Radial distribution systems reconfiguration considering power losses cost and damage cost due to power supply interruption of consumers

Transcription

1 nternatona Journa on Eectrca Engneerng and nformatcs Voume 5, Number 3, September 2013 Rada dstrbuton systems reconfguraton consderng power osses cost and damage cost due to power suppy nterrupton of consumers Sasan Ghasem and Jama Moshtagh Department of Eectrca and Computer Engneerng, nversty of Kurdstan, Sanandaj, PO Box 416, Kurdstan, ran Abstract: Dstrbuton system reconfguraton probem s a compex optmzaton process to fnd a structure wth mnmum osses n whch the satsfacton of both sdes, that s consumers and dstrbuton system companes, need to be met. One of the most sgnfcant parameters n ths regard s to ncrease the reabty of system. Ths parameter, on one hand, ncreases the satsfacton of power consumpton and on the other hand, mproves the economc benefts of dstrbuton companes. Dstrbuton system reconfguraton, consderng the reabty parameters, seems to make the attempts to sove the probem of optmzaton dffcut. n ths paper, a new heurstc approach for dstrbuton system reconfguraton n order to decrease the power osses cost and damage cost due to power suppy nterrupton of consumers has been presented. Rada network constructon and a energzed nodes constrants are the most mportant ones that shoud be consdered n dstrbuton system reconfguraton probem. Hence, n ths paper a new codfcaton s proposed whch s computatonay effcent and guarantees to generate ony feasbe rada topooges a tmes. n order to ustrate the performance of proposed heurstc method, modfed 33bus and 119bus dstrbuton networks have been empoyed whch have ed to the desred resuts. Keywords: Damage cost due to power suppy nterrupton, heurstc agorthm, new codfcaton, power osses cost, reconfguraton, reabty. 1. ntroducton Dstrbuton network reconfguraton refers to the change of operaton confguraton by aterng the topoogca state of open/cosed of some eectrc nes. Network reconfguraton s just feasbe for those networks whch are meshed. n a dstrbuton network the numbers of nes n operaton and out of servce are determned. The states of these sets of nes, subjected to mantanng the rada structure, can change. These changes ought to ead to objectve functon mprovement whch, of course n ths regard, operatng and consumpton power constrants shoud be taken n to account. Paper [1] has empoyed oad transfer from a feeder to neghbor feeder, usng a seres of formuas to assess power osses varaton wthout cacuatng the power fow. n [2] searchng technques s presented whch are based on branch exchange strategy. Modfed Tabu Search has been utzed for dstrbuton system reconfguraton [3]. An optmum power fow concept for actve power osses mnmzaton s used n paper [4] and the same concept s apped n order to mnmze the energy osses [5]. A heurstc approach to fnd structure wth mnmum osses as we as a random waksbased technque n order to osses predcton has been suggested [6]. n order to reduce osses, consderng dstrbuted generaton, a method has been used [7]. Consderng reabty reated ssues n the reconfguraton process s a new approachng manner n the technca terature, wth studes approachng dfferent aspects. n [8], a reconfguraton approach to reduce the nterrupton numbers for a dstrbuton network has been proposed. n [9], network reconfguraton probem, consderng network reabty and power osses has been soved. Reconfguraton modes that mnmze a weghted sum of Receved: May 8 th, Accepted: August 22 nd,

2 Sasan Ghasem, et a. reabty ndex (SAD, SAF and MAF), the expected nterrupton cost (ECOST) and energy not supped (ENS) are deveoped n [10], [11] and [12] respectvey. The man goa of the dstrbuton eectrca networks operaton actvty s to mantan an approprate operaton state of the network eements to secure the suppy of a consumers. Structura and operatona transformatons of the actua power systems have estabshed a compettve framework where the economc aspects are of ncreased mportance. n ths context, the economca and reabe operaton of power systems becomes prmorda. To sove the reconfguraton probem of argeszed or rea dstrbuton systems, many researchers have proposed dfferent codfcaton for metaheurstc technques to mantan the radaty constrant. n [13], Medoza et a. used oop vectors to ensure the generaton of feasbe ndvduas throughout the genetc evouton. Ths drastcay reduces the search space. However, t w produce nfeasbe ndvduas especay whe sovng the reconfguraton probem of argeszed rea dstrbuton network and ths method fas to search the soaton of prncpa nteror nodes of the dstrbuton networks and therefore requres mesh checks whch s a tme consumng approach. n [14], Romero et a., n order to generate rada confguraton, proposed a method based on concept caed pathtonode. Ths method conssts of dentfyng paths nkng between each bus and substaton whch s an exhaustve approach. n [15], Abdeazz et a. presented an agorthm n order to dstngush between feasbe and nfeasbe ndvduas wth the hep of bus ncdence matrx A. They suggested that the vaue of the determnant of A s ether 0 or ±1 for unfeasbe and feasbe rada topooges respectvey. f the ndvdua s nfeasbe the correcton agorthm s very exhaustve as t repaces each swtch subsequenty wth a the swtches of the network. Ths agorthm ooks very handy but for medum and argeszed dstrbuton networks CP tme w ncrease drecty. n [16], Debem et a., usng concepts of graph theory, deveoped an ntegra proposa to dea wth the probem of generatng rada topooges effcenty. However n ths approach, ony the mutaton operator was used and the recombnaton operator was dscarded as t usuay generates nfeasbe ndvduas. n ths paper, n order to recognze network rada confguraton, a new codfcaton has been presented whch ts mpementaton s smpe, quck and precse. Aso, a new heurstc approach for dstrbuton system reconfguraton n order to decrease power osses cost and damage cost due to power suppy nterrupton of consumers has been presented whch acheves desred resuts. 2. Mathematca Mode The mathematca mode of the reconfguraton optmzaton probem has the foowng genera form: Optm{ f } (1) Subject to: V V V, j max mn max j (2) ψ ( n ) = 0 (3) Eq. (1) corresponds to the objectve functon to be optmzed. Eq. (2) consders votage constrants for each node of network and current mt for each branch of network. Eq. (3) deas wth the rada topoogy constrant (f network s rada, so ψ = 0, otherwse ψ = 1). n ths paper, the objectve functon s f that shoud be optmzed, therefore the Eq. (1) becomes: Mn[ LC CC ] + (4) 298

3 Rada dstrbuton systems reconfguraton consderng power osses cost 3. Objectve functon evauaton The objectve functon s a combnaton of two crtera: osses cost (LC) and consumer nterrupton cost (CC). The detas reated to these two crtera are expaned n the next sectons. A. Evauaton of osses cost The power osses can be dentfed by severa components, of whch the most mportant s gven by the technca osses and two of the components can be dentfed n ths category: power osses and energy osses [17]. The actve power osses for a threephase eectrca ne, fowng on the ne s: 2 Poss, = 3R (5) And the energy osses s gven by: W oss, = Poss,. T (6) So LC for ne s obtaned by: LC = c P + c W (7) p oss, w oss, Then the tota osses cost (LC ) for a network branches s: LC = LC (8) B. nterrupton cost evauaton Frst of a, n order for defne the terms successfu and unsuccessfu for consumers suppy connected to a dstrbuton network after faut occurrence n network, we need to be aware of swtchng equpment. Swtchng equpment are defned as foow [17]: Sectonaser: s a swtchng equpment that has been desgned to norma swtch on/off a ne crcut or to separate two crcuts n case of ow ne oad. Crcut breaker: s a swtchng equpment whch s capabe of nterruptng norma or faut currents or estabshng a connecton to cose a crcut. The rada restrcton of the operaton topoogy of the dstrbuton network causes any consumer to be connected through a certan and unque set of nes to the supped source. Addtonay, suppyng power from more than one source s mpossbe. Therefore, to reach a successfu state of the suppyng a consumer, a the ne sectons stuated on the path between the consumer and the source need to be n servce. Aso a ne sectons that drecty connected to ths path and are not abe to be separated from t, have to be n servce. nsuccessfu state and faut path defntons are very compex. Based on current swtchng equpment n the network, we face wth dfferent states reated to nterrupton tme and affected areas by faut (cause to nterrupton). Fgure 1. A rada dstrbuton network. 299

4 Sasan Ghasem, et a. Fgure 1 ustrates an occurred short crcut faut n network whch eads to power suppy nterrupton n downstream consumers. Suppy restoraton can be handed usng dfferent ways. One of these ways s reparng the faut eement of the system and resuppyng through the same path. Another way s to soate the faut and connect one of the downstream consumers to the same source of energy va backup path or to connect to another source of energy. For the upstream consumers the consequences of faut and the energy nterrupton tme depends on swtchng equpment SE. f SE s a sectonaser, the frst equpment that operates after faut s CB whch s stuated on the ongong secton ne from the source. The upstream consumers coud be resupped after the swtchng of SE. Shoud SE s a crcut breaker, after faut occurrence, t tsef w emnate the short crcut. As a resut, the upstream consumers w reman supped wthout experencng an nterrupton, athough they coud be affected n dfferent ways by the transent votage oscatons. A branch between two nodes ncudes an eectrca ne or a transformer and two swtchng equpment at the nodes whch they are each ether sectonaser or crcut breaker. A branch between the nodes and j s characterzed by two reabty ndces (Fgure 2): j faure rate (faure/year) r j faure duraton (h) r Fgure 2. Equvaent reabty parameters for a branch. The faure rate of each branch s cacuated n terms of the faure rates of the component eements, consdered as beng seres connected. Faut occurrence n a branch affects the consumpton nodes dfferenty. Durng the faut cearance, there are four man steps whch are expaned as foow: [18] 1. Locatng the faut and soatng t 2. Resuppyng consumers whch are not n the faut area from source 3. Load transfer to other feeders or energzed nodes through cosng swtchng equpment that are normay open 4. Reparng the equpment and resuppyng the nterrupted consumers through the path before faut Steps 1, 2 and 4 are done after any faut; however, dong step 3 depends on nes capacty and network structure. As a resut, the reabty parameters of branch are [19]: = SE + 0L + SEj (9) = SErSE + 0r0 + SEjr (10) SEj r = (11) For each consumpton node, three prmary reabty parameters are cacuated so that nterrupton duraton of consumpton nodes can be obtaned. For the power nterrupton at a consumpton node, whch connected to the feeder through frstorder cut sets, one of the components of ths cut sets must fa. Consequenty, the components of a second or hgher order cut set are effectvey connected n parae and the unavaabty of a cut set s the product of unavaabty of components n that cut set, assumng the faure events of the components are to be ndependent of each other. n addton, 300

5 Rada dstrbuton systems reconfguraton consderng power osses cost the consumpton node fas f faure of any one of the cut sets occurs, and consequenty, each cut set s effectvey connected n seres wth a other cut sets. Detas of evauatng the reabty at the consumpton node for cut sets of dfferent orders are descrbed here. The unavaabty at the consumpton node s gven by: = (12) e FrstOrder Cut Sets: Fgure 3 shows a set of frstorder cut sets between the feeder and the consumpton node. The unavaabty at the consumpton node due to outage of eements beongng to one or more frstorder cut sets s gven by: e N = (13) = 1 SecondOrder Cut Sets: Fgure 4 reveas a number of second order cut sets between the feeder and the consumpton node. The power nterrupton at a consumpton node due to the faure of a secondorder cut set occurs when both components n the cut set fa, snce they are connected n parae. The unavaabty at the consumpton node due to outage of eements beongng to one or more secondorder cut sets s gven by: N e = (14) = 1 A secondorder cut set can cause a power nterrupton ony when both of ts components fa. Hence = (15) 1 2 Smary, one can cacuate the unavaabty at the consumpton node for thrd and hgher order cut sets N Fgure 3. Frstorder cut sets between feeder and the consumer. e N 2 e N 1 Fgure 4. Secondorder cut sets between feeder and the consumer. The suppy restoraton of consumpton node, through node A, for each faut at any of branches between nodes A and s accompshed after the faut repar. These set of branches are caed Rep for node. For a faut at one of the branches between nodes and n, suppy restoraton of node s performed after the faut soaton. These set of branches s dentfed as so for node. As the network s consdered rada, there s no possbty to restore the suppy of node by transferrng t to other feeders. 301

6 Sasan Ghasem, et a. The equvaent reabty parameters of the consumpton node, are gven by: e, rep =, j e, so j Re p =, e = e, rep + e, so (16) j so j = r, e, so = j r, j, so e = e, rep + e, so (17) e, rep j j, rep j Re p j so r e = e, rep + e, so (18) e, rep e, so So consumer nterrupton cost s: C = e cp( re) + cw ( re) r e P, (19) Hence, the consumers nterrupton cost (CC) for a n consumpton nodes s gven by: CC n = C (20) = 1 The expected energy not supped (EENS) and system average nterrupton duraton ndex (SAD) are of the wdey used reabty ndces n the recent works on addressng the reabty ssues whe reconfgurng the dstrbuton networks. The EENS and SAD may be defned as: EENS = P, N e KWh [ ] consumer.year (21) SAD = N e e N r hours [ ] consumer.year (22) 4. Proposed Codfcaton The rada confguraton, n whch the dstrbuton network operates, shoud not posses any cosed path wth a oads energzed. Exporng the souton of dstrbuton network reconfguraton probem usng some metaheurstc technque, the nta popuaton may be obtaned through the random seecton of N te number of canddate swtches out of tota number of swtches of the dstrbuton network. Most of the tme, t generates nfeasbe ndvduas, partcuary n the case of medum or argeszed dstrbuton networks. Ths certany eads to ncreased computatona burden to create nta popuaton. n dstrbuton network reconfguraton probem, one of the most mportant condtons at frst s to generate the new confguraton whch meets both rada and a node energzed crtera. n the proposed codfcaton, to avod create nfeasbe ndvduas, some graph theorybased rues have been framed. Before framng these rues, the foowng terms must be defned: Consder a network wth n nodes and m branches and K substaton n whch: A s matrx of the order n 1 that the eement a 1 of the matrx A s equa to the number of branches whch drecty are connected to the th node (the te nes are gnored). 302

7 Rada dstrbuton systems reconfguraton consderng power osses cost B s matrx of the order n n. The eement b j of the matrx B can be 1 or 0 as defned beow: b j =1 f =j b j = 1 f node and node j be connected together drecty. (23) b j = 0 Otherwse. C s matrx of order n n. The eement c j of the matrx C can be 1 or 0 as defned beow: c j =1 for; j=1,2,,n; f node s substaton. c j =0 for j=1,2,,n; Otherwse. (24) D s matrx of order n n where D (, j) C (, j) n B (, j) = (25) t s assumed that the summaton of a eements of matrx A for nta condton (wth no oop n network and a nodes energzed) and after any changes n swtches states of the network are equa to a 1 and a 2 respectvey. Now, for new arrangement of swtches, the network remans rada topoogy and wth no any node sanded, as ong as a of the foowng rues are respected: Rue 1: Non of A matrx eements must equa to zero. Rue 2: a 1 =a 2. Rue 3: The coumn summaton of D matrx must not have any zero eements. These rues guarantee to prevent producng ndvduas wth nfeasbe rada topooges. Thus, are necessary to dctate metaheurstc technques throughout the evouton processes wthout nvovng borng mesh checks. Now, the dstrbuton system n Fgure 5 s used to ustrate how the proposed codfcaton works. For nta condton of Fgure 5.1 the A, B, C matrxes and a 1 are: A = [ ] B, = C a 1 =14; =

8 Sasan Ghasem, et a. (a) (b) (c) Fgure 5. Sngene dagram of a sampe test system. (a) nta confguraton (b) The system wth a oop (c) The system wth a oop and two sanded nodes Case 1: n case 1, whch s shown n Fgure 5.2, the test system has a oop and ths structure does not meet crtera for dstrbuton network operaton. Accordng to proposed codfcaton, the rue 2 s not satsfed, because a 2 =16 and t s not equa to a 1. As a resut, case 1 has been rejected. 304

9 Rada dstrbuton systems reconfguraton consderng power osses cost Case 2: n case 2, whch s shown n Fgure 5.3, ndcates a test system whch contans a oop and two sanded nodes. Now Let us compute coumn summaton of D matrx for network confguraton n case 2. The coumn summaton of D matrx s equa to: [ ] As t can be seen, there are two zeros n coumn summaton of D matrx at coumn 7 and 8. t means that nodes 7 and 8 are sanded. Accordng to proposed codfcaton, rue 3 s not met, as a resut ths structure can be rejected. Wth regard to aforementoned cases (cases 1 and 2), ths codfcaton can easy recognze the jursdcton of a structure. Ths codfcaton s aso very easy to be coded n a programmng envronment. n ths paper, ths codfcaton s used to determne mert of the new structures estabshed for dstrbuton network reconfguraton. 5. Proposed Heurstc Agorthm Before expanng proposed heurstc agorthm for reconfguraton, the terms nodepower (np), nodep (n) and teswtch oop (teoop) shoud be expaned. n dstrbuton network, based on rada confguraton, each bus s connected to substaton through a specfed set of branches. Ths set of branches s unque for each bus. t s assumed that the unque set of ne whch connect node to correspondng substaton s L. So, np() and n() are obtaned by: 2 2 np() = R k ( Pk + Qk ) (26) k L n (). p = (27) e, rep, Aso tene oop (teoop) for each tene n the network s a set of nes whch, f the tene s cosed, forms a oop. A. Appcaton of proposed agorthm to fnd a structure wth mnmum osses cost n ths secton, the objectve functon f that shoud be mnmzed s LC. To appy the proposed agorthm n the dstrbuton network reconfguraton, the foowng steps shoud be repeated: Step 1: Defne the nput data: n ths step, the nput data ncudng the network confguraton, nes and oads data, the te nes (tenes vector), teoop for each te ne, number of te nes (N te ), dscarded tenes vector ( DTV = N te 1 ) and k=0. Step 2: Evauatng of objectve functon ( f 1 ): n ths step the vaue of the objectve functon (LC) s evauated usng resuts of the power fow based on the exstng te nes (tenes). Step 3: Computng Δ np : The nodepower dfference ([ Δ np te ], for te =1,2,..., N te ) across a of the open te nes (tenes) are computed. Step 4: f k=n te, then fnsh the agorthm and prnt the vaue of objectve functon (f 1 ) and the te nes vector (tenes), otherwse go to step 5. Step 5: The nodepower dfference ([ Δnp te ]) across such open te nes whch beong to DTV are gnored. Step 6: Swtchng operaton: such open te ne whch has the maxmum nodepower dfference n vector Δnpte s detected and consdered frst. Aso one ends of nodes of ths te ne s detected that has the hghest np. The status of swtches of both sdes of ths node must be changed. The detected te ne s changed n to cosed and ts neghbor ne n correspondng teoop w change to open and create the new arrangement of te nes (tenesnew). 305

10 Sasan Ghasem, et a. Step 7: Constrans checkng: n ths step, the constrants reated to nodes votage, branches current and radaty constrant of the network are checked. f any constrant s voated, then k=k+1 and such te ne whch s seected to swtchng operaton (n step 6), add to DTV vector and return to step 4, otherwse go to step 8. Step 8: Evauatng of objectve functon ( f 2 ): n ths step the new vaue of the objectve functon ( f 2 ) s evauated usng resuts of the power fow based on the new status of te nes (tenesnew). f f 2 f 1, then go to step 9, otherwse k=k+1 and such te ne whch s seected to swtchng operaton (n step 6), add to DTV vector and return to step 4. Step 9: n ths step, the swtchng operaton s accepted (tenes=tenesnew), a members of DTV vector are ceared ( DTV = 1 ), k=0, f 1 =f 2 and go to step 3. N te B. Appcaton of proposed agorthm to fnd a structure wth mnmum damage cost due to power suppy nterrupton n order to fnd an optma confguraton wth mnmum damage cost due to power suppy nterrupton of consumers for the network, the agorthm uses the same process as mentoned n the prevous secton wth tte changes. Here, np and Δ np are repaced wth n and Δn (nodep dfference) respectvey and the objectve functon s changed to mnmzaton of CC. C. Appcaton of proposed agorthm n order to fnd a structure wth mnmum osses cost and damage cost due to power suppy nterrupton Here, the agorthm empoys a combnaton of both above mentoned processes (sectons 5.1 and 5.2). n order to fnd an optma swtchng operaton, n each teraton, the agorthm seects a swtchng operaton from both swtchng operatons, one whch has caused mnmum osses cost (accordng to secton 5.1) and another whch has caused mnmum damage cost due to power faut at consumpton nodes (accordng to secton 5.2), whch w ead to mnmum tota amount of osses cost and damage cost due to power suppy nterrupton. The fow chart of the proposed reconfguraton agorthm s presented n Fgure Case Study Fgure 6. Fow chart of the proposed agorthm 306

11 Rada dstrbuton systems reconfguraton consderng power osses cost Fgure 7. The EEE 33bus test dstrbuton system Effcency of proposed method n ths paper for mut crtera reconfguraton s frst apped on a modfed 33bus dstrbuton system whch shown n Fgure 7. The detaed data for ths system s gven n Appendx A. Ths system work at the nomna votage of kv and the base apparent power s 10 MVA. Aso, the maxmum current mt of the system branches s seected to be 255 A. The proposed method s programmed n MATLAB on a PC Pentum V, 2.8GHz computer wth 512 MB of RAM. n ths paper, n restoraton suppy to power nterrupted consumers processes, the possbty of oad transferrng to another feeder has been taken nto account. n ths network, t has been assumed that there are three crcut breaker (on branch 12, at node 1, on branch 626, at node 6 and on branch 219, at node 19). The other exstng swtchng equpment n the network are sectonaser. The reabty parameters used n cacuatons have been ustrated n Tabe 1. Coeffcents vaue of osses and nterrupton cost are as foows: C p =10 $/kw, C w =0..2 $/kwh, C p =5 $/kw, C w =1 $/kwh. Parameter Component Lne (1 km) Crcut breaker Sectonaaser Tabe 1. Reabty dataa of component. Faure rate Repar tme (f/year) r rep (h) soaton tme r so (h) The study perod (T) s taken on a year bases. The maxmumm capabty of nes and the tme of oad transferrng from one feeder to another are 650 kw and 5 hours respectvey. The resuts of network reconfguraton, consderng LC crteron, CC crteron and both LC and CC crtera at the same tme have been provdedd n Tabe 2. n order to better understand of the resuts, Fgure 8 ndcates the fna vaues of cost osses and damages cost resuted from power nterrupton of consumers for LC, CC and LC+CC crtera. tem Tenes LC ($) CCC ($) LC+CC ($) EENS (kwh/consumer.y) SAD (h/consumer.y) CP tme (s) Tabe 2. Reconfguraton resuts for LC, CC and LC+CC mnmzaton for modfed 33bus dstrbuton system nta condton f=mn[lc] 7,14,9,32, f=mn[cc] 7,13,11,31, f=mn[lc+cc] 7, 14, 9, 31,

12 Sasan Ghasem, et a. Fgure 8. Comparatve resuts for reconfguraton process (Modfed 33bus dstrbuton system). The proposed method s aso apped on the modfed EEE 119node test feeder. Ths test system s a 11 kv dstrbuton system wth 118 sectonazng swtches and 15 te swtches as shown n Fgure 9. The detaed data for ths modfed test system s gven n Appendx A. The test resuts for the modfed EEE 119node test feeder are shown n Tabe 3. n ths case, t has been assumed that there are tweve crcut breaker (on branch 1, at node 1, on branch 5, at node 4, on branch 12, at node 11, on branch 18, at node 11, on branch 30, at node 30, on branch 38, at node 30, on branch 66, at node 68, on branch 78, at node 67, on branch 86, at node 82, on branch 89, at node 68, on branch 101, at node 105 and on branch 115, at node 119). The other exstng swtchng equpment n the network are sectonaser. The optma vaues of LC, CC and LC+CC of reconfguraton for mnmum osses cost, mnmum damages cost resuted from power nterrupton of consumers and mnmum osses cost and damages cost of power nterrupton of consumers are shown n Fgure 10. Fgure 9. The modfed 119bus test system 308

13 Rada dstrbuton systems reconfguraton consderng power osses cost Fgure 10. Comparatve resuts for reconfguraton process (Modfed 119bus dstrbuton system). Tabe 3. Reconfguraton resuts for LC, CC and LC+CC mnmzaton for modfed 119bus dstrbuton system. tem Tenes LC ($) CC ($) LC+CC ($) EENS (kwh/consumer.y) SAD (h/consumer.y) CP tme (s) nta condton f=mn[lc] 43,120,24,51,49, 62,40,126,72,74, 77,83,131,110, f=mn[cc] 44,120,121,54,123, 37,40,96,71,128, 77,108,131,109, f=mn[lc+cc] 46,25,121,54,49, 59,40,96,71,128, 77,130,86,110, Concuson Dstrbuton reconfguraton consderng achevng a structure wth mnmum osses and energy not supped s a compex optmzaton process. Varous factors ncudng the ocaton and types of swtch equpment, the capacty of nes and network structure are effectve n reducng the damage cost of power nterrupton of consumers. n ths work, a mut objectve reconfguraton probem n power dstrbuton systems s studed. Ths mut objectve probem was formuated takng nto account two objectves to be mnmzed: the osses cost and damage cost resuted from power nterrupton of consumers. Addtonay, ths paper has presented a new heurstc approach n order to sove ths mut objectve probem. Aso a new codfcaton has been presented whch avods the creaton of unconnected branches and the formaton of cosed oops when the proposed agorthm s searchng for new confguraton for the network. n most presented artces n ths regard, the possbty of oad transferrng to the neghbor feeders n power suppy restoraton to not supped consumers process has been gnored. However, n ths study, ths possbty has been taken nto account. The proposed method s successfuy apped on modfed 33bus and 119bus dstrbuton networks. 309

14 Sasan Ghasem, et a. Lst of symbos CC the consumers nterrupton cost ($) r j faure duraton for a ne between node and j (h) c p power osses cost($/kw) SAD system average nterrupton duraton (h/consumer.year) c w energy osses cost ($/kw.h) T tme nterva (h) C p cost of the nterrupted power ($/kw) teoop set of nes whch forms a oop C w cost of the energy not supped ($/kw.h) e unavaabty at the consumpton node (faure.h/year) DTV vector of dscarded te nes e unavaabty at the consumpton node (faure.h/year) EENS the expected energy not supped (kwh/consumer.year) e,so unavaabty at the consumpton node resuted from branch set so (faure.h/year) j current n the jth branch (pu) e,rep unavaabty at the consumpton node resuted from branch set Rep (faure.h/year) max maxmum current mt of the jth branch unavaabty at the consumpton node due to j (pu) e outage of eements beongng to one or more frstorder cut sets C nterrupton cost of th consumer ($) e unavaabty at the consumpton node due to outage of eements beongng to one or more secondorder cut sets LC osses cost ($) unavaabty of the branch (faure.h/year) N te number of te nes the unavaabty of the th frstorder cut set (faure.h/year) N the number of consumers connected to unavaabty of the th secondorder cut set node (faure.h/year) N the tota number of frstorder cut sets V votage of the sendng end node of the th branch (pu) N the tota number of secondorder cut V max maxmum specfed system node votage (pu) sets n nodep (kw.faure/year) V mn mnmum specfed system node votage (pu) np nodepower (pu) W oss, energy osses for eectrca ne (kw.h) P, the oads whch connected to node faure rate of eectrca ne (faure/year) (kw) 0 P actve power at sendng end of branch faure rate at the consumpton node (pu) e (faure/year) P oss, actve power osses for eectrca ne faure rate at the consumpton node resuted (pu) e, rep from branch set Rep (faure/year) Q reactve power at sendng end of branch faure rate at the consumpton node resuted (pu) e, so from branch set so (faure/year) R resstance of the th branch (pu) faure rate of the branch (faure/year) r e nterrupton duraton of suppy at faure rates of the swtchng equpment at consumpton node (h) SE nodes (faure/year) r 0 restore tmes of suppyng for a faut on faure rate for a ne between node and j the ne of the branch (h) j (faure/year) r restore tmes of suppyng of the branch ψ ( n ) rada constrant for the nth topoogy (h) r SE restore tmes of suppyng for a faut at Δ np nodepower dfference (pu) the swtchng equpment from the nodes (h) References [1] S. Cvanar, J.J. Granger, H. Yn, S.S.H. Lee, Dstrbuton feeder reconfguraton for oss reducton, EEE Transactons on Power Devery, Vo. 3, No. 3, [2] R. Cherkaou, Méthodes heurstques pour a recherche deconfguratons optmaes d'un réseau éectrque de dstrbuton, Thèse No. 1052, Ecoe Poytechnque Fédérae de Lausanne, [3] A.Y. Abdeazz, F.M. Mohamed, S.F. Mekhamer, M.A.L. Badr, Dstrbuton system reconfguraton usng a modfed Tabu Search agorthm, Eectrc Power Systems Research, Vo. 80, ,

15 Rada dstrbuton systems reconfguraton consderng power osses cost [4] S.K. Goswam, S.K. Bassu, A new Agorthm for the Reconfguraton of Dstrbuton Feeders for Loss Mnmsaton, EEE Transactons on Power Devery, Vo.7, No.3., [5] R. Taesk, D. Rajcc, Dstrbuton Network Reconfguraton for Energy Loss Reducton, EEE Transactons on Power Systems, Vo. 12,No. 1, [6] Crstne Ababe, and Rajesh Kavasser, Effcent Network Reconfguraton sng Mnmum Cost Maxmum FowBased Branch Exchanges and Random WaksBased Loss Estmatons, EEE Transactons on Power Systems, Vo. 26, No. 1, [7] J.H. Cho, J. C. Km, Network Reconfguraton at the Power Dstrbuton System wth Dspersed Generatons for Loss Reducton, EEE Power Engneerng Socety Wnter Meetng, Sngapore, pp , [8]. Trstu, M. Erema, P. meanu, C. Buac, A.. Buac, G. Mazu, n nouveau mode d aborder a reconfguraton des réseaux de dstrbuton urbane, CGRE, Back Sea E Net Regona Meetng, Suceava, Romana, pp.1014, [9] Amanua,, Sakat Chakrabart and S. N. Sngh, Reconfguraton of Power Dstrbuton Systems Consderng Reabty and Power Loss, EEE Transactons on Power Devery, Vo.27, No.2, [10] R. Brown, Dstrbuton Reabty Assesment and Reconfguraton Optmzaton, Transmsson and Dstrbuton Conference Exposton, 2001 EEE/PES, Vo 2, pp , [11] Ye Bn, Wang Xu, Be ZhaoHong, Wang XFan, Dstrbuton Network Reconfguraton for Reabty Worth Enhancement, nternatona Conference on power system Technoogy PowerCon 2002, Vo 4, pp , [12] J. Mendoza, R. Lopez, D. Moraes, E. Lopez and M.Meuner, n Modee de Reconfguraton pour a Mnmsaton de Energe Non Fourne tsant des Agorthms Genetques, Proc, of the EF 2005 Conference, Grenobe, France, [13] J. Mendoza, R. Lopez, D. Moraes, E. Lopez, P. Dessante, R. Moraga, Mnma oss reconfguraton usng genetc agorthms wth restrcted popuaton and addressed operators: rea appcaton, EEE Trans. Power Syst., Vo. 21, No. 2, pp , [14] Romero, A. Gomez, J. Rqueme, F. Lorens, Pathbased dstrbuton network modeng: appcaton to reconfguraton for oss reducton, EEE Trans. Power Syst., Vo. 20, No. 2, pp , [15] A.Y. Abdeazz, F.M. Mohammed, S.F. Mekhamer, M.A.L. Badr, Dstrbuton systems reconfguraton usng amodfed partce swarm optmzaton agorthm, Eectr. Power Syst. Res., Vo. 79, No. 11, pp , [16] A.C.B. Debem, A.C. Pd, L.F. Carvaho, N.G. Bretas, Man chan representaton of evoutonary agorthms apped to dstrbuton system reconfguraton, EEE Trans. Power Syst., Vo. 20, No. 1, pp , [17] on Trstu, Mrcea Erema, Constantn Buac and Lucan Toma, Mutcrtera Reconfguraton of Dstrbuton Eectrca Networks for Mnmzaton of Power Losses and Damage Cost due to Power Suppy nterrupton, EEE PowerTech, [18] J.H. Teng, C.N. Lu, FeederSwtch Reocaton for Consumer nterrupton Cost Mnmzaton, EEE Transactons on Power Devery, Vo. 17, No. 1, pp , [19] R. Bnton, P. Wang, Reabtynetworkequvaent approach to dstrbutonsystemreabty evauaton, EEE ProcGener.Transm. Dstrb., Vo. 145, No. 2, pp ,

16 Appendx A. System data for modfed 33bus dstrbuton network Load at node Length (m) X (Ω) R (Ω) Node j Node Lne # Load at node Length (m) X(Ω) R (Ω) Node j Node Lne # Q(kw) P(kw) Q(kw) P(kw) Sasan Ghasem, et a. 312

17 Rada dstrbuton systems reconfguraton consderng power osses cost System data for modfed 119bus dstrbuton network Lne # Node Node j R (Ω) X(Ω) Load at node Length Load at node (km) P (kw) Q (kw) P (kw) Q (kw) Lne # Node Node j R (Ω) X(Ω) Length (km) 313

18 Sasan Ghasem, et a

19 Rada dstrbuton systems reconfguraton consderng power osses cost Sasan Ghasem receved a M.Sc. degree n eectrca engneerng from Kurdstan nversty, ran, He s currenty wth unversty of Apped Scence and Technoogy of am, ran. Hs areas of nterests are the reabty, reconfguraton and restoraton of power dstrbuton systems. Jama Moshtagh receved a Ph. D. degree n eectrca engneerng from Bath nversty, nted Kngdom, Currenty, he s an Assocate Professor n the Eectrca Engneerngg Department, nversty of Kurdstan, ran. Hs nterest areas are pannng, optmzaton, reabty, and quaty of eectrca systems. 315