Allowed capacity calculation of wind farm based on probabilistic constraint

Transcription

1 COMPUTER MODELLING & NEW TECHNOLOGIES (11) Du Huqu, Wang Jngbo, Ln Zhong-ha, Wang Pngjan, Yan Long Allowed capacty calculaton of wnd farm based on probablstc constrant Huqu Du 1, Jngbo Wang 2 *, Zhong-ha Ln 1, Pngjan Wang 1, Long Yan 1 Abstract 1 School of Informaton and Electroncs Engneerng, Shandong Insttute of Busness and Technology, 191 Bn Ha Road, Yanta, Chna 2 School of Electrcal Engneerng, Yanshan Unversty, 438 Hebe Western Street, Qnhuangdao, Chna Receved 1 October2014, Ths paper presents a method for penetraton capacty calculaton of wnd farm based on probablstc constrant. Accordng to the stochastc programmng theory, under a confdence nterval, a mathematcal model that consders the randomness of wnd speed s establshed based on the statc safety and power qualty constrans. The solvng method s proposed accordng to partcle swarm optmzaton algorthm and stochastc smulaton technque too. Accordng to a real power system n Yunnan, the penetraton capacty of wnd power s calculated under dfferent confdence nterval, and the feasblty and effectveness of ths method are verfed too. The related factors of affectng the penetraton capacty of wnd power are analysed, whch provde the reference for the plannng and desgn of wnd farm. Keywords: penetraton capacty of wnd power, chance constrant, stochastc smulaton, confdence nterval, partcle swarm optmzaton 1 Introducton Energy crss and envronmental polluton have become the two problems that must be faced n the development of modern socety. As a renewable energy, because of low cost and less polluton, wnd energy has receved great attenton around world. In recent years, wth the rapd development of power electronc technology, the technology of wnd power has made great progress. The natonal polcy of strong support for renewable energy has made a perod of rapd development of wnd power constructon n Chna. Wnd power has becomes one of the most mature, large-scale development and commercalzaton of new energy technologes [1-14]. The random, ntermttence and fluctuaton of wnd energy result n the wnd power dspatchng and have a severe mpact on grd securty, stablty and power qualty, whch s the man factor restrctng the nstalled capacty of wnd power and capacty of grd connected. Therefore, to evaluate the maxmum wnd power capacty of system, that s, allowed capacty of wnd power, s the key problem durng the plannng stage of wnd farm. There are no unfed algorthm and formula, because of penetraton capacty calculaton nvolvng many factors. The system was proposed, based on power structure, load and peak load capacty, whch could evaluate the penetraton capacty of wnd power through power grd [4]. The wnd power n Bejng Tanjn Tangshan power grd were assessed comprehensvely through comprehensve analyss of the power structure, load characterstcs, peak load capacty of thermal power, self capacty, pumped storage power staton and te lnes plannng, wthout consderng the effect of ncreasng capacty of wnd farm on the system statc securty. A mathematcal model s establshed for wnd power penetraton lmt n power system based on the statc securty constrans of power system and a new method for solvng the problem s gven based on nteror pont method [5], whle there n no consderng dynamc constrans related to wnd power grd connected operaton, whch may be the key factor determnng the penetraton lmt of wnd power. Accordng to the analyss of envronmental uncertanty of wnd power grd connected and dependent chance programmng theory, the model was establshed that consdered the statc operaton safety, the tradtonal power grd output lmt constrans, the wnd farm power down measures and wnd power capacty. The wnd power allowed capacty was calculated too [7]. In ths paper, we propose a method to calculate the allowed capacty of wnd power, based on probablty constrans. At the same tme, the random of wnd power and equaton constrans of trend are consdered. Accordng to the probablty dstrbuton of wnd speed, the model s establshed and solved, based on the Partcle Swarm Optmzaton (PSO) algorthm of stochastc smulaton technque. 2 The wnd farm and system load model 2.1 WIND FARM The captured wnd power of a fan s a functon of wnd speed at hub heght, and the functon can be expressed as p KSv, (1) *Correspondng author e-mal: duhuqu@126.com 1217

2 COMPUTER MODELLING & NEW TECHNOLOGIES (11) Du Huqu, Wang Jngbo, Ln Zhong-ha, Wang Pngjan, Yan Long p s the captured wnd power; K s the power coeffcent and the nonlnear functon of the tp speed rato and ptch angle; S s swept area of wnd wheel; v s wnd speed at hub heght. The relatonshp between actve power generated by the generator and wnd speed can be expressed as follow 0, v vn,or v vout 3 3 v vn p p, 3 3 n vn v vn, (2) vn vn pn, vn v v out v n, v out, v n denote cuttng n speed, cuttng out speed and the rated wnd speed respectvely; p n s the rated power. Because of random of wnd speed, the power generated by wnd power has the character of random. The probablty of wnd speed between 0~25m/s s very hgh and the annual averaged dstrbuton of wnd speed n YunNan can be expressed by Webull dstrbuton functon [10] k1 k k v v f( v) exp. (3) c c c The probablty dstrbuton of wnd speed s shown n Fgure 1. probablty Speed(m/s) FIGURE 1 The probablty dstrbuton curve of wnd speed 2.2 SYSTEM LOAD MODEL Load changes drectly affect the wnd farm access capacty, expermental results show that, the system load dstrbuton of most area can descrbe accordng to the normal dstrbuton functon n the long run. 2 1 ( pl ) ( pl ) exp[ ], (4) where p L s the system load of the -th node; s the average load of the node; σ s varance. 3 Probablstc constran model of power system of wnd farm The constrant condton manly means that power flow do not overload, the node voltage and the output of actve power and wattles power of conventonal generator are lmted. If the loss of net s not consdered, the summaton of power ncrement of all nodes n the power grd connected wnd farm s zero, n order to meet the power balance. Due to the randomness of actve power output from wnd power and the volatlty of system load, the state varable calculated through system flow s random. The nequalty constrants wth random varable are expressed as the form of probablty, whch s establshed at a specfed confdence level. The confdence level has a general value between 0.9 and 1. The value s smaller, the rsk s bgger. The value s closer to 1.0, the result becomes more conservatve. Takng the accepted largest nstalled capacty of wnd power as goal functon, the goal functon can be expressed as follow: n f max( p ). (5) 1 f The nequalty constrants can be expressed as follow Pr ob{ p p p } x mn xj x max Pr ob{ U mn U U. (6) Pr ob{ Q Q Q } g mn g g max p p p g mn g g max The equalty constrants can be expressed as follow P + P - P U U ( G cos B sn ) G f L j j j j j j Q + Q - Q U U ( G sn B cos ) G f L j j j j j j Prob s the probablty, p xj s the flow of x lne, wnd power of grd connected at node;. (7) p f s the p L s the system load at node; p xj s power flow at j lne; s confdent probablty of nequalty constrants. 4 Partcle Swarm Optmzaton algorthm base on stochastc smulaton 4.1 THE TECHNIQUE OF STOCHASTIC SIMULATION The stochastc smulaton,.e., Monte Carlo smulaton, provdes an effectve way to verfy the probablty constrants. The stochastc varables are sampled from known probablty, whch provdes the bass for decson-makng or tests the decson makng for system. For chance constrants wth stochastc varable Under the condton of constrans contanng random varables, f the decson makng under dsadvantage may not satsfy the constrants, then the decson makng should make the probablty of establshment for constrant condton establshed not less than a certan confdence level [8]. Pr ob{ px mn pxj px Pr ob{ U mn U U. (8) Pr ob{ Qg mn Qg Qg 1218

3 COMPUTER MODELLING & NEW TECHNOLOGIES (11) Du Huqu, Wang Jngbo, Ln Zhong-ha, Wang Pngjan, Yan Long The method of random smulaton can be expressed as follow: n ndependent random ndvdual, for example, v1, v2,... v n are sampled from probablty dstrbuton f(v). The n s the number of satsfyng constrants n n trals. Accordng to the law of large numbers n / n can be used to estmate the value of Equaton (8). If n / n>=, the partcle satsfes the probablty constrants; f n / n<, the partcle volates the probablty constrants, and the value of ftness s penalzed. 4.2 PARTICLE SWARM OPTIMIZATION ALGORITHM Start Intalze the partcle Update partcles No End Output the optmal partcle Yes Iteraton over? 1 2 n Partcle Swarm Optmzaton algorthm (PSO) stems from the research on group prey behavor of brds was proposed by Kennedy and Eberhart n Startng from stochastc soluton, the optmal soluton s searched by means of the teraton and the global optmum can be founded by followng the searched optmal value. The vector X ( x, x,... x ) T denotes the poston of partcle n space; the vector p ( 1, 2,... ) T p p pn denotes the optmal soluton of vector of partcle n teraton; the vector v ( 1, 2,... ) T v v vn denotes the speed of partcle n N dmensonal soluton space. In order to avod fallng nto local optmum, the evoluton route of partcle depends not only on current poston also on the prevous evoluton route. At the same tme, the method of lnear weght s employed, whch ensures fast convergence speed and gets hgher convergence precson. The flow- chart of program s shown n Fgure 2. The evoluton equaton of partcle s expressed as follow v ( t 1) wv ( t) c r [ Z ( t) x ( t)] 1 1 best c r [ G ( t) x ( t)] 2 2 c r[ Z ( t 1) x ( t 1)] 1 c r [ G ( t 1) x ( t 1)] 2 2 best best best, (9) t s the number of teraton; c 1 and c 2 are learnng factor and represent the weght of two optmal solutons respectvely; r 1 and r 2 are ndependent random number between zero and one. The nerta weght s ( ) ( ) w w w N n w N max max mn, (10) n s current cycle number; N s total cycle number. Generate random wnd speed Power flow calculaton Samplng over? Yes No ftness calculaton FIGURE 2 The flowchart of PSO based on stochastc smulaton 5 Analyss of examples In ths paper a certan practcal power grd of Yunnan s used to be analysed and calculated. The system smple topology s shown n Fgure 3. No. 1 generator s defned as the balanced unt. No. 25 and 29 base load generators do not partcpate n the actve power regulaton. The rate of wnd power s 1.5 MW. The system benchmark capacty s 1000 MVA. No.13, 16, 18, 27 etc. are selected as wnd farms and connected grd. The lmt and upper lmt of actve power of conventonal unt parameters for optmzaton are shown n Table 1. TABLE 1 Conventonal unt parameters Unt node Lower lmt of actve power (pu) Upper lmt of actve power (pu) 1(Man wan) (Da chaoshan) (Zong yangha)

4 COMPUTER MODELLING & NEW TECHNOLOGIES (11) Du Huqu, Wang Jngbo, Ln Zhong-ha, Wang Pngjan, Yan Long Cao pu ( 2*750 MVA) Man wan (1650MW) Ha geng (2*180MVA) Wen quan ( 2 *120MVA) ((600 MW) Kun mng power plant J pu (2* MVA) Shang feng ( 180 MVA) Kun gang (3* 120 MVA) Wnd farm Jn daoyng (2 *180MVA) quanfu (180MVA) Dong jao (2*180MVA) Ma anshan ( 3*120MVA) Jn cheng (180MVA) Guo ln ( 2*180MVA) Yang zongha ( 2* 200 MW) Bao feng (2*750MVA) Fu xan ( 2* 180MVA ) Lv chang Q dan ( 2*750MVA) Red-- 500kV Da chashan ( 6* 225 MW) Guan du (150MVA) Blue-- 220kV FIGURE 3 The system smple topology of a certan practcal power grd of Yunnan Yang zongha2 (2* 300 MW) Ths paper analyses the three factors that affect the wnd-power allowed capacty: (1) Dfferent confdence level and connected grd. Average wnd speed μ =7.5m/s, the shape factor k=2, load varance=1. Wnd-power allowed capactes are calculated as shown n Table 2. TABLE 2 Penetraton powers wth dfferent confdence levels and connected grds Connected grd Penetraton powers (pu) α=0.99 α=0.99 α=1.0 13(Ha geng) (Ma anshan) (Fu xan) (Pu j) As seen from Table 3, wnd-power allowed capactes are dfferent when wnd farms are connected nto the system. Dfferent wnd-power allowed capactes can be used to determne the best access pont for maxmzng the acceptance of wnd power. Meanwhle, wnd-power allowed capactes ncrease relatvely wth the confdence probablty reducng. The essence of the phenomenon s to allow some low probabltes, whch volate constrant condtons, thus conservatve calculaton results are avoded. (2) Load levels. To study, the total load of the system s ncreased by 10% compared wth Table 2. Penetraton powers are calculated as shown n Table 3. Due to the demand for electrcal energy ncreasng, wnd-power allowed capactes of most nodes ncrease wth load ncreasng after the system load ncreases. Fgure 4 shows the evoluton curve of the optmal soluton n the 16th node when α=1.0. TABLE 3 The effect of load on wnd power access capacty Connected grd Wnd-power allowed capacty (pu) α=0.95 α=0.99 α=1.0 13(Ha geng) (Ma anshan) (Guo ln) (Pu j)

5 COMPUTER MODELLING & NEW TECHNOLOGIES (11) Du Huqu, Wang Jngbo, Ln Zhong-ha, Wang Pngjan, Yan Long Compared wth Table 2 and Table 3, wnd-power allowed capactes of most nodes ncrease wth load ncreasng after the system load ncreases. Wnd-power allowed capactes of some nodes s not sgnfcantly ncreased because of other restrctons constrants (3) Wnd speed: The confdence probablty s 0.99 n order to nvestgate effects of dfferent average wnd speeds. Other parameters are same as Table 2. Penetraton powers are calculated as shown n Table 4 under dfferent average wnd speeds. TABLE 4 Effect of average wnd speed of wnd power access capacty FIGURE 4 Partcle-swarm optmal evolutons Connected grd Wnd-power allowed capacty (p u) μ=6.5m/s μ=7.5m/s μ=8.5m/s 13(Ha geng) (Ma anshan) (Guo ln) (Pu j) Compared wth Table 2 and Table 4, the fan output ncreases wth the ncrease of the average wnd speed. The level of system dsturbance also ncreases and the wnd-power capacty decreases. 7 Conclusons In ths paper, an analyss method s proposed based on probablty constrants. The optmzaton analyss model of evaluatng allowed capacty s establshed consdered wnd-power randomness under uncertan envronment. The program of MATLAB s developed based on stochastc smulaton technques and partcle-swarm optmzaton algorthms. The analyss of examples demonstrates the feasblty and effecttveness of the algorthm and model. The analytcal method of allowed wnd-power capacty s also sutable for other renewable energy. The lmtaton of ths method s tme consumng because of the use of Monte Cano smulaton technques and only the consderaton of the statc system constrant. The wnd power system dynamc constrant s also a key factor n the decson of the wnd power access capablty. How to consder these dynamc constrants nto the optmzaton model s the focus of future research. Acknowledgments Ths work was fnancally supported by the NSFC ( ) and Natural Scence Foundaton project of Shandong provnce of Chna (ZR2012FL11, ZR2013AL014). References [1] Tan Q-q, Zhu L 2011 The countermeasure to accelerate the development of solar energy ndustry of Yunnan Provnce Goufang Zhnan (3) 125 (n Chnese) [2] Lu Z-w 2007 Research on mpact of large grd-connected wnd farms to the system and maxmum settng capacty Wu Han Huazhong Unversty of Scence and Technology (n Chnese) [3] Lao P, L X-y 2008 A Survey on Calculaton Method of Wnd Power Penetraton Lmt Power System Technology 32(10) 50-3 [4] Sun R-f, Zhang T, Lang J 2011 Evaluaton and Applcaon of Wnd Power Integraton Capacty In Power Grd Automaton of Electrc Power Systems 35(4) 70-6 [5] Le Y-z, Wang W-s, Yn Y-h, Da H-z 2001 An Optmzaton Method for Determnng Wnd Power Penetraton Lmt n Power System Under Statc securty Constrans Proceedng of the CSEE 21(6) 25-8 [6] Guo X-r, Wang D-y, Yang G-q 2011 Maxmum njecton power calculaton based on enhanced partcle swarm optmzaton Electrc Power 44(1) 86-9 [7] Qao J-g, Xu F, Lu Z-x, Mn Y 2008 Optmzaton Analyss Model of Grd-connected Wnd Capacty Based on Chance Programmng Automaton of Electrc Power Systems 32(10) 84-7 [8] Charnes A, Cooper W W 1995 Chance-constraned programmng Management Scence 6(1) 73-9 [9] Lao J-l 2008 Calculaton and Analyss on The Wnd Power Penetraton Lmt Storage Transportaton & Preservaton Of Commodtes 30(5) [10] L Z-y, Wang M, Chen E-y, Gu B-w 1998 Study of Webulldstrbutng Parameters And Wnd Energy Characterstc Value of Wnd Speed Around The Parts Of YunNan In Whch The Wnd Energy Can Be Developed Acta Energy Solars Snca 19(3) 34-9 (n Chnese) [11] Zhang J-h, Yang Q, L W-g 2010 Maxmum Injecton Power Calculaton Of Wnd Farms Connected To Power Systems Based On An Improved Partcle Swarm Optmzaton Algorthms Acta Energlae Solars Snca 31(5) (n Chnese) [12] Wu J, L G-j, Sun Y-z 2007 Maxmum Injecton Power Calculaton Of Wnd Farms Connected To Power Systems Based On Stochastc Programmng Power System Technology 31(14) 15-9 [13] Wang R, Gu W, Sun R, L Q 2011 Analyss On Wnd Power Penetraton Lmt Based On Probablstcally Optmal Power Flow Power System Technology 35(12)

6 COMPUTER MODELLING & NEW TECHNOLOGIES (11) Du Huqu, Wang Jngbo, Ln Zhong-ha, Wang Pngjan, Yan Long Author Huqu Du, Chna Current poston: assocate professor of School of Informaton and Electronc Engneerng, Shandong Insttute of Busness and Technology, Chna. Unversty studes: Master n engneerng precson nstruments and machnery (1985) from Harbn Normal Unversty. Scentfc nterest: robot technology and control. Wang Jngbo, Chna Current poston: major n electrcal engneerng at Yanshan Unversty, Qn Huangdao, Chna Unversty studes: master n electrcal engneerng at Yanshan Unversty, Qn Huangdao, Chna Scentfc nterest: power system economc operaton and rsk management Ln Zhongha, Chna Current poston: assocate professor at Shandong Insttute of Busness and Technology. Unversty studes: doctor's degree n electronc scence and technology from X'an Jao Tong Unversty, X'an, Chna n Scentfc nterest: semconductor materals and devces based on nanotechnology. Wang Pngjan, Chna Current poston: nstructor at Shandong Insttute of Busness and Technology. Unversty studes: the doctor's degree n Condensed matter physcs from nsttute of Sold State Physcs, Chnese Academy of Scence, Hefe, Chna n Scentfc nterest: theory of condensed state physcs. Yan Long Current poston: nstructor at Shandong Insttute of Busness and Technology. Unversty studes: doctor's degree n Mechancal and Electronc Engneerng from Shandong Unversty, Jnan, Chna n Scentfc nterest: machne vson and mage processng. 1222