Study on Distribution Network Reconfiguration with Various DGs

Transcription

1 Inernaonal Conference on Maerals Engneerng and Informaon Technology Applcaons (MEITA 205) Sudy on Dsrbuon ework Reconfguraon wh Varous DGs Shengsuo u a, Y Dng b and Zhru Lang c School of Elecrcal Engneerng, orh Chna Elecrc Power Unversy, Baodng 07003, Chna a nushengsuo@63.com, b dngy49@63.com, c langzr032@63.com Keywords: dsrbued generaon, nework reconfguraon, mproved freworks algorhm, loss. Absrac. In order o research he nfluence of dsrbued generaon access o dsrbuon nework, a mahemacs model of dsrbuon nework reconfguraon wh dsrbued generaon s presened n hs paper. Freworks Algorhm s used o solve hs problem. Accordng o he characersc of dsrbued generaons, ransformng he reconfguraon o mnmum nework loss. Le he swchng sae be he soluon vecor o acheve he purpose of reduce nework loss. IEEE 33 nodes sysem s seleced o make a smulaon es, and he resuls demonsrae ha he mproved freworks algorhm can ge beer convergence effecs. Above all, he mehod n hs paper s suable for opmum he problem of dsrbuon nework reconfguraon.. Inroducon In he recen years, he maor counres all ake her eyes on dsrbued generaon. DG has oceans of dfferences wh radonal cenralzed power generaon, and hey mosly are clean energy. So, all of hese reason make DG becomes more and more mporan. Wh more and more DG access o he dsrbuon nework, he orgnal managemen and operaon wll be nfluenced by hem. On hs background, he radonal dsrbuon nework reconfguraon mehod s no applcable. Reconfguraon enals alerng he opologcal srucure of dsrbuon by changng he saus of he swches (seconalzng swches and e swches) []. We hope ha he enre nework could reduce power loss, elmnae branches congeson, balance lne load and mprove volage qualy. The dsrbuon nework reconfguraon problem can be heorecally conclude o a exremely complcaed nonlnear neger combnaon opmzaon problem [2, 3]. Because of swch combnaon n process of reconfguraon s characerscs of huge quany, herefore, he sngle drec soluon wll fal no he curse of dmensonaly. And due o he soluon space of nework reconfguraon s remendous huge. These wll cause large amoun of calculaon n soluon process, and couldn guaranee he relable convergence. A presen, he solvng mehods of reconfguraon approxmaely dvded no radonal mahemacal mehod, heursc algorhm and arfcal nellgence opmzaon algorhm. Alhough he radonal mahemacal mehod (branch-and-bound mehod, smplex mehod, 0- neger programmng mehod ec.) s more maure n heory, and can ge global opmzaon whou rely on he nal soluon of nework opology. Bu hs mehod wll easly fal no curse of dmensonaly and he consumpon of memory s very large. Heursc algorhm manly conss of wo mehod, one s opmal flow paern, and he oher s branch exchange mehod. These wo mehods mprove he calculaon speed and reduce he amoun of compuaon, bu n some case can guaranee he global opmum. Arfcal nellgence opmzaon algorhm (parcle swarm opmzaon [4], genec algorhm [5], bee colony algorhm [6] and baceral foragng opmzaon algorhm [7] ec.) has he sronger search capables, however, depends on he nal soluon and easly fals no local opmum. In hs paper, mproved freworks opmzaon algorhm s proposed o solve he problem of dsrbuon nework reconfguraon wh varous DGs. In he erave process of hs algorhm, ake he saus of swches o be he soluon vecor. And modfed he amplude equaon of freworks. Accordng o he resuls of smulaon example and exsng mehod, he proposed algorhm offers 205. The auhors - Publshed by Alans Press 766

2 relable convergence and avods fallng no local opmum, n order o propose a new dea o dsrbuon nework reconfguraon wh DGs. Do no number your paper: All manuscrps mus be n Englsh, also he able and fgure exs, oherwse we canno publsh your paper. Please keep a second copy of your manuscrp n your offce. When recevng he paper, we assume ha he correspondng auhors gran us he copyrgh o use he paper for he book or ournal n queson. 2. Problem Formulaon 2. Obecve Funcon of he Problem. The obecve funcon of he dsrbuon nework reconfguraon always ncludes decrease dsrbuon nework loss, ensure elecrcy energy qualy and balance ransmsson lne load. Ths paper focus on he economy of sysem, consderng mnmum he loss as he obecve funcon. + = 2 2 P Q mn F k R () 2 = U where, F s he obecve funcon; s he number of branch; R s he ressance of he h branch; P, Q are he acve and reacve power nec bus ; U s he volage magnude a bus ; k s a bnary varable whch ndcaes he saus of he swch. 2.2 Consran Condons of he Problem. The consran condons of he dsrbuon nework reconfguraon always ncludes power flow consran, node volage consran, DG capacy consran, branch capacy consran and opologcal srucure consran. ) Power Flow Consran P + P Q + Q DG DG = P L = Q + U L + U = = U ( G cosδ U ( G cosδ + B + B sn θ ) sn θ ) 2) ode Volage Consran U mn U U ( =,2,, n) (3) where, U mn and U are he volage lmed value a bus. 3) DG Capacy Consran PDG mn PDG PDG (4) QDG mn QDG QDG where, P DG, Q DG are power of he dsrbued generaons a bus. 4) Branch Capacy Consran P + Q S (5) where, S s he mum allowable capacy of he branch. 5) Topologcal Srucure Consran Afer he reconfguraon, he opology should be radal saus and hs paper doesn consder he solaed sland. Leraure References 3. Modelng Varous DG The radonal nework usually conans wo node ypes, Vθ nodes and PQ nodes. Bu he nework wh DGs wll have some new node ypes[8, 9]. Accordng o he DG accessng ypes and nverer ypes, hs paper ake varous DGs no 4 node ypes, PQ nodes, PV nodes, PI nodes and PQ(V) nodes. ) PQ ode Type PQ node ype ndcaes P and Q are consan. The drec drven synchronous wnd urbnes are always rea as PQ model. Ths ype of DG can be looked upon as negave load. 2) PV ode Type (2) 767

3 PV node ype ndcaes P and V are consan. The nernal combuson and gas urbne whch use he synchronous generaors are always looked upon as PV model. Because of he power flow calculaon mehod n hs paper s forward and backward subsuon mehod, we mus ake he modfcaon o hs ype of model: Q + = Q + ΔQ = Q + f (ΔU ) = X UΔU (6) where, Q s he reacve power of he PV model; s he eraon number; f(δu ) s he reacve power modfcaon ndcaed by volage devaon. Fnally, he reacon power modfcaon defned as follows: Q Q Q = Q = Q = Q mn + ΔQ Q + ΔQ Q Q + ΔQ Q Q Q mn + ΔQ Q mn 3) PI ode Type PI node ype ndcaes P and I are consan. In general case, he phoovolac sysem, fuel cell and mcro gas urbne whch equpped wh curren nverer always rea as PI model. Q + = I (8) ( U ) P where, U s he volage of he h eraon. 4) PQ(V) ode Type Fxed speed and slp conrolled asynchronous wnd urbnes whch absorb reacve power from power sysem o buld magnec feld don have he ably of volage regulaon. So, hese ypes of DG are consdered as PQ(V) ype. The reacve power of PQ(V) model s calculaed by U. P = Ps (9) + Q = ( f U ) In hs secon, hs paper ake he new node ypes no PQ model. In hs way, he forward and backward subsuon mehod could be used. 4. Improved Freworks Algorhm 4. Overvew of Freworks Algorhm. Freworks algorhm (FWA) s a swarm nellgence based on he freworks exploson, proposed by Yng Tan and Yuanchun Zhou [0]. The cenral dea of Freworks Algorhm s pu he opmal problem of soluon space rea as a search n he local space around a specfc pon where he frework s se off hrough he sparks generaed n he exploson. Then calculaon he fness funcon o ge he opmal soluon of hs eraon. Afer he numbers of eraon, he fnal sparks reaches a farly desred opmum.freworks algorhm manly conss exploson operaor, muaon operaon, mappng rules and selecon sraegy. Sage : exploson operaor. The number of sparks of freworks and he amplude of exploson are defned as follows: Y f ( x ) + ε S = m (0) ( Y f ( x )) + ε A = Aˆ f ( x ) Ymn + ε () ( f ( x ) Ymn ) + ε = = where, m and  s a parameer; Y and Y mn are mum value and mnmum value of he fness funcon of hs swarm; f(x ) s he fness value of x ; ε s a smalles consan. To ensure he number of sparks, we should lm each freworks: round( a m) s < am sˆ = round( b m) s > bm, a < b < (2) round( S ) oherwse (7) 768

4 where, round() s negral funcon; a and b are consan. Then calculaed he dsplacemen of freworks n he exploson amplude. k k Δx = x + rand(0, A ) (3) where, rand(0, A ) s random number n exploson amplude. Sage 2: muaon operaon. To keep he dversy, nroducng Gaussan muaon. k k x = x (,) (4) where, (,) s Gaussan dsrbuons. Sage 3: mappng rules. If he sparks ou of he feasble regon, we should pu hem back hrough mappng rules. k k k k k x = x + x x x ) (5) mn %( mn where, % s modular arhmec. Sage 4: selecon sraegy. Afer assure he sparks n feasble regon, hen selec he nex generaon. = K K d( x x ) = = = R( x ) x x (6) where, R(x ) s he sum of he dsances of freworks whch away from x ; K s he se of all curren locaons of boh freworks and sparks. The probables of freworks selecon are defned as follows: R( x ) p( x ) = (7) R( x K ) 4.2 Improved Freworks Algorhm. In he orgnal FWA, he freworks whch have beer fness value could explosve more sparks. Correspondngly, he smaller he amplude of exploson, he beer opmzaon wll have. For hese reason, hs paper modfed he amplude equaon of exploson n order o oban he beer opmzaon speed. Aˆ A ) A Aˆ ( mn = (8) T where, T s consan; A mn s he lower bound of frework exploson amplude. The modfed amplude equaon can warran he bgger exploson amplude n early eraon. However, n he elophase, wh he curren eraon approachng he mum number of eraons, algorhm wll ge he smaller amplude, ha s more focused on he opmzaon of he bes freworks explode around he pon. 4.3 Improved FWA Appled o Reconfguraon Problem. The algorhmc framework o opmze he dsrbuon nework reconfguraon problem are presened as follows: Sep : Inalzaon he parameers of dsrbuon nework, DGs and he mproved FWA algorhm. Sep 2: Randomly generae nal populaon. Trea he saues of each seconalzng swches and e swches as he soluon vecor. Sep 3: Calculae he power flow hrough he opology generaed by soluon vecor, and calculae fness value. Sep 4: Calculae he number of sparks ha he frework regon accordng o (2). Through equaon (4) and (5) oban he locaon of sparks. Selec he generaon of bes fness value and keep for he nex generaon. Sep 5: Accordng o equaon (7), randomly selec n- locaons o be he nex generaon wh he selecon n sep 4. Sep 6: Calculae he fness value of new locaon and updae he opmal soluon. Sep 7: Check f he eraon mee he mum value. If mee ha value, oupu he resuls; f no, go o sep

5 5. Resuls and Dscussons The proposed mehod s es on IEEE-33 es sysem. The bus daa for hs sysem are gven n [].To verfy he performance of mproved FWA and compare wh [2] (calculae power flow by [3]) and [4]. Table Reconfguraon resuls comparson of 3 knds of algorhm Mehod Open Swches Power Loss(kW) Inal ework (8,2), (9,5), (2,22), (8,33), (25,29) OFP [2] (7,8), (0,), (4,5), (32,33), (25,29) Sparsy Leveragng [4] (7,8), (0,), (4,5), (32,33), (25,29) Improved FWA (7,8), (9,0), (4,5), (32,33), (25,29) Scenaro 2 Table 2 The relaed nformaon abou DG Oupu Power DG canddae bus Acve Power Reacve Power number Power Loss(kW) I s observed ha he mehod of [2] and [4] fnally opmal he power loss o 40.28kW, reduced by 30.79%. However, proposed mehod opmal he power loss reach 39.56kW, reduced by 3.5%. The mnmum volage s ncreased from 0.93p.u. o p.u. To examne he applcably of he proposed mehod n solvng he dsrbuon nework reconfguraon wh DG. Accordng o some documens, he DG generally access n he relavely heavy load nodes. The DG canddae bus number and oupu power are shown n able 2. Fg. Reconfguraon opology of scenaro 2 Fg. 2 Comparson of volage for orgnal nework and wo scenaros The reconfguraon resuls are shown n able 2. And wh he same example, he refne adapve genec algorhm obans kW, he parcle swarm opmzaon algorhm obans 770

6 kW. Accordng hese resuls, we could know ha he proposed mehod can solve he dsrbuon nework reconfguraon problem n a effecve way. And from he Fg.2, shows ha afer he DGs access o dsrbuon nework, hey can sgnfcanly reduce he sysem power loss and mprove qualy of power supply. 6. Conclusons Ths paper has researched he applcaon of nework reconfguraon echnque n dsrbuon nework wh DGs and proposed mproved FWA. Ths algorhm execue mulple pon search hrough smulae freworks exploson. On hs bass, hs paper modfed he frework amplude equaon, fnally realzed he arge of mprovng he ables of global search. The algorhm n hs paper s esed n IEEE-33 es sysem, he resuls show he applcably and accuracy of proposed algorhm. References []. J. Lu, P.X. B, W.Y. Yang, e al. Theores of Dsrbuon Sysems and Ther Applcaons. Chna Waer & Power Press, 2007, p [2]. H.J. Lu, L.C. L, C.S. Zhang. Reconfguraon of Dsrbuon ework wh Dsrbued Generaons Based on Varous Load Modes. Power Sysem Proecon and Conrol. Vol.40 (2007) o., p [3]. J.J. Zhao, X. L, Y. Peng, e al. A Comprehensve Opmzaon Algorhm for Inecon Power of Dsrbued Generaon and Dsrbuon ework Reconfguraon Based on Parcle Swarm Opmzaon. Power Sysem Technology. Vol.33 (2009) o.7, p [4]. Z.K. L, X.Y. Chen, K. Yu, e al. Hybrd Parcles Swarm Opmzaon for Dsrbuon ework Reconfguraon. Proceedngs of CSEE. Vol.28 (2008) o.3, p [5]. B.C. Zou, Q.W. Gong, X. L, e al. Research on ework Reconfguraon GA n Dsrbuon Sysem Based on Load Balancng. Power Sysem Proecon and Conrol. Vol.39 (20) o.6, p [6]. M.M. Aman, G.B. Jamson, A.H.A. Bakar, e al. Opmum ework Reconfguraon Based on Maxmzaon of Sysem Loadably Usng Connuaon Power Flow Theorem. Inernaonal Journal of Elecrcal Power & Energy Sysems. Vol.54 (204), p [7]. K.S. Kumar, T. Jayabharah. Power Sysem Reconfguraon and Loss Mnmzaon for an Dsrbuon Sysems Usng Baceral Foragng Opmzaon Algorhm. Inernaonal Journal of Elecrcal Power & Energy Sysems. Vol.36 (202) o., p [8]. W. Wang: Research of Power Flow and ework Loss for he Dsrbuon ework wh he Dsrbued Generaon (Maser, Lanzhou Unversy, Chna 204). p.3. [9]. M. Dng, X.F. Guo. Three-phase Power Flow for he Weakly Meshed Dsrbuon ework wh he Dsrbued Generaon. Advanced n Swarm Inellgence. Vol.29 (2009) o.3, p [0]. Y. Tan, Y.C. Zhu. Freworks Algorhm for Opmzaon. Advances n Swarm Inellgence. Beng, June 2-5, 200, p []. Q. Wang: Dsrbuon ework Reconfguraon wh Dsrbued Generaon (Maser, orh Chna Elecrc Power Unversy, Chna 202). p.33. [2]. F.V. Gomes, S. Carnero, J. Perera, e al. A ew Dsrbuon Sysem Reconfguraon Approach Usng Opmum Power Flow and Sensvy Analyss for Loss Reducon. IEEE Transacons on Power Sysems. Vol.24 (2006) o.4, p [3]. A.Y. Lam, B. Zhang, A. Domnguez-Garca, e al. Opmal Dsrbued Volage Regulaon n Power Dsrbuon eworks. IEEE Transacons on Power Sysems. Vol.5 (202) o.4, p [4]. E. Dall Anese, G.B. Gannaks. Sparsy Leveragng Reconfguraon of Smar Dsrbuon Sysems. IEEE Transacons on Power Delvery. Vol.29 (204) o.3, p