9.pdf

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 2, FEBRUARY 2010 341

Model-Based Predictive Direct Power Control ofDoubly Fed Induction Generators

Dawei Zhi, Student Member, IEEE, Lie Xu, Senior Member, IEEE, and Barry W. Williams

Abstract—This paper presents a predictive direct power controlstrategy for doubly fed induction generators (DFIGs). The methodpredicts the DFIG’s stator active and reactive power variationswithin a fixed sampling period, which is used to directly calculatethe required rotor voltage to eliminate the power errors at the endof the following sampling period. Space vector modulation is thenused to generate the required switching pulses within the fixedsampling period that results in a constant switching frequency.The impact of sampling delay on the accuracy of the sampled ac-tive and reactive powers is analyzed, and detailed compensationmethods are proposed to improve the power control accuracy andsystem stability. Experimental results for a 1.5-kW DFIG systemdemonstrate the effectiveness and robustness of the proposed con-trol strategy during power steps, and variations of rotating speedand machine parameters. System performance for tracking vary-ing stator power references further illustrates the dynamic perfor-mance of the proposed method.

Index Terms—Doubly fed induction generator (DFIG), directpower control (DPC), predictive, pulsewidth-modulated (PWM)converter, wind energy.

NOMENCLATURE

Is, Ir Stator, rotor current vectors.Lm ,Rm Magnetizing inductance, resistance.Lσs, Lσr Stator, rotor leakage inductance.Ls, Lr Stator, rotor self-inductance.Ps,Qs Stator active and reactive power.Rs,Rr Stator, rotor resistance.V s,V r Stator, rotor voltage vectors.ψs,ψr Stator, rotor flux vectors.ω1 , ωr , ωs Synchronous, rotor, slip angular frequency.θs, θr Stator flux, rotor angles in the stationary

frame.θ Angle between the rotor and stator flux

vectorsSuperscriptss, r Synchronous, rotor reference frames.∗ Reference value.Subscriptsd, q Synchronous d–q axes.s, r Stator, rotor.

Manuscript received February 19, 2009; revised June 11, 2009. Currentversion published February 12, 2010. Recommended for publication byAssociate Editor J. M. Guerrero.

D. Zhi and B. W. Williams are with the Department of Electronic and Elec-trical Engineering, University of Strathclyde, Glasgow G1 1XW, U.K. (e-mail:[email protected]; [email protected]).

L. Xu is with the School of Electronics, Electrical Engineering and Com-puter Science, Queen’s University of Belfast, Belfast BT9 5AH, U.K. (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.2009.2028139

I. INTRODUCTION

DOUBLY fed induction generator (DFIG) based wind tur-bines currently dominate the wind energy market due to

their four-quadrant active/reactive power control, variable speedoperation, low converter cost, and reduced power loss comparedto other solutions such as fixed-speed induction generators orfully rated converter systems. A schematic diagram of a DFIG-based wind energy generation system is shown in Fig. 1.

Traditionally, DFIG control is achieved by vector control(VC) [1]–[5], which decouples the rotor currents into activepower (or torque) and reactive power (or flux) components, andadjusts them separately in a reference frame fixed to either thestator flux [1]–[3] or voltage [4], [5]. Current controllers arethen utilized to regulate the rotor currents. The main drawbackfor VC is its linear nature that does not consider the discreteoperation of voltage source converters (VSCs). Thus, in orderto maintain system stability over the whole operation range,and adequate dynamic response under both normal and abnor-mal conditions, the current controller and its control parametersmust be carefully tuned [3]. This could reduce the robustnessof the VC algorithm during erroneous parameters and changingoperation conditions.

Direct torque control (DTC) [6] and direct power control(DPC) [7], [8] that originated from DTC for induction ma-chines [9], [10] have been proposed for the DFIG. Such strate-gies provide direct control of the machine’s torque or power,and reduce the complexity of the VC algorithm. Such DTCand DPC methods involve torque/power hysteresis control, andconverter outputs are selected through a predetermined lookuptable (LUT). However, the converter switching frequency varieswith operating conditions such as rotor speed and system outputpower, which complicates the design of the power circuit ac har-monics filters as they have to be designed to absorb broadbandharmonics. In addition, a high sampling frequency is used forDTC/DPC to guarantee acceptable steady-state and dynamicperformances [6]–[8]. Several modified DTC/DPC strategies,incorporating space vector modulation (SVM), have been pro-posed to achieve a constant switching frequency for inductionmachine drives [11]–[14] and grid-connected VSC [15]–[17].However, additional drawbacks are introduced by such control,e.g., complicated online calculation [11], [15], [16], additionalPI controller parameters [12], [13], [17], and weak robustness tomachine parameter variations [11]–[14]. Several DPC strategieswith constant switching frequency have also been proposed forthe DFIG [18]–[21]. The switching states were initially selectedbased on conventional LUT in [18] and [19], whereas their dura-tions were calculated based on the objectives of reduced torqueand flux oscillation. However, it required complicated online

0885-8993/$26.00 © 2010 IEEE

342 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 25, NO. 2, FEBRUARY 2010

Fig. 1. Schematic diagram of a DFIG-based wind energy generation system.

calculations and has oscillation problems when the DFIG is op-erated around its synchronous speed. Zhi et al. [20], Zhi andXu [21] and Zhi et al. [22] proposed simple constant switchingfrequency DPC strategies for VSC and DFIG. However, onlypreliminary simulation studies were carried out in [21] and [22],and no detailed effect of various voltage vectors on power vari-ation or the impact of practical aspects such as sampling delay,etc., on system performance was considered.

Similar to DTC and DPC methods, predictive current control(PCC) incorporating SVM techniques has been proposed forVSC [23]–[26] and ac machine drives [27]–[29]. The perfor-mance of the current controller for a three-phase grid-connectedVSC in distributed generation systems [23] was improved byconsidering the control delay due to sampling and computation.A unified approach of the PCC method for a VSC is proposedin [24] that uses a predictive current observer with an adaptiveinternal model to compensate the control delay, and improvecontrol bandwidth and stability. The performance of the PCCmethod for an active power filter was improved in [25] by com-pensating the phase error of the harmonic components caused bydiscrete sampling and finite nonnegligible execution time delay.However, a simple linear approximation of the current error wasused in [23]–[25] that can cause system instability due to thenonlinear nature of SVM operation. The least square method ofan online parameter calculation was used in [26] to estimate theload resistance and inductance in a phase-controlled rectifier inorder to guarantee zero steady-state error under PCC.

This paper proposes a predictive DPC (PDPC) strategy forDFIG-based wind energy generation systems, with a fixedswitching frequency, and improved transient and steady-stateperformances. In Section II, the basic principles of PDPC areoutlined. The issues related to PDPC in practical systems andvarious compensation methods are proposed in Section III,based on the detailed analysis of active and reactive powervariations within each pulsewidth-modulated (PWM) period.Verifying experimental results for a 1.5-kW DFIG system arepresented in Section IV.

II. MODEL-BASED PDPC FOR DFIG

A. DFIG’s Active and Reactive Power Flow

As shown in the DFIG’s equivalent circuit in Fig. 2, in thesynchronous reference frame, the stator and rotor voltage vectorscan be expressed as

V ss = RsI

ss + jω1ψ

ss + ψ̇

s

s (1)

V sr = RrI

sr + j(ω1 − ωr )ψs

r + ψ̇s

r (2)

Fig. 2. Equivalent circuit of a DFIG in the synchronous d–q reference frame.

Fig. 3. Spatial relationship of stator flux, rotor flux, and rotor voltage.

From Fig. 2, the DFIG’s stator and rotor flux vectors can beexpressed as

ψss = LsI

ss + Lm Is

r (3a)

ψsr = LrI

sr + Lm Is

s. (3b)

Combining (3a) and (3b) yields

Iss =

ψss

σLs− Lm ψs

r

σLsLr(4)

where σ = (LsLr − L2m )

/LsLr is the leakage factor.

The amplitude of the stator flux can also be calculated as

|ψs | =∣∣∣∣

∫(V s − RsIs) dt

∣∣∣∣ ≈

∣∣∣∣

∫V sdt

∣∣∣∣ . (5)

Assuming the network voltage is constant and neglecting thestator copper loss, the stator flux amplitude shown in (5) canbe regarded as constant. Thus, combining (1) and (4), the statoractive and reactive power inputs from the network are givenas [8]

Ps = −kσω1 |ψs | |ψr | sin θ

Qs = kσω1 |ψs |(|ψr | cos θ − Lr

Lm|ψs |

)(6)

where kσ = 1.5Lm /(σLsLr ), and θ is the angle between therotor and stator flux vectors shown in Fig. 3.

As shown in Fig. 3, where the d-axis of the synchronousreference frame is fixed to the stator flux that results in |ψs | =ψsd , (6) can also be expressed using d–q components as

Ps = −kσω1ψsdψrq

Qs = −kσω1Lr

Lmψ2

sd + kσω1ψsdψrd . (7)

ZHI et al.: MODEL-BASED PREDICTIVE DIRECT POWER CONTROL OF DOUBLY FED INDUCTION GENERATORS 343

Thus, (7) indicates that the stator active and reactive pow-ers can be controlled independently by adjusting ψrq and ψrd ,respectively.

B. Principles of PDPC

The principle of the proposed PDPC method involves thefollowing aspects:

1) to directly calculate the required rotor voltage over a fixedsampling period Ts based on the predictive power modeldeveloped in (7);

2) to generate appropriate voltage vectors over the fixed sam-pling period to approximate the effect of the required rotorvoltage. This is usually achieved using SVM.

Thus, fast dynamic response of power control and a constantswitching frequency are achieved.

Assuming at the beginning of the kth sampling period, theexisting active and reactive power errors are given by

δPs(k) = P ∗s (k) − Ps(k)

δQs(k) = Q∗s(k) − Qs(k). (8)

The objective for the following fixed period Ts is to controlthe stator active and reactive powers such that at the end of theperiod Ts , i.e., the (k + 1)th sampling instance, their errors areeliminated, viz

δPs (k + 1) = P ∗s (k + 1) − Ps (k + 1) = 0

δQs (k + 1) = Q∗s (k + 1) − Qs (k + 1) = 0. (9)

Thus, the changes of the active and reactive powers duringthe period Ts in order to satisfy (9) are

∆Ps(k) = Ps (k + 1) − Ps(k)

= P ∗s (k + 1) − P ∗

s (k) + δPs(k)

∆Qs(k) = Qs (k + 1) − Qs(k)

= Q∗s (k + 1) − Q∗

s(k) + δQs(k). (10)

If zero-order sample and hold is used for the stator powerreferences, i.e., P ∗

s (k + 1) = P ∗s (k) and Q∗

s (k + 1) = Q∗s(k),

the required power changes in the kth sampling period are

∆Ps(k) = δPs(k)

∆Qs(k) = δQs(k). (11)

Thus, the aim of the proposed PDPC strategy is to generate therequired power changes shown in (11) by applying the correctrotor voltage. According to (7) and taking into account the factthat the stator flux is usually constant, the active and reactivepower changes over a small sampling period Ts can be predictedas

∆Ps(k) = −kσω1ψsd(k)∆ψrq (k)

∆Qs(k) = kσω1ψsd(k)∆ψrd(k). (12)

According to (2), the rotor flux changes within period Ts canbe calculated by integrating both sides of (2) as

∆ψsr =

∫

Ts

(V sr − RrI

sr − jωsψ

sr) dt. (13)

For a short period Ts , (13) can be approximated using Eulerbackward method in the d–q axes as

∆ψrd(k) = ψrd (k + 1) − ψrd(k)

= [Vrd(k) − RrIrd(k) + ωsψrq (k)] Ts

∆ψrq (k) = ψrq (k + 1) − ψrq (k)

= [Vrq (k) − RrIrq (k) − ωsψrd(k)] Ts. (14)

Substituting (14) into (12) yields the required rotor voltagefor the following period Ts

Vrd(k) = RrIrd(k) − ωsψrq (k) +1Ts

∆Qs(k)kσω1ψsd(k)

Vrq (k) = RrIrq (k) + ωsψrd(k) − 1Ts

∆Ps(k)kσω1ψsd(k)

(15a)

V sr(k) = Vrd(k) + jVrq (k)

= RrIsr(k) + jωsψ

sr(k) +

1Ts

∆Qs(k) − j∆Ps(k)kσω1ψsd(k)

.

(15b)

Neglecting the rotor resistance, (15a) and (15b) can be sim-plified as

Vrd(k) = −ωsψrq (k) +1Ts

∆Qs(k)kσω1ψsd(k)

Vrq (k) = ωsψrd(k) − 1Ts

∆Ps(k)kσω1ψsd(k)

(16a)

V sr(k) = jωsψ

sr(k) +

1Ts

∆Qs(k) − j∆Ps(k)kσω1ψsd(k)

.

(16b)

Under ideal conditions, the corresponding sampling point atwhich the DFIG’s voltages and currents are sampled, and thePWM update instance when the rotor control voltage for thefollowing period is applied should be identical, as shown inFig. 4. This ensures that the acting rotor voltage corresponds tothe real measured power errors and guarantees the effectivenessof the PDPC method.

III. PRACTICAL CONSIDERATIONS

A. Voltage Vector Calculation Using SVM

For a two-level rotor-side converter, the rotor output three-phase voltages can be represented by a voltage vector, and ac-cording to the output voltage levels of each phase, there are sixactive voltage vectors with amplitudes of 2Vdc/3 and two zerovectors [30]. Fig. 5 shows these eight voltage vectors denotedas V 0–V 7 , where the subscript of V is derived from the binary


Fig. 4. Ideal timing of the proposed PDPC control strategy.

Fig. 5. Spatial relationship of stator flux, rotor flux, and rotor voltage vectors.

number expressing the switching pattern in the phase sequence(a, b, and c). With each sampling period, it is necessary to calcu-late the required switching voltage vectors and their respectivedurations based on the required average rotor voltage vectorcalculated in (16). SVM technique is usually employed.

For the example shown in Fig. 5, where the average rotorvoltage vector Vr is located between V6 and V2 , the voltagevectors required to resemble Vr are V7 ,V6 ,V2 , and V0 , andtheir respective durations are calculated as [30]

ta =√

3kvTs sin(π

3− δ

)

tb =√

3kvTs sin (δ)

t01 = t02 =Ts

2

[1 −

√3kv sin

(π

3+ δ

)](17)

where kv = |V r|/Vdc and 0 ≤ δ < π/3.

B. Power Variations Within PWM Periods

Due to the discrete nature of the converter operation, theactive and reactive powers vary within each sampling period.Based on (16) and Fig. 5, the variations of active and reactivepowers during a short period of T for the voltage vector Vx canbe predicted as

∆Ps = kσω1ψsd(ωsψrd − Vrq−V x)T

∆Qs = kσω1ψsd(ωsψrq + Vrd−V x)T (18)

where Vx represents one of the eight voltage vectors, Vrd−V x

and Vrq−V x are the d- and q-axis components of V x.The following analysis assumes that the DFIG is operating at

a point, as shown in Fig. 5, i.e., both the rotor and stator fluxare presented in Section (I), whereas the desired rotor voltage ispresented in Section (II). The rotor flux leads the stator flux as the

Fig. 6. Active and reactive power variations within a PWM period.

DFIG is in the generation mode and operating at subsynchronousspeed.

According to (18), during the effective period of the zerovoltage vectors V0 and V7 , the power variations are given as

∆Ps = kσω1ψsdωsψrdT

∆Qs = kσω1ψsdωsψrqT. (19)

For normal operation, the angle θ between the stator and rotorflux is relatively small. Thus, the rotor d-axis flux componentψrd is much bigger than its q-axis component ψrq . Therefore,(19) indicates that the active power variation is much greaterthan the reactive power variation under zero-voltage vectors.The direction of the power variation is determined by the signof the rotor slip. In a subsynchronous operation case, both theactive and reactive powers increase (reducing generated activeand absorbed reactive powers) under zero voltage vectors V 0

and V 7 .As can be seen in Fig. 5, for voltage vectors V 2 and V 6 ,

their q-axis components Vrq−V 2 and Vrq−V 6 are both positive,and usually greater than ωsψrd . Thus, according to (17), bothdecrease the active power. Their d-axis components Vrd−V 2 andVrd−V 6 have opposite signs, and therefore, different impact onthe reactive power, e.g., V 6 increases it while V 2 reduces it.

Fig. 6 shows a schematic diagram of the active and reactivepower variations during a PWM period for the case studied. Atthe start and end of each sampling period Ts , the active andreactive power is maintained at their reference values, e.g., atthe kth sampling instant, Ps(k) = P ∗

s(k) and Qs(k) = Q∗s(k).

Whereas during the period, the active and reactive powers varyaccording to the directions analyzed previously.

According to (18), Fig. 6, and as analyzed previously, theamplitudes of active and reactive power ripples within eachsampling period can be estimated. It is assumed that the statorand rotor flux angle θ is small, and the rotor voltage leads therotor flux by 90◦. Under this condition, the amplitude of theactive power ripple can be considered to equal the variation


Fig. 7. Typical sampling and PWM update for PDPC in a practical system.

during one of the zero vectors as

|∆Ps | ≈ kσω1ψsdωsψrdTs

2

[1 −

√3kv sin

(π

3+ δ

)]. (20)

Thus, according to (20), the active power ripple reaches itsmaximum when δ = 0, i.e., the rotor voltage is located close tothe sector boundaries, and it is given as

|∆Ps |max = kσω1ψsdωsψrdTs

2

[1 − 3

2kv

]. (21)

According to (18) and Fig. 6, the reactive power ripple withineach sampling period can be considered to be determined by theactive voltage vectors as

|∆Qs | = kσω1ψsd

[ωsψrq +

23Vdc cos

(π

2− δ + θ

)]ta

≈ kσω1ψsd23Vdc cos

(π

2− δ

)√3kvTs sin

(π

3− δ

)

= kσω1ψsd2√3|V r|Ts sin (δ) sin

(π

3− δ

). (22)

According to (22), maximum reactive power ripple is pro-duced when δ = π/6, i.e., the rotor voltage is located in themiddle of each 60◦ sector, and is given as

|∆Qs |max ≈ 12√

3kσω1ψsd |V r|Ts. (23)

C. Sampling in Practical Systems

The ideal sampling and PWM update sequence mentionedin Fig. 4 cannot be implemented due to the time required fordata sampling and the necessary calculations. A realistic timesequence for a practical system is shown in Fig. 7, where thesampling points are in advance of the PWM update points bya period td during which the necessary voltage and currentare sampled, and the required rotor voltage calculations forthe following period Ts are carried out. Thus, td has to belong enough to ensure that all the required activities can beaccomplished. However, it indicates that the actual power errorwhen the rotor control voltage starts to take effect (update PWM)differs from the one sampled and used to calculate the rotorcontrol voltage. Thus, it is important to examine the impact ofsuch a delay on PDPC performance and provide appropriatecompensation if necessary.

Fig. 8. Sampled power errors due to the delay td .

Fig. 9. Schematic diagram of the proposed PDPC for a DFIG system.

D. Compensation of the Control Delay

Fig. 8 shows the sampled, and desired active and reactivepower feedback using the typical sampling sequence shown inFig. 7. As shown in Fig. 8 and as previously described, theideal power feedbacks required in the control system are Ps(k)′

and Qs(k)′, i.e., at the PWM update instant. However, due tothe td delay, the actual sampled power available to the controlsystem are Ps(k) and Qs(k). If the error between the ideal andactual power feedback is significant, it can result in considerablecontrol errors. Depending on the operating conditions and delaylength, various voltage vectors can be effective within the tdperiod. In general, longer td period has greater impact on thesampled power error.

The power errors due to the sampling delay can be compen-sated to eliminate steady-state error and possible oscillation.

At any sampling instance, the PWM pattern for the previousPWM period including the delay period, the effective voltagevectors, their sequence, and duration times are known. There-fore, the possible power variation during the period td can be pre-dicted. Assuming that the voltage vector sequence and the cor-responding duration times are V 0 ,V a,V b,V 7 , and t01 , ta , tb ,and t02 , respectively, the effective voltage vector duration within


Fig. 10. Schematic diagram of the experimental system.

TABLE IPARAMETERS OF THE TESTED DFIG

the delay period td can be expressed as

tV 0tV b

tV a

=

[td , 0, 0]T , if td < t02[t02 , td − t02 , 0]T , if (t02 + tb) > td > t02[t02 , tb , td − t02 − tb ]T , if td > (t02 + tb)

(24)

where tV 0 , tV b , and tV a are the effective durations of V 7 ,V b,and V a during the td period, respectively.

In the synchronous reference frame, the d- and q-axis com-ponents of V a and V b, namely, Vad, Vaq , Vbd , and Vbq can becalculated. The sampled power errors due to the delay period tdcan then be predicted based on (18) as

∆Pcomp = kσω1ψsd (ωsψrdtd − Vbq tV b − Vaq tV a)

∆Qcomp = kσω1ψsd (ωsψrq td + VbdtV b + VadtV a) . (25)

Thus, the active and reactive powers at the ideal (k′)th point(PWM update instance) can be calculated based on the kthsampled and the predicted values shown in (25) as

Ps(k)′ = Ps(k) + ∆Pcomp(k)

Qs(k)′ = Qs(k) + ∆Qcomp(k). (26)

E. Compensation Due to Rotating Reference Frame

As shown in (16b), the rotor voltage contains two parts,specifically, the first term (namely, V s

r1) that ensures the ro-tor flux rotates at the same angular speed as the stator flux, andkeeps the stator active and reactive powers at constant, whilethe second term (namely, V s

r2) generates the desired powerchanges.

Similarly, as shown in [22], the two rotor voltage compo-nents need to be phase-shifted due to the stator flux movement(synchronous d–q reference frame) within each sampling period

V s′

r = V sr1e

j (∆θ/2) + V sr2e

j∆θ (27)

where ∆θ = ωsTs .To further improve the power control accuracy, an integral

controller with a large time constant Ti can be added to therotor voltage generation module to compensate errors due tomachine parameters mismatch, improper compensation, or nu-merical error as

V s′

r3 =1Ti

(∫∆Qsdt − j

∫∆Psdt

). (28)

The integrator’s inputs are the active and reactive power er-rors, while the outputs from the integrator are added to Vs

r2 .This has little impact on system dynamics due to its large timeconstant Ti . However, the steady-state power errors are reducedso as to achieve precise stator active and reactive power control.Thus, the required rotor voltage in the synchronous referenceframe is given as

V s′′

r = V sr1e

j (∆θ/2) + (V sr2 + V s

r3) ej∆θ . (29)

The completed schematic diagram of the proposed PDPC isshown in Fig. 9.

IV. EXPERIMENTAL STUDIES

The schematic diagram of the experimental rig is shown inFig. 10. The system contains a 1.5-kW DFIG with its rotor cou-pled directly to a dc machine. The DFIG’s parameter values arelisted in Table I. The speed of the dc machine is controlled bya commercial thyristor drive, providing either speed or torque


Fig. 11. Experimental results under various stator active and reactive powersteps with ωr = 1200 r/min. (1): Stator active power input (1 kW/div); (2):stator reactive power input (1 kvar/div); (3): stator phase current (5 A/div);and (4): rotor phase current (10 A/div). (a) Ps step from 0 to −1.0 kW withQs = −1.0 kvar. (b) Qs step from 0 to −1.0 kvar with Ps = 0 W.

Fig. 12. Stator current and background voltage spectra, Ps = −1.5 kW, Qs =−1.0 kvar, ωr = 1200 r/min. (a) LUT-DPC, average switching frequency =2.3 kHz, THD = 6.13%. (b) PDPC, THD = 4.15%. (c) Conventional VC, THD= 4.51%. (d) Background voltage, THD = 1.43%.

control. Two 3-phase variacs are used, one supplying the statorwinding and the other connecting the grid-side converter (GSC).The GSC uses VC and controls the dc-link voltage at 80 V. Therotor-side converter (RSC) and GSC are controlled separatelyby two TI TMS320F2812 DSPs. The sampling and switchingfrequencies for both converters are 5 and 2.5 kHz, respectively,while the delay time td is 25 µs. Due to the relatively smallmagnetizing impedance of the tested DFIG, it absorbs consider-able active and reactive powers even when the rotor is an opencircuit, e.g., 130 W (absorbing) and −1.5 kvar (inductive).

Fig. 13. Experimental results during rotor speed variation (from 1200 to1800 r/min), Ps = −1.0 kW and Qs = −0.5 kvar. (a) (1): DC-link voltage(40 V/div); (2) GSC line-to-line voltage (50 V/div); (3) GSC phase current(5 A/div). (b) (1): Ps (1 kW/div); (2): Qs (1 kvar/div); (3): stator line-to-linevoltage (1 kV/div); (4): stator phase current (5 A/div). (c) (1)–(3): Rotor phasea, b, and c currents (10 A/div); (4): rotor slip (0.2 pu/div).

First, the dynamic performance of the proposed PDPC strat-egy was studied for active and reactive power steps. For com-parison, system response with traditional LUT-DPC and con-ventional VC were also tested. The sampling frequency forLUT-DPC was 20 kHz, whereas VC used the same samplingand switching frequencies as PDPC, i.e., 5 and 2.5 kHz, respec-tively. The hysteresis power control band for LUT-DPC was setat ±4% of 1.5 kVA. The test results are compared in Fig. 11


Fig. 14. Comparison of the impact of different compensation methods on active and reactive power errors, Ps = −1.0 kW and Qs = −0.5 kvar. (a) Activepower errors versus speed (Ps base defined as −1.5 kW). (b) Reactive power errors versus speed (Qs base defined as −1.5 kvar).

with the rotor speed constant at 1200 r/min. For Fig. 11(a), theactive power was stepped from 0 to −1 kW (generating) withthe reactive power fixed at −1 kvar (inductive). For Fig. 11(b),the active power was kept constant at 0 with the reactive powerstepped from 0 to −1 kvar. As seen, the dynamic responses dur-ing active and reactive power steps for the two DPC strategiesare similar, both within a few milliseconds. In contrast, the dy-namic response of VC is slower, over 10 ms in the tests, and ishighly dependent on the tuning of the control parameters.

The stator current harmonic spectra for the three differentcontrol strategies are shown in Fig. 12 together with the back-ground voltage harmonic spectrum. For LUT-DPC, the harmon-ics are spread over a wide frequency range, whereas PDPC andVC have similar harmonic spectra with the dominant harmon-ics concentrated around the 2.5 kHz switching frequency andmultiples thereof. The low-order harmonics, e.g., below 1 kHzare largely due to the background harmonics in the supply volt-age as substantiated from Fig. 12(d). The harmonics around1.5 kHz are generated by the stator and rotor slotting, and existeven when the DFIG’s rotor is an open circuit, i.e., the RSCis disconnected. Tests have also been carried out at differentoperating speeds, and the results are similar to those shown inFigs. 11 and 12.

The performance of the PDPC is also examined during vary-ing the rotor speed from 1200 to 1800 r/min, as shown in Fig. 13.During the test, the stator active and reactive powers are con-stant at −1.0 kW and −0.5 kvar, respectively. As can be seen,during the speed variation, the stator active and reactive powersare controlled, as are the stator and rotor currents. The rotorcurrent frequency initially decreases due to the reduced rotorslip, reaching zero at the synchronous speed of 1500 r/min,and increases after passing 1500 r/min. From Fig. 13, the com-mon dc voltage is also maintained by the GSC. The differentamplitude of the GSC current at 1200 r/min (+0.2 slip) and1800 r/min (−0.2 slip) is due the fact that the power consump-tion in the rotor resistors has opposite sign during sub- andsupersynchronous operations, which affects the active powerexchange between the rotor and the RSC. Consequently, thepower exchange between the GSC and the grid is different forsub- and supersynchronous operations.

Fig. 15. Comparison of dynamic response during Ps step from 0 to −1 kWwith and without delay compensation, Qs = −1.0 kvar and ωr = 1200 r/min.(1): Ps (1 kW/div); (2): Qs (1 kvar/div); (3): stator phase current (5 A/div);(4): rotor phase current (10 A/div). (a) With delay compensation. (b) Withoutdelay compensation.

To validate the effectiveness of the proposed compensationmethods, active and reactive powers were measured for differentoperating speed and different compensation. Four different caseswere considered, which are as follows.

Case 1: Without any compensation.Case 2: With the angle shift shown in (29) and integrator with

an 18-s time constant.Case 3: With delay time td compensation only.Case 4: Fully compensated, cases 2 and 3.

Fig. 14 compares the measured steady-state power errors forthe four cases. As shown in Fig. 14(a), for case 1 without anycompensation, there exists significant active power error. Oncethe angle shift and integrator are implemented in case 2, theactive power error is shifted a fixed value across the operatingspeed range and the error is proportional to the rotor slip. Withdelay compensation, case 3, only a fixed error exists. This alsoproves that the error introduced by the delay time is proportionalto the rotor slip as indicated in (18), since only a zero-voltagevector is effective in the period td in the experiments. In case4, with all the compensation methods applied, the active powererror is reduced to near zero.

For the reactive power shown in Fig. 14(b), again, case 1results in a steady-state error. As previously analyzed, due tothe effective zero voltage vector during the delay time, it has


Fig. 16. Comparison of system performance with Lm errors. (a) During rotor speed variation from 1200–1800 r/min, Ps = −1.0 kW, and Qs = −1.0 kvar.(1): Ps (1 kW/div); (2) Qs (1 kvar/div); (3)–(4) rotor phase a and b currents (10 A/div); (5) rotor slip (0.4 pu/div). (b) During Qs step change from 0 to −1.0 kvarwith Ps = 0 W. (1): Ps (1 kW/div); (2): Qs (1 kvar/div); (3): stator phase current (5 A/div); (4): rotor phase current (10 A/div).

little impact on the reactive power. Thus, as seen from Fig. 14(b),applying td compensation in case 3 has little impact on reactivepower error. Thus, cases 2 and 4 result in a similar performance.From Fig. 14, precise control of both the active and reactivepowers has been achieved with the proposed PDPC method.

Fig. 15(a) and (b) compares the dynamic performance duringan active power step with and without delay td compensation. Ascan be seen, without compensation, the reactive power oscillatesduring the active power step, whereas with compensation, itbecomes more stable and less oscillatory.

Tests on the impact of the variation of mutual inductance thatcan occur due to possible machine saturation and temperaturevariation, etc., on system performance with the PDPC, werealso carried out. The test results are compared in Fig. 16(a)and (b) with the mutual inductance values used in the control

system varied by ±20%. As can be seen in Fig. 16, such errorshave minimal influence on system dynamic and steady-stateperformances. The responses are almost identical for the threedifferent inductance values, which indicate that the proposedPDPC is robust to inductance variation with excellent dynamicand static performances.

As shown in (15b), rotor resistance variation could affect therotor control voltage. Due to the small rotor resistance, its im-pact during system transient is insignificant. Under steady state,rotor resistance error generates a static rotor voltage error, andconsequently, it results in small steady-state power errors if nointegral compensator is applied. However, such static powererrors can be easily compensated by the proposed integral con-troller since the variation of rotor resistance due to temperaturevariation is a slow process. Further tests with the rotor resistance


Fig. 17. Comparison between the PDPC and VC during small-sourceharmonic distortion (5th: 0.5%, 7th: 0.4%, 11th: 0.3%), Ps = −1 kW,and Qs = −500 var. (1): Active power (500 W/div); (2) reactive power(500 var/div); (3) stator phase current (2 A/div).

value used in the control system being twice the actually valueproved its insignificant effect on both steady-state and transientperformances of the proposed method.

Tests during small-source voltage harmonic distortion havealso been carried out, and Fig. 17 compares the results withPDPC and VC. As shown, due to the limited control bandwidth,the generated stator active and reactive powers with VC containconsiderable oscillations in the presence of small-source voltageharmonics (mainly, the fifth and the seventh). However, with thePDPC strategies, the power oscillations are insignificant due tothe direct control of the active and reactive power.

With varying active and reactive power references, furthertests have been conducted, and Fig. 18 compares the measuredwaveforms with PDPC and VC. In Fig. 18(a), with the reactivepower maintained at −1 kvar, the active power reference con-tains an average dc value of −1 kW and a 100 Hz sinusoidalsignal with an amplitude of 300 W. Similarly, in Fig. 18(b),with the active power maintained at −1 kW, a 100-Hz-/300-varsinusoidal signal was injected on to the average reactive powerreference of −1 kvar. As can be seen, due to the high band-width of the PDPC, it results in a much high accuracy withsmall power errors. In contrast, the conventional VC schemeresults in significant control errors due to its insufficient controlbandwidth.

For practical megawatt (MW) DFIG systems, their parameterscan differ significantly from those of the prototype system in thefollowing categories.

Fig. 18. Comparison between the PDPC and VC during active and reac-tive power tracking, average Ps = −1 kW, average Qs = −1 kvar, ωr =1200 r/min. (a) Varying active power reference. (1): Ps reference (1 kW/div);(2): Ps measured (1 kW/div); (3): active power error (1 kW/div). (b) Varyingreactive power reference. (1): Qs reference (1 kvar/div); (2) Qs (1 kvar/div);(3) reactive power error (1 kvar/div).

1) Smaller Rs and Rr than the prototype.2) Bigger Ls, Lr , and Lm than the prototype.3) Bigger Rm and smaller no-load loss than the prototype.As the inductance values have been fully taken into account in

deriving the equations, their differences should have negligibleimpact on system control. Smaller stator and rotor resistancesin MW DFIGs can result in slightly higher accuracy for powercontrol than the prototype as the derivations of (6), (7), and (18)neglect Rs and Rr . Much larger Rm in practical MW systemsalso indicates higher accuracy than that for the prototype, asthe theoretical model shown in Fig. 2 assumed infinite Rm .Nevertheless, full simulation studies using typical parametersseen in practical systems were conducted, and the results matchthe prototype tests well. The simulation results are not shownhere due to space limitations.

V. CONCLUSION

A PDPC strategy for DFIGs has been proposed in this pa-per. A DFIG model that defines the stator active and reactivepower flow was presented. Based on such a model, a DFIG’s ac-tive and reactive power variations with a fixed sampling periodwere predicted, which was then used to directly calculate therequired rotor voltage to eliminate stator power errors at the endof the sampling period. The practical impact of sampling delayon the accuracy of the sampled active and reactive power wasanalyzed, and detailed compensation methods were proposedto improve both the steady-state and dynamic performances ofthe PDPC method. Experimental results from a 1.5-kW DFIGtest system proved the dynamic performance and power controlaccuracy of the PDPC method. System performance during pa-rameter variation and with varying reference further illustratedthe performance of the PDPC method.

REFERENCES

[1] W. Leonhard, Control of Electrical Drives. London, U.K.: Springer-Verlag, 2001.

[2] R. Pena, J. C. Clare, and G. M. Asher, “Doubly fed induction generatorusing back-to-back PWM converters and its application to variable-speedwind-energy generation,” Inst. Electr. Eng. Proc. Electr. Power Appl.,vol. 143, no. 3, pp. 231–241, May 1996.


[3] A. Petersson, L. Harnefors, and T. Thiringer, “Evaluation of current controlmethods for wind turbines using doubly-fed induction machines,” IEEETrans. Power Electron., vol. 20, no. 1, pp. 227–235, Jan. 2005.

[4] H. Akagi and H. Sato, “Control and performance of a doubly-fed inductionmachine intended for a flywheel energy storage system,” IEEE Trans.Power Electron., vol. 17, no. 1, pp. 109–116, Jan. 2002.

[5] R. W. De Doncker, S. Muller, and M. Deicke, “Doubly fed inductiongenerator systems for wind turbines,” IEEE Ind. Appl. Mag., vol. 8, no. 3,pp. 26–33, May/Jun. 2002.

[6] K. P. Gokhale, D. W. Karraker, and S. J. Heikkila, “Controller for a woundrotor slip ring induction machine,” U.S. Patent 6 448 735 B1, Sep. 2002.

[7] R. Datta and V. T. Ranganathan, “Direct power control of grid-connectedwound rotor induction machine without rotor position sensors,” IEEETrans. Power Electron., vol. 16, no. 3, pp. 390–399, May 2001.

[8] L. Xu and P. Cartwright, “Direct active and reactive power control of DFIGfor wind energy generation,” IEEE Trans. Energy Convers., vol. 21, no. 3,pp. 750–758, Sep. 2006.

[9] I. Takahashi and T. Noguchi, “A new quick-response and high-efficiencycontrol strategy of an induction motor,” IEEE Trans. Ind. Appl., vol.IA-22, no. 5, pp. 820–827, Oct. 1986.

[10] M. Depenbrock, “Direct self-control (DSC) of inverter-fed induction ma-chine,” IEEE Trans. Power Electron., vol. PE-3, no. 4, pp. 420–429, Jul.1988.

[11] T. G. Habetler, F. Profumo, M. Pastorelli, and L. M. Tolbert, “Directtorque control of induction machines using space vector modulation,”IEEE Trans. Ind. Appl., vol. 28, no. 5, pp. 1045–53, Oct. 1992.

[12] Y. S. Lai and J. H. Chen, “A new approach to direct torque control of in-duction motor drives for constant inverter switching frequency and torqueripple reduction,” IEEE Trans. Energy Convers., vol. 16, no. 3, pp. 220–227, Sep. 2001.

[13] N. R. N. Idris and A. H. M. Yatim, “Direct torque control of inductionmachines with constant switching frequency and reduced torque ripple,”IEEE Trans. Ind. Electron., vol. 51, no. 4, pp. 758–767, Aug. 2004.

[14] J. Kang and S. Sul, “New direct torque control of induction motor forminimum torque ripple and constant switching frequency,” IEEE Trans.Ind. Appl., vol. 35, no. 5, pp. 1076–1082, 1999.

[15] S. Aurtenechea, M. A. Rodrı́guez, E. Oyarbide, and J. R. Torrealday,“Predictive control strategy for DC/AC converters based on direct powercontrol,” IEEE Trans. Ind. Electron., vol. 54, no. 3, pp. 1261–1271, Jun.2007.

[16] S. Vazquez, J. A. Sanchez, J. M. Carrasco, J. I. Leon, and E. Galvan,“A model-based direct power control for three-phase power converters,”IEEE Trans. Ind. Electron., vol. 55, no. 4, pp. 1647–1657, Apr. 2008.

[17] M. Malinowski, M. Jasinski, and M. P. Kazmierkowski, “Simple directpower control of three-phase PWM rectifier using space-vector modulation(DPC-SVM),” IEEE Trans. Ind. Electron., vol. 51, no. 4, pp. 447–454,Apr. 2004.

[18] G. Abad, M. A. Rodrı́guez, and J. Poza, “Two-level VSC-based predictivedirect power control of the doubly fed induction machine with reducedpower ripple at low constant switching frequency,” IEEE Trans. EnergyConvers., vol. 23, no. 2, pp. 570–580, Jun. 2008.

[19] G. Abad, M. A. Rodrı́guez, and J. Poza, “Two-level VSC-based predictivetorque control of the doubly fed induction machine with reduced torqueand flux ripples at low constant switching frequency,” IEEE Trans. PowerElectron., vol. 23, no. 3, pp. 1050–1061, May 2008.

[20] D. Zhi, L. Xu, and B. W. Williams, “Improved direct power control ofgrid-connected DC/AC converters,” IEEE Trans. Power Electron., vol. 24,no. 5, pp. 1280–1292, May 2009.

[21] D. Zhi and L. Xu, “Direct power control of DFIG with constant switchingfrequency and improved transient performance,” IEEE Trans. EnergyConvers., vol. 22, no. 1, pp. 110–118, Mar. 2007.

[22] D. Zhi, L. Xu, and J. Morrow, “Improved direct power control of doubly-fed induction generator based wind energy system,” in Proc. IEMDC,2007, pp. 1–6.

[23] Q. Zeng and L. Chang, “An advanced SVPWM-based predictive currentcontroller for three-phase inverters in distributed generation systems,”IEEE Trans. Ind. Electron., vol. 53, no. 3, pp. 1235–1246, Mar. 2008.

[24] Y. A.-R. I. Mohamed and E. F. El-Saadany, “Robust high bandwidthdiscrete-time predictive current control with predictive internal model—A unified approach for voltage-source PWM converters,” IEEE Trans.Power Electron., vol. 23, no. 1, pp. 126–136, Jan. 2008.

[25] S. G. Jeong and M. H. Woo, “DSP-based active power filter with predictivecurrent control,” IEEE Trans. Ind. Electron., vol. 44, no. 3, pp. 329–336,Jun. 1997.

[26] S. J. Jeong and S. H. Song, “Improvement of predictive current con-trol performance using online parameter estimation in phase controlledrectifier,” IEEE Trans. Power Electron., vol. 22, no. 5, pp. 1820–1825,Sep. 2007.

[27] H. T. Moon, H. S. Kim, and M. J. Youn, “A discrete-time predictivecurrent control for PMSM,” IEEE Trans. Power Electron., vol. 18, no. 1,pp. 464–472, Jan. 2003.

[28] P. Wipasuramonton, Z. Q. Zhu, and D. Howe, “Predictive current controlwith current-error correction for PM brushless AC drives,” IEEE Trans.Ind. Appl., vol. 42, no. 4, pp. 1071–1079, Jul./Aug. 2006.

[29] M. W. Naouar, A. A. Naassani, E. Monmasson, and T. S. Belkhodja,“FPGA-based predictive current controller for synchronous machinespeed drive,” IEEE Trans. Power Electron., vol. 23, no. 4, pp. 2115–2126, Jul. 2008.

[30] H. W. Van De Broeck, H. C. Skudelny, and G. V. Stanke, “Analysis andrealization of a pulsewidth modulator based on voltage space vectors,”IEEE Trans. Ind. Appl., vol. 24, no. 1, pp. 142–150, Jan./Feb. 1988.

Dawei Zhi (S’07) received the B.Sc. and M.Sc. de-grees from Zhejiang University, Hangzhou, China, in2000 and 2003, respectively. He is currently work-ing toward the Ph.D. degree at the University ofStrathclyde, Glasgow, U.K.

From 2004 to 2005, he was with Delta Power Elec-tronics Center, Shanghai, China.

Lie Xu (M’03–SM’06) received the B.Sc. degreefrom Zhejiang University, Hangzhou, China, in 1993,and the Ph.D. degree from the University of Sheffield,Sheffield, U.K., in 1999.

From 2007 to 2008, he was with the Univer-sity of Strathclyde, Glasgow, U.K. He is currently aSenior Lecturer in the School of Electronics, Elec-trical Engineering and Computer Science, Queen’sUniversity of Belfast, Belfast, U.K. His current re-search interests include power electronics, wind en-ergy generation and grid integration, and application

of power electronics to power systems.

Barry W. Williams received the Ph.D. degree in elec-trical and electronic engineering from the Universityof Cambridge, Cambridge, U.K., in 1980.

He is currently a Professor in the Department ofElectronic and Electrical Engineering, University ofStrathclyde, Glasgow, U.K. His current research in-terests include application of power electronics.

Documents

9.pdf