Controller Design of STATCOM for Power System Stability ... - JART

Controller Design of STATCOM for Power System StabilityImprovement Using Honey Bee Mating OptimizationA. Safari *1 , A. Ahmadian 2 , M. A. A. Golkar 31Department of Electrical Engineering, Ahar Branch,Islamic Azad University, Ahar, Iran*a-safari@iau-ahar.ac.ir2, 3 The Electrical Engineering Department of K. N. ToosiUniversity of Technology, Tehran, IranABSTRACTDamping of low frequency electromechanical oscillations is very important for a safe system operation. The fastacting, of a static synchronous compensator (STATCOM) which is capable of improving both steady state anddynamic performance permits newer approaches to system stabilization. This paper presents a novel methodology fortuning STATCOM based damping controller in order to enhance the damping of system low frequency oscillations.The design of STATCOM parameters are considered an optimization problem according to the time domain-basedobjective function solved by a Honey Bee Mating Optimization (HBMO) algorithm that has a strong ability to find themost optimistic results. To validate the results accuracy, a comparison with Genetic Algorithm (GA) has been made.The effectiveness of the proposed controller is demonstrated through nonlinear time-domain simulation and someperformance indices studies over a wide range of loading conditions. The simulation study shows that the designedcontroller by HBMO performs better than GA in finding the solution. Moreover, the system performance analysis underdifferent operating conditions shows that the φ based controller is superior to the C based controller.Keywords: STATCOM, honey bee mating optimization, power oscillation damping controller, low frequencyoscillations.NomenclatureDCE' qE fdFACTSFDGAGTOHBMOITAEKK AMP ePIP mPSOSMIBSTATCOMSVCTADirect currentInternal voltage behind transientreactanceEquivalent excitation voltageFlexible alternating currenttransmission systemsFigure of demeritGenetic algorithmGate turn off thyristorHoney bee mating optimizationIntegral of time multiplied absolutevalue of the errorProportional gain of the controllerRegulator gainMachine inertia coefficientElectrical output powerProportional integralMechanical input powerParticle swarm optimizationSingle machine infinite busStatic synchronous compensatorStatic var compensatorRegulator time constantT' doT eT sV dcVVSCδφ∆P e∆V dc1. IntroductionTime constant of excitation circuitElectric torqueSettling time of speed deviationDc capacitor voltageTerminal voltageVoltage source converterRotor speedRotor angleExcitation phase angleElectrical power deviationDC voltage deviationLeading in recent years, flexible alternativecurrent transmission systems (FACTS) devicesare one of the most effective ways to improvepower system operation controllability and powertransfer limits. Through the modulation of busvoltage, phase shift between buses, andtransmission line reactance, the FACTS devicescan cause a substantial increase in powertransfer limits during steady state [1]. Thesedevices are an addition to normally steady-statecontrol of a power system but, due to their fast144Vol. 11, February 2013

Controller Design of STATCOM for Power System Stability Improvement Using Honey Bee Mating Optimization, A. Safari et al. / 144‐155response, the FACTS can also be used for powersystem stability enhancement through improveddamping of power swings [2]. The real power flowwith primary function of FACTS devices can beregulated to reduce the low frequency oscillationand enhance power system stability. Recently,several FACTS devices have been implementedand installed in practical power systems [3-5].STATCOM is a member of the FACTS family thatis connected in shunt with the system. From theviewpoint of the power system dynamic stability,the STATCOM provides better dampingcharacteristics than the SVC. It is able toexchange transiently reactive power with thesystem, it can improve oscillation stability betterthan SVC [6, 7]. The STATCOM is based on theprinciple that a voltage source inverter generatesa controllable AC voltage source behind atransformer-leakage reactance hence, that thevoltage difference across the reactance canproduce active and reactive power exchangebetween the STATCOM and the transmissionnetwork. Several trials have been reported in theliterature of dynamic models of STATCOM inorder to design suitable controllers for power flow,voltage and damping controls [8]. Wang [9]established the linearized Phillips–Heffron modelof a power system installed with a STATCOM anddemonstrated the application of the model inanalyzing the damping effect of the STATCOM.Furthermore, seems that no efforts have beenmade to identify the most suitable STATCOMcontrol parameter, in order to arrive at a robustdamping controller. Intelligent controllers have thepotential of overcoming the above mentionedproblems. Fuzzy-logic-based controllers, forexample, have been used for controlling aSTATCOM [7, 10, 11]. The performance of suchcontrollers can be improved by adaptivelyupdating their parameters. Although using therobust control methods [12], the uncertainties aredirectly introduced to the synthesis. Due to thelarge model order of power systems, the orderresulting controller will be very large in generalwhich is not feasible because of the computationaleconomical problems when implementing. Thus,one important issue, in this respect, is the tuningof the controller parameters of the STATCOM. Forthis reason, usually a linearized model of thesystem around a single operation is used forSTATCOM controller design.Many of the optimization techniques such as PSO[13, 14], GA and HBMO are used for optimizationproblems. The HBMO algorithm can be used tosolve many of the same kind of problems as GA [15]and does not suffer from of GA’s problems. ThoughGA methods have been employed successfully tosolve complex optimization problems, a recentresearch has identified deficiencies on itsperformance [16, 17]. In order to overcome thesedrawbacks, the HBMO algorithm is proposed tooptimal tune of controller parameters to improvepower system stability in this paper. The HBMOalgorithm is a very strong method for optimizationand has emerged as a useful tool for engineeringoptimization. Hence, this method is efficient inhandling large and complex search spaces [18, 19].In this study, the problem of designing a robustlySTATCOM based damping controller is consideredas an optimization problem and both, HBMO and GAtechniques are used for searching optimizedparameters. The effectiveness and robustness of theproposed controller are demonstrated throughnonlinear time-domain simulation and someperformance indices studying the damp lowfrequency oscillations under different operatingconditions. Evaluation results show that the HBMObased tuned damping controller achieved goodperformance for a wide range of operating conditionsand is superior to the controller designed using GAtechnique.2. Honey bee mating optimizationThe honey bee is one of the social insects that onlycan survive as a member of a colony. The activityof honey bee suggests many characteristics suchas; team work and communication. A honey beecolony is normally compossed by a single egglayingqueen whose life-span is longer than that ofany other bee; and depending on the season,regularly lays around 60,000 workers . A colonymay contain only one queen during its life-cycle.That is called monogynous. Only the queen is fedwith “royal jelly.” “Nurse bees” take care of thisgland and feed the queen with it. The royal jellyallows the queen bee to become the biggest bee inthe hive [20].Several hundred drones live with the queen andits workers. Queen bee’s life-span is about 5 or 6years, whereas for the rest of the bees, speciallyJournal of Applied Research and Technology 145

Controller Design of STATCOM for Power System Stability Improvement Using Honey Bee Mating Optimization, A. Safari et al. / 144‐155worker bees, their life-spam do not reach 1 year.The drones die after the mating process.The drones play the father role in the colony thatare haploid and amplify or multiply their mother’sgenome without changing their geneticcombinations, except for mutation. Hence, dronesare agents that anticipate one of the mother’sgametes and by the sake of that female can playgenetically the males´s role. Broods, cared byworkers, improve from fertilized or unfertilizedeggs. They represent potential queens andprospective drones, respectively. In the marriageprocess, the queens in mating period, fly from thenest to far places. Insemination ends with thegradual death of drones, and by the sake of thosequeens receive the “mating sign.” Any drone cantake part in the mating process just onece, but thequeens mate several times. These features makebee mating process very interesting among otherinsects.2. Working principle and mathematicalpresentationThe queen plays the most important role in themating process in nature likewise the HBMOalgorithm. The spermatheca is a place for spermof drones and queen’s, all drones, however areoriginally haploid; after successful mating, thedrone’s sperm is stored in the queen’sspermatheca. A brood is reproduced by coming ofsome genes of drone’s into the brood genotype. Abrood has only one genotype [21].Therefore, an HBMO algorithm would beconstructed by the following five important stages:1. The algorithm starts with a mating flight,where a queen selects dronesprobabilistically from the spermatheca. Adrone is selected from list randomly forthe generating broods.2. Generating new broods by combiningdrone’s with queen´s genotypes .3. Using workers to carry on local searchingon broods.4. Adaptation of worker’s ability, based onthe improvement of broods.5. Substitution of queen’s workers bystronger and aptitude broods.When all queens have completed their matingflights, the breeding begins. All the broods afterthe generation are sorted according to fitness, i.e.their weakness or health. The best brood isreplaced by the worst queens until all queens willbe the best and there is no need of broods. Afterthe completion of mating, the remaining broodsfinally are killed hence, a new mating processbegins.2.2 Original HBMO algorithmA drone mates with a queen probabilistically usingan annealing function like this:Pr ob ( D , Q ) exp( f / S ( t ))(1)Where Prob(D,Q) is the probability of addingdrone’s sperm D to queen’s spermatheca Q, ∆(f)is the perfect difference of fitness D of queen, ands(t) is the speed of the queen at time t. Themating is high whether queen’s speed level ishigh, or drone’s fitness is equal to queen’s. Afterevery transition, the speed of queen will decreaseaccording to the following equations:s( t1) s( t)Et ( 1) Et ( ) (2)(3)Where: α is a factor ε(0,1) and γ is the amount ofenergy, E(t) reduction after each transition.The algorithm starts with three user-definedparameters and one predefined parameter. Thepredefined parameter is the number of workers (W),representing the number of heuristics encoded in theprogram. The three user-defined parameters are thenumber of queens, the queen’s spermatheca sizerepresenting the maximum number of mating perqueen in a single mating flight, and the number ofbroods that will be born by all queens. The energyand speed of each queen at the beginning of eachmating flight is initialized at random. A number ofmating flights are realized. At the commencement ofa mating flight, drones are generated randomly andthe queen selects a drone using the probabilistic rulein Equation (1). If the mating is done successfully,146Vol. 11, February 2013

Controller Design of STATCOM for Power System Stability Improvement Using Honey Bee Mating Optimization, A. Safari et al. / 144‐155the storage of drone’s sperm in queen’sspermatheca occurs. The combination of drone’sand queen’s genotypes, generate a new brood,which can be improved later on by employingworkers to carry on a local search. One of the maindifferences between HBMO algorithm and classicevolutionary algorithms is that by storing manydifferent drone’s sperm in the spermatheca for thequeen to use it , some of them create a new solutionfor the fittest broods, and gives the possibility tohave the fittest broods.The role of the workers is brood caring and for thesake of it, they are not separated from thepopulation and are used to grow the broodsgenerated by the queen. Every worker hasdifferent capability for producting in solutions. Thecomputational flow chart of HBMO algorithm isshown in Figure 1.startDefine the model input parameters:a) algorithm parameters, b) model parametersRandom generation of a set of initial solutionsRank the solutions based on the penalized objective function, keeping the bestone the predefined number of trial solutionsUse simulated annealing to select the set of solutions from the search space tomake a mating pool for possible information exchange between the best presetsolution and the selected trial solutionsGenerate new set of solutions by employing different predefined crossoveroperators and heuristic functions between the best present solutions and the trialsolutions according to their fitness valuesImprove the newly generated set of solutions employing different heuristicfunctions and mutation operators according to their fitness valuesUpdating the fitness value of the heuristic functions for next iteration, giving morechance to the more effective heuristic function in solution improvementSubstitute thebest solutionYesIs the new bestsolution better thanthe previous one?NoKeep the previousbest solutionTerminationcriteria satisfiedYesFinishNoAll previous trial solutions are discarded and new trial solutions aregenerated using: a) remaining generated solution, b) randomgenerationFigure 1. Flowchart of the HBMO algorithm.Journal of Applied Research and Technology 147

Controller Design of STATCOM for Power System Stability Improvement Using Honey Bee Mating Optimization, A. Safari et al. / 144‐1553. Power system modelingA SMIB power system installed with a STATCOMshown in Figure 2, is widely used for studies ofpower system oscillations, it is adopted in thispaper to demonstrate the proposed method. Thesynchronous generator delivers power to theinfinite-bus through a double circuit transmissionline and a STATCOM. The system data is given inthe appendix. The system consists of a step downtransformer with a leakage reactance X SDT , athree phase GTO-based voltage source converter,and a DC capacitor [9].VtV EtL1VmL3Vbi Loq are the d-and q-components of the STATCOMcurrent, respectively.The dynamics of the generator and the excitationsystem are expressed through a third order modelgiven as [9, 15]: ( 1)0(7). ( Pm Pe D)/M ,(8).Eq ( Eq E fd ) / Tdo ,(9)L2L4VSCf cV dc.E fd ( Efd Ka(VrefVt))/ Ta,(10)The expressions for the power output, terminalvoltage, and the d-q axes currents in thetransmission line and STATCOM, respectively, are:Figure 2. SMIB power system equippedwith STATCOM.The VSC generates a controllable AC voltagesource behind the leakage reactance. The voltagedifference between the STATCOM bus ACvoltage, v L(t) and v 0(t) produces active and reactivepower exchange between the STATCOM and thepower system, which can be controlled byadjusting the magnitude V 0 and the phase angleφ. The dynamic relation between the capacitorvoltage and current in the STATCOM circuit areexpressed as [9]:ILo (4)ILod jILoq,V o cVdc(cos j sin) cVdc,(5)IdccV dc ( ILodcos ILoqsin),CdcC(6)dcWhere for the PWM inverter c = mk and k is theratio between AC and DC voltage depending onthe inverter structure, m is the modulation ratiodefined by the PWM and the magnitude c is alsodefined by the PWM. The C dc is the dc capacitorvalue and I dc is the capacitor current while i Lod andX(1 LB X ) e LBq mVdcsinVbcosX SDT X SDTItld,X tL XX(1 LBtL X LB ) xdX LB X SDTX LB mVdccosVbsinX SDTItlq,X tL XX(1 LBtL X LB ) xqX LB X SDT(11)(12)eq ( xd X tL ) ItLq mVdcsinI Lod ,(13)X SDTmVdccos ( xd XtL)ItLqILoq,X SDTXtL(14)XLXL XT ; XLB ,(15)22X T , x' d and x q are the transmission line reactance,d-axis transient reactance, and q-axis reactance,respectively. A linear dynamic model is obtainedby linearizing the nonlinear model round anoperating condition.3.1 Power system linearized modelA linear dynamic model is obtained by linearizingthe nonlinear model around an operating148Vol. 11, February 2013

Controller Design of STATCOM for Power System Stability Improvement Using Honey Bee Mating Optimization, A. Safari et al. / 144‐155condition. The linearized model of power systemis given as follows:V DC (16) 0, ( P e D)/M ,(17)// Eq ( Eq Efd ) / Tdo,(18)∆ωPODV DCref∆u∆VKp dc K i dcsK s1 sTS∆φφ 0φE ( K ( v v) E )/ T(19)fd A ref fd AFigure 4. STATCOM PI controller for dc voltaje./vdc K7 K8Eq K9vdc K dcc K d, (20)V LrefV L/Pe K 1 K 2 Eq K pdc vdc(21) K pc c K p ,/Eq/K 4 K3Eq K qdc vdc K qcc K q, (22)/Vt K 5 K 6 Eq K vdc vdc(23) K vc c K v ,Where, K 1 ,K 2 ,...,K 9 , K pu , K qu and K vu are linearizationconstants. The state space model and blockdiagram of the linearized dynamic model of SMIBpower system with STATCOM is given by [15, 22].3.2 STATCOM based controllersThe POD controller, that is better than the PIDcontroller [23], is designed to produce an electricaltorque in phase with the speed deviationaccording to the phase compensation method.The speed deviation ∆ω is considered as theinput to the damping controller. The structure ofthe POD controller is given in Figure 3. Thiscontroller may be considered as a lead-lagcompensator. It comprises gain block, signalwashoutblock and lead-lag compensator. Theblock diagram of STATCOM dc voltage PIcontroller with power oscillation damping stabilizer(φ based controller) is shown in Figure 4. Settingof capacitor voltage is on the controlling part,which in relation to capacitor reference voltageand in comparison to the capacitor voltage, theamount of the angle phase of the converter canbe computed.InputsignalsT W 1sT 1 1 sT 3K1 sT W 1 sT 2 1 sT 4 Figure 3. Power oscillation damping controller.∆u∆ωFigure 5. STATCOM PI controller for ac voltaje.The DC-voltage regulator controls the DC voltageacross the DC capacitor of the STATCOM. Figure5 illustrates the block diagram of STATCOM acvoltage PI controller with a power oscillationdamping stabilizer (C based controller).3.3 STATCOM controllers design using HBMOIn the proposed method, we must tune theSTATCOM controller parameters optimally toimprove overall system dynamic stability. The twosignal control of the STATCOM (φ and c) can bemodulated in order to produce the damping torque,since the selection of the parameter for STATCOMbased damping controller is a complexoptimization problem. To acquire an optimalcombination, this paper employs the HBMO toimprove optimization synthesis and find the globaloptimum value of objective function. For ouroptimization problem, the objective function is atime domain-based objective function:J Np t sim i1 0POD. tdti∆u∆VKp ac K i acsK s1 sT(24)Where, the t sim is the time range of simulation andN p is the total number of operating points for whichthe optimization is carried out. It is aimed tominimize this objective function in order to improvethe system response in terms of the settling timeand overshoots. The design problem can beS∆cC 0cJournal of Applied Research and Technology 149

Controller Design of STATCOM for Power System Stability Improvement Using Honey Bee Mating Optimization, A. Safari et al. / 144‐155formulated as the following constrained optimizationproblem, where the constraints are the controllerparameters bounds:Minimize J Subject to:minmaxG1 G1 G1minmaxG2 G2 G2minmaxG3 G3 G3minmaxG4 G4 G4minmaxG G G5 5 5The proposed approach employs HBMO to solvethis optimization problem and search for anoptimal set of controller parameters. Theoptimization of controller parameters are carriedout by evaluating the objective function as given inEquation 24, which considers a multiple ofoperating conditions. The operating conditions aregiven in Table 1.LoadingconditionP e (pu) Q e(pu) X LCase 1 0.8 0.15 0.3Case 2 0.2 0.01 0.3Case 3 1.2 0.4 0.3Case 4 0.5 0.1 0.6Case 5 0.9 0.1 0.6Case 6 0.5 -0.2 0.3Table 1. Loading conditionsType of controllerParametersHBMO algorithm Genetic algorithmC based φ based C based φ basedcontroller controller controller controllerK 95.692 181.44 169.55 181.23T 1 0.9154 0.13633 0.3811 0.3633T 2 0.3191 0.16796 0.930 0.6791T 3 0.0524 0.043 0.6622 0.1143T 4 0.6994 0.9368 0.2812 0.4466Kp dc --- 99.78 --- 105.23Ki dc --- 0.4762 --- 0.4851Kp ac 2.365 --- 1.48 ---Ki ac 0.0271 --- 0.099 ---Table 2. The optimal parameter settings of theproposed controllersIn order to acquire a better performance, thenumber of queen, N drone , N brood , the size of thequeen’s spermatheca, the decreasing factor andN workers are chosen as 1, 100, 100, 50, 0.98 and1000, respectively [21]. In order to facilitate thecomparison with genetic algorithm (see appendixB), the design and tuning of the dampingcontroller for STATCOM are used. The finalvalues of the optimized parameters with objectivefunction, J, are given in Table 2.4. Nonlinear time domain simulationIn this section, the performance of the proposedcontroller under transient conditions is verified byapplying a 6-cycle three-phase fault at t= 0.6 sec,at the middle of the L 3 transmission line. The faultis cleared by permanent tripping of the faultedline. The performance of the controllers when theHBMO is used in the design is compared to that ofthe controllers designed using the GA. Thesimulation results at all cases loading conditionsdue to designed controller based on the φ basedcontroller and C based controller are shown inFigures 6-11. It can be seen that the proposedcontroller has good performance in damping lowfrequency oscillations and stabilizes the systemquickly. Moreover, from the above conductedtests, it can be concluded that the φ basedcontroller is superior to the C based controller.To demonstrate performance and robustness ofthe proposed controller, two performance indices:ITAE and FD based on the system performancecharacteristics are defined as:ITAEt sim1000 . . t dt0(25)FD ( OS 500) ( US 2000) Ts2 2 2(26)Where, speed deviation (∆ω), Overshoot (OS),Undershoot (US) and settling time of speeddeviation of the machine is considered forevaluation of the ITAE and FD indices. It is worthto mention that, the lower the value of theseindices, the better the system response in termsof time-domain characteristics. Numerical resultsof the performance and robustness for all systemloading cases are shown in Figures 11 and 12. Itcan be seen that the application of both PSS andSTATCOM damping controllers where the150Vol. 11, February 2013

Controller Design of STATCOM for Power System Stability Improvement Using Honey Bee Mating Optimization, A. Safari et al. / 144‐155controllers are tuned by the proposed coordinateddesign approach which gives the best response interms of overshoot, undershoot and settling time.5. ConclusionsThe honey bee mating optimization (HBMO)algorithm has been successfully applied to theoptimal design of STATCOM based dampingcontrollers. The design problem of the controller isconverted into an optimization problem which issolved by a HBMO technique with the time domainbasedobjective function. The robust design hasbeen found to be very effective for a range ofoperating conditions of the power system. Theeffectiveness of the proposed STATCOMcontrollers for improving transient stabilityperformance of a power system are demonstratedby a weakly connected example system subjectedto severe disturbance. The system performancecharacteristics in terms of ITAE and FD indicesrevealed that using both, the proposed HBMO andthe GA based controllers, the overshoot, theundershoot ,the settling time and speed deviationsof the machine are greatly reduced at variousoperating conditions. The nonlinear time domainsimulation results show the robustness of theproposed controller and their ability to provide gooddamping of low frequency oscillations. It can beseen that the HBMO based STATCOM controllerachieves good robust performance, providessuperior damping in comparison with the GA basedSTATCOM controller and greatly enhances thedynamic stability of power system. Moreover, theφ-based controller provides better dampingcharacteristics and greatly enhances the first swingstability compared to the C-based controller.(a) (b) (c)Figure 6. Dynamic responses for ∆ω at (a) case 1, (b) case 2, (c) case 3, loading conditions; solid (HBMObased C controller) and dashed (GA based C controller).(a)(b)Figure 7. Dynamic responses for ∆ω at (a) case 1, (b) case 2, (c) case 3 loading conditions; solid (HBMObased φ controller) and dashed (GA based φ controller).(c)Journal of Applied Research and Technology 151

Controller Design of STATCOM for Power System Stability Improvement Using Honey Bee Mating Optimization, A. Safari et al. / 144‐155(a) (b) (c) (d)Figure 8. Dynamic responses at case 1 loading; solid (HBMO Controller) and dashed (GA Controller); (a)∆Pe (C parameter), (b) ∆δ (C parameter), (c) ∆Pe (φ parameter) and (d) ∆δ (φ parameter).(a) (b) (c)Figure 9. Dynamic responses for ∆ω at (a) case 4, (b) case 5, (c) case 6 loading conditions; solid (HBMObased C controller) and dashed (GA based C controller).(a) (b) (c)Figure 10. Dynamic responses for ∆ω at (a) case 4, (b) case 5, (c) case 6 loading conditions; solid (HBMObased φ controller) and dashed (GA based φ controller).152Vol. 11, February 2013

Controller Design of STATCOM for Power System Stability Improvement Using Honey Bee Mating Optimization, A. Safari et al. / 144‐155(a)Figure 11. Value of performance index with C controller: a) ITAE and b) FD.(b)(a)(b)Figure 12. Value of performance index with φ controller: a) ITAE and b) FD.Appendix A:The nominal parameters of the system are listed inTable 3.M 8 MJ/MVA do 5 . 044GeneratorX d 1 puX q 0 . 6 p.u X d 0 . 3 pu D 0Excitation system K 50a T 0 . 05 saTransformers X 0.1puX SDT T 0 . 1 puTransmission lineX 0 . 4 puqDC link parameter V DC 1 pu C 1 p uDCSTATCOM parameterC 0 .25 52K s = 1 T s = 0.05Table 3. System parameters.Appendix B:Genetic algorithms are stochastic searchtechniques based on the mechanism of naturalselection and survival of the fittest [23]. Further,they combine function evaluation with randomizedand/or well-structured exchange of informationamong solutions to arrive at global optimum. Thearchitecture of GA implementation can besegregated into three constituent phases namely:initial population generation, fitness evaluation andgenetic operations. The GA control parameters,such as population size, crossover probability andmutation probability are selected, and an initialpopulation of binary strings of finite length isJournal of Applied Research and Technology 153

Controller Design of STATCOM for Power System Stability Improvement Using Honey Bee Mating Optimization, A. Safari et al. / 144‐155randomly generated. Given a random initialpopulation GA operates in cycles calledgenerations, as follows [25]:- Each member of the population is evaluatedusing a fitness function.- The population undergoes reproduction in anumber of iterations. One or more parents arechosen stochastically, but strings with higherfitness values have higher probability ofcontributing with an offspring.- Genetic operators, such as crossover andmutation are applied to parents to produce offspring.- The offspring are inserted into the population andthe process is repeated.The crossover is the kernel of genetic operations.It promotes the exploration of new regions in thesearch space using randomized mechanism ofexchanging information between strings. Twoindividuals placed in the mating pool duringreproduction are randomly selected. A crossoverpoint is then randomly selected and informationfrom one parent up to the crossover point isexchanged with the other parent. Theperformance method is illustrated below for theused simple crossover technique.Parent 1: 1011↓ 1110 offspring 1: 10111011startSpecify the parameters forGAGenerate the initiall tiGen=1Calculate the fitness value ofeach individualGen > MaxGenYesOptimal value of thecontroller parameterFinishNoGen = Gen+1Apply GA operations:selection, crossoverand mutationParent 2: 1010 ↓1011 offspring 2: 1010 1110Another process also considered in this work is themutation process of randomly changing encodedbit information for a newly created populationindividual. Mutation is generally considered as asecondary operator to extend the search spaceand cause escape from a local optimum whenused prudently with the selection and crossoverschemes. For the purpose of optimization ofEquation 24. routine from GA [24] is used.Using each set of controller parameters, the timedomain simulation is performed and the fitnessfunction value is determined. The computationalflow chart of GA algorithm is shown in Figure 13.While applying GA, a number of parameters arerequired to be specified. Optimization is terminatedby the pre-specified number of generations forgenetic algorithm.Figure 13. Flowchart of the genetic Algorithm.AcknowledgementsThe authors would like to thank the anonymousreviewers for their helpful criticisms and suggestions forimproving the earlier version of this paper.References[1] A.T. Al-Awami et al., A particle-swarm based approachof power system stability enhancement with unified powerflow controller, International Journal of Electrical Power andEnergy System, Vol. 29, pp. 251-259, 2007.[2] J. Machowski and J. W. Bialek, State variable control ofshunt FACTS devices using phasor measurements, ElectricPower Systems Research, Vol. 78, pp. 39-4, 2008.[3] A. E. Hammad, Analysis of power system stabilityenhancement by static VAR compensators, IEEETransaction. Power System, No.4, pp. 222- 227, 1986.154Vol. 11, February 2013

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