A Modified Newton Raphson Algorithm of Three-Phase Power Flow Analysis in Unsymmetrical Distribution Networks with Distributed Generation

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1 J. Basc. Al. Sc. Res. 3(9) TextRoad ublcaton ISSN Journal of Basc and Aled Scentfc Research A Modfed Newton Rahson Algorthm of Three-hase ower Flow Analyss n Unsymmetrcal strbuton Networks wth strbuted Generaton A-R. Ghasem * R. Ebrahm A. Babaee M. Hoseynoor Bushehr Branch Islamc Azad Unversty Bushehr Iran ABSTRACT There has been a great nterest n use of dstrbuted generaton (G) recently because of some advantages such as loss reducton and mrovement of voltage rofle. Ths requres new software tools to smulate the mact of the G on the system erformance. Therefore ths aer resents a ower flow analyss method for unsymmetrcal dstrbuton systems wth G based on mroved Newton-Rahson method. ue to the unbalanced dstrbuton network t s necessary to consder three-hase model of each comonent of system. Therefore dfferent arts of network are evaluated comletely and arorate models are resented for network load. The roosed method ntroduces a dstrbuton slack bus model through scalar artcaton factors by alyng the concet of generator domans. Also an nternal convergence loo has been aled n ths method to mrove the convergence seed of the load flow calculaton. The artcaton factors are ncororates nto the three-hase ower flow equatons and the aforementoned method solver s dscussed and mlemented. A software ackage has been develoed by elh software to solve the well behaved of unbalanced dstrbuton networks wth usng the roosed method. The effects of usng nternal convergence loo on convergence seed and Gs resentaton on voltage rofle and loss reducton have been studed by usng ths software on the IEEE 34-bus dstrbuton network. Fnally the results are resented and dscussed. KEWOR: ower flow strbuted generator generator doman artcaton factors dstrbuton network. - INTROUCTION ower flow s a very mortant and fundamental tool for the analyss of any electrcal system and s used n the oeratonal as well as lannng stages. Certan alcatons artcularly n dstrbuton automaton and otmzaton of an electrcal system requre reeated load flow solutons. In these alcatons t s very mortant to solve the ower flow roblem as effcently as ossble. In transmsson systems utlzng the Newton-Rahson and the Gous-Sydel solver methods are very oular. However these are non-arorate solvers for dstrbuton network because of ts roertes lke radal structure hgh R/X rato the exstence of unbalanced load. Therefore due to these dstrbuton network roertes whch most of the tme caused the non-rad convergence the secal methods are needed to solve the load allocaton roblem radly [] and []. In addton accordng to the hgh resstvty of dstrbuton systems the network losses should be consdered duraton of the load allocaton [3]. In reference [4] the symmetrcal comonent method and remodelng the network based on ths technque are resented n order to solve the unsymmetrcal-network and unbalanced-load roblems. Ths method has some drown back such as the large tme duraton needed for changes the hased varables nto symmetrcal comonent and vce versa. In reference [5] the enhanced Newton-Rahson method wth admttance matrx and extenson of the frst and second terms of the Taylor seres s roosed as an effcent and rad convergence method. Another roblem whch makes useless the tradtonal ower flow solvers s exstence of Gs. In these years the ntegraton of G nto exstng networks has assocated several techncal economcal and regulatory questons [6]. Therefore tradtonal ower system lannng and oeratng face substantal challenges and new request. In ths new envronment many studes are erformed on dstrbuton ower flow wth resence of Gs. In most of them the am of these studes s concentrated on fndng the ways to handle G unts n ower flow calculatons [7] and [8]. Reference [9] dscussed about otmzaton of mult-tye G caacty and locaton. Ths research used the Newton Rahson (NR) load flow method for balanced dstrbuton network. Reference [0] roosed a methodology for stochastc ower flow n a dstrbuton lne wth dsersed hotovoltac (V) enetraton. Both load and V generaton are stochastc rocesses and the methodology uses a robablstc model for load demand based on measured data and an extensve stochastc modelng of V based on hstorcal meteorologcal data and commercal avalable V anels. In reference [] a fast and also robust load flow method for balanced ower dstrbuton systems wth dstrbuted generaton sources s roosed. Tycal dstrbuton generaton models and dstrbuton load models are ncluded. Also a hybrd drect and ndrect soluton technque s used to acheve effcency and robustness of the algorthm. The author n [] resented SO based dstrbuted Corresondng Author: A-R. Ghasem Bushehr Branch Islamc Azad Unversty Bushehr Iran. 36

2 Ghasem et al.03 generator lacement technque n a balanced dstrbuton system to acheve the best voltage stablty and mrove the short crcut level of system. In ths aer an teratve ower flow was used for calculaton of the mentoned arameters whch can only consder the balanced dstrbuton networks wth Gs. The roosed load flow analyss n [3] s bascally a modfed form of backward forward roagaton method of a radal dstrbuton system to take account for G. Hence the method takes the advantage of both the smlcty of radal dstrbuton system as well as consderaton of G. An effcent backward and forward swee algorthm based on the Krchhoff s crcut laws for the three-hase ower flow s roosed n [4]. For analyss of weakly meshed dstrbuton system the comensaton method s used to break meshes and to calculate the current njectons at each end bus created by breakng the mesh. In ths aer a modfed algorthm of the load allocaton based on Newton-Rahson s roosed whch can be used n unsymmetrcal and unbalanced dstrbuton network ncluded Gs. However dstrbuton networks are usually unbalanced n revous works assumed balanced so ower flow calculaton was very smle and fast. To overcome ths roblem n the roosed method all network comonents and also G are modeled n three hase to consder the unbalanced dstrbuton networks. Also for comensaton of convergence seed an nternal convergence loo s roosed to ncrease the seed of algorthm and guarantee the ower flow convergence. Snce that G connecton s very mortant n reducton of dstrbuton network losses unlke revous methods the roosed algorthm can dstngush the load and loss contrbuton by each G whch can be very useful n G lacement studes and economc analyss for far rcng. Based on above mentoned the man ssues of ths aer are: ) resent all network comonents and varous load models mathematcally for unbalanced three hase ower flow. ) Imlement an nternal convergence loo to ncrease the seed of the roosed algorthm. 3) efne and determne artcaton factors for calculaton of load and loss contrbuton by each G. 4) Extend the unbalanced dstrbuton ower flow equatons to nclude Gs n two Q and V modes. The remander of the aer s organzed as follows: In secton an arorate model for each network comonents such as dstrbuton lnes transformers loads and G s resented. In secton 3 the modfed load allocaton algorthm wth assumtons constrans and requred equatons s dscussed and resented n flowchart. Then n secton 4 results from the method s alcaton to a test network are resented and dscussed. Fnally conclusons are drawn n Secton 5. - ISTRIBUTION NETWORK MOELING strbuton systems are usually unbalanced due to unsymmetrcal network and unbalanced loads of consumers so t s necessary to consder three-hase model of each arts. In ths secton dfferent arts of the network are evaluated comletely and an arorate model for the load allocaton s resented. -- strbuton Lnes Estmaton and comutaton of the overhead lnes medances s a sgnfcant ste n re-analyzng the dstrbuton networks. Because of the exstence sngle-hase double-hase three-hase lnes wthout transosng and also unbalanced loads n any dstrbuton system t s needed to consder the return or ground lne n the mentoned lnes studes. Fgure shows a detaled three-hase lne model n dstrbuton systems. Fgure. The detaled model of three-hase lne n dstrbuton networks. In ths aer the Carson's method s used n order to calculate self and mutual medances of overhead lnes whch the more detals have shown n reference [4]. Therefore the followng equatons are used for self and mutual medances calculaton resectvely: 4 3 Z r f j.560 f.(ln ln ) () GMR f 37

3 J. Basc. Al. Sc. Res. 3(9) Z j f j f.(ln j where f s the network frequency and s the secfc earth resstance. ln ) f () -- strbuton Transformers Transformers are one of the most sgnfcant and comlcated tems to modelng. Consderng tems such as the tye of connecton ta-changers the cols and core losses lays an mortant role to solve the load allocaton roblem. The core abc losses and seres admttance ( T ) matrces can be used to acheve the comlete modelng of transformer [5]. Fgure- llustrates the comlete model of transformer. abc T Fgure. Comlete model of transformer. --- Core losses modelng Based on ERI researches [] the core losses can be formulated by equaton (3) therefore calculaton of the transformers core losses can be wrtten as: S (. u.) S S Q(. u.) S n b n b ( AV ( V Be Ee C V F V where: V: bus voltage n er umt S n = nomnal transformer caacty n kva S b = based ower n kva Other constant values are: A B E ) ) 9 3 C 3.5 F The admttance matrx Another art of transformer model n fgure s seres admttance matrx. The formaton of ths matrx such as delta - star connecton s shown n table. The sub matrces are: I 0 0 II III 0 (4) In addton f the transformer ta rato were equal to : (ntal: secondary) the seres admttance matrx corrected as fallowng: The total arrays of ntal self-admttance matrx dvde on The total arrays of secondary self-admttance matrx dvde on. The total arrays of the mutual-admttance matrx dvde on. (3) 38

4 Ghasem et al.03 Table-. Sub-matrces aled n three-hase transformer admttance matrx. rmary () g g g Connecton tye Secondary (s) g g g Mutualadmttance Selfadmttance abc abc s I I I I -3- Network load modelng Conventonally dstrbuton network feeders suly the loads wth the transformers located on dfferent arts of the lne. It s unsutable to consder the loads one by one n case of the nodes regardng to the large number of them. So n order to reduce the number of nodes a model of the dstrbuted loads s used. The converson of dstrbuted load to a sot load s shown n fgure 3. abc s - I - I - - I t III t III - abc s - I - t III - - t III I I - Fgure 3. Modelng of dstrbuted load to sot load. Regardng to fgure 3 dstrbuted loads can be formulated as: ( )( ) ( ) (5) jq jq V V ( ) 0 (6) ( ) V Ln V V V V V By assumngv V aroxmately s about 0.5. Therefore the half of total dstrbuted feeder load locates at the end and the other half locates at the ntal art. Other tyes of the sot load models whch are used n ths aer are constant ower constant medance constant current and the comlex of them. etals about sot loads model exressed n [3]. -4- G modelng The G n networks s notced by two models: Non-artcatng Gs (Q model). artcatng G (V model). The frst grou (Q) has no control on ts termnal voltages and t ales to the network n the shae of the constant Q loads wth negatve value. The second grou has enhanced technology and the ablty of adjustng the voltage and control the real ower outut where the G buses are modeled as a new tye of V buses shown n followng algorthm [3]: The total njected real ower (the sum of three-hase real ower or nut mechancal ower) s adjustable and remans constant n each rrtaton. Voltage magntudes of each hase of V are equal and secfed. Three voltage hase angles are unknown so equaton (7) shows: c a b a artcaton factors and generator domans artcaton factors are roosed to quantfy the orton of losses for each generator and network source. These factors consderng the network toology evaluate the load dstrbuton and source caactes (ncludng G and network source). The artcaton factors are shown as bellow: (7) 39

5 J. Basc. Al. Sc. Res. 3(9) loss G K 0... m Loss where: m 0 K loss G loss a G loss b G m: Number of artcated Gs n the system : Total real ower losses n the system Loss loss G : Loss assocated wth generator loss c G loss G : Loss assocated wth generator n hase It should be noted that n above equatons ndex 0 belongs to substaton. The defnton of generator doman s the assocate ortons of the electrcal network ther losses and loads to dfferent generators. Regardng dscussed defnton for each generator: load loss G G G 0... m load load a load b load c G G G G where: : the load assocated wth generator load G load G : the load assocated wth generator hase ue to clarfyng the regon of each generator n each hase obtaned ndvdually. In order to estmate the generator doman evaluate the ostve drecton of flow ower n each lne s needed. If the equaton () for each art was correct the drecton of real ower s ostve: Re( V I * j V j I * j ) 0 In ths aer to calculate the generator doman only the real ower s consdered. After estmatng the ostve drectons the factor related to each lne and the bus wth ostve flow ower of generator s determned and the total load and losses ortons for each hase s evaluated as: load G loss G n j0 k j j j j lossj 0... m 0... m where: K and n+: The number of buses and lnes n the system resectvely. : The load assocated wth bus j hase. j lossj : The losses assocated wth lne j hase. j and j : orton load and the Loss assocated wth generator n hase resectvely. 3- The Load Flow Algorthm In ths secton n order to ntroduce the load allocaton algorthm the assumtons constrans and the requred equatons are dscussed at frst. Then the algorthm of rogram n addton to ts flowchart s resented. The system assumtons exressed as fallowng: - System has n+ bus. - System has m generator buses (V). - Bus 0 s the substaton bus. - Generator buses are from number to m. Also the fallowng constran should be satsfed: (8) (9) (0) () () (3) 40

6 Ghasem et al.03 Mn Max Mn Max G G G QG QG QG (4) Regardng to ths equaton for all generators the real (actve) and reactve ower are lmted. The Newton-Rahson solver equaton can be defned by Jacoban matrx as fallowng: F J. x (5) where x shows the unknown factors of the system consst fallowng tems: : The system total real ower loss Loss a... m : The angle of generator buses V m... وn a b c : The angle and the voltage of load buses F s also known and can be dscussed as fallowng equaton for both system substaton and generator buses: c load f ( G KLoss ) m For the load buses: f 0 f Q Q Q 0 a c a m m... n Regardng to mutual medance effects between the lnes we have: n c q q q q V Vk gk cos( k ) bk sn( k ) k 0qa In above equatons and (6) (7) n c q q q q Q V Vk gk sn( k ) bk cos( k ) k 0qa Q are the real ower (actve) and reactve ower of bus n hase resectvely. The algorthm stes are as fallows: Ste) Intal values assumed such as the voltages magntudes equal to the system total losses and angles are equal to 0. Ste) Set the teraton counter k=0 Ste3) esred and ntal for each generator set as: load rated ( k ) G G K In addton ths arameter for substaton shows as fallowng: n c m load load ( k ) G0 G K0 0 a ( k ) ( k ) Ste4) Evaluate F ( x ). Ste5) Sto when (k ) F <tolerance. ( k ) Ste6) Evaluate of J ( F / x) ( k ). x x ( k ) ( k ) ( k ) Ste7) Solve the equaton J x F. ( k ) ( k ) ( k ) Ste8) Correct the voltage magntudes and angels by x x x Ste9) Increase the counter value to K+. Ste0) Evaluate the real and reactve ower bounds of artcatng Gs. Ste) Consder the generator doman for the substaton and artcatng Gs and fnd the ostve drecton of ower flow. ( k ) (k ) Ste) Comutaton K 0 K and go to ste 4. In ths aer due to the Gs artcatng factors lmtaton n both real and reactve ower and the adjustng tas voltage the defned algorthm n reference [3] s comleted and corrected. These correctons whch ncrease the algorthm alance as fallows: If the calculated actve/reactve ower: The outut reactve ower of each generator volated from ts lmted convert the generator nto the generator wth constant ower. (8) (9) 4

7 J. Basc. Al. Sc. Res. 3(9) The outut actve ower of each generator volated from ts lmted convert the generator from roosed V-Slak mode ( K 0 ) nto V mode ( K 0 ) where K s the artcatng factor. In the network wth the V buses the load allocaton results may oscllate between two convergence onts and the calculated owers n authorzed lmtaton maybe varable. Then t ncreases the numbers of the teratons to acheve desred convergence. Therefore due to ncreasng n numbers of the V buses the convergence onts are rased wth the same rato. Two lmtaton nternal and external bounds can be defned to do ths task. At frst V buses suosed as no-lmtaton arameters untl the results acheves an accetable convergence answers ( error t ) then the lmtaton ales and ths rocess contnues to reach the desrable convergence ( error t ). Above technque can be used also for evaluatng the voltage of adjustng tas. By consderng the dscussed theores n ths aer the flowchart of algorthm has shown n fgure 4. Fgure 4. The dagram of corrected algorthm of the load allocaton. 4- RESULTS AN ISCUSSION In ths aer by usng the elh software new software develoed to solve the well behaved of unsymmetrcal and unbalanced dstrbuton networks wth G. In ths software all network arts are modeled based on dslayed equatons frstly then mentoned three-hase load allocaton s erformed accordng to flowchart of fgure 4. In ths secton regardng to the mortance of Gs n convergence seed the advantages of alyng nternal loo and ts effects on some of network roertes and system losses are dscussed. In ths aer the 34-bus standard IEEE network wth voltage level of 4.9 kv s consdered to nvestgate the mact of G unts on the dstrbuton system. Consdered network s llustrated n fgure 5 and the detaled techncal data are shown n reference [6]. 4

8 Ghasem et al.03 Fgure 5. The standard 34-bus IEEE network. In order to avod the oscllatons n both obtaned results of generators from ther lmtatons an nternal loo wth larger convergence than desred can be used. In ths mode the other buses voltages of network wll be closed to desred values and the accetable results wth lower number of teratons can be obtaned after alyng lmtatons nto the generators. Tables and 3 wth two and three Gs have shown the number of teratons for desred convergence due to the dfferent values of the nternal convergence ( t ). The value of 0 for t means runnng algorthm wthout usng the nternal loo and the for t means omsson generators lmtaton. Table. The nternal loo convergence effect (Case wth two Gs) t numbers of teraton Table 3. The nternal loo convergence effect (Case wth three Gs) t numbers of teraton dvergence dvergence The obtaned results n Table have shown that for the ntal values of t the load allocaton erforms wth lower number of teratons n comare to values of 0. and more than t. It should be noted that n ths case (Case ) the G volated from ts outut lmtatons and consdered as a negatve Q load. Snce the load allocaton would be more comlex by ncreasng the Gs numbers the nternal loo would be more benefcal. Therefore accordng to the obtaned results n Table 3 (case ) exstence of three Gs n network wth no nternal loo caused dvergence due to the answer oscllatons. Also the results of Table 3 have shown that for an nternal convergence of 0.00 n ste of the rad convergence occurs due to the generators lmtatons consderaton the evaluated results are nvald. Therefore t seems that the nternal convergence loo shouldn t be very close to the fnal convergence value. At frst to evaluate the effect of the G on network voltage rofle the roosed algorthm has aled on 34 bus IEEE network wthout any Gs and the results have shown n fgure 6. Fgure 6.The voltage rofle of network wthout any Gs. 43

9 J. Basc. Al. Sc. Res. 3(9) As fgure 6 llustrates voltage dro n some buses are unaccetable so the default system s voltage rofle of ths feeder s not wthn the lmts. The reason of ths result s exstence of the large loads and ther far dstances from the substaton bus n the 34 IEEE system. Also due to the exstence of unbalanced load n dstrbuton network voltage rofle for each hase s dfferent from each other whch ths roblem s obvously shown n fgure 6. To nvestgate the effect of G on voltage rofle of ths feeder a G wth 900 kw caacty s assumed n bus 6. Fgure 7 shows the voltage rofle of network n ths condton. Fgure 7. The voltage rofle of network wth a G n bus 6. By comarson between fgures 6 and 7 t can be seen that G connecton to the network mroved the voltage rofle whch s more consderable for termnals buses. In next ste t s assumed that the above G s connected n bus 3. By alyng the roosed algorthm n ths condton the effect of G on the voltage rofle of network can be seen n fgure 8. From fgures 6 and 8 t can be seen that n lke fgure 7 the resence of generator has consderable effects on voltage rofle of buses. By comarng the obtaned results from fgures 7 and 8 t can be seen that G connecton n bus 3 mroved the voltage buses better than when connected n bus 6. Also fgure 8 llustrates that system s voltage rofle of ths feeder s well wthn the desred lmts (5% for both voltage sag or over voltage). Fgure 8. The voltage rofle of network wth a G n bus 3. One sgnfcant results of deloyng G n dstrbuton networks s to mnmse the total system real ower loss due to ower generaton close to the consumng. Therefore n addton of voltage buses calculaton of network losses s consdered n the reared software. As shown n fgures 9 to the real outut ower of substaton generators (f Gs exst) and network losses n dfferent modes are studed. In fgure 9 the real outut ower of substaton and the total network losses are shown when there are no Gs n network. Also the ortons of the real ower and network losses by substaton and G when located on bus 6 have shown n fgure 0. 44

10 Ghasem et al.03 Fgure 9. The losses orton and the three-hase real outut ower of substaton wth no G. Fgure 0. The losses orton and the three-hase real outut ower of substaton and G where located n bus 6. Comarson between fgures 9 and 0 ndcates that the actve ower losses consderable decreased by exstence a G n network. Also n obtaned results because of unbalanced loads exstence n consdered network the outut actve ower and actve ower losses are dfferent for each hase of network. In next ste the locaton of G s changed to bus 3 and the actve ower losses and outut actve ower have shown by the reared software n fgure. Fgure. The losses orton and the three-hase real outut ower of substaton and G where located n bus 3. The obtaned results from fgure shows that lke revous condton usng the G caused the consderable decreasng of total network losses. However n ths condton G has no contrbuton n actve ower losses. In fact n ths condton G desred reactve ower s more than ts lmt so consdered as a negatve Q node whch has no contrbuton on actve ower losses of network. Consequently from the all results exressed n ths secton t can be concluded that the resence of G n dstrbuton network cause the voltage rofle mrovement and reducng the system losses. 45

11 J. Basc. Al. Sc. Res. 3(9) CONCLUSION In ths aer an accurate aroach for consderng Gs n unbalanced ower flow studes s roosed. Frst an accurate modelng of dstrbuton network comonents and dfferent load models were roosed. Then the modfed Newton-Rahson method by alyng an nternal convergence loo defnton of artcatng factors and generaton doman was roosed mathematcally. In contnue based on the roosed algorthm a ractcal rogram was develoed n elh and was aled to a 34-bus test system n order to demonstrate ts alcablty. Based on obtaned results the arorate selecton of the nternal convergence loo rate secally n systems wth Gs lays the notceable role on the numbers of teraton to acheve desred convergence. In the other hand unarecated values lead to the nvald answers. Accordng to the obtaned results by resence of G n consdered dstrbuton network buses voltage rofle mroved whch ths mrovement deends on locaton and sze of the generaton unt. Also the smulaton results have shown that ower generaton n dstrbuton network has been a sgnfcant effect n ower loss decreasng as well as transmtted ower reducton from the substaton to consumers whch defers the network nvestment. Therefore G lacement would be roftable n vew ont of economcal n addtonal of techncal advantages. The obtaned results n dfferent cases have shown that the G sze and locaton effects on ower flow results as well as the other network arameters. Thus n order to brng the most dfferent economc and techncal benefts the best G s sze and locaton can be fned by exert algorthms lke fuzzy or genetc algorthm. ACKNOWLEGMENT Ths research aer has been fnancally suorted by the offce of vce chancellor for research of Bushehr branch Islamc Azad Unversty Bushehr Iran. REFERENCES. M. S. Srnvas 000. strbuton Load Flows: A Bref Revew. ower Engneerng Socety Wnter Meetng : Zhu K.Tomosv 00. Adatve ower Flow Method for strbuton Systems wth sersed Generaton. IEEE Transactons on ower elvery 7(3): S. Tong K. N. Mu 005. A Network-Based strbuted Slack Bus Model for Gs n Unbalanced ower Flow Studes. IEEE Transactons on ower Systems 0(): J. C. M. Vera W. Fretas A. Morelato 004. hase-decouled Method for Three-hase ower Flow Analyss of Unbalanced strbuton Systems. IEE roc.-gener. Transm. strb. 5(5): H. L. Nguyen 997. Newton-Rahson Method n Comlex Form. IEEE Transactons on ower Systems (3): R. E. Abyaneh R. A. Habbabad M. Bavafa 0. A Relablty Methodology for strbuton Systems wth G Journal of Basc and Aled Scentfc Research (JBASR) (9): S. Khushalan J. M. Solank N. N. Schulz 007. eveloment of three-hase unbalanced ower flow usng V and Q models for dstrbuted generaton and study of the mact of G models IEEE Transactons on ower Systems (3): S. M. Moghaddas-Tafresh E. Mashhour 009. strbuted generaton modelng for ower flow studes and a three-hase unbalanced ower flow soluton for radal dstrbuton systems consderng dstrbuted generaton Electrc ower Systems Research 79(4): usran M. Abdllah M. Ashar A. Soerjanto 0. Otmzaton of Mult-Tye strbuted Generaton Caacty and Locaton Based on Bnary Encodng Genetc Algorthm-Newton Rahson Method Journal of Basc and Aled Scentfc Research (JBASR) (7): A. G. Marnooulos M. C. Alexads. S. okooulos 0. Energy losses n a dstrbuton lne wth dstrbuted generaton based on stochastc ower flow Electrc ower Systems Research 8(0): H. Suna. Nkovskb T. Ohnoc T. Takanoc. Kojmac 0. A Fast and Robust Load Flow Method for strbuton Systems wth strbuted Generatons Energy roceda : M. Nafar 0. SO-Based Otmal lacement of Gs n strbuton Systems Consderng Voltage Stablty and Short Crcut Level Imrovement Journal of Basc and Aled Scentfc Research (JBASR) (): Bhujel B. Adhkary A. K. Mshra 0. A Load Flow Algorthm for Radal strbuton System wth strbuted Generaton IEEE Thrd Internatonal Conference on Sustanable Energy Technologes (ICSET) : W. H. Kerestng 00. strbuton system modelng and analyss. CRC ress New ork. 5. Tsa-Hsang Chen Mo-Shng Chen Tosho Inoue aul Kotas Ele A. Chebl 99. Three-hase Cogenerator and Transformer Models for strbuton System Analyss. IEEE Treansactons on ower elvery 6(4): R. M. Crc L. F. Ochoa A. adlla-feltrn and H. Nour 005. Fault analyss n four-wre dstrbuton networks. roceedng IEE Gener. Transm. strb. 5(6):