A Combination of STATCOM and Distribution Transformer With Passivity-based Control for Reactive Power Compensation

Transcription

1 Intrnational Confrnc on Enrgy and Environmntal Protction (ICEEP 216) A Combination of SACOM and Distribution ransformr With Passivity-basd Control for Ractiv Powr Compnsation Jinmu Lai1, a, Xianggn Yin 1, b, Ertao Li 1, c and Yu Chn 1, d 1 Stat Ky Laboratory of Advancd Elctromagntic Enginring and chnology, Huazhong Univrsity of Scinc and chnology, Wuhan 4374, China. a laijinmu@126.com, bxgyin@hust.du.cn, clirtao28@163.com, d @qq.com Kywords: Distribution ransformr, SACOM, Ractiv Powr Compnsation, Passivity-Basd control, Injction Damping. Abstract. his papr studis static synchronous compnsator (SACOM) accssd in th systm via intrmdiat taps on transformr high voltag wingdings. For Dyn11 typ transformrs, th proposd circuit configuration of D-SACOM is analyzd, and th function of ractiv powr compnsation is vrifid. hn, th Eulr-Lagrangian (EL) modl of a distribution transformr-static synchronous compnsator (D-SACOM) is stablishd. his papr also proposs an improvd ip-iq currnt dtction mthod. Manwhil, th passivity-basd control (PBC) law which can dcoupl activ and ractiv powr is provd. By slcting propr injcting damping, w can optimiz th dynamic prformanc and raliz fast compnsation of ractiv powr. Finally, simulation rsults show th ffctivnss of th proposd structur with PBC in ractiv powr compnsation. Introduction Static synchronous compnsator (SACOM) is an important dvic for ractiv powr compnsation. Currntly, thr ar two trnds for SACOM tchnology. On is th dvlopmnt of high voltag transmission-typ SACOM (-SACOM) [1,2] with th goal of high-voltag transmission systm ractiv powr compnsation and voltag support; th othr is distributd-sacom (D-SACOM) [3,4] to improv th powr quality of th consumr sid. Howvr, both mthods hav advantags and disadvantags. Bsids, distribution transformr is widly usd in distribution ntwork, and its ractiv powr consumption can t b ignord at low load factor (lss than.3) [5]. his papr proposs a novl intgratd structur of SACOM and distribution transformr. SACOM is connctd to th winding taps on th primary windings for compnsation currnt injction. h structur is hlpful to mak full us of th spar capacity of th transformr and incras th capacity utilization. h ractiv powr cost of th transformr itslf can also b compnsatd. At th sam tim, a suitabl windings taps can b slctd to rduc th voltag strss, which is hlpful to dcras th cascad count of H-bridg clls. It is important to dsign control algorithm of SACOM which dirctly affcts th prformanc of ractiv powr compnsation. Currntly, th rsarch of control algorithm is conductd in-dpth by domstic and forign scholars. Although linar control stratgis hav bn widly usd in th SACOM systm and hav obtaind th crtain achivmnts, it is not robust to th paramtr variations which may advrsly affct th prformanc. In fact, SACOM is a non-linar, strong coupling, multivariabl systm. Nonlinar control has alrady bn usd in SACOM systm. Dspit thir satisfactory prformanc, nonlinar control mthods suffr from th complxity in implmntation which is difficult to apply in th nginring projcts. h aformntiond control mthods show various advantags and disadvantags rlatd to stability, dynamic rspons, stady stat rror, robustnss against paramtr variations, switching frquncy and control complxity. Howvr, th dissipation proprtis of SACOM which ar inhrntly xistd in its physical structur ar not takn into considration by aformntiond mthods. Passivity is a rstatmnt of nrgy consrvation in SACOM systm, and plays an important rol in dsigning controllr to attain global asymptotic stability and command currnt tracking. Passivity-basd control mthod (PBC) is an ffctiv tool for nonlinar systm, and was first introducd into powr lctronics 216. h authors - Publishd by Atlantis Prss 336

2 control by Ortga. R. [6]. PBC mthod rshaps nrgy storag and injcts damping [7-9]. It can mak SACOM systm convrg to th dsird stabl quilibrium points and acclrat nrgy dissipation. his papr proposs a novl ractiv currnt calculating mthod which applis to D-SACOM basd on th instantanous ractiv powr thory. Furthrmor, th mathmatical modl of D-SACOM systm basd on E-L function is stablishd and a PBC mthod which is vrifid by Lyapunov stability is proposd for D-SACOM. Finally, th simulation tsts basd on Matlab/Simulink show that th proposd structur of D-SACOM and control mthod which applis to systm hav a good compnsation prformanc. Structur of D-SACOM Currntly, th distribution transformrs ar mainly catgorizd into Dyn-typ, Yyn-typ and Yzn-typ by winding connction. In ordr to improv th nduranc ability of unbalancd load and harmonic, Dyn11 typ distribution transformr is widly usd in distribution ntwork. Hnc, this papr primarily discusss Dyn11-typ distribution transformr intgratd with SACOM. 1kV grid ransformr 38V grid A u SA,B,C i SA,B,C A B C a b c * * A1 B1 * C1 n ila,b,c C1 A1 h A-phas clustr u A i A L R u A u B i B L R ub L R u C i C u C C B1 Fig.2 Phasor diagram of lin voltag at HV sid B u CA1 u CA2 Bridg cll 2 u CA5... Bridg cll 5 u A1 u A2 u A5 h B-phas clustr Fig.1. Circuit configuration of th proposd D-SACOM. O h C-phas clustr O b c C B Fig.3. Phasor diagram of Dyn11 transformr. Notic that, u SA, u SB, and u SC ar thr phas voltag of grid systm. i SA, i SB, and i SC ar thr phas currnt of grid systm. u A, u B, and u C ar thr phas voltags at connctd taps of HV sid of transformr. i A, i B, and i C ar thr phas injctd currnt of SACOM at connctd taps. u a, u b, and u c ar thr phas voltag at low sid of transformr. i la, i lb, and i lc ar thr phas currnt of load. L is th filtr inductor. R is th quivalnt rsistanc of filtr inductor. C is th dc capacitor. Fig. 1 shows th proposd circuit configuration of D-SACOM which includs a thr-phas CPS-SPWM ractiv powr compnsation dvic, filtr and Dyn-typ distribution transformrs with intrmdiat taps. SACOM can b connctd to thr taps (shown as A 1, B 1, C 1 in Fig.1) on high-voltag (HV) windings of th transformr. Du to lack of nutral point at th primary sid of Dyn transformr, th stting of th taps at HV sid should guarant that lin voltags of SACOM ar symmtrical, as shown in Fig. 2. In this structur, w can slct a suitabl connctd voltag lvl which can rduc costs and simplify th powr circuit of SACOM, but th minimum of connctd lin voltag is half of th lin voltag. Although SACOM is locatd at HV sid of transformr which is diffrnt from load point, only if th compnsation currnt of SACOM matchs th U a A a θ γ U SA A1 337

3 systm ndd, th purpos of dynamic ractiv powr compnsation which includs ractiv powr of loads and that of transformr consumd can b achivd. Control Mthod Dsign Basd on PBC A. Improvd Ractiv Currnt Dtction Mthod For th D-SACOM, th compnsation currnts ar injctd via th winding taps on th primary windings. h currnt injctd point and load point ar not th sam point. hr ar amplitud and phas angl dviation btwn th load currnt and compnsation currnt. hrfor, th traditional currnt dtction mthod can t b usd dirctly. According to th charactristics of th Dyn11-typ transformr, th supply voltag u SA is lagging bhind th load voltag u a by 3, as shown in Fig. 3. Whn th cntral taps ar chosn as th connction points, th cntral taps voltag is lagging bhind th load voltag u a byγ (γ= 9 ). Manwhil, th amplitud dviation causd by transformr ratio must b compnsatd. h load currnts must b convrtd to th injctd taps via i i - ql qrf = (1) K whr K is th transformr voltag ratio. According to th analysis abov, th schmatic diagram of improvd ractiv currnt dtction mthod is shown as Fig. 4. B. Systm Modling sin/cos PLL + u A sin/cos + Compnsation Load sid γ sid i al i dl i i d arf i bl i 1/K brf i cl i i ql q i crf Fig. 4. Schmatic diagram of improvd i p -i q currnt dtction mthod. h mathmatical modl of th D-SACOM in ABC coordinat is dia L u i R u dt dib L u i R u dt dic L u i R u dt whr 5 A A A B B B C C C u u, k A, B, C (3) k kn n1 Applying th d_q transformation matrix to (2), w can obtain did L ud Liq id R ud dt diq L uq Lid iqr uq dt whr i d and i q ar th d-axis and q-axis componnts of compnsation currnt. u d and u q ar th d-axis and q-axis componnts of SACOM clustr voltag. u d and u q ar th d-axis and q-axis componnts of thr phas voltags at connctd taps of HV sid of transformr. rprsnts th powr grid angular frquncy. 338 (2) (4)

4 h E-L systm could dscrib th charactristics of th systm which is hard to b xprssd by linarization control mthod. Equation (4) can b xprssd as E-L systm modl, and w will obtain (5) by slcting i d and i q as stat variabls. Mx Jx Rx F (5) whr M= M,R R,J J = L L R ud ud id M,,,, J R F x L L R uq uq iq h passivity systm indicats that th accumulatd nrgy of th systm is always lss than th sum of nrgy injctd from th outsid. PBC mthod basd on E-L modl involvs two important parts which ar nrgy rshaping and damping injction to acclrat dissipation for systm. Enrgy rshaping part is to maintain th nrgy distribution at a dsird quilibrium point. h damping injction part can acclrat nrgy dissipation of invrtr systm and assur that th nw working point is globally asymptotically stabl. h storag nrgy function of SACOM can b dscribd as H( x( )) x Mx ( Lid Liq ) (6) 2 2 By taking th drivativ of H( x( )) and substituting (5) into (6) H( x()) Lid id Liq iq x ( F Jx Rx) x F x Rx (7) hn (7) can b rwrittn in intgral form (8). x F x Rx (8) H( x()) H( x()) d d whr mans th initial tim to th currnt tim. Equation (8) indicats that th accumulation nrgy [ H( x( )) H( x ()) ] is always lss than th supply loss is x F x Rx d, and th dissipation which includs th quivalnt rsistanc loss and th switching d. hus, th SACOM is strictly passiv, and th controllr can b dsignd for D-SACOM with th PBC thory. C. Passivity-basd Control Dsign From quation (4), th modl of SACOM is undractuatd systm bcaus th dimnsion of th control vctors of systm (u d, u q ) is lss than that of th systm (i d, i q, u dc ). hus, DC capacitor voltag must b controlld by th indirct control mthod such as proportional-intgral (PI) mthod. By dfining th dsird rfrnc currnt x [ i i ], th spac vctor of rror systm can b obtaind as d i d id id x x x (9) iq iq iq h Lyapunov function of th rror systm can b dscribd as 1 H( x()) x Mx (1) 2 Substituting (9) into (5), th dynamic rror function can b dscribd as M( x x ) J( x x ) R( x x ) F (11) q 339

5 Equation (11) can b rwrittn as Mx Jx Rx F ( Mx Jx Rx ) (12) According to (12), th dsird stabl point works whn x =. h convrgnc spd of systm is dtrmind by th valu of R. It can acclrat nrgy dissipation of th systm and mak th systm astring to xpctd stabl quilibrium point by injcting damping. h injctd dissipation damping is shown as R x ( R R) x (13) dnw d whr R dnw is th xpctation damping of control systm, R d is th injctd positiv dfinit damping. hn function (12) can b xprssd as (14) dnw d Mx Jx R x F ( Mx Jx Rx R x ) (14) In ordr to dcoupl th d-axis and th q-axis currnt, lt = Jx. hrfor, nw control law basd on PBC thory can b achivd as F ( Mx J( x + x ) Rx R x ) (15) d W know that H ( x ()) bcaus of positiv dfinit of M. h drivativ of (1) is achivd as ( - - dnw )=- dnw H ( x( )) x Jx R x x R x (16) Dynamic rror quation systm (1) is stabl according to Lyapunov stability thorm whn H, H. hn, substitut th D-SACOM paramtrs into th nw control law (17) u L Li Ri R i i u dt * did * * d q d a1( d d ) d * diq * * q d q a2( q q ) q u L Li Ri R i i u dt (17) Sourc... u dcn (n=1...15) i d lin SACOM pulss 6 CPS- SPWM u dcn 15 (n=1...15) Individual u dca,u dcb,u dcc balancing control 3 Clustr balancing control transformr sin(ωt +γ) sin(ω t) PLL u ABC i ABC u d, u q u d, u q + + Equ.(28) γ i d, i q 1/K Load i L i qrf abl 1 Simulation paramtrs componnts paramtrs Grid voltag 1 [kv] Grid frquncy 5 [Hz] Lin impdanc.5 [Ω],1.2 [mh] ransformr 1[MVA], 1kV/.4kV ap voltag 5 [kv](cntral taps) Filtr inductor 16 [mh] (1%) Equivalnt rsistanc of.2 [Ω] Filtr inductor DC capacitor 8 [ F] Cascad count pr clustr 5 PWM carrir frq cy 2 [khz] u dcn (n=1...15) u dcrf Ovrall voltag control i drf Fig.5. Diagram of th improvd D-SACOM control systm basd on PBC. 34

6 Fig. 6. Simulation rsults of supply voltag and currnt. Fig. 9. h powr factor of supply sid Fig. 7. Simulation rsults of supply voltag and currnt whn th load dcrass by 5%. Fig. 1. Harmonic spctrum of th supply currnt in phas-a. Fig. 8. Simulation rsults of supply voltag and currnt whn th load incrass by 5%. Fig. 11. Dynamic rspons of SACOM with diffrnt dampings R d From th abov analysis, Fig. 5 shows th passiv controllr for D-SACOM basd on th thory of E-L to compnsat th ractiv powr at connctd taps. In addition, th clustr balancing control and individual balancing control algorithm in [1] ar applid. Simulation Rsults h D-SACOM structur with PBC is vrifid by simulation in Matlab/Simulink nvironmnt. Schmatic diagram of th improvd D-SACOM systm for simulation tst is dpictd in Fig. 5. h spcific paramtrs of th simulation ar shown in abl 1. Fig. 6 illustrats th prformanc of th D-SACOM in rspons to a stp load chang. Spcifically, it can b sn from Fig.8 that th supply voltag and currnt ar in phas with ach othr aftr SACOM is put into opration at t=.1s. Fig.7 shows th dynamic prformanc of SACOMfor th load (inductiv load) dcrasing by 5% at t=.2 s. Fig. 8 shows th load (inductiv load) incrass by 5% at t=.2 s. h currnt of th supply sid coms to stady stat within 3ms. h dynamic rspons of D-SACOM is vry fast. Fig. 9 shows th powr factor (PF) at supply sid. As it can b sn, th PF incrass from.61 to.99 aftr compnsation. h harmonic spctrum of th supply currnt shows that total harmonic distortion (HD) is about 2.4%, as shown in Fig. 1. Harmonic is mainly distributd in th switching frquncy and its multipls spctrum. Fig. 11 shows dynamic rspons of SACOM with diffrnt injctd damping R d. It can b obsrvd that th largr damping is chosn, th fastr rspons of controllr will gt. h initial valu of R d1 and R d2 ar st to a rlativ small on and fin tun to mt th rquirmnt of th systm. h final paramtrs of R d1 and R d2 ar R d1 = R d2 =5. 341

7 Summary In this papr, th mchanism and control of D-SACOM systm ar analyzd in-dpth. An improvd i p -i q currnt dtction mthod is proposd to liminat th ratio and phas angl dviation causd by th transformr. h improvd PBC basd on E-L modl is dsignd for innr currnt control loop. It can acclrat nrgy dissipation and improv th dynamic rspons of SACOM systm by injcting damping. h simulation rsults hav vrifid th ffctivnss of proposd D-SACOM. Also, th PBC mthod has good stady and dynamic prformanc. It is asy to tun th gains of th controllr. Acknowldgmnts his work was financially supportd by national natural scinc foundation of China (No ). Rfrncs [1] Gultkin, B.; Ermis, M., "Cascadd multilvl convrtr-basd transmission SACOM: systm dsign mthodology and dvlopmnt of a 12 kv ±12 MVAr powr stag," Powr Elctronics, IEEE ransactions on, vol.28, no.11, pp , Nov [2] Prira, M., t al. "SVC PLUS: An MMC SACOM for ntwork and grid accss applications." Powrch, 211 IEEE rondhim IEEE, 211:1-5. [3] Bilgin, H.F.; Ermis, M., "Dsign and implmntation of a currnt-sourc convrtr for us in industry applications of D-SACOM," Powr Elctronics, IEEE ransactions on, vol.25, no.8, pp , Aug. 21. [4] Ctin, A.; Ermis, M., "VSC-basd D-SACOM with slctiv harmonic limination," Industry Applications, IEEE ransactions on, vol.45, no.3, pp.1-115, May-jun 29. [5] Wang, C.; Yin, X.; Zhang, Z.; Wn, M., "A novl compnsation tchnology of static synchronous compnsator intgratd with distribution transformr," Powr Dlivry, IEEE ransactions on, vol.28, no.2, pp , Apr [6] Ortga R,Loria A,Nicklasson P J,t al. Passivity-basd control of Eulr-Lagrang systms: mchanical lctrical and lctromchanical application. London,UK:Springr-Vrlag,1998: [7] Rong Xu; Yong Yu; Rongfng Yang, t al. "A novl control mthod for transformrlss H-bridg cascadd SACOM with star configuration," Powr Elctronics, IEEE ransactions on, vol.3, no.3, pp , Mar [8] Kun Mu; Xiaoyu Ma; Xiaobin Mu; Dali Zhu, "Study on passivity-basd control of voltag sourc PWM DC/AC invrtr," Elctronic and Mchanical Enginring and Information chnology (EMEI), 211 Intrnational Confrnc on, vol.8, pp , Aug [9] Mhrasa M., Adabi M.E., Poursmail E., Adabi J, "Passivity-basd control tchniqu for intgration of DG rsourcs into th powr grid," Int. J. Elctr. Powr Enrgy Syst., vol 58, no.5, pp , 214. [1] H. Akagi, S. Inou and. Yoshii, "Control and prformanc of a transformrlss cascad PWM SACOM with star configuration," IEEE ransactions on Industry Applications, vol. 43, no. 4, pp , Jul.-Aug