Preventive Corrective Rescheduling for Reactive Power Reserve Maximization using Generation Participation Factors

Transcription

1 Internatnal urnal f ChemTech Research CODEN( USA): ICRGG ISSN : l.5, N., , Arl-une 03 ICGSEE-03[ 6 March 03] Internatnal Cnference n Glbal Scenar n Envrnment and Energy Preventve Crrectve Reschedulng fr Reactve Pwer Reserve Maxmzatn usng Generatn Partcatn Factrs Pushendra Sngh *, L S Ttare, L D Arya 3 Deartment f Electrcal Engg., ITS, Satna, MP 85 00, Inda, emal: Deartment f Electrcal Engg., GEC, abalur, MP 8 00, Inda, 3 Deartment f Electrcal Engg., SGSITS, Indre, MP 5 003, Inda. *Crres.aur: ersngh@redffmal.cm Abstract: Ths aer resents an evlutnary-based arach fr reventve cntrl f lad bus vltage. Develed algrm tmzes a set f reactve wer cntrl varables and maxmzes reactve reserve avalable at generatng buses. ltage deendent reactve wer lmts have been accunted. The tmal settngs f reactve wer cntrl varables have been btaned fr next nterval redcted ladng cndtn. These tmzed settngs satsfy e eratng nequalty cnstrants n redcted lad cndtn as well as n resent base ladng cndtns. Dfferental evlutnary algrm s a smle ulatn-based search algrm fr glbal tmzatn and has a mnmum number f cntrl arameters. A ulatn based dfferental evlutnary (DE) strategy has been used fr tmzatn. Obtaned results usng DE have been cmared w se btaned usng aner ulatn based technques PSO and CAPSO. Keywrds: Reactve wer reserve, generatn artcatn factr, dfferental evlutnary algrm, statc vltage stablty lmt.. Intrductn: The rblem f reactve wer tmzatn has layed an mrtant rle n tmal eratn f wer system. The adjustment meds f reactve wer flw cnsst f e adjustments f generatr vltages, transfrmer tas, shunt caactrs and nductrs. Snce e generatr vltages are cntnuus, e transfrmer rats and shunt caactrs and nductrs are dscrete. Reactve wer tmzatn (RPO) has cmlex and nn -lnear characterstcs w large number f nequalty cnstrants. Cnventnal tmzatn technques, such as lnear rgrammng and nnlnear rgrammng take advantages n cmutng seed and cnvergence w e bjectve functn f cntnuus, dfferentable and sngle eak value. Yet cnventnal meds cannt handle e dscrete cntnuus rblem n reactve wer tmzatn. Recently, cmutatnal ntellgence-based technques have been rsed n e alcatn f reactve wer tmzatn such as genetc algrm (GA), Tabu search, smulated annealng, artcle swarm tmzatn (PSO) a nd dfferental evlutn (DE). These are cnsdered ractcal and werful slutn schemes t btan e glbal r quas-glbal tmum slutn t engneerng tmzatn rblems. At tmes such schemes are termed as heurstc tmzatn technques. Dfferental evlutn algrm can btan hgh-qualty slutns wn shrt calculatn tme and have stable cnvergence erfrmance. Wu et al 3 rsed tmal reactve wer dsatch usng an adatve genetc algrm. aradarajan and Swaru rsed dfferental evlutn algrm fr tmal reactve

2 Pushendra Sngh et al/int..chemtech Res.03,5() 00 wer dsatch. Zhang et al 5 have resented dynamc mult-gru self-adatve dfferental evlutn algrm fr reactve wer tmzatn. The rblem was a mxed-nteger, nn-lnear tmzatn rblem w nequalty cnstrants. Avalablty f reactve wer at surces and netwrk transfer caablty are tw mrtant asects, whch shuld be cnsdered whle reschedulng f reactve wer cntrl varables. Nedwck et al 6 have resented a reactve management rgram fr a ractcal wer system. They have dscussed a lannng gal f sulyng system reactve demand by nstallatn f adequately szed and adequately lcated caactr banks whch wll ermt e generatng unt near t unty wer factr. Dng et al 7 develed an tmzed reactve reserve management scheme usng Bender s decmstn technque. Yang et al 8 resented a technque fr reactve wer lannng based n chance cnstraned rgrammng accuntng uncertan factrs. Generatr ututs and lad demands mdeled as secfed rbablty dstrbutn. Mnte-Carl smulatn alng w genetc algrm has been used fr slvng e tmzatn rblem. Wu et al 9 descrbed an OPF based arach fr assessng e mnmal reactve wer surt fr generatrs n deregulated wer systems. HE et al 0 rsed a med t tmze reactve wer flw (ORPF) w resects t multle bjectves whle mantanng vltage securty. Zhang et al develed a cmutatnal med fr reactve wer market clearng. Reactve wer reserve avalable at a surce s an mrtant and necessary requrement fr mantanng a desred level f vltage stablty margn. Pwer netwrk may have e transfer caablty f reactve wer but f reserve s nt avalable and reactve wer lmt vlatn ccurs an e statc vltage stablty lmt may be nadequate. Furer reactve reserves avalable at surces wll nt be f much hel n mantanng desred level f stablty margn, f netwrk transfer caablty s lmted. Ths aer rses a medlgy fr vltage stablty enhancement accuntng netwrk ladng cnstrant as well as tmzng reactve wer reserves at varus surces n rrtn t er artcatn factrs decded based n ncremental lad mdel. ltage deendent reactve wer mdel has been used fr determnng reactve wer reserves, whch utlzes feld heatng as well as armature heatng lmt. Inequalty cnstrants n base as well as fr next redcted nterval ladng cndtn have been cnsdered n antcatn. Sectn- exlans rblem frmulatn. Sectn-3 resents mlementatn f e develed algrm fr tmzng bjectve functn. Sectn- gves results and dscussns. Sectn-5 gves cnclusns and hghlghts f e aer.. Prblem frmulatn. Maematcal frmulatn The reactve reserve tmzatn rblem s frmulated as a search rblem whse bjectve s t maxmze e effectve reactve reserve subject t varus eratng and stablty cnstrants,3. Objectve functn s gven as fllws: ) () k ( Abve bjectve functn s tmzed subject t fllwng cnstrants: () Pwer flw cnstrants under current eratng cndtn as well as next redcted ladng cndtn, accuntng reactve wer reschedulng: P f (, ) g(, ) () Inequalty cnstrant n lad bus vltages n resent as well as fr next redcted nterval lad at s lad bus vltages are wn lmt, accuntng reactve wer reschedulng: () NL (3) - lad bus vltage under base ladng cndtn., lad bus vltage - Lwer an uer bund n - lad bus vltage fr redcted next nterval ladng cndtn.

3 Pushendra Sngh et al/int..chemtech Res.03,5() 0 () Inequalty cnstrant n mnmum egen value f lad flw acban at current eratng nt as well as next redcted lad cndtn accuntng reactve wer reschedulng: mn mn mn mn (v) Reactve wer generatn cnstrant under base cndtn as well as at next redcted ladng cndtn accuntng reactve wer reschedulng: k,,..., NG, -Lwer an uer bund n reactve wer generatn at - Reactve wer generatn at - Reactve wer generatn at () (5) k bus. k bus fr redcted next nterval lad. k bus under base ladng cndtn It s stressed here at s vltage deendent. It s furer clarfed at based n mnmum rtr current lmter, e urse f whch s t avd very small rtr current (ese may cause rblem fr exctatn systems) are f nterest fr synchrnus cmensatrs nt fr synchrnus generatrs. (v) Inequalty cnstrant n cntrl varables: X X X (6) NC NL and NC dentes set f lad buses and number f cntrl varables. In bjectve functn relatn (), dentes reactve wer generates at k generatr bus and s e generatr artcatn factr fr k generatr bus.. Determnatn f generatr artcatn factr: s generatn artcatn factr whch s btaned at next redcted lad as fllws: () Obtan mnmum egen value and crresndng egen vectr f reduced lad flw acban. The reduced lad flw acban s btaned as fllws: 3 = 0 0 (7) [ 3 ][ ] [ ] R (8) 3

4 Pushendra Sngh et al/int..chemtech Res.03,5() 0 Mnmum egen value f R and asscated egen vectr [ ] Obtan / s calculated as: ( ) / Calculate and Calculate reactve wer njectn changes at e generatr buses as fllws: are btaned en ut []. g, k.obtan generatn artcatn factr max ) (9) /( g, 3. Imlementatn f dfferental evlutnary algrm t slve frmulated rblem: Ste-: Data nut; Reactve wer cntrl varables and system arameters (resstance, reactance, and suscetance etc.) Ste-: lad flw slutn s btaned. Ste-3: Next nterval redcted lad. Ste-: Lad flw fr e redcted next nterval lad Ste-5: Intalzatn; Generate ulatn f sze M fr cntrl varables [ X, X,..., X M ] frm unfrm dstrbutn between X X X, j,,..., NC j(mn) j j(max) Ste-6: Run lad flw fr each samled vectr X,,..., M. Ste-7: If a vectr satsfes all nequalty cnstrants n base cndtn as well as n next redcted nterval call t F (feasble) erwse call t NF (nt- feasble). Ste-8: Select target vectr. Ste-9: Select base vectr X base whch s feasble and gves e best value f bjectve functn usng Eq. (). Ste-0: Select tw vectrs X and X such at base q Ste-: Obtan a mutated vectr k ( k ) ( k ) ( k ) ( k ) X base ( X X q q - s knwn as scale factr usually les n e range [0, ]. X and selected vectrs. X base Ste-: Generate tral vectr - s knwn as base vectr. k t ) - s a mutant vectr. X q - are tw randmly ( k ) v, j, f ( rand j C r r. j j rand ) ( k ) t, j ( k ) x, j, Oerwse Crssver rbablty ( C r ) les n e range [0, ]. Ste-3: If any cmnents f e tral vectr crsses e bundary en aly bunce back technque used. Thus t s assumed at all cmnents f tral vectrs are wn lmt. Ste-: The tral vectr t s selected n e new ulatn accrdng t Lamnen s crtera.

5 Pushendra Sngh et al/int..chemtech Res.03,5() 03. Results & Dscussns The develed algrm has been mlemented n 6-bus IEEE standard test systems. 6-Bus System Ths system cnssts f tw generatr buses and fur lad buses. Ths system has n all sx reactve wer cntrl varables namely tw generatr bus vltages, shunt cmensatns at buses and 6 and OLTCs at lne number and 7. Maxmum nternal vltages and synchrnus reactances were assumed as Emax. 0 u, Emax. 05u, X d. 00 u and X d. 5u. The lmts f P-bus vltages, shunt cmensatns and OLTCs have been assumed as 0.95u t.5 u, 0.00 u t u and t.0 resectvely. Reactve wer lmts (lwer and uer) f generatng bus, lyng between u t.0000 u and generatng bus are lyng between u t.0000 u 5. Ttal base real and reactve wer lad n e system are.3973u and 0.33 u resectvely. alue f rxmty ndcatr at base cndtn s mn and bjectve functn. 03. The statc vltage stablty lmt s.07u. Table shws P- bus vltage and all er lad bus vltages under base cndtn. The desred range f lad bus vltage s 0.95u and.05 u. Threshld value f rxmty ndcatr has been assumed as mn, Intally, 00 ulatns f each cntrl varable have been generated randmly usng Excel sftware accrdng dstrbutn characterstc f cntrl varable. Only fve artcles (cntrl varables) were selected whch satsfed all nequalty cnstrants. Fg. gves a lt between reactve wer cntrl varables (,, Bsh, Bsh6, Ta, Ta7 ) satsfyng all nequalty cnstrants and bjectve functn ( ). Fg. shws varatn f bjectve functn ( ) w resect t number f teratn f a selected samle whch has and c r After 57 teratns n varatn s fund n bjectve functn ( ). Table gves tmzed set f cntrl varables and all lad bus vltages. Ttal reactve reserve avalable s.77 u. Statc vltage stablty lmt has been btaned as.3573u. Best ntal slutn (artcle) selected as u,. 088u, B SH 0. 00u, B u SH , TAP 9350 u 0. and TAP7. 063u. Reactve reserves at bus N. and w best ntal slutn were.35 u and u resectvely. Whereas, w tmzed slutn ese reactve reserves are btaned as.5095u and u resectvely. Magntude f rxmty ndcatr w tmzed slutn s , bjectve functn s Table 3 shws e cmarsn f dfferental evlutnary w PSO & CAPSO meds based n rxmty ndcatr, stablty lmts and reactve reserves. Table- Lad flw slutn fr 6-bus test system under stressed cndtn. Ttal lad ( P d ). 360 u, Prxmty ndcatr ( mn ) Statc vltage stablty lmt. =.07u S. N Cntrl varables Cntrl varables magntude(u) Lad bus vltages Lad bus vltage magntude(u) * BSH * BSH * 5 TAP TAP7.063 * - Lad bus vltage level belw e secfed lmt

6 Pushendra Sngh et al/int..chemtech Res.03,5() 0 Reactve wer cntrlvarable & bjectve functn Bsh Bsh6 Ta Ta7 3 5 Number f samle Fgure Intal ulatn f artcles (reactve wer cntrl varables) whch satsfy all secfed nequalty cnstrants fr 6-bus test system Objectve Functn Number f teratn Fgure Plt f bjectve functn () w resect t number f teratns fr 6-bus system. Table- Otmzed set f cntrl varables and all lad bus vltages fr 6-bus system. Ttal lad P d. 360 u, Prxmty ndcatr mn S. N Cntrl varables Cntrl varables Magntudes (u) Lad bus vltages Lad bus vltages Magntudes (u) BSH BSH TAP TAP Table-3 Cmarsn f Dfferental Evlutnary med w PSO & CAPSO meds fr 6-bus test system. S. N. Medl gy Prxmty Indcatr Stablty Lmt (u) Objectve Functn ( ) N f Iteratn Reactve reserve (u) Otmzed Otmzed Otmzed Otmzed PSO CAPSO DE Cnclusn Ths aer has resented an algrm fr maxmzatn f reactve wer reserves n rder t mantan vltage rfle fr e next redcted ladng cndtn. Ths has been acheved va a DE algrm. Advantage f DE algrm s at ts mechanzatn s smle wut much maematcal cmlexty. Mrever glbal tmal slutn s btaned and lcal tmal slutn s avded va bunce back search rcedure. Imrtant abut e medlgy s at nt nly reactve reserve s tmzed but nequalty cnstrant n rxmty ndcatr

7 Pushendra Sngh et al/int..chemtech Res.03,5() 05 rvdes requred statc vltage stablty margn. Netwrk as well as surce caabltes are mrtant frm vltage nstablty vewnt. Result and erfrmance f e DE based algrm have been cmared w er tw ulatn based n PSO and CAPSO. References. Mmh.A., El-Hawary M.E. and Adaa R., A revew f selected tmal wer flw lterature t 993. II. Newtn, lnear rgrammng and nterr nt meds, IEEE Trans. n Pwer Systems, 999, (), Deb K., Mult bjectve tmzatn usng evlutnary algrms,. W. & Sns, Wu.H., Ca Y.. and Wen.Y., Otmal reactve wer dsatch usng an adatve genetc algrm, Int.. f Electrcal Pwer & Energy Systems, 998, 0(8), aradarajan M. and Swaru K.S., Dfferental evlutnary algrm fr tmal reactve wer dsatch, Int.. f Electrcal Pwer & Energy Systems, 008, 30(8), Zhang X., Chen W., Da C., and Ca W., Dynamc mult-gru self-adatve dfferental evlutn algrm fr reactve wer tmzatn, Int.. f Electrcal Pwer & Energy Systems, 00, 3, Nedwck P., Mstr r A.F. and Crasdale E.B., Reactve management a key t survval n e 990s, IEEE Trans. n Pwer Systems, 995, 0(), Dng F., Chwdhury B.H., Crw M.L. and Acar L., Imrvng vltage stablty by reactve wer reserve management, IEEE Trans. n Pwer Systems, 005, 0 (), Yang N., Yu C.W., Wen F. and Chung C.Y., An nvestgatn f reactve wer lannng based n chance cnstraned rgrammng, Int.. f Electrcal Pwer & Energy Systems, 007, 9(9), Wu H., Yu C.W., Xu N. and Ln X.., An OPF based arach fr assessng e mnmal reactve wer surt fr generatrs n deregulated wer systems, Int.. f Electrcal Pwer & Energy Systems, 008, 30(), He R., Taylr G.A. and Sng Y.H., Mult-bjectve tmal reactve wer flw ncludng vltage securty and demand rfle classfcatn, Int.. f Electrcal Pwer & Energy Systems, 008, 30(5), Zhang T., Elkasrawy A. and enkatesh B., A new cmutatnal med fr reactve wer marked clearng, Int.. f Electrcal Pwer & Energy Systems, 009, 3, Kundur P., Pwer System Stablty and Cntrl, New Yrk: Mc Graw-Hll Inc.; Arya L.D., Ttare L.S., and Kar D.P., Imrved artcle swarm tmzatn aled t reactve wer reserve maxmzatn, Int.. f Electrcal Pwer & Energy Systems, 00, 3, Lamnen., A cnstrant handlng arach fr dfferental evlutn algrm, Prc. f 00 cngress n evlutnary cmutatn (CEC-00),, Bjwe P.R., Kar D.P. and Arya L.D., Allevatn f lne ver lads and vltage varatns by crrectve reschedulng, Prc. IEEE Part-C 993, 0(), *****