An Approach to the Performance-Oriented Model of Variable-Speed Wind Turbines

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1 An Approach o h Prformanc-Ornd Modl of Varabl-Spd Wnd Trbn Aljandro Rolán, Sdn Mmbr, IEEE, Álvaro na, oan Rocabr, Sdn Mmbr, IEEE, anl Alar, and Grardo Vázqz, Sdn Mmbr, IEEE Elcrcal parmn of Ennrn Tchncal Unvry of Caalona Colom - 08-Trraa, Span Conac Ahor: aljandro.rolan@pc.d Abrac- Th am of h ork o v an approach o h Prformanc-Ornd Modl of Varabl-Spd Wnd rbn (VSWT) qppd h prmann man ynchrono nraor (PMSG), and compar o h componn-ornd modl. In h prn ork ll b analyzd ho a chan n h nd pd affc h por dlvrd from h nraor by man of o approach: frly, h componn-ornd modl of h VSWT-bad PMSG vn,.. h dynamc qaon of h ym ar hon, and hn, dcd ho o oban an qvaln ranfr fncon of h hol ym. A comparon bn boh approach dcd n h ork. I. INTROUCTION Alhoh h lzaon of nd nry ha a vry lon radon, a no nl h nd of h 990 ha nd nry bcam on of h mo mporan anabl nry rorc, parly bca of h ncran prc of h ol, cry concrn of nclar por and abov all aarn abo h clma chan. Th la on of h man raon ha hav lad o a fll rarch no rnal nry orc o provd h lcrcy dmand arond h orld. Morovr, a nd nry abndan and ha an nxhabl ponal, on of h b chnolo oday o provd a anabl pply o h orld dvlon. Th of nd por ha roh condrably drn la yar. By h nd of 996 h oal capacy of nd por a arond 6 GW, hra n 008 rprnd mor han 0 GW, prodcn 4 TWh of lcrcy []. I v an da of h mporanc ha h rnal nry ha noaday. Th fr p o dy h nraon of nd nry no h lcrcal rd o modl h hol ym proprly and mla. Noaday hr x vral por ym mlaon ool,.. PSS/E, SIENT, SABER or PSCA/EMTC (n h prn ork h mlaon ha bn carrd o va PSCA/EMTC mlaon ool). A comparon bn h la o mlaon ool don n []. Th ool ncld bl-n modl of h dffrn componn of a nd por plan, hch ar convnn for load flo and dynamc mlaon of por ym. Hovr, ncary o dvlop nd rbn and nd por plan modl o analyz h nrconncon of h ym o h lcrcal rd. pndn on h m fram of h mlaon, hch drmnd by h prpo of h mlaon, h lvl of h dal of h modl var [3]. A a rl, h m cal of h mlaon ll b from f mllcond o vral mn. Wh h ypcal m fram d n lar por ym ably d, hch approxmaly 0. [4], no praccal o modl a nd rbn or a nd por plan ha rqr a vry mall m p. Normally, hn h complxy of h modl ncra, ncary a mallr nraon m. Takn no accon h obrvaon, a prformanc-ornd modl [5] for a nd rbn ha bn propod a an alrnav o a componn-ornd modl. Th approach rqr a dald knold of h WTGS a ll a h por ym analy o b carrd o. For h raon, bfor dvlopn h prformanc ornd modl of h nd rbn, ncary o dcrb h componn ornd modl of h WTGS. Th ork foc on h modl of VSWT qppd h PMSG bca h mo promn opon for h lcrcy pply a far a nd nry concrnd. In fac, PMSG hav h ndn xcd by man of prmann man locad on h roor, mann hhr ffcncy and l mannanc. Wha mor, ml-pol PMSG can b d ho a arbox, hch mpl a rdcon of h h of h nacll a ll a a rdcon n co. Th roor arodynamc, drv ran and nraor and conrol ll b modlld, hra h nraon of h ym o h lcrcal rd ll no b condrd. A comparon bn h componn-ornd modl and h prformanc-ornd don n h papr. II. SYSTEM ESCRIPTION Th ym analyzd a VSWT bad on a ml-pol PMSG, dpcd n F.. o h lo nraor pd, h roor haf copld drcly o h nraor, hch man ha no arbox ndd /0/$ IEEE 3853

2 ym of a nd rbn, namly h blad lmn mhod, c p lookp abl, nd pd-mchancal por lookp abl and analycal calclaon []. In h ork, h la approach akn no accon. Th da o approxma h c p (λ, θ) characrc by h follon form F.. Elcrcal chm of a varabl pd nd rbn qppd h a PMSG. Th nraor conncd o h rd va a back-o-back convrr, hch con of o convnonal pl-dh modlad (PWM) vola orc convrr (VSC). Th capacor bn h nvrr and rcfr prm o dcopl h conrol of h o nvrr. Th nraor-d convrr conrolld o rla h nraor pd and h acv por ppld by h nraor [6][7], hra h oal of h rd-d convrr o conrol h racv por njcon o h rd [8][9]. Th crrn flrd bfor bn ppld o h rd (harmonc m b rdcd) and a ranformr, hch locad bn h nvrr and h pon of common conncon (PCC) ra h vola n ordr o avod lo n h ranpor of h crrn. I hold b nod ha h dy ddcad o modl and mla h ym from h nd rbn o h PMSG (h h conrol of nraor-d convrr). For h raon, dclnk, ranformr, rd, rcfr, nvrr modl and conrol a ll a pch anl conrol ll no b condrd. III. THE COMPONENT-ORIENTE MOE Th dynamc qaon ha dcrb h modl of h ach par of h ym ar dcrbd blo.. Wnd Spd Modl A compl pd modl con of h m of for componn (conan, ramp, and no) [0]. Hovr, ally akn no accon a p chan n h nd pd n ordr o analyz f h ym bhav proprly d o h chan.. Arodynamc Modl Th arodynamc modl vry ll docmnd n h lrar. For xampl, n [] on can fnd ha h rlaon bn h por xracd from h nd and h nd pd, hch knon a h roor arodynamc P 3 cp Av () hr P h por xracd from h nd (W), ρ h ar dny, hch qal o.5 k/m 3 a a lvl a mprar T = 88 K, c P h por coffcn, v h nd pd pram of h roor (m/) and A h ara p by h roor [m ] (A=πR, bn R h rad of h blad n m). Thr ar for alrnav for modlln h arodynamc c6 x c p (, ) cc c3 c4 c5 () Snc h fncon dpnd on h nd rbn roor yp, h coffcn c -c 6 and x can b dffrn for varo WTGS. Th propod coffcn [] ar: c = 0.5, c = 6, c 3 = 0.4, c 4 = 0, c 5 = 5, c 6 = (x no d bca c 4 = 0). Addonally, h paramr β alo dfnd n varo ay. For xampl, h paramr β n [] dfnd a Whr θ h pch anl (rad), hch h anl bn h plan of roaon and h blad cro-con chord, and h p-pd rao λ dfnd a R (3) (4) v hr ω h anlar vlocy of roor (rad/), R h roor rad (m) and v h nd pd pram of h roor (m/). An xampl of h c p (λ, θ) characrc compd akn no accon (-4) and h abov paramr c - c 6 for a vn roor damr R, roor pd ω and for dffrn val of blad pch anl θ prnd n F.. Th amon of arodynamc orq (τ ) n N m vn by h rao bn h por xracd from h nd (P ), n W, and h rbn roor pd (ω ), n rad/, a follo F.. c p crv for dffrn pch anl. P (5) 3854

3 3. rv Tran Modl A drv ran of a WTGS can b n a a ml-ma ym, conn of 6-ma, 3-ma, -ma or nl-ma modl []. Th 6-ma modl ha x nra, namly hr blad nra, hb nra, arbox nra and nraor nra. Th 3-ma modl con of hr nra, hch ncld h nraor roor, h rbn hb and h blad. In h -ma modl, h drv ran modlld a o nra, corrpondn o ho of rbn and nraor. If a 6-ma or 3-ma modl lzd, h complxy of h modl ncra, hch no drd n por ym ably d. In fac, only h lor frqncy of nr n ch a dy. A concldd n [] a o-ma modl ffcn for rprnn h dynamc of a rbn drv-ran for a por ym ably analy. F. 3 ho a chm of a mchancal drv ran, conn of o ma. I can b obrvd h prnc of hr dampn componn, namly rbn lf dampn (rprnn h arodynamc ranc akn plac n h blad), nraor lf dampn (hch corrpond o mchancal frcon and nda) and dampn coffcn of h haf (rprnn h dynamc ha occr bca of h dffrn pd bn h nraor roor and h rbn haf). All of dampn coffcn ar mard n N m /rad. F. 3. Schm of a o-ma drv ran. Th mahmacal qaon of a o-ma drv ran modl, nlcn h rbn and h nraor lf dampn, ar vn by [3] d K d d K d d d d d hr and ar h rbn and h nraor nra conan (boh n k m ), rpcvly; K h haf ffn (N m/rad); ω and ω ar h rbn and h nraor roor pd (rad/), rpcvly; τ and τ ar h orq prodcd (6) by h roor and h nraor on h lo pd and hh pd haf (N m), rpcvly; and θ and θ dno h rbn and h nraor roor anl (rad), rpcvly. I hold b nod ha all rm ar rfrrd o h hh pd haf (h rm ar dnod h h prcrp ). In h ca, h follon ranformaon ar d [3] n n ar ar ; ; n ar n K ; K nar ; n hr n ar h arbox rao. If h haf ffn and mal dampn ar nlcd, h on-ma modl of h drv ran oband. In h ca, hr only a nl nra, rprnn h m of h rbn and nraor nra. Th mahmacal qaon of h on-ma modl of h drv ran [4]: n ar d d ar I hold b nod ha h o-ma modl ak no accon h pd and por flcaon ha appar hn non-normal condon ak plac. 4. Gnraor Modl Th la componn ha on o b modlld h nraor, pcfcally h prmann man ynchrono nraor (PMSG). Whn drd o oban a dynamc modl of a PMSG on m ak no accon ha only h lcrcal qaon of h aor ar condrd (bca n h roor hr ar no ndn). I rl n a ym of hr qaon, nlk h ond roor hr-pha ynchrono machn, n hch for qaon ar ndd o b d. Hovr, dp h rdcon n h nmbr of qaon, hold b nod ha old b vry dffcl o ork h h lcrcal qaon of h PMSG n h ac abc rfrnc-fram, bca h qaon old dpnd on h mchancal anl θ (hch h anl bn h roor poon n an nan of m and h a-ax), rqrn a ra dal of mlaon m [5]. In ordr o avod h problm, h qaon ar ranformd from a ac hr-pha rfrnc fram o a o-pha roan rfrnc fram, by man of h Park ranformaon [5][6]. Thn, h dynamc modl of h PMSG drvd from h o-pha roan rfrnc fram, n hch h d-ax alnd h h vcor of h flx prodcd by h prmann man and h q-ax 90º ahad of h d-ax h rpc o h drcon of roaon, a F. 4 dpc. Th rfrnc fram cold b namd roor-ornd rfrnc fram, bca h flx crad by h prmann man roa a h am pd han ha of h roor. ar (7) (8) 3855

4 To compl h mahmacal modl of h PMSG h mchancal qaon ndd, and dcrbd by h follon lcromanc orq τ qaon [5]:.5 p[( ) ] () d q d q q A ad bfor, h PMSG amd o b a rond-roor machn, o ndcanc n d- and q-ax hav xacly h am val ( d = q = ). Takn no accon h mplfcaon, h lcrcal qaon (9), rn n h ady-a form [8], and h mchancal qaon () can b rn a follo F. 4. Schm of a PMSG, h abc-ac rfrnc fram and dq-roan rfrnc fram. Th mahmacal modl of h PMSG bad on h follon ampon [5][6][7]: h roor ha no dampr ndn; h machn ymmrc (hr x a paraon of 0º bn h aor ndn and hy hav h am ndcanc); hr no laka flx n h aor ndn, o h laka ndcanc of h ndn condrd o b zro; h manc fld ha a nodal drbon alon h ar ap; hr a conan ar ap (d o h fac ha h prmann man ar locad a h rfac of h roor, o bhav a a rond-roor machn); manc hyr and araon ffc ar nlbl (h manc characrc of h ron condrd o b lnal); h manc prmably of h ron vry hh, hch man ha h manc rlcanc nlbl compard o ha of h ar ap. Takn no accon h mplfcaon and condrn h roor-ornd rfrnc fram, h mahmacal modl of h PMSG can b xprd by h follon qaon [5]: d q r r d q d q d d d d d q q d q d hr bcrp d and q rfr o h phycal qan ha hav bn ranformd no h dq-roan rfrnc fram; d and q ar h aor vola (V); d and q ar h aor crrn (A); r h aor ranc (Ω), d and q ar h aor ndcanc (H) n h d and q ax, rpcvly; Ψ h prmann manc flx (Wb); and ω h lcrcal roan pd of h nraor (rad/), hch vn by: (9) p (0) hr p h nmbr of pol par of h nraor and ω h roaonal pd of h roor (rad/). d d d d d q.5 p q r r d q q d d q () Th acv por P n (W) and racv por Q n (VAr) of h PMSG ar [5]: P Q n n.5.5 d q d d IV. THE PERFORMANCE-ORIENTE MOE q d d q (3) Th prformanc-ornd [5] ha arn a an alrnav o h componn-ornd modl n ordr o rdc h complxy of h modl by rdcn h nraon m of h mlaon, hch ally n h ran from o 0 mllcond. Th da o rprn h nd rbn a a crrn orc, hch dpnd on varo paramr (nd pd, mchancal paramr, c.). Th modl bacally con of a of ranfr fncon characrzn h nd rbn prformanc. Th fnal modl ll con on a nq ranfr fncon ha bhav a f r a WTGS. In fac, a nd rbn can b dcrbd h a cond ordr qvaln ranfr fncon [9], akn no accon dffrn mplfcaon. In [0] prnd a mplfcaon of h WTGS by obann a mplfd qvaln modl for boh h acv and racv por bhavor, onc h prformanc of h nd rbn ha bn analyzd. Th mplfcaon ha hav o b appld n ordr o oban a prformanc-ornd modl of h WTGS ar a follo [5][0]: nd pd amd conan; varablpd opraon n carrd o hn procon n; dcopln bn por and pd,.. pch anl conrol arodynamc rprnaon and mchancal par can b nlcd; h nraor dynamc nlcd, o can b rprnd a a lnar an (for por ym ably, h fa aor flx rann of h nraor no condrd): n 3856

5 [], h nraor and convrr ar mply rprnd a an albrac xpron ha bjcd o por lmaon drn a fal vn; nc h nraor dynamc nlcd, h dynamc rpon vn by h rpon of h por convrr, hch can b rad a conrolld crrn orc; h procon mplfd o V/f procon n. All h ampon lad o a noabl rdcon n h complxy of h ym. Tabl I [5] ho h dffrnc bn h componn-ornd modl and h prformancornd modl. TABE I IFFERENCES BETWEEN PERFORMANCE MOE AN COMPONENT MOE Far Componn modl Prformanc modl Gnraor ynamc modl nar an Pch Pch conrol No ncldd qaon (-5). I hold b nod from ha qaon ha h arodynamc orq rman n a conan val provdd ha h nd pd do no chan. So, a p chan n nd pd man a p chan n arodynamc orq, hch mpl a chan n acv nrad por by man of h nral ranfr fncon of h ym (h np h nd pd, hra h op h arodynamc orq). 7. rv Tran Tranfr Fncon Takn no accon ha h -ma modl drv ran qaon (6) ar lnar qaon, hy can b xprd n h follon form A C B (4) hr A, B, C and ar h follon ranfr fncon Mchancal ym Procon Conrol Paramr con -ma non-lnar modl Vola, frqncy, ovr crrn and ovr pd Por conrollr and nnr crrn loop daa pon n look p abl for arodynamc Inrnal a 6 Tm p lmaon -ma lnarzd modl Vola and frqncy Por conrollr 37 < m -0 m A B C K K K K K K K K (5) I can b n ha condrn h prformanc-ornd modl, nfcan rdcon n modl complxy achvd. Hovr rqr an ndrandn of h opraon of h hol modl, a ll a h nd o kno h corrc daa. Anyay, h mlaon m rdcd condrably. 5. Tranfr Fncon of h VSWT Th ranfr fncon of h hol ym an n-ordr fncon n hch h np val h arodynamc orq and h op val h acv por dlvrd by h nraor. F. 5 ho h concp. Th ranfr fncon h rl of opran h h ranfr fncon of h dffrn par of h ym, hch ll b dcrbd blo. τ H () F. 5. Wnd rbn xprd a a ranfr fncon. P n 6. Wnd Spd and Arodynamc Tranfr Fncon Thr ar no ranfr fncon rlad o nd pd and arodynamc bca hr no dynamc n h rpcv hr (6) A can b n, h -ma modl drv ran can b condrd a for ranfr fncon, hch man ha hr ar o np (orq) and o op (pd). 8. PMSG Tranfr Fncon Th PMSG can b xprd a a ranfr fncon n hch h np h nraor pd and h op h acv por dlvrd o h rd. In ordr o oban h qvaln ranfr fncon of h PMSG, on m play h h qaon () and (3), obann h xpron ha ar ld blo. Nx, by combnn h qaon ohr h (4-6) pobl o oban h qvaln ranfr fncon of h VSWT-bad PMSG,.. h prformanc ornd modl. d d r q (7) 3857

6 P q.5 p n.5 p.5.5 q d r d q r r r d r r r d d d d q d q r r r d r r r q q d r q r.5 r r q d r q r r r d r V. CONCUSIONS (8) (9) (0) Th qaon ha xplan h bhavor of a varablpd nd rbn-bad prmann man ynchrono nraor hav bn prnd (h approach namd h componn-ornd modl). Th prformanc-ornd modl ha bn commnd by man of h ranfr fncon of h bym n hch a nd rbn con. Th da of h approach o rprn h nd rbn a a crrn orc, hch dpnd on varo paramr. Th modl con of a of ranfr fncon characrzn h nd rbn prformanc. p h complxy hon by h qaon hold b nod ha h dynamc ha hy ho ar h am a h on prnd by h dynamc modl. Th da o mplfy h ranfr fncon and o oban an qvaln ranfr fncon ha bhav a f r a nd rbn. ACKNOWEGMENT Th rarch ork ha bn dvlopd ndr h ran ENE C04-03/AT from h Spanh Mnry of Scnc and Tchnoloy. REFERENCES [] Global Wnd 008 Rpor, Global Wnd Enry Concl (GWEC), Tch. Rp., March 009. Avalabl: hp://.c.n/ []. A. Fn, A. Molna, F. Rz, E. Gómz, and F. ménz, Wnd Trbn Modln: Comparon of Advancd Tool for Trann Analy, IEEE Por Ennrn Socy Gnral Mn, Tampa, Florda, n 007, pp. -6. [3]. O. Tand, Grd Inraon of Wnd Farm, Wnd Enry, vol. 6, no. 3, pp. 8-95, n 003. [4] M. Cro and. Chn, Th Mlra Mhod for Smlaon of Por Sym ynamc, IEEE Tranacon on Por Sym, vol. 9, no. 3, pp , A 994. [5] P. Nln, G. K. Andrn, K.. Hamann, K. Ska, and. Bch, A Prformanc Ornd Wnd Trbn Modl for Grd Sably Sd, h Eropan Confrnc on Por Elcronc and Applcaon (EPE), Aalbor, nmark, Spmbr 007, pp. -0. [6] M. Chnchlla, S. Arnal, and. Bro, Conrol of Prmann- Man Gnraor Appld o Varabl-Spd Wnd-Enry Sym Conncd o h Grd, IEEE Tranacon on Enry Convron, vol., no., pp , March 006. [7] G. Ramharan, N. nkn, and O. Anaya-ara, Modlln and Conrol of Synchrono Gnraor for Wd-ran Varabl-pd Wnd Trbn, Wnd Enry, vol. 0, no. 3, pp. 3-46, March 007. [8] A.. Hann and G. Mchalk, Modlln and Conrol of Varabl- Spd Ml-pol Prmann Man Synchrono Gnraor Wnd Trbn, Wnd Enry, vol, no. 5, pp , May 008. [9] S. Achll and M. Pöllr, rc rv Synchrono Machn Modl for Sably Amn of Wnd Farm, 4h Inrnaonal Workhop on ar-cal Inraon of Wnd Por and Tranmon Nork for Offhor Wnd Farm, Bllnd, nmark, Ocobr 003, pp. -9. [0] P. M. Andron and A. Bo. Sably Smlaon of Wnd Trbn Sym, IEEE Tranacon on Por Appara and Sym, vol. PAS-0, no., cmbr 983. [] S. Hr, Grd Inraon of Wnd Enry Convron Sym. nd Ed. Chchr: ohn Wly & Son, 006. [] S. M. Myn, Md. H. Al, R. Takahah, T. Mraa,. Tamra, Y. Tomak, A. Sakahara, and E. Saano, Comparav dy on rann ably analy of nd rbn nraor ym n dffrn drv ran modl, IET Rnabl Por Gnraon, vol., no., pp. 3-4, n 007. [3] G. Mchalk, Varabl Spd Wnd rbn Modlln, Conrol, and Impac on Por Sym, Ph.. Th, p. Rn. Enr., Tchnch Unvrä armad, armad, Grmany, Aprl 008. [4] A. Prdana, ynamc Modl of Wnd Trbn, Ph.. Th, p. Enr. And Env., Chalmr Unvry of Tchnoloy, Göbor, Sdn, 008. [5] C. Kra, Analy of Elcrc Machnry and rv Sym. nd Ed. N York: Wly-Inrcnc, 00. [6] P. Kndr, Por Sym Sably and Conrol. N York: McGra-Hll, 994. [7]. G. Sloo, S. W. H. d Haan, H. Polndr, and W.. Kln, Gnral Modl for Rprnn Varabl Spd Wnd Trbn n Por Sym ynamc Smlaon, IEEE Tranacon on Por Sym, vol. 8, no., pp. 44-5, Fbrary 003. [8] A. Rolán, A. na, G. Vázqz,. Alar and G. Azvdo, Modln of a Varabl Spd Wnd Trbn h a Prmann Man Synchrono Gnraor, IEEE Inrnaonal Sympom on Indral Elcronc (ISIE), Sol, Kora, ly 009, pp [9] C. ach and S. M. Ilam, Idnfcaon of a Rdcd Ordr Wnd Trbn Tranfr Fncon from h Trbn Sp Rpon, Aralaan Unvr Por Ennrn Confrnc (AUPEC), Hobar, Tamana, Arala, Spmbr 005, pp. -4. [0]. Son,. rn, and R. Blman, Eqvaln Tranfr Fncon for a Varabl Spd Wnd Trbn n Por Sym ynamc Smlaon, Inrnaonal ornal of rbd Enry Sorc, vol., no., pp. -3, Novmbr 004. [] M. Bhnk and E. Mljad, Rdcd Ordr ynamc Modl for Varabl-Spd Wnd Trbn h Synchrono Gnraor and Fll Por Convron Topoloy, Inrnaonal Confrnc on Fr Por Sym, Amrdam, Th Ndrland, Novmbr 005, pp