A novel parameter estimation method for metal oxide surge arrester models

Transcription

1 Sādhanā Vol. 36, Part 6, December 2011, pp c Indan Academy of Scences A novel parameter estmaton method for metal oxde surge arrester models MEHDI NAFAR 1,, GEVORK B GHAREHPETIAN 2 and TAHER NIKNAM 1 1 Department of Electrcal Engneerng, Marvdasht Branch, Islamc Azad Unversty, Marvdasht, Iran 2 Electrcal Engneerng Department, Amrkabr Unversty of Technology, Tehran, Iran e-mal: mnafar@mau.ac.r MS receved 9 September 2010; revsed 12 January 2011; accepted 12 May 2011 Abstract. Accurate modellng and exact determnaton of Metal Oxde (MO) surge arrester parameters are very mportant for arrester allocaton, nsulaton coordnaton studes and systems relablty calculatons. In ths paper, a new technque, whch s the combnaton of Adaptve Partcle Swarm Optmzaton (APSO) and Ant Colony Optmzaton (ACO) algorthms and lnkng the MATLAB and EMTP, s proposed to estmate the parameters of MO surge arrester models. The proposed algorthm s named Modfed Adaptve Partcle Swarm Optmzaton (MAPSO). 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 and the cogntve and the socal parameters are self-adaptvely adjusted. Also, to mprove the global search capablty and prevent the convergence to local mnma, ACO algorthm s combned to the proposed APSO algorthm. The transent models of MO surge arrester have been smulated by usng ATP-EMTP. The results of smulatons have been appled to the program, whch s based on MAPSO algorthm and can determne the ftness and parameters of dfferent models. The valdty and the accuracy of estmated parameters of surge arrester models are assessed by comparng the predcted resdual voltage wth expermental results. Keywords. EMTP. Metal oxde surge arrester models; PSO; ACO; parameter estmaton; 1. Introducton Metal oxde (MO) surge arresters are wdely used as protectve devces aganst swtchng and lghtnng over-voltages n power systems. The proper nonlnear voltage-current characterstcs, For correspondence 941

2 942 Mehd Nafar et al gnorable power losses, hgh level relablty n the operaton tme, hgh speed response to the over-voltages and long lfe tme are some advantages of MO surge arresters. Accurate modellng and smulaton of ther dynamc characterstcs are very mportant for arrester allocaton, systems relablty and nsulaton coordnaton studes (IEEE WG 1992; Pncet & Gannetton 1999; Martnez & Durbak 2005). For swtchng over voltages studes, the surge arresters can be represented by ther nonlnear V-I characterstcs. However, such a presentaton would not be sutable for fast front transent and lghtnng surge studes. Because the MO surge arrester exhbts 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 current peaks (IEEE WG 1992). Typcally, the resdual voltage for an mpulse current havng a front tme equal to 1 μs s 8 12% hgher than that of predcted for an mpulse current havng a front tme equal to 8 μs. The resdual voltage for longer tme-to-crests between 45 and 60 μs, s 2 4% lower than that of a 8 μs current mpulse (Martnez & Durbak 2005). In order to reproduce the MO surge arrester dynamc characterstcs mentoned prevously, a lot of researches have been done on modellng and smulaton of MO surge arresters (Martnez & Durbak 2005). A dynamc model has been presented based on the data base of (IEEE WG 1992) for fast mpulse currents (tme-to-crest of μs). To estmate the model parameters, an teratve tral and error procedure has been proposed, whch matches the peak of dscharge voltage obtaned wth 8/20 μs mpulse current. The startng values for the parameters determnaton process, has been determned by consderng the heght and the number of column of the arrester, for fve lnear elements, and two V -I curves for the nonlnear elements. Ths method s usually tme consumng and only applcable to the IEEE model (Martnez & Durbak 2005). The IEEE model was changed and smplfed to other models by researchers (Pncet & Gannetton 1999; Fernandez & Daz 2001; Popov et al 2002). The man problem of proposed models s essentally ther parameters calculaton and estmaton (L et al 2002; Znk et al 2005). Numercal method has been proposed for estmatng the parameters of the surge arrester models n (L et al 2002). Ths method s based on comparng resdual voltages of smulaton and expermental results. The measurement of the resdual voltage when a 8/20 μs mpulse current s appled to the arrester s the start pont of ths method (L et al 2002). In ths paper, an adaptve parameter control s used for nerta weght by usng a fuzzy logcal controller and the cogntve and the socal parameters are self-adaptvely evaluated. Also, n order to avod trappng n local optma, Ant Colony Optmzaton (ACO) algorthm s combned to Adaptve PSO (APSO) to explore the search space much more effcently. Usng the proposed algorthm and lnkng the MATLAB and EMTP programs, parameters of MO surge arrester models are dentfed. The estmated parameters of models are verfed by comparng the results of smulatons by EMTP (EMTP Role Book 1997) wth the expermental results. The results show the ablty of the proposed algorthm n estmatng the surge arrester parameters. 2. Surge arrester models In ths paper, dynamc models of surge arresters are nvestgated n the followng paragraphs. The IEEE WG group proposed the model of fgure 1, ncludng the nonlnear resstances A 0 and A 1, whch are separated by a RL low pass flter (IEEE WG 1992). The parameters calculaton procedure of ths model has been presented n (Martnez & Durbak 2005). It s based on the estmated heght of the arrester, the number of columns of MO dsks and the curves shown n fgure 2.

3 A novel parameter estmaton method for metal oxde surge arrester models 943 Fgure 1. IEEE model. The model, shown n fgure 3, has been proposed by Pncet Ganetton (Pncet & Gannetton 1999). Ths model s based on IEEE model wth some dfferences. In ths model the resstance R 0 stablzes the numercal oscllatons. The nonlnear resstors A 0 and A 1 can be estmated by usng curves shown n fgure 2. The calculaton procedure of nductances for ths model has been presented n (Pncet & Gannetton 1999). Fernandez & Daz (2001) have presented other model whch s based on IEEE model too. Ths model s shown n fgure 4. In Fernandez Daz model, the rato I 0 to I 1 s assumed to be remaned constant all over the voltage range of ther protecton characterstcs where I 0 and I 1 are the currents followng A 0 and A 1 respectvely and the voltage percentage ncreasng of the nput termnal depends only on the nductance L 1. The detals of the calculaton procedure of ths model have been presented n (Fernandez & Daz 2001). The model, shown n fgure 5, has been proposed by Popov for swtchng studes (Popov et al 2002). To estmate the parameters of ths model, an teratve tral and error procedure has been proposed n (Popov et al 2002). Above mentoned procedures do not always result n the best parameters, but these procedures can provde a good estmaton (a startng pont) (L et al 2002). It should be mentoned that these procedures and ther applcatons are lmted to mentoned models. Fgure 2. Nonlnear characterstcs of A 0 and A 1.

4 944 Mehd Nafar et al Fgure 3. Pncet Ganetton model. In recent years, dfferent researches have been presented for determnng the parameters of all arrester models (L et al 2002; Znk et al 2005). A numercal method was proposed for estmatng the parameters of the three suggested models n (L et al 2002). Ths technque s based on comparson of the smulaton results of resdual voltages and the results derved from 8/20 μs expermental measurements (L et al 2002). In ths method, surge arrester parameters are estmated by mnmzng the followng objectve functon: E = T 0 W (t)[v (t, x) Vm(t)] 2 dt, (1) where E s the sum of the quadratc error, T s the duraton of njected mpulse current sgnal, V (t, x) s the predcted resdual voltage obtaned from smulaton results, V m (t) s the measured resdual voltage, x s the state varable vector (parameters of surge arrester model) and W (t) s the weghtng functon, derved from numercal expermentaton. It can take the followng form for dfferent models: ( πt W (t) = cos 3T + π ) ( ) 6 πt W (t) = cos 2T W (t) = 1.0. (2) In ths method, the non-lnear resstances have presented by pece-wse 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 smulated voltage. In ths paper, a new technque based on heurstc algorthms s proposed to estmate the best parameters of surge arresters models. Proposed method s general and can be appled to all surge arrester models. Unlke exstng methods, formulaton or equaton and nformaton on the MO surge arrester dmensons are not necessary. Also, the applcaton of the weghtng functon s not necessary n the proposed method and the non-lnear resstances can be presented by an Fgure 4. Fernandez Daz model.

5 A novel parameter estmaton method for metal oxde surge arrester models 945 Fgure 5. Popov model. exponental voltage current characterstc, as expressed by the equaton (3) (Znk et al 2005) ( ) V q I = p, (3) V ref 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. 3. Objectve functon In ths paper, the ATP-EMTP software s used as a smulaton tool. The 10 ka, 8/20 μs current s appled to the smulated models of surge arresters. The resdual voltage of each model s compared to the expermental results obtaned from (Schmdt et al 1989;Km et al 1996; Hnrchsen 2001) and the parameters of surge arrester models can be estmated by mnmzng the followng equaton: E = T 0 [V (t, x) Vm(t)] 2 dt. (4) Ths objectve functon s smlar to the objectve functon proposed n (L et al 2002). Only n (L et al 2002) an addtonal term (weghtng functon) has been consdered to ncrease the convergence speed. In proposed MAPSO method, the applcaton of the weghtng functon s not necessary. Usually, the measured resdual voltage s a dscrete functon. Accordngly, the objectve functon (4) can be rewrtten as follows: E = N [V ( j t, x) V m ( j t)] 2 t, (5) j=1 where N s the number of dscrete ponts and the t = T / N s the tme nterval.

6 946 Mehd Nafar et al 4. Optmzaton procedure 4.1 ACO algorthm Ants are nsects whch lve together. Beng blnd, they fnd the shortest path from nest to food usng the pheromone. Pheromone, a chemcal materal deposted by the ants, serves as a crtcal communcaton faclty among ants whch help them n ther path recognton. Densty of pheromone deposted by ants, determnes the shortest path of ther ways to food (Nknam et al 2005). Generally, the state transton probablty to select the next path could be expressed, as follows: P j = NA j=1, j = (τ j ) γ 2(1/L j ) γ 1 (τ j ) γ 2(1/L j ) γ 1. (6) After choosng the next path, updatng the tral densty of pheromone s by the followng equaton: τ j (k + 1) = ρτ j (k) + τ j, (7) 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 + 1and τ j s the amount of pheromone tral added to τ j by ants. 4.2 PSO algorthm PSO s a populaton based stochastc optmzaton algorthm developed by Eberhart and Kennedy, nspred by socal behavour of brd flockng or fsh schoolng. It s a useful technque to solve many optmzaton problems (Kennedy & Eberhart 1995; Eberhart & Sh 2001; Gang 2003; Park 2005). PSO shares many smlartes wth evolutonary computaton technques such as Genetc Algorthms (GA). The system s ntalzed wth 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 solutons, called partcles, fly through the problem space by followng the current optmum partcles. Equaton (8) could descrbe the content of ths concept. Vel (t+1) = ω.vel (t) + c 1.rand 1 (.).(Pbest X (t) + c 2.rand 2 (.).(Gbest X (t) ) X (t+1) = X (t) + Vel (t+1), (8) where Vel t s velocty of the th partcle, rand 1 (.) and rand 2 (.) are random numbers between 0 and 1, Pbest s best prevous experence of the th partcle that recorded and Gbest s best partcle among the entre populaton. The constants c 1 and c 2 are postve weghtng coeffcents of the stochastc acceleraton terms whch stmulate each partcle towards Pbest and Gbest postons. Low values allow partcles to

7 A novel parameter estmaton method for metal oxde surge arrester models 947 go far from the target regon and hgh values result n abrupt movements toward, or backward the target regon. The nerta weght ω presents the degree of the partcles momentum. The approprate selecton of nerta weght ω n (8) 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. 4.3 Adaptve PSO As gven n equaton (8), three parameters ω, c 1 and c 2 have great nfluence on the PSO algorthm performance and control the behavour and effcacy of the PSO algorthm. The nerta weght ω s used to control the mpact of the prevous hstory of veloctes on the current velocty. Proper choce of the ω provdes a balance between global and local optmum ponts (Nknam et al 2010). The factors c 1 and c 2 determne the effect of the personal best Pbest, j and global best Gbest. Snce c 1 represents how much the partcle trusts ts own hstorcal experence, t s called cogntve parameter. On the other hand, c 2 represents the socal nfluence that pushes the swarm to converge to the current globally best regon, and s called socal parameter. Also, on each dmenson, partcle veloctes are lmted to mnmum and maxmum veloctes, whch are userdefned parameters as follows: Vel j,mn Vel t+1 j Vel j,max. (9) To control excessve roamng of partcles outsde the search space, usually, Vel j,mn s assumed as Vel j,max.ifvel j,max s too hgh, partcles may fly past good solutons. If Vel j,max s too small, partcles may not explore suffcently beyond local solutons. In many experences wth PSO, Vel j,max was often set at 10 20% of the dynamc range on each dmenson. The approprate choce of control parameters s very mportant for the success n ths type of evolutonary algorthms. In Arumugam & Rao (2008) have descrbed two ways of modfyng the parameter control; adaptve parameter control and self-adaptve parameter control. Adaptve parameter control, takes place when there s some form of feedback from the search that s used to determne the drecton and/or magntude of the change to the strategy parameter. In ths method, the parameter change (accordng to a heurstc rule) takes feedback from the current search state. The nformaton of current state s usually the current teraton of the search, the operator s performance, and/or the dversty of the populaton. For example, n (Eberhart & Kennedy 1995; Arumugam & Rao 2008), lnearly decreasng nerta over the generatons s used as adaptve nerta weght control and n (Nknam et al 2010) a fuzzy logcal controller has been used. Whle n self-adaptve parameter control, the parameters of the meta-heurstc are ncorporated nto the representaton of the soluton. Thus, the values of the parameters evolve together wth the solutons of the populaton. In ths paper, a fuzzy-adaptve parameter control for the nerta weght s used. Also, the other parameters of the evoluton varables, are nvestgated, n order to self adaptvely control them. 4.3a 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.

8 948 Mehd Nafar et al Fgure 6. Membershp functons of nputs and outputs; (a)nfv,(b) ω and (c) ω. 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 (Nknam et al 2010). In ths paper, a fuzzy IF/THEN rules are 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. 4.3b Fuzzfcaton: The fuzzfcaton comprses the process of transformng crsp values nto grades of membershp for lngustc terms of fuzzy sets. For each nput and output varable selected, 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 6. All the membershps of nput are presented n three lngustc levels; S, M, and L for small, medum, Table 1. Fuzzy rules for varatons of nerta weght. ω ω S M L NFV S ZE NE NE M PE ZE NE L PE ZE NE

9 A novel parameter estmaton method for metal oxde surge arrester models 949 and large, respectvely n table 1. 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 6 (Nknam et al 2010). 4.3c 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 1 are used to select the nerta weght correcton ( ω). Each rule represents a mappng from the nput space to the output space. 4.3d 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 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 varable, 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: NFV = FV FV mn. (10) FV max FV mn In the frst teraton, the calculated value of FV may be as FV mn for the next teratons. In equaton (10), FV max s the worst soluton to the mnmzaton process. Typcal nerta weght value s 0.4 ω 0.9. 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. (11) 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. 4.3e 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 shown n fgure Self-adaptve parameter control In order to obtan a self-adaptve parameter control, the parameters must be encoded wthn the soluton of the problem. A self-adaptve control of c 1, c 2 and V max s consdered to avod the cumbersome task of frst localzng and then fne-tunng these three parameters. Approprate tunng of c 1 and c 2 n equaton (8) may mprove effcency, accelerate the search process and reduce the rsk of settlng n one of the local mnma. A study of these acceleraton parameters s gven for PSO n (Kennedy 1999). As default values, c 1 = c 2 = 2 were proposed, but next researches ndcated that alternatve confguratons, dependng on the applcaton, may produce superor performance. Recent work has been shown that t mght be even better to select a larger

10 950 Mehd Nafar et al cogntve parameter, c 1, than a socal parameter, c 2, wth constrant c 1 + c 2 4. In (Arumugam & Rao 2008), t s suggested that the acceleraton coeffcents should nether set to a constant value nor set as a lnearly decreasng tme varyng functon. Instead, these parameters are defned as a functon of local best and global best values of the ftness functon of a mnmzaton problem. In ths paper, the acceleraton coeffcents and the clampng velocty are nether set to a constant value (lke n standard PSO) nor set as a tme varyng functon (lke n adaptve PSO varants). Instead they are ncorporated nto the optmzaton problem, as explaned below. The parameters of partcle wll be allowed to self-adapt by usng the same process used by PSO gven by equatons (8). To ths end, these three parameters are consdered as three new varables that are added wth poston vectors Xj. In general, f N g s the dmenson of the problem and p s the number of self-adaptng parameters, the new poston vector for partcle j wll be, as fallows: X new j =[x j,1, x j,2,..., x j,ng, x j,ng+1,..., x j,ng+p ]. (12) It s obvous that the frst N g varables correspond to the real poston vector of the partcle n the search space, whle the last p varables for ts personal acceleraton constants and velocty lmt. Obvously, these self-adaptng parameters do not enter the ftness functon but are manpulated usng the same mxed ndvdual socal learnng paradgm as the one used n PSO. Also, dmenson of Vel j and Pbest, j, whch represent the velocty and best poston so far for partcle j, respectvely, ncrease as follows: V new j = [v j,1,v j,2,..., v j,ng,v j,ng+1,..., x j,ng+p ], (13) Pbest, new j = [P best,1, P best,2,..., P best,ng, P best,ng+1,..., P best,ng+p ]. (14) Usng equaton (8), each partcle would be addtonally endowed wth the ablty of adaptng ts parameters by amng at both the parameters t had when t got ts best poston n the past and the parameters of the leader, whch managed to brng ths best partcle to ts advantaged poston. 5. Proposed MAPSO 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 Smulated Annealng (SA) along wth the PSO (Gang 2003; Park 2005). 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 and the cogntve and the socal parameters are self-adaptvely evaluated. Also, n order to avod trappng n local optma, ACO algorthm s combned to APSO 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 Adaptve Partcle Swarm Optmzaton (MAPSO) s used to mnmze

11 A novel parameter estmaton method for metal oxde surge arrester models 951 the cost functon of the surge arrester parameters estmaton problem. The proposed MAPSO 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 Populaton = X 2... X NSwarm X = [x,1, x,2,..., x,ng, x,ng+1,..., x,ng+p ] x, j = rand(.) (x max j x mn j ) + x mn j j = 1, 2,..., (Ng + p); = 1, 2,..., N swarm ; p = 3, (15) Velocty = Vel 1 Vel 2... Vel NSwarm Vel = [vel,1,vel,2,..., vel,ng,vel,ng+1,..., vel,ng+p] = rand(.) (vel max j vel mn j ) + vel mn j j = 1, 2,..., (Ng + p); = 1, 2,..., N swarm ; p = 3, (16) vel, j where N swarm s the number of the swarms, Ng s the number of the state varable, x max s the maxmum of th state varable, x mn s the mnmum of th state varable, v max s the maxmum velocty of th state varable and v mn s the 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: Tral_Intensty =[τ j ] NSwarm N Swarm τ j = τ 0, (17) 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 MAPSO-based developed program to calculate the objectve functon. Step 4: Calculate the objectve functon The objectve functon (.e., equaton (5)) s calculated for each ndvdual by usng the smulaton results obtaned n the step 3. (Only the frst Ng varables enter the ftness functon.) 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.

12 952 Mehd Nafar et al Step 6: Select the best global poston The surge arrester parameters n addtonal self-adaptve parameters are represented the poston of partcle n the swarm. 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. Step 8: Update the parameters In ths algorthm, the proper choce of nerta weght, ω, s updated by the fuzzy rules and the other parameters are tunng by self-adaptve parameters. Step 9: Select the th ndvdual The th ndvdual s selected and neghbours of ths partcle should be dynamcally defned as follows: S = x j x x j 2D0 1 1 exp ( ) at t max, = j, (18) where, D 0 s the ntal neghbourhood radus and a s the parameter used to tune the neghbourhood 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: [ Probablty ] = [P 1, P 2,..., P,M ] 1 M P j = (τ j) γ 2(1/L j ) γ 1 M (τ j ) γ 2(1/L j ) γ 1 L j = j=1 1 F(x ) F(x j ). (19) Then the cumulatve probabltes are calculated as follows: where C 1 C 2 [Cumulatve probablty] =[C 1, C 2,..., C M ] 1 M, = P 1 = C 1 + P 2... C j = C j 1 + P j... C M = C M 1 + P M, (20)

13 A novel parameter estmaton method for metal oxde surge arrester models 953 where, M s the number of members n S and Cj 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 compared wth the calculated cumulatve probabltes. The frst term of the cumulatve probabltes (Cj), 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: Vel (t+1) x (t+1) = ω.vel (t) + c 1.rand 1 ( ).(Pbest x (t) + c 2.rand 2 ( ).(x j x (t) = x (t) + Vel (t+1). The presumed pheromone level between X and Xj s updated n the next stage: ) ) (21) τ j (t + 1) = ρ.τ j (t) + P j. (22) Approach B) f S = {}, whch means there s not any ndvdual n partcle s neghbourhood. In ths case, the th partcle s moved accordng to the followng rules: Vel (t+1) = ω.vel (t) + c 1.rand 1 ( ).(Pbest x (t) ) + c 2.rand 2 ( ).(Gbest x (t) x (t+1) = x (t) + Vel (t+1). Then, the tral ntensty s updated, as follows: ) (23) τ j (t + 1) = ρ.τ j (t) + r; 0.1 r 0.5, (24) 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 wth the new populaton of swarms and then the algorthm goes back to step 3. Step 13: ThelastGbest s the soluton of the problem. 6. Lnkng EMTP wth MAPSO algorthm n MATLAB Both EMTP and MATLAB are currently avalable on popular computer for electrcal engneerng applcatons. It can be sad that the best optmzaton methods can be easly developed n

14 954 Mehd Nafar et al MATLAB and transent models of power system equpments can be smulated by EMTP. To use the ablty of both software, a lnk between these programs s necessary. In Mahseredjan et al (1998), several technques for lnkng EMTP wth MATLAB are presented, where MATLAB functons can be called as EMTP. But, n ths paper, ATP fle s called as an nput fle of MAT- LAB. Ths approach s much easer than the other one. The parameters of surge arrester models have been determned by usng MAPSO algorthm developed n MATLAB and the surge arrester models have been smulated by EMTP. A FORTRAN code fle (ATP fle) s developed for each EMTP Smulaton fle. By usng nput/output functons of MATLAB, ATP fle can be called n Fgure 7. Lnk between MATLAB and EMTP n the proposed method.

15 A novel parameter estmaton method for metal oxde surge arrester models 955 Table 2. Estmated parameters based on expermental results of (Schmdt et al 1989). Parameter IEEE Model Pncet Model Fernandez Model Popov Model R 0 ( ) R 1 ( ) L 0 (μh) L 1 (μh) C(nF) p q p q Vreff 0 [V ] Vreff 1 [V ] MATLAB and can be modfed. So, the surge arrester parameters can be modfed accordng to MAPSO outputs. Usng SYSTEM command, the modfed ATP fle can be run n MATLAB. After runnng the ATP fle, a LIS fle s generated. The smulaton outputs of surge arrester models (for example, resdual voltage) are n ths fle. Then, usng nput/output functon, LIS fle can be opened n MATLAB and the resdual voltage of smulaton can be returned to MAPSO algorthm n MATLAB. Ths procedure has been shown n the fgure Parameter determnaton of surge arrester models In ths secton, the proposed method s used to estmate parameters of the transent models of MO surge arresters. The surge arrester models have been smulated by EMTP. The surge arrester parameters, determned by MAPSO algorthm n MATLAB, are mported to the EMTP. The smulaton s performed by usng the (10 ka, 8/20 μs) mpulse current. Durng optmzaton, the resdual voltage of the model s determned by EMTP and then t s transferred to MAPSO algorthm n MATLAB to evaluate the ftness functon. Ths procedure contnues untl the optmal soluton has been determned for parameters. The resdual voltage of smulatons has been compared wth the expermental data of from references (Schmdt et al 1989; Km et al 1996; Table 3. Estmated parameters based on expermental results of Km et al (1996). Parameter IEEE Model Pncet Model Fernandez Model Popov Model R 0 ( ) R 1 ( ) L 0 (μh) L 1 (μh) C(nF) p q p q Vreff 0 [V ] Vreff 1 [V ]

16 956 Mehd Nafar et al Table 4. Estmated parameters based on expermental results of Hnrchsen (2001). Parameter IEEE Model Pncet Model Fernandez Model Popov Model R 0 ( ) R 1 ( ) L 0 (μh) L 1 (μh) C(nF) p q p q Vreff 0 [V ] Vreff 1 [V ] Hnrchsen 2001). The expermental data of the arresters used n ths paper have been lsted n table 8. The estmated parameters of dfferent surge arrester models, whch have been determned by usng the expermental data of (Schmdt et al 1989; Km et al 1996; Hnrchsen 2001), are lsted n tables 2 4. A comparson among expermental and the smulated resdual voltage obtaned by estmated parameters of the models of (IEEE WG 1992; Pncet & Gannetton 1999; Fernandez & Daz 2001; Popov et al 2002) s presented n fgures Fgure 8. Comparson of resdual voltage determned by estmated models and measured by Schmdt et al (1989).

17 A novel parameter estmaton method for metal oxde surge arrester models 957 Fgure 9. Comparson of resdual voltage determned by estmated models and measured by Km et al (1996). It s obvous from these fgures that the smulaton of models usng the estmated parameters results n resdual voltages whch have a good agreement wth the expermental data. It should be noted that, usng proposed algorthm, parameters of all models can be properly estmated. 8. Error analyss In ths secton, by usng the expermental data obtaned from (Km et al 1996), the ablty of the proposed method to dentfy the parameters of surge arrester models and the ablty of models to smulate the arrester dynamc behavour are presented. Surge arresters have dynamc characterstcs n whch rsng rate of resdual voltage depend on the tme to crest and peak value of current. These characterstcs become mportant n consderng the nsulaton coordnaton studes. In ths secton, the models of (IEEE WG 1992; Pncet & Gannetton 1999; Fernandez & Daz 2001; Popov et al 2002), have been compared based on the estmated parameters of table 3. The mpulse current peak values are 2.5 ka, 5 ka and 10 ka and the selected rse and fall tmes are 1/2 μs, 4/10 μs and 8/20 μs. The 1/2 μs mpulse current has been appled to the surge arrester models and the smulaton results have been used to determne the error by the followng equaton: Error% = VR sm VR meas VR meas 100, (25)

18 958 Mehd Nafar et al Fgure 10. Comparson of resdual voltage determned by estmated models and measured by Hnrchsen (2001). Table 5. Comparson between smulated results and expermental results of Km et al (1996). 1/2 μs mpulse current Models Peak of resdual Error% voltage (kv) P.C. = 2.58 ka IEEE P.V. = 7.46 kv Fernandez Pncet Popov P.C. = 5.04 ka IEEE P.V. = 7.97 kv Fernandez Pncet Popov P.C. = ka IEEE P.V. = 8.62 kv Fernandez Pncet Popov

19 A novel parameter estmaton method for metal oxde surge arrester models 959 Table 6. Comparson between smulated results and expermental results of Km et al (1996). 1/2 μs mpulse current Models Peak of resdual Error% voltage (kv) P.C. = 2.95 ka IEEE P.V. = 7.26 kv Fernandez Pncet Popov P.C. = 4.98 ka IEEE P.V. = 7.62 kv Fernandez Pncet Popov P.C. = ka IEEE P.V. = 8.22 kv Fernandez Pncet Popov where VR sm and VR meas are the smulated and measured values, respectvely. The result of ths calculaton has been presented n table 5. The same smulatons and calculatons have been repeated for 4/10 μs and 8/20 μs currents. The results are presented n tables 6 and 7, respectvely. 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 can be drawn: The Popov model can not smulate dynamcs behavour of MO surge arresters properly. Because ths model s a very smplfed verson of the IEEE model, and also, ths model has been proposed for swtchng studes (Popov et al 2002). Table 7. Comparson between smulated results and expermental results of Km et al (1996). 1/2 μs mpulse current Models Peak of resdual Error% voltage (kv) P.C. = 2.50 ka IEEE P.V. = 7.01 kv Fernandez Pncet Popov P.C. = 5.01 ka IEEE P.V. = 7.49 kv Fernandez Pncet Popov P.C. = ka IEEE P.V. = 8.08 kv Fernandez Pncet Popov

20 960 Mehd Nafar et al Table 8. Expermental data of (Schmdt et al 1989; Km et al 1996; Hnrchsen 2001). Tme (μs) Expermental data of Expermental data of Expermental data of (Schmdt et al 1989) (kv) (Km et al 1996) (kv) (Hnrchsen 2001) (kv) The Error n IEEE model and Pncet model ncreases when the peak of the mpulse current decreases. Models of (IEEE WG 1992; Pncet & Gannetton 1999; Fernandez & Daz 2001) smulate the dynamc behavour of surge arresters properly. The proposed algorthm (MAPSO) can be appled to all models. The proposed algorthm s a powerful tool to estmate parameters of MO surge arrester models. 9. Concluson In ths paper a new method, based on APSO and ACO algorthms has been proposed by lnkng the MATLAB and EMTP. Usng ths method t s possble to determne the parameters of dfferent surge arrester models. In ths method, the proposed optmzaton algorthm known as MAPSO can be mplemented easly and the parameters of surge arrester models are estmated based on the MO surge arrester resdual voltage measurements. The proposed method has been appled to dfferent models of surge arresters. It s shown that the estmated parameters of all surge arrester models lead to smulaton results whch are n agreement wth the resdual voltage measurements. It should be mentoned that the prevous studes were lmted to specal models but the proposed method s general and can be appled to all exstng models. References Arumugam M S, Rao M V C 2008 On the mproved performances of the partcle swarm optmzaton algorthms wth adaptve parameters, cross-over operators and root mean square (RMS) varants for computng optmal control of a class of hybrd systems. Appled Soft Comp. 8(1):

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