Loss Minimization Control for Doubly-Fed Induction Generators in Variable Speed Wind Turbines

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1 Th 33d Annual Confnc of th IEEE Indutal Elctonc Soct (IECON) Nov. 5-8, 7, Tap, Tawan o Mnmzaton Contol fo Doubl-Fd Inducton Gnato n Vaabl Spd Wnd Tubn Ahmd G. Abo- Khall, Hong-Guk Pak, Dong-Choon Dpt. of Elctcal Eng., Yungnam Unv. 14-1, Dadong, Gongan, Gongbuk, Koa dcl@u.ac.k Sung-Po Ru, S-Hun Elcto-Mchancal Rach Inttut Hunda Hav Indut Co. td, Gongk, Koa pu@hh.co.k Abtact- In th pap, a novl contol algothm fo mnmzng th opatng lo of doubl fd nducton gnato (DFIG) fo vaabl pd wnd tubn pntd. At ft, th gnato lo a modld, whch cont of th copp lo and th on lo. Thn, a tato d-ax cunt dvd whch mnmz th total gnato lo. Bad on th cunt, th tato actv pow lvl contolld. Th xpmntal ult fo a 3kW DFIG wnd tubn mulato how that th amount of pow avng appoach to 3% at 5[m/] wnd pd, whch mo gnfcant at low wnd pd. Fg. 1. Pow flow n wnd pow gnaton tm. I. INTRODUCTION Wnd pow ha povn to b a potntal clan and nwabl ouc fo gnaton of lctct wth mnmal nvonmntal mpact. In cnt a, th ha bn a wdpad gowth n th xplotaton of wnd ng, whch qu th dvlopmnt of lag and mo obut wnd tubn tm [1]. It pfabl to un th wnd ng gnaton tm (WEGS) at a vaabl gnato pd to maxmz th captud wnd pow. Fo th maxmum pow pont tackng (MPPT), th optmum tp-pd ato [] o ach-bad mthod [1] hav bn ud, whch adjut th actv pow fnc of th gnato to th optmum valu fo th gvn wnd pd. Compad wth th contant pd opaton, vaabl pd opaton of wnd tubn wth th MPPT povd 1~15[%] hgh ng output, low mchancal t, and l pow fluctuaton [3]. Snc th WEGS cont of dffnt mchancal componnt lk dv tan, gabox, gnato, and o on, numou lo can b found n th tm. Th total WEGS lo a dvdd nto two man catgo, mchancal and lctcal lo. A gnal pow flow dagam fo a WEGS hown n Fg. 1. Rcntl, attnton ha bn pad to mpov th opatng ffcnc of gnato n WEGS b mnmzng th lctcal lo. Th DFIG now on of th man gnato fo hgh-pow vaabl-pd wnd ng convon tm. It ha man advantag compad wth th qul-cag nducton gnato [4]-[6]: th oto-d convt opat at th lp fqunc and th pow convt poc onl ± 3% of th atd pow of th gnato wth th convt cot ducd; th gnatd actv and actv pow can b contolld ndpndntl. Contol of DFIG lo ha bn potd n [7] and [8]. In [7], th tato d-ax cunt fo mnmum copp lo dvd and thn ud to obtan th actv pow fnc. Howv, Fg.. Confguaton of DFIG wnd pow tm. th man tagt n [7] th gnato actv and actv pow contol n tad tat and tannt wthout howng th ffct of th njctd actv pow on th copp lo ducton. In [8], th lo ducton achvd b hang th gnato and gd actv pow btwn th two convt on th oto ccut. Howv, th hang ato a functon of th flt capacto cunt, pow facto, and gnato paamt, whch mak t dffcult to dtmn th optmum hang ato fo all pow facto and opatng condton. In th pap, a contol algothm popod to mnmz th total lo of th DFIG. Th copp and on lo of th DFIG a modld a a functon of th tato flux and d-ax cunt. Thn, a tato d-ax cunt whch mnmz th total gnato lo dvd. Th mulaton ult fo a [MW] DFIG how a ducton n th gnato lo up to 3% at 5[m/] wnd pd. Th xpmntal ult fo a 3kW wnd tubn mulato how ng avng of 3% at th am wnd pd. II. MODEING AND CONTRO OF DFIG Confguaton of th ovall wnd gnaton tm ung DFIG hown n Fg.. Th tato of DFIG dctl connctd to th gd and th oto connctd though th back-to-back PWM convt /7/$. 7 IEEE 119

2 Tubn Gd P P * - t Gabox 1:n Pow contoll Encod 1 - * q l l q - a j b l v a q-ax Cunt Contoll PWM Convt v b v c SVPWM v q v d Vdc Q Q * - Ractv pow contoll d * - d d-ax Cunt Contoll Fg. 3. Equvalnt ccut of DFIG. Fg. 3 how th d-q quvalnt ccut of DFIG. In a nchonoul otatng d-q fnc fam, th tato flux and voltag can b xpd a [9] dq = dq mdq (1) d v = dq R dq dq j dq dt ω () wh m : Magntzng nductanc; : Stato lf-nductanc; : Stato d-q ax flux lnkag; dq v dq : Stato d-q ax cunt; dq : Stato d-q ax voltag; ω : Souc angula fqunc. Fo coodnat tanfomaton, th angl btwn two fnc fam qud. Th pha angl θ of th tato flux vcto whch otat at th nchonou pd gvn b dq = ( vdq Rdq ) dt (3) q θ = tan 1 (4) d wh th upcpt ndcat quantt n th tatona fnc fam. Alo, th oto flux and voltag can b xpd a dq = dq mdq (5) d v = dq R dq dq j( ) dq dt ω ω (6) wh : Roto lf-nductanc; : Roto d-q ax flux lnkag; v dq dq dq : Roto d-q ax cunt; : Roto d-q ax voltag; Fg. 4. Contol. block dagam of DFIG. ω : Roto angula fqunc. Fo tanfomaton of th oto quantt, th lp angl ( θ l ) qud, whch can b xpd a θ l = θ θ, wh θ th oto angula poton. Th gnato toqu xpd a P m T = 1.5 ( dq qd) (7) and th tato actv and actv pow can b xpd a 3 P = ( v v ) (8) q q d d 3 Q = ( v v ) (9) q d d q III. CONTRO OF ROTOR-SIDE CONVERTER Stato-flux ontd vcto contol uuall adoptd n DFIG contol, wh th tato flux vcto algnd wth th d-ax. In th ca, th d-q ax flux can b xpd a =, and q d = (1) Th q-ax componnt of th oto cunt can contol th th gnato toqu o th tato actv pow. On th oth hand, th oto d-ax cunt componnt can contol dctl th tato actv pow. Condng v d = fom (1) and ubttutng th oto cunt whch ult fom (1) and (1) nto (8) and (9), th tato actv and actv pow can b xpd a 3 m P = vq (11) q 3 m Q = vq ( m d ) (1) wh m th magntzng cunt, whch contant fo contant. d Thfo, th abov quaton how that tato actv and actv pow can b contolld ndpndntl b contollng q and d, pctvl. Fg. 4 how th chmatc confguaton of th DFIG wnd 111

3 Fg. 5. Pow contol block dagam. (a) Actv pow contol (b) Ractv pow contol. tubn tm and t mplfd contol chm [11]. Th * optmum output pow P of th DFIG ud a th fnc valu fo th pow contol loop. In th contoll, th out tato pow contol loop poduc a fnc valu,, fo th nn cunt contol loop a hown n Fg. 5(a). Nomall, th tato actv pow n th DFIG wnd pow tm contolld to b zo to kp unt pow facto at th tato d. Howv, th tato actv pow Q contolld to th valu o a to poduc th d-ax oto cunt fnc a hown n Fg. 5(b). IV. OSS MINIMIZATION OF DFIG Fld-ontd contol dcbd abov allow th MPPT wth th actv pow contol. B adjutng a ha of th gnato actv pow uppld though th tato and oto at th appopat valu, th gnato lo can b mnmzd [8]. Th machn copp lo can b xpd a P = 1.5( ) R 1.5( ) R (13) cu _ lo d q d Subttutng d and q fom (1) and (1) n (13), th copp lo can b xpd a P = 1.5 [( R ( / ) R ) R / cu _ lo m d d d m (( T/ Kt ) ) R ( T / Ktm) R) d ( d / m ) R ) ] q 3 m v q * q (14) A to that pnt th on lo connctd n paalll to th magntc banch. Such an appoach ha alad bn ud to analz th nducton machn lo [1]. Fom Fg. 3, th tato flux lnkag n th d-q fnc fam a a d = dm ld (15) q = qm lq = (16) Voltag quaton n magntc banch a xpd a ddm Rd = ω qm dt (17) d qm Rq = ω (18) dm dt wh R th quvalnt on lo tanc. Th tato d- ax flux n a nchonou fnc fam nal contant a th tato connctd to th tff gd wth a contant voltag and contant fqunc, whl th q-ax flux nal zo n th d-ax flux ontd contol. Thfo th flux vaaton n nchonou fnc fam can b nglctd and th cunt flowng n th co lo banch can b xpd a R d = ωqm (19) R q = ωdm () Subttutng (15) and (16) nto (19) and (), d = ωlq / R (1) q = ω ( d ld) / R () Th gnato on lo can b xpd a P on _ lo = 1.5( d q ) R (3) Subttutng (1) and () nto (3), P on _ lo = 1.5[( ) Th total lo gvn b l l d t d d l d ( T / K ) ] ω / R d (4) Ptotal _ lo = Pcu _ lo Pon _ lo (5) Eqn. (5) a functon of d and. In (1), a functon d d of and d d and t contant n tato-flux ontd vcto contol. Snc th hang of magntzng cunt fom d and nflunc th lo dffntl vn though d d contant, th hang ffct of and d hould b takn nto d condaton on th dvatv fo th mnmum lo. Fo th, hould b xpd a a functon of d d o vc va. Howv, t dffcult to gt an dct latonhp btwn and d d, o t aumd that th hang of magntzng cunt btwn d and whch poduc th d d don t nflunc th lo. Th aumpton ha bn ud n [7]. To gt th valu of d fo lo mnmzaton, takng th dvatv of th total gnato lo wth gad to d and qualng to zo, dptotal _ lo / d d = (6) Fom (6), th tato d-ax cunt fnc fo mnmum lo gvn b * ( RR mωl) d d = (7) RR RR ω m m l 1111

Total lo Total lo 1.6k Total o Pcupp Pon.k <Unttld> 1.4k 1.8k 1.k P Total lo 1.6k 1.4k 1.k (a) 1.k.8k.6k.4k P cu lo P on lo 1.k.k.8k..5 3. 3.5 4. 1.5..5 3. 3.5 4. 4.5 5.

(b) Magntzng, oto and tato d-ax cunt [A]. Th cunt contant gadl of th opatng condton, whch ult fom th aumpton that th hang of magntzng cunt btwn d and d don t nflunc th lo a mntond abov.

4 Total lo Total lo 1.6k Total o Pcupp Pon.k <Unttld> 1.4k 1.8k 1.k P Total lo 1.6k 1.4k 1.k (a) 1.k.8k.6k.4k P cu lo P on lo 1.k.k.8k Id Id Id Id 8 Idp Id 7 Idp_ Id <Unttld> (b) 4 d d <Unttld> amda amq.8 Fg. 6. DFIG lo fo dffnt d-ax cunt. (a) Total lo[w]. (b) Magntzng, oto and tato d-ax cunt [A]. Th cunt contant gadl of th opatng condton, whch ult fom th aumpton that th hang of magntzng cunt btwn d and d don t nflunc th lo a mntond abov. Snc th aumpton mak om o about to 3% fom th actual mnmzaton, t can b calld a qua-mnmzaton of th gnato lo. Wth (7), th actv pow fnc n (9) gvn b * 3 * Q = vqd (9) V. SIMUATION RESUTS To vf th dvlopd algothm, mulaton cad out fo a DFIG wnd gnaton tm ung PSCAD oftwa. Th atng and paamt of th DFIG a ltd n Tabl I and th tubn paamt a ltd n Tabl II. Fg. 6 how pow lo chaacttc wth gad to th tato d-ax cunt at 6[m/] wnd pd. In th wnd pd, th onl on d-ax cunt valu whch gv a mnmum pow lo. Th oto d-ax cunt can b ducd fom th atd valu to duc th total lo and thb th tm opatng ffcnc ncad. A th oto d-ax cunt dcad, th tato d-ax cunt nca and th total lo dca a hown n Fg. 6 (b). Fg. 7(a) how th gnato pfomanc at 5[m/] wnd pd. Th DFIG tat wth th zo actv pow fnc, and thn th lo mnmzaton algothm actvatd at 3[c] and man actvatd. Both on and copp lo dca a th gnato actv pow t to th optmum valu. Th pow lo dcad fom 14[W] to 95[W], t man pow avng of about 3% obtand. In Fg. 7(b), th oto d-ax cunt dcad a th tato d-ax cunt nca. Snc th tato flux a dtmnd b th tato voltag and fqunc, t man contant vn aft actvaton of lo mnmzaton, a hown n Fg. 7(c). Th oto flux chang du to th cunt chang a hown n Fg. 7(d). It notcabl (c) (d) () (f) amq d Tm [] Fg. 7 o mnmzaton contol at 5 m/ wnd pd. (a) Gnato lo [W]. (b) Stato and oto d-ax cunt [A]. (c) Stato flux [Wb]. (d) Roto flux [Wb]. () Toqu [p.u.]. (f) Spd [pm]. d q Roto flux amd q that th toqu and pd a contant du to complmnta chang of th d and q-ax cunt a hown n Fg. 7 () and (f), pctvl. Fg. 8 how th ult of lo mnmzaton contol at vaabl wnd pd. Dung vaabl wnd pd, th lo mnmzaton contol wok wll a hown n Fg. 8(b). Th tato d-ax cunt n (c) ocllat lghtl du to th tato q- ax cunt vaaton. 111

5 <Unttld> Wnd pd Total lo 3.5k Total o Pcupp Pon 3.k.5k.k 1.5k 1.k.5k Fg. 1. Gnato pow vaaton (a) v. oto d-ax cunt (b) Id Id 5 Idp_ Id 4 (a) [W] 5 [W]/dv 3 1 (b) [A] [A]/dv Fg. 8. DFIG lo at vaabl wnd pd. (a) Wnd pd [m/]. (b) Gnato lo [W]. (c) Roto, tato d-ax cunt [A]. Pow lo [W]] C onvntonalcontol o m nm zaton contol Wnd pd [m/] Fg. 9. Compaon of pow lo vu wnd pd (mulaton). (c) (d) () [VAR] [A] [Nm] [VAR]/dv 8 [A]/dv [Nm]/dv Fg. 9 how th compaon of pow lo wth gad to th wnd pd. It hown that th lo ducton mo gnfcant at low wnd pd. VI. EXPERIMENTA RESUTS To vf th fablt of th popod contol chm, om xpmnt w pfomd fo a 3[kW] laboato pototp. Th tato of th DFIG connctd to th utlt gd. Th oto connctd to th gd though back-to-back PWM convt. Th convt wtchng fqunc 5[kHz] and th amplng pod of th nn cunt and out pow contol loop a 1 [ µ ], 1 [m], pctvl. Th atng and paamt of th DFIG a ltd n Tabl I and th tubn paamt a ltd n Tabl II. Fg. 1 how th ffct of contollng th tato actv pow on th total gnato lo. Th gnato lo dca a th oto d-ax cunt ducd a hown n Fg. 1(a).1 []/dv Fg. 11. Gnato lo mnmzaton at 5 m/ wnd pd. (a) Total lo. (b) Roto d-ax cunt. (c) Stato actv pow. (d) Stato d-ax cunt. () Gnato toqu. and (b). If th oto d-ax cunt dca futh l than th optmum valu, th gnato lo nca accodngl. Fg. 11 how th gnato pfomanc at 5[m/] wnd pd. Th DFIG tat wth th zo actv pow fnc, and thn th lo mnmzaton algothm actvatd and man actv. A th gnato actv pow t to th optmum valu, th total gnato lo dca to th optmum valu a hown n Fg. 11(a). Th pow lo dcad fom 13[W] to 1[W], whch man pow avng of about 3% obtand. Th gnato dnamc pfomanc nvtgatd a hown n Fg. 11(). It notcabl that th toqu kpt contant a th oto d-ax cunt dcad. Fg. 1 how th gnato pfomanc at 7[m/] wnd pd, jut th am a Fg. 11. Th pow lo dcad 1113

6 fom 148[W] to 11[W], wh pow avng about % obtand. Fg. 13 how th pow lo vu th wnd pd. Th ducton of pow lo ffctv mot of th wnd pd ang. Howv, t magn dca at hgh wnd pd. VII. CONCUSIONS It wll known that wnd gnaton tm ma opat at a facton of th atd pow mot of th tm. Rducng th gnato lo ctcal u fo ducng th cot of ng n uch condton. In th pap, a lo mnmzaton algothm fo wnd dvn doubl-fd nducton gnato wa popod. Th gnato total lo a mnmzd though contollng th tato actv pow. To vf th ffctvn of th popod algothm, th mulaton hav bn pfomd fo a [MW] doubl-fd nducton gnato tm. Th mulaton ult hav hown that t pobl to duc th pow lo up to 3% at 5[m/] wnd pd. Th popod algothm povd valdt to duc th gnato up to 3% at 5[m/] ung 3[kW] pototp. APPENDIX TABE I PARAMETERS OF DFIG Paamt Valu Ratd Pow [MW] 3[kW] Ratd n voltag 69[V] [V] Stato tanc.48[p.u].6[ω] Roto tanc.549[p.u].713[ω] Ion lo tanc.18[p.u] 155[Ω] Stato lakag nductanc.941[p.u].3313[h] Roto lakag nductanc.9955[p.u].3313[h] Mutual nductanc [p.u].63443[H] Momnt of nta 48[kg m ].51[kg m ] TABE II PARAMETERS OF TURBINE BADE MODE Paamt Valu Ratd Pow [MW] 3[kW] Blad adu 4[m].95[m] Max. pow conv. coff Optmal tp-pd ato 7 7 Cut-n pd 4[m /] 4[m /] Ratd wnd pd 1[m /] 13[m /] Ga ato 8 ACKNOWEDGMENT Th wok ha bn uppotd b th KEMCO (Koa Eng Managmnt Copoaton) und pojct gant (4- N-WD1-P ). REFERENCES [1] Q. Wang and. Chang, An ntllgnt maxmum pow xtacton algothm fo nvt-bad vaabl pd wnd tubn tm, IEEE Tan. Pow Elcton., vol. 19, No. 5, pp , Spt. 4. [] F. F. M. El-Sou, M. Oab, and H. Godah, Maxmum pow pont tackng contol chm fo gd connctd vaabl pd wnd dvn Fg. 1. Gnato lo mnmzaton at 7 m/ wnd pd. (a) Total lo. (b) Roto d-ax cunt. (c) Stato actv pow. (d) Stato d- ax cunt. Pow lo [W]] Convntonal contol o mnmozaton contol Wnd pd [m/] Fg. 13. Compaon of pow lo vu wnd pd. lf-xctd nducton gnato, KIPE Jounal of Pow Elcton., vol. 6, no. 1, pp.45-51, Jan. 6. [3] H. Akag and H. Sato, Contol and pfomanc of a doubl-fd nducton machn ntndd fo a flwhl ng toag tm, IEEE Tan. on Pow Elcton., vol. 17, no. 1, pp , Jan.. [4] M. Yamamoto and O. Motooh, Actv and actv pow contol fo doubl-fd wound oto nducton gnato, IEEE Tan. on Pow Elcton., vol. 6, no. 4, pp , Oct [5] R. Pna, J. C. Cla, and G. M. Ah, Doubl fd nducton gnato ung back-to-back PWM convt and t applcaton to vaabl- pd wnd-ng gnaton, IEE Poc., vol. 143, no. 3, pp , [6] A. Tapa, G. Tapa, J. X. Otolaza, and J. R. Sanz, Modlng and contol of a wnd tubn dvn doubl-fd nducton gnato, IEEE Tan. Eng Conv., vol. 18, no., pp , Jun 3. [7]. Xu and Y. Tang, A flxbl actv and actv pow contol tatg fo a vaabl pd contant fqunc gnatng tm, IEEE Tan. on Pow Elcton., vol. 1, no.4, pp , Jul, [8] B. Rablo, W. Hofmann, and. Pnho, o ducton mthod fo doubl-fd nducton gnato dv fo wnd tubn, IEEE SPEEDAM Conf. Poc., vol. 3, 6, pp [9] W. Hofmann and F. Okafo, Optmal contol doubl fd full contolld nducton wnd gnato wth hgh ffcnc, IEEE IECON Conf. Poc., vol., 1, pp [1] S-D. W, M-H. Shn, and D-S. Hun, Stato-flux-ontd contol of nducton moto condng on lo, IEEE Tan. on Ind. Elcton., vol. 48, no.3, pp , Jun, 1. [11] Ahmd G. Abo-Khall, Dong-Choon, and S-Hun, Gd conncton of doubl-fd nducton gnato n wnd ng convon tm, IPEMC, Shangha, vol. 3, 6, pp

TRANSIENT PROCESSES AND DYNAMIC OF VARIABLE SPEED PUMP STORAGE UNIT

TRANSIENT PROCESSES AND DYNAMIC OF VARIABLE SPEED PUMP STORAGE UNIT Ol Shal, 203, Vol. 30, No. 2S, pp. 244 256 ISSN 020889X do: 0.376/ol.203.2S.05 203 Etonan Acadmy ublh TRANSIENT ROCESSES AND DYNAMIC OF VARIABLE SEED UM STORAGE UNIT RIMANTAS RANAS DEKSNYS *, DARIUS ALIŠAUSKAS