A PARTICLE SWARM OPTIMIZATION FOR REACTIVE POWER AND VOLTAGE CONTROL CONSIDERING VOLTAGE SECURITY ASSESSMENT

Transcription

1 A PARTICLE SWARM OPTIMIZATION FOR REACTIVE POWER AND VOLTAGE CONTROL CONSIDERING VOLTAGE SECURITY ASSESSMENT Hrotaka Yoshda Kench Kawata IEEE Trans. on Power Systems, Vol.15, No.4, pp , November 2001, presented at IEEE PES Wnter Meetng, Columbus, Jan.28-Feb.1, 2001 Yoshkazu Fukuyama, member, IEEE Shnch Takayama, Yosuke Nakansh, member, IEEE Techncal Research Center, Power Technology Lab. The Kansa Electrc Power Co., Inc. Fuj Electrc Corporate R & D, Ltd , Nakoj, Amagasak, Hyogo, 661 Japan No. 1, Fuj-mach, Hno-cty, Tokyo, Japan Abstract: Ths paper presents a partcle swarm optmzaton (PSO) for reactve power and voltage control (Volt/Var Control: VVC) consderng voltage securty assessment (VSA). VVC can be formulated as a mxed-nteger nonlnear optmzaton problem (MINLP). The proposed method expands the orgnal PSO to handle a MINLP and determnes an on-lne VVC strategy wth contnuous and dscrete control varables such as automatc voltage regulator (AVR) operatng values of generators, tap postons of on-load tap changer (OLTC) of transformers, and the number of reactve power compensaton equpment. The method consders voltage securty usng a contnuaton power flow and a contngency analyss technque. The feasblty of the proposed method s demonstrated and compared wth reactve tabu search (RTS) and the enumeraton method on practcal power system models wth promsng results. Key words: Partcle Swarm Optmzaton, Evolutonary Computaton, Reactve Power and Voltage Control, Mxed- Integer Nonlnear Optmzaton Problem, Voltage Securty Assessment, Contnuaton Power Flow I. INTRODUCTION One of the mportant operatng tasks of power utltes s to keep voltage wthn an allowable range for hgh qualty customer servces. Electrc power loads vary from hour to hour and voltage can be vared by change of the power load. Power utlty operators n control centers handle varous equpment such as generators, transformers, statc condenser (SC), and shunt reactor (ShR), so that they can nject reactve power and control voltage drectly n target power systems n order to follow the load change. VVC determnes an on-lne control strategy for keepng voltage of target power systems consderng the load change and reactve power balance n target power systems. Current practcal VVC n control centers s often realzed based on power flow senstvty analyss of the operaton pont usng lmted executon tme and avalable data from the actual target power system. Reducton of power generaton cost s one of the current nterested ssues of power utltes. Therefore, an optmal control to mnmze power transmsson loss s requred for VVC nstead of smple power flow senstvty analyss. Snce many voltage collapse accdents have been occurred over the last three decades [1], voltage securty problems have been domnated and the consderaton of the problem has been requred n VVC problem [2,3]. Two evaluatons should be performed to consder voltage securty. Frst one s to calculate the dstance between the current operatng pont and the voltage collapse pont. The calculaton can be realzed by drawng a P-V curve usng the contnuaton power flow (CPFLOW) technque [4]. The authors has been developed a practcal CPFLOW and verfed t wth practcal power systems [5]. Another one s to suppose varous faults for the current operatng pont n the target power system and calculate the dstance between the post-fault operatng ponts and voltage collapse ponts for each contngency. The calculaton s called voltage contngency analyss [1]. If a suffcent dstance can be kept for both calculatons, the new operatng condton calculated by VVC can be evaluated as a secure one. Thus, the advanced VVC requres optmal control strategy consderng power loss mnmzaton and voltage securty. VVC can be formulated as a MINLP wth contnuous state varables such as AVR operatng values and dscrete state varables such as OLTC tap postons and the number of reactve power compensaton equpment such as SC and ShR. The objectve functon can be vared accordng to the power system condton. For example, the functon can be mnmzaton of power transmsson loss of the target power system for the normal operatng condton as descrbed above. Conventonally, the methods for VVC problem have been developed usng varous methods such as fuzzy, expert 1

2 system, mathematcal programmng, and senstvty analyss [6-11]. However, a practcal method for a VVC problem formulated as a MINLP wth contnuous and dscrete state varables has been eagerly awated. PSO s one of the evolutonary computaton (EC) technques [12]. The method s mproved and appled to varous problems [13-16]. The orgnal method s able to handle contnuous state varables easly. Moreover, the method can be expanded to handle both contnuous and dscrete varables easly. Therefore, the method can be applcable to VVC formulated as a MINLP. Varous methods have been developed for a MINLP such as generalzed benders decomposton (GBD) [17] and OA/ER [18]. Usng the conventonal methods, whole problem s usually dvded to sub-problems and varous methods are utlzed for solvng each sub-problem. On the contrary, PSO can handle the whole MINLP easly and naturally and t s easy to apply to varous problems compared wth the conventonal methods. Moreover, VVC requres varous constrants that are dffcult to be handled by mathematcal ways. PSO s expected to be sutable for VVC because t can handle such constrants easly. Ths paper presents a PSO for VVC formulated as a MINLP consderng VSA. Voltage securty assessment s consdered usng a CPFLOW technque and a fast voltage contngency selecton method. The feasblty of the proposed method for VVC s demonstrated and compared wth RTS [19][20] and the enumeraton method on practcal system models wth promsng results. II. PROBLEM FORMULATION OF VVC Problem Formulaton VVC for a normal power system condton can be formulated as follows: mnmze f ( x, y) = Loss c n = 1 where, n: the number of branches, x: contnuous varables, y: dscrete varables, Loss : power loss (ploss) at branch, subject to (a) Voltage constrant Voltage magntude at each node must le wthn ts permssble range to mantan power qualty. (b) Power flow constrant Power flow of each branch must le wthn ts permssble range. (c) Voltage securty The Determned VVC strategy should keep voltage securty of the target power system. Ploss of the target power system s calculated for a certan VVC strategy usng load flow calculaton wth both contnuous varables (AVR operatng values) and dscrete (1) varables (OLTC tap postons and the number of reactve power compensaton equpment). Voltage and power flow constrants can be checked at the load flow calculaton and penalty values are added f the constrants are volated. P-V curves for the determned VVC strategy and varous contngences are generated and checked whether the VVC canddate can keep suffcent voltage securty margns. The constant power load model s used because the load model s the severest to the voltage securty problem. However, f a more complcated load model s requred, the proposed method can be easly expanded usng a ZIP load model [21]. State Varables The followng control equpment s consdered n the VVC problem. (a) AVR operatng values (contnuous varable) (b) OLTC tap poston (dscrete varable) (c) The number of reactve power compensaton equpment (dscrete varable) The above state varables are treated n load flow calculaton as follows: AVR operatng values are treated as voltage specfcaton values. OLTC tap postons are treated as tap rato to each tap poston. The number of reactve power compensaton equpment s treated as correspondng susceptance values. III. OVERVIEW OF PARTICLE SWARM OPTIMIZATION [12][13] PSO has been developed through smulaton of smplfed socal models. The features of the method are as follows: (a) The method s based on researches about swarms such as fsh schoolng and a flock of brds. (b) It s based on a smple concept. Therefore, the computaton tme s short and t requres few memores. (c) It was orgnally developed for nonlnear optmzaton problems wth contnuous varables. However, t s easly expanded to treat problems wth dscrete varables. Therefore, t s applcable to a MINLP wth both contnuous and dscrete varables such as VVC. The above feature (c) s sutable for the VVC problem because practcally effcent methods have not been developed for VVC wth both contnuous and dscrete varables. The above features allow PSO to handle the VVC problem and requre short computaton tme. Accordng to the research results for a flock of brds, brds fnd food by flockng (not by each ndvdual). The observaton leads the assumpton that every nformaton s shared nsde flockng. Moreover, accordng to observaton of behavor of human groups, behavor of each ndvdual (agent) s also based on behavor patterns authorzed by the groups such as customs and other behavor patterns accordng to the experences by each ndvdual. The 2

3 assumpton s a basc concept of PSO. PSO s bascally developed through smulaton of a flock of brds n twodmenson space. The poston of each agent s represented by XY-axs poston and the velocty (dsplacement vector) s expressed by vx (the velocty of X-axs) and vy (the velocty of Y-axs). Modfcaton of the agent poston s realzed by usng the poston and the velocty nformaton. Searchng procedures by PSO based on the above concept can be descrbed as follows: a flock of agents optmzes a certan objectve functon. Each agent knows ts best value so far (pbest) and ts XY poston. Moreover, each agent knows the best value n the group (gbest) among pbests, namely the best value so far of the group. The modfed velocty of each agent can be calculated usng the current velocty and the dstance from pbest and gbest as shown below: k v + 1 k k = w v + c rand ( pbest s ) 1 k + c rand ( gbest s ) (2) 2 where, k v : current velocty of agent at teraton k, k+1 v : modfed velocty of agent, rand : random number between 0 and 1, k s : current poston of agent at teraton k, pbest : pbest of agent, gbest : gbest of the group, w : weght functon for velocty of agent, c : weght coeffcents for each term. Usng the above equaton, a certan velocty that gradually gets close to pbests and gbest can be calculated. The current poston (searchng pont n the soluton space) can be modfed by the followng equaton: k+ 1 k k+ 1 s = s + v (3) Fg. 1 shows the above concept of modfcaton of searchng ponts. Dscrete varables can be handled n (2) and (3) wth lttle modfcaton. Dscrete numbers can be used to express Y vk s k v k+1 v pbest s k+1 v gbest S k : current searchng pont, s k+1 : modfed searchng pont, V k : current velocty, V k+1 : modfed velocty, Vpbest : velocty based on pbest Vgbest :velocty based on gbest Fg.1 Concept of modfcaton of a searchng pont. X the current poston and velocty. If a dscrete random number s used n (2) and the whole calculaton of rght-hand sde (RHS) of (2) s dscretzed to the exstng dscrete number, both contnuous and dscrete number can be handled n the algorthm wth no nconsstency. The features of the searchng procedure can be summarzed as follows: (a) PSO utlzes several searchng ponts lke genetc algorthm (GA) and the searchng ponts gradually get close to the optmal pont usng ther pbests and the gbest. (b) The frst term of RHS of (2) s correspondng to dversfcaton n the search procedure. The second and thrd terms of that are correspondng to ntensfcaton n the search procedure. Namely, the method has a wellbalanced mechansm to utlze dversfcaton and ntensfcaton n the search procedure effcently. (c) The orgnal PSO can be appled to the only contnuous problem. However, the method can be expanded to the dscrete problem usng dscrete numbers lke grds for XY poston and ts velocty easly. (d) There s no nconsstency n searchng procedures even f contnuous and dscrete state varables are utlzed wth contnuous axes and grds for XY postons and veloctes. Namely, the method can be appled to a MINLP wth contnuous and dscrete state varables naturally and easly. (e) The above concept s explaned usng only XY-axs (twodmenson space). However, the method can be easly appled to n-dmenson problem. The above feature (b) can be explaned as follows [13]. The RHS of (2) conssts of three terms. The frst term s the prevous velocty of the agent. The second and thrd terms are utlzed to change the velocty of the agent. Wthout the second and thrd terms, the agent wll keep on flyng n the same drecton untl t hts the boundary. Namely, t tres to explore new areas and, therefore, the frst term s correspondng to dversfcaton n the search procedure. On the other hand, wthout the frst term, the velocty of the flyng agent s only determned by usng ts current poston and ts best postons n hstory. Namely, the agents wll try to converge to the ther pbests and/or gbest and, therefore, the terms are correspondng to ntensfcaton n the search procedure. The concept of expanded PSO for MINLP s shown n fg. 2. The orgnal PSO has been appled to a learnng problem of neural networks and Schaffer f6, the X 1 Agent (Contnuous) (Contnuous) X 2 X 3 (Dscrete) X n (Contnuous) Fg. 2 Concept of expanded PSO for MINLP. 3

4 famous benchmark functon for GA, and effcency of the method has been confrmed [12]. IV. VOLTAGE SECURITY ASSESSMENT The statc P-V curve represents the relaton between load ncrease and voltage drop. Namely, the P-V curve can be calculated by ncreasng total loads n the target power system gradually and plottng the dropped voltage. CPFLOW utlzes power system loads as parameters and calculates the P-V curve by modfcaton of the parameters usng a contnuaton method. The contnuaton method s one of the methods n appled mathematcs and t calculates transton of equlbrum ponts (e.g. P-V curve) by modfcaton of parameters. In order to avod the ll-condton around the saddle node bfurcaton pont (nose pont), an arclength along the P-V curve s ntroduced as an addtonal state varable and the power flow equaton s expanded. The contnuaton method s appled to the expanded power flow equaton and the P-V curve can be generated rapdly wthout ll-condton around the nose pont. CPFLOW can generate a P-V curve automatcally and can be appled to large-scale power systems easly [4][5]. The proposed method generates a P-V curve usng the CPFLOW technque and calculates a MW margn, dstance between the current operatng pont and the nose pont, for the determned control strategy. The proposed method also utlzes the fast voltage contngency analyss method usng CPFLOW [22]. Then, the method checks whether the MW margn s enough or not compared wth the predetermned value. The procedure for voltage securty assessment can be expressed as follows: Step. 1 Evaluaton of the control strategy It s checked whether the new power system condton after applyng the current control strategy has an enough MW margn or not. Step. 2 Evaluaton of varous contngences The several severe contngences for the new power system condton after applyng the current control strategy are selected by the fast voltage contngency analyss method. The MW margn for the only severe contngences are calculated usng CPFLOW. If the MW margns for the current control strategy and the severe contngences are large enough, the current control strategy s selected. Otherwse t s not selected. Usng the procedure, the method checks whether the target power system can keep voltage securty by the control or not. VSA conssts of statc and dynamc VSA and the proposed method only consders the statc VSA because of the lmted calculaton tme for on-lne VVC. If the dynamc VSA s stll requred, the VSA used n the proposed method can be replaced wth a dynamc VSA tool such as QSS descrbed n [1]. However, n such a case, we have to face the problem of executon tme and we may have to develop a parallel computaton method for the VSA based on dstrbuted memory tools such as PVM [23] and MPI [24] or shared memory tools such as OpenMP [25]. V. FORMULATION OF VVC USING PSO Treatment of State Varables Each varable s treated n PSO as follows: Intal AVR operatng values are generated randomly between upper and lower bounds of the voltage specfcaton values. The value s also modfed n the search procedure between the bounds. OLTC tap poston s ntally generated randomly between the mnmum and maxmum tap postons. The value s modfed n the search procedure among exstng tap postons. Then, the correspondng mpedance of the transformer s calculated for the load flow calculaton. The number of reactve power compensaton equpment s also generated from 0 to the number of exstng equpment at the substaton ntally. The value s also modfed n the search procedure between 0 and the number of exstng equpment. VVC algorthm usng PSO The proposed VVC algorthm usng PSO can be expressed as follows: Step 1. Intal searchng ponts and veloctes of agents are generated usng the above-mentoned state varables randomly. Step 2. Ploss to the searchng ponts for each agent s calculated usng the load flow calculaton. If the constrants are volated, the penalty s added to the loss (evaluaton value of agent). Step 3. Pbest s set to each ntal searchng pont. The ntal best evaluated value (loss wth penalty) among pbests s set to gbest. Step 4. New veloctes are calculated usng (2). Step 5. New searchng ponts are calculated usng (3). Step 6. Ploss to the new searchng ponts and the evaluaton values are calculated. Step 7. If the evaluaton value of each agent s better than the prevous pbest, the value s set to pbest. If the best pbest s better than gbest, the value s set to gbest. All of gbests are stored as canddates for the fnal control strategy. Step 8. If the teraton number reaches the maxmum teraton number, then go to Step 9. Otherwse, go to Step 4. Step 9. P-V curves for the control canddates and varous contngences are generated usng the best gbest among the stored gbests (canddates). If the MW margn s larger than the predetermned value, the control s determned as the fnal soluton. Otherwse, select the next gbest and repeat the VSA procedure mentoned above. If the voltage and power flow constrants are volated, the absolute volated value from the maxmum and mnmum boundares s largely weghted and added to the objectve 4

5 functon (1). The maxmum teraton number should be determned by pre-smulaton. As mentoned below, PSO requres less than 100 teratons even for large-scale problems. There are several ways to formulate VVC consderng VSA. Maxmzaton of MW margn nstead of loss mnmzaton s one opton. However, the purpose of the paper s to develop VVC algorthm for steady state operaton. In ths case, we can thnk that we stll have enough voltage stablty margn. Therefore, the authors decded to use only loss mnmzaton as the objectve functon and check whether the control strategy has enough voltage stablty margns or not after loss mnmzaton. Moreover, evaluaton for each state s extremely tme-consumng consderng VSA durng optmzaton procedure, and t s dffcult to realze on-lne VVC. Consderng the trade-off between the optmal control and the executon tme, the proposed method selected the way to handle the contngences after generaton of the optmal control canddates. If maxmzaton of MW margn s requred as the objectve functon, approxmaton method such as the look-ahead method wth parallel computaton should be used durng the search procedure for on-lne VVC. VI. NUMERICAL EXAMPLES The proposed method has been appled to several power system models compared wth RTS and the enumeraton method. Our target VVC problem s formulated as a MINLP wth dscrete and contnuous varables. OPF bascally only handles contnuous varables and some papers such as [26] tred to handle dscrete varables n OPF formulaton. Unfortunately, the authors do not have OPF program wth such treatment. Therefore, we compared the proposed method wth the avalable combnatoral optmzaton software n the smulaton. IEEE 14 bus system (1) Smulaton condtons Fg. 3 A modfed IEEE 14 bus system. Fg. 3 shows a modfed IEEE 14 bus system. Table 1 shows the operatng condton of the system. The followngs are control varables. (a) Contnuous AVR operatng values of node 2,3,6, and 8: Upper and lower bounds are 0.9 and 1.1 [pu]. (b) Dscrete tap postons of transformers between node 4-7, 4-9, and 5-6: These transformers are assumed to have 20 tap postons. (c) Dscrete number of nstalled SC n node 9 and 14: Each node s assumed to have three 0.06 [pu] SC. The proposed method tres to generate an optmal control for the operatng condton. Ploss of the orgnal system s [pu]. Generaton of the VVC canddates (Step 1-7 n the proposed VVC algorthm) by the proposed PSO based method, RTS, and the enumeraton method s compared n the smulaton. The followng parameters are utlzed n the smulaton accordng to the pre-smulaton. The coeffcent functon w of (2) s set to the followng equaton [13]: wmax w w = wmax ter max mn ter where, w max =0.9, w mn =0.4, ter max : maxmum teraton number, ter : current teraton number. c 1 and c 2 of (2) are set to 2.0. w max and w mn are set to 0.9 and 0.4 accordng to the pre-smulaton as shown below. Number of agents for PSO s 10. The parameters for RTS are also determned to approprate values through pre-smulaton. The ntal tabu length s 10 and ncrease/decrease rate for tabu length s 0.2 for RTS n the smulaton. The results are compared wth 300 searchng teratons. RTS and the Table 1 Operatng condton of IEEE 14 bus system. Bus No. Vol. [pu] Node specfcaton SC [pu] P [pu] Q [pu] 1 * * * * * * *3 *1 : Node 1 s slack *2 : PV specfcaton node *3 : 0.06 [pu] * 3 SC (4) 5

6 enumeraton method utlzes dgtzed AVR operatng values and the nterval s 0.01 [pu]. The nterval corresponds to 5 [kv] n 500 [kv] system. The formulaton as the combnatoral optmzaton problem (COP) has about 10 9 combnatons n the problem. The system has been developed usng C language (egsc ver.1.1.1) and all smulaton s performed usng EWS (SPECnt95: 12.3). (2) Smulaton results Table 2 shows the best results by the proposed method, RTS, and the enumeraton method. Table 3 shows Table 2 The optmal control for IEEE 14 bus system. Method PSO RTS enumeraton Cont. method Varables AVR AVR AVR AVR Tap Tap Tap SC SC AVR 2 : AVR operatng values [pu] at node 2 Tap 4-7 : Tap rato between node 4 and 7 SC 9 : Susceptance [pu] at node 9 Table 3 Summary of calculaton results by the proposed method and reactve tabu search. Method compared tem IEEE 14 bus system 112 bus system PSO Mnmum loss value Average loss value Cal. Tme RTS Mnmum loss value Cal. Tme loss value : actve power loss [pu] cal. tme : average calculaton tme [s] the loss values and calculaton tme of the results. The best result by RTS s smlar to that by the enumeraton method (the optmal result formulated as a COP). However, the loss value calculated by PSO s smaller than the optmal value and a tap poston s dfferent between the results. When VVC s formulated as a COP, only solutons to dscrete values are searched and the objectve functon shape between the dscretzed nterval s out of concern. Therefore, as t s usually ponted out, the optmal soluton formulated as a MINLP and a COP s dfferent. The results ndcate necessty of formulaton of VVC as a MINLP. PSO can generate smaller loss values than RTS wth 15 % possblty. The calculaton tme by PSO s about 15 % faster than that by RTS. Table 4 shows the parameter senstvty analyss of PSO. In the smulaton, w max and w mn of (4) and c of (2) s changed. The average and mnmum Ploss wth 100 searchng teratons n 100 trals for each case are shown n the table. The results reveal that the approprate values for w max and w mn are 0.9 and 0.4. The approprate value for c s 1.5. However, the mnmum Ploss for 1.5, 2.0, and 2.5 are smlar and 2.0 s utlzed n the smulaton accordng to the suggested value n [13]. Consequently, the approprate parameter values for the problem are the same as the ones suggested n [13]. The proposed method generates a P-V curve for the optmal control strategy usng the CPFLOW technque and performs the voltage contngency analyss. It s verfed that Voltage [pu] Load [pu] Fg. 4 A P-V curve of the optmal control (Node 12) for IEEE 14 bus system. w max w mn Table 4 Parameter senstvty analyss for IEEE 14 bus system (100 trals). C ave mn ave mn ave mn

7 the strategy can keep voltage securty when the load margn to 0.95 [pu] voltage s larger than 10 % load ncrease pont n the smulaton. The evaluaton crtera depend on the target power system and they should be determned for each system through pre-smulaton. Fg. 4 shows an example of a P-V curve for node 12 wth the optmal control strategy Frequences The optmal result by RTS s ncluded n ths range. Practcal 112 bus model system (1) Smulaton condtons The proposed method s appled to a practcal model system wth 112 buses. The system models the EHV system of Kansa Electrc Practcal system. The model system has 11 generators for AVR control, 47 OLTCs wth 9 to 27 tap postons, and 13 SC nstalled buses wth 33 SCs for VVC. The number of agents for PSO s set to 30 n order to get a hgh qualty soluton wthn 1 [mn]. PSO and RTS are compared n 100 searchng teratons. The same parameters for IEEE 14 bus system except the above values are utlzed n the smulaton Actve Power loss nterval [pu] Fg. 5 Statstcal results by PSO (100 trals) for practcal 112 bus system (2) Smulaton results Fg. 5 shows the statstcal evaluaton results by the proposed method n 100 trals. Table 3 shows the loss values and calculaton tme of the results. The average loss value by the proposed method s smaller than the best result by RTS. PSO generates better soluton than RTS wth 96 % possblty. Fg. 6 shows typcal convergence characterstcs (Ploss transton of gbest by PSO and the best result by RTS). It s clear from the fgure that the soluton by PSO s converged to hgh qualty solutons at the early teratons (about 20 teratons). The average teraton to the best result by the proposed method s On the contrary, RTS reaches the best result gradually. The average calculaton tme by PSO s about 4 tmes faster than that by RTS. RTS generates neghborng solutons (canddates for the next searchng pont) n the soluton space. It performs load flow calculaton for each canddate and evaluates volaton of operatng constrants and tabu status for all canddates. Therefore, canddates that should be evaluated are ncreased exponentally as the dmenson of the problem ncreases. On the contrary, PSO just evaluate (2) and (3) for each agent and the number of load flow calculaton s the same for IEEE14 and practcal 112 bus system f the same number of agents are utlzed for the smulaton. The characterstc of PSO s sutable for the applcaton to practcal system. The determned VVC strategy canddate s evaluated as a secure one usng a CPFLOW technque. Voltage contngency analyss s also performed for the canddate and t s evaluated as secure. The calculaton tme for voltage contngency rankng s 11.0 [s] (112 contngences) and the tme for one CPFLOW calculaton s 2.0 [s] for the 112 bus model system. Therefore, for example, the total calculaton tme for voltage securty assessment s 19.0 [s] f CPFLOW s performed for the severest three contngences (one CPFLOW calculaton, contngency rankng and three CPFLOW calculaton). As descrbed above, large penalty s added at Ploss[pu] Iteraton PSO RTS Fg. 6 Convergence characterstcs by PSO and RTS for practcal 112 bus system. the evaluaton of the objectve functon f the voltage and power flow constrants are volated. Therefore, all of the best solutons by both PSO and RTS wthn 100 searchng teratons are feasble solutons wthout voltage and power flow constrants volaton n the smulaton. Although the best VVC strategy s evaluated as secure n the model system, voltage securty assessment can become more mportant when the utlzaton rate of power equpment s ncreased and n the deregulaton envronment. Large-scale 1217 bus model system (1) Smulaton condtons The proposed method has been developed to apply the practcal EHV system. Therefore, the applcablty of the proposed method to the target system s already evaluated wth the 112 bus system. However, n order to evaluate the applcablty of the proposed method to large-scale systems, t has been appled to a 1217 bus system. The model system s composed by doublng the full scale Kansa Electrc power system. The system has 84 generators for AVR control, 388 7

8 Number of states OLTCs, and 82 SCs for VVC. The parameters for evaluated methods are the same as that utlzed for the 112 bus model system. (2) Smulaton results Convergence characterstcs for the 1217 bus system by RTS and PSO are the same as Fg. 6. RTS requres about 7.6 [hour] for 100 teratons. On the contrary, the average executon tme for obtanng the optmal results (the average number of teratons for that s 27.5) by PSO s about 230 [s]. Fg. 7 shows the number of states to be evaluated at each teraton by RTS and PSO. The fgure assumes that the number of agent s 30 n all cases. The number by RTS s the number of neghborng states of the current state at each teraton. Therefore, t ncreases drastcally by ncrease of the dmenson of the problem. On the contrary, the number by PSO corresponds to the number of agents. Therefore, t s the same even for large dmensonal problems. Consequently, although PSO only evaluates the lmted number of states usng (2) and (3), the evaluaton s effcent even for the largescale problems and realzes the quck convergence characterstc to sub-optmal solutons. The characterstc ndcates the applcablty of PSO to large-scale problems. The calculaton tme for evaluaton of one state s ncreasng as the dmenson of the problem ncreases. Therefore, f speed-up of the whole executon tme have to be realzed, parallel computaton methods based on dstrbuted memory tools such as PVM [22] and MPI [23] or shared memory tools such as OpenMP [24] can be utlzed for the optmzaton part n a smlar manner for the VSA part. VII. CONCLUSIONS RTS PSO Number of nodes Fg.7 The number of states evaluated at each teraton by RTS and PSO. Ths paper presents a partcle swarm optmzaton (PSO) for reactve power and voltage control (VVC) consderng voltage securty assessment (VSA). The proposed method formulates VVC as a mxed nteger nonlnear optmzaton problem (MINLP) and determnes a control strategy wth contnuous and dscrete control varables such as AVR operatng values, OLTC tap postons, and the number of reactve power compensaton equpment. The method also consders voltage securty usng a contnuaton power flow (CPFLOW) and a voltage contngency analyss technque. The feasblty of the proposed method for VVC s demonstrated on practcal power systems wth promsng results. The results can be summarzed as follows: (a) Ths paper shows the practcal applcablty of PSO to a MINLP and sutablty of PSO for applcaton to largescale VVC problems. PSO has several parameters. Accordng to the smulaton results, t s not requred severe parameter tunng and especally, PSO only requres less than 50 teratons for obtanng sub-optmal solutons even for large-scale systems. Many power system problems can be formulated as a MINLP and the results ndcate the possblty of PSO as a practcal tool for varous MINLPs of power system operaton and plannng. (c) VVC s sometmes formulated as a combnatoral optmzaton problem. However, dscrete varables of the optmal result formulated as a MINLP and those formulated as a combnatoral optmzaton problem are dfferent. Therefore, t ndcates the effcency of formulaton of VVC as a MINLP. (d) Consderaton of VSA s one of the mportant practcal functons of VVC. The results reveal that the possblty of treatment of the securty by the proposed PSO-based method n VVC. In addton to the proposed method, the followng addtonal features make the proposed VVC more practcal. (d) Avodance of control concentraton to a specfc equpment (e) Trackng to load change (f) Look-ahead control usng load forecast Especally, for handlng (e)(f), an optmal control strategy n several control ntervals should be consdered smultaneously. Improvement of the proposed method consderng the above features and parallel computaton are one of the future works. ACKNOWLEDGEMENTS The authors would lke to acknowledge Prof. Hsao- Dong Chang of Cornell Unversty for hs techncal supports to develop the voltage securty assessment functon. REFERENCES [1] T. Van Cutsem, T. and C. Vournas, Voltage Stablty of Electrc Power Systems, Kluwer Academc Publshers, [2] T. Van Cutsem, "An Approach to Correctve Control of Voltage Instablty Usng Smulaton and Senstvty", IEEE Transacton on Power Systems, Vol. 10, No. 2, pp , May [3] B. D. Thukaram, et al., "Optmal Reactve Power Dspatch Algorthm for Voltage Stablty Improvement", Internatonal Journal of Electrcal Power & Energy Systems, Vol. 18, No. 7, pp , July

9 [4] H. D. Chang, et al., "CPFLOW: A Practcal Tool for Tracng Power System Steady-State Statonary Behavor Due to Load and Generaton Varatons", IEEE Transacton on Power Systems, Vol. 10, No. 2, pp , May [5] H. Yoshda, Y. Fukuyama, et al., "A Practcal Contnuaton Power Flow for Large-Scale Power System Analyss", Proceedngs of IEE of Japan Annual Conventon Record, No. 1313, 1998 (n Japanese). [6] K. Tomsovc, "A Fuzzy Lnear Programmng Approach to the Reactve Power / Voltage Control Problem", IEEE Transacton on Power Systems, Vol. 7, No. 1, pp , February [7] B. Cova, et al., "Contngency Constraned Optmal Reactve Power Flow Procedures for Voltage Control n Plannng and Operaton", IEEE Transacton on Power Systems, Vol. 10, No. 2, pp , May [8] J. L. M. Ramos, et al., "A Hybrd Tool to Assst the Operator n Reactve Power / Voltage Control and Operaton", IEEE Transacton on Power Systems, Vol. 10, No. 2, pp , May [9] Q. H. Wu, et al., "Power System Optmal Reactve Power Dspatch Usng Evolutonary Programmng", IEEE Transacton on Power Systems, Vol. 10, No. 3, pp , August [10] H. Vu, et al., "An Improved Voltage Control on Large- Scale Power System", IEEE Transacton on Power Systems, Vol. 11, No. 3, pp , August [11] T. L. Le et al., "Network Equvalents and Expert System Applcaton for Voltage and VAR Control n Large - Scale Power Systems", IEEE Transacton on Power Systems, Vol. 12, No. 4, pp , November [12] J. Kennedy and R. Eberhart, "Partcle Swarm Optmzaton", Proceedngs of IEEE Internatonal Conference on Neural Networks, Vol. IV, pp , Perth, Australa, [13] Y. Sh and R. Eberhart, "A Modfed Partcle Swarm Optmzer", Proceedngs of IEEE Internatonal Conference on Evolutonary Computaton, pp.69-73, Anchorage, May [14] H. Zhenya, et al., "Extractng Rules from Fuzzy Neural Network by Partcle Swarm Optmzaton", Proceedngs of IEEE Internatonal Conference on Evolutonary Computaton, pp.74-77, Anchorage, May [15] J. Kennedy and W. Spears, "Matchng Algorthm to Problems: An Expermental Test of the Partcle Swarm Optmzaton and Some Genetc Algorthms on the Multmodal Problem Generator", Proceedngs of IEEE Internatonal Conference on Evolutonary Computaton, pp.78-83, Anchorage, May [16] P. Angelne, "Usng Selecton to Improve Partcle Swarm Optmzaton", Proceedngs of IEEE Internatonal Conference on Evolutonary Computaton, Anchorage, pp.84-89, May [17] A. M. Geoffron, "Generalzed Benders Decomposton", Journal of Operaton Theory and Applcatons, Vol.10, No.4, pp , [18] G. R. Kocs and I. E. Grossmann, "Computatonal Experence wth DICOP solvng MINLP Problems n Process Systems Engneerng", Computer Chemcal Engneerng, Vol.13, No.3, pp , [19] R. Battt, "The Reactve Tabu Search", ORSA Journal of Computng, Vol.6, No.2, pp , [20] Y. Fukuyama, et al., "A Reactve Tabu Search for Servce Restoraton n Electrc Power Dstrbuton Systems", Proceedngs of IEEE Internatonal Conference on Evolutonary Computaton, Anchorage, pp , May [21] H. D. Chang, H. Yoshda, Y. Fukuyama, et al., "The Generaton of ZIP-V Curves for Tracng Power System Steady State Statonary Behavor to Load and Generaton Varatons", Proc. of IEEE Summer Meetng, July [22] H. D. Chang, et al., "Look-ahead Voltage and Load Margn Contngency Selecton Functons for Largescale Power Systems", IEEE Transacton on Power Systems, Vol.12, No.1, pp , February [23] J. Dongarra, et al., PMV 3 User's Gude and Reference Manual, Oak Rdge Natonal Laboratory, May [24] W. Gropp, et al., Usng MPI, The MIT Press, [25] OpenMP C and C++ Applcaton Program Interface Verson 1.0, OpenMP Archtecture Revew Board, October [26] W. E. Lu, A. D. Papalexopoulos, and W. F. Tnney, "Dscrete Shunt Controls n a Newton Optmal Power Flow", IEEE Trans. on Power Systems, Vol.7, No.4, November HIROTAKA YOSHIDA receved M.S. degree n electrcal engneerng n 1976 from Doshsha Unversty, Kyoto, Japan. He has been workng at The Kansa Electrc Power Co. from Hs research nterests nclude analyss, plannng, and operaton of power systems. He s a member of IEE of Japan. KENICHI KAWATA receved M.S. degrees n electroncs engneerng n 1977 from Osaka Unversty, Osaka, Japan. He has been workng at The Kansa Electrc Power Co. from Hs research nterests nclude development of operaton and control method n power systems. YOSHIKAZU FUKUYAMA (M'90) receved the B.S., M.S., and Ph.D. degrees n electrcal engneerng n 1985, 1987, and 1997, respectvely, from Waseda Unversty, Tokyo, Japan. He has been workng at Fuj Electrc Co. R&D Japan from He was a vstng scentst at Cornell Unversty from 1993 to Hs research nterests nclude applcaton of ntellgent systems to power systems and power system analyss. He s a member of IEEE and IEE of Japan. SHINICHI TAKAYAMA receved the B.S. and M.S. degrees n electrcal engneerng n 1996 and 1998, respectvely, from Hose Unversty, Tokyo, Japan. He has been workng at Fuj 9

10 Electrc Co. R&D Japan from Hs research nterests nclude applcaton of modern heurstc technques to power systems. He s a member of IEE of Japan. YOSUKE NAKANISHI (M'88) was born n Hyogo, Japan on January 6, He receved B.S. and M.S. n Electrcal Engneerng from Waseda Unversty and Ph.D. from Tokyo Metropoltan Unversty n 1978, 1980, 1996, respectvely. He joned Fuj Electrc Co. n 1980 and s currently workng as a senor engneer at Fuj Electrc Co. R&D. Hs research nterests nclude smulaton and analyss of voltage problems of electrc power systems. He s a member of the IEE of Japan and IEEE. 10

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