USING MODIFIED FUZZY PARTICLE SWARM OPTIMIZATION ALGORITHM FOR PARAMETER ESTIMATION OF SURGE ARRESTERS MODELS

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1 Internatonal Journal of Innovatve Computng, Informaton and Control ICIC Internatonal c 2012 ISSN Volume 8, Number 1(B), January 2012 pp USING MODIFIED FUZZY PARTICLE SWARM OPTIMIZATION ALGORITHM FOR PARAMETER ESTIMATION OF SURGE ARRESTERS MODELS Mehd Nafar 1, Gevork B. Gharehpetan 2 and Taher Nknam 3 1 Department of Electrcal Engneerng Scence and Research Branch Islamc Azad Unversty Tehran, Iran m.nafar@srbau.ac.r 2 Electrcal Engneerng Department Amrkabr Unversty of Technology Tehran, Iran grptan@aut.ac.r 3 Department of Electrcal and Electronc Engneerng Shraz Unversty of Technology Shraz, Iran nknam@sutech.ac.r Receved September 2010; revsed January 2011 Abstract. Accurate modelng and parameters dentfcaton of Metal Oxde Surge Arrester (MOSA) are very mportant for arrester allocaton, systems relablty and nsulaton coordnaton studes. Several models wth acceptable accuracy have been proposed to descrbe ths behavor. It should be mentoned that the estmaton of nonlnear elements of MOSAs s very mportant for all models. In ths paper, a new method, whch s the combnaton of Fuzzy Partcle Swarm Optmzaton (FPSO) and Ant Colony Optmzaton (ACO) methods, s proposed to estmate the parameters of MOSA models. The proposed method s named Modfed Fuzzy Partcle Swarm Optmzaton (MFPSO). In the proposed algorthm, to overcome the drawback of the PSO algorthm (convergence to local optma), the nerta weght s tuned by usng fuzzy rules. Also, to mprove the global search capablty and prevent the convergence to local mnma, ACO algorthm s combned to proposed FPSO algorthm. The transent models of MOSA have been smulated by usng ATP-EMTP. The results of smulatons have been appled to the program, whch s based on MFPSO method and can determne the ftness and parameters of dfferent models. The valdty and the accuracy of the estmated parameters are assessed by comparng the predcted resdual voltage wth the expermental results. Also, Usng proposed algorthm, dfferent surge arrester models and V-I characterstcs determnaton methods have been compared. Keywords: Surge arrester models, PSO, ACO, Fuzzy rules, Parameter estmaton 1. Introducton. MOSAs are wdely used as protectve devces aganst lghtnng and swtchng over-voltages. Accurate modelng and smulaton of ther dynamc characterstcs s very mportant for arrester allocaton, systems relablty and nsulaton coordnaton studes [1-7]. For swtchng surge studes, MOSAs can be modeled by ther nonlnear V -I characterstcs [1,2]. However, such a presentaton would not be approprate for fast front transent and lghtnng surge studes. Because the MOSA shows dynamc characterstcs such that the voltage across the surge arrester ncreases as the tme-to-crest of the arrester current decreases and the voltage of arrester reaches a peak before the arrester 567

2 568 M. NAFAR, G. B. GHAREHPETIAN AND T. NIKNAM current peaks [6]. Typcally, the resdual voltage of an mpulse current havng a front tme equal to 1 µs s 8-12% hgher than that predcted for an mpulse current havng a front tme equal to 8 µs. The resdual voltage of a longer tme-to-crest between 45 and 60 µs, s 2-4% lower than that of a 8 µs current mpulse [6]. In order to reproduce the MOSA dynamc characterstcs, many studes have been focused on modelng and smulaton of MOSAs [1-6]. In [1], a dynamc model has been presented by IEEE, whch s based on database for fast mpulse currents (tme-to-crest of µs). The IEEE model has been smplfed and changed to other models by other researchers [2,3]. The man problem of these models s essentally ther parameters calculaton and estmaton [1-7]. It should be noted that the determnaton of nonlnear resstors of MOSA s very mportant for the proposed models. These resstors could be presented by voltage-current tables gven n [1]. Also, the voltage-current characterstc of a nonlnear resstor could be presented by an exponental equaton [6]. In ths paper, the combnaton of algorthms has been proposed to determne the best parameters for MOSAs models. One of the evolutonary algorthms that have shown great potental and good perspectve for the soluton of varous optmzaton problems s Partcle Swarm Optmzaton (PSO) [8]. The PSO algorthm was developed through smulaton of a smplfed socal system such as socal behavor of brds flockng or fsh schoolng [8]. PSO has been found to be robust n solvng contnuous nonlnear optmzaton problems. However, the performance of the standard PSO greatly depends on ts parameters, such as nerta weght, cogntve and the socal parameters, and t often suffers from the problem of beng trapped n the local optma. Eben et al. [11] descrbed two ways of defnng the parameter values: adaptve parameter control and self-adaptve parameter control. In the former, the parameter values change accordng to a heurstc rule that takes feedback from the current search state, whle n the latter, the parameters of the meta-heurstc are ncorporated nto the representaton of the soluton. Thus, the parameter values evolve together wth the solutons of the populaton. In ths paper, an adaptve parameter control s used for nerta weght usng a fuzzy logcal controller. Also, n order to avod trappng n local optma, Ant Colony Optmzaton (ACO) algorthm s combned to Fuzzy PSO (FPSO) to explore the search space much more effcently. Usng the proposed algorthm and lnkng the MATLAB and EMTP programs, parameters of MOSA models are estmated. Based on the estmated parameters, the models have been smulated and then the results of smulatons have been compared wth the expermental results. The results show the ablty of the proposed algorthm n determnng the surge arrester parameters. Also, usng proposed algorthm, dfferent surge arrester models and V -I characterstcs determnaton methods have been compared. The man contrbutons of ths paper are as follows: () Present a new method for parameters estmaton of all surge arrester models wthout the need for the formulaton, equaton and nformaton on the surge arrester dmensons. () Present a new modfed evolutonary optmzaton algorthm based on PSO and ACO algorthms and fuzzy rules. () Apply the proposed optmzaton algorthm on parameter estmaton of surge arrester problem by usng a new method for lnkng the MATLAB and EMTP programs. 2. Surge Arresters Modelng. The transent models of MOSAs are necessary for nsulaton coordnaton and relablty studes of power systems. Several surge arrester models have been proposed to descrbe the transent behavor of surge arresters [1-3]. In ths paper, transent models are nvestgated n the followng text. The model, shown n Fgure 1, has been suggested by IEEE WG group [1]. As t s shown n ths fgure, the nonlnear V -I characterstcs has been modeled by two

3 USING MODIFIED FPSO ALGORITHM FOR PARAMETER ESTIMATION 569 nonlnear resstors A 0 and A 1 whch are separated by a RL low pass flter. The calculaton of parameters of ths model has been presented n [4]. It s based on the estmated heght of the arrester column, the number of columns of MO dsks and Table 1. Table 1. V -I characterstcs for A 0 and A 1 (V 10 s the dscharge voltage (n kv) for a 10 ka, 8/20 µs current) Current Voltage (per unt of V 10 ) (ka) A 0 A Fgure 1. IEEE model The model, shown n Fgure 2, has been proposed by Pncet [2]. calculaton procedure for ths model has been presented n [2]. The parameters Fgure 2. Pncet model In [3], Fernandez et al. have presented another model whch s based on IEEE model too. Ths model s shown n Fgure 3. An teratve tral and error procedure has been proposed n [3], to determne the model parameters.

4 570 M. NAFAR, G. B. GHAREHPETIAN AND T. NIKNAM Fgure 3. Fernandez model The dentfcaton of nonlnear parts of MOSAs s mportant for the proposed models. The voltage-current characterstcs of a nonlnear resstor can be drectly expressed by Equaton (1) [6]. I = p (V/V ref) q (1) where p and q are constant values, V and I are voltage and current of surge arrester, respectvely, and V ref s an arbtrary reference voltage. For the models based on IEEE model, the ntal nonlnear V -I characterstcs values of A 0 and A 1 could be determned by Table 1 [1,4-6]. The procedures mentoned above, do not always result n the best parameters, but they can provde a good estmaton (a startng pont) [1-6]. It should be noted that these methods are lmted to mentoned models. In recent years, several researches have been presented for estmatng the parameters of all models [5,6]. A numercal method has been proposed for dentfyng the parameters of three suggested models n [5]. Ths method s based on comparson of the smulaton results of resdual voltages and the results derved from 8/20 µs expermental measurements [5]. In ths method, parameters of surge arrester models are estmated by mnmzng the followng objectve functon: F = T 0 W (t) [V (t, x) V m(t)] 2 dt (2) where F s sum of the quadratc error, T s duraton of appled mpulse current sgnal, V (t, x) s the estmated resdual voltage obtaned from smulaton results, V m(t) s the measured voltage, x s the state varable vector (surge arrester model parameters) and W (t) s the weghtng functon, derved from numercal expermentaton. In ths method, the non-lnear resstances have been presented by pecewse functons and consequently a lnearzaton has been adopted. The problem of optmzaton has been solved n two stages wth an am of avodng possble numercal oscllatons of the predcted voltage. In ths paper, a new method based on heurstc algorthms s suggested to estmate the best parameters of MOSAs models. Proposed method s general and can be appled to all surge arrester models. Unlke exstng procedures, equaton or formulaton and nformaton on the surge arrester dmensons are not necessary. Also, the applcaton of the weghtng functon s not necessary n suggested method and the non-lnear resstors can be represented based on Equaton (1) or based on Table 1. Also, usng proposed algorthm, nonlnear characterstcs of surge arrester are estmated va Equaton (1) and then they are compared wth the results of the IEEE method (usng Table 1). 3. Objectve Functon. The ATP-EMTP software has been used as the smulaton tool. The 8/20 µs mpulse current s appled to the smulated models of surge arresters. The smulated resdual voltage of each model s compared wth the expermental data obtaned

5 USING MODIFIED FPSO ALGORITHM FOR PARAMETER ESTIMATION 571 from [7]. The comparson method s based on Equaton (3), as follows: F = T 0 [V (t, x) V m(t)] 2 dt (3) Ths objectve functon can be rewrtten n the dscrete form, as follows: F = N [V (j t, x) V m (j t)] 2 t (4) j=1 where N s the number of dscrete ponts and the t = T/N s computaton tme step. The parameters of surge arrester Models ( x), determned by proposed algorthm n MATLAB, are mported to the EMTP. In ths paper, the smulaton s carred out by usng the 10 ka, 8/20 µs mpulse current. The chosen step tme n smulaton s 0.5 µs. So, the resdual voltage vector of each model (V (t, x)) s determned by EMTP and then s compared wth the measured voltage vector (V m(t)). The objectve functon s evaluated and mnmzed by usng the proposed algorthm and the best parameters of surge arrester models ( x) are estmated. 4. Algorthm of Optmzaton ACO algorthm. Snce ants are blnd nsects, whch lve together, they fnd the shortest path from the nest to the food wth the ad of pheromone. A chemcal materal deposted by the ants, pheromone serves as a crtcal communcaton faclty among ants whch help them n ther path recognton. Pheromone ntensty deposted by ants determnes the shortest path n ther way to food. Generally, the state transton probablty to select the next path can be expressed, as follows: (τ j ) γ 2 (1/L j ) γ 1 P j = (5) NA (τ j ) γ 2 (1/L j ) γ 1 j=1,j After choosng the next path, updatng the tral ntensty of pheromone s as: τ j (k + 1) = ρτ j (k) + τ j (6) where τ j s the ntensty of pheromone between the nodes j and, L j s the length of path between the nodes j and, γ 1 s the control parameter for determnng the weght of tral ntensty, γ 2 s the control parameter for determnng the weght of the length of path, NA s the number of ants, ρ s a coeffcent such that (1 ρ) represents evaporaton of tral between tme k and k + 1 and τ j s the amount of pheromone tral added to τ j by ants Standard PSO algorthm. PSO s a populaton based stochastc optmzaton algorthm, nspred by socal behavor of brd flockng or fsh schoolng, developed by Eberhart and Kennedy. It s a useful technque to solve many optmzaton problems [8-10]. PSO shares many smlartes wth evolutonary computaton technques such as Genetc Algorthms (GA). The system s ntalzed by a populaton of random solutons and searches for optma by updatng generatons. However, unlke GA, PSO has no evoluton operators such as crossover and mutaton. In PSO algorthm, the potental

6 572 M. NAFAR, G. B. GHAREHPETIAN AND T. NIKNAM solutons, called partcles, fly through the problem space by followng the current optmum partcles. Equaton (7) could descrbe the content of ths concept. ( ) ( ) V (t+1) = ω.v (t) + c 1.rand 1 (.). P best X (t) + c 2.rand 2 (.). Gbest X (t) (7) X (t+1) = X (t) + V (t+1) where rand 1 (.) and rand 2 (.) are random number between 0 and 1, Pbest s best prevously recorded experence of the th partcle, Gbest s best partcle among the entre populaton and the constants c 1 and c 2 are weghtng coeffcents of the stochastc acceleraton terms whch stmulate each partcle towards Pbest and Gbest postons. Low values allow partcles to go far from the target regon [13,14]. The coeffcents c 1 and c 2 are often set to 2.0 accordng to prevous experences [8-10]. The approprate selecton of nerta weght ω n Equaton (7) provdes a proper global and local search as t s essental to mnmze teraton average to acheve a suffcent optmal soluton. Approxmately the coeffcent ω often decreases lnearly from 0.9 to 0.4 durng a run. Generally, Equaton (8) could present the nerta weght ω as follows: ω (t+1) ωmax ωmn = ωmax t (8) t max where ω max and ω mn are maxmum and mnmum of the nerta weght, respectvely, and t max s maxmum number of teratons Fuzzy adaptve nerta weght factor. In PSO, the search process s a nonlnear and dynamc procedure. Therefore, when the envronment tself s dynamcally changed over the tme, the optmzaton algorthm should be able to adapt dynamcally to the changng envronment. The change of the partcle s stuaton s drectly correlated to the nerta weght. Proper choce of the nerta weght ω provdes a balance between global and local optmum ponts [10]. Several methods have been appled to handle the nerta weght durng the progresson of the optmzaton process. Constant nerta weght, lnearly decreasng nerta weght and random nerta weght are some examples [12,13]. In ths paper, a fuzzy IF/THEN rules s used to adaptvely control the nerta weght of PSO. Four steps are taken to create the fuzzy system: fuzzfcaton, fuzzy rules, fuzzy reasonng and defuzzfcaton. These steps are descrbed n the followng subsectons. (1) Fuzzfcaton. The fuzzfcaton comprses the process of transformng crsp values nto grades of membershp for lngustc terms of fuzzy sets [14]. For each nput and output selected varable, two or more membershp functons are descrbed. Normally, they are three but can be more. In ths paper, among a set of membershp functons, left-trangle, trangle and rght trangle membershp functons are used for every nput and output as shown n Fgure 4. All the membershps of nput are presented n three lngustc levels; S, M and L for small, medum and large, respectvely n Table 2. The output varable has been presented n three fuzzy sets of lngustc values; NE (negatve), ZE (zero) and PE (postve) wth assocated membershp functons, as shown n Fgure 4 [12]. (2) Fuzzy rules. The fuzzy rules are a seres of IF-THEN statements. These statements are usually derved by an expert to acheve optmum results. In ths paper, the Mamdan-type fuzzy rules have been used to evaluate the condtonal statements that comprse fuzzy logc. For example: f (NFV s L) and (ω s M) THEN ( ω s ZE), where NFV s normalzed ftness value and NFV s an nput varable between 0 and 1. The fuzzy rules of Table 2 are used to select the nerta weght correcton ( ω). Each rule represents a mappng from the nput space to the output space. (3) Fuzzy reasonng. In ths paper, Mamdan s fuzzy nference method s used to map the nputs to the outputs. The AND operator s used for the combnaton of membershp

7 USING MODIFIED FPSO ALGORITHM FOR PARAMETER ESTIMATION 573 (a) (b) (c) Fgure 4. Membershp functons of nputs and outputs: (a) NFV, (b) ω and (c) ω Table 2. Fuzzy rules for varatons of nerta weght ω NFV ω S M L S ZE NE NE M PE ZE NE L PE ZE NE values for each fred rule to generate the membershp values for the fuzzy sets of output varables n the consequent part of the rule. Snce there may be several rules fred n the rule sets for some fuzzy sets of the output varables there may be dfferent membershp values obtaned from dfferent fred rules. To obtan a better nerta weght under the fuzzy system, the current best performance evaluaton and current nerta weght are selected as nputs varables; where as the output varable s the change n the nerta weght. The NFV s used as an nput varable between 0 and 1, and s defned as: NF V = F V F V mn (9) F V max F V mn In the frst teraton, the calculated value of F V may be selected as F V mn for the next teratons. In Equaton (9), F V max s the worst soluton for the mnmzaton process. Typcal nerta weght value s n range of Both postve and negatve correctons lmts are requred for the nerta weght. Therefore, a range of [ ] has been chosen for the nerta weght correcton. ω t+1 = ω t + ω (10) In order to choose an approprate representatve value as the fnal output (crsp values), defuzzfcaton must be done. It wll be llustrated at a later pont. (4) Defuzzfcaton. In order to obtan a crsp value, the output must be defuzzyfed. For defuzzfcaton of every nput and output, the method of centrod (center-of-sums) has been used for the membershp functons as shown n Fgure Proposed MFPSO algorthm. The PSO method should be consdered as a useful method, whch s powerful enough to handle varous knds of nonlnear optmzaton problems. Nevertheless, t may be trapped nto local optma, f over a number of teratons, global best and local best postons are equal to the poston of the partcle. Recently, numerous deas have been used to overcome ths drawback usng other global optmzaton algorthms such as Evolutonary Programmng (EP), Genetc Algorthm (GA) or

8 574 M. NAFAR, G. B. GHAREHPETIAN AND T. NIKNAM Smulated Annealng (SA) along wth the PSO [9]. The performance of the standard PSO greatly depends on ts parameters, such as nerta weght, cogntve and the socal parameters, and t often suffers from the problem of beng trapped n the local optma. In ths paper, an adaptve parameter control s used for nerta weght by usng a fuzzy logcal controller. Also, n order to avod trappng n local optma, ACO algorthm s combned to FPSO to explore the search space much more effcently. Ths new algorthm proposes the applcaton of the ntellgent decson-makng structure of ACO algorthm to the APSO algorthm such that a unque global best poston s obtaned for each partcle. However, t uses random selecton procedure of ACO algorthm to determne dfferent global best postons of each dstnct agent. Ths algorthm, called Modfed Fuzzy Partcle Swarm Optmzaton (MFPSO) s used to mnmze the cost functon of the surge arrester parameters estmaton problem. The proposed MFPSO algorthm has the followng steps: Step 1: Generate the ntal populaton and ntal velocty. The ntal populaton and ntal velocty of each partcle are randomly generated, as follows: x 1 P opulaton = x 2..., x = [x ] 1 n (11) x NSwarm x = rand(.) (x max x mn V 1 V elocty = V 2... V NSwarm ) + x mn, V = [v ] 1 n (12) v = rand(.) (v max v mn ) + v mn where N Swarm s the number of the swarms, n s the number of the state varable, x max and x mn are the maxmum and mnmum of th state varable, respectvely and v max and v mn are the maxmum and mnmum velocty of th state varable. Step 2: Generate the ntal tral ntensty. In ths ntalzaton phase, t s assumed that the tral ntensty between each par of swarms s the same and s generated, as follows: T ral Intensty = [τ j ] NSwarm N Swarm, τ j = τ 0 (13) where τ 0 s the ntal tral ntensty. Step 3: Couplng to EMTP. The surge arrester model s smulated by EMTP usng the gven data (parameters). Then, the smulaton results are transferred to the MFPSO-based developed program to calculate the objectve functon. Step 4: Calculate the objectve functon. The objectve functon (.e., Equaton (4)) s calculated for each ndvdual by usng the smulaton results obtaned n Step 3. Step 5: Sort the ntal populaton. In ths step, the ntal populaton s sorted n ascendng order consderng the value of the objectve functon of each ndvdual. Step 6: Select the best global poston. The ndvdual that has the mnmum value of the objectve functon s selected as the best global poston (.e., Gbest). Step 7: Select the best local poston. The best local poston (Pbest) s selected for each ndvdual.

9 USING MODIFIED FPSO ALGORITHM FOR PARAMETER ESTIMATION 575 Step 8: Update the parameters. In ths algorthm, the proper choce of nerta weght, ω, s updated by the fuzzy rules. Step 9: Select the th ndvdual. The th ndvdual s selected and neghbors of ths partcle should be dynamcally defned as follows: S = x j x x j 2D 0 1 ( ) at, j (14) 1 exp where D 0 s the ntal neghborhood radus and a s the parameter used to tune the neghborhood radus. Step 10: Calculate the next poston for the th ndvdual. There are two approaches to calculate the next poston, as follows: Approach A) f S {}, where {} stands for the null set In ths case, the transton probabltes between x and each ndvdual n S are calculated by the followng equaton: t max [P robablty] = [P 1, P 2,..., P,M ] 1 M, P j = (τ j) γ 2 (1/L j ) γ 1, L M j = (τ j ) γ 2 (1/L j ) γ 1 j=1 1 F (x ) F (x j ) (15) Then, the cumulatve probabltes are calculated as follows: [Cumulatve probablty] = [C 1, C 2,..., C M ] 1 M C 1 = P 1, C 2 = C 1 + P 2,..., C j = C j 1 + P j,..., C M = C M 1 + P M (16) where M s the number of members n S and C j s the cumulatve probablty for the j th ndvdual n S. The roulette wheel s used for the stochastc selecton of the best global poston, as follows: A number between 0 and 1 s randomly generated and s compared wth the calculated cumulatve probabltes. The frst term of the cumulatve probabltes (C j ), whch s greater than the generated number, s selected and the assocated poston s consdered as the best global poston. Then, the th partcle s moved accordng to followng rules, f x j s selected as the best: V (t+1) x (t+1) ( ) = ω.v (t) + c 1.rand 1 ( ). P best x (t) ( ) + c 2.rand 2 ( ). x j x (t) = x (t) + V (t+1) (17) The presumed pheromone level between X and X j s updated n the next stage: τ j (t + 1) = ρ.τ j (t) + P j (18) Approach B) f S = {}, whch means there s not any ndvdual n partcle s neghborhood.

10 576 M. NAFAR, G. B. GHAREHPETIAN AND T. NIKNAM In ths case, the th partcle s moved accordng to the followng rules: ( ) V (t+1) = ω.v (t) + c 1.rand 1 ( ). P best x (t) ( ) + c 2.rand 2 ( ). Gbest x (t) x (t+1) = x (t) + V (t+1) Then, the tral ntensty s updated as follows: (19) τ j (t + 1) = ρ.τ j (t) + r; 0.1 r 0.5 (20) where ndex j represents the best partcle ndex n the group. The modfed poston for the th ndvdual s checked wth ts lmt. Step 11: If all ndvduals have been selected, go to the next step, otherwse, = + 1 and go back to Step 5. Step 12: Check the termnaton crtera. If the current teraton number reaches the predetermned maxmum teraton number, the search procedures should be stopped; otherwse the ntal populaton s replaced by the new populaton of swarms and then the algorthm goes back to Step 3. The last Gbest s the soluton of the problem. 5. Lnk between EMTP and MATLAB. Both ATP-EMTP and MATLAB are currently avalable on popular computer for engneerng applcatons. It could be sad that the best optmzaton algorthms can be easly developed n MATLAB and transent models of power system elements can be smulated by ATP-EMTP. To use the ablty of both soft wares, a lnk between these programs s necessary. In [16], several technques for lnk between EMTP and MATLAB have been presented, where MATLAB functons can be called n EMTP. However, n ths paper, ATP fles have been called as an nput fle of MATLAB. Ths approach s much easer than the other one. The surge arrester parameters have been estmated by usng MFPSO algorthm developed n MATLAB and the surge arrester models have been smulated by EMTP [15]. A FORTRAN code fle (ATP fle) has been developed for each EMTP Smulaton fle. By usng nput/output functons of MATLAB, ATP fle can be called n MATLAB and can be modfed. So, the surge arrester parameters can be modfed accordng to MFPSO outputs. Usng SYSTEM command, the modfed ATP fle can be run n MATLAB. After runnng the ATP fle, a LIS fle s generated whch contans the smulaton outputs of surge arrester models are n ths fle. Then, usng nput/output functon, LIS fle could be opened n MATLAB and the resdual voltage of smulaton could be returned to MFPSO algorthm n MATLAB. Ths procedure can be repeated. 6. Parameter Estmaton of Surge Arrester Models. The surge arrester models have been smulated by ATP-EMTP. Equaton (1) can be used to determne V -I characterstc of A 0 and A 1 n MOSA models. In ths equaton, three parameters (p, q and V reff ) must be dentfed for each nonlnear resstor. Accordng to data gven n Table 1, V -I characterstcs of A 0 and A 1 can also be determned. In ths case, the frst step of the smulaton s multplyng the per unt values of voltages by V 10 and then the coeffcents (V reff ) of A 0 and A 1 are selected such that the smulated voltage and the expermental results are approached. So, n ths case, a V reff must be determned for each nonlnear element. In ths secton, MOSAs parameters models (lnear and nonlnear parameters) have been estmated by the suggested algorthm for models of [1-3]. The surge arrester parameters, estmated by MFPSO algorthm n MATLAB, are mported to the EMTP.

11 USING MODIFIED FPSO ALGORITHM FOR PARAMETER ESTIMATION 577 The smulaton s carred out usng the 10 ka, 8/20 µs mpulse current. Durng optmzaton, the resdual voltage of each model s determned by EMTP and then t s transferred to MFPSO algorthm n MATLAB to evaluate the ftness functon. Ths procedure contnues untl the optmal soluton s determned for parameters of that model. The resdual voltage of smulatons s compared to the expermental data gven on [7]. The estmated parameters of all models, determned usng Equaton (1) and the expermental data of [7], are lsted n Table 3. A comparson among expermental and the smulated resdual voltage obtaned by estmated parameters of the models of [1-3] based on Equaton (1) s shown n Fgure 5. Fgure 5. Comparson between measured and smulated results based on Equaton (1) Table 3. Estmated parameters (usng Equaton (1)) parameter Model of [1] Model of [2] Model of [3] R 0 (Ω) R 1 (Ω) L 0 (µh) L 1 (µh) C (nf ) p q p q V reff 0 [V ] V reff 1 [V ] Accordng to the results of [7], the nonlnear V -I characterstcs of A 0 and A 1 for the models of [1-3] have been estmated by usng the data of Table 1. The results have been lsted n Table 4. The resdual voltages determned by estmated surge arrester models and measured by [7] have been shown n Fgure 6.

12 578 M. NAFAR, G. B. GHAREHPETIAN AND T. NIKNAM Table 4. Estmated parameters (usng data of Table 1) parameter Model of [1] Model of [2] Model of [3] R 0 (Ω) R 1 (Ω) L 0 (µh) L 1 (µh) C (nf ) V reff 0 [V ] V reff 1 [V ] Fgure 6. Comparson between measured and smulated results based on Table 1 Comparng Fgures 5 and 6, t can be seen that V -I characterstcs of nonlnear parts of all surge arrester models can be determned by both methods. As t can be seen n ths fgure, the smulaton results have a good agreement wth the expermental data. As t could be seen n these fgures, for IEEE model, the result obtaned by Equaton (1) s more accurate than the IEEE method, especally for the end part of the curve. It should be sad that both methods are accurate enough for nsulaton coordnaton studes. However, the model accordng to Equaton (1) can determne the energy absorpton of surge arrester better than the IEEE method. For the Pncet model, both methods are accurate enough but for the Fernandez model, the model based on Equaton (1) has a better agreement wth expermental data. It should be noted that, usng proposed method, parameters of all surge arrester models could be properly estmated. 7. Error Analyss. In [7], measurements were performed to get the response of surge arrester block for two types of mpulse currents. These currents are steep front wave mpulse (1/2 µs) and standard mpulse (8/20 µs) mpulse currents. The peak values of mpulse currents were changed n each mpulse test. The peak values of measured resdual voltages of arrester block for these mpulses are presented n Tables 5 and 6. In ths secton, usng these expermental data, the ablty of the proposed method to estmate the parameters of surge arrester models and the ablty of models to smulate

13 USING MODIFIED FPSO ALGORITHM FOR PARAMETER ESTIMATION 579 the arrester dynamc behavor are presented. The models of [1-3], have been smulated n EMTP based on the estmated parameters of Tables 3 and 4. The current peak values n smulaton are 2.5 ka, 5 ka and 10 ka and the selected rse and fall tmes are 1/2 µs and 8/20 µs. The 1/2 µs mpulse current has been appled to the models and the smulaton results have been used to determne the error by the followng equaton: Error% = V sm V meas V meas 100 (21) where V sm and V meas are the peak values of smulated and measured resdual voltage, respectvely. The results of ths calculaton have been presented n Table 5. The same smulatons and calculatons have been repeated for 8/20 µs mpulses. The results are presented n Table 6. In these tables, P.C. and P.V. stand for peak of mpulse current and peak of measured resdual voltage, respectvely. Accordng to the results of these tables, the followng ponts could be drawn: The surge arrester models based on the data of table1 are more accurate n comparson wth the models based on Equaton (1); All surge arrester models smulate the dynamc behavor of MOSA properly; The suggested procedure can be appled to all surge arrester models and; The proposed algorthm (MFPSO) s a powerful tool for dentfyng parameters of all surge arrester models. Table 5. Comparson between measured and smulated results P.C. = 2.58 ka P.V. = 7.46 kv P.C. = 5.04 ka P.V. = 7.97 kv P.C. = ka P.V. = 8.62 kv 1/2 µs mpulse current Models Based on Equaton (1) Based on data of Table 1 Peak of Resdual Error % Peak of Resdual Error % IEEE Fernandeze Pncet IEEE Fernandeze Pncet IEEE Fernandeze Pncet Conclusons. In ths paper, a new algorthm based on the combnaton of Fuzzy partcle swarm optmzaton (FPSO) and ant colony optmzaton (ACO) has been proposed to mprove the performance of PSO algorthm. In ths proposed algorthm, known as MFPSO, to overcome the problem of the premature convergence observed n many applcatons of PSO, the nerta weght has been tuned by usng fuzzy rules. Also, to mprove the global search capablty and prevent the convergence to local mnma, ACO algorthm has been combned to proposed FPSO algorthm. A new method based on the MFPSO algorthm, and lnkng the MATLAB and EMTP programs has been proposed to estmate the parameters of MOSA models. Usng the proposed algorthm, the parameters are estmated based on the MOSA resdual voltage measurements. Also, usng MFPSO algorthm, a comparatve study among dfferent methods of the surge arrester nonlnear V -I characterstcs modelng has been conducted n ths paper. It s show that the result obtaned by usng Equaton (1) s more accurate for energy absorpton studes of surge

14 580 M. NAFAR, G. B. GHAREHPETIAN AND T. NIKNAM Table 6. Comparson between measured and smulated results P.C. = 2.50 ka P.V. = 7.01 kv P.C. = 5.01 ka P.V. = 7.49 kv P.C. = ka P.V. = 8.08 kv 8/20 µs mpulse current Models Based on Equaton (1) Based on data of Table 1 Peak of Resdual Error % Peak of Resdual Error % IEEE Fernandeze Pncet IEEE Fernandeze Pncet IEEE Fernandeze Pncet arrester. However, the IEEE method (for V -I characterstcs determnaton) s more accurate for nsulaton coordnaton studes. Also, t s shown that the estmated parameters of all models n the smulaton results are n a good agreement wth the resdual voltage measurements. It should be noted that the prevous studes were lmted to specal models but the proposed algorthm s general and comparng wth other algorthms, t can be easly mplemented and ts convergence speed s consderable. Acknowledgment. Ths work s partally supported by Islamc Azad Unversty, Scence and Research Branch, Tehran, Iran. The authors also gratefully acknowledge the helpful comments and suggestons of the revewers, whch have mproved the presentaton. REFERENCES [1] IEEE WG , Modelng of metal oxde surge arrester, IEEE Trans. on Power Delvery, vol.7, pp , [2] P. Pncet and M. Gannetton, A smplfed model for znc oxde surge arresters, IEEE Trans. on Power Delvery, vol.14, pp , [3] F. Fernandez and R. Daz, Metal oxde surge arrester model for fast transent smulaton, Proc. of the Internatonal Conference on Power System Transents, pp , [4] J. A. Martnez and D. W. Durbak, Parameter determnaton for modelng systems transents Part V: Surge arrester, IEEE Trans. on Power Delvery, vol.20, no.3, pp , [5] H. J. L, S. Brlasekaran and S. S. Cho, A parameter dentfcaton technque for metal-oxde surge arrester models, IEEE Trans. on Power Delvery, vol.17, no.3, pp , [6] M. Nafar, G. B. Gharehpetan and T. Nknam, A new parameter estmaton algorthm for metal oxde surge arrester, Journal of Electrc Power Components and Systems, vol.39, no.7, pp , [7] I. Km, T. Funabash, H. Sasak and T. Hagwara, Study of ZnO arrester model for steep front wave, IEEE Trans. on Power Delvery, vol.11, pp , [8] J. Kennedy and R. Eberhart, Partcle swarm optmzaton, IEEE Internatonal Conf. on Neural Networks, pp , [9] Z.-L. Gang, Partcle swarm optmzaton to solvng the economc dspatch consderng the generator constrants, IEEE Trans. on Power System, vol.18, pp , [10] Y. Sh and R. Eberhart, A modfed partcle swarm optmzer, Proc. of the IEEE World Congress on Computatonal Intellgence, pp.69-73, [11] A. E. Eben, R. Hnterdng and Z. Mchalewcz, Parameter control n evolutonary algorthms, IEEE Transactons on Evolutonary Computaton, vol.3, pp , [12] P. Bajpa and S. N. Sngh, Fuzzy adaptve partcle swarm optmzaton for bddng strategy n unform prce spot market, IEEE Trans. on Power System, vol.22, pp , 2007.

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