Impact of phase-locked loop on stability of active damped LCL-filter-based grid-connected inverters with capacitor voltage feedback

Transcription

1 J. Mod. Power Syt. Clean Energy (217) 5(4): DOI 1.17/ Impat of phae-loked loop on tablty of atve damped LCL-flter-baed grd-onneted nverter wth apator voltage feedbak Xaoqang GUO 1, Shhao LIU 2, Xaoyu WANG 3 Abtrat Atve damped LCL-flter-baed nverter have been wdely ued for grd-onneted dtrbuted generaton (DG) ytem. In weak grd, however, the phae-loked loop (PLL) dynam may detrmentally affet the tablty of grd-onneted nverter due to nteraton between the PLL and the ontroller. In order to olve the problem, the mpat of PLL dynam on mall-gnal tablty nvetgated for the atve damped LCL-fltered grd-onneted nverter wth apator voltage feedbak. The ytem loed-loop tranfer funton etablhed baed on the Norton equvalent model by takng the PLL dynam nto aount. Ung an etablhed model, the ytem tablty boundary dentfed from the vewpont of PLL bandwdth and urrent regulator gan. The auray of the range of tablty for the PLL bandwdth and urrent regulator gan verfed by both mulaton and expermental reult. CroChek date: 23 May 217 Reeved: 17 January 217 / Aepted: 23 May 217 / Publhed onlne: 8 July 217 Ó The Author() 217. Th artle an open ae publaton & Xaoqang GUO gxq@yu.edu.n Shhao LIU lu@bjtu.edu.n Xaoyu WANG xaoyuw@doe.arleton.a Department of Eletral Engneerng, Yanhan Unverty, Qnhuangdao, Chna Shool of Mehanal, Eletron, and Control Engneerng, Bejng Jaotong Unverty, Bejng, Chna Department of Eletron, Carleton Unverty, Ottawa, ON K1S 5B6, Canada Keyword Phae-loked loop, Small-gnal tablty, Grd-onneted nverter, Atve dampng, LCL flter, Tranfer funton 1 Introduton LCL-flter-baed grd-onneted nverter have been wdely dued n [1 4]. One of the mportant ue ther tablty. Ref. [5] propoed a robut pave dampng method for LLCL-flter-baed grd-onneted nverter, o a to mnmze the effet of harmon voltage on the grd. Another nteretng flter wa propoed n [6] for optmzng the ytem performane and tablty. A reent revew of pave flter for grd-onneted onverter wa preented n [7], and dfferent pave dampng method were dued. In order to avod the loe reultng from pave dampng, apator-urrent feedbak atve dampng wa propoed n [8] to enhane the tablty of LCL-type grd-onneted nverter. Ref. [9] preented an nteretng atve dampng method that an handle tablty wth only grd-urrent feedbak ontrol. In [1], a vrtual RC dampng method wa preented wth extended eletve harmon ompenaton. Note that thee oluton are for voltage-oure nverter. In prate, there are alo urrentoure nverter [11 13]. An nteretng atve dampng oluton wa preented n [14]. However, whle the above method are nghtful for tablty analy, the mpat of phae-loked loop (PLL) dynam on the tablty of grdonneted nverter ha been negleted. The PLL ued to trak the phae angle of the voltage at the pont of ommon ouplng (PCC) and thu to aheve grd ynhronzaton for the nverter [15]. In ae of hgh grd mpedane, t ha been found that the tablty of a voltage oure onverter (VSC) an be affeted by PLL parameter [16, 17]. In

2 Impat of phae-loked loop on tablty of atve damped LCL-flter-baed grd-onneted 575 VSC-baed hgh voltage dret urrent (HVDC) tranmon ytem, the PLL parameter have been found to lmt the maxmum power tranfer apablty [18]. In [19], the mpat of hort-rut rato and phae-loked-loop parameter on mall-gnal behavor nvetgated, However, t only take L-flter-baed nverter nto aount. In ummary, thee early work have dued the nfluene of PLL parameter on the ytem tablty. However, they only foued on grd-onneted nverter ytem wth L or LC flter. In fat, an LCL flter preferred n grd-onneted nverter, due to t better hgher frequeny attenuaton and redued phyal ze of the ndutor [2]. In prate, the LCL flter uually uffer from reonane problem, whh reult n ytem ntablty. In order to deal wth the problem, atve dampng ontroller have been ued [21]. Under weak grd ondton, the urrent regulator and the PLL dynam of the atve damped nverter may nterat a the grd urrent pae the grd mpedane, epeally n ae of a hgh bandwdth PLL. In fat, fat grd ynhronzaton and PLL mportant for operatng the grd-onneted nverter. Inreang PLL bandwdth helpful for the fat and aurate grd ynhronzaton. The PLL bandwdth hould be large enough for the fat grd ynhronzaton, and th why dvere PLL degn have been propoed, a hown n [22 28]. However, when the PLL bandwdth nreaed beyond a ertan lmt, the ytem may beome untable due to reonane between the nverter and the weak grd. Therefore, the nteraton between fat PLL dynam and urrent regulaton deerve further nvetgaton. The objetve of th paper to ontrbute both analytal and expermental verfaton on the nteraton of PLL dynam and urrent regulaton n three-phae grdonneted atve damped nverter wth LCL flter under weak grd ondton. Ung the Norton Theorem, a loedloop tranfer funton etablhed to model the whole grd-onneted nverter ytem nludng the PLL dynam. By analyzng the pole of the loed-loop tranfer funton, the range of tablty of the PLL bandwdth and the urrent regulator gan are obtaned. Both a mulaton and expermental reult from a three-phae grd-onneted nverter are provded to verfy the effetvene of the propoed model. The remander of th paper organzed a follow. In Set. 2, a mall-gnal model etablhed for the three-phae grd-onneted LCL-flter-baed nverter wth apator voltage feedbak and atve dampng. In Set. 3, the mall-gnal tablty of the nverter dued n term of the PLL dynam and the urrent regulator. In Set. 4, the analytal reult are verfed through mulaton and expermental tet. Fnally, onluon are preented n Set Inverter ytem model Fgure 1 how the truture of a typal three-phae grd-onneted nverter ytem. S 1 * S 6 are the wthe; L 1 the nverter-de flter ndutane; C the flter apatane; L 2 the grd-de flter ndutane; L g the grd lne ndutane; V Ca, V Cb, V C are the apator voltage n the grd frame ab ; I ga, I gb, I g are the grd urrent n the grd frame ab. In the grd dq frame, h 1 the PLL output phae angle; x 1 the angular frequeny; V C, I g, I L, V PCC, V g are the voltage vetor at the flter apator, grd urrent vetor, nverter-de flter urrent vetor, voltage vetor at the pont of ommon ouplng, and voltage vetor of the grdde voltage oure, repetvely. In the nverter dq frame, the PLL output phae angle denoted a h, whh almot the ame a h 1 n teady-tate ondton. Other varable n the nverter dq frame are labeled wth a uperrpt, when referred n the grd dq frame. A urrent referene are ontant, n both dq frame, they are denoted a I ref. Let V C denote the apatane voltage n the ab frame. V C ¼ e jh 1 V C when t n the grd dq frame, and V C = e jh V C n the nverter dq frame. Then, the followng relatonhp obtaned: VC ¼ e jdh V C ð1þ Dh ¼ h h 1 where Dh the phae angle dfferene n thee two dq frame and approxmately equal to zero when the grdonneted nverter operate n teady tate. The PLL dynam, however, make Dh depart from zero. Conequently, t mportant to nvetgate the mpat of the PLL on the dynam tablty of the grd-onneted nverter under weak grd ondton. DC power upply S 1 S 3 S 5 L 1 S 4 S 6 S 2 I qref C V Ca V Cb V C F PWM F PLL F θ I ga ab dq I gb PI dq ab I g I dref L 2 PCC L g ~ ~ ~ Fg. 1 Struture of a three-phae grd-onneted nverter ytem

3 576 Xaoqang GUO et al. 2.1 Current regulaton wth atve dampng A hown n Fg. 2, the urrent regulator for the nverter ytem nlude a PI regulator and an atve dampng ontroller, whoe tranfer funton F(). Note that an atve damped LCL flter nreae the ytem omplexty whle nreang the tablty of the nverter. Pave dampng an alo be ued, but t nur addtonal power loe. Therefore, n th paper, atve dampng ued due to avod thee power loe, and t baed on apator voltage feedbak, where the apator voltage dfferentated by and multpled by a gan K before beng fed bak to the urrent regulator output. The tranfer funton F ðþ KC. In prate, the dfferental term may reult n a hghfrequeny dturbane. To avod th problem, a partally dfferentaton ued n the form þ1, where a tme ontant parameter. It loe to a dfferental element when very mall. Th gve the atve dampng ontroller a tranfer funton of the form F ðþ¼ K C þ1. The nverter output voltage derbed a follow: V PWM ðþ¼ I ref ðþ I g ðþ k p þ k þ F ðþv C ðþ Vd 2 From Fg. 2, the ytem varable relatonhp an be derbed by the followng open-loop tranfer funton [29]: I L ðþ¼h 1ðÞV PWM ðþþh 2 ðþv PCC ðþ I g ðþ¼h 3ðÞV PWM ðþþh 4 ðþv PCC ðþ ð2þ V C ðþ¼h 5ðÞV PWM ðþþh 6 ðþv PCC ðþ where the tranfer funton H 1 () * H 6 () are L 2 C 2 þ 1 H 1 ðþ¼ L 1 L 2 C 3 þ ðl 1 þ L 2 Þ ; H 1 2ðÞ¼ L 1 L 2 C 3 þ ðl 1 þ L 2 Þ ; 1 H 3 ðþ¼ L 1 L 2 C 3 þ ðl 1 þ L 2 Þ ; H L 1 C 2 þ 1 4ðÞ¼ L 1 L 2 C 3 þ ðl 1 þ L 2 Þ ; L 2 H 5 ðþ¼ L 1 L 2 C 3 þ ðl 1 þ L 2 Þ ; H L 1 6ðÞ¼ L 1 L 2 C 3 þ ðl 1 þ L 2 Þ : Baed on the above equaton, the grd urrent an be obtaned a: I g ðþ¼g TðÞI ref ðþ Y ðþv C ðþ ð3þ I g ðþ¼ g tðþ I g t ðþ ref ðþ y ðþ y ðþ fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} G T ðþ Y ðþ V C ðþ where g t () and y () an be expreed a: 8 V d k p þ k H3 H 6 V d k p þ k H4 H 5 >< g t ¼ 2H 6 þ V d k p þ k H3 H 6 V d k p þ k H4 H 5 V d FðÞH 4 H 5 2H 4 V d FðÞH 3 H 6 >: y ¼ 2H 6 þ V d k p þ k H3 H 6 V d k p þ k H4 H 5 ð4þ ð5þ The mall-gnal tranfer funton an be expreed a: DI g ¼ y ðþ DV y ðþ C ð6þ fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} Y ðþ where DI g a grd urrent dturbane and DV C a apator voltage dturbane n the nverter dq frame. 2.2 Small-gnal model of PLL dynam Fgure 3 llutrate the PLL loed-loop ontrol ytem ued n the three-phae grd-onneted nverter. A PI regulator ued to enable the q-ax element of the apator voltage to follow the zero nput referene V q *, whle V Ca,V Cb,V C are the PLL nput; x the bae phae angular veloty; f and h are the PLL output frequeny and phae angle, repetvely. The output of the PI regulator V * q = Fg. 3 PLL ytem Flter PI V Ca VCb V C VCq VCd dq ab ω αβ αβ 1/2π 1 Ollator f θ whh n vetor matrx form : Z L1 () V PCC () I gref PI /2 V d V PWM F() G v () VC I g () V C () I g G T ()I ref () Z eq () V C () I g () Z g () V g () Fg. 2 Struture of nverter urrent regulator Fg. 4 Equvalent Norton model of nverter ytem

4 Impat of phae-loked loop on tablty of atve damped LCL-flter-baed grd-onneted 577 Imagnary ax Imagnary ax Real ax (a) Root lou Real ax (a) Root lou Imagnary ax 5-5 Imagnary ax Real ax (b) Detal near the orgn Real ax (b) Detal near the orgn Fg. 5 Root lou of the ytem a PLL bandwdth hange the ntantaneou angular veloty dturbane Dx n the followng form: Dx ¼ k ppll þ k PLL Im V C ð7þ fflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflffl} F PLL ðþ where k ppll and k PLL are the proportonal and ntegral gan of the PI regulator, repetvely. It an be nterpreted from Fg. 3 that, by ntegratng Dx? x, the followng relatonhp obtaned, where F PLL ðþ defned n (7): dh dt ¼ x þ Dx ¼ x þ F PLL ðþim V C ð8þ Baed on (1), the apator voltage an be wrtten a Fg. 6 Root lou of the ytem a urrent regulator gan hange V C ¼ e jdh V C ð1 jdhþ VC þ DV C ¼ VC þ DV C jdhvc ð9þ ) Im V C ¼ Im f DVC g DhVC where V C the teady-tate apator voltage and DV C the apator voltage dturbane. The apator voltage dturbane n the nverter dq frame DV C : DV C ¼ DV C jdhvc ¼ DV C jvc G PLLðÞIm fdv C g ð1þ where G PLL () gven n the followng equaton: F PLL ðþ Dh ¼ þ VC F ImfDV C g ð11þ PLLðÞ fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} G PLL ðþ

5 578 Xaoqang GUO et al. The vetor matrx form of DV C DV C ¼ 1 1 VC G DV PLLðÞ C Smlarly, the grd urrent dturbane DI g expreed a follow: ð12þ an be DI g ¼ DI g jdhig ¼ DI g jig G PLLðÞIm fdv C g ð13þ where I g the teady-tate value of the grd urrent and DI g the urrent dturbane n the grd dq frame. The vetor matrx form of (13) an be wrtten a: DI g ¼ DI g I ref G PLL ðþ DV C ð14þ Wth (12), (13) and (14), the nverter nput mpedane Z eq an be obtaned: 1¼ Z eq ¼ DV C DI g I ref G PLL ðþ þ y ð15þ ðþ 1 y ðþ 1 VC G PLLðÞ Then wth (14) and (15), the grd urrent an be expreed a I g ðþ¼g T ðþi ref ðþ Z eq ðþ 1 V C ðþ ð16þ Table 2 Control parameter Varable Value Varable Value f 5 Hz f wth 1 khz T 5 l I gref 5A k 1 K k p.1 3 Small gnal tablty analy In general, a weak grd ondton mean the grd ha a hgh mpedane. In th eton, a mall gnal tablty analy arred out for the grd-onneted nverter ytem wth hgh grd mpedane. More pefally, the range of the PLL bandwdth and the urrent regulator gan k p requred to keep the nverter ytem table are nvetgated. It hould be noted that optmzed degn of the urrent regulator and the PLL gan beyond the ope of th paper. 3.1 Impat of PLL bandwdth When the urrent regulator gan k p =.1 and the PLL regulator gan k ppll vared wthn the range from 2 to 22, The equvalent Norton model of the nverter ytem hown n Fg. 4. In Fg. 4, Z L1 () denote the grd-de flter ndutane and Z g () denote the grd lne mpedane: 8 Z L1 ðþ¼ 1=L 2 >< 1=L 2 Z g ðþ¼ L ð17þ g >: L g The fnal tranfer funton of the loed-loop ytem an be obtaned from Fg. 4 a follow: Ig (A) I ga Igb I g.1 t () (a) Introde the atve dampng funton.15 GðÞ¼V PCC ðþi ½ ref ðþ Z L1 þ Z g Zeq Z eq ¼ G T þ V g ði ref Z eq þ Z L1 þ Z g Z eq þ Z L1 þ Z g Š 1 Þ 1 ð18þ Ig (A) 5 I g I ga I gb Table 1 Sytem parameter Varable Value Per unt Varable Value Per unt V d 2 V 1 p.u. V g 8 V 1 p.u. L mh.5 L g 6.5 mh.12 L 1 3 mh.6 C 9.4 lf t () (b) Remove the atve dampng funton.15 Fg. 7 Smulated nput urrent waveform n the grd-onneted nverter

6 Impat of phae-loked loop on tablty of atve damped LCL-flter-baed grd-onneted 579 beome le table a the PLL bandwdth nreae. Therefore, under weak grd ondton, a relatvely mall PLL bandwdth hould be hoen to enure ytem tablty for the nverter. 3.2 Impat of urrent regulator gan When the PLL bandwdth fxed at 5 Hz and the urrent regulator gan kp vared wthn the range from to.1, the root lo of the loed-loop tranfer funton (18) are hown n Fg. 6. The arrow ndate the dreton of dereang gan, and the ntereton wth the vertal ax at kp =.4. A an be een from th fgure, the pole of the loed-loop ytem are all n the left half de of the omplex plane, and the ytem table when kp greater than.4. It an be oberved that, when the PLL bandwdth ontant, the ytem tend to be le table a the urrent regulator gan dereae. Fg. 8 Smulated dynam of Ig and VPCC when PLL bandwdth 3 Hz 4 Smulaton and expermental verfaton Baed on the reult of the mall-gnal tablty analy, t an be een that the PLL dynam may gnfantly affet the nverter ytem tablty under weak grd ondton. In th eton, tme-doman mulaton and expermental tet are onduted to verfy the theoretal reult. Parameter of a three-phae grd-onneted nverter ytem wth the truture hown n Fg. 1 are lted n Table 1 and Smulaton reult In order to verfy the effetvene of the atve dampng ontroller, the followng two tet ae were mulated wth amplng perod T = 5 l and wth ntegral gan of the PI-type urrent regulator k = 1: Fg. 9 Smulated dynam of Ig and VPCC when PLL bandwdth 125 Hz the root lo of the loed-loop tranfer funton (18) are hown n Fg. 5. The arrow ndate the dreton of nreang PLL bandwdth, and the ntereton wth the vertal ax at kppll = 12. A an be een from the root lo, the pole of the loed-loop ytem are all n the left half de of the omplex plane, and the ytem table, when kppll wthn the range from 2 to 12 (equally, the PLL bandwdth le than 9 Hz). It hould be noted that when the urrent regulator gan fxed, the ytem tend to Cae 1 The nverter ntally only equpped wth a PItype urrent regulator, then the atve dampng funton added at t =.5. Cae 2 The nverter ntally ntalled wth a PI-type urrent regulator and the atve dampng funton, then the dampng funton removed at t =.1. A hown n Fg. 7, the ytem beome table a oon a the atve dampng funton added, and t beome untable after the atve dampng funton removed. To evaluate the mpat of the PLL bandwdth, wth a fxed urrent regulator gan kp =.1, the mulaton were onduted wth PLL bandwdth of 3 Hz and 125 Hz. The

7 Xaoqang GUO et al. (5 A/dv), V (1 V/dv) 58 VPCC La ga Tme (1 m/dv) Fg. 1 Smulated dynam of Ig and VPCC when kp =.1 (5 A/dv), V (1 V/dv) (a) Cae 1 VPCC La ga Tme (1 m/dv) (b) Cae 2 Fg. 13 Expermental waveform for the grd-onneted nverter Fg. 11 Smulated dynam of Ig and VPCC when kp =.2 Fg. 14 Expermental waveform when the PLL bandwdth 3 Hz and the urrent regulator gan kp =.1 PCC Lg DC power upply L1 L2 C Fg. 12 Shemat dagram of the expermental etup reultng dynam of grd urrent Ig and voltage at PCC VPCC are hown n Fg. 8 and 9 repetvely. In Fg. 8, when the PLL bandwdth 3 Hz, the nverter table and the ollaton of Ig and VPCC are mall. However, n Fg. 9, when the PLL bandwdth nreaed to 125 Hz, the dynam of both Ig and VPCC dverge and the ytem beome untable. Baed on thee mulaton reult, for a gven urrent regulator gan, t an be een that the tablty margn of the nverter ytem bgger when the PLL bandwdth maller. Th onluon verfe the reult of the mall-gnal analy. To evaluate the effet of the urrent regulator gan, keepng the PLL bandwdth fxed at 5 Hz, the mulaton

8 Impat of phae-loked loop on tablty of atve damped LCL-flter-baed grd-onneted 581 were onduted wth k p =.1 and k p =.2. The reultng dynam of grd urrent I g and voltage at PCC V PCC are hown n Fg. 1 and 11 repetvely. The grd-onneted nverter ytem table when k p =.1, a hown n Fg. 1. However, the dynam of both I g and V PCC dverge and the grd-onneted nverter ytem beome untable when k p =.2, a hown n Fg. 11. The onluon agan verfe the reult of the mall-gnal analy. Thee obervaton alo ndate that the nverter ytem may beome untable when the PLL bandwdth beyond t table range, even when the urrent regulaton gan wthn t table range. Therefore, t mportant to take the PLL dynam nto aount. reult verfy the effetvene of atve dampng regardng the reonane whh reult from the LCL flter. The nteraton between the PLL dynam and the urrent regulator wa alo expermentally teted. Frt of all, the urrent regulator gan wa fxed a k p =.1, and expermental tet were arred out wth the PLL bandwdth et to 3 Hz and 125 Hz. The reult are hown n Fg. 14 and 15 repetvely. It an be oberved that the waveform of V PCC, I g, and L are table when the PLL bandwdth 3 Hz. However, when the PLL bandwdth 4.2 Expermental reult A 3 kva expermental platform ytem wa bult to further verfy the mpat of the PLL dynam and the urrent regulator. The hemat dagram of the expermental etup hown n Fg. 12. The nverter ontrolled by a 32-bt fxed-pont 15 MHz TMS32F2812 DSP. The ytem parameter are the ame a thoe mulated above, lted n Table 1 and 2. The effetvene of the atve dampng ontroller wa verfed ung two tet ae mlar to thoe mulated, a follow: Cae 1 The nverter ytem ntally only equpped wth a PI type urrent regulator, then the atve dampng funton added at t =.23. Cae 2 The nverter ytem ntally ntalled wth a PI type urrent regulator and the atve dampng funton, then the dampng funton removed at t =.25. A hown n Fg. 13, the ytem beome table a oon a the atve dampng funton added, and t beome untable after the dampng funton removed. Thee Fg. 16 Expermental waveform when hangng the PLL bandwdth Fg. 15 Expermental waveform when the PLL bandwdth 125 Hz and the urrent regulator gan k p =.1 Fg. 17 Expermental waveform when the urrent regulator gan k p =.1 and the PLL bandwdth 5 Hz

9 582 Xaoqang GUO et al. 125 Hz, V PCC, I g, and L tart dvergng and operate untably. Th ontent wth the theoretal analy and mulaton reult that, for a fxed urrent regulator gan, the ytem more table wth a maller PLL bandwdth. The ame good agreement wth theory wa oberved (5 A/dv), V (1 V/dv) La ga V PCC when the PLL bandwdth wa hanged onlne, a hown n Fg. 16. Seondly, the PLL bandwdth wa fxed at 5 Hz, and expermental tet were arred out wth the urrent regulator gan et to k p =.1 and k p =.2. The reult are hown n Fg. 17 and 18 repetvely. It an be oberved from Fg. 17 that the waveform of V PCC, I g, and L are table when k p =.1. However, the ytem beome untable when k p =.2, wth V PCC, I g, and L dvergng and howng rregular behavor. Th ontent wth the theoretal analy and mulaton reult that, when the PLL bandwdth fxed, the ytem more table for a larger urrent regulator gan. When the urrent regulator gan wa hanged onlne, a hown n Fg. 19, the ame good agreement wth theory wa oberved. Tme (1 m/dv) Fg. 18 Expermental waveform when the urrent regulator gan k p =.2 and the PLL bandwdth 5 Hz 5 Conluon In th paper, the nteraton of phae-loked loop (PLL) dynam and the urrent regulator on ytem tablty ha been nvetgated for atve damped LCL-flter-baed grdonneted nverter wth apator voltage feedbak under weak grd ondton. To effently model the ytem nludng the PLL dynam, an equvalent Norton model wa appled to obtan the loed-loop tranfer funton of the whole ytem. By nvetgatng the pole of the tranfer funton, t ha been found that the ytem tend to be ntable a the PLL bandwdth nreae wth a fxed urrent regulator gan. Alo, when the PLL bandwdth fxed, the ytem tend to be ntable a the urrent regulator gan dereae. The range of tablty of the PLL bandwdth and the urrent regulator gan have been dentfed. The effetvene of the degned atve dampng ontrol method ha been verfed by both mulaton and expermental reult ung a three-phae grd-onneted nverter ytem. Future reearh an nlude tablty analy wth a low amplng frequeny under dfferent ontrol and operatng mode. Aknowledgement Th work wa upported by Sene Foundaton for Dtnguhed Young Sholar of Hebe Provne (No. E ) and Hundred Exellent Innovaton Talent Support Program of Hebe Provne (No. SLRC21759). Fg. 19 Expermental waveform when hangng the urrent regulator gan k p Open Ae Th artle dtrbuted under the term of the Creatve Common Attrbuton 4. Internatonal Lene ( reatveommon.org/lene/by/4./), whh permt unretrted ue, dtrbuton, and reproduton n any medum, provded you gve approprate redt to the orgnal author() and the oure, provde a lnk to the Creatve Common lene, and ndate f hange were made.

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IEEE Tran Power Eletron 28(1): Xaoqang GUO reeved the B.S. and Ph.D. degree n Eletral Engneerng from Yanhan Unverty, Qnhuangdao, Chna, n 23 and 29, repetvely. He ha been a Potdotoral Fellow wth the Laboratory for Eletral Drve Applaton and Reearh (LEDAR), Ryeron Unverty, Toronto, ON, Canada. He urrently an aoate profeor wth the Department of Eletral Engneerng, Yanhan Unverty, Chna. H urrent reearh nteret nlude hgh-power onverter and a drve, eletr vehle hargng taton, and renewable energy power onveron ytem. Shhao LIU reeved the B.S. and M.S. degree from Harbn Engneerng Unverty, Harbn, Chna, n 27 and 21, repetvely, and the Ph.D. degree from Carleton Unverty, Ottawa, ON, Canada, n 214. H reearh nteret nlude networked ontrol ytem, energy management, and optmzaton of mrogrd. Xaoyu WANG reeved the B.S. and M.S. degree from Tnghua Unverty, Bejng, Chna, n 2 and 23, repetvely, and the Ph.D. degree from the Unverty of Alberta, Edmonton, AB, Canada, n 28. He urrently an Aoate Profeor wth the Department of Eletron, Faulty of Engneerng and Degn, Carleton Unverty, Ottawa, ON, Canada. H reearh nteret nlude the ntegraton of dtrbuted energy reoure and power qualty.