Coordinated Control of Dfig Rsc and Gsc Under Generalized Unbalanced and Distorted Grid Voltage...

2808 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 60, NO. 7, JULY 2013

Coordinated Control of DFIG’s RSC andGSC Under Generalized Unbalanced and

Distorted Grid Voltage ConditionsJiabing Hu, Member, IEEE, Hailiang Xu, Student Member, IEEE, and Yikang He, Senior Member, IEEE

Abstract—This paper proposes a coordinated control of therotor-side converter (RSC) and grid-side converter (GSC) of adoubly fed induction generator (DFIG)-based wind-turbine gen-eration system under generalized unbalanced and/or distortedgrid voltage conditions. The system behaviors of the RSC andGSC during supply imbalance and distortion are investigated. Toenhance the fault ride-through operation capability, the RSC isproperly controlled to eliminate the torque oscillations, whereasthe GSC is carefully designed to ensure constant active poweroutput from the overall DFIG generation system. To achieve si-multaneous regulation of the positive-/negative-sequence currentsand fifth-/seventh-order harmonic currents for both the RSCand GSC, a novel current controller, consisting of a conventionalproportional–integral regulator and a dual-frequency resonantcompensator, is proposed and implemented in the positive (dq)+

reference frame. The simulation and experiment studies demon-strate the correctness of the developed model and the effectivenessof the suggested control strategy for DFIG-based wind-turbinesystems under such adverse grid conditions.

Index Terms—Converter, coordinated control, distortion,doubly fed induction generator (DFIG), imbalance, modeling,wind turbine.

NOMENCLATURE

U s, Is Stator voltage and current vectors.U r, Ir Rotor voltage and current vectors.Ug, Ig Grid-side voltage and current vectors.ψs,ψr Stator and rotor flux linkage vectors.ω1, ωr, ωs Stator, rotor, and slip angular frequencies.θs, θg, θr Stator flux, grid voltage, and rotor angles.Ps, Qs Stator output active and reactive powers.

Manuscript received March 1, 2012; revised May 18, 2012; acceptedAugust 11, 2012. Date of publication September 7, 2012; date of current versionFebruary 28, 2013. This work was supported in part by the National NaturalScience Foundation of China under Grant 50577056 and Grant 51277196, bythe Power Electronics Science and Education Development Program of theDelta Environmental and Educational Foundation under Grant DREG2012004,and by the Fundamental Research Funds for the Central Universities underGrant HUST-2012TS062.

J. Hu was with the College of Electrical Engineering, Zhejiang University,Hangzhou 310027, China. He is now with the School of Electrical and Elec-tronic Engineering and the State Key Laboratory of Advanced ElectromagneticEngineering and Technology, Huazhong University of Science and Technology,Wuhan 430074, China (e-mail: [email protected]).

H. Xu and Y. He are with the College of Electrical Engineering,Zhejiang University, Hangzhou 310027, China (e-mail: [email protected];[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/TIE.2012.2217718

Pg, Qg Grid-side output active and reactive powers.Pt, Qt Total output active and reactive powers of the

doubly fed induction generator (DFIG) system.Ls, Lr Stator and rotor self-inductances.Lσs, Lσr Stator and rotor leakage inductances.Lm Mutual inductance.Rs, Rr Stator and rotor resistances.Lg, Rg Input inductance and resistance of the grid-side

converter (GSC).Subscriptsα, β Stationary αβ-axis.d, q Synchronous dq-axis.s, r Stator and rotor.+,−, 5−, 7+ Positive, negative, fifth-order, and seventh-

order components.Superscripts+,−, 5−, 7+ Positive (dq)+, negative (dq)−, negative

(dq)5−, and positive (dq)7+ reference frames.∗ Reference value.∧ Conjugate complex.

I. INTRODUCTION

DUE TO THEIR outstanding merits, including competi-tive durability, flexible power control, and low converter

cost, DFIGs have been widely equipped in the wind-turbinegeneration systems, compared with other solutions such asfixed-speed induction generators or the ones with fully ratedconverters. However, the DFIG-based generation systems havebeen found to be more sensitive and vulnerable to grid distur-bance [1]–[4].

Nowadays, with the gradually wide use of unbalanced ornonlinear loads, particularly some unsymmetrical grid faults,imbalance and harmonic distortion (typically the fifth and sev-enth orders) become two kinds of adverse disturbances in thevoltage supply, which can even coexist in the rural grid anddistribution network. As to DFIG-based generation systems,without grid voltage imbalance or distortion considered in thecontrol strategy, wind turbines might have to be disconnectedfrom this faulty supply from overcurrents and overvoltages[5], [6], which, however, is not allowed by the latest gridcodes [1], [7]. Therefore, from both academic and industrialpoints of view, under generalized unbalanced and distorted gridvoltage conditions, it is quite valuable and extremely urgentto evaluate system behaviors in detail and, consequently, to

0278-0046/$31.00 © 2012 IEEE

HU et al.: CONTROL OF RSC AND GSC UNDER UNBALANCED AND DISTORTED GRID VOLTAGE CONDITIONS 2809

propose associated control strategies for the DFIG-based wind-turbine system.

There have been many concepts on the enhanced control andoperation of DFIG-based wind turbines under unbalanced ordistorted grid voltage conditions. However, as far as the authorsknow, the existing studies have several limits, which can beoutlined as follows.

1) The adverse grid condition was assumed either unbal-anced [8], [9], [14]–[17] or harmonically distorted only[10]–[13], [18], without being considered. Therefore, nodetailed model was proposed for the integrated DFIGsystem under generalized unbalanced and distorted net-work conditions. Furthermore, system behaviors undersuch complex network conditions are left unknown.

2) The proposed control strategies mainly focus on therotor-side converter (RSC) but seldom take the GSC intoaccount. For instance, the RSC was usually designedto eliminate DFIG torque pulsations under unbalancednetworks [8], [9], whereas in [10] and [11], its functionwas to eliminate the stator or rotor current harmonics. In[12] and [13], the RSC was controlled to compensate har-monic voltages at the point of common coupling (PCC)in stand-alone conditions. To reduce the pulsations in theDFIG torque and total active power outputting from thesystem, coordinated control strategies for the GSC andRSC were initially studied in [14] and [15]. However, thesuggested control was only applicable for the unbalancednetwork and not available to any harmonically distortedconditions.

3) Various control targets, including minimizing the stator orrotor current imbalance and distortion, reducing the statoractive and reactive power pulsations, or eliminating thetorque oscillations, were proposed in [16]–[18]. However,as indicated in [17], due to the limited control variablesof the RSC, it is impossible to achieve simultaneouselimination or smoothing of the active power and torqueoscillations. However, more control variables could beacquired from the GSC, and the expected optimized con-trol and operation are possibly achieved by coordinatingcontrol of the RSC and GSC.

By coordinating the control between RSC and GSC, thispaper presents the enhanced operation and control for theDFIG-based wind-turbine systems under generalized unbal-anced and/or distorted grid voltage conditions. This paper is or-ganized as follows. In Section II, the dynamic behaviors of theDFIG’s RSC and GSC are illustrated, whereas the coordinatedcontrol scheme is put forward to improve system operationperformance in Section III. Section IV introduces a typicalproportional–integral (PI) regulator plus a dual-frequency res-onant (R) (DFR) compensator, named the PI-DFR controller,which is applied to regulate the positive-/negative-sequencecurrents and fifth-/seventh-order harmonic currents simultane-ously. Simulation studies and experimental validations are con-ducted in Sections V and VI, respectively. Finally, Section VIIsummarizes the conclusions.

Fig. 1. Spatial relationships among the coordinates of (αβ)s, (αβ)r , (dq)+,(dq)−, (dq)5−, and (dq)7+.

II. DYNAMIC BEHAVIORS OF DFIG’s RSC AND GSC

In this paper, the grid voltage is assumed to be si-multaneously unbalanced and distorted, with the fifth- andseventh-order harmonics considered but without regard to thezero-sequence component in a three-phase three-wire system.In order to understand the dynamic behaviors of a DFIG-basedwind-turbine system under such adverse network, it is essentialto establish an integrated mathematical model for the DFIG’stwo converters.

A. RSC (DFIG) Model

During an unbalanced and distorted grid voltage, all of thestator/rotor fluxes, voltages, and currents contain positive- andnegative-sequence and harmonic components. For convenience,a variable F is usually defined to represent one of the aforemen-tioned DFIG vectors, and thus, F can be expressed in the statorstationary (αβ)s coordinate as

F αβ(t) =F αβ+(t) + F αβ−(t) + F αβ5−(t) + F αβ7+(t)

= |F αβ+(t)| ej(ω1t+ϕ+) + |F αβ−(t)| e−j(ω1t+ϕ−)

+ |F αβ5−(t)| e−j(5ω1t+ϕ5−)

+ |F αβ7+(t)| ej(7ω1t+ϕ7+) (1)

where the subscripts “+,” “−,“5−,” and “7+” represent thepositive- and negative-sequence components and the fifth- andseventh-order harmonic components, respectively, with ϕ+,ϕ−, ϕ5−, and ϕ7+ being their initial phase shifts, respectively.In addition, F can also be re-expressed in the rotor (αβ)r

coordinate, the positive synchronous (dq)+ coordinate, thenegative synchronous (dq)− coordinate, or the harmonic (dq)5−

and (dq)7+ coordinates. For clear illustrations, Fig. 1 shows thespatial relationships among these different coordinates, fromwhich the following transformations can be found:

F+dq =F αβe

−jω1t F+dq = F r

αβe−j(ω1−ωr)t (2a)

F−dq =F αβe

jω1t F−dq = F r

αβej(ω1+ωr)t (2b)

F 5−dq =F αβe

j5ω1t F 5−dq = F r

αβej(5ω1+ωr)t (2c)

F 7+dq =F αβe

−j7ω1t F 7+dq = F r

αβe−j(7ω1−ωr)t (2d)


Fig. 2. “T-representation” of the DFIG equivalent circuit in the (dq)+ coor-dinate rotating at an angular speed of ω1.

where the superscripts “r,“+,“−,“5−,” and “7+” representthe coordinates of (αβ)r, (dq)+, (dq)−, (dq)5−, and (dq)7+,respectively.

According to Fig. 1 and (2), the stator/rotor flux, voltage,and current vectors can be rewritten in terms of their positive-/negative-sequence and harmonic components in the (dq)+

frame as⎧⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎩

F+sdq = F+

sdq+ + F+sdq− + F+

sdq5− + F+sdq7+

= F+sdq+ + F−

sdq−e−j2ω1t + F 5−

sdq5−e−j6ω1t

+ F 7+sdq7+e

j6ω1t

F+rdq = F+

rdq+ + F+rdq− + F+

rdq5− + F+rdq7+

= F+rdq+ +F−

rdq−e−j2ω1t + F 5−

rdq5−e−j6ω1t

+ F 7+rdq7+e

j6ω1t

(3)

From (3), it is obvious that, in the (dq)+ coordinate, thenegative-sequence components behave as ac components pul-sating at the frequency of 2ω1 while the fifth- and seventh-orderquantities behave as ac components pulsating at the frequencyof 6ω1 in the opposite rotating directions with each other.

Fig. 2 shows the equivalent circuit of a DFIG in the (dq)+ co-ordinate, and accordingly, the stator and rotor voltage equationscan be expressed as{

U+sdq = RsI

+sdq + dΨ+

sdq/dt+ jω1Ψ+sdq

U+rdq = RrI

+rdq + dΨ+

rdq/dt+ jωsΨ+rdq

(4)

while the stator and rotor flux equations are given by{Ψ+

sdq = LsI+sdq + LmI+

rdq

Ψ+rdq = LmI+

sdq + LrI+rdq.

(5)

Under unbalanced and distorted grid voltage conditions,the instantaneous stator active and reactive powers can beexpressed as [15], [17]⎧⎨

⎩Ps = −1.5Re

[U+

sdqI+

sdq

]Qs = −1.5Im

[U+

sdqI+

sdq

].

(6)

Ignoring the voltage drop across Rs, according to (3) and (4),the stator voltage U+

sdq can be re-expressed as

U+sdq ≈ d

(Ψ+

sdq+ +Ψ−sdq−e

−j2ω1t +Ψ5−sdq5−e

−j6ω1t

+Ψ7+sdq7+e

j6ω1t)/dt

+ jω1

(Ψ+

sdq+ +Ψ−sdq−e


−j6ω1t

+Ψ7+sdq7+e

j6ω1t)

= jω1

(Ψ+

sdq+ −Ψ−sdq−e

−j2ω1t − 5Ψ5−sdq5−e

−j6ω1t

+7Ψ7+sdq7+e

j6ω1t). (7)

Similarly, according to (3) and (5), the stator current I+sdq can

be calculated as

I+sdq =

(Ψ+

sdq − LmI+rdq

)/Ls

=(Ψ+

sdq+ +Ψ−sdq−e


−j6ω1t

+Ψ7+sdq7+e

j6ω1t)/Ls

− Lm

(I+sdq+ + I−

sdq−e−j2ω1t + I5−

sdq5−e−j6ω1t

+I7+sdq7+e

j6ω1t)/Ls. (8)

Consequently, by substituting (7) and (8) into (6), the statoractive and reactive powers can then be calculated and furtherdecomposed into different components according to the pulsat-ing frequencies, i.e.,

Ps =Ps,dc +∑

i=2,4,6,8,12

Ps,cos i cos(iω1t)

+∑

i=2,4,6,8,12

Ps,sin i sin(iω1t) (9a)

Qs =Qs,dc +∑

i=2,4,6,8,12

Qs,cos i cos(iω1t)

+∑

i=2,4,6,8,12

Qs,sin i sin(iω1t) (9b)

where the subscripts “s,dc” and “s, cos i”/“s, sin i” stand forthe dc component and the cosine/sine components at the fre-quencies of iω1 (i = 2, 4, 6, 8, 12).

In addition, it can be derived from Fig. 2 that the electromag-netic power is equal to the sum of the powers exported from theequivalently controlled voltage sources jω1ψ

+sdq and jωsψ

+rdq ,

i.e.,

Pe = − 1.5Re[jω1ψ

+sdq × I

+

sdq + jωsψ+rdq × I

+

rdq

]= − 1.5ωr

(Lm

Ls

)Im

(ψ+sdq × I

+

rdq

). (10)

Similarly, according to (3) and (5), the electromagneticpower can also be calculated and decomposed as

Pe =Pe,dc +∑

i=2,4,6,8,12

Pe,cos i cos(iω1t)

+∑

i=2,4,6,8,12

Pe,sin i sin(iω1t). (11)

Consequently, the electromagnetic torque can be obtained as

Te = p× Pe/ωr (12)

where p is the number of pole pairs.


All of the coefficients of the dc and ac components in (9)and (11) are given in matrix forms, as shown in Appendix I.Since the stator flux orientation is adopted, i.e., ψ+

sq+ = 0, thecoefficient matrices in Appendix I can be further simplified.From the aforementioned discussion, it can be concluded that,under such adverse grid conditions, if no corresponding controlmeasure were designed, both the stator active/reactive powersand the torque would contain oscillations at the frequencies of2ω1, 4ω1, 6ω1, 8ω1, and 12ω1, respectively, with the stator/rotorcurrents harmfully unbalanced and distorted.

B. GSC Model

Under unbalanced and distorted network conditions, similarto that of a grid-connected voltage-source converter system[19], the instantaneous active and reactive powers exportedfrom the GSC to the network can be expressed as

Pg + jQg = − 1.5U+gdq × I

+

gdq

= − 1.5(U+

gdq+ +U−gdq−e

−j2ω1t

+U5−gdq5−e

−j6ω1t +U7+gdq7+e

j6ω1t)

×(I+

gdq+ + I−gdq−e

j2ω1t

+I5−gdq5−e

j6ω1t + I7+

gdq7+e−j6ω1t

). (13)

Similar to that of the RSC, both the active and reactivepowers of the GSC contain oscillations at the frequencies of2ω1, 4ω1, 6ω1, 8ω1, and 12ω1. Thus, (13) can be rearranged as

Pg =Pg,dc +∑

i=2,4,6,8,12

Pg,cos i cos(iω1t)

+∑

i=2,4,6,8,12

Pg,sin i sin(iω1t) (14a)

Qg =Qg,dc +∑

i=2,4,6,8,12

Qg,cos i cos(iω1t)

+∑

i=2,4,6,8,12

Qg,sin i sin(iω1t). (14b)

Refer to the authors’ previous work [19] for the detailedderivation process, and the coefficients in (14) are shown inAppendix II with the grid voltage orientation adopted, i.e.,U+gq+ = 0.Neglecting the copper losses of the stator and rotor windings,

the power flowing through the capacitor can be formulated as

CdcdVdc

dtVdc

=Pe−Ps−Pg

=(Pe,dc−Ps,dc−Pg,dc)

+∑

i=2,4,6,8,12

(Pe,cos i−Ps,cos i−Pg,cos i) cos(iω1t)

+∑

i=2,4,6,8,12

(Pe,sin i−Ps,sin i−Pg,sin i) sin(iω1t). (15)

III. COORDINATED CONTROL OF RSC AND GSC

As for the RSC, there are eight rotor current components,i.e., I+rd+, I+rq+, I−rd−, I−rq−, I5−rd5−, I5−rq5−, I7+rd7+, and I7+rq7+, thatcan be controlled to improve system responses, as representedin Appendix I. In addition to the controlled average active andreactive powers, i.e., Ps,dc and Qs,dc, six more variables canbe used for control. According to the grid codes and operationrequirements of wind-turbine systems, the oscillations of thestator active and reactive powers and torque, which deterioratethe power quality and increase extra mechanical stress on thebearing parts, are likely to be the main concerns. However,the oscillations in the torque and powers are impossible tobe eliminated simultaneously due to the limited controllablevariables. Thus, it is quite indispensable to evaluate the influ-ence of each oscillating component and to define the controltarget.

As shown in Appendix I, compared with the ac componentsof 2ω1 and 6ω1 in the stator active power, the ones of 4ω1,8ω1, and 12ω1 are only calculated by the negative-sequence andharmonic components and, thus, are much less significant andcan be ignored in the system control. Similar conclusions canbe drawn for the stator reactive power and the torque.

Therefore, the RSC is primarily controlled to eliminatethe oscillating components of 2ω1 and 6ω1 in the torque,i.e., Pe,cos 2 = 0, Pe,sin 2 = 0, Pe,cos 6 = 0, and Pe,sin 6 = 0.Considering the fact that the pulsating components of 2ω1

in the reactive power can be simultaneously eliminated, i.e.,Qs,cos 2 = 0 and Qs,sin 2 = 0, by setting Pe,cos 2 = 0, Pe,sin 2 =0 (see Appendix I); hence, the other two rotor current variablescan be utilized to cancel the pulsating components of 6ω1 inthe reactive power, i.e., Qs,cos 6 = 0 and Qs,sin 6 = 0. As aresult, according to (11) and Appendix I, the eight rotor currentreferences can be computed by

⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

I−∗rd− = −kd1I

+rd+ − kq1I

+rq+

I−∗rq− = kq1I

+rd+ − kd1I

+rq+

I5−∗rd5− =

−2ψ5−sd5−+4ψ7+

sd7+

Lm+ (3kd5 − 4kd7)I

+rd+

+ (3kq5 − 4kq7)I+rq+

I5−∗rq5− =

−2ψ5−sq5−−4ψ7+

sq7+

Lm+ (3kq5 + 4kq7)I

+rd+

− (3kd5 + 4kd7)I+rq+

I7+∗rd7+ =

−2ψ5−sd5−+4ψ7+

sd7+

Lm+ (2kd5 − 3kd7)I

+rd+

+ (2kq5 − 3kq7)I+rq+

I7+∗rq7+ =

2ψ5−sq5−+4ψ7+

sq7+

Lm− (2kq5 + 3kq7)I

+rd+

+ (2kd5 + 3kd7)I+rq+

(16)

where kd1 = ψ−sd−/ψ

+sd+, kq1 = ψ−

sq−/ψ+sd+, kd5 =

ψ5−sd5−/ψ

+sd+, kq5 = ψ5−

sq5−/ψ+sd+, kd7 = ψ7+

sd7+/ψ+sd+, and

kq7 = ψ7+sq7+/ψ

+sd+.

Similar to that of the RSC, there are eight GSC currentcomponents, i.e., I+gd+, I+gq+, I−gd−, I−gq−, I5−gd5−, I5−gq5−, I7+gd7+,

and I7+gq7+, that can be used to optimize the system operation,as shown in Appendix II. Apart from the controlled averageactive and reactive powers Pg,dc and Qg,dc, the remnant sixvariables are available for other controlling purposes. The GSC


is designed to cancel the oscillations outputting from the statoractive power and the oscillations at 6ω1 in the reactive power aswell, corresponding to the RSC’s control target. Consequently,the following equations can be formulated with different orien-tation schemes:

⎧⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎩

Pg,cos 2 − Ps,cos 2 = 0Pg,sin 2 − Ps,sin 2 = 0Pg,cos 6 − Ps,cos 6 = 0Pg,sin 6 − Ps,sin 6 = 0Qg,cos 6 = 0Qg,sin 6 = 0.

(17)

According to (17) and Appendixes I and II, the GSC’s currentreferences can be assigned as⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

I−∗gd− =

2Ps,cos 2

3U+gd+

− λd1I+gd+ − kq1I

+gq+

I−∗gq− =

2Ps,sin 2

3U+gd+

− λq1I+gd+ + λd1I

+gq+

I5−∗gd5− =

Ps,cos 6

3U+gd+

− λd7I+gd+ + λq7I

+gq+

I5−∗gq5− =

Ps,sin 6

3U+gd+

+ λq7I+gd+ − λd7I

+gq+

I7+∗gd7+ =

Ps,cos 6

3U+gd+

− λd5I+gd+ − λq5I

+gq+

I7+∗gq7+ = −Ps,sin 6

3U+gd+

+ λq5I+gd+ − λd5I

+gq+

(18)

where λd1 = U−gd−/U

+gd+, λq1 = U−

gq−/U+gd+, λd5 =

U5−gd5−/U

+gd+, λq5 = U5−

gq5−/U+gd+, λd7 = U7+

gd7+/U+gd+,

and λq7 = U7+gq7+/U

+gd+.

From (15), it is evident that, once the oscillations in thetorque and overall active power are eliminated, the ripples inthe dc link voltage will also be substantially minimized.

IV. CONTROL DESIGN

A. Current Controller

In order to obtain the current references in (16) and (18), animportant and necessary processing is to extract the positive-and negative-sequence and harmonic stator fluxes ψ+

sdq+,

ψ−sdq−, ψ5−

sdq5−, and ψ7+sdq7+ and the grid voltage components

U+gdq+, U−

gdq−, U5−gdq5−, and U7+

gdq7+ accurately and rapidlyfrom the original vectors ψsαβ and Ugαβ . A new decomposingscheme based on multiple second-order generalized integratorsand a frequency-locked loop (MSOGI-FLL) is introduced, andthe detailed implementations can be found in [20].

Once the RSC and GSC current references are acquired forthe coordinated control target, a precise current controller mustbe designed to regulate them accurately and rapidly. As men-tioned previously, the negative-sequence components and thefifth- and seventh-order harmonic components in the (dq)+ ref-erence frame behave as the ac components pulsating at 2ω1 and6ω1, respectively. For this reason, the current controller appliedshould be capable of not only regulating the dc components butalso nullifying the error of the ac components at 2ω1 and 6ω1.Based on the PI-R controller in [15], a PI-DFR controller isdeveloped in this paper, in which the PI regulator is the same

as a conventional PI controller whereas the DFR compensatorconsists of two resonant regulators tuned at double and sixtimes the grid frequency, respectively. As illustrated in [15],the resonant regulator is a generalized ac integrator and canprovide infinite gain at the resonant frequency. Undoubtedly,the positive-/negative-sequence components and fifth-/seventh-order harmonic components can be simultaneously regulatedin the (dq)+ coordinate by the proposed current controller.The complete transfer function of the PI-DFR regulator isgiven as

CPI−DFR(s) =Kp +Ki

s+

sωc1Kr1

s2 + 2ωc1s+ (±2ω1)2

+sωc2Kr2

s2 + 2ωc2s+ (±6ω1)2(19)

where Kp, Ki, and Kr1 and Kr2 are the proportional, integral,and resonant parameters, respectively; ωc1 and ωc2, namedcutoff frequencies, are introduced into the resonant part toreduce its sensitivity against slight frequency variations at theresonant poles. In practice, a cutoff frequency of 5–15 rad/s isfound to be satisfactory with both rapid response and preferablestability [21]. Additionally, it is worth noting that the proposedPI-DFR controller is insensitive to parameter variations, whichcan be derived from the authors’ previous paper [18], wherea PI-R controller is adopted with its parameter robustnessfully discussed through theoretical analysis and simulationstudies.

B. Modulated Voltages of RSC and GSC

According to (4) and (5), the rotor voltage of a DFIG duringunbalanced and distorted network voltage can be represented inthe (dq)+ coordinate as

U+rdq =RrI

+rdq + σLr

(dI+

rdq/dt+ jωsI+rdq

)+ Lm

(U+

sdq −RsI+sdq − jωrψ

+sdq

)/Ls

=σLrV+rdq +E+

rdq (20)

where V +rdq is the output of the PI-DFR controller and given as

V +rdq =

d

dtI+rdq = CPI−DFR(s)

(I+∗rdq − I+

rdq

)(21)

and E+rdq is the equivalent rotor back electromagnetic force,

acting as a disturbance to the PI-DFR controller and possiblygiven by

E+rdq =

(RrI

+rdq + jωsσLrI

+rdq

)+ Lm

(U+sdq −RsI

+sdq − jωrψ

+sdq

)/Ls. (22)

The overall rotor control voltage is then transformed from the(dq)+ reference frame to the rotor (αβ)r frame as [14], [17]

U rrαβ = U+

rdqej(θs−θr). (23)


Fig. 3. Schematic diagram of the proposed current controllers.

Similar to that of the RSC, the controlled voltage of the GSCcan be calculated as [19]

E+gdq = −RgI

+gdq − LgV

+gdq − jω1LgI

+gdq +U+

gdq (24)

where V +gdq is the PI-DFR controller output and given as

V +gdq =

d

dtI+gdq = CPI−DFR(s)

(I+∗gdq − I+

gdq

). (25)

The GSC’s controlled voltage is then transformed from thesynchronous (dq)+ frame to the stationary frame as [19]

Egαβ = E+gdqe

jθg . (26)

C. System Implementation

Fig. 3 shows the schematic diagram of the proposed currentcontrollers for the RSC and GSC. It is necessary to pointout that, since the current references in (16) and (18) arenot in the same reference frame, the negative-sequence andharmonic components should be transformed to the identical(dq)+ coordinate so as to be regulated simultaneously, i.e.,

I+∗r(g)dq = I+∗

r(g)dq+ + I+∗r(g)dq− + I+∗

r(g)dq5− + I+∗r(g)dq7+

= I+∗r(g)dq + I−∗

r(g)dq−e−j2θs(g) + I5−∗

r(g)dq5−e−j6θs(g)

+ I7+∗r(g)dq7+e

j6θs(g) . (27)

Finally, with the modulated voltages given in (23) and (26), aspace vector modulation (SVM) technique can be introducedto produce the required switching voltage vectors with theirrespective duration times.

V. SIMULATION STUDIES

To validate the correctness of the developed model and theeffectiveness of the proposed control strategy, simulation stud-ies were first conducted using Matlab/Simulink. The parametersof the DFIG and its converter controllers are listed in Tables Iand II, respectively, while the system’s schematic diagram isshown in Fig. 4. The nominal dc link voltage is 1050 V, and the

TABLE IPARAMETERS OF THE SIMULATED DFIG

TABLE IIPARAMETERS OF THE RSC AND GSC CONTROLLERS

Fig. 4. Schematic diagram of the simulated DFIG system.

switching frequencies for both the RSC and GSC are 3 kHz.Considering that the mechanical time constant is much largerthan the electromagnetic one, the rotor speed can be assumedto be fixed at 1.2 p.u. during simulations. In addition, a three-phase programmable voltage source is employed to emulatethe adverse grid. Fig. 5 shows the simulation results with 4%voltage imbalance and 3% fifth-order harmonic content, wherethe following three different control modes are adopted andcompared.

1) Mode I (t = 0–0.2 s): Conventional vector control with-out considering the voltage imbalance or distortion forboth the RSC and GSC, i.e., the DFR compensators forthe RSC and GSC are disabled.


Fig. 5. Simulation results with different control modes. (a) Three-phase stator voltages (in per unit). (b) Three-phase rotor currents (in per unit). (c) d+-axisrotor current reference and response (in per unit). (d) q+-axis rotor current reference and response (in per unit). (e) Electromagnetic torque (in per unit). (f) DClink voltage (in per unit). (g) Three-phase stator currents (in per unit). (h) Three-phase GSC currents (in per unit). (i) Three-phase total currents (in per unit).(j) Stator active and reactive powers (in per unit). (k) GSC active and reactive powers (in per unit). (l) Total active and reactive powers (in per unit).

2) Mode II (t = 0.2–0.4 s): The DFR compensator for theRSC is enabled for minimizing the torque oscillation,whereas the DFR compensator for the GSC is disabled.

3) Mode III (t = 0.4–0.6 s): The DFR compensators forboth the RSC and GSC are enabled, i.e., adopting theproposed coordinated control strategy.

As can be seen in Fig. 5, under Mode I, both the stator andgrid currents contain negative-sequence and harmonic compo-nents. Consequently, the total current at the PCC, i.e., Itabc,is unbalanced and distorted. Additionally, the stator active andreactive powers Ps and Qs and the GSC’s active and reactivepowers Pg and Qg all contain oscillating components of 2ω1

and 6ω1, as well as other less significant ones of 4ω1, 8ω1, and12ω1. As a result, the torque Te and the total active and reactivepowers Pt and Qt oscillate badly. Furthermore, oscillationsalso appear in the common dc link voltage. However, as canbe seen in Fig. 5(d) and (e), when the DFR compensator forthe RSC is enabled at 0.2 s, the rotor negative-sequence andharmonic currents are immediately regulated according to theoptimized target. Consequently, the oscillations in the torqueand stator reactive power are quickly eliminated, as shown inFig. 5(e) and (j). However, there are still oscillations with 100and 300 Hz existing significantly in the total active power andthe dc link voltage during Mode II control. At 0.4 s, the controlmethod is switched to Mode III, and the oscillation of the GSCactive power compensates that of the stator active power; conse-quently, the 100- and 300-Hz oscillations in the generated totalactive power of the system diminish immediately, as shownin Fig. 5(k) and (l). Moreover, the dc voltage oscillation issubstantially minimized under Mode III, as shown in Fig. 5(f).

TABLE IIICOMPARISON AMONG DIFFERENT CONTROL MODES DURING

UNBALANCED AND DISTORTED GRID VOLTAGE

For clear comparison, Table III summarizes the total har-monic distortion (THD) of the system output current, the os-cillation amplitudes of the total active and reactive powers, theelectromagnetic torque, and the dc link voltage with differentcontrol modes. It is evident that the proposed control strategycan significantly improve the control and operation behaviorsof DFIG systems under unbalanced and distorted grid supplyconditions.

Further tests with the conventional control, i.e., Mode I,and the proposed strategy, i.e., Mode III, were carried outand compared during a larger transient voltage imbalance of7.5% and a fifth-order harmonic of 4.5% within t = 0.1–0.5 s,as shown in Fig. 6(a) and (b), respectively. As can be seen,compared with the conventional control, the proposed methodis capable of achieving much idealized operation during suchtransient grid imbalance and distortion. However, it is worthpointing out that, compared with the conventional control, theproposed method with the voltage imbalance and distortioncompensated requires a relatively higher voltage for both the


Fig. 6. Simulated results during a transient imbalance of 7.5% and a fifth-order harmonic of 4.5% within 0.1–0.5 s. (a) Conventional control. (b) Coordinatedcontrol.

Fig. 7. Schematic diagram of the tested DFIG system.

RSC and GSC, which could exceed the voltage capability of thetwo converters. In other words, the compensation capability ofthe proposed control is limited by the converters’ voltage rating.

VI. EXPERIMENTAL VALIDATIONS

Experimental tests were conducted on a 5.5-kW DFIG setupas schematically shown in Fig. 7. The DFIG is driven by adc motor at the desired speed with its stator connected via aY/Δ-type step-up transformer to a developed programmable

TABLE IVPARAMETERS OF THE TESTED DFIG

power supply (PPS), which can provide the desired three-phasevoltage with negative-sequence and harmonic components su-perposed flexibly on its fundamentals. The parameters of thetested DFIG are listed in Table IV. The RSC and GSC are con-trolled respectively by two Texas Instruments TMS320F2812DSPs, and the switching frequency for both converters is2.5 kHz with a sampling frequency of 10 kHz. SVM is adoptedto generate the switching pulses. Additionally, the dc linkcapacitor has 1100 μF. A low-pass filter module, composedof 3-mH inductors L1 and 25-μF capacitors C1, is connected


Fig. 8. Measured waveforms of system steady responses with Mode I and Mode II. (CH1) One-phase stator voltage (200 V/div). (CH2) One-phase stator current(10 A/div). (CH3) and (CH4) Two-phase rotor currents (10 A/div). (CH5) DC link voltage (40 V/div). (CH6) Electromagnetic torque (10 N · m/div). (CH7) and(CH8) Stator active and reactive powers (2 kW/div and 2 kvar/div, respectively). (a) Mode I. (b) Mode II.

Fig. 9. Measured waveforms of system transient responses. (CH1) One-phase stator voltage (200 V/div). (CH2) One-phase stator current (10 A/div). (CH3) and(CH4) Two-phase rotor currents (10 A/div). (CH5) DC link voltage (40 V/div). (CH6) Electromagnetic torque (10 N · m/div). (CH7) and (CH8) Stator activeand reactive powers (2 kW/div and 2 kvar/div, respectively). (a) Control mode change (from Mode I to Mode II). (b) Generator speed variation (from 800 to1200 r/min) with Mode II.

with the GSC to reduce the switching frequency harmonics out-putting from the converters. All the waveforms were acquiredby a YOKOGAWA eight-channel DL750 oscilloscope.

Fig. 8 shows a comparison of the measured waveformsimplemented by Mode I and Mode II, where the contents ofnegative sequence and fifth-order harmonic were set as 4%and 3%, respectively. The average stator active and reactivepowers outputting from the DFIG were Ps,dc = 1.5 kW andQs,dc = 0.5 kvar (inductive). The DFIG speed was fixed at800 r/min with the corresponding synchronous speed being1000 r/min. Compared with Mode I, i.e., Fig. 8(a), where thestator and rotor currents are badly distorted with obvious statoractive/reactive power and torque oscillations, Mode II achieveda much smoother operation with reduced torque and poweroscillations, as shown in Fig. 8(b).

To evaluate the dynamic response of the proposed controller,tests were carried out with control mode change and speed

variation, respectively, where more seriously adverse voltageconditions were implemented, viz., the negative-sequence con-tent and fifth-order harmonic content were set as 7% and 5%,respectively. As shown in Fig. 9(a), when the control methodis changed from Mode I to Mode II, the 100- and 300-Hzoscillations in the generator torque and stator reactive powerare removed rapidly. Fig. 9(b) shows the system response withthe rotor’s speed gradually changed from 800 to 1200 r/min,where the stator active and reactive powers were fixed at 0.5 kWand 0.5 kvar (inductive), respectively, for simplified analysis. Itis evident that the proposed controller provides well dynamicresponse during the speed variations.

Further tests were carried out under different contents ofnegative-sequence and/or harmonic components in the gridvoltage. The measured results behave similarly to those inFigs. 8 and 9. The waveforms are not provided here due to spacelimitation.


However, since the dc link capacitor used in the tested setupis larger than the required one, the voltage oscillation in thedc link voltage was not so apparent during the tests. Due tothe signal communication incapability of the two converters,the GSC current references, designed to compensate statorpower oscillations, could not be obtained in the laboratory atthe moment. Thus, unfortunately, tests with Mode III are notgiven in this paper, which will be included in the authors’successive work with the setup improvement in the near future.However, the effectiveness of the proposed control scheme hasbeen initially validated by the experimental results.

VII. CONCLUSION

In this paper, a coordinated control strategy for a DFIG-based wind power generation system under unbalanced anddistorted grid voltage conditions has been investigated in detail.The simulation studies and experimental results demonstratethe correctness of the developed model and the effectivenessof the proposed control strategies. As a result, the followingconclusions can be summarized and highlighted.

1) Under unbalanced and distorted grid voltage conditions,if no corresponding control measures are taken, the to-tal current output from a DFIG-based system will bebadly distorted. In addition, the total output active and

reactive powers, the electromagnetic torque, and thedc link voltage will all contain ac components, par-ticularly the pulsations at the frequencies of 2ω1 and6ω1, which can not only deteriorate the heating con-dition and power quality but also reduce the lifetimeof the turbine shaft system and the dc link electrolyticcapacitor.

2) To provide an optimized and smooth operation, the RSCis controlled to eliminate the torque oscillations, whereasthe GSC is designed to obtain constant active power out-put and to minimize the oscillations in the dc link voltageas well. A current controller, consisting of a typical PIregulator and a DFR compensator, is implemented in thepositive (dq)+ frame, which is capable of simultaneouslyregulating the positive-/negative-sequence currents andfifth-/seventh-order harmonic currents for both the RSCand GSC.

3) The control strategies, proposed in this paper, are notonly applicable for the coexisting conditions of gridvoltage imbalances and distortions but also workablefor either unbalanced or distorted cases. Although nocomplete experimental results are provided in this paper,the effectiveness of the proposed control has been wellverified by simulation results and initial experimentaltests.

⎡⎢⎣Ps,cos 2

Ps,sin 2

Qs,cos 2

Qs,sin 2

⎤⎥⎦= − 3ω1

2Ls

⎡⎢⎣

ψ−sq− −ψ−

sd− −ψ+sq+ ψ+

sd+

−ψ−sd− −ψ−

sq− −ψ+sd+ −ψ+

sq+


sq− ψ+sd+ ψ+

sq+

−ψ−sq− ψ−

sd− −ψ+sq+ ψ+

sd+

⎤⎥⎦⎛⎜⎝⎡⎢⎣ψ+

sd+

ψ+sq+

ψ−sd−

ψ−sq−

⎤⎥⎦− Lm

⎡⎢⎣I+rd+I+rq+I−rd−I−rq−

⎤⎥⎦⎞⎟⎠ (A1)

⎡⎢⎣Ps,cos 4

Ps,sin 4

Qs,cos 4

Qs,sin 4

⎤⎥⎦= − 3ω1

2Ls

⎡⎢⎣

5ψ5−sq5− −5ψ5−

sd5− ψ−sq− −ψ−

sd−−5ψ5−

sd5− −5ψ5−sq5− ψ−

sd− ψ−sq−

−5ψ5−sd5− −5ψ5−

sq5− −ψ−sd− −ψ−

sq−−5ψ5−

sq5− 5ψ5−sd5− ψ−

sq− −ψ−sd−

⎤⎥⎦⎛⎜⎝⎡⎢⎣

ψ−sd−

ψ−sq−

ψ5−sd5−

ψ5−sq5−

⎤⎥⎦− Lm

⎡⎢⎣

I−rd−I−rq−I5−rd5−I5−rq5−

⎤⎥⎦⎞⎟⎠ (A2)

⎡⎢⎣Ps,cos 8

Ps,sin 8

Qs,cos 8

Qs,sin 8

⎤⎥⎦= − 3ω1

2Ls

⎡⎢⎣−7ψ7+

sq7+ 7ψ7+sd7+ ψ−

sq− −ψ−sd−

−7ψ7+sd7+ −7ψ7+

sq7+ −ψ−sd− −ψ−

sq−7ψ7+

sd7+ 7ψ7+sq7+ −ψ−

sd− −ψ−sq−

−7ψ7+sq7+ 7ψ7+

sd7+ −ψ−sq− ψ−

sd−

⎤⎥⎦⎛⎜⎝⎡⎢⎣

ψ−sd−

ψ−sq−

ψ7+sd7+

ψ7+sq7+

⎤⎥⎦− Lm

⎡⎢⎣

I−rd−I−rq−I7+rd7+I7+rq7+

⎤⎥⎦⎞⎟⎠ (A3)

⎡⎢⎣Ps,cos 12

Ps,sin 12

Qs,cos 12

Qs,sin 12

⎤⎥⎦= − 3ω1

2Ls

⎡⎢⎣−7ψ7+

sq7+ 7ψ7+sd7+ 5ψ5−

sq5− −5ψ5−sd5−

−7ψ7+sd7+ −7ψ7+

sq7+ −5ψ5−sd5− −5ψ5−

sq5−7ψ7+

sd7+ 7ψ7+sq7+ −5ψ5−

sd5− −5ψ5−sq5−

−7ψ7+sq7+ 7ψ7+

sd7+ −5ψ5−sq5− 5ψ5−

sd5−

⎤⎥⎦⎛⎜⎝⎡⎢⎣ψ5−

sd5−ψ5−

sq5−ψ7+

sd7+

ψ7+sq7+

⎤⎥⎦− Lm

⎡⎢⎣I5−rd5−I5−rq5−I7+rd7+I7+rq7+

⎤⎥⎦⎞⎟⎠ (A4)

⎡⎢⎢⎢⎢⎣

Ps,dc

Qs,dc

Ps,cos 6

Ps,sin 6

Qs,cos 6

Qs,sin 6

⎤⎥⎥⎥⎥⎦= − 3ω1

2Ls

⎡⎢⎢⎢⎢⎢⎣

0 0 0 0ψ+

sd+ ψ+sq+ −ψ−

sd− −ψ−sq−

5ψ5−sq5− − 7ψ7+

sq7+ −5ψ5−sd5− + 7ψ7+

sd7+ 0 0

−5ψ5−sd5− − 7ψ7+

sd7+ −5ψ5−sq5− − 7ψ7+

sq7+ 0 0

−5ψ5−sd5− + 7ψ7+

sd7+ −5ψ5−sq5− + 7ψ7+

sq7+ 0 0

−5ψ5−sq5− − 7ψ7+

sq7+ 5ψ5−sd5− + 7ψ7+

sd7+ 0 0

0 0 0 0−5ψ5−

sd5− −5ψ5−sq5− 7ψ7+

sd7+ 7ψ7+sq7+

−ψ+sq+ ψ+

sd+ −ψ+sq+ ψ+

sd+

−ψ+sd+ −ψ+

sq+ ψ+sd+ ψ+

sq+

ψ+sd+ ψ+

sq+ ψ+sd+ ψ+

sq+

−ψ+sq+ ψ+

sd+ ψ+sq+ −ψ+

sd+

⎤⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

ψ+sd+

ψ+sq+

ψ−sd−

ψ−sq−

ψ5−sd5−

ψ5−sq5−

ψ7+sd7+

ψ7+sq7+

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦+3Lmω1

2Ls


×

⎡⎢⎢⎢⎢⎢⎣

−ψ+sq+ ψ+

sd+ ψ−sq− −ψ−

sd−ψ+

sd+ ψ+sq+ −ψ−

sd− −ψ−sq−

5ψ5−sq5− − 7ψ7+

sq7+ −5ψ5−sd5− + 7ψ7+

sd7+ 0 0

−5ψ5−sd5− − 7ψ7+

sd7+ −5ψ5−sq5− − 7ψ7+

sq7+ 0 0

−5ψ5−sd5− + 7ψ7+

sd7+ −5ψ5−sq5− + 7ψ7+

sq7+ 0 0

−5ψ5−sq5− − 7ψ7+

sq7+ 5ψ5−sd5− + 7ψ7+

sd7+ 0 0

5ψ5−sq5− −5ψ5−

sd5− −7ψ7+sq7+ 7ψ7+

sd7+

−5ψ5−sd5− −5ψ5−

sq5− 7ψ7+sd7+ 7ψ7+

sq7+

−ψ+sq+ ψ+

sd+ −ψ+sq+ ψ+

sd+

−ψ+sd+ −ψ+

sq+ ψ+sd+ ψ+

sq+

ψ+sd+ ψ+

sq+ ψ+sd+ ψ+

sq+

−ψ+sq+ ψ+

sd+ ψ+sq+ −ψ+

sd+

⎤⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

I+rd+I+rq+I−rd−I−rq−I5−rd5−I5−rq5−I7+rd7+I7+rq7+

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(A5)

⎡⎢⎢⎢⎢⎣

Pe,dc

Pe,cos 2

Pe,cos 4

Pe,cos 6

Pe,cos 8

Pe,cos 12

⎤⎥⎥⎥⎥⎦= − 3Lmωr

2Ls

⎡⎢⎢⎢⎢⎢⎣

ψ+sq+ −ψ+

sd+ ψ−sq− −ψ−

sd−ψ−

sq− −ψ−sd− ψ+

sq+ −ψ+sd+

0 0 ψ5−sq5− −ψ5−

sd5−ψ5−

sq5− + ψ7+sq7+ −ψ5−

sd5− − ψ7+sd7+ 0 0

0 0 ψ7+sq7+ −ψ7+

sd7+

0 0 0 0

ψ5−sq5− − ψ5−

sd5− ψ7+sq7+ −ψ7+

sd7+

0 0 0 0ψ−

sq− −ψ−sd− 0 0

ψ+sq+ −ψ+

sd+ ψ+sq+ −ψ+

sd+

0 0 ψ−sq− −ψ−

sd−ψ7+

sq7+ −ψ7+sd7+ ψ5−

sq5− −ψ5−sd5−

⎤⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣


⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(B1)

⎡⎢⎢⎣

Pe,sin 2

Pe,sin 4

Pe,sin 6

Pe,sin 8

Pe,sin 12

⎤⎥⎥⎦= − 3Lmωr

2Ls

⎡⎢⎢⎢⎣


sq− ψ+sd+ ψ+

sq+

0 0 −ψ5−sd5− −ψ5−

sq5−−ψ5−

sd5− + ψ7+sd7+ −ψ5−

sq5− + ψ7+sq7+ 0 0

0 0 ψ7+sd7+ ψ7+

sq7+

0 0 0 0

0 0 0 0ψ−

sd− ψ−sq− 0 0

ψ+sd+ ψ+

sq+ −ψ+sd+ −ψ+

sq+

0 0 −ψ−sd− −ψ−

sq−ψ7+

sd7+ ψ7+sq7+ −ψ5−

sd5− −ψ5−sq5−

⎤⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣


⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(B2)

⎡⎢⎣Pg,cos 2

Pg,sin 2

Qg,cos 2

Qg,sin 2

⎤⎥⎦= − 3

2

⎡⎢⎢⎣

U−gd− U−

gq− U+gd+ U+

gq+

U−gq− −U−

gd− −U+gq+ U+

gd+

U−gq− −U−

gd− U+gq+ −U+

gd+

−U−gd− −U−

gq− U+gd+ U+

gq+

⎤⎥⎥⎦⎡⎢⎣I+gd+I+gq+I−gd−I−gq−

⎤⎥⎦ (C1)

⎡⎢⎣Pg,cos 4

Pg,sin 4

Qg,cos 4

Qg,sin 4

⎤⎥⎦= − 3

2

⎡⎢⎢⎣

U5−gd5− U5−

gq5− U−gd− U−

gq−U5−

gq5− −U5−gd5− −U−

gq− U−gd−

U5−gq5− −U5−

gd5− U−gq− −U−

gd−−U5−

gd5− −U5−gq5− U−

gd− U−gq−

⎤⎥⎥⎦⎡⎢⎣

I+gd+I+gq+I5−gd5−I5−gq5−

⎤⎥⎦ (C2)

⎡⎢⎣Pg,cos 8

Pg,sin 8

Qg,cos 8

Qg,sin 8

⎤⎥⎦= − 3

2

⎡⎢⎢⎣

U7+gd7+ U7+

gq7+ U−gd− U−

gq−−U7+

gq7+ U7+gd7+ U−

gq− −U−gd−

U7+gq7+ −U7+

gd7+ U−gq− −U−

gd−U7+

gd7+ U7+gq7+ −U−

gd− −U−gq−

⎤⎥⎥⎦⎡⎢⎣

I−gd−I−gq−I7+gd7+I7+gq7+

⎤⎥⎦ (C3)

⎡⎢⎣Pg,cos 12

Pg,sin 12

Qg,cos 12

Qg,sin 12

⎤⎥⎦= − 3

2

⎡⎢⎢⎣

U7+gd7+ U7+

gq7+ U5−gd5− U5−

gq5−−U7+

gq7+ U7+gd7+ U5−

gq5− −U5−gd5−

U7+gq7+ −U7+

gd7+ U5−gq5− −U5−

gd5−U7+

gd7+ U7+gq7+ −U5−

gd5− −U5−gq5−

⎤⎥⎥⎦⎡⎢⎣I5−gd5−I5−gq5−I7+gd7+I7+gq7+

⎤⎥⎦ (C4)

⎡⎢⎢⎢⎢⎣

Pg,dc

Qg,dc

Pg,cos 6

Pg,sin 6

Qg,cos 6

Qg,sin 6

⎤⎥⎥⎥⎥⎦= − 3

2

⎡⎢⎢⎢⎢⎢⎢⎣

U+gd+ U+

gq+ U−gd− U−

gq−U+

gq+ −U+gd+ U−

gq− −U−gd−

U5−gd5− + U7+

gd7+ U5−gq5− + U7+

gq7+ 0 0

−U5−gq5− + U7+

gq7+ U5−gd5− − U7+

gd7+ 0 0

U5−gq5− − U7+

gq7+ −U5−gd5− − U7+

gd7+ 0 0

−U5−gq5− + U7+

gq7+ U5−gd5− − U7+

gd7+ 0 0

U5−gd5− U5−

gq5− U7+gd7+ U7+

gq7+

U5−gq5− −U5−

gd5− U7+gq7+ −U7+

gd7+

U+gd+ −U+

gq+ U+gd+ U+

gq+

U+gd+ U+

gq+ U+gd+ U+

gq+

U+gq+ −U+

gd+ U+gq+ −U+

gd+

U+gq+ −U+

gd+ −U+gq+ U+

gd+

⎤⎥⎥⎥⎥⎥⎥⎦

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

I+gd+I+gq+I−gd−I−gq−I5−gd5−I5−gq5−I7+gd7+I7+gq7+

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦

(C5)


APPENDIX I

The coefficients of the dc and ac components in (9) and (11)are given in (A1)–(A5), (B1), and (B2), shown on the previoustwo pages.

APPENDIX II

The coefficients in (14) are given in (C1)–(C5), shown on theprevious page.

REFERENCES

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Jiabing Hu (S’05–M’10) received the B.Sc. andPh.D. degrees from the College of Electrical En-gineering, Zhejiang University, Hangzhou, China,in 2004 and 2009, respectively.

From 2007 to 2008, he was a Visiting Scholarwith the Department of Electronic and Electrical En-gineering, University of Strathclyde, Glasgow, U.K.From April 2010 to August 2011, he was a Postdoc-toral Research Associate with the Sheffield SiemensWind Power Research Centre and the Departmentof Electronic and Electrical Engineering, The Uni-

versity of Sheffield, Sheffield, U.K. Since September 2011, he has been aProfessor with the School of Electrical and Electronic Engineering, HuazhongUniversity of Science and Technology, Wuhan, China. His current researchinterests include ac machine drives, control of renewable energy generations,and grid integration of large-scale wind farms.

Hailiang Xu (S’10) received the B.Sc. degree fromthe College of Information and Control Engineering,China University of Petroleum, Dongying, China,in 2008. He has been working toward the Ph.D.degree in the College of Electrical Engineering,Zhejiang University, Hangzhou, China, since 2009.

His current research interests include power elec-tronics and enhanced control and operation ofvariable-speed constant-frequency wind power gen-eration systems.

Yikang He (SM’90) was born in Changsha, China.He received the B.Sc. degree from the Depart-ment of Electrical Engineering, Tsinghua University,Beijing, China, in 1964.

In 1964, he joined the College of Electrical Engi-neering, Zhejiang University, Hangzhou, China, asa Teacher, where he is currently a Professor. Hiscurrent research interests include electric machin-ery, motor control, power electronics, and renewableenergy conversion.

Coordinated Control of Dfig Rsc and Gsc Under Generalized Unbalanced and Distorted Grid Voltage...

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