An active damper for stabilizing power electronics-based AC systems Wang, Xiongfei; Blaabjerg, Frede; Liserre, Marco; Chen, Zhe; He, J.; LI, Y.
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1 Aalborg Unverstet An actve damper for stablzng power electroncs-based AC systems Wang Xongfe; Blaabjerg Frede; Lserre Marco; Chen Zhe; He J.; LI Y. Publshed n: 8th Annual IEEE Appled Power Electroncs Conference and Exposton APEC 13 DOI (lnk to publcaton from Publsher): 1.119/APEC Publcaton date: 13 Document Verson Early verson also known as pre-prnt Lnk to publcaton from Aalborg Unversty Ctaton for publshed verson (APA): Wang X. Blaabjerg F. Lserre M. Chen Z. He J. & LI Y. (13). An actve damper for stablzng power electroncs-based AC systems. In 8th Annual IEEE Appled Power Electroncs Conference and Exposton APEC 13 (pp ). IEEE Press. I E E E Appled Power Electroncs Conference and Exposton. Conference Proceedngs DOI: 1.119/APEC General rghts Copyrght and moral rghts for the publcatons made accessble n the publc portal are retaned by the authors and/or other copyrght owners and t s a condton of accessng publcatons that users recognse and abde by the legal requrements assocated wth these rghts.? Users may download and prnt one copy of any publcaton from the publc portal for the purpose of prvate study or research.? You may not further dstrbute the materal or use t for any proft-makng actvty or commercal gan? You may freely dstrbute the URL dentfyng the publcaton n the publc portal? Take down polcy If you beleve that ths document breaches copyrght please contact us at vbn@aub.aau.dk provdng detals and we wll remove access to the work mmedately and nvestgate your clam. Downloaded from vbn.aau.dk on: aprl 5 18
2 An Actve Damper for Stablzng Power Electroncs- Based AC Systems X. Wang F. Blaabjerg M. Lserre and Z. Chen Department of Energy Technology Aalborg Unversty Pontoppdanstraede 11 9 Aalborg Denmark Emal: {xwa fbl ml zch}@et.aau.dk J. He and Y. L Department of Electrcal and Computer Engneerng Unversty of Alberta Edmonton Canada Emal: {hjnwe yunwe.l}@ualberta.ca Abstract The mutual nteractons between the parallel grdconnected converters coupled through the grd mpedance tend to result n a number of stablty and power qualty challenges. To address them ths paper proposes an actve damper concept based on a low-power hgh-bandwdth power converter. The basc dea behnd ths proposal s to dynamcally adjust the grd mpedance seen from the pont of common couplng of the grdconnected converters such that the potental nstabltes and resonance propagaton can be effectvely mtgated. Smulaton and laboratory tests on three parallel grd-connected converters are carred out. The results valdate the stablzng performance of the actve damper. I. INTRODUCTION Over the last years the power electroncs converters are ganng a wde acceptance as an effcent grd nterface for connectng renewable energy systems and at the load sde as electrc drves [1] []. The mutual nteractons between the controllers of the parallel grd-connected converters coupled va the grd mpedance such as the wnd turbnes converters n wnd farms [3] the Photovoltac (PV) nverters n PV power plants [4] and the locomotve converters n the electrc ralway networks [5] wll nevtably arse whch may result n small-sgnal oscllatons. Furthermore due to the popular use of LCL-flters addtonal resonances may occur n the parallel grd-connected converters and vary wth the dfferent number of converters. Ths fact n turn reduces the allowed bandwdth of the converters and also n some cases tends to ntroduce undamped resonances [6]-[8]. There s consequently an urgent need to develop effectve measures to address the aforementoned challenges. In [9] the mpedance-based stablty analyss method orgnatng from the Mddlebrook s Extra Element Theorem [1] provdes a powerful tool to gan the nsght of the converter nteractons. It has been shown that a non-negatve real part of the nput admttance of a grd-connected converter s usually requred for the dampng of oscllatons [11]. Hence to dampen out the addtonal resonances brought by the parallel-connected LCLflters the Resstve-Actve Power Flter (R-APF) method s adopted for the parallel grd-connected PV nverters n [1] where the nverters are controlled to behave as resstve loads at the non-fundamental frequences. However n ths case a hgh-bandwdth current controller s needed n order to cover the changes of resonant frequences whch may be dffcult to realze for the hgh power converter applcatons. Also the performance of the R-APF approach s affected by the grdsde nductances n the LCL-flters [13]. As opposte to the use of the vrtual resstance loop a flter-based method s reported n [3] where a wdeband notch flter coverng the resonance frequences s nserted nto the current controller and thus the resonances n a wnd power plant can be damped. The man drawback of ths method s the desgn of the wdeband notch flter whch s hghly dependent on the system condtons and the stablzng performance tends to be degraded under the system parameters varatons. In ths work nstead of reshapng the nput mpedances of grd-connected converters by usng the dfferent control loops an actve damper based on a low-power hgh-frequency and hgh-bandwdth power electronc converter s proposed. Ths actve damper s connected to the Pont of Common Couplng (PCC) of the grd converters and ams to dynamcally adjust the grd mpedance va the varable resstances at the resonance frequences whch appear. Hence the nstabltes and resonances resultng from the nteractons n the parallel grd-connected converters can effectvely be mtgated. Ths paper frst presents a small-sgnal stablty analyss of a power electroncs-based AC system n Secton II ncludng two parallel actve rectfers wth the LCL-flters. The mutual nteractons between the rectfers and the nfluence of the grd mpedance varatons are evaluated by the Nyqust stablty crteron. Then n lght of the analyss results the operaton prncple of the proposed actve damper concept s dscussed n Secton III ncludng the basc confguraton and the control schemes. Ths s followed by an assessment on the dampng effect of the actve damper n the frequency-doman. Fnally n Secton IV to further valdate the stablzng performance of the actve damper smulatons and laboratory tests on the two parallel actve rectfers as well as the actve damper are performed. The results show that the resonances rased n the system are damped by the actve damper.
3 Fg. 1. A three-phase power electroncs-based AC system. II. STABILITY ANALYSIS OF PARALLEL GRID-CONNECTED CONVERTERS WITH LCL-FILTERS Fg. 1 llustrates a three-phase power electroncs-based AC system where two actve rectfers are connected n parallel respectvely to the Pont of Common Couplng (PCC) and a Power Factor Correcton (PFC) capactor C PFC s nstalled at the PCC. In such a system the presence of shunt-connected capactors n the LCL-flters and the PFC capactor may lead to resonances at the dfferent frequences than the case of sngle actve rectfer [5]. These addtonal resonances n turn reduce the stablty margns of the control loops of the rectfers and even result n unstable oscllatons. To clarfy the nature of such resonances and small-sgnal oscllatons the mpedancebased stablty analyss that s based on the termnal behavoral models of the converters s carred out [9] [14]. A. Modelng of Parallel Grd-Connected Converters Fg. represents the smplfed crcut for the -th (=1 ) actve rectfer. The converter s represented by the modulated voltage source V M and the grd-sde current s controlled for a better stablty of the control system [15]. Thus the frequency behavor of the LCL-flter at the PCC can be expressed by the followng admttances Fg.. Smplfed crcut for the -th (=1 ) actve rectfer. Fg. 3. Block dagram of the current control loop for the -th actve rectfer. Y M Y o Ig ZCf V Z Z Z Z Z Z M V Cf Lf Lg Lf Cf Lg PCC I g 1 V Z Z Z Z Z Z PCC V M Cf Lf Lg Lf Cf Lg where Z Lf Z Cf and Z Lg are the mpedances for the nductor L f the capactor C f and the nductor L g respectvely. Fg. 3 shows the block dagram of the current control loop for the -th actve rectfer whch s appled n the synchronous dq-frame. Snce the dynamcs of the outer DC voltage control loop the reactve power control loop and the phase lockedloop are much slower than the current control loop the effects of these control loops are neglected for the sake of smplcty. Consequently the termnal behavor of the -th rectfer can be represented by a Norton equvalent crcut as shown n Fg. 4 (1) () Fg. 4. The Norton equvalent crcut for the -th actve rectfer wth the grd-sde current control loop closed. whch are derved as follows I G I Y V (3) g cl g oc PCC G Y T c cl (4) 1 Tc Y o oc (5) 1 Tc where I g s the current reference of the -th converter G cl s the closed-loop gan of the current control loop and Y oc s
4 the closed-loop nput admttance. T c s the open-loop gan of the current control loop whch s derved as T G G Y (6) c c d M where G c s the Proportonal-Integral (PI) current controller and G d s the approxmated 1.5 samplng perod (T s ) delay n the dgtal control whch are expressed as follows G G K c c Kpc (7) 1.5T / 1 ss Tss Tss d e 1.75Ts s 1.5 Ts s/ 1 s (8) Substtutng the actve rectfers shown n Fg. 1 by the Norton equvalent crcuts the closed-loop model of the power electroncs-based system can be obtaned as shown n Fg.5. Y C s the admttance of the PFC capactor C PFC Z S s the grd mpedance ncludng L S and R S. It s clear that there are three closed-loop gans for characterzng the responses of the grdsde current n the -th actve rectfer whch are expressed as G T T V I I I cl m m S g g g j 1Tm 1Tm 1Tm ZS where the term j denotes the other actve rectfer ( j). T m s the derved mnor-loop gan used for the mpedance-based stablty analyss [14] whch s gven by oc m t C oc j Yt ZS (9) Y 1 T Y Y Y (1) where Y t s the total sum of the closed-loop nput admttance of the other j-th rectfer and the grd admttance as well as the admttance of the PFC capactor. B. Impedance-based Stablty Analyss To confrm the correctness of the derved mnor-loop gan the mutual nteractons between the two actve rectfers and the effect of grd mpedance varatons are assessed n both the frequency- and tme-doman. Table I summarzes the electrcal constants for the power electroncs-based AC system shown n Fg. 1. The man controller parameters of the actve rectfers are lsted n Table II. Fg. 6 depcts the frequency response of the open-loop gan of the current control loop T c n the -th actve rectfer. It s seen that a stable closed-loop termnal behavor of the rectfer s obtaned at the PCC. Then consderng the effect of grd mpedance sngle actve rectfer wth the PFC capactor at the PCC s evaluated. Fg. 7 compares the Nyqust plots for the mnor-loop gans T m whch s derved wth the dfferent grd nductances. It s shown that the current control loop becomes unstable when the grd nductance L S s equal to.6 mh. Fg. 8 shows the Nyqust plots of the mnor-loop gans by Fg. 5. Closed-loop model of the power electroncs-based AC system. Magntude (db) Phase (deg) Frequency (Hz) Fg. 6. Frequency response of the open-loop gan of the current control loop n the -th rectfer Ls=.3 mh Ls=.6 mh Ls=1. mh Fg. 7. Nyqust plots of the mnor-loop gans derved wth the dfferent grd nductance n the case of sngle actve rectfer. takng the nput admttance of the other paralleled rectfer nto account. Snce n the case of L S equal to.6 mh the current control loop s already unstable for sngle actve rectfer t s not nvolved n Fg. 8. It s nterestng to notce that the current control loop s unstable n the case that L S s equal to 1. mh rather than margnally stable as shown n Fg. 6. Furthermore n order to dentfy the resonance frequences n ths case Fg. 9 depcts the frequency responses of Y oc and Y t. It s seen that two admttances ntersect at 174 Hz wth a negatve phase margn whch ndcates that a resonance wll arse around ths frequency. To further confrm the above frequency-doman analyss the tme-doman smulatons of the parallel actve rectfers are performed wth SIMULINK and PLECS. Fg. 1 shows the smulated currents n the case of sngle actve rectfer wth the dfferent grd nductances from whch a good match wth the Nyqust plots shown n Fg. 7 can be observed. Fg. 11 shows
5 Ls=.3 mh Ls=1. mh TABLE I. SYSTEM ELECTRICAL CONSTANTS Electrcal Parameters Values Grd mpedance (Z S ) L S 1. mh R S.4 Ω PFC capactor C PFC μf L f1= L f 1.5 mh LCL-flters C f1= C f 4.7 μf L g1= L g 1.8 mh DC voltages V dc1= V dc 7 V DC loads R 1= R 4 Ω Fg. 8. Nyqust plots of the mnor-loop gans wth the effect of the nput admttance of the other parallel actve rectfer. Magntude (db) - -4 Yoc Yto TABLE II. MAIN CONTROLLER PARAMETERS OF ACTIVE RECTIFIERS Controller Parameters Values Swtchng frequency f sw 1 khz Samplng perod T S 1-4 s PI current controller K pc1= K pc 18 K c1= K c 9 DC voltage controller K p_dc1 = K p_dc.5 K _dc1 = K _dc Phase (deg) Frequency (Hz) Fg. 9. Frequency responses of Y oc and Y t n the unstable case (L S = 1. mh) for dentfyng the resonance pont. LS =.3 mh (a) (a) LS =.6 mh (b) (b) LS = 1. mh Fg. 11. Smulated currents of the parallel actve rectfers. (a) L S =.3 mh. (b) L S = 1. mh. 1. Rectfer 1.5 (c) Fg. 1. Smulated current waveforms n the case of sngle actve rectfer. (a) L S =.3 mh. (b) L S =.6 mh. (c) L S = 1. mh Rectfer the smulated currents of the parallel actve rectfers. It s seen that the resonances arse when L S s equal to 1. mh. Fg. 1 gves the current harmonc spectra n the unstable case whch valdates the resonance frequency analyss n Fg Frequency (Hz) Fg. 1. Current harmonc spectra n the unstable case (L S = 1. mh).
6 Fg. 13. Basc confguraton of the proposed actve damper. III. PROPOSED ACTIVE DAMPER From (1) t s known that the grd mpedance Z S results n a couplng between the parallel actve rectfers. As n the case of an deally stff power grd there are no nteractons between the controllers of rectfers. Thus the dea behnd the proposed actve damper s to ntroduce a varable dampng resstance va the power converter nto the grd mpedance profle n order to effectvely dampen out the system resonances. A. Operaton Prncple Fg. 13 shows a basc confguraton of the proposed actve damper whch conssts of a three-phase two-level voltage source converter and a resonance dampng controller. Snce there s no addtonal energy storage element at the DC-lnk only the actve power responsble for keepng a constant DC voltage s consumed by the actve damper. Furthermore the actve damper s only responsble for the dampng of resonances caused by the controller nteractons n the parallel grd-connected converters whch s dfferent from the conventonal actve power flters for steady-state harmonc current compensaton. The power ratng of the actve damper s thus lower than actve power flters whch allows operatng wth a hgh swtchng frequency. As a consequence a hghbandwdth controller whch covers a wde varety of resonance frequences can be acheved. Fg. 14 llustrates two types of control block dagrams for realzng such an actve damper functon. The frst opton s based on a conventonal Resstve-Actve Power Flter (R- APF) method [16] as shown n Fg. 14 (a). However nstead of emulatng resstance at all the non-fundamental frequences as usual only the resonant components of the PCC voltage are detected and dvded by a vrtual conductance n ths scheme. Fg. 14 (b) shows the block dagram of the second control scheme where multple frequency-adaptve resonant voltage controllers are employed to acheve the drect resonant voltage compensaton. The outputs of the resonant voltage controllers are passed drectly to the duty cycle of the actve damper thus a fast response of resonance dampng can be obtaned. Also the desgn of the nner current controller s easer compared to the R-APF method whch s merely to ensure a constant DC voltage of the actve damper. It s worthy to menton that the resonance detecton plays (a) (b) Fg. 14. Two control block dagrams for realzng the proposed actve damper functon. (a) R-APF method. (b) Drect voltage compensaton scheme. an mportant role n the above two control schemes. A couple of research works have been reported on the dentfyng the resonance frequences [17] [18]. To reduce the computaton tme the resonant controller wth a wde band can be used to extract or compensate the resonant voltage components. B. Stablzng Effect of Actve Damper To see the stablzng effect of the proposed actve damper the mnor-loop gan s evaluated wth the dampng resstance provded by the actve damper. In lght of the analyss result n Fg. 9 the wde band-pass flter wth the center frequency at 174 Hz and a bandwdth of 1 Hz s used to synthesze the dampng resstance. As a consequence the actve damper can be represented n the frequency-doman as follow R s R c de dref s cs (11)
7 where R de and R dref are the effectve and referenced dampng resstance provded by the actve damper respectvely. ω and ω c denote the center frequency and the bandwdth of the bandpass flter respectvely. Fg. 15 depcts the Nyqust plots for the mnor-loop gans wth the dfferent dampng resstances of the actve damper. It s shown that for the unstable case of parallel actve rectfers (L S = 1. mh) the system s stablzed wth the decrease of the dampng resstance. Also the frequency responses of Y oc and Y to are shown n Fg. 16 from whch t can be seen that the ntersecton ponts between the two admttances dsappear when R dref s equal to 5 Ω. IV. SIMULATION AND EXPERIMENTAL RESULTS To further valdate the performance of the proposed actve damper the tme-doman smulatons and laboratory tests are performed on three grd-connected converters. Two converters are used to buld the parallel actve rectfers shown n Fg.6 and the last converter s controlled as the actve damper. Table III gves the man parameters of the actve damper. A. Smulaton Results Correspondng to the smulated currents shown n Fg. 11 and Fg.1 the stablzng performances of the actve damper are evaluated n the cases of sngle actve rectfer and parallel actve rectfers respectvely. The drect voltage compensaton scheme s tested. Fg. 17 shows the smulated PCC voltage and current for the unstable case of sngle actve rectfer (L S =.6 mh) before and after applyng the proposed actve damper. In ths case the actve damper s enabled at the tme nstant of.4 s. It s obvous that the resonance resultng from the grd mpedance varaton s damped by the actve damper. Fg. 18 shows the smulated currents for the unstable case of parallel actve rectfers (L S =1. mh) after usng the actve damper. Compared to Fg. 11 t can be seen that the mutual nteractons between the two actve rectfers are stablzed by the actve damper. The change of the PCC voltage when the actve damper s appled at the nstant of.4 s s shown n Fg.9. An effectve resonance dampng on the PCC voltage can be observed. In ths case the output current of the actve damper and the assocated harmonc spectra are depcted n Fg.. It can be TABLE III. MAIN PARAMERRES OF ACTIVE DAMPER Parameters Values Flter nductance L fd 3 mh DC capactor C dcd 66 μf Swtchng frequency f sw khz Samplng perod T S s DC voltage V dcd 7 V PR current controller K p_ 3 K r_ 6 DC voltage controller K p_dcd.5 K _dcd.5 Resonant controllers K r_v ω r 35π rad/s Imagnary Axs Rdref= ohm Rdref=1 ohm Rdref=5 ohm Real Axs Fg. 15. Nyqust plots of the mnor-loop gans wth the dfferent dampng resstances of the actve damper. Magntude (db) Phase (deg) Yoc Yto (Rdref= ohm) Yto (Rdref=1 ohm) Yto (Rdref=5 ohm) Frequency (Hz) Fg. 16. Frequency responses of the nput admttance of one rectfer and the total sum of the other admttances consderng the effect of the actve damper. Voltage (V) Current (A) Fg. 17. Smulated PCC voltage and current for the unstable case of sngle actve rectfer (L S=.6 mh) before and after applyng the actve damper. seen that the fundamental frequency current s low due to the absence of the energy storage element n the DC sde whle the resonant current components are relatvely large compared to the fundamental frequency current. Ths fact mples that the actve damper has to absorb a certan amount of resonance currents for stablzng the parallel actve rectfers.
8 Fg. 18. Smulated currents for the unstable case of parallel actve rectfers (L S =1. mh) after usng the actve damper. Fg. 1. Measured PCC voltage waveform wthout applyng the actve damper (1 V/dv 4 ms/dv). Fg. 19. The change of the PCC voltage when the actve damper s appled at the tme nstant.4 s. Current waveform Fg.. Harmonc spectra of the measured voltage wthout applyng the actve damper ( V RMS /dv 15 Hz/dv). (a) Harmonc spectra (b) Fg.. Smulated current of the actve damper and the assocated harmonc spectra. (a) Current waveform. (b) Harmonc spectra. B. Expermental Results In the laboratory test setup three parallel grd-connected Danfoss converters are used to buld the power electroncsbased system shown n Fg. 1 as well as the proposed actve damper. The control systems are mplemented n the DS16 dspace system where the DS511 dgtal waveform output board s used to generate the swtchng pulses. Fg. 1 depcts the tested PCC voltage waveform wthout applyng the proposed actve damper and Fg. gves the harmonc spectra of the measured PCC voltage waveform. It s clearly shown that a low-order harmonc resonance (65 Hz) s rased n ths case. Also the tested output currents of the two actve rectfers are shown n Fg. 3. It can be observed that the same low-order harmonc resonance components arse n the output currents. Fg. 3. Measured output current waveforms of the parallel actve rectfers wthout applyng the actve damper. ( A/dv 4 ms/dv). Ths fact s due to the use of the twelfth harmonc resonant current controller n the synchronous frame for the harmonc current compensaton. In the case of sngle actve rectfer ths harmonc resonant current controller works well. However when the two actve rectfers are connectng n parallel the measured current waveforms ndcate that the phase margns of the current control loops are reduced because of the mutual nteractons between the two rectfers. Fg. 4 shows the measured PCC voltage waveform after applyng the actve damper. It s evdent that the harmonc resonance s effectvely damped by the actve damper. Fg. 5 shows the measured output currents of the parallel actve rectfers. It can be seen that the low-order harmonc currents
9 shown and have confrmed the stablzng performance of the proposed actve damper. Fg. 4. Measured PCC voltage waveform after applyng the actve damper (1 V/dv 4 ms/dv) Fg. 5. Measured output current waveforms of the parallel actve rectfers after applyng the actve damper. ( A/dv 4 ms/dv) are compensated by usng the harmonc resonant controllers. It valdates that the proposed actve damper can help to stablze the mutual nteractons between the current control loops of the parallel grd-connected converters. V. CONCLUSIONS Ths paper has dscussed the resonance propagaton n the multple parallel grd-connected converters. An actve damper for stablzng the power electroncs-based AC systems has been proposed. Although a number of actve stablzaton methods have been reported n prevous work most of them are embedded n the control systems of the converters. As a consequence the performances of those approaches are ether lmted by the characterstcs of converters or senstve to the system condtons whch may cause addtonal resonances. In contrast the proposed actve damper ams to provde a versatle devce that can be plug-and-play for the dfferent applcatons. Furthermore n comparson to the conventonal actve power flters the actve damper only takes effect for the resonance dampng whch allows a low-power hgh control bandwdth desgn. Two control optons for realzng the actve damper functon have been dscussed. Notce that the drect voltage compensaton scheme can perform the same functon as the resstve-actve power flter method by choosng the gans of the resonant controllers based on the desred dampng resstances. Smulatons and expermental results have been REFERENCES [1] F. Blaabjerg Z. Chen and S. B. Kjaer Power electroncs as effcent nterface n dspersed power generaton systems IEEE Trans. Power Electron. vol. 19 pp Sep. 4. [] J. Rocabert A. Luna F. Blaabjerg and P. Rodrguez Control of power converters n AC mcrogrds IEEE Trans. Power Electron. vol. 7 pp Nov. 1. [3] P. Brogan The stablty of multple hgh power actve front end voltage sourced converters when connected to wnd farm collector system n Proc. EPE 1 pp [4] J. Agorreta M. Borrega J. Lopez and L. Marroyo Modelng and control of N-paralleled grd-connected nverters wth LCL flter coupled due to grd mpedance n PV plants IEEE Trans. Power Electron. vol. 6 pp Mar. 11. [5] E. Mollerstedt and B. Bernhardsson Out of control because of harmoncs An analyss of the harmonc response of an nverter locomotve IEEE Control Sys. Mag. vol. pp Aug.. [6] X. Lu M. Lserre K. Sun F. Blaabjerg R. Teodorescu and L. Huang Resonance propagaton of parallel-operated DC-AC converters wth LCL flters n Proc. IEEE APEC 1 pp [7] R. Turner S. Walton and R. Duke Stablty and bandwdth mplcatons of dgtally controlled grd-connected parallel nverters IEEE Trans. Ind. Electron. vol. 57 pp Nov. 1. [8] F. Wang J. L. Duarte M. A. M. Hendrx and P. F. Rbero Modelng and analyss of grd harmonc dstorton mpat of aggeragated DG nverters IEEE Trans. Power Electron. vol. 6 pp Mar. 11. [9] J. Sun Small-sgnal methods for AC dstrbuted power systems a revew IEEE Trans. Power Electron. vol. 4 pp Nov. 9. [1] R. D. Mddlebrook V. Vorperan and L. Lndal The N extra element theorem IEEE Trans. Crcuts Syst. I: Fundam. Theory Appl. vol. 45 pp Sep [11] L. Harnefors M. Bongorno and S. Lundberg Input-admttance calculaton and shapng for controlled voltage-source converters IEEE Trans. Ind. Electron. vol. 54 pp Dec. 7. [1] J. He Y. W. L D. Bosnjak and B. Harrs Investgaton and actve dampng of multple resonances n a parallel-nverter-based mcrogrd IEEE Trans. Power Electron. vol. 8 pp Jan. 13. [13] X. Wang F. Blaabjerg and Z. Chen Synthess of varable harmonc mpedance n nverter-nterfaced dstrbuted generaton unt for harmonc dampng througout a dstrbuton network IEEE Trans. Ind. Appl. vol. 48 pp Jul./Aug. 1. [14] J. Sun Impedance-based stablty crteron for grd-connected covnerters IEEE Trans. Power Electron. vol. 6 pp Nov. 11. [15] J. Yn S. Duan and B. Lu Stablty analyss of grd-connected nverter wth LCL flter adoptng a dgtal sngle-loop controller wth nherent dampng characterstc IEEE Trans. Ind. Inform. Early Access Artcles. [16] H. Akag H. Fujta and K. Wada A shunt actve flter based on votlage detecton for harmonc termnaton of a radal power dstrbuton lne IEEE Trans. Ind. Appl. vol. 35 pp May/Jun [17] L. Asmnoae R. Teodorescu F. Blaabjerg and U. Borup A dgtal controlled PV-nverter wth grd mpedance estmaton for ENS detecton IEEE Trans. Power Electron. vol. pp Nov. 5. [18] X. Zhou J. Fan and A. Q. Huang Hgh-frequency resonance mtgaton for plug-n hybrd electrc vehcles ntegraton wth a wde range of grd condtons IEEE Trans. Power Electron. vol. 7 pp Nov. 1.
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