Multiobjective Fuzzy Optimal Power Dispatch Incorporated TCSC and Load Model 1

Transcription

1 roceedgs of the 5th WSEAS Iteratoal Coferece o Appled Coputer Scece, Hagzhou, Cha, Aprl 6-8, 006 (pp78-786) Multobectve Fuzzy Optal ower Dspatch Icorporated ad Load Model Ru Ma, Hogwe Ya Chagsha Uversty of Scece ad Techology Chlg Road 45, Chagsha, Cha Abstract: - Ths paper presets a ult-obectve optal dspatch odel based o optal flow wth the Thyrstor Cotrolled Seres Capactor () ad load statc voltage characterstc. The ze of the pool cost, polluto esso ad actve losses are solved dvdually order to defe the ebershp fucto of obectve, the, the ult-obectve proble s reforulated to a ew stadard olear proble by the fuzzy sets theory ad ax- operator, fally, t s solved by teror pot ethod ad the results that atch wth ultobectve proble s gaed. The effect of o the optal dspatch s also vestgated ths paper. The test results show that the proposed odel ore atch wth the syste operato ad ca esure the ult-factor partalty of Geerato Copay. The test results also show that corporato of ca ot oly utlze the exstg les, but also chage the results of optal dspatch of syste. Key-Words: - ower syste,, Multobectve optal flow, Fuzzy sets theory, Iteror pot ethod Itroducto As ope access arket prcples are appled to syste, syste has chaged fro the cost based operatos to bd based operatos. It created copetto ad tradg echass for arket partcpats. There exst four types of partcpats the arket. They are Idepedet Syste Operator (ISO), Geerato Copay (GeCo), Dstrbuto Copay (DsCo) ad Trassso Copay (TrasCo). Uder the deregulato evroet, arket partcpats pursut of axal proft for theselves. Wth past ad curret dffcultes buldg ew trassso les ad the sgfcat crease trasacto assocated wth copettve electrcty arkets, atag syste securty s ore tha before. A operato pot of a syste ot oly s a stable equlbru of dfferetal ad algebrac equatos (DAE), but also ust satsfy all the of statc costrats at the equlbru, such as upper ad lower buds of geerators, voltage of all bus ad trasfer capablty of all trassso les. Ths operato pot syste s solved by Optal ower Flow (OF) proble that cosderg securty costrats [-]. I other words, OF s to ze operatg costs of syste, trassso losses or other approprate obectve fuctos at the specfed te stace subect to statc equatos ad equaltes. I addto, the creasg publc awareess of the evroet protecto ad the passage of the Clear Ar Act Aedets of 990 have forced the utltes to odfy ther desg or operatos strateges to reduce polluto ad atospherc essos of the theral plats. I [3] evroetal/ecooc dspatch (EED) proble s solved by fuzzy sets theory. I [4] EED proble s solved by a stregth pareto evolutoary algorth. I [5], EED proble s solve by fuzzy satsfacto-axzg approach. However, ths approach are ot based o OF, so, syste securty s ot take to cosderato. I [6], the authors proposed a ultobectve trasacto odel corporated the load statc voltage characterstc to ze for the pool cost ad polluto esso, However, t ot vestgates the effects of ad ot cosders the actve losses. The Electrc ower Research Isttute (ERI) the U.S. foralzed the broad cocept of Flexble AC Trassso Syste (FACTS) [7] the late 980s. The acroy FACTS detfes alteratg curret trassso systes corporatg electrocs-based cotrollers to ehace the cotrollablty ad crease trasfer capablty. Secto II presets the ultobectve optal Ths work s partally supported by the Hua rovce Scece Foudato Grat #05JJ40088 ad the Foudatoal Research Fuds ofchagsha Uversty of Scece ad Techology

2 roceedgs of the 5th WSEAS Iteratoal Coferece o Appled Coputer Scece, Hagzhou, Cha, Aprl 6-8, 006 (pp78-786) dspatch odel based OF cosderg the ad load voltage characterstc, ths secto also descrbes the steady operato odel of s. I secto III, ultobectbe optsato algorth based fuzzy theory for solvg the proposed odel s troduced. Secto I presets the results of applyg the proposed approach to the test syste. Secto s coclusos. Forualto of ultobectve OF corporatg ad load voltage chacterstc. The Model of for ower Flow Cotrol s a seres copesato copoet. Wth the frg cotrol of the thyrstors, t ca chage ts apparet reactace soothly ad rapdly. There are ay papers o the odels of, cludg the steady state odel [7] ad the dyac oe [8]. The steady state odel we used ths paper s show Fg.., ad are the teral buses of the trassso le, s the reactace of the le, R s the resstace of the le. I the odel, we treat as a capactor/ductor whose reactace ca vary betwee 0.5 ad 0.5 tes the oal reactace of the brach. Assue the s stalled the le ad earby, the correspodg actve ad reactve ecto as (),(): p = sθ () = ( cos θ ) p = s θ = ( cos θ ) () s ode voltage of bus, s ode voltage of bus, s the reactace of, θ = θ θ s the phase agle dfferece of bus ad bus. The actve ad reactve balace equatos of the correspodg ode as (3),(4): = s ( Gcosθ+ Bs θ) = 0 (3) = ( G sθ B cos θ ) = 0 (4) s. Obectve Fucto..Mzato of ool urchase Cost the total pool cost ca be expressed as (5): M F = ( f ( ) ) (5) =, f ( g) = ag + b s the bddg fucto of geeratg ut, g s the output of geerator ut, s the uber of total geeratg ut, respectvely...mzato of olluto Esso the atospherc pollutats such as sulpher oxdes SO x ad troge oxdes NO x caused by fossl-fueled theral uts ca be odel separately. However total to esso to ca be expressed as (6) M F = ( α g + βg + γ ) (6) = γ, β, α are esso characterstcs coeffcets of geeratg ut...3 Mzato of Actve ower Losses the total actve losses ca be expressed as (7): 3 g L g (7) L = l= M F = = L LN ( p ( ) p ( ) p3 ) + N +, s the LN N actve dead of bus, N s the ratg voltage of bus ; p, p, p s the coeffcets of 3 polyoal or ZI load odel by load odellg Measureet-based or Statstc-based, p + p + p =. 3.3 Costras.3.Geerato Real ower Lts: For short-ter operato, ut cotet ad hydrotheral plag are gve to the operatg codto. Cosequetly, ay o load ad out-out-ert cost cosderatos that fluece the ut cotet are out the scope of ths paper. g

3 roceedgs of the 5th WSEAS Iteratoal Coferece o Appled Coputer Scece, Hagzhou, Cha, Aprl 6-8, 006 (pp78-786) Therefore the real output lts of geerator are forulated as: g (8) g g ax s the lts of geeratg ut g, g ax.3.oltage Cotrol ad Reactve Support. oltage lts refer to the requreet for the syste bus voltage to rea wth a arrow rage of levels, buses feedg load through ULTC trasforers that hold the load sde voltage wth a very bad-wth, however, buses feedg load through fxed tap trasforer s affected by load odels. oltage s affected by reactve flows. The voltage lts ad reactve output lts ca be expressed as (8) ad (9), we assued the factor of load bus s costat, so reactve copesato s cosdered ths paper. g g gax (9) ax (0) g, g, g ax are stad for reactve output, axal ad al reactve lt of geeratg ut respectvely.,, ax are stad for ode voltage, al ad axal lts of voltage respectvely..3.3 Securty Cotrol Trassso cogesto ay forced the syste operator to buy ore expesve geerato ad polluto stead of cheaper ad cleaer alteratves. Krchoff s law requre that real ad reactve flows balaces at each bus through the syste, addto, ad ZI load odel s corporated to the flow equato, therefore, the aggregate load odel of dstrbuto syste s cosdered OF. Real balace: ( p ( ) + p ( ) + p ) ( G cosθ + Bsθ ) = () G = LN 3 0 N N Reactve balace: = + G LN( q ( ) q ( ) + q3 ) ( Gs B cosθ ) = 0 N N θ () LN, LN s the real reactve dead of bus respectvely, LN = LNtgϕN ; N s the ratg voltage of bus ;, p, p, q, q q s the p 3, 3 coeffcets of ZI load odel by load odelg Measureet-based ad Statstc-based, p + p + p3 =, q + q + q3 =. The ode bus actve ad reactve balace equatos of the correspodg as (3),(4) Trassso costrats: (3) l l lax l = G ( Gcosθ + Bs θ), l, are l ax stad for the real of trassso le l, lts of trasfer capacty of trassso les l.that s, etwork cogesto are odeled by ths costrat. (4) ax, s the cotrol lts of TCAC ax. 3 Algorth of Multobectve OF Icorporatg ad Load oltage Chacterstc 3.Fuzzy Sets Theory for Multobectve Optzato roble By optzg the above-forulated obectve fuctos, we wll obta ot a sgle optal soluto, but a set of areto optal solutoswe troduce the ebershp fuctos that represet the goals of each obectve fucto as follows: F c0 c0 + 0 F µ ( F) = c0 < F < c0 + (5) F c0 + 0 F s the obectve fucto, c 0, 0 s the obectve fucto of sgle-obectve optal ad the acceptable obectve fucto value, respectvely. 3.The proposed approach for solvg the ultobectve OF proble I ths secto, we troduces a approach that cobed the fuzzy sets theory ad the teror pt ethod to solve the ult-obectve proble of (5)-(4). Step: Solve each sgle-obectve proble usg teror pot ethod, respectvely. The process ca be troduced as follows: solve sgle-obectve for pool cost, that s, the proble s forulated by (5) ad (8)-(4), the pool cost C 0 ad bddg results are gaed, thus, the esso value

4 roceedgs of the 5th WSEAS Iteratoal Coferece o Appled Coputer Scece, Hagzhou, Cha, Aprl 6-8, 006 (pp78-786) ' C 0 s also ca bee coputato based o (6); the actve losses C s also gaed based o (7), 0 we solve sultobectve OF odel for zato of esso, the proble ca be odel by (6) ad (8)-(4), the esso C ad bddg results are also get, thus, the pool cost obectve value C ', the actve lossess C are gaed. I the sae way, we solve sultobectve OF odel for zato of actve lossess, the proble ca be odel by (7) ad (8)-(4), the actve losses C ad bddg results are also ' get, thus, the pool cost obectve value C, the polluto esso C are gaed. Step-: Defe ebershp fucto for each obectve. Because of pool cost, esso ad actve losses are all cost type dex, that s, the saller of obectve value, the better of results of operato plag. therefore, we let F ( pg ) c0 + 0 represets a precse upper boud o the axu perssble pool cost. 0 s the tolerace paraeter that s a easure of fuzzess ths costrats, t s very portat to ult-obectve optal ' ' results, 0 ax{ C, C} C.So we ca use the 0 followg atheatcal forulato for ths ebershp fucto: F c0 c + F µ ( F ) = c < F < c + 0 F c (6) the sae way, we let F ( pg ) c + represets a precse upper boud o the axu perssble esso. s the tolerace paraeter that s a easure of fuzzess ths ' costrats, ax{ C0, C} C.So we ca defe a lear ebershp fucto as follows: F c c + F (7) µ ( F ) = c < F < c + 0 F c + we let F 3 c + represets a precse upper boud o the axu perssble esso. s the tolerace paraeter that s a easure of fuzzess ths costrats, ax{ C0, C} C.So we ca defe a lear ebershp fucto as follows: F3 c c + F3 µ ( F3 ) = c < F3 < c + (8) 0 F3 c + STE3: Buld a fuzzy ultobectve optzato operato plag odel based o the fuzzy set theory ad ax- operator, ths proble ca be forulated as follows: Obectve fucto: µ (9) Subectve to: ' ' ( f ( g ) g ) + 0µ ax{ C, C } (0) = ' α + βpg + γpg + µ ax{ C0, C} () = L g L + µ C0 C = l= () ( ) ax{, } 0 µ (3) (3),(4),(8)-(5) Step4: Use the teror pot ethod to solve the ew sgle-obectve odel for axze ebershp degree s bult by step3, thus, the bddg results that atch wth the three obectves are gaed. 4 Exaple Aalyss I ths paper, a 5-bus -geerator test syste s used to sulato. The sgle-le dagra of syste ad paraeters are gve [6], s stalled le betwee ode 4, 5 ad earby the ode 4, the paraeters of are gve [8].The value of bddg prce ad esso coeffcets are gve Table The paraeters of load dead ad ZI load odel coeffcets are gve Table. Table Geerator bddg prce ad esso coffcets G G Cost a b Esso α β γ Table araters of load dead ad coeffcets of ZI load odell Bus LN LN I the sulato results, Table3 shows the coparso of obectve fucto values by sgle /ult obectve optzato wth or wthout ; 3

5 roceedgs of the 5th WSEAS Iteratoal Coferece o Appled Coputer Scece, Hagzhou, Cha, Aprl 6-8, 006 (pp78-786) Table 3 Coparso of obectve values by sgle/ult obectve optzato wth/wthout Actve ool olluto esso losses cost Mze of actve Wth Wthout losses Mze of pool cost Mze of polluto esso Mult-obec tve optzato Wth Wthout Wth Wthout Wth Wthout Table 4 Coparso of bddg of bddg results by sgle/ult obectve optzato wth/wthout Mze of actve Wth Wthout losses Mze of pool cost Mze of polluto esso Mult -obectve Wth Wthout Wth Wthout Wth optal hout Fro Table 3 ad Table 4, Results of obectve values ad bddg results are dfferece betwee wth ad wthout ult-obectve optal flow dspatch odel. 5 Coclusos Ths paper presets a ult-obectve optal dspatch odel wth the Thyrstor Cotrolled Seres Capactor () ad load statc voltage characterstc. The proposed odel s forulated as ult-obectve optal flow (MOF) proble wth copetg pool cost, polluto esso ad actve losses pact obectves. The ze of the pool cost, polluto esso ad actve losses are solved dvdually order to defe the ebershp fucto of obectve, the, the ult-obectve proble s reforulated to a ew stadard olear proble by the fuzzy sets theory ad ax- operator, fally, t s solved by teror pot ethod ad the results that atch wth ult-obectve proble s gaed. The effect of o the optal dspatch s also vestgated ths paper. The test results show that the proposed odel ore atch wth the syste operato. The test results also show that corporato of ca ot oly utlze the exstg les, but also chage the results of optal dspatch of syste. I cocluso, the proposal odel ths paper ca ake evroetal, ecooc ad actve losses are ult-obectve optzato. Moreover, the proposed odel base fuzzy set theory ths paper takes the ecooc, evroetal etwork ste characterstc of Geerato Copay to accout, therefore, the proposed odel ca esure the ult-factors partalty of Geerato Copay. Refereces: []S. Taur, S. Iwaoto, ad Y. Taur. Optal dspatchg of reactve syste plag ad operato. Tras. st. Electr. Eg.Jp.,vol.04-B,o.3,984. []Y C.M.Huag, H.T.Yag, ad C.L.Huag. B-obectve dspatchg usg fuzzy satsfacto-axzg decso approach. IEEE Tras. ower Syste, vol., pp. 75-7,997. [3]Abdo,M.A Evroetal/ecooc dspatch usg ult-obectve evolutoary algorths. IEEE Tras. o ower Syste..vol.8,o.4,pp:59-537,0.. [4]Ma Ru. A ovel b-obectve fuzzy optal short-ter trade plag odel cosderg evroet proecto ad ecooy proft deregulated syste. roceedg of the CSEE,vo. o.4,pp.04-08,0. [5]Ma Ru, He Reu, et al. Multobectve optsato traacto odel corporatg load statc voltage characterstcs. roceedg of the CSEE,vo. o.9,pp.-5,0. [6]G M Huag, N C Nar, oltage stablty costraed load curtalet procedure to evaluate syste relablty easures, roc. IEEE/ES Wter Meetg Ja 0, NewYork [7]G Huag, Ya The pacts of ad SC o ower Syste Load Curtalets, roc. IEEE/ES Suer Meetg, July 00,Caada. [8]L A. S. lotto, W. W. g, A. R. Carvalho, A. Wey, W. F. Log, F. L. Alvarado, A. Edrs, Deterato of eeded FACTS cotrollers that crease asset utlzato of systes, IEEE Tras. ower Delvery, vol., o., Ja. 997, pp