Electrical Power and Energy Systems 63 (2014) 132–139

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Electrical Power and Energy Systems

journal homepage: www.elsevier .com/locate / i jepes

An integrated approach for optimal placement and tuning of powersystem stabilizer in multi-machine systems

http://dx.doi.org/10.1016/j.ijepes.2014.05.0720142-0615/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author at: Department of Electrical Engineering, NajafabadBranch, Islamic Azad University, Najafabad, Iran. Tel.: +98 9179517691.

E-mail address: vahid_keumarsi@yahoo.com (V. Keumarsi).

Vahid Keumarsi ⇑, Mohsen Simab, Ghazanfar ShahgholianDepartment of Electrical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, IranDepartment of Electrical Engineering, College of Engineering, Fars Science and Research Branch, Islamic Azad University, Fars, Iran

a r t i c l e i n f o a b s t r a c t

Article history:Received 4 August 2013Received in revised form 23 May 2014Accepted 27 May 2014

Keywords:Power system stabilizerTuning and placement of PSSPSO algorithmFuzzy logicMulti-machine system

In this paper, a hybrid approach for tuning and placement of power system stabilizers (PSS) inmulti-machine power systems is provided with the aim of reducing low-frequency oscillations (LFO)and improving power system dynamic stability with wide range of changes in system parameters andoperating point of the system. PSS parameters are adjusted using Particle Swarm Optimization algorithm(PSO), and using Takagi–Sugeno (TS) fuzzy, optimal location for the PSS is determined. The employedfuzzy system has two inputs, the real part and the damping coefficient of network eigenvalues. Theresults of test on a grid four machine-two area sample, show optimal performance of the proposedmethod in improving system stability and reducing low-frequency oscillations of local and inter-areamodes.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The power system is a complex and nonlinear system.Mechanical nature of the power systems produces low-frequencyoscillations (LFO) in the system, which will negatively affect thestability and performance of the system and will restrict the capac-ity of the transmission line [1]. In order to solve this problem, asupplementary controller is employed in the excitation system ofthe generators. This supplementary controller, known as PSS, iswidely used to reduce the LFO and improve system stability [2].Many new intelligent methods such as neural networks [3] andfuzzy logic [4,5] have been used in PSS design. Modern controlmethods such as adaptive control have also been used in PSSdesign [6]. In [7], an approach based on state feedback control ispresented for tuning PSS parameters. Pole placement has also beenemployed to design PSS for multi-machine power systems in coor-dination with FACTS devices [8]. In [9], PSO was used to tune PSSfor interconnected power systems. In [10], the use of adaptiveneuro-fuzzy inference was proposed for PSS design to enhancethe damping issue of the conventional PSSs. Bacterial swarmoptimization is the other approach used for the design of PSS incoordination with thyristor controlled series capacitor (TCSC) for

multi-machine power systems [11]. A fuzzy PI Takagi–Sugenostabilizer is presented in [12]. An optimal power system stabilizer(OPSS) based on second-order linear regulator with conventionallead-lag compensation structure is also proposed in [13]. The mod-ified particle optimization (MPSO) is the other method proposed toadjust the stabilizer parameters [14].

In [15] presented a method to determine the optimal locationand the number of multi-machine power system stabilizers (PSSs)using participation factor (PF) and genetic algorithm (GA). A type-2fuzzy logic power system stabilizer with differential evolutionalgorithm presented in [16]. In [17], the design of a conventionalpower system stabilizer (CPSS) is carried out using the bat algo-rithm (BA). In [18] presents an enhanced indirect adaptive fuzzysliding mode based power system stabilizer for damping localand inter-area modes of oscillations for multi-machine power sys-tems. In [19] presented a new technique named cultural algo-rithms (CAs) to tune the PSS parameters. In [20] present thedesign and implementation of Power System Stabilizers in amulti-machine power system based on innovative evolutionaryalgorithm overtly as Breeder Genetic Algorithm with AdaptiveMutation.

This paper presents a hybrid approach to tune and place PSSs inmulti-machine systems. PSS parameters are adjusted using PSOalgorithm, according to the operating point of the network. Theoptimal location for PSS installation is then determined by fuzzyTakagi–Sugeno (TS) system. The fuzzy system has two inputs, thereal part and the damping coefficient of network eigenvalues.

V. Keumarsi et al. / Electrical Power and Energy Systems 63 (2014) 132–139 133

Network eigenvalues are obtained by the linearization of differen-tial–algebraic equations of the power system. The experimentalresults on a four machine-two area network show the good perfor-mance of the proposed method improving system stability andreducing low frequency oscillations of local and inter-area modes.

Power system modeling equations are presented in section‘Power system modelling’ and the algorithm used for tuning andplacement of PSSs is given in section ‘PSS tuning and placement’.Simulation results and conclusions are described in sections‘Experimental results and Conclusion’, respectively.

Power system modelling

In order to analyze the power system, linearization of Differen-tial–Algebraic Equations (DAE) around the operating point is used[21].

Generator equations

For each generator, the following fourth-order model has beenconsidered:

ddi

dt¼ xi �xs ð1Þ

dxi

dt¼ TMi

Mi�ðE0qi � X0diIdiÞIqi

Mi�ðE0di þ X 0qiIqiÞIdi

Mi� Diðxi �xsÞ

Mið2Þ

dE0qi

dt¼ �

E0qi

T 0doi

� ðXdi � X 0diÞIdi

T 0doi

þ Efdi

T 0doi

ð3Þ

dE0di

dt¼ � E0di

T 0qoii

þ Iqi

T 0qoii

ðXqi � X0qiÞ ð4Þ

ω

ωsTsT+1 2

111sTsT

++ outputinput

PSSK4

311sTsT

++

Fig. 1. Structure of power system stabilizer.

Exciter equation

Exciter equation is:

dEfdi

dt¼ � Efdi

T 0doi

� ðXdi � X0diÞT 0doi

Idi þEfdi

T 0doi

ð5Þ

A detailed description of all symbols and quantities can befound in [21]. By the linearization of the power system equation,explained in [21], and by the addition of PSS equations, the powersystem model is:

D _x ¼ Axþ Bu ð6Þ

Dy ¼ Cxþ Du ð7Þ

where A is the state variables matrix, B is the input matrix, C is theoutput matrix, D is the feed-forward matrix, x is the vector of statevariables, u is the vector of control inputs, and y is the output. Here,the gole of PSS design is to place the eigenvalues of matrix A in theleft half of the complex plane. Eigenvalues of the system can beevaluated from matrix A:

ki ¼ ri � jxi ð8Þ

where i = 1, 2, 3,. . ., n and n denotes the total number of eigenvalues.The eigenvalues may be real or complex. The imaginary part of thecomplex eigenvalue (x) is the radian frequency of the oscillationsand the real part (r) is the decrement rate. Then, the damping ratio(nj) of the jth eigenvalue is defined with the following equation:

ni ¼�riffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

r2i þx2

i

q ð9Þ

PSS structure

The PSSs used here possess a conventional lead-lag structureand have speed deviation input [22–24]. The Gain of stabilizer(KPSS) determines the amount of damping created by PSS. Like ahigh-pass filter with time constant Tw, the Filtering block(washout) passes the cross speed deviations and blocks steady-state values of the speed. The two-level compensation blocks pro-vide an appropriate lead characteristic, in order to compensate thelag characteristic between the input excitation control and theelectrical torque of the generator. Five parameters of PSS, includingT1–T4 (time constant) and KPSS, are optimized by PSO algorithm andTw is considered to be constant. Fig. 1 shows the PSS structure.

PSS tuning and placement

The classical PSS tuning methods are usually used for specificfrequency and operating point, and hence, any change in systemoperating point degrades the performance of PSS. In this paper,Particle Swarm Optimization algorithm (PSO) is used to adjustPSS parameters.

Particle Swarm Optimization (PSO) algorithm

PSO is an evolutionary computation algorithm, inspired fromthe nature and based on repetition [25]. The PSO algorithm is com-posed of fixed number of particles taking random initial values.Two values are assigned to each particle, position (Xk

i ) and velocity(Vk

i ). These particles repetitively move in the n-dimensional space(corresponding to the number of parameters) to look for new pos-sible answer choices by calculating the optimality of each particlebased on the objective function. At each step, the best position ofeach particle (pbestk

i ) and the best position among all particles(gbestk

i ) are stored. New speed (Vkþ1i ) and new position (Xkþ1

i ) ofeach particle will be updated using following equations [26]:

Vkþ1i ¼ w� Vk

i þ c1 � r1 � pbestki � Xk

i

� �þ c2 � r2

� gbestki � Xk

i

� �ð10Þ

Xkþ1i ¼ Xk

i þ Vkþ1i ð11Þ

where c1 and c2 are positive numbers illustrating the weight of theacceleration of each term, guiding each particle toward the bestindividual (pbest) and the best swarm (gbest) positions, r1 and r2 aretwo random number in the range [01], and w is the inertia calcu-lated by the following equation [26]:

w ¼ wmax �wmax �wmin

kmax

� �� k ð12Þ

where wmax and wmin are the maximum and minimum values of w,kmax is the maximum number of iterations and k is the current iter-ation number.

Objective function

The Stability of a power system can be determined based on itseigenvalues. Eigenvalues with large negative real parts ensure sys-tem stability. the overshoot and oscillations values are determined

-15 -12 -9 -6 -3 0 3 5

0

0.2

0.4

0.6

0.8

1

Real Part

Deg

ree

of m

embe

rshi

p

NB NM NS ZE PS

Fig. 3. Membership functions for realpart.

Table 1Fuzzy system rules.

r n

PB PM PS ZE NS

NB Mf1 Mf1 Mf2 Mf3 Mf3NM Mf1 Mf1 Mf2 Mf3 Mf3NS Mf1 Mf2 Mf2 Mf3 Mf4ZE Mf2 Mf3 Mf3 Mf4 Mf5PS Mf3 Mf4 Mf4 Mf5 Mf5

134 V. Keumarsi et al. / Electrical Power and Energy Systems 63 (2014) 132–139

by the damping coefficient of the system, where any increase in thedamping coefficient reduces oscillations and improves the stabilityof the system. In this paper, the objective function is a combinationof the two indices; the damping coefficient and the real part ofeigenvalues, which are considered as follows [27]:

Minimize J ¼ J1 þ aJ2 ða ¼ 10Þ ð13Þ

J1 ¼Xn

i¼1

ðri � r0Þ2 for ri � r0; ðr0 ¼ �3Þ ð14Þ

J2 ¼Xn

i¼1

ðn0 � niÞ2 for ni � n0; ðn0 ¼ 0:3Þ ð15Þ

n denotes the total number of eigenvalues. term J1 in the objectivefunction controls the real part (r) of eigenvalues and generally leadsthe eigenvalues of the system to the left side of imaginary axis in anarea less than r0. The term J2 in the objective function brings thedamping (n) of eigenvalues to the desired damping (n0) and controlsthe overshoot of the system. value of a obtained by experimenta-tion and considered constant equal to 10 [27].

Optimal PSS placement using TS fuzzy

Optimal PSS Locating in multi-machine systems is the impor-tant issues which can improve PSS performance and increasedynamic stability of the power system. The TS fuzzy system is sui-ted for mathematical analysis such as nonlinear systems modeling[28]. The output of a TS fuzzy system is defined as a function ofinputs:

If x1 is M and x2 is L then output ¼ ax1 þ bx2 þ c ð16Þ

where L and M are fuzzy sets; x1 and x2 are fuzzy system inputs; anda, b and c are constants. In this paper, the TS fuzzy system deter-mines the optimal location for PSS installation by proper design ofmembership functions and fuzzy rules. The zero-order TS fuzzy sys-tem (a, b = 0) is used, and thus the output of each rule is a constant.The TS fuzzy system inputs are the damping coefficient and the realpart of power system eigenvalues. Five linguistic variables wereconsidered for each input. The membership functions of the damp-ing coefficient and the real part inputs can be seen in Figs. 2 and 3,respectively. Also, the 25 rules defined for fuzzy output are shownin Table 1. In this paper, it is assumed that a fixed number of PSSs,k, are installed among the m generators of the network. Variouscases of PSS location in network, defined as position index variable(PlaceIndex), are obtained by enumeration of k stabilizers among mgenerators. The maximum possible value for PlaceIndex is obtainedby Eq. (17):

PlaceIndexmax ¼k

m

� �¼ m!

k! ðm� kÞ! ð17Þ

1 � PlaceIndex � PlaceIndexmax ð18Þ

-1 -0.7 -0.4 -0.1 0.2 0.5 0.8 1

0

0.2

0.4

0.6

0.8

1

Damping Ratio

Deg

ree

of m

embe

rshi

p

NS ZE PS PM PB

Fig. 2. Membership functions for damping coefficient.

In order to determine the best location for PSS, all possible loca-tions are determined by (17) and (18) and are stored in PlaceIndexvariable. Then, according to the algorithm shown in Fig. 5, enumer-ation of variable PlaceIndex is performed for each PlaceIndex. Ineach enumeration step, after tuning PSS parameters, the eigen-values of the system are calculated and sorted based on the leastdamping. The first eight eigenvalues (corresponding to the quan-tity of mechanical modes), having the least damping coefficientsare sent to the fuzzy system. Receiving the damping coefficientand the real part of eigenvalues by the fuzzy system as inputs, itcalculates the out(i), output corresponding to the ith eigenvalue.Also FuzzyPlace(k), corresponding to the kth placeIndex at eachenumeration step, can be calculated using Eq. (19):

FuzzyPlaceðkÞ ¼ 10outðiÞ þ 8outðiþ 1Þþ6outðiþ 2Þ þ . . .þ outð8Þ for i ¼ 1;2;3; . . . ;8

ð19Þ

The variable FuzzyPlace(k) indicates the fitness of the kth forinstalling PSS and a large FuzzyPlace(k) shows a better place forPSS installation. Finally, the best place for PSS installation is deter-mined based on the maximum value of FuzzyPlace(k). The algo-rithm used PSS tuning and finding its location can be observed inFig. 5.

Experimental results

In order to study the performance of the proposed method, thefour machine-two area network shown in Fig. 4 is simulated. Thisbenchmark system is introduced to study inter-area oscillationsand their effects on the system dynamic stability. It consists oftwo areas, each having two generators. The two areas are con-nected by a double communication line. About 400 MW of poweris transferred through the communication lines between the twoareas. All the simulations have been carried out by Matlab soft-ware. In this system, there are two generation areas, which havetwo generators, and two loads interconnected by transmissionlines. details of the power system can be seen in reference [29].

PSS tuning

The results of using PSO algorithm to tune the stabilizer param-eters (PSOPSS) are compared with those of using classical methods(CPSS) and Genetic Algorithm (GAPSS). PSO and GA parameters

Fig. 4. Network four machine-two areas.

Fig. 5. Simultaneous PSS tuning and locating algorithm.

V. Keumarsi et al. / Electrical Power and Energy Systems 63 (2014) 132–139 135

considered in this comparison can be seen in Table 2. Eigenvaluesand the damping coefficients of network modes for cases of nostabilizers (No PSS), CPSS, PSOPSS and GAPSS are illustrated inTable 3.

It can be seen that in NoPSS case, some of the network modeshave very weak damping. Moving up to the CPSS case, relative

improvement in the weak modes of network is observed, suggest-ing the positive impact of PSS on network stability. As the resultsshow, optimizing PSS parameters, significantly improves thedamping of network modes. It can also be observed that usingPSO algorithm results in more favorable results than using othermethods to tune PSS parameters.

Table 2PSO and GA parameters.

Parameters PSO GA

Npop 20 20Iter 300 300c1 2 –c2 2 –xmin 0.45 –xmax 0.95 –Pcrossover – 0.7Pmutation – 0.05

Table 3Eigenvalues and damping coefficients.

Method Eigenvalues Damping

NoPSS �0.0907 ± 4.3183i 0.0210�0.2851 ± 6.1351i 0.0464�0.4054 ± 6.2126i 0.0651

CPSS �0.4708 ± 4.4266i 0.1058�0.7694 ± 6.3661i 0.1200�0.7954 ± 6.3383i 0.1245

GAPSS �2.5545 ± 8.6985i 0.2818�2.5440 ± 7.8648i 0.3078�3.0023 ± 8.1775i 0.3446

PSOPSS �2.9973 ± 7.9819i 0.3515�2.9764 ± 7.1223i 0.3856�3.5894 ± 8.1883i 0.4015

Table 4Best place of PSS.

No. PSS Best place (�) Fuzzy place

3PSS �G1, G3, G4 349.5003G2, G3, G4 332.9920G1, G2, G3 320.7537G1, G2, G4 318.4545

2PSS �G1, G3 263.7264G1, G4 259.143G2, G3 254.7809G2, G4 247.361G1, G2 247.2790G3, G4 236.9329

1 PSS �G1 201.8627G2 194.7218G3 183.9345G4 180.6046

Table 5PSS parameters and damping.

No Place KPSS T1 T2 T3 T4 nmin

1 PSS G1 21.25 0.184 0.041 1.384 0.037 0.047

2 PSS G3 36.23 0.276 0.042 0.522 0.014 0.067G1 31.38 0.805 0.013 0.241 0.077

3 PSS G1 17.97 0.333 0.038 0.957 0.084 0.151G3 19.02 1.175 0.047 0.235 0.017G4 6.783 1.066 0.011 0.563 0.077

4PSS G1 10.62 0.911 0.034 0.710 0.200 0.352G2 20.07 0.309 0.068 0.822 0.020G3 6.706 0.559 0.102 1.399 0.013G4 6.312 1.451 0.036 0.436 0.049

Table 6Two different operating cases.

CaseNumber

Description

Case 1 Single line between 8 and 9 out of service, and a three-phaseshort circuit is applied to bus 8 for 0.1 s

Case 2 Single line between 7 and 9 out of service, and a three-phaseshort circuit is applied to bus 9 for 0.15 s

136 V. Keumarsi et al. / Electrical Power and Energy Systems 63 (2014) 132–139

PSS locating

As a common rule, not all the generators in a network areequipped by PSSs, but the minimum number of PSSs used in a net-work equals to half of the total generators used in it [30]. In thispaper, one, two and three PSSs are considered for the powersystem. The optimal location for installing PSSs in each case ispresented in Table 4, obtained using the TS fuzzy system. The3rd column of the table shows the fitness value of each PlaceIndex,with larger values showing better locations for PSS. As observed inTable 4, generators G1, G3, G4 are the best PSS locations for thecase of using three generators, while generators G1, G3 and gener-ator G1 are the best places for PSS installation for the cases of usingtwo and one generators, respectively. The tuned PSS parameters ineach case, best installation position, and the least network damp-ing coefficient are summarized in Table 5.

As observed in Table 5, the minimum damping coefficients incases of using one and two PSSs in network are 0.047 and 0.067,respectively, suggesting a network with weakly damping modes.These values increase to 0.151, a suitable value, for the case ofusing three PSSs and 0.352 when using four PSSs. As a conclusion,installing three PSSs in the network yields to acceptable dampingof oscillatory and weak network modes.

Time domain simulations

In order to study the performance of the proposed algorithm insetting and placing PSSs in power systems, some time domain sim-ulations have been performed on the network under study. Mean-while, to investigate the proposed method performance when theoperating point of the system changes, two different operatingcases are considered for the system (Table 6).

PSS tuningAll generators of the studied network are equipped by PSSs.

Dynamic behavior fluctuations of inter-area modes are depicted

in Figs. 6 and 7 with different methods of setting PSS parameters,including CPSS, GAPSS, PSOPSS and without PSS simulations.

According to Figs. 6 and 7 tuning PSS parameters by PSO algo-rithm provides suitable results and results in more favorabledamping for network compared to the use of CPSS and GAPSS. Ana-lyzing system eigenvalues, shown in Table 3, in combination withthe dynamical simulation performed, suggests the good perfor-mance of the proposed PSOPSS method tuning PSS, improvingdamping and reducing local and inter-area network oscillations.

PSS locatingIn order to study the performance of the proposed method find-

ing the best location for PSS, some time domain simulations hasbeen applied to the network under study. The experiments wereperformed for the cases of installing two and three PSSs in thenetwork.

Investigating the speeds of generators. Figs. 8–15, show the speedsof generators with three and two PSSs in the network for differentinstallation locations and load conditions in the network.

According to Figs. 8–15, the best locations for installing threeand PSSs in the network are generators G1, G3, G4.

0 2 4 6 8 10 12

-2

0

2

x 10-3

Time (sec)

w1-

w3

(pu)

w1- w3 - 4pss (case1)

NoPSSCPSSGAPSSPSOPSS

Fig. 6. Inter-area modes w1–w3, case 1, 4 PSSs installed.

0 2 4 6 8 10 12

-2

0

2

x 10-3

Time (sec)

w2-

w3

(pu)

w2-w3 - 4pss (case1)

NoPSSCPSSGAPSSPSOPSS

Fig. 7. Inter-area modes w2–w3, case 1, 4 PSSs installed.

0 2 4 6 8 10 12

1

1.002

1.004

1.006

1.008

Time (sec)

Spe

ed (

pu)

speed G1 - 3pss (case1)

No psspss in G1,G2,G3pss in G1,G2,G4pss in G1,G3,G4pss in G2,G3,G4

Fig. 8. G1 speed, case1, 3 PSSs installed.

0 2 4 6 8 10 12

1

1.002

1.004

1.006

1.008

Time (sec)

Spe

ed (

pu)

speed G1 - 3pss (case2)No psspss in G1,G2,G3pss in G1,G2,G4pss in G1,G3,G4pss in G2,G3,G4

Fig. 9. G1 speed, case 2, 3 PSSs installed.

0 2 4 6 8 10 12

1

1.002

1.004

1.006

1.008

Time (sec)

Spe

ed (

pu)

speed G2 - 3pss (case1)No psspss in G1,G2,G3pss in G1,G2,G4pss in G1,G3,G4pss in G2,G3,G4

Fig. 10. G2 speed, case 1, 3 PSSs installed.

0 2 4 6 8 10 12

1

1.002

1.004

1.006

1.008

Time (sec)

Spe

ed (

pu)

speed G2 - 3pss (case2)No psspss in G1,G2,G3pss in G1,G2,G3pss in G1,G2,G3pss in G1,G2,G3

Fig. 11. G2 speed, case 2, 3 PSSs installed.

0 2 4 6 8 10 12

1

1.002

1.004

1.006

1.008

1.01

Time (sec)

Spe

ed (

pu)

speed G3 - 3pss (case1)No psspss in G1,G2,G3pss in G1,G2,G4pss in G1,G3,G4pss in G2,G3,G4

Fig. 12. G3 speed, case 1, 3 PSSs installed.

0 2 4 6 8 10 12

1

1.002

1.004

1.006

1.008

1.01

Time (sec)

Spe

ed (

pu)

speed G3 - 3pss (case2)No pss

pss in G1,G2,G3pss in G1,G2,G4

pss in G1,G3,G4

pss in G2,G3,G4

Fig. 13. G3 speed, case 2, 3 PSSs installed.

0 2 4 6 8 10 12

1

1.002

1.004

1.006

1.008

1.01

Time (sec)

Spe

ed (

pu)

speed G4 - 3pss (case1)No psspss in G1,G2,G3pss in G1,G2,G4pss in G1,G3,G4pss in G2,G3,G4

Fig. 14. G4 speed, case 1, 3 PSSs installed.

0 2 4 6 8 10 12

1

1.002

1.004

1.006

1.008

1.01

Time (sec)

Spe

ed (

pu)

speed G4 - 3pss (case2)No psspss in G1,G2,G3pss in G1,G2,G4pss in G1,G3,G4pss in G2,G3,G4

Fig. 15. G4 speed, case 2, 3 PSSs installed.

V. Keumarsi et al. / Electrical Power and Energy Systems 63 (2014) 132–139 137

Inter-area modes. Figs. 16–21, show inter-area oscillations (w1–w3)and (w2–w3), with three and two PSSs in the network with differ-ent installation locations and loading conditions.

0 2 4 6 8 10 12

-4

-2

0

2

4x 10-3

Time (sec)

w1-

w3

(pu)

w1- w3 - 3pss (case1)No PSSpss in G1,G2,G3pss in G1,G2,G4pss in G1,G3,G4pss in G2,G3,G4

Fig. 16. Inter-area modes w1–w3, case 1, 3 PSSs installed.

0 2 4 6 8 10 12

-4

-2

0

2

4x 10-3

Time (sec)

w1-

w3

(pu)

w1-w3 - 3pss (case2)No psspss in G1,G2,G3pss in G1,G2,G4pss in G1,G3,G4pss in G2,G3,G4

Fig. 17. Inter-area modes w1–w3, case 2, 3 PSSs installed.

0 2 4 6 8 10 12

-4

-2

0

2

4x 10-3

Time (sec)

w2-

w3

(pu)

w2-w3 - 3pss (case1)No psspss in G1,G2,G3pss in G1,G2,G4pss in G1,G3,G4pss in G2,G3,G4

Fig. 18. Inter-area modes w2–w3, case 1, 3 PSSs installed.

0 2 4 6 8 10 12

-4

-2

0

2

4x 10-3

Time (sec)

w2-

w3

(pu)

w2-w3 - 3pss (case2)No psspss in G1,G2,G3pss in G1,G2,G4pss in G1,G3,G4pss in G2,G3,G4

Fig. 19. Inter-area modes w2–w3, case 2, 3 PSSs installed.

0 2 4 6 8 10 12-3

-2

-1

0

1

2

x 10-3

Time (sec)

w1-

w3

(pu)

w1-w3 - 2pss (case1)pss in G1,G2pss in G1,G3pss in G1,G4pss in G2,G3pss in G2,G4pss in G3,G4

Fig. 20. Inter-area modes w1–w3, case 1, 2 PSSs installed.

0 2 4 6 8 10 12

-2

-1

0

1

2

x 10-3

Time (sec)

w2-

w3

(pu)

w2-w3 - 2pss (case1)pss in G1,G2pss in G1,G3pss in G1,G4pss in G2,G3pss in G2,G4pss in G3,G4

Fig. 21. Inter-area modes w2–w3, case 1, 3 PSSs installed.

0 2 4 6 8 10 120.998

1

1.002

1.004

1.006

1.008

1.01

Time (sec)

Spe

ed (

pu)

generators speed - No pssG1G2G3G4

Fig. 22. Generators speed, No PSS.

0 2 4 6 8 10 120.998

1

1.002

1.004

1.006

1.008

1.01

Time (sec)

Spe

ed (

pu)

generators speed - 3pss (case2)G1G2G3G4

Fig. 23. Generators speed, case 2, 3 PSSs installed.

0 2 4 6 8 10 12

-2

0

2

x 10-3

Time (sec)

Spe

ed (

pu)

Inter-Area Mods - No pssw1-w3w1-w4w2-w3w2-w4

Fig. 24. Inter-area modes, No PSS installed.

0 2 4 6 8 10 12

-2

0

2

x 10-3

Time (sec)

Spe

ed (

pu)

Inter-Area Mods - 3pss (case2)w1-w3w1-w4w2-w3w2-w4

Fig. 25. Inter-area modes, case 2, 3 PSSs installed.

138 V. Keumarsi et al. / Electrical Power and Energy Systems 63 (2014) 132–139

Figs. 20 and 21, show inter-area oscillations (w1–w3) and(w2–w3), with two PSSs installed:

Figs. 16–21 confirm the previously obtained optimized loca-tions for installing three and two PSSs in the network. Time domainsimulations, shown in Figs. 8–21, introduce generators G1, G3, G4,

and G1, G3 as the best installing locations in the network for thecases of using three and two PSSs, respectively. By comparing theseresults to Table 4, which shows the installing locations determinedusing fuzzy systems, the optimal performance of the proposedfuzzy method to determine the best places for PSSs in the system

V. Keumarsi et al. / Electrical Power and Energy Systems 63 (2014) 132–139 139

is confirmed. In order to study the performance of the proposedmethod improving system stability, reducing local and inter-areaoscillations of the system, a simulation assuming three PSSsinstalled in the network is performed. PSS parameters and opti-mized installation locations are determined by the proposed algo-rithm, and PSSs are installed on the generators G1, G3, G4. Figs. 22–25 show the speeds of generators and inter-area oscillations forcases of no PSS and three PSSs installed.

Figs. 22–25 show the favorable performance of the proposedmethod setting and placing PSSs in the network with the aim ofimproving the system dynamic stability.

Conclusions

In this paper, a hybrid approach for simultaneous PSS settingand placing in multi-machine systems is proposed. PSS parametersare adjusted using PSO optimization algorithm and the optimal PSSinstallation locations are determined by Takagi–Sugeno fuzzy sys-tem. The TS fuzzy system employs damping coefficients and realparts of network eigenvalues as its two inputs. A sample four-machine, two-area network is employed to investigate theeffectiveness of the proposed method, in different operating pointconditions. Analysis of the system eigenvalues and dynamic simu-lation of the network, confirmed optimal performance of the pro-posed method (PSOPSS) setting PSS parameters and improvingdamping modes (particularly mechanical oscillating modes), com-pared to the cases of use of classical methods (CPSS) and GeneticAlgorithm (GAPSS). The proposed fuzzy method was applied todetermine the PSS installation locations, and the obtained resultsshowed optimal performance of the proposed method to simulta-neously determine the best PSS adjustments and installation loca-tions, providing appropriate damping for the system. The proposedmethod is robust against changes in network operating point,improves dynamic performance of the network, reduces local andinter-area low-frequency oscillations of the system, and is suitablefor a wide range of power systems.

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