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Multi-band power system stabilizer design by using CPCE algorithmfor multi-machine power system
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Electric Power Systems Research 101 (2013) 36– 48
Contents lists available at SciVerse ScienceDirect
Electric Power Systems Research
jou rn al hom epage: www.elsev ier .com/ locate /epsr
ulti-band power system stabilizer design by using CPCE algorithmor multi-machine power system
min Khodabakhshian ∗, Reza Hemmati, Majid Moazzamiepartment of Electrical Engineering, University of Isfahan, Isfahan, Iran
a r t i c l e i n f o
rticle history:eceived 29 November 2012eceived in revised form 24 March 2013ccepted 25 March 2013vailable online 19 April 2013
eywords:ulti-band power system stabilizer
a b s t r a c t
Synchronous generators are generally equipped with power system stabilizers (PSS) to damp out lowfrequency oscillations. Among different types of PSSs it has been recently shown that the new advancedstabilizer, called multi-band PSS (MB-PSS), has a better performance to cope with all global, inter areaand local modes. All different types of PSSs are mainly designed based on one operating point of thesystem using a linear model. However, power system is inherently nonlinear and its operating conditionsfrequently change and the PSS performance may deteriorate. This paper develops a new design for MB-PSSin which the parameters are tuned by using a new Meta-heuristic optimization algorithm based on the
PCE algorithmultural algorithm (CA)SO algorithmo-evolutionary algorithm (CEA).
combination of culture algorithm, particle swarm optimization (PSO) and co-evolutionary algorithms.In this new culture-PSO-co evolutionary (CPCE) algorithm, the characteristics of all three mentionedalgorithms are combined and a new strong optimization technique is obtained. The proposed MB-PSS istested on a multi-machine power system and results are compared with PSO-based MB-PSS (PSO-MB-PSS) and conventional MB-PSS (C-MB-PSS). Simulation results confirm the effectiveness of the proposedoptimization tuning method for improving the power system dynamic stability.
. Introduction
Nowadays, modern power systems can reach the stressed con-itions more easily than the past for the sake of increasing poweremand. Therefore, it is necessary to increase power system sta-ility margin by using supplementary controllers. PSS is a commonost-effective method to provide the auxiliary control signal for theVR system of synchronous generators to enhance electromechan-
cal oscillations damping and to improve dynamic stability [1,2].The parameters of CPSS are generally tuned by using a linearized
odel. However, power system topology and loadings continu-usly change and in these conditions the CPSS cannot performfficiently for damping all modes, especially inter-area oscillations3]. In order to overcome this drawback and to have a robust PSS,everal researches have been carried out in recent years. Thesetudies are usually categorized in two groups; (i) presenting a newethod for tuning CPSS parameters and (ii) presenting a new struc-
ure for PSS.The first group of studies presents a new method for PSS coef-
cient tuning to guarantee having enough damping for power
∗ Corresponding author. Tel.: +98 3117934548.E-mail addresses: [email protected], [email protected]
A. Khodabakhshian), [email protected] (R. Hemmati), [email protected] (M. Moazzami).
378-7796/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.epsr.2013.03.011
© 2013 Elsevier B.V. All rights reserved.
system oscillations in a wide range of operating conditions. Classiccontrol methods based on lead–lag controllers [4], non linear [5,6]and adaptive control algorithms [7,8], robust control approaches[9–11], artificial intelligent [1,8,12] and meta-heuristic optimiza-tion methods [13–18] are the common approaches in the firstcategory. The second group presents a new PSS structure such asclassic PID-base PSS [10], fuzzy logic-based PID PSS [19], algebraic-based PSS [20], multi-input PSS [17,18,21] and MB-PSS [22,23] toimprove the PSS performance.
In Ref. [1] a systematical approach for tuning the parameters ofa fuzzy logic PSS by using differential evolution algorithm (DEA) ispresented. This method is developed to minimize the overshoot ofthe rotor angle response. A new recurrent adaptive control (RAC)scheme has been proposed in Ref. [8]. RAC is inspired based onthe similarity of adaptive control system and recurrent neuralnetworks (RNNs). An adaptive PSS based on fuzzy logic has beenreported in Ref. [12] in which its parameters are tuned online byusing neural networks.
Meta-heuristic and evolutionary computation based methodsrecently attract more attention for solving optimization problemsin power system. Bacterial foraging algorithm (BFA) and particleswarm optimization (PSO) [13], chaotic optimization algorithms
(COA) [14], ant colony optimization [15] and genetic algorithm (GA)[17] with a high degree of adaptation and robustness have beencommon approaches to overcome the deficiencies of CPSS tuning.Two classical bio-inspired PSO and BFA algorithms are presented
ower Systems Research 101 (2013) 36– 48 37
iiambdmaf
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ctbtietas
hPsei4tfMwtttmvmtep
Table 1System loading conditions.
Light load Nominal load Heavy load
Total active power is Nominal active Total active power is
A. Khodabakhshian et al. / Electric P
n Ref. [13] for the simultaneous design of multiple optimal PSSsn a two-area four-machine power system. In this structure, bothlgorithms have used time domain data from the PSCAD/EMTDCodels for the online optimization of PSS coefficients. The COA
ased on Lozi map is employed in Ref. [14] for eigenvalue and timeomain-based objective functions for tuning PSS coefficients in aulti-machine power system. In Ref. [15] a novel mixed-integer
nt direction hybrid differential evolution algorithm is proposedor PSS design in multi-machine systems.
A robust PID-based PSS is proposed in Ref. [10]. In this study constrained structure of Lyapunov function and generalizedtatic output feedback gain matrix are used. Iterative linear matrixnequality (ILMI) is employed for optimal tuning of controllerarameters. A hybrid fuzzy PID PSS has been investigated in Ref.19]. The fuzzy logic is used for on-line tuning of PID parame-ers. An algebraic method for assembling and the coordination ofSSs is reported in Ref. [20]. The coordination of PSS parameterss carried out based on state-space representations and differentperating scenarios. For this purpose, a combined non linear timeomain simulations and a constrained optimization method haveeen considered.
The CPSS is usually designed based on one input signal whichan be speed or active power changes. However, it has been shownhat by applying more input signals to PSS its damping ability cane increased [17,18]. In Ref. [17] a comparative study for differentypes of PSSs such as CPSS, IEEE PSS2B, PSS3B and PSS4B modelss carried out. In this study the rotor speed variation �ω and gen-rator electric power Pe or torque Te are two input signals [17]. Ahree dimensional PSS (3D-PSS) with employing rotor speed devi-tion �ω, rotor acceleration a and load angle deviation �ı inputignals has been also studied in Ref. [18].
Power system oscillations may contain low, intermediate andigh frequency sub-signals. The conventional PSSs including CPSS,SSS2B and PSS3B have only one frequency band for passing thetabilizing signal. Therefore, a PSS which can separately deal withach frequency part is more suitable. In this regard, MB-PSS wasntroduced as a new type of dual input stabilizer model in IEEE Std.21.5 [22,23]. This PSS utilizes three low, medium and high pass fil-ers to cover a wide range of oscillations with different frequenciesor more effective damping of all global, inter area and local modes.
otivated by this desirable structure of MB-PSS and also copingith nonlinearities and time varying conditions of power system
his paper proposes a new MB-PSS design in which its parame-ers are tuned by using CPCE algorithm. This new optimizationechnique contains the characters of three different optimization
ethods and leads to a better optimal solution [24]. Fast con-ergence in finding optimal solution, avoiding falling into local
inima and finding more accurate solution are the main adjec-ives of this new algorithm [24]. The proposed CPCE-MB-PSS isvaluated against PSO-MB-PSS and C-MB-PSS in a multi-machineower system. Simulation results clearly show the effectiveness of
G1
G2
T1
T2
BUS 1 BUS 2 BUS 3
New PSS
Line 1 Line 3
Line 2
Line 4
Load
New PSS
Fig. 1. The single-line diagram of two-are
decreased by 20% power decreased by 20%Total reactive power is
decreased by 15%Nominal reactivepower
Total reactive power isdecreased by 15%
the proposed method for damping power system oscillations andimproving dynamic stability.
2. Illustrative test system
To show the effectiveness of the proposed method for improvingpower system dynamic stability, a two-area four-machine powersystem is considered as the case study [4]. The single line diagram ofthis system is shown in Fig. 1. The nominal system parameters areavailable in Ref. [4]. All generators have been originally equippedwith CPSS. However, for current study, the type of PSS changes tothe proposed PSS model as depicted in Fig. 1. To study the sys-tem performance, three loading conditions are considered as heavy,nominal and light and are listed in Table 1.
2.1. Dynamic model of the system
A two-axis, three-order model is employed for simulating allgenerators. The power system can be modelled by a set of nonlineardifferential equations as Eq. (1).
x = f (x, u) (1)
In Eq. (1) x = [ı, ω, E′q] is state variables and u represents the
vector of the PSS output signals. This nonlinear dynamic model canbe rewritten as Eq. (2).⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩
.ωi = (Pm − Pe − Dω)
M.
ıi = ω0(ω − 1)
.
E′qi
= (−Eq + Efd)T ′
do.
Efdi= −Efd + Ka(Vref − Vt)
Ta
(2)
where ω shows per unit rotor speed. ıi and ωi are rotor angle androtor speed of generator ith (pu). Pm and Pe represent mechanicalinput power and electrical output power in terms of p.u. X ′
dis the
per unit transient reactance of d axis. Also E′q and Efd are per unit
values of the internal voltage behind x′d
and equivalent excitationvoltage respectively. T ′
do, Ta and Ka are the time constant of theexcitation circuit (s), regulator time constant (s) and regulator gainrespectively.
G4
G3
T3
T4
BUS 4 BUS 5 BUS 6
Line 5Line 6
Load
New PSSNew PSS
a four-machine power system [4].
38 A. Khodabakhshian et al. / Electric Power Systems Research 101 (2013) 36– 48
PSSU
2
1
sT1
sT1
++
4
3
sT1
sT1
++KPSS
+ref
lactua
Speed
Sensor
ash-ou
W
W
sT1
sT
+
S bloc
3
3
si
U
wwnTofispK
3
iidpbtt
Overall Gain W
Fig. 2. CPS
. Power system stabilizer
.1. Conventional power system stabilizer
The CPSS structure is depicted in Fig. 2, where the generatorpeed is usually used as the input signal [4]. The CPSS is mathemat-cally formulated as follows:
PSS = KPSSSTW
1 + STW
1 + ST1
1 + ST2
1 + ST3
1 + ST4�ω (3)
here �ω is the speed deviation in p.u. The CPSS consists of aashout filter and a dynamic compensator [4]. The UPSS output sig-al is fed to the excitation system as a supplementary input signal.he high pass washout filter is employed to reset the steady stateffset in the PSS output. The value of time constant (Tw) is usuallyxed and is considered as 10 s in this study. Also T1 − T4 and KPSShow the time constants and the gain of two stages lead–lag com-ensator respectively. Then, the design problem will be to obtainDC and T1 − T4.
.2. Multi-band PSS
Fig. 3 shows MB-PSS 4B structure based on multiple work-ng frequency bands. This figure comprises three separate low,ntermediate and high-frequency bands. These signals are used foramping the global, inter area and local modes. A differential band
ass filter, a gain and a limiter are used in each band. The finallock signal is limited by the final VSTmin/VSTmax limiter. For cap-uring different frequency dynamics of local and torsional modes,wo speed transducers have been used. According to Fig. 3, first theSpeed
transducer
KL1
KL2
L
/L
sT1
sT1
++ R
R*L
L
sT1
sT1
++
Kl1
Kl2
KH1
KH2
Speed
transducer
2L
1L11
sT1
sTKL
++
8L
7L17
sT1
sTKL
++
lW
lW
sT1
sT
+
lW
lW
sT1
sT
+
HW
HW
sT1
sT
+
HW
HW
sT1
sT
+
l
/l
sT1
sT1
++ R
R*l
l
sT1
sT1
++
H
/H
sT1
sT1
++ R
R*H
H
sT1
sT1
++
1V
2V
Pe
lL
H
Fig. 3. MB-PSS IEEE 4B b
Limitert Lead-Lag 1 Lead-Lag 2
k diagram.
rotor speed deviation passes from a speed transducer and �ωL–I iscreated. This signal is fed to the low and intermediate bands. Also,by passing Pe from speed transducer �ωH is available and is fedto the high-frequency band. Fig. 4 shows the concept of capturing�ωL–I and �ωH.
Six parameters must be tuned in MB-PSS 4B filters. These param-eters include symmetrical band pass filters at the center frequencyFL, FI, FH and the peak magnitude of the frequency responses withthree gains KL, KI, and KH. Therefore, MB-PSS4B with a flexiblemulti-band transfer function structure provides more degree offreedom for achieving a robust PSS over a wide frequency rangesin different power system contingency conditions. As mentionedbefore, a new optimization method is used to adjust the PSS param-eters. This method is described in the next section.
4. Hybrid CPCE algorithm
CPCE is a hybrid meta-heuristic optimization algorithm for usingthe advantages of PSO, CA and CEA [24]. Fig. 5 shows the main struc-ture of this algorithm in which a new co-evolutionary mechanismbetween two cultural algorithms is built. Then, PSOs are introducedinto the framework of the cultural algorithm in the sub spaces ofBelief spaces 1 and 2, and Population spaces 1 and 2.
A set of individuals which are called shared global belief space(SGBS) (into the co-evolutionary mechanism) are employed for thecoordination of population’s knowledge and experience. In each
generation of the algorithm, all sub-belief spaces 1 and 2 particlesare collected together into the SGBS. Then, the excellent particles ofSGBS are kept and the bad ones are replaced by reinitialized parti-cles. The Affect operations are used in SGBS for two sub-populationL6
L5
sT1
sT1
++
L12
L11
sT1
sT1
++
KL
l6
l5
sT1
sT1
++
l12
l11
sT1
sT1
++
Kl
H6
H5
sT1
sT1
++
H12
H11
sT1
sT1
++
KH
+
LF Band
IF Band
HF Band
maxVL
minVL
maxVl
minVl
maxVH
minVH
+
+
+
+
++
maxVST
minVST
VSTVS
LLVS
LlVS
LHVS
-
-
-
lock diagram [20].
A. Khodabakhshian et al. / Electric Power Systems Research 101 (2013) 36– 48 39
Speed
transducer
+Σ
ωΔ
IL−Δω
HωΔ
maxVL
minVL
axV Im
inV Im
maxVH
maxVST
minVST
VSTab
LK
IL−Δω
IK
HK
LF
F
F
++
+
ent fre
sii
4
ddN
⎧⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎩
(fbaa
Fig. 4. The idea of capturing differ
paces 1 and 2. Now, the experiences of two sub-population spacesn each generation are exchanged. Details of the CPCE algorithm arentroduced in the following subsections.
.1. Structure and details of CPCE algorithm
In this algorithm N particles are used for searching in a D-imensional space of optimization problem. These particles areivided to two equal parts. These two parts are divided again to11, N12, N21 and N22 particles using Eq. (4).
N = (N11 + N12) + (N21 + N22)
N11 + N12 = N21 + N22
BR1 = N11
N12
BR2 = N21
N22
(4)
Particles N11 and N21 are used for searching in Belief space 1B1) and (B2) respectively. Also N12 and N22 particles are utilized
or searching in Population spaces 1 (P1) and 2 (P2). The ratiosetween the numbers of particles in sub-spaces of B1, P1, B2 and P2re determined by using BR1 and BR2 coefficients. These coefficientsre generally in the range of 0.4–0.5. Each space contains a particleEvol
BeliefSpace 1
Population Space 1
Communication
ProtocolAccept ( )
Shared global bel
Share
Affect ( )
Affect ( )
A
Evaluate ( )
Evaluate ( )
Evolve ( )
Evolve ( )
Exchange Exper
Fig. 5. Block diagram o
minVH
quency signal in MB-PSS IEEE 4B.
swarm. For updating particles in each generation for each space,PSO operations are employed using Eqs. (5) and (6).
vk+1id
= wvkid + c1r1(pk
id − xkid) + c2r2(pk
gd − xkid) (5)
xk+1id
= xkid + vk+1
id(6)
In Eqs. (5) and (6) vkid
and xkid
represent the velocity and the posi-tion of ith particle respectively and w is inertia weight, c1 and c2are acceleration coefficients, r1 and r2 are two random numbers dis-tributed in (0, 1). Also pk
idshows the position with the best fitness
found so far by the ith particle and called pbest, pkgd
is the positionwith the best fitness found so far by all particles in the population,usually called gbest.
4.2. Cultural operations
Two cultural-algorithm-populations implement cultural Acceptand Affect operations in each generation of the algorithm.
4.2.1. Accept operations
Accept operation is implemented according to the value of Acp,which is the probability of accept operation in each generation.If rand ≤ Acp, for P1 and B1, the worst particle in B1 (B2) will bereplaced by the best particle in P1 (P2).
ve ( )Evaluate ( )
BeliefSpace 2
Population Space 2
Communication
ProtocolAccept ( )Affect ( )
iefspace
Share
ffect ( )
Evaluate ( )
Evolve ( )
iences
f CPCE algorithm.
4 ower
4
airrtab
4a
S
0 A. Khodabakhshian et al. / Electric P
.2.2. Affect operationsIt is supposed that Afp represents the probability of Affect oper-
tion and Afn is a nonnegative integer parameter. Affect operations performed considering the value of Afp in each generation. Ifand ≤ Afp, for P1 and B1, the bad Afn particles in P1 (P2) will beeplaced by the excellent Afn particles in B1 (B2). For exchanginghe useful knowledge and experience of swarms in each culturallgorithm-population, PSO swarms are associated with each otherased on the Accept and Affect operations.
.3. Co-evolutionary mechanism between two cultural
lgorithmsIn this step, first SGBS is designed. Then, Affect operations fromGBS to P1 and P2 are performed. Finally experiences between P1
Start
Generate the initial spaces and parametersP1, B1, P2, B2, SGBS,
Acp, Afp, Afn, SAfp, SAfn1, SAfn2, Eep, EEn
Randomly generate the initial population withN particles
Evaluate the population
Update the velocity and position for population
Rand<Acp
The best particle in P1 replaces the worstparticle in B1
The best particle in P2 replaces the worstparticle in B2
Rand<Acp
Rand<Afp
The excellent Afn particles ibad Afn particles
The excellent Afn particles ibad Afn particles
Rand<Afp
Put the particles in B1 and B2new SGBS
Reinitialize the ith particle xifitness
Fitness (xi)<T
The SAfn1 excellent particlesthe bad SAfn1 partic
The SAfn2 reinitialized parreplace the other bad SAfn2
Rand<SAfp
Yes
Yes
Yes
Yes
Yes
Yes
No
No
Fig. 6. The CPCE
Systems Research 101 (2013) 36– 48
and P2 are exchanged. Each step is described in the following sub-sections.
4.3.1. Design of the SGBSThere are N0 particles in the SGBS and are determined by using
Eq. (7).
N0 = N11 + N21 (7)
Velocities and positions of each particle in SGBS are set arbi-
trarily. Now SGBS is updated after cultural operations of twocultural-algorithm-populations in each generation according toSection 4.2. Two steps for updating SGBS are needed. First a newSGBS is created including B1 and B2 particles. Then, the excellentn B1 replace thein P1
n B2 replace thein P2
together and get
and evaluate its
V
in SGBS replaceles in P1ticles in SGBS particles in P1
The SAfn1 excellent particles in SGBS replacethe bad SAfn1 particles in P2
The SAfn2 reinitialized particles in SGBSreplace the other bad SAfn2 particles in P2
Rand<SAfp
The EEn excellent particles in P1 replace thebad EEn particles in P2
The EEn excellent particles in P2 replace thebad EEn particles in P1
Rand<EEp
Stopping criteria ismet?
End
Yes
Yes
Yes
No
No
No
No
No
No
No
flowchart.
ower
pp
T
(vtfb
4
gSSbSo
4
bpetcEcaopp
5
tf
A. Khodabakhshian et al. / Electric P
article is reserved and the bad ones are replaced by reinitializedarticles. Let TV be the mean fitness value of particles in SGBS.
V =N0∑i=1
fitness(xi)N0
(8)
TV threshold value is used for reserving or reinitializing. In Eq.8), xi and fitness(xi) are the ith particle in SGBS and its fitnessalue respectively. The value of fitness(xi) is evaluated by usinghe objective function considered for optimization problem. Thenor each particle in SGBS if fitness(xi) ≤ TV, the ith particle (xi) wille reserved or reinitialized.
.3.2. Affect operations from SGBS to P1 and P2Affect operation from SGBS to P1 and P2 is implemented in each
eneration based on the probability value of SAfp. Let SAfn1 andAfn2 be the mean values of two nonnegative integer numbers. ForGBS and P1 (P2), if rand ≤ SAfp, bad SAfn1 particles in P1 (P2) wille replaced by the best particles of SAfn1 in SGBS. Also other badAfn2 particles in P1 (P2) are replaced by the reinitialized particlesf SAfn2 in SGBS.
.3.3. Experience exchanging operation between P1 and P2After Affect operations from SGBS to P1 and P2, experience
etween P1 and P2 is exchanged in each generation. It is sup-osed that the probability of implementing operation of experiencexchange is EEp. Also EEn is the number of particles joined inhis operation. Now for P1 and P2, if rand ≤ EEp, the bad parti-les of EEn in P2 (P1) will be replaced by the best particles ofEn in P1 (P2). This co-evolutionary mechanism associates twoultural-algorithm-populations with each other. Useful knowledgend experience are exchanged between multi-swarms to guidether swarms to achieve a better optimal solution. For this pur-ose, the randomly reinitialized particles are also placed into theopulation. The flowchart of CPCE algorithm is shown in Fig. 6.
. Design methodology
CPCE method is used for tuning the MB-PSS parameters on theest system given in Section 2. For this purpose, first the objectiveunction is defined.
Fig. 7. MB-PSS IEEE 4B
Systems Research 101 (2013) 36– 48 41
5.1. Objective function
The integral of time multiplied absolute error (ITAE) is used asthe objective function [25]. This index is shown in Eq. (9).
J =M=4∑i=1
∫ t
0
(t∣∣�ωri
∣∣)dt (9)
It is evident that the controller with lower ITAE will be betterthan the other ones. Parameter M represents the number of powersystem machines in the system. Therefore, the design procedurecan be formulated as a constrained optimization problem of min-imizing the ITAE which is subject to Kimin
< Ki < Kimax and Timin<
Ti < Timax . The Ki and Ti represent all gains and time constantsshown in Fig. 3.
5.2. PSS tuning
The CPCE algorithm is carried out to tune the proposed MB-PSS parameters. All four generators are equipped with MB-PSS andPSSs are simultaneously tuned. In order to have less computationsfor tuning, the MB-PSS structure is rearranged as shown in Fig. 7and also parameters T2, T4, T6 and T8 are fixed as 0.01. Each MB-PSScontains 21 parameters and all four PSSs have 84 parameters whichshould be simultaneously tuned. In the simulation, the settingparameters of the CPCE algorithm are given in Table 2. It should benoted that CPCE algorithm is run several times and then the optimalset of parameters are selected. In the optimization process, differentdisturbances such as three-phase fault, single phase short circuit,the step change in the reference mechanical power and the stepchange in the reference voltage are applied. After the simulationof different disturbances and also different setting parameters ofalgorithm, the final result which has the lowest objective function(ITAE) is chosen as the final solution. The optimum values of param-eters obtained by using CPCE are shown in Table 3. The parameterswhich have not been presented are chosen as the values given inRef. [26], such as the parameters of speed transducer, washout and
limiters. The proposed CPCE-MB-PSS is compared with PSO-MB-PSS and C-MB-PSS. The PSO-MB-PSS parameters are tuned by usingPSO method and the objective function is also considered as Eq. (9).The setting parameters of PSO are shown in Table 4. The optimumblock diagram.
42 A. Khodabakhshian et al. / Electric Power Systems Research 101 (2013) 36– 48
Table 2Parameter settings of CPCE algorithm.
Population size P1 B1 P2 B2 Afp Afn Acp SAfp SAfn1 SAfn2 EEp EEn
60 20 10 20 10 0.4 3 0.4 0.1 1 1 0.1 1
Table 3MB-PSS parameters by using CPCE.
T1 T3 T5 T7 K1 K2 K
G1 High pass section 0.011 0.005 0.834 0.01 1.00 1.00 1.00Intermediate pass section 0.005 0.01 0.657 0.01 1.50 2.32 2.72Low pass section 0.591 0.01 0.005 0.01 9.40 1.17 3.18
G2 High pass section 0.01 0.914 0.005 0.01 1.93 1.00 1.00Intermediate pass section 0.005 0.01 0.01 0.079 1.00 2.82 1.31Low pass section 0.01 0.005 0.526 0.01 2.37 1.31 1.01
G3 High pass section 0.01 0.005 0.01 0.803 4.73 1.00 1.00Intermediate pass section 0.01 0.005 0.01 0.005 1.55 1.00 1.67Low pass section 0.01 0.005 0.01 0.005 1.00 1.93 1.70
G4 High pass section 0.01 0.005 0.01 0.005 1.36 1.27 1.00Intermediate pass section 0.847 0.01 0.647 0.01 1.07 1.00 2.78Low pass section 0.01 0.005 0.01 0.005 1.00 1.17 1.00
Table 4Parameter settings of PSO algorithm.
Population size c1 c2 c w
vtPp
6
SMeeipctwca
Table 6MB-PSS parameters based on Fig. 3.
Parameter Value
High and intermediatespeed transducer
(−0.0017s + 1)/(0.00013s2 + 0.018s + 1)
Low speed transducer (80s2)/(s3 + 82s2 + 161s + 80)VLmax 0.075VLmin −0.075VImax 0.15VImin −0.15VHmax 0.15VHmin −0.15VSTmax −0.25VSTmin −0.25KL11 1TL1 1.67TL2 2KL17 1TL7 2TL8 2.4
TM
60 2 3 1 Linearly decreasing from 0.9 to 0.4
alues of the PSO-MB-PSS parameters are shown in Table 5. Also,he C-MB-PSS parameters can be found in Ref. [26]. The other MB-SS parameters such as washout and transducer parameters areresented in Table 6.
. Simulation results
The simulation results are carried out on the test system given inection 2. In order to get clear results, first CPCE-MB-PSS and PSO-B-PSS are compared. Then, the CPCE-MB-PSS and C-MB-PSS are
valuated. Also, in order to have a comprehensive study, four differ-nt disturbances are considered as disturbance 1: 5% step increasen reference voltage of generator 1; disturbance 2: 10 cycle three-hase short circuit in the middle of line 3; disturbance 3: 10% stephange in load of bus 3 (area 1) for three different loading condi-
ions and; disturbance 4: line 3 is disconnected at second 1 andill be reconnected after 1000 ms. It should be noted that in loadhange scenario (disturbance 3), the load is increased at second 5nd then is driven back to the nominal load at second 45.
able 5B-PSS parameters by using PSO.
T1 T3
G1 High pass section 0.011 0.006
Intermediate pass section 0.005 0.01
Low pass section 0.6992 0.011
G2 High pass section 0.005 0.01
Intermediate pass section 0.005 0.012
Low pass section 0.005 0.01
G3 High pass section 0.6793 0.01
Intermediate pass section 0.294 0.01
Low pass section 0.01 0.005
G4 High pass section 0.01 0.05
Intermediate pass section 0.01 0.05
Low pass section 0.1479 0.01
TWH 0.012TW1 1
6.1. Comparing CPCE-MB-PSS and PSO-MB-PSS
In this section, the CPCE-MB-PSS and PSO-MB-PSS are stud-ied. Table 7 shows the ITAE for both MB-PSSs. It is seen that theCPCE-MB-PSS has got a lower ITAE index than the other MB-PSS.
T5 T7 K1 K2 K
0.1751 0.011 1.47 3.93 3.400.206 0.01 5.50 4.86 2.190.005 0.01 13.39 1.54 2.13
0.01 0.005 1.00 3.80 3.130.081 0.01 3.90 1.80 1.000.05 0.0098 2.34 2.24 3.76
0.005 0.01 1.00 1.66 4.250.1046 0.011 1.00 1.00 1.910.01 0.05 1.00 1.00 1.83
0.01 0.05 1.82 4.45 4.380.01 0.05 1.22 1.60 1.000.005 0.01 7.52 3.77 2.99
A. Khodabakhshian et al. / Electric Power Systems Research 101 (2013) 36– 48 43
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150.999
0.9992
0.9994
0.9996
0.9998
1
1.0002
1.0004
1.0006
Spp
ed G
1(pu
)
Time(s)0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0.999
0.9992
0.9994
0.9996
0.9998
1
1.0002
1.0004
1.0006
Spp
ed G
1(pu
)
Time(s)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150.9988
0.999
0.9992
0.9994
0.9996
0.9998
1
1.0002
1.0004
1.0006
Spp
ed G
1(pu
)
Time(s)
A B
C
Fig. 8. G1 speed following disturbance 1 (solid: CPCE-MB-PSS; dashed: PSO-MB-PSS). (A) Light, (B) nominal and (C) heavy.
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150.9995
0.9996
0.9997
0.9998
0.9999
1
1.0001
1.0002
Spp
ed G
2(pu
)
Time(s)0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0.9995
0.9996
0.9997
0.9998
0.9999
1
1.0001
1.0002
Spp
ed G
2(pu
)
Time(s)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150.999
0.9995
1
1.0005
Spp
ed G
2(pu
)
Time(s)
A B
C
Fig. 9. G2 speed following disturbance 1 (solid: CPCE-MB-PSS; dashed: PSO-MB-PSS). (A) Light, (B) nominal and (C) heavy.
44 A. Khodabakhshian et al. / Electric Power Systems Research 101 (2013) 36– 48
0 1 2 3 4 5 6 7 8 9 100.997
0.998
0.999
1
1.001
1.002
1.003
1.004
1.005
Spp
ed G
3(pu
)
Time(s)0 1 2 3 4 5 6 7 8 9 10
0.996
0.997
0.998
0.999
1
1.001
1.002
1.003
1.004
1.005
Spp
ed G
3(pu
)
Time(s)
0 1 2 3 4 5 6 7 8 9 100.997
0.998
0.999
1
1.001
1.002
1.003
1.004
1.005
Spp
ed G
3(pu
)
Time(s)
A B
C
Fig. 10. G3 speed following disturbance 2 (solid: CPCE-MB-PSS; dashed: PSO-MB-PSS). (A) Light, (B) nominal and (C) heavy.
0 1 2 3 4 5 6 7 8 9 100.996
0.997
0.998
0.999
1
1.001
1.002
1.003
1.004
1.005
Spp
ed G
4(pu
)
Time(s)0 `1 2 3 4 5 6 7 8 9 10
0.998
0.999
1
1.001
1.002
1.003
1.004
Spp
ed G
4(pu
)
Time(s)
0 1 2 3 4 5 6 7 8 9 100.997
0.998
0.999
1
1.001
1.002
1.003
Spp
ed G
4(pu
)
Time(s)
A B
C
Fig. 11. G4 speed following disturbance 2 (solid: CPCE-MB-PSS; dashed: PSO-MB-PSS). (A) Light, (B) nominal and (C) heavy.
A. Khodabakhshian et al. / Electric Power Systems Research 101 (2013) 36– 48 45
Table 7The values of performance index (ITAE).
Disturbance 1 Disturbance 2
Light Nominal Heavy Light Nominal Heavy
0.30.7
BMc
st
CPCE-MB-PSS 0.2699 0.1582
PSO-MB-PSS 0.4032 0.2287
y changing the operating condition to heavy loading, the CPCE-B-PSS gives a more suitable performance and shows the robust
haracteristics.The simulation results are depicted in Figs. 8–12. Figs. 8 and 9
how the responses under disturbance 1 and Figs. 10 and 11 showhe responses under disturbance 2. The results for disturbance
0 10 20 30 40 50 60 70 800.997 5
0.99 8
0.998 5
0.99 9
0.999 5
1
1.000 5
1.00 1
1.001 5
1.00 2
Spp
ed G
2(pu
)
Time(s)
0 10 20 30 0.997 5
0.99 8
0.998 5
0.99 9
0.999 5
1
1.000 5
1.00 1
1.001 5
1.00 2
Spp
ed G
2(pu
)
Tim
A B
C
Fig. 12. G2 speed following disturbance 3 (solid: CPCE-MB-PSS; d
5 15 25 35 45 55 65 750.9995
0.9996
0.9997
0.9998
0.9999
1
1.0001
1.0002
1.0003
Spp
ed G
2(pu
)
Time(s)
A B
Fig. 13. Generators speed in the nominal operating condition following di
475 0.9913 0.6870 0.7341105 1.3782 0.7202 1.0971
3 are shown in Fig. 12 for generator 2. Also, each figure containsthree loading conditions. The ability of CPCE-MB-PSS in damping
of oscillations following different disturbances and under differentloading conditions can be easily seen in these figures. The proposedCPCE-MB-PSS greatly enhances power system stability and dampsout the oscillations. The simulation results demonstrate that the0 10 20 30 40 50 60 70 800.99 8
0.998 5
0.99 9
0.999 5
1
1.000 5
1.00 1
Spp
ed G
2(pu
)
Time(s)
40 50 60 70 80e(s)
ashed: PSO-MB-PSS). (A) Light, (B) nominal and (C) heavy.
5 15 25 35 45 55 65 750.999
0.9995
1
1.0005
Spp
ed G
1(pu
)
Time(s)
sturbance 1 (solid: CPCE-MB-PSS; dashed: C-MB-PSS). (A) G1 (B) G2.
46 A. Khodabakhshian et al. / Electric Power Systems Research 101 (2013) 36– 48
5 15 25 35 45 55 65 750.988
0.99
0.992
0.994
0.996
0.998
1
1.002
1.004
1.006
Spp
ed G
4(pu
)
Time(s)5 15 25 35 45 55 65 75
0.99
0.995
1
1.005
Spp
ed G
3(pu
)
Time(s)
C D
Fig. 14. Generators speed in the nominal operating condition following disturbance 2 (solid: CPCE-MB-PSS; dashed: C-MB-PSS). (C) G3 (D) G4.
0 1 2 3 4 5 6 7 8 9 100.99 7
0.99 8
0.99 9
1
1.00 1
1.00 2
1.00 3
1.00 4
1.00 5
Spp
ed G
3(pu
)
Time(s)0 1 2 3 4 5 6 7 8 9 10
0.99 8
0.998 5
0.99 9
0.999 5
1
1.000 5
1.00 1
1.001 5
1.00 2
1.002 5
Spp
ed G
1(pu
)
Time(s)
A B
Fig. 15. Generators speed under nominal operating condition following disturbance 4 (solid: CPCE-MB-PSS; dashed: C-MB-PSS). (A) G1 (B) G3.
High passPSS
High passfilter
Intermediate
pass PSSIntermediate
pass filter
Low pass
PSS
Low pass
filter
Fig. 16. Separation of MB-PSS output signals.
A. Khodabakhshian et al. / Electric Power Systems Research 101 (2013) 36– 48 47
10-2
10-1
100
101
102
10
20
30
40
50
dB
PSS Frequency Response
10-2
10-1
100
10 1
10 2
-200
0
200
400
Deg
rees
Frequency (Hz)
10-2
10-1
100
10 1
-20
-10
0
10
20
Deg
rees
Frequency (Hz)
solid:
Pib
6
sMro
Faitlp
pop
6
irgMtiA
Fig. 17. Bode diagrams (
SO-MB-PSS performance goes to fluctuations under heavy operat-ng condition, while the CPCE-MB-PSS performance is not affectedy changing the system operating condition.
.2. Comparing CPCE-MB-PSS and C-MB-PSS
In this section the CPCE-MB-PSS and C-MB-PSS are compared. Ithould be mentioned that all three methods (CPCE-MB-PSS, PSO-B-PSS and C-MB-PSS) could be evaluated at the same time and
esults could be depicted in one figure. However, since the resultsf C-MB-PSS are larger than other methods, figures will not be clear.
In this case, the simulation results are depicted in Figs. 13–15.ig. 13A and B shows the responses under disturbance 1 and Fig. 14And B show the responses under disturbance 2. Also, different load-ng conditions are considered. Fig. 15 also represents the results forhe case of disturbance 4. It is to be noted that in this case since theoad of bus 3 is supplied through line 2 and the load of bus 4 isrocured through line 5, system will be stable.
The results demonstrate the superior performance of the pro-osed CPCE-MB-PSS for all cases where the oscillations are dampedut very fast and the magnitude of oscillations is very low in com-arison with C-MB-PSS.
.3. Comparing CPCE-MB-PSS and CPSS
In the previous sections different MB-PSSs were compared. Its useful to study the internal performance of the MB-PSS and theesults are also compared with the CPSS. The CPSS parameters areiven in [26]. Fig. 16 shows the injected signal by each section of
B-PSS installed on G1 as an example. It can be seen from Fig. 16hat each section injects its relative stabilizing signal. Thus, this PSSnjects a stronger signal than CPSS and naturally performs better.lso, the bode diagrams of CPSS and MB-PSS are depicted in Fig. 17.
MB-PSS; dashed: CPSS).
These figures clearly show that the bandwidth of MB-PSS is widerthan CPSS confirming its superiority performance. In low frequen-cies, the MB-PSS performs with a suitable magnitude, while theCPSS magnitude is very low. Thus, The MB-PSS is able to performmuch better performance under a wider range of frequencies andit can inject a stronger stabilizing signal.
7. Conclusions
In this paper, a multi-band PSS was successfully tuned by using anew optimization method and simulated. A multi-machine powersystem containing different loading conditions was considered toevaluate the proposed MB-PSS. This new algorithm was executedseveral times to find out the best solution. To show the ability ofthe proposed CPCE-MB-PSS, it was compared with PSO-MB-PSS andC-MB-PSS. A complete comparison between MB-PSS and CPSS wasalso performed and discussed. The simulation results demonstratedthe ability of MB-PSS in damping oscillations under different dis-turbances and loading conditions.
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