Fault-Current Study of the Wind-Turbine-Driven Doubly-Fed Induction Generator with the Crowbar Protection Xiangping Kong, Zhe Zhang State Key Laboratory ofAdvanced Electromagnetic Engineering and Technology (Huazhong University of Science and Technology), Wuhan 430074, Hubei, China Email: kongxphust@163.com Abstract. The crowbar protection is commonly used for wind turbines with a doubly-fed induction generator (DFIG) to enhance the low-voltage ride-through capability of the wind turbines. Thus, the fault-current characteristics of DFIG with the crowbar protection under symmetric- and asymmetric-fault states are studied in this paper. Firstly, a DFIG dynamic model in the stator stationary reference frame is developed and the dynamic characteristics of DFIG stator flux linkage are studied when the crowbar protection is activated. Based on it, the DFIG fault-current characteristics under symmetric- and asymmetric-fault states are analyzed and analytical expressions are obtained. Finally, the simulation results show that the accuracy of the theoretical analysis results is satisfactory to meet the requirements of the study of the relay-protection principle and calculation. Keywords: doubly-fed induction generator (DFIG), crowbar protection, stator flux linkage, fault-current characteristics Zaščita delovanja vetrnih elektrarn z dvojno napajanim asinhronskim generatorjem ob kratkostičnih motnjah Najpogostejši način zaščite vetrnih elektrarn z dvojno napajanim asinhronskim generatorjem ob kratkostičnih motnjah v sistemu je zaščita pretvornika v rotorskem tokokrogu s premostitvenim uporom in polprevodniškim stikalom (angl. crowbar). V članku analiziramo kratkostično tokovno karakteristiko vetrnih elektrarn ob simetričnih in nesimetričnih motnjah. V ta namen najprej razvijemo dinamični model dvojno napajanega asinhronskega generatorja v statorskem referenčnem koordinatnem sistemu, na podlagi katerega analiziramo dinamično obnašanje statorskih magnetnih sklepov ob aktivaciji zaščite. Nato razvijemo ustrezne analitične izraze, ki služijo podrobni analizi obnašanja vetrnih elektrarn ob simetričnih in nesimetričnih motnjah v sistemu. Na koncu podamo še simulacijske rezultate, ki kažejo ustrezno obnašanje in zadostujejo kriterijem nastavitve zaščit. 1 Introduction Recently, as the most commercialized one of the renewable energy sources, the wind-power generation has been developed greatly all over the world. The most common type of the wind turbine which has been widely applied is the doubly-fed induction generator (DFIG), since it has the advantages of a small capacity of the converter, high energy-conversion efficiency and flexible power control [1-3]. DFIG comprises a wound-rotor induction generator with its stator windings connected to the power grid directly and rotor windings interfaced to the power grid with an AC/DC/AC converter. The AC/DC/AC converter consists of a rotorside converter (RSC) and a grid-side converter (GSC) connected back-to-back by a dc-link capacitor. However, with the increasing grid-connected windpower capacity, in order to ensure safe operation of the power gird and wind turbines, the power system operators have issued new grid codes to require the wind turbines to have the low-voltage ride-through (LVRT) capability [4]-[6]. In order to enhance the LVRT capability and ensure safe DFIG operation during a grid fault, one commonly used approach is to install the crowbar protection [7]. When the power-grid fault makes the rotor current too large or the dc-link voltage too high, the crowbar protection is activated to short-circuit the rotor windings with the crowbar resistance and divert the current from RSC. Activation of the crowbar protection causes the loss of the excitation current and consequently makes DFIG change from the generator to the motor. Meanwhile, introduction of the crowbar resistance makes the coupling between the stator and the rotor windings increase significantly. Hence, the DFIG operating characteristics are much different not only from those of the synchronous generator, but also from those of the induction motor. Moreover, the DFIG operating characteristics under the LVRT state considerably affect the characteristics of the fault voltage and fault current, which causes many Received 9 January 2014 Accepted 27 February 2014 new challenges to the traditional relay protection of the power grid [8]. Hence, in order to address the relay protection issues and ensure the safe operation of the power grid with DFIGs, the operating and the fault-current characteristics of DFIG under the LVRT state should be studied. So far, many scholars have carried out research works to study the DFIG fault-current characteristics under the three-phase short-circuit state [9-13]. However, the existing research results are either qualitative or obtained by the analogy with the fault-current characteristics of the conventional synchronous generator or induction motor. It means that the DFIG inherent features when the crowbar protection is activated are not taken into account. Furthermore, there is little literature discussing the DFIG fault-current characteristics under asymmetric-fault states. However, the possibility of the asymmetric-faults occurrence is much larger than the symmetric faults. The study of the DFIG fault-current characteristics under the asymmetric-fault states is the important part of the comprehensive analysis of the DFIG fault-current characteristics. In order to fill the gap, the DFIG fault current under the states of the symmetric and asymmetric faults is analyzed in this paper. During a grid fault, the fault current provided by DFIG consists of the stator-side fault current and the grid-side fault current of GSC. However, the fault current provided by GSC is very small, since the capacity of GSC is only 25-30% of the rated capacity of the wind turbine. Hence, only the stator fault current is taken into account in this paper. In Section II, a dynamic model of DFIG in the stator stationary reference frame is developed. In Section III, the dynamic characteristics of the stator flux linkage of DFIG are studied when the crowbar protection is activated and a simplified calculation model of the stator flux linkage is built. Then the DFIG fault-current characteristics under the states of symmetric and asymmetric faults are analyzed and the analytical expressions are obtained in Section IV. Finally, the simulation cases are studied in Section V to validate the theoretical analysis results. 2 DFIG Dynamic Model The generalized voltage and flux-linkage equations of DFIG are expressed in (1) and (2). It is noted that the motor convention is adopted both for the stator and rotor windings. (Us ' ( ** 0 IU J 0 v \Rr (L Y d +— dt v frn \ 1 s w. v r J Jr, v r l Y i Y sr 1 L W Y w ' j j v I J (1) (2) where Us, Ur, Is, Ir, Ws and Wr are the matrices of the voltage, current and flux linkage respectively of the stator and rotor windings. Since the mutual inductance matrix between the stator and rotor windings is time-varying, it is difficult to be solved. The method commonly used in the existing literatures is to perform a synchronous (i.e. dq ) coordinate transformation to (1) and (2). However, in this context, both the reference frame rotating at a positive synchronous speed and the reference frame rotating at a negative synchronous speed are needed under the asymmetric-fault states [14]. Meanwhile, the positive- and the negative-sequence components should be extracted. Hence, when an asymmetric-fault occurs, implementation of dq coordinate transformation would result in a severe complexity to the fault-current study of DFIG. Since the structure and electromagnetic property of the DFIG rotor windings are symmetrical, the stator stationary reference frame should be adopted for coordinate transformation to simplify the analysis. Under the stator stationary (i.e. a.p) reference frame, the DFIG voltage and flux-linkage equations are given in (3) and (4). (3) usa \RS ' ] ^sa dWsJ dt usp Rs\ hp + dyspl dt ura \R 'ra dWrJdt + ®rVrp urp _ [ ! R J }rP _ dVrpjdt -mrWra Wsa ~L_ Lm tsa Ws_p_ L_ Lm 's_ Wra Lm Lr tra Wr__ Lm Lr _ (4) where ar = (1 - s)a1 , representing the rotor angular speed; s is the slip and a1 is the synchronous angular frequency. Taking the stator flux linkage and rotor flux linkage as the state variables, the DFIG state equations are given by (5) Wsa Wsa usa d Ws_ = A Ws_ + us_ dt Wra Wra ura Wr_ _ Wr_ _ ur__ lsa Lr \ Lm Wsa ' s_ 1 Lr \ Lm Wi_ l ra = L -Lm \ 4 Wra h_ _ Lm i Ls _ Wr_ (6) where Lt = LL - L ~RsLr/Lt RsLJLt - RSLr/Lt RsLm 1 Lt RrLJLt - RrLjLt -®r RrLm /Lt ®r -RrLjLt A = As it is known, the damping time constants and oscillation frequencies of the stator flux- linkage and rotor flux linkage are determined by the eigenvalues of the system matrix A . Meanwhile, the damping time constants and oscillation frequencies of the transient components of the stator- and rotor-fault currents are also determined by the eigenvalues of the system matrix A . 3 Study of the Stator Flux Linkage 3.1 Characteristics analysis of the stator flux linkage In matrix A , the terms RsLmlLt and RrLm/Lt indicate the coupling between the stator flux linkage and rotor flux linkage. Under a normal operating state, since both the stator and rotor resistances are small, RsLm/Lt and RrLm/Lt are also very small. It means that the coupling between the stator flux linkage and rotor flux linkage can be neglected under a normal operating state. Hence, the matrix A can be rewritten as -RsLr/Lt A = (7) -RsLr/L, , - RrLJLt -Wr Wr -RrLJLt The eigenvalues of the matrix A are given by |Pl,2 = -VTAs ± jWAs = -RsLr/Lt l P3,4 = -V TAr ± jWAr = -RrLJ Lt ± JWr where tas is the damping time constant of the transient (8) components of the stator flux linkage, Mr is the results of the DFIG fault current based on the simplification that the impact of the stator and rotor resistances can be neglected [9] or by the analogy with the fault-current characteristics of the induction motor [10,11] cannot agree with the reality very well. Replacing Rr in (7) with R'r, a new system matrix Ac after activation of the crowbar protection can be obtained. The corresponding eigenvalues are expressed in (10). Pc1,2 = -VTAcs ± jWAcs , Pc3,4 = -1/TAcr ± jWAcr (10) Specifically for 1.5 MW-rated DFIG (the detailed parameters are given in Appendix A), Table 1 shows the impact of the crowbar resistance on the eigenvalues of matrix Ac . As seen from Table 1, though the crowbar resistance affects both the real and the imaginary parts of the eigenvalues of matrix Ac , the impact of the crowbar resistance on the imaginary part (i.e. oscillation frequencies of the transient components) is rather small. The maximum value of wAcs is 3.68rad/s and the minimum value of wAcr is 373.31 rad/s, hence, it can be approximately considered that WAcs ~ 0 , WAcr ~Wr (11) i.e., there are only an ac component with the frequency of wr and a dc component in the transient components of the stator and rotor fault currents. Table 1 .The eigenvalues of the system matrix Rc/Rr eigenvalues Pc1,2 Pc3,4 10 -8.39 ±j 1.31 -66.88 ±j375.68 20 -7.85±j2.34 -128.08±j374.66 40 -6.30±j3.55 -250.82±j373.44 80 -3.79±j3.68 -495.79±j373.31 120 -2.57±j3.08 -739.47±j373.61 160 -1.99±j2.54 -982.52±j374.45 damping time constant of the transient components of the rotor flux linkage, tas is the damping time constant of the transient components of the stator flux linkage and wAr is the oscillation frequency of the transient components of the rotor flux linkage. In this context, the stator flux linkage and rotor flux linkage can be studied according to two independent second-order systems. If a severe fault occurs near DFIG, the crowbar protection is activated to ensure safe DFIG operation. By introducing the crowbar resistance, the equivalent resistance of the rotor windings R'r is R'r= Rr + Rc (9) where Rc is the crowbar resistance. This makes the coupling between the stator flux linkage and rotor flux linkage increase significantly, which can no longer be neglected. Hence, the research By increasing the crowbar resistance, TAcs increases and TAcr decreases. It means that by increasing the crowbar resistance, the damping speed of the dc component in the stator fault current decreases and the damping speed of the ac component with the frequency of wr increases. Moreover, the damping speed of the ac component with frequency of wr is much larger than that of the dc component. Since the eigenvalues of matrix Ac are affected by the crowbar resistance, and the coupling between the stator flux linkage and rotor flux linkage cannot be neglected, the analysis of the stator flux linkage after the crowbar protection is activated is very complicated. Hence, it is necessary to establish a simplified calculation model of the stator flux linkage. 3.2 A Simplified calculation model of the DFIG stator flux linkage In order to analyze the DFIG stator flux linkage under any kind of fault states (including the asymmetric and symmetric faults), the DFIG stator voltage during a grid fault can be expressed as ''sa = Usa sm fat + «1) 'hb = Usb sin fat + «2 ) (12) Usc = Usc sm fat + «3 ) As noted, there are no special requirements on the amplitudes and phase angles of the three-phase voltages. Hence, (12) is the universal expression of the stator voltage that can be applied to any kind of the fault states. Performing coordinate transformation to (12), the stator voltage under the a/3 reference frame is given by \Us« = Usa Sin fat + 01) \Usp=~Usp C0S (fat + 02 ) where: Usa = ^Ua+USar/3, 0i = arctan (^/^«2), Usal = Usa Sin«1 ~Usb sina2/2 ~Usc Sin «3/2 , Usa2 = Usa CoS «1 ~Usb C0S «2/2 "Usc C0S «3 /2 , Us/ = + U/ )/3 , 0 = arctan (Us/llUs/2 ) , Us/1 = Usb COS «2 - Usc COS «3 , Us/2 = Usc Sin «3 " Usb Sin «2 . Though the equivalent resistance of the rotor windings is large at activation of the crowbar protection, the stator resistance is still very small and can be neglected. By substituting (13) to (3), the expressions of the stator flux linkage with no consideration of damping are given by Vaa (t) = + — COS 0i - Usa COS (fat + Ô! ) fa fa VSp (t) = + — sin Ô2--— Sm (faVt + Ô2 ) fa fa (14) Actually, the dc components in the stator flux linkage always decay with time due to the stator resistance. With consideration of damping, the expressions of the stator flux linkage can be rewritten as Vaa (t) = V—(t ) = V,a0 + —cos^ \e fa U. ,-t/ V—0- — fa sinÔ2 \e U fa U -cos (fat + Ô ) -t/h _ U — Sin (fat + 0) (15) In [9-11], it is assumed that the damping-time constant in (15) is the same as the equivalent-time constant of the stator windings, i.e. rs = Ltj(LrRs) . However, as stated in the previous sub-section, the dynamic characteristics of the stator flux linkage are very complicated after the crowbar protection is activated. Using the handling method for the damping-time constant given in [9-11] would result in a large error. Assuming rs = Ltj(LrRs) , Fig. 1 shows a comparison between the simulation and theoretical results of the stator flux linkage at a symmetric voltage dip. As shown in Fig. 1, using the handling method that makes the damping-time constant in (15) equal to the equivalent-time constant of stator windings would result in a larger error. Hence, employing the above handling method to calculate the damping time constant is not reasonable. Compromising between the accuracy and simplicity, rAcs is adopted as the damping-time constant of the transient components of the stator flux linkage. Fig. 2 demonstrates a comparison between the simulation result and the corresponding theoretical result of the stator flux linkage. "5.02 5.04 5.06 5.08 5.1 5.12 5.14 5.16 5.18 5.2 Time [s] Fig. 1 Stator winding flux for a conventional simplification ■-] -0.4 à a S-" -0.6 -0.8 1 -simulation result ..........theoretical result ^ A A - V \ \ \J w v V V * 5.02 5.04 5.06 5.08 5.1 5.12 5.14 5.16 5.18 5.2 Time [s] Fig. 2 Stator winding flux for the proposed simplification As shown in Fig. 2, due to the impact of the coupling between the stator flux linkage and rotor flux linkage, the dynamic characteristics of the stator flux linkage are very complicated and cannot be simply described by (15). However, using the handling method that equals damping-time constant in (15) with rAcs can assure a high accuracy in the first four cycles. It means that it is reasonable to employ the proposed handling method for the damping-time constant in the first four cycles. Moreover, the proposed handling method is of great significance for the calculation of the maximum value 0 -0.2 -0.4 -0.6 -0.8 0 -0.2 of the fault current and performance evaluation of a fast relaying protection. Furthermore, though introduction of the crowbar resistance makes the dynamic characteristics of the stator flux linkage very complicated, the steady-state features of the stator flux linkage are not affected by the crowbar resistance. It means that the steady-state components expressed in (15) are accurate. 4 Study of the DFIG Stator Fault Current 4.1 Characteristics analysis of the stator flux linkage The following equations can be obtained according to (4). | ira = ysalLm - LsisalLm ^^ \irp = WsfilLm - Ls'sp/Lm | yra = LrysalLm - LtisalLm ^^ [Vrp = LrVsp /Lm - Ltis^Lm After activation of the crowbar protection, the rotor voltage is zero, which means Ura= 0 , Urp = 0 (18) Substituting (16), (17) and (18) to the last two equations in (3), the following equations are obtained: 0 = R'rVaa + Lr dVaa /dt + CrLWsp -R'rLsisa - Lt disJdt - ®Msp .. i (19) 0 = KVsp + Lr dVsp/dt - ®rLrWsa , - R'rLshp - Lt disp /dt + arLt'sa Consequently, the expressions of the stator current are given by ha (t) = aa0e'tT' + ^ (aa1 sinart + aa2 ) + aa3 sin®jt + aa4 cos®1t isp (t) = ap0e-tT' + e-Tr (aB1 sin a>rt + ap2 cos a>rt) + ap3 sin a>1t + ap4cosa1t (20) where zr = L'r/ R'r , representing the equivalent damping-time constant of the rotor windings. The coefficients are given in Appendix B. The three-phase stator currents can be obtained by performing coordinate transformation to (20). As shown in Eq. (20), the dc components in the stator current maintain the stator flux linkage before and after activation of the crowbar protection. Likewise, in order to maintain the rotor flux linkage, there should be the dc components in the rotor current. In order to counteract the alternating flux linkage caused by the dc components in the rotor current, there are the ac components with the frequency of ar in the stator current, as shown in (20). Both the dc component and the ac component decay with time. Moreover, it can be seen that the ac damping component in the DFIG stator current is different from the damping component with the frequency of o\ in the stator current of the conventional synchronous generator. The initial values of the dc and the ac components are related to the fault-occurrence time, the voltage amplitude after the fault occurrence and the DFIG rotor speed. Besides for the damped ac component with the frequency of cor and damped dc component, there is also a steady-state component with the frequency of cc1 in the DFIG stator current. The amplitude of the steady-state component current is determined by the voltage amplitude after the fault occurrence and the DFIG rotor speed. Though the steady-state components in the DFIG stator current are obtained with the simplified calculation model of the stator flux linkage, they are very accurate, since the steady-state components of the stator flux linkage expressed in (15) are accurate as well. It means that the steady-state components of the stator current expressed in (20) can accurately reflect the steady-state features of the stator current under real fault states. 4.2 Case study In order to validate the above theoretical results, a DFIG simulation model is made in PSCAD/EMTDC. The DFIG parameters are given in Appendix A. The three-phase and two-phase voltage dips are used to implement the simulation case studies. Several simulation cases under different voltage dip depth states are studied. However, considering the manuscript length, only the cases where voltages drop to 0.2 p.u. are illustrated in this paper. It is noted that DFIG is in its rated operating state and the rotor speed is 1.2 p.u. before the fault occurrence. With the three-phase voltages all dropped to 0.2 p.u., Fig. 3 provides a comparison between the simulation and the theoretical results of the three-phase stator currents. With the voltages of phase B and phase C both dropped to 0.2 p.u., Fig. 4 shows a comparison between the simulation and the theoretical results of three-phase stator currents. As shown in Figs. 3 and 4, the theoretical result of the stator fault current obtained with the proposed simplified calculation model of the stator flux linkage agrees with the simulation result very well in the first two cycles after the fault occurrence. After the transient components in the stator fault current decay completely, the waveform of the steady-state components of the stator current obtained according to (20) exactly match the simulation waveform. Hence, the above theoretical results are validated. According to the requirements of the principle study and calculation of the relay protection, the maximum and the steady-state values of the fault current are very important parameters. As stated above, the accuracy of the analytical expressions of the DFIG stator current is rather high in the first two cycles after the fault occurrence and during the steady-state period. Moreover, the maximum value of the fault current usually occurs in the first cycle after the fault occurrence. This means that the calculation results of the maximum and the steady-state values of the fault current obtained with the simplified calculation model of the stator flux linkage are accurate enough for the relay protection study. Hence, the analytical expressions of the DFIG stator current given in (20) meet the requirements of principle study and calculation of relay protection. It should be noted that there are no approximation and assumption of the grid voltage made for the above theoretical analysis. Hence, the above theoretical analysis results can be applied for any kind of fault states. 3r 2 -7 !" à 0 ' - 3 2 7 1 0 ■J-1 i-2 5. 3 2 7 1 à o -2 - simulation result "theoretical result 5.06 6.56 6.57 6.58 6.59 - simulation result theoretical result 5.06 6.56 6.57 6.58 6.59 - simulation result theoretical result 5.03 5.04 5.07 5.08 5.1 6.66 6.67 6.68 6.69 6.7 - simulation result "theoretical result 5.07 5.08 5.1 6.66 6.67 6.68 6.69 6.7 simulation result theoretical result 5.07 5.08 5.09 5.1 6.66 6.67 6.68 6.69 6.7 Time [s] 5.05 5.06 6.56 6.57 6.58 6.59 6.6 Time [s] Fig. 3 Three-phase stator currents for the three-phase voltage dips 5 Conclusions In order to meet the needs of the DFIG fault-current analysis under any kind of fault states, a DFIG dynamic model in the stator stationary reference frame is developed. Based on it, the dynamic characteristics of the stator flux linkage and characteristics of the stator fault current are studied. Finally, the analytical expressions of the stator current are obtained. 1) Since introduction of the crowbar resistance significantly increases the coupling between the stator and the rotor flux linkage, the dynamic characteristics of the stator flux linkage are very complicated. The stator flux linkage in the first four cycles after the fault occurrence and during the steady-state period can be studied accurately with the proposed calculation model. 2) Using the proposed calculation model of the stator flux linkage provides analytical expressions for the DFIG stator current under any kind of fault states. The simulation results show that the accuracy of the analytical expressions is rather high in the first two cycles after the fault occurrence and during the steady-state period, thus meeting the requirements of the principle study and calculation of relay protection. Fig. 4 Three-phase stator currents for the two-phase voltage dips 3) Besides for the steady-state component with the frequency of o\ and the damped dc component, there is also the damped ac component with the frequency of cr in the DFIG stator current. It means that the DFIG fault-current characteristics differ from those of the conventional synchronous generator. The research results proposed in this paper are of great significance for setting an approximate relay protection system for the power grid with DFIG penetration. Acknowledgements This work was supported by the National Natural Science Foundation of China (Grant No. 51177058). Appendix A The parameters of DFIG are Rated capacity: 1.5 MVA Rated voltage: 690 V Stator resistance (p.u.): 0.00756 Stator leakage reactance (p.u.): 0.1425 Rotor resistance (p.u.): 0.00533 Rotor leakage reactance (p.u.):0.1425 Mutual reactance (p.u.): 2.1767 Rated rotor speed (p.u.):1.2 Appendix B Let t = L'r/R'r a = -y zr + V t U„ b = mr-m1 , c = mr + m1 , C1 =ysa0 +cos$ m C = U, L2 R ' U U C2 =^ , C3 =^0 sin $2 , C4 ^2 ' 4 m, m. C =- C =- 5 L2 ' b2 +1 rr2 ' 7 c2 +1 rr2 C _ HTV C _ CQ / o , Cû 8 b2 +1 Ty 9 c2 +1 Tr2' 06 5.09 -3 — 5.02 5.03 5.04 5.05 6.6 02 5.03 5.04 5.05 6.6 b c The coefficients in (17) are respectively « = C + — + CC m °a0 L m2 + a2 m2 + a2 °al C1C5 2 2 + C3C5 2 2 'spo T, m + o m + o L„ C C C C + -2^sm0i(C8 -C9) + -L-LCOs0i(C6 + C7) C C C C + 4—(C8 + C9) + ^cos^ (C6 -C7) a = -CC aa2 a a2 W1W5 2 . 2 cot + a 2 -cos ?1 (C8 + C9 )-% + C^sindl (C6 - C7 )-+ Co 2 m + a C C C C + CC-^sin^(C6 + C7)---5cos02(Cs -C9) C C C a*3 = "^7sin^1--y^cos01 (C6 - C7 ) C C C C - (C8 + C9) + --5sin02 (C9 -C8) cos62 (C6 + C7 ) C C C aaA = —^fcos^ + ^ 5 cos 6, ( C8 + C9 ) C C C4 C 5 L' 2 C C C C + C^sin01 (C7 -C6)-—-sin^ (C6 + C7) + C^cos^C, - C ) 2 C a = C1 + C C _ ap0 T! +C3C5 2 2 p L' m; + a - CC 5 2 2 m: + a Ci L' a„, =--— cos 6 - P3 r r 2 CC — sin 6 (C6 - C7 ) CC + _^±cos6 (Cs + C9) + -^cos6 (C8 -C9) Cn Cck 61 (C6 + C7 ) ap4 =-Cism^ + ^^ (C8 + Q) Ls 2 + QQco^2 (C6 -C7)+ C^L^ (Cfi + C7) + C^sin^1 (C8 -C9) where, , , ^0 and ^po are respectively the initial values of stator current and stator flux linkage under ap reference frame when the fault occurs. 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Xu, Coordinated control of DFIG's rotor and grid side converters during network unbalance, IEEE Transactions on Power Electronics, vol. 22, no. 3, pp. 1041-1049, 2008. Xiangping Kong is currently working towards his Ph.D. degree at Huazhong University of Science and Technology (HUST), Wuhan, China. His research interest is in protection of the power grid with penetration of distributed generators. Zhe Zhang received his Ph.D. degree in electrical engineering from HUST, Wuhan, China, in 1992. Currently, he is a professor at the School of Electrical and Electronic Engineering, HUST. His interest is in protective relaying. 0 m 2