Analysis and Compensation of Current Measurement Errors in a Doubly Fed Induction Generator

Transcription

1 J Elctr Eng Tchnol Vol. 8, No.?: 74-?, 0 SSN(Print) SSN(Onlin) Analyi and Compnation of Currnt Maurmnt Error in a Doubly Fd nduction Gnrator Yung-Dug Son*, Won-Sang m *, Han-Sok Pk ** and Jang-Mok Kim Abtract t i ncy to maur th currnt of rotor for controlling th activ and ractiv powr gnratd by th tator id of th doubly fd induction gnrator (DFG) ytm. Thr offt and caling rror in th currnt maurmnt. Th offt and caling rror cau on and two tim currnt rippl of lip frquncy in th ynchronou rfrnc fram of vctor control, rpctivly. Thi papr propo a compnation mthod to rduc thir rippl. Th tator currnt i viabl according to th wind forc but th rotor currnt i almot contant. Thrfor input of th rotor currnt i mor uful for a compnation mthod. Th propod mthod adopt th ynchronou d-axi currnt of th rotor a th input ignal for compnation. Th rippl of th maurmnt rror can b calculatd by intgrating th ynchronou d-axi tator currnt. Th calculatd rror addd to th rfrnc currnt of rotor a input of th currnt rgulator, thn th rippl rducd. Exprimntal rult how th ffctivn of th propod mthod. Kyword: DFG, Rippl rror, Currnt nor rror, Offt, Scaling, Synchronou d-axi rotor currnt. ntroduction A doubl fd induction gnrator (DFG) i a popul wind turbin ytm du to it high nrgy fficincy, rducd mchanical tr on th wind turbin, and rlativly low powr rating of th connctd powr lctronic convrtr of low cot [-4]. Th vctor control of th rotor currnt i ud to control th activ and ractiv powr indpndntly and tably uing a rotating rfrnc fram fixd on th gap flux [5-7]. Thrfor, prci maurmnt of th rotor currnt i vry important in th vctor control [8, 9]. Th rotor- and grid-id currnt maurd from th currnt nor of th convrtr through low pa filtr and A/D convrtr. n thi proc, currnt maurmnt rror can b gnratd du to th non-linity of th currnt nor, quantization rror of A/D convrtr, and th thrmal drift of th analog lctric lmnt. Th rror cau th rippl in th producd powr of th DFG [0, 7]. Th rror can b claifid a offt rror, caling rror and non-linity rror. n th rotor id control, th rippl by offt and caling rror hav on and two tim componnt of th fundamntal rotor currnt frquncy, rpctivly. Thn th rippl of th rotor id lad to th fluctuation of th tator id. Th rippl frquncy by th offt rror i am a th Corrponding Author: Dpt. of Elctrical Enginring, Puan National Univrity, Kora. (jmok@puan.ac.kr) * Dpt. of Elctrical Enginring, Puan National Univrity, Kora. (ydon@puan.ac.kr, won4@ puan.ac.kr) ** Dpt. of Elctrical Enginring, Pukyong National Univrity, Kora. (phanok@pknu.ac.kr Rcivd: Augut 8, 0; Accptd: Octobr, 0 diffrnc btwn th grid frquncy and th lip frquncy, and it by th caling rror i am a th diffrnc btwn th grid frquncy and two tim of th lip frquncy [8]. n [9], a mthod wa propod in ordr to olv th problm of th offt and caling rror in th DFG ytm. Th mthod obtain th two rror dirctly from th pha currnt of th rotor id, and compnat th two rror on th currnt maurmnt path. t can improv th tady tat prformanc of th DFG by liminating th ffct of th offt and caling rror. Howvr, thi mthod cannot guant th complt compnation in th tranint tat bcau th pha currnt of th tationy rfrnc fram ud a input for th calculation of th rror. Thi papr analyz th rror componnt of th offt and th caling on th bai of th ynchronou rfrnc fram of th DFG, and propo a compnation mthod to rduc th ffct of th rror. Th propod mthod adopt th ynchronou d-axi currnt of th rotor a th input ignal for compnation du to th vral advantag. Thi mthod can b imply implmntd by calculating th vral intgral and ubtracting opration. Alo th mthod i wll opratd not only undr th tady tat but alo undr th tranint tat, and robut to th viation of th machin pamtr. Th validity of th propod mthod i vrifid through th xprimnt.. Dcription of DFG [-7] Fig. illutrat th configuration of a DFG ytm. A hown in Fig., th tator magntizing currnt i obtaind 74

2 Yung-Dug Son, Won-Sang m, Han-Sok Pk and Jang-Mok Kim λd i Q ωλd m dr () A known in () and (), th ynchronou d- and q- axi currnt of th rotor dirctly proportional to th ractiv and activ powr of a DFG, rpctivly. n thi papr, two rotor currnt nor ud for th vctor control of back-to-back convrtr of a DFG. Fig.. Configuration of DFG ytm from th grid. Th voltag quation and th tator flux of th ynchronou rfrnc fram givn in (-) and (4). λd ω λq d vd Rid + () dt dλ q v q Riq + + ω λ () d dt λ i + i () d q d q m dr miqr λ i + (4) whr ω i th ynchronou angul pd, i th lfof tator and m i inductanc th magntizing inductanc. Th voltag quation and th rotor flux of th ynchronou rfrnc fram givn in (5-7) and (8).. Effct of Maurmnt Error of Rotor Currnt [9, 0] Fig. how th maurmnt path of th rotor currnt for DFG control. Bcau of th non-linity of th hall nor, th thrmal drift of th analog lmnt, quantization rror of th A/D convrtr, and unbalanc of ach lmnt, th rror gnratd from currnt maurmnt path and invitabl vn if th control ytm i wll dignd and contructd.. Effct of offt rror Fig. how th block diagram of th calculating proc about th influnc of rotor pha currnt offt rror. Th offt rror may b caud by an imbalanc of currnt nor and th maurmnt path or othr problm a mntiond abov. Th offt rror calculatd a: v v dr qr dλdr Rridr + ( ω ωr ) λqr dt (5) dλ qr Rriqr + + ( ω ωr ) λdr dt (6) λ i + i (7) dr qr r dr r qr m d λ i + i (8) m q whr ω r i th angul pd of th rotor. Th producd activ and th ractiv powr of DFG givn by (9) and (0). ( vqiq vdid ) ( v i v i ) P + Q q d d q (9) (0) By uing (-), and (4), th activ and ractiv powr quation of DFG can b rwrittn a follow: P v q m i qr () i abc i abcr Fig.. Path of rotor pha currnt maurmnt DFG Stator Sid Pha Currnt Maurmnt rror Δ Δ br Rotor Sid _offt br_offt / a_offt b_offt / c_offt dr_offt qr_offt l -jl dq λ dq dr_offt qr_offt m dqr d_offt j d_offt q_offt q_offt Fig.. Effct of rotor pha currnt offt rror 74

3 Analyi and Compnation of Currnt Maurmnt Error in a Doubly Fd nduction Gnrator _ offt i +Δ br _ offt ibr +Δbr ( + ) cr _ offt _ offt br _ offt () whr i, i br idal a- and b-pha rotor currnt and Δ, Δ br offt of a- and b-pha, rpctivly. From (), th ynchronou d-q axi rippl currnt of th rotor xprd a: dr _ offt qr _ offt Δ co ωt + ( Δ + Δbr ) in ωt (4) - Δ in ωt + ( Δ + Δbr ) co ωt (5) _ whr ω i th lip angul pd of th rotor, dr offt and qr _ offt th rippl componnt of th rotor currnt du to th offt rror, rpctivly. A known from (4) and (5), th ynchronou d- and q- axi currnt of th rotor hav th fundamntal componnt of th lip frquncy. Th ynchronou d- and q- axi currnt rippl by th offt in th tator can b drivd in (6) and (7), rpctivly. d _ offt d λ λ m d Δ m dr _ offt m q _ offt qr _ offt co ωt + ( Δ + Δ ) in ω t m in t ( br ) co t Δ ω + Δ + Δ ω br (6) (7) Th currnt rippl of th -pha rfrnc fram can b an b obtaind in (8, 9) and (0). m a _ offt [ Δ co( ) ωt + ( Δ + Δbr ) in( ) ωt] (8) of -pha currnt. A known from (8, 9) and (0), th frquncy componnt of th tator ha ( ) du to th offt ffct of th rotor id.. Effct of caling rror Fig. 4 how th block diagram of th calculating proc about th influnc of rotor pha currnt caling rror. f th rotor currnt contain caling rror without offt, thy can b xprd a follow: _ cal Kain( ωt) br _ cal Kbin ωt () whr, i th ral valu of th pha currnt without offt and caling rror, K a and K b dnot th cal factor of a-, and b- pha currnt, rpctivly. From (), th ynchronou d-q axi rippl currnt of th rotor can b drivd a: dr _ cal qr _ cal ( K K ) ( K K ) b a b a in ωt + () 6 ( K K ) ( K + K ) b a b a in ωt + + () Th ynchronou d- and q- axi currnt rippl by th caling rror in th tator can b drivd in (4) and (5), rpctivly. ( K K ) λ d m b a d _ cal in ωt (4) 6 ( K K ) m b a q _ cal in ωt + (5) Th currnt rippl of th -pha rfrnc fram can b obtaind in (6, 7) and (8). m b _ offt - [ Δbr co( -) ωt ( Δ - Δbr ) + in( - ) ωt ] Δ +Δ [ in( ) ω t m br c _ offt +Δ ( +Δ )co( ) ωt] br (9) (0) whr _, a offt b _ offt and c offt _ th offt rror Fig. 4. Effct of rotor pha currnt caling rror 744

4 Yung-Dug Son, Won-Sang m, Han-Sok Pk and Jang-Mok Kim m Kb- Ka a _ cal - [ in(- ) ωt ( Kb- Ka) - co( - ) ω t ] 6 m ( Kb Ka) b _ cal [ in( ) ωt ( Kb Ka) co( ) ω t ] c _ cal (6) (7) m ( Kb + Ka ) [ co( ) ωt] (8) whr a _ cal, b _ cal and c _ cal th cal rror of -pha currnt. A known from (6), (7) and (8), th frquncy componnt of th tator ha ( ) du to th caling rror of th rotor id. 4. Dtction and Compnation of Currnt Error 4. nput ignal adoption for compnation Among prviou quation, th ynchronou d- and q- axi currnt of th rotor and tator can b lctd for th input ignal of th compnator. Th q-axi of th tator currnt i not uitabl for th input ignal of th propod compnator bcau th ynchronou q-axi currnt of th tator i alway fluctuating according to th intnity of th wind. Th offt rror of th rotor and tator givn in (4) and (6), rpctivly. Th caling rror of th rotor and tator givn in () and (4), rpctivly. A known from (4, 6, ) and (4), th amplitud of th tator currnt i lowr than that of th rotor currnt. Morovr, th ynchronou d-axi currnt of th rotor i nly zro or contant for th vctor control. Thrfor, th input ignal of th propod compnator u th ynchronou d-axi currnt of th rotor in thi papr a hown in Tabl. 4. Compnation of currnt maurmnt rror () compnatd automatically, rpctivly. Thrfor, th front in trm can b only conidrd rgdl of th r DC trm in () and (). Thi compnation mthod uing th Tabl and i vry impl but difficult to bring th rliabl rror valu du to th ffct of inaccurat ampling point and th witching noi of GBT. Howvr, th propod compnation mthod can hav high accuracy and rliability du to th u of th avrag valu through continuou intgral. n ordr to compnat th maurmnt rror, two pt of th intgrating opration ndd. Th firt i th intgral of dtcting th offt rror, and th cond i dtcting th caling rror. Th firt pt dividd into two tp a hown in Fig. 5, and Fig. 6. Th firt tp i th intgral of th ynchronou d-axi currnt of th rotor according to th Tabl. Dtction of offt rror on a pcific lip angl θ l Rotor d-axi currnt θ 0 _ Δ θl θl θl l 6 dr offt dr _ offt Δ + Δbr dr _ offt Δ + Δbr dr _ offt Δ + Δbr Tabl. Dtction of cal rror on a pcific lip angl θ l θ l 0 dr _ θl θl θl 6 Rotor d-axi currnt ( K K ) 6 ( K K ) ( K K ) ( K K ) b a cal b a dr _ cal 4 b a dr _ cal b a dr _ cal Th offt and caling rror ( Δ, Δ, K a K b ) can b obtaind from th lctd (4) and () according to th pcific rotor lip angl a hown in Tabl and. Du to th proportional intgral (P) currnt rgulator of th ynchronou d-and q-axi, DC componnt of () and Tabl. nput ignal adoption for compnation nput d-axi dr _ offt (0) qr _ offt () dr _ offt () qr _ offt () currnt Ca Ca : uitabl : unuitabl Ca: q-axi currnt i alway viabl according to th wind intnity Ca: Amplitud of th tator currnt i lowr than that of rotor currnt Fig. 5. Dtction of offt-a (Δ ) 745

5 Analyi and Compnation of Currnt Maurmnt Error in a Doubly Fd nduction Gnrator lip angl θ l from / to / a hown in th ctor of Fig. 5. A hown in (9), th calculation mak th cancllation of th in trm of (4), and can obtain th offt-a, Δ. ε Δidrdθl Δ coθldθl ( Δ Δbr ) in θldθl + + Δ (9) Aftr acquiring th offt-a ( Δ ), th cond tp i th intgral of th currnt of (4) from 0 to according to th lip angl a hown in th ctor of Fig. 6. n thi intgral calculation, th coin trm of (4) i rmovd, and th offt-b ( Δ ) can b obtaind a hown in (0). br ε Δi dθ Δ in 0 θ dθ 4 Δ br dr l br l l (0) Aftr that, th caling rror of th rotor currnt can b obtaind from th cond pt. A hown in Fig. 7, th rror i acquird by intgrating th currnt (8) from / to 5/6 a hown in (). 5 6 Δ dr _ cal l 5 ( ) 6 b a ε i dθ K K in θl + dθl 6 () ( Kb Ka) Fig. 8 how th block diagram of th propod compnation chm. Th ynchronou d-axi currnt of th rotor id i ud for an input ignal of th intgrator a hown in Fig. 8. Th offt rgulator conit of two tp. On i for compnating th a-pha offt rror, and th othr i for th b-pha offt rror. Th two hav intgral typ rgulator (K offt /). Th intgral rgulator forc ε and ε to b zro a hown in Fig. 8. Th controllr for compnating th caling rror alo ha th am rgulator of th offt rror, and forc ε to b zro. Th intgral controllr hav a mmory function to tor th compnatd valu of th offt and caling, rpctivly. Th propod algorithm automatically compnat th offt and caling rror by uing th intgral typ rgulator a hown in Fig. 8. Th gain (K offt and K cal ) of th compnator can b t btwn 0 and, rpctivly. Th mallr th gain i givn, th lowr th rpon and mor accurat th compnating prformanc can b obtaind. Th final compnating quation achivd a in () from th output (Offt_a, Offt_b, Scal_a,b) of th intgral rgulator a hown in Fig. 8. a _ n Scal _ a Offt _ a Scal _ b Offt _ b br b _ n () Fig. 6. Dtction of offt-b (Δ br ) Fig. 7. Dtction of cal rror (K a, K b ) Fig. 8. Block diagram of propod compnation chm 746

6 Yung-Dug Son, Won-Sang m, Han-Sok Pk and Jang-Mok Kim 5. Exprimntal Rult Fig. 9 how th xprimntal tup. Exprimntal tt wr prformd in a.-kw DFG tt rig. Th DFG i coupld to th prmannt magnt ynchronou motor (PMSM) of -kw controlld by a viabl pd drivr providing torqu and pd rgulation. Th rotor of DFG and PMSM controlld patly by microprocor. Th witching frquncy of both convrtr i 5 khz. Spac vctor PWM i ud for witching pul gnration with a ampling frquncy of 0 khz. Th pamtr of th xprimntal ytm hown in Tabl 4. Fig. 0 how th tator pha currnt, th ynchronou d-axi rotor currnt and thir FFT rult undr th following condition; Δ 0.5, Δ br 0.5, K a 0.99, and K b.05. Th rotor i rotating at 50Hz and th ynchronou pd of thi induction gnrator i 60 Hz. Hnc, th lip frquncy i 0 Hz. Fig. 0(b) i th d-axi currnt of th rotor id and it FFT rult. Th d-axi currnt ha on and two tim rippl of th lip frquncy, f l, by th offt and caling rror, rpctivly. A th rult, th a- and b- pha currnt of th tator id in Fig. 0(a) hav ( ) and ( ) tim rippl of th ynchronou frquncy, f, rpctivly a hown in Fig. 0(c) and (d). Fig. how th ynchronou d-axi rotor currnt and it FFT rult bfor th compnation of two rror. Th xprimntal rult wr obtaind undr th rror condition; Δ 0., Δ br 0., K a 0.99, and K b.05. Th condition th maximum tolrabl rror of th wort ca bad on thir dataht of th currnt nor, low pa filtr, matching circuit, and A/D convrtr. A hown in FFT rult of Fig., th ynchronou d-axi currnt ha on and two tim of th lip frquncy of th rotor. f th FFT rult i compd with th prviou wavform, th two tim rippl by caling rror ha th am amplitud and th on tim rippl by th offt rror i dcrad du to th rducd offt. Fig. how thr output valu of th compnator in th block diagram of Fig 8. At firt, th offt-a and -b valu calculatd by th two intgrator, rpctivly. Aftr that, th third intgrator obtain th caling rror by intgrating th two tim rippl componnt until it i nly zro. n thi papr, K offt 0. and K cal 0.05 chon for tabl and prci opration. Fig. 0. Stator pha currnt, ynchronou d-axi rotor currnt and thir FFT rult Fig. 9. Configuration of xprimntal ytm Tabl 4. Th Exprimntal Pamtr Pamtr of DFG Pamtr of PMSM Ratd Powr. [kw] Numbr of pol pair 84.4 [mh] r 84.4 [mh] m 74.7 [mh] R [Ω] R r [Ω] Ratd Powr.0 [kw] Numbr of pol pair 4 R [Ω].4 [mh] Fig.. Synchronou d-axi rotor currnt bfor compnating opration 747

7 Analyi and Compnation of Currnt Maurmnt Error in a Doubly Fd nduction Gnrator frquncy of th rotor. Thn th caling rror compnator bcom activ. A th rult, th rippl componnt by both th offt and caling rror nly compnatd in th ynchronou d-axi currnt of th rotor a hown in Fig.4. Thrfor, powr quality i improvd and th vibration of th gnrator by low frquncy rippl rducd bcau th tator pha currnt do not hav th low frquncy rippl by offt and caling rror. 5. Concluion Fig.. Chactritic of compnation Thi papr propod a compnation mthod to olv th offt and caling problm by th maurmnt rror of th currnt nor in a DFG. Th principal fatur of th propod mthod i uing th ynchronou d-axi currnt of th rotor a an input ignal of th compnator. Thrfor, th propod mthod ha th vral attractiv fatur: robutn with rgd to th viation of th machin viabl, application to th tady and tranint tat, ay implmntation. Th faibility and ffctivn of th propod compnating mthod wr vrifid through xprimntation. Acknowldgmnt Thi work wa upportd by th National Rch Foundation of Kora(NRF) grant fundd by th Kora govrnmnt. (No.0065) Fig.. D-axi currnt aftr compnating offt rror Fig. 4. D-axi currnt aftr compnating caling rror Fig. how th compnation rult rmovd th offt rror of Fig.. A hown in th FFT rult, th rippl of th lip frquncy i liminatd, and th ynchronou d-axi currnt ha only two tim of th lip Rfrnc [] ihui Yang, Zhao Xu, and Zhao Yang Dong, Advancd Control Stratgy of DFG Wind Turbin for Powr Sytm Fault Rid Through, EEE Tran. Powr Sytm, Vol. 7, No., pp. 7-7, 0 [] S.Mullr, M.Dick, and R. W. D Donckr, Doubly fd inductioin gnrator ytm for wind turbin, EEE ndutry Application Magazin, Vol. 8, No., pp. 6-, 00. [] Kiani. M, and W.J., Effct of Voltag Unbalanc and Sytm hmonic on th Prformanc of Doubly Fd nduction Wind Gnrator, ndutry Application Socity Annual Mting, pp. -7, Oct [4] Young-Do Choy, Byung-Moon Han,Jun-Young and Giloo Jang, Ral-Tim Hdw Simulator for Grid-Tid PMSG Wind Powr Sytm, Journal of Elctrical Enginring & Tchnology, Vol. 6, No., pp. 75~8, 0 [5] M. Yamamoto and O. Motoyohi, Activ and Ractiv Powr Control for Doubly-Fd Wound Rotor nduction Gnrator, EEE Tran. Powr 748

8 Yung-Dug Son, Won-Sang m, Han-Sok Pk and Jang-Mok Kim Elctronic, Vol. 6, No 4, pp Oct 99. [6] R. Pna, J.C. Cl and G.M. Ahr, A doubly-fd induction gnrator uing two back-to-back PWM convrtr and it application to viabl pd wind nrgy ytm, EE Proc. Vol. 4, No., pp. - 4, May, 996. [7] Hofman. W and Okafor. F, Optimal control doubly fd full controlld induction wind gnrator with high fficincy, ECON '0, 7th annual Confrnc of th EEE, Vol., No., pp.-8, Dc, 00 [8] G. Saccomando, J. Svnon, and A. Sannino, mproving Voltag Diturbanc Rjction for Viablpd Wind Turbin, EEE Tran. Enrgy Convrion, vol. 7, no., pp. 4-48, Sp. 00. [9] Gwang-Sob Kim, Kyo-Bum, Dong-Choon and Jang-Mok Kim, Fault Diagnoi and Fault- Tolrant Control of DC-link Voltag Snor for Twotag Thr-Pha Grid-Connctd PV nvrtr, Journal of Elctrical Enginring & Tchnology, Vol. 8, No. 4: , 0. [0] Bhzad Mirzaian Dhkordi, Amir Frokh Payam, Mohammad N Hahmnia and Sung-Ki Sul, Dign of an Adaptiv Backtpping Controllr for Doubly-Fd nduction Machin Driv, Journal of Powr Elctronic, Vol. 9, No., pp. 4-5, May [] Han-Su Jung, Son-Hwan Hwang, Jang-Mok Kim, Chul-U Kim and Chol Choi, Diminution of Currnt-Maurmnt Error for Vctor-Controlld AC Motor Driv, EEE Tran. ndutry Application, Vol. 4, No. 5, pp , Spt.-Oct [] Da-Woong Chung and Sung-Ki Sul, Analyi and Compnation of Currnt Maurmnt Error in Vctor-Controlld AC Motor Drivr, EEE Tran. ndutry Application, Vol. 4, No., pp , 998. [] B. H. am, S. K. Panda, J. X. Xu and K. W. im, Torqu rippl minimization in PM ynchronou motor uing itrativ lning control, in procding of th 999 ndutrial Elctronic Socity Annual Confrnc of th EEE, vol., pp , 999. [4] Robrto Bro and Ping Hu, Torqu rippl compnation of induction motor undr fild orintd control, EEE APEC Confrnc, Vol., pp. 57-5, 997. [5] Wizh Qian, S. K. Panda and J. X. Xu, Rduction of priodic torqu rippl in PM ynchronou motor uing lning viabl tructur control, EEE ECON Conf., vol., pp. 0-07, 00. [6] Jong-Woo Choi, Sang-Sup, Sang-Yop Yu and Sok-Joo Kang, Novl priodic torqu rippl compnation chm in vctor controlld AC motor driv, EEE APEC Confrnc, Vol., pp.8-85, 998. [7] Sol-Bin, Kyo-Bum, Dong-Choon and Jang-Mok Kim, An mprovd Control Mthod for a DFG in a Wind Turbin undr an Unbalancd Grid Voltag Condition, Journal of Elctrical Enginring & Tchnology, Vol. 5, No. 4, pp. 64-6, 00. [8] Young-l Kim, Son-Hwan Hwang, Jang-Mok Kim, Sung-Ho Song, Chan-Ki Kim and Young-Do Choy, Rduction of currnt rippl du to currnt maurmnt rror in a doubly fd induction gnrator, EEE Applid Powr Elctronic Confrnc and Expoition(APEC) 008, pp , 008. [9] Gui-Gun Pk, Son-Hwan Hwang, Jang-Mok Kim, Kyo-Bum and Dong-Choon, Rduction of Currnt Rippl du to Currnt Maurmnt Error in a Doubly Fd nduction Gnrator, Journal of Powr Elctronic, Vol. 0, No., pp. -9, May [0] Won-Sang m, Son-Hwan Hwang, Jang-Mok Kim and Jaho Choi, Analyi and compnation of currnt maurmnt rror in a doubly fd induction gnrator, EEE Enrgy convrion congr and Expoition(ECCE) 009, pp. 7-79, 009. Yung-Dug Son H wa born in Buan, Kora, in 97. H rcivd th B.S. dgr in Control and ntrumntation Enginring from Kora Mitim Univrity in 997. H wa a tudnt rchr with Tokyo ntitut of Tchnology, Japan, in 998, and rcivd th M.S. dgr in from Kob Univrity of Mrcantil Ocan Elctro-Mchanical, Japan, in 00. From 00 to 009, h wa a Snior Rch Enginr with Hyundai Havy ndutri Co., td. H i currntly working towd th Ph.D. dgr in Elctrical Enginring from Puan National Univrity, Kora. H i a Profional Enginr Building Elctrical Faciliti and a Profional Enginr Elctric Application. Hi rch intrt includ powr convrion, lctric machin driv, lctrical faciliti and rnwabl powr ytm. Won-Sang m H wa born in Buan, Kora, in 98. H rcivd th B.S., M.S. and Ph.D. dgr in Elctrical Enginring from Puan National Univrity, Buan, Kora, in 007, 009 and 0, rpctivly. H i currntly a Potdoctoral Rchr with Klipch chool of Elctrical and Computr Enginring in Nw Mxico Stat Univrity, a Cruc. Hi rch intrt includ powr convrion, lctric machin driv, and thir diagnoi and fault-tolranc. 749

9 Analyi and Compnation of Currnt Maurmnt Error in a Doubly Fd nduction Gnrator Han-Sok Pk H rcivd hi B.S. and M.S. dgr in Elctrical Enginring from Chung-Ang Univrity, Soul, Kora, in 98, 98, and Ph.D. dgr from th dptmnt of Elctrical Enginring, from Kora Mitim Univrity, Buan, Kora, in 996, rpctivly. Sinc 986, h ha bn with th School of Elctrical Enginring, Pukyong National Univrity (PKNU), whr h i currntly a profor. Hi currnt intrt includ th control of lctric machin, nrgy convrion and rch intrt includ th lctric machin dign & control, rnwabl nrgy ytm. Jang-Mok Kim H rcivd hi B.S. from Puan National Univrity (PNU), Kora, in 988, and th M.S. and Ph.D. dgr from th dptmnt of Elctrical Enginring, Soul National Univrity, Soul, Kora, in 99 and 996, rpctivly. From 997 to 000, h wa a Snior Rch Enginr with th Kora Elctrical Powr Rch ntitut (KEPR). Sinc 00, h ha bn with th School of Elctrical Enginring, PNU, whr h i currntly a Rch Mmbr of th Rch ntitut of Computr nformation and Communication, a Faculty Mmbr, and a had of G lctronic Smt Control Cntr. A a Viiting Schol, h joind th Cntr for Advancd Powr Sytm (CAPS), Florida Stat Univrity, in 007. Hi currnt intrt includ th control of lctric machin, lctric vhicl propulion, and powr quality. 750