OPTIMAL SECTIONALIZERS PLACEMENT IN THE PRESENCE OF DISTRIBUTED GENERATION SOURCES BY BINARY DIFFERENTIAL EVOLUTIONARY ALGORITHM

Transcription

1 OPTIMAL SECTIONALIZERS PLACEMENT IN THE PRESENCE OF DISTRIBUTED ENERATION SOURCES BY BINARY DIFFERENTIAL EVOLUTIONARY ALORITHM BABAK NAJAFI 1, NORADIN HADIMI 2, MOHAMMMAD KARIMI 1, PAYAM FARHADI 1 Key words: Dfferental evolutonary algorthm, Optmal sectonalzer placement, Relablty mprovement. Ths paper proposes a novel structure for dfferental evolutonary algorthm (DEA) to maxmze the customer satsfacton by optmal sectonalzer placement (OSP) n the presence of dstrbuted generaton (D) unts. To acheve ths goal, the bnary DEA (BDEA) s suggested by addng sgmod functon to smple DEA that makes the algorthm more robust and faster for OSP problem whch has only two statuses: open/close (zero/one). The OSP problem has been formulated as a functon of relablty ndex and sectonalzer cost and these terms have been presented as membershp functons whch are related by weghtng factors. Smulaton results have been performed n Roy Bllnton Test System (RBTS), the prorty of the BDEA has been compared wth the ant colony optmzaton (ACO) technque 1. INTRODUCTION The most blackouts of customers are related to the network dstrbuton whch s due to large sze of ths network. Approprate strateges have been consdered to reduce the outage n recent years. One of the strateges for relablty mprovement s a proper placement of sectonalzer n the presence of dstrbuted generaton (D). The sectonalzer let the other parts of system to be fed through man feeder by usng D and solatng the fault zone. Ths approach not only decreases the annual expected energy not suppled (EENS), but also ncreases the customer satsfacton. Installng sectonalzer n dstrbuton networks can beneft the system wth mproved relablty, managed confguraton along wth effectve fault solaton and network reconfguraton [1, 2]. In ths secton, the lterature has been revewed to explore the related researches related to sectonalzer allocaton. They have been categorzed nto four major groups based on ther selected objectve functon: cost, relablty, multobjectve functon and mult-objectve functon n the presence of D(s). 1 Islamc Azad Unversty, Parsabad Moghan Branch, Department of Electrcal Engneerng, Parsabad Moghan, Iran 2 Islamc Azad Unversty, Ardabl Branch,Young Researchers and Elte Club, Ardabl, Iran Rev. Roum. Sc. Techn. Électrotechn. et Énerg., 60, 1, p , Bucarest, 2015

2 70 Babak Najaf et al. 2 In [3], objectve functon of sectonalzer placement has been formulated as a cost based formula. Other set of formulaton of sectonalzer allocaton s based on relablty ndces whch have been presented n [4 9]. Thrd category of the formulaton methods of optmal sectonalzer allocaton, namely multobjectve functons, combned the sectonalzer cost and the relablty ndex to formulate the optmum objectve functon [10 13]. Due to mprovement of relablty ndces by Ds, other category of papers has placed sectonalzer n the presence of D unts. Mao et al. have proposed graph-based algorthm to solve the optmal sectonalzer n the presence of Ds by consderng customer prorty [14]. Fnally, a fuzzy multobjectve functon has been solved by ACO algorthm to mprove the relablty ndex (.e. EENS) and reduce the swtch cost n presence of D n [15]. 4 bus Roy Bllnton Test System (RBTS) and a practcal radal dstrbuton network has been used as test system and several scenaros have been appled on these systems to llustrate the mpact of D sze/locaton on objectve functon as well as the number and locaton of sectonalzer and system average nterrupton duraton ndex (SAIDI). Man contrbuton of ths paper s based on suggestng a novel structure for dfferental evolutonary algorthm (DEA) to adaptve of sectonalzer optmal locaton n the presence of Ds problem. The proposed bnary DEA (BDEA) has been desgned by applyng sgmod functon after crossover operator of smple DEA. Relablty of the proposed algorthm s confrmed by testng on several test functons. The optmal sectonalzer allocaton n the presence of D unt has been formulated as a multobjectve functon whch conssts of two objectves. Frst objectve s to mprove the network relablty ndex through reducng the EENS ndex. Second objectve s to mnmze the sectonalzer cost. The second objectve wll be obtaned by reducng the number of nstalled sectonalzer. These objectves have been presented as membershp functons. The results of the BDEA have been compared wth related values of ACO technque n a standard system. 2. THE OPTIMAL SECTIONALIZER PLACEMENT PROBLEM In formulaton of optmal sectonalzer placement (OSP) problem, two objectves have been set. These objectves are presented as membershp functons and related together by weghtng factors [15]. Frst objectve s mprovng the relablty of dstrbuton network. Ths target s amed to mprove the EENS and has been deployed as a relablty ndex, n kwh/yr. Usng ths ndex, tme and unsuppled load wll be ntegrated n one ndex whch s the man advantage of EENS than two tradtonal ndces (.e. SAIFI and SAIDI). Equaton (1) defne ntalzng µ EENS based on mnmum value of EENS, EENS mn. accordngly, f µ EENS s less than EENS mn, the membershp functon s 1, else µ EENS s equal to exponental value of normalzed dfference between EENS and EENS mn.

3 3 Optmal sectonalzers placement problem for electrcal networks 71 1, μ EENS = EENS EENS EENS EENS mn exp, otherwse. EENSmn Equaton 2 shows swtch cost, of project. Ths equaton has two terms, The total swtch cost mnmzaton (SCM) conssts of two terms, these are determned based on polcy of reducton of the number of new nstalled swtch, NS new, and old nstalled swtch (NS old ). Cost of plan s a functon of the number of nstalled swtch. There are numerous swtches whose locaton wll change after nstallng D unts. Also, varaton of loads, and network confguraton ncrease the relocaton probablty of these equpment. Man goal n swtch nstallaton polcy s to mnmze the new nstallatons because new swtches ncur new nvestments and t affects the relablty and cost reducton. Then frst term of SCM s the dfference between the number of new and old nstalled swtches multpled by new swtch nvestment cost, SIC. Second term of total swtch cost mnmzaton s functon of status of old nstalled swtch, SS, n a new plan and related cost, (RCS ). SCM = ( NS NS ) SIC + SS RCS, (2) new old = 1 where n s the number of new nstalled swtches and SS s defned as n 0 f new swtch has been nstalled n old locaton SS =. (3) 1 otherwse Second objectve s to mnmze the sectonalzer cost whch can be obtaned by reducng the number of nstalled sectonalzer(s). If SCM s less/equal wth zero or more than SCM max, the membershp value s 1 or zero, respectvely. Whle between zero and SCM max s functon of values of SCM and SCM max (see Eq.(4)) μ SCM 1, SCM 0 SCM max SCM = 0 SCM SCM max. SCM max 0, SCM max SCM Equaton (5) has been suggested to determne the maxmum swtch cost ( ) max max old, mn (1) (4) SCM = NS NS SIC (5) where, NS max s the maxmum number of swtches whch can be nstalled n the network and can be determned accordng to specfc crtera such as avalable budget. It s evdent that f there s no restrcton n selectng NS max, the parameter wll be equal to the number of canddate stes for swtch nstallaton [10]. Two membershp functons of relablty ndex whch are µ EENS and sectonalzer cost, are ntroduced to formulate the objectve functon as fuzzy set.

4 72 Babak Najaf et al. 4 These objectves are weghted by two arbtrary factors: w 1 and w 2 and they represent the mportance of each term n each desgn. OF = Max{ w1 μeens + w2μ SCM}, (6) where, w 1 +w 2 =1. 3. BINARY DIFFERENTIAL EVOLUTIONARY ALORITHM Evolutonary algorthms (EAs) are of the most famous branches of ntellgent computng whch use some operators (crossover, mutaton and other operators) to obtan the optmal soluton from ntal populaton. The DEA s a member of EA famly whch was proposed orgnally n 1997 [16]. enerally, the DEA technque has fve stages and along wth a sgmod functon whch wll be ntegrated n the algorthm, the BDEA algorthm could be obtaned. So, the BDEA technque has sx stages [16 17]. Stage Intalzaton: Ths algorthm s a populaton based algorthm, therefore, ntal populaton s produced by Eq. (7) to start the optmzaton process. Dmensons of DEA depends on the numbers of populaton(p), and varable (V). MIN MAX MIN Zk, = ZL + rand ( ZL ZL ), [ 1, P], L [ 1, V ] (7) where Z L MIN and Z L MAX are lower and upper boundares, respectvely, whch have been selected based on the problem requrements and rand produces a value between [0,1] randomly. P and V are the numbers of parameter and varable, respectvely. Stage Mutaton. The ntalzed populaton wll mutate usng Eq. (8). Mutaton operator helps algorthm to escape from local mnma. For ths, three vectors are selected from ntal populaton, randomly, called Z 1, Z 2 and Z 3 so that components of these vectors are not equal. Man crteron n producton of mutated matrx s scalng factor (F). Ths parameter s selected n the range [0, 2]. The mpact of second and thrd selected vectors, Z 2 and Z 3, n mutaton process are controlled by F, Z + 1 m, = Z 1 + F ( Z 2 Z 3 ). (8) Stage Crossover. By crossover operator, pror populaton (parent) s composed and the next populaton wll be produced (chldren). Crossover operator won t be appled on all populaton, and applyng crtera s the crossover rate(cr). Ths parameter s a real value n the range [0, 1]. If crossover rate s hgher than a random value, vectors from mutaton step are selected; otherwse, selecton s performed from ntal populaton,

5 5 Optmal sectonalzers placement problem for electrcal networks Z f α j CR or j = γ Z c, j =, Z otherwse = 1,..., P ; j= 1,..., V (9) where, α j and γ are chosen randomly from [1,, V]. Stage v Sgmod Functon. By applyng sgmod functon to the obtaned vectors from crossover operator, the populaton s transferred n bnary space;.e. zero and/or one. Ths work s carred out due to the performance nature of sectonalzeres whch are open and/or close. 1, f rand < sgmod( Z Z j, = 0, otherwse 1 sgmod( Z j, ) = Z j, 1+ e j, ). (10) Stage v Selecton. In ths stage, the algorthm uses the selecton operator to choose the optmal soluton that has been acheved so far. In other words, selecton operator decdes between ntal matrx, Z, and crossover matrx, Z j. If related soluton of crossover vector, f (Z c, ), s less than or equal to the soluton correspondng wth ntal populaton, f(z ), the crossover vector wll be selected. Ths concept has been shown n Eq. (11) Z + 1 Z = Z c, f f ( Z c, ) otherwse f ( Z ) = 1,..., P. (11) Stage v Termnaton Crtera. To termnate the algorthm, there are two ways; reachng to the optmal soluton or reachng the maxmum allowed number of teraton. In optmzaton problem, the second crteron has been used. 4. SOLVIN THE OSP PROBLEM BY THE BDEA TECHNIQUE The concept and equatons of objectve functon and BDEA approach have been presented n Sectons 3 4, respectvely. In ths secton, solvng the OSP problem by BDEA has been ntroduced. To start the optmzaton process, the nput data s appled; for ths purpose, two sets of nputs are defned: data of problem and algorthm. These data consst of lnes length, falure rate, repar tme average, canddate locatons for swtch nstallaton (problem data), the numbers of populaton and generaton, and crossover rate CR (algorthm data) are defned.

6 74 Babak Najaf et al. 6 Due to the fact that there s no possblty to nstall the sectonalzer, some sectons are removed manually. The length of lne and the locaton of D unts have been determned. In ths stage, the sectonalzng devce lst can be prepared. The locaton and number of sectonalzers have been presented through formed matrx of sectonalzer. The subprograms of zonng and then relablty ndex calculaton are performed. The value of objectve functon wll be computed based on these data. To start the optmzaton stage, the random ntal populaton s generated based on the numbers of populaton and sectonalzer. Then, the number and locaton of sectonalzer wll be calculated and zonng subprogram wll be carred out, agan. By placng D unts whch have been removed n prevous desgn, relablty ndex are rerunnng to create a novel lst of the number of sectonalzer. The objectve functon wll be calculated based on the ntal populaton. Three operators of mutaton, crossover and sgmod wll be appled on the populaton and the objectve functon wll be recalculated. The selecton operator selects the best soluton between two obtaned objectve functon. The termnaton crteron s examned, f does not satsfed, teraton wll be contnued untl satsfacton. The optmal possble solutons for objectve functon, the number and locaton of sectonalzer and relablty ndces are prnted. 5. CASE STUDY The results of solvng OSP problem wth the proposed algorthm have been compared wth the related parameters of ACO technque [15] n Bus 4 of the RBTS. Second case s a feeder of Meshkn-Shahr dstrbuton network n northwest of Iran. The numbers of generaton and populaton of the BDEA are 50 and 40, respectvely. The crossover rate s 0.1. BUS 4 OF RBTS. The sngle lne dagram of the bus 4 of the RBTS n rated voltage 33 kv and ts data have been presented n [15]. The total average load s MW wth power factor equal to 0.9. It should be noted that n ths system, all sectonalzers are removed and the number and locaton of these swtches have been determned wthout old sectonalzer. Also, both sdes of all sectons are consdered as canddates for swtch nstallaton. Three cases have been ntroduced on the test system and have been dscussed the number and locaton of nstalled sectonalzers. Case I. Base system study; Case II. Weghtng factor senstvty analyss; Case III. D unt sze senstvty analyss. In all above cases, the maxmum avalable sectonalzer (NS max ) s 20.

7 7 Optmal sectonalzers placement problem for electrcal networks CASE I BASE SYSTEM STUDY Man objectve of ths case s to study the mpact of the presence and absence of D unts on objectve functon value and the locaton and number of sectonalzeres. In ths case, to produce the smlar objectve, the weghtng factors have been assumed 0.5. Table 1 llustrates the results of BDEA and ACO technques n frst Case for OSS problem. In all tables, D Cap./Loc s capacty and locaton of D, respectvely. Table 1 Results of Case I on RBTS test system test Tech. D Cap./Loc. w 1 w 2 EENS µ EENS µ SCM OF Optmal sectonalzer locaton ACO , 26-27, 18-33, I-I BDEA ,18-33, 26-27, ACO ,18-19,21-24,26-27,18-33,44-46 I-II BDEA 1000/ , 18-33, By consderng values of Table 1, results of two tests show meanngful dfference. The number and locaton of sectonalzeres of two algorthms are the same n the frst case whle n the second they are dfferent. The number of sectonalzer of BDEA s 3 fewer than the number of swtch of ACO approach. The sectonalzer locatons of BDEA s as the same as the locatons of ACO algorthm CASE II WEIHTIN FACTOR SENSITIVITY ANALYSIS Man objectve of ths case s to study the mpact of weghtng factors changes on satsfacton level and the locaton and number of sectonalzng devces. For ths purpose, four test cases have been ntroduced where w 1 and w 2 change between 0.2 and 0.8. Other parameter values are smlar to frst case. Table 2 shows results of applyng the second scenaro on RBTS test system by the proposed algorthm and comparson of the results wth the related values of ACO algorthm. Table 2 Results of Case II on RBTS test system D test Tech. Cap./Loc w 1 w 2 EENS µ EENS µ SCM OF Optmal sectonalzer locaton ACO 1000/ , II-I BDEA 1000/ ACO 1000/ , 33-18,21-24, II-II BDEA 1000/ , 21-19, ACO 1000/ , 33-18, 27-26, 21-24, 19-18, 10-8 II-III BDEA 1000/ , 27-26, 24-26, 33-18, 19-18, , 24-21, 19-18, 18-15, 13-12, 10-8, ACO 1000/ , 44-26, 38-35, 33-18, II-IV , 24-21, 33-18, 19-18, 16-12, 51-49, BDEA 1000/ , 29-27, 44-26, 27-26

8 76 Babak Najaf et al. 8 By consderng the lsted values n Table 2, weghng factors varaton have mpact on objectve functon. The numbers of sectonalzer are the same n the thrd and fourth tests whle n the frst and second tests the number of sectonalzer of BDEA s less than the related value of ACO algorthm CASE III D UNIT SIZE SENSITIVITY ANALYSIS Man objectve of ths case s to study the mpact of changes of D sze on the optmal locaton and number of sectonalzng devce and ts objectve functon. For ths, three Ds of 2000, 3000 and 4000 W n bus 26 are nstalled whle other parameters are smlar to frst case. Results of case III by BDEA and ACO technques have been lsted n Table 3. Table 3 Results of Case III on RBTS test system test Tech. Sze/Loc EENS µ EENS µ SCM OF Optmal sectonalzer locaton ACO , 18-19, 24-26, 26-27, III-I BDEA 2000/ , 18-33, 24-26, 26-27, ACO ,15-18,18-19,24-26,26-27,35-38,26-44 III-II BDEA 3000/ , 18-19, 14-26, 26-27, ACO ,15-18,18-19,24-26, 26-27,44-46 III-III BDEA 4000/ ,15-18,18-19,24-26, 26-27,44-46 Regardng to lsted values n Table 3, the proposed technque presents better soluton than ACO algorthm, especally n thrd test of ths case. In second test the number of swtches n BDEA s 2 fewer than related value of ACO algorthm whle n frst an thrd tests, these values are equal. The smlar locatons of sectonalzer by two algorthms are: 4, 3 and 5 n 1 st, 2 nd, and 3 rd tests of thrd case, respectvely. 6. CONCLUSION In ths work, optmal sectonalzers placement (OSP) has been performed based on a fuzzy multobjectve functon by bnary dfferental evolutonary algorthm. By dong smulaton n standard and practcal test system t can be confrmed that: The proposed algorthm presents better soluton than ACO algorthm [15]. In frst case, the satsfacton level of two algorthms s equal n 1 st test whle n 2 nd test the objectve functon of BDEA s % more than related value of ACO algorthm. In frst to fourth tests of second case, the objectve functon values of the proposed algorthm are %, %, % and % more than related values of ACO algorthm, respectvely. These ncrements are % and % as well as 8.758% for 1 st to 3 rd tests of thrd case, respectvely. Changng weghtng factors shows that better satsfacton can be obtaned when dfference between two these weghtng factors s relatvely greater. In other

9 9 Optmal sectonalzers placement problem for electrcal networks 77 words, the relablty membershp functon s more than swtch cost membershp and thus f the values of two weghtng factors s close, the satsfacton level reduces. EENS wll decrease by reducng the number of sectonalzer(s) and also ncrement of the nstalled D capacty helps ths to EENS reducton. From Table 3 n frst and second tests of 3 rd case, the number of nstalled sectonalzer s equal whle EENS of frst test s more than related value of second test. The numbers of nstalled sectonalzer of BDEA and ACO technques n four tests s equal (I-I, II-IV, III-I and III-III) and n other tests, the BDEA has presented fewer sectonalzers wth respect to ACO algorthm (I-II, II I, II II, II III, III II). Receved on September 27, 2013 REFERENCES 1. R. Bllnton, R. N. Allan, Relablty evaluaton of power systems, Ptman Books, New York, London, Westnghouse Electrc Corporaton, Electrc utlty reference book dstrbuton systems, 3, East Pttsburgh, Levtn, M. T. Shmuel, D. Elmaks, Optmal sectonalzer allocaton n electrc dstrbuton systems by genetc algorthm, Electrc Power Systems Research, 31, pp , A. Morad., M. Fotuh-Fruzabad, Optmal swtch placement n dstrbuton systems usng trnary partcle swarm optmzaton algorthm, IEEE Transactons on Power Delvery, 23, 1, pp , A. Abr-Jahrom, M. Fotuh-Fruzabad, M. Parvana, M. Mosleh, Optmzed sectonalzng swtch placement strategy n dstrbuton systems, IEEE Transactons on Power Delvery, 27, 1, pp , Z. Rajc, V. Flpovc, Approxmate calculaton of backup supply proftablty n medum voltage power dstrbuton plannng, IEE Proc.-eneraton, Transmsson and Dstrbuton, 151, 6, pp , J. H. Teng, Y. H. Lu, A novel ACS-based optmum swtch relocaton method, IEEE Transactons on Power Systems, 18, 1, pp , J. H. Teng, Ch. N. Lu, Feeder-swtch relocaton for customer nterrupton cost mnmzaton, IEEE Transactons on Power Delvery, 17, 1, pp , Cell, F. Plo, Optmal sectonalzng swtches allocaton n dstrbuton networks, IEEE Transactons on Power Delvery, 14, 3, pp , P. Wang, R. Bllnton, Demand-sde optmal selecton of swtchng devces n radal dstrbuton system plannng, IEE Proc.-eneraton, Transmsson and Dstrbuton, 145, 4, pp , R. Bllnton, S. Jonnavthula, Optmal swtchng devce placement n radal dstrbuton systems, IEEE Transactons on Power Delvery, 11, 3, pp , Ch. Sh. Chen, Ch. H. Ln, H. J. Chuang, Ch. Sh. L, Huang M. Y., Huang Ch. W., Optmal placement of lne swtches for dstrbuton automaton systems usng mmune algorthm, IEEE Transactons on Power Systems, 21, 3, pp , 2006.

10 78 Babak Najaf et al W. Tppachon, D. Rerkpreedapong, Multobjectve optmal placement of swtches and protectve devces n electrc power dstrbuton systems usng ant colony optmzaton, Electrc Power Systems Research, 79, pp , Y. Mao, K. N.Mu, Swtch placement to mprove system relablty for radal dstrbuton systems wth dstrbuted generaton, IEEE Transactons on Power Systems, 18, 4, pp , H. Falagh, M. R. Haghfam, Ch. Sngh, Ant colony optmzaton-based method for placement of sectonalzng swtches n dstrbuton networks usng a fuzzy multobjectve approach, IEEE Transactons on Power Delvery, 24, 1, pp , R. Storn, K. Prce, Dfferental evoluton a smple and effcent heurstc for global optmzaton over contnuous spaces, Journal of lobal Optmzaton, 11, pp , R. Hossenzadehdehkord, M. Eskandar Nasab, H. Shayegh, M. Karm, P. Farhad, Optmal Szng and Sttng of Shunt Capactor Bank by a New Improved Dfferental Evolutonary Algorthm, Internatonal Transactons on Electrcal Energy Systems, 2013; DOI: / etep.1762).