Direct Power Control of a Doudly Fed Induction Generator with a Fixed Switching Frequency

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1 Dict Pow Contol of a Doudly Fd Induction Gnato with a Fixd Switching Fquncy Won-Sang i, Sung-Tak Jou, yo-bu L School of Elctical and Coput Engining Ajou Univity, Suwon, oa kyl@ajou.ac.k Stv Watkin Fladh Elctonic Ltd Abtact Thi pap pnt th iplntation of a dict activ and activ pow contol of a doubly fd induction gnato (DFIG) applid to a wind gnation yt a an altnativ to th claical fild ointd contol (FOC). Th FOC i known to hav coplx contol tuctu, which conit of cunt contoll, pow contoll and fa tanfoation, and alo dpnd highly on paat vaiation uch a oto and tato itanc and inductanc. Th popod dict pow contol (DPC) thod poduc a fat and obut pow pon without calling fo coplx tuctu and algoith. Howv, it ha high pow ippl duing tady tat. In thi pap, activ and activ pow contoll and pac-vcto odulation (SVM) a cobind to plac th hyti contoll ud in th oiginal DPC iv, ulting in th fixd witching fquncy of pow convt. Th iulation ult with FOC and DPC fo a 3kW DFIG a givn and dicud and xpintal ult fo th a achin a hown to illutat th faibility of th popod contol tatgy. ywod-dict pow contol, doubly fd induction gnato, fild ointd contol, fa tanfoation, paat vaiation, pac-vcto odulation, hyti contoll, fixd withing fquncy I. INTRODUCTION Th concpt of a doubly fd induction gnato applid to a wind gnation yt i an intting option with a ignificant akt potntial. Thi yt allow vaiabl pd opation ov a lag, but tictd ang. Th ot ipotant it of vaiabl pd wind tubin copad to convntional fixd pd wind tubin a incad ngy captu, ipovd pow quality and ducd chanical t on th wind tubin [1]. A DFIG conit of a wound oto induction gnato (WRIG) with th tato winding dictly connctd to a thpha pow gid and with th oto winding ountd to a bidictional back-to-back IGBT fquncy convt. A chatic diaga of vaiabl pd wind tubin yt with a DFIG i hown in Fig. 1. Th pow convt conit of th oto-id convt and th gid-id convt, in which th oto-id convt contol th activ and activ pow and th gid-id convt contol th DC-link voltag and nu a convt opation at unity pow facto []. Contol of a DFIG i taditionally achivd though th contol of th coponnt of th voltag vcto in a fild-ointd contol (FOC), which i achivd by a oto cunt contoll [3-6]. On ain aw back of thi yt i that it pfoanc dpnd gatly on accuat achin paat uch a tato, oto itanc, and inductanc. R S T Wind DFIG Gid Roto Sid Convt DC-Link Ntwok Tanfo Gid Sid Convt AC filt Fig. 1. Schatic diaga of vaiabl pd wind tubin yt with a DFIG. Thu, pfoanc dgad whn actual achin paat dpat fo valu ud in th contol yt. Dict pow contol (DPC) abandon th oto cunt contol philoophy, chaactitic of FOC and achiv bang-bang activ and activ pow contol by odulating th oto voltag in accodanc with th activ and activ pow o. DPC i chaactizd by fat dynaic pon, ipl tuctu and obut pon againt paat vaiation. It do not ploy a oto cunt contoll and SVM [7], [8]. On awback with th baic DPC i that it diplay lag cunt, activ and activ pow ippl, ulting in vibation and acoutic noi. Anoth awback fo DPC i convt witching fquncy vaiation that ignificantly coplicat pow cicuit dign. In o to obtain a ooth opation and fixd witching fquncy, dict pow contol i /08/$ IEEE 1

2 P ωσl l Iq ω ( L I σl I ) l I q I V V q j l θ V V abc C I j l I q θ I I abc ω l ω d / θ l θ θ V I ω V abc I abc P V I j θ V I I 1/ L λ d Fig. 3. Fild ointd contol (FOC) tuctu fo th oto id convt of a DFIG. I d cobind with a SVM tatgy bad on th pincipl of th DPC thod. Thi pap pnt a nw dict activ and activ pow contol bad on SVM fo a DFIG-bad wind tubin yt. Th contol tatgy dictly calculat fnc oto contol voltag with ach witching piod, uing th tiatd tato flux, th calculatd activ and activ pow and thi o. Siulation ult fo a 3 kw a hown to dontat and xpintal ult fo a 3 kw a hown to dontat th pfoanc of th popod contol tatgy. II. A. Modling of th DFIG V I R Ll jωλ FOC REVIEW L j( ω ω ) λ L l R I V Th d-q odl in th abitay fnc fa i xpd a follow. dλ V = RI jωλ (1) dλ V = RI j( ω ω) λ () λ = λd jλq, λ = λ jλq λd = LI d LI, λq = LI q LIq (3) λ = LI L Id, λq = LI q LIq wh Id, Iq, I, I q and λd, λq, λ, λq a th cunt and th flux of th tato and oto in d- and q-ax, R and R a th itanc of th tato and oto winding, ω i th oto pd. An quivalnt cicuit i t up by an of th voltag and flux quation of th abitay fnc fa, a hown in Fig.. Fig.. An quivalnt cicuit in th abitay fnc fa. Th DFIG i a wound oto induction gnato, in which th oto cicuit i connctd to th gid though two back-toback convt with a coon DC link capacito bank. Th ability to ubtact and upply pow fo th oto ak it poibl to opat th DFIG at ub-ynchonou o upynchonou pd whil kping a contant voltag and fquncy on th tato [9]. B. FOC fo th DFIG Th oto-id convt i contolld in a ynchonouly otating dq-axi fa, with th d-axi ointd along th tato flux vcto poition. In thi way, a dcoupld contol btwn th tato activ and activ pow i obtaind. Th influnc of th tato itanc can b nglctd and tato flux can b contant a th tato i connctd to th gid. Fo uch a fnc fa lction, th DFIG odl can b ivd a

3 V = 0, V = ωλ (4) d q d L di V R R I L L I = ( ) σ ωlσ q L L di V ( R R ) I L ( L I L I ) λ q = q q σ ωl L σ (5) = LI = LI LI, λ = LI LI = 0(6) d d q q q L λ = I σ L I λ = σ L I (7) L, q q wh σ = 1 L / LL, L = L / L, ωl = ω ω i th lip fquncy, ω i th lctical angula vlocity of th tato, I i th agntizing cunt of th gnato. Th DFIG tato activ and activ pow ay b coputd a follow. 3 3 L P = ( V I V I ) = V I L d d q q q q 3 3 Vq L = ( VqId Vd Iq ) = Vq ( I ). ω L L (8) ingl doinant nonzo pol. In thi condition, a taightfowad appoach fo digning a PI-contoll i to plac th zo of th PI-contoll to appoxiatly cancl th doinant pol of th plant, ulting in th clod-loop tanf function of th ovall contol yt. P P = 3 L Vq PPPC ( ) L PP 3 L 3 L ( PC Vq PP PC) Vq PC L L A can b n fo (9), th vaiation of achin paat, pcially utual inductanc, ha ipact on th pow dynaic. III. PROPOSED DPC STRATEGY FOR THE DFIG In th popod contol tatgy, th d-axi of th ynchonou fa i fixd to th tato flux, a hown in Fig. 5. Sinc th tato i dictly connctd to th gid, and th influnc of th tato itanc can b nglctd, th tato flux can b conid contant.. (9) Du to contant tato voltag, th tato activ and activ pow a contolld via I q and I pctivly. In th DFIG voltag quation (5), th oto cunt I q and I can b contolld uing V q and V pctivly. Th contol ch conit of inn cunt contoll and out pow contoll. Fig. 3 how th FOC ch fo th oto-id convt of a DFIG. q β β λ λ = λ d d ω ω I P, IC PP PC p I 3 L V L q λ q θ l θ λ θ α α P, Fig. 4. Ovall contol yt fo th FOC. Th pol-placnt thod i utilizd to dign PIcontoll in cunt contol loop and pow contol loop [11]. Conquntly, th ulting ovall contol yt iplntd on th DFIG copond to th block diaga ktchd in Fig. 4. It i n fo th contol yt that all th plant fo th cunt contol loop a tabl with only on Fig. 5. Stato and oto flux vcto in th ynchonou d-q fa. Fo (1), fo a ynchonou fa ( ω = ω - th tato flux pd, λ = λ ), th tato voltag vcto i givn a d V = V = ωλ. (10) q d Bad on (3), th tato cunt i givn by 3

4 P ωl k σ ωλ d L ωl ( λd ) L ωλ P - P k σ d - PI PI Pow contoll V V q j l θ θ l V V abc abc,, Convt /3 SVM C ω λ d - θ Stato flux tiation [8] θ V I 3/ V I abc abc ω DFIG Stato pow calculation [10] Fig. 6. Schatic diaga of th popod DPC fo a DFIG yt. I L λ L λ λ L λ = =. LL L σl σll (11) Uing (8) and (11), th tato activ and activ pow input fo th ntwok can b calculatd a P = k ωλ λ σ d q L = kσωλ ( λ λ ) L d d wh k = 1.5 L /( σ L L ). σ (1) Sinc th tato flux ain contant, accoding to (1), th activ and activ pow chang ov a contant piod of T a givn by Cobining (1), (13) and (14) and nglcting th oto itanc, th oto voltag quid to liinat th pow o in th d-q fnc fa i calculatd a V = ( P I / )( ) ωl V P P P kσωλ d L q = ( PP / )( ) ωl ( λd ). L kσωλ d (15) Th fit t on th ight-hand id duc pow o whil th cond t copnat fo th oto lip that cau th diffnt otating pd of th tato and oto flux. A can b n, calculation qui only ipl ultiplication and no coplicatd athatic. P = k ωλ λ σ d q = k ωλ λ. σ d (13) A hown in Fig. 5, in th ynchonou d-q fnc fa, th oto voltag i givn by P, P, PP V 1/ Fig. 7. Ovall contol yt fo th DPC. k σ ωλ d λ dλ V = RI jωλ l. (14) Th chatic diaga of th popod DPC fo a DFIG yt i hown in Fig. 6. Th contoll contain two PI contoll, -on fo activ pow and on fo activ pow-, and a SVM unit. Th tato activ and activ pow can b calculatd dictly. Th tato flux i tiatd uing th 4

5 aud tato voltag and cunt in th tationay fnc. Coniing (1), (14) and (15), block diaga diplay th dynaic xiting btwn P and V q, on th on hand, and V, on th oth hand. Th ovall contol tuctu of a DPC i ntially contitutd by on pow contoll. Fig. 7 vidnc that both dynaic tun out to b xactly th a. Futho, thi tato flux ay b gadd a a contant ditubanc, who ffct on ay b aily ovd jut by cloing th activ pow contolloop via a copnato including an intgal action. It i fundantal to not that th o ignal fding th PI contoll a coputd by ubtacting th t-point of th vaiabl to b contolld - o P - fo it actual valu - o P, pctivly. Thi i du to th fact that and a tictly ngativ. A a ult, both and P clod-loop dynaic can b pntd by th uniqu cond-o tanf function givn nxt. (a) (b) (c) (A) With noinal L (B) With 0.5 L Fig. 8. Siulation ult of pow tp pon (a), tato cunt (b) and DC-link voltag (c) in th FOC iv. 5

6 (a) (b) (c) (A) With noinal L (B) With 0.5 L Fig. 9. Siulation ult of pow tp pon (a), tato cunt (b) and DC-link voltag (c) in th DPC iv. k ωλ ( ) P P k k PP σ d PP = PP σωλ d σωλ d (16) Fo th tanf function (16), dynaic can b ainly influncd by th contant k σ that a ind by th tato and oto lakag and utual inductanc. Subtituting tato and oto inductanc (3), th paat k σ i wittn a follow. 3 L 3 1 = σ LL L Ll L k (17) Sinc th lakag path i ainly ai, th vaiation of achin paat ha littl ipact on th pow dynaic. 6

7 (a) Schatic diaga of th xpintal tup. (b) Ral pictu of xpintal tup Fig. 10. Expintal tup of th DPC yt. IV. SIMULATION RESULTS Siulation of th popod contol tatgy fo a DFIGbad gnation yt i pfod to how that th DPC iv i abl to opat with fat dynaic pon and obutn of activ and activ pow contol in copaion with th convntional FOC iv. Th DPC and FOC tatgi a iulatd fo a 3kW, 0V, 14.7A, 60Hz foupol achin and th paat R = Ω, R = 0.65 Ω, L = 67.3 H, L = 67.3H and L = 63.7H. Fig. 8 and 9 how pow pon of th FOC iv and th DPC iv whn th activ and activ pow a tp changd fo -600Va to 600Va at 0. and fo -100W to -700W at 0.4, pctivly ( - f gnating activ pow and abobing activ pow). An ipov opation in t of fat dynaic pon can b noticd with DPC. Th FOC iv i nitiv to chang in th utual inductanc a hown in Fig. 8(A) and (B). In Fig. 8(B), th activ pow dviat fo th contol whn th fnc pow -600Va i applid and th ovhoot of both th tato cunt and th activ pow occu un tanint condition. Howv, Fig. 9(A) and (B) how th obutn of th DPC iv whn th utual inductanc ha L and 0.5L pctivly. It do not dpnd on th utual inductanc vaiation and ha a obut chaactitic againt paat vaiation. 7

8 V. EXPERIMENTAL RESULTS Th xpintal tup of th DPC yt i hown in Fig. 10. Th atd valu and paat of a DFIG a a a th iulation. Th gnato i ivn by 4.96kW, 0V, 3000p PMSM fd by an AC invt. Th pow lctonic tag conit of two back-to-back convt uing intllignt pow odul (M). Th oto-id voltag ouc PWM convt i intd in th oto winding and th gid-id voltag ouc PWM convt i connctd to th tato winding via an AC filt. Th convt a 3kW atd IGBT bidg with a 400µF DC-link capacito, who apling ti i 00µ and witching fquncy i 5kHz. Th digital contoll i bad on a digital ignal poco (TMS30VC33 DSP) and a 1-bit analog-to-digital (A/D) convt poviding fat pocing fo floating-point calculation. Hall no a ployd in th cunt aunt, and th fnc voltag a ynthizd fo th gulatd DC-link voltag and SVM ignal of th convt. Sapling ti duing th xpint i 100µ and th oto id convt witching ti i 00µ. Dai copnation i alo includd. Duing th xpint, two poc a caid out bfo th tato winding i connctd to th gid via a agntic contacto (MC). Fitly, at low oto pd, th pow gnation fo DFIG i not nough to upply to th gid. Th agntic contacto i activatd whn th oto pd ach a t oto pd. Scondly, th tato winding i connctd to th gid whn th tato voltag, fquncy and pha a alignd to th gid. Fig. 11 how that th tato winding i connctd to th gid within 0.4. Th DPC contoll gain ud a a follow: Fig. 11. Expintal ult of th connction to th gid. P = 0.5, I = 500, PP = 0.5, = 500; To vify th popod contol tatgy, th xpintal invtigation i focud on th activ and activ pow pon and th tato cunt ippl. Th activ and activ pow fnc a tp changd fo -3kW to -.kw at 0.5 and fo -0.kVa to 0.9kVa at 0.7, pctivly. It i notd that th i no ovhoot duing tanint opation and th tady-tat o i aintaind contant. Th ffctivn of th popod DPC tatgy i confid in Fig. 1. Fo th axiu pow tacking (MPPT) cuv of vaiabl-pd wind tubin [1], tt fo a coplt gnation yt a caid out. Th DFIG i t in pow contol. Givn a oto-pd aunt uing an nco, activ pow fnc a calculatd fo th MPPT cuv and ipod on th DFIG aft copnating fo th pow lo. Fig. 13 how th xpintal ult whn th oto pd chang fo 1480 to 1550p. In Fig. 13, th gnation yt opatd wll and achivd th MPPT cuv duing oto pd vaiation. Fig. 1. Expintal ult of th popod DPC tp pon. 8

9 Intnational Jounal of Elctonic, vol. 93, no. 11, pp , Nov [6], -B. L and F. Blaabjg, Ipovd Dict Toqu Contol fo Snol Matix Convt Div with Contant Switching Fquncy and Toqu Rippl Rduction, Intnational Jounal of Contol, Autoation, and Syt, vol. 4, no. 1, pp , Fb [7] R. Datta and V. T. Ranganathan, Dict Pow Contol of Gid- Connctd Wound Roto Induction Machin without Roto Poition Sno, IEEE Tanaction on Pow Elctonic, Vol. 16, No. 3, May 001. [8] M. Malinowki, M. P. azikowki, S. Hann, F. Blaabjg, and G. D. Maqu, Vitual-flux-bad dict pow contol of th-pha PWM ctifi, IEEE Tanaction on Induty Application, vol. 37, no. 4 pp , Jul./Aug [9] A. Tapia, G. Tapia, J. X. Otolaza, and Jo Raon Sanz, Modling and Contol of a Wind Tubin Divn Doubly Fd Induction Gnato, IEEE Tanaction on Engy Convion, vol. 18, no., pp , Jun 003. [10] Y. Li, A. Mullan, G. Lightbody, and R. Yacaini, Modling of th Wind Tubin With a Doubly Fd Induction Gnato fo Gid Intgation Studi, IEEE Tanaction on Engy Convion, vol. 1, no. 1, Ma [11] G. Tapia, A. Tapia, J. X. Otolaza, Two Altnativ Modling Appoach fo th Evaluation of Wind Fa Activ and Ractiv Pow Pfoanc,, IEEE Tanaction on Engy Convion, vol. 1, no. 4, pp , Dc [1] L. Miht-Popa, F. Blaabjg and I. Bolda, Wind Tubin Gnato Modling and Siulation Wh Rotational Spd i th Contolld Vaiabl IEEE Tanaction on Induty Application, vol. 40, no. 1, pp. 3-10, Jan/Fb Fig. 13. Expintal ult of a coplt gnation yt. VI. CONCLUSION A dict pow contol thod fo DFIG iv wa popod to contol th activ and activ pow dictly without fa tanfoation and cunt contoll ud in th FOC iv, and achiv obutn. Siulatd ult and xpintal ult how th validity of th DPC algoith with a fixd witching fquncy. Copaing th FOC iv, th popod contol tatgy can povid fat dynaic pon un tanint condition and obut chaactitic againt paat vaiation. REFERENCES [1] T. Ackann, Wind Pow in Pow Syt. John Wily and Son, 005. [] I. Bolda, Elctic Div. Taylo & Fanci, 006. [3] S. Analt, J. C. Bugo and J. L. R. Ando, Dict Toqu Contol of a Doubly-Fd Induction Gnato fo Vaiabl Spd Wind Tubin, Elctic Pow Coponnt and Syt, vol. 30, pp , 00. [4]. P. Gokhal, D. W. aak, and S. J. Hikkila, Contoll fo a Wound Roto Slip Ring Induction Machin, U. S. Patnt, no. US003/ , Ap [5]. -B. L, C. -H. Ba, and F. Blaabjg, An ipovd DTC-SVM thod fo atix convt iv uing a dadbat ch, 9