VTPH30

3206 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 28, NO. 7, JULY 2013

DC-Voltage Fluctuation Elimination Througha DC-Capacitor Current Control for DFIG

Converters Under Unbalanced GridVoltage Conditions

Changjin Liu, Dehong Xu, Senior Member, IEEE, Nan Zhu, Frede Blaabjerg, Fellow, IEEE,and Min Chen, Member, IEEE

AbstractUnbalanced grid voltage causes a large second-orderharmonic current in the dc-link capacitors as well as dc-voltagefluctuation, which potentially will degrade the lifespan and re-liability of the capacitors in voltage source converters. This pa-per proposes a novel dc-capacitor current control method for agrid-side converter (GSC) to eliminate the negative impact of un-balanced grid voltage on the dc-capacitors. In this method, a dc-capacitor current control loop, where a negative-sequence resonantcontroller is used to increase the loop gain, is added to the conven-tional GSC current control loop. The rejection capability to theunbalanced grid voltage and the stability of the proposed controlsystem are discussed. The second-order harmonic current in the dccapacitor as well as dc-voltage fluctuation is very well eliminated.Hence, the dc capacitors will be more reliable under unbalancedgrid voltage conditions. A modular implementation method of theproposed control strategy is developed for the DFIG controller.Finally, experiments are presented to validate the theoreticalanalysis.

Index TermsControl analysis, dc-capacitor current, doubly fedinduction generator (DFIG), resonant controller, unbalanced gridvoltage.

NOMENCLATUREs Stator flux.us, ug ur Grid, GSC, and rotor ac-voltages.udc DC voltage of the dc link.ig , is , ir GSC, stator, and rotor ac currents.igdc , irdc GSC and RSC dc currents.icap Second-order harmonic dc-capacitor

current.Lg , Lm ,Ls, Lr GSC, mutual, stator, and rotor induc-

tances.

Manuscript received May 10, 2012; revised August 7, 2012; acceptedOctober 1, 2012. Date of current version December 24, 2012. This work wassupported in part by the National Natural Science Foundation of China underGrant 51277163 and in part by the Zhejiang Key Science and Technology Inno-vation Group Program under Grant 2010R50021. Recommended for publicationby Associate Editor B. Wu.

C. Liu is with General Electric Global Research, Shanghai 201203, China(e-mail: [email protected]).

D. Xu, N. Zhu, and M. Chen are with the College of Electrical Engineering,Zhejiang University, Hangzhou 310027, China (e-mail: [email protected];[email protected]; [email protected]).

F. Blaabjerg is with the Department of Energy Technology, Aalborg Univer-sity, Aalborg DK-9220, Denmark (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2012.2223829

Rg ,Rs,Rr GSC, stator, and rotor resistances.C Capacitance of a dc capacitor.s, r , sl Grid, rotor, and rotor slip angular frequen-

cies.s Grid voltage phase.P,Q Active and reactive power.sl Rotor slip.Superscripts Reference value. Conjugate complex.(0), (2) DC and second-order harmonic compo-

nents.(+1), (1) Positive-sequence and negative-sequence

fundamental components.(+2), (2) Positive-sequence and negative-sequence

second-order harmonic components.Subscriptsd, q Synchronous d- and q-axis.cap, g, s, r Capacitor, GSC, grid/stator, and rotor.

I. INTRODUCTION

W ITH the continuous increased capacity of installed windpower, the effects of wind power generation on the gridare more and more considerable [1]. As a consequence, thegrid codes issued by more and more power system operatorsspecify that the wind turbines should withstand certain voltagedisturbances such as voltage unbalance and voltage distortionwithout tripping. In order to do this, the wind turbine systemsmust continuously develop and improve their performance [2],[3].

A large number of wind turbine systems are increasingly be-ing installed in remote areas in China. Many wind farms arelocated in the terminal of power transmission systems. The gen-erated wind power is required to be transferred to load centerswith long transmission lines, whose connections may be weak.The presence of voltage unbalance is more severe in these weaktransmission lines [4]. However, Chinese standards issued in2012 require that large-scale wind turbines should withstand asteady-state voltage unbalance of 2% and a short-time voltageunbalance of 4% without tripping [5], which can also be foundin some international standards, e.g., EN-50160 [6]. Moreover,the wind turbines must remain connected even during transientunbalanced voltage dips.

0885-8993/$31.00 2012 IEEE

LIU et al.: DC-VOLTAGE FLUCTUATION ELIMINATION THROUGH A DC-CAPACITOR CURRENT CONTROL 3207

Fig. 1. Active power flow in a DFIG wind turbine.

Since the stator of a doubly fed induction generator (DFIG)is directly connected to the grid, a negative sequence is addedto the stator flux under unbalanced grid voltage conditions. As aconsequence, larger negative-sequence currents flow throughthe stator and rotor, which cause a significant second-orderharmonic fluctuation in the electromagnetic torque and pow-ers [4], [7]. Then, the torque fluctuations cause wear and tearof the mechanical components such as gearbox and shaft [8]. Inaddition, the active power fluctuations, which flow through thecapacitors of the dc link from both grid-side converter (GSC)and rotor-side converter (RSC), as shown in Fig. 1, cause a largesecond-order harmonic current in the dc capacitors as well asvoltage ripples in the dc link [9]. It results in higher power lossin the dc capacitors and higher operating temperature, whichwill speed up evaporation of the electrolytes liquid and shortentheir lifespan. Further, low-frequency ripple current is moredetrimental than high frequency [10], [11].

Hence, under the unbalanced conditions, the large low-frequency current and voltage ripple in the dc-link capacitors ofthe back-to-back converter is one of the most critical problemsof DFIG [8], [9]. The control of dc voltage used in the GSC forthe DFIG is slightly different to the grid-connected convertersunder the unbalanced conditions, because the dc-voltage ripplesare caused not only by the unbalanced grid voltage but also by theactive power fluctuations from the RSC. In order to obtain con-stant dc voltage, the GSC should reject these two disturbances,i.e., the unbalanced grid voltage and the RSC fluctuating ac-tive power. Several control techniques have been presented forthe GSC controller to reduce the voltage ripple during the volt-age unbalance, which can be divided into three categories: 1)feed-forward methods; 2) dual current control methods; and 3)resonant controller methods.

The feed-forward methods include a grid voltage feed-forward control [12], [13] and an RSC dc-current (i.e., a loadcurrent for GSC) feed-forward control [14][17]. The impactof the grid voltage unbalance on the dc capacitors is reducedby the grid voltage feed-forward control, and the impact of theRSC active power fluctuations on the dc capacitors is reducedby the RSC dc-current feed-forward control. However, the con-trol delay may degrade the control performance of the feed-forward methods, and the feed-forward terms may also includehigh-frequency noise. Moreover, in order to detect the RSC dccurrent, additional hardware of the load current detection maybe needed [15], [16]. To avoid additional detection circuits, an

alternative approach is that the GSC controller calculates thereal-time RSC active power based on the rotor current and rotorvoltage reference [14], [17]. This requires that the GSC con-troller and the RSC controller should be integrated into onecontroller, which loses the modularity of the DFIG converters.It is worth noting that large-scale DFIG converters usually havea modular structure for higher reliability and maintenance.

Dual current control is a popular method for regulating thepositive-sequence current and negative-sequence current at thesame time [9], [18][20]. The positive and negative current ref-erences are calculated from the desired powers and the gridvoltages. Multiple control targets are available by setting ofthe references, such as constant stator power, balanced sta-tor currents, constant electromagnetic torque, and constant dc-voltage [19], [20]. Under the unbalance conditions, to obtainconstant dc voltage, the output fluctuating active power of theGSC must be equal to that of the RSC. Then, the current refer-ences of the GSC depend on the fluctuating active power of theRSC [9], [19]. As a result, this method cannot be implementedin wind power converters with a modular structure.

Since the frequency of the dc-voltage ripple is twice of thegrid frequency, a resonant controller is added to the original dc-voltage controller to increase the dc-voltage loop gain exactlyat twice the grid frequency in [21] and [22]. By doing so, thecontrol loop gain is large enough to reject the disturbances.Then, a constant dc voltage is obtained. However, the addedresonant controller may reduce the phase margin of the systemwhen the resonant frequency is close to or below the crossoverfrequency of the dc-voltage loop due to a phase step change of180 around the resonant frequency [23]. Since the bandwidthof the dc-voltage outer loop is normally lower than 100 Hzfor large-scale DFIG converters, whose switching frequencyis typically around 23 kHz, the resonant controller used in adc-voltage controller is not a good option for DFIG converterswhen considering system stability. Moreover, the dynamic ofthe outer loop is slow.

In order to make the dc capacitors more reliable under un-balanced conditions, this paper is focused on the second-orderdc-capacitor harmonic current elimination by using a robust andmodular control method for the GSC. First, negative impacts ofthe unbalanced grid voltage on the dc capacitors are discussed.Then, a dc-capacitor current control method with a negative-sequence resonant controller is proposed to reduce the im-pact and implemented in the grid-voltage-oriented dq-frame. A


modular implementation method of the proposed control strat-egy is developed for the DFIG controller. The rejection capabil-ity to the unbalanced grid voltage and the stability of the systemare discussed. Finally, experiments are presented to validate thetheoretical analysis.

II. IMPACT OF UNBALANCED VOLTAGE ON DC CAPACITORSA typical DFIG configuration of a wind turbine is shown

in Fig. 1. The stator is directly connected to the low-voltagegrid and the rotor is interfaced through a back-to-back converterthat consists of an RSC, a GSC, and a common dc link [24].The RSC controller is used to control the power output of thegenerator, and the GSC controller is used to keep the dc-linkvoltage stable regardless of the magnitude and the directionof the rotor power [25]. Neglecting conductor power losses,the output grid active power Po at the wind turbine terminal isequal to the sum of the GSC active power Pg and the stator activepower Ps . The direction references of the power and current arealso defined as Fig. 1.

Under unbalanced grid voltage conditions, the grid volt-age comprises positive-, negative-, and zero-sequences. In thispaper, a voltage unbalance factor is defined as the negative-sequence magnitude divided by the positive-sequence mag-nitude in percentage [6]. During grid voltage unbalance, theactive power flow in DFIG wind turbines fluctuates. Sincezero-sequence voltage cannot induce zero-sequence current in athree-phase three-line system, the effect of zero-sequence volt-age is ignored in this paper. The grid voltage can be presented by(1) in the grid voltage synchronous reference frame (dq-frame)as

usdq = u(+1)sdq + u

(1)sdq e

j2s t (1)

where ej2s t means that the negative-sequence componentrotates at clockwise direction with twice the grid frequency inthe dq-frame. It is assumed that the input voltage of the GSC is

ugdq = u(+1)gdq + u

(1)gdq e

j2s t . (2)

Consequently, the input ac current of the GSC might becomposed of a positive-sequence component and a negative-sequence component that depends on the rejection capability ofthe control loop to disturbances at twice the grid frequency:

igdq = i(+1)gdq + i

(1)gdq e

j2s t . (3)

The active power of the GSC Pg can be obtained by using (2)and (3)

Pg = 1.5 Re{ugdq igdq

}

= 1.5 Re{u

(+1)gdq i

(+1)gdq + u

(1)gdq i

(1)gdq

}

+ 1.5 Re{u

(+1)gdq i

(1)gdq e

j2s t + u(1)gdq i(+1)gdq e

j2s t}

= P (0)g + P(2)g (4)

where P (0)g and P (2)g are the fundamental and second-orderactive powers of the GSC, respectively

P(0)g = 1.5 Re

{u

(+1)gdq i

(+1)gdq + u

(1)gdq i

(1)gdq

}

P(2)g = 1.5 Re

{u

(+1)gdq i

(1)gdq e


j2s t}

.

(5)Similar to the GSC, the active power of the RSC Pr can be

expressed as

Pr = 1.5 Re{urdq irdq

}

= 1.5 Re{u

(+1)rdq i

(+1)rdq + u

(1)rdq i

(1)rdq

}

+ 1.5 Re{u

(+1)rdq i

(1)rdq e

j2s t + u(1)rdq i(+1)rdq e

j2s t}

= P (0)r + P(2)r (6)

where P (0)r and P (2)r are the fundamental and second-orderactive powers of the RSC, respectively

P(0)r = 1.5 Re

{u

(+1)rdq i

(+1)rdq + u

(1)rdq i

(1)rdq

}

P(2)r = 1.5 Re

{u

(+1)rdq i

(1)rdq e


j2s t}

.

(7)As the positive-sequence rotor voltage u(+1)rdq approximates

to slu(+1)sdq [24], i.e., u

(+1)rdq

= slu(+1)sdq , the second-order activepower of the RSC can be rewritten as

P (2)r = 1.5 Re{slu

(+1)sdq i

(1)rdq e


j2s t}

(8)where sl is rotor slip, and it is defined as the ratio of the rotorslip angular frequency sl to the grid angular frequency s , i.e.,sl

= sl/s = (s r )/s .According to Fig. 1 and neglecting the power losses of the

GSC and the RSC, the active power that flows into the dccapacitor is

Pcap =udcicap =Pg Pr =(P (0)g P (0)r

)+

(P (2)g P (2)r

).

(9)Since the GSC can well regulate the fundamental active

power P (0)g to track the fundamental active power P (0)r , theterm (P (0)g P (0)r ) in (9) can be neglected. By doing so, thedc-capacitor active power Pcap is found to be

Pcap = P (2)g P (2)r . (10)Substituting (5) and (8) into (10) yields

Pcap = 1.5 Re(u

(+1)gdq i

(1)gdq e


j2s t)

1.5 Re(slu

(+1)sdq i

(1)rdq e


j2s t)

.

(11)From the dc-capacitor power of (11), the terms

i(1)gdq , i

(1)rdq , u

(1)gdq , and u

(1)rdq are strongly dependent on the con-

trol. A grid-voltage-oriented vector control method by using a


Fig. 2. Conventional control of the GSC using a PI-controller in the dq-frame [25], [26].

Fig. 3. Conventional control of the DFIG using a PI-controller in the dq-frame [3], [24].

PI-controller is selected to be analyzed in this paper, which isa common control method for DFIG wind turbine systems, asshown in Fig. 2 for the GSC and Fig. 3 for the DFIG.

The GSC model, which can be found in [26], is shown withinthe dashed box in Fig. 2. The conventional control strategyfor the GSC is described in [25]. From Fig. 2, the d-axis con-trol loop is composed of a dc-link voltage control loop anda d-axis current (i.e., active current component) control loop,which is used to realize the stable control of the dc-link volt-age, and the q-axis current control loop determines the powerfactor of the GSC. The plant for the current control loop isgiven by Ggp(s) = 1/(Lgs + Rg ), and the control delay isdenoted by Gd(s) = esTd , where Td is the delay time. TheDFIG model, which can be found in [3], is described as thedashed box in Fig. 6, where G1(s) = 1/(s + js), G2(s) =(s + jsl)Lm/Ls , and Gp(s) = 1/(Lrs + Rr ); is the leak-age factor, = 1 L2m/(LsLr ). Both of the GSC model andthe DFIG model are derived by using an averaged switch mod-eling method [27], where the discrete switch network is aver-aged over one switching period for converting to the continuousmodel.

The PI-controller transfer functions GgPI(s) and GrPI(s) inFigs. 2 and 3 are given by

GgPI(s) = Kgp +Kgis

GrPI(s) = Krp +Kris

.(12)

From Figs. 2 and 3, the rejection capabilities of the ac currentto the grid voltage disturbance for the GSC and the DFIG aredefined, respectively, by

Ggui(s) =igdq (s)usdq (s)

(13)

Grui(s) =irdq (s)usdq (s)

. (14)

By neglecting the current decoupling term, the ac voltage ofthe GSC and the RSC can also be yielded from Figs. 2 and 3,respectively

ugdq (s) = GgPI(s)Gd(s)(igdq (s) igdq (s)

) (15)urdq (s) = GrPI(s)Gd(s)

(irdq (s) irdq (s)

). (16)

The minus sign in (15) is because the reference direction ofthe GSC current is defined as input into the GSC.

If s = j2s , which represents the negative-sequence com-ponent in the dq-frame, substituting (13)(16) into (11), andassuming igdq (j2s) = 0 and irdq (j2s) = 0 by using theconventional control methods, the expression of the dc-capacitorpower can be rewritten by using these transfer functions

Pcap = 1.5 Re{u

(+1)sdq u

(1)sdq Gg u i (j2s )ej 2 s t

+(i(+1)g dq u

(1)sdq GgPI(j2s )Gd (j2s )

)Ggu i (j2s )ej 2 s t

}

1.5 Re{u

(+1)sdq u

(1)sdq sl Gr u i (j2s )ej 2 s t

(i(+1)r dq u

(1)sdq GrPI(j2s )Gd (j2s )

)Gru i (j2s )ej 2 s t

}.

(17)At steady-state operation, the amplitude of the dc-capacitor

current can be calculated by

Icapm =|Pcap |Udc

. (18)

It should be noted that the dc-capacitor current also containsthe switching ripples, which are not related to the control meth-ods but to the modulation methods. Therefore, the switchingripples are not included when we discuss the control of thedc-capacitor current in this paper.

As can be seen from (17) and (18), the amplitude of the dc-capacitor current depends on the grid voltages u(+1)sdq and u

(1)sdq ,

the positive-sequence currents i(+1)gdq and i(+1)rdq , and the rejections

Ggui(j2s) and Grui(j2s). The grid voltages u(+1)sdq andu

(1)sdq are related to the grid condition and the positive-sequence

currents i(+1)gdq and i(+1)rdq are due to wind power, both of which

do not depend on the converter control loops. On the contrary,the rejections Ggui(j2s) and Grui(j2s) strongly dependon the converter control loops: if the control loops have a highrejection to the negative-sequence grid voltage disturbances,the dc-capacitor current will be smaller, so the impact of theunbalanced grid voltage on the dc capacitor can be suppressed.


TABLE IPARAMETERS OF 1.5 MW DFIG FOR A WIND TURBINE

TABLE IIPARAMETERS OF A DFIG CONVERTER

Fig. 4. Rejection capability to the negative-sequence grid voltage in the dq-frame by using a conventional PI-controller. (a) Rejection of Ggu i (s) for GSC.(b) Rejection of Gru i (s) for DFIG.

A 1.5-MW DFIG with a 500-kW back-to-back converter isselected in this paper, whose parameters are listed in Tables I andII. In order to prevent significant impact of the switching actionon the current loop stability, the current loop bandwidth shouldbe smaller than one-fourth of the switching frequency [28]. Inthis case, the bandwidth is selected to be 100, 250, and 500 Hz,in order to evaluate the performance of the conventional controlmethods. Then, the rejection capabilities ofGgui(s) andGrui(s)to the negative-sequence grid voltage are shown in Fig. 4, wheres = j2f . It is seen that the rejection capability is increasedby the increased bandwidths of the current loop by regulat-ing the PI-controller. But they are still too small to suppress the

negative-sequence current caused by the negative-sequence gridvoltage. Moreover, the rejection capability of Grui(j2s) inthe DFIG is much smaller than that of Ggui(j2s) in the GSCwhen the bandwidth is the same, because the EMF voltage inthe rotor induced by the negative-sequence grid voltage is pro-portional to its rotor slip, which has a high value of (2 sl) [7].Thus, according to (17) and (18), a small negative-sequence gridvoltage will cause a high fluctuating dc-capacitor current if itis not considered unbalanced control. This problem will hindersafe and reliable operation of DFIG wind turbine systems, be-cause the low-frequency ripple currents in the dc-link capacitorsshorten their lifespan.

III. PROPOSED DC-CAPACITOR CURRENT CONTROLSCHEME FOR GSCS

In order to improve the reliability of DFIG wind turbines, theimpacts of the unbalanced grid voltage on the dc capacitor needto be eliminated. To achieve this goal, a proper control strategyshould be implemented to increase the negative-sequence rejec-tion capability of the system. Moreover, the control structureshould contribute to a modular structure design for large-scaleDFIG converters.

A. Control Method to Eliminate Second-Order HarmonicCurrent in DC Capacitors

A basic control loop of the GSC with current decoupling isshown in Fig. 2. It is seen that there are two disturbances in thecontrol loop, i.e., the grid voltage usdq and the RSC dc currentirdc . During grid voltage unbalance, the dc-capacitor currenticap might have the second-order harmonic, which is caused bythese disturbances. According to the feedback control principle,if the disturbance is included by the closed-loop and the loopgain is large enough, the disturbance will be rejected [29]. InFig. 2, the disturbances usdq and irdc are indeed included by theouter dc-voltage control loop, but the loop gain is too small toreject the disturbances due to a low loop bandwidth of the outerdc-voltage control loop, which is usually between one-tenthand one-fifth of the inner current control loop. It is said thatthe bandwidth of the dc-voltage control loop is normally lowerthan 100 Hz for large-scale DFIG converters, whose switchingfrequency is around 23 kHz.

In order to reject the disturbances and to maintain a high-phase margin, this paper proposes a dc-capacitor current controlmethod by using a resonant controller, as shown in Fig. 5. Basedon Fig. 2, a dc-capacitor current control loop is added to the con-ventional control structure. The output of the dc-capacitor cur-rent control loop is added to the output of the current control loopas a component of the GSC voltage command. Consequently,the dc-capacitor current control loop is a closed loop that in-cludes both the disturbances usdq and irdc . Since the frequencyof the dc-capacitor current caused by the unbalanced grid volt-age is twice the grid voltage frequency, a second-order resonantcontroller G(2)R (s) is selected as the loop controller. In orderto eliminate the dc-capacitor current, the dc-capacitor currentreference icap is set to zero. By doing so, the disturbances usdqand irdc will be rejected if the gain of the resonant controller


Fig. 5. Proposed dc-capacitor current control method by using a second-order negative-sequence resonant controller in the dq-frame for the GSC.

is large enough. As a consequence, the second-order harmonicdc-capacitor current as well as the fluctuating dc-voltage will beeliminated.

The overall GSC current control loop consists of a funda-mental current control loop and a dc-capacitor current controlloop. According to the proposed method in Fig. 5, the voltagereference of the GSC be calculated as

ugdq = (uPIgdq + u

Rgdq + u

Cgdq

). (19)

It can be seen that the voltage reference ugdq consists ofthree components: uPIgdq which is the fundamental componentproduced by the PI-controller of the fundamental current loop,uRgdq which is the second-order harmonic component producedby the resonant controller of the dc-capacitor current loop, anduCgdq = jsLg igdq which is the decoupling voltage component.Under the unbalanced grid condition, the dc-capacitor currentmay contain the second-order harmonic component. Since thegain of the resonant controller is large and the phase of theresonant controller is zero at frequency 2s , the resonantcontroller output uRgdq will be an ac signal with an angularfrequency of 2s in the steady state.

Since any sinusoidal scalar can be expressed by the additionof two vectors that rotate in the opposite directions accordingto Eulers formula, the output of the dc-capacitor current loopwill contain not only a negative-sequence component whosefrequency is 2s but also a positive-sequence componentwhose frequency is 2s when using a normal resonant controller.The former is converted to the negative-sequence voltage, whilethe latter is converted to the third-order positive-sequence volt-age which will produce third-order harmonic current in theGSC ac current [21]. To prevent this problem, a second-ordernegative-sequence resonant controller can be adopted insteadof the normal resonant controller [21], [30]. The expression ofthe second-order negative-sequence resonant controller with acut-off frequency c [31] is given by

G(2)R (s)=

2Kr1 + (s + j2s)/c

=2Krc(s + c j2s)

s2 + 2cs + 2c + (2s)2.

(20)

If c


Fig. 6. Overall block diagram of the proposed dc-capacitor current control strategy.

then the corresponding second-order harmonic dc-capacitor cur-rent can be given as

icap(t) = Cd

dtudc(t)

= Cd

dt

(Udc + U

(2)dcm sin(2st + 0)

)

= 2sC U (2)dcm cos(2st + 0)= 2sC u(2)dc (t Ts/8) (23)

where U (2)dcm is the amplitude of the second-order harmonic dcvoltage u(2)dc , 0 is the initial phase angle of u

(2)dc , and Ts is the

grid voltage period. Hence, the amplitude of the dc-capacitorcurrent is equal to the product of coefficient 2sC and U (2)dcm ,and the phase of the dc-capacitor current is obtained by meansof a delayed dc voltage u(2)dc of Ts/8, i.e., 2.5 ms for 50 Hz grid.It is fast enough to meet the dynamic requirements. Moreover,by doing so, a differential operation is avoided, so the noiseintroduced by the differential operation can be prevented. From(23), it can also be found that the dc-voltage fluctuation will beeliminated if the dc-capacitor current is canceled.

The overall block diagram of the proposed dc-capacitor cur-rent control strategy based on the negative-sequence resonantcontroller and the delay detection method is shown in Fig. 6.The control system consists of two inner fundamental currentcontrol loops for d- and q-axis currents, a dc-capacitor cur-rent control loop, and an outer dc-voltage control loop. The dcvoltage will be controlled by both the dc-voltage control loopand the dc-capacitor current control loop. The dc-voltage con-trol loop is used to make the dc-voltage stable by regulatingthe fundamental active current reference igd ; the dc-capacitorcurrent control loop is used to eliminate the dc-voltage fluctu-ation which may be present during the grid voltage unbalance.The d- and q-axis fundamental currents are controlled by PI-controllers. The dc-capacitor current control loop is highlightedby the dashed box in Fig. 6. It consists of a dc-capacitor current

detection by means of the dc-voltage delayed operation and anegative-sequence resonant controller. Regarding the resonantcontroller implementation, the outputs of the real part G(2)Rx (s)and the imaginary part G(2)Ry (s) are added to the outputs of thed- and q-axis current loops, respectively. The decoupling currentfeed-forward terms sLg igd and sLg igq are used to eliminatethe interactions between the d- and q-axis components of thecurrent in the dq-frame. Then, the obtained GSC voltage refer-ences ugd and ugq are used to control the GSC via an inversepark transformation and a space vector modulation (SVM).

From Fig. 6, it is clear that the GSC controller is able to elimi-nate the dc-voltage fluctuation regardless of the RSC controller.Thus, the proposed control method makes the GSC controllerindependent of the RSC controller, so it is a feasible controlmethod for the DFIG converters with a modular structure. Sincethe dc-capacitor current is indirectly detected by means of mea-suring the dc voltage, no additional hardware detection circuitryis necessary, which can save the cost.

IV. CURRENT CONTROL LOOP ANALYSISSince the bandwidth of the dc-voltage outer loop is normally

lower than 100 Hz for large-scale DFIG converters, the rejectioncapability of the dc-voltage control loop to the second-orderharmonic component is very small. Thus, it is not necessary toanalyze the dc-voltage control loop when accessing the rejectioncapacity to the disturbances.

From the overall current control loop in Fig. 5, it is clearthat the dc-capacitor current icap(s) is determined by the GSCcurrent reference igdq (s), the dc-capacitor current referenceicap(s), the grid voltage disturbance usdq (s), and the RSC dccurrent irdc(s). The overall closed-loop transfer function forthis current control system is given by

icap(s) = Ggc(s)igdq (s) + Gcc(s)icap(s)

+ Guc(s)usdq (s)Grc(s)irdc(s) (24)where Ggc(s) is the transfer function from the GSC current ref-erence igdq (s) to the capacitor current icap(s) and represents the


tracking performance of the current loop; Gcc(s) is the transferfunction from the dc-capacitor current reference icap(s) to thecapacitor current icap(s) and represents the tracking perfor-mance of the capacitor current control loop; Guc(s) is the trans-fer function from the grid voltage disturbance usdq (s) to thecapacitor current icap(s) and represents the rejection capabilityof the GSC current loop to the grid voltage disturbance; Grc(s)is the transfer function from the RSC dc current irdc(s) to thecapacitor current icap(s) and represents the rejection capabilityof the GSC current loop to the RSC dc-current disturbance. Thedetailed expressions of these transfer functions are shown asfollows:

Ggc (s) =icap (s)ig dq (s)

=Ku Ggp (s)GgPI(s)Gd (s)

1 + Ggp (s)GgPI(s)Gd (s) + Ku Ggp (s)G(2)R (s)Gd (s)

(25)

Gcc (s) =icap (s)icap (s)

=Ku Ggp (s)G

(2)R (s)Gd (s)

1 + Ggp (s)GPI(s)Gd (s) + Ku Ggp (s)G(2)R (s)Gd (s)

(26)

Guc (s) =icap (s)usdq (s)

=Ku Ggp (s)


(27)

Grc (s) =icap (s)irdc (s)

=1 + Ggp (s)GgPI(s)Gd (s)


(28)where Ku = 1.5Usd/Udc and Ggp(s) = 1/(Rg + sLg ).

The rejection capability of the GSC current loop to the gridvoltage disturbance is derived as

Ggui(s) =igdq (s)usdq (s)

=Guc(s)

Ku. (29)

A. Stability EvaluationIn this study, the PI-controllers of the GSC and the RSC

current control loops are designed to achieve an open-loopcrossover frequency at 250 Hz when using only PI-controllerin per unit system, i.e., Kgp = 0.7,Kgi = 60, and Krp =0.7,Kri = 50. The parameters of the resonant controller areselected as Kr = 15 and c = 3 rad/s. The parameters of theconverter and the DFIG are given in Tables I and II.

The denominator of the transfer functions (25)(28) is thesame and it is defined as the characteristic equation of thecurrent control loop, i.e., = 1 + Ggp(s)GgPI(s)Gd(s) +KuGgp(s)G

(2)R (s)Gd(s). In order to evaluate the stability [29],

the current loop gain Di(s) is introduced as given in

Di(s) = Ggp(s)GgPI(s)Gd(s) + KuGgp(s)G(2)R (s)Gd(s).

(30)From the overall control loop in Fig. 5, and using the transfer

functions of (25) instead of the forward path of the current loop,the dc-voltage loop gain can be obtained as

Du (s) = GuPI(s)Ggc(s)/Cs (31)where GuPI(s) is the transfer function of the PI-controller inthe dc-voltage control loop, GuPI(s) = Kup + Kui/s.

The frequency responses of the current loop gain Di(s) andthe dc-voltage loop gain Du (s) are shown in Fig. 7(a) and (b),respectively. The dashed line presents the conventional controlmethod, and the solid line presents the proposed dc-capacitorcurrent control method. Compared to the conventional controlmethod, it is seen from Fig. 7(a) that the current loop gain at100 Hz, i.e., referring to the negative-sequence frequency inthe dq-frame, is significantly increased by using the proposedcontrol method. Hence, the loop gain becomes large enoughto reject the disturbances in the control loop. Furthermore, thephase margin of the proposed control system changes slightlycompared to using the conventional control method. Therefore,the impact of the introduced dc-capacitor current control schemeon the stability can be ignored.

B. Rejection Capability to DisturbancesFig. 8(a) and (b) shows the rejection capability of the cur-

rent loop to the disturbances in the dc link, usdq and irdc , re-spectively. The dashed line presents the conventional controlmethod, and the solid line presents the proposed dc-capacitorcurrent control method. From Fig. 8(a), by using the conven-tional control method, the rejection of the negative-sequencegrid voltage is only 3 dB, whereas it becomes 27 dB by usingthe proposed control method, which denotes that the proposedcontrol method can significantly reduce the impact of the dis-turbance usdq on the dc link. Meanwhile, the rejection of thesecond-order RSC dc-current fluctuation irdc is increased to30 dB by using the proposed control method, whereas it isonly 0 dB by using the conventional control method. Hence, theproposed control method significantly increases rejection capa-bility to both of the disturbances, usdq and irdc , at twice the gridfrequency.

Using the proposed control method, the dc-capacitor currentcomponent which causes the RSC power fluctuation is alsosuppressed due to the high rejection of Grc(j2s) to irdc .Thus, the dc-capacitor power of (17) can be rewritten as

Pcap = 1.5 Re{u

(+1)sdq u

(1)sdq Gg u i (j2s )ej 2 s t

+(i(+1)g dq u

(1)sdq GgPI(j2s )Gd (j2s )

)Ggu i (j2s )ej 2 s t

}

1.5Grc (j2s ) Re{u

(+1)sdq u

(1)sdq sl Gr u i (j2s )ej 2 s t

(i(+1)r dq u

(1)sdq GrPI(j2s )Gd (j2s )

)Gru i (j2s )ej 2 s t

}.

(32)


Fig. 7. Frequency responses of the current loop gain Di (s) and the dc-voltage loop gain Du (s). (a) Frequency response of the current loop gain Di (s).(b) Frequency response of the dc-voltage loop gain Du (s).

Fig. 8. Rejection capability of the current loop to the disturbances in the dc link. (a) Rejection of Ggu i (s) to the grid voltage disturbance. (b) Rejection ofGrc (s) to the RSC dc-current disturbance.

By doing so, in terms of the dc-capacitor activepower, the rejection capability of the RSC to the unbal-anced grid voltage becomes Grc(j2s)Grui(j2s) andGrc(j2s)Grui(j2s). It seems that the rejection capa-bility of the RSC is increased regardless of whether the realdisturbance rejection capability of the RSC, Grui(j2s), isincreased or not, so the GSC can independently eliminate the dc-capacitor active power. It is not necessary to coordinate the GSCand the RSC for maintaining constant dc voltage. It should bepointed out that the RSC active power can be directly multipliedby Grc(j2s) because the imaginary part of Grc(j2s) isvery small.

By substituting (32) into (18), the amplitude of the dc-capacitor current can be obtained. As an example, Fig. 9 shows

that the amplitude of the dc-capacitor current is varied with theresonant controller gain Kr when the voltage unbalance factoris 40% and the stator active power is 0.5 pu for different valuesof the rotor slip. Note that if Kr = 0, this is identical to usethe conventional control method. From Fig. 9, compared to theconventional control method, the amplitude of the dc-capacitorcurrent is significantly decreased by using the proposed dc-capacitor current control method. The second-order harmonicdc-capacitor current can be completely eliminated when Kr islarger than 20. Therefore, the proposed method can significantlyeliminate the negative impact of the unbalanced voltage on thedc-capacitor current as well as the dc voltage. It is worth not-ing that the dc-capacitor current for sl = 0.2 is larger than thatfor sl = 0.2, when using the conventional control method


Fig. 9. Amplitude of the dc-capacitor current when the voltage unbalancefactor is 40% and the stator active power is 0.5 pu for different rotor slipsl . (a) Rotor slip sl = 0.2 (subsynchronous speed). (b) Rotor slip sl = 0.2(supersynchronous speed).

TABLE IIIPARAMETERS OF A 30 kW DFIG FOR EXPERIMENTAL TESTS

(i.e., Kr = 0). The explanation is that the actual direction ofthe active power component 1.5Re{slu(+1)sdq i

(1)rdq e

j2s t} in (11)is flowing into the RSC when sl = 0.2, so this term is actuallyadded to the GSC active power component P (2)g .

V. EXPERIMENTAL RESULTS

The experimental platform is composed of a 30-kW DFIGwhich is driven by a speed controlled induction machine, and a10-kW back-to-back power converter for the DFIG. The dc volt-age in the power converter is controlled to 650 V. The switchingfrequency of the converter is 2 kHz. The open-loop crossoverfrequency is also set to 250 Hz when using only PI-controller,and the PI-controller parameters are selected as Kgp = 1.3 andKgi = 100. The resonant controller parameters are selected asKr = 15 and c = 3 rad/s in the experiments. Each of theGSC and the RSC control algorithms is implemented in a perunit system with a 32-bit fixed-point DSP TMS320F2808. Theparameters of the DFIG and the DFIG converter are given inTables III and IV, respectively.

TABLE IVPARAMETERS OF A 10 KW DFIG CONVERTER

Fig. 10. DFIG waveforms during the experimental tests.

Fig. 11. Steady-state performance for the conventional control method andthe proposed control method with the stator active power output 10 kW at asubsynchronous speed of 1200 r/min (0.8 pu). (a) Conventional control method.(b) Proposed control method.

During the experiments, the lines of A- and B-phases of theDFIG system are directly connected to the 230 V/50 Hz grid, andthe line of C-phase is connected to the grid through a variableautotransformer. The voltage of C-phase is maintained at 205 Vby regulating the autotransformer in all the experiments. Bydoing so, an unbalanced voltage supply is set up. The unbalancefactor is 4%.

In all the experiments, the conventional control method inFig. 3 is used for the RSC to control the DFIG. The wave-forms of the DFIG output are shown in Fig. 10. The statoractive power is set to 10 kW and the rotor speed is 1200 r/min(0.8 pu). From Fig. 10, under an unbalanced grid voltage condi-tion, an unbalanced and distorted stator current can be found andthe rotor current ripple exists. Consequently, the active powerdelivered to the dc link fluctuates at twice the grid frequency,which is one of the disturbances to the dc-capacitor current aswell as the dc voltage.

The steady-state performance for the conventional controlmethod and the proposed control method is given in Fig. 11(a)


and (b), respectively. The test condition is the same as that ofFig. 10. By using the conventional PI control method, the dcvoltage contains a significant second-order harmonic compo-nent, and the GSC current is unbalanced and also harmonicallydistorted, as shown in Fig. 11(a). These results verify that theGSC control system does not have the control gain to suppressthe second harmonic ripple by using the conventional controlmethod. On the contrary, the dc-voltage fluctuation is signif-icantly suppressed by using the proposed control method, asshown in Fig. 11(b). In Fig. 11(b), the GSC current consistsof two parts: one is the positive-sequence active current corre-sponding to the fundamental active power, and the other is thenegative-sequence active current corresponding to the fluctuat-ing active power from the RSC. If the fluctuating active powerfrom the RSC is large, the GSC current will become significantlyunbalanced, which may exceed its current rating.

The frequency spectrum of the dc-capacitor current is alsoshown in Fig. 11. The RMS value of the second-order harmonicdc-capacitor current is 3.5 A (i.e., 0.25 pu) by using the con-ventional control method in Fig. 11(a), whereas it is reducedto 0.4 A (i.e., 0.03 pu) by using the proposed control methodin Fig. 11(b). It is clear that the second-order harmonic dc-capacitor current is removed by using the proposed dc-capacitorcurrent control, leaving only the switching ripples. Therefore,the impact of the unbalanced grid voltage on the dc-capacitorlifespan can be eliminated. Since the dc capacitor connects theGSC and the RSC in parallel, the characteristic frequency ofthe dc-capacitor current ripples is 4 kHz, which is twice theswitching frequency.

The capacitance of electrolytic capacitors tends to changeover time due to evaporation of electrolyte, and they usuallyhave a tolerance range of 20% [11]. As a result, the coefficientof the dc-capacitor current detection C will deviate from the ac-tual capacitance value. A deviation of20% of the coefficient Cis tested in order to access the proposed control method for suchan event. The experimental results are presented in Fig. 12. It canbe seen that the dc-voltage fluctuation is also suppressed duringthe deviation of the coefficient C. This conclusion can also beobtained from Fig. 9, because the resonant controller can outputan adequate voltage reference to eliminate the dc-capacitor cur-rent if Kr is among 1020 in this case. Therefore, the proposedcontrol method is robust to the capacitance variations.

The GSC transient response when the dc-capacitor currentcontrol loop is enabled is shown in Fig. 13. Once the statorcurrent loop with the resonant controller is enabled, the reso-nant controller produces a second harmonic component in thedq-frame in order to suppress the dc-voltage fluctuation. Simul-taneously, the GSC starts to transfer the fluctuated active powerfrom the RSC to the grid by injecting the negative-sequenceactive current into the grid. Then, the dc-voltage fluctuation isreduced. The transient time is 60 ms, so the control systemexhibits a good transient response.

The dynamic performance during rotor speed variations isalso demonstrated in the experiments. The rotor speed is con-trolled by the adjustable speed drive which is linearly increasedfrom subsynchronous speed 1350 r/min (0.9 pu) to supersyn-chronous speed 1650 r/min (1.1 pu). The stator active power

Fig. 12. Steady-state performance for the proposed control method when thecoefficient C has a deviation of 20% from the actual dc-capacitor value. Fromtop to bottom: dc voltage udc , GSC current ig a , ig b , and ig c , d-axis resonantcontroller output uRgd . (a)20% deviation for coefficient C. (b) +20% deviationfor coefficient C.

Fig. 13. GSC transient performance when the dc-capacitor current controlloop is enabled. From top to bottom: dc voltage udc , GSC current ig a , ig b , andig c , d-axis resonant controller output uRgd .

output is maintained at 10 kW during the rotor speed variations.The experimental results are shown in Fig. 14. The rotor currenthas a large amount of ripples under unbalanced grid voltage con-ditions. However, the dc voltage is kept stable and its fluctuationis eliminated regardless of the change of the rotor current. Theproposed control method can work well in the whole operationspeed range.

Under balanced grid voltage condition, a step change of thestator active power output is used to analyze the dynamic per-formance of the GSC system, which is illustrated in Fig. 15.The stator active power output changes from 0 to 15 kW duringthe test. It is seen that the dc voltage has a sag of 10 V onlyand completely recovers to its normal value 650 V from the sagafter 40 ms later. The overall control system still keeps a gooddynamic performance. Therefore, the impact of the proposedcontrol method on the dynamic performance is very little.


Fig. 14. Dynamic performance when the rotor speed changes linearlyfrom subsynchronous speed 1350 r/min (0.9 pu) to supersynchronous speed1650 r/min (1.1 pu). From top to bottom: dc voltage udc , GSC current ig b , rotorcurrent ir b , stator current isb .

Fig. 15. Dynamic response to a step change of the stator active power from 0to 15 kW. From top to bottom: dc voltage udc , GSC current ig b , rotor currentir b , stator current isb .

Fig. 16. Dynamic behavior for a step change of output active grid power from5 to 15 kW. From top to bottom: dc voltage udc , output grid current io , d-axisGSC current reference ig d , d-axis GSC current ig d .

Fig. 16 shows the dynamic behavior of the proposed controlmethod for a step change of output grid active power Po from 5to 15 kW. The grid voltage is balanced and kept at the rated valueduring the test. From Fig. 16, the d-axis GSC current referencehas a corresponding increase in response to the step change ofthe grid active power. The d-axis GSC current can well track itsreference. As a result, the dc voltage still keeps stable althoughit has a slight sag. To sum up, the proposed control method canalso keep the DFIG system stable even under a step change ofthe output grid active power at a wind turbine terminal.

VI. CONCLUSIONIn order to reduce the negative impact of the second-order

harmonic current in the dc capacitor and thereby increase the

reliability of the dc-link capacitors of the DFIG converters, thispaper proposes a dc-capacitor current control method for a GSC.The dc-capacitor current is obtained by means of detecting thedc voltage fluctuation, so it does not require any additional hard-ware detection, which also contributes to the cost saving in themethod. The proposed dc-capacitor current control algorithm isimplemented in the GSC controller without any power informa-tion from the RSC controller. Therefore, the GSC controller canbe independent of the RSC controller by using the proposed con-trol method. This makes the control method more suitable forlarge-scale DFIG converters with a modular structure. Further-more, the proposed control method has very little impact on thesystem stability. The experimental results show that the second-order dc-capacitor current is eliminated and also the dc-voltagefluctuation is suppressed. Hence, the dc capacitors will be morereliable under unbalanced grid voltage conditions. The exper-imental results also show that the dc-capacitor current controlmethod is robust to the measuring deviation of the dc-capacitorcurrent.

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Changjin Liu received the B.Sc. degree in electri-cal engineering from Tongji University, Shanghai,China, in 2005, and the Ph.D. degree from the Col-lege of Electrical Engineering, Zhejiang University,Hangzhou, China, in 2012, where he performed re-search on the control of DFIG wind turbines andenergy storage for power system.

In 2011, he was a Visiting Scholar in the De-partment of Energy Technology, Aalborg University,Aalborg, Denmark. Since July 2012, he has been withGeneral Electric Global Research, Shanghai, where

he is currently involved in power conversion system control.

Dehong Xu (M94SM10) received the B.Sc.,M.Sc., and Ph.D. degrees from the Depart-ment of Electrical Engineering, Zhejiang Univer-sity, Hangzhou, China, in 1983, 1986, and 1989,respectively.

Since 1996, he has been a Full Professor in theCollege of Electrical Engineering, Zhejiang Univer-sity. He was a Visiting Scholar in the University ofTokyo, Tokyo, Japan, from June 1995 to May 1996.From June 2000 to December 2000, he was a Visit-ing Professor in Center for Power Electronics System,

Virginia Tech, Blacksburg. From February 2006 to April 2006, he was a Visit-ing Professor in ETH, Zurich, Switzerland. He has authored or coauthored fivebooks and more than 350 papers. He owns three U.S. patents and 18 Chinesepatents. His research interests include power electronics topology and control,and power conversion for energy saving and renewable energy.

Dr. Xu received three paper awards of IEEE conferences. He was at-largeAdcom member of the IEEE Power Electronics Society from 2006 to 2008.He is currently a board member of Electrical Engineering Discipline of ChinaState Department Education Degree Committee. He is a Vice President of theChina Power Electronics Society and a Vice Chairman of the editorial com-mittee of the Chinese Journal of Power Electronics. He is an Associate Editorof both IEEE TRANSACTION ON POWER ELECTRONICS and IEEE TRANSACTIONON SUSTAINABLE ENERGY. He was a Technical Program Chair of the IEEEInternational Symposium on Power Electronics for Distributed Generation Sys-tems (PEDG2010), General Cochair of PEDG2012, and General chair of IEEEInternational Symposium on Industrial Electronics (ISIE2012).

Nan Zhu was born in Nanjing, China, in 1989. He re-ceived the B.S. degree from the Department of Elec-trical Engineering, Zhejiang University, Hangzhou,China, in 2011, where he is currently working towardthe Ph.D. degree.

His research interests include wind power gen-eration with doubly-fed induction machines, powerelectronics reliability, and intelligent power modules.

Frede Blaabjerg (S86M88SM97F03) re-ceived the Ph.D. degree from Aalborg University,Aalborg, Denmark, in 1995.

He was with ABB-Scandia, Randers from 1987 to1988. He became an Assistant Professor in 1992, anAssociate Professor in 1996, and a Full Professor inpower electronics and drives in 1998 at Aalborg Uni-versity. He has been a Part-Time Research Leaderat Research Center Risoe in wind turbines. During20062010, he was the Dean of the Faculty of Engi-neering, Science, and Medicine and became a Visiting

Professor at Zhejiang University, Hangzhou, China, in 2009. His research areasare in power electronics and its applications such as wind turbines, PV systems,and adjustable speed drives.

Dr. Blaabjerg has been Editor-in-Chief of the IEEE TRANSACTIONS ONPOWER ELECTRONICS since 2006. He was a Distinguished Lecturer for the IEEEPower Electronics Society during 20052007 and for the IEEE Industry Appli-cations Society from 2010 to 2011. He received the 1995 Angelos Award forhis contribution in modulation technique and the Annual Teacher prize at Aal-borg University. In 1998, he received the Outstanding Young Power ElectronicsEngineer Award from the IEEE Power Electronics Society. He has received tenIEEE Prize paper awards and another prize paper award at PELINCEC Poland2005. He received the IEEE PELS Distinguished Service Award in 2009 andthe EPE-PEMC 2010 Council award.

Min Chen (M06) was born in China, in 1976. Hereceived the B.S. and Ph.D. degrees from the Depart-ment of Electrical Engineering, Zhejiang University,Hangzhou, China, in 1998 and 2004, respectively.

He is currently a Faculty Member of Zhejiang Uni-versity. His research interests include power qualitycontrol, high-frequency high-power conversion, andrenewable energy power conversion system.

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