Published in: Proceedings of the 30th Annual IEEE Applied Power Electronics Conference and Exposition, APEC 2015

Transcription

1 Aalbrg Unertet Small-Sgnal Mdelng, Analy and Tetng f Parallel Three-Phae-Inerter wth A Nel Autnmu urrent Sharng ntrller Guan, Yajuan; Qunter, Juan arl Vaquez; Guerrer, Jep M.; elh, Ernane A. A. Publhed n: Prceedng f the 3th Annual IEEE Appled Pwer Electrnc nference and Exptn, APE 5 DOI (lnk t publcatn frm Publher):.9/APE Publcatn date: 5 Dcument Vern Early ern, al knwn a pre-prnt nk t publcatn frm Aalbrg Unerty tatn fr publhed ern (APA): Guan, Y., Qunter, J.. V., Guerrer, J. M., & elh, E. A. A. (5). Small-Sgnal Mdelng, Analy and Tetng f Parallel Three-Phae-Inerter wth A Nel Autnmu urrent Sharng ntrller. In Prceedng f the 3th Annual IEEE Appled Pwer Electrnc nference and Exptn, APE 5 (pp ). IEEE Pre. I E E E Appled Pwer Electrnc nference and Exptn. nference Prceedng, DOI:.9/APE General rght pyrght and mral rght fr the publcatn made acceble n the publc prtal are retaned by the authr and/r ther cpyrght wner and t a cnn f acceng publcatn that uer recgne and abde by the legal requrement acated wth thee rght.? Uer may dwnlad and prnt ne cpy f any publcatn frm the publc prtal fr the purpe f prate tudy r reearch.? Yu may nt further dtrbute the materal r ue t fr any prft-makng actty r cmmercal gan? Yu may freely dtrbute the UR dentfyng the publcatn n the publc prtal? Take dwn plcy If yu belee that th dcument breache cpyrght pleae cntact u at bn@aub.aau.dk prdng detal, and we wll reme acce t the wrk mmedately and netgate yur clam. Dwnladed frm bn.aau.dk n: augut, 8

2 Small-Sgnal Mdelng, Analy and Tetng f Parallel Three-Phae-Inerter wth A Nel Autnmu urrent Sharng ntrller Yajuan Guan, Juan. Vaquez, Jep M. Guerrer Reearch Prgramme n Mcrgrd Department f Energy Technlgy Department Aalbrg Unerty, Aalbrg, Denmark ygu@et.aau.dk Ernane Antôn Ale elh Pwer Electrnc Reearch Grup Federal Unerty f Uberlânda Uberlânda, razl Abtract A nel mple and effecte autnmu currentharng cntrller fr parallel three-phae nerter emplyed n th paper. The nel cntrller able t endw t the ytem hgh peed repne and precn n cntrat t the cnentnal drp cntrl a t de nt requre calculatng any acte r reacte pwer, ntead t ue a rtual mpedance lp and a SFR phae-lcked lp. The mall-gnal mdel f the ytem wa deelped fr the autnmu peratn f nerter-baed mcrgrd wth the prped cntrller. The deelped mdel hw large tablty margn and fat tranent repne f the ytem. Th mdel can help dentfyng the rgn f each f the mde and pble feedback gnal fr degn f cntrller t mpre the ytem tablty. Expermental reult frm tw parallel. kva nerter erfy the effectene f the nel cntrl apprach. Keywrd three-phae parallel nerter; mdelng; autnmu current cntrl I. INTRODUTION In mcrgrd, drp cntrl methd ha been dmnated the autnmu cntrl f parallel nerter n the lat decade [], []. Althugh th technque nly need lcal nfrmatn t perate, t preented a number f prblem that were led alng the lterature [3]-[9]. The frt ne that the drp ceffcent that regulate frequency and ampltude are bacally prprtnal term, that n rder t ncreae ther range f alue, derate term were added [3]-[5]. The ecnd ne that frequency and ltage are repectely related t acte and reacte pwer when the utput mpedance f the generatr manly nducte, hweer n an nerter the utput mpedance can be fxed by mean f rtual mpedance [6], [7]. The thrd ne that n cae f rete lne/rtual mpedance, acte pwer cntrlled by the nerter ltage ampltude, whle the reacte pwer flw dmnated by the angle [8], [9]. aed n thee three mprement, a cntrl archtecture baed n a rtual retance, P-V and Q-f drp can be ued t deal wth the autnmu cntrl f parallel cnnected nerter [8], []. The tablty f autnmu mcr-grd a crtcal ue cnderng the lw-nerta nature f uch nerter dmnated ytem. Small-gnal-baed tablty analy ha been reprted n [4], []-[5] t tudy the tablty f the autnmu drp-cntrlled mcrgrd ytem. Hweer, pwer drp cntrl ha the nherent drawback that t need t calculate ntantaneu acte and reacte pwer and then aerage thrugh lw pa flter, whe bandwh may mpact the tranent repne f the ytem [6], [3], [6]. T cpe wth thee prblem, a mpler and fater cntrller prped n th paper, whch cnt f a phae-lcked lp (P) and a rtual retance lp that wll prde fr bth ntantaneu current harng and fat dynamc repne f the paralleled nerter ytem. A mall gnal mdel deelped n rder t analyze the ytem tablty and t mde. Smulatn and expermental reult are preented t ealuate the feablty f the nel apprach. II. ONTRO STRUTURE AND PRINIPE Fg. hw the pwer tage f an nerter whch cnt f a three-leg three-phae nerter cnnected t a D lnk, laded by an flter, and cnnected t the A bu. The cntrller nclude a ynchrnu reference frame-baed phae lcked lp (SRF-P) whch ubttute the tw lp drp cntrl, a rtual retance lp (R r ), a D lnk ltage feedfrward lp, and the cnentnal PR nner current and ltage lp (G and G ) that generate a PWM gnal t dre the IGT the nerter. apactr current and ltage are tranfrmed t the tatnary reference frame ( cαβ and cαβ ). The ltage reference generated by ung the ampltude reference ( ) and the phae generated by a SRF- P. The P ha the bjecte t ynchrnze all the nerter near t the ame frequency ( ω ). Een thugh the P tryng t ynchrnze the nerter wth the cmmn A bu, n cae f upplyng reacte lad, the current flwng thrugh the rtual retance wll create unadable ltage drp that wll caue an ncreae f frequency n the P. Th way the mechanm nherently endw an drp charactertc n each nerter. Thu, the relatnhp between I α, I β and R r can be generalzed and expreed fr a number N f cnerter a[7] /5/$3. 5 IEEE 57

3 l D lnk abc αβ c n abc αβ abc αβ ω x abc αβ G c αβ G αβ V ref θ αβ R r Fg.. ntrl tructure f the prped cntrl methd. I R = I R = = I R () α r α r... αn rn I R = I R = = I R () β r β r... βn rn The utput α and β ax utput current f paralleled nerter are nerely prprtnal t ther rtual retance. It can be ealy bered that current harng perfrmance jut nfluenced by the utput mpedance rat ntead f the utput mpedance alue f the tw nerter mdule. III. SMA SIGNA MODE In rder t analy the tablty and parameter entty, the mall-gnal mdel f the nerter wth the prped cntrller ha been deelped n th paper. Each nerter mdeled n t nddual reference frame whe rtatn frequency et by t P. The nerter mdel nclude the reference ltage generatn dynamc, ltage and current cntrller dynamc, flter dynamc, lne mpedance dynamc and P dynamc. In rder t get the equlbrum pnt, the mall-gnal mdel huld be deelped n the ynchrnu rtatng reference frame. Nte that the prprtnal renant (PR) cntrller whch are ued n ltage cntrl lp n tatnary reference frame huld al be tranferred t the ynchrnu reference frame t keep t frequency charactertc. In the fllwng ub-ectn the nternal mdelng dcued n mre detal. A. Vltage reference generatn and rtual mpedance A mentned abe, n the prped cntrller, the ltage reference generated by ung the ampltude reference ( ) and the phae generated by a SRF-P. And then, the ltage reference mdfed by the rtual mpedance lp whch feedback the prduct f the rtual retance wth ther crrepndng utput current cmpnent. In drp-cntrlled parallel nerter, rtual mpedance lp ha al been added t the ltage reference n rder t fx the utput mpedance f the ltage urce nerter (VSI) and t cmpenate the dfference f lne mpedance fr parallel nerter. ede thee, the mt mprtant functnalty f the rtual retr here t determne the lad harng rat f the paralleled nerter. The mdfed ltage reference whch are generated n tatnary reference frame whch can be ealy tranferred t the ynchrnu reference frame can be expreed n crdnate a fllw: = R R ' d d r d ' q = q r q The algebrac equatn f ltage reference generatn can be expreed a: (3) ' Δ = gen Δ Dgen Δ (4) gen R, r = Dgen = R r. Vltage lp cntrller The nner ltage lp cntrller baed n a PR tructure n tatnary reference frame, where generalzed ntegratr are ued t achee zer teady-tate errr. aed n the abc / αβ - crdnate tranfrmatn prncple, a three-phae ytem can be mdeled n tw ndependent ngle-phae ytem. In rder t ntegrate the entre ytem, the PR cntrller need t be tranferred t the ynchrnu reference frame t mantan t (5) 57

4 ' d ' q d q ω ω A d ω A q ω Fg.. Vltage PR cntrller n frame frequency charactertc whch wll make ure the nerter peratng at the zer crng pnt n the bde dagram f the PR cntrller. Fg. hw the ltage cntrller blck dagram n ynchrnu reference frame ncludng all feed-back and feedfrward term. It can be een that there are fur tate A and n Fg.. The crrepndng tate equatn can be expreed a: k p ω ω k p dad ' = ( d d ) ωd ωaq daq ' = ( q q) ω q ω Ad The arable A and d nt hae any partcular phycal meanng but they are tate t deelp the tate-pace mdel. d d d q = A ω d q = A ω A well a the algebrac equatn ( ) ( ) q d d q = K K ' d p d d d = K K ' q p q q q The lnearzed mall-gnal tate-pace mdel f the ltage lp cntrller are preented n (9) t (). k k d q (6) (7) (8) A l l ω ω ω ω, l, ω ω = = = ΔA ' Δ Δ = l D l Δ d Dl Δ Δ D p l = Dl K = K p l K, K, K p = K p () () (). urrent lp cntrller The nner current lp cntrller baed n a prprtnal tructure n tatnary reference frame a hwn n Fg. 3. The algebrac equatn f current lp cntrller can be expreed a: ( ) ( ) = K PWMd p d d = K PWMq p q q (3) The lnearzed mall-gnal tate-pace mdel f the ltage lp cntrller are preented n (4) t (6). D Δ Δ PWM = Dcur Δ Dc ur (4) Δ K Kp = = Kp p cur, Dcur Kp (5) aed n () and (4), the utput f current lp cntrller Δ can be dered a fllw: PWM ΔA ΔA Δ ' = Al l Δ l Δ Δ Δ (9) ΔA ' Δ PWM = Dcurl DcurD l Δ Δ Δ ( DcurDl Dcur ) Δ (6) 573

5 d q Fg. 3. urrent lp cntrller d q k p k p PWMd PWMq D. Three-phae half-brdge crcut and utput flter The tructure f three-phae half-brdge crcut and utput flter hwn n Fg. 4. Here, the three-phae half-brdge crcut equalent t a ltage gan K PWM. The crrepndng tate equatn can be expreed a: dd K = r ω K =r ω dd = ω q d d dq = ω d q q PWM d q PWMd d PWM q d PWMq q (7) The utput arable f the flter are the tate arable. The fllwng equatn repreent the lnearzed mallgnal tate-pace mdel f the three-phae half-brdge crcut and utput flter at the equlbrum pnt. Δ Δ = A Δ PWM Δ Δ Δ A r ω ω r, ω KPWM K =, = = ω PWM (8) (9) In (8), the utput f current lp cntrller Δ PWM can be ubttuted by (6), then the (8) can be expreed a: Δ Δ ΔA A Dcurl = Δ Δ Δ ' DcurD l Δ Δ ( DcurDl Dcur ) Δ Δ () PWMd PWMq K pwm K pwm d q R ω ω R d q d q ω ω Fg. 4. Equalent three-phae half-brdge crcut and flter q Fg. 5. P mdel K P K pp E. ne mpedance The lne mpedance quet mall a there are nly cable between each nerter and cmmn bu. The rtual mpedance whch are equalent t ere cnnectn wth the lne mpedance n th cntrl trategy dmnate the R/X rat. Only the real lne mpedance cndered here, nce the rtual mpedance are already mdeled n part A. The crrepndng tate equatn can be expreed a: dd r = l ω dq r = l ω ω d q d bud l l l q d q buq l l l d q θ () The utput arable f the lne mpedance are the tate arable. The lnearzed mall-gnal tate-pace mdel are a fllw. Δ Δ = Al Δ l l Δbu Δ r l ω l Al =, r ω l l l l l =, l = l l () (3) F. Phae lcked lp (P) The SRF-P an mprtant cntrl lp n th prped cntrller. Een thugh the P tryng t ynchrnze the nerter wth the cmmn A bu, n cae f upplyng reacte lad, the current flwng thrugh the rtual 574

6 retance wll create unadable ltage drp that wll caue an ncreae f frequency n the P. Th way the mechanm nherently endw an I β ω drp charactertc t each nerter. A detaled blck dagram f the SRF-P hwn n Fg. 5. The crrepndng tate equatn can be expreed a: d =KPq dθ = ω = K pp q (4) The arable de nt hae a partcular phycal meanng but t a tate t facltate the deelpment f the tate-pace mdel. The lnearzed mall-gnal mdel f P are gen by A P Δ Δ Δ AP P θ = θ Δ Δ Δ K, P = P = K P (5) (6) G. mbned nerter mdel A cmplete tate-pace mall-gnal mdel f the nerter can be btaned by cmbnng the tate-pace mdel f the ltage reference generatr, ltage cntrller, current cntrller, utput flter, lne mpedance and P, gen by (4), (9), (8), () and (5). There are ttally tate n each nddual nerter mdel. x A x bu [ ] [ ] Δ = Δ Δ Δ (7) T (8) Δ x = ΔA Δ Δ Δ Δ Δ Δθ The (9) are hwn at the bttm f the page. IV. STAIITY ANAYSIS ASED ON ROOT OUS In th ectn, tablty and entty analy are cnducted t undertand the parametrc nfluence n the tablty and dynamc perfrmance f the DG ytem equpped wth the prped cntrller. The tudy baed n the egenalue analy f the deelped ytem tate pace mdel. Three factr are netgated n th paper: the rtual retr, the prprtnal parameter f ltage lp cntrller, and the prprtnal parameter f current lp cntrller. The ytem parameter fr the bae cae are preented n Table I. Fg. 6 hw the trajectre f the mde n functn f the rtual retance alue R r.ntce that th ytem ha x rt: fur cnjugated ple and tw real ple. The arrw ndcate the elutn f the crrepndng ple when the ceffcent ncreae. It can be een that when the parameter ncreang, the cmplex ple becme dmnant, reultng n a near ecnd rder behar. ut t al can be een that the lw enblty f rtual mpedance alue er the ytem dynamc, thrugh the maller mement f egenalue durng the large ncrement f R. r Snce n bth cae the ple reman n the left half-plane n the reanable rtual mpedance alue range, the ytem table n the range f cncern. A abe mentned, by adjutng the rtual retance, the current-harng rat can be fxed, whle they hae neglgble mpact n ytem tablty. Fg. 7 hw that when the parameter K p f the ltage lp PR cntrller ncreae, the dmnant mde whch are n cluter me apart frm real ax. The mde n cluter A and me tward real ax whch wll deterrate the ytem tablty f the parameter K p cntnuuly ncreang. Fg. 8 hw that when the parameter K p f the current lp P cntrller ncreae, the dmnant mde whch are n cluter me apart frm real ax. The mde n cluter A and me tward real ax and hw lw enblty f parameter K p er the ytem dynamc, thrugh the maller mement f egenalue durng the ncrement f K p. TAE I. SYSTEM PARAMETERS Parameter Value Parameter Value U dc 65V 3V.8mH 9uF R r Ω ω 34rad/ K p.53 K 3.4 K p.63 K P K pp 34.4 Al l ldgen lgen Dcurl A ( DcurDl Dcur )] DcurDlDgen DcurDl gen A =, =, = l Al l P AP (9) 575

7 x 5 A x 4 R r = x x Fg. 6. Trace f nde a functn f. R r. x x x Fg. 9. Expermental etup x 4 Fg. 7. Trace f nde a functn f. K p I.5 x x 4 Fg. 8. Trace f nde a functn f. K p x Tme () (a) V. EXPERIMENTA RESUTS In rder t erfy the effectene f the prped cntrller and t tablty, a cale-dwn labratry prttype bult accrdng t Fg.. The expermental etup cnt f tw Danf. kw nerter, a dspase6 cntrl bard, flter, EM enr and tw rete lad, a hwn n Fg.9. The electrcal etup and cntrl ytem parameter are lted n Table I. I Fg. hw the expermental reult f the paralleled nerter ytem when harng a rete lad by ung the prped cntrl cheme. In th cae, the rtual retance (R r ) rat uddenly changed frm : t : and then back t :. It can be een that after abut 4m, the drect current can be precely cntrlled accrdng t the rat f ther rtual retance. Ntce the mth and fat tranent repne f the current. Here, the acte pwer and reacte pwer whch d nt partcpate n the cntrl lp are nly fr berng. I q (b) I d I d I q Fg. hw the tranent repne f the paralleled nerter ytem emplyng the nel cntrller durng uddenly (c) 576

8 P ut I I q q P ut Q ut Q ut I I d d Tme () (c) (d) Fg.. Tranent repne f paralleled nerter harng rete lad durng the rtual retance rat changng. (a) utput current f nerter#, (b) utput current f nerter#, (c) utput drect and quadrature current f nerter#, #, (d) acte and reacte pwer f nerter#, #. 77W lad tep change (frm 5.6A t 8A and back t 5.6A). It can be bered the fat tranent repne f the ytem durng lad tep change, whle mantanng precely current harng perfrmance. Acte Pwer (W) Reacte Pwer (Var) P ut P ut Q ut Q ut (d) Fg.. Tranent repne f paralleled nerter harng rete lad when lad teppng up/dwn. (a) utput current f nerter#, (b) utput current f nerter#, (c) utput drect and quadrature current f nerter#, #, (d) acte and reacte pwer f nerter#, #. Fg. hw the tranent repne f the paralleled nerter ytem emplyng the nel cntrller durng uddenly cnnectng and dcnnectng ne f the VSI. It can be een that the lwet tranent tme arund.6. (a) Output urrent f INV (A) I (b) (a) 577

9 REFERENES I d I d (b) I q (c) P ut P ut Q ut Q ut (d) Fg.. Tranent repne f paralleled nerter harng rete lad when nerter # cnnectng and dcnnectng. (a) utput current f nerter#, (b) utput current f nerter#, (c) utput drect and quadrature current f nerter#, #, (d) acte and reacte pwer f nerter#, #. VI. ONUSION A mpler and fater cntrller whch cnt f a phaelcked lp and a rtual retance lp fr cntrllng utput lad current amng parallel three-phae nerter emplyed. The mall gnal mdel deelped baed n the nel cntrller f nerter- baed mcrgrd. The mdel wa analyzed n term f the ytem egenalue and ther entty n dfferent cenar. Expermental reult erfy the effectene f the prped cntrller. I I q [] aeter, R.H., "McrGrd," Pwer Engneerng Scety Wnter Meetng,. IEEE, l., n., pp.35,-38 l., [] Guerrer, J.M.; handrkar, M.; ee, T.; h, P.., "Adanced ntrl Archtecture fr Intellgent Mcrgrd Part I: Decentralzed and Herarchcal ntrl," Indutral Electrnc, IEEE Tranactn n, l.6, n.4, pp.54,-6, Apr.l 3 [3] J. Guerrer,. de Vcuna, J. Mata, M. atlla, and J. Mret, "A wrele cntrller t enhance dynamc perfrmance f parallel nerter n dtrbuted generatn ytem," IEEE Tran. Pwer Electrn., l. 9, n. 5, pp. 5 3, Sep. 4. [4]. Sa and P. ehn, "Autnmu lad harng f ltage urce cnerter," IEEE Tran. Pwer Del., l., n., pp. 9 6, Apr. 5. [5] Yajuan Guan, Weyang Wu, Xaqang Gu, Herng Gu. "An Impred Drp ntrller fr Grd-nnected Vltage Surce Inerter n Mcrgrd." nd Internatnal Sympum n Pwer Electrnc fr Dtrbuted Generatn Sytem, PEDG, : [6] S. J. hang,. Y. Yen, and K. T. hang, "A multmdule parallelable ere-cnnected PWM ltage regulatr," IEEE Tran. Ind. Electrn., l. 48, n. 3, pp , Jun.. [7] Engler, A.; Sultan, N., "Drp cntrl n V-grd," Future Pwer Sytem, 5 Internatnal nference n, l., n., pp.6 pp.,6, 8-8 N. 5 [8] Guerrer, J.M.; Mata, J.; u Garca de Vcuna; atlla, M.; Mret, J., "Decentralzed ntrl fr Parallel Operatn f Dtrbuted Generatn Inerter Ung Rete Output Impedance," Indutral Electrnc, IEEE Tranactn n, l.54, n., pp.994,-4, Aprl Apr. 7 [9] Karel De rabandere, run len, Jeren Van den Keybu, et al, "A Vltage and Frequency Drp ntrl Methd fr Parallel Inerter," IEEE Tran. Pwer Electrnc, l., n. 4, pp. 7-5, July. 7 [] Vandrn, T..; Meerman,.; Degrte,.; Render,.; Vandeelde,., "A ntrl Strategy fr Ilanded Mcrgrd Wth D-nk Vltage ntrl," Pwer Delery, IEEE Tranactn n, l.6, n., pp.73,- 73, Aprl Apr. [] N. Pgaku, M. Prdanc, and T.. Green, "Mdelng, analy and tetng f autnmu peratn f an nerter-baed mcrgrd," IEEE Tran. Pwer Electrn., l., n., pp , Mar. 7. [] Krutka, N.; Hernandez-Arambur,.A.; Green, T., "State-pace mdel f grd-cnnected nerter under current cntrl mde," Electrc Pwer Applcatn, IET, l., n. 3, pp , May. 7. [3] Alreza Kahrbaean, Yaer Abdel-Rady I. Mhamed, "Analy and Mtgatn f w-frequency Intablte n Autnmu Medum- Vltage nerter-aed Mcrgrd Wth Dynamc ad," IEEE Tran. Indutral Electrnc, l. 6, n. 4, pp , Aprl. 4 [4] elh, E.A.A.; rtz, P..; Garca, P.F.D., "Small-gnal tablty fr parallel-cnnected nerter n tand-alne A upply ytem," Indutry Applcatn, IEEE Tranactn n, l.38, n., pp.533,-54, Mar/Apr. [5] Dng, D.; ryech, D.; Mattaell, P.; Xue, Y. "Analy f Phae- cked p w Frequency Stablty n Three-Phae Grd-nnected Pwer nerter nderng Impedance Interactn," Indutral Electrnc, IEEE Tranactn n, l.pp, n.99, pp., July. 4 [6] Vaquez, J..; Guerrer, J.M.; Saagheb, M.; Ely-Garca, J.; Tedrecu, R., "Mdelng, Analy, and Degn f Statnary- Reference-Frame Drp-ntrlled Parallel Three-Phae Vltage Surce Inerter," Indutral Electrnc, IEEE Tranactn n, l.6, n.4, pp.7,-8, Aprl Apr. 3 [7] Yajuan Guan; Vaquez, J..; Guerrer, J.M, "A Smple Autnmu urrent-sharng ntrl Strategy fr Fat Dynamc Repne f Parallel Inerter n Ilanded Mcrgrd," Energy nference, 4 IEEE Internatnal n, ENERGYON4, 4: