Journal of the Franklin Institute 345 (2008) 166181

Optimal location and controller design of

optimal location and controller parameters for power system stability improvement. The nonlinear

ARTICLE IN PRESS

www.elsevier.com/locate/jfranklin

0016-0032/$32.00 r 2007 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

doi:10.1016/j.jfranklin.2007.08.002

Corresponding author. Tel.: +91 9897563294.

E-mail address: panda_sidhartha@rediffmail.com (S. Panda).simulation results show that optimally located STATCOM improves the transient stability and

coordinated design of STATCOM-based controller and PSSs improve greatly the system damping.

Finally, the coordinated design problem is extended to a four-machine two-area system and the

results show that the inter-area and local modes of oscillations are well damped with the proposed

PSO-optimized controllers.

r 2007 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Keywords: Static synchronous compensator; Transient stability; Optimal location; Particle swarm optimization;

Power system stabilizer; Coordinated design; Power system stabilitySTATCOM for power system stabilityimprovement using PSO

Sidhartha Panda, Narayana Prasad Padhy

Department of Electrical Engineering, Indian Institute of Technology, Roorkee, Uttarakhand-247667, India

Received 14 February 2007; received in revised form 23 July 2007; accepted 1 August 2007

Abstract

The optimal location of a static synchronous compensator (STATCOM) and its coordinated

design with power system stabilizers (PSSs) for power system stability improvement are presented in

this paper. First, the location of STATCOM to improve transient stability is formulated as an

optimization problem and particle swarm optimization (PSO) is employed to search for its optimal

location. Then, coordinated design problem of STATCOM-based controller with multiple PSS is

formulated as an optimization problem and optimal controller parameters are obtained using PSO.

A two-area test system is used to show the effectiveness of the proposed approach for determining the

ARTICLE IN PRESS1. Introduction

Reactive power compensation is an important issue in electrical power systems andshunt exible AC transmission system (FACTS) devices play an important role incontrolling the reactive power ow to the power network and, hence, the system voltageuctuations and stability. Static synchronous compensator (STATCOM) is member ofFACTS family that is connected in shunt with the system. Even though the primarypurpose of STATCOM is to support bus voltage by injecting (or absorbing) reactivepower, it is also capable of improving the power system stability [1]. It has been provedthat shunt FACTS devices give maximum benet from their stabilized voltage supportwhen sited at the mid-point of the transmission line [2]. The rst swing stability of thesystem is greatly inuenced by choice of different models of the transmission line [3]. Forlong transmission lines, when the actual model of the line is considered, the results maydeviate signicantly from those found for the simplied model. With pre-dened directionof real power ow, the shunt FACTS devices need to be placed slightly off-center towardsthe sending end for maximum benet from the transient stability point of view [4,5].Application of GA to determine the optimal location of the shunt FACTS devices fortransient stability improvement has also been reported in the literature [6].Power system stabilizers (PSSs) are one of the most common controls used to damp out

power system oscillations. When a STATCOM is present in a power system to support thebus voltage, a supplementary damping controller could be designed to modulate theSTATCOM bus voltage in order to improve damping of system oscillations [7]. But,the interaction among PSSs and STATCOM-based controller may enhance or degrade thedamping of certain modes of rotors oscillating modes. To improve overall systemperformance, many researches were made on the coordination between PSSs and FACTSpower oscillation damping controllers [811].Although the local control signals are easy to get, they are not as highly controllable and

observable as wide area signals for the inter-area oscillation modes. Due to restriction oflocal measurements, these controllers based on local signals tend to be difcult to offersatisfactory performance under various system operating conditions. With the rapidadvancement in wide area measurement systems technology, fast communication networksand powerful information technology, the widely dispersed signals of power systems can becentralized, processed and distributed even in real time, which makes the wide area signal agood alternative for control input [12]. A number of conventional techniques have beenreported in the literature pertaining to design problems of conventional PSSs: theeigenvalue assignment, mathematical programming, gradient procedure for optimizationand also the modern control theory. Unfortunately, the conventional techniques are timeconsuming as they are iterative and require heavy computation burden and slowconvergence. In addition, the search process is susceptible to be trapped in local minimaand the solution obtained may not be optimal [13]. The evolutionary methods constitutean approach to search for the optimum solutions via some form of directed random searchprocess. A relevant characteristic of the evolutionary methods is that they search forsolutions without previous problem knowledge. Recently, particle swarm optimization(PSO) appeared as a promising evolutionary technique for handling the optimizationproblems. PSO is a population-based stochastic optimization technique, inspired by socialbehavior of bird ocking or sh schooling [14]. This paper proposes to use PSO technique

S. Panda, N.P. Padhy / Journal of the Franklin Institute 345 (2008) 166181 167to determine optimal location of STATCOM for transient stability improvement.

For damping the power system oscillations and for improving the interactions betweenPSSs and STATCOM-based controller, PSO-based optimal tuning approach is employedto coordinately design the proposed damping controllers. The difference of speeddeviations is taken as the input signal for the proposed STATCOM-based controller.The reminder of the paper is organized as follows. A two-area system with a STATCOM

is described in Section 2. In Section 3, a brief overview of PSO is provided. Optimallocation of STATCOM and its optimal controller parameters are formulated asoptimization problems in Section 4. The computer simulation results for system understudy are presented and discussed in Section 5.

2. Two-area system with STATCOM

ARTICLE IN PRESSS. Panda, N.P. Padhy / Journal of the Franklin Institute 345 (2008) 166181168Consider a two-area system (areas 1 and 2), connected by a long transmission line with aSTATCOM as shown in Fig. 1. The direction of real power ow (PL) is assumed to befrom area-1 to -2. If the rating of the STATCOM is large enough to supply the reactivepower required to maintain constant voltage magnitude at the point of connection, iteffectively divides the transmission line into two sections (sections 1 and 2). In Fig. 1, L isthe distance from the sending end, at which the STATCOM is located.The power ows at the sending end and receiving end for a long transmission line with

distributed parameters can be written as [15]

PS K1 cos yB yA K2 cos yB d, (1)

PR K2 cos yB d K3 cos yB yA, (2)where

K1 AV 2S=B; K2 AVSVR=B; K3 AVR=Band

A jAjyA; B jBjyB;VR jVRj0; VS jVSjd.

It is clear from Eq. (2) that the receiving-end real power PR reaches the maximum valuewhen the angle d becomes yB. However, the sending-end real power PS of Eq. (1) becomesmaximum at d 180yB.

Sending-end Receiving-endLoad-1 Load-2

VSC

VS VR

VST

VM

L

section-1 section-2

VDC

iST

Area-1 Area-2

PLFig. 1. Two-area system with STATCOM.

ARTICLE IN PRESSThe power-angle characteristic of the line using the actual line model is shown in Fig. 2(without the STATCOM). Fig. 2 is drawn using Eqs. (1) and (2) by varying the powerangle d, from 01 to 1801. It is noticed that when the angle d increases from zero, both thesending-end power (SEP) and receiving-end powers (REP) are increased. As the lineresistances are not neglected, the angle yB is slightly less than 901. Hence, as d increases,rst the angle d becomes equal to yB, at which point the REP becomes maximum (point ain Fig. 2). With further increase in d, it becomes equal to 180yB, at which point SEPbecomes maximum (point b in Fig. 2). So, REP rst reaches the maximum value at anangle d1 followed by the maximum SEP at an angle d2.Now let us consider that the STATCOM is placed at the mid-point of the line as shown

in Fig. 1, and its rating is large enough to supply the reactive power required to maintain aconstant voltage magnitude at mid-point. So the transmission line is divided into two equalsections and the SEP and REP characteristic of two equal sections are identical. Eachsection can be represented by the same power-angle characteristic curve of Fig. 2. But,

0 50 100 150 2000

5

10

15

Power angle [deg]

SEP

REP

b

ac

213

SE

P &

RE

P [pu]

Fig. 2. Sending-end and receiving-end power-angle characteristics for actual line model.

S. Panda, N.P. Padhy / Journal of the Franklin Institute 345 (2008) 166181 169from Fig. 2, it is clear that maximum value of SEP is more than the maximum value ofREP for a line section. Hence, for the two equal sections with identical power-anglecharacteristic, maximum SEP of section-2 (SEP-2) is more than maximum REP ofsection-1 (REP-1). If section-1 delivers the maximum power at its receiving-end (point a, inFig. 2) the corresponding SEP of section-2 can be represented by the same power level(point c, in Fig. 2). So, even though the section-2 is capable of carrying more power, itcarries that much power which it receives at its receiving-end. Hence the maximum powertransfer capability of the system is limited by the maximum REP-1. The total transmissionangle at the maximum power point is d d1+d3 and if the power angle is further increasedthe power transfer through the line decreases because of the decrease in maximum REP-1and section-1 operates in unstable region. When maximum REP-1 is greater thanmaximum SEP-2, section-2 operates in the unstable region at higher power angles and Pdcharacteristics follows REP curve. However, when maximum REP-1 is less than maximumSEP-2, section-1 operates in the unstable region at higher power angles and Pdcharacteristics follows SEP curve. The above unusual change in the pattern of the Pdcurve which signicantly affects the stability of the system can be utilized to improve thesystem stability. As for a given initial operating condition and fault clearing time the area

ARTICLE IN PRESSbetween the Pd curve and the initial operating power line is a measure of the deceleratingarea. In equal-area criterion method this area is used to determine the stability of thesystem. This area can be increased by shifting the Pd curve towards the left by shiftingthe location of the STATCOM towards the sending-end, and the stability can be furtherimproved.The SEP and REP power-angle characteristics depend upon the length of the line

section. For lower values of L (i.e., as the location of the STATCOM is moved towards thesending end), the length of line section-1 decreases and the length of line section-2increases. Hence, the maximum REP-1 increases while the maximum SEP-2 decreases.Thus the point a in Fig. 2 moves upwards and point b goes downwards. MaximumREP-1 will be equal to maximum SEP-2 at some off-center location of STATCOM. Inother words, as the location of STATCOM is moved towards the sending-end, at somevalue of L, the points a and b become equal and are at the same power level. Thelocation of STATCOM at which the points a and b are equal is the optimal locationfrom transient stability improvement point of view. In the present paper, PSO technique isapplied to determine the optimal location of STATCOM.

3. Overview of particle swarm optimization

PSO method is a member of wide category of swarm intelligence methods for solving theoptimization problems. It is a population-based search algorithm where each individual isreferred to as particle and represents a candidate solution. Each particle in PSO iesthrough the search space with an adaptable velocity that is dynamically modied accordingto its own ying experience and also to the ying experience of the other particles. In PSO,each particle strive to improve itself by imitating traits from their successful peers. Further,each particle has a memory and hence it is capable of remembering the best position in thesearch space ever visited by it. The position corresponding to the best tness is known aspbest and the overall best out of all the particles in the population is called gbest [16,17].The modied velocity and position of each particle can be calculated using the current

velocity and the distance from the pbestj,g to gbestg as shown in the following formulas [18]:

vt1j;g wvtj;g c1r1 pbestj;g xtj;g c2r2 gbestg xtj;g, (3)

xt1j;g xtj;g vt1j;g . (4)

with j 1; 2; . . . ; n and j 1; 2; . . . ;m, where n is the number of particles in a group; m thenumber of members in a particle; t the number of iterations (generations); v

tj;g thevelocity

of particle j at iteration t, Vming pvtj;gpVmaxg ; w the inertia weight factor; c1 and c2 are thecognitive and social acceleration factors, respectively; r1 and r2 are the random numbersuniformly distributed in the range (0, 1); x

tj;g is the current position of particle j at iteration

t; pbestj the pbest of particle j; gbest the gbest of the group.The j-th particle in the swarm is represented by a g-dimensional vector xj

xj;1; xj;2; . . . ;xj;g and its rate of position change (velocity) is denoted by anotherg-dimensional vector vj vj;1; vj;2; . . . ; vj;g. The best previous position of the j-th particlevector pbestj pbestj;1; pbestj;2; . . . ; pbestj;g. The index of best particle among all theparticles in the group is represented by gbestg. In PSO, each particle moves in the search

S. Panda, N.P. Padhy / Journal of the Franklin Institute 345 (2008) 166181170space with a velocity according to its own previous best solution and its groups previous

unstable at all locations of STATCOM.

ARTICLE IN PRESSStep-2: Employ PSO to minimize the objective function JStep-3: Check for stability of the system.Step-4: If the system is unstable, decrease TFC by a small step and repeat from Step-2.

Stop if the system is stable.The system will be stable at TFC TFCF only if the STATCOM is placed at optimal

location obtained by the above method and for TFC4TFCF the system becomes unstable atbest solution. The velocity update in a PSO consists of three parts: momentum, cognitiveand social parts. The balance among these parts determines the performance of a PSOalgorithm. The parameters c1 and c2 determine the relative pull of pbest and gbest and theparameters r1 and r2 help in stochastically varying these pulls. In the above equations,superscripts denote the iteration number.

4. Problem formulation

4.1. Optimal location of STATCOM

As explained in Section 2, the power transfer capability and hence the transient stabilityof the system can be improved by locating STATCOM slightly off-center towards thesending-end instead of the mid-point. For a given initial operating conditions, there will bean optimal location of STATCOM where the maximum sending-end power of section-1 isequal to the maximum receiving-end power of section-2. From transient stability point ofview, the value of maximum sending-end power is important as the power that can bedrawn from generator terminals immediately after fault clearance inuences the transientstability. Therefore, the objective function to maintain transient stability can be written inthe following form:

Objective function J jmaximumDd1 Dd1j, (5)where Dd1 and Dd2 are the rotor angle deviation following a disturbance of generators inareas 1 and 2, respectively, and |maximum(Dd1Dd2)| is the absolute value of maximumrotor angle deviation difference of two areas.If |maximum(Dd1Dd2)|o1801 the system is stable. For objective function calculation,

the time-domain simulation of the nonlinear system model is carried out for the simulationperiod. PSO is employed to search for the location of STATCOM where the value ofobjective function is minimum. The problem constraints are the location bounds.Therefore, the design problem can be formulated as the following optimization problem:

minimize J (6)

subject to

LminpLpLmax, (7)where L is the length of line section from the sending-end to the location of STATCOM.The following steps are followed to search for the optimal location of STATCOM toimprove transient stability:Step-1: Initially set the fault clearing time TFC to a high value so that the system is

S. Panda, N.P. Padhy / Journal of the Franklin Institute 345 (2008) 166181 171all locations.

4.2. Coordinated design of STATCOM-based controller and PSS

The commonly used leadlag structure is chosen in this study as STATCOM-basedcontroller as shown in Fig. 3. The structure consists of: a gain block, a signal washoutblock and two-stage phase-compensation block. The phase-compensation blockprovides the appropriate phase-lead characteristics to compensate for the phase lagbetween input and the output signals. The signal washout block serves as a high-passlter which allows signals associated with oscillations in input signal to pass unchanged.Without it steady changes in input would modify the output. From the viewpointof the washout function the value of washout time constant is not critical and may be inthe range 120 s [19]. In this structure, the washout time constants TWS and thetime constants T2s, T4s are usually prespecied. In the present study, TW 10 s andT2s T4s 0.3 s are used. The controller gain KS and the time constants T1s and T3s are tobe determined.The generic PSS block of the SimPowerSystem (SPS) toolbox is used to add damping to

the rotor oscillations of the synchronous machine by controlling its excitation. The output

ARTICLE IN PRESSS. Panda, N.P. Padhy / Journal of the Franklin Institute 345 (2008) 166181172signal of the PSS is used as an additional input (VS) to the excitation system block. ThePSS input signal can be either the machine speed deviation or acceleration power. The PSSmodel consists of a low-pass lter, a general gain, a washout high-pass lter, a phase-compensation system, and an output limiter as shown in Fig. 4. The general gain KPdetermines the amount of damping produced by the stabilizer. The washout high-pass ltereliminates low frequencies that are present in the input signal and allows the PSS torespond only to changes in the input. The phase-compensation system is used tocompensate the phase lag between the excitation voltage and the electrical torque of thesynchronous machine. In this structure, a washout time constant TWP 3 s is used. Thetime constants T1P and T2P are to be determined.It is worth mentioning that the PSS and STATCOM-based controllers are designed to

minimize the power system oscillations after a large disturbance so as to improve thepower system stability. In the present study, an integral time absolute error of the speed

1 + sTWS

sTWS

1 + sT2S

1 + sT1s

1 + sT4S

1 + sT3SKS

VST

Gain

blockWashout

block

Two-stage

lead-lag block

+

+Input Output

VST_Ref

VST

Vmax

Vmin

ST

ST

Fig. 3. Structure of the STATCOM-based controller.

Gain

block Lead-lag blockWashout

block

InputKP

1 + sTWP

sTWP1 + sT2P

1 + sT1P

Output

VS

VSmax

Vmin

Sensor

SFig. 4. Structure of the generic power system stabilizer.

ARTICLE IN PRESSdeviations is taken as the objective function expressed as follows:

J Z ttsimt0

Doj j tdt, (8)

where Do denotes the speed deviation for a set of controller parameters, and tsim is the timerange of the simulation.For objective function calculation, the time-domain simulation of the nonlinear power

system model is carried out for the simulation period. It is aimed to minimize this objectivefunction in order to improve the system response in terms of the settling time andovershoots.In this study, it is aimed to minimize the proposed objective function J. The problem

constraints are the PSS and STATCOM controller parameter bounds. Therefore, thedesign problem can be formulated as the following optimization problem:

Minimize J (9)

subject to

KminS pKSpKmaxS ,Tmin1S pT1SpTmax1S ,Tmin3S pT3SpTmax3S ,KminP1 pKP1pKmaxP1 ,Tmin1P1pT1P1pTmax1P1 ,Tmin2P1pT2P1pTmax2P1 ,KminP2 pKP2pKmaxP2 ,Tmin1P2pT1P2pTmax1P2 ,Tmin2P2pT2P2pTmax2P2 . 10

The proposed approach employs PSO technique to solve this optimization problem andsearches for the optimal set of PSS and STATCOM-based controller parameters.

5. Results and discussions

The SPSs toolbox is used for all simulations and STATCOM-based controller design.SPS is a MATLAB-based modern design tool that allows scientists and engineers torapidly and easily build models to simulate power systems using Simulink environment.The SPSs main library, powerlib, contains models of typical power equipment such asmachines, governors, excitation systems, transformers, lines and FACTS devices. Thelibrary also contains the powergui block that opens a graphical user interface for thesteady-state analysis of electrical circuits. The load ow and machine initialization optionof the powergui block performs the load ow and the machines initialization [20].In order to determine the optimal location of STATCOM and design the STATCOM-

based controller, the MATLAB/SIMULINK model of the test system depicted in Fig. 1 isdeveloped using SPS blockset. The system consists of two hydraulic generating units, oneof 1400MVA in one area and 700MVA in the other. The generators are represented by a

S. Panda, N.P. Padhy / Journal of the Franklin Institute 345 (2008) 166181 173sixth-order model and both are equipped with hydraulic turbine and governor (HTG)

and excitation system. The HTG represents a nonlinear hydraulic turbine model, a PIDgovernor system, and a servomotor. The excitation system consists of a voltage regulatorand DC exciter, without the exciters saturation function. All the relevant parameters aregiven in Appendix. The generators with output voltages of 13.8 kV are connected by a long500 km transmission line through three-phase step-up transformers. The output voltage oftransformer is 500 kV. The loads in each area are so chosen that the real power ow on thetransmission line is always from area-1 to -2. The STATCOM used for this model is aphasor model with a rating of7200MVA. The pre-fault reference voltage is set to 1 pu for

ARTICLE IN PRESSS. Panda, N.P. Padhy / Journal of the Franklin Institute 345 (2008) 166181174STATCOM (please refer to Appendix for other parameters).

5.1. Application of PSO to determine optimal location

Initial power outputs of the generators chosen are P1 0.75 pu and P2 0.4 pu. Theloads at the area-1 are 160MW and 200MVAR and those at area-2 are 1340MW and500MVAR. The reference voltage of STATCOM is set 1.0 pu. The pre-fault SEP and REPare 918 and 886MW, respectively. A three-phase fault is applied at the sending-end bus attime t 0.1 s. The original system is restored upon the clearance of the fault. Also toimprove transient stability the reference voltage is increased to 1.1 pu immediately after thefault clearance.The optimal location of STATCOM is obtained employing PSO using the steps given in

Section 4.1. For the optimization of objective function given in Eq. (6), routines from PSOtoolbox are used. While applying PSO technique, a number of parameters are required tobe specied. An appropriate choice of the parameters affects the speed of convergence ofthe algorithm. Table 1 shows the parameters used in the present study for the PSOalgorithm.The optimal location of STATCOM is found to be at L 212 km from the sending end

and the corresponding highest critical fault clearing time TFCF 0.079 s by the above PSO-optimization approach. This information about the optimal location is useful during theplanning stage so that the substation can be located at the optimal location (or nearest tothe optimal location as far as possible) to install the STATCOM for maximum benet interms of both transient stability and power handling capacity.To verify the obtained result, the above contingency (three-phase fault at sending-end

at t 0.1 s and cleared at t 0.179 s) is simulated for different locations of STATCOM.Fig. 5 shows the variation of rotor angle difference (d1d2) for different locations ofSTATCOM which conrms that the system is stable for the given initial operatingconditions and fault clearing time only if the STATCOM is placed at the optimal location(L 212 km) and unstable at all other locations.

Table 1

Parameters used for PSO algorithm

PSO parameters Value/type

Swarm size 20

No. of generations 100

c1, c2 2.0, 2.0

w , w 0.9, 0.4start end

ARTICLE IN PRESS5.2. Application of PSO to determine optimal controller parameters

Owing to the recent advances in optical ber communication and global positioningsystem, wide area measurement system can realize phasor measurement synchronously anddeliver it to the control center even in real time, which makes the wide area signal a goodalternative for control input. In view of the above, the difference of speed deviations ofgenerators in the two areas (o1o2) is chosen as the control input of STATCOM-basedcontroller in this paper. Also, accelerating powers of the individual generators are chosenas the input signal for the two PSSs.The parameters of the PSS and the STATCOM-based controller are optimally tuned

Fig. 5. Variation of rotor angle difference for different locations of STATCOM (TFC 0.079 s andSEP 918MW).

S. Panda, N.P. Padhy / Journal of the Franklin Institute 345 (2008) 166181 175using PSO technique. The objective function given in Eq. (8) is evaluated for each individualby simulating the example power system, considering a severe three-phase fault disturbance.The convergence of objective function J with the number of generations is shown in Fig. 6.The obtained parameters of STATCOM-based controller and PSS are shown in Table 2.To evaluate the capability of the PSO-optimized PSS and STATCOM-based controller,

time-domain simulation is performed on the example power system under varioussevere and small disturbances. The system response with controllers without theoptimized parameters is shown with dotted line and the response with controllerswith optimized parameters is shown with solid lines. Note that, in controller without theoptimized parameters case, both STATCOM (with Vref 1.0 pu before fault and 1.1 puafter fault clearance) and PSS are present in the system, but the STATCOM-basedcontroller is not considered and the parameters of the PSSs are not optimized.In order to show the effectiveness of the PSO-optimized controllers, the same

contingency is applied and the variation of (d1d2) against time is shown in Fig. 7. It isclear from Fig. 7 that the power system oscillations are quickly damped out withapplication of proposed PSO-optimized controllers.The effectiveness of the proposed controllers to variation in line power ow is also

examined. By changing the loads in each area, the SEP is increased by 100MW (from 918to 1018MW) and a three-phase fault is applied at the sending-end bus at t 0 s and

ARTICLE IN PRESSS. Panda, N.P. Padhy / Journal of the Franklin Institute 345 (2008) 1661811761.52

1.522Jcleared after 0.077 s. Fig. 8 shows the variation of the rotor angle difference of the twomachines for controllers without the optimized parameters and the controllers with theoptimized parameters.

Table 2

PSO-optimized parameters of STATCOM-based controller and PSSs

STATCOM-base controller PSS-1 parameters PSS-2 parameters

KS T1S T3S KP1 T1P1 T2P1 KP2 T1P2 T2P2

103.6343 0.5703 0.0493 0.9788 0.0837 0.7683 0.3264 0.0893 0.8920

0 10 20 30 40 50 60 70 80 90 1001.51

1.512

1.514

1.516

1.518

Generation

Converg

ence o

f

Fig. 6. Convergence of objective function.

Fig. 7. Variation of rotor angle difference without and with PSO-optimized controllers (TFC 0.079 s andSEP 918MW).

ARTICLE IN PRESS

S. Panda, N.P. Padhy / Journal of the Franklin Institute 345 (2008) 166181 177To show the effectiveness of the PSO-optimized controllers under small disturbance, theload at receiving end is disconnected for 50ms (this simulates a small disturbance). Thevariation of speed deviation difference of the two machines and STATCOM bus voltage(VST) are shown in Figs. 9 and 10. From the gure it is clear that the performance of thepower system has been improved signicantly by modulating the STATCOM bus voltagefollowing the disturbance and the damping has been improved considerably.

5.3. Design problem for Kundurs four-machine, two-area system

The design problem is further extended to Kundurs four-machine, two-area systemshown in Fig. 11 [19]. Speed deviations of generators G1 and G4 are selected as the inputsignal of the STATCOM-based controller. Accelerating power of the individual generatorsare chosen as the input signals for all four PSSs.

Fig. 8. Variation of rotor angle difference without and with PSO-optimized controllers at higher sending-end

power (TFC 0.075 s and SEP 1018MW).

Fig. 9. Variation of rotor speed difference under small disturbance.

ARTICLE IN PRESSFig. 10. Variation of STATCOM reference voltage signal under small disturbance.

S. Panda, N.P. Padhy / Journal of the Franklin Institute 345 (2008) 166181178An integral time absolute error of the speed signals corresponding to the local and inter-area modes of oscillations is taken as the objective function. The objective function isexpressed as

J Z ttsimt0

XDoL

XDoI

tdt, (11)

where DoL and DoI are the speed deviations of local and inter-area modes of oscillations,respectively, and tsim is the time range of the simulation.The parameters of the PSSs and the STATCOM-based controller are optimally tuned

using PSO technique as explained above. The convergence of objective function J with thenumber of generations is shown in Fig. 12. The obtained parameters of STATCOM-basedcontroller and PSS are shown in Table 3.To show the effectiveness of the proposed PSO-optimized controllers based on wide

area signal under extreme conditions, time-domain simulation is performed on thesystem with a three-phase fault applied at the sending end of the circuit betweenbuses 7 and 8 (near bus 7) that is cleared 100ms later. Figs. 13 and 14 show the variationsof the inter-area and local mode of oscillation, against time, respectively. From thesegures, it can be seen that both inter-area and local modes of oscillations are highly

STATCOM

1

2

3

4

G1

G2

G3

G4

Area 1 Area 2

25 km 10 km110 km

25 km10 km5 6

7 9 10 11

L-1 L-2

110 km

8

Fig. 11. Four-machine two-area system with STATCOM.

ARTICLE IN PRESS6.5

S. Panda, N.P. Padhy / Journal of the Franklin Institute 345 (2008) 166181 179oscillatory for the case of controllers without optimized parameters. For the caseof controllers with PSO-optimized parameters, these modal oscillations are quicklydamped out.

0 4020 60 80 100 120 140 160 180 2003.5

4

4.5

5

5.5

6

Generation

Con

verg

ence o

f J

Fig. 12. Convergence of objective function.

Table 3

PSO-optimized parameters of STATCOM-based controller and PSSs for four-machine two-area system

Controller/parameters STATCOM PSS-1 PSS-2 PSS-3 PSS-4

Gain 232.323 3.5952 4.6062 4.3768 4.2875

Time constant 0.2892 0.0801 0.0396 0.0758 0.0699

0.2641 1.7881 0.6691 1.0796 1.2285

Fig. 13. Inter-area mode of oscillation for 100ms three-phase fault near bus 7.

ARTICLE IN PRESS6. Conclusions

In this paper, PSO technique is applied to determine the optimal location and controllerparameters of STATCOM. First, a systematic procedure to determine the optimal locationof STATCOM for transient stability improvement following a severe disturbance isproposed. The proposed algorithm is applied to nd the optimal location of STATCOM in

Fig. 14. Local mode of oscillation for 100ms three-phase fault near bus 7.

S. Panda, N.P. Padhy / Journal of the Franklin Institute 345 (2008) 166181180a two-area system employing PSO. Further, a STATCOM-based damping controller isproposed and the parameter of the proposed controller and PSSs are coordinatelydetermined using PSO. The obtained nonlinear simulation results show that optimallylocated STATCOM extends the critical fault clearing time and hence improve transientstability of the system. Also, coordinated design of STATCOM-based controller and PSSsusing PSO technique, improve greatly the system stability by damping out the powersystem oscillations quickly, under severe and small disturbance conditions. Finally, thecoordinated design problem is extended to a four-machine two-area system. The time-domain simulations have shown that the inter-area and local modes of oscillations are welldamped with the PSO-optimized controllers.

Appendix

The data for various components used in the MATLAB simulation (All data are in puunless specied otherwise; the notations used are as in SimPowerSystem toolbox.):Generator parameters: M1 1400MVA, M2 700MVA, V 13.8KV, f 60Hz,

Xd 1.305, Xd1 0.296, Xd00 0.255, Xq 0.474, Xq00 0.243, X1 0.18.Transformer parameters: T1 1400MVA, T2 700MVA, 13.8/500KV, R2 0.002,

L2 0.12, Rm 500O, Xm 500O.Transmission line parameters per km: R1 0.1755O, R0 0.2758O, L1 0.8737mH,

L0 3.22mH, C1 13.33 nF, C0 8.297 nF.

STATCOM parameters: 500KV, 7200MVAR, R 0.071, L 0.22, VDC 40KV,CDC 3757mF, Vref 1.0, KP 50, Ki 1000.STATCOM controller: DVST

max 1.1 pu, DVSTmin 0.9 pu, T2S T4S 0.3 s, TWS 10 s.PSSs: sensor time constant 0.015 s, VSmax 0.15 pu, VSmin 0.15 pu.

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Optimal location and controller design of STATCOM for power system stability improvement using PSOIntroductionTwo-area system with STATCOMOverview of particle swarm optimizationProblem formulationOptimal location of STATCOMCoordinated design of STATCOM-based controller and PSS

Results and discussionsApplication of PSO to determine optimal locationApplication of PSO to determine optimal controller parametersDesign problem for Kundurs four-machine, two-area system

ConclusionsReferences