Active Damping of LCL-Filter Resonance based on Virtual Resistor for PWM Rectifiers Stability Analysis with Different Filter Parameters

Transcription

1 Acte Dampng o Flter Resonance based on Vrtual Resstor or PWM Recters Stablty Analyss wth Derent Flter Parameters hrstan Wessels, Jörg Dannehl, student member, IEEE and Fredrch W. Fuchs, senor member, IEEE hrstanalbrechtsunersty o Kel Instute o Power Electroncs and Electrcal Dres Kaserstr. 2, Kel, Germany Abstract Ths publcaton presents the nestgaton o acte dampng o resonance oscllatons wth rtual resstor or grdconnected PWM recters wth lter or derent lter parameters. Usng the oltageorented PI current control wth conerter current eedback, addtonal acte dampng o the lter resonance s necessary or stable operaton. In the lterature derent methods are proposed that der n number o sensors and complexty o control algorthms. I hgher dampng o the swtchng rpple current s requred lters wth lower resonance requences can be used. Resultng low ratos between resonance requency and control requency challenge the control wth respect to dampng o resonance. Moreoer, some acte dampng methods are not sutable or these lter settngs. Here the acte dampng concept based on rtual resstor s analyzed concernng stablty or two sgncant lter conguratons. It turns out that t s applcable or conguratons wth hgher resonance requency, whereas systems lower resonance requences can poorly be damped. Addtonally the method exhbts the adantage o smple mplementaton but the dsadantage o addtonal current sensors. Theoretcal analyses and o the selected method wth tmedscrete mplementaton are shown n ths paper. Theory s ered by expermental results. I. INTRODUTION PWM recters are appled where bdrectonal low o energy by conerters s needed, e.g. n arable speed dres wth regenerate brakng or regenerate energy systems. As adantages they oer an adjustable power actor and emt less current harmonc dstorton, compared to passe dode recters. To damp the swtchng harmoncs, grd sde lters are used to connect the PWM recter wth the grd. lters are more nterestng, because they are more costeecte compared to smple lters as smaller nductors can be used to achee the same dampng eect. To oercome the dsadantage o resonance oscllatons o lters, dampng o the lter resonance s necessary. Smple passe dampng wth resstor n seres to the ltercapactor [1] creates addtonal power losses and decreases the system perormance. Thus acte dampng by modyng the control algorthm s preerred because o no addtonal power losses and more lexblty. Derent acte dampng methods are presented n lterature. In [24] the conerter current control wth addtonal eedback o the oltages across the lter capactors s shown. In [5] the lne current control wth addtonal eedback o the current through the lter capactors s presented. In [6,7] the conerter current control usng only the conerter sde current sensors s shown. An oerew about derent multloop approaches can be ound n [810]. In [1113] the control s desgned by usng the complete state normaton. The control methods der n seeral crtera lke number o sensors, complexty o control algorthm and robustness aganst parameter aratons or certan lter conguratons. In [14] lmtatons o control wth conerter current eedback and addtonal acte dampng wth notchlter as presented n [6] are shown. I an lter wth a low resonance requency s chosen or the purpose o hgh dampng o swtchng harmoncs, the desgn o the acte dampng gets ery dcult and a poor robustness s obtaned. A method utlzable or a large set o system parameters s desrable. In ths paper the applcablty o the oltageorented PI control wth acte dampng based on rtual resstor concept [9] s presented ncludng the analyss o stablty or two sgncant lter settngs. The analyss s ered by means o measurement results. The publcaton s organzed as ollows: n secton II the system descrpton and modelng s shown. Secton III descrbes the control structure and n secton IV the rtual resstor concept ncludng theoretcal analyses s shown. Measurement results are presented and analysed n secton V. Fnally, a concluson closes ths publcaton.

2 II. SYSTEM DESRIPTION The nestgated system s shown n Fg. 1. The PWM recter s connected wth the grd a lter. The D sde o the recter conssts o the D capactor and s connected to a load. The system parameters are gen n Tab. I. Here, two lter conguratons wth derent resonance requences are used. hoosng a hgher lter capactor yelds to hgher dampng o the Fg. 1: Grdconnected PWM recter wth Flter swtchng harmoncs, but reduces the resonance requency o the lter as t can be seen n the Bode dagram n Fg. 2. For the purpose o eedback the D lnk oltage as well as the conerter and lne currents are measured. The lne oltage s measured or synchronzng the control wth the grd requency. Here the space ector notaton s used. The threephase alues are transormed nto statonary reerence rame and urther, usng the lne oltage ector, nto rotatng coordnates n order to perorm the oltageorentedcontrol. From control pont o ew t s adantageous to control D alues snce PI controllers can achee reerence trackng wthout steady state errors. As dsadantage the coordnate transormaton leads to current dynamcs couplng. Modelng the lter n a reerence rame ges g c d d d ( R ( R g j c j j g c ) ) (1) For the control desgn the delays caused by the PWM, samplng and computaton are taken nto account by modelng the conerter as one sample delay wth a tme constant o one swtchng perod ( ). Tab. I: System parameters or analyss Symbol Quantty Value Nomnal lne oltage 230 V (rms) Nomnal lne current 15 A (rms) g Grdsde lter nductance 2,0 mh R g Resstance o grdsde lter nductor 30 m c onertersde lter nductance 3,0 mh R c Resstance o conertersde lter 30 m nductor Flter capactance 8 F / 48 F c Swtchng/ontrol requency 4 khz The transer uncton o the conerter s: PWM ( s) * 1 st 1 G (3) For the control loops, PI controllers wth proportonal gan k and tme constant T are used, whch are modeled as shown n equaton (4). G PI ( s) c st 1 st k (4) Due to the dscrete nature o the control algorthm mplementaton the stablty analyses n ths paper are perormed tme dscretely as well n the Zdoman. All other transer unctons are dscretzed wth the zeroorderhold method [15] wth a samplng requency equal to the control requency. ouplngs between current components are neglected or stablty analyss as a decouplng network s used [14]. The copper losses o the nductors are taken nto account by R g and R l. Neglectng the losses o the conerter and o the lter, the power balance between grd sde and D sde ges D D = 3/2 d d. The dynamcs o the D lnk oltage can be expressed by: D d D 3 d d D oad oad (2) 2 D Fg. 2: Bode dagram o transer unctons (conerter output oltage to lne current) o lnelters wth derent resonance requences.

3 III. ONTRO STRUTURE In ths paper the oltageorented PI control [1,16] wth conerter current eedback and addtonal resonance dampng s used to control the PWM recter wth lter. The cascaded control structure s shown n Fg. 3. For the control desgn the conerter s modeled as shown n (3). The PI controller parameter (k I, T I ) are tuned as descrbed n [14] 2 k I k I, opt ; TI ai Tc ; ai 3 (8) 2T c Addtonally, antwndup mechansms are mplemented to aod the arsng problems n case o lmtaton o the current and oltage reerences. Grd synchronzaton s done wth a P algorthm. Fg. 3: Oerew o complete control structure (γ : lne oltage phase angle) To regulate the Doltage o the outer control loop to ts constant alue PI controllers are used. To desgn the PI controller parameters (k D,T D ), the nner control loop s modeled as a rst order delay element wth the delay tme o T nner = 4 T c. and the controller s tuned wth the symmetrcal optmum [17]: 2 * VDD k ; 2 D TD adtnner ; ad 3 (5) 3 a T D nner d The nner current control s perormed n rotatng coordnates wth PI controllers as well. In the low requency range the lter behaes smlar to the lter as shown n [1]. In ths requency range the control wll mostly act. Thereore a desgner needs to model the system n the rotatng rame o the lterbased acte recter or the control and consder the transer uncton o the oerall lter wth dampng or stablty and dynamc purposes [1]. The approxmaton as lter wll be used or the control desgn n ths paper. Assumng the d and qcurrent dynamcs decoupled (2) ges the ollowng dynamcs: IV. VIRTUA RESISTOR ONEPT Applyng the PI control structure wth conerter current eedback wthout addtonal acte dampng yelds the root loc shown n Fg. 6 or lter wth hgh resonance requency and Fg. 8 or low resonance requency. Marked are the system poles or optmal proportonal gan k I =k I,opt. For both sets o parameters the system becomes unstable because the resonant poles all outsde the unty crcle. Acte dampng wth the rtual resstor concept as presented n [9] s based on the dea, that resonance oscllatons n a network can be damped by connectng a real resstor n seres to the lter capactor. By modyng the control algorthm smlar behaor can be acheed wthout usng a real resstor. Thus, no addtonal power losses are generated. The one phase equalentcrcut o a passely damped lter by means o addtonal resstor R s shown n Fg. 4. d d d q d q R d R q d (6) Fg. 4: One phase equalent crcut o lter The block dagram o the lter ollows rom equaton (9) (s) (9) The lne oltage s treated as dsturbance and thereore not taken nto consderaton durng the control desgn process. Thereore the same parameters can be used or the d and qcurrent controller. The control desgn and analyss wll be perormed or the daxs only. Transormng the rst lne o (6) nto the aplace doman yelds the rst order behaor: I 1/ R d G ( s) (7) V s ( / R ) 1 d and s shown n Fg. 5 (upper). Rearrangng the block dagram yelds the one shown n Fg. 5 (lower). It can be seen that n order to emulate a real resstor R n seres to an addtonal dampng term (s R ) has to be added to the conerter current reerence. The new system behaes lke a network wth dampng resstor, but nstead o a real resstor, addtonal current sensors and derentaton are needed. It should be noted that, nstead o usng measured alues, capactor current estmaton s known rom [10] but complcates the control algorthm.

4 By dscretzng the derentaton wth backwardsderenceapproxmaton [15] wth as the system samplng tme the conerter reerence current becomes: (10) Fg. 5: Block dagram o Flter wth real dampng resstor n seres to capactance (upper) and rearrangement to rtual dampng resstor (lower) A derentator may cause nose problems n the control because t wll amply hghrequency sgnals [9], but nether n smulaton nor expermental results problems were notced n ths work. In the laboratory the ltercapactorcurrent c s calculated as derence o the conerter current and the lne current. As already mentoned, some acte dampng methods are not applcable or lne lter conguratons wth a low resonance requency. To nestgate the applcablty o the presented rtual resstor concept, the analyses are done or two sgncant lter settngs wth derent parameters, one wth a hgh resonance requency and the other wth a low resonance requency. Fg. 7 shows the pole zero map o the closed current control loop or hgh resonance requency wth derent rtual resstor alues aryng rom R =0 to R =15 and constant proportonal gan k I,opt. Fg. 6: Root locus wthout rtual resstor or lter wth hgh resonance requency ( res=1,6 khz) Fg. 8: Root locus wthout rtual resstor or lter wth low resonance requency ( res=660 Hz) Fg. 7: Pole zero map wth rtual resstor (R =0 15 n steps) or lter wth hgh resonance requency ( res=1,6 khz) Fg. 9: Pole zero map wth rtual resstor (R =6 6 n steps) or lter wth low resonance requency ( res=660 Hz)

5 For zero rtual resstance the acte dampng s neecte and the same system pole conguraton as marked n Fg. 6 wthout acte dampng can be seen. For ncreasng alues o rtual resstor the resonant poles are attracted nto the nner unty crcle and the system gets stablzed. A rtual resstance o R =10 yelds eecte acte dampng. Further ncrease o R leads to nstablty agan, because the system pole on the magnary axs moe outsde the unty crcle. Fg. 9 shows the same pole zero map or low resonance requency lter parameters and derent rtual resstances rom R = 6 to R =6. By aryng the rtual resstor alue the system poles can be moed, but they are not attracted nto the nner unty crcle, thus the system stablty cannot be ncreased. Stable system operaton can only be acheed by lowerng the proportonal gan o the current control, whch reduces the system bandwh, or by usng other acte dampng methods lke state space controllers, whch s not presented here. V. EXPERIMENTA RESUTS To ery the theoretcal analyss measurement results are taken at a test bench o the system as shown n Fg. 1. The control algorthm s mplemented on a dspae DS 1006 board. The selbult 22 kwpwm recter s loaded by an nertered 4pole nducton motor. The eecte D lnk capactance s 4450 F. Fg. 10 shows the lne and conerter currents or the lter wth hgh resonance requency ( =8 F) wthout acte dampng (upper) and wth acte dampng by rtual resstor (lower). The eecteness o the rtual resstor becomes clear as the resonance s well damped. The current spectra wth acte dampng n Fg. 12 and wthout acte dampng n Fg. 13 also llustrate a good resonance dampng. Fgure 16 shows the currents durng actaton o acte dampng. Obously, the resonance oscllatons are damped ast and eectely by the rtual resstor. Fg. 10: Measured conerter (ch 2) and lne currents (ch 4) wthout (upper) and wth rtual resstor (lower) or lter wth hgh resonance requency ( res=1,6 khz) (20A/d) Fg. 11: Measured conerter (ch 2) and lne currents (ch 4) wthout (upper) and wth rtual resstor (lower) or lter wth low resonance requency ( res=660 Hz) (20A/d)

6 Fg. 12: Measured conerter (upper) and lne (lower) current spectra wthout rtual resstor or lter wth hgh resonance requency ( res=1,6 khz) Fg. 14: Measured conerter (upper) and lne (lower) current spectra wthout rtual resstor or lter wth low resonance requency ( res=660 Hz) Fg. 13: Measured conerter (upper) and lne (lower) current spectra wth rtual resstor (R =15 ) or lter wth hgh resonance requency ( res=1,6 khz) Fg. 15: Measured conerter (upper) and lne (lower) current spectra wth rtual resstor (R =2 ) or lter wth low resonance requency ( res=660 Hz) Theoretcally, no stable operaton s possble wth the lter wth low resonance requency ( = 48 F) as the system poles are outsde the unty crcle or all PI gans (see root locus n Fg. 8). But due to addtonal natural dampng o the lter elements whch s not modeled n ths work operaton wth reduced PI gan s possble. Fg. 11 shows measurement results obtaned wth the lter wth low resonance requency ( = 48 F) and reduced PI gan (k I =0,8 k I,opt ). Fg. 14 and 15 show the spectra. The resonance oscllatons are manly sble n the conerter current and can be damped by a small rtual resstor. Hgher rtual resstor alues leads to nstablty agan ery easly. The system s close to the stablty lmt and small ncrease o R or k I lead to nstablty makng the conerter trppng. ne current s more dstorted by low grd harmoncs (5 th and 7 th ). Due to the low PI gan the low requency dstortons are damped worse. Fg. 16: Measured conerter (ch 2) and lne currents (ch 4) durng actaton o rtual resstor (ch 3) or lter wth hgh resonance requency ( res=1,6 khz) (20A/d)

7 VI. ONUSION In ths paper the oltageorented PI control wth conerter current eedback and addtonal resonance dampng s used to control the PWM recter wth grd sde lter. The acte dampng method based on the rtual resstor concept s analysed or two sgncant settngs o lne lter parameters. Ths method oers the adantage o smple mplementaton but the dsadantage o addtonal needed current sensors. To show the nstablty wthout addtonal acte dampng the system s analyzed n root locus. The tunng procedure o the rtual resstor and ts result on the control perormance s presented n the pole zero map. The perormance o the nestgated control system s ered by measurements at a test dre. From theoretcal analyss and expermental results t becomes clear, that acte dampng wth rtual resstor damps resonance eectely only or hgh resonance requency lter. For lter wth low resonance requency the system stablty can only be acheed by lowerng the proportonal gan o the current controller, whch reduces the system bandwh or by usng more complex control algorthms lke state space control, whch s not consdered here. AKNOEDGMENT Ths work has partly been nanced by European Socal Fund / Innoaton Fund SchleswgHolsten and carred out as part o E wnd, competence centre wnd energy Schleswg Holsten REFERENES [1] M. serre, F. Blaabjerg, and S. Hansen, Desgn and control o an lterbased threephase acte recter, IEEE Trans. on Industry Applcatons, ol. 41, no. 5, pp , [2] V. Blasko and V. Kaura, A noel control to actely damp resonance n nput lter o a threephase oltage source conerter, IEEE Trans. on Industry Applcatons, ol. 33, no. 2, pp , [3] M. serre, A. Dell Aqula, and F. Blaabjerg, Stablty mproement o an lter based threephase acte recter, n Proc. Power Electroncs Specalst onerence, ol.3, pp , [4] M. Malnowsk, M.P. Kazmerkowsk, W. Szczygel, and S. Bernet, Smple Sensorless Acte Dampng Soluton or threephase PWM Recter wth Flter, Proc. IEEE Industral Electroncs onerence, pp ,2005. [5] E. Twnng and D.G. Holmes, Grd urrent Regulaton o a ThreePhase Voltage Source Inerter wth an Input Flter, IEEE Trans. on Power Electroncs, ol. 18, no. 3, [6] M. serre, R. Teodorescu, and F. Blaabjerg, Stablty o Photooltac and Wnd Turbne Grdonnected Inerters or a arge Set o Grd Impedance Values, IEEE Trans. on Power Electroncs, ol. 21, no. 1, pp , [7] J. Dannehl, F.W. Fuchs, and S. Hansen, PWM Recter wth Flter usng derent urrent ontrol Structures, Proc. European onerence on Power Electroncs and Applcatons, DROM, 2007.# [8] P.. oh and D.G. Holmes, Analyss o multloop control strateges or //ltered oltagesource and currentsource nerters, IEEE Trans. on Industry Applcatons, ol. 41, no. 5, pp , [9] P.A. Dahono, A control method to damp oscllaton n the nput lter, n Proc. Power Electroncs Specalst onerence, ol. 4, pp , [10] W. Gullk,. Norum, R. Nlsen, Acte Dampng o Resonance Oscllatons n Flters Based on Vrtual Flux and Vrtual Resstor, Proc. European onerence on Power Electroncs and Applcatons, DROM, [11] M. Bojrup, P. Karlsson, M. Alakula, and. Gertmar, A multple rotatng ntegrator controller or acte lters, Proc. European onerence on Power Electroncs and Applcatons, DROM, [12] F.A. Magueed and J. Sensson, ontrol o VS connected to the grd through lter to achee balanced currents, Proc. IEEE Industry Applcatons Socety Annual Meetng, ol. 1, pp. 5728, [13] E. Wu and P.W. ehn, Dgtal current control o a oltage source conerter wth acte dampng o resonance, IEEE Trans. on Power Electroncs, ol. 21, no. 5, pp , [14] J. Dannehl,. Wessels, F.W. Fuchs, mtatons o VoltageOrented PI urrent ontrol o Grdonnected PWM Recters wth Flter, IEEE Trans. on Industral Electroncs (submtted), 2008 [15] K.J. Aaström and B. Wttenmark, omputercontrolled systems: theory and desgn, Prentce Hall, [16] M.P. Kazmerkowsk, R. Krshnan, and F. Blaabjerg, ontrol n Power Electroncs: Selected Problems, Academc Press, [17] D. Schröder, Elektrsche Antrebe 2, Regelung on Antrebssystemen, Sprnger, 2001.