Research ArticlePerformance Evaluation of Antlion OptimizerBased Regulator in Automatic Generation Control ofInterconnected Power System

Esha Gupta and Akash Saxena

Department of Electrical Engineering Swami Keshvanand Institute of Technology Management and GramothanOffice No AC-201 Ramnagaria Jagatpura Jaipur Rajasthan 302017 India

Correspondence should be addressed to Esha Gupta eshaguptaoutlookcom

Received 26 November 2015 Accepted 4 May 2016

Academic Editor Chung-Liang Chang

Copyright copy 2016 E Gupta and A Saxena This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper presents an application of the recently introduced Antlion Optimizer (ALO) to find the parameters of primary governorloop of thermal generators for successful Automatic Generation Control (AGC) of two-area interconnected power system Twostandard objective functions Integral Square Error (ISE) and Integral TimeAbsolute Error (ITAE) have been employed to carry outthis parameter estimation process The problem is transformed in optimization problem to obtain integral gains speed regulationand frequency sensitivity coefficient for both areasThe comparison of the regulator performance obtained fromALO is carried outwith Genetic Algorithm (GA) Particle Swarm Optimization (PSO) and Gravitational Search Algorithm (GSA) based regulatorsDifferent types of perturbations and load changes are incorporated to establish the efficacy of the obtained design It is observedthat ALO outperforms all three optimization methods for this real problem The optimization performance of ALO is comparedwith other algorithms on the basis of standard deviations in the values of parameters and objective functions

1 Introduction

With the increase in the interconnection of the utilities com-plexity in power system operation and control has emerged asa challenging problem in front of design engineers Variationof the system parameters (voltage and frequency) from theirnominal values can present a potential threat to the systemstability To control these deviations intelligent design isrequired at generation transmission and distribution endHence Automatic Generation Control (AGC) of intercon-nected power network is a major thrust area of research Tokeep frequency and tie-line power exchanges in a nominalrange AGC of the interconnected power system is required[1 2] The prime objective of the successful power systemoperation is to transmit distribute and utilize the electricalpower within the nominal range of frequency and terminalvoltage Normally the interconnection of different powerplants (nuclear thermal and hydro) introduces differentcomplexities in the operation of power system Hydro powerplants are less operative in developing countries like India

as the availability of the water for irrigation purpose is acritical issue Moreover the constraints related to regulationshinder the participation of hydro power plants in the AGCHigh efficiency of nuclear units prevents the participation ofthese units in AGCThe role of AGC is prominent in thermalpower plants Control of generator consists in functioning oftwomajor loops Automatic Voltage Regulator (AVR) loop tomaintain the nominal voltage and Load Frequency Control(LFC) loop to maintain the system frequency

In 1970 the concept of modern optimal control wasintroduced by Elgerd [1] In the modern optimal control thedetermination of the parameters of primary governor loopis performed to enhance the systemrsquos damping performanceIn recent years this field has emerged as a potential area ofresearch Approaches employed for AGC can be subdividedinto two categories First the application of supervised learn-ing models and expert systems was employed to obtain anintelligent control of interconnected power system Secondthe applications of metaheuristic techniques to obtain thecontroller settings were explored A rich literature survey on

Hindawi Publishing CorporationJournal of EngineeringVolume 2016 Article ID 4570617 14 pageshttpdxdoiorg10115520164570617

2 Journal of Engineering

AGC is provided in [3] A philosophy of AGC is explainedin [4 5] Some of the approaches for effective AGC werebased on Pole Placement Technique [6] Coefficient DiagramMethod (CDM) [7 8] Neural Networks (NN) [9ndash11] FuzzyLogic (FL) [12ndash15] and Super Magnetic Energy Storage(SMES) Devices [16] Calculation of CDM coefficients forlarge interconnected units involves heavy computationsThese approaches require large data sets and observationsfor training and rule formation Moreover fuzzy approachesare based on approximations AGC of a power system isa responsible operation minute changes in the controllersettings can put a question mark on the reliable operationof the power system Hence Neural Network and FuzzyLogic based approaches are not suitable in modern powersystemrsquos context As ldquonature is the best teacherrdquo by mim-icking the biological behavior of plants insects and speciessome beautiful analogies were developed and simulated byresearchers in the form of mathematical paradigms Someof these approaches include Gravitational Search Algorithm(GSA) [17] based on Newtonrsquos law of attraction ParticleSwarm Optimization (PSO) [18] based on the behavior offlock and swarm fishes Genetic Algorithm (GA) [19] basedon Darwinianrsquos survival of the fittest and natural evolutionBacterial Foraging (BF) [20] based on foraging behaviorof bacteria Differential Evolution (DE) [21] Artificial BeeColony (ABC) [22] based on the behavior of bees FireflyAlgorithm (FA) [23] and Cuckoo Search (CS) [24] Somehybrid approaches are also reported in which the Fuzzy Logicis combined with the PI controllers Majorly the propor-tional and integral gains of a controller were considered asparameters of interest in the optimization process Howeverin the literature parameters of primary governor loop werealso optimized in [20] The effect of speed regulation onthe performance of the regulator was also discussed in [25]Recently Teaching Learning Based Optimization (TLBO)is applied to find the scaling factors and integral gains fortwo thermal unitsrsquo interconnected power systems in [26]Recently Grey Wolf Optimizer (GWO) is applied to find outthe optimal settings of PID controller for three thermal unitsby Sharma and Saikia [27] In the work frequency droop wasobserved in the presence of solar power plants Bat algorithmis applied to find the regulator settings of multiarea thermalpower system in [28] The author employed PD-PID cascadecontrollers to obtain the AGC From the literature review itis clear that application of metaheuristic algorithm in AGCregulator design is a potential area The search of a properset of parameters (integral and differential gains primaryloop parameters) by which Area Control Error (ACE) can bereduced to zero is a major objective to solve AGC problemIn the literature two objective functions (design criteria)were employed to carry out the estimation process To findthe minima of these functions by considering the gains andother parameters as variables is the essence of AGC problemEvolutionary algorithms search for global optima of thefunction by the combined actions of agents and decidingoperator in a predefined search space Hence the quality ofexploration and exploitation is a major deciding factor in theperformance of the algorithm Another noteworthy feature ofthese algorithms is randomness although randomness gives

different results in each run they can yet be able to avoid thelocal minima trap

Recently Mirjalili proposed an AntlionOptimizer (ALO)algorithm on the behavior inspired from antlions [29] ALOhas been successfully applied over 19 benchmark func-tions along with four classical engineering problems Thisalgorithm is based on the foraging behavior of antlionsMoreover salient features of algorithms are the effectiveexploration of the search space by random walk and randomselection of agents Similarly exploitation of the search spaceis assured by adaptive boundaries of traps Since it is apopulation based algorithm the avoidance of local optima isindispensable Fewer parameters gradient-free structure andadaptive intensity with iterations are some salient features ofthe algorithm In view of the above literature survey salientfeatures and computational efficacy of the ALOmotivated usto employ ALO in AGC regulator design for the very firsttime The following are the objectives of this research work

(1) To solve the optimization process by ISE and ITAEobjective functions to find out the parameters of pri-mary governor loop that is speed regulation constant(119877) frequency bias (119863) and integral gains (119870

119868)

(2) To test the efficacy of the objective functions withthe help of damping performance obtained by ALOregulators

(3) To test the robustness and efficacy of the proposeddesign with other recently employed regulators andtest the design for various types of perturbations andtopological changes

This paper is organized as followsThe details of systemmod-eling are presented in brief in Section 2 In Section 3 detailsof ALO along with the functioning of operators are explainedin a lucid manner Section 4 discusses the simulation resultsand analysis Section 5 provides the comparative analysis ofthe optimization process for all the algorithms And finallyin Section 6 conclusions and future scope of the work arepointed out

2 System Modeling

21 AGC Model The two-area nonreheat thermal inter-connected power system is shown in Figure 1 The maincomponents of the power system include speed governorturbine rotating mass and load The inputs of the powersystem are controller output 119906 load disturbance Δ119875

119871 and

tie-line power Δ119875tie and the outputs are frequency deviationsΔ119891 and Area Control Error (ACE) The ACE signal controlsthe steady state errors of frequency deviation and tie-powerdeviation Mathematically ACE can be defined as

ACE = 119861Δ119891 + Δ119875tie (1)

where 119861 indicates the frequency bias parameterThe operating behavior of the power system is dynamic

so it must be assumed that the parameters of the system arelinear For mathematical modeling the transfer function isused

Journal of Engineering 3

B1

B2

ACE1

PI controller

PI controller

Controller

Controller

u1

+ +

+

+

minus minus

minus

minus

minus

minus

minus

1

R1

1

R2

1

1 + sTg1

1

1 + sTg2

1

1 + sTt1

1

1 + sTt2

ΔPg1

ΔPg2

ΔPL1

ΔPL2

ΔP12

ΔP21

Kp1

1 + sTp1

Kp2

1 + sTp2

Load

Load

TurbineGovernor

TurbineGovernor

ΔF1

ΔF2

ACE2

++

+u2

2120587T12s

a12a12

ΔPtie

sum

sum

sumsumsum

sum sum

Figure 1 Transfer function model of two-area nonreheat thermal interconnected system

The transfer function of a governor is represented by [1]

119866119892 (119904) =

1

1 + 119904119879119892

(2)

The turbine is represented by the transfer function as [1]

119866119905 (119904) =

1

1 + 119904119879119905

(3)

The transfer function of rotating mass and load [1] is asfollows

119866119871 (119904) =

119870119901

1 + 119904119879119901

(4)

where 119879119901= 2119867119891119863 and119870

119901= 1119863

Δ119875119866and Δ119875

119871are the two inputs of rotating mass and load

and Δ119891(119904) is the output and is represented by [1]

Δ119891 (119904) = 119866119871(119904) [Δ119875

119866(119904) minus Δ119875

119871(119904)] (5)

22 The System Investigated The system was investigated ontwo equal thermal areas connected by a weak tie line havingthe same generation capacity of 1000MVA The parametersof the system are taken from [4] A sudden step perturbationof 01875 pu occurs in area 1 and another one of 01275 puoccurs in area 2 The transfer function model of the two-area thermal system is shown in Figure 1 The system isimplemented using MATLAB 2013 and run on a Pentium IVCPU 269GHz and 184GB RAM computer [30]

23The Proposed Approach The controller used in AGC sys-tem is PI controller as it determines the difference between setpoint and reference point and removes the steady state errorFor the design of PI controller the parameters proportionalgain (119870

119875) and integral gain (119870

119868) are essential However in this

work for the ease and simplicity of the optimization processwe consider proportional gain 1 Area Control Errors are theinput of the controllers for area 1 and area 2 and are definedas

ACE1= 1198611Δ1198911+ Δ119875tie

ACE2= 1198612Δ1198912+ Δ119875tie

(6)

where 1198611= 1119877

1+ 1198631and 119861

2= 1119877

2+ 1198632

The outputs of the controllers are 1199061and 119906

2and are

obtained as follows

1199061= 1198701198751ACE1+ 1198701198681intACE

1

1199062= 1198701198752ACE2+ 1198701198682intACE

2

(7)

In this paper the estimation of integral gains and parametersof primary governor loop is based on two objective functions(ITAE and ISE) which are given in (8) These objective

4 Journal of Engineering

functions aim to reduce the steady state error to zero andmaximize the damping ratio of the system Hence

1198691= ITAE = int

119879

0

(1003816100381610038161003816Δ1198911

1003816100381610038161003816 +1003816100381610038161003816Δ1198912

1003816100381610038161003816 +1003816100381610038161003816Δ119875tie

1003816100381610038161003816) sdot 119905 119889119905

1198692= ISE = int

119879

0

(1003816100381610038161003816Δ1198911

1003816100381610038161003816

2+1003816100381610038161003816Δ1198912

1003816100381610038161003816

2+1003816100381610038161003816Δ119875tie

1003816100381610038161003816

2) 119889119905

(8)

The problematic constraints are the parameters of AGCregulator which contains integral gains speed regulationsand the frequency sensitivity coefficients as they are boundedwith the limits These parameters are system specific Hencethe design problem can be formulated as follows

Minimize 119869

Subjected to 119870119868minle 119870119868le 119870119868max

119877min le 119877 le 119877max

119863min le 119863 le 119863max

(9)

119869 is the objective function (1198691and 1198692)

3 Antlion Optimizer

A novel algorithm inspired by nature named Antlion Opti-mizer (ALO) is presented in this section This techniquewas proposed by Mirjalili [29] in 2015 In ALO the huntingmechanism of antlions is mimicked Antlions belong toMyrmeleontidae family of class net winged insects ALOemploys five main steps of hunting that is random walkof ants building trap entrapment of ants in trap catchingprey and rebuilding traps The ALO algorithm is a gradient-free algorithm which also provides greater exploration andexploitation of search space Exploration is guaranteed bythe random selection of antlions and random walks of antsaround them whereas exploitation is guaranteed by adaptiveshrinking boundaries of antlionrsquos trap With the help ofroulette wheel and random walks ALO has high probabilityto resolve local optima stagnation The life cycle of antlionsconsists of two main phases larvae and adults Total naturallifespan can take up to 3 years which mostly occurs inlarvae and only 3ndash5 weeks in adulthood Antlions undergometamorphosis in a cocoon to become adult They mostlyhunt in larvae and the adulthood period is for reproductionAn antlion larva digs a cone shaped pit in sand by movingalong a circular path and throwing out sand with its massivejaw After digging the trap the larvae hide underneath thebottom of the cone and wait for the insect (preferably ant)to be trapped in the pit The edge of the cone is sharp enoughfor insects to fall to the bottom of the trap easily Figure 2illustrates the hunting behavior in which antlions wait for theants to be trapped in the cone shaped pit

Once the antlion realizes that the prey is in the trap it triesto catch it Another interesting behavior in the lifestyle of antbehavior is the relevancy of size of the trap level of hungerand shape of the moon Antlions dig out larger traps as theybecome more hungry and when the moon is full And in thisway they improve their chance of survival

Figure 2 The hunting behavior of antlion

31 Mathematical Modeling of the ALO Algorithm

(a) RandomWalks of Ants Randomwalks of ants are given in

119883(119905) = [0 cumsum (2119903 (1199051) minus 1)

cumsum (2119903 (1199052) minus 1) cumsum (2119903 (119905

119899) minus 1)]

(10)

where 119899 is the maximum number of iterations cumsumcalculates the cumulative sum and 119905 is the step of randomwalk Hence

119903 (119905) =

1 if rand gt 05

0 if rand lt 05(11)

Here 119903(119905) is a stochastic function and rand is a randomnumber generated with uniform distribution in the intervalof [0 1]

The positions of ants are saved and utilized duringoptimization in the matrix

119872Ant =

[[[[[[[[[[

[

1198601111986012sdot sdot sdot sdot sdot sdot 119860

1119889

1198602111986022sdot sdot sdot sdot sdot sdot 119860

2119889

11986011989911198601198992sdot sdot sdot sdot sdot sdot 119860

119899119889

]]]]]]]]]]

]

(12)

where119872Ant is the matrix for saving the position of each ant119860119894119895

shows the value of the 119895th variable of 119894th ant 119899 is thenumber of ants and 119889 is the number of variables

At each step of optimization ants update their positionaccording to random walk Equation (10) cannot be directlyused for updating position of ants The random walks arenormalized using the following equation (min-max normal-ization)

119883119905

119894=(119883119905

119894minus 119886119894) times (119889

119894minus 119888119905

119894)

(119889119905

119894minus 119886119894)

+ 119888119894 (13)

Journal of Engineering 5

Table 1 Optimized parameters of AGC regulator

Parameters ALO GSA [17] PSO [18] GA [19]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

1198701198681

03260 04002 03817 04171 03131 04498 03031 065251198701198682

02135 02010 02153 02028 01091 02158 03063 079601198771

00491 00404 00401 00435 00581 00201 00794 005031198772

00699 00509 00657 00635 00531 003 00737 006091198631

04457 04884 05889 04778 04756 05910 07591 072161198632

08770 08975 08946 08744 06097 08226 08950 08984

where 119886119894is the minimum of random walk of 119894th variable

119889119894is the maximum of random walk of 119894th variable 119888119905

119894is

the minimum of 119894th variable at 119905th iteration and 119889119905119894is the

maximum of 119894th variable at 119905th iteration

(b) Trapping in Antlionrsquos Pit Random walks of ants areaffected by antlionsrsquo trap Mathematical modeling of trappingin antlionrsquos pit is proposed by the following equations

119888119905

119894= Antlion119905

119895+ 119888119905

119889119905

119894= Antlion119905

119895+ 119889119905

(14)

where 119888119905 represents the minimum of all variables at 119905thiteration 119889119905 indicates the vector including the maximum ofall variables at 119905th iteration 119888119905

119894is the minimum of all variables

for 119894th ant 119889119905119894is the maximum of all variables for 119894th ant and

Antlion119905119895shows the position of the selected 119895th antlion at 119905th

iteration

(c) Building Trap For building trap a roulette wheel isemployed to model the hunting capability of antlions TheALO algorithm is required to utilize a roulette wheel operatorfor selecting antlions based on their fitness during optimiza-tion This mechanism provides high chances to the fitterantlions for catching ants

(d) Sliding Ants towards Antlion Antlions are able to buildtraps which are proportional to their fitness and ants arerequired to move randomly Once the antlion realizes that anant is in the trap it shoots sand out the centre of the pit Theants which are trying to escape slide down the trapThe radiusof the antrsquos randomwalks hypersphere is decreased adaptivelyin the mathematical modeling The following equations areproposed for this

119888119905=119888119905

119868

119889119905=119889119905

119868

(15)

where 119868 is a ratio 119888119905 is the minimum of all variables at 119905thiteration and 119889119905 indicates the vector including the maximumof all variables at 119905th iteration

(e) Catching Prey and Rebuilding the Pit This is the finalstage of hunt At this stage an ant reaches the bottom of

the pit and is caught in the antlionrsquos jaw After this stage theantlion pulls the ant inside the sand and consumes its bodyCatching the prey occurs when the ant goes inside the sandand becomes fitter than its corresponding antlion Accordingto the position of the latest hunted ant the antlions updatetheir position to enhance the chances of catching new preyMathematically the following equations can be proposed inthis regard

Antlion119905119895= Ant119905

119894if 119891 (Ant119905

119894) gt 119891 (Antlion119905

119895) (16)

where 119905 represents the current iteration Antlion119905119895is the

position of the selected 119895th antlion at 119905th iteration and Ant119905119894

represents the position of 119894th ant at 119905th iteration

(f) Elitism For any evolutionary algorithm elitism is animportant feature that allows antlions to maintain the bestsolution obtained at any stage of optimization process Inthis algorithm the best obtained antlion during the entireiteration is saved and is considered as an elite Since thefittest antlion is elite it affects the movement of all the antsduring iteration Hence it is assumed that every ant walksrandomly around a selected antlion by roulette wheel and theelite simultaneously as follows

Ant119905119894=119877119905

119860+ 119877119905

119864

2 (17)

where 119877119905119860is the random walk around the antlion selected by

the roulette wheel at 119905th iteration119877119905119864is the randomwalk and

Ant119905119894represents the position of 119894th ant at 119905th iteration

The following section presents analysis of simulationresults

4 Results and Analysis

This section presents simulation results and analysis of AGCregulator performance on two-area thermal interconnectedpower system with different step perturbations and loadingconditions Different AGC regulator settings are obtainedwith the application of four algorithms (GA PSO GSA andALO) on two standard objective functions (ISE and ITAE)Table 1 shows the values of optimized parameters of regulatorwith the application of the abovementioned algorithms ontwo objective functions

Table 2 shows the values of systemrsquos minimum dampingratio and eigenvalues after the application of these AGC

6 Journal of Engineering

Table2Eigenvaluesa

ndminim

umdamping

ratio

Parameter

ALO

GSA

[17]

PSO[18]

GA[19

]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

Syste

mmod

es

minus58548

minus59604

minus58468

minus5976

minus5846

minus65657

minus56586

minus5808

minus42219

minus44165

minus4313

minus44257

minus444

43minus48155

minus42083

minus42168

minus03805plusmn17

191119894

minus02885plusmn18

854119894

minus03994plusmn17

029119894

02511plusmn19

124119894

minus040

10plusmn17

004i

minus00030plusmn26953119894minus04925plusmn13

799119894

minus02024plusmn16

817119894

minus03007plusmn14

854119894

minus02088plusmn17

320119894

minus02606plusmn16

066119894

minus01924plusmn17420119894

minus024

06plusmn17

718i

minus00220plusmn21889119894minus02491plusmn14

729119894

003

61plusmn15

786i

minus03716

minus04624

minus03395

minus05169

minus009

83plusmn00157i

minus046

66minus01353

minus01058

minus0117

9minus00910

minus0110

2minus00884

minus03521

minus00494

minus03294

minus07991

minus02256

minus02351

minus02061

minus02416

minus02144

minus03712

minus09209

Minim

umdamping

ratio

01984

01197

01601

01098

01345

00011

01668

00229

Journal of Engineering 7

regulators Eigenvalue analysis plays an important role instability studies Complex conjugate eigenvalues are alsoknown as swing modes and these eigenvalues are responsiblefor oscillatory instability when the real part of the eigen-value is positive From Table 2 it is observed that whenoptimization process is carried out with the application ofGA on 119869

2system mode contains a swing mode with positive

eigenvalue (0361) Real positive part of eigen is the indicationof oscillations of growing amplitudeTheminimum dampingratios obtained from the application of different regulatorswith 119869

1and 119869

2criteria are shown in Table 2 For PSO

regulator minimum damping ratios obtained from thesecriteria are (01345 00011) similarly the ratios for GA are(01668 00229) for GSA are (01601 01098) and for ALOare (01984 01197) It can be said that a considerable amountof damping is enhanced in each case when the regulatorparameters are obtained with criterion 119869

1 Overall damping

of the system is the highest with ALO regulator (1198691) (01984)

Prima facie it can be concluded that the regulator designobtained from criterion 119869

1is more effective as the damping

enhanced by this regulator is higher In eigenvalue analysisboth real and imaginary parts have their interpretation andphysical significance The real part of the complex conjugateeigenvalue shows the damping behavior which represents thedamp oscillations whichmeans the larger themagnitude thehigher the rate of decay Imaginary components show thefrequency of oscillations It can be observed from Table 2that high frequency oscillations are associated with setting1198692 Higher frequency oscillations are bad for equipment

health and often cause the damage of physical structure ofcontrollers In this case for 119869

2 GA frequency of oscillations

is (157 168) for PSO (269 218) for GSA (191 174) and(188 173) for ALO It is observed that although frequencyof oscillations is in moderate range for GA regulator theamplitude of the oscillation is growing with time as it has apositive real part of eigenvalue However the other regulatorshave high frequency of oscillations modes as comparedwith ALO To show this analysis in a more prominent wayAGC regulators are designed with ALO algorithm and testedfor different levels of perturbations Figures 3(a) and 3(b)show the dynamic responses of frequency deviations inareas 1 and 2 when area 1 observes a step disturbance of001 pu Figures 3(c) and 3(d) show the frequency deviationcurves of both areas with both regulator settings 119869

1and

1198692when area 2 is perturbed with 002 pu Similarly for

both regulator settings the dynamic responses obtainedfrom both areas are self-explanatory It is observed that 119869

1

setting is promising The overshoot and settling time of thefrequency deviation curves of both areas are less with 119869

1

regulator It is also empirical to judge that the variationsof tie-line power exchanges are nominal with both types ofperturbation with 119869

1regulator Hence it is concluded that 119869

1

optimization criterion is suitable for the designing of theAGCregulator

To exhibit the comparative performance of the ALO reg-ulator with other regulators four different loading scenariosare simulated in this work These loading conditions aresummarized below

Case 1 Load changes in area 1 by 10Thedynamic responsesof Δ119865

1 Δ1198652 and Δ119875tie are given in Figures 4ndash6 for all the

algorithms

Case 2 Load changes in area 2 by 20 Figures 7ndash9 show thedynamic responses of the system

Case 3 Load is increased in area 1 by 25 In Figures 10ndash12the system dynamic responses are shown

Case 4 Load is decreased in area 1 by 25 and the systemdynamic responses are given in Figures 13ndash15

Dynamic responses along with the system eigenvalues forthese conditions are exhibited in Table 3 It is observed thatagain with setting 119869

2few eigenvalues possess positive real part

when optimized with GA (00370 00382 and 00368) Thereal part of swing mode varies from minus02823 to minus04567 forALO regulator from minus02541 to minus04632 for GSA regulatorfrom minus00982 to minus4587 for PSO regulator and from minus02511to minus05411 for GA regulator with criterion 119869

1 It is of note

here that the real part of the eigenvalue observes a largevariation in case of GA under different loading conditionsThis spread put a question mark on the performance ofthe regulator and robustness of the regulator also Moder-ate spread has been observed with ALO regulator For allcases higher numeric values of real part of the eigenvaluessuggest that the system is more stable In Case 1 thesevalues are (minus04278 minus02823) for ALO (minus04288 minus02570)for GSA (minus04277 minus02395) for PSO and (minus02588 minus05271)for GA It can be predicted that for Case 1 the robustsetting is achieved by ALO Similarly in Case 4 the realparts of eigenvalues (swing modes) are (minus03276 minus02879)for ALO and (minus03106 minus02589) for GSA and an addi-tional swing mode with PSO setting has been observed(1198691) (minus03055 minus02459 00983) and (minus0440 02680) for GA

From this it is also observed that a higher degree ofrobustness can be achieved by ALO regulator To understandthe dynamic response of the frequency deviation curvesa conventional index Figure of Demerit (FOD) is usedin this paper Figure of Demerit is the summation of thesquare of the overshoot and settling time of the deviationcurves It is observed that for almost all loading cases thevalues of settling time overshoot and FODs are low forALO based regulators as compared with other regulatordesigns It is observed from Figures 4ndash6 that ALO basedcontroller exhibits better dynamic performance as comparedwith others The percentage of overshoot and settling timeis much less in these cases The low oscillatory responseexhibited by ALO is best suited for the equipmentrsquos healthFOD values are considered as a close replica of dynamicperformance of controller Higher values of FOD show poordynamic performance and vice versa It is also empiricalto mention here that for frequency deviation in area 1 thesettling time and FOD obtained from ALO are 38 and 1444respectively whereas from GSA PSO and GA the settlingtime and FOD are 56 50 and 49 and 3136 25 and 2401respectively The frequency deviation in area 2 also showsthat the values of settling time and FOD are less when ALO

8 Journal of Engineering

Table3Syste

mmod

esfore

achcase

ofallthe

algorithm

s

Parameters

ALO

GSA

[17]

PSO[18]

GA[19

]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

Case

1

minus58014

minus58014

minus57891

minus59112

minus57884

minus64711

minus55532

minus5752

minus42274

minus42274

minus4313

minus44257

minus444

43minus48155

minus41792

minus42168

minus04924plusmn16

361119894

minus04924plusmn16

361119894

minus04288plusmn16

043119894

minus02773plusmn18

079119894

minus04277plusmn16

059119894

minus00430plusmn25784119894

minus02588plusmn14

307119894

minus02211plusmn15

866119894

minus02842plusmn14

933119894

minus02842plusmn14

933119894

minus02570plusmn16

085119894

minus01941plusmn1746

0119894minus02395plusmn17

695119894

minus00222plusmn21888119894

minus05271plusmn11657119894

00370plusmn15

795119894

minus01208

minus01208

minus03454

minus05259

minus00983plusmn00157119894

minus04806

minus01466

minus01058

minus02021

minus02021

minus0110

1minus00884

minus03584

minus00494

minus03344

minus09221

minus02229

minus02229

minus02062

minus02416

minus02144

minus0401

minus08182

Case

2

minus58597

minus59843

minus58468

minus5976

minus5846

minus6564

minus55965

minus5808

minus41275

minus42672

minus42059

minus43093

minus43269

minus46691

minus40832

minus41155

minus046

46plusmn17

341119894

minus02906plusmn19

218119894

minus040

02plusmn17

063119894

minus02534plusmn19

127119894

minus03943plusmn17

014119894

000

14plusmn26941119894

minus05108plusmn12

557119894

minus02029plusmn16

828119894

minus03315plusmn13

466119894

minus01072plusmn15

609119894

minus03117plusmn14

571119894

minus02466plusmn15

904119894

minus03057plusmn16

218119894

minus00944plusmn20213119894

minus03032plusmn12

918119894

minus00013plusmn14

380119894

minus01204

minus00879

minus03394

minus05169

minus00986plusmn00155119894

minus04774

minus01467

minus01059

minus02047

minus044

98minus0110

1minus00884

minus03521

minus00494

minus0344

minus08003

minus02234

minus05752

minus02096

minus0245

minus02155

minus03879

minus09453

Case

3

minus57282

minus58373

minus57167

minus58312

minus5716

minus6353

minus54991

minus56819

minus42274

minus43812

minus4313

minus44278

minus444

43minus48155

minus41792

minus42168

minus05297plusmn15

095119894

minus03560plusmn16

872119894

minus04632plusmn14

784119894

minus03257plusmn16

774119894

minus04587plusmn14

794119894

minus00990plusmn24269119894

minus02590plusmn14

294119894

minus02413plusmn14

636119894

minus02816plusmn14

943119894

minus00567plusmn17

151119894

minus02541plusmn16

063119894

minus01938plusmn17

505119894

minus02396plusmn17679119894

minus00228plusmn21889119894

minus05411plusmn10

386119894

003

82plusmn15

795119894

minus01204

minus00878

minus0355

minus05367

minus00982plusmn00157119894

minus04855

minus01462

minus01058

minus02039

minus046

72minus011

minus00886

minus03686

minus00494

minus03357

minus09251

minus02252

minus05609

minus02063

minus02401

minus02144

minus04258

minus08475

Case

4

minus60556

minus62024

minus6041

minus61949

minus604

01minus68711

minus57445

minus59969

minus42274

minus43812

minus4313

minus44278

minus444

43minus48155

minus41792

minus42168

minus03695plusmn20323119894

minus01897plusmn22365119894

minus03106plusmn20088119894

minus01627plusmn22305119894

minus03055plusmn20076119894

01510plusmn30616119894

minus044

40plusmn15

429119894

minus01319plusmn19

807119894

minus02838plusmn14

894119894

minus00573plusmn17

122119894

minus02589plusmn16

017119894

minus01958plusmn1744

2119894minus02459plusmn17

656119894

minus00217plusmn21890119894

minus02680plusmn14

339119894

003

68plusmn15

765119894

minus01216

minus00879

minus03261

minus04948

minus00983plusmn00158119894

minus04698

minus01478

minus01059

minus01971

minus0434

minus0110

5minus00886

minus03379

minus00494

minus03276

minus07544

minus02194

minus05605

minus02059

minus024

minus02144

minus03632

minus09192

Journal of Engineering 9

J

J1

2

2 4 6 81 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(a)

J

J1

2

2 4 6 80 10

Time (s)

minus005

0

005

ΔF2

(Hz)

(b)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(c)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

minus005

0

005

ΔF2

(Hz)

(d)

J

J1

2

2 4 6 80 10

Time (s)

ΔP

tie(p

u)

minus002

0

002

(e)

J

J1

2

2 4 6 80 10

Time (s)

minus001

0

001

ΔP

tie(p

u)

(f)

Figure 3 Dynamic responses obtained from ALO

regulator is used The value of settling time with frequencydeviation in area 2 is observed as 60 for ALO 72 for GSA76 for PSO and 80 for GA It is also interesting to observethat with the 10 increase in the load PSO gives erroneousresults and the flow of tie-line power behaves in a differentmanner Hence critical analysis of dynamic responses clearlyreveals that better dynamic performance is exhibited by ALOBy examining the responses in Figures 7ndash9 it is clearly seenthat the settling time and peak overshoot are less whenload changes in area 2 by 20 It can be observed fromFigure 8 that when area 2 observes 20 increase GA basedcontroller is not able to mitigate the frequency oscillationsThis inculcates oscillatory instability in the system HoweverALO based controller shows a better dynamic response andyields satisfactory performance over a wide range of loading

conditions For Case 2 the settling time of ALO is 36 and is53 42 and 58 for GSA PSO andGA respectively Similarlythe FOD is also very low in case of ALO that is 1296whereas it is 1764 and 3364 in case of PSO and GA Figures10 and 11 show the frequency deviations of areas 1 and 2From dynamic responses of overshoot settling time andFOD it is clear that ALO provides competitive results Thedynamic responses for Case 4 are shown in Figures 13ndash15 andit has been observed that ALO tuned controller yields betterdynamic performanceThe minimum settling time and FODobtained from ALO are 51 and 2601 for frequency deviationin area 1 and 60 and 3600 for frequency deviation in area 2However in case of GSA the settling time is 79 and FOD is198 An oscillatory response is obtained by the GA GSA andPSO tuned controllers

10 Journal of Engineering

ALOGSA [17]

PSO [18]GA [19]

2 4 6 8 10 120Time (s)

minus004

minus003

minus002

minus001

0

001

ΔF1

(Hz)

Figure 4 Change in frequency of area 1 by 10 load increase in area1

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

2 4 6 80 1210

Time (s)

ALOGSA [17]

PSO [18]GA [19]

Figure 5 Change in frequency of area 2 by 10 load increase in area1

5 Optimization Performance

To judge the efficiency of the optimization process carried outby all algorithms 100 trials of optimization are carried outTo provide a fair comparison the population size (100) andthe maximum number of iterations (1000) are kept the sameStopping criterion for the optimization process is maximumrun of the iteration To observe the optimization process in acritical way the standard deviations of optimized parametersof the regulator along with the values of objective functionsare calculated and shown in Table 4 It is observed thathigh values of standard deviations are obtained in regulator

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 6 Change in tie-line power by 10 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 7 Change in frequency of area 1 by 20 load increase in area2

parameters and values of objective functions when optimiza-tion process is handled by GA (009729) Comparatively largevalues of standard deviations are found in GA and PSOwhenthey are compared with ALO We observed high values ofstandard deviation in speed regulation parameters after eachrun of optimization obtained with GA regulators (119869

1and

1198692) Speed regulation parameter is a vulnerable parameter

in power system dynamics studies It affects the systemdynamics in a very prominent way Large values of standarddeviations in the calculation of such vulnerable parametersare not acceptable The values for standard deviations are010256 (GSA 119869

1) and 01550 (GA 119869

2) and similarly for

1198772 they are 00081 (ALO 119869

1) 002 (GSA) 038 (PSO) and

Journal of Engineering 11

Table 4 Standard deviation of optimized parameters of the regulator

Parameters ALO GSA [17] PSO [18] GA [19]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

1198701198681

002923 003773 002425 007720 002604 008461 009729 0206871198631

004107 003315 004475 009833 008416 004759 018872 0213131198771

000582 000102 000045 000168 000153 001403 000892 0007171198701198682

001763 004563 010256 000769 009639 008158 005800 0155501198632

008957 008807 004916 011771 016726 008363 017955 0079451198772

000343 000174 000173 000385 000280 001080 000310 00105937000184 716E minus 06 00212 0000419 038 0011 176 0013

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

ALOGSA [17]

PSO [18]GA [19]

Figure 8 Change in frequency of area 2 by 20 load increase in area2

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 9 Change in tie-line power by 20 load increase in area 2

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 10 Change in frequency of area 1 by 25 load increase inarea 1

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 11 Change in frequency of area 2 by 25 load increase inarea 1

12 Journal of Engineering

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 12 Change in tie-line power by 25 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus005

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 13 Change in frequency of area 1 by 25 load decreases inarea 1

176 for GA The impact of speed regulation parameters onthe dynamic response is shown in [25] The lowest valuesof standard deviations are observed when the parametersare optimized by ALO This basically means that in eachrun of optimization ALO exhibits precision in computingthe parameters The standard deviations in the values ofintegral gains for area 1 by 119869

1and 119869

2are minimum for

ALO (0041 0033) for GA these values are (018 and 0213)and similarly (0044 009) for GSA and (008 and 0047)for PSO It can be concluded that regulator setting integralgain observes the least variation in numerical values whenthe parameter is optimized through ALO (119869

1) The values

of standard deviations in objective functions 1198691and 119869

2are

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 14 Change in frequency of area 1 by 25 load decreases inarea 1

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 15 Change in tie-line power by 25 load decreases in area 1

the lowest for ALO process and the highest for GA Thevalues of standard deviations in the values of 119869

1for GA PSO

GSA and GWO are 00972 00264 00242 and 002 andfor 1198692are 02068 00846 00772 and 03773 It has been

observed that the values obtained by ALO are precise and theoptimization processes are reliable enough for obtaining theregulator design However high values of standard deviationsin parameters of regulator (176 with 119877

2) and in the objective

functions show that the optimization process loses its rele-vance when it is handled by GA Hence it is concluded fromthe eigenvalue analysis anddynamic response of the deviationcurves that ALO shows a promising response to obtainregulator settingwith optimization criterion 119869

1The following

Journal of Engineering 13

section summarizes the contribution of this research workand proposes a solid milieu for future work

6 Conclusion

This paper presents an application of the recently introducedalgorithm ALO to find optimal parameters of the AGCregulator The ALO regulator is employed on a test system oftwo thermal units connected with a weak tie line of limitedcapacity for AGCThe following are the major findings of thework

(A) Comparison of the application of two objective func-tions namely ISE and ITAE in optimization processfor finding the regulator parameters under differ-ent contingencies is investigated Results reveal thatITAE is a better choice to optimize the regulatorparameters

(B) Eigenvalue analysis is performed to test the effec-tiveness of the proposed approach and to comparethe results of the proposed approach with recentlypublished approaches It is observed that the dampingobtained from ALO regulator is more positive ascompared with the other algorithms

(C) ALO shows promising results in terms of overshootsettling time obtained from the frequency responsesof both areas under different loading cases standarddeviations in regulatorrsquos parameter values ISE andITAE values and optimization performance

(D) Damping performance is evaluated with differentcontingencies load changes and step disturbancesin both areas PI controller setting obtained throughALO exhibits better dynamic performance and over-all low settling time

Application of other new metaheuristic algorithms in AGCregulator design on different models of the power systemconsidering different renewable energy power sources lies inthe future scope

Nomenclature

119894 Subscript referring to area 119894 (1 2)Δ119865119894 Frequency deviation in area 119894 (Hz)

Δ119875119866119894 Incremental generation of area 119894 (pu)

Δ119875119871119894 Incremental load change in area 119894 (pu)

ACE119894 Area Control Error of area 119894

119861119894 Frequency bias parameter of area 119894

119877119894 Speed regulation of the governor of area 119894

(Hzpu MW)119879119892119894 Time constant of governor of area 119894 (s)

119879119905119894 Time constant of turbine of area 119894 (s)

119870119901119894 Gain of generator and load of area 119894

119879119901119894 Time constant of generator and load of

area 119894 (s)Δ119875tie Incremental change in tie line (pu)11987912 Synchronizing coefficient

119879 Simulation time (s)119905 Current iteration

Competing Interests

The authors declare that they have no competing interests

References

[1] O I Elgerd Energy Systems Theory An Introduction McGraw-Hill New Delhi India 1983

[2] IEEE Standard Committee ldquoIEEE Standard definitions of termsfor automatic generation control on electric power systemsrdquoIEEE Transactions on Power Apparatus and Systems vol 89 no6 pp 1356ndash1364 1970

[3] A Ibraheem P Kumar and D P Kothari ldquoRecent philosophiesof automatic generation control strategies in power systemsrdquoIEEE Transactions on Power Systems vol 20 no 1 pp 346ndash3572005

[4] H Sadat Power System Analysis McGraw-Hill New York NYUSA 1999

[5] J Nanda and B Kaul ldquoAutomatic generation control of aninterconnected power systemrdquo Proceedings of the Institution ofElectrical Engineers vol 125 no 5 pp 385ndash390 1978

[6] A Y Sivaramakrishnan M V Hariharan and M C SrisailamldquoDesign of variable-structure load-frequency controller usingpole assignment techniquerdquo International Journal of Controlvol 40 no 3 pp 487ndash498 1984

[7] M Z Bernard T H Mohamed Y S Qudaih and Y MitanildquoDecentralized load frequency control in an interconnectedpower system using Coefficient Diagram Methodrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 63pp 165ndash172 2014

[8] R Ali T HMohamed Y S Qudaih and YMitani ldquoA new loadfrequency control approach in an isolated small power systemsusing coefficient diagram methodrdquo International Journal ofElectrical Power and Energy Systems vol 56 pp 110ndash116 2014

[9] I Vajk M Vajta L Keviczky R Haber J Hetthessy andK Kovacs ldquoAdaptive load-frequency control of the hungarianpower systemrdquo Automatica vol 21 no 2 pp 129ndash137 1985

[10] J Kanniah S C Tripathy O P Malik and G S HopeldquoMicroprocessor-based adaptive load-frequency controlrdquo IEEProceedings CmdashGeneration Transmission and Distribution vol131 no 4 pp 121ndash128 1984

[11] M L Kothari P S Satsangi and J Nanda ldquoSampled-dataautomatic generation control of interconnected reheat thermalsystems considering generation rate constraintsrdquo IEEE Transac-tions on Power Apparatus and Systems vol 100 no 5 pp 2334ndash2342 1981

[12] S Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001

[13] B K Sahu S Pati P K Mohanty and S Panda ldquoTeaching-learning based optimization algorithm based fuzzy-PID con-troller for automatic generation control of multi-area powersystemrdquo Applied Soft Computing Journal vol 27 pp 240ndash2492015

[14] K R Sudha and R Vijaya Santhi ldquoLoad frequency control of aninterconnected reheat thermal systemusing type-2 fuzzy systemincluding SMES unitsrdquo International Journal of Electrical Poweramp Energy Systems vol 43 no 1 pp 1383ndash1392 2012

[15] A Banerjee V Mukherjee and S P Ghoshal ldquoIntelligentcontroller for load-tracking performance of an autonomous

14 Journal of Engineering

power systemrdquo Ain Shams Engineering Journal vol 5 no 4 pp1167ndash1176 2014

[16] S Padhan R K Sahu and S Panda ldquoAutomatic generationcontrol with thyristor controlled series compensator includingsuperconducting magnetic energy storage unitsrdquo Ain ShamsEngineering Journal vol 5 no 3 pp 759ndash774 2014

[17] R K Sahu S Panda and S Padhan ldquoOptimal gravitationalsearch algorithm for automatic generation control of intercon-nected power systemsrdquo Ain Shams Engineering Journal vol 5no 3 pp 721ndash733 2014

[18] Y L Abdel-Magid and M A Abido ldquoAGC tuning of intercon-nected reheat thermal systems with particle swarm optimiza-tionrdquo in Proceedings of the 10th IEEE International Conferenceon Electronics Circuits and Systems (ICECS rsquo03) pp 376ndash379December 2003

[19] Y L Abdel-Magid and M M Dawoud ldquoOptimal AGC tuningwith genetic algorithmsrdquo Electric Power Systems Research vol38 no 3 pp 231ndash238 1996

[20] J Nanda S Mishra and L C Saikia ldquoMaiden application ofbacterial foraging-based optimization technique in multiareaautomatic generation controlrdquo IEEE Transactions on PowerSystems vol 24 no 2 pp 602ndash609 2009

[21] U K Rout R K Sahu and S Panda ldquoDesign and analysisof differential evolution algorithm based automatic generationcontrol for interconnected power systemrdquo Ain Shams Engineer-ing Journal vol 4 no 3 pp 409ndash421 2013

[22] H Gozde M C Taplamacioglu and I Kocaarslan ldquoCompara-tive performance analysis of Artificial Bee Colony algorithm inautomatic generation control for interconnected reheat thermalpower systemrdquo International Journal of Electrical Power andEnergy Systems vol 42 no 1 pp 167ndash178 2012

[23] S Debbarma L Chandra Saikia and N Sinha ldquoSolution toautomatic generation control problem using firefly algorithmoptimized I120582D120583 controllerrdquo ISA Transactions vol 53 no 2 pp358ndash366 2014

[24] P Dash L C Saikia and N Sinha ldquoComparison of per-formances of several Cuckoo search algorithm based 2DOFcontrollers in AGC of multi-area thermal systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 55 pp 429ndash436 2014

[25] A Saxena M Gupta and V Gupta ldquoAutomatic generationcontrol of two area interconnected power system using Geneticalgorithmrdquo in Proceedings of the 3rd IEEE International Con-ference on Computational Intelligence and Computing Research(ICCIC rsquo12) Coimbatore India December 2012

[26] B K Sahu T K Pati J R Nayak S Panda and S K KarldquoA novel hybrid LUS-TLBO optimized fuzzy-PID controllerfor load frequency control of multi-source power systemrdquoInternational Journal of Electrical Power amp Energy Systems vol74 pp 58ndash69 2016

[27] Y Sharma and L C Saikia ldquoAutomatic generation controlof a multi-area STmdashthermal power system using Grey WolfOptimizer algorithm based classical controllersrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 853ndash862 2015

[28] P Dash L C Saikia and N Sinha ldquoAutomatic generationcontrol of multi area thermal system using Bat algorithmoptimized PDndashPID cascade controllerrdquo International Journal ofElectrical Power amp Energy Systems vol 68 pp 364ndash372 2015

[29] S Mirjalili ldquoThe ant lion optimizerrdquo Advances in EngineeringSoftware vol 83 pp 80ndash98 2015

[30] MATLAB httpwwwmathworkscom

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

2 Journal of Engineering

AGC is provided in [3] A philosophy of AGC is explainedin [4 5] Some of the approaches for effective AGC werebased on Pole Placement Technique [6] Coefficient DiagramMethod (CDM) [7 8] Neural Networks (NN) [9ndash11] FuzzyLogic (FL) [12ndash15] and Super Magnetic Energy Storage(SMES) Devices [16] Calculation of CDM coefficients forlarge interconnected units involves heavy computationsThese approaches require large data sets and observationsfor training and rule formation Moreover fuzzy approachesare based on approximations AGC of a power system isa responsible operation minute changes in the controllersettings can put a question mark on the reliable operationof the power system Hence Neural Network and FuzzyLogic based approaches are not suitable in modern powersystemrsquos context As ldquonature is the best teacherrdquo by mim-icking the biological behavior of plants insects and speciessome beautiful analogies were developed and simulated byresearchers in the form of mathematical paradigms Someof these approaches include Gravitational Search Algorithm(GSA) [17] based on Newtonrsquos law of attraction ParticleSwarm Optimization (PSO) [18] based on the behavior offlock and swarm fishes Genetic Algorithm (GA) [19] basedon Darwinianrsquos survival of the fittest and natural evolutionBacterial Foraging (BF) [20] based on foraging behaviorof bacteria Differential Evolution (DE) [21] Artificial BeeColony (ABC) [22] based on the behavior of bees FireflyAlgorithm (FA) [23] and Cuckoo Search (CS) [24] Somehybrid approaches are also reported in which the Fuzzy Logicis combined with the PI controllers Majorly the propor-tional and integral gains of a controller were considered asparameters of interest in the optimization process Howeverin the literature parameters of primary governor loop werealso optimized in [20] The effect of speed regulation onthe performance of the regulator was also discussed in [25]Recently Teaching Learning Based Optimization (TLBO)is applied to find the scaling factors and integral gains fortwo thermal unitsrsquo interconnected power systems in [26]Recently Grey Wolf Optimizer (GWO) is applied to find outthe optimal settings of PID controller for three thermal unitsby Sharma and Saikia [27] In the work frequency droop wasobserved in the presence of solar power plants Bat algorithmis applied to find the regulator settings of multiarea thermalpower system in [28] The author employed PD-PID cascadecontrollers to obtain the AGC From the literature review itis clear that application of metaheuristic algorithm in AGCregulator design is a potential area The search of a properset of parameters (integral and differential gains primaryloop parameters) by which Area Control Error (ACE) can bereduced to zero is a major objective to solve AGC problemIn the literature two objective functions (design criteria)were employed to carry out the estimation process To findthe minima of these functions by considering the gains andother parameters as variables is the essence of AGC problemEvolutionary algorithms search for global optima of thefunction by the combined actions of agents and decidingoperator in a predefined search space Hence the quality ofexploration and exploitation is a major deciding factor in theperformance of the algorithm Another noteworthy feature ofthese algorithms is randomness although randomness gives

different results in each run they can yet be able to avoid thelocal minima trap

Recently Mirjalili proposed an AntlionOptimizer (ALO)algorithm on the behavior inspired from antlions [29] ALOhas been successfully applied over 19 benchmark func-tions along with four classical engineering problems Thisalgorithm is based on the foraging behavior of antlionsMoreover salient features of algorithms are the effectiveexploration of the search space by random walk and randomselection of agents Similarly exploitation of the search spaceis assured by adaptive boundaries of traps Since it is apopulation based algorithm the avoidance of local optima isindispensable Fewer parameters gradient-free structure andadaptive intensity with iterations are some salient features ofthe algorithm In view of the above literature survey salientfeatures and computational efficacy of the ALOmotivated usto employ ALO in AGC regulator design for the very firsttime The following are the objectives of this research work

(1) To solve the optimization process by ISE and ITAEobjective functions to find out the parameters of pri-mary governor loop that is speed regulation constant(119877) frequency bias (119863) and integral gains (119870

119868)

(2) To test the efficacy of the objective functions withthe help of damping performance obtained by ALOregulators

(3) To test the robustness and efficacy of the proposeddesign with other recently employed regulators andtest the design for various types of perturbations andtopological changes

This paper is organized as followsThe details of systemmod-eling are presented in brief in Section 2 In Section 3 detailsof ALO along with the functioning of operators are explainedin a lucid manner Section 4 discusses the simulation resultsand analysis Section 5 provides the comparative analysis ofthe optimization process for all the algorithms And finallyin Section 6 conclusions and future scope of the work arepointed out

2 System Modeling

21 AGC Model The two-area nonreheat thermal inter-connected power system is shown in Figure 1 The maincomponents of the power system include speed governorturbine rotating mass and load The inputs of the powersystem are controller output 119906 load disturbance Δ119875

119871 and

tie-line power Δ119875tie and the outputs are frequency deviationsΔ119891 and Area Control Error (ACE) The ACE signal controlsthe steady state errors of frequency deviation and tie-powerdeviation Mathematically ACE can be defined as

ACE = 119861Δ119891 + Δ119875tie (1)

where 119861 indicates the frequency bias parameterThe operating behavior of the power system is dynamic

so it must be assumed that the parameters of the system arelinear For mathematical modeling the transfer function isused

Journal of Engineering 3

B1

B2

ACE1

PI controller

PI controller

Controller

Controller

u1

+ +

+

+

minus minus

minus

minus

minus

minus

minus

1

R1

1

R2

1

1 + sTg1

1

1 + sTg2

1

1 + sTt1

1

1 + sTt2

ΔPg1

ΔPg2

ΔPL1

ΔPL2

ΔP12

ΔP21

Kp1

1 + sTp1

Kp2

1 + sTp2

Load

Load

TurbineGovernor

TurbineGovernor

ΔF1

ΔF2

ACE2

++

+u2

2120587T12s

a12a12

ΔPtie

sum

sum

sumsumsum

sum sum

Figure 1 Transfer function model of two-area nonreheat thermal interconnected system

The transfer function of a governor is represented by [1]

119866119892 (119904) =

1

1 + 119904119879119892

(2)

The turbine is represented by the transfer function as [1]

119866119905 (119904) =

1

1 + 119904119879119905

(3)

The transfer function of rotating mass and load [1] is asfollows

119866119871 (119904) =

119870119901

1 + 119904119879119901

(4)

where 119879119901= 2119867119891119863 and119870

119901= 1119863

Δ119875119866and Δ119875

119871are the two inputs of rotating mass and load

and Δ119891(119904) is the output and is represented by [1]

Δ119891 (119904) = 119866119871(119904) [Δ119875

119866(119904) minus Δ119875

119871(119904)] (5)

22 The System Investigated The system was investigated ontwo equal thermal areas connected by a weak tie line havingthe same generation capacity of 1000MVA The parametersof the system are taken from [4] A sudden step perturbationof 01875 pu occurs in area 1 and another one of 01275 puoccurs in area 2 The transfer function model of the two-area thermal system is shown in Figure 1 The system isimplemented using MATLAB 2013 and run on a Pentium IVCPU 269GHz and 184GB RAM computer [30]

23The Proposed Approach The controller used in AGC sys-tem is PI controller as it determines the difference between setpoint and reference point and removes the steady state errorFor the design of PI controller the parameters proportionalgain (119870

119875) and integral gain (119870

119868) are essential However in this

work for the ease and simplicity of the optimization processwe consider proportional gain 1 Area Control Errors are theinput of the controllers for area 1 and area 2 and are definedas

ACE1= 1198611Δ1198911+ Δ119875tie

ACE2= 1198612Δ1198912+ Δ119875tie

(6)

where 1198611= 1119877

1+ 1198631and 119861

2= 1119877

2+ 1198632

The outputs of the controllers are 1199061and 119906

2and are

obtained as follows

1199061= 1198701198751ACE1+ 1198701198681intACE

1

1199062= 1198701198752ACE2+ 1198701198682intACE

2

(7)

In this paper the estimation of integral gains and parametersof primary governor loop is based on two objective functions(ITAE and ISE) which are given in (8) These objective

4 Journal of Engineering

functions aim to reduce the steady state error to zero andmaximize the damping ratio of the system Hence

1198691= ITAE = int

119879

0

(1003816100381610038161003816Δ1198911

1003816100381610038161003816 +1003816100381610038161003816Δ1198912

1003816100381610038161003816 +1003816100381610038161003816Δ119875tie

1003816100381610038161003816) sdot 119905 119889119905

1198692= ISE = int

119879

0

(1003816100381610038161003816Δ1198911

1003816100381610038161003816

2+1003816100381610038161003816Δ1198912

1003816100381610038161003816

2+1003816100381610038161003816Δ119875tie

1003816100381610038161003816

2) 119889119905

(8)

The problematic constraints are the parameters of AGCregulator which contains integral gains speed regulationsand the frequency sensitivity coefficients as they are boundedwith the limits These parameters are system specific Hencethe design problem can be formulated as follows

Minimize 119869

Subjected to 119870119868minle 119870119868le 119870119868max

119877min le 119877 le 119877max

119863min le 119863 le 119863max

(9)

119869 is the objective function (1198691and 1198692)

3 Antlion Optimizer

A novel algorithm inspired by nature named Antlion Opti-mizer (ALO) is presented in this section This techniquewas proposed by Mirjalili [29] in 2015 In ALO the huntingmechanism of antlions is mimicked Antlions belong toMyrmeleontidae family of class net winged insects ALOemploys five main steps of hunting that is random walkof ants building trap entrapment of ants in trap catchingprey and rebuilding traps The ALO algorithm is a gradient-free algorithm which also provides greater exploration andexploitation of search space Exploration is guaranteed bythe random selection of antlions and random walks of antsaround them whereas exploitation is guaranteed by adaptiveshrinking boundaries of antlionrsquos trap With the help ofroulette wheel and random walks ALO has high probabilityto resolve local optima stagnation The life cycle of antlionsconsists of two main phases larvae and adults Total naturallifespan can take up to 3 years which mostly occurs inlarvae and only 3ndash5 weeks in adulthood Antlions undergometamorphosis in a cocoon to become adult They mostlyhunt in larvae and the adulthood period is for reproductionAn antlion larva digs a cone shaped pit in sand by movingalong a circular path and throwing out sand with its massivejaw After digging the trap the larvae hide underneath thebottom of the cone and wait for the insect (preferably ant)to be trapped in the pit The edge of the cone is sharp enoughfor insects to fall to the bottom of the trap easily Figure 2illustrates the hunting behavior in which antlions wait for theants to be trapped in the cone shaped pit

Once the antlion realizes that the prey is in the trap it triesto catch it Another interesting behavior in the lifestyle of antbehavior is the relevancy of size of the trap level of hungerand shape of the moon Antlions dig out larger traps as theybecome more hungry and when the moon is full And in thisway they improve their chance of survival

Figure 2 The hunting behavior of antlion

31 Mathematical Modeling of the ALO Algorithm

(a) RandomWalks of Ants Randomwalks of ants are given in

119883(119905) = [0 cumsum (2119903 (1199051) minus 1)

cumsum (2119903 (1199052) minus 1) cumsum (2119903 (119905

119899) minus 1)]

(10)

where 119899 is the maximum number of iterations cumsumcalculates the cumulative sum and 119905 is the step of randomwalk Hence

119903 (119905) =

1 if rand gt 05

0 if rand lt 05(11)

Here 119903(119905) is a stochastic function and rand is a randomnumber generated with uniform distribution in the intervalof [0 1]

The positions of ants are saved and utilized duringoptimization in the matrix

119872Ant =

[[[[[[[[[[

[

1198601111986012sdot sdot sdot sdot sdot sdot 119860

1119889

1198602111986022sdot sdot sdot sdot sdot sdot 119860

2119889

11986011989911198601198992sdot sdot sdot sdot sdot sdot 119860

119899119889

]]]]]]]]]]

]

(12)

where119872Ant is the matrix for saving the position of each ant119860119894119895

shows the value of the 119895th variable of 119894th ant 119899 is thenumber of ants and 119889 is the number of variables

At each step of optimization ants update their positionaccording to random walk Equation (10) cannot be directlyused for updating position of ants The random walks arenormalized using the following equation (min-max normal-ization)

119883119905

119894=(119883119905

119894minus 119886119894) times (119889

119894minus 119888119905

119894)

(119889119905

119894minus 119886119894)

+ 119888119894 (13)

Journal of Engineering 5

Table 1 Optimized parameters of AGC regulator

Parameters ALO GSA [17] PSO [18] GA [19]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

1198701198681

03260 04002 03817 04171 03131 04498 03031 065251198701198682

02135 02010 02153 02028 01091 02158 03063 079601198771

00491 00404 00401 00435 00581 00201 00794 005031198772

00699 00509 00657 00635 00531 003 00737 006091198631

04457 04884 05889 04778 04756 05910 07591 072161198632

08770 08975 08946 08744 06097 08226 08950 08984

where 119886119894is the minimum of random walk of 119894th variable

119889119894is the maximum of random walk of 119894th variable 119888119905

119894is

the minimum of 119894th variable at 119905th iteration and 119889119905119894is the

maximum of 119894th variable at 119905th iteration

(b) Trapping in Antlionrsquos Pit Random walks of ants areaffected by antlionsrsquo trap Mathematical modeling of trappingin antlionrsquos pit is proposed by the following equations

119888119905

119894= Antlion119905

119895+ 119888119905

119889119905

119894= Antlion119905

119895+ 119889119905

(14)

where 119888119905 represents the minimum of all variables at 119905thiteration 119889119905 indicates the vector including the maximum ofall variables at 119905th iteration 119888119905

119894is the minimum of all variables

for 119894th ant 119889119905119894is the maximum of all variables for 119894th ant and

Antlion119905119895shows the position of the selected 119895th antlion at 119905th

iteration

(c) Building Trap For building trap a roulette wheel isemployed to model the hunting capability of antlions TheALO algorithm is required to utilize a roulette wheel operatorfor selecting antlions based on their fitness during optimiza-tion This mechanism provides high chances to the fitterantlions for catching ants

(d) Sliding Ants towards Antlion Antlions are able to buildtraps which are proportional to their fitness and ants arerequired to move randomly Once the antlion realizes that anant is in the trap it shoots sand out the centre of the pit Theants which are trying to escape slide down the trapThe radiusof the antrsquos randomwalks hypersphere is decreased adaptivelyin the mathematical modeling The following equations areproposed for this

119888119905=119888119905

119868

119889119905=119889119905

119868

(15)

where 119868 is a ratio 119888119905 is the minimum of all variables at 119905thiteration and 119889119905 indicates the vector including the maximumof all variables at 119905th iteration

(e) Catching Prey and Rebuilding the Pit This is the finalstage of hunt At this stage an ant reaches the bottom of

the pit and is caught in the antlionrsquos jaw After this stage theantlion pulls the ant inside the sand and consumes its bodyCatching the prey occurs when the ant goes inside the sandand becomes fitter than its corresponding antlion Accordingto the position of the latest hunted ant the antlions updatetheir position to enhance the chances of catching new preyMathematically the following equations can be proposed inthis regard

Antlion119905119895= Ant119905

119894if 119891 (Ant119905

119894) gt 119891 (Antlion119905

119895) (16)

where 119905 represents the current iteration Antlion119905119895is the

position of the selected 119895th antlion at 119905th iteration and Ant119905119894

represents the position of 119894th ant at 119905th iteration

(f) Elitism For any evolutionary algorithm elitism is animportant feature that allows antlions to maintain the bestsolution obtained at any stage of optimization process Inthis algorithm the best obtained antlion during the entireiteration is saved and is considered as an elite Since thefittest antlion is elite it affects the movement of all the antsduring iteration Hence it is assumed that every ant walksrandomly around a selected antlion by roulette wheel and theelite simultaneously as follows

Ant119905119894=119877119905

119860+ 119877119905

119864

2 (17)

where 119877119905119860is the random walk around the antlion selected by

the roulette wheel at 119905th iteration119877119905119864is the randomwalk and

Ant119905119894represents the position of 119894th ant at 119905th iteration

The following section presents analysis of simulationresults

4 Results and Analysis

This section presents simulation results and analysis of AGCregulator performance on two-area thermal interconnectedpower system with different step perturbations and loadingconditions Different AGC regulator settings are obtainedwith the application of four algorithms (GA PSO GSA andALO) on two standard objective functions (ISE and ITAE)Table 1 shows the values of optimized parameters of regulatorwith the application of the abovementioned algorithms ontwo objective functions

Table 2 shows the values of systemrsquos minimum dampingratio and eigenvalues after the application of these AGC

6 Journal of Engineering

Table2Eigenvaluesa

ndminim

umdamping

ratio

Parameter

ALO

GSA

[17]

PSO[18]

GA[19

]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

Syste

mmod

es

minus58548

minus59604

minus58468

minus5976

minus5846

minus65657

minus56586

minus5808

minus42219

minus44165

minus4313

minus44257

minus444

43minus48155

minus42083

minus42168

minus03805plusmn17

191119894

minus02885plusmn18

854119894

minus03994plusmn17

029119894

02511plusmn19

124119894

minus040

10plusmn17

004i

minus00030plusmn26953119894minus04925plusmn13

799119894

minus02024plusmn16

817119894

minus03007plusmn14

854119894

minus02088plusmn17

320119894

minus02606plusmn16

066119894

minus01924plusmn17420119894

minus024

06plusmn17

718i

minus00220plusmn21889119894minus02491plusmn14

729119894

003

61plusmn15

786i

minus03716

minus04624

minus03395

minus05169

minus009

83plusmn00157i

minus046

66minus01353

minus01058

minus0117

9minus00910

minus0110

2minus00884

minus03521

minus00494

minus03294

minus07991

minus02256

minus02351

minus02061

minus02416

minus02144

minus03712

minus09209

Minim

umdamping

ratio

01984

01197

01601

01098

01345

00011

01668

00229

Journal of Engineering 7

regulators Eigenvalue analysis plays an important role instability studies Complex conjugate eigenvalues are alsoknown as swing modes and these eigenvalues are responsiblefor oscillatory instability when the real part of the eigen-value is positive From Table 2 it is observed that whenoptimization process is carried out with the application ofGA on 119869

2system mode contains a swing mode with positive

eigenvalue (0361) Real positive part of eigen is the indicationof oscillations of growing amplitudeTheminimum dampingratios obtained from the application of different regulatorswith 119869

1and 119869

2criteria are shown in Table 2 For PSO

regulator minimum damping ratios obtained from thesecriteria are (01345 00011) similarly the ratios for GA are(01668 00229) for GSA are (01601 01098) and for ALOare (01984 01197) It can be said that a considerable amountof damping is enhanced in each case when the regulatorparameters are obtained with criterion 119869

1 Overall damping

of the system is the highest with ALO regulator (1198691) (01984)

Prima facie it can be concluded that the regulator designobtained from criterion 119869

1is more effective as the damping

enhanced by this regulator is higher In eigenvalue analysisboth real and imaginary parts have their interpretation andphysical significance The real part of the complex conjugateeigenvalue shows the damping behavior which represents thedamp oscillations whichmeans the larger themagnitude thehigher the rate of decay Imaginary components show thefrequency of oscillations It can be observed from Table 2that high frequency oscillations are associated with setting1198692 Higher frequency oscillations are bad for equipment

health and often cause the damage of physical structure ofcontrollers In this case for 119869

2 GA frequency of oscillations

is (157 168) for PSO (269 218) for GSA (191 174) and(188 173) for ALO It is observed that although frequencyof oscillations is in moderate range for GA regulator theamplitude of the oscillation is growing with time as it has apositive real part of eigenvalue However the other regulatorshave high frequency of oscillations modes as comparedwith ALO To show this analysis in a more prominent wayAGC regulators are designed with ALO algorithm and testedfor different levels of perturbations Figures 3(a) and 3(b)show the dynamic responses of frequency deviations inareas 1 and 2 when area 1 observes a step disturbance of001 pu Figures 3(c) and 3(d) show the frequency deviationcurves of both areas with both regulator settings 119869

1and

1198692when area 2 is perturbed with 002 pu Similarly for

both regulator settings the dynamic responses obtainedfrom both areas are self-explanatory It is observed that 119869

1

setting is promising The overshoot and settling time of thefrequency deviation curves of both areas are less with 119869

1

regulator It is also empirical to judge that the variationsof tie-line power exchanges are nominal with both types ofperturbation with 119869

1regulator Hence it is concluded that 119869

1

optimization criterion is suitable for the designing of theAGCregulator

To exhibit the comparative performance of the ALO reg-ulator with other regulators four different loading scenariosare simulated in this work These loading conditions aresummarized below

Case 1 Load changes in area 1 by 10Thedynamic responsesof Δ119865

1 Δ1198652 and Δ119875tie are given in Figures 4ndash6 for all the

algorithms

Case 2 Load changes in area 2 by 20 Figures 7ndash9 show thedynamic responses of the system

Case 3 Load is increased in area 1 by 25 In Figures 10ndash12the system dynamic responses are shown

Case 4 Load is decreased in area 1 by 25 and the systemdynamic responses are given in Figures 13ndash15

Dynamic responses along with the system eigenvalues forthese conditions are exhibited in Table 3 It is observed thatagain with setting 119869

2few eigenvalues possess positive real part

when optimized with GA (00370 00382 and 00368) Thereal part of swing mode varies from minus02823 to minus04567 forALO regulator from minus02541 to minus04632 for GSA regulatorfrom minus00982 to minus4587 for PSO regulator and from minus02511to minus05411 for GA regulator with criterion 119869

1 It is of note

here that the real part of the eigenvalue observes a largevariation in case of GA under different loading conditionsThis spread put a question mark on the performance ofthe regulator and robustness of the regulator also Moder-ate spread has been observed with ALO regulator For allcases higher numeric values of real part of the eigenvaluessuggest that the system is more stable In Case 1 thesevalues are (minus04278 minus02823) for ALO (minus04288 minus02570)for GSA (minus04277 minus02395) for PSO and (minus02588 minus05271)for GA It can be predicted that for Case 1 the robustsetting is achieved by ALO Similarly in Case 4 the realparts of eigenvalues (swing modes) are (minus03276 minus02879)for ALO and (minus03106 minus02589) for GSA and an addi-tional swing mode with PSO setting has been observed(1198691) (minus03055 minus02459 00983) and (minus0440 02680) for GA

From this it is also observed that a higher degree ofrobustness can be achieved by ALO regulator To understandthe dynamic response of the frequency deviation curvesa conventional index Figure of Demerit (FOD) is usedin this paper Figure of Demerit is the summation of thesquare of the overshoot and settling time of the deviationcurves It is observed that for almost all loading cases thevalues of settling time overshoot and FODs are low forALO based regulators as compared with other regulatordesigns It is observed from Figures 4ndash6 that ALO basedcontroller exhibits better dynamic performance as comparedwith others The percentage of overshoot and settling timeis much less in these cases The low oscillatory responseexhibited by ALO is best suited for the equipmentrsquos healthFOD values are considered as a close replica of dynamicperformance of controller Higher values of FOD show poordynamic performance and vice versa It is also empiricalto mention here that for frequency deviation in area 1 thesettling time and FOD obtained from ALO are 38 and 1444respectively whereas from GSA PSO and GA the settlingtime and FOD are 56 50 and 49 and 3136 25 and 2401respectively The frequency deviation in area 2 also showsthat the values of settling time and FOD are less when ALO

8 Journal of Engineering

Table3Syste

mmod

esfore

achcase

ofallthe

algorithm

s

Parameters

ALO

GSA

[17]

PSO[18]

GA[19

]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

Case

1

minus58014

minus58014

minus57891

minus59112

minus57884

minus64711

minus55532

minus5752

minus42274

minus42274

minus4313

minus44257

minus444

43minus48155

minus41792

minus42168

minus04924plusmn16

361119894

minus04924plusmn16

361119894

minus04288plusmn16

043119894

minus02773plusmn18

079119894

minus04277plusmn16

059119894

minus00430plusmn25784119894

minus02588plusmn14

307119894

minus02211plusmn15

866119894

minus02842plusmn14

933119894

minus02842plusmn14

933119894

minus02570plusmn16

085119894

minus01941plusmn1746

0119894minus02395plusmn17

695119894

minus00222plusmn21888119894

minus05271plusmn11657119894

00370plusmn15

795119894

minus01208

minus01208

minus03454

minus05259

minus00983plusmn00157119894

minus04806

minus01466

minus01058

minus02021

minus02021

minus0110

1minus00884

minus03584

minus00494

minus03344

minus09221

minus02229

minus02229

minus02062

minus02416

minus02144

minus0401

minus08182

Case

2

minus58597

minus59843

minus58468

minus5976

minus5846

minus6564

minus55965

minus5808

minus41275

minus42672

minus42059

minus43093

minus43269

minus46691

minus40832

minus41155

minus046

46plusmn17

341119894

minus02906plusmn19

218119894

minus040

02plusmn17

063119894

minus02534plusmn19

127119894

minus03943plusmn17

014119894

000

14plusmn26941119894

minus05108plusmn12

557119894

minus02029plusmn16

828119894

minus03315plusmn13

466119894

minus01072plusmn15

609119894

minus03117plusmn14

571119894

minus02466plusmn15

904119894

minus03057plusmn16

218119894

minus00944plusmn20213119894

minus03032plusmn12

918119894

minus00013plusmn14

380119894

minus01204

minus00879

minus03394

minus05169

minus00986plusmn00155119894

minus04774

minus01467

minus01059

minus02047

minus044

98minus0110

1minus00884

minus03521

minus00494

minus0344

minus08003

minus02234

minus05752

minus02096

minus0245

minus02155

minus03879

minus09453

Case

3

minus57282

minus58373

minus57167

minus58312

minus5716

minus6353

minus54991

minus56819

minus42274

minus43812

minus4313

minus44278

minus444

43minus48155

minus41792

minus42168

minus05297plusmn15

095119894

minus03560plusmn16

872119894

minus04632plusmn14

784119894

minus03257plusmn16

774119894

minus04587plusmn14

794119894

minus00990plusmn24269119894

minus02590plusmn14

294119894

minus02413plusmn14

636119894

minus02816plusmn14

943119894

minus00567plusmn17

151119894

minus02541plusmn16

063119894

minus01938plusmn17

505119894

minus02396plusmn17679119894

minus00228plusmn21889119894

minus05411plusmn10

386119894

003

82plusmn15

795119894

minus01204

minus00878

minus0355

minus05367

minus00982plusmn00157119894

minus04855

minus01462

minus01058

minus02039

minus046

72minus011

minus00886

minus03686

minus00494

minus03357

minus09251

minus02252

minus05609

minus02063

minus02401

minus02144

minus04258

minus08475

Case

4

minus60556

minus62024

minus6041

minus61949

minus604

01minus68711

minus57445

minus59969

minus42274

minus43812

minus4313

minus44278

minus444

43minus48155

minus41792

minus42168

minus03695plusmn20323119894

minus01897plusmn22365119894

minus03106plusmn20088119894

minus01627plusmn22305119894

minus03055plusmn20076119894

01510plusmn30616119894

minus044

40plusmn15

429119894

minus01319plusmn19

807119894

minus02838plusmn14

894119894

minus00573plusmn17

122119894

minus02589plusmn16

017119894

minus01958plusmn1744

2119894minus02459plusmn17

656119894

minus00217plusmn21890119894

minus02680plusmn14

339119894

003

68plusmn15

765119894

minus01216

minus00879

minus03261

minus04948

minus00983plusmn00158119894

minus04698

minus01478

minus01059

minus01971

minus0434

minus0110

5minus00886

minus03379

minus00494

minus03276

minus07544

minus02194

minus05605

minus02059

minus024

minus02144

minus03632

minus09192

Journal of Engineering 9

J

J1

2

2 4 6 81 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(a)

J

J1

2

2 4 6 80 10

Time (s)

minus005

0

005

ΔF2

(Hz)

(b)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(c)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

minus005

0

005

ΔF2

(Hz)

(d)

J

J1

2

2 4 6 80 10

Time (s)

ΔP

tie(p

u)

minus002

0

002

(e)

J

J1

2

2 4 6 80 10

Time (s)

minus001

0

001

ΔP

tie(p

u)

(f)

Figure 3 Dynamic responses obtained from ALO

regulator is used The value of settling time with frequencydeviation in area 2 is observed as 60 for ALO 72 for GSA76 for PSO and 80 for GA It is also interesting to observethat with the 10 increase in the load PSO gives erroneousresults and the flow of tie-line power behaves in a differentmanner Hence critical analysis of dynamic responses clearlyreveals that better dynamic performance is exhibited by ALOBy examining the responses in Figures 7ndash9 it is clearly seenthat the settling time and peak overshoot are less whenload changes in area 2 by 20 It can be observed fromFigure 8 that when area 2 observes 20 increase GA basedcontroller is not able to mitigate the frequency oscillationsThis inculcates oscillatory instability in the system HoweverALO based controller shows a better dynamic response andyields satisfactory performance over a wide range of loading

conditions For Case 2 the settling time of ALO is 36 and is53 42 and 58 for GSA PSO andGA respectively Similarlythe FOD is also very low in case of ALO that is 1296whereas it is 1764 and 3364 in case of PSO and GA Figures10 and 11 show the frequency deviations of areas 1 and 2From dynamic responses of overshoot settling time andFOD it is clear that ALO provides competitive results Thedynamic responses for Case 4 are shown in Figures 13ndash15 andit has been observed that ALO tuned controller yields betterdynamic performanceThe minimum settling time and FODobtained from ALO are 51 and 2601 for frequency deviationin area 1 and 60 and 3600 for frequency deviation in area 2However in case of GSA the settling time is 79 and FOD is198 An oscillatory response is obtained by the GA GSA andPSO tuned controllers

10 Journal of Engineering

ALOGSA [17]

PSO [18]GA [19]

2 4 6 8 10 120Time (s)

minus004

minus003

minus002

minus001

0

001

ΔF1

(Hz)

Figure 4 Change in frequency of area 1 by 10 load increase in area1

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

2 4 6 80 1210

Time (s)

ALOGSA [17]

PSO [18]GA [19]

Figure 5 Change in frequency of area 2 by 10 load increase in area1

5 Optimization Performance

To judge the efficiency of the optimization process carried outby all algorithms 100 trials of optimization are carried outTo provide a fair comparison the population size (100) andthe maximum number of iterations (1000) are kept the sameStopping criterion for the optimization process is maximumrun of the iteration To observe the optimization process in acritical way the standard deviations of optimized parametersof the regulator along with the values of objective functionsare calculated and shown in Table 4 It is observed thathigh values of standard deviations are obtained in regulator

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 6 Change in tie-line power by 10 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 7 Change in frequency of area 1 by 20 load increase in area2

parameters and values of objective functions when optimiza-tion process is handled by GA (009729) Comparatively largevalues of standard deviations are found in GA and PSOwhenthey are compared with ALO We observed high values ofstandard deviation in speed regulation parameters after eachrun of optimization obtained with GA regulators (119869

1and

1198692) Speed regulation parameter is a vulnerable parameter

in power system dynamics studies It affects the systemdynamics in a very prominent way Large values of standarddeviations in the calculation of such vulnerable parametersare not acceptable The values for standard deviations are010256 (GSA 119869

1) and 01550 (GA 119869

2) and similarly for

1198772 they are 00081 (ALO 119869

1) 002 (GSA) 038 (PSO) and

Journal of Engineering 11

Table 4 Standard deviation of optimized parameters of the regulator

Parameters ALO GSA [17] PSO [18] GA [19]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

1198701198681

002923 003773 002425 007720 002604 008461 009729 0206871198631

004107 003315 004475 009833 008416 004759 018872 0213131198771

000582 000102 000045 000168 000153 001403 000892 0007171198701198682

001763 004563 010256 000769 009639 008158 005800 0155501198632

008957 008807 004916 011771 016726 008363 017955 0079451198772

000343 000174 000173 000385 000280 001080 000310 00105937000184 716E minus 06 00212 0000419 038 0011 176 0013

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

ALOGSA [17]

PSO [18]GA [19]

Figure 8 Change in frequency of area 2 by 20 load increase in area2

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 9 Change in tie-line power by 20 load increase in area 2

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 10 Change in frequency of area 1 by 25 load increase inarea 1

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 11 Change in frequency of area 2 by 25 load increase inarea 1

12 Journal of Engineering

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 12 Change in tie-line power by 25 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus005

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 13 Change in frequency of area 1 by 25 load decreases inarea 1

176 for GA The impact of speed regulation parameters onthe dynamic response is shown in [25] The lowest valuesof standard deviations are observed when the parametersare optimized by ALO This basically means that in eachrun of optimization ALO exhibits precision in computingthe parameters The standard deviations in the values ofintegral gains for area 1 by 119869

1and 119869

2are minimum for

ALO (0041 0033) for GA these values are (018 and 0213)and similarly (0044 009) for GSA and (008 and 0047)for PSO It can be concluded that regulator setting integralgain observes the least variation in numerical values whenthe parameter is optimized through ALO (119869

1) The values

of standard deviations in objective functions 1198691and 119869

2are

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 14 Change in frequency of area 1 by 25 load decreases inarea 1

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 15 Change in tie-line power by 25 load decreases in area 1

the lowest for ALO process and the highest for GA Thevalues of standard deviations in the values of 119869

1for GA PSO

GSA and GWO are 00972 00264 00242 and 002 andfor 1198692are 02068 00846 00772 and 03773 It has been

observed that the values obtained by ALO are precise and theoptimization processes are reliable enough for obtaining theregulator design However high values of standard deviationsin parameters of regulator (176 with 119877

2) and in the objective

functions show that the optimization process loses its rele-vance when it is handled by GA Hence it is concluded fromthe eigenvalue analysis anddynamic response of the deviationcurves that ALO shows a promising response to obtainregulator settingwith optimization criterion 119869

1The following

Journal of Engineering 13

section summarizes the contribution of this research workand proposes a solid milieu for future work

6 Conclusion

This paper presents an application of the recently introducedalgorithm ALO to find optimal parameters of the AGCregulator The ALO regulator is employed on a test system oftwo thermal units connected with a weak tie line of limitedcapacity for AGCThe following are the major findings of thework

(A) Comparison of the application of two objective func-tions namely ISE and ITAE in optimization processfor finding the regulator parameters under differ-ent contingencies is investigated Results reveal thatITAE is a better choice to optimize the regulatorparameters

(B) Eigenvalue analysis is performed to test the effec-tiveness of the proposed approach and to comparethe results of the proposed approach with recentlypublished approaches It is observed that the dampingobtained from ALO regulator is more positive ascompared with the other algorithms

(C) ALO shows promising results in terms of overshootsettling time obtained from the frequency responsesof both areas under different loading cases standarddeviations in regulatorrsquos parameter values ISE andITAE values and optimization performance

(D) Damping performance is evaluated with differentcontingencies load changes and step disturbancesin both areas PI controller setting obtained throughALO exhibits better dynamic performance and over-all low settling time

Application of other new metaheuristic algorithms in AGCregulator design on different models of the power systemconsidering different renewable energy power sources lies inthe future scope

Nomenclature

119894 Subscript referring to area 119894 (1 2)Δ119865119894 Frequency deviation in area 119894 (Hz)

Δ119875119866119894 Incremental generation of area 119894 (pu)

Δ119875119871119894 Incremental load change in area 119894 (pu)

ACE119894 Area Control Error of area 119894

119861119894 Frequency bias parameter of area 119894

119877119894 Speed regulation of the governor of area 119894

(Hzpu MW)119879119892119894 Time constant of governor of area 119894 (s)

119879119905119894 Time constant of turbine of area 119894 (s)

119870119901119894 Gain of generator and load of area 119894

119879119901119894 Time constant of generator and load of

area 119894 (s)Δ119875tie Incremental change in tie line (pu)11987912 Synchronizing coefficient

119879 Simulation time (s)119905 Current iteration

Competing Interests

The authors declare that they have no competing interests

References

[1] O I Elgerd Energy Systems Theory An Introduction McGraw-Hill New Delhi India 1983

[2] IEEE Standard Committee ldquoIEEE Standard definitions of termsfor automatic generation control on electric power systemsrdquoIEEE Transactions on Power Apparatus and Systems vol 89 no6 pp 1356ndash1364 1970

[3] A Ibraheem P Kumar and D P Kothari ldquoRecent philosophiesof automatic generation control strategies in power systemsrdquoIEEE Transactions on Power Systems vol 20 no 1 pp 346ndash3572005

[4] H Sadat Power System Analysis McGraw-Hill New York NYUSA 1999

[5] J Nanda and B Kaul ldquoAutomatic generation control of aninterconnected power systemrdquo Proceedings of the Institution ofElectrical Engineers vol 125 no 5 pp 385ndash390 1978

[6] A Y Sivaramakrishnan M V Hariharan and M C SrisailamldquoDesign of variable-structure load-frequency controller usingpole assignment techniquerdquo International Journal of Controlvol 40 no 3 pp 487ndash498 1984

[7] M Z Bernard T H Mohamed Y S Qudaih and Y MitanildquoDecentralized load frequency control in an interconnectedpower system using Coefficient Diagram Methodrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 63pp 165ndash172 2014

[8] R Ali T HMohamed Y S Qudaih and YMitani ldquoA new loadfrequency control approach in an isolated small power systemsusing coefficient diagram methodrdquo International Journal ofElectrical Power and Energy Systems vol 56 pp 110ndash116 2014

[9] I Vajk M Vajta L Keviczky R Haber J Hetthessy andK Kovacs ldquoAdaptive load-frequency control of the hungarianpower systemrdquo Automatica vol 21 no 2 pp 129ndash137 1985

[10] J Kanniah S C Tripathy O P Malik and G S HopeldquoMicroprocessor-based adaptive load-frequency controlrdquo IEEProceedings CmdashGeneration Transmission and Distribution vol131 no 4 pp 121ndash128 1984

[11] M L Kothari P S Satsangi and J Nanda ldquoSampled-dataautomatic generation control of interconnected reheat thermalsystems considering generation rate constraintsrdquo IEEE Transac-tions on Power Apparatus and Systems vol 100 no 5 pp 2334ndash2342 1981

[12] S Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001

[13] B K Sahu S Pati P K Mohanty and S Panda ldquoTeaching-learning based optimization algorithm based fuzzy-PID con-troller for automatic generation control of multi-area powersystemrdquo Applied Soft Computing Journal vol 27 pp 240ndash2492015

[14] K R Sudha and R Vijaya Santhi ldquoLoad frequency control of aninterconnected reheat thermal systemusing type-2 fuzzy systemincluding SMES unitsrdquo International Journal of Electrical Poweramp Energy Systems vol 43 no 1 pp 1383ndash1392 2012

[15] A Banerjee V Mukherjee and S P Ghoshal ldquoIntelligentcontroller for load-tracking performance of an autonomous

14 Journal of Engineering

power systemrdquo Ain Shams Engineering Journal vol 5 no 4 pp1167ndash1176 2014

[16] S Padhan R K Sahu and S Panda ldquoAutomatic generationcontrol with thyristor controlled series compensator includingsuperconducting magnetic energy storage unitsrdquo Ain ShamsEngineering Journal vol 5 no 3 pp 759ndash774 2014

[17] R K Sahu S Panda and S Padhan ldquoOptimal gravitationalsearch algorithm for automatic generation control of intercon-nected power systemsrdquo Ain Shams Engineering Journal vol 5no 3 pp 721ndash733 2014

[18] Y L Abdel-Magid and M A Abido ldquoAGC tuning of intercon-nected reheat thermal systems with particle swarm optimiza-tionrdquo in Proceedings of the 10th IEEE International Conferenceon Electronics Circuits and Systems (ICECS rsquo03) pp 376ndash379December 2003

[19] Y L Abdel-Magid and M M Dawoud ldquoOptimal AGC tuningwith genetic algorithmsrdquo Electric Power Systems Research vol38 no 3 pp 231ndash238 1996

[20] J Nanda S Mishra and L C Saikia ldquoMaiden application ofbacterial foraging-based optimization technique in multiareaautomatic generation controlrdquo IEEE Transactions on PowerSystems vol 24 no 2 pp 602ndash609 2009

[21] U K Rout R K Sahu and S Panda ldquoDesign and analysisof differential evolution algorithm based automatic generationcontrol for interconnected power systemrdquo Ain Shams Engineer-ing Journal vol 4 no 3 pp 409ndash421 2013

[22] H Gozde M C Taplamacioglu and I Kocaarslan ldquoCompara-tive performance analysis of Artificial Bee Colony algorithm inautomatic generation control for interconnected reheat thermalpower systemrdquo International Journal of Electrical Power andEnergy Systems vol 42 no 1 pp 167ndash178 2012

[23] S Debbarma L Chandra Saikia and N Sinha ldquoSolution toautomatic generation control problem using firefly algorithmoptimized I120582D120583 controllerrdquo ISA Transactions vol 53 no 2 pp358ndash366 2014

[24] P Dash L C Saikia and N Sinha ldquoComparison of per-formances of several Cuckoo search algorithm based 2DOFcontrollers in AGC of multi-area thermal systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 55 pp 429ndash436 2014

[25] A Saxena M Gupta and V Gupta ldquoAutomatic generationcontrol of two area interconnected power system using Geneticalgorithmrdquo in Proceedings of the 3rd IEEE International Con-ference on Computational Intelligence and Computing Research(ICCIC rsquo12) Coimbatore India December 2012

[26] B K Sahu T K Pati J R Nayak S Panda and S K KarldquoA novel hybrid LUS-TLBO optimized fuzzy-PID controllerfor load frequency control of multi-source power systemrdquoInternational Journal of Electrical Power amp Energy Systems vol74 pp 58ndash69 2016

[27] Y Sharma and L C Saikia ldquoAutomatic generation controlof a multi-area STmdashthermal power system using Grey WolfOptimizer algorithm based classical controllersrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 853ndash862 2015

[28] P Dash L C Saikia and N Sinha ldquoAutomatic generationcontrol of multi area thermal system using Bat algorithmoptimized PDndashPID cascade controllerrdquo International Journal ofElectrical Power amp Energy Systems vol 68 pp 364ndash372 2015

[29] S Mirjalili ldquoThe ant lion optimizerrdquo Advances in EngineeringSoftware vol 83 pp 80ndash98 2015

[30] MATLAB httpwwwmathworkscom

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Engineering 3

B1

B2

ACE1

PI controller

PI controller

Controller

Controller

u1

+ +

+

+

minus minus

minus

minus

minus

minus

minus

1

R1

1

R2

1

1 + sTg1

1

1 + sTg2

1

1 + sTt1

1

1 + sTt2

ΔPg1

ΔPg2

ΔPL1

ΔPL2

ΔP12

ΔP21

Kp1

1 + sTp1

Kp2

1 + sTp2

Load

Load

TurbineGovernor

TurbineGovernor

ΔF1

ΔF2

ACE2

++

+u2

2120587T12s

a12a12

ΔPtie

sum

sum

sumsumsum

sum sum

Figure 1 Transfer function model of two-area nonreheat thermal interconnected system

The transfer function of a governor is represented by [1]

119866119892 (119904) =

1

1 + 119904119879119892

(2)

The turbine is represented by the transfer function as [1]

119866119905 (119904) =

1

1 + 119904119879119905

(3)

The transfer function of rotating mass and load [1] is asfollows

119866119871 (119904) =

119870119901

1 + 119904119879119901

(4)

where 119879119901= 2119867119891119863 and119870

119901= 1119863

Δ119875119866and Δ119875

119871are the two inputs of rotating mass and load

and Δ119891(119904) is the output and is represented by [1]

Δ119891 (119904) = 119866119871(119904) [Δ119875

119866(119904) minus Δ119875

119871(119904)] (5)

22 The System Investigated The system was investigated ontwo equal thermal areas connected by a weak tie line havingthe same generation capacity of 1000MVA The parametersof the system are taken from [4] A sudden step perturbationof 01875 pu occurs in area 1 and another one of 01275 puoccurs in area 2 The transfer function model of the two-area thermal system is shown in Figure 1 The system isimplemented using MATLAB 2013 and run on a Pentium IVCPU 269GHz and 184GB RAM computer [30]

23The Proposed Approach The controller used in AGC sys-tem is PI controller as it determines the difference between setpoint and reference point and removes the steady state errorFor the design of PI controller the parameters proportionalgain (119870

119875) and integral gain (119870

119868) are essential However in this

work for the ease and simplicity of the optimization processwe consider proportional gain 1 Area Control Errors are theinput of the controllers for area 1 and area 2 and are definedas

ACE1= 1198611Δ1198911+ Δ119875tie

ACE2= 1198612Δ1198912+ Δ119875tie

(6)

where 1198611= 1119877

1+ 1198631and 119861

2= 1119877

2+ 1198632

The outputs of the controllers are 1199061and 119906

2and are

obtained as follows

1199061= 1198701198751ACE1+ 1198701198681intACE

1

1199062= 1198701198752ACE2+ 1198701198682intACE

2

(7)

In this paper the estimation of integral gains and parametersof primary governor loop is based on two objective functions(ITAE and ISE) which are given in (8) These objective

4 Journal of Engineering

functions aim to reduce the steady state error to zero andmaximize the damping ratio of the system Hence

1198691= ITAE = int

119879

0

(1003816100381610038161003816Δ1198911

1003816100381610038161003816 +1003816100381610038161003816Δ1198912

1003816100381610038161003816 +1003816100381610038161003816Δ119875tie

1003816100381610038161003816) sdot 119905 119889119905

1198692= ISE = int

119879

0

(1003816100381610038161003816Δ1198911

1003816100381610038161003816

2+1003816100381610038161003816Δ1198912

1003816100381610038161003816

2+1003816100381610038161003816Δ119875tie

1003816100381610038161003816

2) 119889119905

(8)

The problematic constraints are the parameters of AGCregulator which contains integral gains speed regulationsand the frequency sensitivity coefficients as they are boundedwith the limits These parameters are system specific Hencethe design problem can be formulated as follows

Minimize 119869

Subjected to 119870119868minle 119870119868le 119870119868max

119877min le 119877 le 119877max

119863min le 119863 le 119863max

(9)

119869 is the objective function (1198691and 1198692)

3 Antlion Optimizer

A novel algorithm inspired by nature named Antlion Opti-mizer (ALO) is presented in this section This techniquewas proposed by Mirjalili [29] in 2015 In ALO the huntingmechanism of antlions is mimicked Antlions belong toMyrmeleontidae family of class net winged insects ALOemploys five main steps of hunting that is random walkof ants building trap entrapment of ants in trap catchingprey and rebuilding traps The ALO algorithm is a gradient-free algorithm which also provides greater exploration andexploitation of search space Exploration is guaranteed bythe random selection of antlions and random walks of antsaround them whereas exploitation is guaranteed by adaptiveshrinking boundaries of antlionrsquos trap With the help ofroulette wheel and random walks ALO has high probabilityto resolve local optima stagnation The life cycle of antlionsconsists of two main phases larvae and adults Total naturallifespan can take up to 3 years which mostly occurs inlarvae and only 3ndash5 weeks in adulthood Antlions undergometamorphosis in a cocoon to become adult They mostlyhunt in larvae and the adulthood period is for reproductionAn antlion larva digs a cone shaped pit in sand by movingalong a circular path and throwing out sand with its massivejaw After digging the trap the larvae hide underneath thebottom of the cone and wait for the insect (preferably ant)to be trapped in the pit The edge of the cone is sharp enoughfor insects to fall to the bottom of the trap easily Figure 2illustrates the hunting behavior in which antlions wait for theants to be trapped in the cone shaped pit

Once the antlion realizes that the prey is in the trap it triesto catch it Another interesting behavior in the lifestyle of antbehavior is the relevancy of size of the trap level of hungerand shape of the moon Antlions dig out larger traps as theybecome more hungry and when the moon is full And in thisway they improve their chance of survival

Figure 2 The hunting behavior of antlion

31 Mathematical Modeling of the ALO Algorithm

(a) RandomWalks of Ants Randomwalks of ants are given in

119883(119905) = [0 cumsum (2119903 (1199051) minus 1)

cumsum (2119903 (1199052) minus 1) cumsum (2119903 (119905

119899) minus 1)]

(10)

where 119899 is the maximum number of iterations cumsumcalculates the cumulative sum and 119905 is the step of randomwalk Hence

119903 (119905) =

1 if rand gt 05

0 if rand lt 05(11)

Here 119903(119905) is a stochastic function and rand is a randomnumber generated with uniform distribution in the intervalof [0 1]

The positions of ants are saved and utilized duringoptimization in the matrix

119872Ant =

[[[[[[[[[[

[

1198601111986012sdot sdot sdot sdot sdot sdot 119860

1119889

1198602111986022sdot sdot sdot sdot sdot sdot 119860

2119889

11986011989911198601198992sdot sdot sdot sdot sdot sdot 119860

119899119889

]]]]]]]]]]

]

(12)

where119872Ant is the matrix for saving the position of each ant119860119894119895

shows the value of the 119895th variable of 119894th ant 119899 is thenumber of ants and 119889 is the number of variables

At each step of optimization ants update their positionaccording to random walk Equation (10) cannot be directlyused for updating position of ants The random walks arenormalized using the following equation (min-max normal-ization)

119883119905

119894=(119883119905

119894minus 119886119894) times (119889

119894minus 119888119905

119894)

(119889119905

119894minus 119886119894)

+ 119888119894 (13)

Journal of Engineering 5

Table 1 Optimized parameters of AGC regulator

Parameters ALO GSA [17] PSO [18] GA [19]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

1198701198681

03260 04002 03817 04171 03131 04498 03031 065251198701198682

02135 02010 02153 02028 01091 02158 03063 079601198771

00491 00404 00401 00435 00581 00201 00794 005031198772

00699 00509 00657 00635 00531 003 00737 006091198631

04457 04884 05889 04778 04756 05910 07591 072161198632

08770 08975 08946 08744 06097 08226 08950 08984

where 119886119894is the minimum of random walk of 119894th variable

119889119894is the maximum of random walk of 119894th variable 119888119905

119894is

the minimum of 119894th variable at 119905th iteration and 119889119905119894is the

maximum of 119894th variable at 119905th iteration

(b) Trapping in Antlionrsquos Pit Random walks of ants areaffected by antlionsrsquo trap Mathematical modeling of trappingin antlionrsquos pit is proposed by the following equations

119888119905

119894= Antlion119905

119895+ 119888119905

119889119905

119894= Antlion119905

119895+ 119889119905

(14)

where 119888119905 represents the minimum of all variables at 119905thiteration 119889119905 indicates the vector including the maximum ofall variables at 119905th iteration 119888119905

119894is the minimum of all variables

for 119894th ant 119889119905119894is the maximum of all variables for 119894th ant and

Antlion119905119895shows the position of the selected 119895th antlion at 119905th

iteration

(c) Building Trap For building trap a roulette wheel isemployed to model the hunting capability of antlions TheALO algorithm is required to utilize a roulette wheel operatorfor selecting antlions based on their fitness during optimiza-tion This mechanism provides high chances to the fitterantlions for catching ants

(d) Sliding Ants towards Antlion Antlions are able to buildtraps which are proportional to their fitness and ants arerequired to move randomly Once the antlion realizes that anant is in the trap it shoots sand out the centre of the pit Theants which are trying to escape slide down the trapThe radiusof the antrsquos randomwalks hypersphere is decreased adaptivelyin the mathematical modeling The following equations areproposed for this

119888119905=119888119905

119868

119889119905=119889119905

119868

(15)

where 119868 is a ratio 119888119905 is the minimum of all variables at 119905thiteration and 119889119905 indicates the vector including the maximumof all variables at 119905th iteration

(e) Catching Prey and Rebuilding the Pit This is the finalstage of hunt At this stage an ant reaches the bottom of

the pit and is caught in the antlionrsquos jaw After this stage theantlion pulls the ant inside the sand and consumes its bodyCatching the prey occurs when the ant goes inside the sandand becomes fitter than its corresponding antlion Accordingto the position of the latest hunted ant the antlions updatetheir position to enhance the chances of catching new preyMathematically the following equations can be proposed inthis regard

Antlion119905119895= Ant119905

119894if 119891 (Ant119905

119894) gt 119891 (Antlion119905

119895) (16)

where 119905 represents the current iteration Antlion119905119895is the

position of the selected 119895th antlion at 119905th iteration and Ant119905119894

represents the position of 119894th ant at 119905th iteration

(f) Elitism For any evolutionary algorithm elitism is animportant feature that allows antlions to maintain the bestsolution obtained at any stage of optimization process Inthis algorithm the best obtained antlion during the entireiteration is saved and is considered as an elite Since thefittest antlion is elite it affects the movement of all the antsduring iteration Hence it is assumed that every ant walksrandomly around a selected antlion by roulette wheel and theelite simultaneously as follows

Ant119905119894=119877119905

119860+ 119877119905

119864

2 (17)

where 119877119905119860is the random walk around the antlion selected by

the roulette wheel at 119905th iteration119877119905119864is the randomwalk and

Ant119905119894represents the position of 119894th ant at 119905th iteration

The following section presents analysis of simulationresults

4 Results and Analysis

This section presents simulation results and analysis of AGCregulator performance on two-area thermal interconnectedpower system with different step perturbations and loadingconditions Different AGC regulator settings are obtainedwith the application of four algorithms (GA PSO GSA andALO) on two standard objective functions (ISE and ITAE)Table 1 shows the values of optimized parameters of regulatorwith the application of the abovementioned algorithms ontwo objective functions

Table 2 shows the values of systemrsquos minimum dampingratio and eigenvalues after the application of these AGC

6 Journal of Engineering

Table2Eigenvaluesa

ndminim

umdamping

ratio

Parameter

ALO

GSA

[17]

PSO[18]

GA[19

]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

Syste

mmod

es

minus58548

minus59604

minus58468

minus5976

minus5846

minus65657

minus56586

minus5808

minus42219

minus44165

minus4313

minus44257

minus444

43minus48155

minus42083

minus42168

minus03805plusmn17

191119894

minus02885plusmn18

854119894

minus03994plusmn17

029119894

02511plusmn19

124119894

minus040

10plusmn17

004i

minus00030plusmn26953119894minus04925plusmn13

799119894

minus02024plusmn16

817119894

minus03007plusmn14

854119894

minus02088plusmn17

320119894

minus02606plusmn16

066119894

minus01924plusmn17420119894

minus024

06plusmn17

718i

minus00220plusmn21889119894minus02491plusmn14

729119894

003

61plusmn15

786i

minus03716

minus04624

minus03395

minus05169

minus009

83plusmn00157i

minus046

66minus01353

minus01058

minus0117

9minus00910

minus0110

2minus00884

minus03521

minus00494

minus03294

minus07991

minus02256

minus02351

minus02061

minus02416

minus02144

minus03712

minus09209

Minim

umdamping

ratio

01984

01197

01601

01098

01345

00011

01668

00229

Journal of Engineering 7

regulators Eigenvalue analysis plays an important role instability studies Complex conjugate eigenvalues are alsoknown as swing modes and these eigenvalues are responsiblefor oscillatory instability when the real part of the eigen-value is positive From Table 2 it is observed that whenoptimization process is carried out with the application ofGA on 119869

2system mode contains a swing mode with positive

eigenvalue (0361) Real positive part of eigen is the indicationof oscillations of growing amplitudeTheminimum dampingratios obtained from the application of different regulatorswith 119869

1and 119869

2criteria are shown in Table 2 For PSO

regulator minimum damping ratios obtained from thesecriteria are (01345 00011) similarly the ratios for GA are(01668 00229) for GSA are (01601 01098) and for ALOare (01984 01197) It can be said that a considerable amountof damping is enhanced in each case when the regulatorparameters are obtained with criterion 119869

1 Overall damping

of the system is the highest with ALO regulator (1198691) (01984)

Prima facie it can be concluded that the regulator designobtained from criterion 119869

1is more effective as the damping

enhanced by this regulator is higher In eigenvalue analysisboth real and imaginary parts have their interpretation andphysical significance The real part of the complex conjugateeigenvalue shows the damping behavior which represents thedamp oscillations whichmeans the larger themagnitude thehigher the rate of decay Imaginary components show thefrequency of oscillations It can be observed from Table 2that high frequency oscillations are associated with setting1198692 Higher frequency oscillations are bad for equipment

health and often cause the damage of physical structure ofcontrollers In this case for 119869

2 GA frequency of oscillations

is (157 168) for PSO (269 218) for GSA (191 174) and(188 173) for ALO It is observed that although frequencyof oscillations is in moderate range for GA regulator theamplitude of the oscillation is growing with time as it has apositive real part of eigenvalue However the other regulatorshave high frequency of oscillations modes as comparedwith ALO To show this analysis in a more prominent wayAGC regulators are designed with ALO algorithm and testedfor different levels of perturbations Figures 3(a) and 3(b)show the dynamic responses of frequency deviations inareas 1 and 2 when area 1 observes a step disturbance of001 pu Figures 3(c) and 3(d) show the frequency deviationcurves of both areas with both regulator settings 119869

1and

1198692when area 2 is perturbed with 002 pu Similarly for

both regulator settings the dynamic responses obtainedfrom both areas are self-explanatory It is observed that 119869

1

setting is promising The overshoot and settling time of thefrequency deviation curves of both areas are less with 119869

1

regulator It is also empirical to judge that the variationsof tie-line power exchanges are nominal with both types ofperturbation with 119869

1regulator Hence it is concluded that 119869

1

optimization criterion is suitable for the designing of theAGCregulator

To exhibit the comparative performance of the ALO reg-ulator with other regulators four different loading scenariosare simulated in this work These loading conditions aresummarized below

Case 1 Load changes in area 1 by 10Thedynamic responsesof Δ119865

1 Δ1198652 and Δ119875tie are given in Figures 4ndash6 for all the

algorithms

Case 2 Load changes in area 2 by 20 Figures 7ndash9 show thedynamic responses of the system

Case 3 Load is increased in area 1 by 25 In Figures 10ndash12the system dynamic responses are shown

Case 4 Load is decreased in area 1 by 25 and the systemdynamic responses are given in Figures 13ndash15

Dynamic responses along with the system eigenvalues forthese conditions are exhibited in Table 3 It is observed thatagain with setting 119869

2few eigenvalues possess positive real part

when optimized with GA (00370 00382 and 00368) Thereal part of swing mode varies from minus02823 to minus04567 forALO regulator from minus02541 to minus04632 for GSA regulatorfrom minus00982 to minus4587 for PSO regulator and from minus02511to minus05411 for GA regulator with criterion 119869

1 It is of note

here that the real part of the eigenvalue observes a largevariation in case of GA under different loading conditionsThis spread put a question mark on the performance ofthe regulator and robustness of the regulator also Moder-ate spread has been observed with ALO regulator For allcases higher numeric values of real part of the eigenvaluessuggest that the system is more stable In Case 1 thesevalues are (minus04278 minus02823) for ALO (minus04288 minus02570)for GSA (minus04277 minus02395) for PSO and (minus02588 minus05271)for GA It can be predicted that for Case 1 the robustsetting is achieved by ALO Similarly in Case 4 the realparts of eigenvalues (swing modes) are (minus03276 minus02879)for ALO and (minus03106 minus02589) for GSA and an addi-tional swing mode with PSO setting has been observed(1198691) (minus03055 minus02459 00983) and (minus0440 02680) for GA

From this it is also observed that a higher degree ofrobustness can be achieved by ALO regulator To understandthe dynamic response of the frequency deviation curvesa conventional index Figure of Demerit (FOD) is usedin this paper Figure of Demerit is the summation of thesquare of the overshoot and settling time of the deviationcurves It is observed that for almost all loading cases thevalues of settling time overshoot and FODs are low forALO based regulators as compared with other regulatordesigns It is observed from Figures 4ndash6 that ALO basedcontroller exhibits better dynamic performance as comparedwith others The percentage of overshoot and settling timeis much less in these cases The low oscillatory responseexhibited by ALO is best suited for the equipmentrsquos healthFOD values are considered as a close replica of dynamicperformance of controller Higher values of FOD show poordynamic performance and vice versa It is also empiricalto mention here that for frequency deviation in area 1 thesettling time and FOD obtained from ALO are 38 and 1444respectively whereas from GSA PSO and GA the settlingtime and FOD are 56 50 and 49 and 3136 25 and 2401respectively The frequency deviation in area 2 also showsthat the values of settling time and FOD are less when ALO

8 Journal of Engineering

Table3Syste

mmod

esfore

achcase

ofallthe

algorithm

s

Parameters

ALO

GSA

[17]

PSO[18]

GA[19

]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

Case

1

minus58014

minus58014

minus57891

minus59112

minus57884

minus64711

minus55532

minus5752

minus42274

minus42274

minus4313

minus44257

minus444

43minus48155

minus41792

minus42168

minus04924plusmn16

361119894

minus04924plusmn16

361119894

minus04288plusmn16

043119894

minus02773plusmn18

079119894

minus04277plusmn16

059119894

minus00430plusmn25784119894

minus02588plusmn14

307119894

minus02211plusmn15

866119894

minus02842plusmn14

933119894

minus02842plusmn14

933119894

minus02570plusmn16

085119894

minus01941plusmn1746

0119894minus02395plusmn17

695119894

minus00222plusmn21888119894

minus05271plusmn11657119894

00370plusmn15

795119894

minus01208

minus01208

minus03454

minus05259

minus00983plusmn00157119894

minus04806

minus01466

minus01058

minus02021

minus02021

minus0110

1minus00884

minus03584

minus00494

minus03344

minus09221

minus02229

minus02229

minus02062

minus02416

minus02144

minus0401

minus08182

Case

2

minus58597

minus59843

minus58468

minus5976

minus5846

minus6564

minus55965

minus5808

minus41275

minus42672

minus42059

minus43093

minus43269

minus46691

minus40832

minus41155

minus046

46plusmn17

341119894

minus02906plusmn19

218119894

minus040

02plusmn17

063119894

minus02534plusmn19

127119894

minus03943plusmn17

014119894

000

14plusmn26941119894

minus05108plusmn12

557119894

minus02029plusmn16

828119894

minus03315plusmn13

466119894

minus01072plusmn15

609119894

minus03117plusmn14

571119894

minus02466plusmn15

904119894

minus03057plusmn16

218119894

minus00944plusmn20213119894

minus03032plusmn12

918119894

minus00013plusmn14

380119894

minus01204

minus00879

minus03394

minus05169

minus00986plusmn00155119894

minus04774

minus01467

minus01059

minus02047

minus044

98minus0110

1minus00884

minus03521

minus00494

minus0344

minus08003

minus02234

minus05752

minus02096

minus0245

minus02155

minus03879

minus09453

Case

3

minus57282

minus58373

minus57167

minus58312

minus5716

minus6353

minus54991

minus56819

minus42274

minus43812

minus4313

minus44278

minus444

43minus48155

minus41792

minus42168

minus05297plusmn15

095119894

minus03560plusmn16

872119894

minus04632plusmn14

784119894

minus03257plusmn16

774119894

minus04587plusmn14

794119894

minus00990plusmn24269119894

minus02590plusmn14

294119894

minus02413plusmn14

636119894

minus02816plusmn14

943119894

minus00567plusmn17

151119894

minus02541plusmn16

063119894

minus01938plusmn17

505119894

minus02396plusmn17679119894

minus00228plusmn21889119894

minus05411plusmn10

386119894

003

82plusmn15

795119894

minus01204

minus00878

minus0355

minus05367

minus00982plusmn00157119894

minus04855

minus01462

minus01058

minus02039

minus046

72minus011

minus00886

minus03686

minus00494

minus03357

minus09251

minus02252

minus05609

minus02063

minus02401

minus02144

minus04258

minus08475

Case

4

minus60556

minus62024

minus6041

minus61949

minus604

01minus68711

minus57445

minus59969

minus42274

minus43812

minus4313

minus44278

minus444

43minus48155

minus41792

minus42168

minus03695plusmn20323119894

minus01897plusmn22365119894

minus03106plusmn20088119894

minus01627plusmn22305119894

minus03055plusmn20076119894

01510plusmn30616119894

minus044

40plusmn15

429119894

minus01319plusmn19

807119894

minus02838plusmn14

894119894

minus00573plusmn17

122119894

minus02589plusmn16

017119894

minus01958plusmn1744

2119894minus02459plusmn17

656119894

minus00217plusmn21890119894

minus02680plusmn14

339119894

003

68plusmn15

765119894

minus01216

minus00879

minus03261

minus04948

minus00983plusmn00158119894

minus04698

minus01478

minus01059

minus01971

minus0434

minus0110

5minus00886

minus03379

minus00494

minus03276

minus07544

minus02194

minus05605

minus02059

minus024

minus02144

minus03632

minus09192

Journal of Engineering 9

J

J1

2

2 4 6 81 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(a)

J

J1

2

2 4 6 80 10

Time (s)

minus005

0

005

ΔF2

(Hz)

(b)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(c)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

minus005

0

005

ΔF2

(Hz)

(d)

J

J1

2

2 4 6 80 10

Time (s)

ΔP

tie(p

u)

minus002

0

002

(e)

J

J1

2

2 4 6 80 10

Time (s)

minus001

0

001

ΔP

tie(p

u)

(f)

Figure 3 Dynamic responses obtained from ALO

regulator is used The value of settling time with frequencydeviation in area 2 is observed as 60 for ALO 72 for GSA76 for PSO and 80 for GA It is also interesting to observethat with the 10 increase in the load PSO gives erroneousresults and the flow of tie-line power behaves in a differentmanner Hence critical analysis of dynamic responses clearlyreveals that better dynamic performance is exhibited by ALOBy examining the responses in Figures 7ndash9 it is clearly seenthat the settling time and peak overshoot are less whenload changes in area 2 by 20 It can be observed fromFigure 8 that when area 2 observes 20 increase GA basedcontroller is not able to mitigate the frequency oscillationsThis inculcates oscillatory instability in the system HoweverALO based controller shows a better dynamic response andyields satisfactory performance over a wide range of loading

conditions For Case 2 the settling time of ALO is 36 and is53 42 and 58 for GSA PSO andGA respectively Similarlythe FOD is also very low in case of ALO that is 1296whereas it is 1764 and 3364 in case of PSO and GA Figures10 and 11 show the frequency deviations of areas 1 and 2From dynamic responses of overshoot settling time andFOD it is clear that ALO provides competitive results Thedynamic responses for Case 4 are shown in Figures 13ndash15 andit has been observed that ALO tuned controller yields betterdynamic performanceThe minimum settling time and FODobtained from ALO are 51 and 2601 for frequency deviationin area 1 and 60 and 3600 for frequency deviation in area 2However in case of GSA the settling time is 79 and FOD is198 An oscillatory response is obtained by the GA GSA andPSO tuned controllers

10 Journal of Engineering

ALOGSA [17]

PSO [18]GA [19]

2 4 6 8 10 120Time (s)

minus004

minus003

minus002

minus001

0

001

ΔF1

(Hz)

Figure 4 Change in frequency of area 1 by 10 load increase in area1

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

2 4 6 80 1210

Time (s)

ALOGSA [17]

PSO [18]GA [19]

Figure 5 Change in frequency of area 2 by 10 load increase in area1

5 Optimization Performance

To judge the efficiency of the optimization process carried outby all algorithms 100 trials of optimization are carried outTo provide a fair comparison the population size (100) andthe maximum number of iterations (1000) are kept the sameStopping criterion for the optimization process is maximumrun of the iteration To observe the optimization process in acritical way the standard deviations of optimized parametersof the regulator along with the values of objective functionsare calculated and shown in Table 4 It is observed thathigh values of standard deviations are obtained in regulator

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 6 Change in tie-line power by 10 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 7 Change in frequency of area 1 by 20 load increase in area2

parameters and values of objective functions when optimiza-tion process is handled by GA (009729) Comparatively largevalues of standard deviations are found in GA and PSOwhenthey are compared with ALO We observed high values ofstandard deviation in speed regulation parameters after eachrun of optimization obtained with GA regulators (119869

1and

1198692) Speed regulation parameter is a vulnerable parameter

in power system dynamics studies It affects the systemdynamics in a very prominent way Large values of standarddeviations in the calculation of such vulnerable parametersare not acceptable The values for standard deviations are010256 (GSA 119869

1) and 01550 (GA 119869

2) and similarly for

1198772 they are 00081 (ALO 119869

1) 002 (GSA) 038 (PSO) and

Journal of Engineering 11

Table 4 Standard deviation of optimized parameters of the regulator

Parameters ALO GSA [17] PSO [18] GA [19]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

1198701198681

002923 003773 002425 007720 002604 008461 009729 0206871198631

004107 003315 004475 009833 008416 004759 018872 0213131198771

000582 000102 000045 000168 000153 001403 000892 0007171198701198682

001763 004563 010256 000769 009639 008158 005800 0155501198632

008957 008807 004916 011771 016726 008363 017955 0079451198772

000343 000174 000173 000385 000280 001080 000310 00105937000184 716E minus 06 00212 0000419 038 0011 176 0013

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

ALOGSA [17]

PSO [18]GA [19]

Figure 8 Change in frequency of area 2 by 20 load increase in area2

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 9 Change in tie-line power by 20 load increase in area 2

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 10 Change in frequency of area 1 by 25 load increase inarea 1

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 11 Change in frequency of area 2 by 25 load increase inarea 1

12 Journal of Engineering

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 12 Change in tie-line power by 25 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus005

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 13 Change in frequency of area 1 by 25 load decreases inarea 1

176 for GA The impact of speed regulation parameters onthe dynamic response is shown in [25] The lowest valuesof standard deviations are observed when the parametersare optimized by ALO This basically means that in eachrun of optimization ALO exhibits precision in computingthe parameters The standard deviations in the values ofintegral gains for area 1 by 119869

1and 119869

2are minimum for

ALO (0041 0033) for GA these values are (018 and 0213)and similarly (0044 009) for GSA and (008 and 0047)for PSO It can be concluded that regulator setting integralgain observes the least variation in numerical values whenthe parameter is optimized through ALO (119869

1) The values

of standard deviations in objective functions 1198691and 119869

2are

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 14 Change in frequency of area 1 by 25 load decreases inarea 1

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 15 Change in tie-line power by 25 load decreases in area 1

the lowest for ALO process and the highest for GA Thevalues of standard deviations in the values of 119869

1for GA PSO

GSA and GWO are 00972 00264 00242 and 002 andfor 1198692are 02068 00846 00772 and 03773 It has been

observed that the values obtained by ALO are precise and theoptimization processes are reliable enough for obtaining theregulator design However high values of standard deviationsin parameters of regulator (176 with 119877

2) and in the objective

functions show that the optimization process loses its rele-vance when it is handled by GA Hence it is concluded fromthe eigenvalue analysis anddynamic response of the deviationcurves that ALO shows a promising response to obtainregulator settingwith optimization criterion 119869

1The following

Journal of Engineering 13

section summarizes the contribution of this research workand proposes a solid milieu for future work

6 Conclusion

This paper presents an application of the recently introducedalgorithm ALO to find optimal parameters of the AGCregulator The ALO regulator is employed on a test system oftwo thermal units connected with a weak tie line of limitedcapacity for AGCThe following are the major findings of thework

(A) Comparison of the application of two objective func-tions namely ISE and ITAE in optimization processfor finding the regulator parameters under differ-ent contingencies is investigated Results reveal thatITAE is a better choice to optimize the regulatorparameters

(B) Eigenvalue analysis is performed to test the effec-tiveness of the proposed approach and to comparethe results of the proposed approach with recentlypublished approaches It is observed that the dampingobtained from ALO regulator is more positive ascompared with the other algorithms

(C) ALO shows promising results in terms of overshootsettling time obtained from the frequency responsesof both areas under different loading cases standarddeviations in regulatorrsquos parameter values ISE andITAE values and optimization performance

(D) Damping performance is evaluated with differentcontingencies load changes and step disturbancesin both areas PI controller setting obtained throughALO exhibits better dynamic performance and over-all low settling time

Application of other new metaheuristic algorithms in AGCregulator design on different models of the power systemconsidering different renewable energy power sources lies inthe future scope

Nomenclature

119894 Subscript referring to area 119894 (1 2)Δ119865119894 Frequency deviation in area 119894 (Hz)

Δ119875119866119894 Incremental generation of area 119894 (pu)

Δ119875119871119894 Incremental load change in area 119894 (pu)

ACE119894 Area Control Error of area 119894

119861119894 Frequency bias parameter of area 119894

119877119894 Speed regulation of the governor of area 119894

(Hzpu MW)119879119892119894 Time constant of governor of area 119894 (s)

119879119905119894 Time constant of turbine of area 119894 (s)

119870119901119894 Gain of generator and load of area 119894

119879119901119894 Time constant of generator and load of

area 119894 (s)Δ119875tie Incremental change in tie line (pu)11987912 Synchronizing coefficient

119879 Simulation time (s)119905 Current iteration

Competing Interests

The authors declare that they have no competing interests

References

[1] O I Elgerd Energy Systems Theory An Introduction McGraw-Hill New Delhi India 1983

[2] IEEE Standard Committee ldquoIEEE Standard definitions of termsfor automatic generation control on electric power systemsrdquoIEEE Transactions on Power Apparatus and Systems vol 89 no6 pp 1356ndash1364 1970

[3] A Ibraheem P Kumar and D P Kothari ldquoRecent philosophiesof automatic generation control strategies in power systemsrdquoIEEE Transactions on Power Systems vol 20 no 1 pp 346ndash3572005

[4] H Sadat Power System Analysis McGraw-Hill New York NYUSA 1999

[5] J Nanda and B Kaul ldquoAutomatic generation control of aninterconnected power systemrdquo Proceedings of the Institution ofElectrical Engineers vol 125 no 5 pp 385ndash390 1978

[6] A Y Sivaramakrishnan M V Hariharan and M C SrisailamldquoDesign of variable-structure load-frequency controller usingpole assignment techniquerdquo International Journal of Controlvol 40 no 3 pp 487ndash498 1984

[7] M Z Bernard T H Mohamed Y S Qudaih and Y MitanildquoDecentralized load frequency control in an interconnectedpower system using Coefficient Diagram Methodrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 63pp 165ndash172 2014

[8] R Ali T HMohamed Y S Qudaih and YMitani ldquoA new loadfrequency control approach in an isolated small power systemsusing coefficient diagram methodrdquo International Journal ofElectrical Power and Energy Systems vol 56 pp 110ndash116 2014

[9] I Vajk M Vajta L Keviczky R Haber J Hetthessy andK Kovacs ldquoAdaptive load-frequency control of the hungarianpower systemrdquo Automatica vol 21 no 2 pp 129ndash137 1985

[10] J Kanniah S C Tripathy O P Malik and G S HopeldquoMicroprocessor-based adaptive load-frequency controlrdquo IEEProceedings CmdashGeneration Transmission and Distribution vol131 no 4 pp 121ndash128 1984

[11] M L Kothari P S Satsangi and J Nanda ldquoSampled-dataautomatic generation control of interconnected reheat thermalsystems considering generation rate constraintsrdquo IEEE Transac-tions on Power Apparatus and Systems vol 100 no 5 pp 2334ndash2342 1981

[12] S Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001

[13] B K Sahu S Pati P K Mohanty and S Panda ldquoTeaching-learning based optimization algorithm based fuzzy-PID con-troller for automatic generation control of multi-area powersystemrdquo Applied Soft Computing Journal vol 27 pp 240ndash2492015

[14] K R Sudha and R Vijaya Santhi ldquoLoad frequency control of aninterconnected reheat thermal systemusing type-2 fuzzy systemincluding SMES unitsrdquo International Journal of Electrical Poweramp Energy Systems vol 43 no 1 pp 1383ndash1392 2012

[15] A Banerjee V Mukherjee and S P Ghoshal ldquoIntelligentcontroller for load-tracking performance of an autonomous

14 Journal of Engineering

power systemrdquo Ain Shams Engineering Journal vol 5 no 4 pp1167ndash1176 2014

[16] S Padhan R K Sahu and S Panda ldquoAutomatic generationcontrol with thyristor controlled series compensator includingsuperconducting magnetic energy storage unitsrdquo Ain ShamsEngineering Journal vol 5 no 3 pp 759ndash774 2014

[17] R K Sahu S Panda and S Padhan ldquoOptimal gravitationalsearch algorithm for automatic generation control of intercon-nected power systemsrdquo Ain Shams Engineering Journal vol 5no 3 pp 721ndash733 2014

[18] Y L Abdel-Magid and M A Abido ldquoAGC tuning of intercon-nected reheat thermal systems with particle swarm optimiza-tionrdquo in Proceedings of the 10th IEEE International Conferenceon Electronics Circuits and Systems (ICECS rsquo03) pp 376ndash379December 2003

[19] Y L Abdel-Magid and M M Dawoud ldquoOptimal AGC tuningwith genetic algorithmsrdquo Electric Power Systems Research vol38 no 3 pp 231ndash238 1996

[20] J Nanda S Mishra and L C Saikia ldquoMaiden application ofbacterial foraging-based optimization technique in multiareaautomatic generation controlrdquo IEEE Transactions on PowerSystems vol 24 no 2 pp 602ndash609 2009

[21] U K Rout R K Sahu and S Panda ldquoDesign and analysisof differential evolution algorithm based automatic generationcontrol for interconnected power systemrdquo Ain Shams Engineer-ing Journal vol 4 no 3 pp 409ndash421 2013

[22] H Gozde M C Taplamacioglu and I Kocaarslan ldquoCompara-tive performance analysis of Artificial Bee Colony algorithm inautomatic generation control for interconnected reheat thermalpower systemrdquo International Journal of Electrical Power andEnergy Systems vol 42 no 1 pp 167ndash178 2012

[23] S Debbarma L Chandra Saikia and N Sinha ldquoSolution toautomatic generation control problem using firefly algorithmoptimized I120582D120583 controllerrdquo ISA Transactions vol 53 no 2 pp358ndash366 2014

[24] P Dash L C Saikia and N Sinha ldquoComparison of per-formances of several Cuckoo search algorithm based 2DOFcontrollers in AGC of multi-area thermal systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 55 pp 429ndash436 2014

[25] A Saxena M Gupta and V Gupta ldquoAutomatic generationcontrol of two area interconnected power system using Geneticalgorithmrdquo in Proceedings of the 3rd IEEE International Con-ference on Computational Intelligence and Computing Research(ICCIC rsquo12) Coimbatore India December 2012

[26] B K Sahu T K Pati J R Nayak S Panda and S K KarldquoA novel hybrid LUS-TLBO optimized fuzzy-PID controllerfor load frequency control of multi-source power systemrdquoInternational Journal of Electrical Power amp Energy Systems vol74 pp 58ndash69 2016

[27] Y Sharma and L C Saikia ldquoAutomatic generation controlof a multi-area STmdashthermal power system using Grey WolfOptimizer algorithm based classical controllersrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 853ndash862 2015

[28] P Dash L C Saikia and N Sinha ldquoAutomatic generationcontrol of multi area thermal system using Bat algorithmoptimized PDndashPID cascade controllerrdquo International Journal ofElectrical Power amp Energy Systems vol 68 pp 364ndash372 2015

[29] S Mirjalili ldquoThe ant lion optimizerrdquo Advances in EngineeringSoftware vol 83 pp 80ndash98 2015

[30] MATLAB httpwwwmathworkscom

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 Journal of Engineering

functions aim to reduce the steady state error to zero andmaximize the damping ratio of the system Hence

1198691= ITAE = int

119879

0

(1003816100381610038161003816Δ1198911

1003816100381610038161003816 +1003816100381610038161003816Δ1198912

1003816100381610038161003816 +1003816100381610038161003816Δ119875tie

1003816100381610038161003816) sdot 119905 119889119905

1198692= ISE = int

119879

0

(1003816100381610038161003816Δ1198911

1003816100381610038161003816

2+1003816100381610038161003816Δ1198912

1003816100381610038161003816

2+1003816100381610038161003816Δ119875tie

1003816100381610038161003816

2) 119889119905

(8)

The problematic constraints are the parameters of AGCregulator which contains integral gains speed regulationsand the frequency sensitivity coefficients as they are boundedwith the limits These parameters are system specific Hencethe design problem can be formulated as follows

Minimize 119869

Subjected to 119870119868minle 119870119868le 119870119868max

119877min le 119877 le 119877max

119863min le 119863 le 119863max

(9)

119869 is the objective function (1198691and 1198692)

3 Antlion Optimizer

A novel algorithm inspired by nature named Antlion Opti-mizer (ALO) is presented in this section This techniquewas proposed by Mirjalili [29] in 2015 In ALO the huntingmechanism of antlions is mimicked Antlions belong toMyrmeleontidae family of class net winged insects ALOemploys five main steps of hunting that is random walkof ants building trap entrapment of ants in trap catchingprey and rebuilding traps The ALO algorithm is a gradient-free algorithm which also provides greater exploration andexploitation of search space Exploration is guaranteed bythe random selection of antlions and random walks of antsaround them whereas exploitation is guaranteed by adaptiveshrinking boundaries of antlionrsquos trap With the help ofroulette wheel and random walks ALO has high probabilityto resolve local optima stagnation The life cycle of antlionsconsists of two main phases larvae and adults Total naturallifespan can take up to 3 years which mostly occurs inlarvae and only 3ndash5 weeks in adulthood Antlions undergometamorphosis in a cocoon to become adult They mostlyhunt in larvae and the adulthood period is for reproductionAn antlion larva digs a cone shaped pit in sand by movingalong a circular path and throwing out sand with its massivejaw After digging the trap the larvae hide underneath thebottom of the cone and wait for the insect (preferably ant)to be trapped in the pit The edge of the cone is sharp enoughfor insects to fall to the bottom of the trap easily Figure 2illustrates the hunting behavior in which antlions wait for theants to be trapped in the cone shaped pit

Once the antlion realizes that the prey is in the trap it triesto catch it Another interesting behavior in the lifestyle of antbehavior is the relevancy of size of the trap level of hungerand shape of the moon Antlions dig out larger traps as theybecome more hungry and when the moon is full And in thisway they improve their chance of survival

Figure 2 The hunting behavior of antlion

31 Mathematical Modeling of the ALO Algorithm

(a) RandomWalks of Ants Randomwalks of ants are given in

119883(119905) = [0 cumsum (2119903 (1199051) minus 1)

cumsum (2119903 (1199052) minus 1) cumsum (2119903 (119905

119899) minus 1)]

(10)

where 119899 is the maximum number of iterations cumsumcalculates the cumulative sum and 119905 is the step of randomwalk Hence

119903 (119905) =

1 if rand gt 05

0 if rand lt 05(11)

Here 119903(119905) is a stochastic function and rand is a randomnumber generated with uniform distribution in the intervalof [0 1]

The positions of ants are saved and utilized duringoptimization in the matrix

119872Ant =

[[[[[[[[[[

[

1198601111986012sdot sdot sdot sdot sdot sdot 119860

1119889

1198602111986022sdot sdot sdot sdot sdot sdot 119860

2119889

11986011989911198601198992sdot sdot sdot sdot sdot sdot 119860

119899119889

]]]]]]]]]]

]

(12)

where119872Ant is the matrix for saving the position of each ant119860119894119895

shows the value of the 119895th variable of 119894th ant 119899 is thenumber of ants and 119889 is the number of variables

At each step of optimization ants update their positionaccording to random walk Equation (10) cannot be directlyused for updating position of ants The random walks arenormalized using the following equation (min-max normal-ization)

119883119905

119894=(119883119905

119894minus 119886119894) times (119889

119894minus 119888119905

119894)

(119889119905

119894minus 119886119894)

+ 119888119894 (13)

Journal of Engineering 5

Table 1 Optimized parameters of AGC regulator

Parameters ALO GSA [17] PSO [18] GA [19]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

1198701198681

03260 04002 03817 04171 03131 04498 03031 065251198701198682

02135 02010 02153 02028 01091 02158 03063 079601198771

00491 00404 00401 00435 00581 00201 00794 005031198772

00699 00509 00657 00635 00531 003 00737 006091198631

04457 04884 05889 04778 04756 05910 07591 072161198632

08770 08975 08946 08744 06097 08226 08950 08984

where 119886119894is the minimum of random walk of 119894th variable

119889119894is the maximum of random walk of 119894th variable 119888119905

119894is

the minimum of 119894th variable at 119905th iteration and 119889119905119894is the

maximum of 119894th variable at 119905th iteration

(b) Trapping in Antlionrsquos Pit Random walks of ants areaffected by antlionsrsquo trap Mathematical modeling of trappingin antlionrsquos pit is proposed by the following equations

119888119905

119894= Antlion119905

119895+ 119888119905

119889119905

119894= Antlion119905

119895+ 119889119905

(14)

where 119888119905 represents the minimum of all variables at 119905thiteration 119889119905 indicates the vector including the maximum ofall variables at 119905th iteration 119888119905

119894is the minimum of all variables

for 119894th ant 119889119905119894is the maximum of all variables for 119894th ant and

Antlion119905119895shows the position of the selected 119895th antlion at 119905th

iteration

(c) Building Trap For building trap a roulette wheel isemployed to model the hunting capability of antlions TheALO algorithm is required to utilize a roulette wheel operatorfor selecting antlions based on their fitness during optimiza-tion This mechanism provides high chances to the fitterantlions for catching ants

(d) Sliding Ants towards Antlion Antlions are able to buildtraps which are proportional to their fitness and ants arerequired to move randomly Once the antlion realizes that anant is in the trap it shoots sand out the centre of the pit Theants which are trying to escape slide down the trapThe radiusof the antrsquos randomwalks hypersphere is decreased adaptivelyin the mathematical modeling The following equations areproposed for this

119888119905=119888119905

119868

119889119905=119889119905

119868

(15)

where 119868 is a ratio 119888119905 is the minimum of all variables at 119905thiteration and 119889119905 indicates the vector including the maximumof all variables at 119905th iteration

(e) Catching Prey and Rebuilding the Pit This is the finalstage of hunt At this stage an ant reaches the bottom of

the pit and is caught in the antlionrsquos jaw After this stage theantlion pulls the ant inside the sand and consumes its bodyCatching the prey occurs when the ant goes inside the sandand becomes fitter than its corresponding antlion Accordingto the position of the latest hunted ant the antlions updatetheir position to enhance the chances of catching new preyMathematically the following equations can be proposed inthis regard

Antlion119905119895= Ant119905

119894if 119891 (Ant119905

119894) gt 119891 (Antlion119905

119895) (16)

where 119905 represents the current iteration Antlion119905119895is the

position of the selected 119895th antlion at 119905th iteration and Ant119905119894

represents the position of 119894th ant at 119905th iteration

(f) Elitism For any evolutionary algorithm elitism is animportant feature that allows antlions to maintain the bestsolution obtained at any stage of optimization process Inthis algorithm the best obtained antlion during the entireiteration is saved and is considered as an elite Since thefittest antlion is elite it affects the movement of all the antsduring iteration Hence it is assumed that every ant walksrandomly around a selected antlion by roulette wheel and theelite simultaneously as follows

Ant119905119894=119877119905

119860+ 119877119905

119864

2 (17)

where 119877119905119860is the random walk around the antlion selected by

the roulette wheel at 119905th iteration119877119905119864is the randomwalk and

Ant119905119894represents the position of 119894th ant at 119905th iteration

The following section presents analysis of simulationresults

4 Results and Analysis

This section presents simulation results and analysis of AGCregulator performance on two-area thermal interconnectedpower system with different step perturbations and loadingconditions Different AGC regulator settings are obtainedwith the application of four algorithms (GA PSO GSA andALO) on two standard objective functions (ISE and ITAE)Table 1 shows the values of optimized parameters of regulatorwith the application of the abovementioned algorithms ontwo objective functions

Table 2 shows the values of systemrsquos minimum dampingratio and eigenvalues after the application of these AGC

6 Journal of Engineering

Table2Eigenvaluesa

ndminim

umdamping

ratio

Parameter

ALO

GSA

[17]

PSO[18]

GA[19

]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

Syste

mmod

es

minus58548

minus59604

minus58468

minus5976

minus5846

minus65657

minus56586

minus5808

minus42219

minus44165

minus4313

minus44257

minus444

43minus48155

minus42083

minus42168

minus03805plusmn17

191119894

minus02885plusmn18

854119894

minus03994plusmn17

029119894

02511plusmn19

124119894

minus040

10plusmn17

004i

minus00030plusmn26953119894minus04925plusmn13

799119894

minus02024plusmn16

817119894

minus03007plusmn14

854119894

minus02088plusmn17

320119894

minus02606plusmn16

066119894

minus01924plusmn17420119894

minus024

06plusmn17

718i

minus00220plusmn21889119894minus02491plusmn14

729119894

003

61plusmn15

786i

minus03716

minus04624

minus03395

minus05169

minus009

83plusmn00157i

minus046

66minus01353

minus01058

minus0117

9minus00910

minus0110

2minus00884

minus03521

minus00494

minus03294

minus07991

minus02256

minus02351

minus02061

minus02416

minus02144

minus03712

minus09209

Minim

umdamping

ratio

01984

01197

01601

01098

01345

00011

01668

00229

Journal of Engineering 7

regulators Eigenvalue analysis plays an important role instability studies Complex conjugate eigenvalues are alsoknown as swing modes and these eigenvalues are responsiblefor oscillatory instability when the real part of the eigen-value is positive From Table 2 it is observed that whenoptimization process is carried out with the application ofGA on 119869

2system mode contains a swing mode with positive

eigenvalue (0361) Real positive part of eigen is the indicationof oscillations of growing amplitudeTheminimum dampingratios obtained from the application of different regulatorswith 119869

1and 119869

2criteria are shown in Table 2 For PSO

regulator minimum damping ratios obtained from thesecriteria are (01345 00011) similarly the ratios for GA are(01668 00229) for GSA are (01601 01098) and for ALOare (01984 01197) It can be said that a considerable amountof damping is enhanced in each case when the regulatorparameters are obtained with criterion 119869

1 Overall damping

of the system is the highest with ALO regulator (1198691) (01984)

Prima facie it can be concluded that the regulator designobtained from criterion 119869

1is more effective as the damping

enhanced by this regulator is higher In eigenvalue analysisboth real and imaginary parts have their interpretation andphysical significance The real part of the complex conjugateeigenvalue shows the damping behavior which represents thedamp oscillations whichmeans the larger themagnitude thehigher the rate of decay Imaginary components show thefrequency of oscillations It can be observed from Table 2that high frequency oscillations are associated with setting1198692 Higher frequency oscillations are bad for equipment

health and often cause the damage of physical structure ofcontrollers In this case for 119869

2 GA frequency of oscillations

is (157 168) for PSO (269 218) for GSA (191 174) and(188 173) for ALO It is observed that although frequencyof oscillations is in moderate range for GA regulator theamplitude of the oscillation is growing with time as it has apositive real part of eigenvalue However the other regulatorshave high frequency of oscillations modes as comparedwith ALO To show this analysis in a more prominent wayAGC regulators are designed with ALO algorithm and testedfor different levels of perturbations Figures 3(a) and 3(b)show the dynamic responses of frequency deviations inareas 1 and 2 when area 1 observes a step disturbance of001 pu Figures 3(c) and 3(d) show the frequency deviationcurves of both areas with both regulator settings 119869

1and

1198692when area 2 is perturbed with 002 pu Similarly for

both regulator settings the dynamic responses obtainedfrom both areas are self-explanatory It is observed that 119869

1

setting is promising The overshoot and settling time of thefrequency deviation curves of both areas are less with 119869

1

regulator It is also empirical to judge that the variationsof tie-line power exchanges are nominal with both types ofperturbation with 119869

1regulator Hence it is concluded that 119869

1

optimization criterion is suitable for the designing of theAGCregulator

To exhibit the comparative performance of the ALO reg-ulator with other regulators four different loading scenariosare simulated in this work These loading conditions aresummarized below

Case 1 Load changes in area 1 by 10Thedynamic responsesof Δ119865

1 Δ1198652 and Δ119875tie are given in Figures 4ndash6 for all the

algorithms

Case 2 Load changes in area 2 by 20 Figures 7ndash9 show thedynamic responses of the system

Case 3 Load is increased in area 1 by 25 In Figures 10ndash12the system dynamic responses are shown

Case 4 Load is decreased in area 1 by 25 and the systemdynamic responses are given in Figures 13ndash15

Dynamic responses along with the system eigenvalues forthese conditions are exhibited in Table 3 It is observed thatagain with setting 119869

2few eigenvalues possess positive real part

when optimized with GA (00370 00382 and 00368) Thereal part of swing mode varies from minus02823 to minus04567 forALO regulator from minus02541 to minus04632 for GSA regulatorfrom minus00982 to minus4587 for PSO regulator and from minus02511to minus05411 for GA regulator with criterion 119869

1 It is of note

here that the real part of the eigenvalue observes a largevariation in case of GA under different loading conditionsThis spread put a question mark on the performance ofthe regulator and robustness of the regulator also Moder-ate spread has been observed with ALO regulator For allcases higher numeric values of real part of the eigenvaluessuggest that the system is more stable In Case 1 thesevalues are (minus04278 minus02823) for ALO (minus04288 minus02570)for GSA (minus04277 minus02395) for PSO and (minus02588 minus05271)for GA It can be predicted that for Case 1 the robustsetting is achieved by ALO Similarly in Case 4 the realparts of eigenvalues (swing modes) are (minus03276 minus02879)for ALO and (minus03106 minus02589) for GSA and an addi-tional swing mode with PSO setting has been observed(1198691) (minus03055 minus02459 00983) and (minus0440 02680) for GA

From this it is also observed that a higher degree ofrobustness can be achieved by ALO regulator To understandthe dynamic response of the frequency deviation curvesa conventional index Figure of Demerit (FOD) is usedin this paper Figure of Demerit is the summation of thesquare of the overshoot and settling time of the deviationcurves It is observed that for almost all loading cases thevalues of settling time overshoot and FODs are low forALO based regulators as compared with other regulatordesigns It is observed from Figures 4ndash6 that ALO basedcontroller exhibits better dynamic performance as comparedwith others The percentage of overshoot and settling timeis much less in these cases The low oscillatory responseexhibited by ALO is best suited for the equipmentrsquos healthFOD values are considered as a close replica of dynamicperformance of controller Higher values of FOD show poordynamic performance and vice versa It is also empiricalto mention here that for frequency deviation in area 1 thesettling time and FOD obtained from ALO are 38 and 1444respectively whereas from GSA PSO and GA the settlingtime and FOD are 56 50 and 49 and 3136 25 and 2401respectively The frequency deviation in area 2 also showsthat the values of settling time and FOD are less when ALO

8 Journal of Engineering

Table3Syste

mmod

esfore

achcase

ofallthe

algorithm

s

Parameters

ALO

GSA

[17]

PSO[18]

GA[19

]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

Case

1

minus58014

minus58014

minus57891

minus59112

minus57884

minus64711

minus55532

minus5752

minus42274

minus42274

minus4313

minus44257

minus444

43minus48155

minus41792

minus42168

minus04924plusmn16

361119894

minus04924plusmn16

361119894

minus04288plusmn16

043119894

minus02773plusmn18

079119894

minus04277plusmn16

059119894

minus00430plusmn25784119894

minus02588plusmn14

307119894

minus02211plusmn15

866119894

minus02842plusmn14

933119894

minus02842plusmn14

933119894

minus02570plusmn16

085119894

minus01941plusmn1746

0119894minus02395plusmn17

695119894

minus00222plusmn21888119894

minus05271plusmn11657119894

00370plusmn15

795119894

minus01208

minus01208

minus03454

minus05259

minus00983plusmn00157119894

minus04806

minus01466

minus01058

minus02021

minus02021

minus0110

1minus00884

minus03584

minus00494

minus03344

minus09221

minus02229

minus02229

minus02062

minus02416

minus02144

minus0401

minus08182

Case

2

minus58597

minus59843

minus58468

minus5976

minus5846

minus6564

minus55965

minus5808

minus41275

minus42672

minus42059

minus43093

minus43269

minus46691

minus40832

minus41155

minus046

46plusmn17

341119894

minus02906plusmn19

218119894

minus040

02plusmn17

063119894

minus02534plusmn19

127119894

minus03943plusmn17

014119894

000

14plusmn26941119894

minus05108plusmn12

557119894

minus02029plusmn16

828119894

minus03315plusmn13

466119894

minus01072plusmn15

609119894

minus03117plusmn14

571119894

minus02466plusmn15

904119894

minus03057plusmn16

218119894

minus00944plusmn20213119894

minus03032plusmn12

918119894

minus00013plusmn14

380119894

minus01204

minus00879

minus03394

minus05169

minus00986plusmn00155119894

minus04774

minus01467

minus01059

minus02047

minus044

98minus0110

1minus00884

minus03521

minus00494

minus0344

minus08003

minus02234

minus05752

minus02096

minus0245

minus02155

minus03879

minus09453

Case

3

minus57282

minus58373

minus57167

minus58312

minus5716

minus6353

minus54991

minus56819

minus42274

minus43812

minus4313

minus44278

minus444

43minus48155

minus41792

minus42168

minus05297plusmn15

095119894

minus03560plusmn16

872119894

minus04632plusmn14

784119894

minus03257plusmn16

774119894

minus04587plusmn14

794119894

minus00990plusmn24269119894

minus02590plusmn14

294119894

minus02413plusmn14

636119894

minus02816plusmn14

943119894

minus00567plusmn17

151119894

minus02541plusmn16

063119894

minus01938plusmn17

505119894

minus02396plusmn17679119894

minus00228plusmn21889119894

minus05411plusmn10

386119894

003

82plusmn15

795119894

minus01204

minus00878

minus0355

minus05367

minus00982plusmn00157119894

minus04855

minus01462

minus01058

minus02039

minus046

72minus011

minus00886

minus03686

minus00494

minus03357

minus09251

minus02252

minus05609

minus02063

minus02401

minus02144

minus04258

minus08475

Case

4

minus60556

minus62024

minus6041

minus61949

minus604

01minus68711

minus57445

minus59969

minus42274

minus43812

minus4313

minus44278

minus444

43minus48155

minus41792

minus42168

minus03695plusmn20323119894

minus01897plusmn22365119894

minus03106plusmn20088119894

minus01627plusmn22305119894

minus03055plusmn20076119894

01510plusmn30616119894

minus044

40plusmn15

429119894

minus01319plusmn19

807119894

minus02838plusmn14

894119894

minus00573plusmn17

122119894

minus02589plusmn16

017119894

minus01958plusmn1744

2119894minus02459plusmn17

656119894

minus00217plusmn21890119894

minus02680plusmn14

339119894

003

68plusmn15

765119894

minus01216

minus00879

minus03261

minus04948

minus00983plusmn00158119894

minus04698

minus01478

minus01059

minus01971

minus0434

minus0110

5minus00886

minus03379

minus00494

minus03276

minus07544

minus02194

minus05605

minus02059

minus024

minus02144

minus03632

minus09192

Journal of Engineering 9

J

J1

2

2 4 6 81 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(a)

J

J1

2

2 4 6 80 10

Time (s)

minus005

0

005

ΔF2

(Hz)

(b)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(c)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

minus005

0

005

ΔF2

(Hz)

(d)

J

J1

2

2 4 6 80 10

Time (s)

ΔP

tie(p

u)

minus002

0

002

(e)

J

J1

2

2 4 6 80 10

Time (s)

minus001

0

001

ΔP

tie(p

u)

(f)

Figure 3 Dynamic responses obtained from ALO

regulator is used The value of settling time with frequencydeviation in area 2 is observed as 60 for ALO 72 for GSA76 for PSO and 80 for GA It is also interesting to observethat with the 10 increase in the load PSO gives erroneousresults and the flow of tie-line power behaves in a differentmanner Hence critical analysis of dynamic responses clearlyreveals that better dynamic performance is exhibited by ALOBy examining the responses in Figures 7ndash9 it is clearly seenthat the settling time and peak overshoot are less whenload changes in area 2 by 20 It can be observed fromFigure 8 that when area 2 observes 20 increase GA basedcontroller is not able to mitigate the frequency oscillationsThis inculcates oscillatory instability in the system HoweverALO based controller shows a better dynamic response andyields satisfactory performance over a wide range of loading

conditions For Case 2 the settling time of ALO is 36 and is53 42 and 58 for GSA PSO andGA respectively Similarlythe FOD is also very low in case of ALO that is 1296whereas it is 1764 and 3364 in case of PSO and GA Figures10 and 11 show the frequency deviations of areas 1 and 2From dynamic responses of overshoot settling time andFOD it is clear that ALO provides competitive results Thedynamic responses for Case 4 are shown in Figures 13ndash15 andit has been observed that ALO tuned controller yields betterdynamic performanceThe minimum settling time and FODobtained from ALO are 51 and 2601 for frequency deviationin area 1 and 60 and 3600 for frequency deviation in area 2However in case of GSA the settling time is 79 and FOD is198 An oscillatory response is obtained by the GA GSA andPSO tuned controllers

10 Journal of Engineering

ALOGSA [17]

PSO [18]GA [19]

2 4 6 8 10 120Time (s)

minus004

minus003

minus002

minus001

0

001

ΔF1

(Hz)

Figure 4 Change in frequency of area 1 by 10 load increase in area1

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

2 4 6 80 1210

Time (s)

ALOGSA [17]

PSO [18]GA [19]

Figure 5 Change in frequency of area 2 by 10 load increase in area1

5 Optimization Performance

To judge the efficiency of the optimization process carried outby all algorithms 100 trials of optimization are carried outTo provide a fair comparison the population size (100) andthe maximum number of iterations (1000) are kept the sameStopping criterion for the optimization process is maximumrun of the iteration To observe the optimization process in acritical way the standard deviations of optimized parametersof the regulator along with the values of objective functionsare calculated and shown in Table 4 It is observed thathigh values of standard deviations are obtained in regulator

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 6 Change in tie-line power by 10 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 7 Change in frequency of area 1 by 20 load increase in area2

parameters and values of objective functions when optimiza-tion process is handled by GA (009729) Comparatively largevalues of standard deviations are found in GA and PSOwhenthey are compared with ALO We observed high values ofstandard deviation in speed regulation parameters after eachrun of optimization obtained with GA regulators (119869

1and

1198692) Speed regulation parameter is a vulnerable parameter

in power system dynamics studies It affects the systemdynamics in a very prominent way Large values of standarddeviations in the calculation of such vulnerable parametersare not acceptable The values for standard deviations are010256 (GSA 119869

1) and 01550 (GA 119869

2) and similarly for

1198772 they are 00081 (ALO 119869

1) 002 (GSA) 038 (PSO) and

Journal of Engineering 11

Table 4 Standard deviation of optimized parameters of the regulator

Parameters ALO GSA [17] PSO [18] GA [19]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

1198701198681

002923 003773 002425 007720 002604 008461 009729 0206871198631

004107 003315 004475 009833 008416 004759 018872 0213131198771

000582 000102 000045 000168 000153 001403 000892 0007171198701198682

001763 004563 010256 000769 009639 008158 005800 0155501198632

008957 008807 004916 011771 016726 008363 017955 0079451198772

000343 000174 000173 000385 000280 001080 000310 00105937000184 716E minus 06 00212 0000419 038 0011 176 0013

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

ALOGSA [17]

PSO [18]GA [19]

Figure 8 Change in frequency of area 2 by 20 load increase in area2

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 9 Change in tie-line power by 20 load increase in area 2

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 10 Change in frequency of area 1 by 25 load increase inarea 1

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 11 Change in frequency of area 2 by 25 load increase inarea 1

12 Journal of Engineering

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 12 Change in tie-line power by 25 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus005

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 13 Change in frequency of area 1 by 25 load decreases inarea 1

176 for GA The impact of speed regulation parameters onthe dynamic response is shown in [25] The lowest valuesof standard deviations are observed when the parametersare optimized by ALO This basically means that in eachrun of optimization ALO exhibits precision in computingthe parameters The standard deviations in the values ofintegral gains for area 1 by 119869

1and 119869

2are minimum for

ALO (0041 0033) for GA these values are (018 and 0213)and similarly (0044 009) for GSA and (008 and 0047)for PSO It can be concluded that regulator setting integralgain observes the least variation in numerical values whenthe parameter is optimized through ALO (119869

1) The values

of standard deviations in objective functions 1198691and 119869

2are

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 14 Change in frequency of area 1 by 25 load decreases inarea 1

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 15 Change in tie-line power by 25 load decreases in area 1

the lowest for ALO process and the highest for GA Thevalues of standard deviations in the values of 119869

1for GA PSO

GSA and GWO are 00972 00264 00242 and 002 andfor 1198692are 02068 00846 00772 and 03773 It has been

observed that the values obtained by ALO are precise and theoptimization processes are reliable enough for obtaining theregulator design However high values of standard deviationsin parameters of regulator (176 with 119877

2) and in the objective

functions show that the optimization process loses its rele-vance when it is handled by GA Hence it is concluded fromthe eigenvalue analysis anddynamic response of the deviationcurves that ALO shows a promising response to obtainregulator settingwith optimization criterion 119869

1The following

Journal of Engineering 13

section summarizes the contribution of this research workand proposes a solid milieu for future work

6 Conclusion

This paper presents an application of the recently introducedalgorithm ALO to find optimal parameters of the AGCregulator The ALO regulator is employed on a test system oftwo thermal units connected with a weak tie line of limitedcapacity for AGCThe following are the major findings of thework

(A) Comparison of the application of two objective func-tions namely ISE and ITAE in optimization processfor finding the regulator parameters under differ-ent contingencies is investigated Results reveal thatITAE is a better choice to optimize the regulatorparameters

(B) Eigenvalue analysis is performed to test the effec-tiveness of the proposed approach and to comparethe results of the proposed approach with recentlypublished approaches It is observed that the dampingobtained from ALO regulator is more positive ascompared with the other algorithms

(C) ALO shows promising results in terms of overshootsettling time obtained from the frequency responsesof both areas under different loading cases standarddeviations in regulatorrsquos parameter values ISE andITAE values and optimization performance

(D) Damping performance is evaluated with differentcontingencies load changes and step disturbancesin both areas PI controller setting obtained throughALO exhibits better dynamic performance and over-all low settling time

Application of other new metaheuristic algorithms in AGCregulator design on different models of the power systemconsidering different renewable energy power sources lies inthe future scope

Nomenclature

119894 Subscript referring to area 119894 (1 2)Δ119865119894 Frequency deviation in area 119894 (Hz)

Δ119875119866119894 Incremental generation of area 119894 (pu)

Δ119875119871119894 Incremental load change in area 119894 (pu)

ACE119894 Area Control Error of area 119894

119861119894 Frequency bias parameter of area 119894

119877119894 Speed regulation of the governor of area 119894

(Hzpu MW)119879119892119894 Time constant of governor of area 119894 (s)

119879119905119894 Time constant of turbine of area 119894 (s)

119870119901119894 Gain of generator and load of area 119894

119879119901119894 Time constant of generator and load of

area 119894 (s)Δ119875tie Incremental change in tie line (pu)11987912 Synchronizing coefficient

119879 Simulation time (s)119905 Current iteration

Competing Interests

The authors declare that they have no competing interests

References

[1] O I Elgerd Energy Systems Theory An Introduction McGraw-Hill New Delhi India 1983

[2] IEEE Standard Committee ldquoIEEE Standard definitions of termsfor automatic generation control on electric power systemsrdquoIEEE Transactions on Power Apparatus and Systems vol 89 no6 pp 1356ndash1364 1970

[3] A Ibraheem P Kumar and D P Kothari ldquoRecent philosophiesof automatic generation control strategies in power systemsrdquoIEEE Transactions on Power Systems vol 20 no 1 pp 346ndash3572005

[4] H Sadat Power System Analysis McGraw-Hill New York NYUSA 1999

[5] J Nanda and B Kaul ldquoAutomatic generation control of aninterconnected power systemrdquo Proceedings of the Institution ofElectrical Engineers vol 125 no 5 pp 385ndash390 1978

[6] A Y Sivaramakrishnan M V Hariharan and M C SrisailamldquoDesign of variable-structure load-frequency controller usingpole assignment techniquerdquo International Journal of Controlvol 40 no 3 pp 487ndash498 1984

[7] M Z Bernard T H Mohamed Y S Qudaih and Y MitanildquoDecentralized load frequency control in an interconnectedpower system using Coefficient Diagram Methodrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 63pp 165ndash172 2014

[8] R Ali T HMohamed Y S Qudaih and YMitani ldquoA new loadfrequency control approach in an isolated small power systemsusing coefficient diagram methodrdquo International Journal ofElectrical Power and Energy Systems vol 56 pp 110ndash116 2014

[9] I Vajk M Vajta L Keviczky R Haber J Hetthessy andK Kovacs ldquoAdaptive load-frequency control of the hungarianpower systemrdquo Automatica vol 21 no 2 pp 129ndash137 1985

[10] J Kanniah S C Tripathy O P Malik and G S HopeldquoMicroprocessor-based adaptive load-frequency controlrdquo IEEProceedings CmdashGeneration Transmission and Distribution vol131 no 4 pp 121ndash128 1984

[11] M L Kothari P S Satsangi and J Nanda ldquoSampled-dataautomatic generation control of interconnected reheat thermalsystems considering generation rate constraintsrdquo IEEE Transac-tions on Power Apparatus and Systems vol 100 no 5 pp 2334ndash2342 1981

[12] S Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001

[13] B K Sahu S Pati P K Mohanty and S Panda ldquoTeaching-learning based optimization algorithm based fuzzy-PID con-troller for automatic generation control of multi-area powersystemrdquo Applied Soft Computing Journal vol 27 pp 240ndash2492015

[14] K R Sudha and R Vijaya Santhi ldquoLoad frequency control of aninterconnected reheat thermal systemusing type-2 fuzzy systemincluding SMES unitsrdquo International Journal of Electrical Poweramp Energy Systems vol 43 no 1 pp 1383ndash1392 2012

[15] A Banerjee V Mukherjee and S P Ghoshal ldquoIntelligentcontroller for load-tracking performance of an autonomous

14 Journal of Engineering

power systemrdquo Ain Shams Engineering Journal vol 5 no 4 pp1167ndash1176 2014

[16] S Padhan R K Sahu and S Panda ldquoAutomatic generationcontrol with thyristor controlled series compensator includingsuperconducting magnetic energy storage unitsrdquo Ain ShamsEngineering Journal vol 5 no 3 pp 759ndash774 2014

[17] R K Sahu S Panda and S Padhan ldquoOptimal gravitationalsearch algorithm for automatic generation control of intercon-nected power systemsrdquo Ain Shams Engineering Journal vol 5no 3 pp 721ndash733 2014

[18] Y L Abdel-Magid and M A Abido ldquoAGC tuning of intercon-nected reheat thermal systems with particle swarm optimiza-tionrdquo in Proceedings of the 10th IEEE International Conferenceon Electronics Circuits and Systems (ICECS rsquo03) pp 376ndash379December 2003

[19] Y L Abdel-Magid and M M Dawoud ldquoOptimal AGC tuningwith genetic algorithmsrdquo Electric Power Systems Research vol38 no 3 pp 231ndash238 1996

[20] J Nanda S Mishra and L C Saikia ldquoMaiden application ofbacterial foraging-based optimization technique in multiareaautomatic generation controlrdquo IEEE Transactions on PowerSystems vol 24 no 2 pp 602ndash609 2009

[21] U K Rout R K Sahu and S Panda ldquoDesign and analysisof differential evolution algorithm based automatic generationcontrol for interconnected power systemrdquo Ain Shams Engineer-ing Journal vol 4 no 3 pp 409ndash421 2013

[22] H Gozde M C Taplamacioglu and I Kocaarslan ldquoCompara-tive performance analysis of Artificial Bee Colony algorithm inautomatic generation control for interconnected reheat thermalpower systemrdquo International Journal of Electrical Power andEnergy Systems vol 42 no 1 pp 167ndash178 2012

[23] S Debbarma L Chandra Saikia and N Sinha ldquoSolution toautomatic generation control problem using firefly algorithmoptimized I120582D120583 controllerrdquo ISA Transactions vol 53 no 2 pp358ndash366 2014

[24] P Dash L C Saikia and N Sinha ldquoComparison of per-formances of several Cuckoo search algorithm based 2DOFcontrollers in AGC of multi-area thermal systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 55 pp 429ndash436 2014

[25] A Saxena M Gupta and V Gupta ldquoAutomatic generationcontrol of two area interconnected power system using Geneticalgorithmrdquo in Proceedings of the 3rd IEEE International Con-ference on Computational Intelligence and Computing Research(ICCIC rsquo12) Coimbatore India December 2012

[26] B K Sahu T K Pati J R Nayak S Panda and S K KarldquoA novel hybrid LUS-TLBO optimized fuzzy-PID controllerfor load frequency control of multi-source power systemrdquoInternational Journal of Electrical Power amp Energy Systems vol74 pp 58ndash69 2016

[27] Y Sharma and L C Saikia ldquoAutomatic generation controlof a multi-area STmdashthermal power system using Grey WolfOptimizer algorithm based classical controllersrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 853ndash862 2015

[28] P Dash L C Saikia and N Sinha ldquoAutomatic generationcontrol of multi area thermal system using Bat algorithmoptimized PDndashPID cascade controllerrdquo International Journal ofElectrical Power amp Energy Systems vol 68 pp 364ndash372 2015

[29] S Mirjalili ldquoThe ant lion optimizerrdquo Advances in EngineeringSoftware vol 83 pp 80ndash98 2015

[30] MATLAB httpwwwmathworkscom

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Engineering 5

Table 1 Optimized parameters of AGC regulator

Parameters ALO GSA [17] PSO [18] GA [19]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

1198701198681

03260 04002 03817 04171 03131 04498 03031 065251198701198682

02135 02010 02153 02028 01091 02158 03063 079601198771

00491 00404 00401 00435 00581 00201 00794 005031198772

00699 00509 00657 00635 00531 003 00737 006091198631

04457 04884 05889 04778 04756 05910 07591 072161198632

08770 08975 08946 08744 06097 08226 08950 08984

where 119886119894is the minimum of random walk of 119894th variable

119889119894is the maximum of random walk of 119894th variable 119888119905

119894is

the minimum of 119894th variable at 119905th iteration and 119889119905119894is the

maximum of 119894th variable at 119905th iteration

(b) Trapping in Antlionrsquos Pit Random walks of ants areaffected by antlionsrsquo trap Mathematical modeling of trappingin antlionrsquos pit is proposed by the following equations

119888119905

119894= Antlion119905

119895+ 119888119905

119889119905

119894= Antlion119905

119895+ 119889119905

(14)

where 119888119905 represents the minimum of all variables at 119905thiteration 119889119905 indicates the vector including the maximum ofall variables at 119905th iteration 119888119905

119894is the minimum of all variables

for 119894th ant 119889119905119894is the maximum of all variables for 119894th ant and

Antlion119905119895shows the position of the selected 119895th antlion at 119905th

iteration

(c) Building Trap For building trap a roulette wheel isemployed to model the hunting capability of antlions TheALO algorithm is required to utilize a roulette wheel operatorfor selecting antlions based on their fitness during optimiza-tion This mechanism provides high chances to the fitterantlions for catching ants

(d) Sliding Ants towards Antlion Antlions are able to buildtraps which are proportional to their fitness and ants arerequired to move randomly Once the antlion realizes that anant is in the trap it shoots sand out the centre of the pit Theants which are trying to escape slide down the trapThe radiusof the antrsquos randomwalks hypersphere is decreased adaptivelyin the mathematical modeling The following equations areproposed for this

119888119905=119888119905

119868

119889119905=119889119905

119868

(15)

where 119868 is a ratio 119888119905 is the minimum of all variables at 119905thiteration and 119889119905 indicates the vector including the maximumof all variables at 119905th iteration

(e) Catching Prey and Rebuilding the Pit This is the finalstage of hunt At this stage an ant reaches the bottom of

the pit and is caught in the antlionrsquos jaw After this stage theantlion pulls the ant inside the sand and consumes its bodyCatching the prey occurs when the ant goes inside the sandand becomes fitter than its corresponding antlion Accordingto the position of the latest hunted ant the antlions updatetheir position to enhance the chances of catching new preyMathematically the following equations can be proposed inthis regard

Antlion119905119895= Ant119905

119894if 119891 (Ant119905

119894) gt 119891 (Antlion119905

119895) (16)

where 119905 represents the current iteration Antlion119905119895is the

position of the selected 119895th antlion at 119905th iteration and Ant119905119894

represents the position of 119894th ant at 119905th iteration

(f) Elitism For any evolutionary algorithm elitism is animportant feature that allows antlions to maintain the bestsolution obtained at any stage of optimization process Inthis algorithm the best obtained antlion during the entireiteration is saved and is considered as an elite Since thefittest antlion is elite it affects the movement of all the antsduring iteration Hence it is assumed that every ant walksrandomly around a selected antlion by roulette wheel and theelite simultaneously as follows

Ant119905119894=119877119905

119860+ 119877119905

119864

2 (17)

where 119877119905119860is the random walk around the antlion selected by

the roulette wheel at 119905th iteration119877119905119864is the randomwalk and

Ant119905119894represents the position of 119894th ant at 119905th iteration

The following section presents analysis of simulationresults

4 Results and Analysis

This section presents simulation results and analysis of AGCregulator performance on two-area thermal interconnectedpower system with different step perturbations and loadingconditions Different AGC regulator settings are obtainedwith the application of four algorithms (GA PSO GSA andALO) on two standard objective functions (ISE and ITAE)Table 1 shows the values of optimized parameters of regulatorwith the application of the abovementioned algorithms ontwo objective functions

Table 2 shows the values of systemrsquos minimum dampingratio and eigenvalues after the application of these AGC

6 Journal of Engineering

Table2Eigenvaluesa

ndminim

umdamping

ratio

Parameter

ALO

GSA

[17]

PSO[18]

GA[19

]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

Syste

mmod

es

minus58548

minus59604

minus58468

minus5976

minus5846

minus65657

minus56586

minus5808

minus42219

minus44165

minus4313

minus44257

minus444

43minus48155

minus42083

minus42168

minus03805plusmn17

191119894

minus02885plusmn18

854119894

minus03994plusmn17

029119894

02511plusmn19

124119894

minus040

10plusmn17

004i

minus00030plusmn26953119894minus04925plusmn13

799119894

minus02024plusmn16

817119894

minus03007plusmn14

854119894

minus02088plusmn17

320119894

minus02606plusmn16

066119894

minus01924plusmn17420119894

minus024

06plusmn17

718i

minus00220plusmn21889119894minus02491plusmn14

729119894

003

61plusmn15

786i

minus03716

minus04624

minus03395

minus05169

minus009

83plusmn00157i

minus046

66minus01353

minus01058

minus0117

9minus00910

minus0110

2minus00884

minus03521

minus00494

minus03294

minus07991

minus02256

minus02351

minus02061

minus02416

minus02144

minus03712

minus09209

Minim

umdamping

ratio

01984

01197

01601

01098

01345

00011

01668

00229

Journal of Engineering 7

regulators Eigenvalue analysis plays an important role instability studies Complex conjugate eigenvalues are alsoknown as swing modes and these eigenvalues are responsiblefor oscillatory instability when the real part of the eigen-value is positive From Table 2 it is observed that whenoptimization process is carried out with the application ofGA on 119869

2system mode contains a swing mode with positive

eigenvalue (0361) Real positive part of eigen is the indicationof oscillations of growing amplitudeTheminimum dampingratios obtained from the application of different regulatorswith 119869

1and 119869

2criteria are shown in Table 2 For PSO

regulator minimum damping ratios obtained from thesecriteria are (01345 00011) similarly the ratios for GA are(01668 00229) for GSA are (01601 01098) and for ALOare (01984 01197) It can be said that a considerable amountof damping is enhanced in each case when the regulatorparameters are obtained with criterion 119869

1 Overall damping

of the system is the highest with ALO regulator (1198691) (01984)

Prima facie it can be concluded that the regulator designobtained from criterion 119869

1is more effective as the damping

enhanced by this regulator is higher In eigenvalue analysisboth real and imaginary parts have their interpretation andphysical significance The real part of the complex conjugateeigenvalue shows the damping behavior which represents thedamp oscillations whichmeans the larger themagnitude thehigher the rate of decay Imaginary components show thefrequency of oscillations It can be observed from Table 2that high frequency oscillations are associated with setting1198692 Higher frequency oscillations are bad for equipment

health and often cause the damage of physical structure ofcontrollers In this case for 119869

2 GA frequency of oscillations

is (157 168) for PSO (269 218) for GSA (191 174) and(188 173) for ALO It is observed that although frequencyof oscillations is in moderate range for GA regulator theamplitude of the oscillation is growing with time as it has apositive real part of eigenvalue However the other regulatorshave high frequency of oscillations modes as comparedwith ALO To show this analysis in a more prominent wayAGC regulators are designed with ALO algorithm and testedfor different levels of perturbations Figures 3(a) and 3(b)show the dynamic responses of frequency deviations inareas 1 and 2 when area 1 observes a step disturbance of001 pu Figures 3(c) and 3(d) show the frequency deviationcurves of both areas with both regulator settings 119869

1and

1198692when area 2 is perturbed with 002 pu Similarly for

both regulator settings the dynamic responses obtainedfrom both areas are self-explanatory It is observed that 119869

1

setting is promising The overshoot and settling time of thefrequency deviation curves of both areas are less with 119869

1

regulator It is also empirical to judge that the variationsof tie-line power exchanges are nominal with both types ofperturbation with 119869

1regulator Hence it is concluded that 119869

1

optimization criterion is suitable for the designing of theAGCregulator

To exhibit the comparative performance of the ALO reg-ulator with other regulators four different loading scenariosare simulated in this work These loading conditions aresummarized below

Case 1 Load changes in area 1 by 10Thedynamic responsesof Δ119865

1 Δ1198652 and Δ119875tie are given in Figures 4ndash6 for all the

algorithms

Case 2 Load changes in area 2 by 20 Figures 7ndash9 show thedynamic responses of the system

Case 3 Load is increased in area 1 by 25 In Figures 10ndash12the system dynamic responses are shown

Case 4 Load is decreased in area 1 by 25 and the systemdynamic responses are given in Figures 13ndash15

Dynamic responses along with the system eigenvalues forthese conditions are exhibited in Table 3 It is observed thatagain with setting 119869

2few eigenvalues possess positive real part

when optimized with GA (00370 00382 and 00368) Thereal part of swing mode varies from minus02823 to minus04567 forALO regulator from minus02541 to minus04632 for GSA regulatorfrom minus00982 to minus4587 for PSO regulator and from minus02511to minus05411 for GA regulator with criterion 119869

1 It is of note

here that the real part of the eigenvalue observes a largevariation in case of GA under different loading conditionsThis spread put a question mark on the performance ofthe regulator and robustness of the regulator also Moder-ate spread has been observed with ALO regulator For allcases higher numeric values of real part of the eigenvaluessuggest that the system is more stable In Case 1 thesevalues are (minus04278 minus02823) for ALO (minus04288 minus02570)for GSA (minus04277 minus02395) for PSO and (minus02588 minus05271)for GA It can be predicted that for Case 1 the robustsetting is achieved by ALO Similarly in Case 4 the realparts of eigenvalues (swing modes) are (minus03276 minus02879)for ALO and (minus03106 minus02589) for GSA and an addi-tional swing mode with PSO setting has been observed(1198691) (minus03055 minus02459 00983) and (minus0440 02680) for GA

From this it is also observed that a higher degree ofrobustness can be achieved by ALO regulator To understandthe dynamic response of the frequency deviation curvesa conventional index Figure of Demerit (FOD) is usedin this paper Figure of Demerit is the summation of thesquare of the overshoot and settling time of the deviationcurves It is observed that for almost all loading cases thevalues of settling time overshoot and FODs are low forALO based regulators as compared with other regulatordesigns It is observed from Figures 4ndash6 that ALO basedcontroller exhibits better dynamic performance as comparedwith others The percentage of overshoot and settling timeis much less in these cases The low oscillatory responseexhibited by ALO is best suited for the equipmentrsquos healthFOD values are considered as a close replica of dynamicperformance of controller Higher values of FOD show poordynamic performance and vice versa It is also empiricalto mention here that for frequency deviation in area 1 thesettling time and FOD obtained from ALO are 38 and 1444respectively whereas from GSA PSO and GA the settlingtime and FOD are 56 50 and 49 and 3136 25 and 2401respectively The frequency deviation in area 2 also showsthat the values of settling time and FOD are less when ALO

8 Journal of Engineering

Table3Syste

mmod

esfore

achcase

ofallthe

algorithm

s

Parameters

ALO

GSA

[17]

PSO[18]

GA[19

]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

Case

1

minus58014

minus58014

minus57891

minus59112

minus57884

minus64711

minus55532

minus5752

minus42274

minus42274

minus4313

minus44257

minus444

43minus48155

minus41792

minus42168

minus04924plusmn16

361119894

minus04924plusmn16

361119894

minus04288plusmn16

043119894

minus02773plusmn18

079119894

minus04277plusmn16

059119894

minus00430plusmn25784119894

minus02588plusmn14

307119894

minus02211plusmn15

866119894

minus02842plusmn14

933119894

minus02842plusmn14

933119894

minus02570plusmn16

085119894

minus01941plusmn1746

0119894minus02395plusmn17

695119894

minus00222plusmn21888119894

minus05271plusmn11657119894

00370plusmn15

795119894

minus01208

minus01208

minus03454

minus05259

minus00983plusmn00157119894

minus04806

minus01466

minus01058

minus02021

minus02021

minus0110

1minus00884

minus03584

minus00494

minus03344

minus09221

minus02229

minus02229

minus02062

minus02416

minus02144

minus0401

minus08182

Case

2

minus58597

minus59843

minus58468

minus5976

minus5846

minus6564

minus55965

minus5808

minus41275

minus42672

minus42059

minus43093

minus43269

minus46691

minus40832

minus41155

minus046

46plusmn17

341119894

minus02906plusmn19

218119894

minus040

02plusmn17

063119894

minus02534plusmn19

127119894

minus03943plusmn17

014119894

000

14plusmn26941119894

minus05108plusmn12

557119894

minus02029plusmn16

828119894

minus03315plusmn13

466119894

minus01072plusmn15

609119894

minus03117plusmn14

571119894

minus02466plusmn15

904119894

minus03057plusmn16

218119894

minus00944plusmn20213119894

minus03032plusmn12

918119894

minus00013plusmn14

380119894

minus01204

minus00879

minus03394

minus05169

minus00986plusmn00155119894

minus04774

minus01467

minus01059

minus02047

minus044

98minus0110

1minus00884

minus03521

minus00494

minus0344

minus08003

minus02234

minus05752

minus02096

minus0245

minus02155

minus03879

minus09453

Case

3

minus57282

minus58373

minus57167

minus58312

minus5716

minus6353

minus54991

minus56819

minus42274

minus43812

minus4313

minus44278

minus444

43minus48155

minus41792

minus42168

minus05297plusmn15

095119894

minus03560plusmn16

872119894

minus04632plusmn14

784119894

minus03257plusmn16

774119894

minus04587plusmn14

794119894

minus00990plusmn24269119894

minus02590plusmn14

294119894

minus02413plusmn14

636119894

minus02816plusmn14

943119894

minus00567plusmn17

151119894

minus02541plusmn16

063119894

minus01938plusmn17

505119894

minus02396plusmn17679119894

minus00228plusmn21889119894

minus05411plusmn10

386119894

003

82plusmn15

795119894

minus01204

minus00878

minus0355

minus05367

minus00982plusmn00157119894

minus04855

minus01462

minus01058

minus02039

minus046

72minus011

minus00886

minus03686

minus00494

minus03357

minus09251

minus02252

minus05609

minus02063

minus02401

minus02144

minus04258

minus08475

Case

4

minus60556

minus62024

minus6041

minus61949

minus604

01minus68711

minus57445

minus59969

minus42274

minus43812

minus4313

minus44278

minus444

43minus48155

minus41792

minus42168

minus03695plusmn20323119894

minus01897plusmn22365119894

minus03106plusmn20088119894

minus01627plusmn22305119894

minus03055plusmn20076119894

01510plusmn30616119894

minus044

40plusmn15

429119894

minus01319plusmn19

807119894

minus02838plusmn14

894119894

minus00573plusmn17

122119894

minus02589plusmn16

017119894

minus01958plusmn1744

2119894minus02459plusmn17

656119894

minus00217plusmn21890119894

minus02680plusmn14

339119894

003

68plusmn15

765119894

minus01216

minus00879

minus03261

minus04948

minus00983plusmn00158119894

minus04698

minus01478

minus01059

minus01971

minus0434

minus0110

5minus00886

minus03379

minus00494

minus03276

minus07544

minus02194

minus05605

minus02059

minus024

minus02144

minus03632

minus09192

Journal of Engineering 9

J

J1

2

2 4 6 81 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(a)

J

J1

2

2 4 6 80 10

Time (s)

minus005

0

005

ΔF2

(Hz)

(b)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(c)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

minus005

0

005

ΔF2

(Hz)

(d)

J

J1

2

2 4 6 80 10

Time (s)

ΔP

tie(p

u)

minus002

0

002

(e)

J

J1

2

2 4 6 80 10

Time (s)

minus001

0

001

ΔP

tie(p

u)

(f)

Figure 3 Dynamic responses obtained from ALO

regulator is used The value of settling time with frequencydeviation in area 2 is observed as 60 for ALO 72 for GSA76 for PSO and 80 for GA It is also interesting to observethat with the 10 increase in the load PSO gives erroneousresults and the flow of tie-line power behaves in a differentmanner Hence critical analysis of dynamic responses clearlyreveals that better dynamic performance is exhibited by ALOBy examining the responses in Figures 7ndash9 it is clearly seenthat the settling time and peak overshoot are less whenload changes in area 2 by 20 It can be observed fromFigure 8 that when area 2 observes 20 increase GA basedcontroller is not able to mitigate the frequency oscillationsThis inculcates oscillatory instability in the system HoweverALO based controller shows a better dynamic response andyields satisfactory performance over a wide range of loading

conditions For Case 2 the settling time of ALO is 36 and is53 42 and 58 for GSA PSO andGA respectively Similarlythe FOD is also very low in case of ALO that is 1296whereas it is 1764 and 3364 in case of PSO and GA Figures10 and 11 show the frequency deviations of areas 1 and 2From dynamic responses of overshoot settling time andFOD it is clear that ALO provides competitive results Thedynamic responses for Case 4 are shown in Figures 13ndash15 andit has been observed that ALO tuned controller yields betterdynamic performanceThe minimum settling time and FODobtained from ALO are 51 and 2601 for frequency deviationin area 1 and 60 and 3600 for frequency deviation in area 2However in case of GSA the settling time is 79 and FOD is198 An oscillatory response is obtained by the GA GSA andPSO tuned controllers

10 Journal of Engineering

ALOGSA [17]

PSO [18]GA [19]

2 4 6 8 10 120Time (s)

minus004

minus003

minus002

minus001

0

001

ΔF1

(Hz)

Figure 4 Change in frequency of area 1 by 10 load increase in area1

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

2 4 6 80 1210

Time (s)

ALOGSA [17]

PSO [18]GA [19]

Figure 5 Change in frequency of area 2 by 10 load increase in area1

5 Optimization Performance

To judge the efficiency of the optimization process carried outby all algorithms 100 trials of optimization are carried outTo provide a fair comparison the population size (100) andthe maximum number of iterations (1000) are kept the sameStopping criterion for the optimization process is maximumrun of the iteration To observe the optimization process in acritical way the standard deviations of optimized parametersof the regulator along with the values of objective functionsare calculated and shown in Table 4 It is observed thathigh values of standard deviations are obtained in regulator

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 6 Change in tie-line power by 10 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 7 Change in frequency of area 1 by 20 load increase in area2

parameters and values of objective functions when optimiza-tion process is handled by GA (009729) Comparatively largevalues of standard deviations are found in GA and PSOwhenthey are compared with ALO We observed high values ofstandard deviation in speed regulation parameters after eachrun of optimization obtained with GA regulators (119869

1and

1198692) Speed regulation parameter is a vulnerable parameter

in power system dynamics studies It affects the systemdynamics in a very prominent way Large values of standarddeviations in the calculation of such vulnerable parametersare not acceptable The values for standard deviations are010256 (GSA 119869

1) and 01550 (GA 119869

2) and similarly for

1198772 they are 00081 (ALO 119869

1) 002 (GSA) 038 (PSO) and

Journal of Engineering 11

Table 4 Standard deviation of optimized parameters of the regulator

Parameters ALO GSA [17] PSO [18] GA [19]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

1198701198681

002923 003773 002425 007720 002604 008461 009729 0206871198631

004107 003315 004475 009833 008416 004759 018872 0213131198771

000582 000102 000045 000168 000153 001403 000892 0007171198701198682

001763 004563 010256 000769 009639 008158 005800 0155501198632

008957 008807 004916 011771 016726 008363 017955 0079451198772

000343 000174 000173 000385 000280 001080 000310 00105937000184 716E minus 06 00212 0000419 038 0011 176 0013

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

ALOGSA [17]

PSO [18]GA [19]

Figure 8 Change in frequency of area 2 by 20 load increase in area2

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 9 Change in tie-line power by 20 load increase in area 2

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 10 Change in frequency of area 1 by 25 load increase inarea 1

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 11 Change in frequency of area 2 by 25 load increase inarea 1

12 Journal of Engineering

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 12 Change in tie-line power by 25 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus005

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 13 Change in frequency of area 1 by 25 load decreases inarea 1

176 for GA The impact of speed regulation parameters onthe dynamic response is shown in [25] The lowest valuesof standard deviations are observed when the parametersare optimized by ALO This basically means that in eachrun of optimization ALO exhibits precision in computingthe parameters The standard deviations in the values ofintegral gains for area 1 by 119869

1and 119869

2are minimum for

ALO (0041 0033) for GA these values are (018 and 0213)and similarly (0044 009) for GSA and (008 and 0047)for PSO It can be concluded that regulator setting integralgain observes the least variation in numerical values whenthe parameter is optimized through ALO (119869

1) The values

of standard deviations in objective functions 1198691and 119869

2are

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 14 Change in frequency of area 1 by 25 load decreases inarea 1

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 15 Change in tie-line power by 25 load decreases in area 1

the lowest for ALO process and the highest for GA Thevalues of standard deviations in the values of 119869

1for GA PSO

GSA and GWO are 00972 00264 00242 and 002 andfor 1198692are 02068 00846 00772 and 03773 It has been

observed that the values obtained by ALO are precise and theoptimization processes are reliable enough for obtaining theregulator design However high values of standard deviationsin parameters of regulator (176 with 119877

2) and in the objective

functions show that the optimization process loses its rele-vance when it is handled by GA Hence it is concluded fromthe eigenvalue analysis anddynamic response of the deviationcurves that ALO shows a promising response to obtainregulator settingwith optimization criterion 119869

1The following

Journal of Engineering 13

section summarizes the contribution of this research workand proposes a solid milieu for future work

6 Conclusion

This paper presents an application of the recently introducedalgorithm ALO to find optimal parameters of the AGCregulator The ALO regulator is employed on a test system oftwo thermal units connected with a weak tie line of limitedcapacity for AGCThe following are the major findings of thework

(A) Comparison of the application of two objective func-tions namely ISE and ITAE in optimization processfor finding the regulator parameters under differ-ent contingencies is investigated Results reveal thatITAE is a better choice to optimize the regulatorparameters

(B) Eigenvalue analysis is performed to test the effec-tiveness of the proposed approach and to comparethe results of the proposed approach with recentlypublished approaches It is observed that the dampingobtained from ALO regulator is more positive ascompared with the other algorithms

(C) ALO shows promising results in terms of overshootsettling time obtained from the frequency responsesof both areas under different loading cases standarddeviations in regulatorrsquos parameter values ISE andITAE values and optimization performance

(D) Damping performance is evaluated with differentcontingencies load changes and step disturbancesin both areas PI controller setting obtained throughALO exhibits better dynamic performance and over-all low settling time

Application of other new metaheuristic algorithms in AGCregulator design on different models of the power systemconsidering different renewable energy power sources lies inthe future scope

Nomenclature

119894 Subscript referring to area 119894 (1 2)Δ119865119894 Frequency deviation in area 119894 (Hz)

Δ119875119866119894 Incremental generation of area 119894 (pu)

Δ119875119871119894 Incremental load change in area 119894 (pu)

ACE119894 Area Control Error of area 119894

119861119894 Frequency bias parameter of area 119894

119877119894 Speed regulation of the governor of area 119894

(Hzpu MW)119879119892119894 Time constant of governor of area 119894 (s)

119879119905119894 Time constant of turbine of area 119894 (s)

119870119901119894 Gain of generator and load of area 119894

119879119901119894 Time constant of generator and load of

area 119894 (s)Δ119875tie Incremental change in tie line (pu)11987912 Synchronizing coefficient

119879 Simulation time (s)119905 Current iteration

Competing Interests

The authors declare that they have no competing interests

References

[1] O I Elgerd Energy Systems Theory An Introduction McGraw-Hill New Delhi India 1983

[2] IEEE Standard Committee ldquoIEEE Standard definitions of termsfor automatic generation control on electric power systemsrdquoIEEE Transactions on Power Apparatus and Systems vol 89 no6 pp 1356ndash1364 1970

[3] A Ibraheem P Kumar and D P Kothari ldquoRecent philosophiesof automatic generation control strategies in power systemsrdquoIEEE Transactions on Power Systems vol 20 no 1 pp 346ndash3572005

[4] H Sadat Power System Analysis McGraw-Hill New York NYUSA 1999

[5] J Nanda and B Kaul ldquoAutomatic generation control of aninterconnected power systemrdquo Proceedings of the Institution ofElectrical Engineers vol 125 no 5 pp 385ndash390 1978

[6] A Y Sivaramakrishnan M V Hariharan and M C SrisailamldquoDesign of variable-structure load-frequency controller usingpole assignment techniquerdquo International Journal of Controlvol 40 no 3 pp 487ndash498 1984

[7] M Z Bernard T H Mohamed Y S Qudaih and Y MitanildquoDecentralized load frequency control in an interconnectedpower system using Coefficient Diagram Methodrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 63pp 165ndash172 2014

[8] R Ali T HMohamed Y S Qudaih and YMitani ldquoA new loadfrequency control approach in an isolated small power systemsusing coefficient diagram methodrdquo International Journal ofElectrical Power and Energy Systems vol 56 pp 110ndash116 2014

[9] I Vajk M Vajta L Keviczky R Haber J Hetthessy andK Kovacs ldquoAdaptive load-frequency control of the hungarianpower systemrdquo Automatica vol 21 no 2 pp 129ndash137 1985

[10] J Kanniah S C Tripathy O P Malik and G S HopeldquoMicroprocessor-based adaptive load-frequency controlrdquo IEEProceedings CmdashGeneration Transmission and Distribution vol131 no 4 pp 121ndash128 1984

[11] M L Kothari P S Satsangi and J Nanda ldquoSampled-dataautomatic generation control of interconnected reheat thermalsystems considering generation rate constraintsrdquo IEEE Transac-tions on Power Apparatus and Systems vol 100 no 5 pp 2334ndash2342 1981

[12] S Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001

[13] B K Sahu S Pati P K Mohanty and S Panda ldquoTeaching-learning based optimization algorithm based fuzzy-PID con-troller for automatic generation control of multi-area powersystemrdquo Applied Soft Computing Journal vol 27 pp 240ndash2492015

[14] K R Sudha and R Vijaya Santhi ldquoLoad frequency control of aninterconnected reheat thermal systemusing type-2 fuzzy systemincluding SMES unitsrdquo International Journal of Electrical Poweramp Energy Systems vol 43 no 1 pp 1383ndash1392 2012

[15] A Banerjee V Mukherjee and S P Ghoshal ldquoIntelligentcontroller for load-tracking performance of an autonomous

14 Journal of Engineering

power systemrdquo Ain Shams Engineering Journal vol 5 no 4 pp1167ndash1176 2014

[16] S Padhan R K Sahu and S Panda ldquoAutomatic generationcontrol with thyristor controlled series compensator includingsuperconducting magnetic energy storage unitsrdquo Ain ShamsEngineering Journal vol 5 no 3 pp 759ndash774 2014

[17] R K Sahu S Panda and S Padhan ldquoOptimal gravitationalsearch algorithm for automatic generation control of intercon-nected power systemsrdquo Ain Shams Engineering Journal vol 5no 3 pp 721ndash733 2014

[18] Y L Abdel-Magid and M A Abido ldquoAGC tuning of intercon-nected reheat thermal systems with particle swarm optimiza-tionrdquo in Proceedings of the 10th IEEE International Conferenceon Electronics Circuits and Systems (ICECS rsquo03) pp 376ndash379December 2003

[19] Y L Abdel-Magid and M M Dawoud ldquoOptimal AGC tuningwith genetic algorithmsrdquo Electric Power Systems Research vol38 no 3 pp 231ndash238 1996

[20] J Nanda S Mishra and L C Saikia ldquoMaiden application ofbacterial foraging-based optimization technique in multiareaautomatic generation controlrdquo IEEE Transactions on PowerSystems vol 24 no 2 pp 602ndash609 2009

[21] U K Rout R K Sahu and S Panda ldquoDesign and analysisof differential evolution algorithm based automatic generationcontrol for interconnected power systemrdquo Ain Shams Engineer-ing Journal vol 4 no 3 pp 409ndash421 2013

[22] H Gozde M C Taplamacioglu and I Kocaarslan ldquoCompara-tive performance analysis of Artificial Bee Colony algorithm inautomatic generation control for interconnected reheat thermalpower systemrdquo International Journal of Electrical Power andEnergy Systems vol 42 no 1 pp 167ndash178 2012

[23] S Debbarma L Chandra Saikia and N Sinha ldquoSolution toautomatic generation control problem using firefly algorithmoptimized I120582D120583 controllerrdquo ISA Transactions vol 53 no 2 pp358ndash366 2014

[24] P Dash L C Saikia and N Sinha ldquoComparison of per-formances of several Cuckoo search algorithm based 2DOFcontrollers in AGC of multi-area thermal systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 55 pp 429ndash436 2014

[25] A Saxena M Gupta and V Gupta ldquoAutomatic generationcontrol of two area interconnected power system using Geneticalgorithmrdquo in Proceedings of the 3rd IEEE International Con-ference on Computational Intelligence and Computing Research(ICCIC rsquo12) Coimbatore India December 2012

[26] B K Sahu T K Pati J R Nayak S Panda and S K KarldquoA novel hybrid LUS-TLBO optimized fuzzy-PID controllerfor load frequency control of multi-source power systemrdquoInternational Journal of Electrical Power amp Energy Systems vol74 pp 58ndash69 2016

[27] Y Sharma and L C Saikia ldquoAutomatic generation controlof a multi-area STmdashthermal power system using Grey WolfOptimizer algorithm based classical controllersrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 853ndash862 2015

[28] P Dash L C Saikia and N Sinha ldquoAutomatic generationcontrol of multi area thermal system using Bat algorithmoptimized PDndashPID cascade controllerrdquo International Journal ofElectrical Power amp Energy Systems vol 68 pp 364ndash372 2015

[29] S Mirjalili ldquoThe ant lion optimizerrdquo Advances in EngineeringSoftware vol 83 pp 80ndash98 2015

[30] MATLAB httpwwwmathworkscom

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Journal of Engineering

Table2Eigenvaluesa

ndminim

umdamping

ratio

Parameter

ALO

GSA

[17]

PSO[18]

GA[19

]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

Syste

mmod

es

minus58548

minus59604

minus58468

minus5976

minus5846

minus65657

minus56586

minus5808

minus42219

minus44165

minus4313

minus44257

minus444

43minus48155

minus42083

minus42168

minus03805plusmn17

191119894

minus02885plusmn18

854119894

minus03994plusmn17

029119894

02511plusmn19

124119894

minus040

10plusmn17

004i

minus00030plusmn26953119894minus04925plusmn13

799119894

minus02024plusmn16

817119894

minus03007plusmn14

854119894

minus02088plusmn17

320119894

minus02606plusmn16

066119894

minus01924plusmn17420119894

minus024

06plusmn17

718i

minus00220plusmn21889119894minus02491plusmn14

729119894

003

61plusmn15

786i

minus03716

minus04624

minus03395

minus05169

minus009

83plusmn00157i

minus046

66minus01353

minus01058

minus0117

9minus00910

minus0110

2minus00884

minus03521

minus00494

minus03294

minus07991

minus02256

minus02351

minus02061

minus02416

minus02144

minus03712

minus09209

Minim

umdamping

ratio

01984

01197

01601

01098

01345

00011

01668

00229

Journal of Engineering 7

regulators Eigenvalue analysis plays an important role instability studies Complex conjugate eigenvalues are alsoknown as swing modes and these eigenvalues are responsiblefor oscillatory instability when the real part of the eigen-value is positive From Table 2 it is observed that whenoptimization process is carried out with the application ofGA on 119869

2system mode contains a swing mode with positive

eigenvalue (0361) Real positive part of eigen is the indicationof oscillations of growing amplitudeTheminimum dampingratios obtained from the application of different regulatorswith 119869

1and 119869

2criteria are shown in Table 2 For PSO

regulator minimum damping ratios obtained from thesecriteria are (01345 00011) similarly the ratios for GA are(01668 00229) for GSA are (01601 01098) and for ALOare (01984 01197) It can be said that a considerable amountof damping is enhanced in each case when the regulatorparameters are obtained with criterion 119869

1 Overall damping

of the system is the highest with ALO regulator (1198691) (01984)

Prima facie it can be concluded that the regulator designobtained from criterion 119869

1is more effective as the damping

enhanced by this regulator is higher In eigenvalue analysisboth real and imaginary parts have their interpretation andphysical significance The real part of the complex conjugateeigenvalue shows the damping behavior which represents thedamp oscillations whichmeans the larger themagnitude thehigher the rate of decay Imaginary components show thefrequency of oscillations It can be observed from Table 2that high frequency oscillations are associated with setting1198692 Higher frequency oscillations are bad for equipment

health and often cause the damage of physical structure ofcontrollers In this case for 119869

2 GA frequency of oscillations

is (157 168) for PSO (269 218) for GSA (191 174) and(188 173) for ALO It is observed that although frequencyof oscillations is in moderate range for GA regulator theamplitude of the oscillation is growing with time as it has apositive real part of eigenvalue However the other regulatorshave high frequency of oscillations modes as comparedwith ALO To show this analysis in a more prominent wayAGC regulators are designed with ALO algorithm and testedfor different levels of perturbations Figures 3(a) and 3(b)show the dynamic responses of frequency deviations inareas 1 and 2 when area 1 observes a step disturbance of001 pu Figures 3(c) and 3(d) show the frequency deviationcurves of both areas with both regulator settings 119869

1and

1198692when area 2 is perturbed with 002 pu Similarly for

both regulator settings the dynamic responses obtainedfrom both areas are self-explanatory It is observed that 119869

1

setting is promising The overshoot and settling time of thefrequency deviation curves of both areas are less with 119869

1

regulator It is also empirical to judge that the variationsof tie-line power exchanges are nominal with both types ofperturbation with 119869

1regulator Hence it is concluded that 119869

1

optimization criterion is suitable for the designing of theAGCregulator

To exhibit the comparative performance of the ALO reg-ulator with other regulators four different loading scenariosare simulated in this work These loading conditions aresummarized below

Case 1 Load changes in area 1 by 10Thedynamic responsesof Δ119865

1 Δ1198652 and Δ119875tie are given in Figures 4ndash6 for all the

algorithms

Case 2 Load changes in area 2 by 20 Figures 7ndash9 show thedynamic responses of the system

Case 3 Load is increased in area 1 by 25 In Figures 10ndash12the system dynamic responses are shown

Case 4 Load is decreased in area 1 by 25 and the systemdynamic responses are given in Figures 13ndash15

Dynamic responses along with the system eigenvalues forthese conditions are exhibited in Table 3 It is observed thatagain with setting 119869

2few eigenvalues possess positive real part

when optimized with GA (00370 00382 and 00368) Thereal part of swing mode varies from minus02823 to minus04567 forALO regulator from minus02541 to minus04632 for GSA regulatorfrom minus00982 to minus4587 for PSO regulator and from minus02511to minus05411 for GA regulator with criterion 119869

1 It is of note

here that the real part of the eigenvalue observes a largevariation in case of GA under different loading conditionsThis spread put a question mark on the performance ofthe regulator and robustness of the regulator also Moder-ate spread has been observed with ALO regulator For allcases higher numeric values of real part of the eigenvaluessuggest that the system is more stable In Case 1 thesevalues are (minus04278 minus02823) for ALO (minus04288 minus02570)for GSA (minus04277 minus02395) for PSO and (minus02588 minus05271)for GA It can be predicted that for Case 1 the robustsetting is achieved by ALO Similarly in Case 4 the realparts of eigenvalues (swing modes) are (minus03276 minus02879)for ALO and (minus03106 minus02589) for GSA and an addi-tional swing mode with PSO setting has been observed(1198691) (minus03055 minus02459 00983) and (minus0440 02680) for GA

From this it is also observed that a higher degree ofrobustness can be achieved by ALO regulator To understandthe dynamic response of the frequency deviation curvesa conventional index Figure of Demerit (FOD) is usedin this paper Figure of Demerit is the summation of thesquare of the overshoot and settling time of the deviationcurves It is observed that for almost all loading cases thevalues of settling time overshoot and FODs are low forALO based regulators as compared with other regulatordesigns It is observed from Figures 4ndash6 that ALO basedcontroller exhibits better dynamic performance as comparedwith others The percentage of overshoot and settling timeis much less in these cases The low oscillatory responseexhibited by ALO is best suited for the equipmentrsquos healthFOD values are considered as a close replica of dynamicperformance of controller Higher values of FOD show poordynamic performance and vice versa It is also empiricalto mention here that for frequency deviation in area 1 thesettling time and FOD obtained from ALO are 38 and 1444respectively whereas from GSA PSO and GA the settlingtime and FOD are 56 50 and 49 and 3136 25 and 2401respectively The frequency deviation in area 2 also showsthat the values of settling time and FOD are less when ALO

8 Journal of Engineering

Table3Syste

mmod

esfore

achcase

ofallthe

algorithm

s

Parameters

ALO

GSA

[17]

PSO[18]

GA[19

]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

Case

1

minus58014

minus58014

minus57891

minus59112

minus57884

minus64711

minus55532

minus5752

minus42274

minus42274

minus4313

minus44257

minus444

43minus48155

minus41792

minus42168

minus04924plusmn16

361119894

minus04924plusmn16

361119894

minus04288plusmn16

043119894

minus02773plusmn18

079119894

minus04277plusmn16

059119894

minus00430plusmn25784119894

minus02588plusmn14

307119894

minus02211plusmn15

866119894

minus02842plusmn14

933119894

minus02842plusmn14

933119894

minus02570plusmn16

085119894

minus01941plusmn1746

0119894minus02395plusmn17

695119894

minus00222plusmn21888119894

minus05271plusmn11657119894

00370plusmn15

795119894

minus01208

minus01208

minus03454

minus05259

minus00983plusmn00157119894

minus04806

minus01466

minus01058

minus02021

minus02021

minus0110

1minus00884

minus03584

minus00494

minus03344

minus09221

minus02229

minus02229

minus02062

minus02416

minus02144

minus0401

minus08182

Case

2

minus58597

minus59843

minus58468

minus5976

minus5846

minus6564

minus55965

minus5808

minus41275

minus42672

minus42059

minus43093

minus43269

minus46691

minus40832

minus41155

minus046

46plusmn17

341119894

minus02906plusmn19

218119894

minus040

02plusmn17

063119894

minus02534plusmn19

127119894

minus03943plusmn17

014119894

000

14plusmn26941119894

minus05108plusmn12

557119894

minus02029plusmn16

828119894

minus03315plusmn13

466119894

minus01072plusmn15

609119894

minus03117plusmn14

571119894

minus02466plusmn15

904119894

minus03057plusmn16

218119894

minus00944plusmn20213119894

minus03032plusmn12

918119894

minus00013plusmn14

380119894

minus01204

minus00879

minus03394

minus05169

minus00986plusmn00155119894

minus04774

minus01467

minus01059

minus02047

minus044

98minus0110

1minus00884

minus03521

minus00494

minus0344

minus08003

minus02234

minus05752

minus02096

minus0245

minus02155

minus03879

minus09453

Case

3

minus57282

minus58373

minus57167

minus58312

minus5716

minus6353

minus54991

minus56819

minus42274

minus43812

minus4313

minus44278

minus444

43minus48155

minus41792

minus42168

minus05297plusmn15

095119894

minus03560plusmn16

872119894

minus04632plusmn14

784119894

minus03257plusmn16

774119894

minus04587plusmn14

794119894

minus00990plusmn24269119894

minus02590plusmn14

294119894

minus02413plusmn14

636119894

minus02816plusmn14

943119894

minus00567plusmn17

151119894

minus02541plusmn16

063119894

minus01938plusmn17

505119894

minus02396plusmn17679119894

minus00228plusmn21889119894

minus05411plusmn10

386119894

003

82plusmn15

795119894

minus01204

minus00878

minus0355

minus05367

minus00982plusmn00157119894

minus04855

minus01462

minus01058

minus02039

minus046

72minus011

minus00886

minus03686

minus00494

minus03357

minus09251

minus02252

minus05609

minus02063

minus02401

minus02144

minus04258

minus08475

Case

4

minus60556

minus62024

minus6041

minus61949

minus604

01minus68711

minus57445

minus59969

minus42274

minus43812

minus4313

minus44278

minus444

43minus48155

minus41792

minus42168

minus03695plusmn20323119894

minus01897plusmn22365119894

minus03106plusmn20088119894

minus01627plusmn22305119894

minus03055plusmn20076119894

01510plusmn30616119894

minus044

40plusmn15

429119894

minus01319plusmn19

807119894

minus02838plusmn14

894119894

minus00573plusmn17

122119894

minus02589plusmn16

017119894

minus01958plusmn1744

2119894minus02459plusmn17

656119894

minus00217plusmn21890119894

minus02680plusmn14

339119894

003

68plusmn15

765119894

minus01216

minus00879

minus03261

minus04948

minus00983plusmn00158119894

minus04698

minus01478

minus01059

minus01971

minus0434

minus0110

5minus00886

minus03379

minus00494

minus03276

minus07544

minus02194

minus05605

minus02059

minus024

minus02144

minus03632

minus09192

Journal of Engineering 9

J

J1

2

2 4 6 81 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(a)

J

J1

2

2 4 6 80 10

Time (s)

minus005

0

005

ΔF2

(Hz)

(b)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(c)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

minus005

0

005

ΔF2

(Hz)

(d)

J

J1

2

2 4 6 80 10

Time (s)

ΔP

tie(p

u)

minus002

0

002

(e)

J

J1

2

2 4 6 80 10

Time (s)

minus001

0

001

ΔP

tie(p

u)

(f)

Figure 3 Dynamic responses obtained from ALO

regulator is used The value of settling time with frequencydeviation in area 2 is observed as 60 for ALO 72 for GSA76 for PSO and 80 for GA It is also interesting to observethat with the 10 increase in the load PSO gives erroneousresults and the flow of tie-line power behaves in a differentmanner Hence critical analysis of dynamic responses clearlyreveals that better dynamic performance is exhibited by ALOBy examining the responses in Figures 7ndash9 it is clearly seenthat the settling time and peak overshoot are less whenload changes in area 2 by 20 It can be observed fromFigure 8 that when area 2 observes 20 increase GA basedcontroller is not able to mitigate the frequency oscillationsThis inculcates oscillatory instability in the system HoweverALO based controller shows a better dynamic response andyields satisfactory performance over a wide range of loading

conditions For Case 2 the settling time of ALO is 36 and is53 42 and 58 for GSA PSO andGA respectively Similarlythe FOD is also very low in case of ALO that is 1296whereas it is 1764 and 3364 in case of PSO and GA Figures10 and 11 show the frequency deviations of areas 1 and 2From dynamic responses of overshoot settling time andFOD it is clear that ALO provides competitive results Thedynamic responses for Case 4 are shown in Figures 13ndash15 andit has been observed that ALO tuned controller yields betterdynamic performanceThe minimum settling time and FODobtained from ALO are 51 and 2601 for frequency deviationin area 1 and 60 and 3600 for frequency deviation in area 2However in case of GSA the settling time is 79 and FOD is198 An oscillatory response is obtained by the GA GSA andPSO tuned controllers

10 Journal of Engineering

ALOGSA [17]

PSO [18]GA [19]

2 4 6 8 10 120Time (s)

minus004

minus003

minus002

minus001

0

001

ΔF1

(Hz)

Figure 4 Change in frequency of area 1 by 10 load increase in area1

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

2 4 6 80 1210

Time (s)

ALOGSA [17]

PSO [18]GA [19]

Figure 5 Change in frequency of area 2 by 10 load increase in area1

5 Optimization Performance

To judge the efficiency of the optimization process carried outby all algorithms 100 trials of optimization are carried outTo provide a fair comparison the population size (100) andthe maximum number of iterations (1000) are kept the sameStopping criterion for the optimization process is maximumrun of the iteration To observe the optimization process in acritical way the standard deviations of optimized parametersof the regulator along with the values of objective functionsare calculated and shown in Table 4 It is observed thathigh values of standard deviations are obtained in regulator

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 6 Change in tie-line power by 10 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 7 Change in frequency of area 1 by 20 load increase in area2

parameters and values of objective functions when optimiza-tion process is handled by GA (009729) Comparatively largevalues of standard deviations are found in GA and PSOwhenthey are compared with ALO We observed high values ofstandard deviation in speed regulation parameters after eachrun of optimization obtained with GA regulators (119869

1and

1198692) Speed regulation parameter is a vulnerable parameter

in power system dynamics studies It affects the systemdynamics in a very prominent way Large values of standarddeviations in the calculation of such vulnerable parametersare not acceptable The values for standard deviations are010256 (GSA 119869

1) and 01550 (GA 119869

2) and similarly for

1198772 they are 00081 (ALO 119869

1) 002 (GSA) 038 (PSO) and

Journal of Engineering 11

Table 4 Standard deviation of optimized parameters of the regulator

Parameters ALO GSA [17] PSO [18] GA [19]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

1198701198681

002923 003773 002425 007720 002604 008461 009729 0206871198631

004107 003315 004475 009833 008416 004759 018872 0213131198771

000582 000102 000045 000168 000153 001403 000892 0007171198701198682

001763 004563 010256 000769 009639 008158 005800 0155501198632

008957 008807 004916 011771 016726 008363 017955 0079451198772

000343 000174 000173 000385 000280 001080 000310 00105937000184 716E minus 06 00212 0000419 038 0011 176 0013

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

ALOGSA [17]

PSO [18]GA [19]

Figure 8 Change in frequency of area 2 by 20 load increase in area2

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 9 Change in tie-line power by 20 load increase in area 2

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 10 Change in frequency of area 1 by 25 load increase inarea 1

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 11 Change in frequency of area 2 by 25 load increase inarea 1

12 Journal of Engineering

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 12 Change in tie-line power by 25 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus005

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 13 Change in frequency of area 1 by 25 load decreases inarea 1

176 for GA The impact of speed regulation parameters onthe dynamic response is shown in [25] The lowest valuesof standard deviations are observed when the parametersare optimized by ALO This basically means that in eachrun of optimization ALO exhibits precision in computingthe parameters The standard deviations in the values ofintegral gains for area 1 by 119869

1and 119869

2are minimum for

ALO (0041 0033) for GA these values are (018 and 0213)and similarly (0044 009) for GSA and (008 and 0047)for PSO It can be concluded that regulator setting integralgain observes the least variation in numerical values whenthe parameter is optimized through ALO (119869

1) The values

of standard deviations in objective functions 1198691and 119869

2are

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 14 Change in frequency of area 1 by 25 load decreases inarea 1

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 15 Change in tie-line power by 25 load decreases in area 1

the lowest for ALO process and the highest for GA Thevalues of standard deviations in the values of 119869

1for GA PSO

GSA and GWO are 00972 00264 00242 and 002 andfor 1198692are 02068 00846 00772 and 03773 It has been

observed that the values obtained by ALO are precise and theoptimization processes are reliable enough for obtaining theregulator design However high values of standard deviationsin parameters of regulator (176 with 119877

2) and in the objective

functions show that the optimization process loses its rele-vance when it is handled by GA Hence it is concluded fromthe eigenvalue analysis anddynamic response of the deviationcurves that ALO shows a promising response to obtainregulator settingwith optimization criterion 119869

1The following

Journal of Engineering 13

section summarizes the contribution of this research workand proposes a solid milieu for future work

6 Conclusion

This paper presents an application of the recently introducedalgorithm ALO to find optimal parameters of the AGCregulator The ALO regulator is employed on a test system oftwo thermal units connected with a weak tie line of limitedcapacity for AGCThe following are the major findings of thework

(A) Comparison of the application of two objective func-tions namely ISE and ITAE in optimization processfor finding the regulator parameters under differ-ent contingencies is investigated Results reveal thatITAE is a better choice to optimize the regulatorparameters

(B) Eigenvalue analysis is performed to test the effec-tiveness of the proposed approach and to comparethe results of the proposed approach with recentlypublished approaches It is observed that the dampingobtained from ALO regulator is more positive ascompared with the other algorithms

(C) ALO shows promising results in terms of overshootsettling time obtained from the frequency responsesof both areas under different loading cases standarddeviations in regulatorrsquos parameter values ISE andITAE values and optimization performance

(D) Damping performance is evaluated with differentcontingencies load changes and step disturbancesin both areas PI controller setting obtained throughALO exhibits better dynamic performance and over-all low settling time

Application of other new metaheuristic algorithms in AGCregulator design on different models of the power systemconsidering different renewable energy power sources lies inthe future scope

Nomenclature

119894 Subscript referring to area 119894 (1 2)Δ119865119894 Frequency deviation in area 119894 (Hz)

Δ119875119866119894 Incremental generation of area 119894 (pu)

Δ119875119871119894 Incremental load change in area 119894 (pu)

ACE119894 Area Control Error of area 119894

119861119894 Frequency bias parameter of area 119894

119877119894 Speed regulation of the governor of area 119894

(Hzpu MW)119879119892119894 Time constant of governor of area 119894 (s)

119879119905119894 Time constant of turbine of area 119894 (s)

119870119901119894 Gain of generator and load of area 119894

119879119901119894 Time constant of generator and load of

area 119894 (s)Δ119875tie Incremental change in tie line (pu)11987912 Synchronizing coefficient

119879 Simulation time (s)119905 Current iteration

Competing Interests

The authors declare that they have no competing interests

References

[1] O I Elgerd Energy Systems Theory An Introduction McGraw-Hill New Delhi India 1983

[2] IEEE Standard Committee ldquoIEEE Standard definitions of termsfor automatic generation control on electric power systemsrdquoIEEE Transactions on Power Apparatus and Systems vol 89 no6 pp 1356ndash1364 1970

[3] A Ibraheem P Kumar and D P Kothari ldquoRecent philosophiesof automatic generation control strategies in power systemsrdquoIEEE Transactions on Power Systems vol 20 no 1 pp 346ndash3572005

[4] H Sadat Power System Analysis McGraw-Hill New York NYUSA 1999

[5] J Nanda and B Kaul ldquoAutomatic generation control of aninterconnected power systemrdquo Proceedings of the Institution ofElectrical Engineers vol 125 no 5 pp 385ndash390 1978

[6] A Y Sivaramakrishnan M V Hariharan and M C SrisailamldquoDesign of variable-structure load-frequency controller usingpole assignment techniquerdquo International Journal of Controlvol 40 no 3 pp 487ndash498 1984

[7] M Z Bernard T H Mohamed Y S Qudaih and Y MitanildquoDecentralized load frequency control in an interconnectedpower system using Coefficient Diagram Methodrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 63pp 165ndash172 2014

[8] R Ali T HMohamed Y S Qudaih and YMitani ldquoA new loadfrequency control approach in an isolated small power systemsusing coefficient diagram methodrdquo International Journal ofElectrical Power and Energy Systems vol 56 pp 110ndash116 2014

[9] I Vajk M Vajta L Keviczky R Haber J Hetthessy andK Kovacs ldquoAdaptive load-frequency control of the hungarianpower systemrdquo Automatica vol 21 no 2 pp 129ndash137 1985

[10] J Kanniah S C Tripathy O P Malik and G S HopeldquoMicroprocessor-based adaptive load-frequency controlrdquo IEEProceedings CmdashGeneration Transmission and Distribution vol131 no 4 pp 121ndash128 1984

[11] M L Kothari P S Satsangi and J Nanda ldquoSampled-dataautomatic generation control of interconnected reheat thermalsystems considering generation rate constraintsrdquo IEEE Transac-tions on Power Apparatus and Systems vol 100 no 5 pp 2334ndash2342 1981

[12] S Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001

[13] B K Sahu S Pati P K Mohanty and S Panda ldquoTeaching-learning based optimization algorithm based fuzzy-PID con-troller for automatic generation control of multi-area powersystemrdquo Applied Soft Computing Journal vol 27 pp 240ndash2492015

[14] K R Sudha and R Vijaya Santhi ldquoLoad frequency control of aninterconnected reheat thermal systemusing type-2 fuzzy systemincluding SMES unitsrdquo International Journal of Electrical Poweramp Energy Systems vol 43 no 1 pp 1383ndash1392 2012

[15] A Banerjee V Mukherjee and S P Ghoshal ldquoIntelligentcontroller for load-tracking performance of an autonomous

14 Journal of Engineering

power systemrdquo Ain Shams Engineering Journal vol 5 no 4 pp1167ndash1176 2014

[16] S Padhan R K Sahu and S Panda ldquoAutomatic generationcontrol with thyristor controlled series compensator includingsuperconducting magnetic energy storage unitsrdquo Ain ShamsEngineering Journal vol 5 no 3 pp 759ndash774 2014

[17] R K Sahu S Panda and S Padhan ldquoOptimal gravitationalsearch algorithm for automatic generation control of intercon-nected power systemsrdquo Ain Shams Engineering Journal vol 5no 3 pp 721ndash733 2014

[18] Y L Abdel-Magid and M A Abido ldquoAGC tuning of intercon-nected reheat thermal systems with particle swarm optimiza-tionrdquo in Proceedings of the 10th IEEE International Conferenceon Electronics Circuits and Systems (ICECS rsquo03) pp 376ndash379December 2003

[19] Y L Abdel-Magid and M M Dawoud ldquoOptimal AGC tuningwith genetic algorithmsrdquo Electric Power Systems Research vol38 no 3 pp 231ndash238 1996

[20] J Nanda S Mishra and L C Saikia ldquoMaiden application ofbacterial foraging-based optimization technique in multiareaautomatic generation controlrdquo IEEE Transactions on PowerSystems vol 24 no 2 pp 602ndash609 2009

[21] U K Rout R K Sahu and S Panda ldquoDesign and analysisof differential evolution algorithm based automatic generationcontrol for interconnected power systemrdquo Ain Shams Engineer-ing Journal vol 4 no 3 pp 409ndash421 2013

[22] H Gozde M C Taplamacioglu and I Kocaarslan ldquoCompara-tive performance analysis of Artificial Bee Colony algorithm inautomatic generation control for interconnected reheat thermalpower systemrdquo International Journal of Electrical Power andEnergy Systems vol 42 no 1 pp 167ndash178 2012

[23] S Debbarma L Chandra Saikia and N Sinha ldquoSolution toautomatic generation control problem using firefly algorithmoptimized I120582D120583 controllerrdquo ISA Transactions vol 53 no 2 pp358ndash366 2014

[24] P Dash L C Saikia and N Sinha ldquoComparison of per-formances of several Cuckoo search algorithm based 2DOFcontrollers in AGC of multi-area thermal systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 55 pp 429ndash436 2014

[25] A Saxena M Gupta and V Gupta ldquoAutomatic generationcontrol of two area interconnected power system using Geneticalgorithmrdquo in Proceedings of the 3rd IEEE International Con-ference on Computational Intelligence and Computing Research(ICCIC rsquo12) Coimbatore India December 2012

[26] B K Sahu T K Pati J R Nayak S Panda and S K KarldquoA novel hybrid LUS-TLBO optimized fuzzy-PID controllerfor load frequency control of multi-source power systemrdquoInternational Journal of Electrical Power amp Energy Systems vol74 pp 58ndash69 2016

[27] Y Sharma and L C Saikia ldquoAutomatic generation controlof a multi-area STmdashthermal power system using Grey WolfOptimizer algorithm based classical controllersrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 853ndash862 2015

[28] P Dash L C Saikia and N Sinha ldquoAutomatic generationcontrol of multi area thermal system using Bat algorithmoptimized PDndashPID cascade controllerrdquo International Journal ofElectrical Power amp Energy Systems vol 68 pp 364ndash372 2015

[29] S Mirjalili ldquoThe ant lion optimizerrdquo Advances in EngineeringSoftware vol 83 pp 80ndash98 2015

[30] MATLAB httpwwwmathworkscom

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Engineering 7

regulators Eigenvalue analysis plays an important role instability studies Complex conjugate eigenvalues are alsoknown as swing modes and these eigenvalues are responsiblefor oscillatory instability when the real part of the eigen-value is positive From Table 2 it is observed that whenoptimization process is carried out with the application ofGA on 119869

2system mode contains a swing mode with positive

eigenvalue (0361) Real positive part of eigen is the indicationof oscillations of growing amplitudeTheminimum dampingratios obtained from the application of different regulatorswith 119869

1and 119869

2criteria are shown in Table 2 For PSO

regulator minimum damping ratios obtained from thesecriteria are (01345 00011) similarly the ratios for GA are(01668 00229) for GSA are (01601 01098) and for ALOare (01984 01197) It can be said that a considerable amountof damping is enhanced in each case when the regulatorparameters are obtained with criterion 119869

1 Overall damping

of the system is the highest with ALO regulator (1198691) (01984)

Prima facie it can be concluded that the regulator designobtained from criterion 119869

1is more effective as the damping

enhanced by this regulator is higher In eigenvalue analysisboth real and imaginary parts have their interpretation andphysical significance The real part of the complex conjugateeigenvalue shows the damping behavior which represents thedamp oscillations whichmeans the larger themagnitude thehigher the rate of decay Imaginary components show thefrequency of oscillations It can be observed from Table 2that high frequency oscillations are associated with setting1198692 Higher frequency oscillations are bad for equipment

health and often cause the damage of physical structure ofcontrollers In this case for 119869

2 GA frequency of oscillations

is (157 168) for PSO (269 218) for GSA (191 174) and(188 173) for ALO It is observed that although frequencyof oscillations is in moderate range for GA regulator theamplitude of the oscillation is growing with time as it has apositive real part of eigenvalue However the other regulatorshave high frequency of oscillations modes as comparedwith ALO To show this analysis in a more prominent wayAGC regulators are designed with ALO algorithm and testedfor different levels of perturbations Figures 3(a) and 3(b)show the dynamic responses of frequency deviations inareas 1 and 2 when area 1 observes a step disturbance of001 pu Figures 3(c) and 3(d) show the frequency deviationcurves of both areas with both regulator settings 119869

1and

1198692when area 2 is perturbed with 002 pu Similarly for

both regulator settings the dynamic responses obtainedfrom both areas are self-explanatory It is observed that 119869

1

setting is promising The overshoot and settling time of thefrequency deviation curves of both areas are less with 119869

1

regulator It is also empirical to judge that the variationsof tie-line power exchanges are nominal with both types ofperturbation with 119869

1regulator Hence it is concluded that 119869

1

optimization criterion is suitable for the designing of theAGCregulator

To exhibit the comparative performance of the ALO reg-ulator with other regulators four different loading scenariosare simulated in this work These loading conditions aresummarized below

Case 1 Load changes in area 1 by 10Thedynamic responsesof Δ119865

1 Δ1198652 and Δ119875tie are given in Figures 4ndash6 for all the

algorithms

Case 2 Load changes in area 2 by 20 Figures 7ndash9 show thedynamic responses of the system

Case 3 Load is increased in area 1 by 25 In Figures 10ndash12the system dynamic responses are shown

Case 4 Load is decreased in area 1 by 25 and the systemdynamic responses are given in Figures 13ndash15

Dynamic responses along with the system eigenvalues forthese conditions are exhibited in Table 3 It is observed thatagain with setting 119869

2few eigenvalues possess positive real part

when optimized with GA (00370 00382 and 00368) Thereal part of swing mode varies from minus02823 to minus04567 forALO regulator from minus02541 to minus04632 for GSA regulatorfrom minus00982 to minus4587 for PSO regulator and from minus02511to minus05411 for GA regulator with criterion 119869

1 It is of note

here that the real part of the eigenvalue observes a largevariation in case of GA under different loading conditionsThis spread put a question mark on the performance ofthe regulator and robustness of the regulator also Moder-ate spread has been observed with ALO regulator For allcases higher numeric values of real part of the eigenvaluessuggest that the system is more stable In Case 1 thesevalues are (minus04278 minus02823) for ALO (minus04288 minus02570)for GSA (minus04277 minus02395) for PSO and (minus02588 minus05271)for GA It can be predicted that for Case 1 the robustsetting is achieved by ALO Similarly in Case 4 the realparts of eigenvalues (swing modes) are (minus03276 minus02879)for ALO and (minus03106 minus02589) for GSA and an addi-tional swing mode with PSO setting has been observed(1198691) (minus03055 minus02459 00983) and (minus0440 02680) for GA

From this it is also observed that a higher degree ofrobustness can be achieved by ALO regulator To understandthe dynamic response of the frequency deviation curvesa conventional index Figure of Demerit (FOD) is usedin this paper Figure of Demerit is the summation of thesquare of the overshoot and settling time of the deviationcurves It is observed that for almost all loading cases thevalues of settling time overshoot and FODs are low forALO based regulators as compared with other regulatordesigns It is observed from Figures 4ndash6 that ALO basedcontroller exhibits better dynamic performance as comparedwith others The percentage of overshoot and settling timeis much less in these cases The low oscillatory responseexhibited by ALO is best suited for the equipmentrsquos healthFOD values are considered as a close replica of dynamicperformance of controller Higher values of FOD show poordynamic performance and vice versa It is also empiricalto mention here that for frequency deviation in area 1 thesettling time and FOD obtained from ALO are 38 and 1444respectively whereas from GSA PSO and GA the settlingtime and FOD are 56 50 and 49 and 3136 25 and 2401respectively The frequency deviation in area 2 also showsthat the values of settling time and FOD are less when ALO

8 Journal of Engineering

Table3Syste

mmod

esfore

achcase

ofallthe

algorithm

s

Parameters

ALO

GSA

[17]

PSO[18]

GA[19

]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

Case

1

minus58014

minus58014

minus57891

minus59112

minus57884

minus64711

minus55532

minus5752

minus42274

minus42274

minus4313

minus44257

minus444

43minus48155

minus41792

minus42168

minus04924plusmn16

361119894

minus04924plusmn16

361119894

minus04288plusmn16

043119894

minus02773plusmn18

079119894

minus04277plusmn16

059119894

minus00430plusmn25784119894

minus02588plusmn14

307119894

minus02211plusmn15

866119894

minus02842plusmn14

933119894

minus02842plusmn14

933119894

minus02570plusmn16

085119894

minus01941plusmn1746

0119894minus02395plusmn17

695119894

minus00222plusmn21888119894

minus05271plusmn11657119894

00370plusmn15

795119894

minus01208

minus01208

minus03454

minus05259

minus00983plusmn00157119894

minus04806

minus01466

minus01058

minus02021

minus02021

minus0110

1minus00884

minus03584

minus00494

minus03344

minus09221

minus02229

minus02229

minus02062

minus02416

minus02144

minus0401

minus08182

Case

2

minus58597

minus59843

minus58468

minus5976

minus5846

minus6564

minus55965

minus5808

minus41275

minus42672

minus42059

minus43093

minus43269

minus46691

minus40832

minus41155

minus046

46plusmn17

341119894

minus02906plusmn19

218119894

minus040

02plusmn17

063119894

minus02534plusmn19

127119894

minus03943plusmn17

014119894

000

14plusmn26941119894

minus05108plusmn12

557119894

minus02029plusmn16

828119894

minus03315plusmn13

466119894

minus01072plusmn15

609119894

minus03117plusmn14

571119894

minus02466plusmn15

904119894

minus03057plusmn16

218119894

minus00944plusmn20213119894

minus03032plusmn12

918119894

minus00013plusmn14

380119894

minus01204

minus00879

minus03394

minus05169

minus00986plusmn00155119894

minus04774

minus01467

minus01059

minus02047

minus044

98minus0110

1minus00884

minus03521

minus00494

minus0344

minus08003

minus02234

minus05752

minus02096

minus0245

minus02155

minus03879

minus09453

Case

3

minus57282

minus58373

minus57167

minus58312

minus5716

minus6353

minus54991

minus56819

minus42274

minus43812

minus4313

minus44278

minus444

43minus48155

minus41792

minus42168

minus05297plusmn15

095119894

minus03560plusmn16

872119894

minus04632plusmn14

784119894

minus03257plusmn16

774119894

minus04587plusmn14

794119894

minus00990plusmn24269119894

minus02590plusmn14

294119894

minus02413plusmn14

636119894

minus02816plusmn14

943119894

minus00567plusmn17

151119894

minus02541plusmn16

063119894

minus01938plusmn17

505119894

minus02396plusmn17679119894

minus00228plusmn21889119894

minus05411plusmn10

386119894

003

82plusmn15

795119894

minus01204

minus00878

minus0355

minus05367

minus00982plusmn00157119894

minus04855

minus01462

minus01058

minus02039

minus046

72minus011

minus00886

minus03686

minus00494

minus03357

minus09251

minus02252

minus05609

minus02063

minus02401

minus02144

minus04258

minus08475

Case

4

minus60556

minus62024

minus6041

minus61949

minus604

01minus68711

minus57445

minus59969

minus42274

minus43812

minus4313

minus44278

minus444

43minus48155

minus41792

minus42168

minus03695plusmn20323119894

minus01897plusmn22365119894

minus03106plusmn20088119894

minus01627plusmn22305119894

minus03055plusmn20076119894

01510plusmn30616119894

minus044

40plusmn15

429119894

minus01319plusmn19

807119894

minus02838plusmn14

894119894

minus00573plusmn17

122119894

minus02589plusmn16

017119894

minus01958plusmn1744

2119894minus02459plusmn17

656119894

minus00217plusmn21890119894

minus02680plusmn14

339119894

003

68plusmn15

765119894

minus01216

minus00879

minus03261

minus04948

minus00983plusmn00158119894

minus04698

minus01478

minus01059

minus01971

minus0434

minus0110

5minus00886

minus03379

minus00494

minus03276

minus07544

minus02194

minus05605

minus02059

minus024

minus02144

minus03632

minus09192

Journal of Engineering 9

J

J1

2

2 4 6 81 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(a)

J

J1

2

2 4 6 80 10

Time (s)

minus005

0

005

ΔF2

(Hz)

(b)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(c)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

minus005

0

005

ΔF2

(Hz)

(d)

J

J1

2

2 4 6 80 10

Time (s)

ΔP

tie(p

u)

minus002

0

002

(e)

J

J1

2

2 4 6 80 10

Time (s)

minus001

0

001

ΔP

tie(p

u)

(f)

Figure 3 Dynamic responses obtained from ALO

regulator is used The value of settling time with frequencydeviation in area 2 is observed as 60 for ALO 72 for GSA76 for PSO and 80 for GA It is also interesting to observethat with the 10 increase in the load PSO gives erroneousresults and the flow of tie-line power behaves in a differentmanner Hence critical analysis of dynamic responses clearlyreveals that better dynamic performance is exhibited by ALOBy examining the responses in Figures 7ndash9 it is clearly seenthat the settling time and peak overshoot are less whenload changes in area 2 by 20 It can be observed fromFigure 8 that when area 2 observes 20 increase GA basedcontroller is not able to mitigate the frequency oscillationsThis inculcates oscillatory instability in the system HoweverALO based controller shows a better dynamic response andyields satisfactory performance over a wide range of loading

conditions For Case 2 the settling time of ALO is 36 and is53 42 and 58 for GSA PSO andGA respectively Similarlythe FOD is also very low in case of ALO that is 1296whereas it is 1764 and 3364 in case of PSO and GA Figures10 and 11 show the frequency deviations of areas 1 and 2From dynamic responses of overshoot settling time andFOD it is clear that ALO provides competitive results Thedynamic responses for Case 4 are shown in Figures 13ndash15 andit has been observed that ALO tuned controller yields betterdynamic performanceThe minimum settling time and FODobtained from ALO are 51 and 2601 for frequency deviationin area 1 and 60 and 3600 for frequency deviation in area 2However in case of GSA the settling time is 79 and FOD is198 An oscillatory response is obtained by the GA GSA andPSO tuned controllers

10 Journal of Engineering

ALOGSA [17]

PSO [18]GA [19]

2 4 6 8 10 120Time (s)

minus004

minus003

minus002

minus001

0

001

ΔF1

(Hz)

Figure 4 Change in frequency of area 1 by 10 load increase in area1

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

2 4 6 80 1210

Time (s)

ALOGSA [17]

PSO [18]GA [19]

Figure 5 Change in frequency of area 2 by 10 load increase in area1

5 Optimization Performance

To judge the efficiency of the optimization process carried outby all algorithms 100 trials of optimization are carried outTo provide a fair comparison the population size (100) andthe maximum number of iterations (1000) are kept the sameStopping criterion for the optimization process is maximumrun of the iteration To observe the optimization process in acritical way the standard deviations of optimized parametersof the regulator along with the values of objective functionsare calculated and shown in Table 4 It is observed thathigh values of standard deviations are obtained in regulator

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 6 Change in tie-line power by 10 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 7 Change in frequency of area 1 by 20 load increase in area2

parameters and values of objective functions when optimiza-tion process is handled by GA (009729) Comparatively largevalues of standard deviations are found in GA and PSOwhenthey are compared with ALO We observed high values ofstandard deviation in speed regulation parameters after eachrun of optimization obtained with GA regulators (119869

1and

1198692) Speed regulation parameter is a vulnerable parameter

in power system dynamics studies It affects the systemdynamics in a very prominent way Large values of standarddeviations in the calculation of such vulnerable parametersare not acceptable The values for standard deviations are010256 (GSA 119869

1) and 01550 (GA 119869

2) and similarly for

1198772 they are 00081 (ALO 119869

1) 002 (GSA) 038 (PSO) and

Journal of Engineering 11

Table 4 Standard deviation of optimized parameters of the regulator

Parameters ALO GSA [17] PSO [18] GA [19]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

1198701198681

002923 003773 002425 007720 002604 008461 009729 0206871198631

004107 003315 004475 009833 008416 004759 018872 0213131198771

000582 000102 000045 000168 000153 001403 000892 0007171198701198682

001763 004563 010256 000769 009639 008158 005800 0155501198632

008957 008807 004916 011771 016726 008363 017955 0079451198772

000343 000174 000173 000385 000280 001080 000310 00105937000184 716E minus 06 00212 0000419 038 0011 176 0013

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

ALOGSA [17]

PSO [18]GA [19]

Figure 8 Change in frequency of area 2 by 20 load increase in area2

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 9 Change in tie-line power by 20 load increase in area 2

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 10 Change in frequency of area 1 by 25 load increase inarea 1

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 11 Change in frequency of area 2 by 25 load increase inarea 1

12 Journal of Engineering

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 12 Change in tie-line power by 25 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus005

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 13 Change in frequency of area 1 by 25 load decreases inarea 1

176 for GA The impact of speed regulation parameters onthe dynamic response is shown in [25] The lowest valuesof standard deviations are observed when the parametersare optimized by ALO This basically means that in eachrun of optimization ALO exhibits precision in computingthe parameters The standard deviations in the values ofintegral gains for area 1 by 119869

1and 119869

2are minimum for

ALO (0041 0033) for GA these values are (018 and 0213)and similarly (0044 009) for GSA and (008 and 0047)for PSO It can be concluded that regulator setting integralgain observes the least variation in numerical values whenthe parameter is optimized through ALO (119869

1) The values

of standard deviations in objective functions 1198691and 119869

2are

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 14 Change in frequency of area 1 by 25 load decreases inarea 1

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 15 Change in tie-line power by 25 load decreases in area 1

the lowest for ALO process and the highest for GA Thevalues of standard deviations in the values of 119869

1for GA PSO

GSA and GWO are 00972 00264 00242 and 002 andfor 1198692are 02068 00846 00772 and 03773 It has been

observed that the values obtained by ALO are precise and theoptimization processes are reliable enough for obtaining theregulator design However high values of standard deviationsin parameters of regulator (176 with 119877

2) and in the objective

functions show that the optimization process loses its rele-vance when it is handled by GA Hence it is concluded fromthe eigenvalue analysis anddynamic response of the deviationcurves that ALO shows a promising response to obtainregulator settingwith optimization criterion 119869

1The following

Journal of Engineering 13

section summarizes the contribution of this research workand proposes a solid milieu for future work

6 Conclusion

This paper presents an application of the recently introducedalgorithm ALO to find optimal parameters of the AGCregulator The ALO regulator is employed on a test system oftwo thermal units connected with a weak tie line of limitedcapacity for AGCThe following are the major findings of thework

(A) Comparison of the application of two objective func-tions namely ISE and ITAE in optimization processfor finding the regulator parameters under differ-ent contingencies is investigated Results reveal thatITAE is a better choice to optimize the regulatorparameters

(B) Eigenvalue analysis is performed to test the effec-tiveness of the proposed approach and to comparethe results of the proposed approach with recentlypublished approaches It is observed that the dampingobtained from ALO regulator is more positive ascompared with the other algorithms

(C) ALO shows promising results in terms of overshootsettling time obtained from the frequency responsesof both areas under different loading cases standarddeviations in regulatorrsquos parameter values ISE andITAE values and optimization performance

(D) Damping performance is evaluated with differentcontingencies load changes and step disturbancesin both areas PI controller setting obtained throughALO exhibits better dynamic performance and over-all low settling time

Application of other new metaheuristic algorithms in AGCregulator design on different models of the power systemconsidering different renewable energy power sources lies inthe future scope

Nomenclature

119894 Subscript referring to area 119894 (1 2)Δ119865119894 Frequency deviation in area 119894 (Hz)

Δ119875119866119894 Incremental generation of area 119894 (pu)

Δ119875119871119894 Incremental load change in area 119894 (pu)

ACE119894 Area Control Error of area 119894

119861119894 Frequency bias parameter of area 119894

119877119894 Speed regulation of the governor of area 119894

(Hzpu MW)119879119892119894 Time constant of governor of area 119894 (s)

119879119905119894 Time constant of turbine of area 119894 (s)

119870119901119894 Gain of generator and load of area 119894

119879119901119894 Time constant of generator and load of

area 119894 (s)Δ119875tie Incremental change in tie line (pu)11987912 Synchronizing coefficient

119879 Simulation time (s)119905 Current iteration

Competing Interests

The authors declare that they have no competing interests

References

[1] O I Elgerd Energy Systems Theory An Introduction McGraw-Hill New Delhi India 1983

[2] IEEE Standard Committee ldquoIEEE Standard definitions of termsfor automatic generation control on electric power systemsrdquoIEEE Transactions on Power Apparatus and Systems vol 89 no6 pp 1356ndash1364 1970

[3] A Ibraheem P Kumar and D P Kothari ldquoRecent philosophiesof automatic generation control strategies in power systemsrdquoIEEE Transactions on Power Systems vol 20 no 1 pp 346ndash3572005

[4] H Sadat Power System Analysis McGraw-Hill New York NYUSA 1999

[5] J Nanda and B Kaul ldquoAutomatic generation control of aninterconnected power systemrdquo Proceedings of the Institution ofElectrical Engineers vol 125 no 5 pp 385ndash390 1978

[6] A Y Sivaramakrishnan M V Hariharan and M C SrisailamldquoDesign of variable-structure load-frequency controller usingpole assignment techniquerdquo International Journal of Controlvol 40 no 3 pp 487ndash498 1984

[7] M Z Bernard T H Mohamed Y S Qudaih and Y MitanildquoDecentralized load frequency control in an interconnectedpower system using Coefficient Diagram Methodrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 63pp 165ndash172 2014

[8] R Ali T HMohamed Y S Qudaih and YMitani ldquoA new loadfrequency control approach in an isolated small power systemsusing coefficient diagram methodrdquo International Journal ofElectrical Power and Energy Systems vol 56 pp 110ndash116 2014

[9] I Vajk M Vajta L Keviczky R Haber J Hetthessy andK Kovacs ldquoAdaptive load-frequency control of the hungarianpower systemrdquo Automatica vol 21 no 2 pp 129ndash137 1985

[10] J Kanniah S C Tripathy O P Malik and G S HopeldquoMicroprocessor-based adaptive load-frequency controlrdquo IEEProceedings CmdashGeneration Transmission and Distribution vol131 no 4 pp 121ndash128 1984

[11] M L Kothari P S Satsangi and J Nanda ldquoSampled-dataautomatic generation control of interconnected reheat thermalsystems considering generation rate constraintsrdquo IEEE Transac-tions on Power Apparatus and Systems vol 100 no 5 pp 2334ndash2342 1981

[12] S Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001

[13] B K Sahu S Pati P K Mohanty and S Panda ldquoTeaching-learning based optimization algorithm based fuzzy-PID con-troller for automatic generation control of multi-area powersystemrdquo Applied Soft Computing Journal vol 27 pp 240ndash2492015

[14] K R Sudha and R Vijaya Santhi ldquoLoad frequency control of aninterconnected reheat thermal systemusing type-2 fuzzy systemincluding SMES unitsrdquo International Journal of Electrical Poweramp Energy Systems vol 43 no 1 pp 1383ndash1392 2012

[15] A Banerjee V Mukherjee and S P Ghoshal ldquoIntelligentcontroller for load-tracking performance of an autonomous

14 Journal of Engineering

power systemrdquo Ain Shams Engineering Journal vol 5 no 4 pp1167ndash1176 2014

[16] S Padhan R K Sahu and S Panda ldquoAutomatic generationcontrol with thyristor controlled series compensator includingsuperconducting magnetic energy storage unitsrdquo Ain ShamsEngineering Journal vol 5 no 3 pp 759ndash774 2014

[17] R K Sahu S Panda and S Padhan ldquoOptimal gravitationalsearch algorithm for automatic generation control of intercon-nected power systemsrdquo Ain Shams Engineering Journal vol 5no 3 pp 721ndash733 2014

[18] Y L Abdel-Magid and M A Abido ldquoAGC tuning of intercon-nected reheat thermal systems with particle swarm optimiza-tionrdquo in Proceedings of the 10th IEEE International Conferenceon Electronics Circuits and Systems (ICECS rsquo03) pp 376ndash379December 2003

[19] Y L Abdel-Magid and M M Dawoud ldquoOptimal AGC tuningwith genetic algorithmsrdquo Electric Power Systems Research vol38 no 3 pp 231ndash238 1996

[20] J Nanda S Mishra and L C Saikia ldquoMaiden application ofbacterial foraging-based optimization technique in multiareaautomatic generation controlrdquo IEEE Transactions on PowerSystems vol 24 no 2 pp 602ndash609 2009

[21] U K Rout R K Sahu and S Panda ldquoDesign and analysisof differential evolution algorithm based automatic generationcontrol for interconnected power systemrdquo Ain Shams Engineer-ing Journal vol 4 no 3 pp 409ndash421 2013

[22] H Gozde M C Taplamacioglu and I Kocaarslan ldquoCompara-tive performance analysis of Artificial Bee Colony algorithm inautomatic generation control for interconnected reheat thermalpower systemrdquo International Journal of Electrical Power andEnergy Systems vol 42 no 1 pp 167ndash178 2012

[23] S Debbarma L Chandra Saikia and N Sinha ldquoSolution toautomatic generation control problem using firefly algorithmoptimized I120582D120583 controllerrdquo ISA Transactions vol 53 no 2 pp358ndash366 2014

[24] P Dash L C Saikia and N Sinha ldquoComparison of per-formances of several Cuckoo search algorithm based 2DOFcontrollers in AGC of multi-area thermal systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 55 pp 429ndash436 2014

[25] A Saxena M Gupta and V Gupta ldquoAutomatic generationcontrol of two area interconnected power system using Geneticalgorithmrdquo in Proceedings of the 3rd IEEE International Con-ference on Computational Intelligence and Computing Research(ICCIC rsquo12) Coimbatore India December 2012

[26] B K Sahu T K Pati J R Nayak S Panda and S K KarldquoA novel hybrid LUS-TLBO optimized fuzzy-PID controllerfor load frequency control of multi-source power systemrdquoInternational Journal of Electrical Power amp Energy Systems vol74 pp 58ndash69 2016

[27] Y Sharma and L C Saikia ldquoAutomatic generation controlof a multi-area STmdashthermal power system using Grey WolfOptimizer algorithm based classical controllersrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 853ndash862 2015

[28] P Dash L C Saikia and N Sinha ldquoAutomatic generationcontrol of multi area thermal system using Bat algorithmoptimized PDndashPID cascade controllerrdquo International Journal ofElectrical Power amp Energy Systems vol 68 pp 364ndash372 2015

[29] S Mirjalili ldquoThe ant lion optimizerrdquo Advances in EngineeringSoftware vol 83 pp 80ndash98 2015

[30] MATLAB httpwwwmathworkscom

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Journal of Engineering

Table3Syste

mmod

esfore

achcase

ofallthe

algorithm

s

Parameters

ALO

GSA

[17]

PSO[18]

GA[19

]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

Case

1

minus58014

minus58014

minus57891

minus59112

minus57884

minus64711

minus55532

minus5752

minus42274

minus42274

minus4313

minus44257

minus444

43minus48155

minus41792

minus42168

minus04924plusmn16

361119894

minus04924plusmn16

361119894

minus04288plusmn16

043119894

minus02773plusmn18

079119894

minus04277plusmn16

059119894

minus00430plusmn25784119894

minus02588plusmn14

307119894

minus02211plusmn15

866119894

minus02842plusmn14

933119894

minus02842plusmn14

933119894

minus02570plusmn16

085119894

minus01941plusmn1746

0119894minus02395plusmn17

695119894

minus00222plusmn21888119894

minus05271plusmn11657119894

00370plusmn15

795119894

minus01208

minus01208

minus03454

minus05259

minus00983plusmn00157119894

minus04806

minus01466

minus01058

minus02021

minus02021

minus0110

1minus00884

minus03584

minus00494

minus03344

minus09221

minus02229

minus02229

minus02062

minus02416

minus02144

minus0401

minus08182

Case

2

minus58597

minus59843

minus58468

minus5976

minus5846

minus6564

minus55965

minus5808

minus41275

minus42672

minus42059

minus43093

minus43269

minus46691

minus40832

minus41155

minus046

46plusmn17

341119894

minus02906plusmn19

218119894

minus040

02plusmn17

063119894

minus02534plusmn19

127119894

minus03943plusmn17

014119894

000

14plusmn26941119894

minus05108plusmn12

557119894

minus02029plusmn16

828119894

minus03315plusmn13

466119894

minus01072plusmn15

609119894

minus03117plusmn14

571119894

minus02466plusmn15

904119894

minus03057plusmn16

218119894

minus00944plusmn20213119894

minus03032plusmn12

918119894

minus00013plusmn14

380119894

minus01204

minus00879

minus03394

minus05169

minus00986plusmn00155119894

minus04774

minus01467

minus01059

minus02047

minus044

98minus0110

1minus00884

minus03521

minus00494

minus0344

minus08003

minus02234

minus05752

minus02096

minus0245

minus02155

minus03879

minus09453

Case

3

minus57282

minus58373

minus57167

minus58312

minus5716

minus6353

minus54991

minus56819

minus42274

minus43812

minus4313

minus44278

minus444

43minus48155

minus41792

minus42168

minus05297plusmn15

095119894

minus03560plusmn16

872119894

minus04632plusmn14

784119894

minus03257plusmn16

774119894

minus04587plusmn14

794119894

minus00990plusmn24269119894

minus02590plusmn14

294119894

minus02413plusmn14

636119894

minus02816plusmn14

943119894

minus00567plusmn17

151119894

minus02541plusmn16

063119894

minus01938plusmn17

505119894

minus02396plusmn17679119894

minus00228plusmn21889119894

minus05411plusmn10

386119894

003

82plusmn15

795119894

minus01204

minus00878

minus0355

minus05367

minus00982plusmn00157119894

minus04855

minus01462

minus01058

minus02039

minus046

72minus011

minus00886

minus03686

minus00494

minus03357

minus09251

minus02252

minus05609

minus02063

minus02401

minus02144

minus04258

minus08475

Case

4

minus60556

minus62024

minus6041

minus61949

minus604

01minus68711

minus57445

minus59969

minus42274

minus43812

minus4313

minus44278

minus444

43minus48155

minus41792

minus42168

minus03695plusmn20323119894

minus01897plusmn22365119894

minus03106plusmn20088119894

minus01627plusmn22305119894

minus03055plusmn20076119894

01510plusmn30616119894

minus044

40plusmn15

429119894

minus01319plusmn19

807119894

minus02838plusmn14

894119894

minus00573plusmn17

122119894

minus02589plusmn16

017119894

minus01958plusmn1744

2119894minus02459plusmn17

656119894

minus00217plusmn21890119894

minus02680plusmn14

339119894

003

68plusmn15

765119894

minus01216

minus00879

minus03261

minus04948

minus00983plusmn00158119894

minus04698

minus01478

minus01059

minus01971

minus0434

minus0110

5minus00886

minus03379

minus00494

minus03276

minus07544

minus02194

minus05605

minus02059

minus024

minus02144

minus03632

minus09192

Journal of Engineering 9

J

J1

2

2 4 6 81 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(a)

J

J1

2

2 4 6 80 10

Time (s)

minus005

0

005

ΔF2

(Hz)

(b)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(c)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

minus005

0

005

ΔF2

(Hz)

(d)

J

J1

2

2 4 6 80 10

Time (s)

ΔP

tie(p

u)

minus002

0

002

(e)

J

J1

2

2 4 6 80 10

Time (s)

minus001

0

001

ΔP

tie(p

u)

(f)

Figure 3 Dynamic responses obtained from ALO

regulator is used The value of settling time with frequencydeviation in area 2 is observed as 60 for ALO 72 for GSA76 for PSO and 80 for GA It is also interesting to observethat with the 10 increase in the load PSO gives erroneousresults and the flow of tie-line power behaves in a differentmanner Hence critical analysis of dynamic responses clearlyreveals that better dynamic performance is exhibited by ALOBy examining the responses in Figures 7ndash9 it is clearly seenthat the settling time and peak overshoot are less whenload changes in area 2 by 20 It can be observed fromFigure 8 that when area 2 observes 20 increase GA basedcontroller is not able to mitigate the frequency oscillationsThis inculcates oscillatory instability in the system HoweverALO based controller shows a better dynamic response andyields satisfactory performance over a wide range of loading

conditions For Case 2 the settling time of ALO is 36 and is53 42 and 58 for GSA PSO andGA respectively Similarlythe FOD is also very low in case of ALO that is 1296whereas it is 1764 and 3364 in case of PSO and GA Figures10 and 11 show the frequency deviations of areas 1 and 2From dynamic responses of overshoot settling time andFOD it is clear that ALO provides competitive results Thedynamic responses for Case 4 are shown in Figures 13ndash15 andit has been observed that ALO tuned controller yields betterdynamic performanceThe minimum settling time and FODobtained from ALO are 51 and 2601 for frequency deviationin area 1 and 60 and 3600 for frequency deviation in area 2However in case of GSA the settling time is 79 and FOD is198 An oscillatory response is obtained by the GA GSA andPSO tuned controllers

10 Journal of Engineering

ALOGSA [17]

PSO [18]GA [19]

2 4 6 8 10 120Time (s)

minus004

minus003

minus002

minus001

0

001

ΔF1

(Hz)

Figure 4 Change in frequency of area 1 by 10 load increase in area1

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

2 4 6 80 1210

Time (s)

ALOGSA [17]

PSO [18]GA [19]

Figure 5 Change in frequency of area 2 by 10 load increase in area1

5 Optimization Performance

To judge the efficiency of the optimization process carried outby all algorithms 100 trials of optimization are carried outTo provide a fair comparison the population size (100) andthe maximum number of iterations (1000) are kept the sameStopping criterion for the optimization process is maximumrun of the iteration To observe the optimization process in acritical way the standard deviations of optimized parametersof the regulator along with the values of objective functionsare calculated and shown in Table 4 It is observed thathigh values of standard deviations are obtained in regulator

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 6 Change in tie-line power by 10 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 7 Change in frequency of area 1 by 20 load increase in area2

parameters and values of objective functions when optimiza-tion process is handled by GA (009729) Comparatively largevalues of standard deviations are found in GA and PSOwhenthey are compared with ALO We observed high values ofstandard deviation in speed regulation parameters after eachrun of optimization obtained with GA regulators (119869

1and

1198692) Speed regulation parameter is a vulnerable parameter

in power system dynamics studies It affects the systemdynamics in a very prominent way Large values of standarddeviations in the calculation of such vulnerable parametersare not acceptable The values for standard deviations are010256 (GSA 119869

1) and 01550 (GA 119869

2) and similarly for

1198772 they are 00081 (ALO 119869

1) 002 (GSA) 038 (PSO) and

Journal of Engineering 11

Table 4 Standard deviation of optimized parameters of the regulator

Parameters ALO GSA [17] PSO [18] GA [19]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

1198701198681

002923 003773 002425 007720 002604 008461 009729 0206871198631

004107 003315 004475 009833 008416 004759 018872 0213131198771

000582 000102 000045 000168 000153 001403 000892 0007171198701198682

001763 004563 010256 000769 009639 008158 005800 0155501198632

008957 008807 004916 011771 016726 008363 017955 0079451198772

000343 000174 000173 000385 000280 001080 000310 00105937000184 716E minus 06 00212 0000419 038 0011 176 0013

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

ALOGSA [17]

PSO [18]GA [19]

Figure 8 Change in frequency of area 2 by 20 load increase in area2

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 9 Change in tie-line power by 20 load increase in area 2

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 10 Change in frequency of area 1 by 25 load increase inarea 1

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 11 Change in frequency of area 2 by 25 load increase inarea 1

12 Journal of Engineering

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 12 Change in tie-line power by 25 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus005

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 13 Change in frequency of area 1 by 25 load decreases inarea 1

176 for GA The impact of speed regulation parameters onthe dynamic response is shown in [25] The lowest valuesof standard deviations are observed when the parametersare optimized by ALO This basically means that in eachrun of optimization ALO exhibits precision in computingthe parameters The standard deviations in the values ofintegral gains for area 1 by 119869

1and 119869

2are minimum for

ALO (0041 0033) for GA these values are (018 and 0213)and similarly (0044 009) for GSA and (008 and 0047)for PSO It can be concluded that regulator setting integralgain observes the least variation in numerical values whenthe parameter is optimized through ALO (119869

1) The values

of standard deviations in objective functions 1198691and 119869

2are

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 14 Change in frequency of area 1 by 25 load decreases inarea 1

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 15 Change in tie-line power by 25 load decreases in area 1

the lowest for ALO process and the highest for GA Thevalues of standard deviations in the values of 119869

1for GA PSO

GSA and GWO are 00972 00264 00242 and 002 andfor 1198692are 02068 00846 00772 and 03773 It has been

observed that the values obtained by ALO are precise and theoptimization processes are reliable enough for obtaining theregulator design However high values of standard deviationsin parameters of regulator (176 with 119877

2) and in the objective

functions show that the optimization process loses its rele-vance when it is handled by GA Hence it is concluded fromthe eigenvalue analysis anddynamic response of the deviationcurves that ALO shows a promising response to obtainregulator settingwith optimization criterion 119869

1The following

Journal of Engineering 13

section summarizes the contribution of this research workand proposes a solid milieu for future work

6 Conclusion

This paper presents an application of the recently introducedalgorithm ALO to find optimal parameters of the AGCregulator The ALO regulator is employed on a test system oftwo thermal units connected with a weak tie line of limitedcapacity for AGCThe following are the major findings of thework

(A) Comparison of the application of two objective func-tions namely ISE and ITAE in optimization processfor finding the regulator parameters under differ-ent contingencies is investigated Results reveal thatITAE is a better choice to optimize the regulatorparameters

(B) Eigenvalue analysis is performed to test the effec-tiveness of the proposed approach and to comparethe results of the proposed approach with recentlypublished approaches It is observed that the dampingobtained from ALO regulator is more positive ascompared with the other algorithms

(C) ALO shows promising results in terms of overshootsettling time obtained from the frequency responsesof both areas under different loading cases standarddeviations in regulatorrsquos parameter values ISE andITAE values and optimization performance

(D) Damping performance is evaluated with differentcontingencies load changes and step disturbancesin both areas PI controller setting obtained throughALO exhibits better dynamic performance and over-all low settling time

Application of other new metaheuristic algorithms in AGCregulator design on different models of the power systemconsidering different renewable energy power sources lies inthe future scope

Nomenclature

119894 Subscript referring to area 119894 (1 2)Δ119865119894 Frequency deviation in area 119894 (Hz)

Δ119875119866119894 Incremental generation of area 119894 (pu)

Δ119875119871119894 Incremental load change in area 119894 (pu)

ACE119894 Area Control Error of area 119894

119861119894 Frequency bias parameter of area 119894

119877119894 Speed regulation of the governor of area 119894

(Hzpu MW)119879119892119894 Time constant of governor of area 119894 (s)

119879119905119894 Time constant of turbine of area 119894 (s)

119870119901119894 Gain of generator and load of area 119894

119879119901119894 Time constant of generator and load of

area 119894 (s)Δ119875tie Incremental change in tie line (pu)11987912 Synchronizing coefficient

119879 Simulation time (s)119905 Current iteration

Competing Interests

The authors declare that they have no competing interests

References

[1] O I Elgerd Energy Systems Theory An Introduction McGraw-Hill New Delhi India 1983

[2] IEEE Standard Committee ldquoIEEE Standard definitions of termsfor automatic generation control on electric power systemsrdquoIEEE Transactions on Power Apparatus and Systems vol 89 no6 pp 1356ndash1364 1970

[3] A Ibraheem P Kumar and D P Kothari ldquoRecent philosophiesof automatic generation control strategies in power systemsrdquoIEEE Transactions on Power Systems vol 20 no 1 pp 346ndash3572005

[4] H Sadat Power System Analysis McGraw-Hill New York NYUSA 1999

[5] J Nanda and B Kaul ldquoAutomatic generation control of aninterconnected power systemrdquo Proceedings of the Institution ofElectrical Engineers vol 125 no 5 pp 385ndash390 1978

[6] A Y Sivaramakrishnan M V Hariharan and M C SrisailamldquoDesign of variable-structure load-frequency controller usingpole assignment techniquerdquo International Journal of Controlvol 40 no 3 pp 487ndash498 1984

[7] M Z Bernard T H Mohamed Y S Qudaih and Y MitanildquoDecentralized load frequency control in an interconnectedpower system using Coefficient Diagram Methodrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 63pp 165ndash172 2014

[8] R Ali T HMohamed Y S Qudaih and YMitani ldquoA new loadfrequency control approach in an isolated small power systemsusing coefficient diagram methodrdquo International Journal ofElectrical Power and Energy Systems vol 56 pp 110ndash116 2014

[9] I Vajk M Vajta L Keviczky R Haber J Hetthessy andK Kovacs ldquoAdaptive load-frequency control of the hungarianpower systemrdquo Automatica vol 21 no 2 pp 129ndash137 1985

[10] J Kanniah S C Tripathy O P Malik and G S HopeldquoMicroprocessor-based adaptive load-frequency controlrdquo IEEProceedings CmdashGeneration Transmission and Distribution vol131 no 4 pp 121ndash128 1984

[11] M L Kothari P S Satsangi and J Nanda ldquoSampled-dataautomatic generation control of interconnected reheat thermalsystems considering generation rate constraintsrdquo IEEE Transac-tions on Power Apparatus and Systems vol 100 no 5 pp 2334ndash2342 1981

[12] S Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001

[13] B K Sahu S Pati P K Mohanty and S Panda ldquoTeaching-learning based optimization algorithm based fuzzy-PID con-troller for automatic generation control of multi-area powersystemrdquo Applied Soft Computing Journal vol 27 pp 240ndash2492015

[14] K R Sudha and R Vijaya Santhi ldquoLoad frequency control of aninterconnected reheat thermal systemusing type-2 fuzzy systemincluding SMES unitsrdquo International Journal of Electrical Poweramp Energy Systems vol 43 no 1 pp 1383ndash1392 2012

[15] A Banerjee V Mukherjee and S P Ghoshal ldquoIntelligentcontroller for load-tracking performance of an autonomous

14 Journal of Engineering

power systemrdquo Ain Shams Engineering Journal vol 5 no 4 pp1167ndash1176 2014

[16] S Padhan R K Sahu and S Panda ldquoAutomatic generationcontrol with thyristor controlled series compensator includingsuperconducting magnetic energy storage unitsrdquo Ain ShamsEngineering Journal vol 5 no 3 pp 759ndash774 2014

[17] R K Sahu S Panda and S Padhan ldquoOptimal gravitationalsearch algorithm for automatic generation control of intercon-nected power systemsrdquo Ain Shams Engineering Journal vol 5no 3 pp 721ndash733 2014

[18] Y L Abdel-Magid and M A Abido ldquoAGC tuning of intercon-nected reheat thermal systems with particle swarm optimiza-tionrdquo in Proceedings of the 10th IEEE International Conferenceon Electronics Circuits and Systems (ICECS rsquo03) pp 376ndash379December 2003

[19] Y L Abdel-Magid and M M Dawoud ldquoOptimal AGC tuningwith genetic algorithmsrdquo Electric Power Systems Research vol38 no 3 pp 231ndash238 1996

[20] J Nanda S Mishra and L C Saikia ldquoMaiden application ofbacterial foraging-based optimization technique in multiareaautomatic generation controlrdquo IEEE Transactions on PowerSystems vol 24 no 2 pp 602ndash609 2009

[21] U K Rout R K Sahu and S Panda ldquoDesign and analysisof differential evolution algorithm based automatic generationcontrol for interconnected power systemrdquo Ain Shams Engineer-ing Journal vol 4 no 3 pp 409ndash421 2013

[22] H Gozde M C Taplamacioglu and I Kocaarslan ldquoCompara-tive performance analysis of Artificial Bee Colony algorithm inautomatic generation control for interconnected reheat thermalpower systemrdquo International Journal of Electrical Power andEnergy Systems vol 42 no 1 pp 167ndash178 2012

[23] S Debbarma L Chandra Saikia and N Sinha ldquoSolution toautomatic generation control problem using firefly algorithmoptimized I120582D120583 controllerrdquo ISA Transactions vol 53 no 2 pp358ndash366 2014

[24] P Dash L C Saikia and N Sinha ldquoComparison of per-formances of several Cuckoo search algorithm based 2DOFcontrollers in AGC of multi-area thermal systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 55 pp 429ndash436 2014

[25] A Saxena M Gupta and V Gupta ldquoAutomatic generationcontrol of two area interconnected power system using Geneticalgorithmrdquo in Proceedings of the 3rd IEEE International Con-ference on Computational Intelligence and Computing Research(ICCIC rsquo12) Coimbatore India December 2012

[26] B K Sahu T K Pati J R Nayak S Panda and S K KarldquoA novel hybrid LUS-TLBO optimized fuzzy-PID controllerfor load frequency control of multi-source power systemrdquoInternational Journal of Electrical Power amp Energy Systems vol74 pp 58ndash69 2016

[27] Y Sharma and L C Saikia ldquoAutomatic generation controlof a multi-area STmdashthermal power system using Grey WolfOptimizer algorithm based classical controllersrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 853ndash862 2015

[28] P Dash L C Saikia and N Sinha ldquoAutomatic generationcontrol of multi area thermal system using Bat algorithmoptimized PDndashPID cascade controllerrdquo International Journal ofElectrical Power amp Energy Systems vol 68 pp 364ndash372 2015

[29] S Mirjalili ldquoThe ant lion optimizerrdquo Advances in EngineeringSoftware vol 83 pp 80ndash98 2015

[30] MATLAB httpwwwmathworkscom

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Engineering 9

J

J1

2

2 4 6 81 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(a)

J

J1

2

2 4 6 80 10

Time (s)

minus005

0

005

ΔF2

(Hz)

(b)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

ΔF1

(Hz)

minus005

0

005

(c)

J

J1

2

2 4 6 80 12 14 16 18 20 2210

Time (s)

minus005

0

005

ΔF2

(Hz)

(d)

J

J1

2

2 4 6 80 10

Time (s)

ΔP

tie(p

u)

minus002

0

002

(e)

J

J1

2

2 4 6 80 10

Time (s)

minus001

0

001

ΔP

tie(p

u)

(f)

Figure 3 Dynamic responses obtained from ALO

regulator is used The value of settling time with frequencydeviation in area 2 is observed as 60 for ALO 72 for GSA76 for PSO and 80 for GA It is also interesting to observethat with the 10 increase in the load PSO gives erroneousresults and the flow of tie-line power behaves in a differentmanner Hence critical analysis of dynamic responses clearlyreveals that better dynamic performance is exhibited by ALOBy examining the responses in Figures 7ndash9 it is clearly seenthat the settling time and peak overshoot are less whenload changes in area 2 by 20 It can be observed fromFigure 8 that when area 2 observes 20 increase GA basedcontroller is not able to mitigate the frequency oscillationsThis inculcates oscillatory instability in the system HoweverALO based controller shows a better dynamic response andyields satisfactory performance over a wide range of loading

conditions For Case 2 the settling time of ALO is 36 and is53 42 and 58 for GSA PSO andGA respectively Similarlythe FOD is also very low in case of ALO that is 1296whereas it is 1764 and 3364 in case of PSO and GA Figures10 and 11 show the frequency deviations of areas 1 and 2From dynamic responses of overshoot settling time andFOD it is clear that ALO provides competitive results Thedynamic responses for Case 4 are shown in Figures 13ndash15 andit has been observed that ALO tuned controller yields betterdynamic performanceThe minimum settling time and FODobtained from ALO are 51 and 2601 for frequency deviationin area 1 and 60 and 3600 for frequency deviation in area 2However in case of GSA the settling time is 79 and FOD is198 An oscillatory response is obtained by the GA GSA andPSO tuned controllers

10 Journal of Engineering

ALOGSA [17]

PSO [18]GA [19]

2 4 6 8 10 120Time (s)

minus004

minus003

minus002

minus001

0

001

ΔF1

(Hz)

Figure 4 Change in frequency of area 1 by 10 load increase in area1

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

2 4 6 80 1210

Time (s)

ALOGSA [17]

PSO [18]GA [19]

Figure 5 Change in frequency of area 2 by 10 load increase in area1

5 Optimization Performance

To judge the efficiency of the optimization process carried outby all algorithms 100 trials of optimization are carried outTo provide a fair comparison the population size (100) andthe maximum number of iterations (1000) are kept the sameStopping criterion for the optimization process is maximumrun of the iteration To observe the optimization process in acritical way the standard deviations of optimized parametersof the regulator along with the values of objective functionsare calculated and shown in Table 4 It is observed thathigh values of standard deviations are obtained in regulator

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 6 Change in tie-line power by 10 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 7 Change in frequency of area 1 by 20 load increase in area2

parameters and values of objective functions when optimiza-tion process is handled by GA (009729) Comparatively largevalues of standard deviations are found in GA and PSOwhenthey are compared with ALO We observed high values ofstandard deviation in speed regulation parameters after eachrun of optimization obtained with GA regulators (119869

1and

1198692) Speed regulation parameter is a vulnerable parameter

in power system dynamics studies It affects the systemdynamics in a very prominent way Large values of standarddeviations in the calculation of such vulnerable parametersare not acceptable The values for standard deviations are010256 (GSA 119869

1) and 01550 (GA 119869

2) and similarly for

1198772 they are 00081 (ALO 119869

1) 002 (GSA) 038 (PSO) and

Journal of Engineering 11

Table 4 Standard deviation of optimized parameters of the regulator

Parameters ALO GSA [17] PSO [18] GA [19]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

1198701198681

002923 003773 002425 007720 002604 008461 009729 0206871198631

004107 003315 004475 009833 008416 004759 018872 0213131198771

000582 000102 000045 000168 000153 001403 000892 0007171198701198682

001763 004563 010256 000769 009639 008158 005800 0155501198632

008957 008807 004916 011771 016726 008363 017955 0079451198772

000343 000174 000173 000385 000280 001080 000310 00105937000184 716E minus 06 00212 0000419 038 0011 176 0013

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

ALOGSA [17]

PSO [18]GA [19]

Figure 8 Change in frequency of area 2 by 20 load increase in area2

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 9 Change in tie-line power by 20 load increase in area 2

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 10 Change in frequency of area 1 by 25 load increase inarea 1

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 11 Change in frequency of area 2 by 25 load increase inarea 1

12 Journal of Engineering

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 12 Change in tie-line power by 25 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus005

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 13 Change in frequency of area 1 by 25 load decreases inarea 1

176 for GA The impact of speed regulation parameters onthe dynamic response is shown in [25] The lowest valuesof standard deviations are observed when the parametersare optimized by ALO This basically means that in eachrun of optimization ALO exhibits precision in computingthe parameters The standard deviations in the values ofintegral gains for area 1 by 119869

1and 119869

2are minimum for

ALO (0041 0033) for GA these values are (018 and 0213)and similarly (0044 009) for GSA and (008 and 0047)for PSO It can be concluded that regulator setting integralgain observes the least variation in numerical values whenthe parameter is optimized through ALO (119869

1) The values

of standard deviations in objective functions 1198691and 119869

2are

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 14 Change in frequency of area 1 by 25 load decreases inarea 1

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 15 Change in tie-line power by 25 load decreases in area 1

the lowest for ALO process and the highest for GA Thevalues of standard deviations in the values of 119869

1for GA PSO

GSA and GWO are 00972 00264 00242 and 002 andfor 1198692are 02068 00846 00772 and 03773 It has been

observed that the values obtained by ALO are precise and theoptimization processes are reliable enough for obtaining theregulator design However high values of standard deviationsin parameters of regulator (176 with 119877

2) and in the objective

functions show that the optimization process loses its rele-vance when it is handled by GA Hence it is concluded fromthe eigenvalue analysis anddynamic response of the deviationcurves that ALO shows a promising response to obtainregulator settingwith optimization criterion 119869

1The following

Journal of Engineering 13

section summarizes the contribution of this research workand proposes a solid milieu for future work

6 Conclusion

This paper presents an application of the recently introducedalgorithm ALO to find optimal parameters of the AGCregulator The ALO regulator is employed on a test system oftwo thermal units connected with a weak tie line of limitedcapacity for AGCThe following are the major findings of thework

(A) Comparison of the application of two objective func-tions namely ISE and ITAE in optimization processfor finding the regulator parameters under differ-ent contingencies is investigated Results reveal thatITAE is a better choice to optimize the regulatorparameters

(B) Eigenvalue analysis is performed to test the effec-tiveness of the proposed approach and to comparethe results of the proposed approach with recentlypublished approaches It is observed that the dampingobtained from ALO regulator is more positive ascompared with the other algorithms

(C) ALO shows promising results in terms of overshootsettling time obtained from the frequency responsesof both areas under different loading cases standarddeviations in regulatorrsquos parameter values ISE andITAE values and optimization performance

(D) Damping performance is evaluated with differentcontingencies load changes and step disturbancesin both areas PI controller setting obtained throughALO exhibits better dynamic performance and over-all low settling time

Application of other new metaheuristic algorithms in AGCregulator design on different models of the power systemconsidering different renewable energy power sources lies inthe future scope

Nomenclature

119894 Subscript referring to area 119894 (1 2)Δ119865119894 Frequency deviation in area 119894 (Hz)

Δ119875119866119894 Incremental generation of area 119894 (pu)

Δ119875119871119894 Incremental load change in area 119894 (pu)

ACE119894 Area Control Error of area 119894

119861119894 Frequency bias parameter of area 119894

119877119894 Speed regulation of the governor of area 119894

(Hzpu MW)119879119892119894 Time constant of governor of area 119894 (s)

119879119905119894 Time constant of turbine of area 119894 (s)

119870119901119894 Gain of generator and load of area 119894

119879119901119894 Time constant of generator and load of

area 119894 (s)Δ119875tie Incremental change in tie line (pu)11987912 Synchronizing coefficient

119879 Simulation time (s)119905 Current iteration

Competing Interests

The authors declare that they have no competing interests

References

[1] O I Elgerd Energy Systems Theory An Introduction McGraw-Hill New Delhi India 1983

[2] IEEE Standard Committee ldquoIEEE Standard definitions of termsfor automatic generation control on electric power systemsrdquoIEEE Transactions on Power Apparatus and Systems vol 89 no6 pp 1356ndash1364 1970

[3] A Ibraheem P Kumar and D P Kothari ldquoRecent philosophiesof automatic generation control strategies in power systemsrdquoIEEE Transactions on Power Systems vol 20 no 1 pp 346ndash3572005

[4] H Sadat Power System Analysis McGraw-Hill New York NYUSA 1999

[5] J Nanda and B Kaul ldquoAutomatic generation control of aninterconnected power systemrdquo Proceedings of the Institution ofElectrical Engineers vol 125 no 5 pp 385ndash390 1978

[6] A Y Sivaramakrishnan M V Hariharan and M C SrisailamldquoDesign of variable-structure load-frequency controller usingpole assignment techniquerdquo International Journal of Controlvol 40 no 3 pp 487ndash498 1984

[7] M Z Bernard T H Mohamed Y S Qudaih and Y MitanildquoDecentralized load frequency control in an interconnectedpower system using Coefficient Diagram Methodrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 63pp 165ndash172 2014

[8] R Ali T HMohamed Y S Qudaih and YMitani ldquoA new loadfrequency control approach in an isolated small power systemsusing coefficient diagram methodrdquo International Journal ofElectrical Power and Energy Systems vol 56 pp 110ndash116 2014

[9] I Vajk M Vajta L Keviczky R Haber J Hetthessy andK Kovacs ldquoAdaptive load-frequency control of the hungarianpower systemrdquo Automatica vol 21 no 2 pp 129ndash137 1985

[10] J Kanniah S C Tripathy O P Malik and G S HopeldquoMicroprocessor-based adaptive load-frequency controlrdquo IEEProceedings CmdashGeneration Transmission and Distribution vol131 no 4 pp 121ndash128 1984

[11] M L Kothari P S Satsangi and J Nanda ldquoSampled-dataautomatic generation control of interconnected reheat thermalsystems considering generation rate constraintsrdquo IEEE Transac-tions on Power Apparatus and Systems vol 100 no 5 pp 2334ndash2342 1981

[12] S Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001

[13] B K Sahu S Pati P K Mohanty and S Panda ldquoTeaching-learning based optimization algorithm based fuzzy-PID con-troller for automatic generation control of multi-area powersystemrdquo Applied Soft Computing Journal vol 27 pp 240ndash2492015

[14] K R Sudha and R Vijaya Santhi ldquoLoad frequency control of aninterconnected reheat thermal systemusing type-2 fuzzy systemincluding SMES unitsrdquo International Journal of Electrical Poweramp Energy Systems vol 43 no 1 pp 1383ndash1392 2012

[15] A Banerjee V Mukherjee and S P Ghoshal ldquoIntelligentcontroller for load-tracking performance of an autonomous

14 Journal of Engineering

power systemrdquo Ain Shams Engineering Journal vol 5 no 4 pp1167ndash1176 2014

[16] S Padhan R K Sahu and S Panda ldquoAutomatic generationcontrol with thyristor controlled series compensator includingsuperconducting magnetic energy storage unitsrdquo Ain ShamsEngineering Journal vol 5 no 3 pp 759ndash774 2014

[17] R K Sahu S Panda and S Padhan ldquoOptimal gravitationalsearch algorithm for automatic generation control of intercon-nected power systemsrdquo Ain Shams Engineering Journal vol 5no 3 pp 721ndash733 2014

[18] Y L Abdel-Magid and M A Abido ldquoAGC tuning of intercon-nected reheat thermal systems with particle swarm optimiza-tionrdquo in Proceedings of the 10th IEEE International Conferenceon Electronics Circuits and Systems (ICECS rsquo03) pp 376ndash379December 2003

[19] Y L Abdel-Magid and M M Dawoud ldquoOptimal AGC tuningwith genetic algorithmsrdquo Electric Power Systems Research vol38 no 3 pp 231ndash238 1996

[20] J Nanda S Mishra and L C Saikia ldquoMaiden application ofbacterial foraging-based optimization technique in multiareaautomatic generation controlrdquo IEEE Transactions on PowerSystems vol 24 no 2 pp 602ndash609 2009

[21] U K Rout R K Sahu and S Panda ldquoDesign and analysisof differential evolution algorithm based automatic generationcontrol for interconnected power systemrdquo Ain Shams Engineer-ing Journal vol 4 no 3 pp 409ndash421 2013

[22] H Gozde M C Taplamacioglu and I Kocaarslan ldquoCompara-tive performance analysis of Artificial Bee Colony algorithm inautomatic generation control for interconnected reheat thermalpower systemrdquo International Journal of Electrical Power andEnergy Systems vol 42 no 1 pp 167ndash178 2012

[23] S Debbarma L Chandra Saikia and N Sinha ldquoSolution toautomatic generation control problem using firefly algorithmoptimized I120582D120583 controllerrdquo ISA Transactions vol 53 no 2 pp358ndash366 2014

[24] P Dash L C Saikia and N Sinha ldquoComparison of per-formances of several Cuckoo search algorithm based 2DOFcontrollers in AGC of multi-area thermal systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 55 pp 429ndash436 2014

[25] A Saxena M Gupta and V Gupta ldquoAutomatic generationcontrol of two area interconnected power system using Geneticalgorithmrdquo in Proceedings of the 3rd IEEE International Con-ference on Computational Intelligence and Computing Research(ICCIC rsquo12) Coimbatore India December 2012

[26] B K Sahu T K Pati J R Nayak S Panda and S K KarldquoA novel hybrid LUS-TLBO optimized fuzzy-PID controllerfor load frequency control of multi-source power systemrdquoInternational Journal of Electrical Power amp Energy Systems vol74 pp 58ndash69 2016

[27] Y Sharma and L C Saikia ldquoAutomatic generation controlof a multi-area STmdashthermal power system using Grey WolfOptimizer algorithm based classical controllersrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 853ndash862 2015

[28] P Dash L C Saikia and N Sinha ldquoAutomatic generationcontrol of multi area thermal system using Bat algorithmoptimized PDndashPID cascade controllerrdquo International Journal ofElectrical Power amp Energy Systems vol 68 pp 364ndash372 2015

[29] S Mirjalili ldquoThe ant lion optimizerrdquo Advances in EngineeringSoftware vol 83 pp 80ndash98 2015

[30] MATLAB httpwwwmathworkscom

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Journal of Engineering

ALOGSA [17]

PSO [18]GA [19]

2 4 6 8 10 120Time (s)

minus004

minus003

minus002

minus001

0

001

ΔF1

(Hz)

Figure 4 Change in frequency of area 1 by 10 load increase in area1

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

2 4 6 80 1210

Time (s)

ALOGSA [17]

PSO [18]GA [19]

Figure 5 Change in frequency of area 2 by 10 load increase in area1

5 Optimization Performance

To judge the efficiency of the optimization process carried outby all algorithms 100 trials of optimization are carried outTo provide a fair comparison the population size (100) andthe maximum number of iterations (1000) are kept the sameStopping criterion for the optimization process is maximumrun of the iteration To observe the optimization process in acritical way the standard deviations of optimized parametersof the regulator along with the values of objective functionsare calculated and shown in Table 4 It is observed thathigh values of standard deviations are obtained in regulator

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 6 Change in tie-line power by 10 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 7 Change in frequency of area 1 by 20 load increase in area2

parameters and values of objective functions when optimiza-tion process is handled by GA (009729) Comparatively largevalues of standard deviations are found in GA and PSOwhenthey are compared with ALO We observed high values ofstandard deviation in speed regulation parameters after eachrun of optimization obtained with GA regulators (119869

1and

1198692) Speed regulation parameter is a vulnerable parameter

in power system dynamics studies It affects the systemdynamics in a very prominent way Large values of standarddeviations in the calculation of such vulnerable parametersare not acceptable The values for standard deviations are010256 (GSA 119869

1) and 01550 (GA 119869

2) and similarly for

1198772 they are 00081 (ALO 119869

1) 002 (GSA) 038 (PSO) and

Journal of Engineering 11

Table 4 Standard deviation of optimized parameters of the regulator

Parameters ALO GSA [17] PSO [18] GA [19]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

1198701198681

002923 003773 002425 007720 002604 008461 009729 0206871198631

004107 003315 004475 009833 008416 004759 018872 0213131198771

000582 000102 000045 000168 000153 001403 000892 0007171198701198682

001763 004563 010256 000769 009639 008158 005800 0155501198632

008957 008807 004916 011771 016726 008363 017955 0079451198772

000343 000174 000173 000385 000280 001080 000310 00105937000184 716E minus 06 00212 0000419 038 0011 176 0013

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

ALOGSA [17]

PSO [18]GA [19]

Figure 8 Change in frequency of area 2 by 20 load increase in area2

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 9 Change in tie-line power by 20 load increase in area 2

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 10 Change in frequency of area 1 by 25 load increase inarea 1

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 11 Change in frequency of area 2 by 25 load increase inarea 1

12 Journal of Engineering

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 12 Change in tie-line power by 25 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus005

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 13 Change in frequency of area 1 by 25 load decreases inarea 1

176 for GA The impact of speed regulation parameters onthe dynamic response is shown in [25] The lowest valuesof standard deviations are observed when the parametersare optimized by ALO This basically means that in eachrun of optimization ALO exhibits precision in computingthe parameters The standard deviations in the values ofintegral gains for area 1 by 119869

1and 119869

2are minimum for

ALO (0041 0033) for GA these values are (018 and 0213)and similarly (0044 009) for GSA and (008 and 0047)for PSO It can be concluded that regulator setting integralgain observes the least variation in numerical values whenthe parameter is optimized through ALO (119869

1) The values

of standard deviations in objective functions 1198691and 119869

2are

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 14 Change in frequency of area 1 by 25 load decreases inarea 1

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 15 Change in tie-line power by 25 load decreases in area 1

the lowest for ALO process and the highest for GA Thevalues of standard deviations in the values of 119869

1for GA PSO

GSA and GWO are 00972 00264 00242 and 002 andfor 1198692are 02068 00846 00772 and 03773 It has been

observed that the values obtained by ALO are precise and theoptimization processes are reliable enough for obtaining theregulator design However high values of standard deviationsin parameters of regulator (176 with 119877

2) and in the objective

functions show that the optimization process loses its rele-vance when it is handled by GA Hence it is concluded fromthe eigenvalue analysis anddynamic response of the deviationcurves that ALO shows a promising response to obtainregulator settingwith optimization criterion 119869

1The following

Journal of Engineering 13

section summarizes the contribution of this research workand proposes a solid milieu for future work

6 Conclusion

This paper presents an application of the recently introducedalgorithm ALO to find optimal parameters of the AGCregulator The ALO regulator is employed on a test system oftwo thermal units connected with a weak tie line of limitedcapacity for AGCThe following are the major findings of thework

(A) Comparison of the application of two objective func-tions namely ISE and ITAE in optimization processfor finding the regulator parameters under differ-ent contingencies is investigated Results reveal thatITAE is a better choice to optimize the regulatorparameters

(B) Eigenvalue analysis is performed to test the effec-tiveness of the proposed approach and to comparethe results of the proposed approach with recentlypublished approaches It is observed that the dampingobtained from ALO regulator is more positive ascompared with the other algorithms

(C) ALO shows promising results in terms of overshootsettling time obtained from the frequency responsesof both areas under different loading cases standarddeviations in regulatorrsquos parameter values ISE andITAE values and optimization performance

(D) Damping performance is evaluated with differentcontingencies load changes and step disturbancesin both areas PI controller setting obtained throughALO exhibits better dynamic performance and over-all low settling time

Application of other new metaheuristic algorithms in AGCregulator design on different models of the power systemconsidering different renewable energy power sources lies inthe future scope

Nomenclature

119894 Subscript referring to area 119894 (1 2)Δ119865119894 Frequency deviation in area 119894 (Hz)

Δ119875119866119894 Incremental generation of area 119894 (pu)

Δ119875119871119894 Incremental load change in area 119894 (pu)

ACE119894 Area Control Error of area 119894

119861119894 Frequency bias parameter of area 119894

119877119894 Speed regulation of the governor of area 119894

(Hzpu MW)119879119892119894 Time constant of governor of area 119894 (s)

119879119905119894 Time constant of turbine of area 119894 (s)

119870119901119894 Gain of generator and load of area 119894

119879119901119894 Time constant of generator and load of

area 119894 (s)Δ119875tie Incremental change in tie line (pu)11987912 Synchronizing coefficient

119879 Simulation time (s)119905 Current iteration

Competing Interests

The authors declare that they have no competing interests

References

[1] O I Elgerd Energy Systems Theory An Introduction McGraw-Hill New Delhi India 1983

[2] IEEE Standard Committee ldquoIEEE Standard definitions of termsfor automatic generation control on electric power systemsrdquoIEEE Transactions on Power Apparatus and Systems vol 89 no6 pp 1356ndash1364 1970

[3] A Ibraheem P Kumar and D P Kothari ldquoRecent philosophiesof automatic generation control strategies in power systemsrdquoIEEE Transactions on Power Systems vol 20 no 1 pp 346ndash3572005

[4] H Sadat Power System Analysis McGraw-Hill New York NYUSA 1999

[5] J Nanda and B Kaul ldquoAutomatic generation control of aninterconnected power systemrdquo Proceedings of the Institution ofElectrical Engineers vol 125 no 5 pp 385ndash390 1978

[6] A Y Sivaramakrishnan M V Hariharan and M C SrisailamldquoDesign of variable-structure load-frequency controller usingpole assignment techniquerdquo International Journal of Controlvol 40 no 3 pp 487ndash498 1984

[7] M Z Bernard T H Mohamed Y S Qudaih and Y MitanildquoDecentralized load frequency control in an interconnectedpower system using Coefficient Diagram Methodrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 63pp 165ndash172 2014

[8] R Ali T HMohamed Y S Qudaih and YMitani ldquoA new loadfrequency control approach in an isolated small power systemsusing coefficient diagram methodrdquo International Journal ofElectrical Power and Energy Systems vol 56 pp 110ndash116 2014

[9] I Vajk M Vajta L Keviczky R Haber J Hetthessy andK Kovacs ldquoAdaptive load-frequency control of the hungarianpower systemrdquo Automatica vol 21 no 2 pp 129ndash137 1985

[10] J Kanniah S C Tripathy O P Malik and G S HopeldquoMicroprocessor-based adaptive load-frequency controlrdquo IEEProceedings CmdashGeneration Transmission and Distribution vol131 no 4 pp 121ndash128 1984

[11] M L Kothari P S Satsangi and J Nanda ldquoSampled-dataautomatic generation control of interconnected reheat thermalsystems considering generation rate constraintsrdquo IEEE Transac-tions on Power Apparatus and Systems vol 100 no 5 pp 2334ndash2342 1981

[12] S Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001

[13] B K Sahu S Pati P K Mohanty and S Panda ldquoTeaching-learning based optimization algorithm based fuzzy-PID con-troller for automatic generation control of multi-area powersystemrdquo Applied Soft Computing Journal vol 27 pp 240ndash2492015

[14] K R Sudha and R Vijaya Santhi ldquoLoad frequency control of aninterconnected reheat thermal systemusing type-2 fuzzy systemincluding SMES unitsrdquo International Journal of Electrical Poweramp Energy Systems vol 43 no 1 pp 1383ndash1392 2012

[15] A Banerjee V Mukherjee and S P Ghoshal ldquoIntelligentcontroller for load-tracking performance of an autonomous

14 Journal of Engineering

power systemrdquo Ain Shams Engineering Journal vol 5 no 4 pp1167ndash1176 2014

[16] S Padhan R K Sahu and S Panda ldquoAutomatic generationcontrol with thyristor controlled series compensator includingsuperconducting magnetic energy storage unitsrdquo Ain ShamsEngineering Journal vol 5 no 3 pp 759ndash774 2014

[17] R K Sahu S Panda and S Padhan ldquoOptimal gravitationalsearch algorithm for automatic generation control of intercon-nected power systemsrdquo Ain Shams Engineering Journal vol 5no 3 pp 721ndash733 2014

[18] Y L Abdel-Magid and M A Abido ldquoAGC tuning of intercon-nected reheat thermal systems with particle swarm optimiza-tionrdquo in Proceedings of the 10th IEEE International Conferenceon Electronics Circuits and Systems (ICECS rsquo03) pp 376ndash379December 2003

[19] Y L Abdel-Magid and M M Dawoud ldquoOptimal AGC tuningwith genetic algorithmsrdquo Electric Power Systems Research vol38 no 3 pp 231ndash238 1996

[20] J Nanda S Mishra and L C Saikia ldquoMaiden application ofbacterial foraging-based optimization technique in multiareaautomatic generation controlrdquo IEEE Transactions on PowerSystems vol 24 no 2 pp 602ndash609 2009

[21] U K Rout R K Sahu and S Panda ldquoDesign and analysisof differential evolution algorithm based automatic generationcontrol for interconnected power systemrdquo Ain Shams Engineer-ing Journal vol 4 no 3 pp 409ndash421 2013

[22] H Gozde M C Taplamacioglu and I Kocaarslan ldquoCompara-tive performance analysis of Artificial Bee Colony algorithm inautomatic generation control for interconnected reheat thermalpower systemrdquo International Journal of Electrical Power andEnergy Systems vol 42 no 1 pp 167ndash178 2012

[23] S Debbarma L Chandra Saikia and N Sinha ldquoSolution toautomatic generation control problem using firefly algorithmoptimized I120582D120583 controllerrdquo ISA Transactions vol 53 no 2 pp358ndash366 2014

[24] P Dash L C Saikia and N Sinha ldquoComparison of per-formances of several Cuckoo search algorithm based 2DOFcontrollers in AGC of multi-area thermal systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 55 pp 429ndash436 2014

[25] A Saxena M Gupta and V Gupta ldquoAutomatic generationcontrol of two area interconnected power system using Geneticalgorithmrdquo in Proceedings of the 3rd IEEE International Con-ference on Computational Intelligence and Computing Research(ICCIC rsquo12) Coimbatore India December 2012

[26] B K Sahu T K Pati J R Nayak S Panda and S K KarldquoA novel hybrid LUS-TLBO optimized fuzzy-PID controllerfor load frequency control of multi-source power systemrdquoInternational Journal of Electrical Power amp Energy Systems vol74 pp 58ndash69 2016

[27] Y Sharma and L C Saikia ldquoAutomatic generation controlof a multi-area STmdashthermal power system using Grey WolfOptimizer algorithm based classical controllersrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 853ndash862 2015

[28] P Dash L C Saikia and N Sinha ldquoAutomatic generationcontrol of multi area thermal system using Bat algorithmoptimized PDndashPID cascade controllerrdquo International Journal ofElectrical Power amp Energy Systems vol 68 pp 364ndash372 2015

[29] S Mirjalili ldquoThe ant lion optimizerrdquo Advances in EngineeringSoftware vol 83 pp 80ndash98 2015

[30] MATLAB httpwwwmathworkscom

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Engineering 11

Table 4 Standard deviation of optimized parameters of the regulator

Parameters ALO GSA [17] PSO [18] GA [19]1198691

1198692

1198691

1198692

1198691

1198692

1198691

1198692

1198701198681

002923 003773 002425 007720 002604 008461 009729 0206871198631

004107 003315 004475 009833 008416 004759 018872 0213131198771

000582 000102 000045 000168 000153 001403 000892 0007171198701198682

001763 004563 010256 000769 009639 008158 005800 0155501198632

008957 008807 004916 011771 016726 008363 017955 0079451198772

000343 000174 000173 000385 000280 001080 000310 00105937000184 716E minus 06 00212 0000419 038 0011 176 0013

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

minus002

minus0015

minus001

minus0005

0

0005

001

0015

ALOGSA [17]

PSO [18]GA [19]

Figure 8 Change in frequency of area 2 by 20 load increase in area2

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 9 Change in tie-line power by 20 load increase in area 2

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 10 Change in frequency of area 1 by 25 load increase inarea 1

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 11 Change in frequency of area 2 by 25 load increase inarea 1

12 Journal of Engineering

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 12 Change in tie-line power by 25 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus005

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 13 Change in frequency of area 1 by 25 load decreases inarea 1

176 for GA The impact of speed regulation parameters onthe dynamic response is shown in [25] The lowest valuesof standard deviations are observed when the parametersare optimized by ALO This basically means that in eachrun of optimization ALO exhibits precision in computingthe parameters The standard deviations in the values ofintegral gains for area 1 by 119869

1and 119869

2are minimum for

ALO (0041 0033) for GA these values are (018 and 0213)and similarly (0044 009) for GSA and (008 and 0047)for PSO It can be concluded that regulator setting integralgain observes the least variation in numerical values whenthe parameter is optimized through ALO (119869

1) The values

of standard deviations in objective functions 1198691and 119869

2are

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 14 Change in frequency of area 1 by 25 load decreases inarea 1

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 15 Change in tie-line power by 25 load decreases in area 1

the lowest for ALO process and the highest for GA Thevalues of standard deviations in the values of 119869

1for GA PSO

GSA and GWO are 00972 00264 00242 and 002 andfor 1198692are 02068 00846 00772 and 03773 It has been

observed that the values obtained by ALO are precise and theoptimization processes are reliable enough for obtaining theregulator design However high values of standard deviationsin parameters of regulator (176 with 119877

2) and in the objective

functions show that the optimization process loses its rele-vance when it is handled by GA Hence it is concluded fromthe eigenvalue analysis anddynamic response of the deviationcurves that ALO shows a promising response to obtainregulator settingwith optimization criterion 119869

1The following

Journal of Engineering 13

section summarizes the contribution of this research workand proposes a solid milieu for future work

6 Conclusion

This paper presents an application of the recently introducedalgorithm ALO to find optimal parameters of the AGCregulator The ALO regulator is employed on a test system oftwo thermal units connected with a weak tie line of limitedcapacity for AGCThe following are the major findings of thework

(A) Comparison of the application of two objective func-tions namely ISE and ITAE in optimization processfor finding the regulator parameters under differ-ent contingencies is investigated Results reveal thatITAE is a better choice to optimize the regulatorparameters

(B) Eigenvalue analysis is performed to test the effec-tiveness of the proposed approach and to comparethe results of the proposed approach with recentlypublished approaches It is observed that the dampingobtained from ALO regulator is more positive ascompared with the other algorithms

(C) ALO shows promising results in terms of overshootsettling time obtained from the frequency responsesof both areas under different loading cases standarddeviations in regulatorrsquos parameter values ISE andITAE values and optimization performance

(D) Damping performance is evaluated with differentcontingencies load changes and step disturbancesin both areas PI controller setting obtained throughALO exhibits better dynamic performance and over-all low settling time

Application of other new metaheuristic algorithms in AGCregulator design on different models of the power systemconsidering different renewable energy power sources lies inthe future scope

Nomenclature

119894 Subscript referring to area 119894 (1 2)Δ119865119894 Frequency deviation in area 119894 (Hz)

Δ119875119866119894 Incremental generation of area 119894 (pu)

Δ119875119871119894 Incremental load change in area 119894 (pu)

ACE119894 Area Control Error of area 119894

119861119894 Frequency bias parameter of area 119894

119877119894 Speed regulation of the governor of area 119894

(Hzpu MW)119879119892119894 Time constant of governor of area 119894 (s)

119879119905119894 Time constant of turbine of area 119894 (s)

119870119901119894 Gain of generator and load of area 119894

119879119901119894 Time constant of generator and load of

area 119894 (s)Δ119875tie Incremental change in tie line (pu)11987912 Synchronizing coefficient

119879 Simulation time (s)119905 Current iteration

Competing Interests

The authors declare that they have no competing interests

References

[1] O I Elgerd Energy Systems Theory An Introduction McGraw-Hill New Delhi India 1983

[2] IEEE Standard Committee ldquoIEEE Standard definitions of termsfor automatic generation control on electric power systemsrdquoIEEE Transactions on Power Apparatus and Systems vol 89 no6 pp 1356ndash1364 1970

[3] A Ibraheem P Kumar and D P Kothari ldquoRecent philosophiesof automatic generation control strategies in power systemsrdquoIEEE Transactions on Power Systems vol 20 no 1 pp 346ndash3572005

[4] H Sadat Power System Analysis McGraw-Hill New York NYUSA 1999

[5] J Nanda and B Kaul ldquoAutomatic generation control of aninterconnected power systemrdquo Proceedings of the Institution ofElectrical Engineers vol 125 no 5 pp 385ndash390 1978

[6] A Y Sivaramakrishnan M V Hariharan and M C SrisailamldquoDesign of variable-structure load-frequency controller usingpole assignment techniquerdquo International Journal of Controlvol 40 no 3 pp 487ndash498 1984

[7] M Z Bernard T H Mohamed Y S Qudaih and Y MitanildquoDecentralized load frequency control in an interconnectedpower system using Coefficient Diagram Methodrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 63pp 165ndash172 2014

[8] R Ali T HMohamed Y S Qudaih and YMitani ldquoA new loadfrequency control approach in an isolated small power systemsusing coefficient diagram methodrdquo International Journal ofElectrical Power and Energy Systems vol 56 pp 110ndash116 2014

[9] I Vajk M Vajta L Keviczky R Haber J Hetthessy andK Kovacs ldquoAdaptive load-frequency control of the hungarianpower systemrdquo Automatica vol 21 no 2 pp 129ndash137 1985

[10] J Kanniah S C Tripathy O P Malik and G S HopeldquoMicroprocessor-based adaptive load-frequency controlrdquo IEEProceedings CmdashGeneration Transmission and Distribution vol131 no 4 pp 121ndash128 1984

[11] M L Kothari P S Satsangi and J Nanda ldquoSampled-dataautomatic generation control of interconnected reheat thermalsystems considering generation rate constraintsrdquo IEEE Transac-tions on Power Apparatus and Systems vol 100 no 5 pp 2334ndash2342 1981

[12] S Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001

[13] B K Sahu S Pati P K Mohanty and S Panda ldquoTeaching-learning based optimization algorithm based fuzzy-PID con-troller for automatic generation control of multi-area powersystemrdquo Applied Soft Computing Journal vol 27 pp 240ndash2492015

[14] K R Sudha and R Vijaya Santhi ldquoLoad frequency control of aninterconnected reheat thermal systemusing type-2 fuzzy systemincluding SMES unitsrdquo International Journal of Electrical Poweramp Energy Systems vol 43 no 1 pp 1383ndash1392 2012

[15] A Banerjee V Mukherjee and S P Ghoshal ldquoIntelligentcontroller for load-tracking performance of an autonomous

14 Journal of Engineering

power systemrdquo Ain Shams Engineering Journal vol 5 no 4 pp1167ndash1176 2014

[16] S Padhan R K Sahu and S Panda ldquoAutomatic generationcontrol with thyristor controlled series compensator includingsuperconducting magnetic energy storage unitsrdquo Ain ShamsEngineering Journal vol 5 no 3 pp 759ndash774 2014

[17] R K Sahu S Panda and S Padhan ldquoOptimal gravitationalsearch algorithm for automatic generation control of intercon-nected power systemsrdquo Ain Shams Engineering Journal vol 5no 3 pp 721ndash733 2014

[18] Y L Abdel-Magid and M A Abido ldquoAGC tuning of intercon-nected reheat thermal systems with particle swarm optimiza-tionrdquo in Proceedings of the 10th IEEE International Conferenceon Electronics Circuits and Systems (ICECS rsquo03) pp 376ndash379December 2003

[19] Y L Abdel-Magid and M M Dawoud ldquoOptimal AGC tuningwith genetic algorithmsrdquo Electric Power Systems Research vol38 no 3 pp 231ndash238 1996

[20] J Nanda S Mishra and L C Saikia ldquoMaiden application ofbacterial foraging-based optimization technique in multiareaautomatic generation controlrdquo IEEE Transactions on PowerSystems vol 24 no 2 pp 602ndash609 2009

[21] U K Rout R K Sahu and S Panda ldquoDesign and analysisof differential evolution algorithm based automatic generationcontrol for interconnected power systemrdquo Ain Shams Engineer-ing Journal vol 4 no 3 pp 409ndash421 2013

[22] H Gozde M C Taplamacioglu and I Kocaarslan ldquoCompara-tive performance analysis of Artificial Bee Colony algorithm inautomatic generation control for interconnected reheat thermalpower systemrdquo International Journal of Electrical Power andEnergy Systems vol 42 no 1 pp 167ndash178 2012

[23] S Debbarma L Chandra Saikia and N Sinha ldquoSolution toautomatic generation control problem using firefly algorithmoptimized I120582D120583 controllerrdquo ISA Transactions vol 53 no 2 pp358ndash366 2014

[24] P Dash L C Saikia and N Sinha ldquoComparison of per-formances of several Cuckoo search algorithm based 2DOFcontrollers in AGC of multi-area thermal systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 55 pp 429ndash436 2014

[25] A Saxena M Gupta and V Gupta ldquoAutomatic generationcontrol of two area interconnected power system using Geneticalgorithmrdquo in Proceedings of the 3rd IEEE International Con-ference on Computational Intelligence and Computing Research(ICCIC rsquo12) Coimbatore India December 2012

[26] B K Sahu T K Pati J R Nayak S Panda and S K KarldquoA novel hybrid LUS-TLBO optimized fuzzy-PID controllerfor load frequency control of multi-source power systemrdquoInternational Journal of Electrical Power amp Energy Systems vol74 pp 58ndash69 2016

[27] Y Sharma and L C Saikia ldquoAutomatic generation controlof a multi-area STmdashthermal power system using Grey WolfOptimizer algorithm based classical controllersrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 853ndash862 2015

[28] P Dash L C Saikia and N Sinha ldquoAutomatic generationcontrol of multi area thermal system using Bat algorithmoptimized PDndashPID cascade controllerrdquo International Journal ofElectrical Power amp Energy Systems vol 68 pp 364ndash372 2015

[29] S Mirjalili ldquoThe ant lion optimizerrdquo Advances in EngineeringSoftware vol 83 pp 80ndash98 2015

[30] MATLAB httpwwwmathworkscom

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Journal of Engineering

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 12 Change in tie-line power by 25 load increase in area 1

2 4 6 80 1210

Time (s)

ΔF1

(Hz)

minus005

minus004

minus003

minus002

minus001

0

001

ALOGSA [17]

PSO [18]GA [19]

Figure 13 Change in frequency of area 1 by 25 load decreases inarea 1

176 for GA The impact of speed regulation parameters onthe dynamic response is shown in [25] The lowest valuesof standard deviations are observed when the parametersare optimized by ALO This basically means that in eachrun of optimization ALO exhibits precision in computingthe parameters The standard deviations in the values ofintegral gains for area 1 by 119869

1and 119869

2are minimum for

ALO (0041 0033) for GA these values are (018 and 0213)and similarly (0044 009) for GSA and (008 and 0047)for PSO It can be concluded that regulator setting integralgain observes the least variation in numerical values whenthe parameter is optimized through ALO (119869

1) The values

of standard deviations in objective functions 1198691and 119869

2are

2 4 6 80 1210

Time (s)

ΔF2

(Hz)

times10minus3

minus20

minus15

minus10

minus5

0

5

ALOGSA [17]

PSO [18]GA [19]

Figure 14 Change in frequency of area 1 by 25 load decreases inarea 1

2 4 6 80 1210

Time (s)

ΔP

tie(p

u)

minus003

minus002

minus001

0

001

002

ALOGSA [17]

PSO [18]GA [19]

Figure 15 Change in tie-line power by 25 load decreases in area 1

the lowest for ALO process and the highest for GA Thevalues of standard deviations in the values of 119869

1for GA PSO

GSA and GWO are 00972 00264 00242 and 002 andfor 1198692are 02068 00846 00772 and 03773 It has been

observed that the values obtained by ALO are precise and theoptimization processes are reliable enough for obtaining theregulator design However high values of standard deviationsin parameters of regulator (176 with 119877

2) and in the objective

functions show that the optimization process loses its rele-vance when it is handled by GA Hence it is concluded fromthe eigenvalue analysis anddynamic response of the deviationcurves that ALO shows a promising response to obtainregulator settingwith optimization criterion 119869

1The following

Journal of Engineering 13

section summarizes the contribution of this research workand proposes a solid milieu for future work

6 Conclusion

This paper presents an application of the recently introducedalgorithm ALO to find optimal parameters of the AGCregulator The ALO regulator is employed on a test system oftwo thermal units connected with a weak tie line of limitedcapacity for AGCThe following are the major findings of thework

(A) Comparison of the application of two objective func-tions namely ISE and ITAE in optimization processfor finding the regulator parameters under differ-ent contingencies is investigated Results reveal thatITAE is a better choice to optimize the regulatorparameters

(B) Eigenvalue analysis is performed to test the effec-tiveness of the proposed approach and to comparethe results of the proposed approach with recentlypublished approaches It is observed that the dampingobtained from ALO regulator is more positive ascompared with the other algorithms

(C) ALO shows promising results in terms of overshootsettling time obtained from the frequency responsesof both areas under different loading cases standarddeviations in regulatorrsquos parameter values ISE andITAE values and optimization performance

(D) Damping performance is evaluated with differentcontingencies load changes and step disturbancesin both areas PI controller setting obtained throughALO exhibits better dynamic performance and over-all low settling time

Application of other new metaheuristic algorithms in AGCregulator design on different models of the power systemconsidering different renewable energy power sources lies inthe future scope

Nomenclature

119894 Subscript referring to area 119894 (1 2)Δ119865119894 Frequency deviation in area 119894 (Hz)

Δ119875119866119894 Incremental generation of area 119894 (pu)

Δ119875119871119894 Incremental load change in area 119894 (pu)

ACE119894 Area Control Error of area 119894

119861119894 Frequency bias parameter of area 119894

119877119894 Speed regulation of the governor of area 119894

(Hzpu MW)119879119892119894 Time constant of governor of area 119894 (s)

119879119905119894 Time constant of turbine of area 119894 (s)

119870119901119894 Gain of generator and load of area 119894

119879119901119894 Time constant of generator and load of

area 119894 (s)Δ119875tie Incremental change in tie line (pu)11987912 Synchronizing coefficient

119879 Simulation time (s)119905 Current iteration

Competing Interests

The authors declare that they have no competing interests

References

[1] O I Elgerd Energy Systems Theory An Introduction McGraw-Hill New Delhi India 1983

[2] IEEE Standard Committee ldquoIEEE Standard definitions of termsfor automatic generation control on electric power systemsrdquoIEEE Transactions on Power Apparatus and Systems vol 89 no6 pp 1356ndash1364 1970

[3] A Ibraheem P Kumar and D P Kothari ldquoRecent philosophiesof automatic generation control strategies in power systemsrdquoIEEE Transactions on Power Systems vol 20 no 1 pp 346ndash3572005

[4] H Sadat Power System Analysis McGraw-Hill New York NYUSA 1999

[5] J Nanda and B Kaul ldquoAutomatic generation control of aninterconnected power systemrdquo Proceedings of the Institution ofElectrical Engineers vol 125 no 5 pp 385ndash390 1978

[6] A Y Sivaramakrishnan M V Hariharan and M C SrisailamldquoDesign of variable-structure load-frequency controller usingpole assignment techniquerdquo International Journal of Controlvol 40 no 3 pp 487ndash498 1984

[7] M Z Bernard T H Mohamed Y S Qudaih and Y MitanildquoDecentralized load frequency control in an interconnectedpower system using Coefficient Diagram Methodrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 63pp 165ndash172 2014

[8] R Ali T HMohamed Y S Qudaih and YMitani ldquoA new loadfrequency control approach in an isolated small power systemsusing coefficient diagram methodrdquo International Journal ofElectrical Power and Energy Systems vol 56 pp 110ndash116 2014

[9] I Vajk M Vajta L Keviczky R Haber J Hetthessy andK Kovacs ldquoAdaptive load-frequency control of the hungarianpower systemrdquo Automatica vol 21 no 2 pp 129ndash137 1985

[10] J Kanniah S C Tripathy O P Malik and G S HopeldquoMicroprocessor-based adaptive load-frequency controlrdquo IEEProceedings CmdashGeneration Transmission and Distribution vol131 no 4 pp 121ndash128 1984

[11] M L Kothari P S Satsangi and J Nanda ldquoSampled-dataautomatic generation control of interconnected reheat thermalsystems considering generation rate constraintsrdquo IEEE Transac-tions on Power Apparatus and Systems vol 100 no 5 pp 2334ndash2342 1981

[12] S Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001

[13] B K Sahu S Pati P K Mohanty and S Panda ldquoTeaching-learning based optimization algorithm based fuzzy-PID con-troller for automatic generation control of multi-area powersystemrdquo Applied Soft Computing Journal vol 27 pp 240ndash2492015

[14] K R Sudha and R Vijaya Santhi ldquoLoad frequency control of aninterconnected reheat thermal systemusing type-2 fuzzy systemincluding SMES unitsrdquo International Journal of Electrical Poweramp Energy Systems vol 43 no 1 pp 1383ndash1392 2012

[15] A Banerjee V Mukherjee and S P Ghoshal ldquoIntelligentcontroller for load-tracking performance of an autonomous

14 Journal of Engineering

power systemrdquo Ain Shams Engineering Journal vol 5 no 4 pp1167ndash1176 2014

[16] S Padhan R K Sahu and S Panda ldquoAutomatic generationcontrol with thyristor controlled series compensator includingsuperconducting magnetic energy storage unitsrdquo Ain ShamsEngineering Journal vol 5 no 3 pp 759ndash774 2014

[17] R K Sahu S Panda and S Padhan ldquoOptimal gravitationalsearch algorithm for automatic generation control of intercon-nected power systemsrdquo Ain Shams Engineering Journal vol 5no 3 pp 721ndash733 2014

[18] Y L Abdel-Magid and M A Abido ldquoAGC tuning of intercon-nected reheat thermal systems with particle swarm optimiza-tionrdquo in Proceedings of the 10th IEEE International Conferenceon Electronics Circuits and Systems (ICECS rsquo03) pp 376ndash379December 2003

[19] Y L Abdel-Magid and M M Dawoud ldquoOptimal AGC tuningwith genetic algorithmsrdquo Electric Power Systems Research vol38 no 3 pp 231ndash238 1996

[20] J Nanda S Mishra and L C Saikia ldquoMaiden application ofbacterial foraging-based optimization technique in multiareaautomatic generation controlrdquo IEEE Transactions on PowerSystems vol 24 no 2 pp 602ndash609 2009

[21] U K Rout R K Sahu and S Panda ldquoDesign and analysisof differential evolution algorithm based automatic generationcontrol for interconnected power systemrdquo Ain Shams Engineer-ing Journal vol 4 no 3 pp 409ndash421 2013

[22] H Gozde M C Taplamacioglu and I Kocaarslan ldquoCompara-tive performance analysis of Artificial Bee Colony algorithm inautomatic generation control for interconnected reheat thermalpower systemrdquo International Journal of Electrical Power andEnergy Systems vol 42 no 1 pp 167ndash178 2012

[23] S Debbarma L Chandra Saikia and N Sinha ldquoSolution toautomatic generation control problem using firefly algorithmoptimized I120582D120583 controllerrdquo ISA Transactions vol 53 no 2 pp358ndash366 2014

[24] P Dash L C Saikia and N Sinha ldquoComparison of per-formances of several Cuckoo search algorithm based 2DOFcontrollers in AGC of multi-area thermal systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 55 pp 429ndash436 2014

[25] A Saxena M Gupta and V Gupta ldquoAutomatic generationcontrol of two area interconnected power system using Geneticalgorithmrdquo in Proceedings of the 3rd IEEE International Con-ference on Computational Intelligence and Computing Research(ICCIC rsquo12) Coimbatore India December 2012

[26] B K Sahu T K Pati J R Nayak S Panda and S K KarldquoA novel hybrid LUS-TLBO optimized fuzzy-PID controllerfor load frequency control of multi-source power systemrdquoInternational Journal of Electrical Power amp Energy Systems vol74 pp 58ndash69 2016

[27] Y Sharma and L C Saikia ldquoAutomatic generation controlof a multi-area STmdashthermal power system using Grey WolfOptimizer algorithm based classical controllersrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 853ndash862 2015

[28] P Dash L C Saikia and N Sinha ldquoAutomatic generationcontrol of multi area thermal system using Bat algorithmoptimized PDndashPID cascade controllerrdquo International Journal ofElectrical Power amp Energy Systems vol 68 pp 364ndash372 2015

[29] S Mirjalili ldquoThe ant lion optimizerrdquo Advances in EngineeringSoftware vol 83 pp 80ndash98 2015

[30] MATLAB httpwwwmathworkscom

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Engineering 13

section summarizes the contribution of this research workand proposes a solid milieu for future work

6 Conclusion

This paper presents an application of the recently introducedalgorithm ALO to find optimal parameters of the AGCregulator The ALO regulator is employed on a test system oftwo thermal units connected with a weak tie line of limitedcapacity for AGCThe following are the major findings of thework

(A) Comparison of the application of two objective func-tions namely ISE and ITAE in optimization processfor finding the regulator parameters under differ-ent contingencies is investigated Results reveal thatITAE is a better choice to optimize the regulatorparameters

(B) Eigenvalue analysis is performed to test the effec-tiveness of the proposed approach and to comparethe results of the proposed approach with recentlypublished approaches It is observed that the dampingobtained from ALO regulator is more positive ascompared with the other algorithms

(C) ALO shows promising results in terms of overshootsettling time obtained from the frequency responsesof both areas under different loading cases standarddeviations in regulatorrsquos parameter values ISE andITAE values and optimization performance

(D) Damping performance is evaluated with differentcontingencies load changes and step disturbancesin both areas PI controller setting obtained throughALO exhibits better dynamic performance and over-all low settling time

Application of other new metaheuristic algorithms in AGCregulator design on different models of the power systemconsidering different renewable energy power sources lies inthe future scope

Nomenclature

119894 Subscript referring to area 119894 (1 2)Δ119865119894 Frequency deviation in area 119894 (Hz)

Δ119875119866119894 Incremental generation of area 119894 (pu)

Δ119875119871119894 Incremental load change in area 119894 (pu)

ACE119894 Area Control Error of area 119894

119861119894 Frequency bias parameter of area 119894

119877119894 Speed regulation of the governor of area 119894

(Hzpu MW)119879119892119894 Time constant of governor of area 119894 (s)

119879119905119894 Time constant of turbine of area 119894 (s)

119870119901119894 Gain of generator and load of area 119894

119879119901119894 Time constant of generator and load of

area 119894 (s)Δ119875tie Incremental change in tie line (pu)11987912 Synchronizing coefficient

119879 Simulation time (s)119905 Current iteration

Competing Interests

The authors declare that they have no competing interests

References

[1] O I Elgerd Energy Systems Theory An Introduction McGraw-Hill New Delhi India 1983

[2] IEEE Standard Committee ldquoIEEE Standard definitions of termsfor automatic generation control on electric power systemsrdquoIEEE Transactions on Power Apparatus and Systems vol 89 no6 pp 1356ndash1364 1970

[3] A Ibraheem P Kumar and D P Kothari ldquoRecent philosophiesof automatic generation control strategies in power systemsrdquoIEEE Transactions on Power Systems vol 20 no 1 pp 346ndash3572005

[4] H Sadat Power System Analysis McGraw-Hill New York NYUSA 1999

[5] J Nanda and B Kaul ldquoAutomatic generation control of aninterconnected power systemrdquo Proceedings of the Institution ofElectrical Engineers vol 125 no 5 pp 385ndash390 1978

[6] A Y Sivaramakrishnan M V Hariharan and M C SrisailamldquoDesign of variable-structure load-frequency controller usingpole assignment techniquerdquo International Journal of Controlvol 40 no 3 pp 487ndash498 1984

[7] M Z Bernard T H Mohamed Y S Qudaih and Y MitanildquoDecentralized load frequency control in an interconnectedpower system using Coefficient Diagram Methodrdquo Interna-tional Journal of Electrical Power and Energy Systems vol 63pp 165ndash172 2014

[8] R Ali T HMohamed Y S Qudaih and YMitani ldquoA new loadfrequency control approach in an isolated small power systemsusing coefficient diagram methodrdquo International Journal ofElectrical Power and Energy Systems vol 56 pp 110ndash116 2014

[9] I Vajk M Vajta L Keviczky R Haber J Hetthessy andK Kovacs ldquoAdaptive load-frequency control of the hungarianpower systemrdquo Automatica vol 21 no 2 pp 129ndash137 1985

[10] J Kanniah S C Tripathy O P Malik and G S HopeldquoMicroprocessor-based adaptive load-frequency controlrdquo IEEProceedings CmdashGeneration Transmission and Distribution vol131 no 4 pp 121ndash128 1984

[11] M L Kothari P S Satsangi and J Nanda ldquoSampled-dataautomatic generation control of interconnected reheat thermalsystems considering generation rate constraintsrdquo IEEE Transac-tions on Power Apparatus and Systems vol 100 no 5 pp 2334ndash2342 1981

[12] S Wu M J Er and Y Gao ldquoA fast approach for automaticgeneration of fuzzy rules by generalized dynamic fuzzy neuralnetworksrdquo IEEE Transactions on Fuzzy Systems vol 9 no 4 pp578ndash594 2001

[13] B K Sahu S Pati P K Mohanty and S Panda ldquoTeaching-learning based optimization algorithm based fuzzy-PID con-troller for automatic generation control of multi-area powersystemrdquo Applied Soft Computing Journal vol 27 pp 240ndash2492015

[14] K R Sudha and R Vijaya Santhi ldquoLoad frequency control of aninterconnected reheat thermal systemusing type-2 fuzzy systemincluding SMES unitsrdquo International Journal of Electrical Poweramp Energy Systems vol 43 no 1 pp 1383ndash1392 2012

[15] A Banerjee V Mukherjee and S P Ghoshal ldquoIntelligentcontroller for load-tracking performance of an autonomous

14 Journal of Engineering

power systemrdquo Ain Shams Engineering Journal vol 5 no 4 pp1167ndash1176 2014

[16] S Padhan R K Sahu and S Panda ldquoAutomatic generationcontrol with thyristor controlled series compensator includingsuperconducting magnetic energy storage unitsrdquo Ain ShamsEngineering Journal vol 5 no 3 pp 759ndash774 2014

[17] R K Sahu S Panda and S Padhan ldquoOptimal gravitationalsearch algorithm for automatic generation control of intercon-nected power systemsrdquo Ain Shams Engineering Journal vol 5no 3 pp 721ndash733 2014

[18] Y L Abdel-Magid and M A Abido ldquoAGC tuning of intercon-nected reheat thermal systems with particle swarm optimiza-tionrdquo in Proceedings of the 10th IEEE International Conferenceon Electronics Circuits and Systems (ICECS rsquo03) pp 376ndash379December 2003

[19] Y L Abdel-Magid and M M Dawoud ldquoOptimal AGC tuningwith genetic algorithmsrdquo Electric Power Systems Research vol38 no 3 pp 231ndash238 1996

[20] J Nanda S Mishra and L C Saikia ldquoMaiden application ofbacterial foraging-based optimization technique in multiareaautomatic generation controlrdquo IEEE Transactions on PowerSystems vol 24 no 2 pp 602ndash609 2009

[21] U K Rout R K Sahu and S Panda ldquoDesign and analysisof differential evolution algorithm based automatic generationcontrol for interconnected power systemrdquo Ain Shams Engineer-ing Journal vol 4 no 3 pp 409ndash421 2013

[22] H Gozde M C Taplamacioglu and I Kocaarslan ldquoCompara-tive performance analysis of Artificial Bee Colony algorithm inautomatic generation control for interconnected reheat thermalpower systemrdquo International Journal of Electrical Power andEnergy Systems vol 42 no 1 pp 167ndash178 2012

[23] S Debbarma L Chandra Saikia and N Sinha ldquoSolution toautomatic generation control problem using firefly algorithmoptimized I120582D120583 controllerrdquo ISA Transactions vol 53 no 2 pp358ndash366 2014

[24] P Dash L C Saikia and N Sinha ldquoComparison of per-formances of several Cuckoo search algorithm based 2DOFcontrollers in AGC of multi-area thermal systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 55 pp 429ndash436 2014

[25] A Saxena M Gupta and V Gupta ldquoAutomatic generationcontrol of two area interconnected power system using Geneticalgorithmrdquo in Proceedings of the 3rd IEEE International Con-ference on Computational Intelligence and Computing Research(ICCIC rsquo12) Coimbatore India December 2012

[26] B K Sahu T K Pati J R Nayak S Panda and S K KarldquoA novel hybrid LUS-TLBO optimized fuzzy-PID controllerfor load frequency control of multi-source power systemrdquoInternational Journal of Electrical Power amp Energy Systems vol74 pp 58ndash69 2016

[27] Y Sharma and L C Saikia ldquoAutomatic generation controlof a multi-area STmdashthermal power system using Grey WolfOptimizer algorithm based classical controllersrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 853ndash862 2015

[28] P Dash L C Saikia and N Sinha ldquoAutomatic generationcontrol of multi area thermal system using Bat algorithmoptimized PDndashPID cascade controllerrdquo International Journal ofElectrical Power amp Energy Systems vol 68 pp 364ndash372 2015

[29] S Mirjalili ldquoThe ant lion optimizerrdquo Advances in EngineeringSoftware vol 83 pp 80ndash98 2015

[30] MATLAB httpwwwmathworkscom

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

14 Journal of Engineering

power systemrdquo Ain Shams Engineering Journal vol 5 no 4 pp1167ndash1176 2014

[16] S Padhan R K Sahu and S Panda ldquoAutomatic generationcontrol with thyristor controlled series compensator includingsuperconducting magnetic energy storage unitsrdquo Ain ShamsEngineering Journal vol 5 no 3 pp 759ndash774 2014

[17] R K Sahu S Panda and S Padhan ldquoOptimal gravitationalsearch algorithm for automatic generation control of intercon-nected power systemsrdquo Ain Shams Engineering Journal vol 5no 3 pp 721ndash733 2014

[18] Y L Abdel-Magid and M A Abido ldquoAGC tuning of intercon-nected reheat thermal systems with particle swarm optimiza-tionrdquo in Proceedings of the 10th IEEE International Conferenceon Electronics Circuits and Systems (ICECS rsquo03) pp 376ndash379December 2003

[19] Y L Abdel-Magid and M M Dawoud ldquoOptimal AGC tuningwith genetic algorithmsrdquo Electric Power Systems Research vol38 no 3 pp 231ndash238 1996

[20] J Nanda S Mishra and L C Saikia ldquoMaiden application ofbacterial foraging-based optimization technique in multiareaautomatic generation controlrdquo IEEE Transactions on PowerSystems vol 24 no 2 pp 602ndash609 2009

[21] U K Rout R K Sahu and S Panda ldquoDesign and analysisof differential evolution algorithm based automatic generationcontrol for interconnected power systemrdquo Ain Shams Engineer-ing Journal vol 4 no 3 pp 409ndash421 2013

[22] H Gozde M C Taplamacioglu and I Kocaarslan ldquoCompara-tive performance analysis of Artificial Bee Colony algorithm inautomatic generation control for interconnected reheat thermalpower systemrdquo International Journal of Electrical Power andEnergy Systems vol 42 no 1 pp 167ndash178 2012

[23] S Debbarma L Chandra Saikia and N Sinha ldquoSolution toautomatic generation control problem using firefly algorithmoptimized I120582D120583 controllerrdquo ISA Transactions vol 53 no 2 pp358ndash366 2014

[24] P Dash L C Saikia and N Sinha ldquoComparison of per-formances of several Cuckoo search algorithm based 2DOFcontrollers in AGC of multi-area thermal systemrdquo InternationalJournal of Electrical Power and Energy Systems vol 55 pp 429ndash436 2014

[25] A Saxena M Gupta and V Gupta ldquoAutomatic generationcontrol of two area interconnected power system using Geneticalgorithmrdquo in Proceedings of the 3rd IEEE International Con-ference on Computational Intelligence and Computing Research(ICCIC rsquo12) Coimbatore India December 2012

[26] B K Sahu T K Pati J R Nayak S Panda and S K KarldquoA novel hybrid LUS-TLBO optimized fuzzy-PID controllerfor load frequency control of multi-source power systemrdquoInternational Journal of Electrical Power amp Energy Systems vol74 pp 58ndash69 2016

[27] Y Sharma and L C Saikia ldquoAutomatic generation controlof a multi-area STmdashthermal power system using Grey WolfOptimizer algorithm based classical controllersrdquo InternationalJournal of Electrical Power and Energy Systems vol 73 pp 853ndash862 2015

[28] P Dash L C Saikia and N Sinha ldquoAutomatic generationcontrol of multi area thermal system using Bat algorithmoptimized PDndashPID cascade controllerrdquo International Journal ofElectrical Power amp Energy Systems vol 68 pp 364ndash372 2015

[29] S Mirjalili ldquoThe ant lion optimizerrdquo Advances in EngineeringSoftware vol 83 pp 80ndash98 2015

[30] MATLAB httpwwwmathworkscom

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of