Optimal Phase Arrangement of Distribution Feeders Using Immune Algorithm

Transcription

1 The 4th Internatonal Conference on Intellgent System Applcatons to Power Systems, ISAP 2007 Optmal Phase Arrangement of Dstrbuton Feeders Usng Immune Algorthm C.H. Ln, C.S. Chen, M.Y. Huang, H.J. Chuang, M.S. Kang, C.Y. Ho and C.W. Huang Abstract-- In ths paper, the mmune algorthm (IA) s proposed to derve the rephasng strategy arrangement of laterals and dstrbuton transformers to enhance three phase balancng of dstrbuton systems. The mult-objectve functon s formulated by consderng the unbalance of phasng currents, the customer servce nterrupton cost and labor cost to perform the optmal rephasng strategy. To demonstrate the effectveness of the proposed methodology to enhance three-phase balancng of dstrbuton systems, a practcal dstrbuton feeder n Tapower wth 523 customers s selected for computer smulaton. By mnmzng the objectve functon subjected to the operaton constrants, the rephasng strategy has been derved by selectng the laterals and dstrbuton transformers for phasng adjustment. The phase currents and neutral currents of test feeder before and after the executon of proposed rephasng strategy have been measured and collected by the SCADA system n Tapower. It s found that the neutral current of test feeder has been reduced to be less than the over neutral current lmt by executng the rephasng of laterals and dstrbuton transformers. Index Terms Immune algorthm, Outage management system, Customer nformaton system. W I. INTRODUCTION th the dramatcally load growth of resdental and commercal customers for the past decade n Tapower dstrbuton system, the unbalance of three phase currents of dstrbuton feeders has become an crtcal ssue and often causes feeder servce trppng due to over neutral current. Besdes, the executon of non-nterruptble load transfer between feeders for scheduled outage and servce restoraton after fault contngency has even caused further feeder trppng because the resultant neutral current of supportng feeder after load transfer s larger than the LCO relay settng. Furthermore, the voltage rse on the system neutral lne due to over neutral current may ntroduce personnel hazard problem. It s the conventonal practce for dstrbuton engneers to perform phase swappng of dstrbuton laterals and transformers to mprove phase loadng balance based on system operaton experence wth try and error methods, whch s very labor ntensve and tme-consumng. Wth the stochastc varaton of power consumpton by customers, the phase balancng of C.H. Ln s wth the Department of Electrcal Engneerng, Natonal Kaohsung Unversty of Appled Scences, Kaohsung 807, Tawan (e-mal: chln@mal.ee.kuas.edu.tw). C.S. Chen and M.Y. Huang are wth the Department of Electrcal Engneerng, Natonal Sun Yat-Sen Unversty, Kaohsung, Tawan. M.S. Kang, H.J. Chuang, and C.Y. Ho are wth the Department of Electrcal Engneerng, Kao Yuan Unversty, Lu Chu, Tawan. C.W. Huang s wth the Power Research Insttute, Tawan Power Company. dstrbuton systems has to be evaluated for all tme perods to avod the feeder trppng unexpectedly due to over neutral current. To enhance the three phase balance of dstrbuton systems, the rephasng strategy of dstrbuton feeders should be derved by consderng the study case wth the worst unbalance scenaros. To mprove the three-phase balance of dstrbuton systems, two approaches have been presented n the prevous research works [], [2]. In [3], Chen et al. presented a genetc algorthm to optmze the phase arrangement of dstrbuton transformers connected to the prmary feeder. The rephasng of dstrbuton transformers and laterals s a drect and effectve way to acheve three phase balance for dstrbuton feeders by consderng phase loadng of dstrbuton transformers. However, the labor cost and cost of scheduled power outages related to the customer servce nterrupton have to be ncluded n the dervaton of rephasng strategy by consderng the number of customers affected, the amount of loadng dsconnected and the outage duraton tme. By consderng the customer servce nterrupton cost and the labor cost nvolved as well as the enhancement of three phase balancng n the objectve functon for phase re-arrangement, the proper cost effectveness of the rephasng problem can be obtaned. Because of the stochastc load characterstcs of customers over study tme perod, the phase current loadngs of dstrbuton transformers, laterals, and whole feeder wll be tme varant. It s the conventonal practce to solve the optmzaton of phase arrangement by consderng the study hour wth the worst scenaros of 3-φ unbalance. The effectveness of mmune algorthm (IA) to solve the complcated optmzaton problems has been llustrated n the prevous study [4]. In ths paper, a relablty based objectve functon has been formulated by ncludng the labor cost, the customer servce nterrupton cost and the equvalent cost of neutral current reducton for each feasble scenaro of phasng adjustment. The IA s then used to determne the rephasng strategy of dstrbuton transformers and laterals to reduce three phase unbalance of dstrbuton feeders wth best cost effectveness. In ths paper, the objectve functon wth subjected constrants for the optmal phase arrangement of dstrbuton feeders s expressed as the antgen nputs and the feasble rephasng strateges are represented as the antbodes for the IA. An nteger codng system s developed to accelerate the speed to acheve hgh-qualty soluton wthout usng long bnary strng. The genetc operators ncludng crossover and mutaton are then processed for the producton of antbodes n 7

2 The 4th Internatonal Conference on Intellgent System Applcatons to Power Systems, ISAP 2007 a feasble space. Wth the operaton of IA algorthm on the Table I memory cell, the fast convergence of optmzaton problem Vald rephasng schemes for varous types of laterals wll be obtaned durng the searchng process by applyng the nformaton entropy as a measure of dversty for the populaton to avod fallng nto a local suboptmal soluton. The effectveness of the proposed IA to solve the phase balancng problem s then verfed by comparng to the classcal genetc algorthm (GA). (2) II. PROCESS OF OPTIMAL REPHASING FOR DISTRIBUTION FEEDERS To derve the rephasng strategy for dstrbuton transformers and laterals to mprove three phase balance of dstrbuton feeders, the phase currents and neutral current of all prmary trunk lne sectons, laterals and transformers have been smulated n ths paper. The attrbutes of dstrbuton components such as lne segments, dstrbuton transformers, etc., have been retreved from the faclty database of outage management system (OMS) n Tapower. The network confguraton of dstrbuton feeder s then dentfed by performng the topology process accordng to the connectvty attrbutes of dstrbuton components. The daly load patterns of customer classes, whch have been derved by load survey study, and the monthly energy consumpton of customers n the database of customer nformaton system (CIS) are used to solve the hourly power demand of each customer. Wth the customer-to-transformer mappng, the hourly loadng of each dstrbuton transformer s solved by ntegratng the power profles of all customers served. By executng the three phase load flow analyss, the three phase currents and neutral current of each prmary trunk lne secton and each lateral can be calculated. The objectve functon for rephasng of dstrbuton transformers and laterals s then formulated by ncludng the number of customers affected, the total load demand nterrupton and the tme duraton to complete the rephasng works. III. THE PROPOSED IMMUNE ALGORITHM TO DERIVE THE REPHASING STRATEGY OF DISTRIBUTION FEEDERS A. Phasng arrangement In ths paper, the notaton (X, Y, Z) s used to represent the phasng arrangement of each lateral. The possble connecton schemes for varous types of phasng arrangement are lsted n Table I for the sngle-phase, two-phase, and three-phase laterals. To prevent damage of three phase motor loads due to reverse operaton after rephasng, same phase sequence (postve or negatve) has to be consdered n the dervaton of rephasng strategy. For nstance, an open-wye, open-delta (OYD) transformer wth the prmary sde connected to A and B phases (A,B,*) can be rephased as B and C phases (*,A,B) or C and A phases (B,*,A) to mantan the same phase sequence for the motor loads served by the OYD transformer at the secondary sde. By the same way, a 3-φ lateral wth orgnal phasng (A,B,C) can be rephasng ether as (B,C,A) or (C,A,B) only. B. Objectve functon The objectve functon of the proposed IA methodology for rephrasng of dstrbuton feeders s formulated by consderng the followng costs. ) Penalty cost functon of neutral current The neutral current of a dstrbuton feeder s the summaton of three phase currents. I n = I a + Ib + Ic () To prevent the neutral current from exceedng the LCO relay settng, whch s 70 A n ths study, the penalty cost functon of neutral current s expressed as a cubc equaton n (2). A penalty cost wll be ntroduced f the neutral current I n, s larger than 40 A at rephasng node. An nfnte penalty value s appled when I n, s larger than 70A, whch mples that all possble rephasng of laterals and dstrbuton transformers wll be consdered for the reducton of neutral current at node. 0 In, 40A 3 Cub, = w( In, 40) 40A < In, < 70A (2) 70A I n, where w represents the equvalent cost of neutral current, whch can be adjusted by dstrbuton engneers. 2) Customer servce nterrupton cost The customer servce nterrupton cost (CIC) for the outage due to rephasng engneerng works of laterals or dstrbuton transformers s expressed as (3). n CIC = IC j j= n = C j ( t ) L j j= where n: total number of affected nodes for rephasng work at node, IC j : the customer nterrupton cost of node j due to rephasng outage at node, C j : per unt nterrupton cost of node j, t : the duraton tme to complete the rephasng work at node, L j : the total load demand at of node j. The C j (t ) n (3) represents the ntegrated per unt nterrupton costs of dfferent types of customers at node, whch have been derved n [5] for the resdental, commercal, and ndustral customers respectvely. Besdes, three dfferent categores of key customers wth hgh servce prorty levels (3) 72

3 The 4th Internatonal Conference on Intellgent System Applcatons to Power Systems, ISAP 2007 are consdered n ths paper. The rephasng scheme whch nvolves key customers wth hgher servce prorty wll be ssued a very hgh nterrupton cost n the objectve functon. Level : the customers wth power outage could be affected by nconvenence or publc concern (schools, supermarkets, sport and entertanment facltes, etc.) Level 2: the customers wth power outage could result n serous fnancal damage (banks, ol refnery plants, hgh technology plants, etc.) Level 3: the customers wth power outage could jeopardze the publc securty (hosptals, polce statons, fre statons, mportant telecommuncatons, etc.) The customer nterrupton cost at node j by ncludng the key customers s represented n (4). C j ( t ) = ( Res j f R ( t ) + Com j fc ( t ) 3 (4) l + Ind f ( t ) + Pr f ( t )) j I l= where Res, Com, Ind, Pr: the load percentage of resdental, commercal, ndustral, and key customers at node j, f R, f C, f I, f P : the nterrupton cost functon of resdental, commercal, ndustral, and key customers, l: the prorty level of key customers. To solve the load percentages of Res, Com, Ind, Pr customers wthn each servce zone, the customer-totransformer mappng s retreved from the faclty database of OMS system. The daly load patterns of dfferent customer classes and the energy consumpton of each customer retreved from the CIS database are used to solve the hourly loadng of each servce zone by ntegratng the power profles of all customers served. 3) Labor cost The labor cost CL to execute the rephasng at node s estmated based on the per unt crew payment, total crew members requred and the tme duraton to complete the rephasng work. C. Mult-Objectve Functon To derve the rephasng strategy for dstrbuton feeders to enhance the 3-φ balance, the objectve functon of optmal phase balancng problem s formulated as (5) by consderng the feeder neutral current, the customer servce nterrupton cost and labor cost to perform the rephasng for laterals and dstrbuton transformers. Mn OPT = n n Cub + = = n = l j, CIC + CL (5) In ths paper, the followng constrants are also taken nto consderaton for rephasng.. No man transformers, feeders and lne swtches become overloaded after rephasng. 2. Radal network confguraton must be mantaned for dstrbuton feeders. 3. All servce zones are connected and served by the feeder. P IV. IMMUNE ALGORITHM The mmune algorthm (IA) has been wdely used to solve the optmzaton problems by applyng the same operaton prncple of human mmune system. The capablty of IA method for pattern recognton and memorzaton does provde a more effcent way to solve the dscrete optmzaton problem as compared to the genetc algorthm. The objectve functon and lmt constrants are represented as antgen nputs, whle the soluton process s smulated by antbody producton n the feasble space through the genetc operaton mechansm. The calculaton of affnty between antbodes s embedded wthn the algorthm to determne the promoton/suppresson of antbody producton. Through the IA computaton, the antbody whch most fts the antgen s consdered as the soluton for the optmzaton problem. A. The structures of genes and chromosomes An mmune algorthm based decson makng [6] s proposed n ths study to fnd the optmal rephasng strategy of laterals and dstrbuton transformers. The populaton of memory cells s a collecton of the antbodes (feasble solutons) accessble toward the optmalty, whch s the key factor to acheve fast convergence for global optmzaton. In ths paper, the genetc codng structure of the mmune algorthm s adopted and the dversty and affnty of the antbodes are calculated durng the decson makng process to fnd the optmal rephasng strategy. The data structure of genes can be depcted as shown n Fg.. For a feeder wth N possble strateges of phase arrangement nvolvng M object nodes, t wll generate N antbodes havng M genes n the antbody pool. The gene node() conssts of a sequence of alternatng unsgn nteger numbers representng the canddate connecton schemes of n branches connectng node. Fg.. Data structure of genes wth correspondng nformaton entropy for IA based rephasng strategy. B. Dversty The dversty of feasble strateges n the populaton s measured between the antbodes and t wll be ncreased to prevent local optmzaton durng the searchng process of optmal rephasng strategy. For each evolvng generaton, the new antbodes are generated to strengthen the dversty of antbody populaton n the memory cell. Wth the data structure of genes n Fg., the entropy E j of the jth gene (j=, 2,, M) s defned as (6) E j = N Pj = log P (6) where N s the quantty of antbodes and P j s the probablty j 73

4 The 4th Internatonal Conference on Intellgent System Applcatons to Power Systems, ISAP 2007 that the jth allele comes out at the jth gene. If all alleles at the jth gene are the same, the entropy of the jth becomes zero. From (6), the dversty of all genes s calculated as the mean value of nformatve entropy. M E = E j (7) M j= C. Affnty The affnty of antbodes s an mportant ndex for the mmune algorthm durng the optmzaton process. If the affnty of some antbodes s the same durng mmune process, t wll nfluence the searchng effcency of optmzaton for the plannng of phase arrangement. Two types of affnty are calculated for the proposed IA n ths paper. One s the affnty between antbodes: ( Ab) j = (8) + E(2) where E(2) s the nformaton entropy of these two antbodes. The genes of the th antbody and the jth antbody wll be the same when E(2) s equal to zero. The affnty between the th antbody and the jth antbody, (AB) j, wll be wthn the range [0, ]. The other one s the affnty between antbody (canddate of phase arrangement of objectve nodes) and antgen (the objectve functons). ( Ag) = (9) + OPT where OPT s the total cost evaluated by (5) to represent the connecton between the antgen and antbody. The antgen wth the maxmum affnty (Ag) wll be the optmal phase arrangement wthn the feasble space. D. Computaton procedures The process to solve the objectve functon for optmal rephasng strategy of laterals and dstrbuton transformers s smulated by the nteracton of antbody and antgen n the mmune algorthm. Durng evoluton of genes, the canddates of rephasng strategy wth hgh affnty are selected and ncluded n the memory cells, whch wll be used to generate new canddate rephasng strategy. The computaton procedure of IA method s executed as follows: Step Recognton of antgens To solve the optmal rephasng strategy of dstrbuton feeders, the total cost of objectve functon for each possble soluton subject to operaton constrants s calculated n ths step. The nteger codng s adopted for the antgen pattern to represent the relatonshp of genes and physcal rephasng of laterals and transformers n the objectve functon for the computaton process. Step 2 Producton of ntal antbody populaton A random number generator s appled to generate the antbodes n the feasble space. All of antbodes and a group of genes are consdered to form the antbody pool. Some of the antbodes wth hgher affnty wll be selected from the memory cells durng the searchng process to generate a new set of antbodes. Each par of gene and antbody represents a possble soluton for the optmal rephasng problem n an objectve node. Step 3 Calculaton of Affnty In ths step, the affnty between antbodes (Ab) j and the affnty between antbodes and antgens (Ag) are calculated by (7) and (8) respectvely as the references n the followng evaluaton process. Step 4 Evaluaton and selecton The antbody havng hgh affnty wth the antgen s added to the new memory cells. To mantan the sze of memory cells and ensure the speed of convergence, the dversty of memory cells s calculated and the antbody wth hgh affnty (namely, (Ab) j close ) s removed so that the volaton of sze constrant of memory cells can be prevented. A roulette selecton algorthm s mplemented by consderng the affnty of antbodes to form a new antbody pool by spnnng the desred roulette. Snce most of the selected antbodes have hgher affntes wth the antgen, the average affnty of the new populaton pool wll be hgher than that of the orgnal pool to obtan better evoluton durng IA optmzaton process. Step 5 Crossover and mutaton After the selecton of antbody generaton, the operatons of crossover and mutaton for the new generated antbodes are performed. The crossover operaton s performed by applyng the one-cut-pont method, whch randomly selects the matng pont and exchanges the gene arrays of the rght-hand porton of the matng ponts between two antbodes. The matng operaton wll prevent the search process from local optmzaton by ncreasng the dversty of antbody populaton. Accordng to the predefned mutaton rate, mutaton s executed to perform the occasonal random alteraton of the value for an antbody poston. Step 6 Decson of optmal rephasng strategy Durng the mmune process, the antbody havng hgh affntes wth the antgen wll be added to the new memory cell, whch wll be mantaned after applyng the operaton of crossover, mutaton and selecton for the populaton. The search process of optmzaton contnues untl no further mprovement n relatve affnty can be obtaned and the antbody wth the hghest affnty n the memory cell wll be the optmal strategy for the rephasng of laterals and dstrbuton transformers. V. NUMERICAL RESULTS To demonstrate the effectveness of the proposed IA methodology to derve the optmal rephasng strategy to enhance the three phase balance of servce zones, laterals and dstrbuton feeders, a practcal dstrbuton feeder n Fengshan Dstrct of Tapower n Fg. 2 has been selected for computer smulaton. Feeder BC34 s a kv overhead feeder wth total length of 0.5 km. There are three prmary trunk sectons (T,T2,T3), two laterals (L,L2) wth 46 OYD transformers and 73 -φ transformers to provde the servce to the low voltage customers. In addton, fve hgh voltage customers are served by ths feeder too. By usng so many OYD transformers to serve both -φ and 3-φ customers wth stochastc load behavor, serous three phase unbalance has been ntroduced as descrbed n Fg. 3. The phasng 74

5 The 4th Internatonal Conference on Intellgent System Applcatons to Power Systems, ISAP 2007 rearrangement of laterals and dstrbuton transformers has to be performed so that the neutral current can be reduced to be less than the lmt of 70 A. To perform the search of optmal rephasng strategy, the parameters of antbody pool sze, the crossover rate and the mutaton rate have been determned as 00, 0.8, and 0. respectvely based on the smulaton of varous case studes n ths paper. After executng the search of optmal rephasng strategy for Feeder BC34 by the proposed IA methodology, Table II shows the proposed rephasng of laterals and dstrbuton transformers. It s found that the phase of lateral L2 should be changed from (A,B,C) to (C,A,B) and the phases of two OYD transformers at nodes N86 and N90 are changed from (A,*,C) and (*,B,C) to (*,C,A) and (C,*,B) respectvely. TABLE II THE PROPOSED REPHASING SCHEME FOR FEEDER BC34 : dstrbuton transformers Table III shows the change of neutral currents, the customer servce nterrupton cost and the labor cost to perform the rephasng work for the test feeder. The maxmum neutral current has been reduced from 84A to 47A, whch s less than the over neutral current lmt of 70A and the customer servce nterrupton cost and ntroduced labor cost are $7,82 and $462 respectvely. TABLE III THE CHANGE OF NEUTRAL CURRENTS (8 PM), THE CUSTOMER SERVICE INTERRUPTION COST AND LABOR COST BY EXECUTING THE PROPOSED REPHASING SCHEME Fg. 2. The one-lne dagram of Feeder BC34. Fg. 3. Three-phase currents and neutral current of Feeder BC34 before rephasng. Besdes the phase currents and neutral current of test feeder, n Fg. 3, whch have been collected by DDCC system n Tapower, the phase currents of prmary trunk sectons and laterals have also been calculated by executng three phase load flow analyss. After applyng the proposed rephasng strategy, Fg. 4 llustrates the actual hourly neutral currents of Feeder BC34, whch have been collected by DDCC system n Tapower. By comparng the hourly neutral currents of the test feeder before the proposed rephasng scheme, the three phase balance has been mproved sgnfcantly for each study hour. The average neutral current of the test feeder has been reduced from 67 A to 37 A. To llustrate the convergence of search process for optmal rephasng strategy, Fg. 5 shows the reducton of total cost of objectve functon (OPT) wth evoluton generatons solved by the proposed IA methodology and the genetc algorthm (GA) [3]. More sgnfcant mprovement of OPT has been obtaned by the IA methodology, and the mnmum value of has been resulted n ths study. Although same optmal rephasng strategy has been derved by both methodologes, the proposed IA method converges at the 2th generaton whle 45 generatons s requred for the GA method. 75

6 The 4th Internatonal Conference on Intellgent System Applcatons to Power Systems, ISAP 2007 Fg. 4 Three-phase currents and neutral current of Feeder BC34 after rephasng. currents of servce zones, laterals and prmary trunk sectons have been derved. To solve the optmal rephasng strategy for dstrbuton feeders to enhance the three phase balance, the objectve functon has been developed by ncludng the equvalent cost of neutral current, the labor cost and the customer servce nterrupton cost to perform the rephasng of laterals and dstrbuton transformers. By executng the optmal rephasng strategy wth the proposed IA methodology for an actual feeder n Tapower, one of the laterals and two dstrbuton transformers have been dentfed for phasng adjustment. After adjustng the phasng of lateral and dstrbuton transformers by Tapower crews, the phase currents and neutral currents of the test feeder have been collected by the SCADA system. By comparng the hourly phase currents and neutral currents of the test feeder before and after rephasng, t s found that three phase balance has been mproved sgnfcantly. The worst neutral current at the peak hour perod has been reduced from 3 A to 67 A whch mples that the problem of feeder trppng due to over neutral current volaton has been solved successfully. Fg. 5. Total cost of objectve functon (OPT) wth evoluton generatons. VI. CONCLUSION To mprove the three phase balance of dstrbuton feeders, the optmal rephasng strategy of laterals and dstrbuton transformers has been proposed by applyng the IA methodology n ths paper. The hourly loadng of each dstrbuton transformer and each hgh voltage customer have been solved accordng to the typcal load patterns of customer classes and bllng nformaton of customers served. The attrbutes of dstrbuton components are retreved from the database of outage management system n Tapower to determne the feeder network topology and to prepare the nput data fle for computer smulaton. By executng the three phase load flow analyss, the phase currents and neutral VII. REFERENCES [] J. Zhu, M. Y. Chow, and F. Zhang, "Phase balancng usng mxednteger programmng," IEEE Trans. Power Systems, vol. 3, no. 4, pp , Nov [2] J. Zhu, G.. Blbro, and M. Y. Chow, "Phase balancng usng smulated annealng," IEEE Trans. Power Systems, vol. 4, no.4, pp , Nov [3] T.H. Chen and J.T. Cherng, "Optmal phase arrangement of dstrbuton transformers connected a prmary feeder for system unbalance mprovement and loss reducton usng a genetc algorthm," IEEE Trans. on Power Systems, vol. 5, no. 3, pp.994~000, Aug [4] S.J. Huang, An mmune-based optmzaton method to capactor placement n a radal dstrbuton system, IEEE Trans. on Power Delvery, 2000, 5, (2), pp [5] G. Toefson, R. Bllnton. G. Wacker, E. Chan, and J. Aweya, A Canadan customer survey to assess power system relablty worth, IEEE Trans. on Power System, Vol. 9, Feb. 994, pp [6] C.H. Ln, C.S. Chen, C.J. Wu, M.S. Kang, "Applcaton of mmune algorthm to optmal feeder reconfguraton under multple objectves," IEE Proceedngs Gener. Transm. Dstrb., vol. 50, no. 2, pp.83~89, March