IMPROVED THREE PHASE POWER FLOW METHOD FOR CALCULATION OF POWER LOSSES IN UNBALANCED RADIAL DISTRIBUTION NETWORK

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1 24 th tertol Coferee o Eletrty struto Glsgow, Jue 217 er 489 MROE HREE HAE OWER FLOW MEHO FOR CALCULAON OF OWER LOE N UNBALANCE RAAL RBUON NEWORK omslv ALNJAK v AC Kruo RUNC HE O Crot FER - Crot HE O - Crot tomslv.lk@he.hr v.v@fer.hr kruo.tru@he.hr ABRAC Reetly, the eed for mrovg the effey of dstruto etwork terms of ower losses s eg emhszed. A lrge shre of totl ower losses refers to low voltge etworks whh re usully uled. For the ower flow lyss t s eessry to use three hse modelg. hs er resets modelg of dstruto etwork elemets d ther mlemetto kwrd/forwrd swee (BF) ower flow method. A mrovemet of BF method s develoed y usg the redth-frst serh method for etwork reumerg d reto of modfed dee mtrx. he mroved method mmzes the red elemets of eh terto d results sgft reduto of totl lulto tme wthout ury loss. hs mrovemet mkes ths method more sutle for usg rel tme lultos. he roosed method s used for lulto of ower losses uled d symmetrl etwork whh re omred. he urose of ths test s to show the dvtge of three hse ower flow lyss omred to symmetrl model. NROUCON Reetly, ower loss reduto d rese of dstruto etwork effey of dstruto etworks re eg emhszed. struto etworks re mostly rdl systems tht re hrterzed wth short rhes wth my lterls, lrge umer of odes, three hse d sgle hse users tht use uled lods. ue to resg eetrto of dstruted geerto ower flow oth dretos of rdl system tht lso mts o eletrl odtos d further omltes the mgemet of dstruto etwork. o esure dstruto etwork rellty, rese ts effey d to ele oetos of dstruted geerto t s eessry to rese etwork utomto d mlemet tve dstruto mgemet tht lso ludes otmsto of ower losses. For otmsto of ower losses t s eessry to mke ower flow lyss. ue to hgh R/X rto of dstruto etwork, ower flow methods tht re ommoly used for trsmsso etwork lyss, lke Guss-edel or Newto-Rhso, re ot sutle euse they do t lwys overge. For ower flow lyss of dstruto etworks re rther used BF method d ldder etwork theory method tht re oth desred [1]. Comrso of these methods s mde my reserhes d my of them more refer BF method lke [2] d [3]. Alyss of uled etworks y usg symmetrl model use urte results whh re rtulrly exressed low voltge etworks. Hee, for etter ury t s eessry to use three hse models. he urose of ths er s to reset the wy of modellg of three hse dstruto etwork elemets ludg les, trsformers d lods. el se s low voltge etwork tht s four wred le wth eutrl wre. Hee t hs to e trsformed three hse model so t e used the sme lulto wth three hse models of mddle voltge etworks. After defg three hse models tertve three hse ower flow BF method lgorthm wll e desred. ht method wll e used for lulto of totl ower losses dstruto etworks. For lrge etworks lulto tme e sgftly resed so t mkes some dffultes mlemetto of ths method rel tme lyss. ths er uthors mde mrovemet of the ommoly used BF method y reumerg of etwork odes d rhes y usg redth-frst serh grh theory method. he roosed method mmzes the umer of red elemets of dee mtrx, whh s srse mtrx, d thus redues the lulto tme. Comrso of lulto tme of the ommoly used BF method d the roosed method wll e mde for etworks wth vrous umers of odes. eveloed lgorthm wll e used for omrso of the results of ower losses lulto y usg symmetrl model d the three hse model. he lyss wll e mde o rel low voltge etwork d the results wll rove the dvtges of three hse model. HREE HAE RBUON NEWORK ELEMEN Le model struto mddle voltge les ossts of three hse odutors whle low voltge les ossts of three hse d o eutrl odutor. For three hse model of le t s eessry to defe mede d dmtte mtrx, oth wth dmesos 3 3. For four wred low voltge etwork tl mede d dmtte mtrx hve dmeso 4 4 d they eed to e trsformed to mtres wth dmeso 3 3. Fg. 1 resets four wred le seto model etwee odes d. he odutor medes etwee odes d of the sme hse re lled self-oulg medes d medes etwee odutors of dfferet hses re lled mutul-ouled medes. CRE 217 1/5

2 24 th tertol Coferee o Eletrty struto Glsgow, Jue 217 er 489 ( 1 ) (7) where (8) 1 (8) Fg. 1 Le model of four wred etwork For the utlty freuey of 5 Hz the formul for selfoulg medes s (1) d for mutul-oulg medes s (2) [4]: 93 R1,5,628l / km (1) Flly, mede mtrx e redued to dmesos 3 3 (9) [5]: (9) Fg. 2 resets the le seto model wth hse to hse d hse to groud shut tes: 93,5,628l / km (2) where R 1 resste of the odutor [Ω/km], r Erth resstvty [Ωm], Geometr Me Rdus of odutor [m], dste etwee hses d [m]. hese medes re used for reto of mede mtrx 4 4 (3) (3) Kro reduto s used for reduto of ths mtrx to dmesos 3 3. oltge euto etwee odes d s (4) [5]: Mtres re dvded loks y les so t e lso wrtte s (5): f the eutrl wre s grouded, the eul d the result s (6): 1 sertg (6) (5) gves (7): d (4) (5) re (6) Fg. 2 Le seto model wth shut tes elf d mutul otetl oeffets re defed s (1) d (11) [1]: l km F (1) / l km F (11) / where dste from odutor to ts mge [m], rdus of odutor [m], dste from odutor to the mge of odutor [m], dste from odutor to odutor [m]. hese otetl oeffets re used for reto of dmtte mtrx of ode (12): 1 B B B B B B (12) B B B f the vlues of self d mutul dmttes re kow, dmtte mtrx s eul to (13): 1,,, 2 (13) CRE 217 2/5

3 24 th tertol Coferee o Eletrty struto Glsgow, Jue 217 er 489 hut urrets ode re eul to (14): sh sh (14) sh sh ot lod models hree hse model of str oeted lod wth ostt ower t ode e exressed s (15): lod lod lod lod (15) gle hse lod urrets re lulted y usg (15) ut oly hse where the lod s oeted, whle the urret other two hses s eul to zero. eedg o the trsformer oeto vetor grou the model s derved y oetg three sgle hse models. Oe of the most ommoly used trsformers dstruto etwork s y5. ts three hse model s show Fg. 4 d ts urret-voltge euto s (18): A B C A B C (18) Curret d voltge le eutos otl urret tht flows through le seto s eul to sum of ll shut urrets ode, ll lod urrets ode d urrets of ll rhes tht ext from ode ext (16): lod sh ext (16) lod sh ext lod sh ext oltge euto s eul to (17): (17) rsformer model A sgle hse trsformer s modeled s four-ole model (Fg. 3). Fg. 3 A sgle hse trsformer model Fg. 4 Euvlet model of three hse trsformer y5 OLUON ALGORHM he roosed method s sed o BF method. ut rmeters re feeder voltge, lods ll odes, le rmeters d msmth tolere. Modfed dee mtrx he frst ste fter tlzto s to rete dee mtrx of the etwork. struto etworks re usully rdl wth lterls. her dee mtrx s srse mtrx where zero elemets me o oeto, -1 reresets sedg odes whh re loted o mtrx dgol d 1 reresets reevg odes. Redg of ll the elemets sgftly rologs lulto tme. he umer of red elemets NRE for every ste of BF s eul to umer of o-dgol elemets of uertrgulr mtrx ( ): ( 1) NRE (19) 2 CRE 217 3/5

4 24 th tertol Coferee o Eletrty struto Glsgow, Jue 217 er 489 he de of the roosed method s to rete modfed dee mtrx MM y usg redth-frst serh method where ll the o-dgol d o-zero elemets of eh row wll e sorted seuetly d thus mmze NRE. he method wll e exled o 9- ode smle etwork o Fg. 5. Fg. 5 A 9-ode smle etwork he umers elow the odes re ode lels. he frst ste of the method s to gve the ordl umers to odes d rhes. he frst ode s the feeder ode (usully usr or sustto) d the frst rh s tht whh eters the feeder ode. he odes tht re oeted to the frst ode re suessvely ssged wth ext ordl umers, d the ordl umers of rhes re eul to the ordl umer of the ode tht they eter. he for eh of these odes ther eghour odes re serhed d they get the ext free ordl umer. erhg s fshed whe the ed ode of the etwork s rehed. Fg. 5 the ode ordl umers re led ove the odes d the rh umers re led rles. A sheme of reumerg for the smle etwork s show Fg. 6. Fg. 6 Reumerg sheme for 9-ode smle etwork New ordl umers re used to rete MM. he th ode s led o the dgol elemet of the th row of the dee mtrx. he dgol elemets rereset reevg odes of rhes. All odes tht re oeted to the th ode re led the uer-trgulr rt of the mtrx the olum tht s eul to ther ordl umer. Fg. 7 reresets dee mtrx d ts modfto MM d the le oets oly elemets tht re red every loo. Fg. 7 dee mtrx d ts modfto BF method After reto of MM tertve roess of BF strts. eh terto k the frst ste s lulto of odl urrets ll odes (2): (k 1) 1) (k (k1) (2) (k 1) he ext ste s kwrd swee whh strts from the ed ode d suessvely moves to the feeder ode. he rh urrets re lulted s sum of odl urrets reevg ode d urrets of ll rhes tht ext the reevg ode (21): ext (21) he thrd ste s forwrd swee whh strts from the feeder ode d moves towrds the ed ode. Nodl voltges re lulted y usg (22): (22) Fl ste of eh terto s lulto of voltge msmth for every ode (23): (k1) 1,2,..., (23) f the voltge msmth for every ode ll hses s lower th tolere lmt, terto roess stos. otl ower losses re lulted s sum of ower losses ll rhes d losses shut tes (24): loss loss (24) loss, E REUL rh shut erforme test rogrm ode of ommoly used BF d the roosed method s mde MALAB order to omre ther exeuto tmes for etworks wth vrous umers of odes. All tests re mde o omuter wth AM Athlo 64 X2 dul ore roessor 2.5 GHz d 6. GB RAM. he erforme tests re mde o smle three hse dstruto grds wth 9, 34, 1, 25, 5 d 1 odes. Eh test s erformed for overgee tolere ε=.1. Clulto durtos re omred le. Gve results re verge vlues of te oseutve lultos. otl umers of dee mtrx elemets tht re red durg the terto roess (NRE) for oth methods re omred le. CRE 217 4/5

5 24 th tertol Coferee o Eletrty struto Glsgow, Jue 217 er 489 le Comrso of lulto durtos (ε =.1) ε =.1 Nodes me roosed tertos BF (s) reduto method (s) (%) % % % % % % le Comrso of totl NRE (ε =.1) ε =.1 Nodes roosed Numer BF method reduto (%) % % % % % % Bsed o test results t e oluded tht the roosed method s sgftly more effet, d the effey s more emhszed lrger etworks. For the etwork wth 1 odes tht overges 6 tertos the roosed method redues umer of dee mtrx red elemets for more th seve tmes whh uses the three tmes shorter exeuto tme omrso wth the ommoly used BF method. ower losses lyss of uled etworks Oe of the gols of ths er s to omre results of ower losses lulto uled dstruto etworks wth three hse model d symmetrl model. est ws erformed for fve ses of dly dgrm of low voltge uled etwork tht s suled from sustto 1/.4 k v. Mte er lvosk Brod, Crot, wth 64 three hse d 18 sgle hse ustomers (Fg. 8) d test results re show le. Fg. 8 Low voltge,4 k etwork of sustto 1/.4 k v. Mte le Comrso of ower losses lulto results y three hse model d symmetrl model otl otl ower losses (ka) me Msmth ower (h) hree (%) (ka) ymmetr hse 1: : : : : For ower losses lyss of uled etworks three hse model s more urte euse t dstgushes three hse d sgle hse lods s well s symmetry of three hse lods. Bsed o test results t e oluded tht the more uled lod of the etwork uses greter msmth etwee the results. hus, for ower losses lyss of uled dstruto etworks, eselly of low voltge etworks, t s reommeded to use three hse model. CONCLUON hs er resets how to use three hse ower flow lulto BF method for uled dstruto etworks. he uthors develoed mrovemet of ommoly used BF y modfto of dee mtrx y redth-frst serh method whh resulted sgft reduto of rogrm exeuto tme. he roosed method s used for lulto of ower losses uled etworks d the oluso s tht t s more urte th symmetrl model. Although three hse lulto model s more omlex th symmetrl model, d thus t lsts loger, mrovemet reseted ths er, whh sgftly shortes rogrm exeuto tme, mkes the roosed method sutle for lto rel tme lyss. REFERENCE [1] W.H. Kerstg, 22, struto system modellg d lyss, CRC ress, Bo Rto, UA [2] K. Krush Murthy,.. Jy Rm Kumr, 212, hree hse uled rdl dstruto lod flow method, tertol refereed Jourl of Egeerg d ee, ol. 1, No. 1, [3] A. Alsd, B. Gholm, 29, A effetve roh for dstruto system ower flow soluto, tertol Jourl of Eletrl, Comuter, Eerget, Eleltro d Commuto Egeerg, ol. 3, 1-5 [4]. v, 211, rofz roru tokov sg, Udze sveulst u greu, gre, Crot [5] J.B.. urhmym, 29, Lod flow soluto of uled rdl dstruto systems, Jourl of heoretl d Aled formto ehology, ol. 6, No. 1, 4-51 CRE 217 5/5