Optimal Network Reconfiguration with Distributed Generation Using NSGA II Algorithm

Transcription

1 (IJARAI) Internatonal Journal of Advanced Research n Artfcal Intellgence, Optmal Network Reconfguraton wth Dstrbuted Generaton Usng NSGA II Algorthm Jasna Hvzefendć Faculty of Engneerng and Informaton Technologes Internatonal Burch Unversty Sarajevo, Bosna and Herzegovna Amr Hadžmehmedovć Unversty of Tuzla Tuzla, Bosna and Herzegovna Majda Tešanovć Faculty of Electrcal Engneerng Unversty of Tuzla Tuzla, Bosna and Herzegovna Abstract Ths paper presents a method to solve electrcal network reconfguraton problem n the presence of dstrbuted generaton (DG) wth an objectve of mnmzng real power loss and energy not suppled functon n dstrbuton system. A method based on NSGA II mult-objectve algorthm s used to smultaneously mnmze two objectve functons and to dentfy the optmal dstrbuton network topology. The constrants of voltage and branch current carryng capacty are ncluded n the evaluaton of the objectve functon. The method has been tested on radal electrcal dstrbuton network wth 213 nodes, 248 lnes and 72 swtches. Numercal results are presented to demonstrate the performance and effectveness of the proposed methodology. Keywords radal dstrbuton network; dstrbuted generaton; genetc algorthms; NSGA II; loss reducton I. INTRODUCTION Newly formed market condtons artculate the need for adjusted approach n managng dstrbuton network n order to meet not only the requrements mposed by techncal condtons of the system but also the requrements mposed by consumers and network regulators. Sgnfcant changes n dstrbuton system have been caused by nstallng dstrbuton generaton unts whch have consderable mpact on system voltage profle and power losses, both beng mportant quanttes n the process of plannng and reconfguraton of electrcal network. DGs are grd-connected or stand-alone electrc generaton unts located wthn the electrc dstrbuton system at or near the end user. The ntegraton of DGs n dstrbuton system would lead to mprovng the voltage profle, relablty mprovement such as servce restoraton and unnterruptble power supply and ncrease n energy effcency. The dstrbuton feeder reconfguraton (DFR) s one of the most sgnfcant control schemes n the dstrbuton networks whch can be affected by the nterconnecton of DGs [1]. Generally, the DFR s defned as alterng the topologcal structure of dstrbuton feeders by changng the open/closed status of automatc and te swtches or protectve devces located n strategc places n dstrbuton system. By changng the statuses of the sectonalzng and te swtches, the confguraton of dstrbuton system s vared, and loads are transferred among the feeders whle the radal confguraton format of electrcal supply s stll mantaned. Network reconfguraton s a very effectve and effcent way to ensure more even load dstrbuton of network s elements, mprove system relablty and voltage profle, and to reduce power losses. All modes are subject to reconfguraton: normal, crtcal and falure. Provded that all varables are wthn acceptable lmts, network reconfguraton wll acheve optmal workng condtons n normal mode. Takng nto consderaton a large number of swtches n dstrbuton network, whose on/off swtchng affects the network topology, reconfguraton problem can be defned as a complex combnatoral, non-dfferentable, and constraned mult-objectve optmzaton problem. Radal network condtons, explct voltage constrants n all node, lne capactes, etc. are vewed as some of the constrants that have to be taken nto consderaton. In recent years, dfferent methods and approaches have been used to solve the problem of dstrbuton system reconfguraton wth dstrbuton generators nstalled. The lterature related to ths problem manly refers to applcaton of heurstc algorthms and artfcal ntellgence-based algorthms such as Genetc algorthms, Fuzzy logc, Partcle swarm optmzaton, Tabu search, etc. [2-7]. Most cases address reducng power losses and load balancng, takng nto account the effect of generators dstrbuted n the network, whle very lttle attenton s pad to system relablty. However, specal attenton should been pad to the ssue of relablty of power supply, n order to ncrease economc effcency of dstrbuton companes [14]. Network reconfguraton process can be used as one possblty to mprove network relablty ndcators. Furthermore, relablty mprovement by DGs s possble when ntended slandng operaton s allowed [8]. In paper [15] NSGA II (Non-Domnated Genetc Algorthm II) s appled to the plannng of dstrbuton electrcal network problem. Ths paper s focused on the applcaton of NSGA II on resolvng the problem of reconfguraton of dstrbuton network wth dstrbuted generaton. The effect of dstrbuted generaton on voltage n the network, takng nto account two objectve functons: power losses and relablty functon s presented. Dependng on characterstcs of the power dstrbuton networks (network parameters, characterstcs of power lnes, falure rates, types of consumers, etc) smultaneous optmzaton of these 6 P a g e

2 (IJARAI) Internatonal Journal of Advanced Research n Artfcal Intellgence, functons can be dsagreeng, that s the optmum topology for one objectve can be very dfferent by the optmum obtaned wth the other functon. Snce the proposed method optmzes two objectve functons smultaneously, the problem s defned as mult-objectve problem takng nto account the defned system constrants. The effectveness of the methodology s demonstrated on real dstrbuton network consstng of 213- buses showng ts potental of applcablty to the large dstrbuton systems. The problem formulaton s dscussed n detal n secton II. The network reconfguraton algorthm usng a multobjectve NSGA II s descrbed n secton III. The smulaton results n terms of power loss and energy not suppled are dscussed n Secton IV and fnally the last secton presents the concluson of the study. II. PROBLEM FORMULATION The objectve of the proposed soluton model for reconfguraton of dstrbuton network problem s to mnmze two functons as follows: power losses functon and relablty functon presented by Energy not suppled ndex (ENS). The optmal results of the defned functons do not lead to the same optmal network topology what creates tradeoff between relablty and power losses functon. Electrcal power losses are one of the most mportant factors whch pont to busness cost-effectveness and qualty of dstrbuton. Energy losses n electrcal dstrbuton network n the amount of 1% cause the ncrease n company s busness costs of up to 2% to supply energy to cover the losses [9]. Therefore, the reducton of power losses s one of the most mportant ssues n dstrbuton system operaton. In addton to the power losses functon, relablty functon s also defned n the paper, wth the objectve to ncrease relablty n consumers supply by mnmzng expected energy not suppled due to power nterruptons. The essental attrbutes of nterruptons n the power supply of the customers are the frequency and duraton. Whle duraton s predomnantly nfluenced by the dstrbuton system structure (radal, meshed, weak meshed) and the exstng automatons, the frequency s manly nfluenced by the adopted operatonal confguraton; t can be mnmzed by the sutable choce of the effectve confguraton [7]. Snce there s no 100% relable system, t s n the best nterest of both supplers and consumers to mnmze power supply nterruptons. Ths functon wll be presented through Energy not Suppled functon (ENS). These two objectves can be met by dentfyng optmal network topology. Effcent soluton of the descrbed problem requres the choce of optmal topology of radal network wthn the set of possble solutons. A. MathematcalFormulaton of Problem The purpose of dstrbuton network reconfguraton s to fnd optmal radal operatng structure that mnmzes two functons: the system power losses and ENS functon wthn the operatng constrants. Accorndg to the lterature [2], [14] thus the problem can be formulated as follows: n mn P ( I D I ) R (1) loss 1 where D = 1 f lne, otherwse s equal to 0. N V 1 DI mn f P r (2) ens where P loss s total real power losses functon, f ens s the ENS functon, I current n the branch ; R resstance n the branch ; α s set of branches connected to the dstrbuton generators node m, P real power flow through branch ; λ falure rate of branch (number of falure per year and per klometer of branch ); r falure duraton of branch ; N v number of branches. The DG produces actve current I DI, and for a radal network t changes only the actve component of current of branch set α. Subject to the system constrants: - I I max branch capacty, V V V - mn j max - the current n each branch cannot exceed the - voltage constrant. The voltage n each load buses n the system has to be wthn the defned lmts. The mnmum voltage s 0.95 and maxmum voltage s 1.05 (±5%). n - PS Pg, P Ploss - power balance constrant 1 n 1 - n 1 - topologcal constrant. Electrcal dstrbuton systems are operated n radal confguraton. Generator operaton constrants: DG unts are only allowed to operate wthn the acceptable mn lmt where P and P are the lower and upper bound of DG output and P mn max g max P P. The search space for ths problem s the set of all possble network confguratons. In order to check the defned constrants, voltage magntude and angle at each bus n the system have to be known at any tme. When the voltage magntude at any bus n the system s not wthn the defned lmts, network confguraton cannot be consdered as a possble soluton. Snce ths nformaton s ncluded n the state varable x, t can be presented as follows: x = [q 2, q 3,,q n, V, 2 V,..., 3 V n [ T (3) and state space as s IR 6(n-1), where a b c T a b c V, V V and T,, V, are voltage magntude and angels respectvely for load buses, and the bus 1 s substaton P a g e

3 (IJARAI) Internatonal Journal of Advanced Research n Artfcal Intellgence, For three-phase dstrbuton network wth n buses, bus 1 presents substaton and buses 2, 3,...n, are load buses. Equaton (3) can be solved by power flow calculaton solvng the system of (6n-6) non-lnear algebrac equatons. To calculate the second objectve functon, ENS ndex due to nterrupton n supply, t s necessary to consder two elements: falure rate and the length of nterrupton n power supply for each load pont. The latter s conssted of two components: tme necessary to locate falure and the tme necessary to repar t. Automatc sectonalzers and swtches separate the part of the network where the falure occurred, reducng the rsk for other consumers n the network. The tme needed to repar the falure s usually the tme needed to solate the falure, to connect the affected consumers to reserve power supply (f possble) and to repar the fault tself [10]. In order to calculate ths functon, load flow studes should be performed to calculate not-dstrbuted energy n all consumer nodes wthout supply, whch are located under the fault n the network. III. OPTIMIZATION METHOD FOR MULTI-OBJECTIVE RECONFIGURATION NETWORK The development of heurstc algorthms and computer performances have contrbuted towards solvng the problem of mult-objectve optmzaton. Whle solvng mult-objectve optmzaton problems, t s necessary to pay attenton to convergence to optmal set of solutons (Pareto set) and mantan dversty of solutons wthn the set of current solutons [11]. Suggested methodology for solvng the defned mult-objectve optmzaton problem s based on multobjectve Non-Domnated Sortng Genetc Algorthm II. (NSGA II). Genetc algorthms use populaton of solutons n every optmzaton path wthn optmzaton process. The objectve s to come as close as possble to the true Pareto-front and smultaneously gan as many solutons as possble. Ths ensures that the decson-maker wll have a wder choce of qualty solutons wth a better overvew of all possble optmal topologes of a dstrbuton network [11]. A. NSGA II Algorthm Mult-objectve evolutonary algorthms are sutable for mult-objectve optmzaton due to ther ablty to handle complex problems, nvolvng features such as dscontnutes, multmodalty, dsjont feasble spaces and nose functons evaluaton [12]. NSGA II s a mult-objectve genetc algorthm developed by Deb, 2003 [13]. Basc advantage of NSGA II over other mult-objectve genetc algorthms s reflected n possbltes for dversty preservaton of populaton, whch further enables unform dstrbuton of solutons wthn Pareto front. The crowdng dstance approach s ntroduced nto NSGA II as the ftness measure to make comparson of solutons n the same Front. Ths approach estmates the densty of solutons surroundng a partcular soluton by calculatng the average dstance of two ponts on ether sde of the observed soluton for all objectve functons defned for partcular problem. The fast non-domnated sort strategy s used to evaluate soluton domnance and classfy the soluton nto Pareto fronts that corresponds to the cluster wth the same soluton domnance. Furthermore, NSGA II uses elte strategy that sgnfcantly helps n speedng up the performance of the genetc algorthm [13]. B. Proposed Methodology Algorthm starts wth randomly selected radal functonal soluton that s typcal for electrcal dstrbuton network, as a bass for a frst generaton of trade-offs n the part of a genetc algorthm code. By applyng NSGA II algorthm new potental solutons of the network are generated. The bnary alphabet has been used to mplement the optmzaton model, n whch every bte of chromosome represents the status of swtches (open/closed). Every bte can have value of 0 or 1, whch dentfes the status of every electrc lne, 0-open, 1-closed. In the reconfguraton network problems, only a certan number of lnes have a changeable bt n chromosome, and therefore only those lnes are subject to genetc operators, crossover and mutaton, whle other lnes have a fxed value n chromosome (always have the value of 1 n operaton). If newly created solutons meet topologcal constrants (radal condtons), evaluaton of the objectve functons s carred out,.e. power flow and calculaton of objectve functons are performed. Power flow calculaton s done n MATLAB. For that purpose, a part of the code for power flow calculaton based on Newton-Raphson method s modfed for the need of objectve functons evaluaton, transfer of varables, storage of dvergng solutons and vsualzaton. Based on the power flow results, convergence of specfc network confguraton s verfed, as well as other constrants whch refer to the capactes of lnes, power statons and dstrbuted generatons. Solutons whch do not satsfy defned constrants are elmnated or penalzed, dependng on convergence of power flow calculaton. For other solutons, whch meet defned lmts, evaluaton of objectve functon s done. The procedure s repeated untl stoppng crtera are met. The crtera for stoppng calculaton can be based on a maxmum number of generatons, mnmum of evaluated solutons, tme lmts to smulaton, average change n soluton dstrbuton, etc. Suggested model uses the concept of Pareto domnaton n the evaluaton of the objectve functons. Input data to descrbe mult-objectve optmzaton problem are system parameters and constrants, lnes, the loads, relablty parameters, falure rates, and the repar tmes. MATLAB functons for genetc algorthms whch are used for calculaton are modfed for specfc dscrete functon for calculatng power flow, power losses and testng system s constrants for network solutons. CPU tme spent for calculatng and dentfyng the set of possble solutons depends on the tme necessary for the objectve functons evaluaton, tme for verfcaton of defned constrants by power flow calculaton and actve losses. To speed up the calculaton, parallel processng of genetc algorthm, n the part of evaluaton of the objectve functon and constrants, s done. 8 P a g e

4 (IJARAI) Internatonal Journal of Advanced Research n Artfcal Intellgence, Fg. 1. Part of a dstrbuton network wth dstrbuted generaton Takng nto consderaton that evaluaton of one ndvdual (soluton) s completely ndependent of some other ndvdual, ndependent of some other ndvdual, evaluaton of the entre populaton s dstrbuted to 8 avalable processors, whch sgnfcantly speeds up the calculaton process. The results of the descrbed algorthm s a Pareto front of possble optmal topologcal solutons for the electrcal dstrbuton network IV. CASE STUDY AND NUMERICAL RESULTS The test system for the case study s 10 KV radal dstrbuton network wth dstrbuted generaton (Fg. 1.) wth 213 buses, 248 lnes and 72 swtches. Dstrbuted generaton s connected to the node 213 and generates the actve power of 5 MW. It s assumed that DG does not generate reactve power to the network. All smulatons are done on Intel Xeon E5-2699V3 wth 32 GB RAM, that enables parallel data processng on 18 processor unts. In ntal network topology, presented n Fg. 1., swtches 2 3, 5 6, 9, 13, 15, 22, 25, 28 29, 32 33, 36, 38 46, 49 51, 53 55, 57 59, 61, and 72 are closed, whle 1, 4, 7-8, 10 12, 14, 16 21, 23 24, 26 27, 30 31, 34 35, 37, 47 48, 52, 56, 60, swtches are open. For ntal solutons, total power losses are KW and ENS due to nterrupton n supply s KWh. NSGA II parameters In the consderaton of optmal parameters 60 smulatons were run wth dfferent values. Only the best performng parameters are presented n ths paper and they are: ntal populaton sze s 150, crossover probablty pc s 0.8, maxmum number of generaton s 200 and Pareto fracton s Tournament selecton s used, as well as two-pont crossover. The stoppng crteron of the algorthm s an mposed maxmum number of generatons or lmt of the average change n dstrbuton of solutons wthn the Pareto set (less than 10). Certan number of smulatons s done by usng adaptve mutaton whch search the larger soluton space n the smaller number of generaton (n ths case the number of generaton was 114), but evaluaton tme s longer. After the multple ndependent runs of algorthm, t was concluded that the best results are acheved wth fxed mutaton probablty of Furthermore, t was observed that ftness values sgnfcantly mprove n early generatons, when the solutons are farther from optmal values. The best ftness values slowly mprove n later generatons, whose populaton s closer to the optmal solutons. Number of generatons for acheved solutons was n the range from generatons, for all tests wth fxed crossover and mutaton factor. 9 P a g e

5 (IJARAI) Internatonal Journal of Advanced Research n Artfcal Intellgence, A. Result Analyss Applcaton of the descrbed methodology to dentfy optmal network confguraton based on NSGA II algorthm resulted n a set of possble solutons, out of whch 9 Pareto optmal solutons are presented n Fg. 2. Pareto set of optmal solutons s acheved for 138 generatons, whle total number of acheved possble solutons s 49. Total algorthm executon tme on 18 processor unts was 15 mnutes and 36 seconds. Table 1. shows values of objectve functons for solutons from Pareto optmal set, as well as the on/off change of swtches. Fg. 2. Pareto optmal solutons for network reconfguraton wth dstrbuted generaton TABLE I. VALUES OF OBJECTIVE FUNCTION FOR PARETO OPTIMAL SOLUTIONS FROM FIG. 2 No. Swtch on Swtch off Losses NS KW Wh Consderng the results shown n Table 1, the best soluton for losses functon s soluton 1. However, ths s the worst soluton for ENS functon. It s evdent that changes n the value for ENS functon are smaller than for losses functon. Therefore, based on practcal network topology mplementaton, functonal and economcal beneft the best compromse soluton can be soluton 3, gven the evdent small changes n ENS functon between solutons 3, 4 and 5, whle the dfference n losses functon s somewhat bgger. Soluton 3 has power losses of KW, whle ENS s KWh. The acheved near-optmal solutons show trats of each soluton from the Pareto front (the fact that not a sngle ndvdual soluton from Pareto front can be mproved for one functon wthout affectng the other n the opposte manner). Ths trat does not apply for all permssble searched solutons. The character of the acheved searched and near-optmal solutons depends on all set values, where dfferent ntenstes and length of fault on lnes are of specal mportance. If ntensty and fault length at all lnes are equal, the varablty of soluton would be consderably lower, wth a unque optmum for both functons. It s obvous that many searched solutons can be smultaneously mproved from the aspect of both functons whch are optmzed; subsequently, the consdered objectves are not necessarly n conflct wth each other. Ths does not provde values whch are approxmately optmal for ether of the objectve functons. Objectve functon assessng relablty, nterruptons n supply, s ncdental. Therefore, when descendng sort order strategy s appled, the probablty for local mnmum s hgher for relablty crteron that for power losses functon. Optmal mnmzaton of losses wll be acheved when the voltage n lnes s closer to the maxmum allowed value U max. Snce calculatons were done wth assumed constant load values (values of peak loads), mantanng voltage at lnes as closer as possble to U max ensures consderably less values for losses n the network. If voltage lmtaton s U max = 1.20, losses values for soluton 3 would be KW. Power losses for lne for ntal soluton are 0.73 KW, and for the dentfed optmal soluton t s 0.49 KW (soluton 3). Values for losses at the same lne wthout dstrbuted generaton connected s 0.58 KW wth the same swtch state. Snce dstrbuted generaton s of small capacty n relaton to the strength of dstrbutve network nto whch t s connected, there s a reducton n the losses n the lne onto whch t s connected. Impact on voltage On Fg. 3. s shown voltage profle of bus system for soluton 3 from Table 1. It s clear that the voltage s wthn the allowed lmts. On Fg. 4. s shown the change n voltage n network nodes when dstrbuted generaton s not connected nto the network (voltage shown n blue) and when the dstrbuted generaton s connected (voltage shown n red). The shapes of voltage profles are almost the same n both cases, except for mnor changes n the voltage strength at end lnes, whch s a consequence of connected dstrbuted generaton. Lnes wth dstrbutve generaton connected have an ncrease n voltage from p.u. to p.u. after nstallng the dstrbuted generaton nto the network. Fg. 3. Voltage profle for soluton P a g e

6 (IJARAI) Internatonal Journal of Advanced Research n Artfcal Intellgence, Fg. 4. Voltage profle wth dstrbuted generaton connected and dsconnected V. CONCLUSION Reconfguraton represents one of the most mportant measures whch can mprove performance n the operaton of a dstrbuton system. The paper shows applcaton of multobjectve genetc algorthm NSGA II on resolvng the problem of reconfguraton of dstrbutve network wth dstrbuted generaton, n order to dentfy optmal topologcal soluton takng nto account the set lmtatons. Algorthm s tested on a part of a network wth 213 nodes, 248 lnes and 72 swtches. Mult-objectve problem s formulated n order to decrease overall network losses and mprove system relablty through mnmzng ENS. The acheved results show the effcency of the proposed methodology. Identfcaton of near-optmal network confguraton s presented. It s evdent n decreasng overall network losses and ENS ndex compared to network ntal state. The paper also shows the effect of dstrbuted generaton on voltage profle n dstrbutve network. The results show that network reconfguraton n the presence of DG mprove the voltage profle n the network. It s obvous that applcaton of the proposed methodology enables a more complex approach to mprovng the operatonal condtons n dstrbutve networks, compared to tradtonal methods. The methodology proposed s also a useful tool for quck dentfcaton of optmal network confguraton n case of faults, and t can also be benefcal for plannng and upgradng exstng network. So, both the NSGA II effcency n fndng solutons and the ncreased effcency of the the dstrbuton network after usng NSGA II are presented n the paper. The acheved results for both objectve functons can be represented n fnancal terms as well, and these are economc ndcators to mprove effcency n managng a dstrbutve network. REFERENCES [1] W. M. Dahalan, H. Mokhls, Network Reconfguraton for Loss Reducton wth Dstrbuted Generatons Usng PSO, IEEE Internatonal Conference on Power and Energy (PECon), Malaysa, pp G, December [2] N. Rugthacharoencheep, S. Srsumranukul, Optmal Feeder Reconfguraton wth Dstrbuted Generaton n Three-Phase Dstrbuton System by Fuzzy Multobjectve and Tabu Search, Energy Technology and Management, 1 st ed, Tauseef Azed, ISBN , October, 2011 under CC BY-NC-SA 3.0 lcense [3] M. N. M. Nasr, N. M. Shahrn, M. F. Sulama, M. H. Jal, M. F. Baharoma, Optmum Network Reconfguraton and DGs Szng Wth Allocaton Smultaneously by Usng Partcle Swarm Optmzaton (PSO), Internatonal Journal of Engneerng and Technology (IJET), Vol 6, No 2, pp , Apr-May [4] T.P. Sa Sree, N.P. Chandra Rao, Optmal Network Reconfguraton and Loss Mnmzaton Usng Harmony Search Algorthm In The Presence Of Dstrbuted Generaton, Internatonal Journal of Electrcal and Electroncs Research, Vol. 2, Issue 3, pp ,July - September [5] Y. Shu-jun, Y.Zh, W.Yan, Y. Yu-xn, S.Xao-yan, Dstrbuton network reconfguraton wth dstrbuted power based on genetc algorthm, 4th Internatonal Conference on Electrc Utlty Deregulaton and Restructurng and Power Technologes (DRPT),,pp , 6-9 July [6] A.Hajzadeh, E. Hajzadeh, PSO-Based Plannng of Dstrbuton Systems wth Dstrbuted Generators, World Academy of Scence, Engneerng and Technology 45, pp , [7] B. Tomoagă, M. Chndrş, A. Sumper, A. Sudra-Andreu, R. Vllafafla-Robles, Pareto Optmal Reconfguraton of Power Dstrbuton Systems Usng a Genetc Algorthm Based on NSGA-II, Energes 2013, 6, pp , 2013., [8] S.M. Cho, H.S. Shn, J.H. Park, J.C. Km, Dstrbuton System Reconfguraton Consderng Customer and DG Relablty Cost, Journal of Electrcal Engneerng & Technology Vol. 7, No. 4, pp. 486~492, [9] K.Šmleša, Z.Vrančć, A.Matkovć, F.Lulć, G.Juretć, Gubtak elektrčne energje u dstrbucjskoj elektroenergetskoj mrež, CIRED hrvatsk ogranak, 1. savjetovanje, S01-2, Šbenk, Croata [10] A.Hajzadeh, E.Hajzadeh : PSO-based Plannng of Dstrbuton Systems wth Dstrbuted Generators, World Academy of Scence, Engneerng and Technology, No. 45, pp , [11] F.Rvas-Davalos, E.Moreno-Goyta, G.Guterrez-Alacaraz, J.Tovar- Hernandez, Evolutonary Mult-Objectve Optmzaton n Power Systems: State-of-the-Art, Proceedngs on IEEE PowerTech Conference, pp , Lausanne, Swtzerland, [12] C.M.Fonseca, P.J.Flemng, An overvew of evolutonary algorthms n multobjectve optmzaton, Evolutonary Computaton, pp.1-16, 3(1), Sprng [13] K.Deb, A.Pratpat, S.Agarwal, T.Meyarvan, A Fast and Eltst Mult- Objectve Genetc Algorthm: NSGA-II, IEEE Transacton on Evolutonary Computaton, Vol. 6, No2, pp , [14] I.J.Ramrez-Rosado, J.L.Bernal-Agustn, Relablty and Costs Optmzaton for Dstrbuton Networks Expanson Usng an Evolutonary Algorthm, IEEE Power Engneerng Revew, Vol. 21, pp , 2001 [15] Muhammad Ahmad, Ashkan Yousef, Alreza Soroud, Mehd Ehsan, Mult Objectve Dstrbuted Generaton Plannng Usng NSGA-II, 13th Internatonal Power Electroncs and Moton Control Conference EPE-PEMC, pp , P a g e