How To Write A Power Flow Model For A Power Plant

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1 tertiol Jourl of Adves i Egieerig & Teholog, Mrh JAET N: POWER FLOW ANALY OF THREE PHAE UNBALANCED RADAL DTRBUTON YTEM Puthiredd Umpthi Redd 1, irigiri ivgru 2, Prdhmm gmeswrru 3 1 Deprtmet of Eletril d Eletrois Egieerig, ree idieth Egieerig College, Tirupti , di. 2 Deprtmet of Eletril d Eletrois Egieerig, Jwhrll Nehru Tehologil Uiversit College of Egieerig Kid, Kid , di. 3 Deprtmet of Eletril d Eletrois Egieerig, ri eteswr Uiversit College of Egieerig, Tirupti , di. ABTRACT This pper provides ew pproh for power flow d modelig lsis of three phse uled rdil distriutio sstems (URD) usig the simple forwrd/wrd sweep-sed lgorithm. A three phse lod flow solutio is proposed osiderig voltge regultor d trsformer with detiled lod modelig, for the trsformer modelig smmetril ompoets theor is used d ero seuee-voltge d-urret updtig for the sweep-sed methods is show. The vlidit d effetiveess of the proposed method is demostrted simple 19-us uled sstem for grouded we-delt d delt grouded we trsformer oetios. Results re i greemets with the literture d show tht the proposed model is vlid d relile. KEYWORD: Distriutio stem, Forwrd-Bwrd sweep-sed methods, Three-phse lod model lsis, Power flow lsis.. NTRODUCTON Power distriutio sstems hve differet hrteristis from trsmissio sstems [1],[2].The re hrteried s Rdil/wel meshed strutures, Uled etwors/lods: sigle, doule d three phse lods, High resiste/rete(r/x) rtio of the lies, Extremel lrge umer of rhes/odes, hut pitor s d distriutio trsformers, Low voltge levels ompred with those of trsmissio sstems d distriuted geertors[3].[4]. Beuse of the iheret uled ture of the power distriutio sstem, eh us m e hvig lods tht e threephse grouded we or ugrouded delt oeted, two-phse grouded or sigle-phse grouded [5]. The uled ture of power distriutio sstems reuires speil three phse ompoet d sstem models [6]. The opertio d plig studies of distriutio sstem reuires sted stte oditios of sstem e otied from the lod flow solutio[7],[8].the effiie of the etire proess depeds hevil o the effiie d pilit of the lod flow progrm used for this purpose[9]. Most of the reserhers preseted tehiues, espeill to oti the lod flow solutio of distriutio etwors [10],[11] hve proposed lod flow solutio method writig lgeri eutio for us voltge mgitude. However this method is suitle for sigle-phse lsis [12]. A few reserhers hve proposed lod flow solutio tehiues[17] to le uled distriutio etwors [13],[14] hve formulted lod flow prolem s set of o lier power mismth eutios s futio of the us voltges. These eutios hve ee solved Newto s method [15],[16] hve proposed three phse power flow lgorithm sed o the forwrd d word wl log the etwor. The method osiders some spets of three phse modellig of rhes d detiled lod modellig [18],[19]. P. Arvidhu, proposed method [20], A ew fst deoupled 514 ol. 3, ssue 1, pp

2 tertiol Jourl of Adves i Egieerig & Teholog, Mrh JAET N: power flow method for distriutio sstems. mprovemets i the represettio of P uses o three-phse distriutio power flow [21] re proposed. A ew pproh hve give [22], [23] for three-phse Fst Deoupled Lod Flow for Uled Distriutio stems. T.H. Che, N.C. Yg, proposed three-phse power-flow diret ZBR method for uled rdil distriutio sstems [24]. A imple d Diret Approh for Uled Rdil Distriutio stem three phse Lod Flow olutio [25] hve ee explied. The sigifie of this power flow lsis is to ppl lod flow dt for pitor plemet, etwor reofigurtio, voltge regultor plemet et. i URD. This pper presets lgorithm for solvig lod model d power flow lsis of three-phse uled rdil distriutio sstems. The lgorithm is ple of solvig for sstems with m feeders emtig from grid susttio with lrge umer of odes d rhes. This pper osiders ll tpes of lod modellig i.e distriutio sstem lie model, lie shut dmitte model distriuted lod model, pitor model, trsformer modelig, Forwrd-Bwrd weep (FB) lod flow, lgorithm for lod flow, results d disussio, olusios d referees. Bsed o the proposed lgorithm, omputer progrm hs ee developed usig MATLAB d results re preseted for tpil etwor of 19-ode URD.. MODELNG OF UNBALANCED RADAL DTRBUTON YTEM Rdil distriutio sstem e modeled s etwor of uses oeted distriutio lies, swithes or trsformers. Eh us m lso hve orrespodig lod, shut pitor d/or ogeertor oeted to it. This model e represeted rdil iteroetio of opies of the si uildig lo show i Figure 1. ie give rh m e sigle-phse, two-phse, or three-phse, eh of the leled utities is respetivel omplex slr, 2 1, or 3 1 omplex vetor. The model osist of distriutio lie with re without voltge regultor or with or Trsformer. Figure 1. Bsi uildig lo of uled rdil distriutio sstem ilusio of ll models 2.1 Distriutio sstem lie model For the lsis of power trsmissio lie, two fudmetl ssumptios re mde, mel: Threephse urrets re led d Trspositio of the odutors to hieve led lie prmeters. A geerl represettio of distriutio sstem with N odutors e formulted resortig to the Crso s eutios, ledig to N N primitive impede mtrix. The stdrd method used to form this mtrix is the Kro redutio, sed o the Kirhhoff s lws. For iste four-wire grouded str oeted overhed distriutio lie show i figure 2 results i 4 4 impede mtrix. The orrespodig eutios re 515 ol. 3, ssue 1, pp

3 tertiol Jourl of Adves i Egieerig & Teholog, Mrh JAET N: Bus p p p p } } } Bus Figure 2. Model of the three-phse four wire distriutio lie p p = + (1) p p t e represeted i mtrix form s Z p = + (2) T p f the eutrl is grouded, the voltge p d e osidered to e eul. From the l st row of e. (2) it is possile to oti 1 T = (3) d sustitutig e.(3) ito e. (2), the fil form orrespodig to the Kro s redutio eomes Ze p = + (4) Where e e e 1 T Ze = Z = e e e (5) e e e is the Curret vetor through lie etwee odes p d e eul to the sum of the lod urrets of ll the odes eod lie etwee ode p d plus the sum of the hrgig urrets of ll the uses eod lie etwee ode p d, of eh phse. Therefore the us voltge e omputed whe we ow the us p voltge, mthemtill, rewritig e. (4) 516 ol. 3, ssue 1, pp

4 tertiol Jourl of Adves i Egieerig & Teholog, Mrh JAET N: e p = p e p e e e e e e e (6) 2.2 Lie shut dmitte model These urret ietios for represetig lie hrgig, whih should e dded to the respetive ompestio urret ietios t odes p d, re give sh sh sh = 1 2 ( + + ) 2.3 Distriutio stem Lod Model ( + + ) ( + + ) Costt Power: Rel d retive power ietios t the ode re ept ostt. This lod orrespods to the trditiol PQ pproximtio i sigle-phse lsis. Costt mpede: These tpes of lods re useful to model lrge idustril lods. The impede of the lod is lulted the speified rel d retive power t omil voltge d is ept ostt. Costt Curret: The mgitude of the lod urret is lulted the speified rel d retive power t omil voltge d is ept ostt Distriuted lod model ometimes the primr feeder supplies lods through distriutio trsformers tpped t vrious lotios log lie setio. f ever lod poit is modeled s ode the there re lrge umer of odes i the sstem. o these lods re represeted s lumped lods. At oe fourth legth of lie from sedig ode, where two thirds of the lod is oeted. For this dumm ode is reted. Oe third lods is oeted t the reeivig ode. the uled distriutio sstem, lods e uiforml distriuted log lie. Whe the lods re uiforml distriuted it is ot eessr to model eh d ever lod i order to determie the voltge drop from the soure ed to the lst lods. 2.4 Cpitor model hut pitor s re ommol used i distriutio sstems to help i voltge regultio d to provide retive power support. The pitor s re modeled s ostt suseptes oeted i either str or delt. imilr to the lod model, ll pitor s re modeled s three-phse s with the urrets of the missig phses set to ero for sigle-phse d two-phse s. 2.5 Trsformer modelig Three-phse trsformer is represeted two los show i Figure 3. Oe lo represets the per uit lege dmitte mtrix Y d the other lo models the ore loss s futio of T voltge o the seodr side. (7) 517 ol. 3, ssue 1, pp

5 tertiol Jourl of Adves i Egieerig & Teholog, Mrh JAET N: Figure 3. Geerl Three-phse Trsformer Model Now tht Y is ot sigulr, the o ero seuee ompoets of the voltges o the primr P side e determied -1 = Y Y (8) P P s imilr results e otied for forwrd sweep lultio -1 = Y Y (9) s P P Where is the oero seuee ompoet of, Y is sme s Y, exept htt the lst row is repled with [1 1 1 ], d s Y re otied settig the elemets i P the lst row of d Y P to 0, respetivel. Oe the oero-seuee ompoets of or P re lulted, ero-seuee ompoets re dded to them to form the lie-toeutrl voltges so tht the forwrd/wrd sweep proedure otiued.. FORWARD - BACKWARD WEEP (FB) LOAD FLOW METHOD 3.1 Bwrd weep: The purpose of the wrd sweep is to updte rh urrets i eh setio, osiderig the previous itertio voltges t eh ode. Durig wrd propgtio voltge vlues re held ostt t the vlues otied i the forwrd pth d updted rh urrets re trsmitted wrd log the feeder usig wrd pth. Bwrd sweep strts from extreme ed rh d proeeds log the forwrd pth. p e L C Figure 4.igle phse lie setio with lod oeted t ode etwee phse & eutrl. Figure 4 shows phse of three-phse sstem where lies etwee odes p d feed the ode d ll the other lies oetig ode drw urret from lie etwee ode p d. 518 ol. 3, ssue 1, pp

6 tertiol Jourl of Adves i Egieerig & Teholog, Mrh JAET N: Durig this propgtio differet lod urrets d pitor urrets (if exist) re lulted usig mthemtil models of lods d pitors preseted i setio 2.1. The lie hrgig urrets of ll the rhes re dded to the lod urret. Figure 5 show rh of the distriutio etwor, oeted etwee two odes p d d M su-lterls re oeted th to it. The pret rh urret feeds the lod t the ode d the su-lterls oeted to the pret rh. This urret e lulted usig E. (10). Figure 5. Brh of distriutio etwor oeted to M su-lterls 1 = L + + m Y (10) sh m M m M m m Where Y is the hlf lie shut dmitte of the rh i sh th itertio. m is the rh urret vetor i lie setio i th itertio. m is the urret vetor i rh m efore updtig i th itertio. 1 is the voltge vetor of the rh m i (-1) th itertio. m M represets the set of lie setios oeted to th rh f pitor is pled t the reeivig ed of the rh the pitor urret should lso e iluded. Tle 1. shows mthemtil Models of differet lods(str & delt oeted) whih gives ostt power, ostt impede d ostt urret. Aother dvtge of the proposed method is ll the dt is stored i vetor form, thus svig mout of omputer memor. The proposed method fids extesive use i etwor reofigurtio, pitor plemet d voltge regultor plemet studies. Tle 1. Mthemtil Models of differet lods 519 ol. 3, ssue 1, pp

7 tertiol Jourl of Adves i Egieerig & Teholog, Mrh JAET N: Forwrd weep The purpose of the forwrd sweep is to lulte the voltges t eh ode strtig from the soure ode. The soure ode voltge is set s 1.0 per uit d other ode voltges re lulted s = + p Ze Y sh p (11) Where, p re the voltge vetors of phses for p th d th odes respetivel i th itertio. e e e Ze = e e e e e e is the urret vetor i th rh i th itertio. These lultios will e rried out till the voltge t eh us is withi the speified limits. Therefore the rel d retive power losses i the lie etwee odes p d m e writte s: ( )( ) * = p (12) Where is vetor of power loss with three, two or sigle phse p d re voltge vetor of three phses t odes p d is the rh urret vetor of three phses for the setio oeted i etwee p th d th ode 3.3 Forwrd Bwrd sweep method lgorithm tep 1: Red iput dt regrdig the uled rdil distriutio sstem. tep 2: Determie forwrd Bwrd propgtio pths. tep 3: itilie the voltge mgitude t ll odes s 1 p.u d voltge gles to e 0 0, , d for phse A, phse B d phse C respetivel. tep 4: Determie forwrd Bwrd propgtio pths. tep 5: itilie the voltge mgitude t ll odes s 1 p.u d voltge gles to e 0 0, , d for phse A, phse B d phse C respetivel. tep 6: et itertio out =1 d = tep 7: Clulte lod urrets d pitor urrets(if exist) t ll odes. tep 8: Clulte the rh urrets usig e. (10) i the wrd sweep. tep 9: Clulte ode voltges usig e. (11) i the forwrd sweep tep10: Che for the overgee, if the differee etwee the voltge mgitudes i two oseutive itertios is less th the go to step 9 else set =+1 d go to step 5. tep11: Clulte rel d retive power loss i eh rh. tep12: Prit voltges d power losses t eh ode. tep13: top. 520 ol. 3, ssue 1, pp

8 tertiol Jourl of Adves i Egieerig & Teholog, Mrh JAET N: REULT AND DCUON This method omputes the power flow solutio for its give rdil etwor with its lodigs d illustrted with 19 ode test sstem of uled rdil distriutio sstem. The outome of this pper is to ppl lod flow dt for pitor plemet, etwor reofigurtio, voltge regultor plemet et. i URD re ver useful. 4.1 Exmple 1 A 19 ode uled rdil distriutio sstem is show i Figure 6. The lie d lod dt re give i [23]. For the lod flow the se voltge d se MA re hose s 11 d 1000 A respetivel. Tle2: oltge d Phse gles of 19 ode URD Node No. Existig method [23] Proposed method Phse A Phse B Phse C Phse A Phse B Phse C Figure 6. igle lie digrm of 19 ode URD 521 ol. 3, ssue 1, pp

9 tertiol Jourl of Adves i Egieerig & Teholog, Mrh JAET N: Tle3: Ative d Retive Power flows of 19 ode URD Tle4: ummr of test results of 19 ode URD Desriptio Phse A Phse B Phse C Miimum oltge Mx. oltge regultio (%) Totl Ative Power Loss (W) Totl Retive Power Loss (Ar) Totl Ative Power Demd (W) Totl Retive Power Demd (Ar) Totl Feeder Cpit (A) oltge profile with ompriso of the proposed method with existig method d tive d retive Power flows of 19 ode URD re give i tle 2 d 3. oltge vritio is give i tle 2, whih gives etter mgitudes re otied i proposed method. The tive power flow gives higher power flow pit with proposed method show i Tle 3. The Tle 4 gives summr of test results for 19 ode uled rdil distriutio sstems. From tle 4 it hs ee oserved tht the miimum voltge i phses A, B, C is , d t ode 19. The mximum peretge voltge regultio i phses A, B d C re 4.82%, 5.01% d 4.93%. The totl tive power loss i phses of A, B d C re 4.34, 4.42 d 4.54 W d the totl retive power loss i phses of A, B d C re 1.95,1.90 d 1.94 A respetivel. The rel power losses i phses A, B d C re 3.64%, 3.96% d 3.78% d the retive power losses re 3.32%, 3.34% d 3.33% of their totl lods. The solutio is overged i 4 itertios d time te is seods for 19 ode URD. The proposed method is ple of solvig for sstems with m feeders emtig from grid susttio with lrge umer of odes ompred with the existig method [23] d results re foud stisftor.. CONCLUON this pper, simple lgorithm hs ee preseted to solve power flow d lod modelig i.e distriutio sstem lie model, lie shut dmitte model, Distriuted lod model, pitor model d trsformer modelig of uled rdil distriutio etwors. The proposed method hs good 522 ol. 3, ssue 1, pp

10 tertiol Jourl of Adves i Egieerig & Teholog, Mrh JAET N: overgee propert for prtil distriutio etwors with prtil R/X rtio. Computtioll, this method is extremel effiiet; s it solves simple lgeri reursive eutios for voltge phsers d other dvtge is ll the dt is stored i vetor form, thus svig omputer memor. The Forwrd-Bwrd weep (FB) lgorithm is ple of solvig for sstems with m feeders emtig from grid susttio with lrge umer of odes d rhes. A omputer progrm hs ee developed usig MATLAB d results re preseted for tpil etwor of 19-ode URD. REFERENCE [1] W.H.Kerstig, A method to the desig d opertio of distriutio sstem, EEE Trs. o Power Apprtus d stems, ol.pa , pp [2] Che. T. H, Che M., Hwg. K. J, Kots. P, Cheli. E. A., "Distriutio sstem power flow lsis- rigid pproh," EEE Trs. o Power Deliver, vol. 6, o. 3, pp , Jul [3] Che. T. H, Che M., Hwg. K. J, Kots. P, Cheli. E. A, Three phse geertor d trsformer models for distriutio lsis EEE Trs. power Del., vol. 6, o. 4, pp , Ot [4] Bishop. M.T, Foster J.D, Dow D. A, "The pplitio of sigle phse voltge regultors o threephse distriutio sstems," Rurl Eletri Power Coferee, pp. C2/1- C2/7, April [5] Ds.D, Kothri.P, Klm.A, "imple d effiiet method for lod flow solutio of rdil distriutio sstems," Eletril Power d Eerg stems, vol. 17, o. 5, pp , Ot [6] hirmohmmdi. D, Crol. Cheg. A, A Three phse power flow method for rel time distriutio sstem lsis, EEE Trs. o Power stem, ol. 10, No. 2, M [7] Zimmerm. R. D, Chig. H. D, "Fst deoupled power flow for uled rdil distriutio sstems," EEE-PE Witer Meetig, pper o. 95, New Yor, [8] Ghosh., Ds.D, Method for lod flow solutio of rdil distriutio etwors, EE Pro. Geertio, Trsmissio d Distriutio, ol. 146, No. 6, pp , [9] Goswm.. K, Bsu, "Diret solutio of distriutio sstems," EE Pro., pt. C, vol. 188, o. 1, pp , [10] Thurm. D, Wieoo Bd. H.M, Jerome.J, "A Roust three phse power flow lgorithm for rdil distriutio sstems," Eletri Power stem Reserh, vol. 50, o. 3, pp , Ju [11] Li. W.M, u. Y., Chi.H.C, Teg. J.H, "Three-Phse uled distriutio power flow solutios with miimum dt preprtio," EEE Trs. o Power stems, vol. 14, o. 3, pp , Aug [12] Li.W. M, Teg. J. H., "Three-Phse distriutio etwors fst deoupled power flow solutios," Eletri Power d Eerg stems, vol. 22, o. 5, pp , Ju [13] Gri. P. A. N, Perei. J. L. R, Cmerio., Dost.. M, Mrti. N., "Three-Phse power flow lultios usig the urret ietio method," EEE Trs. o Power stems,vol. 15, o. 2, pp , M [14] Mui K. N, Chig H. D, Existee, uiueess d mootoi properties of the fesile power flow solutio for rdil three phse distriutio etwors, EEE Trs. Ciruit d st., vol.47, o.10, pp , Ot [15] Teg. J. H, A Networ-Topolog-sed Three-Phse Power Flow for Distriutio stems, Proeedigs of Ntiol iee Couil ROC (A), vol.24, o.4, pp , [16] Kerstig W. H, Distriutio stem Modelig d Alsis, CRC Press [17] Gri. P. A. N, Perei. J. L. R, Cmerio., oltge otrol devies models for distriutio power flow lsis, EEE Trs. Power st., vol. 16, o. 4, pp , Nov [18] Teg. J. H, "A Modified guss- seidel lgorithm of three phse power flow lsis i distriutio etwor," Eletril Power d Eerg stems, vol. 24, o. 2, pp , Fe [19]. Herri, L. i, d J. Clu, Review of hrmoi lod flow formultios, EEE Trs.Power Del., vol. 18, o. 3, pp , Jul [20] P. Arvidhu, A ew fst deoupled power flow method for distriutio sstems, Eletri power Compoets d stems, vol.31, o. 9, pp , [21] Gri. P. A. N, Perei. J. L. R, Cmerio, mprovemets i the represettio of P uses o three-phse distriutio power flow, EEE Trs. Power Del., vol. 19, o. 2, pp , Apr [22] Je-Ho Teg, Chuo-Ye Chg, Bwrd/Forwrd weep-bsed Hrmoi Alsis method for Distriutio stems EEE Trs. Power Del.,vol. 22, o. 3, pp , Jul [23] A. R. Htmi d M. Prs Moghddm, Three-Phse Fst Deoupled Lod Flow for Uled Distriutio stems, ri Jourl of Eletril d Computer Egieerig, vol. 6,o.1,witer-sprig ol. 3, ssue 1, pp

11 tertiol Jourl of Adves i Egieerig & Teholog, Mrh JAET N: [24] T.H. Che,N.C. Yg, Three-phse power-flow diret ZBR method for uled rdil distriutio sstems, ET Geertio Trsmissio Distriutio, ol. 3, ssue 10, pp , [25] J.B.. urhmm, C. Rdhrish d K. Pduumr, A imple d Diret Approh or Uled Rdil Distriutio stem three phse Lod Flow olutio Reserh Jourl of pplied iees, Egieerig d Teholog, vol. 2, o.5, pp , Augest,2010. Authors P.UMAPATH REDDY: He Reeived B.E from Adr Uiversit d M.Teh.,(Eletril Power stems) from Jwhrll Nehru Tehologil Uiversit, Atpur, di i 1998 d 2004 respetivel, Now he is pursuig Ph.D. ree. Curretl he is with Deprtmet of Eletril d Eletrois Egieerig, ree idieth Egieerig College, Tirupti, di. His reserh iterest iludes Power distriutio stems d Power stem opertio d otrol. He is Life Memer of di oiet for Tehil Edutio..ivg Ru: He reeived B.E from Adr Uiversit d M.Teh.ree i 2000 from T, Khrgpur d did his Ph.D from Jwhrll Nehru Tehologil Uiversit, Atpur, di i He is presetl worig s Assoite professor i J.N.T.U.College of Egieerig Kid,(Autoomous) Kid, Adrprdesh, di. He reeived two tiol wrds (Pdit Md Moh Mlvi memoril Prie d est pper prie wrd from the stitute of Egieers (di) for the er He is referee for EEE ourls. He hs roud 75 Ntiol d tertiol ourls i his redit. His reserh iterest iludes Power distriutio Automtio d Power stem opertio d otrol. P. gmeswr Ru: He is presetl worig s professor i..u. College Egieerig, Tirupti. Otied his diplom d B.Teh i eletril Egieerig, M.Teh i power sstem opertio d otrol d Ph.d i.. Uiversit, Tirupti. is res of iterest re power sstem opertio, plig d pplitio of fu logi to power sstem, pplitio of power sstem lie o-lier otrollers. 524 ol. 3, ssue 1, pp