Impact Analysis of Transmission Capacity Constraints on Wind Power Penetration and Production Cost in Generation Dispatch

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1 The 14th Internton Conference on Integent ystem Appctons to ower ystems, IA 2007 ovember 4-8, 2007, Kohsung, Twn Imp Anyss of Trnsmsson Cpcty Constrnts on Wnd ower enetrton nd roducton Cost n Generton sptch Chun-Lung Chen Tsung-Yng Lee, Member, IEEE Abstr-- Wnd power penetrton n Twn power system fces sgnfcnt brrers due to mted trnsmsson cpbty. One of the most mportnt future chenges seems to be the mngement of the ntegrton of fuctutons n the eectrcty producton from wnd energy sources. In ths pper, penty functon-drect serch method (-M s deveoped to further modfy the drect serch method (M to mprove computton effcency. The -M gorthm s used to fctte economc shrng of generton nd reserve cross res, nd mnmze the tot generton cost n the mut-re wnd-therm coordnton dsptch probem. ever technque constrnts re pped to determne the optm proporton of wnd genertor cpcty tht cn be ntegrted nto the mut-re soted system. umerc experments re ncuded to understnd the effects of wnd genertor cpcty n producton cost nyss nd to ustrte the mps of trnsmsson cpcty mts on wnd power penetrton eve n ech re. Index Terms Wnd-therm coordnton dsptch, wnd power penetrton eve, re spnnng reserve, trnsmsson cpcty mts, penty functon-drect serch method. W I. ITROCTIO ITH the dvnce n wnd turbne technooges, wnd energy hs become compettve wth other fue-bsed generton resources. nce the cost of wnd turbne genertors (WTGs hs been reduced to gret extent, nstton of WTGs s fue svers s economcy nd envronmenty ttrve n wndy regons. It woud be benefc to ncrese the power suppy cpcty n Twn by the nstton of power pnts usng wnd energy sources [1], [2]. espte vrous benefts of the wnd power, the ntermttency nd unpredctbty of wnd power generton cretes dffcuty n the contro of fuency nd schedung of generton. Ths my cuse operton ssues nd wste usbe cpcty when the nstton of the wnd generton ncreses. It cn be expected tht mny probems w rse n the renewbe energy bsed hybrd power system, prtcury n system operton nd pnnng [3]-[9]. Wnd power penetrton n Twn power system fces sgnfcnt brrers due to mted trnsmsson cpbty. g. C. L. Chen s wth the eprtment of Eectrc Engneerng, Mnghsn nversty of cence nd Technoogy, Hsn-Chu, Twn, R.O.C. (x , e-m: ccung@must.edu.tw T. Y. Lee s wth the eprtment of Eectrc Engneerng, Mnghsn nversty of cence nd Technoogy, Hsn-Chu, Twn, R.O.C. (x , e-m: tyee@must.edu.tw 1 shows smpe network mode of Twn power system. It cn be dvded nto three res; the southern re, the centr re nd the northern re. ote tht bout 50% of tot od demnd nd ony 30% of tot power generton re n the northern re. Are power unbnce, resutng n undesrbe hevy fows mong the three res, w ncur hgh trnsmsson osses nd cuse nstbty. In ddton, n ntegrton of wnd generton nto the mut-re eectrc grd s dffcut to mnge. The mn chenge ssoctes wth ts vrbty nd unpredctbty. To ensure the securty nd rebty of the system, mntnng suffcent emergency reserve cross sever unts n ech re s much more cpbe of respondng fuency devtons nd system od pck-up foowng contngency for n soted system such s Twn power system. gnfcnt mounts of wnd power generton w be ured for the schedung ddton generton reserves to cover the unpredctbe wnd genertor output vrtons. Besdes, the re spnnng reserve ured ncreses wth the u re wnd power generton. Both of them re nterreted, not seprtey. To further tke dvntge of resources, t my be dvntgeous for the system to fctte economc shrng of generton nd reserve cross res, nd vod dsptched reserve beng trpped by severe trnsmsson bottenecks. These compex condtons mke t very dffcut for sovng the extended wnd-therm coordnton probem to cheve optm utzton of wnd energy sources n the mut-re Twn power system. Incorportng ddton physc nd economc operton constrnts nto the generton schedung probem dds further compexty to the souton methodoogy. The terture on ppcton of optmzton methods for generton dsptch s vst [10]-[14]. To de effectvey wth the coupng constrnts of the probem, penty functon-drect serch method (-M s deveoped n ths pper to sove the mut-re economc generton nd reserve dsptch probem consderng wnd power generton. The proposed gorthm cn mnmze the tot generton cost when the optm wnd power penetrton eve n ech re s reched. Test resuts re provded to ustrte the merts of the proposed method nd to ustrte the mps of trnsmsson cpcty mts on wnd power penetrton eve n ech re wthn the Twn power system. 353

2 The 14th Internton Conference on Integent ystem Appctons to ower ystems, IA 2007 ovember 4-8, 2007, Kohsung, Twn j (30% of tot generton C j C (30% of tot generton (40% of tot generton j g. 1. A smpe network mode of Twn power system. II. ROBLEM ORMLATIO The optm dsptch of generton n mut-re wndtherm system nvoves the dsptchng of generton mong wnd pnts nd therm pnts n order to mnmze the tot producton costs whe stsfy constrnts. Genery, the fue cost of therm generton unt w be second order poynom functon. The generton cost of WTGs from the pubc utty s the chepest becuse t needs no fue. Becuse of the ntermttency nd unpredctbty of wnd power generton, ddton physc nd economc operton constrnts must be tken nto consderton to rech compromse between system securty nd tot opertng cost. Accordng to the network shown n g. 1, the mthemtc mode of the mut-re wnd-therm coordnton dsptch cn be stted s foow. Objecton functon: Mnmze T = T = 1 orthern Are,, Centr Are, C, C ( (1 T s the tot generton cost; s the ndex for therm unts; T s the number of therm unts n system; ( s the producton cost functon of therm unt ; nd s the generton of therm unt. subject to the foowng constrnts. C outhern Are C R R (50% of tot od demnd R C R C (20% of tot od demnd R R (30% of tot od demnd + C = j (b Are up reserve urement constrnts R R, C, (5 R = R + AR (, C, (6 j R +, R C +, C, C R, C (c Are down reserve urement constrnts R R, C, (10 R = AR(, C, (11 j R +, R C +, C, C R, C (4 (7 (8 (9 (12 (13 (14 (d Trnsmsson cpcty mts constrnts, C (15 = +,,, C (16, C, re the northern, centre nd south respectvey; C,, re the od demnd n ech re;, re the trnsfer power nd fow mts from centr re to northern re respectvey; nd C, re the trnsfer power nd fow C mts from southern re to centr re respectvey.,, re the trnsfer up nd down reserves from centr, re to northern re respectvey;, C, re the trnsfer, C up nd down reserves from southern re to centr re respectvey; R, RC, R re the up-spnnng reserve urements n ech re (consderng wnd power C generton; R, R, R re the up-spnnng reserve urements n ech re (not consderng wnd power C generton; AR, AR, AR re the ddton up-reserve urements n ech re (consderng wnd power generton; R, RC, R re the down-spnnng reserve urements n ech re (consderng wnd power C generton; nd AR, AR, AR re the ddton downreserve urements n ech re (consderng wnd power generton. 1 ystem Constrnts ( Import/export power bnce constrnts + + = C j + + C = j C C (2 (3 2 Therm Genertor Constrnts (e nt s mum up/down reserve contrbuton constrnts = d% (17 = d% (18 (f nt s up/down spnnng reserve contrbuton constrnts 354

3 The 14th Internton Conference on Integent ystem Appctons to ower ystems, IA 2007 {, } mn { }, = mn (19 = mn (20 (g nt cpcty constrnts mn (21 s the mum up-reserve contrbuton of therm unt ; s the mum down-reserve contrbuton of therm unt ; contrbuton of therm unt ; nd s the up-reserve s the down-reserve contrbuton of therm unt. s the upper generton mt of therm unt ; mn s the ower generton mt of therm unt ; nd d % s the percentge of mum unt cpcty. 3 Wnd Genertor Constrnts (h Wnd power curve constrnts 0 v vij or v > voj * = ϕ j ( v vij v v (22 Rj vrj v voj ( Actu wnd generton mt constrnts * 0 (23 j s the ndex for wnd unts; W s the number of wnd unts n system; s the upper generton mt of wnd unt j; * s the vbe generton of wnd unt j; nd s the u generton of wnd unt j. v s the wnd speed; v s the cut n wnd speed of wnd unt j; Ij v Rj s the rted wnd speed of wnd unt j; v s the cut out wnd speed Oj of wnd unt j; nd ϕ ( s the wnd power curve of wnd unt j. j III. OLTIO METHO A IMLEMETATIO O -M The drect serch method (M, frst ntroduced by Chen nd Chen, hs been successfuy pped to E probem consderng trnsmsson cpcty constrnts [12]. urthermore, n tertve M s so proposed to sove the probem of wnd-therm coordnton dsptch n hybrd power system [15]. The proposed tertve M gorthm decomposes the coordnton probem nto wnd nd therm sub-probems. These schemes terte between the two subprobems unt the soutons converge. However, the prevous work negected the modeng of trnsmsson networks, whch re very mportnt n wnd-therm coordnton ppctons. In ddton, the probem s further compcted to the generton schedung mposed by the presence of coupng constrnts, such s the retonshp between the re spnnng reserve urements nd the re u wnd power generton. These compex condtons mke the conventon M gorthm very dffcut to sove the mut-re wndtherm coordnton probem n rge sze soted system. Besdes, the tertve M gorthm, however, tkes onger tme for convergence. To further speed up the souton process, penty functon-drect serch method (-M s proposed for hndng coupng constrnts propery. To ccount for re up reserve urement votons (5, re 355 down reserve urement votons (10 nd trnsmsson cpcty mt votons (15, the tot opertng cost s ugmented by nonnegtve penty terms C1, C2 nd C3, respectvey, penzng constrnt votons. Thus, the ugmented cost functon s formed nd T A = C1 T = 1, C, C2, C, C3, C ( + C1+ C2 + C3 (24 ( R R R ( R R R ( H ( R H( R H( T = 1 ovember 4-8, 2007, Kohsung, Twn R R (25 (26 (27 ( (28 nd H(x s the Hevsde (unt step functon. The penty terms C1, C2 nd C3 re proporton to the correspondng votons nd zero n cse of no voton. There re chosen hgh enough s to mke constrnt votons prohbtve n the fn souton. Another nequty nd equty constrnts of the probem cn be hnded propery n the enhnced drect serch procedure. The over procedure of the proposed mut-re wnd-therm coordnton gorthm cn be stted s foows: tep 1 Generte n nt souton for ech re. tep 2 et nt ccuton step 1 nd reduced for K. tep 3 =1. tep 4 erform n enhnced drect serch procedure. tep 5 Is greter thn predefned resoutonε? Yes, =/K, go to step 4; otherwse, go to step 6. tep 6 rnt resuts. The proposed -M gorthm cn be stted n det s foows: A. Int outon Estmte for Ech Are In ppyng the -M to sove the generton schedung probem, t s qute key tht rndomy nt souton s nfesbe owng to the rge set of operton constrnts nherent n the mut-re wnd-therm coordnton dsptch probem. In ths pper, smpe procedure s used to determne the proper nt souton estmte of ech re. The computton steps of the nt souton estmte re shown s foows. tep 1 rt of the od demnd s frst dstrbuted to the wnd power generton nd the mnmum generton mts of the therm unts n ech re. tep 2 egectng the re up/down reserve urement constrnts nd trnsmsson cpcty constrnts, therm unts wth hgh effcency re chosen to ncrese ther outputs by mum steps for stsfyng ther own re generton urements. If the u re generton s greter thn the re od demnd, export s much economc excess power s possbe to other res to stsfy other re generton urements.

4 The 14th Internton Conference on Integent ystem Appctons to ower ystems, IA 2007 ovember 4-8, 2007, Kohsung, Twn tep 3 Ccute the nt opertng cost (ncudng producton cost nd penty cost. ote tht the penty cost cn be evuted by ppyng the Eqs. (25-(27. B. etermne the Optm Wnd ower Generton for Ech Are Becuse of the unpredctbe rse nd f n wnd genertor output, sgnfcnt mounts of wnd generton w be ured for the schedung of ddton emergency reserves to mntn dequte fuency contro. The system rmpng cpcty, the od demnd nd the sze of the power system re mportnt fors n determnng the proporton of wnd genertor cpcty tht cn be ntegrted nto the mut-re soted system. In ths pper, sever technque constrnts re pped to decde the optm wnd power generton for ech re. rst, the vbe wnd genertor power output s functon of the wnd veocty. econd, the u re wnd power generton must stsfy the mnmum permssbe power of therm genertors nd the re down-spnnng reserve urement. More specfcy, the re wnd power penetrton s restrcted by the system mum up/down spnnng reserve contrbuton of therm unts nd by the trnsmsson cpcty mts constrnts. Consderng these constrnts on the re wnd power generton, the optm wnd power penetrton eve cn be evuted propery by usng the drect serch procedure. As resut, the optm wnd-therm generton coordnton probem cn be overcome through the use of procedure bsed on the enhnced drect serch process to ugment the serchng technque for determnng the optm wnd power penetrton eve n ech re. C. Enhnced rect erch rocedure Exporton on ntzton begns wth fndng the best drecton for mprovement. To fnd drecton tht reduces the tot opertng cost nd eds to pont wthn the fesbe regon, nother procedure my be needed to ugment the serchng technque wth ght computton expenses. Onet--tme serch s n effectve strtegy of drect serch procedure for hndng coupng constrnts effectvey wthout ntroducng ny mutpers. The computton steps of the enhnced drect serch procedure re shown s foows: tep 1 nts, wthout votng the mum or mnmum generton mts re to ncrese or decrese ther outputs by the predefned step for ccutng ther ncrement costs (IC nd decrement costs (C. Ths s shown s foows: ( + ( IC =, therm genertor (29 IC = 0, j wnd genertor ( ( C =, therm genertor (30 C = 0, j wnd genertor subject to mn + nd, therm genertor (31 * + nd 0, j wnd genertor =1, 2,, T; j=1, 2,, W tep 2 A unts re exmned to check f there s ny mprovement. If no more mprovement cn be cheved, then stop; otherwse, go to step 3. tep 3 An ndependent unt wth mnmum ncrement cost ICx (ssume unt x s chosen to ncrese ts output by the predefned step, nd then, ony dependent unt Cy (ssume unt y, y x whe gnng the most reducton n the tot opertng cost T A, shoud be seected to reduce ts output to stsfy the od bnce equton. ote tht the penty cost s wys ccuted frst t ech possbe step. tep 4 The outputs of ths prtcur pr of unts w be djusted gn by the predetermned step f they do not vote the generton mts, nd ony the ncrement cost of unt x nd the decrement cost of unt y need to be reccuted. tep 5 Go to step 2. IV. MERICAL EXERIMET To exmne the merts of the proposed method, the prc Twn power system wth 52 therm genertng unts ws studed [12], [15]. The percentges of tot system od t ech re re shown n g. 1. The fow mts from centr re to northern re nd from southern re to centr re re set to be 3000 MW. The up spnnng reserve urements n ech re re ssumed to be 900 MW, nd the mum up/down spnnng reserve of ny snge unt coud not exceed more thn 10 percent of ts rted cpcty (d%=10%. In ths study, the ncresed re up/down spnnng reserve urements re ccuted s smpe fron of the predcted re wnd generton (r%=20%. It s ssumed tht wnd genertor does not provde reserve. The prmeters of -M re seected s: the nt ccuton step 1 =80 MW, the reduced for K=5 nd the predetermned resouton ε =0.01 MW. A the computton s performed on C entum IV-3.0 GHz computer, nd computer progrms were deveoped n ORTRA. These cses re stted n det s foows. A. Effect of Wnd ower Generton Integrton on Generton chedung The frst cse s to ustrte the mp of ncorportng wnd genertors nto the system on the exstng utty generton schedung probem. Tbe I gves comprson of resuts consderng wnd power generton or not for the od of MW. Ignorng the wnd power generton, ony the up-reserve urement (900 MW s ured n ech re to respond to unt forced outges nd od forecstng errors. However, sgnfcnt mount of wnd power generton w ure the schedung of ddton generton reserves. As shown n the thrd coumn of Tbe I, t cn be seen tht 1000 MW of re wnd generton cuses 200 MW ncrese n the need for re up/down reserve to operte the soted Twn power system reby nd effcenty. It cn so be seen tht 1000 MW of re wnd power generton ncreses the bty of therm genertors to provde reserve. It shoud be notced tht the northern re hs mted generton cpcty n ths cse study nd rge mount of power fows through 345 kv trnsmsson nes from southern re nd centr re to northern re. Even wth suffcent reserve of the system, most of spnnng reserves n the other res my not contrbute to the northern re due to te-ne congeston. To stsfy 356

5 The 14th Internton Conference on Integent ystem Appctons to ower ystems, IA 2007 ovember 4-8, 2007, Kohsung, Twn northern re up-reserve urement, the ne fow from centr re to northern re must be reduced to mke room for reserves ( =2398 MW nd unts n the northern re so hve to chnge ther generton to ncrese oc spnnng reserve. Therefore, the up-reserve urements for northern re (1100 MW cn be stsfed through the sum of oc (498 MW nd mported reserves (602 MW. In ths test cse, the fue svng vue s bout 2,206,836 T$/h when the wnd power generton (1000 MW n ech re s consdered. To demonstrte the good convergence property of proposed gorthm, Tbe II gves comprson of tot number of tertons ured nd operton costs consderng the wnd genertor cpcty durng ech convergence eve t the od eve of MW n the cse 1.2. rom ths resut, votons of the system constrnts re emnted n the frst convergence eve ( 1 = 80 MW nd the soutons re cose to optm souton durng corse convergence eve. Ony bout 0.15 sec ws needed to rrve t ts fn souton n ths test cse. TABLE I COMARIO O RELT COIERIG THE WI OWER GEERATIO OR OT OR THE LOA O MW Cse Avbe Are Wnd Generton (orth/centre/outh (MW 0 / 0 / /1000 /1000 Actu Are Wnd Generton (orth/centre/outh (MW 0 / 0 / /1000 /1000 ow Lmt ( / (MW C 3000 / /3000 Lne ow ( / (MW C 2501 / /529 Are p Reserve Requrement (orth/centre/outh (MW 900 / 900 / /1100 /1100 Loc p pnnng Reserve (orth/centre/outh (MW 401 / 181 / /610 / 318 Are own Reserve Requrement (orth/centre/outh (MW 0 /0 / 0 200/200 /200 Loc own pnnng Reserve (orth/centre/outh (MW 680 /575 / /575/324 roducton Cost (T$/h TABLE II COMARIO O ITERATIO A ROCTIO COT OR VARIO I THE CAE 1.2 Itertons roducton enty Cost Tot Cost Convergence Cost (T$/h (T$/h (T$/h Intzton = 80 MW = 16 MW =3.2 MW = 0.64 MW =0.128 MW = MW = MW B. urther tudy for Are Wnd Generton enetrton t Lghty Lod emnd Tbe III gves good nsght bout the mp of technque constrnts on the wnd power penetrton n ech re t ghty od demnd (12000 MW. In the cse 2.1, the vbe wnd generton n the northern re, centr re nd southern re re ssumed to be 0 MW, 2000 MW nd 2000 MW, respectvey. ote tht bout 50% of tot od demnd nd most of ess economc unts re octed n the northern re so tht t s dvntgeous for northern re to mport economc wnd power from other res subject to the trnsmsson cpcty constrnts. However, the mount of u wnd power generton n centr re nd southern re woud need to be curted snce sever technque constrnts must be observed. Besdes, the u wnd power generton n centr re nd southern re hs to rech n equbrum (1681 MW to reduce the spnnng reserve urement for ech re s more economc wnd power trnsfer re be to fow between res. It shoud be notced tht the te-nes crry generton, up-reserve nd down-reserve t the sme tme. To stsfy northern re up-reserve urement nd centr re down-reserve urement, the ne fow from centr re to northern re must be reduced ( =2695 MW to mke room for up-reserve nd down-reserve. Therefore, the up-reserve urements for northern re (900 MW cn be stsfed through the sum of oc (743 MW nd mported reserves (157 MW. The down-reserve urement for centr re (336 MW s just ony stsfed through the mported reserves whch re provded by southern re nd northern re wth 188 MW nd 148 MW respectvey. ote tht 42 MW (190 MW-148 MW of down-reserve n the northern re my not contrbute to the centr re due to te-ne congeston. The resuts show tht the gorthm s rebe pproch, nd the souton s resonbe. In the cse 2.2, the vbe wnd generton n the northern re, centr re nd southern re re ssumed to be 900 MW, 2000 MW nd 3000 MW, respectvey. In order to stsfy the 275 MW down-reserve urement of southern re, 91 MW s provded by oc re. The remnng 184 MW s provded by northern re nd centr re wth 184 MW nd 0 MW respectvey. The sum of ndvdu oc down-reserves s just equ to the down-reserve urement of southern re (or centr re. Athough wnd unts n centr re (or southern re generte power chepy, the mum wnd power penetrton s restrcted to be 1375 MW becuse of the mum down-spnnng reserve contrbuton of therm genertors. Ths resuts n wnd power curtments n centr re nd southern re even f the system hs suffcent trnsmsson cpcty mong the three res. The sutbeness of the gorthm presented n ths pper to the souton of the optm wnd power penetrton eve n ech re s, thus, confrmed. C. Imps of Trnsmsson Cpcty Lmts on roducton Cost In the st cse, g. 2 depcts the numerc experment resuts under vrous od demnds to ustrte the effect of trnsmsson cpcty mts on producton cost. The vbe wnd generton n the northern re, centr re nd southern re re ssumed to be 1500 MW, 1500 MW nd 2500 MW, respectvey. or the ghty od demnd (12000 MW, the system hs suffcent trnsmsson cpcty nd the producton cost re sme when the trnsmsson cpcty mts re greter thn 2000 MW. When the od demnd s rsed to MW, the trnsfer power nto northern re s ncresed nd the hgher producton cost my be obtned to refect te-ne congeston. However, the producton cost my rech n equbrum when rger trnsmsson cpcty mts s chosen (4000 MW, but n hevy od demnd (19000 MW, the producton cost my be fr from those when sm trnsmsson cpcty mts re chosen (1500 MW. umerc resuts gve good ndctor to provde vube nformton for nstton of WTGs s fue svers n the 357

6 The 14th Internton Conference on Integent ystem Appctons to ower ystems, IA 2007 ovember 4-8, 2007, Kohsung, Twn Twn power system. TABLE III RTHER TY OR AREA WI GEERATIO EETRATIO AT LIGHTLY LOA EMA Cse Avbe Are Wnd Generton (orth/centre/outh (MW 0 / 2000 / / 2000 / 3000 Actu Are Wnd Generton (orth/centre/outh (MW 0 / 1681 / / 1375 / 1375 ow Lmt ( / (MW 3000 / /3000 C Lne ow ( / (MW 2695 / / 1394 C Are p Reserve Requrement (orth/centre/outh (MW 900 / 1236 / / 1175 / 1175 Loc p pnnng Reserve (orth/centre/outh (MW 743 / 610 / / 610 / 642 Are own Reserve Requrement (orth/centre/outh (MW 0 / 336 / / 275 / 275 Loc own pnnng Reserve (orth/centre/outh (MW 190 / 0 / / 0 / 91 roducton Cost (T$/h C Tme (s roducton Cost (T$/h MW MW MW ow Lmt (MW g. 2. Comprson of resuts under vrous trnsmsson cpcty mts n Twn power system.v. Concusons The go of ths reserch s to deveop mut-re wndtherm coordnton gorthm for sovng the optm generton dsptch probem n n soted power system wth rge ntegrton of wnd energy sources. Becuse of the ntermttency nd unpredctbty of wnd power generton, ddton physc nd economc operton constrnts must be tken nto consderton to rech compromse between system securty nd tot opertng cost. To de effectvey wth the coupng constrnts of the probem, ths pper presents penty functon-drect serch method (-M to provde coordnton of wnd nd therm generton schedung probem. The proposed gorthm cn mnmze the tot generton cost when the optm wnd power penetrton eve n ech re s reched. The resuts show tht the gorthm s rebe pproch nd the souton s resonbe. umerc experments re ncuded to provde vube nformton n both operton nd pnnng probems nd to gve good ndctor to nvest n new power pnts usng wnd energy sources for the Twn power system n the future. REERECE [1] C.. Yue, C.M. Lu nd M.L. Lou Erc, A trnston towrd sustnbe energy future: fesbty ssessment nd deveopment strteges of wnd power n Twn, Energy ocy, vo. 29, pp , [2] T.J. Chng, Y.T. Wu, H.Y. Hsu, C.R. Chu nd C.M. Lo, Assessment of wnd chrerstcs nd wnd turbne chrerstcs n Twn, Renewbe Energy, vo. 28, pp , [3] A.G. Bkrtzs nd.. okopouos, hort Term Generton chedung n m Autonomous ystem wth nconventon Energy ources, IEEE Trns. ower ystems, vo. 3, no. 3, pp , Aug., 1988 [4] G.C. Contxs nd J. Kbours, hort Term chedung n Wnd/ese Autonomous Energy ystem, IEEE Trns. ower ystems, vo. 6, no. 3, pp , Aug., [5] E.. Gvndou, A. G. Bkrtzs nd.. okopouos, A robbstc Method for the Evuton of the erformnce of Wnd- ese Energy ystems, IEEE Trns. ower ystems, vo. 7, no. 3, pp , ep., [6] M. Bouzguend nd. Rhmn, Vue nyss of ntermttent generton sources from the system opertons perspectve, IEEE Trns. on Energy Converson, vo. 8, no, 3, pp , [7].. okopouos, A.C. rmourtss nd A. G. Bkrtzs, redcton nd Evuton of the erformnce of Wnd-ese Energy ystems, IEEE Trns. Energy Converson, vo. 11, no. 2, pp , June., [8].H. Krk, R.B. Chedd nd. Rmdn, robbstc roducton Costng of ese-wnd Energy Converson ystems, IEEE Trns. Energy Converson, vo. 15, no.3, pp , ep., [9] R. oherty nd M. O Mey, A new pproch to quntfy reserve demnd n systems wth sgnfcnt nsted wnd cpcty, IEEE Trns. ower ystems, vo. 20, no. 2, pp , [10] C.L. Chen nd. Chen, Mut-Are Economc Generton nd Reserve sptch, roceedngs IEEE ICA Conference My 2001, pp [11] A.J. Wood nd B.. Woenberg, ower Generton Operton nd Contro, John Wey & ons, Inc., ew York 1984 [12] C. L. Chen nd. Chen, rect erch Method for ovng Economc sptch robem consderng Trnsmsson Cpcty Constrnts, IEEE Trnson on ower ystems, Vo. 16, o. 4, pp , [13]. treffert, Mut-Are Economc sptch wth Te Lne Constrnts, IEEE Trns. on ower ystems, Vo. 10, o. 4, pp , ovember, [14] J. n, nd L. Zhng, Re-Tme Economc sptch wth Lne ow nd Emsson Constrnts sng Qudrtc rogrmmng, IEEE Trns. on ower ystems, Vo. 13, o. 2, pp , My, [15] C. L. Chen, T. Y. Lee nd R. M. Jn, Optm wnd-therm coordnton dsptch n soted power systems wth rge ntegrton of wnd cpcty, Energy Convers nd Mnge, vo. 47 (18-19, pp , BIOGRAHIE Chun-Lung Chen ws born n Twn, Repubc of Chn, He receved hs BEE degree from ton Twn Insttute of Technoogy n 1990, MEE from ton Twn nversty n 1992, nd h.. from ton Twn nversty of cence nd Technoogy n nce 2001, he hs been n ssocte professor t the eprtment of Eectrc Engneerng, Mnghsn nversty of cence nd Technoogy. Hs res of mjor nterests re demnd sde mngement, unt commtment, economc dsptch, nd wnd energy systems. Tsung-Yng Lee ws born n Twn, Repubc of Chn, He receved hs MEE nd h.. degree from ton Twn nversty of cence nd Technoogy n 1992 nd He hs been n ssocte professor t the eprtment of Eectrc Engneerng, Mnghsn nversty od cence nd Technoogy, snce Hs reserch nterest s n the operton nd pnnng of power systems. ACKOWLEGMET The uthor deepy pprectes the support of Twn ower Compny for provdng the system dt nd test cses. 358

Pattern Generation for Two Dimensional. cutting stock problem.

Pattern Generation for Two Dimensional. cutting stock problem. Internton Journ of Memtcs Trends nd Technoogy- Voume3 Issue- Pttern Generton for Two Dmenson Cuttng Stock Probem W N P Rodrgo, W B Dundseker nd A A I Perer 3 Deprtment of Memtcs, Fty of Scence, Unversty