Allocation of optimal distributed generation using GA for minimum system losses in radial distribution networks

Transcription

1 MultCraft Internatonal Journal of Engneerng, Scence and Technology Vol., No. 3, 010, pp INTERNATIONA JOURNA OF ENGINEERING, SCIENCE AND TECHNOOGY MultCraft mted. All rghts reserved Allocaton of optmal dstrbuted generaton usng GA for mnmum system losses n radal dstrbuton networks T. N. Shukla 1*, S.. Sngh, K. B. Nak 3 *1 Department of Electrcal Engneerng, Kamla Nehru Insttute of Technology, Sultanpur, (U..), INDIA Department of Electrcal Engneerng, Insttute of Technology, Banaras Hndu Unversty, Varanas (U..), INDIA 3 Drector, College of Engneerng Scence and Technology, ucknow (U..), INDIA * Correspondng Author: e-mal: tns_shukla55@yahoo.com, tns.shukla@gmal.com,tel , Mob Abstract The dstrbuted generaton (DG) s one of the vable optons for mtgaton of problems of load growth, overloadng of lnes, qualty of supply and relablty n tern extendng equpment mantenance ntervals and to reduce lne losses. However, the lne loss reducton s the obvous parameter easly expressble n terms of system parameters. Therefore, ths paper ams to mnmze actve power loss by placng DG strategcally n a radal dstrbuton system. The problem s formulated as an optmzaton problem and soluton s obtaned usng genetc algorthm (GA). The strategc locatons are decded on the bass of loss senstvty to actve power necton at varous nodes. Ths approach helps n reducng the computatonal efforts of selectng approprate locaton(s). The performance of the method s tested on 33-bus test system and comparson of the results wth a reported method reveals that the proposed method yelds superor results. In addton, long term economc beneft of optmal DG placement s also demonstrated. Keywords: dstrbuted generaton, lne loss reducton, optmal locaton, radal dstrbuton networks. 1. Introducton Earler the dstrbuton networks had been desgned to convey electrcal energy from hgh voltage transmsson networks, whereby the maorty of electrcal generaton plants were connected, to the customers (Jenkns, 1996). By the addton of embedded generaton plants to dstrbuton networks, voltage profle of the network s mproved and energy demand decreases from the utlty network. Also, passve dstrbuton networks are transformed nto actve networks after embedded unts have been added to them (Iumba et al., 1999; Mlanovc and Davd, 00). Tradtonally load growth s forecasted by dstrbuton companes untl a predetermned amount s reached, whereby a new capacty must be added to the network. Ths new capacty s usually the addton of new substatons or expandng exstng substatons capactes and ther assocated new feeders or both. However, the flexblty, technologes, techncal & monetary benefts and concepts of DG plannng s challengng ths state of matter and ganng credblty as a soluton to the dstrbuton plannng problems wth the prohbtvely hgh cost of power curtalment n the changng regulatory and economc scenaros and enhancng DG as an attractve dstrbuton plannng opton that avods causng degradaton of power qualty, relablty and control of the utlty systems (Dugan et al.,001 and Racklffe, 000). Qunta et al. (1993) and Khator and eung (1997) reported that the dstrbuton system plannng problem s to dentfy a combnaton of expanson proects for the least cost network nvestment that satsfes load growth requrements wthout volatng any system and operatonal constrants. The DG benefts (Daly and Morsson, 001 and Chradega and Ramkumar,004) are numerous and the reasons (Jenksn,000) for mplementng DGs are an energy effcency or ratonal use of energy, deregulaton or competton polcy, dversfcaton of energy sources, avalablty of modular generatng plant, ease of fndng stes for smaller generators, shorter constructon tme and lower captal costs of smaller plants and proxmty of the generaton plant to heavy loads, whch reduces transmsson costs. Dstrbuted generaton (DG) can offer an alternatve plannng approach to utltes to satsfy demand growth and dstrbuton network securty, plannng and management ssues. As DG may provde many benefts for dstrbuton network operators that can choose where to place t, as well as controllng ts operatng pattern through peak load

2 95 Shukla et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 010, pp operaton, the recognton of DG deferment benefts [by ccolo and Sano (009)] may nfluence the optmal connecton of new generaton wthn exstng networks. Brown et al. (1997) suggested that proper stng of DG may defer T&D expanson. Also t s accepted by many countres n Kyoto rotocol (1997) that the reducton n gaseous emssons (manly CO ) offered by DGs s maor legal drver for DG mplementaton. DG are ncreasngly becomng an attractve alternatve to network renforcement and expanson for ther small sze, low nvestment cost, modularty and ablty to explot renewable energy sources and due to ther hgh effcency. Numerous studes used dfferent approaches to evaluate the benefts from DGs to a network n the form of loss reducton and loadng level reducton. In the optmzaton process, Díaz-Dorado et al. (00) proposed to solve MV networks wth rng, clasp, and nter-connectve confguratons, consderng nvestment and losses costs takng nto account the constrants of conductor capactes and voltage drop. The paper of Mardaneh and Gharehpetan (004) deals wth the task of fndng the optmal stng and szng of dstrbuted generaton (DG) unts for a gven dstrbuton network to mnmze the cost of actve and reactve power generaton. Cell et al (005) proposed a mult-obectve formulaton based on the applcaton of GA for the stng and szng of DG resources nto exstng dstrbuton networks. They consdered the power loss cost and the cost of servce nterruptons (.e. number and duraton) as the master obectve functon. GA based optmzaton technque (whch can gve near optmal results), sutable for multobectve problems lke DG allocaton wth optmal power flow (OF) calculatons has been used by Slvestr et al. (1999). A hybrd GA-OF approach was proposed by Harrson et al. (008) for fndng optmal locaton for connectng a predefned numbers of DGs n a dstrbuton network. Jabr and al (009) presented an ordnal optmzaton (OO) method for specfyng the locatons and capactes of dstrbuted generaton (DG) such that a trade-off between loss mnmzaton and DG capacty maxmzaton s acheved. Acharya et al (006) suggested a heurstc method to select approprate locaton and optmal value of DG capacty for mnmum real power losses of the system by calculatng DG sze at dfferent buses. Though the method s effectve n selectng locaton, t requres more computatonal effort. The heurstc method used to calculate DG sze s based on approxmate loss formula and t may lead to an napproprate soluton. Sze and locaton of DG are crucal factors n the applcaton of DG for ts maxmum benefts. In the present work, GA based technque has been proposed and an attempt has been made to determne optmal DG sze for mnmzaton of real power losses n a radal dstrbuton network and ts monetary benefts. The number of canddate locatons s decded from the results of loss senstvty obtaned by nectng real power nto the network.. roblem Formulaton The nstallaton of DG unts at non-optmal places may not result as benefcal as t could have been otherwse. Snce the mpacts of dstrbuted generaton on system performance depend on system operatng condtons and the characterstcs of the dstrbuted generaton, t s necessary to use some solutons n plannng and operaton to attan the best performance. In large dstrbuton systems to select best place(s) for nstallaton of optmal sze DG unts s a complex combnatoral optmzaton problem..1. Selecton of ocaton In order to reduce the efforts to select approprate nodes for placement of dstrbuted generaton devces a pror, senstveness of nodes towards the change n actve power loss wth respect to change n actve power necton at varous nodes are dentfed. The loss senstvty factors at dfferent buses have been evaluated to select approprate nodes for DG plannng by usng load flow program sutable to radal networks suggested by Afsar et al. (00). These senstvty factors reflect how the feeder power losses change f more real power s nected at a partcular node and t also allows obtanng the canddate nodes to locate DG. oss senstvty factors are evaluated for the base case frst to decde the frst approprate locaton. In order to select next canddate locaton(s), successve senstvty analyss (computaton of loss senstvty of varous buses takng nto account the prevously selected locaton(s) at whch DG could be placed) has been used. Ths process s repeated tll optmum number of locatons s ascertaned. The optmal number of locatons s that number of buses whch gves maxmum benefts (savng) for optmal sze DGs placed at selected locatons. The expresson for lne losses descrbe by Elgard (1971) has been used for the purpose. The change n actve power loss of the system due to change n actve power necton at a node s expressed as n oss = ( α β Q ) (1) = 1.. oss Mnmzaton Among the many benefts of dstrbuted generaton, reducton n system lne losses s one of them. Nevertheless, reactve power loss s obvously not less mportant. Ths s due to the fact that reactve power flow n the system needs to be mantaned at a certan amount for suffcent voltage level. Consequently, reactve power makes t possble to transfer real power through transmsson and dstrbuton lnes to customers. Normally, the real power loss draws more attenton for the utltes, as t reduces the effcency of transmttng energy to customers. System loss reducton by strategcally placed DG along the network feeder, can be very useful f the decson maker s commtted to reduce losses and to mprove network performance (e.g. on the level of losses and/or relablty) mantanng nvestments to a reasonable low level. Ths feature may be very useful n case of revenue recovered

3 96 Shukla et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 010, pp by dstrbuton company (DISCO) whch s not only based on the asset value but also on network performance. So n the present work, real power necton at selected locaton(s) through DGs s consdered to acheve the obectve. An establshed loss formula; Elgard (1971) based on loss coeffcents α and β s represented n Eq. () and has been used for the calculaton of real power loss n the present work. n n oss = = 1 = 1 α ( + Q Q ) + β ( Q Q ) The obectve functon s to mnmze the actve power loss usng Equaton (10) and formulated as to Mnmze Subect to N oss = oss n n G = 1 = 1 mn V V k = 1 + k ( ) max oss V (5) I I (6) scheduled.3. Demand Curve Energy losses are usually accounted per year. Snce constant loadng condton of a dstrbuton system s not realstc and varaton of load demand can also not be predcted, load duraton curve can be constructed usng the demand curve data and can be approxmated n dscrete levels. Day to day demand curves vary as per the demand of loads. Seasonal varatons, socal commoton, economc and envronmental aspects also dctate the changes n demand curve. Snce the fnal soluton depends on proper choce of demand curve, a careful analyss s requred. In order to acheve the obectve, a steady demand curve s consdered n ths work wheren annual demand curve s approxmated by 360 daly demand varaton curves and s used to compute energy loss. The pecewse lnear load duraton curve s assumed to nclude the effect of varyng loads () and s dvded nto three load levels as average (1), base () and peak load (3) condtons of 6.5%, 100% and 15% of scheduled system loads of duraton 1000 hrs, 6760 hrs and 1000 hrs respectvely as shown n Fgure 1and the these descrpton wth the base case loss and the lowest voltage are also shown n Table 1. All the ndvdual buses demand curves are consdered dentcal to the demand curve taken at substaton. Ths assumpton s really necessary because ndvdual demand curves for each bus are rarely avalable. In addton, ths assumpton does not nterfere n the result sgnfcantly, especally when the feeder supples many loads and the nfluence area s homogenous lke a resdental, commercal, rural or ndustral area. () (3) (4) Table1: Duraton of varous load levels and other detals for the consdered systems oad evels 1 3 oad level Duraton tme(hrs) oss wthout DG (kw) owest voltage V

4 97 Shukla et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 010, pp oad evel 3 1 T 1 T T3 Tme Fgure 1: Approxmated oad Duraton Curve 3. Genetc Algorthm Genetc Algorthm smulates the bologcal processes that allows the consecutve generatons n a populaton to adapt to ther envronment. Genetc Algorthms are unconstraned optmzaton methods, whch model the evolutonary adaptaton n nature. They work wth a populaton of solutons and create new generatons of solutons by approprate genetc operators. In depth descrpton of the method s not provded here as GA has been appled n several problems and excellent texts; Goldenberg (1989) and Kalyanmoy Deb (1995), are avalable. However, ts mplementaton for DG allocaton problem s delneated n followng sectons. GA s effectve parameter search technques. They are consdered when conventonal technques have not acheved the desred speed, accuracy or effcency. GA s dfferent from conventonal optmzaton and search procedures n the followng ways. GA work wth codng of parameters rather than the parameters themselves. GA search from a populaton of ponts rather than a sngle pont. GA use only obectve functons rather than addtonal nformaton such as ther dervatves. GA use probablstc transton rules, and not determnstc rules. Followng are the advantages of GA. They requre no knowledge of gradent nformaton about the response surface. They are resstant to becomng trapped n local optma therefore can be employed for a wde varety of optmzaton problems. It can quckly scan a vast soluton set. Bad proposals do not affect the end soluton negatvely as they are smply dscarded. It doesn't have to know any rules of the problem - t works by ts own nternal rules. For the advantages of parallel searchng, robust searchng, and searchng mechansm based on the prncple of natural evoluton, genetc algorthm has found applcatons n many areas and has become one of the most successful optmzaton algorthms. The GA become partcularly sutable for the problem posed here due to above mentoned features Codng Strategy It s expected that the GA should produce optmal values of actve power to be nected from the DG nstalled at approprate locaton(s) n the network. Snce the soluton varables are coded n bnary form n GA mplementaton, t becomes mperatve to represent soluton varables (.e. DG values n present study) n bnary coded form. The codng of actve power to be nected n the system at the canddate buses through DGs s done n bnary form usng 1 bnary bts for sngle locaton to take care of real power capacty of 4096 kw avalable at the source node (substaton) of example test system dscussed n secton 5. These 1 bts would get repeated as many tmes as the number of locatons n case of more than one locaton. 3.. Ftness Functon The ftness functon n GA mplementaton plays a maor role and generally expressed n terms of obectve functon to be optmzed. Snce n the present work, obectve functon s to mnmze actve power loss, the ftness functon s defned as the nverse of obectve functon.

5 98 Shukla et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 010, pp Selecton of GA parameters Selecton of approprate GA parameters s crucal for ts faster convergence. In absence of any gude lne to choose these parameters, some mechansm has to be devsed. However, the types of crossover and mutaton are based on user choce. In present mplementaton, one pont crossover and constant mutaton types have been chosen. In order to quantfy the values of crossover and mutaton probabltes, effect of varatons n mutaton probablty at fxed value of crossover probablty and crossover probablty at fxed value of mutaton probablty on convergence propertes have been studed and demonstrated n Fgure and Fgure 3. The populaton sze and number of generatons for these studes have been chosen to be 100 and 50 respectvely. It can be observed from Fgure that the mutaton probablty of appears to be the most sutable as obectve functon value declnes fast and attans lowest value at the earlest compared to other values of mutaton. Wth ths value of mutaton probablty, convergence propertes at varous crossover probabltes were plotted as shown n Fgure 3. The best performance was found at 0.85 crossover probablty. Therefore the fnal value of crossover and mutaton probabltes was chosen 0.85 and respectvely for the present studes. In order to confrm the sutablty of chosen value of populaton sze, the performance was further studed at varous values of populaton sze at cross over and mutaton probabltes 0.85 and respectvely and best performance was observed at populaton sze of 100. Therefore, ths combnaton of 100, 50, 0.85 and respectvely for populaton sze, number of generatons, crossover probablty and mutaton probablty was taken as the fnal value for further studes.

6 99 Shukla et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 010, pp GA Implementaton The GA technology s partcularly sutable for the soluton of combnatoral optmzaton problems. The advantages of usng GA are that they requre no knowledge of gradent nformaton about the response surface; they are resstant to becomng trapped n local optma and can be employed for a wde varety of optmzaton problems. The GA methodology dscussed above s mplemented usng followng steps. Step 0: Intalzed number of locatons to unty. Step 1: Determnaton of canddate locatons: Input the dstrbuton system branch mpedances and complex bus powers. Determne the senstvty factors. Arrange the buses n descendng order of ther senstvtes. Bus at the top s selected as the present locaton for DG placement. Step : Input genetc algorthm control data. Step 3: Intalze populaton wth random strngs and copy nto matng pool. Step 4: Do whle generaton number s less than maxmum number of generaton taken Do whle populaton number s less than populaton sze ck up the strng correspondng to populaton number from matng pool and decode t nto test confguraton Apply load demand Call dstrbuton load flow solver Check voltage constrants Compute ftness functon Increment populaton number by one Use matng pool to create new populaton for next generaton Carry out reproducton, cross over and mutaton n matng pool Increment generaton number by one Step5: Obtan desred soluton.e. optmal DG sze, mnmum system loss and savngs Step 6: If the savng s more than the prevous value, ncrement number of locatons by one. Otherwse go to step 7. Step 7: Stop 4. Results and Dscusson 4.1. System and other detals Effectveness of the proposed methodology s tested on the wdely used 33 bus-3 branch test system at dfferent loadng condtons. The system data for ths system has been taken from Kashem et al (000). The actve power (sum of total connected load and the base system losses) at the source node n the begnnng of the perod s about 3936 kw. The entre algorthm has been wrtten n Vsual C++ language and mplemented on dual core.56 MHz, 1 GB C. In order to demonstrate the long term mpact of DG, plannng perod of 10 years have been consdered wth a unform load growth of.5% per year and mantanng same confguraton of the network. DG sources are assumed to be always avalable throughout the plannng perod. The cost benefts of optmally allocated DG for a utlty are explaned by a reducton n the energy bought by the amount produced by the DG unts. Ths also mples a reducton n losses and savng n energy that the utlty avods buyng from large generators because of self producton. The cost of DG generated power of US $30.00 per kw has been arbtrarly taken for ths study whch ncludes captal cost of DG wth nstallaton, operaton and mantenance cost. The generaton cost may be low however, t can be consdered approprate for demonstraton of the effectveness of the methodology n terms of energy savngs. The rate of energy cost has been consdered equal to US $0.05 per kwh for the cost beneft analyss. It should be hghlghted that n presence of lberalzed electrcty market, dfferent retal sales rate of the energy produced by a DG unt should be consdered. These retal sales depend on the technology adopted (mn gas turbne, CH, wnd turbne, etc.), the regulatory actons and the wllngness to harness renewable energy. Energy savng cost (ESC) has been calculated as the dfference of energy loss cost wthout DG and the energy loss cost wth DG for varable loads (EC) and the monetary benefts are calculated as a dfference of ESC and the DG cost whch ncludes cost of DG and ts nstallaton, and the expendture ncurred towards ther operaton & mantenance.

7 100 Shukla et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 010, pp The base case loss senstvty results of sx most senstve buses arranged n descendng order are shown n Table for the system studed. Although ths paper ams to llustrate techncal and economc benefts of DG allocaton at multple locatons, the demonstraton deals wth sngle locaton case also n order to compare t wth results reported n lterature by Acharya (006). 4.. Dscusson Bus no. 6 beng the most senstve mode as seen n Table, s selected as frst canddate locaton for DG placement n ths system. The same node has also been selected as the most suted locaton by Acharya (006) usng heurstc method. Results of DG capacty, loss reducton and energy savngs are reported n Table 3 for proposed and heurstc methods. Acharya et al. (006) reported the base case system loss of 11.0 kw s based on an approxmate load flow method Dstflow used by the authors. However, ths value was found to be kw usng backward sweep power flow method and the same s shown n Table 3 for far comparson. The optmal DG sze of 380 kw was obtaned by proposed method whereas 490 kw has been reported by Acharya (006). The system loss dropped from 16 kw to kw n heurstc method and kw n proposed method. It s to be noted that the evaluated DG capacty s much less than the reported n heurstc method wth hgher loss reducton though margnal. It can also be seen that the energy savngs obtaned for one year by proposed method s $ whle t s $ by heurstc method. Table : Senstvty Analyss Results Bus No Senstvty values Table 3: Summary for 33 bus system wth rated loads for Sngle locaton ower oss(n KW) oss Energy Methodology Optmal DG sze Wthout Wth reducton Savngs ($) locaton (kw) DG DG (kw) Heurstc 13] roposed GA In order to study the effect of DG nstallaton n radal network, an attempt has been made to place DG at more than one locaton (multple locatons). The next locaton has been decded on the bass of successve senstvty explaned n secton.1. Followng ths procedure, bus no. 8 was found to be the next locaton for allocatng DG at two locatons. The GA produced DG value of 1718 kw and 840 kw at buses 6 and 8 respectvely. roceedng n ths manner, analyss was carred out up-to four locatons consderng the varable loads and results are shown n Table 4. It can be seen from ths table that the lne loss decreases as the number of locatons ncreases. However, amount of decrease n lne loss reduces n successve locatons. The savng n energy cost (ESC) follows the reverse trend. It ncreases wth ncrease n number of locatons but at hgher number of locatons ths ncrease s margnal. Snce margnal reducton n loss and margnal ncrease n energy savng cost was observed when the number of locatons was ncreased to four, further ncrease n number of locatons were not consdered. Optmal values of DG to be placed for varous loadng condtons were obtaned usng proposed technque. Effect of varatons n number of locatons on DG values for three consdered loadng condtons are also tabulated n Table 5. It s observed that the losses reduce at all load levels wth the mproved voltage profle as the number of locatons ncrease. The value of loss reducton becomes smaller and smaller as the number of locatons ncrease whch can be seen from Table 5. Table 4: Effect of no. of locatons on DG sze, losses, voltage profle and one year EC, ESC No. of locaton 1 (6) (6,8) 3 (6,8,0) 4 (6,8,0,4) osses (kw) at varous load levels owest Voltage (p. u.) Cost of Energy oss (EC) n $ Cost of Energy Savng (ESC) n $ Another advantage of mprovement n voltage profles due to nstallaton of DG (at the end of plannng perod of 10 years) has also been demonstrated n Table 5. One can see the varaton n voltage profle at varous loadng condtons wth the varaton n

8 101 Shukla et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 010, pp number of locatons. It can be very well understood that the voltage profles get mproved as the number of locatons ncreases. Ths ncrease has been observed from p. u. (wthout DG) to p. u. (wth DG placed at four locatons) at peak load level (3). It can further be observed that the values of loss reducton reduced by 0.381kW, 0.91kW and 1.550kW at load levels 1, & 3 respectvely when number of locatons was ncreased from three to four whle the correspondng values of loss reducton when number of locatons was ncreased from one to three can be observed equal to kw, kw and kw respectvely. It suggests that the loss reducton reduces as the number of locatons ncreases and beyond certan number of locatons, the loss reducton may cease. However, the lmtng number s decded on the bass of economc benefts as dscussed n the next secton. DGs nstalled ones wll reman n system as long as ther performance s satsfactory. Thus the money nvested once on DG wll help nvestor to harness ts beneft throughout ts lfe. Although the systems losses reduce as the number of DG at varous locatons ncrease, the nvestment on DG also ncrease. Thus the reducton n cost of energy loss s acheved at addtonal nvestment on DG and nvestor can be only benefted as long as savng s more than nvestment. Therefore, there must be some lmt on number of DG beyond whch t may be uneconomcal. In order to nvestgate ths lmt, economc analyss has been performed. The beneft acheved was obtaned wth varyng loads and varyng number of DG locatons. Consderng the load growth of.5% per year, the loads at peak loadng condton have rsen to about 1.5 tmes the base case loadng of the consdered system at the end of 10 year plannng perod. The results of energy loss cost (EC) and the benefts n US$ are shown n Fgure 4. It can be seen that the beneft ncreases f the number of locatons s ncreased from one to three. However, the value of the beneft (compensaton) gets reduced beyond three no. of locatons. To assess the speed of GA for the soluton of present problem for the DG placed at multple locatons, computatonal tme was also recorded and has been plotted n Fgure 5 for one year and ten year plannng perods. It can be observed that the computatonal tme ncreases wth ncrease n locatons but there s margnal ncrease n tme for ten years plannng perod compared to one year perod. Table 5: Effect of optmally located DG on DG sze, losses and voltage profle for dfferent locatons No. of locatons one Two Three four oad DG Sze (kw) at bus no. osses owest evels (kw) voltage (p.u)

9 10 Shukla et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 010, pp Conclusons lacement of DG n radal dstrbuton network has been demonstrated n ths paper. The approprate locaton of DG had been decded on the bass of senstvty of actve power loss wth respect to real power necton through DG. In case of multple locatons, successve senstvty had been made use of usng same algorthm. The problem s formulated as an optmzaton problem wth mnmzaton of real power loss (hence evaluaton of monetary benefts) subect to equalty and nequalty constrants and solved for optmal value of DG usng GA. It s demonstrated that the beneft ncreases wth ncrease number of locatons wthn certan locatons beyond whch t s uneconomcal. Sgnfcant mprovement n voltage profle as an addtonal advantage of optmal DG placement has also been observed and demonstrated. Nomenclature r ( r) System resstance per unt length, R = Total resstance of the lne, Total length of the lne, N Number of lne sectons, oss k Real power loss n secton k, oss SG ne loss from source to DG locaton,

10 103 Shukla et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 010, pp oss G ne loss from the locaton of DG to load and Q th Real and reactve power demands at bus respectvely, G and Q G Real and reactve power generaton by DG placed at bus respectvely, oss System real power loss, N Number of buses, I Current carryng capacty of lne secton connected between nodes and. V And mn V scheduled δ voltage magntude and angle at th bus respectvely. V, V Acceptable voltage lmt at bus max System phase voltage, th Z = r + x ; Z matrx Elements of [ ] BUS α, β are the loss coeffcents represented as α = r cos( δ δ ) /V V β = r Sn( δ δ ) / VV Appendx A.1 oss Savng Analyss oss savngs are classfed as ether capacty or energy loss savngs. Capacty loss savngs reduce load on T&D and generaton system equpment. Ths lessens the need for captal upgrades. They are calculated by developng feeder and transformer loss savngs equatons and evaluatng them durng peak load condtons. Energy loss savngs reduce electrcty generaton requrements. Ther value s the cost savngs realzed by reducng operaton and mantenance expenses of exstng plants. A. System Modelng Ths secton focuses on lne loss reducton analyss. In ths study, one-concentrated load s assumed at the end of the lne. Wth the ntroducton of DG, lne loss reducton can be expected. Ths factor s analyzed, quantfed and presented n ths paper for multple locatons of the DG along the feeder. Two smple radal systems are consdered: ) System wthout DG ) System wth the ncluson of DG. Both systems have a concentrated load at the lne end. The total length of the lne s assumed to be km. Schematcs of the two cases are shown n Fgure A.1 and Fgure A.. Fgure A.1: A smple radal dstrbuton system wthout WTG. For the system wth DG, the locaton of DG s assumed to be G km from source.

11 104 Shukla et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 010, pp Fgure A.: Schematc of a radal system wth the ncluson of DG. The followng assumptons are made n the study: 1) oad s Y-connected; lne current s the same as phase current; I = I ) oad absorbs real power at some specfed power factor 3) DG produces real power at a laggng or leadng or unty power factor 4) V s the RMS load phase voltage. V s the reference phasor. The load complex power s S = + Q, therefore, the current absorbed by the load s I = ( Q ) 3V (A.1) A.3 ne oss Reducton Analyss Electrcal lne loss occurs when current flows through transmsson and dstrbuton systems. The magntude of the loss depends on amount current flow and the lne resstance. Therefore, lne loss can be decreased by reducng ether lne current or resstance or both. If DG s used to provde energy locally to the load, lne loss can be reduced because of the decrease n current flow n some part of the network. The real power necton at a bus, n, consdered here as the dfference between real power generaton and the real power demand at that bus, and can be expressed as n =, G (A.) From the schematc of the system shown n Fgure 1, nstantaneous base case losses for a three-phase system can be expressed as r ( + Q ) oss ( B ) = (A.3) 3V Now n case of lne loss wth DG, assumng that the lne s short, voltage drop along the lne s neglected. Schematc of ths system s shown n Fgure. The output current of DG supplyng complex power {S G = G + Q G } s gven by G Q G I = (A.4) G 3V The lne loss wth the ntegraton of DG s a combnaton (sum) of two parts: ) ne loss from source to the locaton of DG. ) ne loss from DG locaton to the locaton of load. In presence of DG (Fgure A.), the feeder current I S wll be the dfference of load current I and DG output current I G. The lne loss from source to DG locaton can be expressed as rg ( + Q + + Q Q Q ) G G G G oss SG = rg (A.5) 3V Agan, the lne loss from the locaton of DG to load ( oss ) wll be oss G G r ( G ) ( + Q ) = (A.6) 3V The total lne loss ( oss ( AT ) ) n presence of DG placed at a X dstance from the source can be calculated by combnng Equatons (A.5) and (A.6) and expressed as

12 105 Shukla et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 010, pp X ( + ) R oss ( AT ) = + Q + G Q G G Q Q G (A.7) 3V Instantaneous loss savngs (S) at any pont on a feeder can be represented as the dfference between losses wthout DG and losses wth DG. S = oss (B) - oss (AT). Hence, ( + Q Q Q ) RX S = (A.8) G G G G 3V The postve sgn of S ndcates that system loss reduces wth the ntegraton of DG but the negatve sgn mples that DG causes hgher loss n the system. References Acharya N., Mahat., Mthulanathan N., 006. An analytcal approach for DG allocaton n prmary dstrbuton network, Electrc ower and Energy Systems, Vol. 8, pp Afsar, M., Sngh, S.., Rau, G.S. and Rao, G.K. 00. A fast power flow soluton of radal dstrbuton networks, Electrc ower Components and Systems (USA), Vol. 30, No.10, Brown R.E., an J., Feng X., and Koutlev K., Stng dstrbuted generaton to defer T&D expanson, roc. IEE. Generaton, Transmsson and Dstrbuton, Vol. 1, pp Chradea., Ramakumar R An approach to quantfy the techncal benefts of dstrbuted generaton, IEEE Transactons on Energy Converson, Vol. 19, No. 4, pp Cell G., Ghan E., Mocc S., and lo F., 005. A multobectve evolutonary algorthm for the szng and stng of dstrbuted generaton, IEEE Transactons on ower Systems, Vol. 0, No., pp Dugan R.C., McDermott T.E. and G.J. Ball 001. lannng for dstrbuted generaton, IEEE Industral Applcaton Magazne, Vol. 7, pp Daly.A., Morrson J. 9 Aprl 1May 001. Understandng the potental benefts of dstrbuted generaton on power delvery systems, Rural Electrc ower Conference, pp. A11 A13. Daz-Dorado E., J. Cdras, E. Mguez 00. Applcaton of evolutonary algorthms for the plannng of urban dstrbuton networks of medum voltage, IEEE Transacton on ower Systems, Vol. 17, No. 3, pp Elgerd O.I., Electrc energy system theory: an ntroducton, McGraw- Hll Inc. Goldenberg D. E Genetc Algorthm n Search, Optmzaton and Machne earnng: Addton-Wesley ublshng Co. Inc Harrson G.., ccolo A., Sano., Wallace A.R Hybrd GA and OF evaluaton of network capacty for dstrbuton generaton connectons, Electrcal ower Energy System, Vol. 78, pp Iumba NM, Jmoh AA, Nkabnde M (1999). Influence of Dstrbuton Generaton on Dstrbuton Networks erformance, roceedng of AFRICON 99, : Jenkns N (1996). Embedded Generaton-art, IEE ower Engne. J., pp Jabr, R. A., al, B. C Ordnal optmzaton approach for locatng and szng of dstrbuted generaton, IET proceedngs Generaton, Transmsson & Dstrbuton, Vol. 3, No. 8, pp Khator K. and eung,.c ower dstrbuton plannng: A revew of models and ssues, IEEE Transacton on ower Systems, Vol. 1, No. 3, pp Kyoto rotocol to the Unted Natons Framework Conventon on clmate change, Dec Kalyanmoy Deb, Optmzaton for engneerng desgn: Algorthm and Examples: rentce Hall of Inda td., New Delh. Kashem M. A., Ganpathy, V., Jamson, G.B., Buhar, M. I A novel method for loss mnmzaton n dstrbuton networks, roc. Internatonal Conference on Electrc Utlty Deregulaton and Restructurng and ower Technologes, pp Mardaneh, M., Gharehpetan G. B..004, Stng and szng of DG unts usng GA and OF based technque, TENCON. IEEE Regon 10 Conference, Vol. 3, pp , 1-4. Mlanovc JV, Davd TM (00). Stablty of Dstrbuton Networks wth Embedded Generators and Inducton Motors, roceedng of the IEEE ES Wnter Meetng, : ccolo, A. Sano, Evaluatng the mpact of network nvestment deferral on dstrbuted generaton expanson, IEEE Transactons on ower System, Vol. 4 No. 3, pp Quntana V.H., Temraz H.K., Hpel K.W Two stage power system dstrbuton plannng algorthm, roc. IEE Generaton, Transmsson and Dstrbuton, Vol. 140, No. 1, pp Racklffe G Gudelnes for plannng dstrbuted generaton systems, roc. of IEEE ower Engneerng Socety Summer Meetng, vol. 3. Seattle (WA, USA): pp Slvestr A., Berzz, S., Buonanno, Dstrbuted generaton plannng usng genetc algorthms, Electrc ower Engneerng, ower Tech Budapest 99, Inter. Conference, pp.57.

13 106 Shukla et al. / Internatonal Journal of Engneerng, Scence and Technology, Vol., No. 3, 010, pp Bographcal notes: T. N. Shukla was born n Inda n He receved hs B.E. and M.E. n Electrcal Engneerng from Allahabad Unversty n 1976 and 1981 respectvely. resently he s pursung hs h. D. from U Techncal Unversty, ucknow. He oned the Electrcal Engneerng Department at Kamla Nehru Insttute of Technology, Sultanpur, as lecturer n 198 where he s presently servng as rofessor. He s currently pursung hs h.d. from U.. Techncal Unversty, ucknow. Hs man research nterests are n optmal operaton and AI applcatons to power dstrbuton systems. S.. Sngh was born n Inda n He receved hs B.E. and M.E. n Electrcal Engneerng from Allahabad Unversty n 1978 and 1981 respectvely. He obtaned hs h.d. from Banaras Hndu Unversty n 1990.He was ost Doctoral scholar at Unversty of Calgary, Canada durng He oned the Electrcal Engneerng Department of Banaras Hndu Unversty as faculty n 1981 where he s presently servng as rofessor. Hs man research nterests are n secure and optmal operatons of power systems, deregulaton, dstrbuton automaton and AI applcatons to power systems. Dr. Sngh s a Fellow of Insttuton of Engneers (Inda), Senor Member of IEEE and lfe member of Systems Socety of Inda. K.B.Nak was born n Inda n He receved hs B.E. from Kanpur Unversty and M.E. from Nagpur Unversty n Electrcal Engneerng. He obtaned hs h.d. from Kanpur Unversty n He oned the Electrcal Engneerng Department at Kamla Nehru Insttute of Technology, Sultanpur, as professor n 1986 and served as professor tll Jan He has also been the Drector of the nsttute for about sx years. After retrement of hs servce, presently he s servng as the Drector of College of Engneerng, Scences and Technology, ucknow (U), Inda. Hs man research nterests are n optmal operaton, power electroncs and AI applcatons to power dstrbuton systems. Receved December 009 Accepted March 010 Fnal acceptance n revsed form March 010