Branch Exchange Approach to Power Loss Reduction in Reconfiguration Problem of Balanced Distribution Networks

Transcription

1 Int. J. Mech. Eng. Autom. olume, Number 3, 015, pp Receved: December 8, 014; Publshed: March 5, 015 Internatonal Journal of Mechancal Engneerng and Automaton Branch Exchange Approach to Power Loss Reducton n Reconfguraton Problem of Balanced Dstrbuton Networks Branko Stojanovć Department for Mltary Electronc Systems, Sector of Electroncs, Techncal Testng Center, Belgrade 11000, Serba Correspondng author: Branko Stojanovć (elektronka@toc.vs.rs; stojanovc.branko@rocketmal.com) Abstract: Network reconfguraton s done by changng the status of the swtches, manly for two reasons, actve power loss reducton and load balancng. It attracts attenton of dstrbuton engneers for qute a long perod of tme. In ths paper, solvng method for the actve power loss reducton s gven. Searchng of the radal confguratons s done by the branch exchange method. To ad the search, two approxmate power flow methods wth varyng degree of accuracy have been developed. Appled Fortran programs are very fast but can be used only as ndcaton for the loss estmaton because of the nsuffcent method accuraces. At each teraton end t s necessary to run effcent power flow algorthm to determne the real stuaton concernng loss reducton and go on from ths pont of calculaton. Numercal example for Baran and Wu network s gven at the end of the work. Though only ndcatve, developed methods converge to the global optmum. The tme duraton of the used methods depends thoroughly on the fast manpulaton of ncomng data. Ths flaw makes methods nterestng for the tme beng only n plannng stage when the duraton s not of prmary mportance. Keywords: Network confguraton, swtches, actve power loss, power flow algorthm, branch exchange. 1. Introducton In radal dstrbuton networks sectonalzng swtches are used for protecton, to solate fault or to reconfgure network. In Fg. 1, dstrbuton network wth sectonalzng swtches s presented. Load s connected at the spots. There are two types of sectonalzng swtches, normally closed swtches that connect feeders (CB1-CB6) and normally open that connect two prmary feeders (CB7) or two substatons (CB8) or laterals that form loop (CB9). Early papers concernng reconfguraton for power loss reducton were done by Wu [1], Shrmohammad and Hong []. In Ref. [], the authors start from network where all swtches are closed and then successvely open them to elmnate loops. The choce s done, whch swtch to open, after optmal flow pattern applcaton. The number of swtches for open/close acton s much less than a branch number. In Ref. [3], sophstcatedly based Smulated Annealng method s presented (wth specal coolng and perturbaton mechansm) for the large scale systems reconfguraton problem. Km [4] uses combned Smulated Annealng method wth taboo search for mnmzaton of the losses n dstrbuton systems. Fg. 1 Typcal dstrbuton system layout.

2 Branch Exchange Approach to Power Loss Reducton n Reconfguraton Problem of Balanced Dstrbuton Networks 143 Su, Chang and Chou [5] use an ant colony search algorthm for the power loss reconfguraton problem. Fuzzy mutated genetc algorthm for the optmal reconfguraton problem wth mult-objectve functon n the form of dscrete mult-objectve optmzaton s presented n Ref. [6]. One of the greatest problems that authors face s achevng the radal network confguraton by enablng all consumers to be suppled. Determnaton of the network reconfguraton as a fuzzy genetc algorthm wth mult-objectve functon whch takes normal states as well as faults nto consderaton s gven n Ref. [7]. Genetc algorthm s appled n Ref. [8]. Tabu search s used n Ref. [9], n whch new defnton of soluton neghborhood structure to avod too many confguratons search s appled. Fast reconfguraton of dstrbuton systems consderng loss mnmzaton s mplemented n Ref. [10]. Fuzzy approach to reconfguraton wth quadruple objectve functon (load balancng, loss mnmzaton, node voltage devaton mnmzaton, branch current lmtaton) s gven n Ref. [11]. Dstrbuton system mnmum loss reconfguraton n the Hyper-Cube Ant Colony Optmzaton framework s presented n Ref. [1]. In all stated lterature complcated software s appled that s not presented and s run on fast PC-s (Pentum-I), especally n recent references. In ths paper, network reconfguraton for the power loss reducton s presented. The approach n Ref. [1] s completely adopted. Two methods for the power flow approxmaton after load transfer between two supply feeders or two laterals are gven. New power flow equatons developed for radal dstrbuton networks are presented [13]. These approxmate power flow methods are used to calculate actve power loss reducton [14]. In ths reference lstngs, A and B of developed programs are gven. Slow but precse algorthm, exhaustve search s mostly nconvenent because number of 37 confguratons whch ought to be searched s of 5 order that amounts 435,897 whle the number of possble states for the same example s 37 whch to tell the truth do not need to be analyzed all (just these that are connected and radal).. Problem Formulaton.1 Statng the Problem In order to consder power loss reconfguraton problem as an optmzaton, t s necessary to note that radal confguraton corresponds to spannng tree as a graph representng the network topology. So we come to the mnmal spannng tree problem that can be nterpreted n the followng way. The graph s gven, fnd such spannng tree to mnmze the objectve functon takng followng constrants nto consderaton: (1) voltage constrants, () current constrants, (3) relablty constrants. Ths s a combnatoral optmzaton problem.. Power Flow Equatons Consder radal network n Fg.. Lnes wll be represented by the mpedances z l = r l + jx l, (ths s a smplfcaton compared wth schematc dagram) and consumers wll be modeled as constant power loads S L = P L + jq L. Power flow n the radal dstrbuton network can be represented wth the recursve equatons called DstFlow branch equatons, whch use actve power, reactve power and voltage at the entrance of the branch P, Q, respectvely to note the same varables at the end of the branch n the followng manner: P Q P 1 P r P L1 (1) Fg. Radal network sngle lne dagram.

3 144 Branch Exchange Approach to Power Loss Reducton n Reconfguraton Problem of Balanced Dstrbuton Networks P Q Q () 1 Q x Q L1 P 1 ( r P xq ) ( r x ) Q (3) So, f varables P 0, Q 0, 0 at the frst node are known or estmated, the same varables n other nodes can be calculated by the successve applcaton of the above mentoned equatons. Ths s called a forward sweep. DstFlow branch equatons can be wrtten n backward sweep also, usng actve power, reactve power and voltage effectve value at the end of the branch P, Q, to determne the same values at the branch entrance. The result s recursve formulae, called backward sweep branch equatons. where P P' Q' 1 P r P' Q' 1 Q x Q r P x Q P L Q x 1 ( ' ' ) ( ) P ' P P Q r Q Q. ' L, L L P ' Q ' (4) (5) (6) As forward sweep, the backward sweep can be defned as start upgradng wth the last node of the network supposng values P n, Q n, n n that pont for known and carry on wth the backward sweep calculatng the same varables n other nodes by the successve applcaton of Eqs. (4)-(6). Upgradng process s fnshed wth the frst node (slack node), n whch new upgraded njected values are determned P 0, Q 0. In the course of reconfguraton, confguratons wth sub-laterals can be obtaned for the power flow algorthm [15] to be appled..3 Objectve Functon Calculaton For the power loss reducton the purpose s to mnmze total r losses whch can be calculated as follows: n 1 LP = 0 r P Q 3. Branch Exchange Search On the way to the soluton, t s necessary to fnd the most convenent tree among all (the one whose operatng pont satsfes constrants and mnmzes the objectve functon). It s clear that the search of all spannng trees gves soluton but t s practcally mpossble because the number of the possble spannng trees generated by the branch exchange s too bg for practcal problems and for each partcular tree t s necessary to apply power flow wth ntrnsc nput data (system data) accompaned by enumeraton of the nodes unless some other power flow s used for whch enumeraton s not necessary [16]. The mstakes n the course of enumeraton are also possble [17]. Branch exchange can be appled to generate relevant spannng trees from the ntal one. For gven spannng tree T 0 to each open branch, we assgn loop as f t s closed. Fg. 3 shows such loop to whch open branch b s assgned. Branch exchange creates a new tree by closng the open branch (branch b from the fgure) and openng of loop closed branch (branch m from the fgure for example). Basc dea of searchng scheme whch uses branch exchange s to start wth (feasble) tree and then create a new one successvely applyng one branch exchange at a tme. On each level the best branch exchange s chosen (the one whch mnmzes objectve functon, not volatng constrants) among all trees (chldren) that can be generated from the ntal tree by the branch exchange. By search we do not check all possble trees. On our way to global optmum soluton sometmes generates local optma. Sometmes for savng, we get postve value whle actual power flow shows that t s negatve. Fg. 3 Loop wth open branch b.

4 Branch Exchange Approach to Power Loss Reducton n Reconfguraton Problem of Balanced Dstrbuton Networks 145 Computng effcency depend on two thngs, choosng of branch m whch ought to be open because t effects a number of trals that have to be done and n the same tme at each searchng level (when the best soluton for that level s chosen) the actual power flow should be run whch s most tme consumng because of the nput data fles. Although effcent power flow s adopted for runnng, the best wll be not to use t, when t s not necessary because t s obvous that t s very tme consumng. Searchng n the descrbed manner draws falures as t s only approxmate and searchng wth real effcent power flow wll dffer from one that s adopted. 4. Approxmate Power Flow Algorthms 4.1 Algorthm 1 Smplfed Dst Flow Algorthm DstFlow branch equatons can be smplfed by neglectng the member whch denotes power loss n an actual branch and whch s much smaller than power njected at the entrance and at the end of the branch. So the followng equatons derved. P +1 = P P L+1 (7) Q +1 = Q Q L+1 (8) 1 ( r P xq ) (9) As network s radal the soluton of these equatons s easly obtaned. For the network n Fg., the soluton s as follows: P +1 = Q +1 = n P Lk k n Q Lk k (10) (11) 1 ( r P xq ) (1) These equatons are called smplfed DstFlow equatons and they wll be used n ths chapter for solvng the power flow for certan confguraton from current searchng level. Power loss of a certan branch s possble to calculate, on the bass of the followng formula: P Q LP = r r ( P Q ) (13) Total power loss for the entre network can be calculated by summaton of the losses per each branch,.e., n 1 LP = r ( P Q ) (14) 0 Power loss estmaton because of the branch exchange: For power loss reducton estmaton, because of the branch exchange, consult [14]. 4. Algorthm Updatng of DstFlow Algorthm by Backward and Forward Sweep For nomnal branch exchange b-k n Fg. 3, the method conssts of the followng steps: Step 1. Backward sweep Update power flow along the loop by backward sweep startng from node k and n of the loop applyng backward sweep DstFlow equatons. We start wth ntal values for the power and voltage at the end of the loop whch are calculated by a precse power flow algorthm for network n queston. Let us denote updated values for the power and voltage as follows: ' ' ' ' ' ' P, Q, = k,..., 0k; P, Q, = n,..., 0n; on, ok (15) Step. Forward sweep Calculate the voltage dfference n startng (slack) node (dfference between actual value 0 and updated ' ' on, ok ). If calculated dfference s too bg (bgger than some prevously adopted value max ) apply forward sweep to reduce the error (ths tme startng from the slack node, usng updated values of power and voltage for applyng a forward sweep). Let us denote new updated values wth: " " " " P, Q, = 0k + 1,..., k; P, Q, = 0n + 1,..., n (16) Step 3. Perform correcton of the power flow estmaton n ntal node Use the dfference between backward and forward sweep updated values as a msmatch and update ntal node power value by addton of these msmatches,.e., " ' ' " " ' ' " P0 k P0 k ( Pk Pk ) ; P0 n P0 n ( Pn Pn ) (17) Detals of ths algorthm applcaton are gven n Ref. [1]. Note that backward and forward sweep represent

5 146 Branch Exchange Approach to Power Loss Reducton n Reconfguraton Problem of Balanced Dstrbuton Networks teraton of the Dst Flow equatons mplementaton. In ths case the algorthm s appled for the loop generated by branch exchange. We conclude Method s computatonally faster than a real power flow applcaton; Method precseness depends on a transferred load P k, Q k. Power loss calculaton: To estmate the power loss please observe that " " P 0k - P 0k P k + LP L ; P 0n - P -P 0n k + LP R (18) where LP R and LP L represent power loss reducton n rght (R) and left (L) loop branch respectvely. Then for the total loss reducton we obtan the followng formula: LP = LP L + LP R = (P 0k -P ) + (P 0n -P ) (19) 5. Numercal Results Suggested soluton methods are mplemented n Fortran 77. Approxmate power flow methods, (M1)-smplfed Dst Flow and (M)-DstFlow method updated by backward and forward sweep are used n the course of programmng. Besdes, precse power flow algorthms (M3) [13, 15] are used to check the correctness of M1 and M methods. Tested system s hypothetcal 1.66 k system (gven n Fg. 4) comprsng of 3 buses and 5 te swtches formng 5 dfferent loops when closed. System data are gven n Ref. [14] along wth the voltage pcture of ntal confguraton. Total actve and reactve load of tested network amount to 3,715 kw and,300 kar, respectvely. Total system actve power loss s kw whch s 5.5% of total actve power demand. The lowest voltage of the ntal confguraton s p.u. It s also supposed that each branch can be open or closed by the means of sectonalzng swtch. Result of the appled calculaton [14] s presented n Tables 1 and. In Tables 1 and, each row represents a branch exchange. The branch exchange s defned by the par of fgures n the second column. The row after search level number, row 6 of the Table 1 for example, " 0k " 0n denotes whch branch exchange s chosen n that search level havng maxmal loss reducton n mnd. 6. Conclusons Two dfferent approxmate power flow methods are mplemented. They are used to estmate power loss reducton after branch exchange and are based on the power flow equatons developed for radal dstrbuton network. Numercal results show Both computng methods are very fast but of a dfferent accuracy degree. They nclude both actve and reactve power flow. Both algorthms are only ndcatve regardng estmaton of the actve power losses, they show n whch drecton to move because they do not gve precse losses, t s necessary to run precse power flow. One algorthm (M) s optmstc, gves bgger values than actual for savngs and converges to the same confguraton as algorthm M1. Precse njected powers P0K and P0N nto the loop from slack node can not be obtaned by deducton of the dran powers to generate clean loops as performed n ths artcle. Dependence between the loop actve powers s more complex and for ths reason we get much better results by ths method than real. The second algorthm (M1) ndcates further reconfguraton wth an approxmately mnmal reducton of losses whch appears to be much greater (they are neglected at the very begnnng) so that ts ndcatve characterstc s of ntrnsc value for generatng the acceptable optmum whch n our case s also global optmum [18] whch s the advantage of ths method compared wth the other methods n Refs. [1, 19, 0]. 1 Fg Hypothetcal 1.66 k system

6 Branch Exchange Approach to Power Loss Reducton n Reconfguraton Problem of Balanced Dstrbuton Networks 147 Table 1 Test results, method M. Search level Branch closed-open Loss reducton n kw compared wth ntal confguraton Method M Actual loss reducton (method M3) each each = each = each = each = Conclusons: (1) Confguraton remans as t s, branches 9, 7, 14, 3 and 37 are open and all others are closed; () Total power loss for ths confguraton (Fg. 5) amount kw. Precse calculaton of the loop node voltages by M method s almost senseless. When approxmaton s appled, the same value for all the node voltages we get results that dffer almost neglgbly and as such do not nfluence the accuracy of a method. Ths voltage approxmaton decreases the algorthm executon tme. The lowest voltage of the fnal confguraton s p.u., whch s better than the prevous value p.u., so wth reconfguraton the voltage pcture s only mproved.

7 148 Branch Exchange Approach to Power Loss Reducton n Reconfguraton Problem of Balanced Dstrbuton Networks Table Test results, method M1. Search level Branch closed-open Loss reducton n kw compared wth ntal confguraton Method M1 Actual loss reducton (method M3) each each each = each each 0-37-each = each 0-9-each each 0-37-each = each 0-9-each 0-14-each 0-3-each 0-37-each 0 - Conclusons: (1) Confguraton remans as t s, branches 7, 9, 14, 3 and 37 are open and all others are closed; () Total power loss for ths confguraton (Fg. 5) amount kw what s for kw less, compared wth ntal confguraton, 31.1% savng s acheved compared wth the loss (0.675 kw) of ntal confguraton. The man problem encountered by the author s a problem of nput data for runnng of Fortran programs. For each teraton, actual network confguraton, nput fle was fed n agan, so the real executon s very tme consumng, unless ths dffculty becomes solved by the further automaton development, whch s not a crucal pont n the plannng phase. Both shown algorthms, although ndcatve, converge and fnd global optmum (escapng tme consumng precse power flow algorthm whch wll

8 Branch Exchange Approach to Power Loss Reducton n Reconfguraton Problem of Balanced Dstrbuton Networks Fg. 5 Method M1 and M fnal confguraton that s also the global optmum [18]. be appled on each generated confguraton n the course of calculaton). By the more complete programmng of the developed algorthms [0] notable savng n computng tme wll be acheved and the shown algorthms wll come closer to the real symmetrcal dstrbuton networks problem plannng. It s worth mentonng that by the actve power loss reducton consderable money savngs n consumers delvered electrc energy are acheved. References [1] M.E. Baran, F.F. Wu, Network reconfguraton n dstrbuton systems for loss reducton and load balancng, IEEE Trans. Power Delvery 4 () (1989) [] D. Shrmohammad, H.W. Hong, Reconfguraton of electrc dstrbuton networks for resstve lne losses reducton, IEEE Transactons on Power Delvery 4 () (1989) [3] Y.J. Jeon, J.C. Km, J.O. Km, J.R. Shn, K.Y. Lee, An effcent smulated annealng algorthm for network reconfguraton n large-scale dstrbuton systems, IEEE Transactons on Power Delvery 17 (4) (00) [4] Y.J. Jeon, J.C. Km, Applcaton of smulated annealng and taboo search for loss mnmzaton n dstrbuton systems, Electrc Power and Energy Systems 6 (004) [5] C.T. Su, C.F. Chang, J.P. Chou, Dstrbuton network reconfguraton for loss reducton by ant colony search algorthm, Electrc Power Systems Research 75 (005) [6] K. Prasad, R. Ranjan, N.C. Sahoo, A. Chaturved, Optmal reconfguraton of radal dstrbuton systems usng a fuzzy mutated genetc algorthm, IEEE Transactons on Power Delvery 0 () (005) [7] Y.Y. Hong, S.Y. Ho, Determnaton of network confguraton consderng mult-objectve n dstrbuton systems usng genetc algorthms, IEEE Transactons on Power Systems 0 () (005) [8] M. Stojanovć, D. Tasć, M. učkovć, A. Rstć, Optmal dstrbuton network confguraton choce by genetc algorthm, n: 01 CIRED Conference, Serba, Sept. 3-8, 01. [9] M.A.N. Gumaraes, C.A. Castro, Reconfguraton of dstrbuton systems for loss reducton usng tabu search, n: 15th PSCC, Lege, Aug. -6, 005. [10] H.P. Schmdt, N. Ida, N. Kagan, J.C. Guaraldo, Fast reconfguraton of dstrbuton systems consderng loss mnmzaton, IEEE Transactons on Power Systems 0 (3) (005) [11] D. Das, A fuzzy multobjectve approach for network reconfguraton of dstrbuton systems, IEEE Transactons on Power Delvery 1 (1) (006) [1] E. Carpaneto, G. Chcco, Dstrbuton system mnmum loss reconfguraton n the hyper-cube ant colony optmzaton framework, Electrc Power Systems Research 78 (008) [13] B. Stojanovć, Smulated annealng method and ts applcaton to capactor placement problem n radal dstrbuton networks, Masters Work n Serban, Unversty of Electrcal Engneerng, Belgrade, [14] B. Stojanovć, Network reconfguraton n balanced dstrbuton systems for actve power loss reducton, Elektroprvreda 3 (007) [15] A. Sarć, Artfcal ntellgence applcaton for reactve power and voltage regulaton problem soluton n dstrbuton systems, Doctoral Dssertaton, Unversty of electrcal Engneerng, Belgrade, [16] J.M. Nahman, D.M. Perć, Optmal plannng of radal dstrbuton networks by smulated annealng technque, IEEE Transactons on Power Systems 3 () (008) [17] R.A.W. Ahmed, A new heurstc approach for optmal reconfguraton n dstrbuton systems, Electrc Power Systems Research 81 (011) [18] F.. Gomes, S.Jr. Carnero, J.L.R. Perera, M.P. nagre, P.A.N. Garca, L.R. Araujo, A new heurstc reconfguraton algorthm for large dstrbuton systems, IEEE Transactons on Power Systems 0 (3) (005) [19]. Borozan, D. Rajčć, R. Ačkovsk, Improved method for loss mnmzaton n dstrbuton networks, IEEE Transactons on Power Systems 10 (3) (1995) [0]. Strezosk, Collaborators: Basc power calculatons for analyses and control of dstrbuton networks, Insttute for Power and Electroncs, Unversty of Techncal scence, Nov Sad, 1998.