Research Article Power Frequency Oscillation Suppression...
14
Research Article Power Frequency Oscillation Suppression Using Two-Stage Optimized Fuzzy Logic Controller for Multigeneration System Y. K. Bhateshvar and H. D. Mathur EEE Department, BITS, Pilani Campus, Pilani 333031, India Correspondence should be addressed to Y. K. Bhateshvar; [email protected] Received 8 November 2015; Revised 3 March 2016; Accepted 16 March 2016 Academic Editor: Bosukonda M. Mohan Copyright © 2016 Y. K. Bhateshvar and H. D. Mathur. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. is paper attempts to develop a linearized model of automatic generation control (AGC) for an interconnected two-area reheat type thermal power system in deregulated environment. A comparison between genetic algorithm optimized PID controller (GA- PID), particle swarm optimized PID controller (PSO-PID), and proposed two-stage based PSO optimized fuzzy logic controller (TSO-FLC) is presented. e proposed fuzzy based controller is optimized at two stages: one is rule base optimization and other is scaling factor and gain factor optimization. is shows the best dynamic response following a step load change with different cases of bilateral contracts in deregulated environment. In addition, performance of proposed TSO-FLC is also examined for ±30% changes in system parameters with different type of contractual demands between control areas and compared with GA-PID and PSO-PID. MATLAB/Simulink is used for all simulations. 1. Introduction Electrical power system is day by day gaining complexity due to stress to deliver quality power to consumers. Elec- trical energy is produced and consumed simultaneously and balance between demand and supply must be maintained in this complex scenario. is scenario is termed as automatic generation control (AGC). In interconnected power system, controlling frequency as well as tie line power is a challenge. Aſter restructuring of power system where distribution and generation companies have the freedom to purchase and sell power in competitive energy market, demand and generation balance is treated as one of the ancillary services. Independent system operator (ISO) controls various ancillary services to provide secure, reliable, and economical power transmission. Distribution companies (DISCOs) and generation companies (GENCOs) are coordinating with each other under certain fixed contracts in normal operation. In interconnected multi- area power system, DISCO participation matrix (DPM) helps to visualize the various contracts made between GENCOs and DISCOs. In interconnected power system, tie line flows and frequency being controlled and maintaining them at the scheduled values are the two main prime objectives of AGC. e change in frequency and tie line power flow together is termed as area control error (ACE) which is used as control input for AGC operation. Researchers have exhaustively studied various aspects of AGC in deregulated scenario with different test conditions and control strategies [1–4]. Power system is categorized and modeled in terms of control areas for comprehensive analysis of AGC parameters. Literature available discusses single and multiarea model with and without deregulation aspects but, keeping in view of recent competitive energy market, it is also needed to be modeled with existing complexities, that is, nonlinearity present in the system to have better understanding and to have critical review of the system as a whole [5]. It is shown that governor dead band nonlinearity tends to produce a continuous oscillation in the frequency and tie line power transient response [6]. In deregulated era, power system had to undergo numerous technical challenges. In [7] Christie and Bose described several possible structures Hindawi Publishing Corporation Advances in Fuzzy Systems Volume 2016, Article ID 8308109, 13 pages http://dx.doi.org/10.1155/2016/8308109
Transcript of Research Article Power Frequency Oscillation Suppression...
Research ArticlePower Frequency Oscillation Suppression Using Two-StageOptimized Fuzzy Logic Controller for Multigeneration System
Y K Bhateshvar and H D Mathur
EEE Department BITS Pilani Campus Pilani 333031 India
Correspondence should be addressed to Y K Bhateshvar yogeshbhateshvargmailcom
Received 8 November 2015 Revised 3 March 2016 Accepted 16 March 2016
Academic Editor Bosukonda M Mohan
Copyright copy 2016 Y K Bhateshvar and H D Mathur This is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited
This paper attempts to develop a linearized model of automatic generation control (AGC) for an interconnected two-area reheattype thermal power system in deregulated environment A comparison between genetic algorithm optimized PID controller (GA-PID) particle swarm optimized PID controller (PSO-PID) and proposed two-stage based PSO optimized fuzzy logic controller(TSO-FLC) is presented The proposed fuzzy based controller is optimized at two stages one is rule base optimization and otheris scaling factor and gain factor optimization This shows the best dynamic response following a step load change with differentcases of bilateral contracts in deregulated environment In addition performance of proposed TSO-FLC is also examined for plusmn30changes in system parameters with different type of contractual demands between control areas and compared with GA-PID andPSO-PID MATLABSimulink is used for all simulations
1 Introduction
Electrical power system is day by day gaining complexitydue to stress to deliver quality power to consumers Elec-trical energy is produced and consumed simultaneously andbalance between demand and supply must be maintained inthis complex scenario This scenario is termed as automaticgeneration control (AGC) In interconnected power systemcontrolling frequency as well as tie line power is a challengeAfter restructuring of power system where distribution andgeneration companies have the freedom to purchase and sellpower in competitive energymarket demand and generationbalance is treated as one of the ancillary services Independentsystem operator (ISO) controls various ancillary services toprovide secure reliable and economical power transmissionDistribution companies (DISCOs) and generation companies(GENCOs) are coordinating with each other under certainfixed contracts in normal operation In interconnectedmulti-area power system DISCOparticipationmatrix (DPM) helpsto visualize the various contracts made between GENCOsand DISCOs
In interconnected power system tie line flows andfrequency being controlled and maintaining them at thescheduled values are the two main prime objectives of AGCThe change in frequency and tie line power flow together istermed as area control error (ACE) which is used as controlinput for AGC operation
Researchers have exhaustively studied various aspects ofAGC in deregulated scenario with different test conditionsand control strategies [1ndash4] Power system is categorized andmodeled in terms of control areas for comprehensive analysisof AGC parameters Literature available discusses single andmultiarea model with and without deregulation aspects butkeeping in view of recent competitive energy market itis also needed to be modeled with existing complexitiesthat is nonlinearity present in the system to have betterunderstanding and to have critical review of the system as awhole [5] It is shown that governor dead band nonlinearitytends to produce a continuous oscillation in the frequencyand tie line power transient response [6] In deregulated erapower system had to undergo numerous technical challengesIn [7] Christie and Bose described several possible structures
Hindawi Publishing CorporationAdvances in Fuzzy SystemsVolume 2016 Article ID 8308109 13 pageshttpdxdoiorg10115520168308109
2 Advances in Fuzzy Systems
for AGC in deregulated scenario and also addressed technicalissues in power system operation after deregulation Twodifferent approaches to AGC based on HVDC-link andramp following controller are introduced by Bakken andGrande in [8] for Norway and Sweden interconnected powersystem in deregulated environment A detailed simulationand optimization have been carried out byDonde et al [9] forAGC system after deregulation In their work the concept ofDISCOparticipationmatrix has also been shown for differenttypes of contracts and an optimized integral controller isproposed based on trajectory sensitivity
The other approaches to handle AGC are in terms of vari-ous control strategies There are classical and intelligent waysto address AGCbut as complications are increasingwith inte-gration of renewable sources of energy control solution willalso be highly dynamic in nature The classical control tech-niques alone are difficult to implement in a deregulated powersystem environment because of their fixed structure and it isdifficult to determine satisfactory performance with varyingoperating point With the advent of intelligence in controlsystem researchers are focusing on techniques which mixboth the classical and intelligent approach Roy et al [10]studied the four-area multiunits AGC in restructured powersystem A chaotic ant swarm optimization and real coded GAare used to obtain optimal gain parameters for optimal tran-sient performances Bhatt et al [11] proposed model for AGCin restructured power systemThe concept of DISCO partici-pationmatrix is used to simulate the bilateral contracts in thethree and four areas Hybrid particle swarm optimization isused to obtain optimal gain parameters for optimal transientperformance There are several control techniques based onoptimal intelligent and robust approaches proposed for theAGC system in deregulated power systems in recent times
Various optimization methods have been explored byresearchers for PID controller in [12ndash15] but these conven-tional techniques havemany limitations therefore intelligenttechniques like fuzzy logic neural networks and so forthhave gained popularity Even fuzzy logic controller designsuffers from proper selection of input and output variablersquosmembership functions and rule base which give impetusto optimize fuzzy controller parameters In general theseFLC parameters are determined by either experience ortrial and error and this does not assure an optimal FLCdesign Althoughmany attempts have beenmadewith severaloptimization methods in recent literature to optimize a fuzzylogic controller [14 16 17] this paper presents a comparisonbetween different control algorithms which are developedand implemented in the same model The first controltechnique used is PID controller where gain parameters areoptimized by genetic algorithm (GA-PID) second one alsoused PID controller where gain parameters are optimizedby particle swarm optimization (PSO-PID) and the lastapproach is optimizing fuzzy controller in two differentstages Firstly the rule base is optimized and later scaling andgain factors are optimized by particle swarm optimization(TSO-FLC)
The simulation results show that the TSO-FLC greatlyreduces undershoot and settling time Simulation results also
show better performance of fuzzy controller even with plusmn30variation in system parameters
2 System Examined
The two-area system model is considered in continuousoperation mode and nominal system parameters used forstudy are given in Appendix The schematic block diagram isshown in Figure 1 Each area is containing two GENCOs andtwo DISCOs The contracts between GENCOs and DISCOsare shown in distribution participationmatrix (DPM) [18 19]DPM is also referred to as contract participation factormatrix(cpf matrix) It makes the visualization of contracts Thenumber of rows indicates the number of GENCOs and thenumber of columns indicates the number of DISCOs Herethe 119894119895th entry corresponds to the fraction of the total loadpower contracted by DISCO119895 from GENCO119894 [18]
The cpf matrix is
cpf matrix =
[[[[[
[
cpf11 cpf12 cpf13 cpf14cpf21 cpf22 cpf23 cpf24cpf31 cpf32 cpf33 cpf34cpf41 cpf42 cpf43 cpf44
]]]]]
]
where sum
119895
cpf 119894119895 = 1
(1)
The system output which depends on the area control error(ACE) is
ACE119894 = Δ119875tie119894 + 119887119894Δ119891119894 (2)
where 119887119894 is frequency bias constant Δ119891 frequency deviationand Δ119875tie change in tie line power
The coefficients that distribute area control error (ACE)to several GENCOs are termed as ACE participation factors(apf) and for an integrated power system it is shown inapf matrix as shown in
apf matrix =
[[[[[
[
apf1 0 0 0
0 apf2 0 0
0 0 apf3 0
0 0 0 apf4
]]]]]
]
(3)
where additions of all apfs are equal to 1 within control area
sum
119894
apf 119894 = 1 (4)
The contracted scheduled loads in DISCOs in Area 1 areΔ119875Ld1Cont andΔ119875Ld2Cont and inArea 2 areΔ119875Ld3Cont andΔ119875Ld4Contand represented in the Δ119875LDCont
matrix The uncontractedlocal loads in Area 1 are Δ119875Ld1Uncont and Δ119875Ld2Uncont whereasArea 2 are Δ119875Ld3 Uncont and Δ119875Ld4 Uncont shown in Δ119875LD Uncontmatrix [11]
Δ119875LD Cont =
[[[[[
[
Δ119875Ld1 Cont
Δ119875Ld2 Cont
Δ119875Ld3 Cont
Δ119875Ld4 Cont
]]]]]
]
Advances in Fuzzy Systems 3
PowerSystem 2
Speedgovernor
Reheater
Turbine
Speedgovernor
Reheater
Turbine
PowerSystem 1
Speedgovernor
Reheater
Turbine
Speedgovernor
Reheater
Turbine
TSO-FLC 1 TSO-FLC 2
Ther
mal
-reh
eat G
ENCO
1
Ther
mal
-reh
eat G
ENCO
2
Ther
mal
-reh
eat G
ENCO
3
Ther
mal
-reh
eat G
ENCO
4
Scheduledpower
+ +
+
+
+ +++
+
+
+ + +
Power demandof Area 1
DISCO 1 DISCO 2 DISCO 4DISCO 3
Demand fromGENCO 1
Demand fromGENCO 1
Demand fromGENCO 2
Demand fromGENCO 2
Demand fromGENCO 4
Demand fromGENCO 4
Demand fromGENCO 3
Demand fromGENCO 3
1205731
1
R1
1
R2
1205732a12
1
R3
1
R4
T12s
minus
minus minus
minus
minus minus
minusminus minus
minus
minus minus
cpf 14
cpf 13
cpf 12
cpf 11
cpf 24
cpf 23
cpf 22
cpf 21
cpf 34
cpf 33
cpf 32
cpf 31
cpf 44
cpf 43
cpf 42
cpf 41
apf1 apf2 apf3 apf4
Power demandof Area 2
Δf1 Δf2
Figure 1 Block diagram representing a two-area interconnected power system
Δ119875LD Uncont =
[[[[[
[
Δ119875Ld1 Uncont
Δ119875Ld2 Uncont
Δ119875Ld3 Uncont
Δ119875Ld4 Uncont
]]]]]
]
(5)
The total distributed power by 119895th DISCO
Δ119875Ld(119895) = Δ119875Ld(119895) Cont + Δ119875Ld(119895) Uncont (6)
where Δ119875Ld(119895) Cont is contracted can be shown throughcpf matrix but uncontracted power for 119895th DISCO is out ofscope of cpf matrix
4 Advances in Fuzzy Systems
+ + + + + + ++
+
Contracted demandfrom GENCO 4 to
Area 1 DISCOs
Contracted demandfrom GENCO 2 to
Area 2 DISCOs
Contracted demandfrom GENCO 1 to
Area 2 DISCOs
Contracted demandfrom GENCO 3 to
Area 1 DISCOs
+ + + +
ΔPtie12_sch
ΔP
Ld3_
Con
t
ΔP
Ld3_
Con
t
ΔP
Ld1_
Con
t
ΔP
Ld1_
Con
t
ΔP
Ld2_
Con
t
ΔP
Ld2_
Con
t
ΔP
Ld4_
Con
t
ΔP
Ld4_
Con
t
cpf 13
cpf 14
cpf 23
cpf 24
cpf 31
cpf 32
cpf 41
cpf 42
minus
ΔPLA1rarrA2 ΔPLA2rarrA1
Figure 2 The block diagram representation of scheduled 119875tie12
The total distributed power shown in matrix Δ119875LD is
Δ119875LD = Δ119875LD Cont + Δ119875LD Uncont (7)
Similar to this total generated powers through GENCOs inArea 1 are Δ1198751198921 and Δ1198751198922 and in Area 2 are Δ1198751198923 and Δ1198751198924
and these are shown in the Δ119875119866 matrixThe contracted generated powers in Area
1 are Δ1198751198921 Cont amp Δ1198751198922 Cont and in Area 2 areΔ1198751198923 Cont amp Δ1198751198924 Cont shown in Δ119875119866 Cont matrix
Δ119875119866 Cont =
[[[[
[
Δ1198751198921 ContΔ1198751198922 ContΔ1198751198923 ContΔ1198751198924 Cont
]]]]
]
(8)
Theuncontracted powers demanded under contract violationrequired in Area 1 and Area 2 are referred to as Δ1198751198711LOC andΔ1198751198712LOC is required power by local GENCOs only in thatareaThat required power fromGENCOs shown inΔ119875119866 Uncontmatrix
Δ119875119866 Uncont =
[[[[
[
Δ1198751198921 UncontΔ1198751198922 UncontΔ1198751198923 UncontΔ1198751198924 Uncont
]]]]
]
(9)
where Δ1198751198921 Uncont and Δ1198751198922 Uncont are uncontracted requiredpower from GENCO 1 and GENCO 2 in Area 1 andΔ1198751198923 Uncont and Δ1198751198924 Uncont are uncontracted required powerfrom GENCO 3 and GENCO 4 in Area 2
Δ119875119871(119896)LOC = sum
119894
Δ119875119892(119894) Uncont (10)
where 119894 referred to GENCOs within 119896th control area
And Δ119875119892(119894) Uncont is calculated from equation
Δ119875119892(119894) Uncont = apf 119894 lowast sum
119895
Δ119875Ld(119895) Uncont (11)
Or in matrix form
Δ119875119866 Uncont = apf matrix lowast Δ119875LD Uncont (12)
So total required generation power in matrix form is repre-sented as
Δ119875119866 = Δ119875119866 Cont + Δ119875119866 Uncont
Δ119875119866 = cpfmatrix lowast Δ119875LD Cont + apfmatrix lowast Δ119875LD Uncont(13)
The total generation required of individual GENCOs can becalculated also from equation
Δ119875119892(119894) = sum
119895
(cpf 119894119895 lowast Δ119875Ld(119895) Cont) + apf 119894
lowast sum
119895
Δ119875Ld(119895) Uncont(14)
So total demanded power from GENCOs is shown in Δ119875119866
matrix
Δ119875119866 =
[[[
[
Δ1198751198921
Δ1198751198922
Δ1198751198923
Δ1198751198924
]]]
]
(15)
The scheduled tie line power flow between Areas 1 and 2shown in block diagram in Figure 2 can be represented by
Δ119875tie12 sch = (cpf13 lowast Δ119875Ld3Cont + cpf23 lowast Δ119875Ld3 Cont
+ cpf14 lowast Δ119875Ld4 Cont + cpf24 lowast Δ119875Ld4 Cont)
Advances in Fuzzy Systems 5
Table 1 PID controller gains from optimization method
S no Area 1 PID gains Area 2 PID gains
1 GA optimizedPID controller gains
119870119901 059226 100299119870119894 073350 084666119870119889 062571 045060
2 PSO optimizedPID controller gains
119870119901 067927 095495119870119894 160343 172912119870119889 096307 078236
minus (cpf31 lowast Δ119875Ld1 Cont + cpf41 lowast Δ119875Ld1 Cont
+ cpf32 lowast Δ119875Ld2 Cont + cpf42 lowast Δ119875Ld2 Cont)
(16)
3 Control Strategies
In this paper two different control strategies are exploredThefirst control strategy is conventional proportional-integral-derivative (PID) control and another is artificial intelligencebased fuzzy logic control (FLC) PID controller is optimizedby two different stochastic optimization techniques GA andPSO and later PSO based optimized FLC is proposed whereFLC parameters are optimized in two different stages
31 PID Controller PID controller is selected as controllerfor AGC and GA and PSO are used for optimizing of gainparameters that is 119870119901 119870119894 and 119870119889 ACE119894 is selected ascontroller input and 119880PID is output of controller as given in
119880PID = 119870119901 (ACE119894) + 119870119894 (intACE119894119889119905)
+ 119870119889 (119889ACE119894
119889119905
)
(17)
311 Genetic Algorithm The genetic algorithm (GA) isinspired by the principles of genetics and evolution Itmimics the reproduction behavior observed in biologicalpopulations The GA employs the principle of ldquosurvivalof the fittestrdquo in its search process to select and generateindividuals that are adapted to their environment Thereforeover a number of generations desirable traits will evolveand remain in the genome composition of the populationover traits with weaker undesirable characteristics The GAis well suited to and has been extensively applied to solvecomplex design optimization problems because it can handleboth discrete and continuous variables and nonlinear objec-tive and constrained functions without requiring gradientinformation [13 15ndash17] The AGC modeled has an objective
function for PID optimization as given in (18) which is aimedfor minimization of peak undershoots and settling time offrequency and tie line deviation
119869OBJ = int
119879
0
(120582 (10038161003816100381610038161003816PUΔ119891
1
10038161003816100381610038161003816+
10038161003816100381610038161003816PUΔ119891
2
10038161003816100381610038161003816+ 120583
10038161003816100381610038161003816PUΔ119875tie12
10038161003816100381610038161003816)
+ (STΔ1198911
+ STΔ1198912
+ STΔ119875tie12)) 119889119905
(18)
Here 120582 120583 and 119879 are selected as 10 500 and 50respectively
312 Particle SwarmOptimization Particle swarmoptimiza-tion (PSO) is a heuristic search method which is by theswarming or collaborative behavior of biological populationsIn PSO a set of randomly generated solutions (initial swarm)propagates in the design space towards the optimal solutionover a number of iterations (moves) based on large amount ofinformation about the design space that is assimilated andshared by all members of the swarm PSO is inspired by theability of flocks of birds schools of fish and herds of animalsto adapt to their environment find rich sources of food andavoid predators by implementing an ldquoinformation sharingrdquoapproach hence developing an evolutionary advantage Itsability to converge faster to global solution makes it favorabletechnique compared to other stochastic optimization meth-ods like GA and simulated annealing (SA) [17ndash19] The PIDcontroller gains for both control areas optimized by GA andPSO are shown in Table 1 An algorithm is developed for thesystem under study for optimization with PSO and followingsteps are followed
Algorithm steps for PSO implementation are given below
(1) Setting parameters for PSO
(a) Define dimensions of search space(b) Define boundaries of search space (minimum
and maximum values of variables)(c) Define minimum and maximum values of par-
ticlersquos velocities
(2) Initialize population
(a) Initialize random population of swarm withinboundaries
6 Advances in Fuzzy Systems
Fuzzy logic controller Controlled output
+
+
ACEi Kemin
Ke
Kcemax
Kemax
Kce
Kcemin
Kpumin
Kpu
Kiu
Kpumax
Kiumin
Kiumax
Ui
1
s
d
dt
Figure 3 MISO-type fuzzy logic controller
VN ZMN SP VPMPSN
000
100
050
ACEidACEiUi
120583
minus1 minus075 minus050 minus025 0 025 050 075 1
Figure 4 Membership functions of inputs and output variable
(b) Set random velocities to particles of swarmwithin boundaries
(3) Evaluate the fitness of each particle position as perobjective function selected
(a) Identify each particlersquos best known position(b) Identify the best known position of swarm(c) Update the velocities and positions of particles
(4) Repeat step (3) up to either maximum iterations orconvergence criteria satisfied
32 PSO Optimized Fuzzy Logic Controller Power systemoperation and control have undergoing immense changesfrom earlier times as complexity has increased multifolddue to stress to deliver quality and uninterrupted powerto consumers These reasons have boosted power systemengineers to use intelligent control strategies in operationand control where fuzzy logic has gained popularity amongstothers because of its computing approach based on ldquodegreesof truthrdquo rather than the usual ldquotrue or falserdquo Therefore itis widely used in engineering problems Fuzzy set theoryand fuzzy logic establish the rules of a nonlinear mappingThe fuzzy logic controller modeling consists of three stepsof fuzzification determination of fuzzy control rules anddefuzzification [20] Fuzzy logic is a systematic and easier wayto implement control algorithm for uncertain and indefinitemodels in engineering and suits most AGC problem [21 22]
The comparison between the proposed TSO-FLC andGA-PID and PSO-PID controllers is quantified based on twodynamic performance indices that is peak undershoot andsettling time
Table 2 Fuzzy rules for Area 1 controller
ACEVN MN SN Z SP MP VP
ΔACE
VN VN VN VN VN SN MN SNMN VN MN SN MN VN SN SPSN VN VN VN VN Z Z ZZ MN MN N Z MP MP MPSP Z Z Z VP VP VP VPMP SN SP VP MP SP MP VPVP SP MP SP VP VP VP VP
The multi-input and single-output (MISO) type fuzzycontroller is shown in Figure 3 119870119901119906 and 119870119894119906 are the propor-tional and integral gains respectively Two inputs ACE119894 andderivative of ACE119894 that is (119889ACE119894119889119905) are fed to the fuzzycontrollerThe fuzzy logic process is initiated by fuzzificationofACE119894 and119889ACE119894119889119905Mamdani fuzzy inferencemechanismand centroid method for defuzzification are later used forrespective processes 119880119894 is a crisp value and 119906119894 is a controlsignal for the system
119906119894 = minus119870119901119906119880119894 minus 119870119894119906 int 119880119894119889119905 (19)
Membership functions (MF) specify the degree to which agiven input belongs to a set FLC has used seven membershipfunctions Very Negative (VN) Medium Negative (MN)Small Negative (SN) Zero (Z) Small Positive (SP) MediumPositive (MP) and Very Positive (VP) The membershipfunction sets of FLC for input as well as output variables areshown in Figure 4 Optimized rule base for proposed TSO-FLC for both areas is shown in Tables 2 and 3
Advances in Fuzzy Systems 7
0 5 10 15 20 25 30 35 40 45 50708709
71711712713714715716717718
Iteration
Fitn
ess v
alue
Figure 5 FLC optimization of step 1 for rule base optimization
0 10 20 30 40 50 60 70 80 90 10052545658606264666870
Iteration
Fitn
ess v
alue
Figure 6 FLC optimization of step 2 for scaling and gain factoroptimization
Table 3 Fuzzy rules for Area 2 controller
ACEVN MN SN Z SP MP VP
ΔACE
VN VN VN MN VN SN SN ZMN VN VN VN VN SN Z ZSN VN VN VN MN SN SP SPZ MN MN VN Z VP MP MPSP SN SN SP MP VP VP VPMP Z Z SP VP VP VP VPVP Z SP SP VP MP VP VP
Table 4 Optimized scaling and gain parameters for TSO-FLC
Scaling parameters Gain parameters119870119890 119870119888119890 119870119901119906 119870119894119906
FLC for Area 1 112833 093282 143489 218240FLC for Area 2 188194 056237 056237 210918
Themembership functions of each input and each outputare spread across a linear distribution range from minus1 to +1 Intwo stages FLC is optimized by PSO with objective functiongiven in (18)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
Figure 7 Comparison of GA-PID PSO-PID and TSO-FLC forreheat type two-area thermal power system (Case A) Poolco (a)frequency deviation in Area 1 and (b) frequency deviation in Area 2
Rule BaseOptimization In this step apart from center rule allother rules need to be optimized Only one rule is configuredthat when both inputs are zero then output is also zero Insystem under study out of 49 rules 48 rules are required to beoptimizedThe curve between best fitness values with respectto iteration for rule base optimization is shown in Figure 5
Scaling Factor and Gain Optimization In this second stepoptimum values of two scaling factors (119870119890 and 119870119888119890) and twogain parameters (119870119901119906 and 119870119894119906) are needed to be optimizedof FLC Graphically the best fitness values with respect toiteration are represented in Figure 6 Table 4 shows theoptimized scaling and gain parameters for TSO-FLC
4 Test Cases and Simulations
There are three different test cases of deregulated power sys-tem considered for justification of optimum performance ofproposed TSO-FLC controller as compared to conventionalGA-PID andPSO-PID controllersThese test cases are Poolcobased transactions combination of Poolco and bilateral based
8 Advances in Fuzzy Systems
Table 5 Different test cases for proposed system
Test cases cpf matrixContractedload (pu)(Δ119875LD Cont)
Uncontractedload (pu)(Δ119875LDUncont
)
Load Δ119875LD(pu)
ScheduledGENCOs
power (pu)(Δ119875119866)
Scheduled tieline powerflow (pu)(Δ119875tie12 sch)
Case A(Poolco based transactions)
[[[[[[[[[
[
05 05 0 0
05 05 0 0
0 0 05 05
0 0 05 05
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
000
000
000
000
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
0
Case B(combination of Poolco andbilateral basedtransactions)
[[[[[[[[[
[
025 020 025 0
025 020 0 0
050 030 015 0
0 030 060 1
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
000
000
000
000
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
00070
00045
00095
00190
]]]]]]]]]
]
minus00085
Case C(contract violation)
[[[[[[[[[
[
025 020 025 0
025 020 0 0
050 030 015 0
0 030 060 1
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
0000
0004
0000
0008
]]]]]]]]]
]
[[[[[[[[[
[
0010
0014
0010
0018
]]]]]]]]]
]
[[[[[[[[[
[
00090
00065
00135
00230
]]]]]]]]]
]
minus00085
Table 6 System parameters
Rated power (Area 1 and Area 2) 1198751199031 and 1198751199032 2000MW
Transfer function gain of generator (Area 1 and Area 2) 1198701199011 and 1198701199012 120
Generatorrsquos time constant (Area 1 and Area 2) 1198791199011 and 1198791199012 20
Governorrsquos time constant 1198791198921 008
Governorrsquos time constant 1198791198922 002
Steam turbinersquos time constant 119879119905 03
Regulation of the governor (Area 1 and Area 2) 1198771 and 1198772 24
Frequency bias constant 120573 0425
Synchronizing power coefficient 11988612 1
Synchronization coefficient 11987912 0545
transactions and contract violationThe cpf matrix and loadpower from each DISCO are varied in each test case asdepicted in Table 5 Apart from this all GENCOs are allowedto participate equally in each area for AGC therefore ACEparticipation factor (apf 119894) 05 is considered for simulationpurpose
The total generated power Δ119875119892(119894) required by individualGENCO is composed of all contracted and uncontractedloads Each GENCO shares the uncontracted load of its owncontrol area according to its ACE participation factor Thevalues of system parameters given in Appendix (Table 6)
are used for a comparative study Frequency deviations ofboth areas and tie line deviation after load change as per loaddistribution (Table 5) in each area for test casesA B andC areshown in Figures 7 8 and 9 respectively Two performanceindices (settling time and peak undershoot) were selected forjustification of dynamic performance response of controllersEffect of +30 and minus30 change in parameter values 120573 11987912and 119879119901 (parameters value in Table 7 in Appendix) is alsoexamined Peak undershoot and settling time of both areasand tie line deviation are also determined with +30 andminus30 change in system parameters in each area for test cases
Advances in Fuzzy Systems 9
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 8 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case B) Combination of Poolcoand bilateral contracts (a) frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Table 7 Different cases with different system parameters
119879119901 120573 11987912
Case 1 (nominal value) 20 0425 0545Case 2 (+30 increase) 26 05525 07085Case 3 (minus30 decrease) 14 02975 03815
A B and C shown in Figures 10 11 12 13 14 and 15 Thecomparison of dynamic performances of GA-PID and PSO-PID controllerswith the proposedTSO-FLC controller showsthat proposed TSO-FLC gives better results in terms of lessersettling time and peak undershoot MatlabSimulink is usedfor simulation purpose
In order to examine the performance of controllerspeak undershoot and settling time of both areas and tieline deviation are determined for test cases A B and Cwith standard values of system parameters Apart from this
the effect of +30 and minus30 change in parameter values 12057311987912 and 119879119901 (parameters value in Table 7) is also examinedso further performance indices for +30 and minus30 changein system parameters for different test cases determined areshown in Figures 10 11 12 13 14 and 15 Based on thiscomparison it can be concluded that proposed TSO-FLCgives better results in terms of lesser settling time and peakundershoot compared to GA-PID and PSO-PID controllers
5 Conclusion
In this paper an optimization strategy for FLC is proposedfor AGC This optimization strategy is based on rule baseoptimization and scaling factor and gain factor optimizationof FLC PSO is used as optimization technique The perfor-mance of proposed controller is compared with conventionalPID controller also optimized by two optimization methodsGA and PSO under different test cases based on contractual
10 Advances in Fuzzy Systems
0 5 10 15 20 25 30 35 40 45 50minus0035
minus003minus0025
minus002minus0015
minus001minus0005
00005
001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus004
minus0035minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 9 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case C) Contract violation (a)frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Case AGA-PID 002556 002064 003407 002663 002140 003561PSO-PID 002150 001714 002922 002268 001804 003080TSO-FLC 000972 000750 001380 001118 000865 001579
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)(nominal)Δf1 Δf1 Δf1
(nominal)Δf2 Δf2 Δf2
Figure 10 Peak undershoot comparison at plusmn30 variation insystem parameters for Case A
demands in deregulated power system The dynamic per-formance of proposed controllers is observed on the basisof two performance indices that is settling time and peak
1983015 1751152 2344273 1993948 1761672 23553811340694 1173940 1593159 1340694 1173940 1593159312402 120954 933828 087750 087520 395436
000000
500000
1000000
1500000
2000000
2500000
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)
Settling time (plusmn5)
Δf1 Δf1 Δf2 Δf2(nominal)
Δf1(nominal)
Δf2
Figure 11 Settling time comparison at plusmn30 variation in systemparameters for Case A
undershoot Simulation results show that proposedTSO-FLCcontroller provides a better performance in comparison of
Advances in Fuzzy Systems 11
002645002177000893
002139001732000689
003519002954001269
002714002317001363
002184001847001055
003614003129001913
Case B
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
8500E minus 0
8500E minus 0
8585E minus 0
8500E minus 0
8500E minus 0
8551E minus 0
8500E minus 0
8500E minus 0
8543E minus 0GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal) (nominal) (nominal)
Figure 12 Peak undershoot comparison at plusmn30 variation in system parameters for Case B
19690831301781383480
17569881144269294828
23292181578341545893
20689471391069278520
18352271218930235500
24063641624648279652
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
9006E + 0
2500E + 0
1559E + 0
8092E + 0
2543E + 0
1458E + 0
8668E + 0
2682E + 0
1523E + 0
Settling time (plusmn5)
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal)(nominal)(nominal)
Figure 13 Settling time comparison at plusmn30 variation in system parameters for Case B
GA-PID and PSO-PID controllers Robustness of the TSO-FLC is also justified for +30 and minus30 change in systemparameters for different sets of contractual demands andagain it is observed that TSO-FLC is a suitable controller forAGC in an interconnected power system
Appendix
Speed governor 1(1 + 119904119879119892)
Thermal reheater (1 + 119870119903119904119879119903)(1 + 119904119879119903)
Thermal turbine 1(1 + 119904119879119905)
Power system 119870119901(1 + 119904119879119901)
See Tables 6 and 7
Competing Interests
The authors declare that they have no competing interests
12 Advances in Fuzzy Systems
003448002803001143
002865002275000883
004529003775001625
004000003394001872
003212002700001445
005290004552002641
000000
001000
002000
003000
004000
005000
006000
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
Case C
Peak undershoot
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 14 Peak undershoot comparison at plusmn30 variation in system parameters for Case C
20958661452353404295
18844331286364324176
21740051495980272999
19415891329047232815
25159171748899549258
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
8465E + 0
2550E + 0
1450E + 0
7297E + 0
2553E + 0
1319E + 0
8019E + 0
2730E + 0
1396E + 0
1716E + 0
1082E + 0
2472E + 0
Settling time (plusmn5)
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 15 Settling time comparison at plusmn30 variation in system parameters for Case C
References
[1] F Daneshfar ldquoIntelligent load-frequency control in a deregu-lated environment continuous-valued input extended classifiersystem approachrdquo IET Generation Transmission and Distribu-tion vol 7 no 6 pp 551ndash559 2013
[2] I A Chidambaram and B Paramasivam ldquoOptimized load-frequency simulation in restructured power system with Redoxflow batteries and interline power flow controllerrdquo InternationalJournal of Electrical Power and Energy Systems vol 50 no 1 pp9ndash24 2013
[3] A P Sakis Meliopoulos G J Cokkinides and A G BakirtzisldquoLoad-frequency control service in a deregulated environmentrdquoDecision Support Systems vol 24 no 3-4 pp 243ndash250 1999
[4] F Liu Y H Song J Ma S Mei and Q Lu ldquoOptimalload-frequency control in restructured power systemsrdquo IEEProceedings Generation Transmission andDistribution vol 150no 1 pp 87ndash95 2003
[5] W C Chan and Y Y Hsu ldquoAutomatic generation control ofinterconnected power systems using variable-structure con-trollersrdquo IEE Proceedings C Generation Transmission and Dis-tribution vol 128 no 5 pp 269ndash279 1981
[6] S C Tripathy G S Hope and O P Malik ldquoOptimisationof load-frequency control parameters for power systems withreheat steam turbines and governor deadband nonlinearityrdquoIEE Proceedings C Generation Transmission and Distributionvol 129 no 1 pp 10ndash16 1982
Advances in Fuzzy Systems 13
[7] R D Christie and A Bose ldquoLoad frequency control issues inpower system operations after deregulationrdquo IEEE Transactionson Power Systems vol 11 no 3 pp 1191ndash1200 1995
[8] B H Bakken and O S Grande ldquoAutomatic generation controlin a deregulated power systemrdquo IEEE Transactions on PowerSystems vol 13 no 4 pp 1401ndash1406 1998
[9] V Donde M A Pai and I A Hiskens ldquoSimulation andoptimization in an AGC system after deregulationrdquo IEEETransactions on Power Systems vol 16 no 3 pp 481ndash489 2001
[10] R Roy P Bhatt and S P Ghoshal ldquoEvolutionary computationbased three-area automatic generation controlrdquo Expert Systemswith Applications vol 37 no 8 pp 5913ndash5924 2010
[11] P Bhatt R Roy and S P Ghoshal ldquoOptimized multi areaAGC simulation in restructured power systemsrdquo InternationalJournal of Electrical Power amp Energy Systems vol 32 no 4 pp311ndash322 2010
[12] S P Ghoshal ldquoOptimizations of PID gains by particle swarmoptimizations in fuzzy based automatic generation controlrdquoElectric Power Systems Research vol 72 no 3 pp 203ndash212 2004
[13] I Chiha N Liouane and P Borne ldquoTuning PID controllerusing multiobjective ant colony optimizationrdquo Applied Compu-tational Intelligence and Soft Computing vol 2012 Article ID536326 7 pages 2012
[14] V Mukherjee and S P Ghoshal ldquoIntelligent particle swarmoptimized fuzzy PID controller for AVR systemrdquo Electric PowerSystems Research vol 77 no 12 pp 1689ndash1698 2007
[15] K Naidu H Mokhlis and A H A Bakar ldquoMultiobjective opti-mization using weighted sum Artificial Bee Colony algorithmfor Load Frequency Controlrdquo International Journal of ElectricalPower and Energy Systems vol 55 pp 657ndash667 2014
[16] D Pelusi ldquoOptimization of a fuzzy logic controller using geneticalgorithmsrdquo in Proceedings of the 3rd International Conferenceon IntelligentHuman-Machine Systems andCybernetics (IHMSCrsquo11) pp 143ndash146 Zhejiang China August 2011
[17] T Chaiyatham I Ngamroo S Pothiya and S VachirasricirikulldquoDesign of optimal fuzzy logic-PID controller using bee colonyoptimization for frequency control in an isolated wind-dieselsystemrdquo in Proceedings of the Transmission amp DistributionConference amp Exposition Asia and Pacific vol 1 pp 1ndash4 IEEESeoul The Republic of Korea October 2009
[18] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 2006
[19] M Parida and J Nanda ldquoAutomatic generation control of ahydro-thermal system in deregulated environmentrdquo in Proceed-ings of the 8th International Conference on Electrical Machinesand Systems (ICEMS rsquo05) pp 942ndash947Nanjing China Septem-ber 2005
[20] C C Lee ldquoFuzzy logic in control systems fuzzy logic controllerIIrdquo IEEE Transactions on SystemsMan and Cybernetics vol 20no 2 pp 419ndash435 1990
[21] K R M Vijaya Chandrakala S Balamurugan and K Sankara-narayanan ldquoVariable structure fuzzy gain scheduling based loadfrequency controller for multi source multi area hydro thermalsystemrdquo International Journal of Electrical Power and EnergySystems vol 53 no 1 pp 375ndash381 2013
[22] Y K Bhateshvar and H D Mathur ldquoFrequency stabilizationusing fuzzy logic based controller for multi-area power systemin deregulated environmentrdquo in Proceedings of the 2nd Inter-national Conference on Advances in Control and Optimizationof Dynamical Systems (ACODS rsquo12) pp 1ndash10 Bangalore IndiaFebruary 2012
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
2 Advances in Fuzzy Systems
for AGC in deregulated scenario and also addressed technicalissues in power system operation after deregulation Twodifferent approaches to AGC based on HVDC-link andramp following controller are introduced by Bakken andGrande in [8] for Norway and Sweden interconnected powersystem in deregulated environment A detailed simulationand optimization have been carried out byDonde et al [9] forAGC system after deregulation In their work the concept ofDISCOparticipationmatrix has also been shown for differenttypes of contracts and an optimized integral controller isproposed based on trajectory sensitivity
The other approaches to handle AGC are in terms of vari-ous control strategies There are classical and intelligent waysto address AGCbut as complications are increasingwith inte-gration of renewable sources of energy control solution willalso be highly dynamic in nature The classical control tech-niques alone are difficult to implement in a deregulated powersystem environment because of their fixed structure and it isdifficult to determine satisfactory performance with varyingoperating point With the advent of intelligence in controlsystem researchers are focusing on techniques which mixboth the classical and intelligent approach Roy et al [10]studied the four-area multiunits AGC in restructured powersystem A chaotic ant swarm optimization and real coded GAare used to obtain optimal gain parameters for optimal tran-sient performances Bhatt et al [11] proposed model for AGCin restructured power systemThe concept of DISCO partici-pationmatrix is used to simulate the bilateral contracts in thethree and four areas Hybrid particle swarm optimization isused to obtain optimal gain parameters for optimal transientperformance There are several control techniques based onoptimal intelligent and robust approaches proposed for theAGC system in deregulated power systems in recent times
Various optimization methods have been explored byresearchers for PID controller in [12ndash15] but these conven-tional techniques havemany limitations therefore intelligenttechniques like fuzzy logic neural networks and so forthhave gained popularity Even fuzzy logic controller designsuffers from proper selection of input and output variablersquosmembership functions and rule base which give impetusto optimize fuzzy controller parameters In general theseFLC parameters are determined by either experience ortrial and error and this does not assure an optimal FLCdesign Althoughmany attempts have beenmadewith severaloptimization methods in recent literature to optimize a fuzzylogic controller [14 16 17] this paper presents a comparisonbetween different control algorithms which are developedand implemented in the same model The first controltechnique used is PID controller where gain parameters areoptimized by genetic algorithm (GA-PID) second one alsoused PID controller where gain parameters are optimizedby particle swarm optimization (PSO-PID) and the lastapproach is optimizing fuzzy controller in two differentstages Firstly the rule base is optimized and later scaling andgain factors are optimized by particle swarm optimization(TSO-FLC)
The simulation results show that the TSO-FLC greatlyreduces undershoot and settling time Simulation results also
show better performance of fuzzy controller even with plusmn30variation in system parameters
2 System Examined
The two-area system model is considered in continuousoperation mode and nominal system parameters used forstudy are given in Appendix The schematic block diagram isshown in Figure 1 Each area is containing two GENCOs andtwo DISCOs The contracts between GENCOs and DISCOsare shown in distribution participationmatrix (DPM) [18 19]DPM is also referred to as contract participation factormatrix(cpf matrix) It makes the visualization of contracts Thenumber of rows indicates the number of GENCOs and thenumber of columns indicates the number of DISCOs Herethe 119894119895th entry corresponds to the fraction of the total loadpower contracted by DISCO119895 from GENCO119894 [18]
The cpf matrix is
cpf matrix =
[[[[[
[
cpf11 cpf12 cpf13 cpf14cpf21 cpf22 cpf23 cpf24cpf31 cpf32 cpf33 cpf34cpf41 cpf42 cpf43 cpf44
]]]]]
]
where sum
119895
cpf 119894119895 = 1
(1)
The system output which depends on the area control error(ACE) is
ACE119894 = Δ119875tie119894 + 119887119894Δ119891119894 (2)
where 119887119894 is frequency bias constant Δ119891 frequency deviationand Δ119875tie change in tie line power
The coefficients that distribute area control error (ACE)to several GENCOs are termed as ACE participation factors(apf) and for an integrated power system it is shown inapf matrix as shown in
apf matrix =
[[[[[
[
apf1 0 0 0
0 apf2 0 0
0 0 apf3 0
0 0 0 apf4
]]]]]
]
(3)
where additions of all apfs are equal to 1 within control area
sum
119894
apf 119894 = 1 (4)
The contracted scheduled loads in DISCOs in Area 1 areΔ119875Ld1Cont andΔ119875Ld2Cont and inArea 2 areΔ119875Ld3Cont andΔ119875Ld4Contand represented in the Δ119875LDCont
matrix The uncontractedlocal loads in Area 1 are Δ119875Ld1Uncont and Δ119875Ld2Uncont whereasArea 2 are Δ119875Ld3 Uncont and Δ119875Ld4 Uncont shown in Δ119875LD Uncontmatrix [11]
Δ119875LD Cont =
[[[[[
[
Δ119875Ld1 Cont
Δ119875Ld2 Cont
Δ119875Ld3 Cont
Δ119875Ld4 Cont
]]]]]
]
Advances in Fuzzy Systems 3
PowerSystem 2
Speedgovernor
Reheater
Turbine
Speedgovernor
Reheater
Turbine
PowerSystem 1
Speedgovernor
Reheater
Turbine
Speedgovernor
Reheater
Turbine
TSO-FLC 1 TSO-FLC 2
Ther
mal
-reh
eat G
ENCO
1
Ther
mal
-reh
eat G
ENCO
2
Ther
mal
-reh
eat G
ENCO
3
Ther
mal
-reh
eat G
ENCO
4
Scheduledpower
+ +
+
+
+ +++
+
+
+ + +
Power demandof Area 1
DISCO 1 DISCO 2 DISCO 4DISCO 3
Demand fromGENCO 1
Demand fromGENCO 1
Demand fromGENCO 2
Demand fromGENCO 2
Demand fromGENCO 4
Demand fromGENCO 4
Demand fromGENCO 3
Demand fromGENCO 3
1205731
1
R1
1
R2
1205732a12
1
R3
1
R4
T12s
minus
minus minus
minus
minus minus
minusminus minus
minus
minus minus
cpf 14
cpf 13
cpf 12
cpf 11
cpf 24
cpf 23
cpf 22
cpf 21
cpf 34
cpf 33
cpf 32
cpf 31
cpf 44
cpf 43
cpf 42
cpf 41
apf1 apf2 apf3 apf4
Power demandof Area 2
Δf1 Δf2
Figure 1 Block diagram representing a two-area interconnected power system
Δ119875LD Uncont =
[[[[[
[
Δ119875Ld1 Uncont
Δ119875Ld2 Uncont
Δ119875Ld3 Uncont
Δ119875Ld4 Uncont
]]]]]
]
(5)
The total distributed power by 119895th DISCO
Δ119875Ld(119895) = Δ119875Ld(119895) Cont + Δ119875Ld(119895) Uncont (6)
where Δ119875Ld(119895) Cont is contracted can be shown throughcpf matrix but uncontracted power for 119895th DISCO is out ofscope of cpf matrix
4 Advances in Fuzzy Systems
+ + + + + + ++
+
Contracted demandfrom GENCO 4 to
Area 1 DISCOs
Contracted demandfrom GENCO 2 to
Area 2 DISCOs
Contracted demandfrom GENCO 1 to
Area 2 DISCOs
Contracted demandfrom GENCO 3 to
Area 1 DISCOs
+ + + +
ΔPtie12_sch
ΔP
Ld3_
Con
t
ΔP
Ld3_
Con
t
ΔP
Ld1_
Con
t
ΔP
Ld1_
Con
t
ΔP
Ld2_
Con
t
ΔP
Ld2_
Con
t
ΔP
Ld4_
Con
t
ΔP
Ld4_
Con
t
cpf 13
cpf 14
cpf 23
cpf 24
cpf 31
cpf 32
cpf 41
cpf 42
minus
ΔPLA1rarrA2 ΔPLA2rarrA1
Figure 2 The block diagram representation of scheduled 119875tie12
The total distributed power shown in matrix Δ119875LD is
Δ119875LD = Δ119875LD Cont + Δ119875LD Uncont (7)
Similar to this total generated powers through GENCOs inArea 1 are Δ1198751198921 and Δ1198751198922 and in Area 2 are Δ1198751198923 and Δ1198751198924
and these are shown in the Δ119875119866 matrixThe contracted generated powers in Area
1 are Δ1198751198921 Cont amp Δ1198751198922 Cont and in Area 2 areΔ1198751198923 Cont amp Δ1198751198924 Cont shown in Δ119875119866 Cont matrix
Δ119875119866 Cont =
[[[[
[
Δ1198751198921 ContΔ1198751198922 ContΔ1198751198923 ContΔ1198751198924 Cont
]]]]
]
(8)
Theuncontracted powers demanded under contract violationrequired in Area 1 and Area 2 are referred to as Δ1198751198711LOC andΔ1198751198712LOC is required power by local GENCOs only in thatareaThat required power fromGENCOs shown inΔ119875119866 Uncontmatrix
Δ119875119866 Uncont =
[[[[
[
Δ1198751198921 UncontΔ1198751198922 UncontΔ1198751198923 UncontΔ1198751198924 Uncont
]]]]
]
(9)
where Δ1198751198921 Uncont and Δ1198751198922 Uncont are uncontracted requiredpower from GENCO 1 and GENCO 2 in Area 1 andΔ1198751198923 Uncont and Δ1198751198924 Uncont are uncontracted required powerfrom GENCO 3 and GENCO 4 in Area 2
Δ119875119871(119896)LOC = sum
119894
Δ119875119892(119894) Uncont (10)
where 119894 referred to GENCOs within 119896th control area
And Δ119875119892(119894) Uncont is calculated from equation
Δ119875119892(119894) Uncont = apf 119894 lowast sum
119895
Δ119875Ld(119895) Uncont (11)
Or in matrix form
Δ119875119866 Uncont = apf matrix lowast Δ119875LD Uncont (12)
So total required generation power in matrix form is repre-sented as
Δ119875119866 = Δ119875119866 Cont + Δ119875119866 Uncont
Δ119875119866 = cpfmatrix lowast Δ119875LD Cont + apfmatrix lowast Δ119875LD Uncont(13)
The total generation required of individual GENCOs can becalculated also from equation
Δ119875119892(119894) = sum
119895
(cpf 119894119895 lowast Δ119875Ld(119895) Cont) + apf 119894
lowast sum
119895
Δ119875Ld(119895) Uncont(14)
So total demanded power from GENCOs is shown in Δ119875119866
matrix
Δ119875119866 =
[[[
[
Δ1198751198921
Δ1198751198922
Δ1198751198923
Δ1198751198924
]]]
]
(15)
The scheduled tie line power flow between Areas 1 and 2shown in block diagram in Figure 2 can be represented by
Δ119875tie12 sch = (cpf13 lowast Δ119875Ld3Cont + cpf23 lowast Δ119875Ld3 Cont
+ cpf14 lowast Δ119875Ld4 Cont + cpf24 lowast Δ119875Ld4 Cont)
Advances in Fuzzy Systems 5
Table 1 PID controller gains from optimization method
S no Area 1 PID gains Area 2 PID gains
1 GA optimizedPID controller gains
119870119901 059226 100299119870119894 073350 084666119870119889 062571 045060
2 PSO optimizedPID controller gains
119870119901 067927 095495119870119894 160343 172912119870119889 096307 078236
minus (cpf31 lowast Δ119875Ld1 Cont + cpf41 lowast Δ119875Ld1 Cont
+ cpf32 lowast Δ119875Ld2 Cont + cpf42 lowast Δ119875Ld2 Cont)
(16)
3 Control Strategies
In this paper two different control strategies are exploredThefirst control strategy is conventional proportional-integral-derivative (PID) control and another is artificial intelligencebased fuzzy logic control (FLC) PID controller is optimizedby two different stochastic optimization techniques GA andPSO and later PSO based optimized FLC is proposed whereFLC parameters are optimized in two different stages
31 PID Controller PID controller is selected as controllerfor AGC and GA and PSO are used for optimizing of gainparameters that is 119870119901 119870119894 and 119870119889 ACE119894 is selected ascontroller input and 119880PID is output of controller as given in
119880PID = 119870119901 (ACE119894) + 119870119894 (intACE119894119889119905)
+ 119870119889 (119889ACE119894
119889119905
)
(17)
311 Genetic Algorithm The genetic algorithm (GA) isinspired by the principles of genetics and evolution Itmimics the reproduction behavior observed in biologicalpopulations The GA employs the principle of ldquosurvivalof the fittestrdquo in its search process to select and generateindividuals that are adapted to their environment Thereforeover a number of generations desirable traits will evolveand remain in the genome composition of the populationover traits with weaker undesirable characteristics The GAis well suited to and has been extensively applied to solvecomplex design optimization problems because it can handleboth discrete and continuous variables and nonlinear objec-tive and constrained functions without requiring gradientinformation [13 15ndash17] The AGC modeled has an objective
function for PID optimization as given in (18) which is aimedfor minimization of peak undershoots and settling time offrequency and tie line deviation
119869OBJ = int
119879
0
(120582 (10038161003816100381610038161003816PUΔ119891
1
10038161003816100381610038161003816+
10038161003816100381610038161003816PUΔ119891
2
10038161003816100381610038161003816+ 120583
10038161003816100381610038161003816PUΔ119875tie12
10038161003816100381610038161003816)
+ (STΔ1198911
+ STΔ1198912
+ STΔ119875tie12)) 119889119905
(18)
Here 120582 120583 and 119879 are selected as 10 500 and 50respectively
312 Particle SwarmOptimization Particle swarmoptimiza-tion (PSO) is a heuristic search method which is by theswarming or collaborative behavior of biological populationsIn PSO a set of randomly generated solutions (initial swarm)propagates in the design space towards the optimal solutionover a number of iterations (moves) based on large amount ofinformation about the design space that is assimilated andshared by all members of the swarm PSO is inspired by theability of flocks of birds schools of fish and herds of animalsto adapt to their environment find rich sources of food andavoid predators by implementing an ldquoinformation sharingrdquoapproach hence developing an evolutionary advantage Itsability to converge faster to global solution makes it favorabletechnique compared to other stochastic optimization meth-ods like GA and simulated annealing (SA) [17ndash19] The PIDcontroller gains for both control areas optimized by GA andPSO are shown in Table 1 An algorithm is developed for thesystem under study for optimization with PSO and followingsteps are followed
Algorithm steps for PSO implementation are given below
(1) Setting parameters for PSO
(a) Define dimensions of search space(b) Define boundaries of search space (minimum
and maximum values of variables)(c) Define minimum and maximum values of par-
ticlersquos velocities
(2) Initialize population
(a) Initialize random population of swarm withinboundaries
6 Advances in Fuzzy Systems
Fuzzy logic controller Controlled output
+
+
ACEi Kemin
Ke
Kcemax
Kemax
Kce
Kcemin
Kpumin
Kpu
Kiu
Kpumax
Kiumin
Kiumax
Ui
1
s
d
dt
Figure 3 MISO-type fuzzy logic controller
VN ZMN SP VPMPSN
000
100
050
ACEidACEiUi
120583
minus1 minus075 minus050 minus025 0 025 050 075 1
Figure 4 Membership functions of inputs and output variable
(b) Set random velocities to particles of swarmwithin boundaries
(3) Evaluate the fitness of each particle position as perobjective function selected
(a) Identify each particlersquos best known position(b) Identify the best known position of swarm(c) Update the velocities and positions of particles
(4) Repeat step (3) up to either maximum iterations orconvergence criteria satisfied
32 PSO Optimized Fuzzy Logic Controller Power systemoperation and control have undergoing immense changesfrom earlier times as complexity has increased multifolddue to stress to deliver quality and uninterrupted powerto consumers These reasons have boosted power systemengineers to use intelligent control strategies in operationand control where fuzzy logic has gained popularity amongstothers because of its computing approach based on ldquodegreesof truthrdquo rather than the usual ldquotrue or falserdquo Therefore itis widely used in engineering problems Fuzzy set theoryand fuzzy logic establish the rules of a nonlinear mappingThe fuzzy logic controller modeling consists of three stepsof fuzzification determination of fuzzy control rules anddefuzzification [20] Fuzzy logic is a systematic and easier wayto implement control algorithm for uncertain and indefinitemodels in engineering and suits most AGC problem [21 22]
The comparison between the proposed TSO-FLC andGA-PID and PSO-PID controllers is quantified based on twodynamic performance indices that is peak undershoot andsettling time
Table 2 Fuzzy rules for Area 1 controller
ACEVN MN SN Z SP MP VP
ΔACE
VN VN VN VN VN SN MN SNMN VN MN SN MN VN SN SPSN VN VN VN VN Z Z ZZ MN MN N Z MP MP MPSP Z Z Z VP VP VP VPMP SN SP VP MP SP MP VPVP SP MP SP VP VP VP VP
The multi-input and single-output (MISO) type fuzzycontroller is shown in Figure 3 119870119901119906 and 119870119894119906 are the propor-tional and integral gains respectively Two inputs ACE119894 andderivative of ACE119894 that is (119889ACE119894119889119905) are fed to the fuzzycontrollerThe fuzzy logic process is initiated by fuzzificationofACE119894 and119889ACE119894119889119905Mamdani fuzzy inferencemechanismand centroid method for defuzzification are later used forrespective processes 119880119894 is a crisp value and 119906119894 is a controlsignal for the system
119906119894 = minus119870119901119906119880119894 minus 119870119894119906 int 119880119894119889119905 (19)
Membership functions (MF) specify the degree to which agiven input belongs to a set FLC has used seven membershipfunctions Very Negative (VN) Medium Negative (MN)Small Negative (SN) Zero (Z) Small Positive (SP) MediumPositive (MP) and Very Positive (VP) The membershipfunction sets of FLC for input as well as output variables areshown in Figure 4 Optimized rule base for proposed TSO-FLC for both areas is shown in Tables 2 and 3
Advances in Fuzzy Systems 7
0 5 10 15 20 25 30 35 40 45 50708709
71711712713714715716717718
Iteration
Fitn
ess v
alue
Figure 5 FLC optimization of step 1 for rule base optimization
0 10 20 30 40 50 60 70 80 90 10052545658606264666870
Iteration
Fitn
ess v
alue
Figure 6 FLC optimization of step 2 for scaling and gain factoroptimization
Table 3 Fuzzy rules for Area 2 controller
ACEVN MN SN Z SP MP VP
ΔACE
VN VN VN MN VN SN SN ZMN VN VN VN VN SN Z ZSN VN VN VN MN SN SP SPZ MN MN VN Z VP MP MPSP SN SN SP MP VP VP VPMP Z Z SP VP VP VP VPVP Z SP SP VP MP VP VP
Table 4 Optimized scaling and gain parameters for TSO-FLC
Scaling parameters Gain parameters119870119890 119870119888119890 119870119901119906 119870119894119906
FLC for Area 1 112833 093282 143489 218240FLC for Area 2 188194 056237 056237 210918
Themembership functions of each input and each outputare spread across a linear distribution range from minus1 to +1 Intwo stages FLC is optimized by PSO with objective functiongiven in (18)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
Figure 7 Comparison of GA-PID PSO-PID and TSO-FLC forreheat type two-area thermal power system (Case A) Poolco (a)frequency deviation in Area 1 and (b) frequency deviation in Area 2
Rule BaseOptimization In this step apart from center rule allother rules need to be optimized Only one rule is configuredthat when both inputs are zero then output is also zero Insystem under study out of 49 rules 48 rules are required to beoptimizedThe curve between best fitness values with respectto iteration for rule base optimization is shown in Figure 5
Scaling Factor and Gain Optimization In this second stepoptimum values of two scaling factors (119870119890 and 119870119888119890) and twogain parameters (119870119901119906 and 119870119894119906) are needed to be optimizedof FLC Graphically the best fitness values with respect toiteration are represented in Figure 6 Table 4 shows theoptimized scaling and gain parameters for TSO-FLC
4 Test Cases and Simulations
There are three different test cases of deregulated power sys-tem considered for justification of optimum performance ofproposed TSO-FLC controller as compared to conventionalGA-PID andPSO-PID controllersThese test cases are Poolcobased transactions combination of Poolco and bilateral based
8 Advances in Fuzzy Systems
Table 5 Different test cases for proposed system
Test cases cpf matrixContractedload (pu)(Δ119875LD Cont)
Uncontractedload (pu)(Δ119875LDUncont
)
Load Δ119875LD(pu)
ScheduledGENCOs
power (pu)(Δ119875119866)
Scheduled tieline powerflow (pu)(Δ119875tie12 sch)
Case A(Poolco based transactions)
[[[[[[[[[
[
05 05 0 0
05 05 0 0
0 0 05 05
0 0 05 05
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
000
000
000
000
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
0
Case B(combination of Poolco andbilateral basedtransactions)
[[[[[[[[[
[
025 020 025 0
025 020 0 0
050 030 015 0
0 030 060 1
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
000
000
000
000
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
00070
00045
00095
00190
]]]]]]]]]
]
minus00085
Case C(contract violation)
[[[[[[[[[
[
025 020 025 0
025 020 0 0
050 030 015 0
0 030 060 1
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
0000
0004
0000
0008
]]]]]]]]]
]
[[[[[[[[[
[
0010
0014
0010
0018
]]]]]]]]]
]
[[[[[[[[[
[
00090
00065
00135
00230
]]]]]]]]]
]
minus00085
Table 6 System parameters
Rated power (Area 1 and Area 2) 1198751199031 and 1198751199032 2000MW
Transfer function gain of generator (Area 1 and Area 2) 1198701199011 and 1198701199012 120
Generatorrsquos time constant (Area 1 and Area 2) 1198791199011 and 1198791199012 20
Governorrsquos time constant 1198791198921 008
Governorrsquos time constant 1198791198922 002
Steam turbinersquos time constant 119879119905 03
Regulation of the governor (Area 1 and Area 2) 1198771 and 1198772 24
Frequency bias constant 120573 0425
Synchronizing power coefficient 11988612 1
Synchronization coefficient 11987912 0545
transactions and contract violationThe cpf matrix and loadpower from each DISCO are varied in each test case asdepicted in Table 5 Apart from this all GENCOs are allowedto participate equally in each area for AGC therefore ACEparticipation factor (apf 119894) 05 is considered for simulationpurpose
The total generated power Δ119875119892(119894) required by individualGENCO is composed of all contracted and uncontractedloads Each GENCO shares the uncontracted load of its owncontrol area according to its ACE participation factor Thevalues of system parameters given in Appendix (Table 6)
are used for a comparative study Frequency deviations ofboth areas and tie line deviation after load change as per loaddistribution (Table 5) in each area for test casesA B andC areshown in Figures 7 8 and 9 respectively Two performanceindices (settling time and peak undershoot) were selected forjustification of dynamic performance response of controllersEffect of +30 and minus30 change in parameter values 120573 11987912and 119879119901 (parameters value in Table 7 in Appendix) is alsoexamined Peak undershoot and settling time of both areasand tie line deviation are also determined with +30 andminus30 change in system parameters in each area for test cases
Advances in Fuzzy Systems 9
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 8 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case B) Combination of Poolcoand bilateral contracts (a) frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Table 7 Different cases with different system parameters
119879119901 120573 11987912
Case 1 (nominal value) 20 0425 0545Case 2 (+30 increase) 26 05525 07085Case 3 (minus30 decrease) 14 02975 03815
A B and C shown in Figures 10 11 12 13 14 and 15 Thecomparison of dynamic performances of GA-PID and PSO-PID controllerswith the proposedTSO-FLC controller showsthat proposed TSO-FLC gives better results in terms of lessersettling time and peak undershoot MatlabSimulink is usedfor simulation purpose
In order to examine the performance of controllerspeak undershoot and settling time of both areas and tieline deviation are determined for test cases A B and Cwith standard values of system parameters Apart from this
the effect of +30 and minus30 change in parameter values 12057311987912 and 119879119901 (parameters value in Table 7) is also examinedso further performance indices for +30 and minus30 changein system parameters for different test cases determined areshown in Figures 10 11 12 13 14 and 15 Based on thiscomparison it can be concluded that proposed TSO-FLCgives better results in terms of lesser settling time and peakundershoot compared to GA-PID and PSO-PID controllers
5 Conclusion
In this paper an optimization strategy for FLC is proposedfor AGC This optimization strategy is based on rule baseoptimization and scaling factor and gain factor optimizationof FLC PSO is used as optimization technique The perfor-mance of proposed controller is compared with conventionalPID controller also optimized by two optimization methodsGA and PSO under different test cases based on contractual
10 Advances in Fuzzy Systems
0 5 10 15 20 25 30 35 40 45 50minus0035
minus003minus0025
minus002minus0015
minus001minus0005
00005
001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus004
minus0035minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 9 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case C) Contract violation (a)frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Case AGA-PID 002556 002064 003407 002663 002140 003561PSO-PID 002150 001714 002922 002268 001804 003080TSO-FLC 000972 000750 001380 001118 000865 001579
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)(nominal)Δf1 Δf1 Δf1
(nominal)Δf2 Δf2 Δf2
Figure 10 Peak undershoot comparison at plusmn30 variation insystem parameters for Case A
demands in deregulated power system The dynamic per-formance of proposed controllers is observed on the basisof two performance indices that is settling time and peak
1983015 1751152 2344273 1993948 1761672 23553811340694 1173940 1593159 1340694 1173940 1593159312402 120954 933828 087750 087520 395436
000000
500000
1000000
1500000
2000000
2500000
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)
Settling time (plusmn5)
Δf1 Δf1 Δf2 Δf2(nominal)
Δf1(nominal)
Δf2
Figure 11 Settling time comparison at plusmn30 variation in systemparameters for Case A
undershoot Simulation results show that proposedTSO-FLCcontroller provides a better performance in comparison of
Advances in Fuzzy Systems 11
002645002177000893
002139001732000689
003519002954001269
002714002317001363
002184001847001055
003614003129001913
Case B
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
8500E minus 0
8500E minus 0
8585E minus 0
8500E minus 0
8500E minus 0
8551E minus 0
8500E minus 0
8500E minus 0
8543E minus 0GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal) (nominal) (nominal)
Figure 12 Peak undershoot comparison at plusmn30 variation in system parameters for Case B
19690831301781383480
17569881144269294828
23292181578341545893
20689471391069278520
18352271218930235500
24063641624648279652
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
9006E + 0
2500E + 0
1559E + 0
8092E + 0
2543E + 0
1458E + 0
8668E + 0
2682E + 0
1523E + 0
Settling time (plusmn5)
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal)(nominal)(nominal)
Figure 13 Settling time comparison at plusmn30 variation in system parameters for Case B
GA-PID and PSO-PID controllers Robustness of the TSO-FLC is also justified for +30 and minus30 change in systemparameters for different sets of contractual demands andagain it is observed that TSO-FLC is a suitable controller forAGC in an interconnected power system
Appendix
Speed governor 1(1 + 119904119879119892)
Thermal reheater (1 + 119870119903119904119879119903)(1 + 119904119879119903)
Thermal turbine 1(1 + 119904119879119905)
Power system 119870119901(1 + 119904119879119901)
See Tables 6 and 7
Competing Interests
The authors declare that they have no competing interests
12 Advances in Fuzzy Systems
003448002803001143
002865002275000883
004529003775001625
004000003394001872
003212002700001445
005290004552002641
000000
001000
002000
003000
004000
005000
006000
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
Case C
Peak undershoot
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 14 Peak undershoot comparison at plusmn30 variation in system parameters for Case C
20958661452353404295
18844331286364324176
21740051495980272999
19415891329047232815
25159171748899549258
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
8465E + 0
2550E + 0
1450E + 0
7297E + 0
2553E + 0
1319E + 0
8019E + 0
2730E + 0
1396E + 0
1716E + 0
1082E + 0
2472E + 0
Settling time (plusmn5)
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 15 Settling time comparison at plusmn30 variation in system parameters for Case C
References
[1] F Daneshfar ldquoIntelligent load-frequency control in a deregu-lated environment continuous-valued input extended classifiersystem approachrdquo IET Generation Transmission and Distribu-tion vol 7 no 6 pp 551ndash559 2013
[2] I A Chidambaram and B Paramasivam ldquoOptimized load-frequency simulation in restructured power system with Redoxflow batteries and interline power flow controllerrdquo InternationalJournal of Electrical Power and Energy Systems vol 50 no 1 pp9ndash24 2013
[3] A P Sakis Meliopoulos G J Cokkinides and A G BakirtzisldquoLoad-frequency control service in a deregulated environmentrdquoDecision Support Systems vol 24 no 3-4 pp 243ndash250 1999
[4] F Liu Y H Song J Ma S Mei and Q Lu ldquoOptimalload-frequency control in restructured power systemsrdquo IEEProceedings Generation Transmission andDistribution vol 150no 1 pp 87ndash95 2003
[5] W C Chan and Y Y Hsu ldquoAutomatic generation control ofinterconnected power systems using variable-structure con-trollersrdquo IEE Proceedings C Generation Transmission and Dis-tribution vol 128 no 5 pp 269ndash279 1981
[6] S C Tripathy G S Hope and O P Malik ldquoOptimisationof load-frequency control parameters for power systems withreheat steam turbines and governor deadband nonlinearityrdquoIEE Proceedings C Generation Transmission and Distributionvol 129 no 1 pp 10ndash16 1982
Advances in Fuzzy Systems 13
[7] R D Christie and A Bose ldquoLoad frequency control issues inpower system operations after deregulationrdquo IEEE Transactionson Power Systems vol 11 no 3 pp 1191ndash1200 1995
[8] B H Bakken and O S Grande ldquoAutomatic generation controlin a deregulated power systemrdquo IEEE Transactions on PowerSystems vol 13 no 4 pp 1401ndash1406 1998
[9] V Donde M A Pai and I A Hiskens ldquoSimulation andoptimization in an AGC system after deregulationrdquo IEEETransactions on Power Systems vol 16 no 3 pp 481ndash489 2001
[10] R Roy P Bhatt and S P Ghoshal ldquoEvolutionary computationbased three-area automatic generation controlrdquo Expert Systemswith Applications vol 37 no 8 pp 5913ndash5924 2010
[11] P Bhatt R Roy and S P Ghoshal ldquoOptimized multi areaAGC simulation in restructured power systemsrdquo InternationalJournal of Electrical Power amp Energy Systems vol 32 no 4 pp311ndash322 2010
[12] S P Ghoshal ldquoOptimizations of PID gains by particle swarmoptimizations in fuzzy based automatic generation controlrdquoElectric Power Systems Research vol 72 no 3 pp 203ndash212 2004
[13] I Chiha N Liouane and P Borne ldquoTuning PID controllerusing multiobjective ant colony optimizationrdquo Applied Compu-tational Intelligence and Soft Computing vol 2012 Article ID536326 7 pages 2012
[14] V Mukherjee and S P Ghoshal ldquoIntelligent particle swarmoptimized fuzzy PID controller for AVR systemrdquo Electric PowerSystems Research vol 77 no 12 pp 1689ndash1698 2007
[15] K Naidu H Mokhlis and A H A Bakar ldquoMultiobjective opti-mization using weighted sum Artificial Bee Colony algorithmfor Load Frequency Controlrdquo International Journal of ElectricalPower and Energy Systems vol 55 pp 657ndash667 2014
[16] D Pelusi ldquoOptimization of a fuzzy logic controller using geneticalgorithmsrdquo in Proceedings of the 3rd International Conferenceon IntelligentHuman-Machine Systems andCybernetics (IHMSCrsquo11) pp 143ndash146 Zhejiang China August 2011
[17] T Chaiyatham I Ngamroo S Pothiya and S VachirasricirikulldquoDesign of optimal fuzzy logic-PID controller using bee colonyoptimization for frequency control in an isolated wind-dieselsystemrdquo in Proceedings of the Transmission amp DistributionConference amp Exposition Asia and Pacific vol 1 pp 1ndash4 IEEESeoul The Republic of Korea October 2009
[18] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 2006
[19] M Parida and J Nanda ldquoAutomatic generation control of ahydro-thermal system in deregulated environmentrdquo in Proceed-ings of the 8th International Conference on Electrical Machinesand Systems (ICEMS rsquo05) pp 942ndash947Nanjing China Septem-ber 2005
[20] C C Lee ldquoFuzzy logic in control systems fuzzy logic controllerIIrdquo IEEE Transactions on SystemsMan and Cybernetics vol 20no 2 pp 419ndash435 1990
[21] K R M Vijaya Chandrakala S Balamurugan and K Sankara-narayanan ldquoVariable structure fuzzy gain scheduling based loadfrequency controller for multi source multi area hydro thermalsystemrdquo International Journal of Electrical Power and EnergySystems vol 53 no 1 pp 375ndash381 2013
[22] Y K Bhateshvar and H D Mathur ldquoFrequency stabilizationusing fuzzy logic based controller for multi-area power systemin deregulated environmentrdquo in Proceedings of the 2nd Inter-national Conference on Advances in Control and Optimizationof Dynamical Systems (ACODS rsquo12) pp 1ndash10 Bangalore IndiaFebruary 2012
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Fuzzy Systems 3
PowerSystem 2
Speedgovernor
Reheater
Turbine
Speedgovernor
Reheater
Turbine
PowerSystem 1
Speedgovernor
Reheater
Turbine
Speedgovernor
Reheater
Turbine
TSO-FLC 1 TSO-FLC 2
Ther
mal
-reh
eat G
ENCO
1
Ther
mal
-reh
eat G
ENCO
2
Ther
mal
-reh
eat G
ENCO
3
Ther
mal
-reh
eat G
ENCO
4
Scheduledpower
+ +
+
+
+ +++
+
+
+ + +
Power demandof Area 1
DISCO 1 DISCO 2 DISCO 4DISCO 3
Demand fromGENCO 1
Demand fromGENCO 1
Demand fromGENCO 2
Demand fromGENCO 2
Demand fromGENCO 4
Demand fromGENCO 4
Demand fromGENCO 3
Demand fromGENCO 3
1205731
1
R1
1
R2
1205732a12
1
R3
1
R4
T12s
minus
minus minus
minus
minus minus
minusminus minus
minus
minus minus
cpf 14
cpf 13
cpf 12
cpf 11
cpf 24
cpf 23
cpf 22
cpf 21
cpf 34
cpf 33
cpf 32
cpf 31
cpf 44
cpf 43
cpf 42
cpf 41
apf1 apf2 apf3 apf4
Power demandof Area 2
Δf1 Δf2
Figure 1 Block diagram representing a two-area interconnected power system
Δ119875LD Uncont =
[[[[[
[
Δ119875Ld1 Uncont
Δ119875Ld2 Uncont
Δ119875Ld3 Uncont
Δ119875Ld4 Uncont
]]]]]
]
(5)
The total distributed power by 119895th DISCO
Δ119875Ld(119895) = Δ119875Ld(119895) Cont + Δ119875Ld(119895) Uncont (6)
where Δ119875Ld(119895) Cont is contracted can be shown throughcpf matrix but uncontracted power for 119895th DISCO is out ofscope of cpf matrix
4 Advances in Fuzzy Systems
+ + + + + + ++
+
Contracted demandfrom GENCO 4 to
Area 1 DISCOs
Contracted demandfrom GENCO 2 to
Area 2 DISCOs
Contracted demandfrom GENCO 1 to
Area 2 DISCOs
Contracted demandfrom GENCO 3 to
Area 1 DISCOs
+ + + +
ΔPtie12_sch
ΔP
Ld3_
Con
t
ΔP
Ld3_
Con
t
ΔP
Ld1_
Con
t
ΔP
Ld1_
Con
t
ΔP
Ld2_
Con
t
ΔP
Ld2_
Con
t
ΔP
Ld4_
Con
t
ΔP
Ld4_
Con
t
cpf 13
cpf 14
cpf 23
cpf 24
cpf 31
cpf 32
cpf 41
cpf 42
minus
ΔPLA1rarrA2 ΔPLA2rarrA1
Figure 2 The block diagram representation of scheduled 119875tie12
The total distributed power shown in matrix Δ119875LD is
Δ119875LD = Δ119875LD Cont + Δ119875LD Uncont (7)
Similar to this total generated powers through GENCOs inArea 1 are Δ1198751198921 and Δ1198751198922 and in Area 2 are Δ1198751198923 and Δ1198751198924
and these are shown in the Δ119875119866 matrixThe contracted generated powers in Area
1 are Δ1198751198921 Cont amp Δ1198751198922 Cont and in Area 2 areΔ1198751198923 Cont amp Δ1198751198924 Cont shown in Δ119875119866 Cont matrix
Δ119875119866 Cont =
[[[[
[
Δ1198751198921 ContΔ1198751198922 ContΔ1198751198923 ContΔ1198751198924 Cont
]]]]
]
(8)
Theuncontracted powers demanded under contract violationrequired in Area 1 and Area 2 are referred to as Δ1198751198711LOC andΔ1198751198712LOC is required power by local GENCOs only in thatareaThat required power fromGENCOs shown inΔ119875119866 Uncontmatrix
Δ119875119866 Uncont =
[[[[
[
Δ1198751198921 UncontΔ1198751198922 UncontΔ1198751198923 UncontΔ1198751198924 Uncont
]]]]
]
(9)
where Δ1198751198921 Uncont and Δ1198751198922 Uncont are uncontracted requiredpower from GENCO 1 and GENCO 2 in Area 1 andΔ1198751198923 Uncont and Δ1198751198924 Uncont are uncontracted required powerfrom GENCO 3 and GENCO 4 in Area 2
Δ119875119871(119896)LOC = sum
119894
Δ119875119892(119894) Uncont (10)
where 119894 referred to GENCOs within 119896th control area
And Δ119875119892(119894) Uncont is calculated from equation
Δ119875119892(119894) Uncont = apf 119894 lowast sum
119895
Δ119875Ld(119895) Uncont (11)
Or in matrix form
Δ119875119866 Uncont = apf matrix lowast Δ119875LD Uncont (12)
So total required generation power in matrix form is repre-sented as
Δ119875119866 = Δ119875119866 Cont + Δ119875119866 Uncont
Δ119875119866 = cpfmatrix lowast Δ119875LD Cont + apfmatrix lowast Δ119875LD Uncont(13)
The total generation required of individual GENCOs can becalculated also from equation
Δ119875119892(119894) = sum
119895
(cpf 119894119895 lowast Δ119875Ld(119895) Cont) + apf 119894
lowast sum
119895
Δ119875Ld(119895) Uncont(14)
So total demanded power from GENCOs is shown in Δ119875119866
matrix
Δ119875119866 =
[[[
[
Δ1198751198921
Δ1198751198922
Δ1198751198923
Δ1198751198924
]]]
]
(15)
The scheduled tie line power flow between Areas 1 and 2shown in block diagram in Figure 2 can be represented by
Δ119875tie12 sch = (cpf13 lowast Δ119875Ld3Cont + cpf23 lowast Δ119875Ld3 Cont
+ cpf14 lowast Δ119875Ld4 Cont + cpf24 lowast Δ119875Ld4 Cont)
Advances in Fuzzy Systems 5
Table 1 PID controller gains from optimization method
S no Area 1 PID gains Area 2 PID gains
1 GA optimizedPID controller gains
119870119901 059226 100299119870119894 073350 084666119870119889 062571 045060
2 PSO optimizedPID controller gains
119870119901 067927 095495119870119894 160343 172912119870119889 096307 078236
minus (cpf31 lowast Δ119875Ld1 Cont + cpf41 lowast Δ119875Ld1 Cont
+ cpf32 lowast Δ119875Ld2 Cont + cpf42 lowast Δ119875Ld2 Cont)
(16)
3 Control Strategies
In this paper two different control strategies are exploredThefirst control strategy is conventional proportional-integral-derivative (PID) control and another is artificial intelligencebased fuzzy logic control (FLC) PID controller is optimizedby two different stochastic optimization techniques GA andPSO and later PSO based optimized FLC is proposed whereFLC parameters are optimized in two different stages
31 PID Controller PID controller is selected as controllerfor AGC and GA and PSO are used for optimizing of gainparameters that is 119870119901 119870119894 and 119870119889 ACE119894 is selected ascontroller input and 119880PID is output of controller as given in
119880PID = 119870119901 (ACE119894) + 119870119894 (intACE119894119889119905)
+ 119870119889 (119889ACE119894
119889119905
)
(17)
311 Genetic Algorithm The genetic algorithm (GA) isinspired by the principles of genetics and evolution Itmimics the reproduction behavior observed in biologicalpopulations The GA employs the principle of ldquosurvivalof the fittestrdquo in its search process to select and generateindividuals that are adapted to their environment Thereforeover a number of generations desirable traits will evolveand remain in the genome composition of the populationover traits with weaker undesirable characteristics The GAis well suited to and has been extensively applied to solvecomplex design optimization problems because it can handleboth discrete and continuous variables and nonlinear objec-tive and constrained functions without requiring gradientinformation [13 15ndash17] The AGC modeled has an objective
function for PID optimization as given in (18) which is aimedfor minimization of peak undershoots and settling time offrequency and tie line deviation
119869OBJ = int
119879
0
(120582 (10038161003816100381610038161003816PUΔ119891
1
10038161003816100381610038161003816+
10038161003816100381610038161003816PUΔ119891
2
10038161003816100381610038161003816+ 120583
10038161003816100381610038161003816PUΔ119875tie12
10038161003816100381610038161003816)
+ (STΔ1198911
+ STΔ1198912
+ STΔ119875tie12)) 119889119905
(18)
Here 120582 120583 and 119879 are selected as 10 500 and 50respectively
312 Particle SwarmOptimization Particle swarmoptimiza-tion (PSO) is a heuristic search method which is by theswarming or collaborative behavior of biological populationsIn PSO a set of randomly generated solutions (initial swarm)propagates in the design space towards the optimal solutionover a number of iterations (moves) based on large amount ofinformation about the design space that is assimilated andshared by all members of the swarm PSO is inspired by theability of flocks of birds schools of fish and herds of animalsto adapt to their environment find rich sources of food andavoid predators by implementing an ldquoinformation sharingrdquoapproach hence developing an evolutionary advantage Itsability to converge faster to global solution makes it favorabletechnique compared to other stochastic optimization meth-ods like GA and simulated annealing (SA) [17ndash19] The PIDcontroller gains for both control areas optimized by GA andPSO are shown in Table 1 An algorithm is developed for thesystem under study for optimization with PSO and followingsteps are followed
Algorithm steps for PSO implementation are given below
(1) Setting parameters for PSO
(a) Define dimensions of search space(b) Define boundaries of search space (minimum
and maximum values of variables)(c) Define minimum and maximum values of par-
ticlersquos velocities
(2) Initialize population
(a) Initialize random population of swarm withinboundaries
6 Advances in Fuzzy Systems
Fuzzy logic controller Controlled output
+
+
ACEi Kemin
Ke
Kcemax
Kemax
Kce
Kcemin
Kpumin
Kpu
Kiu
Kpumax
Kiumin
Kiumax
Ui
1
s
d
dt
Figure 3 MISO-type fuzzy logic controller
VN ZMN SP VPMPSN
000
100
050
ACEidACEiUi
120583
minus1 minus075 minus050 minus025 0 025 050 075 1
Figure 4 Membership functions of inputs and output variable
(b) Set random velocities to particles of swarmwithin boundaries
(3) Evaluate the fitness of each particle position as perobjective function selected
(a) Identify each particlersquos best known position(b) Identify the best known position of swarm(c) Update the velocities and positions of particles
(4) Repeat step (3) up to either maximum iterations orconvergence criteria satisfied
32 PSO Optimized Fuzzy Logic Controller Power systemoperation and control have undergoing immense changesfrom earlier times as complexity has increased multifolddue to stress to deliver quality and uninterrupted powerto consumers These reasons have boosted power systemengineers to use intelligent control strategies in operationand control where fuzzy logic has gained popularity amongstothers because of its computing approach based on ldquodegreesof truthrdquo rather than the usual ldquotrue or falserdquo Therefore itis widely used in engineering problems Fuzzy set theoryand fuzzy logic establish the rules of a nonlinear mappingThe fuzzy logic controller modeling consists of three stepsof fuzzification determination of fuzzy control rules anddefuzzification [20] Fuzzy logic is a systematic and easier wayto implement control algorithm for uncertain and indefinitemodels in engineering and suits most AGC problem [21 22]
The comparison between the proposed TSO-FLC andGA-PID and PSO-PID controllers is quantified based on twodynamic performance indices that is peak undershoot andsettling time
Table 2 Fuzzy rules for Area 1 controller
ACEVN MN SN Z SP MP VP
ΔACE
VN VN VN VN VN SN MN SNMN VN MN SN MN VN SN SPSN VN VN VN VN Z Z ZZ MN MN N Z MP MP MPSP Z Z Z VP VP VP VPMP SN SP VP MP SP MP VPVP SP MP SP VP VP VP VP
The multi-input and single-output (MISO) type fuzzycontroller is shown in Figure 3 119870119901119906 and 119870119894119906 are the propor-tional and integral gains respectively Two inputs ACE119894 andderivative of ACE119894 that is (119889ACE119894119889119905) are fed to the fuzzycontrollerThe fuzzy logic process is initiated by fuzzificationofACE119894 and119889ACE119894119889119905Mamdani fuzzy inferencemechanismand centroid method for defuzzification are later used forrespective processes 119880119894 is a crisp value and 119906119894 is a controlsignal for the system
119906119894 = minus119870119901119906119880119894 minus 119870119894119906 int 119880119894119889119905 (19)
Membership functions (MF) specify the degree to which agiven input belongs to a set FLC has used seven membershipfunctions Very Negative (VN) Medium Negative (MN)Small Negative (SN) Zero (Z) Small Positive (SP) MediumPositive (MP) and Very Positive (VP) The membershipfunction sets of FLC for input as well as output variables areshown in Figure 4 Optimized rule base for proposed TSO-FLC for both areas is shown in Tables 2 and 3
Advances in Fuzzy Systems 7
0 5 10 15 20 25 30 35 40 45 50708709
71711712713714715716717718
Iteration
Fitn
ess v
alue
Figure 5 FLC optimization of step 1 for rule base optimization
0 10 20 30 40 50 60 70 80 90 10052545658606264666870
Iteration
Fitn
ess v
alue
Figure 6 FLC optimization of step 2 for scaling and gain factoroptimization
Table 3 Fuzzy rules for Area 2 controller
ACEVN MN SN Z SP MP VP
ΔACE
VN VN VN MN VN SN SN ZMN VN VN VN VN SN Z ZSN VN VN VN MN SN SP SPZ MN MN VN Z VP MP MPSP SN SN SP MP VP VP VPMP Z Z SP VP VP VP VPVP Z SP SP VP MP VP VP
Table 4 Optimized scaling and gain parameters for TSO-FLC
Scaling parameters Gain parameters119870119890 119870119888119890 119870119901119906 119870119894119906
FLC for Area 1 112833 093282 143489 218240FLC for Area 2 188194 056237 056237 210918
Themembership functions of each input and each outputare spread across a linear distribution range from minus1 to +1 Intwo stages FLC is optimized by PSO with objective functiongiven in (18)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
Figure 7 Comparison of GA-PID PSO-PID and TSO-FLC forreheat type two-area thermal power system (Case A) Poolco (a)frequency deviation in Area 1 and (b) frequency deviation in Area 2
Rule BaseOptimization In this step apart from center rule allother rules need to be optimized Only one rule is configuredthat when both inputs are zero then output is also zero Insystem under study out of 49 rules 48 rules are required to beoptimizedThe curve between best fitness values with respectto iteration for rule base optimization is shown in Figure 5
Scaling Factor and Gain Optimization In this second stepoptimum values of two scaling factors (119870119890 and 119870119888119890) and twogain parameters (119870119901119906 and 119870119894119906) are needed to be optimizedof FLC Graphically the best fitness values with respect toiteration are represented in Figure 6 Table 4 shows theoptimized scaling and gain parameters for TSO-FLC
4 Test Cases and Simulations
There are three different test cases of deregulated power sys-tem considered for justification of optimum performance ofproposed TSO-FLC controller as compared to conventionalGA-PID andPSO-PID controllersThese test cases are Poolcobased transactions combination of Poolco and bilateral based
8 Advances in Fuzzy Systems
Table 5 Different test cases for proposed system
Test cases cpf matrixContractedload (pu)(Δ119875LD Cont)
Uncontractedload (pu)(Δ119875LDUncont
)
Load Δ119875LD(pu)
ScheduledGENCOs
power (pu)(Δ119875119866)
Scheduled tieline powerflow (pu)(Δ119875tie12 sch)
Case A(Poolco based transactions)
[[[[[[[[[
[
05 05 0 0
05 05 0 0
0 0 05 05
0 0 05 05
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
000
000
000
000
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
0
Case B(combination of Poolco andbilateral basedtransactions)
[[[[[[[[[
[
025 020 025 0
025 020 0 0
050 030 015 0
0 030 060 1
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
000
000
000
000
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
00070
00045
00095
00190
]]]]]]]]]
]
minus00085
Case C(contract violation)
[[[[[[[[[
[
025 020 025 0
025 020 0 0
050 030 015 0
0 030 060 1
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
0000
0004
0000
0008
]]]]]]]]]
]
[[[[[[[[[
[
0010
0014
0010
0018
]]]]]]]]]
]
[[[[[[[[[
[
00090
00065
00135
00230
]]]]]]]]]
]
minus00085
Table 6 System parameters
Rated power (Area 1 and Area 2) 1198751199031 and 1198751199032 2000MW
Transfer function gain of generator (Area 1 and Area 2) 1198701199011 and 1198701199012 120
Generatorrsquos time constant (Area 1 and Area 2) 1198791199011 and 1198791199012 20
Governorrsquos time constant 1198791198921 008
Governorrsquos time constant 1198791198922 002
Steam turbinersquos time constant 119879119905 03
Regulation of the governor (Area 1 and Area 2) 1198771 and 1198772 24
Frequency bias constant 120573 0425
Synchronizing power coefficient 11988612 1
Synchronization coefficient 11987912 0545
transactions and contract violationThe cpf matrix and loadpower from each DISCO are varied in each test case asdepicted in Table 5 Apart from this all GENCOs are allowedto participate equally in each area for AGC therefore ACEparticipation factor (apf 119894) 05 is considered for simulationpurpose
The total generated power Δ119875119892(119894) required by individualGENCO is composed of all contracted and uncontractedloads Each GENCO shares the uncontracted load of its owncontrol area according to its ACE participation factor Thevalues of system parameters given in Appendix (Table 6)
are used for a comparative study Frequency deviations ofboth areas and tie line deviation after load change as per loaddistribution (Table 5) in each area for test casesA B andC areshown in Figures 7 8 and 9 respectively Two performanceindices (settling time and peak undershoot) were selected forjustification of dynamic performance response of controllersEffect of +30 and minus30 change in parameter values 120573 11987912and 119879119901 (parameters value in Table 7 in Appendix) is alsoexamined Peak undershoot and settling time of both areasand tie line deviation are also determined with +30 andminus30 change in system parameters in each area for test cases
Advances in Fuzzy Systems 9
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 8 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case B) Combination of Poolcoand bilateral contracts (a) frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Table 7 Different cases with different system parameters
119879119901 120573 11987912
Case 1 (nominal value) 20 0425 0545Case 2 (+30 increase) 26 05525 07085Case 3 (minus30 decrease) 14 02975 03815
A B and C shown in Figures 10 11 12 13 14 and 15 Thecomparison of dynamic performances of GA-PID and PSO-PID controllerswith the proposedTSO-FLC controller showsthat proposed TSO-FLC gives better results in terms of lessersettling time and peak undershoot MatlabSimulink is usedfor simulation purpose
In order to examine the performance of controllerspeak undershoot and settling time of both areas and tieline deviation are determined for test cases A B and Cwith standard values of system parameters Apart from this
the effect of +30 and minus30 change in parameter values 12057311987912 and 119879119901 (parameters value in Table 7) is also examinedso further performance indices for +30 and minus30 changein system parameters for different test cases determined areshown in Figures 10 11 12 13 14 and 15 Based on thiscomparison it can be concluded that proposed TSO-FLCgives better results in terms of lesser settling time and peakundershoot compared to GA-PID and PSO-PID controllers
5 Conclusion
In this paper an optimization strategy for FLC is proposedfor AGC This optimization strategy is based on rule baseoptimization and scaling factor and gain factor optimizationof FLC PSO is used as optimization technique The perfor-mance of proposed controller is compared with conventionalPID controller also optimized by two optimization methodsGA and PSO under different test cases based on contractual
10 Advances in Fuzzy Systems
0 5 10 15 20 25 30 35 40 45 50minus0035
minus003minus0025
minus002minus0015
minus001minus0005
00005
001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus004
minus0035minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 9 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case C) Contract violation (a)frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Case AGA-PID 002556 002064 003407 002663 002140 003561PSO-PID 002150 001714 002922 002268 001804 003080TSO-FLC 000972 000750 001380 001118 000865 001579
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)(nominal)Δf1 Δf1 Δf1
(nominal)Δf2 Δf2 Δf2
Figure 10 Peak undershoot comparison at plusmn30 variation insystem parameters for Case A
demands in deregulated power system The dynamic per-formance of proposed controllers is observed on the basisof two performance indices that is settling time and peak
1983015 1751152 2344273 1993948 1761672 23553811340694 1173940 1593159 1340694 1173940 1593159312402 120954 933828 087750 087520 395436
000000
500000
1000000
1500000
2000000
2500000
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)
Settling time (plusmn5)
Δf1 Δf1 Δf2 Δf2(nominal)
Δf1(nominal)
Δf2
Figure 11 Settling time comparison at plusmn30 variation in systemparameters for Case A
undershoot Simulation results show that proposedTSO-FLCcontroller provides a better performance in comparison of
Advances in Fuzzy Systems 11
002645002177000893
002139001732000689
003519002954001269
002714002317001363
002184001847001055
003614003129001913
Case B
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
8500E minus 0
8500E minus 0
8585E minus 0
8500E minus 0
8500E minus 0
8551E minus 0
8500E minus 0
8500E minus 0
8543E minus 0GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal) (nominal) (nominal)
Figure 12 Peak undershoot comparison at plusmn30 variation in system parameters for Case B
19690831301781383480
17569881144269294828
23292181578341545893
20689471391069278520
18352271218930235500
24063641624648279652
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
9006E + 0
2500E + 0
1559E + 0
8092E + 0
2543E + 0
1458E + 0
8668E + 0
2682E + 0
1523E + 0
Settling time (plusmn5)
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal)(nominal)(nominal)
Figure 13 Settling time comparison at plusmn30 variation in system parameters for Case B
GA-PID and PSO-PID controllers Robustness of the TSO-FLC is also justified for +30 and minus30 change in systemparameters for different sets of contractual demands andagain it is observed that TSO-FLC is a suitable controller forAGC in an interconnected power system
Appendix
Speed governor 1(1 + 119904119879119892)
Thermal reheater (1 + 119870119903119904119879119903)(1 + 119904119879119903)
Thermal turbine 1(1 + 119904119879119905)
Power system 119870119901(1 + 119904119879119901)
See Tables 6 and 7
Competing Interests
The authors declare that they have no competing interests
12 Advances in Fuzzy Systems
003448002803001143
002865002275000883
004529003775001625
004000003394001872
003212002700001445
005290004552002641
000000
001000
002000
003000
004000
005000
006000
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
Case C
Peak undershoot
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 14 Peak undershoot comparison at plusmn30 variation in system parameters for Case C
20958661452353404295
18844331286364324176
21740051495980272999
19415891329047232815
25159171748899549258
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
8465E + 0
2550E + 0
1450E + 0
7297E + 0
2553E + 0
1319E + 0
8019E + 0
2730E + 0
1396E + 0
1716E + 0
1082E + 0
2472E + 0
Settling time (plusmn5)
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 15 Settling time comparison at plusmn30 variation in system parameters for Case C
References
[1] F Daneshfar ldquoIntelligent load-frequency control in a deregu-lated environment continuous-valued input extended classifiersystem approachrdquo IET Generation Transmission and Distribu-tion vol 7 no 6 pp 551ndash559 2013
[2] I A Chidambaram and B Paramasivam ldquoOptimized load-frequency simulation in restructured power system with Redoxflow batteries and interline power flow controllerrdquo InternationalJournal of Electrical Power and Energy Systems vol 50 no 1 pp9ndash24 2013
[3] A P Sakis Meliopoulos G J Cokkinides and A G BakirtzisldquoLoad-frequency control service in a deregulated environmentrdquoDecision Support Systems vol 24 no 3-4 pp 243ndash250 1999
[4] F Liu Y H Song J Ma S Mei and Q Lu ldquoOptimalload-frequency control in restructured power systemsrdquo IEEProceedings Generation Transmission andDistribution vol 150no 1 pp 87ndash95 2003
[5] W C Chan and Y Y Hsu ldquoAutomatic generation control ofinterconnected power systems using variable-structure con-trollersrdquo IEE Proceedings C Generation Transmission and Dis-tribution vol 128 no 5 pp 269ndash279 1981
[6] S C Tripathy G S Hope and O P Malik ldquoOptimisationof load-frequency control parameters for power systems withreheat steam turbines and governor deadband nonlinearityrdquoIEE Proceedings C Generation Transmission and Distributionvol 129 no 1 pp 10ndash16 1982
Advances in Fuzzy Systems 13
[7] R D Christie and A Bose ldquoLoad frequency control issues inpower system operations after deregulationrdquo IEEE Transactionson Power Systems vol 11 no 3 pp 1191ndash1200 1995
[8] B H Bakken and O S Grande ldquoAutomatic generation controlin a deregulated power systemrdquo IEEE Transactions on PowerSystems vol 13 no 4 pp 1401ndash1406 1998
[9] V Donde M A Pai and I A Hiskens ldquoSimulation andoptimization in an AGC system after deregulationrdquo IEEETransactions on Power Systems vol 16 no 3 pp 481ndash489 2001
[10] R Roy P Bhatt and S P Ghoshal ldquoEvolutionary computationbased three-area automatic generation controlrdquo Expert Systemswith Applications vol 37 no 8 pp 5913ndash5924 2010
[11] P Bhatt R Roy and S P Ghoshal ldquoOptimized multi areaAGC simulation in restructured power systemsrdquo InternationalJournal of Electrical Power amp Energy Systems vol 32 no 4 pp311ndash322 2010
[12] S P Ghoshal ldquoOptimizations of PID gains by particle swarmoptimizations in fuzzy based automatic generation controlrdquoElectric Power Systems Research vol 72 no 3 pp 203ndash212 2004
[13] I Chiha N Liouane and P Borne ldquoTuning PID controllerusing multiobjective ant colony optimizationrdquo Applied Compu-tational Intelligence and Soft Computing vol 2012 Article ID536326 7 pages 2012
[14] V Mukherjee and S P Ghoshal ldquoIntelligent particle swarmoptimized fuzzy PID controller for AVR systemrdquo Electric PowerSystems Research vol 77 no 12 pp 1689ndash1698 2007
[15] K Naidu H Mokhlis and A H A Bakar ldquoMultiobjective opti-mization using weighted sum Artificial Bee Colony algorithmfor Load Frequency Controlrdquo International Journal of ElectricalPower and Energy Systems vol 55 pp 657ndash667 2014
[16] D Pelusi ldquoOptimization of a fuzzy logic controller using geneticalgorithmsrdquo in Proceedings of the 3rd International Conferenceon IntelligentHuman-Machine Systems andCybernetics (IHMSCrsquo11) pp 143ndash146 Zhejiang China August 2011
[17] T Chaiyatham I Ngamroo S Pothiya and S VachirasricirikulldquoDesign of optimal fuzzy logic-PID controller using bee colonyoptimization for frequency control in an isolated wind-dieselsystemrdquo in Proceedings of the Transmission amp DistributionConference amp Exposition Asia and Pacific vol 1 pp 1ndash4 IEEESeoul The Republic of Korea October 2009
[18] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 2006
[19] M Parida and J Nanda ldquoAutomatic generation control of ahydro-thermal system in deregulated environmentrdquo in Proceed-ings of the 8th International Conference on Electrical Machinesand Systems (ICEMS rsquo05) pp 942ndash947Nanjing China Septem-ber 2005
[20] C C Lee ldquoFuzzy logic in control systems fuzzy logic controllerIIrdquo IEEE Transactions on SystemsMan and Cybernetics vol 20no 2 pp 419ndash435 1990
[21] K R M Vijaya Chandrakala S Balamurugan and K Sankara-narayanan ldquoVariable structure fuzzy gain scheduling based loadfrequency controller for multi source multi area hydro thermalsystemrdquo International Journal of Electrical Power and EnergySystems vol 53 no 1 pp 375ndash381 2013
[22] Y K Bhateshvar and H D Mathur ldquoFrequency stabilizationusing fuzzy logic based controller for multi-area power systemin deregulated environmentrdquo in Proceedings of the 2nd Inter-national Conference on Advances in Control and Optimizationof Dynamical Systems (ACODS rsquo12) pp 1ndash10 Bangalore IndiaFebruary 2012
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
4 Advances in Fuzzy Systems
+ + + + + + ++
+
Contracted demandfrom GENCO 4 to
Area 1 DISCOs
Contracted demandfrom GENCO 2 to
Area 2 DISCOs
Contracted demandfrom GENCO 1 to
Area 2 DISCOs
Contracted demandfrom GENCO 3 to
Area 1 DISCOs
+ + + +
ΔPtie12_sch
ΔP
Ld3_
Con
t
ΔP
Ld3_
Con
t
ΔP
Ld1_
Con
t
ΔP
Ld1_
Con
t
ΔP
Ld2_
Con
t
ΔP
Ld2_
Con
t
ΔP
Ld4_
Con
t
ΔP
Ld4_
Con
t
cpf 13
cpf 14
cpf 23
cpf 24
cpf 31
cpf 32
cpf 41
cpf 42
minus
ΔPLA1rarrA2 ΔPLA2rarrA1
Figure 2 The block diagram representation of scheduled 119875tie12
The total distributed power shown in matrix Δ119875LD is
Δ119875LD = Δ119875LD Cont + Δ119875LD Uncont (7)
Similar to this total generated powers through GENCOs inArea 1 are Δ1198751198921 and Δ1198751198922 and in Area 2 are Δ1198751198923 and Δ1198751198924
and these are shown in the Δ119875119866 matrixThe contracted generated powers in Area
1 are Δ1198751198921 Cont amp Δ1198751198922 Cont and in Area 2 areΔ1198751198923 Cont amp Δ1198751198924 Cont shown in Δ119875119866 Cont matrix
Δ119875119866 Cont =
[[[[
[
Δ1198751198921 ContΔ1198751198922 ContΔ1198751198923 ContΔ1198751198924 Cont
]]]]
]
(8)
Theuncontracted powers demanded under contract violationrequired in Area 1 and Area 2 are referred to as Δ1198751198711LOC andΔ1198751198712LOC is required power by local GENCOs only in thatareaThat required power fromGENCOs shown inΔ119875119866 Uncontmatrix
Δ119875119866 Uncont =
[[[[
[
Δ1198751198921 UncontΔ1198751198922 UncontΔ1198751198923 UncontΔ1198751198924 Uncont
]]]]
]
(9)
where Δ1198751198921 Uncont and Δ1198751198922 Uncont are uncontracted requiredpower from GENCO 1 and GENCO 2 in Area 1 andΔ1198751198923 Uncont and Δ1198751198924 Uncont are uncontracted required powerfrom GENCO 3 and GENCO 4 in Area 2
Δ119875119871(119896)LOC = sum
119894
Δ119875119892(119894) Uncont (10)
where 119894 referred to GENCOs within 119896th control area
And Δ119875119892(119894) Uncont is calculated from equation
Δ119875119892(119894) Uncont = apf 119894 lowast sum
119895
Δ119875Ld(119895) Uncont (11)
Or in matrix form
Δ119875119866 Uncont = apf matrix lowast Δ119875LD Uncont (12)
So total required generation power in matrix form is repre-sented as
Δ119875119866 = Δ119875119866 Cont + Δ119875119866 Uncont
Δ119875119866 = cpfmatrix lowast Δ119875LD Cont + apfmatrix lowast Δ119875LD Uncont(13)
The total generation required of individual GENCOs can becalculated also from equation
Δ119875119892(119894) = sum
119895
(cpf 119894119895 lowast Δ119875Ld(119895) Cont) + apf 119894
lowast sum
119895
Δ119875Ld(119895) Uncont(14)
So total demanded power from GENCOs is shown in Δ119875119866
matrix
Δ119875119866 =
[[[
[
Δ1198751198921
Δ1198751198922
Δ1198751198923
Δ1198751198924
]]]
]
(15)
The scheduled tie line power flow between Areas 1 and 2shown in block diagram in Figure 2 can be represented by
Δ119875tie12 sch = (cpf13 lowast Δ119875Ld3Cont + cpf23 lowast Δ119875Ld3 Cont
+ cpf14 lowast Δ119875Ld4 Cont + cpf24 lowast Δ119875Ld4 Cont)
Advances in Fuzzy Systems 5
Table 1 PID controller gains from optimization method
S no Area 1 PID gains Area 2 PID gains
1 GA optimizedPID controller gains
119870119901 059226 100299119870119894 073350 084666119870119889 062571 045060
2 PSO optimizedPID controller gains
119870119901 067927 095495119870119894 160343 172912119870119889 096307 078236
minus (cpf31 lowast Δ119875Ld1 Cont + cpf41 lowast Δ119875Ld1 Cont
+ cpf32 lowast Δ119875Ld2 Cont + cpf42 lowast Δ119875Ld2 Cont)
(16)
3 Control Strategies
In this paper two different control strategies are exploredThefirst control strategy is conventional proportional-integral-derivative (PID) control and another is artificial intelligencebased fuzzy logic control (FLC) PID controller is optimizedby two different stochastic optimization techniques GA andPSO and later PSO based optimized FLC is proposed whereFLC parameters are optimized in two different stages
31 PID Controller PID controller is selected as controllerfor AGC and GA and PSO are used for optimizing of gainparameters that is 119870119901 119870119894 and 119870119889 ACE119894 is selected ascontroller input and 119880PID is output of controller as given in
119880PID = 119870119901 (ACE119894) + 119870119894 (intACE119894119889119905)
+ 119870119889 (119889ACE119894
119889119905
)
(17)
311 Genetic Algorithm The genetic algorithm (GA) isinspired by the principles of genetics and evolution Itmimics the reproduction behavior observed in biologicalpopulations The GA employs the principle of ldquosurvivalof the fittestrdquo in its search process to select and generateindividuals that are adapted to their environment Thereforeover a number of generations desirable traits will evolveand remain in the genome composition of the populationover traits with weaker undesirable characteristics The GAis well suited to and has been extensively applied to solvecomplex design optimization problems because it can handleboth discrete and continuous variables and nonlinear objec-tive and constrained functions without requiring gradientinformation [13 15ndash17] The AGC modeled has an objective
function for PID optimization as given in (18) which is aimedfor minimization of peak undershoots and settling time offrequency and tie line deviation
119869OBJ = int
119879
0
(120582 (10038161003816100381610038161003816PUΔ119891
1
10038161003816100381610038161003816+
10038161003816100381610038161003816PUΔ119891
2
10038161003816100381610038161003816+ 120583
10038161003816100381610038161003816PUΔ119875tie12
10038161003816100381610038161003816)
+ (STΔ1198911
+ STΔ1198912
+ STΔ119875tie12)) 119889119905
(18)
Here 120582 120583 and 119879 are selected as 10 500 and 50respectively
312 Particle SwarmOptimization Particle swarmoptimiza-tion (PSO) is a heuristic search method which is by theswarming or collaborative behavior of biological populationsIn PSO a set of randomly generated solutions (initial swarm)propagates in the design space towards the optimal solutionover a number of iterations (moves) based on large amount ofinformation about the design space that is assimilated andshared by all members of the swarm PSO is inspired by theability of flocks of birds schools of fish and herds of animalsto adapt to their environment find rich sources of food andavoid predators by implementing an ldquoinformation sharingrdquoapproach hence developing an evolutionary advantage Itsability to converge faster to global solution makes it favorabletechnique compared to other stochastic optimization meth-ods like GA and simulated annealing (SA) [17ndash19] The PIDcontroller gains for both control areas optimized by GA andPSO are shown in Table 1 An algorithm is developed for thesystem under study for optimization with PSO and followingsteps are followed
Algorithm steps for PSO implementation are given below
(1) Setting parameters for PSO
(a) Define dimensions of search space(b) Define boundaries of search space (minimum
and maximum values of variables)(c) Define minimum and maximum values of par-
ticlersquos velocities
(2) Initialize population
(a) Initialize random population of swarm withinboundaries
6 Advances in Fuzzy Systems
Fuzzy logic controller Controlled output
+
+
ACEi Kemin
Ke
Kcemax
Kemax
Kce
Kcemin
Kpumin
Kpu
Kiu
Kpumax
Kiumin
Kiumax
Ui
1
s
d
dt
Figure 3 MISO-type fuzzy logic controller
VN ZMN SP VPMPSN
000
100
050
ACEidACEiUi
120583
minus1 minus075 minus050 minus025 0 025 050 075 1
Figure 4 Membership functions of inputs and output variable
(b) Set random velocities to particles of swarmwithin boundaries
(3) Evaluate the fitness of each particle position as perobjective function selected
(a) Identify each particlersquos best known position(b) Identify the best known position of swarm(c) Update the velocities and positions of particles
(4) Repeat step (3) up to either maximum iterations orconvergence criteria satisfied
32 PSO Optimized Fuzzy Logic Controller Power systemoperation and control have undergoing immense changesfrom earlier times as complexity has increased multifolddue to stress to deliver quality and uninterrupted powerto consumers These reasons have boosted power systemengineers to use intelligent control strategies in operationand control where fuzzy logic has gained popularity amongstothers because of its computing approach based on ldquodegreesof truthrdquo rather than the usual ldquotrue or falserdquo Therefore itis widely used in engineering problems Fuzzy set theoryand fuzzy logic establish the rules of a nonlinear mappingThe fuzzy logic controller modeling consists of three stepsof fuzzification determination of fuzzy control rules anddefuzzification [20] Fuzzy logic is a systematic and easier wayto implement control algorithm for uncertain and indefinitemodels in engineering and suits most AGC problem [21 22]
The comparison between the proposed TSO-FLC andGA-PID and PSO-PID controllers is quantified based on twodynamic performance indices that is peak undershoot andsettling time
Table 2 Fuzzy rules for Area 1 controller
ACEVN MN SN Z SP MP VP
ΔACE
VN VN VN VN VN SN MN SNMN VN MN SN MN VN SN SPSN VN VN VN VN Z Z ZZ MN MN N Z MP MP MPSP Z Z Z VP VP VP VPMP SN SP VP MP SP MP VPVP SP MP SP VP VP VP VP
The multi-input and single-output (MISO) type fuzzycontroller is shown in Figure 3 119870119901119906 and 119870119894119906 are the propor-tional and integral gains respectively Two inputs ACE119894 andderivative of ACE119894 that is (119889ACE119894119889119905) are fed to the fuzzycontrollerThe fuzzy logic process is initiated by fuzzificationofACE119894 and119889ACE119894119889119905Mamdani fuzzy inferencemechanismand centroid method for defuzzification are later used forrespective processes 119880119894 is a crisp value and 119906119894 is a controlsignal for the system
119906119894 = minus119870119901119906119880119894 minus 119870119894119906 int 119880119894119889119905 (19)
Membership functions (MF) specify the degree to which agiven input belongs to a set FLC has used seven membershipfunctions Very Negative (VN) Medium Negative (MN)Small Negative (SN) Zero (Z) Small Positive (SP) MediumPositive (MP) and Very Positive (VP) The membershipfunction sets of FLC for input as well as output variables areshown in Figure 4 Optimized rule base for proposed TSO-FLC for both areas is shown in Tables 2 and 3
Advances in Fuzzy Systems 7
0 5 10 15 20 25 30 35 40 45 50708709
71711712713714715716717718
Iteration
Fitn
ess v
alue
Figure 5 FLC optimization of step 1 for rule base optimization
0 10 20 30 40 50 60 70 80 90 10052545658606264666870
Iteration
Fitn
ess v
alue
Figure 6 FLC optimization of step 2 for scaling and gain factoroptimization
Table 3 Fuzzy rules for Area 2 controller
ACEVN MN SN Z SP MP VP
ΔACE
VN VN VN MN VN SN SN ZMN VN VN VN VN SN Z ZSN VN VN VN MN SN SP SPZ MN MN VN Z VP MP MPSP SN SN SP MP VP VP VPMP Z Z SP VP VP VP VPVP Z SP SP VP MP VP VP
Table 4 Optimized scaling and gain parameters for TSO-FLC
Scaling parameters Gain parameters119870119890 119870119888119890 119870119901119906 119870119894119906
FLC for Area 1 112833 093282 143489 218240FLC for Area 2 188194 056237 056237 210918
Themembership functions of each input and each outputare spread across a linear distribution range from minus1 to +1 Intwo stages FLC is optimized by PSO with objective functiongiven in (18)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
Figure 7 Comparison of GA-PID PSO-PID and TSO-FLC forreheat type two-area thermal power system (Case A) Poolco (a)frequency deviation in Area 1 and (b) frequency deviation in Area 2
Rule BaseOptimization In this step apart from center rule allother rules need to be optimized Only one rule is configuredthat when both inputs are zero then output is also zero Insystem under study out of 49 rules 48 rules are required to beoptimizedThe curve between best fitness values with respectto iteration for rule base optimization is shown in Figure 5
Scaling Factor and Gain Optimization In this second stepoptimum values of two scaling factors (119870119890 and 119870119888119890) and twogain parameters (119870119901119906 and 119870119894119906) are needed to be optimizedof FLC Graphically the best fitness values with respect toiteration are represented in Figure 6 Table 4 shows theoptimized scaling and gain parameters for TSO-FLC
4 Test Cases and Simulations
There are three different test cases of deregulated power sys-tem considered for justification of optimum performance ofproposed TSO-FLC controller as compared to conventionalGA-PID andPSO-PID controllersThese test cases are Poolcobased transactions combination of Poolco and bilateral based
8 Advances in Fuzzy Systems
Table 5 Different test cases for proposed system
Test cases cpf matrixContractedload (pu)(Δ119875LD Cont)
Uncontractedload (pu)(Δ119875LDUncont
)
Load Δ119875LD(pu)
ScheduledGENCOs
power (pu)(Δ119875119866)
Scheduled tieline powerflow (pu)(Δ119875tie12 sch)
Case A(Poolco based transactions)
[[[[[[[[[
[
05 05 0 0
05 05 0 0
0 0 05 05
0 0 05 05
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
000
000
000
000
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
0
Case B(combination of Poolco andbilateral basedtransactions)
[[[[[[[[[
[
025 020 025 0
025 020 0 0
050 030 015 0
0 030 060 1
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
000
000
000
000
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
00070
00045
00095
00190
]]]]]]]]]
]
minus00085
Case C(contract violation)
[[[[[[[[[
[
025 020 025 0
025 020 0 0
050 030 015 0
0 030 060 1
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
0000
0004
0000
0008
]]]]]]]]]
]
[[[[[[[[[
[
0010
0014
0010
0018
]]]]]]]]]
]
[[[[[[[[[
[
00090
00065
00135
00230
]]]]]]]]]
]
minus00085
Table 6 System parameters
Rated power (Area 1 and Area 2) 1198751199031 and 1198751199032 2000MW
Transfer function gain of generator (Area 1 and Area 2) 1198701199011 and 1198701199012 120
Generatorrsquos time constant (Area 1 and Area 2) 1198791199011 and 1198791199012 20
Governorrsquos time constant 1198791198921 008
Governorrsquos time constant 1198791198922 002
Steam turbinersquos time constant 119879119905 03
Regulation of the governor (Area 1 and Area 2) 1198771 and 1198772 24
Frequency bias constant 120573 0425
Synchronizing power coefficient 11988612 1
Synchronization coefficient 11987912 0545
transactions and contract violationThe cpf matrix and loadpower from each DISCO are varied in each test case asdepicted in Table 5 Apart from this all GENCOs are allowedto participate equally in each area for AGC therefore ACEparticipation factor (apf 119894) 05 is considered for simulationpurpose
The total generated power Δ119875119892(119894) required by individualGENCO is composed of all contracted and uncontractedloads Each GENCO shares the uncontracted load of its owncontrol area according to its ACE participation factor Thevalues of system parameters given in Appendix (Table 6)
are used for a comparative study Frequency deviations ofboth areas and tie line deviation after load change as per loaddistribution (Table 5) in each area for test casesA B andC areshown in Figures 7 8 and 9 respectively Two performanceindices (settling time and peak undershoot) were selected forjustification of dynamic performance response of controllersEffect of +30 and minus30 change in parameter values 120573 11987912and 119879119901 (parameters value in Table 7 in Appendix) is alsoexamined Peak undershoot and settling time of both areasand tie line deviation are also determined with +30 andminus30 change in system parameters in each area for test cases
Advances in Fuzzy Systems 9
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 8 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case B) Combination of Poolcoand bilateral contracts (a) frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Table 7 Different cases with different system parameters
119879119901 120573 11987912
Case 1 (nominal value) 20 0425 0545Case 2 (+30 increase) 26 05525 07085Case 3 (minus30 decrease) 14 02975 03815
A B and C shown in Figures 10 11 12 13 14 and 15 Thecomparison of dynamic performances of GA-PID and PSO-PID controllerswith the proposedTSO-FLC controller showsthat proposed TSO-FLC gives better results in terms of lessersettling time and peak undershoot MatlabSimulink is usedfor simulation purpose
In order to examine the performance of controllerspeak undershoot and settling time of both areas and tieline deviation are determined for test cases A B and Cwith standard values of system parameters Apart from this
the effect of +30 and minus30 change in parameter values 12057311987912 and 119879119901 (parameters value in Table 7) is also examinedso further performance indices for +30 and minus30 changein system parameters for different test cases determined areshown in Figures 10 11 12 13 14 and 15 Based on thiscomparison it can be concluded that proposed TSO-FLCgives better results in terms of lesser settling time and peakundershoot compared to GA-PID and PSO-PID controllers
5 Conclusion
In this paper an optimization strategy for FLC is proposedfor AGC This optimization strategy is based on rule baseoptimization and scaling factor and gain factor optimizationof FLC PSO is used as optimization technique The perfor-mance of proposed controller is compared with conventionalPID controller also optimized by two optimization methodsGA and PSO under different test cases based on contractual
10 Advances in Fuzzy Systems
0 5 10 15 20 25 30 35 40 45 50minus0035
minus003minus0025
minus002minus0015
minus001minus0005
00005
001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus004
minus0035minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 9 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case C) Contract violation (a)frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Case AGA-PID 002556 002064 003407 002663 002140 003561PSO-PID 002150 001714 002922 002268 001804 003080TSO-FLC 000972 000750 001380 001118 000865 001579
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)(nominal)Δf1 Δf1 Δf1
(nominal)Δf2 Δf2 Δf2
Figure 10 Peak undershoot comparison at plusmn30 variation insystem parameters for Case A
demands in deregulated power system The dynamic per-formance of proposed controllers is observed on the basisof two performance indices that is settling time and peak
1983015 1751152 2344273 1993948 1761672 23553811340694 1173940 1593159 1340694 1173940 1593159312402 120954 933828 087750 087520 395436
000000
500000
1000000
1500000
2000000
2500000
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)
Settling time (plusmn5)
Δf1 Δf1 Δf2 Δf2(nominal)
Δf1(nominal)
Δf2
Figure 11 Settling time comparison at plusmn30 variation in systemparameters for Case A
undershoot Simulation results show that proposedTSO-FLCcontroller provides a better performance in comparison of
Advances in Fuzzy Systems 11
002645002177000893
002139001732000689
003519002954001269
002714002317001363
002184001847001055
003614003129001913
Case B
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
8500E minus 0
8500E minus 0
8585E minus 0
8500E minus 0
8500E minus 0
8551E minus 0
8500E minus 0
8500E minus 0
8543E minus 0GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal) (nominal) (nominal)
Figure 12 Peak undershoot comparison at plusmn30 variation in system parameters for Case B
19690831301781383480
17569881144269294828
23292181578341545893
20689471391069278520
18352271218930235500
24063641624648279652
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
9006E + 0
2500E + 0
1559E + 0
8092E + 0
2543E + 0
1458E + 0
8668E + 0
2682E + 0
1523E + 0
Settling time (plusmn5)
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal)(nominal)(nominal)
Figure 13 Settling time comparison at plusmn30 variation in system parameters for Case B
GA-PID and PSO-PID controllers Robustness of the TSO-FLC is also justified for +30 and minus30 change in systemparameters for different sets of contractual demands andagain it is observed that TSO-FLC is a suitable controller forAGC in an interconnected power system
Appendix
Speed governor 1(1 + 119904119879119892)
Thermal reheater (1 + 119870119903119904119879119903)(1 + 119904119879119903)
Thermal turbine 1(1 + 119904119879119905)
Power system 119870119901(1 + 119904119879119901)
See Tables 6 and 7
Competing Interests
The authors declare that they have no competing interests
12 Advances in Fuzzy Systems
003448002803001143
002865002275000883
004529003775001625
004000003394001872
003212002700001445
005290004552002641
000000
001000
002000
003000
004000
005000
006000
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
Case C
Peak undershoot
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 14 Peak undershoot comparison at plusmn30 variation in system parameters for Case C
20958661452353404295
18844331286364324176
21740051495980272999
19415891329047232815
25159171748899549258
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
8465E + 0
2550E + 0
1450E + 0
7297E + 0
2553E + 0
1319E + 0
8019E + 0
2730E + 0
1396E + 0
1716E + 0
1082E + 0
2472E + 0
Settling time (plusmn5)
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 15 Settling time comparison at plusmn30 variation in system parameters for Case C
References
[1] F Daneshfar ldquoIntelligent load-frequency control in a deregu-lated environment continuous-valued input extended classifiersystem approachrdquo IET Generation Transmission and Distribu-tion vol 7 no 6 pp 551ndash559 2013
[2] I A Chidambaram and B Paramasivam ldquoOptimized load-frequency simulation in restructured power system with Redoxflow batteries and interline power flow controllerrdquo InternationalJournal of Electrical Power and Energy Systems vol 50 no 1 pp9ndash24 2013
[3] A P Sakis Meliopoulos G J Cokkinides and A G BakirtzisldquoLoad-frequency control service in a deregulated environmentrdquoDecision Support Systems vol 24 no 3-4 pp 243ndash250 1999
[4] F Liu Y H Song J Ma S Mei and Q Lu ldquoOptimalload-frequency control in restructured power systemsrdquo IEEProceedings Generation Transmission andDistribution vol 150no 1 pp 87ndash95 2003
[5] W C Chan and Y Y Hsu ldquoAutomatic generation control ofinterconnected power systems using variable-structure con-trollersrdquo IEE Proceedings C Generation Transmission and Dis-tribution vol 128 no 5 pp 269ndash279 1981
[6] S C Tripathy G S Hope and O P Malik ldquoOptimisationof load-frequency control parameters for power systems withreheat steam turbines and governor deadband nonlinearityrdquoIEE Proceedings C Generation Transmission and Distributionvol 129 no 1 pp 10ndash16 1982
Advances in Fuzzy Systems 13
[7] R D Christie and A Bose ldquoLoad frequency control issues inpower system operations after deregulationrdquo IEEE Transactionson Power Systems vol 11 no 3 pp 1191ndash1200 1995
[8] B H Bakken and O S Grande ldquoAutomatic generation controlin a deregulated power systemrdquo IEEE Transactions on PowerSystems vol 13 no 4 pp 1401ndash1406 1998
[9] V Donde M A Pai and I A Hiskens ldquoSimulation andoptimization in an AGC system after deregulationrdquo IEEETransactions on Power Systems vol 16 no 3 pp 481ndash489 2001
[10] R Roy P Bhatt and S P Ghoshal ldquoEvolutionary computationbased three-area automatic generation controlrdquo Expert Systemswith Applications vol 37 no 8 pp 5913ndash5924 2010
[11] P Bhatt R Roy and S P Ghoshal ldquoOptimized multi areaAGC simulation in restructured power systemsrdquo InternationalJournal of Electrical Power amp Energy Systems vol 32 no 4 pp311ndash322 2010
[12] S P Ghoshal ldquoOptimizations of PID gains by particle swarmoptimizations in fuzzy based automatic generation controlrdquoElectric Power Systems Research vol 72 no 3 pp 203ndash212 2004
[13] I Chiha N Liouane and P Borne ldquoTuning PID controllerusing multiobjective ant colony optimizationrdquo Applied Compu-tational Intelligence and Soft Computing vol 2012 Article ID536326 7 pages 2012
[14] V Mukherjee and S P Ghoshal ldquoIntelligent particle swarmoptimized fuzzy PID controller for AVR systemrdquo Electric PowerSystems Research vol 77 no 12 pp 1689ndash1698 2007
[15] K Naidu H Mokhlis and A H A Bakar ldquoMultiobjective opti-mization using weighted sum Artificial Bee Colony algorithmfor Load Frequency Controlrdquo International Journal of ElectricalPower and Energy Systems vol 55 pp 657ndash667 2014
[16] D Pelusi ldquoOptimization of a fuzzy logic controller using geneticalgorithmsrdquo in Proceedings of the 3rd International Conferenceon IntelligentHuman-Machine Systems andCybernetics (IHMSCrsquo11) pp 143ndash146 Zhejiang China August 2011
[17] T Chaiyatham I Ngamroo S Pothiya and S VachirasricirikulldquoDesign of optimal fuzzy logic-PID controller using bee colonyoptimization for frequency control in an isolated wind-dieselsystemrdquo in Proceedings of the Transmission amp DistributionConference amp Exposition Asia and Pacific vol 1 pp 1ndash4 IEEESeoul The Republic of Korea October 2009
[18] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 2006
[19] M Parida and J Nanda ldquoAutomatic generation control of ahydro-thermal system in deregulated environmentrdquo in Proceed-ings of the 8th International Conference on Electrical Machinesand Systems (ICEMS rsquo05) pp 942ndash947Nanjing China Septem-ber 2005
[20] C C Lee ldquoFuzzy logic in control systems fuzzy logic controllerIIrdquo IEEE Transactions on SystemsMan and Cybernetics vol 20no 2 pp 419ndash435 1990
[21] K R M Vijaya Chandrakala S Balamurugan and K Sankara-narayanan ldquoVariable structure fuzzy gain scheduling based loadfrequency controller for multi source multi area hydro thermalsystemrdquo International Journal of Electrical Power and EnergySystems vol 53 no 1 pp 375ndash381 2013
[22] Y K Bhateshvar and H D Mathur ldquoFrequency stabilizationusing fuzzy logic based controller for multi-area power systemin deregulated environmentrdquo in Proceedings of the 2nd Inter-national Conference on Advances in Control and Optimizationof Dynamical Systems (ACODS rsquo12) pp 1ndash10 Bangalore IndiaFebruary 2012
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Fuzzy Systems 5
Table 1 PID controller gains from optimization method
S no Area 1 PID gains Area 2 PID gains
1 GA optimizedPID controller gains
119870119901 059226 100299119870119894 073350 084666119870119889 062571 045060
2 PSO optimizedPID controller gains
119870119901 067927 095495119870119894 160343 172912119870119889 096307 078236
minus (cpf31 lowast Δ119875Ld1 Cont + cpf41 lowast Δ119875Ld1 Cont
+ cpf32 lowast Δ119875Ld2 Cont + cpf42 lowast Δ119875Ld2 Cont)
(16)
3 Control Strategies
In this paper two different control strategies are exploredThefirst control strategy is conventional proportional-integral-derivative (PID) control and another is artificial intelligencebased fuzzy logic control (FLC) PID controller is optimizedby two different stochastic optimization techniques GA andPSO and later PSO based optimized FLC is proposed whereFLC parameters are optimized in two different stages
31 PID Controller PID controller is selected as controllerfor AGC and GA and PSO are used for optimizing of gainparameters that is 119870119901 119870119894 and 119870119889 ACE119894 is selected ascontroller input and 119880PID is output of controller as given in
119880PID = 119870119901 (ACE119894) + 119870119894 (intACE119894119889119905)
+ 119870119889 (119889ACE119894
119889119905
)
(17)
311 Genetic Algorithm The genetic algorithm (GA) isinspired by the principles of genetics and evolution Itmimics the reproduction behavior observed in biologicalpopulations The GA employs the principle of ldquosurvivalof the fittestrdquo in its search process to select and generateindividuals that are adapted to their environment Thereforeover a number of generations desirable traits will evolveand remain in the genome composition of the populationover traits with weaker undesirable characteristics The GAis well suited to and has been extensively applied to solvecomplex design optimization problems because it can handleboth discrete and continuous variables and nonlinear objec-tive and constrained functions without requiring gradientinformation [13 15ndash17] The AGC modeled has an objective
function for PID optimization as given in (18) which is aimedfor minimization of peak undershoots and settling time offrequency and tie line deviation
119869OBJ = int
119879
0
(120582 (10038161003816100381610038161003816PUΔ119891
1
10038161003816100381610038161003816+
10038161003816100381610038161003816PUΔ119891
2
10038161003816100381610038161003816+ 120583
10038161003816100381610038161003816PUΔ119875tie12
10038161003816100381610038161003816)
+ (STΔ1198911
+ STΔ1198912
+ STΔ119875tie12)) 119889119905
(18)
Here 120582 120583 and 119879 are selected as 10 500 and 50respectively
312 Particle SwarmOptimization Particle swarmoptimiza-tion (PSO) is a heuristic search method which is by theswarming or collaborative behavior of biological populationsIn PSO a set of randomly generated solutions (initial swarm)propagates in the design space towards the optimal solutionover a number of iterations (moves) based on large amount ofinformation about the design space that is assimilated andshared by all members of the swarm PSO is inspired by theability of flocks of birds schools of fish and herds of animalsto adapt to their environment find rich sources of food andavoid predators by implementing an ldquoinformation sharingrdquoapproach hence developing an evolutionary advantage Itsability to converge faster to global solution makes it favorabletechnique compared to other stochastic optimization meth-ods like GA and simulated annealing (SA) [17ndash19] The PIDcontroller gains for both control areas optimized by GA andPSO are shown in Table 1 An algorithm is developed for thesystem under study for optimization with PSO and followingsteps are followed
Algorithm steps for PSO implementation are given below
(1) Setting parameters for PSO
(a) Define dimensions of search space(b) Define boundaries of search space (minimum
and maximum values of variables)(c) Define minimum and maximum values of par-
ticlersquos velocities
(2) Initialize population
(a) Initialize random population of swarm withinboundaries
6 Advances in Fuzzy Systems
Fuzzy logic controller Controlled output
+
+
ACEi Kemin
Ke
Kcemax
Kemax
Kce
Kcemin
Kpumin
Kpu
Kiu
Kpumax
Kiumin
Kiumax
Ui
1
s
d
dt
Figure 3 MISO-type fuzzy logic controller
VN ZMN SP VPMPSN
000
100
050
ACEidACEiUi
120583
minus1 minus075 minus050 minus025 0 025 050 075 1
Figure 4 Membership functions of inputs and output variable
(b) Set random velocities to particles of swarmwithin boundaries
(3) Evaluate the fitness of each particle position as perobjective function selected
(a) Identify each particlersquos best known position(b) Identify the best known position of swarm(c) Update the velocities and positions of particles
(4) Repeat step (3) up to either maximum iterations orconvergence criteria satisfied
32 PSO Optimized Fuzzy Logic Controller Power systemoperation and control have undergoing immense changesfrom earlier times as complexity has increased multifolddue to stress to deliver quality and uninterrupted powerto consumers These reasons have boosted power systemengineers to use intelligent control strategies in operationand control where fuzzy logic has gained popularity amongstothers because of its computing approach based on ldquodegreesof truthrdquo rather than the usual ldquotrue or falserdquo Therefore itis widely used in engineering problems Fuzzy set theoryand fuzzy logic establish the rules of a nonlinear mappingThe fuzzy logic controller modeling consists of three stepsof fuzzification determination of fuzzy control rules anddefuzzification [20] Fuzzy logic is a systematic and easier wayto implement control algorithm for uncertain and indefinitemodels in engineering and suits most AGC problem [21 22]
The comparison between the proposed TSO-FLC andGA-PID and PSO-PID controllers is quantified based on twodynamic performance indices that is peak undershoot andsettling time
Table 2 Fuzzy rules for Area 1 controller
ACEVN MN SN Z SP MP VP
ΔACE
VN VN VN VN VN SN MN SNMN VN MN SN MN VN SN SPSN VN VN VN VN Z Z ZZ MN MN N Z MP MP MPSP Z Z Z VP VP VP VPMP SN SP VP MP SP MP VPVP SP MP SP VP VP VP VP
The multi-input and single-output (MISO) type fuzzycontroller is shown in Figure 3 119870119901119906 and 119870119894119906 are the propor-tional and integral gains respectively Two inputs ACE119894 andderivative of ACE119894 that is (119889ACE119894119889119905) are fed to the fuzzycontrollerThe fuzzy logic process is initiated by fuzzificationofACE119894 and119889ACE119894119889119905Mamdani fuzzy inferencemechanismand centroid method for defuzzification are later used forrespective processes 119880119894 is a crisp value and 119906119894 is a controlsignal for the system
119906119894 = minus119870119901119906119880119894 minus 119870119894119906 int 119880119894119889119905 (19)
Membership functions (MF) specify the degree to which agiven input belongs to a set FLC has used seven membershipfunctions Very Negative (VN) Medium Negative (MN)Small Negative (SN) Zero (Z) Small Positive (SP) MediumPositive (MP) and Very Positive (VP) The membershipfunction sets of FLC for input as well as output variables areshown in Figure 4 Optimized rule base for proposed TSO-FLC for both areas is shown in Tables 2 and 3
Advances in Fuzzy Systems 7
0 5 10 15 20 25 30 35 40 45 50708709
71711712713714715716717718
Iteration
Fitn
ess v
alue
Figure 5 FLC optimization of step 1 for rule base optimization
0 10 20 30 40 50 60 70 80 90 10052545658606264666870
Iteration
Fitn
ess v
alue
Figure 6 FLC optimization of step 2 for scaling and gain factoroptimization
Table 3 Fuzzy rules for Area 2 controller
ACEVN MN SN Z SP MP VP
ΔACE
VN VN VN MN VN SN SN ZMN VN VN VN VN SN Z ZSN VN VN VN MN SN SP SPZ MN MN VN Z VP MP MPSP SN SN SP MP VP VP VPMP Z Z SP VP VP VP VPVP Z SP SP VP MP VP VP
Table 4 Optimized scaling and gain parameters for TSO-FLC
Scaling parameters Gain parameters119870119890 119870119888119890 119870119901119906 119870119894119906
FLC for Area 1 112833 093282 143489 218240FLC for Area 2 188194 056237 056237 210918
Themembership functions of each input and each outputare spread across a linear distribution range from minus1 to +1 Intwo stages FLC is optimized by PSO with objective functiongiven in (18)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
Figure 7 Comparison of GA-PID PSO-PID and TSO-FLC forreheat type two-area thermal power system (Case A) Poolco (a)frequency deviation in Area 1 and (b) frequency deviation in Area 2
Rule BaseOptimization In this step apart from center rule allother rules need to be optimized Only one rule is configuredthat when both inputs are zero then output is also zero Insystem under study out of 49 rules 48 rules are required to beoptimizedThe curve between best fitness values with respectto iteration for rule base optimization is shown in Figure 5
Scaling Factor and Gain Optimization In this second stepoptimum values of two scaling factors (119870119890 and 119870119888119890) and twogain parameters (119870119901119906 and 119870119894119906) are needed to be optimizedof FLC Graphically the best fitness values with respect toiteration are represented in Figure 6 Table 4 shows theoptimized scaling and gain parameters for TSO-FLC
4 Test Cases and Simulations
There are three different test cases of deregulated power sys-tem considered for justification of optimum performance ofproposed TSO-FLC controller as compared to conventionalGA-PID andPSO-PID controllersThese test cases are Poolcobased transactions combination of Poolco and bilateral based
8 Advances in Fuzzy Systems
Table 5 Different test cases for proposed system
Test cases cpf matrixContractedload (pu)(Δ119875LD Cont)
Uncontractedload (pu)(Δ119875LDUncont
)
Load Δ119875LD(pu)
ScheduledGENCOs
power (pu)(Δ119875119866)
Scheduled tieline powerflow (pu)(Δ119875tie12 sch)
Case A(Poolco based transactions)
[[[[[[[[[
[
05 05 0 0
05 05 0 0
0 0 05 05
0 0 05 05
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
000
000
000
000
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
0
Case B(combination of Poolco andbilateral basedtransactions)
[[[[[[[[[
[
025 020 025 0
025 020 0 0
050 030 015 0
0 030 060 1
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
000
000
000
000
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
00070
00045
00095
00190
]]]]]]]]]
]
minus00085
Case C(contract violation)
[[[[[[[[[
[
025 020 025 0
025 020 0 0
050 030 015 0
0 030 060 1
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
0000
0004
0000
0008
]]]]]]]]]
]
[[[[[[[[[
[
0010
0014
0010
0018
]]]]]]]]]
]
[[[[[[[[[
[
00090
00065
00135
00230
]]]]]]]]]
]
minus00085
Table 6 System parameters
Rated power (Area 1 and Area 2) 1198751199031 and 1198751199032 2000MW
Transfer function gain of generator (Area 1 and Area 2) 1198701199011 and 1198701199012 120
Generatorrsquos time constant (Area 1 and Area 2) 1198791199011 and 1198791199012 20
Governorrsquos time constant 1198791198921 008
Governorrsquos time constant 1198791198922 002
Steam turbinersquos time constant 119879119905 03
Regulation of the governor (Area 1 and Area 2) 1198771 and 1198772 24
Frequency bias constant 120573 0425
Synchronizing power coefficient 11988612 1
Synchronization coefficient 11987912 0545
transactions and contract violationThe cpf matrix and loadpower from each DISCO are varied in each test case asdepicted in Table 5 Apart from this all GENCOs are allowedto participate equally in each area for AGC therefore ACEparticipation factor (apf 119894) 05 is considered for simulationpurpose
The total generated power Δ119875119892(119894) required by individualGENCO is composed of all contracted and uncontractedloads Each GENCO shares the uncontracted load of its owncontrol area according to its ACE participation factor Thevalues of system parameters given in Appendix (Table 6)
are used for a comparative study Frequency deviations ofboth areas and tie line deviation after load change as per loaddistribution (Table 5) in each area for test casesA B andC areshown in Figures 7 8 and 9 respectively Two performanceindices (settling time and peak undershoot) were selected forjustification of dynamic performance response of controllersEffect of +30 and minus30 change in parameter values 120573 11987912and 119879119901 (parameters value in Table 7 in Appendix) is alsoexamined Peak undershoot and settling time of both areasand tie line deviation are also determined with +30 andminus30 change in system parameters in each area for test cases
Advances in Fuzzy Systems 9
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 8 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case B) Combination of Poolcoand bilateral contracts (a) frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Table 7 Different cases with different system parameters
119879119901 120573 11987912
Case 1 (nominal value) 20 0425 0545Case 2 (+30 increase) 26 05525 07085Case 3 (minus30 decrease) 14 02975 03815
A B and C shown in Figures 10 11 12 13 14 and 15 Thecomparison of dynamic performances of GA-PID and PSO-PID controllerswith the proposedTSO-FLC controller showsthat proposed TSO-FLC gives better results in terms of lessersettling time and peak undershoot MatlabSimulink is usedfor simulation purpose
In order to examine the performance of controllerspeak undershoot and settling time of both areas and tieline deviation are determined for test cases A B and Cwith standard values of system parameters Apart from this
the effect of +30 and minus30 change in parameter values 12057311987912 and 119879119901 (parameters value in Table 7) is also examinedso further performance indices for +30 and minus30 changein system parameters for different test cases determined areshown in Figures 10 11 12 13 14 and 15 Based on thiscomparison it can be concluded that proposed TSO-FLCgives better results in terms of lesser settling time and peakundershoot compared to GA-PID and PSO-PID controllers
5 Conclusion
In this paper an optimization strategy for FLC is proposedfor AGC This optimization strategy is based on rule baseoptimization and scaling factor and gain factor optimizationof FLC PSO is used as optimization technique The perfor-mance of proposed controller is compared with conventionalPID controller also optimized by two optimization methodsGA and PSO under different test cases based on contractual
10 Advances in Fuzzy Systems
0 5 10 15 20 25 30 35 40 45 50minus0035
minus003minus0025
minus002minus0015
minus001minus0005
00005
001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus004
minus0035minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 9 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case C) Contract violation (a)frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Case AGA-PID 002556 002064 003407 002663 002140 003561PSO-PID 002150 001714 002922 002268 001804 003080TSO-FLC 000972 000750 001380 001118 000865 001579
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)(nominal)Δf1 Δf1 Δf1
(nominal)Δf2 Δf2 Δf2
Figure 10 Peak undershoot comparison at plusmn30 variation insystem parameters for Case A
demands in deregulated power system The dynamic per-formance of proposed controllers is observed on the basisof two performance indices that is settling time and peak
1983015 1751152 2344273 1993948 1761672 23553811340694 1173940 1593159 1340694 1173940 1593159312402 120954 933828 087750 087520 395436
000000
500000
1000000
1500000
2000000
2500000
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)
Settling time (plusmn5)
Δf1 Δf1 Δf2 Δf2(nominal)
Δf1(nominal)
Δf2
Figure 11 Settling time comparison at plusmn30 variation in systemparameters for Case A
undershoot Simulation results show that proposedTSO-FLCcontroller provides a better performance in comparison of
Advances in Fuzzy Systems 11
002645002177000893
002139001732000689
003519002954001269
002714002317001363
002184001847001055
003614003129001913
Case B
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
8500E minus 0
8500E minus 0
8585E minus 0
8500E minus 0
8500E minus 0
8551E minus 0
8500E minus 0
8500E minus 0
8543E minus 0GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal) (nominal) (nominal)
Figure 12 Peak undershoot comparison at plusmn30 variation in system parameters for Case B
19690831301781383480
17569881144269294828
23292181578341545893
20689471391069278520
18352271218930235500
24063641624648279652
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
9006E + 0
2500E + 0
1559E + 0
8092E + 0
2543E + 0
1458E + 0
8668E + 0
2682E + 0
1523E + 0
Settling time (plusmn5)
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal)(nominal)(nominal)
Figure 13 Settling time comparison at plusmn30 variation in system parameters for Case B
GA-PID and PSO-PID controllers Robustness of the TSO-FLC is also justified for +30 and minus30 change in systemparameters for different sets of contractual demands andagain it is observed that TSO-FLC is a suitable controller forAGC in an interconnected power system
Appendix
Speed governor 1(1 + 119904119879119892)
Thermal reheater (1 + 119870119903119904119879119903)(1 + 119904119879119903)
Thermal turbine 1(1 + 119904119879119905)
Power system 119870119901(1 + 119904119879119901)
See Tables 6 and 7
Competing Interests
The authors declare that they have no competing interests
12 Advances in Fuzzy Systems
003448002803001143
002865002275000883
004529003775001625
004000003394001872
003212002700001445
005290004552002641
000000
001000
002000
003000
004000
005000
006000
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
Case C
Peak undershoot
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 14 Peak undershoot comparison at plusmn30 variation in system parameters for Case C
20958661452353404295
18844331286364324176
21740051495980272999
19415891329047232815
25159171748899549258
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
8465E + 0
2550E + 0
1450E + 0
7297E + 0
2553E + 0
1319E + 0
8019E + 0
2730E + 0
1396E + 0
1716E + 0
1082E + 0
2472E + 0
Settling time (plusmn5)
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 15 Settling time comparison at plusmn30 variation in system parameters for Case C
References
[1] F Daneshfar ldquoIntelligent load-frequency control in a deregu-lated environment continuous-valued input extended classifiersystem approachrdquo IET Generation Transmission and Distribu-tion vol 7 no 6 pp 551ndash559 2013
[2] I A Chidambaram and B Paramasivam ldquoOptimized load-frequency simulation in restructured power system with Redoxflow batteries and interline power flow controllerrdquo InternationalJournal of Electrical Power and Energy Systems vol 50 no 1 pp9ndash24 2013
[3] A P Sakis Meliopoulos G J Cokkinides and A G BakirtzisldquoLoad-frequency control service in a deregulated environmentrdquoDecision Support Systems vol 24 no 3-4 pp 243ndash250 1999
[4] F Liu Y H Song J Ma S Mei and Q Lu ldquoOptimalload-frequency control in restructured power systemsrdquo IEEProceedings Generation Transmission andDistribution vol 150no 1 pp 87ndash95 2003
[5] W C Chan and Y Y Hsu ldquoAutomatic generation control ofinterconnected power systems using variable-structure con-trollersrdquo IEE Proceedings C Generation Transmission and Dis-tribution vol 128 no 5 pp 269ndash279 1981
[6] S C Tripathy G S Hope and O P Malik ldquoOptimisationof load-frequency control parameters for power systems withreheat steam turbines and governor deadband nonlinearityrdquoIEE Proceedings C Generation Transmission and Distributionvol 129 no 1 pp 10ndash16 1982
Advances in Fuzzy Systems 13
[7] R D Christie and A Bose ldquoLoad frequency control issues inpower system operations after deregulationrdquo IEEE Transactionson Power Systems vol 11 no 3 pp 1191ndash1200 1995
[8] B H Bakken and O S Grande ldquoAutomatic generation controlin a deregulated power systemrdquo IEEE Transactions on PowerSystems vol 13 no 4 pp 1401ndash1406 1998
[9] V Donde M A Pai and I A Hiskens ldquoSimulation andoptimization in an AGC system after deregulationrdquo IEEETransactions on Power Systems vol 16 no 3 pp 481ndash489 2001
[10] R Roy P Bhatt and S P Ghoshal ldquoEvolutionary computationbased three-area automatic generation controlrdquo Expert Systemswith Applications vol 37 no 8 pp 5913ndash5924 2010
[11] P Bhatt R Roy and S P Ghoshal ldquoOptimized multi areaAGC simulation in restructured power systemsrdquo InternationalJournal of Electrical Power amp Energy Systems vol 32 no 4 pp311ndash322 2010
[12] S P Ghoshal ldquoOptimizations of PID gains by particle swarmoptimizations in fuzzy based automatic generation controlrdquoElectric Power Systems Research vol 72 no 3 pp 203ndash212 2004
[13] I Chiha N Liouane and P Borne ldquoTuning PID controllerusing multiobjective ant colony optimizationrdquo Applied Compu-tational Intelligence and Soft Computing vol 2012 Article ID536326 7 pages 2012
[14] V Mukherjee and S P Ghoshal ldquoIntelligent particle swarmoptimized fuzzy PID controller for AVR systemrdquo Electric PowerSystems Research vol 77 no 12 pp 1689ndash1698 2007
[15] K Naidu H Mokhlis and A H A Bakar ldquoMultiobjective opti-mization using weighted sum Artificial Bee Colony algorithmfor Load Frequency Controlrdquo International Journal of ElectricalPower and Energy Systems vol 55 pp 657ndash667 2014
[16] D Pelusi ldquoOptimization of a fuzzy logic controller using geneticalgorithmsrdquo in Proceedings of the 3rd International Conferenceon IntelligentHuman-Machine Systems andCybernetics (IHMSCrsquo11) pp 143ndash146 Zhejiang China August 2011
[17] T Chaiyatham I Ngamroo S Pothiya and S VachirasricirikulldquoDesign of optimal fuzzy logic-PID controller using bee colonyoptimization for frequency control in an isolated wind-dieselsystemrdquo in Proceedings of the Transmission amp DistributionConference amp Exposition Asia and Pacific vol 1 pp 1ndash4 IEEESeoul The Republic of Korea October 2009
[18] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 2006
[19] M Parida and J Nanda ldquoAutomatic generation control of ahydro-thermal system in deregulated environmentrdquo in Proceed-ings of the 8th International Conference on Electrical Machinesand Systems (ICEMS rsquo05) pp 942ndash947Nanjing China Septem-ber 2005
[20] C C Lee ldquoFuzzy logic in control systems fuzzy logic controllerIIrdquo IEEE Transactions on SystemsMan and Cybernetics vol 20no 2 pp 419ndash435 1990
[21] K R M Vijaya Chandrakala S Balamurugan and K Sankara-narayanan ldquoVariable structure fuzzy gain scheduling based loadfrequency controller for multi source multi area hydro thermalsystemrdquo International Journal of Electrical Power and EnergySystems vol 53 no 1 pp 375ndash381 2013
[22] Y K Bhateshvar and H D Mathur ldquoFrequency stabilizationusing fuzzy logic based controller for multi-area power systemin deregulated environmentrdquo in Proceedings of the 2nd Inter-national Conference on Advances in Control and Optimizationof Dynamical Systems (ACODS rsquo12) pp 1ndash10 Bangalore IndiaFebruary 2012
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
6 Advances in Fuzzy Systems
Fuzzy logic controller Controlled output
+
+
ACEi Kemin
Ke
Kcemax
Kemax
Kce
Kcemin
Kpumin
Kpu
Kiu
Kpumax
Kiumin
Kiumax
Ui
1
s
d
dt
Figure 3 MISO-type fuzzy logic controller
VN ZMN SP VPMPSN
000
100
050
ACEidACEiUi
120583
minus1 minus075 minus050 minus025 0 025 050 075 1
Figure 4 Membership functions of inputs and output variable
(b) Set random velocities to particles of swarmwithin boundaries
(3) Evaluate the fitness of each particle position as perobjective function selected
(a) Identify each particlersquos best known position(b) Identify the best known position of swarm(c) Update the velocities and positions of particles
(4) Repeat step (3) up to either maximum iterations orconvergence criteria satisfied
32 PSO Optimized Fuzzy Logic Controller Power systemoperation and control have undergoing immense changesfrom earlier times as complexity has increased multifolddue to stress to deliver quality and uninterrupted powerto consumers These reasons have boosted power systemengineers to use intelligent control strategies in operationand control where fuzzy logic has gained popularity amongstothers because of its computing approach based on ldquodegreesof truthrdquo rather than the usual ldquotrue or falserdquo Therefore itis widely used in engineering problems Fuzzy set theoryand fuzzy logic establish the rules of a nonlinear mappingThe fuzzy logic controller modeling consists of three stepsof fuzzification determination of fuzzy control rules anddefuzzification [20] Fuzzy logic is a systematic and easier wayto implement control algorithm for uncertain and indefinitemodels in engineering and suits most AGC problem [21 22]
The comparison between the proposed TSO-FLC andGA-PID and PSO-PID controllers is quantified based on twodynamic performance indices that is peak undershoot andsettling time
Table 2 Fuzzy rules for Area 1 controller
ACEVN MN SN Z SP MP VP
ΔACE
VN VN VN VN VN SN MN SNMN VN MN SN MN VN SN SPSN VN VN VN VN Z Z ZZ MN MN N Z MP MP MPSP Z Z Z VP VP VP VPMP SN SP VP MP SP MP VPVP SP MP SP VP VP VP VP
The multi-input and single-output (MISO) type fuzzycontroller is shown in Figure 3 119870119901119906 and 119870119894119906 are the propor-tional and integral gains respectively Two inputs ACE119894 andderivative of ACE119894 that is (119889ACE119894119889119905) are fed to the fuzzycontrollerThe fuzzy logic process is initiated by fuzzificationofACE119894 and119889ACE119894119889119905Mamdani fuzzy inferencemechanismand centroid method for defuzzification are later used forrespective processes 119880119894 is a crisp value and 119906119894 is a controlsignal for the system
119906119894 = minus119870119901119906119880119894 minus 119870119894119906 int 119880119894119889119905 (19)
Membership functions (MF) specify the degree to which agiven input belongs to a set FLC has used seven membershipfunctions Very Negative (VN) Medium Negative (MN)Small Negative (SN) Zero (Z) Small Positive (SP) MediumPositive (MP) and Very Positive (VP) The membershipfunction sets of FLC for input as well as output variables areshown in Figure 4 Optimized rule base for proposed TSO-FLC for both areas is shown in Tables 2 and 3
Advances in Fuzzy Systems 7
0 5 10 15 20 25 30 35 40 45 50708709
71711712713714715716717718
Iteration
Fitn
ess v
alue
Figure 5 FLC optimization of step 1 for rule base optimization
0 10 20 30 40 50 60 70 80 90 10052545658606264666870
Iteration
Fitn
ess v
alue
Figure 6 FLC optimization of step 2 for scaling and gain factoroptimization
Table 3 Fuzzy rules for Area 2 controller
ACEVN MN SN Z SP MP VP
ΔACE
VN VN VN MN VN SN SN ZMN VN VN VN VN SN Z ZSN VN VN VN MN SN SP SPZ MN MN VN Z VP MP MPSP SN SN SP MP VP VP VPMP Z Z SP VP VP VP VPVP Z SP SP VP MP VP VP
Table 4 Optimized scaling and gain parameters for TSO-FLC
Scaling parameters Gain parameters119870119890 119870119888119890 119870119901119906 119870119894119906
FLC for Area 1 112833 093282 143489 218240FLC for Area 2 188194 056237 056237 210918
Themembership functions of each input and each outputare spread across a linear distribution range from minus1 to +1 Intwo stages FLC is optimized by PSO with objective functiongiven in (18)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
Figure 7 Comparison of GA-PID PSO-PID and TSO-FLC forreheat type two-area thermal power system (Case A) Poolco (a)frequency deviation in Area 1 and (b) frequency deviation in Area 2
Rule BaseOptimization In this step apart from center rule allother rules need to be optimized Only one rule is configuredthat when both inputs are zero then output is also zero Insystem under study out of 49 rules 48 rules are required to beoptimizedThe curve between best fitness values with respectto iteration for rule base optimization is shown in Figure 5
Scaling Factor and Gain Optimization In this second stepoptimum values of two scaling factors (119870119890 and 119870119888119890) and twogain parameters (119870119901119906 and 119870119894119906) are needed to be optimizedof FLC Graphically the best fitness values with respect toiteration are represented in Figure 6 Table 4 shows theoptimized scaling and gain parameters for TSO-FLC
4 Test Cases and Simulations
There are three different test cases of deregulated power sys-tem considered for justification of optimum performance ofproposed TSO-FLC controller as compared to conventionalGA-PID andPSO-PID controllersThese test cases are Poolcobased transactions combination of Poolco and bilateral based
8 Advances in Fuzzy Systems
Table 5 Different test cases for proposed system
Test cases cpf matrixContractedload (pu)(Δ119875LD Cont)
Uncontractedload (pu)(Δ119875LDUncont
)
Load Δ119875LD(pu)
ScheduledGENCOs
power (pu)(Δ119875119866)
Scheduled tieline powerflow (pu)(Δ119875tie12 sch)
Case A(Poolco based transactions)
[[[[[[[[[
[
05 05 0 0
05 05 0 0
0 0 05 05
0 0 05 05
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
000
000
000
000
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
0
Case B(combination of Poolco andbilateral basedtransactions)
[[[[[[[[[
[
025 020 025 0
025 020 0 0
050 030 015 0
0 030 060 1
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
000
000
000
000
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
00070
00045
00095
00190
]]]]]]]]]
]
minus00085
Case C(contract violation)
[[[[[[[[[
[
025 020 025 0
025 020 0 0
050 030 015 0
0 030 060 1
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
0000
0004
0000
0008
]]]]]]]]]
]
[[[[[[[[[
[
0010
0014
0010
0018
]]]]]]]]]
]
[[[[[[[[[
[
00090
00065
00135
00230
]]]]]]]]]
]
minus00085
Table 6 System parameters
Rated power (Area 1 and Area 2) 1198751199031 and 1198751199032 2000MW
Transfer function gain of generator (Area 1 and Area 2) 1198701199011 and 1198701199012 120
Generatorrsquos time constant (Area 1 and Area 2) 1198791199011 and 1198791199012 20
Governorrsquos time constant 1198791198921 008
Governorrsquos time constant 1198791198922 002
Steam turbinersquos time constant 119879119905 03
Regulation of the governor (Area 1 and Area 2) 1198771 and 1198772 24
Frequency bias constant 120573 0425
Synchronizing power coefficient 11988612 1
Synchronization coefficient 11987912 0545
transactions and contract violationThe cpf matrix and loadpower from each DISCO are varied in each test case asdepicted in Table 5 Apart from this all GENCOs are allowedto participate equally in each area for AGC therefore ACEparticipation factor (apf 119894) 05 is considered for simulationpurpose
The total generated power Δ119875119892(119894) required by individualGENCO is composed of all contracted and uncontractedloads Each GENCO shares the uncontracted load of its owncontrol area according to its ACE participation factor Thevalues of system parameters given in Appendix (Table 6)
are used for a comparative study Frequency deviations ofboth areas and tie line deviation after load change as per loaddistribution (Table 5) in each area for test casesA B andC areshown in Figures 7 8 and 9 respectively Two performanceindices (settling time and peak undershoot) were selected forjustification of dynamic performance response of controllersEffect of +30 and minus30 change in parameter values 120573 11987912and 119879119901 (parameters value in Table 7 in Appendix) is alsoexamined Peak undershoot and settling time of both areasand tie line deviation are also determined with +30 andminus30 change in system parameters in each area for test cases
Advances in Fuzzy Systems 9
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 8 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case B) Combination of Poolcoand bilateral contracts (a) frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Table 7 Different cases with different system parameters
119879119901 120573 11987912
Case 1 (nominal value) 20 0425 0545Case 2 (+30 increase) 26 05525 07085Case 3 (minus30 decrease) 14 02975 03815
A B and C shown in Figures 10 11 12 13 14 and 15 Thecomparison of dynamic performances of GA-PID and PSO-PID controllerswith the proposedTSO-FLC controller showsthat proposed TSO-FLC gives better results in terms of lessersettling time and peak undershoot MatlabSimulink is usedfor simulation purpose
In order to examine the performance of controllerspeak undershoot and settling time of both areas and tieline deviation are determined for test cases A B and Cwith standard values of system parameters Apart from this
the effect of +30 and minus30 change in parameter values 12057311987912 and 119879119901 (parameters value in Table 7) is also examinedso further performance indices for +30 and minus30 changein system parameters for different test cases determined areshown in Figures 10 11 12 13 14 and 15 Based on thiscomparison it can be concluded that proposed TSO-FLCgives better results in terms of lesser settling time and peakundershoot compared to GA-PID and PSO-PID controllers
5 Conclusion
In this paper an optimization strategy for FLC is proposedfor AGC This optimization strategy is based on rule baseoptimization and scaling factor and gain factor optimizationof FLC PSO is used as optimization technique The perfor-mance of proposed controller is compared with conventionalPID controller also optimized by two optimization methodsGA and PSO under different test cases based on contractual
10 Advances in Fuzzy Systems
0 5 10 15 20 25 30 35 40 45 50minus0035
minus003minus0025
minus002minus0015
minus001minus0005
00005
001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus004
minus0035minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 9 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case C) Contract violation (a)frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Case AGA-PID 002556 002064 003407 002663 002140 003561PSO-PID 002150 001714 002922 002268 001804 003080TSO-FLC 000972 000750 001380 001118 000865 001579
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)(nominal)Δf1 Δf1 Δf1
(nominal)Δf2 Δf2 Δf2
Figure 10 Peak undershoot comparison at plusmn30 variation insystem parameters for Case A
demands in deregulated power system The dynamic per-formance of proposed controllers is observed on the basisof two performance indices that is settling time and peak
1983015 1751152 2344273 1993948 1761672 23553811340694 1173940 1593159 1340694 1173940 1593159312402 120954 933828 087750 087520 395436
000000
500000
1000000
1500000
2000000
2500000
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)
Settling time (plusmn5)
Δf1 Δf1 Δf2 Δf2(nominal)
Δf1(nominal)
Δf2
Figure 11 Settling time comparison at plusmn30 variation in systemparameters for Case A
undershoot Simulation results show that proposedTSO-FLCcontroller provides a better performance in comparison of
Advances in Fuzzy Systems 11
002645002177000893
002139001732000689
003519002954001269
002714002317001363
002184001847001055
003614003129001913
Case B
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
8500E minus 0
8500E minus 0
8585E minus 0
8500E minus 0
8500E minus 0
8551E minus 0
8500E minus 0
8500E minus 0
8543E minus 0GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal) (nominal) (nominal)
Figure 12 Peak undershoot comparison at plusmn30 variation in system parameters for Case B
19690831301781383480
17569881144269294828
23292181578341545893
20689471391069278520
18352271218930235500
24063641624648279652
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
9006E + 0
2500E + 0
1559E + 0
8092E + 0
2543E + 0
1458E + 0
8668E + 0
2682E + 0
1523E + 0
Settling time (plusmn5)
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal)(nominal)(nominal)
Figure 13 Settling time comparison at plusmn30 variation in system parameters for Case B
GA-PID and PSO-PID controllers Robustness of the TSO-FLC is also justified for +30 and minus30 change in systemparameters for different sets of contractual demands andagain it is observed that TSO-FLC is a suitable controller forAGC in an interconnected power system
Appendix
Speed governor 1(1 + 119904119879119892)
Thermal reheater (1 + 119870119903119904119879119903)(1 + 119904119879119903)
Thermal turbine 1(1 + 119904119879119905)
Power system 119870119901(1 + 119904119879119901)
See Tables 6 and 7
Competing Interests
The authors declare that they have no competing interests
12 Advances in Fuzzy Systems
003448002803001143
002865002275000883
004529003775001625
004000003394001872
003212002700001445
005290004552002641
000000
001000
002000
003000
004000
005000
006000
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
Case C
Peak undershoot
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 14 Peak undershoot comparison at plusmn30 variation in system parameters for Case C
20958661452353404295
18844331286364324176
21740051495980272999
19415891329047232815
25159171748899549258
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
8465E + 0
2550E + 0
1450E + 0
7297E + 0
2553E + 0
1319E + 0
8019E + 0
2730E + 0
1396E + 0
1716E + 0
1082E + 0
2472E + 0
Settling time (plusmn5)
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 15 Settling time comparison at plusmn30 variation in system parameters for Case C
References
[1] F Daneshfar ldquoIntelligent load-frequency control in a deregu-lated environment continuous-valued input extended classifiersystem approachrdquo IET Generation Transmission and Distribu-tion vol 7 no 6 pp 551ndash559 2013
[2] I A Chidambaram and B Paramasivam ldquoOptimized load-frequency simulation in restructured power system with Redoxflow batteries and interline power flow controllerrdquo InternationalJournal of Electrical Power and Energy Systems vol 50 no 1 pp9ndash24 2013
[3] A P Sakis Meliopoulos G J Cokkinides and A G BakirtzisldquoLoad-frequency control service in a deregulated environmentrdquoDecision Support Systems vol 24 no 3-4 pp 243ndash250 1999
[4] F Liu Y H Song J Ma S Mei and Q Lu ldquoOptimalload-frequency control in restructured power systemsrdquo IEEProceedings Generation Transmission andDistribution vol 150no 1 pp 87ndash95 2003
[5] W C Chan and Y Y Hsu ldquoAutomatic generation control ofinterconnected power systems using variable-structure con-trollersrdquo IEE Proceedings C Generation Transmission and Dis-tribution vol 128 no 5 pp 269ndash279 1981
[6] S C Tripathy G S Hope and O P Malik ldquoOptimisationof load-frequency control parameters for power systems withreheat steam turbines and governor deadband nonlinearityrdquoIEE Proceedings C Generation Transmission and Distributionvol 129 no 1 pp 10ndash16 1982
Advances in Fuzzy Systems 13
[7] R D Christie and A Bose ldquoLoad frequency control issues inpower system operations after deregulationrdquo IEEE Transactionson Power Systems vol 11 no 3 pp 1191ndash1200 1995
[8] B H Bakken and O S Grande ldquoAutomatic generation controlin a deregulated power systemrdquo IEEE Transactions on PowerSystems vol 13 no 4 pp 1401ndash1406 1998
[9] V Donde M A Pai and I A Hiskens ldquoSimulation andoptimization in an AGC system after deregulationrdquo IEEETransactions on Power Systems vol 16 no 3 pp 481ndash489 2001
[10] R Roy P Bhatt and S P Ghoshal ldquoEvolutionary computationbased three-area automatic generation controlrdquo Expert Systemswith Applications vol 37 no 8 pp 5913ndash5924 2010
[11] P Bhatt R Roy and S P Ghoshal ldquoOptimized multi areaAGC simulation in restructured power systemsrdquo InternationalJournal of Electrical Power amp Energy Systems vol 32 no 4 pp311ndash322 2010
[12] S P Ghoshal ldquoOptimizations of PID gains by particle swarmoptimizations in fuzzy based automatic generation controlrdquoElectric Power Systems Research vol 72 no 3 pp 203ndash212 2004
[13] I Chiha N Liouane and P Borne ldquoTuning PID controllerusing multiobjective ant colony optimizationrdquo Applied Compu-tational Intelligence and Soft Computing vol 2012 Article ID536326 7 pages 2012
[14] V Mukherjee and S P Ghoshal ldquoIntelligent particle swarmoptimized fuzzy PID controller for AVR systemrdquo Electric PowerSystems Research vol 77 no 12 pp 1689ndash1698 2007
[15] K Naidu H Mokhlis and A H A Bakar ldquoMultiobjective opti-mization using weighted sum Artificial Bee Colony algorithmfor Load Frequency Controlrdquo International Journal of ElectricalPower and Energy Systems vol 55 pp 657ndash667 2014
[16] D Pelusi ldquoOptimization of a fuzzy logic controller using geneticalgorithmsrdquo in Proceedings of the 3rd International Conferenceon IntelligentHuman-Machine Systems andCybernetics (IHMSCrsquo11) pp 143ndash146 Zhejiang China August 2011
[17] T Chaiyatham I Ngamroo S Pothiya and S VachirasricirikulldquoDesign of optimal fuzzy logic-PID controller using bee colonyoptimization for frequency control in an isolated wind-dieselsystemrdquo in Proceedings of the Transmission amp DistributionConference amp Exposition Asia and Pacific vol 1 pp 1ndash4 IEEESeoul The Republic of Korea October 2009
[18] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 2006
[19] M Parida and J Nanda ldquoAutomatic generation control of ahydro-thermal system in deregulated environmentrdquo in Proceed-ings of the 8th International Conference on Electrical Machinesand Systems (ICEMS rsquo05) pp 942ndash947Nanjing China Septem-ber 2005
[20] C C Lee ldquoFuzzy logic in control systems fuzzy logic controllerIIrdquo IEEE Transactions on SystemsMan and Cybernetics vol 20no 2 pp 419ndash435 1990
[21] K R M Vijaya Chandrakala S Balamurugan and K Sankara-narayanan ldquoVariable structure fuzzy gain scheduling based loadfrequency controller for multi source multi area hydro thermalsystemrdquo International Journal of Electrical Power and EnergySystems vol 53 no 1 pp 375ndash381 2013
[22] Y K Bhateshvar and H D Mathur ldquoFrequency stabilizationusing fuzzy logic based controller for multi-area power systemin deregulated environmentrdquo in Proceedings of the 2nd Inter-national Conference on Advances in Control and Optimizationof Dynamical Systems (ACODS rsquo12) pp 1ndash10 Bangalore IndiaFebruary 2012
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Fuzzy Systems 7
0 5 10 15 20 25 30 35 40 45 50708709
71711712713714715716717718
Iteration
Fitn
ess v
alue
Figure 5 FLC optimization of step 1 for rule base optimization
0 10 20 30 40 50 60 70 80 90 10052545658606264666870
Iteration
Fitn
ess v
alue
Figure 6 FLC optimization of step 2 for scaling and gain factoroptimization
Table 3 Fuzzy rules for Area 2 controller
ACEVN MN SN Z SP MP VP
ΔACE
VN VN VN MN VN SN SN ZMN VN VN VN VN SN Z ZSN VN VN VN MN SN SP SPZ MN MN VN Z VP MP MPSP SN SN SP MP VP VP VPMP Z Z SP VP VP VP VPVP Z SP SP VP MP VP VP
Table 4 Optimized scaling and gain parameters for TSO-FLC
Scaling parameters Gain parameters119870119890 119870119888119890 119870119901119906 119870119894119906
FLC for Area 1 112833 093282 143489 218240FLC for Area 2 188194 056237 056237 210918
Themembership functions of each input and each outputare spread across a linear distribution range from minus1 to +1 Intwo stages FLC is optimized by PSO with objective functiongiven in (18)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
Figure 7 Comparison of GA-PID PSO-PID and TSO-FLC forreheat type two-area thermal power system (Case A) Poolco (a)frequency deviation in Area 1 and (b) frequency deviation in Area 2
Rule BaseOptimization In this step apart from center rule allother rules need to be optimized Only one rule is configuredthat when both inputs are zero then output is also zero Insystem under study out of 49 rules 48 rules are required to beoptimizedThe curve between best fitness values with respectto iteration for rule base optimization is shown in Figure 5
Scaling Factor and Gain Optimization In this second stepoptimum values of two scaling factors (119870119890 and 119870119888119890) and twogain parameters (119870119901119906 and 119870119894119906) are needed to be optimizedof FLC Graphically the best fitness values with respect toiteration are represented in Figure 6 Table 4 shows theoptimized scaling and gain parameters for TSO-FLC
4 Test Cases and Simulations
There are three different test cases of deregulated power sys-tem considered for justification of optimum performance ofproposed TSO-FLC controller as compared to conventionalGA-PID andPSO-PID controllersThese test cases are Poolcobased transactions combination of Poolco and bilateral based
8 Advances in Fuzzy Systems
Table 5 Different test cases for proposed system
Test cases cpf matrixContractedload (pu)(Δ119875LD Cont)
Uncontractedload (pu)(Δ119875LDUncont
)
Load Δ119875LD(pu)
ScheduledGENCOs
power (pu)(Δ119875119866)
Scheduled tieline powerflow (pu)(Δ119875tie12 sch)
Case A(Poolco based transactions)
[[[[[[[[[
[
05 05 0 0
05 05 0 0
0 0 05 05
0 0 05 05
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
000
000
000
000
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
0
Case B(combination of Poolco andbilateral basedtransactions)
[[[[[[[[[
[
025 020 025 0
025 020 0 0
050 030 015 0
0 030 060 1
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
000
000
000
000
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
00070
00045
00095
00190
]]]]]]]]]
]
minus00085
Case C(contract violation)
[[[[[[[[[
[
025 020 025 0
025 020 0 0
050 030 015 0
0 030 060 1
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
0000
0004
0000
0008
]]]]]]]]]
]
[[[[[[[[[
[
0010
0014
0010
0018
]]]]]]]]]
]
[[[[[[[[[
[
00090
00065
00135
00230
]]]]]]]]]
]
minus00085
Table 6 System parameters
Rated power (Area 1 and Area 2) 1198751199031 and 1198751199032 2000MW
Transfer function gain of generator (Area 1 and Area 2) 1198701199011 and 1198701199012 120
Generatorrsquos time constant (Area 1 and Area 2) 1198791199011 and 1198791199012 20
Governorrsquos time constant 1198791198921 008
Governorrsquos time constant 1198791198922 002
Steam turbinersquos time constant 119879119905 03
Regulation of the governor (Area 1 and Area 2) 1198771 and 1198772 24
Frequency bias constant 120573 0425
Synchronizing power coefficient 11988612 1
Synchronization coefficient 11987912 0545
transactions and contract violationThe cpf matrix and loadpower from each DISCO are varied in each test case asdepicted in Table 5 Apart from this all GENCOs are allowedto participate equally in each area for AGC therefore ACEparticipation factor (apf 119894) 05 is considered for simulationpurpose
The total generated power Δ119875119892(119894) required by individualGENCO is composed of all contracted and uncontractedloads Each GENCO shares the uncontracted load of its owncontrol area according to its ACE participation factor Thevalues of system parameters given in Appendix (Table 6)
are used for a comparative study Frequency deviations ofboth areas and tie line deviation after load change as per loaddistribution (Table 5) in each area for test casesA B andC areshown in Figures 7 8 and 9 respectively Two performanceindices (settling time and peak undershoot) were selected forjustification of dynamic performance response of controllersEffect of +30 and minus30 change in parameter values 120573 11987912and 119879119901 (parameters value in Table 7 in Appendix) is alsoexamined Peak undershoot and settling time of both areasand tie line deviation are also determined with +30 andminus30 change in system parameters in each area for test cases
Advances in Fuzzy Systems 9
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 8 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case B) Combination of Poolcoand bilateral contracts (a) frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Table 7 Different cases with different system parameters
119879119901 120573 11987912
Case 1 (nominal value) 20 0425 0545Case 2 (+30 increase) 26 05525 07085Case 3 (minus30 decrease) 14 02975 03815
A B and C shown in Figures 10 11 12 13 14 and 15 Thecomparison of dynamic performances of GA-PID and PSO-PID controllerswith the proposedTSO-FLC controller showsthat proposed TSO-FLC gives better results in terms of lessersettling time and peak undershoot MatlabSimulink is usedfor simulation purpose
In order to examine the performance of controllerspeak undershoot and settling time of both areas and tieline deviation are determined for test cases A B and Cwith standard values of system parameters Apart from this
the effect of +30 and minus30 change in parameter values 12057311987912 and 119879119901 (parameters value in Table 7) is also examinedso further performance indices for +30 and minus30 changein system parameters for different test cases determined areshown in Figures 10 11 12 13 14 and 15 Based on thiscomparison it can be concluded that proposed TSO-FLCgives better results in terms of lesser settling time and peakundershoot compared to GA-PID and PSO-PID controllers
5 Conclusion
In this paper an optimization strategy for FLC is proposedfor AGC This optimization strategy is based on rule baseoptimization and scaling factor and gain factor optimizationof FLC PSO is used as optimization technique The perfor-mance of proposed controller is compared with conventionalPID controller also optimized by two optimization methodsGA and PSO under different test cases based on contractual
10 Advances in Fuzzy Systems
0 5 10 15 20 25 30 35 40 45 50minus0035
minus003minus0025
minus002minus0015
minus001minus0005
00005
001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus004
minus0035minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 9 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case C) Contract violation (a)frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Case AGA-PID 002556 002064 003407 002663 002140 003561PSO-PID 002150 001714 002922 002268 001804 003080TSO-FLC 000972 000750 001380 001118 000865 001579
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)(nominal)Δf1 Δf1 Δf1
(nominal)Δf2 Δf2 Δf2
Figure 10 Peak undershoot comparison at plusmn30 variation insystem parameters for Case A
demands in deregulated power system The dynamic per-formance of proposed controllers is observed on the basisof two performance indices that is settling time and peak
1983015 1751152 2344273 1993948 1761672 23553811340694 1173940 1593159 1340694 1173940 1593159312402 120954 933828 087750 087520 395436
000000
500000
1000000
1500000
2000000
2500000
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)
Settling time (plusmn5)
Δf1 Δf1 Δf2 Δf2(nominal)
Δf1(nominal)
Δf2
Figure 11 Settling time comparison at plusmn30 variation in systemparameters for Case A
undershoot Simulation results show that proposedTSO-FLCcontroller provides a better performance in comparison of
Advances in Fuzzy Systems 11
002645002177000893
002139001732000689
003519002954001269
002714002317001363
002184001847001055
003614003129001913
Case B
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
8500E minus 0
8500E minus 0
8585E minus 0
8500E minus 0
8500E minus 0
8551E minus 0
8500E minus 0
8500E minus 0
8543E minus 0GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal) (nominal) (nominal)
Figure 12 Peak undershoot comparison at plusmn30 variation in system parameters for Case B
19690831301781383480
17569881144269294828
23292181578341545893
20689471391069278520
18352271218930235500
24063641624648279652
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
9006E + 0
2500E + 0
1559E + 0
8092E + 0
2543E + 0
1458E + 0
8668E + 0
2682E + 0
1523E + 0
Settling time (plusmn5)
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal)(nominal)(nominal)
Figure 13 Settling time comparison at plusmn30 variation in system parameters for Case B
GA-PID and PSO-PID controllers Robustness of the TSO-FLC is also justified for +30 and minus30 change in systemparameters for different sets of contractual demands andagain it is observed that TSO-FLC is a suitable controller forAGC in an interconnected power system
Appendix
Speed governor 1(1 + 119904119879119892)
Thermal reheater (1 + 119870119903119904119879119903)(1 + 119904119879119903)
Thermal turbine 1(1 + 119904119879119905)
Power system 119870119901(1 + 119904119879119901)
See Tables 6 and 7
Competing Interests
The authors declare that they have no competing interests
12 Advances in Fuzzy Systems
003448002803001143
002865002275000883
004529003775001625
004000003394001872
003212002700001445
005290004552002641
000000
001000
002000
003000
004000
005000
006000
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
Case C
Peak undershoot
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 14 Peak undershoot comparison at plusmn30 variation in system parameters for Case C
20958661452353404295
18844331286364324176
21740051495980272999
19415891329047232815
25159171748899549258
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
8465E + 0
2550E + 0
1450E + 0
7297E + 0
2553E + 0
1319E + 0
8019E + 0
2730E + 0
1396E + 0
1716E + 0
1082E + 0
2472E + 0
Settling time (plusmn5)
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 15 Settling time comparison at plusmn30 variation in system parameters for Case C
References
[1] F Daneshfar ldquoIntelligent load-frequency control in a deregu-lated environment continuous-valued input extended classifiersystem approachrdquo IET Generation Transmission and Distribu-tion vol 7 no 6 pp 551ndash559 2013
[2] I A Chidambaram and B Paramasivam ldquoOptimized load-frequency simulation in restructured power system with Redoxflow batteries and interline power flow controllerrdquo InternationalJournal of Electrical Power and Energy Systems vol 50 no 1 pp9ndash24 2013
[3] A P Sakis Meliopoulos G J Cokkinides and A G BakirtzisldquoLoad-frequency control service in a deregulated environmentrdquoDecision Support Systems vol 24 no 3-4 pp 243ndash250 1999
[4] F Liu Y H Song J Ma S Mei and Q Lu ldquoOptimalload-frequency control in restructured power systemsrdquo IEEProceedings Generation Transmission andDistribution vol 150no 1 pp 87ndash95 2003
[5] W C Chan and Y Y Hsu ldquoAutomatic generation control ofinterconnected power systems using variable-structure con-trollersrdquo IEE Proceedings C Generation Transmission and Dis-tribution vol 128 no 5 pp 269ndash279 1981
[6] S C Tripathy G S Hope and O P Malik ldquoOptimisationof load-frequency control parameters for power systems withreheat steam turbines and governor deadband nonlinearityrdquoIEE Proceedings C Generation Transmission and Distributionvol 129 no 1 pp 10ndash16 1982
Advances in Fuzzy Systems 13
[7] R D Christie and A Bose ldquoLoad frequency control issues inpower system operations after deregulationrdquo IEEE Transactionson Power Systems vol 11 no 3 pp 1191ndash1200 1995
[8] B H Bakken and O S Grande ldquoAutomatic generation controlin a deregulated power systemrdquo IEEE Transactions on PowerSystems vol 13 no 4 pp 1401ndash1406 1998
[9] V Donde M A Pai and I A Hiskens ldquoSimulation andoptimization in an AGC system after deregulationrdquo IEEETransactions on Power Systems vol 16 no 3 pp 481ndash489 2001
[10] R Roy P Bhatt and S P Ghoshal ldquoEvolutionary computationbased three-area automatic generation controlrdquo Expert Systemswith Applications vol 37 no 8 pp 5913ndash5924 2010
[11] P Bhatt R Roy and S P Ghoshal ldquoOptimized multi areaAGC simulation in restructured power systemsrdquo InternationalJournal of Electrical Power amp Energy Systems vol 32 no 4 pp311ndash322 2010
[12] S P Ghoshal ldquoOptimizations of PID gains by particle swarmoptimizations in fuzzy based automatic generation controlrdquoElectric Power Systems Research vol 72 no 3 pp 203ndash212 2004
[13] I Chiha N Liouane and P Borne ldquoTuning PID controllerusing multiobjective ant colony optimizationrdquo Applied Compu-tational Intelligence and Soft Computing vol 2012 Article ID536326 7 pages 2012
[14] V Mukherjee and S P Ghoshal ldquoIntelligent particle swarmoptimized fuzzy PID controller for AVR systemrdquo Electric PowerSystems Research vol 77 no 12 pp 1689ndash1698 2007
[15] K Naidu H Mokhlis and A H A Bakar ldquoMultiobjective opti-mization using weighted sum Artificial Bee Colony algorithmfor Load Frequency Controlrdquo International Journal of ElectricalPower and Energy Systems vol 55 pp 657ndash667 2014
[16] D Pelusi ldquoOptimization of a fuzzy logic controller using geneticalgorithmsrdquo in Proceedings of the 3rd International Conferenceon IntelligentHuman-Machine Systems andCybernetics (IHMSCrsquo11) pp 143ndash146 Zhejiang China August 2011
[17] T Chaiyatham I Ngamroo S Pothiya and S VachirasricirikulldquoDesign of optimal fuzzy logic-PID controller using bee colonyoptimization for frequency control in an isolated wind-dieselsystemrdquo in Proceedings of the Transmission amp DistributionConference amp Exposition Asia and Pacific vol 1 pp 1ndash4 IEEESeoul The Republic of Korea October 2009
[18] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 2006
[19] M Parida and J Nanda ldquoAutomatic generation control of ahydro-thermal system in deregulated environmentrdquo in Proceed-ings of the 8th International Conference on Electrical Machinesand Systems (ICEMS rsquo05) pp 942ndash947Nanjing China Septem-ber 2005
[20] C C Lee ldquoFuzzy logic in control systems fuzzy logic controllerIIrdquo IEEE Transactions on SystemsMan and Cybernetics vol 20no 2 pp 419ndash435 1990
[21] K R M Vijaya Chandrakala S Balamurugan and K Sankara-narayanan ldquoVariable structure fuzzy gain scheduling based loadfrequency controller for multi source multi area hydro thermalsystemrdquo International Journal of Electrical Power and EnergySystems vol 53 no 1 pp 375ndash381 2013
[22] Y K Bhateshvar and H D Mathur ldquoFrequency stabilizationusing fuzzy logic based controller for multi-area power systemin deregulated environmentrdquo in Proceedings of the 2nd Inter-national Conference on Advances in Control and Optimizationof Dynamical Systems (ACODS rsquo12) pp 1ndash10 Bangalore IndiaFebruary 2012
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
8 Advances in Fuzzy Systems
Table 5 Different test cases for proposed system
Test cases cpf matrixContractedload (pu)(Δ119875LD Cont)
Uncontractedload (pu)(Δ119875LDUncont
)
Load Δ119875LD(pu)
ScheduledGENCOs
power (pu)(Δ119875119866)
Scheduled tieline powerflow (pu)(Δ119875tie12 sch)
Case A(Poolco based transactions)
[[[[[[[[[
[
05 05 0 0
05 05 0 0
0 0 05 05
0 0 05 05
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
000
000
000
000
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
0
Case B(combination of Poolco andbilateral basedtransactions)
[[[[[[[[[
[
025 020 025 0
025 020 0 0
050 030 015 0
0 030 060 1
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
000
000
000
000
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
00070
00045
00095
00190
]]]]]]]]]
]
minus00085
Case C(contract violation)
[[[[[[[[[
[
025 020 025 0
025 020 0 0
050 030 015 0
0 030 060 1
]]]]]]]]]
]
[[[[[[[[[
[
001
001
001
001
]]]]]]]]]
]
[[[[[[[[[
[
0000
0004
0000
0008
]]]]]]]]]
]
[[[[[[[[[
[
0010
0014
0010
0018
]]]]]]]]]
]
[[[[[[[[[
[
00090
00065
00135
00230
]]]]]]]]]
]
minus00085
Table 6 System parameters
Rated power (Area 1 and Area 2) 1198751199031 and 1198751199032 2000MW
Transfer function gain of generator (Area 1 and Area 2) 1198701199011 and 1198701199012 120
Generatorrsquos time constant (Area 1 and Area 2) 1198791199011 and 1198791199012 20
Governorrsquos time constant 1198791198921 008
Governorrsquos time constant 1198791198922 002
Steam turbinersquos time constant 119879119905 03
Regulation of the governor (Area 1 and Area 2) 1198771 and 1198772 24
Frequency bias constant 120573 0425
Synchronizing power coefficient 11988612 1
Synchronization coefficient 11987912 0545
transactions and contract violationThe cpf matrix and loadpower from each DISCO are varied in each test case asdepicted in Table 5 Apart from this all GENCOs are allowedto participate equally in each area for AGC therefore ACEparticipation factor (apf 119894) 05 is considered for simulationpurpose
The total generated power Δ119875119892(119894) required by individualGENCO is composed of all contracted and uncontractedloads Each GENCO shares the uncontracted load of its owncontrol area according to its ACE participation factor Thevalues of system parameters given in Appendix (Table 6)
are used for a comparative study Frequency deviations ofboth areas and tie line deviation after load change as per loaddistribution (Table 5) in each area for test casesA B andC areshown in Figures 7 8 and 9 respectively Two performanceindices (settling time and peak undershoot) were selected forjustification of dynamic performance response of controllersEffect of +30 and minus30 change in parameter values 120573 11987912and 119879119901 (parameters value in Table 7 in Appendix) is alsoexamined Peak undershoot and settling time of both areasand tie line deviation are also determined with +30 andminus30 change in system parameters in each area for test cases
Advances in Fuzzy Systems 9
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 8 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case B) Combination of Poolcoand bilateral contracts (a) frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Table 7 Different cases with different system parameters
119879119901 120573 11987912
Case 1 (nominal value) 20 0425 0545Case 2 (+30 increase) 26 05525 07085Case 3 (minus30 decrease) 14 02975 03815
A B and C shown in Figures 10 11 12 13 14 and 15 Thecomparison of dynamic performances of GA-PID and PSO-PID controllerswith the proposedTSO-FLC controller showsthat proposed TSO-FLC gives better results in terms of lessersettling time and peak undershoot MatlabSimulink is usedfor simulation purpose
In order to examine the performance of controllerspeak undershoot and settling time of both areas and tieline deviation are determined for test cases A B and Cwith standard values of system parameters Apart from this
the effect of +30 and minus30 change in parameter values 12057311987912 and 119879119901 (parameters value in Table 7) is also examinedso further performance indices for +30 and minus30 changein system parameters for different test cases determined areshown in Figures 10 11 12 13 14 and 15 Based on thiscomparison it can be concluded that proposed TSO-FLCgives better results in terms of lesser settling time and peakundershoot compared to GA-PID and PSO-PID controllers
5 Conclusion
In this paper an optimization strategy for FLC is proposedfor AGC This optimization strategy is based on rule baseoptimization and scaling factor and gain factor optimizationof FLC PSO is used as optimization technique The perfor-mance of proposed controller is compared with conventionalPID controller also optimized by two optimization methodsGA and PSO under different test cases based on contractual
10 Advances in Fuzzy Systems
0 5 10 15 20 25 30 35 40 45 50minus0035
minus003minus0025
minus002minus0015
minus001minus0005
00005
001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus004
minus0035minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 9 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case C) Contract violation (a)frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Case AGA-PID 002556 002064 003407 002663 002140 003561PSO-PID 002150 001714 002922 002268 001804 003080TSO-FLC 000972 000750 001380 001118 000865 001579
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)(nominal)Δf1 Δf1 Δf1
(nominal)Δf2 Δf2 Δf2
Figure 10 Peak undershoot comparison at plusmn30 variation insystem parameters for Case A
demands in deregulated power system The dynamic per-formance of proposed controllers is observed on the basisof two performance indices that is settling time and peak
1983015 1751152 2344273 1993948 1761672 23553811340694 1173940 1593159 1340694 1173940 1593159312402 120954 933828 087750 087520 395436
000000
500000
1000000
1500000
2000000
2500000
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)
Settling time (plusmn5)
Δf1 Δf1 Δf2 Δf2(nominal)
Δf1(nominal)
Δf2
Figure 11 Settling time comparison at plusmn30 variation in systemparameters for Case A
undershoot Simulation results show that proposedTSO-FLCcontroller provides a better performance in comparison of
Advances in Fuzzy Systems 11
002645002177000893
002139001732000689
003519002954001269
002714002317001363
002184001847001055
003614003129001913
Case B
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
8500E minus 0
8500E minus 0
8585E minus 0
8500E minus 0
8500E minus 0
8551E minus 0
8500E minus 0
8500E minus 0
8543E minus 0GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal) (nominal) (nominal)
Figure 12 Peak undershoot comparison at plusmn30 variation in system parameters for Case B
19690831301781383480
17569881144269294828
23292181578341545893
20689471391069278520
18352271218930235500
24063641624648279652
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
9006E + 0
2500E + 0
1559E + 0
8092E + 0
2543E + 0
1458E + 0
8668E + 0
2682E + 0
1523E + 0
Settling time (plusmn5)
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal)(nominal)(nominal)
Figure 13 Settling time comparison at plusmn30 variation in system parameters for Case B
GA-PID and PSO-PID controllers Robustness of the TSO-FLC is also justified for +30 and minus30 change in systemparameters for different sets of contractual demands andagain it is observed that TSO-FLC is a suitable controller forAGC in an interconnected power system
Appendix
Speed governor 1(1 + 119904119879119892)
Thermal reheater (1 + 119870119903119904119879119903)(1 + 119904119879119903)
Thermal turbine 1(1 + 119904119879119905)
Power system 119870119901(1 + 119904119879119901)
See Tables 6 and 7
Competing Interests
The authors declare that they have no competing interests
12 Advances in Fuzzy Systems
003448002803001143
002865002275000883
004529003775001625
004000003394001872
003212002700001445
005290004552002641
000000
001000
002000
003000
004000
005000
006000
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
Case C
Peak undershoot
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 14 Peak undershoot comparison at plusmn30 variation in system parameters for Case C
20958661452353404295
18844331286364324176
21740051495980272999
19415891329047232815
25159171748899549258
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
8465E + 0
2550E + 0
1450E + 0
7297E + 0
2553E + 0
1319E + 0
8019E + 0
2730E + 0
1396E + 0
1716E + 0
1082E + 0
2472E + 0
Settling time (plusmn5)
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 15 Settling time comparison at plusmn30 variation in system parameters for Case C
References
[1] F Daneshfar ldquoIntelligent load-frequency control in a deregu-lated environment continuous-valued input extended classifiersystem approachrdquo IET Generation Transmission and Distribu-tion vol 7 no 6 pp 551ndash559 2013
[2] I A Chidambaram and B Paramasivam ldquoOptimized load-frequency simulation in restructured power system with Redoxflow batteries and interline power flow controllerrdquo InternationalJournal of Electrical Power and Energy Systems vol 50 no 1 pp9ndash24 2013
[3] A P Sakis Meliopoulos G J Cokkinides and A G BakirtzisldquoLoad-frequency control service in a deregulated environmentrdquoDecision Support Systems vol 24 no 3-4 pp 243ndash250 1999
[4] F Liu Y H Song J Ma S Mei and Q Lu ldquoOptimalload-frequency control in restructured power systemsrdquo IEEProceedings Generation Transmission andDistribution vol 150no 1 pp 87ndash95 2003
[5] W C Chan and Y Y Hsu ldquoAutomatic generation control ofinterconnected power systems using variable-structure con-trollersrdquo IEE Proceedings C Generation Transmission and Dis-tribution vol 128 no 5 pp 269ndash279 1981
[6] S C Tripathy G S Hope and O P Malik ldquoOptimisationof load-frequency control parameters for power systems withreheat steam turbines and governor deadband nonlinearityrdquoIEE Proceedings C Generation Transmission and Distributionvol 129 no 1 pp 10ndash16 1982
Advances in Fuzzy Systems 13
[7] R D Christie and A Bose ldquoLoad frequency control issues inpower system operations after deregulationrdquo IEEE Transactionson Power Systems vol 11 no 3 pp 1191ndash1200 1995
[8] B H Bakken and O S Grande ldquoAutomatic generation controlin a deregulated power systemrdquo IEEE Transactions on PowerSystems vol 13 no 4 pp 1401ndash1406 1998
[9] V Donde M A Pai and I A Hiskens ldquoSimulation andoptimization in an AGC system after deregulationrdquo IEEETransactions on Power Systems vol 16 no 3 pp 481ndash489 2001
[10] R Roy P Bhatt and S P Ghoshal ldquoEvolutionary computationbased three-area automatic generation controlrdquo Expert Systemswith Applications vol 37 no 8 pp 5913ndash5924 2010
[11] P Bhatt R Roy and S P Ghoshal ldquoOptimized multi areaAGC simulation in restructured power systemsrdquo InternationalJournal of Electrical Power amp Energy Systems vol 32 no 4 pp311ndash322 2010
[12] S P Ghoshal ldquoOptimizations of PID gains by particle swarmoptimizations in fuzzy based automatic generation controlrdquoElectric Power Systems Research vol 72 no 3 pp 203ndash212 2004
[13] I Chiha N Liouane and P Borne ldquoTuning PID controllerusing multiobjective ant colony optimizationrdquo Applied Compu-tational Intelligence and Soft Computing vol 2012 Article ID536326 7 pages 2012
[14] V Mukherjee and S P Ghoshal ldquoIntelligent particle swarmoptimized fuzzy PID controller for AVR systemrdquo Electric PowerSystems Research vol 77 no 12 pp 1689ndash1698 2007
[15] K Naidu H Mokhlis and A H A Bakar ldquoMultiobjective opti-mization using weighted sum Artificial Bee Colony algorithmfor Load Frequency Controlrdquo International Journal of ElectricalPower and Energy Systems vol 55 pp 657ndash667 2014
[16] D Pelusi ldquoOptimization of a fuzzy logic controller using geneticalgorithmsrdquo in Proceedings of the 3rd International Conferenceon IntelligentHuman-Machine Systems andCybernetics (IHMSCrsquo11) pp 143ndash146 Zhejiang China August 2011
[17] T Chaiyatham I Ngamroo S Pothiya and S VachirasricirikulldquoDesign of optimal fuzzy logic-PID controller using bee colonyoptimization for frequency control in an isolated wind-dieselsystemrdquo in Proceedings of the Transmission amp DistributionConference amp Exposition Asia and Pacific vol 1 pp 1ndash4 IEEESeoul The Republic of Korea October 2009
[18] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 2006
[19] M Parida and J Nanda ldquoAutomatic generation control of ahydro-thermal system in deregulated environmentrdquo in Proceed-ings of the 8th International Conference on Electrical Machinesand Systems (ICEMS rsquo05) pp 942ndash947Nanjing China Septem-ber 2005
[20] C C Lee ldquoFuzzy logic in control systems fuzzy logic controllerIIrdquo IEEE Transactions on SystemsMan and Cybernetics vol 20no 2 pp 419ndash435 1990
[21] K R M Vijaya Chandrakala S Balamurugan and K Sankara-narayanan ldquoVariable structure fuzzy gain scheduling based loadfrequency controller for multi source multi area hydro thermalsystemrdquo International Journal of Electrical Power and EnergySystems vol 53 no 1 pp 375ndash381 2013
[22] Y K Bhateshvar and H D Mathur ldquoFrequency stabilizationusing fuzzy logic based controller for multi-area power systemin deregulated environmentrdquo in Proceedings of the 2nd Inter-national Conference on Advances in Control and Optimizationof Dynamical Systems (ACODS rsquo12) pp 1ndash10 Bangalore IndiaFebruary 2012
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Fuzzy Systems 9
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 8 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case B) Combination of Poolcoand bilateral contracts (a) frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Table 7 Different cases with different system parameters
119879119901 120573 11987912
Case 1 (nominal value) 20 0425 0545Case 2 (+30 increase) 26 05525 07085Case 3 (minus30 decrease) 14 02975 03815
A B and C shown in Figures 10 11 12 13 14 and 15 Thecomparison of dynamic performances of GA-PID and PSO-PID controllerswith the proposedTSO-FLC controller showsthat proposed TSO-FLC gives better results in terms of lessersettling time and peak undershoot MatlabSimulink is usedfor simulation purpose
In order to examine the performance of controllerspeak undershoot and settling time of both areas and tieline deviation are determined for test cases A B and Cwith standard values of system parameters Apart from this
the effect of +30 and minus30 change in parameter values 12057311987912 and 119879119901 (parameters value in Table 7) is also examinedso further performance indices for +30 and minus30 changein system parameters for different test cases determined areshown in Figures 10 11 12 13 14 and 15 Based on thiscomparison it can be concluded that proposed TSO-FLCgives better results in terms of lesser settling time and peakundershoot compared to GA-PID and PSO-PID controllers
5 Conclusion
In this paper an optimization strategy for FLC is proposedfor AGC This optimization strategy is based on rule baseoptimization and scaling factor and gain factor optimizationof FLC PSO is used as optimization technique The perfor-mance of proposed controller is compared with conventionalPID controller also optimized by two optimization methodsGA and PSO under different test cases based on contractual
10 Advances in Fuzzy Systems
0 5 10 15 20 25 30 35 40 45 50minus0035
minus003minus0025
minus002minus0015
minus001minus0005
00005
001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus004
minus0035minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 9 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case C) Contract violation (a)frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Case AGA-PID 002556 002064 003407 002663 002140 003561PSO-PID 002150 001714 002922 002268 001804 003080TSO-FLC 000972 000750 001380 001118 000865 001579
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)(nominal)Δf1 Δf1 Δf1
(nominal)Δf2 Δf2 Δf2
Figure 10 Peak undershoot comparison at plusmn30 variation insystem parameters for Case A
demands in deregulated power system The dynamic per-formance of proposed controllers is observed on the basisof two performance indices that is settling time and peak
1983015 1751152 2344273 1993948 1761672 23553811340694 1173940 1593159 1340694 1173940 1593159312402 120954 933828 087750 087520 395436
000000
500000
1000000
1500000
2000000
2500000
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)
Settling time (plusmn5)
Δf1 Δf1 Δf2 Δf2(nominal)
Δf1(nominal)
Δf2
Figure 11 Settling time comparison at plusmn30 variation in systemparameters for Case A
undershoot Simulation results show that proposedTSO-FLCcontroller provides a better performance in comparison of
Advances in Fuzzy Systems 11
002645002177000893
002139001732000689
003519002954001269
002714002317001363
002184001847001055
003614003129001913
Case B
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
8500E minus 0
8500E minus 0
8585E minus 0
8500E minus 0
8500E minus 0
8551E minus 0
8500E minus 0
8500E minus 0
8543E minus 0GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal) (nominal) (nominal)
Figure 12 Peak undershoot comparison at plusmn30 variation in system parameters for Case B
19690831301781383480
17569881144269294828
23292181578341545893
20689471391069278520
18352271218930235500
24063641624648279652
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
9006E + 0
2500E + 0
1559E + 0
8092E + 0
2543E + 0
1458E + 0
8668E + 0
2682E + 0
1523E + 0
Settling time (plusmn5)
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal)(nominal)(nominal)
Figure 13 Settling time comparison at plusmn30 variation in system parameters for Case B
GA-PID and PSO-PID controllers Robustness of the TSO-FLC is also justified for +30 and minus30 change in systemparameters for different sets of contractual demands andagain it is observed that TSO-FLC is a suitable controller forAGC in an interconnected power system
Appendix
Speed governor 1(1 + 119904119879119892)
Thermal reheater (1 + 119870119903119904119879119903)(1 + 119904119879119903)
Thermal turbine 1(1 + 119904119879119905)
Power system 119870119901(1 + 119904119879119901)
See Tables 6 and 7
Competing Interests
The authors declare that they have no competing interests
12 Advances in Fuzzy Systems
003448002803001143
002865002275000883
004529003775001625
004000003394001872
003212002700001445
005290004552002641
000000
001000
002000
003000
004000
005000
006000
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
Case C
Peak undershoot
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 14 Peak undershoot comparison at plusmn30 variation in system parameters for Case C
20958661452353404295
18844331286364324176
21740051495980272999
19415891329047232815
25159171748899549258
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
8465E + 0
2550E + 0
1450E + 0
7297E + 0
2553E + 0
1319E + 0
8019E + 0
2730E + 0
1396E + 0
1716E + 0
1082E + 0
2472E + 0
Settling time (plusmn5)
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 15 Settling time comparison at plusmn30 variation in system parameters for Case C
References
[1] F Daneshfar ldquoIntelligent load-frequency control in a deregu-lated environment continuous-valued input extended classifiersystem approachrdquo IET Generation Transmission and Distribu-tion vol 7 no 6 pp 551ndash559 2013
[2] I A Chidambaram and B Paramasivam ldquoOptimized load-frequency simulation in restructured power system with Redoxflow batteries and interline power flow controllerrdquo InternationalJournal of Electrical Power and Energy Systems vol 50 no 1 pp9ndash24 2013
[3] A P Sakis Meliopoulos G J Cokkinides and A G BakirtzisldquoLoad-frequency control service in a deregulated environmentrdquoDecision Support Systems vol 24 no 3-4 pp 243ndash250 1999
[4] F Liu Y H Song J Ma S Mei and Q Lu ldquoOptimalload-frequency control in restructured power systemsrdquo IEEProceedings Generation Transmission andDistribution vol 150no 1 pp 87ndash95 2003
[5] W C Chan and Y Y Hsu ldquoAutomatic generation control ofinterconnected power systems using variable-structure con-trollersrdquo IEE Proceedings C Generation Transmission and Dis-tribution vol 128 no 5 pp 269ndash279 1981
[6] S C Tripathy G S Hope and O P Malik ldquoOptimisationof load-frequency control parameters for power systems withreheat steam turbines and governor deadband nonlinearityrdquoIEE Proceedings C Generation Transmission and Distributionvol 129 no 1 pp 10ndash16 1982
Advances in Fuzzy Systems 13
[7] R D Christie and A Bose ldquoLoad frequency control issues inpower system operations after deregulationrdquo IEEE Transactionson Power Systems vol 11 no 3 pp 1191ndash1200 1995
[8] B H Bakken and O S Grande ldquoAutomatic generation controlin a deregulated power systemrdquo IEEE Transactions on PowerSystems vol 13 no 4 pp 1401ndash1406 1998
[9] V Donde M A Pai and I A Hiskens ldquoSimulation andoptimization in an AGC system after deregulationrdquo IEEETransactions on Power Systems vol 16 no 3 pp 481ndash489 2001
[10] R Roy P Bhatt and S P Ghoshal ldquoEvolutionary computationbased three-area automatic generation controlrdquo Expert Systemswith Applications vol 37 no 8 pp 5913ndash5924 2010
[11] P Bhatt R Roy and S P Ghoshal ldquoOptimized multi areaAGC simulation in restructured power systemsrdquo InternationalJournal of Electrical Power amp Energy Systems vol 32 no 4 pp311ndash322 2010
[12] S P Ghoshal ldquoOptimizations of PID gains by particle swarmoptimizations in fuzzy based automatic generation controlrdquoElectric Power Systems Research vol 72 no 3 pp 203ndash212 2004
[13] I Chiha N Liouane and P Borne ldquoTuning PID controllerusing multiobjective ant colony optimizationrdquo Applied Compu-tational Intelligence and Soft Computing vol 2012 Article ID536326 7 pages 2012
[14] V Mukherjee and S P Ghoshal ldquoIntelligent particle swarmoptimized fuzzy PID controller for AVR systemrdquo Electric PowerSystems Research vol 77 no 12 pp 1689ndash1698 2007
[15] K Naidu H Mokhlis and A H A Bakar ldquoMultiobjective opti-mization using weighted sum Artificial Bee Colony algorithmfor Load Frequency Controlrdquo International Journal of ElectricalPower and Energy Systems vol 55 pp 657ndash667 2014
[16] D Pelusi ldquoOptimization of a fuzzy logic controller using geneticalgorithmsrdquo in Proceedings of the 3rd International Conferenceon IntelligentHuman-Machine Systems andCybernetics (IHMSCrsquo11) pp 143ndash146 Zhejiang China August 2011
[17] T Chaiyatham I Ngamroo S Pothiya and S VachirasricirikulldquoDesign of optimal fuzzy logic-PID controller using bee colonyoptimization for frequency control in an isolated wind-dieselsystemrdquo in Proceedings of the Transmission amp DistributionConference amp Exposition Asia and Pacific vol 1 pp 1ndash4 IEEESeoul The Republic of Korea October 2009
[18] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 2006
[19] M Parida and J Nanda ldquoAutomatic generation control of ahydro-thermal system in deregulated environmentrdquo in Proceed-ings of the 8th International Conference on Electrical Machinesand Systems (ICEMS rsquo05) pp 942ndash947Nanjing China Septem-ber 2005
[20] C C Lee ldquoFuzzy logic in control systems fuzzy logic controllerIIrdquo IEEE Transactions on SystemsMan and Cybernetics vol 20no 2 pp 419ndash435 1990
[21] K R M Vijaya Chandrakala S Balamurugan and K Sankara-narayanan ldquoVariable structure fuzzy gain scheduling based loadfrequency controller for multi source multi area hydro thermalsystemrdquo International Journal of Electrical Power and EnergySystems vol 53 no 1 pp 375ndash381 2013
[22] Y K Bhateshvar and H D Mathur ldquoFrequency stabilizationusing fuzzy logic based controller for multi-area power systemin deregulated environmentrdquo in Proceedings of the 2nd Inter-national Conference on Advances in Control and Optimizationof Dynamical Systems (ACODS rsquo12) pp 1ndash10 Bangalore IndiaFebruary 2012
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
10 Advances in Fuzzy Systems
0 5 10 15 20 25 30 35 40 45 50minus0035
minus003minus0025
minus002minus0015
minus001minus0005
00005
001
Time (s)
Chan
ge in
freq
1
GA-PIDPSO-PIDTSO-FLC
(a)
0 5 10 15 20 25 30 35 40 45 50minus004
minus0035minus003
minus0025minus002
minus0015minus001
minus00050
0005
Time (s)
Chan
ge in
freq
2
GA-PIDPSO-PIDTSO-FLC
(b)
0 5 10 15 20 25 30 35 40 45 50minus9minus8minus7minus6minus5minus4minus3minus2minus1
01
Time (s)
GA-PIDPSO-PIDTSO-FLC
times10minus3
Chan
ge in
Ptie12
tie li
ne
(c)
Figure 9 Comparison of GA-PID PSO-PID and TSO-FLC for reheat type two-area thermal power system (Case C) Contract violation (a)frequency deviation in Area 1 (b) frequency deviation in Area 2 and (c) tie line power deviation
Case AGA-PID 002556 002064 003407 002663 002140 003561PSO-PID 002150 001714 002922 002268 001804 003080TSO-FLC 000972 000750 001380 001118 000865 001579
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)(nominal)Δf1 Δf1 Δf1
(nominal)Δf2 Δf2 Δf2
Figure 10 Peak undershoot comparison at plusmn30 variation insystem parameters for Case A
demands in deregulated power system The dynamic per-formance of proposed controllers is observed on the basisof two performance indices that is settling time and peak
1983015 1751152 2344273 1993948 1761672 23553811340694 1173940 1593159 1340694 1173940 1593159312402 120954 933828 087750 087520 395436
000000
500000
1000000
1500000
2000000
2500000
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)
Settling time (plusmn5)
Δf1 Δf1 Δf2 Δf2(nominal)
Δf1(nominal)
Δf2
Figure 11 Settling time comparison at plusmn30 variation in systemparameters for Case A
undershoot Simulation results show that proposedTSO-FLCcontroller provides a better performance in comparison of
Advances in Fuzzy Systems 11
002645002177000893
002139001732000689
003519002954001269
002714002317001363
002184001847001055
003614003129001913
Case B
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
8500E minus 0
8500E minus 0
8585E minus 0
8500E minus 0
8500E minus 0
8551E minus 0
8500E minus 0
8500E minus 0
8543E minus 0GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal) (nominal) (nominal)
Figure 12 Peak undershoot comparison at plusmn30 variation in system parameters for Case B
19690831301781383480
17569881144269294828
23292181578341545893
20689471391069278520
18352271218930235500
24063641624648279652
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
9006E + 0
2500E + 0
1559E + 0
8092E + 0
2543E + 0
1458E + 0
8668E + 0
2682E + 0
1523E + 0
Settling time (plusmn5)
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal)(nominal)(nominal)
Figure 13 Settling time comparison at plusmn30 variation in system parameters for Case B
GA-PID and PSO-PID controllers Robustness of the TSO-FLC is also justified for +30 and minus30 change in systemparameters for different sets of contractual demands andagain it is observed that TSO-FLC is a suitable controller forAGC in an interconnected power system
Appendix
Speed governor 1(1 + 119904119879119892)
Thermal reheater (1 + 119870119903119904119879119903)(1 + 119904119879119903)
Thermal turbine 1(1 + 119904119879119905)
Power system 119870119901(1 + 119904119879119901)
See Tables 6 and 7
Competing Interests
The authors declare that they have no competing interests
12 Advances in Fuzzy Systems
003448002803001143
002865002275000883
004529003775001625
004000003394001872
003212002700001445
005290004552002641
000000
001000
002000
003000
004000
005000
006000
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
Case C
Peak undershoot
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 14 Peak undershoot comparison at plusmn30 variation in system parameters for Case C
20958661452353404295
18844331286364324176
21740051495980272999
19415891329047232815
25159171748899549258
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
8465E + 0
2550E + 0
1450E + 0
7297E + 0
2553E + 0
1319E + 0
8019E + 0
2730E + 0
1396E + 0
1716E + 0
1082E + 0
2472E + 0
Settling time (plusmn5)
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 15 Settling time comparison at plusmn30 variation in system parameters for Case C
References
[1] F Daneshfar ldquoIntelligent load-frequency control in a deregu-lated environment continuous-valued input extended classifiersystem approachrdquo IET Generation Transmission and Distribu-tion vol 7 no 6 pp 551ndash559 2013
[2] I A Chidambaram and B Paramasivam ldquoOptimized load-frequency simulation in restructured power system with Redoxflow batteries and interline power flow controllerrdquo InternationalJournal of Electrical Power and Energy Systems vol 50 no 1 pp9ndash24 2013
[3] A P Sakis Meliopoulos G J Cokkinides and A G BakirtzisldquoLoad-frequency control service in a deregulated environmentrdquoDecision Support Systems vol 24 no 3-4 pp 243ndash250 1999
[4] F Liu Y H Song J Ma S Mei and Q Lu ldquoOptimalload-frequency control in restructured power systemsrdquo IEEProceedings Generation Transmission andDistribution vol 150no 1 pp 87ndash95 2003
[5] W C Chan and Y Y Hsu ldquoAutomatic generation control ofinterconnected power systems using variable-structure con-trollersrdquo IEE Proceedings C Generation Transmission and Dis-tribution vol 128 no 5 pp 269ndash279 1981
[6] S C Tripathy G S Hope and O P Malik ldquoOptimisationof load-frequency control parameters for power systems withreheat steam turbines and governor deadband nonlinearityrdquoIEE Proceedings C Generation Transmission and Distributionvol 129 no 1 pp 10ndash16 1982
Advances in Fuzzy Systems 13
[7] R D Christie and A Bose ldquoLoad frequency control issues inpower system operations after deregulationrdquo IEEE Transactionson Power Systems vol 11 no 3 pp 1191ndash1200 1995
[8] B H Bakken and O S Grande ldquoAutomatic generation controlin a deregulated power systemrdquo IEEE Transactions on PowerSystems vol 13 no 4 pp 1401ndash1406 1998
[9] V Donde M A Pai and I A Hiskens ldquoSimulation andoptimization in an AGC system after deregulationrdquo IEEETransactions on Power Systems vol 16 no 3 pp 481ndash489 2001
[10] R Roy P Bhatt and S P Ghoshal ldquoEvolutionary computationbased three-area automatic generation controlrdquo Expert Systemswith Applications vol 37 no 8 pp 5913ndash5924 2010
[11] P Bhatt R Roy and S P Ghoshal ldquoOptimized multi areaAGC simulation in restructured power systemsrdquo InternationalJournal of Electrical Power amp Energy Systems vol 32 no 4 pp311ndash322 2010
[12] S P Ghoshal ldquoOptimizations of PID gains by particle swarmoptimizations in fuzzy based automatic generation controlrdquoElectric Power Systems Research vol 72 no 3 pp 203ndash212 2004
[13] I Chiha N Liouane and P Borne ldquoTuning PID controllerusing multiobjective ant colony optimizationrdquo Applied Compu-tational Intelligence and Soft Computing vol 2012 Article ID536326 7 pages 2012
[14] V Mukherjee and S P Ghoshal ldquoIntelligent particle swarmoptimized fuzzy PID controller for AVR systemrdquo Electric PowerSystems Research vol 77 no 12 pp 1689ndash1698 2007
[15] K Naidu H Mokhlis and A H A Bakar ldquoMultiobjective opti-mization using weighted sum Artificial Bee Colony algorithmfor Load Frequency Controlrdquo International Journal of ElectricalPower and Energy Systems vol 55 pp 657ndash667 2014
[16] D Pelusi ldquoOptimization of a fuzzy logic controller using geneticalgorithmsrdquo in Proceedings of the 3rd International Conferenceon IntelligentHuman-Machine Systems andCybernetics (IHMSCrsquo11) pp 143ndash146 Zhejiang China August 2011
[17] T Chaiyatham I Ngamroo S Pothiya and S VachirasricirikulldquoDesign of optimal fuzzy logic-PID controller using bee colonyoptimization for frequency control in an isolated wind-dieselsystemrdquo in Proceedings of the Transmission amp DistributionConference amp Exposition Asia and Pacific vol 1 pp 1ndash4 IEEESeoul The Republic of Korea October 2009
[18] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 2006
[19] M Parida and J Nanda ldquoAutomatic generation control of ahydro-thermal system in deregulated environmentrdquo in Proceed-ings of the 8th International Conference on Electrical Machinesand Systems (ICEMS rsquo05) pp 942ndash947Nanjing China Septem-ber 2005
[20] C C Lee ldquoFuzzy logic in control systems fuzzy logic controllerIIrdquo IEEE Transactions on SystemsMan and Cybernetics vol 20no 2 pp 419ndash435 1990
[21] K R M Vijaya Chandrakala S Balamurugan and K Sankara-narayanan ldquoVariable structure fuzzy gain scheduling based loadfrequency controller for multi source multi area hydro thermalsystemrdquo International Journal of Electrical Power and EnergySystems vol 53 no 1 pp 375ndash381 2013
[22] Y K Bhateshvar and H D Mathur ldquoFrequency stabilizationusing fuzzy logic based controller for multi-area power systemin deregulated environmentrdquo in Proceedings of the 2nd Inter-national Conference on Advances in Control and Optimizationof Dynamical Systems (ACODS rsquo12) pp 1ndash10 Bangalore IndiaFebruary 2012
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Fuzzy Systems 11
002645002177000893
002139001732000689
003519002954001269
002714002317001363
002184001847001055
003614003129001913
Case B
000000000500001000001500002000002500003000003500004000
Peak undershoot
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
8500E minus 0
8500E minus 0
8585E minus 0
8500E minus 0
8500E minus 0
8551E minus 0
8500E minus 0
8500E minus 0
8543E minus 0GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal) (nominal) (nominal)
Figure 12 Peak undershoot comparison at plusmn30 variation in system parameters for Case B
19690831301781383480
17569881144269294828
23292181578341545893
20689471391069278520
18352271218930235500
24063641624648279652
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
9006E + 0
2500E + 0
1559E + 0
8092E + 0
2543E + 0
1458E + 0
8668E + 0
2682E + 0
1523E + 0
Settling time (plusmn5)
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12
GA-PIDPSO-PIDTSO-FLC
Δf1 Δf1 Δf1 Δf2 Δf2 Δf2(nominal)(nominal)(nominal)
Figure 13 Settling time comparison at plusmn30 variation in system parameters for Case B
GA-PID and PSO-PID controllers Robustness of the TSO-FLC is also justified for +30 and minus30 change in systemparameters for different sets of contractual demands andagain it is observed that TSO-FLC is a suitable controller forAGC in an interconnected power system
Appendix
Speed governor 1(1 + 119904119879119892)
Thermal reheater (1 + 119870119903119904119879119903)(1 + 119904119879119903)
Thermal turbine 1(1 + 119904119879119905)
Power system 119870119901(1 + 119904119879119901)
See Tables 6 and 7
Competing Interests
The authors declare that they have no competing interests
12 Advances in Fuzzy Systems
003448002803001143
002865002275000883
004529003775001625
004000003394001872
003212002700001445
005290004552002641
000000
001000
002000
003000
004000
005000
006000
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
Case C
Peak undershoot
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 14 Peak undershoot comparison at plusmn30 variation in system parameters for Case C
20958661452353404295
18844331286364324176
21740051495980272999
19415891329047232815
25159171748899549258
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
8465E + 0
2550E + 0
1450E + 0
7297E + 0
2553E + 0
1319E + 0
8019E + 0
2730E + 0
1396E + 0
1716E + 0
1082E + 0
2472E + 0
Settling time (plusmn5)
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 15 Settling time comparison at plusmn30 variation in system parameters for Case C
References
[1] F Daneshfar ldquoIntelligent load-frequency control in a deregu-lated environment continuous-valued input extended classifiersystem approachrdquo IET Generation Transmission and Distribu-tion vol 7 no 6 pp 551ndash559 2013
[2] I A Chidambaram and B Paramasivam ldquoOptimized load-frequency simulation in restructured power system with Redoxflow batteries and interline power flow controllerrdquo InternationalJournal of Electrical Power and Energy Systems vol 50 no 1 pp9ndash24 2013
[3] A P Sakis Meliopoulos G J Cokkinides and A G BakirtzisldquoLoad-frequency control service in a deregulated environmentrdquoDecision Support Systems vol 24 no 3-4 pp 243ndash250 1999
[4] F Liu Y H Song J Ma S Mei and Q Lu ldquoOptimalload-frequency control in restructured power systemsrdquo IEEProceedings Generation Transmission andDistribution vol 150no 1 pp 87ndash95 2003
[5] W C Chan and Y Y Hsu ldquoAutomatic generation control ofinterconnected power systems using variable-structure con-trollersrdquo IEE Proceedings C Generation Transmission and Dis-tribution vol 128 no 5 pp 269ndash279 1981
[6] S C Tripathy G S Hope and O P Malik ldquoOptimisationof load-frequency control parameters for power systems withreheat steam turbines and governor deadband nonlinearityrdquoIEE Proceedings C Generation Transmission and Distributionvol 129 no 1 pp 10ndash16 1982
Advances in Fuzzy Systems 13
[7] R D Christie and A Bose ldquoLoad frequency control issues inpower system operations after deregulationrdquo IEEE Transactionson Power Systems vol 11 no 3 pp 1191ndash1200 1995
[8] B H Bakken and O S Grande ldquoAutomatic generation controlin a deregulated power systemrdquo IEEE Transactions on PowerSystems vol 13 no 4 pp 1401ndash1406 1998
[9] V Donde M A Pai and I A Hiskens ldquoSimulation andoptimization in an AGC system after deregulationrdquo IEEETransactions on Power Systems vol 16 no 3 pp 481ndash489 2001
[10] R Roy P Bhatt and S P Ghoshal ldquoEvolutionary computationbased three-area automatic generation controlrdquo Expert Systemswith Applications vol 37 no 8 pp 5913ndash5924 2010
[11] P Bhatt R Roy and S P Ghoshal ldquoOptimized multi areaAGC simulation in restructured power systemsrdquo InternationalJournal of Electrical Power amp Energy Systems vol 32 no 4 pp311ndash322 2010
[12] S P Ghoshal ldquoOptimizations of PID gains by particle swarmoptimizations in fuzzy based automatic generation controlrdquoElectric Power Systems Research vol 72 no 3 pp 203ndash212 2004
[13] I Chiha N Liouane and P Borne ldquoTuning PID controllerusing multiobjective ant colony optimizationrdquo Applied Compu-tational Intelligence and Soft Computing vol 2012 Article ID536326 7 pages 2012
[14] V Mukherjee and S P Ghoshal ldquoIntelligent particle swarmoptimized fuzzy PID controller for AVR systemrdquo Electric PowerSystems Research vol 77 no 12 pp 1689ndash1698 2007
[15] K Naidu H Mokhlis and A H A Bakar ldquoMultiobjective opti-mization using weighted sum Artificial Bee Colony algorithmfor Load Frequency Controlrdquo International Journal of ElectricalPower and Energy Systems vol 55 pp 657ndash667 2014
[16] D Pelusi ldquoOptimization of a fuzzy logic controller using geneticalgorithmsrdquo in Proceedings of the 3rd International Conferenceon IntelligentHuman-Machine Systems andCybernetics (IHMSCrsquo11) pp 143ndash146 Zhejiang China August 2011
[17] T Chaiyatham I Ngamroo S Pothiya and S VachirasricirikulldquoDesign of optimal fuzzy logic-PID controller using bee colonyoptimization for frequency control in an isolated wind-dieselsystemrdquo in Proceedings of the Transmission amp DistributionConference amp Exposition Asia and Pacific vol 1 pp 1ndash4 IEEESeoul The Republic of Korea October 2009
[18] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 2006
[19] M Parida and J Nanda ldquoAutomatic generation control of ahydro-thermal system in deregulated environmentrdquo in Proceed-ings of the 8th International Conference on Electrical Machinesand Systems (ICEMS rsquo05) pp 942ndash947Nanjing China Septem-ber 2005
[20] C C Lee ldquoFuzzy logic in control systems fuzzy logic controllerIIrdquo IEEE Transactions on SystemsMan and Cybernetics vol 20no 2 pp 419ndash435 1990
[21] K R M Vijaya Chandrakala S Balamurugan and K Sankara-narayanan ldquoVariable structure fuzzy gain scheduling based loadfrequency controller for multi source multi area hydro thermalsystemrdquo International Journal of Electrical Power and EnergySystems vol 53 no 1 pp 375ndash381 2013
[22] Y K Bhateshvar and H D Mathur ldquoFrequency stabilizationusing fuzzy logic based controller for multi-area power systemin deregulated environmentrdquo in Proceedings of the 2nd Inter-national Conference on Advances in Control and Optimizationof Dynamical Systems (ACODS rsquo12) pp 1ndash10 Bangalore IndiaFebruary 2012
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
12 Advances in Fuzzy Systems
003448002803001143
002865002275000883
004529003775001625
004000003394001872
003212002700001445
005290004552002641
000000
001000
002000
003000
004000
005000
006000
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
8500E minus 0
Case C
Peak undershoot
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 14 Peak undershoot comparison at plusmn30 variation in system parameters for Case C
20958661452353404295
18844331286364324176
21740051495980272999
19415891329047232815
25159171748899549258
000000
500000
1000000
1500000
2000000
2500000
3000000
Axi
s titl
e
8465E + 0
2550E + 0
1450E + 0
7297E + 0
2553E + 0
1319E + 0
8019E + 0
2730E + 0
1396E + 0
1716E + 0
1082E + 0
2472E + 0
Settling time (plusmn5)
GA-PIDPSO-PIDTSO-FLC
(+30) (minus30) (+30) (minus30)ΔPtie12
(+30)ΔPtie12
(minus30)ΔPtie12Δf1 Δf1 Δf1 Δf2 Δf2 Δf2
(nominal)(nominal)(nominal)
Figure 15 Settling time comparison at plusmn30 variation in system parameters for Case C
References
[1] F Daneshfar ldquoIntelligent load-frequency control in a deregu-lated environment continuous-valued input extended classifiersystem approachrdquo IET Generation Transmission and Distribu-tion vol 7 no 6 pp 551ndash559 2013
[2] I A Chidambaram and B Paramasivam ldquoOptimized load-frequency simulation in restructured power system with Redoxflow batteries and interline power flow controllerrdquo InternationalJournal of Electrical Power and Energy Systems vol 50 no 1 pp9ndash24 2013
[3] A P Sakis Meliopoulos G J Cokkinides and A G BakirtzisldquoLoad-frequency control service in a deregulated environmentrdquoDecision Support Systems vol 24 no 3-4 pp 243ndash250 1999
[4] F Liu Y H Song J Ma S Mei and Q Lu ldquoOptimalload-frequency control in restructured power systemsrdquo IEEProceedings Generation Transmission andDistribution vol 150no 1 pp 87ndash95 2003
[5] W C Chan and Y Y Hsu ldquoAutomatic generation control ofinterconnected power systems using variable-structure con-trollersrdquo IEE Proceedings C Generation Transmission and Dis-tribution vol 128 no 5 pp 269ndash279 1981
[6] S C Tripathy G S Hope and O P Malik ldquoOptimisationof load-frequency control parameters for power systems withreheat steam turbines and governor deadband nonlinearityrdquoIEE Proceedings C Generation Transmission and Distributionvol 129 no 1 pp 10ndash16 1982
Advances in Fuzzy Systems 13
[7] R D Christie and A Bose ldquoLoad frequency control issues inpower system operations after deregulationrdquo IEEE Transactionson Power Systems vol 11 no 3 pp 1191ndash1200 1995
[8] B H Bakken and O S Grande ldquoAutomatic generation controlin a deregulated power systemrdquo IEEE Transactions on PowerSystems vol 13 no 4 pp 1401ndash1406 1998
[9] V Donde M A Pai and I A Hiskens ldquoSimulation andoptimization in an AGC system after deregulationrdquo IEEETransactions on Power Systems vol 16 no 3 pp 481ndash489 2001
[10] R Roy P Bhatt and S P Ghoshal ldquoEvolutionary computationbased three-area automatic generation controlrdquo Expert Systemswith Applications vol 37 no 8 pp 5913ndash5924 2010
[11] P Bhatt R Roy and S P Ghoshal ldquoOptimized multi areaAGC simulation in restructured power systemsrdquo InternationalJournal of Electrical Power amp Energy Systems vol 32 no 4 pp311ndash322 2010
[12] S P Ghoshal ldquoOptimizations of PID gains by particle swarmoptimizations in fuzzy based automatic generation controlrdquoElectric Power Systems Research vol 72 no 3 pp 203ndash212 2004
[13] I Chiha N Liouane and P Borne ldquoTuning PID controllerusing multiobjective ant colony optimizationrdquo Applied Compu-tational Intelligence and Soft Computing vol 2012 Article ID536326 7 pages 2012
[14] V Mukherjee and S P Ghoshal ldquoIntelligent particle swarmoptimized fuzzy PID controller for AVR systemrdquo Electric PowerSystems Research vol 77 no 12 pp 1689ndash1698 2007
[15] K Naidu H Mokhlis and A H A Bakar ldquoMultiobjective opti-mization using weighted sum Artificial Bee Colony algorithmfor Load Frequency Controlrdquo International Journal of ElectricalPower and Energy Systems vol 55 pp 657ndash667 2014
[16] D Pelusi ldquoOptimization of a fuzzy logic controller using geneticalgorithmsrdquo in Proceedings of the 3rd International Conferenceon IntelligentHuman-Machine Systems andCybernetics (IHMSCrsquo11) pp 143ndash146 Zhejiang China August 2011
[17] T Chaiyatham I Ngamroo S Pothiya and S VachirasricirikulldquoDesign of optimal fuzzy logic-PID controller using bee colonyoptimization for frequency control in an isolated wind-dieselsystemrdquo in Proceedings of the Transmission amp DistributionConference amp Exposition Asia and Pacific vol 1 pp 1ndash4 IEEESeoul The Republic of Korea October 2009
[18] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 2006
[19] M Parida and J Nanda ldquoAutomatic generation control of ahydro-thermal system in deregulated environmentrdquo in Proceed-ings of the 8th International Conference on Electrical Machinesand Systems (ICEMS rsquo05) pp 942ndash947Nanjing China Septem-ber 2005
[20] C C Lee ldquoFuzzy logic in control systems fuzzy logic controllerIIrdquo IEEE Transactions on SystemsMan and Cybernetics vol 20no 2 pp 419ndash435 1990
[21] K R M Vijaya Chandrakala S Balamurugan and K Sankara-narayanan ldquoVariable structure fuzzy gain scheduling based loadfrequency controller for multi source multi area hydro thermalsystemrdquo International Journal of Electrical Power and EnergySystems vol 53 no 1 pp 375ndash381 2013
[22] Y K Bhateshvar and H D Mathur ldquoFrequency stabilizationusing fuzzy logic based controller for multi-area power systemin deregulated environmentrdquo in Proceedings of the 2nd Inter-national Conference on Advances in Control and Optimizationof Dynamical Systems (ACODS rsquo12) pp 1ndash10 Bangalore IndiaFebruary 2012
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Advances in Fuzzy Systems 13
[7] R D Christie and A Bose ldquoLoad frequency control issues inpower system operations after deregulationrdquo IEEE Transactionson Power Systems vol 11 no 3 pp 1191ndash1200 1995
[8] B H Bakken and O S Grande ldquoAutomatic generation controlin a deregulated power systemrdquo IEEE Transactions on PowerSystems vol 13 no 4 pp 1401ndash1406 1998
[9] V Donde M A Pai and I A Hiskens ldquoSimulation andoptimization in an AGC system after deregulationrdquo IEEETransactions on Power Systems vol 16 no 3 pp 481ndash489 2001
[10] R Roy P Bhatt and S P Ghoshal ldquoEvolutionary computationbased three-area automatic generation controlrdquo Expert Systemswith Applications vol 37 no 8 pp 5913ndash5924 2010
[11] P Bhatt R Roy and S P Ghoshal ldquoOptimized multi areaAGC simulation in restructured power systemsrdquo InternationalJournal of Electrical Power amp Energy Systems vol 32 no 4 pp311ndash322 2010
[12] S P Ghoshal ldquoOptimizations of PID gains by particle swarmoptimizations in fuzzy based automatic generation controlrdquoElectric Power Systems Research vol 72 no 3 pp 203ndash212 2004
[13] I Chiha N Liouane and P Borne ldquoTuning PID controllerusing multiobjective ant colony optimizationrdquo Applied Compu-tational Intelligence and Soft Computing vol 2012 Article ID536326 7 pages 2012
[14] V Mukherjee and S P Ghoshal ldquoIntelligent particle swarmoptimized fuzzy PID controller for AVR systemrdquo Electric PowerSystems Research vol 77 no 12 pp 1689ndash1698 2007
[15] K Naidu H Mokhlis and A H A Bakar ldquoMultiobjective opti-mization using weighted sum Artificial Bee Colony algorithmfor Load Frequency Controlrdquo International Journal of ElectricalPower and Energy Systems vol 55 pp 657ndash667 2014
[16] D Pelusi ldquoOptimization of a fuzzy logic controller using geneticalgorithmsrdquo in Proceedings of the 3rd International Conferenceon IntelligentHuman-Machine Systems andCybernetics (IHMSCrsquo11) pp 143ndash146 Zhejiang China August 2011
[17] T Chaiyatham I Ngamroo S Pothiya and S VachirasricirikulldquoDesign of optimal fuzzy logic-PID controller using bee colonyoptimization for frequency control in an isolated wind-dieselsystemrdquo in Proceedings of the Transmission amp DistributionConference amp Exposition Asia and Pacific vol 1 pp 1ndash4 IEEESeoul The Republic of Korea October 2009
[18] P Kundur Power System Stability and Control McGraw-HillNew York NY USA 2006
[19] M Parida and J Nanda ldquoAutomatic generation control of ahydro-thermal system in deregulated environmentrdquo in Proceed-ings of the 8th International Conference on Electrical Machinesand Systems (ICEMS rsquo05) pp 942ndash947Nanjing China Septem-ber 2005
[20] C C Lee ldquoFuzzy logic in control systems fuzzy logic controllerIIrdquo IEEE Transactions on SystemsMan and Cybernetics vol 20no 2 pp 419ndash435 1990
[21] K R M Vijaya Chandrakala S Balamurugan and K Sankara-narayanan ldquoVariable structure fuzzy gain scheduling based loadfrequency controller for multi source multi area hydro thermalsystemrdquo International Journal of Electrical Power and EnergySystems vol 53 no 1 pp 375ndash381 2013
[22] Y K Bhateshvar and H D Mathur ldquoFrequency stabilizationusing fuzzy logic based controller for multi-area power systemin deregulated environmentrdquo in Proceedings of the 2nd Inter-national Conference on Advances in Control and Optimizationof Dynamical Systems (ACODS rsquo12) pp 1ndash10 Bangalore IndiaFebruary 2012
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
