Control strategies for active power filters

Transcription

1 Control strateges for actve ower flters F. Barrero, E. Romero and M. I. Mlanés Deartment of Electronc and Electromechancal Engneerng chool of Indstral Engneerng Unversty of Extremadra Avda Elvas s/n, 66 Badajoz (PAIN) hone: , fax: , e-mal: Abstract. In ths aer a comarson between strateges for extractng the three-hase erence crrents for actve ower flters s shown. The erformance of these strateges wll be evalated nder dfferent sorce and load condtons. The stdy has been aled to a three-hase for-wre system n order to nclde mbalance. It wll be shown that nder balanced and snsodal voltages, harmonc cancellaton and reactve ower comensaton can be acheved by all the methods. However, when the voltages are dstorted and/or nbalanced, the comensaton caabltes are not evalent. It wll be roved that some strateges do not offer an adeate solton when the mans are not deal, ncldng harmoncs or mbalance. Frst, ths aer resents a revson of for control strateges for the extracton of the erence crrents for an actve ower flter connected to a three-hase forwred sorce that sles to a nonlnear load (Fgre ). The for strateges that have been comared are: - Instantaneos actve and reactve ower (- method). - Instantaneos drect and adratre crrent (d method). - Unty Power Factor (UPF) method. - Perfect Harmonc Cancellaton (PHC) method. Fnally, comaratve evalaton s erformed by means of smlaton stdy nder both deal and dstorted mans voltage condtons and varos load condtons. Keywords Actve flterng, erence crrent extracton, - theory, method, nty ower factor method, erfect d harmonc cancellaton method. A a B b C c N n R L Ca Cb Cc Cn L AF PCC La Lb Lc Ln Non-lnear load. Introton C Power electroncs converters, more and more wdely sed n ndstral, commercal as well as domestc alcatons, sffer from the roblem of drawng non snsodal crrent and reactve ower from the sorce. Ths behavor cases voltage dstorton that affects to another loads connected at the same ont of common colng (PCC). Actve ower flters are researched and develoed as a vable alternatve over the conventonal methods to solve ths roblem. Of corse, the sze and cost of actve ower flters deends on harmoncs and reactve ower to be comensated. The control strategy for a shnt actve ower flter (Fgre ) generates the erence crrent that mst be rovded by the ower flter to comensate reactve ower and harmoncs crrents demanded by the load. Ths mles a set of sorce crrent n the hase doman, that wll be tracked generatng the swtchng sgnals aled to the electronc converter (heart of the actve ower flter) by means of the arorate closed-loo swtchng control techne, lke hysteress band control. Fg.. Three-hase for-wre sorce wth non-lnear load and shnt actve ower flter.. Instantaneos - strategy Most of the APF s (actve ower flters) develoed are based on the nstantaneos reactve ower theory (or - theory) to calclate the desred comensaton crrent. Ths theory was roosed frst by Akag and hs coworkers n 984 []. nce then varos nterretatons and mrovements of ths method have been resented [], []. In ths method, a set of voltages ( a, b, c ) and crrents ( a, b, c ) from a three-hase for-wre system, are frst transformed nto three-axs reresentaton --, sng the followng ower nvarant: C htts://do.org/.484/rej.8 4 RE&PQJ, Vol., No., Arl 4

2 a a C b ; C b c c () C where C s the so called transformaton T matrx: C ; C C.. d method L + L + (6) Ths method s also known as ynchronos Reference Frame (RF) [6], [7]. Here, the erence frame d- (d drect axs, adratre axs) s determned by the angle θ wth resect to the - frame sed n the - theory. The transformaton from -- frame to d- frame s gven by: The generalzed nstantaneos actve ower,, and nstantaneos reactve ower,, defned n [], [], n terms of the -- comonents, are gven by the followng exressons: aa bb cc + + The nstantaneos three-hase actve ower has two comonents: the nstantaneos zero-seence actve ower,, and the nstantaneos actve ower de to ostve and negatve seence comonents, e. Accordng to ths: + e + e Moreover, each ower comonent have, n ts trn, a mean vale or comonent and an oscllatng vale or ac comonent. For the system shown n Fgre, the ower comonents rered by the load are: L L L L L d cosθ senθ sen θ cos θ () If d axs s n the drecton of the voltage sace vector, and takng nto accont that the zero-seence comonent s nvarant, the transformaton s gven by: () (4) + + L () The objectve s to get the sorce to gve only the constant actve ower demanded by the load, + L. In addton, the sorce mst delver no zero-seence actve ower,. Theore, the erence sorce crrents n the -- frame can be determned by [8]: d + where, the transformaton matrx, has the - T roertes: ;. Each one of the crrent comonents ( d, ) has an average vale or comonent and an oscllatng vale or ac comonent: d d + d + d The comensatng strategy (for harmonc reton and reactve ower comensaton) mles that the sorce mst only delvers the mean vale of the drect-axs comonent of load crrent. Theore, the comensator crrent wll be: C L Cd Ld + C L L (7) (8) (9) () From eaton (8) the drect-axs comonent of the load crrent s: + L L Ld Ld + Ld + + () htts://do.org/.484/rej.8 4 RE&PQJ, Vol., No., Arl 4

3 The comonent of the above eaton wll be: Ld ( + ) () where the sbscrt mst be nderstood as the mean vale of the exresson nto brackets. The erence sorce crrent mst be n hase wth the sorce voltage and no nbalanced, theore t wll be obtaned, n the -- frame, mltlyng () for an ntary vector n the drecton of voltage sorce sace vector, exclded the zero-seence comonent: Ld + ( ) + + () 4. UPF strategy The comensaton strategy known as the nty ower factor (UPF) method has the objectve that the load ls the comensator mst be vewed by the sorce as a resstance [8], [9]. Ths method s also known as the voltage synchronzaton method becase the crrent sorce sace vector s n hase wth the voltage sorce sace vector. The comensator crrent wll be: C L L K K K + + ) (4) where K s a constant whch vale deends on the sorce voltage and the load. The ower delvered by the sorce wll be: ( () The contance K can be determned wth the crteron that the ower delvered by the sorce eals the comonent of the nstantaneos actve ower of the load, theore: K L ( + + ) + Fnally, the erence crrent sorce wll be gven by: + L K ( + + ). PHC strategy (6) (7) Ths method can be consdered as a modfcaton of the revosly resented theores and has the objectve to comensate all the harmonc crrents and reactve ower demanded by the load; theore, the crrent sorce wll be balanced and wll be n hase wth the fndamental comonent of the voltage sorce, exclded the zeroseence comonent [8]. The comensator erence crrent wll be gven by: where C L L K (8) s the voltage sorce sace vector wth only fndamental comonent wthot zero-seence comonent. The comensator erence crrent wll be gven by: ( ) K K + (9) The constant K vale wll be determned wth the condton that the above ower delvered by the sorce eals the comonent of the nstantaneos actve ower demanded by the load. Theore: K + + () L Fnally, the erence sorce crrent wll be gven by: + L K + 6. Comaratve evalaton () Table I smmarzes the exressons for determnng the erence sorce crrent n the for comensaton strateges consdered. TABLA I. Exressons for determnng the erence sorce crrent. - strategy L + L + d strategy ( + ) + UPF strategy + L ( ) + + PHC strategy + L + htts://do.org/.484/rej.8 44 RE&PQJ, Vol., No., Arl 4

4 For comaratve evalaton, varos smlaton reslts are obtaned nder both deal and dstorted mans voltage and nder dfferent load crrent condtons. In all the cases, the hase angle between the fndamental comonents of sorce voltage and load crrent s º ntve. Followng fgres are based on normalzed anttes. For balanced cases the hase a magntdes wll be shown, for nbalanced cases all three hases magntdes wll be shown. For all cases, the nformaton s organzed n ths manner: orce voltage and load crrent. Freency sectrm of sorce voltage and load crrent. Reference comensator crrent: UPF (ble), - (green), d - (red), PHC (cyan). Reference sorce crrent wth the same colors assgnaton as n. (e) Freency sectrm of for UPF strategy. (f) Freency sectrm of for - strategy. (g) Freency sectrm of for d- strategy. (h) Freency sectrm of for PHC strategy. () Load owers: e (ble), (green), (red). orce owers for UPF: e (ble), (green), (red). orce owers for -: e (ble), (green), (red). orce owers for d-: e (ble), (green), (red). orce owers for PHC: e (ble), (green), (red). Case A. Ideal mans voltage. Balanced and dstorted ( th and 7 th harmonc) load crrent.... (g) ().. L (h), 99 L L, Fg.. mlaton reslts for case A. mlaton reslts for case A are shown n Fgre and Table II. It s observed that both sorce voltages and crrent are snsodals, and are n hase, hence, reactve ower and harmoncs are flly comensated. The sorce sles only the constant ower demanded by the load TABLE II: mmary of vales from smlaton reslts for case A. L UPF - d- PHC 4,46%,6%,4%,4%,44% I (A),77,77,6,6,6 I (A),78,77,6,6,6 cosφ,866 f,84 (VA),44,,99,99,99.. (e) (f) htts://do.org/.484/rej.8 4 RE&PQJ, Vol., No., Arl 4

5 Case B. Balanced and dstorted ( th and 7 th harmonc) sorce voltages. Balanced and dstorted ( th and 7 th harmonc) load crrents. mlaton reslts for case B are shown n Fgre and Table III. It s observed that, for UPF strategy, both sorce voltages and crrents have smlar shae, and are n hase; hence, reactve ower s flly comensated and harmonc levels of the comensated (sorce) crrents are the same as n the sorce voltages. On the other hand, d - and PHC strateges ree dstorton bt the reactve ower s not flly comensated. Wth - strategy, sorce crrents contan harmoncs at freences not resent n load crrents, bt only wth ths strategy the sorce sles the constant ower demanded by the load. TABLA III: mmary of vales from smlaton reslts for case B L UPF - d- PHC 4,46% 4,9%,79% 4,%,4% I (A),77,4,6,6,7 I (A),78,9,6,6,7 cosφ,866 f,768,88,97,97 (VA),9,,79,4,7 4 (g) ()..,, 99 L,76 L,7 L (h) Fg. : mlaton reslts for case B All the strateges correctly comensate the fndamental comonent reactve ower. However, wth PHC strategy the sorce sles oscllatng reactve ower. - - Case C. Balanced and dstorted (7 th harmonc) sorce voltage. Balanced and dstorted ( th harmonc) load crrent (e) (f) htts://do.org/.484/rej.8 46 RE&PQJ, Vol., No., Arl 4

6 TABLA IV: mmary of vales from smlaton reslts for case C L UPF - d- PHC 9,887 4, 4,49,6, I (A),77,89,6,6,6 I (A),7,9,69,68,6 cosφ,866 f,84,98,99,99 (VA),4,74,6,4, Case D. Unbalanced and ndstorted sorce voltages. Unbalanced and ndstorted load crrents. 8 6 (e). (f) (g). (h) () L L, L, () L L L, 99, Fg. 4: mlaton reslts for case C mlaton reslts for case C are shown n Fgre 4 and Table IV. These reslts are smlar to the case B: Note that d - strategy generates non-snsodal erence sorce crrents de to the dfferent harmoncs order n sorce voltages and load crrents Fg. : mlaton reslts for case D htts://do.org/.484/rej.8 47 RE&PQJ, Vol., No., Arl 4

7 mlaton reslts for case D are shown n Fgre and Table V. It s observed that only PHC strategy s able to elmnate nbalance from the load crrents. The freency sectrms n Fgre do not aear becase they are dfferent for each hase, however vales are shown n Table V. The - strategy obtans the worst reslts, nstead. Wth PHC strategy the sorce sles hgh oscllatng reactve ower whch s not demanded by the load TABLA V: mmary of vales from smlaton reslts for case D L UPF - d- PHC I A (A),77 %,6,%,6,96%,6,6%,6,4% I B (A),77 %,86 %,69,76%,66,67%,6 % I C (A),77 %,68 %,6,77%,4,94%,6 % f,866,97,98 (VA),,4,,,97 Case E. Unbalanced and ndstorted sorce voltages. Unbalanced and ndstorted load crrents Fg. 6: mlaton reslts for case E TABLA VI: mmary of vales from smlaton reslts for case E L UPF - d- PHC I A (A),77 %,6,4%,697 4,%,69,8%,677,6% I B (A),99 %,8 %,69 4%,679,9%,67 % I C (A),44 %,67 %,7,9%,7,4%,68 % f,866,97,99 (VA),69,46,478,46, ().. - L L, 47,8 mlaton reslts for case E are shown n Fgre 6 and Table VI. Here, n contrast to case D, there s zeroseence nstantaneos ower. In all strateges the constant ower comonent s sled by the sorce ( e + L ), excet n d - strategy n whch the mentoned ower s sled by the comensator, as can be seen n eaton (). 7. Conclsons The most arorate strategy deends on the correcton objectve. If the comlance of harmonc standards and reactve ower comensaton are looked for, the PHC s the most adeate strategy, becase t acts correctly nder any tlty condtons. If mnmzng the sorce crrents RM vales s desred, the best strategy s UPF, even more n the resence of harmonc voltages at the PCC not cased by the nonlnear load. If constant actve ower from the sorce s desred, the generalzed - theory wll be selected, althogh t mantans or ncrease the sorce crrent harmonc dstorton. The d - theory cold be consdered an ntermedate solton among all strateges becase t mantans all the ratos nder certan lmts. It has been roved that - strategy (maybe the most wdely sed) s the most senstve to dstorton and mbalance n the voltages at the PCC. htts://do.org/.484/rej.8 48 RE&PQJ, Vol., No., Arl 4

8 References [] Akag, H.; Kanazawa, Y.; Nabae, A. Instantaneos Reactve Power Comensators Comrsng wtchng Devces wthot Energy torage Comonents, IEEE Transactons on Indstry Alcatons, Vol., No, May- Jne 984. [] Peng, F.-Z.; Ott, G. W.; Adams, D. J. "Harmonc and Reactve Power Comensaton Based on the Generalzed Instantaneos Reactve Power Theory for Three-Phase For-Wre ystems", IEEE Transactons on Power Electroncs, Vol., No 6, November 998. [] Akag, H.; Ogasawara,.; Km, H. The Theory of Instantaneos Power n Three-Phase For-wre systems: A comrehensve aroach, Conf. Rec. IEEE-IA Annal Meetng,. 4 49, 999. [4] Afonso, J.; Coto, C.; Martns, J. Actve Flters wth Control Based on the - Theory, IEEE Indstral Electroncs ocety Newsletter,.. etember. [] Aredes, M.; Watanabe, E.H. New Control Algorthms for eres and hnt Three-hase Forwre Actve Power Flters, IEEE Transactons on Power Delvery, Vol., No, Jly 99. [6] Nabae, A; Tanaka, T. A New Defnton of Instantaneos Actve-Reactve Crrent anda Power Based on Instantaneos ace Vectors on Polar Coordnates n Three Phase Crcts, IEEE Transactons on Power Delvery, Vol., No, Jly 996. [7] oares, V.; Verdelho, P.; Mares, G. D. An Instantaneos Actve and Reactve Crrent Comonent Method for Actve Flters", IEEE Transactons on Power Electroncs, Vol., Nº 4, Jly. [8] Rafe, M.-R.; Tolyat, H. A.; Ghaz, R.; Goalarathanam, T. An Otmal and Flexble Control trategy for Actve Flterng and Power Factor Correcton Under Non-nsodal Lne Voltages, IEEE Transactons on Power Delvery, Vol. 6, No., 97-, Arl. [9] Cavallan, A.; Montaran, G.C. Comensaton trateges for hnt Actve-flter Control, IEEE Transactons on Power Electroncs, Vol. 9, No 6, November 984. [] Deenbrock, M.; tadt, V.; Wrede, H. A Theoretcal Investgaton of Orgnal and Modfed Instantaneos Power Theory Aled to For-Wre ystems, IEEE Transactons on Indstry Alcatons, Vol. 9, Nº 4, Jly- Agst. htts://do.org/.484/rej.8 49 RE&PQJ, Vol., No., Arl 4