1

Control of DFIG for Rotor Current HarmonicsElimination

Lingling Fan, Senior Member, IEEE, Rajesh Kavasseri, Senior Member, IEEE, Haiping Yin, Chanxia Zhu,Minqiang Hu

Abstract—Unbalanced stator conditions cause rotor currentharmonics and torque pulsations in Doubly-Fed Induction Gen-erators (DFIG) which are used widely in wind energy systems.From a hardware perspective, current control techniques to min-imize the rotor current harmonics include rotor-side converterinjected voltage compensation and grid-side converter compensa-tion. From a software perspective, the current controllers eitheradopt synchronous reference frame for controller design or adoptpositive synchronous (qd+) and negative synchronous referenceframes (qd−) to decompose the harmonics in rotor currentsand control them separately. This paper develops a proportionalresonance (PR) control strategy in the stationary reference frame(αβ) to minimize rotor current harmonics and torque pulsations.The main advantages of the proposed method are (i) only onetransformation (abc/αβ) is required and (ii) harmonic filters arenot required. The proposed control strategy is compared with theproportional integral (PI) control strategy in qd+ and qd− andthe proportional integral and resonant (PIR) control strategy inqd+. Simulations performed in Matlab/Simulink are presentedto illustrate the effectiveness of the proposed control strategy.

Index Terms—Wind Generation, Doubly Fed Induction Gen-erator, harmonics, unbalance, proportional resonance

I. INTRODUCTION

DOUBLY Fed Induction Generators (DFIGs) are widelyused in wind generation. The configuration of a grid-tied

DFIG wind turbine system is shown in Fig. 1. The possibilityof getting a constant frequency AC output from a DFIGwhile driven by a variable speed prime mover improves theefficacy of energy harvest from wind [1]. Unlike a squirrel-cage induction generator, which has its rotor short circuited,a DFIG has its rotor terminals accessible. The rotor of aDFIG is fed by a variable-frequency (fr), variable magnitudethree-phase voltage generated by a PWM converter. This ACvoltage injected into the rotor circuit will generate a flux witha frequency fr if the rotor is standing still. When the rotoris rotating at a speed fm, the net flux linkage will have afrequency fr + fm. When the wind speed changes, the rotorspeed fm will change and in order to have the net flux linkageat a frequency 60 Hz, the rotor injection frequency should alsobe adjusted.

Unbalanced stator conditions in DFIGs give rise to rotorcurrent harmonics and torque pulsations which can causeexcessive shaft stress and winding losses. From a hardwareperspective, current control techniques to minimize the rotor

L. Fan, R. Kavasseri, H. Yin and C. Zhu are with the dept. of Electrical& Computer Engineering, North Dakota State University, Fargo, ND 58105.Email: Lingling.Fan@ndsu.edu, Rajesh.Kavasseri@ndsu.edu. M. Hu is withthe school of Electrical Engineering, Southeast University, Nanjing China210098. Email: mqhu@seu.edu.cn.

DFIGTo Grid

C2C1

C

Crowbar

vr ir

is

PWM Converters

vs

Pg+ jQ g

Wind Turbine

Fig. 1. Grid-tied DFIG wind turbine system.

current harmonics include rotor-side converter injected voltagecompensation [2] and grid-side converter compensation [3].From a software perspective, the current controllers eitheradopt synchronous reference frame for controller design [4]or more sophisticated, adopt synchronous (qd+)and negativesynchronous reference frame (qd−)to decompose the harmon-ics in rotor currents and control them separately [5]. A similarapproach is used in [3] to extract the negative sequencecurrents to the load in qd− reference frame, and then adopt PIcontrollers to compensate the negative sequence current fromgrid-side converters.

The first approach in [2] and [6] uses only one referenceframe qd+ and ultimately dealing with 2ωe frequency har-monics. In [2], the controller design requires careful tuning.While in [6], proportional integral and resonant controllersare adopted to eliminate the 2ωe frequency harmonics. Thesecond approach in [5] and [3] requires two reference framesand filters to trap high frequency harmonics. More recently,for generalized grid converters, αβ reference frame is usedand proportional resonance controller is adopted [7]. WhileProportional Resonance (PR) controllers have been widelyused in converter control (can be considered as ac PI con-trollers [8]), their use for harmonic mitigation in DFIGs hasnot been explored. PR controllers have two advantages overother proposed techniques in that only one transformation isneeded and filters are not required. In this paper, a PR controlstrategy will be developed for the rotor-side converters tosuppress harmonics and minimize torque pulsations. The restof the paper is organized as follows.

978-1-4244-4241-6/09/$25.00 ©2009 IEEE

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In Section II, an analysis of the harmonics in rotor currentsand electromagnetic torque during unbalanced stator conditionis presented. Section III presents the PI control strategy usingtwo reference frames (qd+, qd−), PIR control strategy insynchronous reference frame qd+ and PR control strategyusing αβ reference frame. Simulation results performed withMatlab/Simulink are given in Section IV to demonstrate theeffectiveness of the proposed control strategy. Section Vconcludes the paper.

II. HARMONIC ANALYSIS FOR THE UNBALANCED STATORCONDITION

The purpose of the analysis is to analyze the DFIG op-eration under unbalanced stator conditions and the followingassumptions are made.

1) Rotor voltage injections are sinusoidal and the magni-tude of the injected voltage is constant during the statorunbalance.

2) An inverter with sine PWM is used to generate sinewaveforms for the rotor injection. With slip control, thesynthesized ac voltage will have a frequency fr = fs −

fm where fs = 60 Hz. With sine PWM, the lowest orderharmonics will be at several kHz which is easily filteredout.

3) The stator side voltage frequency is 60 Hz. During theunbalance, the voltage magnitudes of the three phasesmay not be the same. and the relative phase anglesbetween the three voltages may not be 1200.

There are two steps in the analysis. The first step is toidentify the harmonic component in the rotor currents andthe electromagnetic torque and the second step is to estimatethe magnitude of each harmonic component. Using symmetriccomponent theory, the voltage phasors can be decomposed intoa positive sequence, a negative sequence and a zero sequencecomponent. The calculation of harmonic components in therotor current and electromagnetic torque are based on thesequence decomposition as explained below.

A. Harmonics Components in the Rotor CurrentsFor an induction machine, the following rule holds true:

ωr+ωm = ωs, that is, the sum of the rotor injection frequencyand the rotor shaft electrical speed equals to the stator variablefrequency. For the positive sequence voltage set with frequencyωs applied to the stator side, the resulting rotor currents or fluxlinkage have a frequency ωr = ωs −ωm = sωs. The negativesequence voltage set can be seen as a three-phase balanced setwith a negative frequency −ωs. Thus the induced flux linkagein rotor circuit and the rotor currents have a frequency of−ωs−ωm = −(2−s)ωs. The torque, in positive sequence setvariables, is a constant at steady-state. However, in negativesequence set, the torque has (2− s)ωs.

B. Harmonic Components of Electromagnetic TorqueUnder unbalanced stator condition, the stator current has

two components: positive sequence Is+ and negative sequencecomponent Is−. The rotor current also has two components:

positive sequence Ir+ and negative sequence components Ir−.The electromagnetic torque is produced by the interactionbetween the stator flux linkage and the rotor linkage, or thestator current and the rotor current. For interactions betwen thestator and rotor mmfs of the same sequence (+, +) or (-, -),the torque appears as a dc (steady) component. For interactionsbetween stator and rotor mmfs of the opposite sequence (+,-) or (-, +), the torque appears as a pulsating component withfrequency 2ωe. Thus, the resultant torque can be decomposedinto four components:

Te = Te1 + Te2 + Te3 + Te4 (1)

where Te1 is due to the interaction of Is+ and Ir+, Te2 isdue to the interaction of Is− and Ir−, Te3 is due to theinteraction of Is+ and Ir−, and Te4 is due to the interactionof Is− and Ir+. Te1 and Te2 are due to the interaction of thesame harmonic order currents or mmfs. Hence these two aredc components. Te3 and Te4 are pulsating components withfrequency of 2ωe.

This can also be justified by expressing the torque in termsof the stator current induced mmf space vector Fs and therotor current induced mmf space vector Fr [9]:

Te = −P

2

μ0

2

πDl

gFsFr sin δsr (2)

where P is the number of poles, μ0 is the air gap permeability,D is the average diameter of the air gap, l is the length of theconductor and g is the length of the air gap, Fs and Fr arethe peak values of stator- and rotor-mmf waves and δsr is theangle between the two space vectors.

When the two mmf space vectors have the same rotatingspeed, δsr is a constant and the torque is smooth. The positivesequence stator mmf has a rotating speed of ωe. The positivesequence rotor current has a frequency of ωr and the rotoris rotating at a speed of ωm. The resulting rotor mmf in airgap has a speed of ωe (ωr + ωm) as well. Hence Te1 is a dccomponent. The negative sequence stator mmf and the negativesequence rotor mmf have the same speed −ωe. Hence Te2 isa dc component. On the other hand, the positive stator mmfand the negative rotor mmf has an angle of −2ωet + δsr0.Hence the torque produced Te3 has a pulsating frequency of2ωe. Using the same analogy, Te4 has a pulsating frequencyof 2ωe as well.

III. CONTROL STRATEGIES

The positive sequence three-phase voltages will induce aslip frequency sωe in the rotor circuits. The negative sequencevoltage set can be seen as a three-phase balanced set with anegative frequency−ωs. Thus the induced flux linkage in rotorcircuit and the rotor currents have a frequency of −ωs−ωm =−(2− s)ωs.

Observed from the synchronously rotating reference frame,the first component has a frequency of ωe−ωr−sωe = 0, i.e.,a dc component and the second component has a frequencyof ωe − ωr + (2 − s)ωe = 2ωe, i.e., 120 Hz. Using thesame analogy, the frequency components in the rotor currentobserved from the clockwise synchronously rotating reference

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frame and the stationary αβ reference frame can be deter-mined. Table I shows the components in the three referenceframes.

To extract the harmonic components in the rotor current,both a synchronously rotating reference frame and a clockwisesynchronously rotating reference frame (Fig. 2) will be used.

TABLE IROTOR CURRENT COMPONENTS OBSERVED IN VARIOUS REFERENCE

FRAMES

stationary ωe −ωe αβ

Positive sωe 0 −2ωe ωe

Negative −(2− s)ωe 2ωe 0 −ωe

a axis

q qxis (synchronously rotating)

d axis ( synchronously rotating)

q' axis (negatively synchronously )

d' axis (negativelysynchronously)

-2

-ωe

ωe

ωe

Fig. 2. Two reference frames: synchronous and negatively synchronous.

The rotor currents in both reference frames will have a dccomponent and a high frequency component. Low pass filtershave to be used to extract the dc components which corre-sponds to the magnitudes of the two harmonic components.The scheme for extracting the dc components is shown inFig. 3.

ieqr

iedr

low pass filterie +

qr

low pass filterie +

dr

eieqr - ji edr

complexto real

low pass filter

low pass filter

ie - qr

ie - dr

j2ωet

Fig. 3. Scheme for extracting dc components.

A third-order butterworth low-pass filter is used in theextracting strategy. Since the ac components have a frequencyof 120 Hz, the bandwidth of the filter is set to be 100 rad/s.The transfer function of the butterworth filter is expressed:

G(s) =ω3

0

(s + ω0)3(3)

where ω0 = 100 rad/s.

A. PI controllers in dq+ and dq− reference framesThe control scheme using two reference frames: qd+ and

qd− to minimize the negative sequence rotor harmonics is

shown in Fig. 4. Positive- and negative sequence componentsin the rotor currents are extracted through qd+ and qd−

reference frame transformation. Low pass filters are use toget the dc components in each reference frame. The controlpurpose is to use a PI controller and let the negative sequencecurrent component track the reference point - zero. Thiscontrol scheme is used in [5].

B. PIR controllers in dq+ reference framesIn the synchronous reference frame, the positive-, negative-

sequence rotor currents will be observed as dc and ac with−2ωe frequency. It will be reasonable to use a PI controller tobring the dc component of the rotor current to the referencevalue. For the ac component of 2ωe frequency, in order toeliminate it, or bring the ac component to the reference valuewith zero magnitude, a PR controller with resonance frequencyof 2ωe will be used. Hence, the control diagram is shown inFig. 5. This control scheme is used in [6].

C. Proposed PR controllers in αβ reference frameA PR control scheme is proposed in this paper. In αβ sta-

tionary reference frame, the positive- and negative- sequencerotor currents will be observed as components of ωe and−ωe frequency. Hence there only exists one frequency inαβ reference frame. The PR controllers function as ac PIcontrollers to track the ac reference points. Different than theprevious PI control scheme, only one controller for each axiswill be used. The control scheme is shown in Fig. 6. Themain advantages of the proposed method are (i) only onetransformation (abc/αβ) is required and (ii) harmonic filtersare not required.

IV. CASE STUDIES

Matlab/Simulink model of a 3HP DFIG (parameters areshown in Appendix) is developed by the authors [10] andwill be used to test the proposed control strategies. The statorvoltage RMS value is 230 V. At t = 1 second, phase A voltagedrops to 70.7 V. At t = 1.5 second, phase A voltage recoversto the nominal value. Three case studies are simulated:

1) without negative sequence compensation subject to un-balanced stator voltage. The simulation results are shownin Figs. 7-8.

2) with PI control strategy. The simulation results areshown in Figs. 9-11.

3) with PIR control strategy. The simulation results areshown in Figs. 12-13.

4) with PR control strategy. The simulation results areshown in Figs. 14-16.

Fig. 7 shows that under balanced stator voltage condition,the torque is a constant. The phase A stator current has afrequency of 60 Hz and a magnitude about 1.4 pu. The phase Arotor current has a frequency of 3.5 Hz and a magnitude about0.5 pu. During the unbalanced stator condition, the torquenow has a pulsating component with a frequency of 2ωe. Themagnitude of the stator current increases to more than 7 pu.The magnitude of the rotor current increases to 3 pu and there

4

Fig. 4. The two reference frames: synchronous and negatively synchronous.

abc/ qd

2221

)2(ssk

sk

k iiP +

++

PIR

iqr

idr

iqr*

idr*

+

+

-

-vqr

vdrqd/abc

vcr

var

vbr

icr

iar

ibr

2221

)2(ssk

skk ii

P +++

ωe

ωe

θmθm

Fig. 5. Proportional integral plus resonant (PI+R) control scheme.

abc /

22 )(sskk i

P ++

PR

icr

iar

ibr

*

*

+

+

-

-

22 )(sskk i

P ++

abcvcr

var

vbr

ωe

ωe

θmθm

αβ αβ/

iα

iα vα

iβ

iβ vβ

Fig. 6. Proposed Proportional resonant (PR) control scheme.

are two frequency components in the rotor current, one at theslip frequency around 3.5 Hz and the other near 120 Hz.

In Fig. 8, the abc rotor currents are transformed into the syn-chronous reference frame qd+ and the negative synchronousreference frame qd−. It shows that under balanced statorcondition, the rotor currents are seen as constants in qd+

while in qd− they are pulsating currents with a frequency of120 Hz. During unbalanced stator condition, the rotor currents

are shown to have a dc component and a 120 Hz pulsatingcomponent in both reference frames. The magnitude of thepulsating component in ieqr or iedr is seen equivalent to the dccomponent in i−e

qr or i−edr . Hence, by applying a low pass filter,

the dc components in ieqdr and i−eqdr corresponding to ieqdr+ and

i−eqdr− can be extracted.

With the positive and negative components extracted andreflecting in qd+ and qd− reference frames as dc variables,

5

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−4

−2

0

2to

rque

(pu)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−10

−5

0

5

10

i as (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−4

−2

0

2

4

i ar (p

u)

time (sec)

Fig. 7. Dynamic responses of torque, stator current ias and rotor currentiar without negative sequence compensation.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−5

0

5

ie qr (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−5

0

5

ie dr (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−2

0

2

4

i−e qr (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−4

−2

0

2

i−e dr (p

u)

time (sec)

Fig. 8. Dynamic responses of rotor currents in qd+ and qd− referenceframes without negative sequence compensation.

PI controllers can be applied to force these components todesired values. To eliminate the rotor current harmonics, thereference values of the negative sequence rotor currents i∗−e

qr

and i∗−edr are set to be zeros. The simulation results with the

PI control in two reference frames are shown in Figs. 9-11. Itis found that applying the control strategy, during unbalancedstator condition, the high frequency pulsating components intorque and rotor currents are reduced significantly. The controlfunction is realized physically by injecting a negative sequencecomponent in the rotor voltages shown in Fig. 11.

The similar control function can be realized through PIRcontrol strategy in the synchronous reference frame. Thesimulation results are shown in Figs. 12-13.

For the proposed PR control strategy, αβ reference frame isadopted. During unbalanced stator condition, the rotor currentsonly have one frequency component - 60 Hz. PR controllers

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−2

−1

0

1

2

torq

ue (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−10

−5

0

5

10

i as (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−4

−2

0

2

4

i ar (p

u)

time (sec)

Fig. 9. Dynamic responses of torque, stator current ias and rotor currentiar with PI control strategy.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−2

0

2

4

ie qr (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−5

0

5

ie dr (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−5

0

5

i−e qr (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−4

−2

0

2

i−e dr (p

u)

time (sec)

Fig. 10. Dynamic responses of rotor currents in qd+ and qd− referenceframes with PI control strategy.

work as ac PI controller, i.e., they are effective to bring therotor currents to the referenced sinusoidal waveforms. Thereference signals are no longer constants as in the synchronousreference frame, rather, they are transferred into αβ referenceframe and are sinusoidal waveforms of 60 Hz. The simulationresults are shown in Figs. 14-16. The control objective - tominimize the rotor current harmonics - is achieved.

V. CONCLUSION

In this paper, a novel control strategy to minimize rotorcurrent harmonics due to unbalanced stator condition is devel-oped and tested. Analysis of the harmonics in rotor currentsduring unbalanced stator condition is first given. Stationaryreference frame (αβ) is adopted and proportional resonance(PR) control strategy is developed. The proposed controlstrategy is compared with the PI control strategy in qd+ and

6

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.4

−0.2

0

0.2

0.4

0.6ve qr

(pu)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.5

0

0.5

ve dr (p

u)

time (sec)

Fig. 11. Dynamic responses of the injected rotor voltages in qd+ referenceframe with PI control strategy.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−2

−1

0

1

2

torq

ue (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−10

−5

0

5

10

i as (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−4

−2

0

2

4

i ar (p

u)

time (sec)

Fig. 12. Dynamic responses of torque, stator current ias and rotor currentiar with PIR control strategy.

qd−. Simulations performed in Matlab/Simulink are given todemonstrate the effectiveness of the proposed control strategy.The main advantages of the proposed method are (i) only onetransformation (abc/αβ) is required and (ii) harmonic filtersare not required.

APPENDIX

The 3HP induction machine parameters are listed in TableII.

REFERENCES

[1] S. Muller, M. Deicke, and R. W. D. Doncker, “Doubly fed inductiongenerator systems for wind turbine,” IEEE Ind. Appl. Mag., pp. 26–33,May/June 2002.

[2] N. Mohan, First Course on Power Electronics. MNPERE Prentice Hall,2005.

[3] R. Pena, R. Cardenas, and E. Escobar, “Control system for unbalancedoperation of stand-alone doubly fed induction generators,” IEEE Trans.Energy Convers., vol. 22, no. 2, 2007.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.4

−0.2

0

0.2

0.4

0.6

ve qr (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.5

0

0.5

ve dr (p

u)

time (sec)

Fig. 13. Dynamic responses of rotor voltages in qd+ reference frames withPIR control strategy.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−2

−1

0

1

2

torq

ue (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−10

−5

0

5

10

i as (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−4

−2

0

2

4

i ar (p

u)

time (sec)

Fig. 14. Dynamic responses of torque, stator current ias and rotor currentiar with PR control strategy.

TABLE IIINDUCTION MACHINE PARAMETERS

Rs(Ω) 0.435Xls (Ω) 0.754XM (Ω) 26.13X′

lr(Ω) 0.754

r′r (Ω) 0.816J(kg.m2) 0.089

7

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−2

0

2

4ie qr

(pu)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−5

0

5

ie dr (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−5

0

5

i−e qr (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−4

−2

0

2

i−e dr (p

u)

time (sec)

Fig. 15. Dynamic responses of rotor currents in qd+ and qd− referenceframes with PR control strategy.

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.4

−0.2

0

0.2

0.4

0.6

ve qr (p

u)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2−0.5

0

0.5

ve dr (p

u)

time (sec)

Fig. 16. Dynamic responses of the injected rotor voltages in qd+ referenceframe with PR control strategy.

[4] T. K. A. Brekken and N. Mohan, “Control of a doubly fed inductionwind generator under unbalanced grid voltage conditions,” IEEE Trans.Energy Convers., vol. 22, pp. 129–135, March 2007.

[5] L. Xu and Y. Wang, “Dynamic modeling and control of dfig-basedwind turbines under unbalanced network conditions,” IEEE Trans. PowerSyst., vol. 22, no. 1, pp. 314–323, February 2007.

[6] J. Hu and Y. He, “Modeling and enhanced control of DFIG underunbalanced grid voltage conditions,” Eletric Power Systems Research,2008, doi:10.1016/j.epsr.2008.06.017.

[7] ——, “Modeling and control of grid-connected voltage-sourced convert-ers under generalized unbalanced operation conditions,” IEEE Trans.Energy Convers., vol. 23, no. 3, pp. 903–913, Sep. 2008.

[8] R. Teodorescu, F. Blaabjerg, M. Liserre, and P. Loh, “Proportional-resonant controllers and filters for grid-connected voltage-source con-verters,” IEE Proc.-Electr. Power Appl., vol. 153, no. 5, pp. 750–762,Sep. 2006.

[9] A. Fitzgerald, C. Kingsley, and A. Kusko, Electric Machinery.McGraw-Hill Book Company, 1971.

[10] Z. Miao and L. Fan, “The art of modeling high-order induction genera-tors in wind generation applications,” Simulation and Modelling Practiceand Theory, vol. 6, no. 9.

Lingling Fan is an assistant professor in Dept. of Electrical & ComputerEngineering, North Dakota State University. She received the BS, MS degreesin electrical engineering from Southeast University, Nanjing, China, in 1994and 1997, respectively. She received Ph.D. degree in electrical engineeringfrom West Virginia University in 2001. Before joining NDSU, Dr. Fanwas with Midwest ISO, St. Paul, Minnesota. Her research interests includemodeling and control of renewable energy systems, power system reliabilityand economics.

Rajesh Kavasseri received his Ph.D. degree in Electrical Engineering fromWashington State University, Pullman, WA in 2002. He is currently anassociate professor in North Dakota State University. Dr. Kavasseri’s researchareas are power system dynamics and control, nonlinear system, algebraicgeometry application in power system analysis.

Minqiang Hu received his Ph.D. degree in Electrical Engineering fromHuazhong University of Science and Technology, Wuhan China in 1990. Heis currently a full professor in School of Electrical Engineering, SoutheastUniversity, Nanjing, China. His research areas include electric machinemodeling and simulation, protection and control and substation power qualitymonitoring.