06507348.pdf

894 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 29, NO. 2, FEBRUARY 2014

Direct Power Control of Doubly Fed InductionGenerator Under Distorted Grid Voltage

Heng Nian, Member, IEEE, and Yipeng Song

AbstractThis paper presents a direct power control (DPC)strategy for a doubly fed induction generator (DFIG)-based windpower generation system under distorted grid voltage. By ana-lyzing the six times grid frequency power pulsation produced bythe fifth and seventh grid voltage harmonic components, a novelDPC strategy with vector proportional integrated (VPI) regulatorhas been proposed to implement the smooth active and reactivepower output of DFIG. The performance analysis of the proposedDPC strategy, including the steady and dynamic state performance,closed-loop operation stability, and rejection capability for the gridvoltage distorted component and back EMF compensation item hasbeen investigated. The availability of the proposed DPC strategywith a VPI regulator is verified by experiment results of DFIGsystem under harmonically distorted grid condition.

Index TermsDirect power control (DPC), doubly fed induc-tion generator (DFIG), harmonically distorted grid voltage, vectorproportional integrated (VPI) regulator.

NOMENCLATUREU s ,U r Stator and rotor voltage vectors.Is , Ir Stator and rotor current vectors.s ,r Stator and rotor flux linkage vectors.1 , r , s Stator, rotor, and slip angular frequencies.Ps,Qs Stator output active and reactive powers.Ls, Lr Stator and rotor self inductances.Ls, Lr Stator and rotor leakage inductances.Lm Mutual inductance.Rs,Rr Stator and rotor resistances.s, r Stator voltage angle and rotor angle.Subscripts, Stationary , axes.d, q Synchronous d, q axes.s, r Stator, rotor.+, 5,7+, r Fundamental, fifth order, seventh order, and rotor

components.Superscripts+, 5,7+, r (dq)+ , (dq)5,(dq)7+ ,and rotor ()r reference

frames.

Manuscript received January 20, 2013; revised March 11, 2013; acceptedApril 10, 2013. Date of current version August 20, 2013. This work was sup-ported in part by the China National Science and Technology Support Programunder Project 2011AA050204, and the National Natural Science Foundationof China under Project 51277159. Recommended for publication by AssociateEditor V. Staudt.

The authors are with the College of Electrical Engineering, Zhejiang Uni-versity, 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/TPEL.2013.2258943

Reference value. Conjugate complex.T Matrix transpose.

I. INTRODUCTION

W IND power generation based on the doubly-fed induc-tion generator (DFIG) has gained increasing popularitydue to several advantages, including smaller converters ratingaround 30% of the generator rating, variable speed and four-quadrant active and reactive power operation capabilities, lowerconverter cost, and power losses compared with the fixed-speedinduction generators or synchronous generators with full-sizedconverters [1], [2]. Several novel control strategies have beeninvestigated in order to improve the DFIG operation perfor-mance, i.e., the vector oriented control (VOC) [3], direct powercontrol [4], and predictive current control [5].

Up to now, the steady and transient response of DFIG-basedwind power generation system under balanced [6] and unbal-anced [7][11] grid voltage conditions have been discussedwidely. There are mainly two control methods adopted, VOC,and direct power control (DPC). The authors in [7][9] intro-duced the unbalanced control strategy with the VOC technique,in which the detrimental influence on the DFIG system causedby negative component of the grid voltage was also analyzed.Several alternative control targets focusing on the eliminationof negative component of stator/rotor current, as well as statoractive/reactive power and electromagnetic torque pulsation wereproposed. Zhou et al. [10], [11] explicitly illustrated the unbal-anced control strategy using the DPC technique with differentstator power compensation item, in which the five different con-trol targets were proposed to improve the DFIG operation abilityunder transient unbalanced grid voltage.

However, there are always voltage harmonic distorted com-ponents in the transmission system of the power grid. It has beenpointed out that the highly distorted stator/rotor current, signifi-cant electromagnetic torque and power oscillations would occurif grid voltage harmonics are not taken into account by DFIGscontrol strategy [12]. The authors in [13][16] have presenteda theoretical analysis and an improved VOC strategy for DFIG,in which alternative control targets were proposed to keep thethree-phase sinusoidal stator/rotor current, or remove pulsationsin both stator active and reactive powers, or remove pulsationsin the electromagnetic torque and stator reactive power. Fur-thermore, in addition to the conventional rotor current controlloop, a distinctive and independent stator current resonant con-trol loop was also given out in [17] to successfully eliminate thestator current harmonic components.

0885-8993 2013 IEEE

NIAN AND SONG: DIRECT POWER CONTROL OF DOUBLY FED INDUCTION GENERATOR UNDER DISTORTED GRID VOLTAGE 895

Nevertheless, all the aforementioned investigation on theDFIG system under the harmonic voltage is based on the VOCtechnique, which requires the decomposition of grid voltagefundamental and harmonic components; thus, the closed-loopoperation stability and dynamic response of the entire controlsystem will be deteriorated [10], [11]. The DPC technique hasbeen proved to be preponderant for DFIG control, such as sim-ple implementation, fast dynamic response, robustness againstparameter variations, and grid disturbance [18], [19]. In orderto overcome the traditional DPC drawback of variable switch-ing frequency, the DPC integrated with space vector modu-lation (DPC-SVM) has been adopted to decrease the broad-band harmonics injecting into the grid and simplify the filterdesign [20].

For the purpose of achieving excellent DFIG system per-formance with DPC strategy under harmonically distorted gridconditions, it is important to implement the accurate control ofstator active and reactive power. Several regulators are capableof accurately tracking the actual signal according to the ref-erence one, i.e., hysteresis regulator [3], proportional-resonant(PR) [21][25] regulator in stationary frame; traditional PI reg-ulator [21], [22], proportional integral resonant (PIR) regulator[13][15], [21], [22], [26], vector PI (VPI) regulator [21], [22]in the synchronous frame.

Under harmonically distorted grid conditions, the DFIGwould contain six times grid frequency pulsation item and anaverage item of stator active and reactive power. Therefore, PIregulator would not be appropriate due to the insufficient gainat the six times grid frequency. PIR regulator could achieve zerosteady-state error, in which the PI and resonant part is used todeal with the average item and the pulsation item respectively.However, unexpected peak of magnitude response at the fre-quency larger than resonant 300 Hz may arise due to the poledistribution of control object DFIG, which is detrimental to thestable closed-loop operation [22]. Considering that it needs onespecific resonant controller to deal with one specific harmonicsequence in the PR regulator, the control loop structure com-plexity would increase as the number of harmonic sequenceincreases, which is harmful to the stable closed-loop operation.The VPI regulator, based on pole-zero cancellation to avoid theunexpected gain peak [21], [22], can be used to remove theDFIG stator active and reactive power pulsation componentsdue to the adequate closed-loop phase margin and accurate acsignal tracking capability.

This paper investigates the DPC strategy of wind-turbinedriven DFIG generation systems under distorted grid voltageconditions. First, the mathematical model of a DFIG systemunder fifth- and seventh-order harmonically distorted grid sup-ply is briefly mentioned as a foundation. Considering that thewind power generation should focus on the energy quality in-jected into the grid, the stator active and reactive power withoutany oscillation is selected as the harmonic control target. Then,focused on the steady-state tracking accuracy, dynamic perfor-mance analysis, closed-loop operation stability, as well as therejection capability of the grid voltage distorted component andback EMF compensation item, the performance analysis of theproposed DPC control strategy with VPI regulator is conducted.

Fig. 1. Relationship between the (dq)+ , (dq)5, and (dq)7+ reference frames.

Fig. 2. T-representation of the DFIG equivalent circuit in the positive syn-chronous (dq)+ reference frame rotating at the speed of 1 .

Finally, the experimental system on 1 kW laboratory DFIG hasbeen built to validate the availability of the proposed DPC strat-egy using the VPI regulator.

II. MATHEMATICAL MODEL OF DFIG UNDER HARMONICALLYDISTORTED VOLTAGE

In order to investigate the DPC strategy, DFIG mathematicalmodel under harmonically distorted grid condition should be es-tablished first. Under the harmonically distorted grid condition,grid voltage can be decomposed into fundamental frequencycomponent and a series of harmonic frequency components.Considering that the fifth- and seventh-order sequences are themajor harmonic components of the grid voltage [12]; this pa-per would focus on the DPC strategy under these two harmoniccomponents.

Fig. 1 shows the relationship of the fundamental and harmonicsequence coordinate frames, in which (dq)+ is rotated at thespeed of +1 , (dq)5 at the speed of 51 , (dq)7 at the speedof 71 . 1 is the synchronous angular speed of the fundamentalfrequency grid voltage.

The equivalent circuit of DFIG in the (dq)+ reference frameis shown in Fig. 2, in which DFIG stator flux +sdq and rotorflux +rdq can be presented respectively as

+sdq = LsI+sdq + LmI

+rdq (1)

+rdq = LmI+sdq + LrI

+rdq (2)

where is the flux, I is the current, subscripts d, q representcomponents at the d, q axes, subscripts s, r represent statorand rotor components of DFIG, superscripts + represents the(dq)+ reference frames rotating at the angular speed of +1 .


Ls = Ls + Lm and Lr = Lr + Lm are total self-inductancesof stator and rotor winding, Ls, Lr , and Lm are stator and rotorleakage inductances and the mutual inductance, respectively.

Based on (1) and (2), the stator current and rotor current canbe written as

I+sdq =Lm

LrLs L2m

(LrLm

+sdq +rdq)

(3)

I+rdq =Lm

LrLs L2m

(LsLm

+rdq +sdq)

. (4)

According to Fig. 2, the stator and rotor voltages U+sdq andU+rdq in the (dq)+ reference frame can be expressed as

U+sdq = RsI+sdq + d

+sdq /dt + j1

+sdq (5)

U+rdq = RrI+rdq + d

+rdq /dt + js

+rdq (6)

where U is the voltage, Rs and Rr are stator and rotor resis-tances, r is the rotor angular speed, and s = 1r is the slipangular speed.

DFIG stator output instantaneous active and reactive powerscan be expressed as

Ps + jQs =32U+sdq I

+sdq (7)

where I+sdq is the conjugated space vector of I+sdq , Ps , and Qsare stator active and reactive power.

When thed-axis of the synchronous reference frame is alignedwith the stator voltage vector, the deferential of stator flux +sdqwill be zero. And assuming that the stator resistance is ignored,(5) can be written as

U+sdq = j1+sdq = 1+sq = U+sd . (8)

Substituting (6) and (8) into (7), the stator active and reactivepowers can be yielded as

Ps + jQs =32U+sd

LmLrLs L2m

(LrLm

+sdq

+rdq

)

= kU+sd

(LrLm

(+sd j+sq

) (+rd j+rq))

= kU+sd+rd + jkU+sd(

LrLm

U+sd1

+ +rq

)(9)

where k = 32Lm

Ls Lr L2m .Therefore, the stator active power and reactive power can be

written respectively as

Ps = kU+sd+rd (10a)

Qs = kU+sd

(+rq +

LrLm

U+sd1

). (10b)

Based on (10), the rotor flux can be shown as

+rd = 1

kU+sd

Ps (11a)

+rq =Qs

kU+sd

LrLm

U+sd1

. (11b)

Equation (6) can be separated into d-axis and q-axis componentand rewritten as

U+rd = RrI+rd + d

+rd

/dt s+rq (12a)

U+rq = RrI+rq + d

+rq

/dt + s+rd . (12b)

Substituting (4) and (11a) into (12a), rotor voltage d-axiscomponent in the (dq)+ reference frame can be written as

U+rd = RrLs

LsLr L2m+rd + d

+rd

/dt s+rq

=RrLs

LsLr L2m1

kU+sd

Ps 1kU

+sd

dPsdt

s+rq . (13)

The last item of (13) is an equivalent rotor back electromag-netic force which can be regarded as compensation item. Thus,the transfer function of stator output active power to the rotorvoltage d-axis component can be expressed as

Ps(s)U+rd(s)

=3U+sdLm

/2Ls

Rr + sLr. (14a)

Similar mathematical deduction can be conducted to obtainthe transfer function of stator output reactive power to rotorvoltage q-axis component, which is shown as following:

Qs(s)U+rq (s)

=3U+sdLm

/2Ls

Rr + sLr. (14b)

Besides, based on (11), during a constant sampling time pe-riod Ts , the deferential of rotor flux can be calculated as

d+rddt

= 1kU

+sd

dPsdt

= 1kU

+sd

P s PsTs

(15a)

d+rqdt

=1

kU+sd

dQsdt

=1

kU+sd

Qs QsTs

(15b)

where, P s and Qs are the stator active and reactive power ref-erences, respectively.

Substituting (11) and (15) into (12), and neglecting the ro-tor resistance, the rotor control reference voltage for the DFIGcontrol based on DPC can be written as

U+rd = V+rd + E

+rd = Cpower(P s Ps)

s(

Qs

kU+sd

LrU+sd

Lm1

)(16a)

U+rq =V+rq + E

+rq =Cpower(Q

s Qs) s

Ps

kU+sd

(16b)

where, Cpower is the proper stator power regulator to restrainthe power regulation error.

Equation (16) gives out that the rotor control voltage consistsof the stator active and reactive power regulator output V +rdqand the back electromagnetic force E+rdq . It would be essentialto choose the proper regulator Cpower to achieve zero powertracking error under the distorted grid voltage.

Under the distorted grid voltage, the stator voltage containsnot only fundamental, but also the fifth- and seventh-order har-monic components, which would produce the corresponding


Fig. 3. DPC scheme of the DFIG under the distorted grid voltage using theVPI regulator.

harmonic components in the stator current; therefore, the 300 Hzstator output active and reactive power pulsation will be pro-duced as a consequence [13][15].

For the sake of restraining the power pulsation item, the reso-nant regulator, which can be designed to have large control gainat the pulsation frequency (300 Hz), will be proposed for theDPC strategy of DFIG under the harmonic grid condition. Upto now, the PIR and VPI regulators [21], [22] are available forDFIG control under distorted grid voltage conditions to regu-late the average and pulsation power item simultaneously. Con-sidering that the VPI regulator has the advantage of pole-zerocancellation to eliminate the unexpected peak in the closed-loopcontrol response [22] and comparatively larger closed-loop op-eration phase margin (which would be proved in Section III),the VPI regulator is proposed for the power control of the DFIGunder the harmonic voltage; thus, (16) can be modified as

U+rd = V+rd + E

+rd = CVPI(s)(P s Ps)

s(

Qs

kU+sd

LrU+sd

Lm1

)(17a)

U+rq = V+rq + E

+rq = CVPI(s)(Q

s Qs) s

Ps

kU+sd

.

(17b)Equation (17) indicates that both the average component and

300 Hz pulsation component of stator active and reactive powererrors can be suppressed to zero, and consequently, the powerpulsation can be eliminated when the constant active or reactivepower references are given.

III. PERFORMANCE ANALYSIS OF THE DPC STRATEGY WITH AVPI REGULATOR

In order to achieve the smooth stator active and reactive poweroutput under the distorted grid voltage, the DFIG steady anddynamic state performance, as well as the disturbance rejectioncapability of the proposed DPC strategy using the VPI regulatorshould be investigated. Moreover, as the conventional PIR regu-lator would cause the deterioration of closed-loop control phasemargin and may cause instability operation [27]; the closed-loopstability using the VPI regulator should also be discussed.

Based on (5), the stator flux in the (dq)+ reference frame canbe obtained as

+sdq =1

s + jsU+sdq

Rss + js

I+sdq . (18)

If the stator resistance Rs is neglected, (18) can be simplifiedas

+sdq =1

s + jsU+sdq . (19)

According to (1) and (2), the rotor flux in the (dq)+ referenceframe can be expressed as

+rdq =LmLs

+sdq + LrI+rdq . (20)

Based on (6) and (20), the rotor voltage in the (dq)+ referenceframe can be deduced as

U+rdq = (Rr + Lr (s + js)) I+rdq +

LmLs

(s + js)+sdq .

(21)

Therefore, based on (10), (19), (20), and (21), the proposedDPC scheme of the DFIG under the distorted grid voltagecan be shown in Fig. 3, in which it can be seen: 1) the backEMF item E+rd and E+rq of stator active power and reactivepower can be found in (17); 2) the Ps and Qs calculation andthe VPI regulator output V +rdq can be found in (10) and (17);3) the item kLrU+2sd

/1Lm is required for Qs calculation.

Furthermore, the Gp(s) and Gk can be described as the math-ematical model of DFIG, which can also be verified accordingto (14).

The transfer function of VPI regulator can be defined as [21],[22]

CVPI = Kp +Kis

+Kprs

2 + Kirss2 + cs + 20

(22)

where Kp and Ki are proportional and integral coeffi-cient,respectively, for regulating the dc component, c is theresonant bandwidth, 0 is the resonant frequency. Kpr and Kirare proportional and integral coefficient of VPI for regulatingthe harmonic components, in which Kir = KprRr /Lr shouldbe achieved based on the rule of pole-zero cancellation [22].


Fig. 4. Bode diagram of the VPI regulator (a) Kpr = 1(Kir = 157), c =10, 15, 20 rad/s; (b) Kpr = 0.5, 0.75, 1.0(Kir = 78.5, 117.75, 157), and c =15 rad/s.

For the purpose of better investigating the proposed DPCstrategy, it should be pointed out that Kpr ,Kir , and c are theonly parameters of the VPI regulator that can be adjusted in thecontrol loop, while the other parameters such as 0 and DFIGmachine parameters are fixed. Usually, c should be selectedabout 1020 rad/s to improve the resonant peak gain and the ro-bust performance to the grid frequency variation, and Kpr ,Kirshould be selected based on the rule of pole-zero cancellationto achieve the 3050 dB peak gain at the resonant frequency toeliminate ac signal tracking error [23][26].

Fig. 4(a) shows the bode diagram of the VPI regulator withdifferent resonant bandwidth c = 10, 15, 20 rad/s and sameKpr = 1.0 (Kir = 157). The magnitude at the resonant fre-quency 300 Hz would be 45.9, 42.0, and 38.5 dB, which islarge enough to minimize the control error. And the magnituderesponse at the frequency adjacent to the resonant frequencywould remain almost constant regardless of c . Moreover, it

should be pointed out that the VPI regulator phase response at300 Hz would be phase leading of around 90, which is morebeneficial to the control of the DFIG behaving as an inertia unit.

Fig. 4(b) shows the bode diagram of the VPI regulator withdifferent Kpr = 0.5, 0.75, 1.0(Kir = 78.5, 117.75, 157) andsame resonant bandwidth c = 15 rad/s. It can be seen that themagnitude at the resonant frequency 300 Hz would be 36.5, 39.2,and 42.0 dB. Nevertheless, the magnitude response at the adja-cent frequency would become lower than the results in Fig. 4(a),while the phase response remains constant regardless of c .

The magnitude and phase response at the resonant 300 Hzfrequency are mostly important for the harmonic current controlof the DFIG. In Fig. 4, it can be found that, under the condition ofKpr and c variation, the magnitude response would vary withinan acceptable range of 3050 dB so that the satisfactory ac signaltracking error can be ensured, and the phase response wouldremain unchanged of around leading 90 which is favorable tothe control of the DFIG as an inertia unit.

A. Steady-state PerformanceAccording to Fig. 3, the transfer function of stator active and

reactive power reference P s , Qs to actual power Ps Qs can beobtained as following, in which the back EMF E+rdq and gridvoltage U+sdq is regarded as disturbance and neglected

GP s(s) =PsP s

=CVPI(s)Gp(s)Gk

1 + CVPI(s)Gp(s)Gk(23a)

GQs(s) =QsQs

=CVPI(s)Gp(s)Gk

1 + CVPI(s)Gp(s)Gk. (23b)

Fig. 5 shows the closed-loop control bode diagram with thesame parameters in Fig. 4. As shown in Fig. 5(a), with Kpr =1(Kir = 157) and c = 10, 15, and 20 rad/s, the magnituderesponse of GP s(s) and GQs(s) at the dc and 300 Hz point is0 dB, and the phase response at the dc and 300 Hz point is 0,which indicates that the actual stator active and reactive powerwould accurately follow the reference signal.

The closed-loop control bode diagram with Kpr = 0.5, 0.75,1.0(Kir = 78.5, 117.75, 157) and c = 15 rad/s is shown inFig. 5(b). The magnitude and phase response of GP s(s) andGQs(s) at the frequency lower than 300 Hz would be differentfrom the results in Fig. 5(a), while the same magnitude and phaseresponse will be achieved at the resonant frequency 300 Hz,which ensure the accurate tracking of both dc component and300 Hz ac component with 0 dB magnitude response and 0phase response.

Therefore, it can be obtained that the closed-loop controlsteady-state performance of the proposed DPC strategy with theVPI regulator would be satisfactorily accurate regardless of theparameter Kpr and c variation.

B. Dynamic Performance AnalysisIt is also important to make comparison of dynamic response

between the proposed DPC and traditional VOC for the DFIGcontrol under the harmonic voltage. The dynamic performancewith the proposed DPC strategy can be investigated based on


Fig. 5. Bode diagram of GP s (s) and GQs (s) with different parameters:(a) Kpr = 1(Kir = 157), c = 10, 15, 20 rad/s; (b) Kpr = 0.5, 0.75,1.0(Kir = 78.5, 117.75, 157), c = 15 rad/s; (Kp = 1, Ki = 1, c = 10 rad/s,0 = 600 rad/s, U+sd = 110 V, Rr = 0.88 , Ls = Lr = 0.093 H, Lm =0.09 H, = 0.063).

the stator active and reactive power closed-loop control transferfunction as shown in (23). According to [13], considering thatthe DFIG plant transfer function using the VOC strategy can beexpressed identically as Gp (s) in Fig. 3, the major differencebetween DPC and VOC for the dynamic performance analysiswould rely on the different DFIG plant transfer function whenthe same VPI regulator is adopted. Based on [13], the rotorcurrent closed-loop control transfer function with VOC can beexpressed as following:

GclVOC(s) =IrdqIrdq

=CVPI(s)Gp(s)

1 + CVPI(s)Gp(s). (24)

It can be seen that, in (23) and (24), the plant transfer functionwith DPC has one more item of Gk than that with VOC, whichis helpful to enlarge the magnitude gain and widen the controlfrequency spectrum range.

Fig. 6. Bode diagram of the closed-loop control transfer function under VOCand DPC strategy: (a) concerning the 300 Hz ac signal, Kpr = 0.5, 0.75,1.0(Kir = 78.5, 117.75, 157), c = 15 rad/s; 0 = 600 rad/s, U+sd = 110 V,Rr = 0.88 , Ls = Lr = 0.093 H, Lm = 0.09 H, = 0.063; (b) concerningdc signal, Kp = 0.1, Ki = 1, U+sd = 110 V, Rr = 0.88 , Ls = Lr = 0.093 H,Lm = 0.09 H, = 0.063.

The bode diagram of the closed-loop control transfer functionwith VOC and DPC strategy is given in Fig. 6. Considering thatthe cut-off frequency should be with 3 dB magnitude responseand larger cutoff frequency is helpful for the faster dynamicperformance, the effective frequency spectrum with the VOCstrategy would be 285 to 315 Hz as shown in Fig. 6(a), whilethe effective frequency spectrum with the DPC strategy wouldbe 20 to 5000 Hz. It also can be seen that the VPI parametervariation of kpr 0.5, 0.75, and 1.0 has negligible influence onthe dynamic performance of both the VOC and DPC strategy.Similar conclusion can be drawn when considering the dc signalregulation in Fig. 6(b). When VOC is adopted, 3 dB magni-tude response would be obtained at the frequency of 0.16 Hz,and the corresponding cutoff frequency for DPC would be430 Hz, which points out that the DPC would exhibit much faster


dynamic response with the step change of stator output activeand reactive power.

C. Rejection of Grid Voltage Distortion on the Stator Activeand Reactive Power Steady-State Tracking Performance

According to the control scheme shown in Fig. 3, when thegrid voltage distortion is considered, the following equation canbe deduced:

((P s Ps)CVPI(s) U+sdG1(s)G2(s))Gp(s)GkU+sdG1(s)Gt = Ps. (25)

After the mathematical derivation, (25) can be rewritten asP s CVPI(s)Gp(s)Gk + U

+sd(G1(s)G2(s)Gp(s)Gk

G1(s)Gt) = Ps(1 + CVPI(s)Gp(s)Gk ). (26)The stator active power reference P s is usually constant, and

the grid voltage d-axis U+sd contains the average fundamen-tal component and fifth-/seventh-order harmonic components.Therefore, the constant stator active power reference P s and gridvoltage fundamental components can be removed from (26), andthe following equation can be deduced:

U+sd5,7+(G1(s)G2(s)Gp(s)Gk G1(s)Gt)= Ps(1 + CVPI(s)Gp(s)Gk ) (27)

Then, the transfer function of grid voltage distorted compo-nent U+sd5,7+ to stator active power Ps can be given as

GPs Us d (s) =Ps

U+sd5,7+=

G1(s)G2(s)Gp(s)Gk G1(s)Gt1 + CVPI(s)Gp(s)Gk

(28)Fig. 7 demonstrates the grid voltage distortion rejection ca-

pability of the proposed DPC strategy with the considerationof the stator active power steady-state tracking performance.Fig. 7(a) exhibits the similar result as Fig. 5(a), i.e., when cvaries as 10, 15, and 20 rad/s, the magnitude response at 300 Hzwould change slightly as 59.7 dB, 62.2 dB, and 65.7 dB, allof which would be large enough to attenuate the grid voltagedistorted component. Besides, the phase response would alsoremain unchanged while c varies.

As shown in Fig. 7(b) with Kpr = 0.5, 0.75, 1.0(Kir = 78.5,117.75, 157) and c = 15 rad/s, both the magnitude and phaseresponse would change a little when the frequency is lower than300 Hz. While at the 300 Hz frequency point, the magnitudeand phase response would change slightly 56.2, 59.7, and62.2 dB, which validates the satisfactory grid voltage distortionrejection capability on the stator active power tracking.

Similarly, when considering the rejection of grid voltage dis-tortion on the stator reactive power steady-state tracking per-formance, the high attenuation around 60 dB would also beguaranteed, which would not be discussed in detail.

Thus, it can be concluded that the grid voltage distortionrejection capability of the proposed DPC strategy on the sta-tor active and reactive power steady-state tracking performancewould remain satisfactory regardless of the VPI regulator pa-

Fig. 7. Bode diagram of GP s Usd (s) with different parameters: (a) Kpr =1(Kir = 157), c = 10, 15, 20 rad/s; (b) Kpr = 0.5, 0.75, 1.0(Kir = 78.5,117.75, 157), c = 15 rad/s; (Kp = 1, Ki = 1, 0 = 600 rad/s, U+sd = 110 V,Rr = 0.88 , Ls = Lr = 0.093 H, Lm = 0.09 H, = 0.063).

rameter deviation, which results in the satisfactory stator activeand reactive power accurate tracking performance.

D. Stability ConsiderationIt can be found in (23) and (28) that the denominators are

the same which is always defined as characteristic equationof the closed-loop transfer function using the proposed DPCstrategy. Thus, the transfer function used to verify the closed-loop operation stability can be written as

D(s) = CVPI(s)Gp(s)Gk . (29)The closed-loop control stability consideration under the pro-

posed DPC strategy can be found from Fig. 8. It can be seen inFig. 8(a) that, the magnitude and phase response would remainalmost same at the resonant frequency 300 Hz when c varies10, 15, and 20 rad/s, the same results can be found in Fig. 8(b)when Kpr varies 0.5, 0.75, and 1.0 as shown.

Therefore, it can be concluded that the stable closed-loopoperation of the proposed DPC strategy using the VPI regula-tor would always be guaranteed with sufficient phase margin


Fig. 8. Bode diagram of D(s) with different parameters: (a) Kpr = 1(Kir =157), c = 10, 15, 20 rad/s; (b) Kpr = 0.5, 0.75, 1.0(Kir = 78.5, 117.75,157), c = 15 rad/s; (Kp = 1, Ki = 1, c = 10 rad/s, 0 = 600 rad/s, U+sd =110 V, Rr = 0.88 , Ls = Lr = 0.093 H, Lm = 0.09 H, = 0.063).

of around 90 for the stable closed-loop operation under thedistorted grid voltage.

E. Influence of Back EMF on the Steady-State Stator Activeand Reactive Power Tracking Performances

As demonstrated in Fig. 3, the back EMF in (17) can beconsidered as a disturbance to the closed-loop operation; thus,the transfer function of back EMF d-axis E+rd to the stator activepower Ps can be derived as

GPs Er d (s) =Ps

E+rd=

Gp(s)Gk1 + CVPI(s)Gp(s)Gk

. (30)

The back EMF d-axis component for the stator active powercontrol E+rd = s

(Qs

k U+s d

Lr U+s d

Lm 1

)contains constant com-

ponent of s , Qs, k , Lr , Lm and 1 , as well as 300 Hz

Fig. 9. Bode diagram of GP s E rd (s) with different parameters: (a) Kpr =1(Kir = 157), c = 10, 15, 20 rad/s; (b) Kpr = 0.5, 0.75, 1.0(Kir = 78.5,117.75, 157), c = 15 rad/s; (Kp = 1, Ki = 1, c = 10 rad/s, 0 = 600rad/s, U+

sd= 110 V, Rr = 0.88 , Ls = Lr = 0.093 H, Lm = 0.09 H, =

0.063).

ac signal of grid voltage d-axis component U+sd containingfifth- and seventh-order harmonic components in the (dq)+frame.

Fig. 9 shows the influence of back EMF d-axis E+rd on thesteady-state stator active power tracking performance, wherethe 300 Hz harmonic signal would be significantly attenuatedto 42.5, 42.0, and 39.5 dB with c = 10, 15, and 20 rad/sin Fig. 9(a), or attenuated to 36.0, 39.5, and 42.0 dB withKpr = 0.5, 0.75, and 1.0 in Fig. 9(b) respectively. Therefore, itcan be verified that the existence of back EMF d-axis componentas compensation items would have negligible influence on thestator active power tracking precision.

Similar conclusion concerning the influence of back EMFq-axis E+rq on the steady-state stator reactive power trackingperformance can also be obtained, which would not be describedin detail.


Fig. 10. Block diagram of experiment system.

TABLE IPARAMETER OF EXPERIMENTAL DFIG SYSTEM

IV. EXPERIMENTAL VALIDATION

A. Experimental SetupAn experimental system was built on a laboratory prototype

of 1 kW DFIG system as shown in Fig. 10, in which the DFIGis driven by a 1.5 kW squirrel cage induction machine as thewind turbine. The induction machine is driven by a generalconverter. The rotor side converter of DFIG is connected witha dc power supply. A controllable three-phase power grid is setup to simulate the practical harmonic power grid [28]. In theexperiment, fifth- and seventh-order harmonic components areset to be 3.4% and 2.8% each, and the rotor speed is initiallyset to 800 rpm. The control strategy is implemented on the TIDSP TMS320F2812, and the driver for IGBT is SEMIKRONSKHI61. The sampling frequency is 10 kHz, and the IGBTswitching frequency is 5 kHz. The waveforms are acquired by aYOKOGAWA DL750 scope recorder, the harmonic componentanalysis is done by FLUKE NORMA 5000 power analyzer.Parameters of the tested DFIG are listed in Table I.

The proposed DPC control strategy for DFIG system underthe distorted grid voltage is shown in Fig. 11. First, the grid volt-age phase is obtained through phase lock loop (PLL) proposedin [13], the rotor position and speed are achieved by the out-put of an encoder. The stator active and reactive powers can becalculated by sampling three-phase stator voltage and current.The stator active and reactive power control error, which is theinput of the VPI regulator, can be calculated according to the

Fig. 11. Proposed DPC scheme of DFIG under distorted grid voltage usingthe VPI regulator.

actual signal and reference signal. The output of the VPI regula-tor, together with the compensation back electromagnetic force,would be sent to the SVPWM to generate the IGBT switchingsignals to fulfill the control target. The control target in this pa-per is chosen as smooth stator output active and reactive power.It can be seen from the proposed DPC control strategy schemethat no harmonic decomposition is required during the controlprocess, therefore no negative influence on the control systemstability and fast dynamic response would be produced.

However, it should be noted that the practical DFIG machinecontains certain inevitable tooth harmonic, this would inevitablyresult in the nonsinusoidal air gap magnetic field and the corre-sponding stator and rotor harmonic current. Such nonsinusoidalcomponents would always exist during the experiment, and itwould help to better understand the proposed DPC strategy ifthese no-sinusoidal components are considered as the back-ground harmonics.

B. Experimental ResultsDuring the experiment process, the VPI regulator is applied

with the resonant bandwidth c = 15 rad/s, the resonant param-eter Kpr , and Kir is chosen as 1 and 157 based on the rule ofpole-zero cancellation [21], [22].

The DFIG experiment result under ideal power grid (whichstill contains 0.80% and 0.34% fifth and seventh harmonic com-ponents) is shown in Fig. 12. The background harmonic com-ponents caused by the DFIG itself would results in the tinynonsinusoidal components both in the stator and rotor currents,i.e., the fifth- and seventh-order harmonic component of thestator current is 2.13% and 0.54%, respectively. As a conse-quence, tiny stator active and reactive power 300 Hz pulsationwould be produced, 18 W and 15 Var, due to the existenceof nonsinusoidal stator current.

The experimental result under the distorted grid voltage withfifth- and seventh-order harmonic components set as 3.40% and2.80%, respectively, is carried out and shown in Fig. 13. Thestator currents contain harmonic components of 7.52% 250 Hzand 3.69% 350 Hz due to the occurrence of the distorted gridvoltage fifth and seventh harmonic components. Considering


Fig. 12. Experimental result of the DFIG system performance under the idealgrid voltage condition.

Fig. 13. Experimental result of the DFIG system performance under the dis-torted grid voltage condition with VPI disabled.

that the rotor speed is 800 rpm (0.8 p.u., equivalent to 40 Hz),the distorted air gap magnetic field containing 250 and 350 Hzharmonic component in the stationary frame would generate290 (250 + 40 Hz, due to the negative rotation direction of fifthharmonic sequence and positive rotor rotation) and 310 Hz (35040 Hz, due to the positive rotation direction of 7th harmonicsequence and positive rotor rotation) rotor current harmoniccomponent in the rotor position oriented frame. The 290 and310 Hz components of rotor current can be regarded as the29th and 31st-order harmonic component considering the rotorcurrent fundamental frequency of 10 Hz. Corresponding rotorcurrent harmonic components at 290 and 310 Hz are 4.52%and 2.38%, respectively. Most importantly, the stator active andreactive power 300 Hz pulsation would increase to 88 W and85 Var, which is quite unfavorable and harmful to the normaloperation of the power grid. The harmonic analysis result isavailable in Table II.

The experimental result of the proposed DPC strategy withthe harmonic control target of eliminating the stator power pul-sation can be observed from Fig. 14, and the harmonic analysisresult is also listed in Table II. In contrast to Fig. 13, the statoractive and reactive power pulsations are effectively restrainedto 20 W and 14 Var due to the effective operation of the VPI

TABLE IIHARMONIC ANALYSIS DATA WITH THE PROPOSED DPC STRATEGY

Fig. 14. Experimental result of the DFIG system steady performance underthe distorted grid voltage condition with VPI enabled.

regulator, which is close to the experiment result under the idealpower grid condition as shown in Fig. 12. Besides, the statorcurrent fifth-order harmonic component has been significantlyrestrained from 7.52% to 1.08%, and the seventh-order com-ponent increases from 3.69% to 4.73%. Moreover, the statorcurrent THD has been reduced from 8.37% to 4.80%. Simi-lar conclusion can be made when considering the rotor currentharmonic components as shown in Table II.

Fig. 15 shows the experiment result of the DFIG system tran-sient performance at the moment of enabling the VPI regulatorunder the distorted grid voltage condition. It can be seen that,before the enabling moment, severe stator active and reactivepower pulsations of88 W and85 Var, as well as severely dis-torted stator currents can be observed. Nevertheless, when theVPI regulator is enabled, the stator active and reactive powerpulsation can be successfully restrained within about 40 ms to20 W and 14 Var, respectively, and no impulse or instabilityresponse appears.

A stepping of stator active power reference from 300 to 500 Wis used to test the DFIG system transient response under thedistorted grid voltage condition with the VPI regulator, as illus-trated in Fig. 16. Before the stepping moment, the actual valueof stator active power follows precisely to the reference signal,and there is almost no control error in the stator active power.


Fig. 15. Experimental result of the DFIG system transient performance underthe distorted grid voltage condition with VPI enabled.

Fig. 16. Experimental result of the DFIG stator active power reference step-ping transient performance under the distorted grid voltage condition with VPIenabled.

When stator active power stepping happens and large controlerror emerges, the PI part of VPI can successfully minimize thecontrol error and finally regulate the stator active power follow-ing the reference signal. During the transient process, the VPIregulator maintains effectiveness in regulating the 300 Hz acsignal, which verifies the independent working capability of PIpart and the VPI regulator. Therefore, based on the experimentresults shown in Figs. 15 and 16, the fast dynamic responseadvantage of the proposed DPC strategy in terms of both dc and300 Hz ac signals tracking has been validated.

Fig. 17 shows the experimental result of the DFIG operationfrom the subsynchronous state to super-synchronous state withthe VPI regulator under the distorted grid condition. During theprocess of rotor accelerating from 800 (0.8 p.u.) to 1200 rpm(1.2 p.u.), the proposed DPC strategy using the VPI regulatorcan achieve smooth rotor current changing, and the stator out-put active power remains constant during the whole process, thestator power control error also remains zero. This result veri-fies that DFIG using the DPC strategy with the VPI regulatorcan operate normally under both subsynchronous and super-synchronous state.

Fig. 17. Experimental result of the DFIG system operating from subsyn-chronous to super-synchronous state under the distorted grid voltage conditionwith VPI enabled.

V. CONCLUSIONThe paper has presented a VPI-based DPC strategy for a

wind turbine driven DFIG system under the harmonically dis-torted grid voltage. By applying the VPI regulator to suppress thepower pulsation component, the proposed DPC strategy can suc-cessfully implement the smooth active and reactive power outputof DFIG under the harmonic voltage. The steady power trackingprecision and fast dynamic performance of the proposed DPCstrategy are theoretically analyzed and proved experimentally.The proposed DPC strategy also shows an excellent disturbancerejection ability and closed-loop operation stability. Experimentresults have been carried out to validate the excellent dynamicand steady operation performance of the proposed DPC strategy.

REFERENCES

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[25] G. Shen, X. Zhu, J. Zhang, and D. Xu, A new feedback method for PRcurrent control of LCL-filter-based grid-connected inverter, IEEE Trans.Ind. Electron., vol. 57, no. 6, pp. 20332041, Jun. 2010.

[26] C. Liu, D. Xu, N. Zhu, F. Blaabjerg, and M. Chen, DC-voltage fluctuationelimination through a DC-capacitor current control for DFIG convertersunder unbalanced grid voltage conditions, IEEE Trans. Power Electron.,vol. 28, no. 7, pp. 32063218, Jul. 2013.

[27] C. Liu, W. Chen, F. Blaabjerg, and D. Xu, Optimized design of resonantcontroller for stator current harmonic compensation in DFIG wind turbinesystems, in Proc. IEEE Appl. Power Electron. Conf. Expo., Feb. 2012,pp. 20382044.

[28] R. Zeng, H. Nian, and P. Zhou, A three-phase programmable voltage saggenerator for low voltage ride-through capability test of wind turbine,in Proc. IEEE Energy Convers. Cong. Expo., Atlanta, GA, USA, 2010,pp. 305311.

Heng Nian (M09) received the B.Eng. degree andthe M.Eng. degree from the HeFei University of Tech-nology, Hefei, China, and the Ph.D. degree fromZhejiang University, Hangzhou, China, in 1999,2002, and 2005, respectively, all in electricalengineering.

From 2005 to 2007, he was as a Postdoctoral withthe College of Electrical Engineering, Zhejiang Uni-versity, and has been an Associate Professor since2007. His current research interests include the op-timal design and operation control for wind power

generation system.

Yipeng Song was born in Hangzhou, China. He re-ceived the B.Sc. degree from the College of ElectricalEngineering, Zhejiang University, Hangzhou, China,in July 2010, where he is currently working towardthe Ph.D. degree.

His current research interests include motor con-trol with power electronics devices in renewable-energy conversion, particularly the control and op-eration of doubly fed induction generators for windpower generation under adverse grid condition.

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