J. Appl. Envron. Bol. Sc., 5(1)20-27, 2015 2015, TextRoad Publcaton ISSN: 2090-4274 Journal of Appled Envronmental and Bologcal Scences www.textroad.com A Mathematcal Model for Restoraton Problem n Smart Grds Incorporatng Load Sheddng Concept Nada Zendehdel *, Raab Asgharan Ghanad Yazd Department of Electrcal Engneerng, Faculty of Engneerng, Ferdows Unversty of Mashhad, Mashhad, Iran Receved: September 12, 2014 Accepted: December 3, 2014 ABSTRACT The automatc restoraton process s an mportant part of advanced dstrbuton automaton whch seeks to automatcally restore outage loads n smart grds. Ths ablty of the smart grds mproves the relablty and reduces the servce nterrupton perod. Accordng to the mportance of the restoraton problem, ths work focuses on modelng ths problem n a smpler manner whch s approprate for smart grd. Snce the smart grd agents can perform dstrbuted computatonal actvtes and make decsons ndvdually, the proposed model s constructed as a routng problem n a vrtual graph whch s developed based on the out-of-servce areas n the man grd. Ths model s solved nstead of the commonly used NP-hard restoraton problem durng decson makng process to obtan the optmal restoraton plan. The presented routng problem whch s constraned by some power system operatng constrants consders the load sheddng concepts and gves the sheddng program wth respect to the load prortzatons. It can be solved by a lnear bnary programmng technque such as branch and bound. Fnally to demonstrate the desgned restoraton algorthm capabltes, a standard test system s selected and the method s mplemented on t. The gven results show the applcablty of the proposed model. KEYWORDS: Lnear bnary programmng; Load sheddng; Restoraton problem; Smart grd INTRODUCTION In smart grds, servce restoraton s an mportant appearance of advanced dstrbuton automaton whch transfers unfualted and outage loads to other substaton and supples as many customers as possble n the shortest tme automatcally. The automated actons durng restoraton process reduce the nterrupton costs and mprove the qualty of servce usng the exstng mcroprocessor based and automated swtchgear at nodes. These swtches can be dvded nto two types: normally closed sectonalzed swtches and normally opened te swtches. The status of these swtches must be regulated properly such that the radal topology of dstrbuton system s mantaned. Durng emergency operaton, the swtches can be changed autonomously such that power can be served from dfferent feeders to the outage area. Ths ablty s an mportant change of paradgm n dstrbuton networks operaton acheved by smart grds deployments. Accordng to [1], real-tme nformaton whch s avalable by bdrectonal communcatons and automated controls, the out-of-servce areas can be automatcally restored and the servce nterruptons are mtgated. Accordng to the mportance of the restoraton problem, n recent decades, many researches were focused on ths ssue and dfferent approaches have been proposed to obtan the best swtchng operaton plan to reenergze the out-of-servce areas n presence of the operatng lmtatons. Mathematcally, the restoraton problem s a combnatoral non-lnear mult obectve optmzaton problem wth some lnear and non-lnear constrants. The constrants of ths problem are related to the power system physcal and operatonal constrans such as source, lne/cable loadng, nodal voltage and often radal network constrants. The proposed reconfguraton approaches can be categorzed as determnstc mathematcal programmng method [2-6], heurstc technques [7-9] and knowledge-based systems [10]. There are several common characterstcs of these approaches. Frst, all necessary nformaton s collected from felds at a centralzed computer system. Second, large amount of data transferrng and low-latency communcaton are mposed on the system. Thrd, the control center requres expensve computng capablty. These mentoned characterstcs comprse barrers that aggravate even more n the case of medum voltage (MV), manly due to ther extent and substantal branchng and also large number of nodes that have to be montored. As a result, centralzed technques have some dffcultes to be mplemented n smart grd wth real-tme sensor measurements and varous ntellgent electronc devces. Meanwhle, mult agent system (MAS) as a dstrbuted problem solvng approach utlzes a dstrbuted control at the component level and uses peer-to-peer communcaton for collaboratng agents acheve near global obectves and overcome dsadvantages of centralzed technques. Accordng to the dstrbuted ntellgence n smart grd and exstng onlne measurement, MAS seems an approprate solvng method for restoraton problem. Recently, some research has been performed to develop MASs n servce restoraton [11-19]. In [11], MAS archtecture has been utlzed for only the servce restoraton wthout consderng the load Correspondng author: Nada Zendehdel, Department of Electrcal Engneerng, Faculty of Engneerng, Ferdows Unversty of Mashhad, Mashhad, Iran. 20
Zendehdel and Asgharan, 2015 sheddng and prortes. In [12, 13], MAS framework has been developed for the servce restoraton problem, ncorporatng the load sheddng concept. Load varaton and prortzaton have not been consdered n these mentoned two studes. In [14, 15], the restoraton problem has been nvestgated n the MAS archtectures, consderng load prortzaton and sheddng concepts. A completely dstrbuted algorthm has been proposed n [16] for the self-healng mechansm n dstrbuton systems wth dstrbuted energy resources (DES). In [17, 18], an agent based control framework has been presented for controllng the self-healng process consderng the peak load n duraton of the fault repar. A MAS archtecture ncludng agents wth local vews has been proposed n [19] to realze the automatc restoraton mechansm. There are two common characterstcs of the mentoned MAS approaches have been proposed n the past [11-19]. Frst, the decson makng polces n avalable studes are based on the learnng methods or expert-based systems whch often acheve near global obectves. They don't nvestgate the optmalty of ther obtaned dstrbuted solvng approaches. Second, they requre huge databases to restore statstcal data for ther expert-based decson makers. They don't consder the advantages of the mathematcal programmng methods to elmnate ths requrement. To overcome ths barrers a dstrbuted restoraton problem approach s proposed n ths paper to guarantee the optmalty of the obtaned restoraton plan and reduce the amount of necessary nformaton for dstrbuton system restoraton. Ths paper wll explore the agent based restoraton problem and ams to fnd an optmal restoraton plan. In the proposed MAS archtecture, two categores of agents, ncludng zone and feeder agents, negotate together and exchange local nformaton. Furthermore, they make decson usng the receved nformaton through a hybrd decson makng polcy. Ths polcy s desgned based on the expert-based system and mathematcal programmng technques to be ganed from the advantages of both methods smultaneously. At the same tme, the restoraton problem s modeled smply and a novel approach s developed for obtanng an optmal restoraton plan ncorporatng the load prortzaton and sheddng. The presented model s a lnear bnary programmng problem whch ts dmenson s lower than the man mxed nteger NP-hard mathematcal problem commonly used for modelng the restoraton problem. In other words, ths paper focuses on ntroducng a mathematcal model for restoraton problem such that the complexty of the proposed method and ts data accuracy dependence s lower than the commonly mxed nteger programmng method used for solvng restoraton problem. In ths model mportant practcal ssues related to the restoraton problem ncludng load prortzaton and sheddng s consdered. The sutablty and capablty of the developed method s demonstrated by mplementng t on IEEE standard test system. The gven results llustrate the applcablty of the presented algorthm wth accurate restoraton plan and load sheddng program. The rest of ths paper s organzed n sx sectons as follows. Secton 2 ntroduces a mult-agent framework for the self-healng mechansm n the dstrbuton systems. Secton 3 presents the decson makng polcy and advanced mathematcal restoraton model. Secton 4 llustrates the evaluaton of the mult-agent control framework by means of the IEEE 33-node test dstrbuton systems. Fnally, the paper conclusons are drawn n Secton 5. A lst of all the symbols used n the paper s ncluded after the conclusons. Agent Based Control Archtecture In smart grds, the agents are equpped wth the ntellgent ablty to communcate and negotate together to determne the current states of the system and make decson to set the status of ther actuators to reenergze the out-of-servce areas n a shortest perod. Therefore, n ths secton, a MAS control structure s proposed for automated servce restoraton n smart dstrbuton system. In the proposed structure, each dstrbuton feeder s dvded nto some segments, namely zones, wth the locaton of the swtchng devces whch are placed on the boundary of each segment. In the presented MAS, a control agent s assgned to each zone as a zone agent to communcate, make decson and calculaton. Moreover, a feeder agent s assgned to each feeder to determne the operatng stuaton of each feeder and communcate wth other adacent feeder agents. Agents communcate together to coordnate ther performance based on the agent communcaton language (ACL) [20] whch s developed n 1996 by foundaton for ntellgent physcal agents (FIPA) [21]. Each zone agent montors the nodal voltage and branch currents at ts correspondng zone and calculates two mportant factors whch can demonstrate the operatng stuaton of that zone. These two factors can be consdered as mnmum nodal voltage at a zone and mnmum spar current capacty of lnes at a zone. Zone agents send these montored data to ther feeder agent through sendng messages f the relatve feeder agent seeks to calculate ts avalable capacty to reenergze addtonal loads. Furthermore, feeder agent communcates wth other feeder agents whch are connected wth them by a te (normally opened) swtch. Durng the restoraton process, an outage zone can be transferred to a backup feeder to be reenergzed f that feeder has enough avalable capacty to satsfy the requred power consumpton of loads at that outage zone. One of the mportant concepts of restoraton problem s the load prortzaton. Consderng the lack of power supply durng the emergency condton the restoraton process should be started from reenergzng the hghest prorty loads and then other loads are allowed to be restored. If any backup feeder has suffcent capacty to restore the out-of servce areas, the restoraton process s conducted as a group restoraton. Otherwse, the outage areas are dvded nto some parts such that each part s restored va an ndvdual feeder. 21
J. Appl. Envron. Bol. Sc., 5(1)20-27, 2015 In ths work, the load pattern and prortzatons are assumed to be avalable ntally for each zone agent. To guarantee the satsfacton of power system operatng constrant durng the restoraton process the peak load over the restoraton perod s used from the load pattern to fnd the restoraton plan. Coordnaton between Agents The agents coordnate together n the proposed MAS usng the montored and ntated data to fnd the best restoraton plan. After solatng the fault area, the downstream zones are dsconnected from the grd and enter the outage stuaton. The feeder agent montors ths operatng stuaton and starts to negotate wth other neghborng feeder agents whch are connected to them va te swtch as backup feeder agents. The backup feeder agents communcate wth zone agents placed on the relatve feeder and ask them about the avalable capacty. A backup feeder agent wth a maxmum capacty s selected as a leader of decson makers to make some decsons and fnd the swtchng plan. The obtaned restoraton plan s gven to other agents va sendng message. In the proposed MAS, the agents coordnate ther performance usng a hybrd polcy consstng of expertbased system and mathematcal programmng method. On one hand, the polcy s desgned wth respect to the mportant aspects related to the operatonal practces of the restoraton problem. In other words, some expertbased rules are extracted usng these aspects to coordnate the agent performance. On the other hand, to guarantee the optmalty of the performance of the agents durng the restoraton plan, the decson makng process s taken nto account usng the mathematcal programmng technque. To ths end a new usage of ths technque s developed whch s matched wth the dstrbuted nature of the proposed MAS structure. To ths end, a restoraton problem s smply modeled as a lnear bnary optmzaton problem whch ts soluton denotes the optmal swtchng operaton whch should be mplemented by zone agents. The developed hybrd polcy s explaned n the followng of ths secton. Expert-Based Rules In the proposed MAS, consderng some practcal aspects of the restoraton problem guarantees the applcablty of the obtaned plan. These mportant factors are hghlghted as follows. In emergency condton, the avalable capacty of dstrbuton feeders s lmted. Therefore the hghest prorty loads should be restored at frst. Consderng ths fact, a weghtng coeffcent, namely ω, s defned for th zone to dentfy ts load prorty. The radal topology of the dstrbuton system should be mantaned. If t s possble the group restoraton plan s preferred, otherwse the restoraton process should be done usng as mnmum as possble swtchng operaton. Load transferrng durng the restoraton process should be done wthout any voltage and lne current volaton. Therefore, the nodal voltage and lne current lmtatons n each backup feeder should be consdered n determnng the avalable capacty of a feeder [17]. An outage zone can be transfer to a backup feeder f that feeder has enough avalable capacty. If there s no enough capacty to restore the outage areas entrely, the remanng out-of-servce areas should shed. Accordng to the mentoned ponts, the followng expert-based rules are extracted. Rule1. Each feeder agent calculates avalable capacty of the feeder wth respect to the mnmum avalable spar lne current capacty related to zones placed between the substaton node and the zone whch connects to the damaged feeder va a te swtch. The spar current capacty of feeder th, namely SCrC s calculated by a feeder agent as max ( ) SCrC = mn I I, l L (1) l l l In addton, maxmum allowable addtonal voltage drop n a feeder s an mportant factor n determnaton of that feeder capacty. Each feeder agent calculates the allowable addtonal voltage drop of feeder th, namely AAVoD, as ts avalable voltage capacty as follows. AAVoD = v 0.9 p u (2) mn.. Rule2. Each zone agent montors the sensor measurements and determnes two operatng factor for ts correspondng zone ncludng the voltage dfference and the current dfference at both sdes of a zone, namely ΔV and ΔI, respectvely. Rule3. Each zone agent attaches the exchanged nformaton of the next zones to ts zone nformaton and sends the result to the neghborng zone. Rule4. The receved nformaton s classfed as a table consstng of two columns and some rows. The frst column denotes the sender zone agent and the second column ncludes the nformaton such as ΔV and ΔI of a zone or mnmum nodal voltage and spar lne current capacty. The rows llustrate the connectvty of zones n the feeder. 22
Zendehdel and Asgharan, 2015 Rule5.Each zone should be suppled from an entrance node to mantan the radal topology of the dstrbuton network. Rule6. A feeder agent can nvestgate the possblty of reenergzng an addtonal zone usng (3) and (4). In other words, f (3) and (4) are satsfed the th feeder has enough capacty to reenergze the th outage zone. Ths rule enables feeder agent to evaluate the load flow constrants n a dstrbuted manner. V AAVoD (3) I SCrC (4) Rule7. Sheddng the least prorty loads can enable the feeder agents to restore remanng outage loads. Feeder agent gves the sheddng program to relatve zone agents after decson makng process. Lnear Bnary Programmng Technque In the presented MAS structure, the leader feeder agents wth maxmum loadng capacty s responsble to construct a well-defned mathematcal optmzaton model for fndng optmal combnatons of outage zones. To ths end, t utlzes the receved measurements from other zone agents ncludng the load consumpton of outage zones and avalable capacty of other backup feeders. The power consumpton data s sent by zone agents placed n outage areas as a classfed table whch s explaned n prevous secton. Moreover, the data related to the avalable capacty of other backup feeder s sent from feeder agents to the leader. These feeder agents receve a message from the damaged feeder and start to negotate wth zone agents to ask them about the spar current capacty and allowable addtonal voltage drop at the feeder. For more smplfcaton, the leader feeder agent develops a vrtual graph of the out-of-servces area wth the receved nformaton. Ths vrtual graph conssts of some vertces, branches and a capacty node. Outage zones whch are lsted n the classfed table construct the nodes, whle the swtchng devces placed between zones n outage areas bulds the branches of the graph. Moreover, the capacty node s an auxlary node whch s consdered as a source. Ths node can be connected to some zones n the graph wth respect of the connecton zone of te swtches n the man grd. To clarfy the mentoned explanatons, Fg. 2 shows a vrtual graph whch s developed for the out-of-servce areas n the dstrbuton system shown n Fg. 1. As can seen, the connectvty of vertces n the vrtual graph s determned based on the operatng stuaton of the swtchng devces. The capacty node connects to some nodes n the graph based on the status of the te swtch n the grd. These nodes correspond to some zones n outage areas whch are connected to backup feeders va te swtches. Accordng to the desgned decson makng polcy, the man grd s replaced by the constructed vrtual graph and the restoraton problem n the man dstrbuton system s replaced by a smple routng problem n the vrtual graph. Ths new routng problem s a lnear bnary optmzaton problem wth the obectve of fndng mnmum number of paths n the graph for connectng as greatest vertces as possble to the capacty node wthout formng a loop. These paths are selected such that some constrants, whch are developed wth respect to the restoraton problem constrants, are satsfed. Note that, the vrtual graph s smpler and shorter than the man grd. Moreover, the satsfacton of some constrants (.e. load flow constrants) s nvestgated n a dstrbuted manner by agents. Hence, the complexty of the routng problem s more less that the restoraton problem. Accordng to the soluton of the optmzaton problem, each obtaned path represents a restoraton path n the grd and the vertces whch are connected to the capacty node va that path denote the outage zones whch are reenergzed va a backup feeder. Consderng the branch whch the path s connected to the capacty node the backup feeder n the man grd s represented. To develop such a mathematcal model for routng problem, two categores of bnary varables are ntroduced for each zone. The frst one ndcates the possblty of restorng a zone by a specfc backup feeder, namely x, and the second category ncludes a bnary varable denotes the sheddng of the loads at a zone, namely y. Indeed, f an outage zone s determned to be restored by a backup feeder ts relatve varable "x" s set as 1 and ts relatve varable "y" s set as 0. In the followng, the proposed optmzaton model for restoraton problem whch s a routng problem n a smple graph s developed. The restoraton constrants and ts relatve operatonal practces are consdered. A. The obectve functon A restoraton plan commonly ams to energze maxmum loads usng mnmum swtchng operatons. Accordng to the routng problem ponts of vew, ths obectve s equal to fnd mnmum number of paths to connect maxmum vertces of the graph to the capacty node. Max ( ωx Wω y) (5),mn B. Constrants 1. Nodal voltage constrants The model consders the acceptable range n whch nodal voltage can vary wthout volatng any operatng constrant. Durng the restoraton process, load transferrng should not cause to volate the voltage constrant 23
J. Appl. Envron. Bol. Sc., 5(1)20-27, 2015 volaton at any node. In other words, loads can transfers to other backup feeder f t has enough voltage capacty. From the routng problem ponts, the vertces can connect to the capacty node va the th path f (6) s satsfed. ωx V AAVoD (6) 2. Loadng capablty of a backup feeder. The branch current can vary wthout volatng any operatng constrants wthn an acceptable range. Ths constrant s descred mathematcally from the routng problem ponts of vew as follows. ωx I SCrC (7) 3. Radal topology of the grd Regardng ths characterstc, each outage zone should be reenergzed only va one backup feeder. Accordng to the routng problem perspectve, each vertex should be connected to the capacty node va only one path. Ths fact s modeled mathematcally as x 1 (8) 4. Sequental nature of restoraton process In restoraton process, each te swtch agent reenergzes ts closest zone and then, other swtchng devces restore other zones sequentally. From the routng problem vews the vertces can be connected to the capacty node va a path from the nearest to the furthest node. Ths sequence s explaned mathematcally, consderng the topology of the vrtual topology of outage area, as follows. x x 1 0 (9) > 1 5. Restorng as many outage zones as possble Restoraton process ams to reenergze maxmum possble outage zones. Hence, the possblty of reenergzng zones placed n the out-of servce areas should be nvestgated entrely to determne the remanng outage zones whch should be shed because of lack of supply. x I + y I I (10) 6. An outage zone s restored or shed y + x 1 (11) Accordng to (8) and (11), t can be concluded that (11) can descrbe the constrants 3 and 6. The proposed model s an optmzaton model developed to model the restoraton problem n a smple manner. The dmenson of ths model s a more less than the NP-hard combnatoral optmzaton model whch s commonly used for restoraton problem. The ntroduced model s solved by any lnear bnary programmng method such as branch and bound [22]. Snce the mathematcal programmng technques gve the optmal obectve, ths method s used as a decson makng polcy n the proposed MAS by the feeder agents to obtan the optmal restoraton plan. Desgnng the vrtual graph and usng lmted nformaton gven by ntellgent sensors reduce the dmenson of the problem and dscover the dsadvantages of centralzed such technques. In addton, expert-based rules lead to dstrbute some computatonal actvtes among agents and reduce the complexty of the proposed model. Numercal Analyss The developed control method and the proposed mathematcal model for restoraton problem are tested on the IEEE 33-node radal dstrbuton system havng 33 buses and 32 branches. Ths test system s presented n [23]. Fg. 1 shows ths test system wth ts zones. Here, the dstrbuton system s smulated wth Matlab software as a plot power system and the proposed decson makng method s also modeled n ths software. In addton, the model s smulated wth Matlab usng ts Branch-and-Bound solver to fnd the optmal restoraton path. A permanent three phase balanced fault whch s assumed to have occurred at node7, zone4 s solated by operatng swtchng devces, namely SW8 and SW9. Accordng to the proposed algorthm feeder 1 s selected as a leader feeder agent whch s receved some nformaton from outage zone agents and classfes the data as a table. 24
Zendehdel and Asgharan, 2015 Fg 1: IEEE 33-bus test system wth ts zones Moreover, t receves the capacty of other backup feeder from feeder agents. Ths feeder agent constructs the vrtual graph, as shown n Fg 2, and develops the proposed optmzaton problem to fnd the optmal restoraton plan. Ths optmzaton plan f solved by branch and bound technque and ts optmal soluton whch denotes the connectvty stuaton of vertces to the capacty node va some paths. These paths are shown t Fg. 2 by dash lnes. In other words, ths soluton llustrates the restoraton paths and the outage zones whch are restored wth the obtaned plan. Fg 2: Vrtual graph Table I demonstrate the obtaned results gven from solvng the routng optmzaton problem. Table I: Soluton of the optmzaton problem Varable No. x 51 x 52 x 61 x 62 x 71 x 72 y 5 y 6 y 7 Obtaned result 1 0 0 0 0 1 0 1 0 As can be seen, the outage zones 5 s reenergzed va backup feeder 1 and outage zone 7 s reenergzed va backup feeder 2, whle the outage zone 6 should be shed because of the lack of spar current capacty of both avalable backup feeders. Table II llustrates the restoraton plan whch s sent to relatve zone agents to be mplemented. Table II: Restoraton plan Outage zone No. Backup feeder Restoraton status Zone 5 Feeder 1 Reenergzng Zone 6 - Sheddng Zone 7 Feeder 2 Reenergzng Accordng to the obtaned results, Table III represents the swtchng sequence. In ths table number "1" denotes the closed status and number "0" represents the opened status of a swtchng devce. 25
J. Appl. Envron. Bol. Sc., 5(1)20-27, 2015 Table III: Swtchng sequence Swtch No. SW8 SW9 SW11 SW13 SW14 SW15 SW16 SW17 SW18 Other swtches Status 0 0 0 0 0 1 0 0 1 1 The obtaned result demonstrates the applcablty of the proposed model for restoraton problem. Concluson In ths work, a novel model s proposed for restoraton problem s smart grds. Consderng bdrectonal communcaton nfrastructure and ntellgent electronc swtchng devces, the control programs can be mplemented more than prevous and the restoraton actvtes can be conducted automatcally. The ntellgent devces as agents negotate together and exchange local nformaton to make decson n a dstrbuted manner. In such an envronment, the centralzed decson makng technques mpose some dffcultes n applcaton on the system. Analyzng the huge amount of data n a computer center and solvng restoraton problem based on the common avalable NP-hard mathematcal model s not applcable n smart grds. Hence, a smple and lower dmenson model s proposed for restoraton problem ncorporatng the smart grd features and ntellgent ablty of electrcal devces. Unlke the commonly used restoraton model, ths model can be solved by lnear bnary programmng technques and acheve the optmal obectve. Furthermore, the proposed model consders the lack of supply n the grd durng the emergency condton and obtans the load sheddng program based on the load prortzaton. The presented restoraton algorthm s tested on IEEE standard 33-bus test system and the obtaned result demonstrates the applcablty of the method. Symbols AAVoD I l I L max l SCrC v mn W x ΔI ΔV ω The allowable addtonal voltage drop of feeder th The magntude of current flows the l th dstrbuton lne The maxmum allowable branch current magntude The set of lnes placed on the th feeder The spar current capacty of feeder th The lowest voltage magntude of buses n the th backup feeder It s a penalty coeffcent The bnary varable related to the th zone and the th backup feeder The current dfference at both sdes of the th zone The voltage dfference at both sdes of the th zone The prorty coeffcent for th zone REFERENCES [1] Tanyou, L. and X. Bngyn. "The self-healng technologes of smart dstrbuton grd". n Electrcty Dstrbuton (CICED), 2010 Chna Internatonal Conference on. pp. 1-6, 2010. [2] T. Nagata, S. Hatakeyama, M. Yasouka, and H. Sasak An effcent method for power dstrbuton system restoraton based on mathematcal programmng and operaton strategy, n Proceedngs of the Internatonal Conference of Power System Technology, 2000. [3] D. Pal, S. Kumar, B. Tudu, K.K. Mandal and N. Chakraborty Effcent and automatc reconfguraton and servce restoraton n radal dstrbuton system usng dfferental evoluton, Proceedngs of the Internatonal Conference on Fronters of Intellgent Computng: Theory and Applcatons (FICTA) Advances n Intellgent Systems and Computng, vol. 199, pp 365-372, 2013. [4] T. Ananthapadmanabha, R. Prakash, Mano Kumar Puar, A. Gangadhara and M. Gangadhara System reconfguraton and servce restoraton of prmary dstrbuton systems augmented by capactors usng a new level-wse approach, ournal of Electrcal and Electroncs Engneerng Research, vol. 3(3), pp. 42-51, March 2011. [5] R. Perez-Guerrero, G. Heydt, N. Jack, B. Keel, and A. Castelhano Optmal restoraton of dstrbuton systems usng dynamc programmng, IEEE Transactons on Power Delvery, vol. 23, no. 3, pp. 1589 1596, 2008. [6] A. Hussan, M.-S. Cho and S.-J. Lee A Novel Algorthm for Reducng Restoraton Tme n Smart Dstrbuton Systems Utlzng Reclosng Dead Tme, ournal of electrcal engneerng & technology, vol. 9, pp. 742-748, 2014. [7] W.P. Mathas-Neto Dstrbuton system restoraton n a DG envronment usng a heurstc constructve mult-start algorthm, Transmsson and Dstrbuton Conference and Exposton: Latn Amerca (T&D- LA), pp. 86-91, 2010 IEEE/PES. 26
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