International Power, Electronics and Materials Engineering Conference (IPEMEC 2015)

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1 Internatonal Power, Electroncs and Materals Engneerng Conference (IPEMEC 2015) Dynamc Model of Wnd Speed Dstrbuton n Wnd Farm Consderng the Impact of Wnd Drecton and Interference Effects Zhe Dong 1, a, Ran L 1,b and Le Dang 1,c 1 Department of Electrcal Engneerng, North Chna Electrc Power Unversty, Baodng, Hebe, , Chna. a @qq.con, b hss0527@163.com, c dangle_mao@126.com Keywords: Wnd Speed Model, Interference Effect, Dynamc Dstrbuton of Wnd Speed. Abstract. The accurate and practcal wnd speed model of wnd farm s the bass of the relevant research work of wnd power predcton. Ths paper based on the wnd farm and the real-tme data of wnd turbne, put forward a knd of dynamc dstrbuton model of wnd speed that consder the wnd turbne wake and wake flow supermposed effect and tme delay effect, and consderng the relatve space poston of wnd machne n dfferent wnd drecton. Frst analyzng the nfluence of the wake effect, wake flow supermposed effect, tme delay effect and the change of wnd drecton on the wnd speed n theory, establshng the mathematcal model of wnd speed that consdered nterference effects; secondly, based on fan locaton map and the measured wnd speed of an actual wnd farm, usng the establshed the model to take smulaton analyss of the dstrbuton of wnd speed, and takng devaton analyss on the smulaton results and the actual wnd speed data of the dstrbuton dynamc model of wnd speed and the tradtonal wnd speed model put forward by ths paper. The results show that the wnd speed model put forward by ths paper can more accurately smulated the attenuaton, delay of the wnd speed of the wnd farm when the wnd drecton changed, and havng practcablty. Introducton Because the wnd energy source havng randomness and uncontrollablty, the wnd turbne s subjected to great dsturbance almost every tme, the dsturbance makng the output power of wnd turbne power be fluctuated, resultng n that t s dffcult to reach the deal accuracy of power predcton, but also brought mpact to the wnd turbne and power system connected wth t, such as, shortenng the lfe of the wnd machne, reducng the qualty of power of power grd, and even brought voltage flcker problem[1-3]. Therefore, t s necessary to establsh accurate wnd speed model to smulate the changng fluctuaton of wnd speed. The Modelng Sngle Wnd Wake Model. The wake of sngle wnd turbne can be descrbed by usng the Jensen model [4]. The model thnks that the ntal dameter of the cross secton of the wake flow farm s wnd wheel dameter, r expressng the length of wnd turbne blade. Usng d to express the dstance of the downstream of turbne, r w expressng the radus of the cross-secton of wake flow, then the radus of the cross-secton of the wake flow can be expressed as: rw r k* d (1) n whch k beng shape coeffcent, usually the onshore wnd farm takng k 0.075, offshore wnd farm beng k 0.04 [5].Usng v 0, v w0, vw respectvely to expresses the natural wnd speed, the wnd speed of the back of wnd turbne, the speed of wake flow. We can get the wnd speed of the back of wnd turbne by momentum theory: The authors - Publshed by Atlants Press 639

2 vwo a s the nducton factor of axal, a 1 1CT The speed of the wnd turbne n the wake: (1 a) v 0 (2) CT, s thrust coeffcent of wnd turbne. r 2 vw( d) v0[1 a( ) ] (3) r w The Model of Overlay of Wake Flow. For two fans wth the relatve dstance that beng along wnd drecton, the length of the fan blade of downstream beng r, swept area beng A. When the wake flow of a fan of the upstream reached d, the wake radus beng r w(d), the effect area of the wake flow beng A w(d). Regulatng the overlap area of the other two unts s A s, accordng to the degree of overlap, we can dvde the nfluence of the wake flow of upstream fan on the fan of downstream nto three knds: under lap, completng overlap, partal overlap. The overlap area of the former two cases are 0, A. For partal overlap, accordng to the overlappng area t can be dvded nto two cases n fgure 1, and respectvely gvng the calculaton method of overlappng area. ( a) r (d) d r (d) r ( b) r ( d) r d r ( d) w c w w c w Fgure 1 Schematc dagram of overlap of fan Case (a) d d d A r arccos( ) r ( d) arccos( ) d l (4) 2 c a 2 a s w c r rw ( d) Case (b) r d r ( d) r ( d) d r A r r d d l (5) c w 2 w c s arccos w( ) arccos c 2dr c 2 dr c w( d) Accordng to the law of conservaton of momentum, we can calculate the nput speed of any fan n the wnd farm by formula (6): n k 0 wk k k 1 k v v [ v v ( d ) ] (6) n the formula, v expressng the wnd speed effectng on the fan ; v 0 expressng the wnd speed the fan wthout the effect of any wake flow and tower shadow; k beng the rato of the projecton area of the k fan n the wnd wheel of the fan compared wth the area of wnd wheel of the fan: k As k A ; vw kdk beng the wnd speed of wake flow when the k fan effectng on the fan; d k expressng the relatve dstance downwnd between fan and fan k. Tme Delay Model of The Wake Flow of Fan. Consderng the tme delay of wnd speed between fans, thnkng approxmately that the wnd drecton of transmsson beng the current wnd drecton, the route of transmsson beng a straght lne, the transmsson speed beng the wnd speed of the back of the upstream fan, gnorng the loss of wnd speed and the abouchement of natural wnd speed n the transmsson process. We can calculate and get the capturng speed v (t) of unt at the t moment: 640

3 n k 0 wk k k k1 k v () t v () t [ v () t v ( d, t T )] (7) n the formula, Tk vw0 k / dk sad the tme delay effect of the wake flow of unt k to unt. The Dstrbuton Model of Dynamc Space of Fan. In the actual operaton of wnd farm, wnd drecton s dynamc. We must be based on the dstrbuton model of dynamc space of fan that consderng the effect of the change of wnd drecton on the wnd flow. (1)The establshment of the ntal coordnate system Takng the counter-clockwse drecton as the forward drecton, the fan n the north sde of the wnd farm s the pole, takng east drecton as the polar axs. Accordng to the dstrbuton of the fan poston, to obtan the ntal coordnate of n fan n the wnd farm. The coordnate of any fan n the wnd farm s ( r, ), r, respectvely sad the dstance between unt and pole, the ncluded angle between the unt and the polar axs. (2) The transformaton of dynamc coordnate Takng the north drecton as the wnd drecton angle of 0 degree, clockwse drecton s postve, the wnd drecton angle at any tme beng β. Accordng the wnd drecton angle to take aton transformaton on the ntal coordnate, takng clockwse aton angleβon the pole axs of new coordnate to get the pole axs of the ntal coordnate, after transformaton, the coordnate of any fan ' ' ' ' ' n the wnd farm s ( r, ), whch r r,. (3) Calculatng the relatve poston of fan accordng to the locaton of new coordnate The new coordnate after transformaton can be decomposed to obtan the poston of each unt n ' ' ' downwnd and crosswnd drectons. In whch, the coordnate of any fan s ( r, ), the poston of t n the downwnd and crosswnd drecton respectvely beng ds r 'sn ', dc r 'cos '. The downwnd and crosswnd drectons of all n fans n the wnd farm are: DS [ ds 1, ds2,..., dsn], Dc [ dc 1, dc2,..., dcn] (8) Sortng the fans n the wnd farm from small to large accordng to the wnd drecton, we can get the collecton of all the k fans of the upstream of any unt, and can calculate the relatve poston of the downwnd and crosswnd of the relatve unt of the k fans. Assumng that the number of upstream unt as the 1, 2,. k. The relatve poston of the downwnd and crosswnd of the relatve unt of the fan k respectvely are : D [ d, d,..., d ] [ d d, d d,..., d d ] (9) s s1 s2 sk s1 s s2 s sk s D [ d, d,..., d ] [ d d, d d,..., d d ] (10) c c1 c2 ck c1 c c2 c ck c The establshment of the dynamc wnd speed dstrbuton model of wnd farm. The dstrbuton curve of the model of ths paper usng the locaton of wnd farm s accordng to the method of settng model of the above analyss to set the ntal space model, takng the real tme data of anemometer tower as the nput of model. Accordng to the wnd drecton to take the coordnate transformaton, calculatng the relatve space poston of the unt n the current moment, determnng the marshallng sequence of unts of upstream and downstream and the relatve dstance of crosswnd, then calculatng the nteracton of the wake flow of the unts. At the same tme, through the relatve dstance of the downwnd of unts and the wnd speed of the back of the unts to determne the travel tme of the wake flow, calculatng the wake effects of tme delay. Fnally, the model gves the real tme speed of each fan n wnd farm as result. 641

4 Examples Ths paper takes a wnd farm as the research object for the wnd speed modelng and verfcaton, the electrc feld beng equpped wth 33 sets of 1.5MW wnd turbnes, blade length beng 37.5m. Fgure 2 shows the locaton map of part of the fan used n the smulaton of the secton. Fgure 2 The locaton map of partal fans of wnd farm Ths secton took smulaton comparson on the tradtonal dstrbuton model of wnd speed and the dstrbuton model of dynamc wnd speed put forward by ths paper that consderng the wnd drecton and nterference effect of fan. The selected wnd drecton of the tradtonal dstrbuton model of wnd speed s constant and s the man wnd drecton of the current season: north wnd (0 degrees); the dstrbuton model of dynamc wnd speed consderng wnd drecton and nterference effect of fan took the real tme data of anemometer tower as nput. Wnd Speed(m/s Wnd Speed(m/s Fgure 3 The contrast of the smulated wnd speed and the real tme wnd speed of the fan Extractng the wnd speed of WT27 from the output results of two knds model, comparng the actual wnd speed of the fan, the result beng shown n fgure 3. The dstrbuton model of dynamc wnd speed consderng the effect of wnd drecton got that the smulated wnd wave s more consstent wth the real tme wnd speed wave, the ampltude beng bascally dentcal. Fgure 4 and table 1 took devaton analyss on the smulated wnd speed and the real tme wnd speed of the two models. We can see that the devaton between the smulated wnd speed and the real tme wnd speed of the tradtonal model s bascally negatve, namely the actual wnd speed s less than the smulated wnd speed. Ths s because the tradtonal model n the smulaton took the north wnd and made t be unchangeable, and then the locaton of WT27 s bascally not affected by effects of upstream wake flow of fan; and when the wnd n the northwest and northeast slghtly offset, whle the offset angle s small, the fan n ths locaton beng too close, the slghtly change of the relatve poston of the fan WT27 that can make the fan WT27 be n the nfluence range of wake flow of WT26 or WT28, 642

5 resultng n the reduce of wnd speed of fan WT27, showng as that the actual wnd speed s smaller than the smulated wnd speed. And for the dstrbuton model of dynamc wnd speed of the wnd farm put forward n ths paper, because consderng the nfluence of the wnd speed change on the relatve poston of the fan, the devaton beng on the fluctuaton of the 0m/s, the devaton of model was obvously smaller than the devaton of tradtonal model. Table 1 gave the data of devaton of two knds of models, the accuracy of the dstrbuton model of dynamc wnd speed consderng the nfluence of wnd drecton got greatly mproved compared wth the tradtonal model of the wnd speed, can be more accurately to descrbe the dynamc changes of wnd speed of wnd farm. Fgure 4 The devaton analyss of the real tme wnd speed and the smulated wnd speed Table 1 Comparson of the devaton of smulated wnd speed of the two knds of model The bggest devaton The smallest devaton The average devaton Tradtonal model The model of ths paper References [1] Sun Tao, Wang Wesheng, Da Huzhu, et: Power System Technology, n Chnese, Vol.27(2003),p [2] Ma Xnxa, Song Mngzhong, L Yongguang: Journal of Shangha Unversty of Electrc Power, n Chnese, Vol.22(2006),p [3] Ceng Lhua, Wang Feng, Lu Deyou: Proceedngs of the CSEE, n Chnese, Vol.31(2011),p [4] Cao Na, Zhao Haxang, Ren Puchun, et: Proceedngs of the CSEE, n Chnese, Vol.27(2007),p [5] Rathmann O,Barthelme R J,Frandsen S: Turbne wake model forwnd resource software (European Wnd Energy Conference and Exhbton, Athens, 2006). 643