Stepwise Restoration of DG-integrated Distribution Network under Cold Load Pickup

Transcription

1 V. Kumar, R. Kumar.H.C., I. Gupta and H.O. Gupta / GMSARN Internatonal Journal 1 (2007) 1-8 Stepwse Restoraton of DG-ntegrated Dstrbuton Network under Cold Load Pckup Vshal Kumar *, Rohth Kumar. H.C., I. Gupta and H.O. Gupta Abstract A scheme for step-by-step restoraton of a power dstrbuton network under Cold Load Pckup condton has been presented n ths paper. The proposed scheme uses the optmal load sheddng at each step of restoraton process whle takng nto account the effects of dspersed generaton (DG). The load dversty conserved by DG has been effectvely utlzed for qucker restoraton of the network. The optmzaton s performed to acheve multple objectves of mnmum load curtalment and mnmum swtchng operatons whle satsfyng all the network constrants. Genetc Algorthm has been utlzed to search the optmal soluton. A consderable amount of mprovement n the relablty has been observed n case of DG ncorporaton. The proposed scheme has been llustrated on a 33-bus radal dstrbuton network. Keywords Cold load pckup, Dstrbuted generaton, Optmal load sheddng, Power dstrbuton network restoraton. 1. INTRODUCTION Loss of dversty among electrcal loads durng the restoraton followng an extended outage can lead to heavy loadng on system durng post-outage perod. Ths loss of dversty s manly due to thermostatcally controlled loads connected n the system beng swtched ON smultaneously at the nstant of supply restoraton, causng post-outage load-demand to reach 2 to 5 tmes the dversfed load, such a hgh load condton s known as Cold Load Pckup (CLPU) [1]. The proporton of thermostatcally controlled loads s ncreasng at a hgh rate and these loads consttute the major porton of the load on the system today. Such a rase has made the CLPU problem a prevalent feature of dstrbuton system restoraton, especally n the power defcent countres where scheduled and forced power outages are frequent. CLPU has more than sxty years old hstory, however low percentage of thermostatcally controlled loads at that tme dd not make the problem so severe. It was frst recognzed as nrush phenomenon n 1952, and change of relays settngs were proposed [2]-[4]. In the recent past, researchers started payng attenton towards CLPU problem, and several efforts have been made to model the connected loads and also the nterconnectng elements under ths condton [5]. Durng last few years much of research n ths area has been orented towards * Vshal Kumar (correspondng author) s wth Electrcal Engneerng Department (EED), Indan Insttute of Technology Roorkee (IITR), Roorkee , Inda. (Telephone: , e-mal: vshal_saxena72@hotmal.com) Rohth Kumar H.C. s wth EED, IITR, Roorkee , Inda (Telephone: , e-mal: hc_roh@yahoo.com ) Indra Gupta s Assstant Professor n EED, IITR, Roorkee Inda. (Telephone: , e-mal: ndrafee@tr.ernet.n ) H.O.Gupta s Professor n EED, IITR, Roorkee Inda. (Telephone: e-mal: harfee@tr.ernet.n ) optmal desgnng of the dstrbuton network and development of better restoraton technques under CLPU [3], [6]-[9]. A crtcal survey has been conducted recently to hghlght varous aspects of CLPU problem [2]. The CLPU condton manly depends on several factors such as the duraton of outage, type of connected load, weather condton, lvng habts of the user, and thermal characterstcs of the buldng. Researchers have dvded CLPU condton n to four phases: Inrush, motor startng current, motor acceleratng current, and endurng current phase [10]-[12]. Intal three phases are transent n nature and de out wthn few seconds, whereas the endurng phase can last for long duraton thereby causng sgnfcantly hgh loadng on the dstrbuton network elements, thereby volatng voltage and current lmts of the feeder [2]. Hence, all the connected loads can not be swtched ON smultaneously durng the ntaton of restoraton. However, the aggregated load decreases wth tme, and allows more loads to be swtched ON as the network regans dversty gradually. As evdent from the lterature, extensve research n the area of CLPU has been carred out to restore network n mnmum duraton. Several heurstc and non-heurstc approaches have been used to obtan the optmal sequence of restoraton. Ucak and Pahwa [6] amed at mnmzng the total restoraton tme and customer nterrupton duraton by makng use of derved functon between restoraton tme and restoraton order. Further, the authors determned the optmal swtchng order to mnmze customer average nterrupton duraton ndex (CAIDI) by usng adjacent par wse nterchange method [7]. Walklesh and Pahwa [8] performed a cost optmzaton to determne the sze of substaton transformer and number of sectonalzng swtches that mnmze the total annual cost. The same authors also appled Genetc Algorthm (GA) for optmal restoraton of an actual feeder. The capactor banks were used for 1

2 V. Kumar, R. Kumar.H.C., I. Gupta and H.O. Gupta / GMSARN Internatonal Journal 1 (2007) 1-8 boostng the voltage to meet the under-voltage permssble lmt [9]. As the restoraton tme s based on the order n whch sectons are restored, for sequencng the swtches, GA [10] and Ant Colony algorthm [13] have also been exploted. The ssues lke voltage and current constrants of buses and branches, and locaton for placement of sectonalzng swtches have been addressed n a recent paper by Gupta and Pahwa [14], they have taken the base of voltage drop to fnd the locaton of sectonalzng swtches and optmal sze of transformer and feeder, whle mnmzng the restoraton tme. Therefore, t s evdent from the above references that rgorous work has been carred out on transformer overloadng and cost mnmzaton for cold load pckup condton. The man reason for occurrence of CLPU condton s the loss of dversty among the loads. However, n the modern days of ntegrated power system, most of the hgh prorty loads such as hosptals, and commercal complexes etc. prefer to have ther own DG plants to meet ther demand durng outages. These non-utltyowned generators (NUGs) are operated n rollover mode and they conserve load-dversty durng CLPU condton, thereby reducng the total load requrement durng restoraton. Ths paper studes the effect of presence of such NUGs n dstrbuton network durng restoraton under CLPU condton, and proposes a scheme to restore the network quckly by makng use of the dversty conserved by NUGs. The scheme s demonstrated on a 33 bus, 12.66kV radal dstrbuton system. The results obtaned for the network wth and wthout ncorporaton of NUG are compared, and qucker restoraton of the network was acheved. CLPU Model Varety of models for CLPU condton wth varous approaches s avalable n the lterature [15]-[21]. However, n the present work, the delayed exponent model has been consdered [21]. The model characterzes CLPU condton as an exponental functon wth delay. Load S(t) n p.u S U S T S D T 1 T 2 Tme n hours Fg.1. CLPU model represented as a delayed exponent In the delayed exponental model, un-dversfed load S U remans constant from restoraton tme T 1 to T 2, showng delay, and after T 2 t decreases exponentally to dversfed level S D as shown n the above Fg 1. Mathematcally, ths model can be expressed as (1) [14]. - α ( t- T2 ) [ S + ( S - S ) e ] u( t- T2 ) S ( t) = D U D (1) + S [1- u( t- T2 )] u( t- T1 ) U 2. AIM AND APPROACH The am of the present work s to study the effect of presence of NUGs on the restoraton of network under CLPU n a DG-ntegrated dstrbuton system. The approach adopted n the proposed scheme for restoraton of a network under CLPU s based on load curtalment. The loads are curtaled to restart the network and then are restored n step-by-step manner as the loadng of the network elements decays wth tme. It s assumed that all the loads follow the delayed exponent model of CLPU [21] except the loads wth NUG, whch are suppled durng outage and mantan ther dversty. Some predetermned step-ponts are consdered on the load profle, and correspondng locatons for optmal load sheddng/restorng at each step are determned wth the help of GA. Man objectve s to determne the optmal locatons for load curtalment, and the sequence of restoraton of loads as to acheve maxmum utlzaton of the exstng network capacty. Methodology The endurng phase of CLPU condton perssts for much longer perod and causes excessve loadng on substaton transformer, current volaton n the feeders, and voltage volaton at the buses. Hence, loads are pcked up n an optmal sequence so that all the operatonal constrants could be satsfed [3]. However, loads connected to NUG are beng suppled durng the outage, and they mantan ther dversty, hence contrbuton of such loads to the total load demand remans constant durng pre and post outage perod. Here, the methodology s to determne the optmal load sheddng locatons and restore the network n steps, besdes the ncluson of effects of NUG. Consder load at bus, swtched ON at tme step T j, f ths load s not connected wth NUG durng outage perod, then t follows CLPU profle gven by (2.a) on restoraton, else the load dversty s conserved (2.b), and ths ads the process of network restoraton. α( T T ) j S ( t) = [ SD + ( S ) ] ( ) U S D e u t T j = 1... m (2.a) S ( t) = S j = 1... m (2.b) D Here, m s the total number of dstnct dscrete step- 2

3 V. Kumar, R. Kumar.H.C., I. Gupta and H.O. Gupta / GMSARN Internatonal Journal 1 (2007) 1-8 ponts consdered on the CLPU load profle, and the correspondng tmng nstants can be evaluated from (3). 1 j S S ln D Tj = + T, j = 1... m α SU SD (3) The S j s loadng correspondng to predetermned step pont j consdered on CLPU model as shown n Fg. 1. Here, n the case study presented n next secton these are consdered as gven n Table 1. Problem Formulaton The man objectve here s to mnmze the load curtaled at each step whle restorng the network along wth mnmum swtches beng operated. Ths s a case of nonlnear combnatoral problem wth multple objectves. Ths mult-objectve optmzaton problem s converted to a sngle objectve problem wth the help of sutable weghts, and the mathematcal formulaton of the problem s expressed as (5). = S S Total Suppled Mn f W + W I + W V STotal + W S + W SW Load IV V VV V TV TV SW (5) Objectve functon gven by (5) s subjected to operatonal constrants as mentoned below. All the power flow equatons of the network should be satsfed The utlty voltage at each load bus should be wthn permssble lmt (Utlty s standard ANSI Std. C ) (±5%). V V V mn max, { buses of the network} (6) In a feeder or conductor, current cannot be ncreased beyond a specfed lmt, whch s decded by thermal capacty of the conductor. I I Rated, { branches of the network} (7) Here, I Rated s current permssble for branch wthn safe lmt of temperature. The total power suppled to the network must be wthn the substaton transformer capacty lmt. In the proposed scheme for network restoraton, maxmum loadng of the transformer s consdered as the loadng lmt of transformer for no addtonal loss of lfe. S < K S (8) TMax TM T Loadng lmt of the forced ar-cooled transformer for a delayed exponental CLPU model has been explaned for dfferent outage-duraton, and pre-outage and postoutage loadng condtons. The maxmum un-dversfed load for dfferent dversfed loads and outage duraton s also reported, and the maxmum supplyng lmts for one-hour outage wth dfferent pre and post outage load condtons have also been determned [6], [22]. Weghts consdered n (5) reflect the relatve prorty of each term present n the objectve functon. The weghts act as the penalty to be mposed n case of volaton of constrants. However n the present work, the weght s also used to convert mult-objectve optmzaton problem to a sngle objectve problem. Snce the man objectve s to acheve a small quantty of loss of load, heavy penalty s mposed to the frst term. The second and the thrd terms n the objectve functon are steady state securty constrants, and heavy penaltes are appled n case f these lmts are volated. Fourth term s of slghtly lesser sgnfcance n comparson wth second and the thrd, as the dstrbuton transformers are rated for a short perod of overloadng wth no or a very nomnal loss of lfe. Varyng these weghts can lead to alternatve solutons. Genetc Algorthm Genetc algorthms are the computerzed search and optmzaton algorthms based on the mechansm of natural genetcs and selecton [23], [24]. These algorthms work wth a populaton of possble solutons, rather than a sngle pont as n conventonal optmzaton technques. The populaton of possble soluton contnuously undergoes the process of natural changes such as selecton, crossover and mutaton fnally to arrve wth a global optmum soluton. In the present research work, bnary encodng system has been successfully adopted owng to ts smplcty of representaton and ease of understandng. The length of the encoded strng s equal to the total number of buses n the system, and each bt of ths strng represents the status of the load connected at that bus. GA here uses roulette wheel selecton, one-pont crossover and bt-wse mutaton along wth eltsm preservng mechansm [23], [24]. Maxmum number of generatons s used to termnate GA. The algorthm desgned for the determnaton of the optmal locatons for load curtalment/restoraton s explaned as follows. Algorthm Some load-ponts are consdered on the CLPU profle; these load ponts actually represent the steps of restoraton. Followng s the computatonal flow for desgned algorthm usng GA, appled for a load-pont, whch determnes the load sheddng locatons correspondng to that load-pont. The applcaton of the algorthm for each restoraton step enables to know the optmal sequence of restoraton of the loads. 3

4 V. Kumar, R. Kumar.H.C., I. Gupta and H.O. Gupta / GMSARN Internatonal Journal 1 (2007) 1-8 IN P U T : P S IZ E, G e M A X, P C, P M, N G e n e r a te r a n d o m p o p u la to n P 0 o f PS IZ E fo r ( = 1 : G e M A X ) s e t: j= 1 ; W h le ( j PS IZ E ) s e t: k = 1 ; W h le ( k N ) k U p d a te P ( j) b y e q. (2.a ); // f b u s k n o t c o n n e c te d to N U G // k U p d a te P ( j) b y e q. (2.b ); // f b u s k c o n n e c te d to N U G // k + + ; e n d W h le E v a lu a te P (j) fro m e q. (5 ) j+ + ; e n d W h le /* A p p ly g e n e tc o p e r a to r s a s b e lo w * / S e le c t(p ); // S u b r o u tn e fo r R o u le tte w h e e l s e le c to n // X o v e r(p ); // S u b r o u tn e fo r o n e - p o n t c r o s s o v e r // M u ta te (P ); // S u b r o u tn e fo r b t - w s e m u ta to n // E lte (P,P -1 ); // S u b r o u tn e fo r e lts m // + + ; // In c r e m e n t g e n e r a to n c o u n te r // e n d fo r O U T P U T : O p tm a l S w tc h n g lo c a to n s 3. CASE STUDY The proposed scheme s llustrated on a 33-bus, kv radal dstrbuton network [25] wth a substaton transformer capacty of 5. Under CLPU condton, most of the system buses volate the lower voltage lmt, and hence to effectvely utlze the permssble range of the utlty voltage, the substaton voltage has been consdered as p.u.. It s consdered that the network s ntally compensated for reactve power through the optmal placement of capactors at buses, and the correspondng values are gven n Appendx-I [26]. In order to llustrate the effects of presence of NUGs, It s assumed that NUGs are present at buses 14, 17, 25 and 30. Table 1. Values of tme elapsed for the step-ponts Step-pont (j) Tme Elapsed n Mnutes Descrpton of Steppont/(S j ) Outage duraton 0 (Restart) 0 Start of Restoraton 2.50 x S D x S D x S D x S D x S D x S D The typcal values of weghts appled n the objectve functon for the present case-study are: 75.0 for the lost load, for the current volaton, for the voltage volaton, 50.0 for the transformer volaton, and 10.0 for number of swtchng operatons. The proposed scheme utlzes a delayed exponental model as explaned n secton-1. The assocated parameters to the model are taken as α =1 hr -1, T= T 2 - T 1 =30 mnutes, S U = 2.5 p.u., and S D =1.0 p.u., and K TM =1.50. Tme nstances and loadngs correspondng to each step of stepwse restoraton of the network are llustrated n Table RESULTS AND DISCUSSION The current restoraton problem s a nonlnear combnatoral problem and GA has been used to obtan the optmal soluton. GA s appled wth dfferent populaton sze: 60, 80, 100 and 150, and the best result obtaned has been reported here. The correspondng GA convergence curve for step-pont-0 s shown n Fg.2. The followng are the consdered GA parameters F tnes s func to n v a lu e > Populaton sze: 100 Crossover rate: 0.8 Mutaton rate: 0.05 Maxmum no of generatons: No. of Generatons > Fg.2. Convergence curve of GA for step-pont-0 of case-2 Table 2 shows the results obtaned for stepwse restoraton of the network n both the cases, wthout NUGs (Case-1) and wth NUGs (Case-2). It s clear that durng step-wse restoraton of Case-2, restoraton of network takes place n step-pont 3 aganst step-pont-4 for Case-1. Also, the number of loads beng dsconnected s lesser n all the steps n Case-2. Ths s manly because of the reducton n the total load demand owng to conservaton of dversty of loads connected wth NUG durng outage perod. The graphcal vew of step-wse restoraton under both the cases has been presented n Fg.3 and 4; the load suppled by NUG durng the outage s also shown n the fgure. The expected load represents the requred load to be restored for the complete restoraton of the network correspondng to the loadponts. The analyss was conducted by self developed codes wrtten n MATLAB-R2006a package, on PC wth Intel P-IV processor of 2.0 GHz clock frequency, and the average CPU executon tme pertanng to Case-1 and 4

5 V. Kumar, R. Kumar.H.C., I. Gupta and H.O. Gupta / GMSARN Internatonal Journal 1 (2007) 1-8 Case-2 has been reported n Table 3. Table 2. Results of step-wse restoraton of network Step-pont: 0 served n Load at the buses to be dsconnected Total number of swtchng operaton Step-pont: 1 served n Load at the buses to be dsconnected Total number of swtchng operaton Step-pont: 2 served n Load at the buses to be dsconnected Total number of swtchng operaton Step-pont: 3 served n Load at the buses to be dsconnected Case 1 Wth out NUGs Case 2 Wth NUGs ,8,12,13,17,18,31,32,33 14,16,18,29, ,13,17,18,31,32,33 14,18, ,18,32 14, ,32 Nl Table 3. Average CPU Tme per Step-pont Case-1 Case-2 CPU Tme (n sec./step) Load n p.u. Load n p.u Expected Load Restored Load wthout NUGs Step-pont Fg.3. Step-wse restoraton of network n case Expected Load Load Suppled by NUGs Restored Load wth NUGs Step-pont Fg.4. Step-wse restoraton of network n case-2 The presence of DG n dstrbuton network also mproves the relablty ndces of supply. For the purpose of llustraton, a case has been consdered where the total connected load s equal to substaton transformer capacty. An average load per customer of 2kW s assumed and relablty ndces are evaluated. The number of customers restored under both the cases s presented n Fg.5, t s evdent that more number of customers are restored n Case-2. A consderable mprovement n the relablty ndces has been observed n Case-2. To support the prevous statement, few of the basc customer orented relablty ndces such as System Average Interrupton Duraton Index (SAIDI), System Average Interrupton Frequency Index (SAIFI) are evaluated and gven n Table 4. Total number of swtchng operaton Step-pont: 4 served n 2 Nl Table 4. Evaluated Relablty Indces Index Case-1 Case-2 SAIDI (mn/customer) SAIFI (nt/customer)

6 V. Kumar, R. Kumar.H.C., I. Gupta and H.O. Gupta / GMSARN Internatonal Journal 1 (2007) 1-8 No. of Customers served Case-1 Case-2 T 2 u(t) V V W IV W Load W SW W TV W VV Intaton of decay towards S D Unt step functon Sum of the ratos of bus-voltage volatons to the lmtng value Weght for I V Weght for rato of lost load over total load Weght for SW Weght for S TV Weght for V V Step-Pont Fg.5. Number of customers served n both cases 5. CONCLUSION In the present work, the effect of presence of NUGs on network restoraton durng CLPU condton has been nvestgated. A scheme has been proposed, to restore the network under CLPU wth the utlzaton of dversty conserved by the NUGs. The proposed scheme for ncorporaton of NUGs restored the network qucker than the one wthout consderng the NUG, moreover mnmzed the total number of swtchng operatons requred wth maxmum utlzaton of exstng capacty of the system. It s concluded that the presence of NUGs also mproves the relablty ndces. The scheme s llustrated on a 33-bus 12.66kV dstrbuton system. The subject matter dscussed n ths paper s of hgh relevance, as the amount of DG ntegrated network s rsng, as to meet the customers supply requrement durng outages, and the utltes seem to beneft under such scenaro by beng able to restore the network at a faster rate. α Ge MAX I V K TM N NUG NUGs NOMENCLATURE Rate of decay of load under CLPU Maxmum number of generatons Sum of the ratos of lne-current volatons to ts thermal lmt Transformer maxmum loadng factor Total no of buses n the system Non Utlty-owned Generator Non Utlty-owned Generator unts Probablty of crossover Probablty of mutaton Populaton sze k th bus of j th chromosome durng th generaton P C P M P SIZE k P ( j ) S(t) Load Demand wth respect to tme for t T 1 S D S Suppled S T S T Max S Total S TV S U SW T 1 Dversfed Load n p.u. Load suppled durng CLPU Substaton transformer ratng Maxmum transformer loadng Total connected load n the network Transformer loadng-lmt volaton Un-dversfed load n p.u. Number of swtchng operatons Intaton of restoraton REFERENCES [1] Mcdonald, J.E.; Brunng, A.M.; and Maheu, W.R Cold Load Pckup. IEEE Transacton on Power Apparatus and Systems, vol. 98, pp [2] Kumar, V.; Gupta, I.; and Gupta, H.O An Overvew of Cold Load Pckup Issues n Power Dstrbuton Systems. Electrc Power Components & Systems. Vol. 34, No.6, pp [3] Pahwa, A Role of dstrbuton automaton n restoraton of dstrbuton systems after emergences. In Proceedngs of the Transmsson and Dstrbuton Conference and Exposton, IEEE/PES, vol. 2, pp [4] Ramsaur, O A new approach to cold load restoraton. Electrcal World, vol. 138, pp [5] Agneholm, E.; and Daalder, J Cold load pckup of resdental load. IEE Pro. Gener. Transm. Dstrb., vol. 147, no. 1, pp [6] Ucak, C.; and Pahwa, A An analytcal approach for step-by-step restoraton of dstrbuton systems followng extended outages. IEEE Transactons on Power Delvery, vol. 9, no. 3, pp [7] Ucak, C.; and Pahwa, A Optmal step-by-step restoraton of dstrbuton systems durng excessve loads due to cold load pckup, Electrc Power Systems Research, vol. 32, no. 2, pp [8] Wakleh, J. J.; and Pahwa, A Dstrbuton system desgn optmzaton for cold load pckup. IEEE Transactons on Power Systems, vol. 11, no. 4, pp [9] Wakleh, J. J.; and Pahwa, A Optmzaton of dstrbuton system desgn to accommodate cold load pckup, IEEE Transactons on Power Delvery, vol. 12, no. 1, pp , January [10] Chaval, S.; Pahwa, A.; Das, S A Genetc algorthm Approach for Optmal Dstrbuton Feeder Restoraton durng Cold Load Pckup. In Proceedngs, World Congress 011 Computatonal Intellgence, Honolulu, Hawa. [11] Agneholm, E Cold Load Pck-Up, PhD thess, Department of Electrc Power Engneerng, Chalmers Unversty of Technology, Goteborg, Sweden. [12] Mrza, O. H Usage of CLPU curve to deal wth cold load pckup problem. IEEE Transactons on Power Delvery, vol. 12, no. 2, pp [13] Mohanty, I.; Kalta, J.; Das, S.; Pahwa, A.; and Buehler, E Ant algorthms for the optmal restoraton of dstrbuton feeders durng cold load 6

7 V. Kumar, R. Kumar.H.C., I. Gupta and H.O. Gupta / GMSARN Internatonal Journal 1 (2007) 1-8 pckup. In Proceedngs of the Swarm Intellgence Symposum 2003, SIS 03, pp , Aprl [14] Gupta, V.; and Pahwa, A A voltage dropbased approach to nclude cold load pckup n desgn of dstrbuton systems. IEEE Transactons on Power Systems, vol.19, no.2, pp [15] Law, J.; Mnford, D.; Ellott, L.; and Storms, M.; Measured and predcted cold load pck up and feeder parameter determnaton usng the harmonc model algorthm. IEEE Transactons on Power Systems, vol. 10, Issue 4, pp [16] Nehrr, M. H.; Dolan, P. S.; Gerez, V.; and Jameson, W. J Development and valdaton of a physcally-based computer model for predctng wnter electrc heatng loads. IEEE Transactons on Power Systems, Vol. 10, Issue: 1, pp [17] Laurent J. C.; and Malhame, R. P A physcally-based computer model of aggregate electrc water heatng loads. IEEE Transactons on Power Systems, Vol. 9, Issue: 3, pp [18] Athow D.; and Law, J Development and applcatons of a random varable model for cold load pckup. IEEE Transactons on Power Delvery, Vol. 9, Issue: 3, pp [19] Aubn, J.; Bergeron, R.; and Morn, R Dstrbuton transformer overloadng capablty under cold-load pckup condtons. IEEE Transactons on Power Delvery, Vol. 5, Issue: 4, pp [20] Leou, R.C.; Gang, Z. L.; Lu, C. N.; Chang, B. S.; and Cheng, C. L Dstrbuton system feeder cold load pckup model. Electrc Power Systems Research, Vol. 36, Issue 3, pp [21] Lang, W.W.; Anderson M. D.; and Fannn, D.R An Analytcal method for quantfyng the electrcal space heatng component of cold load pckup. IEEE Transactons on Power Apparatus and Systems, vol. PAS-101, no. 4, pp [22] ANSI/IEEE C , Gude for loadng mneral-ol-mmersed power transformer up to and ncludng 100 wth 55 C or 65 C wndng rse, The Insttute of Electrcal and Electroncs Engneers, Inc.,1981 from the World Wde Web: ber=1103&syear=1981. [23] Deb, K Mult-Objectve optmzaton usng evolutonary algorthms. Sngapore: John Wley & Sons. [24] Goldberg, D.E Genetc algorthm n search, optmzaton and machne learnng.-: Addson- Wesley. [25] Mesut, E.B.; and Felx, F.Wu Network Reconfguraton n Dstrbuton System for Loss Reducton and Load Balancng. IEEE Transacton on Power Delvery, Vol.4, No.2. [26] Kumar, V.; Gupta, I.; Gupta, H.O.; and Jhanwar, N Optmal Locaton and Szng of Capactor Banks for Power Dstrbuton Systems. Journal of Internatonal Assocaton on Electrcty Generaton Transmsson & Dstrbuton (Afro-Asan Regon), Vol , No. 1. APPENDIX-I Lstng of the bus numbers and the amount of reactve power compensaton provded [26]. Bus No. Capactor Values n kvar

8 8 V. Kumar, R. Kumar.H.C., I. Gupta and H.O. Gupta / GMSARN Internatonal Journal 1 (2007) 1-8