Optimum Design of Power Converter Current Controllers in Large-Scale Power Electronics Based Power Systems

Transcription

1 Aalborg Unverstet Optmum Desgn of Power Converter Current Controllers n Large-Scale Power Electroncs Based Power Systems Ebrahmzadeh, Esmael; Blåbjerg, Frede; Wang, Xongfe; Bak, Claus Leth Publshed n: I E E E DOI (lnk to publcaton from Publsher): /TIA Publcaton date: 2018 Document Verson Accepted author manuscrpt, peer revewed verson Lnk to publcaton from Aalborg Unversty Ctaton for publshed verson (APA): Ebrahmzadeh, E., Blaabjerg, F., Wang, X., & Bak, C. L. (Accepted/In press). Optmum Desgn of Power Converter Current Controllers n Large-Scale Power Electroncs Based Power Systems. I E E E Transactons on Industry Applcatons. 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 reurements 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.

2 Optmum Desgn of Power Converter Current Controllers n Large-Scale Power Electroncs Based Power Systems Esmael Ebrahmzadeh Member, IEEE Department of Energy Technology Aalborg Unversty ebb@et.aau.dk Frede Blaabjerg Fellow, IEEE Department of Energy Technology Aalborg Unversty fbl@et.aau.dk Xongfe Wang Senor Member, IEEE Department of Energy Technology Aalborg Unversty xwa@et.aau.dk Claus Leth Bak Senor Member, IEEE Department of Energy Technology Aalborg Unversty clb@et.aau.dk Abstract In a large-scale power electronc system lke a wnd farm, the mutual nteractons between the power converter controllers and passve components may lead to nstablty problems or undesred dynamc response. Ths paper presents an optmum parameter desgn procedure for the power converter controllers n a power electronc system n order to guarantee a stable operaton and to guarantee an acceptable dynamc response. In the approach, frst, all oscllatory modes are calculated by a Mult-Input Mult-Output (MIMO) transfer functon matrx of the power system; then, a mult-objectve optmzaton procedure based on the Genetc Algorthm (GA) s presented to place the modes n the desred locatons n order to ncrease the stablty margn and to mprove the dynamc response. Tme-doman smulatons of a 400-MW wnd farm n the PSCAD/EMT envronment confrms the effectveness of the presented desgn approach. Keywords power electronc system, grd-connected converters, stablty, dynamc response, desgn, optmzaton, dampng I. INTRODUCTION The fast growth of renewable energy sources, HV systems, varable-speed drvers, etc., has brought concerns about the stable and relable operaton of the future power system [1]-[6]. A power electronc system contanng many power converters may show an undesred dynamc behavor or even an unstable operaton, whle the ndvdual power converters show an acceptable dynamc characterstc for a strong grd. Recently, Transmsson System Operators (TSOs) n dfferent countres have reported a few tmes that they could not connect a wnd farm to the grd because of harmoncfreuency oscllatons [7]. In such cases, ndvdual wnd turbnes have already passed dfferent tests but the whole wnd farm does not show a stable operaton. The dynamc oscllatons above the fundamental freuency are manly comng from the mutual nteractons between the hgh-bandwdth controllers and the passve components of the system [8], [9]. Therefore, ths paper presents a method for desgnng the power converters to reduce the electrcal oscllatons by consderng some nformaton of the power system. There are two general approaches to analyze a power electronc system: One s the non-lnear tme-doman smulaton analyss, whch s accurate n a wde freuency range but has hgh computatonal burden. The second approach s the lnearzed freuency-doman analyss, whch s accurate n the ntended freuency range and has low computatonal burden [10], [11]. Optmzaton of a large-scale power electronc system n the tme-doman s complex because of too hgh computatonal burden. So far, freuency-doman analyss based on the state-space modelng has been done n varous power electronc systems lke mcrogrds, current source converters, and parallel voltage source nverters [12]- [16]. However, the state-space modelng can be complex for large-scale power electronc systems because t needs the nformaton of each component of the system n detals [17]- [21]. Another tool, for dynamc analyss of the system n the freuency-doman, s the mpedance based modelng [22]-[27]. In ths method, the source output mpedance (Z s ) and the load nput mpedance (Z l) are obtaned and then the nterconnected system stablty s assessed by the Nyust crteron of the rato of Z l(s)/z s(s) [22]- [27]. Therefore, t can just dentfy f the system s stable and can not dentfy how much the stablty margn s. So, the mpedance-based analyss can not be used as a powerful desgn tool for a large number of power converters n a large-scale power electronc system. In order to reduce the electrcal oscllatons and to mprove the dynamc response n a large power electronc system, ths paper presents a freuency-doman based optmum desgn method, whch s smple and has low computatonal burden. The proposed optmzed desgn approach s solved by usng Genetc Algorthm (GA) and ts objectve functon s to ncrease the stablty margn and to mprove the dynamc response. A large-scale power electroncs based system s ntroduced as a Mult-Input Mult-Output (MIMO) transfer functon matrx, whch s smpler than state-space modelng. The dynamc analyss, the dampng and freuences of oscllatory modes are dentfed based on the determnant of the MIMO matrx. In Secton II, a grd-connected power electronc converter s modeled by a Norton euvalent crcut,.e., a current source wth a parallel actve admttance. In Secton III, a large power electronc system s modeled by a MIMO transfer functon matrx. The proposed optmzed parameter desgn s explaned n Secton IV, where the oscllatory modes of the system are placed n desred locatons. In Secton IV, a 400-MW wnd farm s consdered as a case study. In Secton V, the proposed optmum desgn s tested by tme-doman smulatons of the 400-MW wnd farm studed usng the PSCAD/EMT Ths work was supported by European Research Councl (ERC) under the European Unon s Seventh Framework Program (FP/ )/ERC Grant Agreement no. [ Harmony].

3 2 envronment software. II. ADMITTANCE MODEL OF GRID-CONNECTED CONVERTER A smple block-dagram of a grd-connected converter wth an nner control loop s shown n Fg. 1(a), where G cont-k s the current controller, and G delay-k s the delay of the dgtal control mplementaton. Fg. 1(b) shows the block-dagram of the current closed-loop control system, where the PoC voltage (V PoC-k) and the current reference (I ref-k) are the nputs and the grd current (I g-k) s the output. From Fg. 1(b), the grd current can be obtaned from Igk Gc k Iref k Yc kvpoc k (1) where G c-k and Y c-k are T Y ck Lf Gc k, Yc k 1T 1T ck k ck T c-k and Y Lf-k are 1 Tc k Gcont kgdelaykylf k, YLf k (3) sl f k Based on Euaton (1), a grd-connected converter can be modeled by an deal current source along wth a parallel actve admttance (Norton euvalent crcut) as shown n Fg. 1(c). Ths paper focuses on optmum desgn of the current controller, whch s fast and a hgh-bandwdth controller. Therefore, the outer power controllers and grd synchronzaton loops are neglected as they are too slow to have nfluence on current controller dynamcs. In ths paper, G cont-k s consdered to be a Proportonal plus Resonant (PR) current controller and G delay-k s modeled by Pade approxmaton,.e., Kks Gcont k Kpk 2 2 s f 1.5 Ts k (1.5 Ts k ) 2 1 s s (4) 1.5Ts ks G () 2 12 delayk s e Tsk (1.5 Ts k ) 2 1 s s 2 12 where ω f s the fundamental freuency and T s-k s the samplng perod of the dgtal control. 2 (2) (a) grd-connected converter wth the nner control loop (b) closed-loop control of grd current (c) Norton euvalent of the converter Fg. 1. Grd-connected converter wth the nner control loop and ts euvalent crcut. III. A POWER ELECTRONIC SYSTEM AS A MULTI-INPUT MULTI- OUTPUT (MIMO) TRANSFER FUNCTION MATRIX By modelng of every passve element and actve element (power electronc converters) as Norton euvalent crcut, the current-voltage relatonshps n a power electronc system can be obtaned by the nodal admttance matrx as gven n (5). In (5), t s assumed that bus 1 s connected to the electrcal grd and bus 2 to bus n+1 are connected to the power electronc converters. Y c-k (k=1,2,,n), Y,Y j(s) (,j=1,2,,m, and j) are the actve admttance of the k th power electronc converter, the connected admttance to the th bus, the admttance between th bus and j th bus, respectvely. When a component model s black-box, ts euvalent admttance can be obtaned by Y11 Y12 Y13 Y1( n1) Y1( n2) Y 1m 1 V Y21 Y22 Yc 1 Y23 Y2( n1) Y2( n2) Y 2m V2 Y31 Y32 Y33 Yc 2 Y3( n1) Y3( n2) Y 3m V3 I g I c1 Ic2 I Y Y Y Y Y Y Y V cn 0 ( 2)1 ( 2)2 ( 2)3 ( 2)( 1) ( 2)( 2) ( 2) ( 1) Y n Y n Y n Y n n Y n n Y V n m n 0 Ym1 Ym 2 Ym 3 Ymn Ym ( n2) Ymm Vm ( n1)1 ( n1)2 ( n1)3 ( n1)( n1) ( 1)( 2) ( 1) n (5) c n n n n m

4 3 experment (f the component has been bult) or by numercal smulatons (f the component has been desgned but has not been bult yet). Euaton (5) s actually a Mult-Input Mult- Output (MIMO) transfer functon matrx [28], where the outputs are the bus voltages and the nputs are the njected currents,.e, -1 V(s) = G(s) I(s) (6) The poles of the ntroduced MIMO transfer functon can be calculated by solvng the followng euaton: det G(s) 0 p j, p j,, p j where the freuency (f ) and the dampng rato (ζ ) of the poles can be obtaned from f (8) The poles of the MIMO transfer functon matrx bascally are the poles of ts elements,.e, Ps () Gj () s ( s p )( s p ) ( s p ) 1 2 A1 A A 2 ( s p1) ( s p2) ( s p ) (7) (9) Fg. 2. Step response of a smple second-order system for dfferent dampng ratos. The nverse Laplace transform of G j(s) s j p t p t 1 2 G t A e A e A e 1 2 () t j t t j t 1 2 pt A e e A e e A e e t jt (10) Therefore, the poles of G j(s) n the s-doman are related to the oscllatons of the system n the tme-doman. The magnary parts of the poles dentfy the freuences of oscllatons and the real parts dentfy the dampng of the oscllatons. If α (one of the real parts) s postve, the term t jt e A e s a functon wth an ncreasng exponental magntude and the system s unstable. If α s negatve, the term t jt e A e value of zero. s a decayng exponental functon wth a fnal WT MW TSC-1 GSC-1 WT-1 current 690V:33kV Bus-2 33-kV cable L f C f CB-1 T 1 Bus-6 Bus-10 33kV/33kV/150kV WT MW TSC-2 GSC-2 WT-2 current 690V:33kV 33-kV cable Bus-3 L f C f CB-2 T 1 Bus-7 Bus-11 T 2 Bus kV cable PCC voltage 150kV:400kV R g L g 100 MW WT MW WT-4 TSC-3 TSC-4 GSC-3 GSC-4 WT-3 current 690V:33kV 33-kV cable Bus-16 Bus-4 L f C f CB-3 WT-4 current 690V:33kV 33-kV cable Bus-5 L f C f CB-4 T 1 T kV cable Bus-8 Bus-12 33kV/33kV/150kV Bus-9 Bus-13 T 2 Bus-15 T 3 Bus-1 Grd current V g Thevenn s Euvalent of Grd Fg MW wnd farm, whch s studed for the proposed optmum controller desgn method.

5 4 IV. PROPOSED OPTIMUM DESIGN OF CURRENT CONTROLLER A. Guaranteeng stablty Accordng to the prevous dscusson, a power electroncs based system s stable f and only f all ts poles (P 1, P 2,, and P ) have negatve real parts. The mode wth the largest real part can be found by P j Max(,,, ) c c c c 1 2 (11) If P c has a negatve real part, t means that the real parts of all modes are negatve. Therefore, n order to guarantee the stablty, an neualty constrant, H(x), s consdered n GA algorthm to set the real part of P c smaller than zero. The threshold value for stablty s zero mathematcally. However, because of the round-off errors of floatng-pont computatons and the grd varatons, the threshold value should be consdered a value larger than zero to be robust. So, t s consdered to be ten here.,.e., 10 H ( x) 0 c (12) where x, optmzaton varable, can be a vector ncludng the current controller and flter parameters of the grd-connected converter. x [ K, K, L, C ] p f f (13) The optmum parameter vector (x) ncludes the flter parameters to have more freedom degrees and to optmze the system deally. In a case, f the flter parameters can not be redesgned, the vector ncludes only the controller parameters. In ths case, there are less freedom degrees for the optmzaton and may not optmze the system deally. 6.7 MW WT-1A WT-1A WT-1A WT-1B WT-1B WT-1B WT-1C WT-1C WT-1C WT-1D WT-1D WT-1D WT-1E WT-1E WT-1E ZAB, BAB ZBC, BBC ZCD, BCD ZDE, BDE ZET, BET 95-mm 2 Cable 240-mm 2 Cable 400-mm 2 Cable WT-1 Feeder Fg. 4. Ffteen wnd turbnes, whch are located on each 100-MW strng of the wnd farm shown n Fg. 3. WT-1ABCDE WT-1ABCDE WT-1ABCDE 33.3 MW 33.3 MW 33.3 MW ZAT, BAT ZAT, BAT ZAT, BAT WT-1 Feeder 33 kv Collector Bus WT MW Z 33, B kv Collector Bus WT-1 Feeder 33 kv Collector Bus B. Guaranteeng the desred dynamc performance Fg. 2 shows the step response of a smple second-order system for dfferent dampng ratos, whch s used as an example for evaluatng the dynamc response of a system. Fg. 2 shows that the amount of overshoot depends on the dampng rato. The system wth a smaller dampng rato reaches the fnal value faster, but the response oscllates around ths fnal value. A system wth a dampng rato around 0.8 can be a good tradeoff between the speed and oscllaton of the response as shown n Fg. 2. In a power electroncs based systems, low-freuency modes are related to the power converter controllers and the hghfreuency modes are more related to the cables and transformers. As the swtchng freuency (f s) s consdered to be 2.5 khz, the maxmum logcal bandwdth for the current controller would be around 500 Hz (f s/5) [29]. Therefore, In order to guarantee the desred dynamc performance of the power converters n a power electronc system, an objectve functon s consdered to set the dampng ratos of all lowfreuency modes close to 0.8; n fact, the objectve functon s to mnmze F(x) as descrbed n (14). F( x) Max 0.8, 0.8,, j j, f f 500 Hz, j 1,2,..., n j j h j j n (14) (a) Fg. 5. Aggregated model of the ffteen wnd turbnes shown n Fg. 4, (a) aggregated model on each feeder, (b) aggregated model of three feeders. V. A 400-MW WIND FARM AS A CASE STUDY The effectveness of the proposed optmzed desgn approach s studed for a 400-MW wnd farm wth 100-MW aggregated strngs, as shown n Fg. 3. Ffteen Wnd Turbnes (WTs) of 6.7 MW are located on three parallel feeders as shown n Fg. 4. Under the nomnal operaton, the current on the feeder s ncreasng towards the collector bus as the number of the WTs s also ncreasng. Therefore, a closer cable to the collector bus should have larger cross-secton than a farther cable. Conseuently, three dfferent cables (95 mm 2 cable, 240 mm 2 cable, and 400 mm 2 cable) carry the feeder current. Fve WTs of 6.7-MW on each feeder can be aggregated by one 33-MW WT as shown n Fg. 5(a). If t s assumed that the njected power by the WTs on the feeder are the same, the euvalent mpedance parameters of the 33-MW WT can be calculated by Z 4Z 9Z 16Z 25Z Z AT 25 B B B B B B AB BC CD DE ET AT AB BC CD DE ET (15) where, Z AT and B AT are the euvalent seres mpedance and the euvalent shunt susceptance, respectvely. Z AB, Z BC, Z CD, (b)

6 5 Fg. 7. Mode dampng ratos of the ndvdual WT and the wnd farm for the stand-alone desgn, and for the optmum desgn. Fg. 6. Step-response of the desgned GSC for a strong grd. Table I. Parameters of the 400-MW wnd farm and Genetc Algorthm (GA) Solver Parameter Value Transformer T 1 Leakage nductance µh Shunt capactance 3.24 µf Cable 33-kv Seres nductance mh Seres resstance Ω Transformer T 2 Leakage nductance mh Shunt capactance 0.26 µf/km Cable 150-kv ( Cable length = Seres nductance 0.5 mh/km 10 km) Seres resstance Ω/km Transformer T 3 Leakage nductance mh Grd X/R rato 20 SCR 100 Kp 2.5e-3 Current controller K 2 Genetc Algorthm (GA) Solver fs 2.5 khz Populaton Sze 40 Generatons 160 Stall Generatons 80 Functon Tolerance Z DE, and Z ET are the seres mpedances of the sectons and B AB, B BC, B CD, B DE, and B ET are the shunt susceptances (see Fg. 4). Fnally, the aggregated 33.3-MW WTs on three parallel feeders can be aggregated as one 100-MW WT (see Fg. 5(b)). The euvalent seres mpedance and shunt susceptance can be calculated by Z AT Z33 B33 3BAT (16) 3 Snce the dc-lnk s almost constant, the dynamcs of the Turbne-Sde Converters (TSCs) can be neglected. A smple Thévenn euvalent voltage source s used to represent the grd. The transformers are modeled by ts short-crcut mpedances and the cables are modeled by the nomnal π- model. The parameters of the wnd farm are gven n Table I. Short Crcut Rato (SCR) s defned by 2 Vg SCR (17) ZS g base (a) (b) Fg. 8. Dynamc response of GSC. GSC parameters are changed from the optmum desgn to the ntal desgn at t = 0.5 s and the dynamc response of the optmum desgn s also tested at t = 0.4 s, (a) PCC voltage and grd current, (b) FFT analyss of PCC voltage between t = 0.52s to t = 0.54s. Where V g and Z g are the grd voltage and the grd mpedance, and S base s the apparent power njected by the wnd farm. For large X/R rato, Z g = X g = ω 0L g. More detaled nformaton about the model can be found n [29]. The current controller and flter parameters of the Grd-Sde Converters (GSCs) are

7 6 (a) (b) Fg. 9. Robustness of the optmum desgn case (SCR = 100 and Cable length = 10 km) aganst varatons, (a) SCR = 100 (optmzed case) s changed to SCR =50 and SCR =200, (b) Cable length = 10 km (optmzed case) s changed to Cable length = 1 km and Cable length = 15 km. desgned for a desred phase-margn of 45 for stand-alone operaton. Fg. 6 shows the step-response of the GSC for a strong grd, where a desred dynamc response can be observed. The same controllers are used for all GSCs. VI. PROPOSED OPTIMUM DESIGN IN FREQUENCY-DOMAIN AND CORRESPONDING TIME-DOMAIN SIMULATIONS A. Optmum desgn Fg. 7 shows the mode dampng ratos of the ndvdual WT and the wnd farm for the stand-alone desgn (ntal desgn). The dampng ratos of the modes of the wnd farm for the optmzed parameters (Kp = 9.51e-3, K = 4.16, and fres = 357 Hz) are also shown n Fg. 7. As t can be seen, the dampng ratos of the ndvdual WT for the stand-alone desgn s around 0.8, whch confrms that the ndvdual WT for a strong grd has a good stablty margn and an acceptable dynamc response. However, when all WTs are connected to the wnd farm, the dampng ratos for low-freuency modes are too small and the dampng rato for freuency around 900 Hz s negatve, whch shows that the wnd farm s unstable around ths freuency. Therefore, t s necessary to redesgn the controller parameters to mprove the stablty margn and to guarantee a desred dynamc response. As shown n Fg. 7, after settng the GSC parameters based on the proposed optmum desgn procedure, all modes have postve dampng, whch confrms that the wnd farm has a stable operaton. In addton, the low-freuency modes, whch s related to the power converter dynamcs, have sutable dampngs around 0.8, whch depcts that the wnd farm has a desred dynamc performance for the optmum desgn. Fg. 10. Robustness of the optmum desgn. The GSC parameters are optmzed and set for SCR = 100 and Cable length = 10 km but the wnd farm s smulated for another case,.e., SCR = 50 and Cable length = 15 km. At t = 0.5, the GSC parameters are changed to the ntal desgn In Fg. 8, the wnd farm s smulated n the tme-doman usng PSCAD software, where the current controller parameters of the GSCs have been set by the proposed optmum desgn (before t = 0.5 s). At t = 0.4 s, the current reference s changed from 0.25 p.u. to 1 p.u. As t can be seen, the wnd farm has a good dynamc response and a stable operaton for the optmzed parameters. At t = 0.5, the GSC parameters are changed from the optmum desgn to the ntal desgn. As shown n Fg. 8,

8 7 some oscllatons around 900 Hz propagate nto the wnd farm, because of the nstablty problems as predcted n Fg. 7 n the freuency-doman. Therefore, t can be concluded that a good control desgn for an ndvdual power converter cannot guarantee the stable operaton of the whole power electroncs based system as shown n Fg. 8. B. Senstvty analyss wth respect to system varatons In ths secton, the robustness of the optmum desgn case (SCR = 100 and Cable length = 10 km) aganst varatons of the wnd farm s studed. Fg. 9(a) shows the mode dampng ratos of the wnd farm, where SCR = 100 (optmzed case) s changed to SCR =50 and SCR =200. Fg. 9(b) shows the mode dampng ratos, where Cable length = 10 km (optmzed case) s changed to Cable length = 1 km and Cable length = 15 km. As t can be seen, the dampng ratos of modes, partcularly low-freuency modes, are not affected a lot aganst such varatons. The hgh freuency poles are related to the resonance modes resultng from the capactance and the nductance of the cables. By ncreasng the cable length, the capactance and the nductance of the cable ncrease and the resonance freuency decreases. The dampng of these poles s corresponded to the resstance of the cable. As ths resstance s very small, the dampng of these poles s small. In order to confrm the robustness of the optmzed desgn, the tme-doman smulatons have also been performed. Frst, the GSC parameters are optmzed and set for SCR = 100 and Cable length = 10 km. However, the wnd farm s smulated for another SCR and cable lengths,.e., SCR = 50 and Cable length = 15 km. At t = 0.5, the parameters are changed to the ntal desgn. As t can be seen from Fg. 10, the wnd farm wth the optmum controller desgn presents a robust and stable operaton. However, after t = 0.5, the wnd farm wth the ntal parameters s unstable and harmonc-freuency oscllatons propagate nto the grd. VII. CONCLUSION Ths paper presents a mult-objectve desgn procedure for the power converter controllers n order to ncrease the stablty margn n a power electroncs based system. A power electronc system s ntroduced as a Mult-Input Mult-Output (MIMO) transfer functon matrx and the oscllatory modes are dentfed by the determnant of the MIMO matrx. The proposed algorthm put the modes n the desred locatons to mprove the dynamc response of the system. A 400-MW wnd farm s studed as a power electroncs based system for the proposed optmum desgn procedure. Tme-doman smulatons confrm that a good desgn for an ndvdual converter under strong grd cannot guarantee a stable operaton of the whole power electronc system ncludng many other converters and passve components. On the other hand, the proposed desgn technue s a powerful tool to analyze and to mprove the dynamc performance of a large-scale power electronc system lke a wnd farm. 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9 8 [20] L. P. Kunjumuhammed, B. C. Pal, C. Oates, and K. J. Dyke, Electrcal oscllatons n wnd farm systems: analyss and nsght based on detaled modelng, IEEE Trans. Sustan. Energy, vol. 7, no. 1, pp , Jan [21] E. Ebrahmzadeh, F. Blaabjerg, X. Wang, and C. L. Bak, Modelng and dentfcaton of harmonc nstablty problems n wnd farms, n Proc IEEE Energy Converson Congress and Expo. (ECCE), Mlwaukee, WI, pp. 1 [22] J. Sun, Impedance-based stablty crteron for grd-connected nverters, IEEE Trans. Power Electron., vol. 26, no. 11, pp , Nov [23] L. Harnefors, R. Fnger, X. Wang, H. Ba, and F. Blaabjerg, "VSC nputadmttance modelng and analyss above the nyust freuency for passvty-based stablty assessment," IEEE Trans. Ind. Electron., vol. 64, no. 8, pp , Aug [24] X. Wang, F. Blaabjerg, and W. Wu, Modellng and analyss of harmonc stablty n ac power-electroncs-based power system, IEEE Trans. Power Electron., vol. 29, no. 12, pp , Dec [25] M. Cespedes and J. Sun, Impedance modelng and analyss of grd connected voltage-source converters, IEEE Trans. Power Electron., vol. 29, no. 3, pp , Mar [26] X. Wang, L. Harnefors, and F. Blaabjerg, A unfed mpedance model of grd-connected voltage-source converters, IEEE Trans. Power Electron., 2017, early access, do: /TPEL [27] L. Xu, L. Fan and Z. Mao, " mpedance-model-based resonance analyss of a VSC HV system," IEEE Trans. Power Del., vol. 30, no. 3, pp , Jun [28] S. Skogestad and I. Postlethwate, Multvarable feedback control: analyss and desgn, New York: Wley, 2000 [29] S. K. Chaudhary, "Control and protecton of wnd power plants wth VSC-HV connecton," PhD Thess, Aalborg Unversty, Aalborg, Denmark, Esmael Ebrahmzadeh (S 16) receved the M.Sc. degree n Electrcal Engneerng from Unversty of Tehran, Tehran, Iran, where he has also been a lecturer for undergraduate courses. In 2015, he was employed as a PhD Fellow at the Department of Energy Technology, Aalborg Unversty, Aalborg, Denmark, where he s currently an Industral Postdoc. He has been a vstng R&D Engneer at Vestas Wnd Systems A/S, Aarhus, Denmark, n 2017, where he s currently workng as a R&D Control Engneer. Hs research nterests nclude modelng, desgn, and control of power-electronc converters n dfferent applcatons, as well as power ualty and stablty analyss n large wnd power plants. He s an IEEE member and receved the best paper awards at IEEE PEDG 2016 and IEEE PES GM Frede Blaabjerg (S 86 M 88 SM 97 F 03) was wth ABB- Scanda, Randers, Denmark, from 1987 to From 1988 to 1992, he got the PhD degree n Electrcal Engneerng at Aalborg Unversty n He became an Assstant Professor n 1992, an Assocate Professor n 1996, and a Full Professor of power electroncs and drves n From 2017 he became a Vllum Investgator. He s honors causa at Unversty Poltehnca Tmsoara (UPT), Romana and Tallnn Techncal Unversty (TTU) n Estona. Hs current research nterests nclude power electroncs and ts applcatons such as n wnd turbnes, PV systems, relablty, harmoncs and adjustable speed drves. He has publshed more than 600 journal papers n the felds of power electroncs and ts applcatons. He s the co-author of four monographs and edtor of ten books n power electroncs and ts applcatons. He has receved 29 IEEE Prze Paper Awards, the IEEE PELS Dstngushed Servce Award n 2009, the EPE-PEMC Councl Award n 2010, the IEEE Wllam E. Newell Power Electroncs Award 2014 and the Vllum Kann Rasmussen Research Award He was the Edtor-n-Chef of the IEEE TRANSTIONS ON POWER ELECTRONICS from 2006 to He has been Dstngushed Lecturer for the IEEE Power Electroncs Socety from 2005 to 2007 and for the IEEE Industry Applcatons Socety from 2010 to 2011 as well as 2017 to In 2018 he s Presdent Elect of IEEE Power Electroncs Socety. He serves as Vce-Presdent of the Dansh Academy of Techncal Scences. He s nomnated n 2014, 2015, 2016 and 2017 by Thomson Reuters to be between the most 250 cted researchers n Engneerng n the world. Xongfe Wang (S 10-M 13-SM 17) receved the B.S. degree from Yanshan Unversty, Qnhuangdao, Chna, n 2006, the M.S. degree from Harbn Insttute of Technology, Harbn, Chna, n 2008, both n electrcal engneerng, and the Ph.D. degree n energy technology from Aalborg Unversty, Aalborg, Denmark, n Snce 2009, he has been wth the Department of Energy Technology, Aalborg Unversty, where he s currently a Professor and Research Program Leader for Electronc Grd Infrastructure. Hs research nterests nclude modelng and control of grd-connected converters, harmoncs analyss and control, passve and actve flters, stablty of power electronc based power systems. Dr. Wang serves as an Assocate Edtor for the IEEE TRANSTIONS ON POWER ELECTRONICS, the IEEE TRANSTIONS ON INDUSTRY APPLICATIONS, and the IEEE JOURNAL OF EMERGING AND SELECTED TOPICS IN POWER ELECTRONICS. In 2016, he was selected nto Aalborg Unversty Strategc Talent Management Program for the next-generaton research leaders. He receved four IEEE prze paper awards, the outstandng revewer award of IEEE TRANSTIONS ON POWER ELECTRONICS n 2017, and the IEEE PELS Rchard M. Bass Outstandng Young Power Electroncs Engneer Award n Claus Leth Bak was born n Århus, Denmark, on Aprl 13th, He receved the B.Sc. wth honors n Electrcal Power Engneerng n 1992 and the M.Sc. n Electrcal Power Engneerng at the Department of Energy Technology at Aalborg Unversty n After hs studes he worked as a professonal engneer wth Electrc Power Transmsson and Substatons wth specalzatons wthn the area of Power System Protecton at the NV Net Transmsson System Operator. In 1999 he was employed as an Assstant Professor at the Department of Energy Technology, Aalborg Unversty, where he holds a Full Professor poston today. He receved the PhD degree n 2015 wth the thess

10 9 EHV/HV underground cables n the transmsson system. He has supervsed/co-supervsed +35 PhD s and +50 MSc theses. Hs man Research areas nclude Corona Phenomena on Overhead Lnes, Composte Transmsson Towers, Power System Modelng and Transent Smulatons, Underground Cable transmsson, Power System Harmoncs, Power System Protecton and HV-VSC Offshore Transmsson Networks. He s the author/coauthor of app. 310 publcatons. He s a member of Cgré SC C4 AG1 and SC B5 and charman of the Dansh Cgré Natonal Commttee (August 2018). He s an IEEE senor member (M 1999, SM 2007). He receved the DPSP 2014 best paper award and the PEDG 2016 best paper award. He serves as Head of the Energy Technology PhD program (+ 120 PhD s) and as Head of the Secton of Electrc Power Systems and Hgh Voltage and s a member of the PhD board at the Faculty of Engneerng and Scence.