Modeling and Control of DFIG-based Variable-speed Wind-turbine

9
Electric Power Systems Research 78 (2008) 1841–1849 Contents lists available at ScienceDirect Electric Power Systems Research journal homepage: www.elsevier.com/locate/epsr Modeling and control of DFIG-based variable-speed wind-turbine Hee-Sang Ko a,, Gi-Gab Yoon b , Nam-Ho Kyung a , Won-Pyo Hong c a Wind Energy Research Center, Korea Institute of Energy Research, Yuseong-gu Jang-Dong 71-2, Daejeon 305-343, Republic of Korea b Power Distribution Laboratory, Korean Electric Power Research Institute, Republic of Korea c Hanbat National University , Building Services Engineering, Republic of Korea article info Article history: Received 13 April 2007 Received in revised form 22 February 2008 Accepted 27 February 2008 Available online 16 July 2008 Keywords: Doubly fed induction-generator Variable-speed wind-turbine Voltage control Voltage-source converter abstract This paper presents a modeling and a control of doubly fed induction-generator (DFIG)-based variable- speed wind-turbine. A detail dynamic model of a DFIG-based wind-turbine grid-connected system is presented in the dq-synchronous reference frame. Along with conventional control schemes for wind turbine, an innovative voltage control scheme is proposed that manipulates dynamically the reactive power from the voltage-source converter (VSC) with taking into account its operating state and limits. © 2008 Elsevier B.V. All rights reserved. 1. Introduction Increased wind power generation has influenced the overall power system operation and planning in terms of power qual- ity, security, stability, and voltage control [1–6]. The local power flow pattern and the system’s dynamic characteristics change when large wind turbines (WTs) are connected to the utility grid [7]. Both fixed-speed and variable-speed WTs are presently used in Europe and North America. To achieve the required voltage reg- ulation, fixed-speed WTs are often complemented by additional equipment and/or compensating devices that may be installed in close proximity or at a remote location [8–11]. Doubly fed induction generators (DFIGs) are also becoming popular for variable-speed WTs, particularly in North America, with the modern units often exceeding the 3 MW level [12]. Variable-speed WTs utilize power electronic converter technology that in addition to accommodat- ing variable-speed operation also enables rapid control of real and reactive power [13]. In many WT applications, variable-speed operation is achieved by appropriately controlling the back-to-back voltage-source con- verters (VSC). There have been a great number of publications proposing various control solutions to achieve desirable dynamic performance and decoupled control of active and reactive power. Although different in implementation, most commonly used con- verters enable the WTs to maintain the required power factor Corresponding author. E-mail address: [email protected] (H.-S. Ko). (power factor control, PFC) or voltage (local voltage control, LVC) at the terminals [14–17]. The rotor-side converter provides the active and the reactive power necessary to attain the control objectives for either the PFC or the LVC modes. The grid-side converter is connected to electric utility through a filter. Its main objective is to maintain the DC-link capacitor voltage by exchanging the active power with the grid. Consequently, PFC- mode is often used for maximum active power exchange with the grid. Mostly, undesirable interferences with the protection circuitry and/or the trip of WTs are caused when DC-voltage in DC-link reaches its limit. From this point of view, it is desirable to mini- mize and/or suppress the voltage swings at the terminal of WT. To achieve this objective, an innovative reactive power control methodology is presented in the rotor-side converter and the grid- side converter. Without loss of generality, in this paper, a dynamic model of wind power system composed of typical industrial DFIG-based WT is developed to demonstrate and validate the proposed control methodology. Since the focus of this paper is on the wind- energy-system, the detailed PWM switching of converters is not represented, and instead the converters are modeled using con- trollable voltage sources assuming linear modulation region as it is commonly done in literature [13–18]. However, the transient stud- ies are conducted using full-order models of machines and other relevant components of the system. The performance of various controllers is evaluated in the presence of noise. Overall, computer studies demonstrate potential improvements that can be achieved with the proposed supervisory control scheme. 0378-7796/$ – see front matter © 2008 Elsevier B.V. All rights reserved. doi:10.1016/j.epsr.2008.02.018

description

Modeling and Control of DFIG-based Variable-speed Wind-turbine

Transcript of Modeling and Control of DFIG-based Variable-speed Wind-turbine

Page 1: Modeling and Control of DFIG-based Variable-speed Wind-turbine

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Electric Power Systems Research 78 (2008) 1841–1849

Contents lists available at ScienceDirect

Electric Power Systems Research

journa l homepage: www.e lsev ier .com/ locate /epsr

odeling and control of DFIG-based variable-speed wind-turbine

ee-Sang Koa,∗, Gi-Gab Yoonb, Nam-Ho Kyunga, Won-Pyo Hongc

Wind Energy Research Center, Korea Institute of Energy Research, Yuseong-gu Jang-Dong 71-2, Daejeon 305-343, Republic of KoreaPower Distribution Laboratory, Korean Electric Power Research Institute, Republic of KoreaHanbat National University , Building Services Engineering, Republic of Korea

r t i c l e i n f o

rticle history:eceived 13 April 2007eceived in revised form 22 February 2008

a b s t r a c t

This paper presents a modeling and a control of doubly fed induction-generator (DFIG)-based variable-speed wind-turbine. A detail dynamic model of a DFIG-based wind-turbine grid-connected system ispresented in the dq-synchronous reference frame. Along with conventional control schemes for wind

ccepted 27 February 2008vailable online 16 July 2008

eywords:oubly fed induction-generatorariable-speed wind-turbine

turbine, an innovative voltage control scheme is proposed that manipulates dynamically the reactivepower from the voltage-source converter (VSC) with taking into account its operating state and limits.

© 2008 Elsevier B.V. All rights reserved.

(aaocmemg

armTms

wime

oltage controloltage-source converter

. Introduction

Increased wind power generation has influenced the overallower system operation and planning in terms of power qual-

ty, security, stability, and voltage control [1–6]. The local powerow pattern and the system’s dynamic characteristics change when

arge wind turbines (WTs) are connected to the utility grid [7].Both fixed-speed and variable-speed WTs are presently used in

urope and North America. To achieve the required voltage reg-lation, fixed-speed WTs are often complemented by additionalquipment and/or compensating devices that may be installed inlose proximity or at a remote location [8–11]. Doubly fed inductionenerators (DFIGs) are also becoming popular for variable-speed

Ts, particularly in North America, with the modern units oftenxceeding the 3 MW level [12]. Variable-speed WTs utilize powerlectronic converter technology that in addition to accommodat-ng variable-speed operation also enables rapid control of real andeactive power [13].

In many WT applications, variable-speed operation is achievedy appropriately controlling the back-to-back voltage-source con-erters (VSC). There have been a great number of publications

roposing various control solutions to achieve desirable dynamicerformance and decoupled control of active and reactive power.lthough different in implementation, most commonly used con-erters enable the WTs to maintain the required power factor

∗ Corresponding author.E-mail address: [email protected] (H.-S. Ko).

rtcircsw

378-7796/$ – see front matter © 2008 Elsevier B.V. All rights reserved.oi:10.1016/j.epsr.2008.02.018

power factor control, PFC) or voltage (local voltage control, LVC)t the terminals [14–17]. The rotor-side converter provides thective and the reactive power necessary to attain the controlbjectives for either the PFC or the LVC modes. The grid-sideonverter is connected to electric utility through a filter. Itsain objective is to maintain the DC-link capacitor voltage by

xchanging the active power with the grid. Consequently, PFC-ode is often used for maximum active power exchange with the

rid.Mostly, undesirable interferences with the protection circuitry

nd/or the trip of WTs are caused when DC-voltage in DC-linkeaches its limit. From this point of view, it is desirable to mini-ize and/or suppress the voltage swings at the terminal of WT.

o achieve this objective, an innovative reactive power controlethodology is presented in the rotor-side converter and the grid-

ide converter.Without loss of generality, in this paper, a dynamic model of

ind power system composed of typical industrial DFIG-based WTs developed to demonstrate and validate the proposed control

ethodology. Since the focus of this paper is on the wind-nergy-system, the detailed PWM switching of converters is notepresented, and instead the converters are modeled using con-rollable voltage sources assuming linear modulation region as it isommonly done in literature [13–18]. However, the transient stud-

es are conducted using full-order models of machines and otherelevant components of the system. The performance of variousontrollers is evaluated in the presence of noise. Overall, computertudies demonstrate potential improvements that can be achievedith the proposed supervisory control scheme.
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1842 H.-S. Ko et al. / Electric Power Systems

irio

2v

ptcctWwTpa

smdiucrTccr

e[

t

2

w

wωtstlaap

P

2l

bstgnscs

Fig. 1. Grid-connected wind-turbine system.

This paper is organized as follows: The study system is describedn Section 2; in Section 3, the VSC control design is presented; theeactive power control scheme and the control design is proposedn Section 4 and Section 5, respectively; the case studies are carriedut in Section 6; and conclusions are drawn in Section 7.

. Study system of grid-connected DFIG-basedariable-speed wind-turbine

Fig. 1 shows a simplified diagram of system considered in thisaper. Here, the WT is equipped with a step-up 0.69 kV/34.5 kVransformer (TR). The WT is connected to the point-of-commonoupling (PCC, bus 3) by 1 km cable. The WT and the utility grid areonnected through the 132 kV transmission line (TL, 30 km). Here,he utility grid is represented by an infinite-bus. The details of the

T considered in the model are shown in Fig. 2. The data for a 2 MWind turbine considered in this analysis is given in Appendix A [19].

he WT consists of a three-bladed rotor with the correspondingitch controller, a mechanical gearbox, a DFIG with two converters,DC-link capacitor, and a grid filter.

Including the DFIG, the individual components of electrical sub-ystem including a transformer, a cable, and a transmission line areodeled using the dq-synchronous reference frame [20]. Wherein,

-axis is assumed to be aligned to stator flux, and the current com-ng out of the generator is considered positive. The DFIG controllerstilize the concept of disconnection of the active and reactive powerontrols by transformation of the machine parameters into the dq-eference frame and by separating forming of the rotor voltages.hen, the active power can be controlled by influencing the d-axisomponent of the rotor current while the reactive power can beontrolled by influencing the q-axis components of the rotor cur-

ent.

The system parameters, operating conditions, controller gains,tc., are given in Appendix A and also more details can be found in21]. The mathematical models for the electrical components and

Fig. 2. Doubly fed induction-generator wind-turbine.

Research 78 (2008) 1841–1849

he mechanical components are as follows:

.1. Double-fed induction generator

The DFIG was represented by the following equations

1ωb

d ds

dt= Rsids +ωe qs + vds

1ωb

d qsdt

= vqs + Rsiqs −ωe ds

1ωb

d dr

dt= vdr + Rridr +ωs qr

1ωb

d qrdt

= vqr + Rriqr −ωs dr

(1)

ith

ds = −(Ls + Lm)ids − Lmidr, qs = −(Ls + Lm)iqs − Lmiqr dr = −(Lr + Lm)idr − Lmids, qr = −(Lr + Lm)iqr − Lmiqs

(2)

here v is the voltage, R is the resistance, i is the current, ωe ands =ωe −ωr are the stator and slip electrical angular speed, respec-

ively,ωr is the rotor electrical angular speed,ωb is the base angularpeed in rad/s, Lm is the mutual inductance, Ls and Lr are the sta-or and rotor leakage inductance, respectively, and is the fluxinkage. The subscripts d and q indicate the direct and quadraturexis components, respectively. The subscripts s and r indicate statornd rotor quantities, respectively. The electrical active and reactiveower delivered by the stator are given by

s = vdsids + vqsiqs, Qs = vdsiqs − vqsids (3)

.2. Dynamic model of transmission line, transformer, cable, andoad

The mathematical model of a TL, a TR, a cable, and a load cane found from the description of the R, L, C segment into the dq-ynchronous reference frame [19]. The equations of the TL, the TR,he cable, the RL-filter on the grid-side converter, and the load areiven in (4)–(8). For the formulation of the TR and the load, for theumerical purpose, small capacitors (Co = 1 e−6 pu) are used to theending-end with removing two capacitors, and the sending-endapacitors are only considered in the case of formulating the cableince its capacitance contributes to the reactive power (Fig. 3).

Transmission line (TL)

LTL

ωb

didl

dt= vd2 − vd1 − RTLidl +ωeLTLiql

LTL diql = v − v − R i −ωeL i

ωb dt q2 q1 TL ql TL dl

CTL

ωb

dvd1

dt= idc1 +ωeCTLvq1,

CTL

ωb

dvq1dt

= iqc1 −ωeCTLvd1

CTL

ωb

dvd2

dt= idc2 +ωeCTLvq2,

CTL

ωb

dvq2dt

= iqc2 −ωeCTLvd2

(4)

Fig. 3. Lumped TL description in the dq-domain.

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H.-S. Ko et al. / Electric Power Systems Research 78 (2008) 1841–1849 1843

F

3

Arcg

merg

aQa

ttnc

4

Wc

Q

where, j = r, g (here, r and g stands for rotor-side and grid-side,respectively.), Qmax

jis the maximum reactive power (limit) that

the j controller can provide, and �Qpcc is the total reactive powerrequired to support the voltage at the PCC.

ig. 4. Block diagram of the VSC controller showing the input/output variables.

where subscript 1 and 2 corresponds to bus 3 and bus 4, respec-tively.Transformer

Ltr

ωb

didl

dt= vd2 − vd1 − Rtridl +ωeLtriql

Ltr

ωb

diqldt

= vq2 − vq1 − Rtriql −ωeLtridl

Co

ωb

dvd1

dt= idl +ωeCovq1,

Co

ωb

dvq1dt

= iql −ωeCovd1

(5)

where subscript 1 and 2 corresponds to bus 1 and bus 2, respec-tively.Cable

Lca

ωb

didl

dt= vd2 − vd1 − Rcaidl +ωeLcaiql

Lca

ωb

diqldt

= vq2 − vq1 − Rcaiql −ωeLcaidl

Cca

ωb

dvd1

dt= idc1 +ωeCcavq1,

Cca

ωb

dvq1dt

= iqc1 −ωeCcavd1

(6)

where subscript 1 and 2 corresponds to bus 2 and bus 3, respec-tively.RL-filter on the grid-side converter

Lfilt

ωb

did,filt

dt= vd2 − vd1 − Rfiltid,filt +ωeLfiltiq,filt

Lfilt

ωb

diq,filt

dt= vq2 − vq1 − Rfiltiq,filt −ωeLfiltid,filt

(7)

where subscript filt stands for filter (see Fig. 2), and 1 and 2 indi-cate voltage output from the grid-side converter controller and thevoltage of bus 1, respectively.RL load

Lload

ωb

didL

dt= vd1 − RloadidL +ωeLloadiqL

Lload

ωb

diqLdt

= vq1 − RloadiqL −ωeLloadidL

Co

ωb

dvd1

dt= idL +ωeCovq1,

Co

ωb

dvq1dt

= iqL −ωeCovd1

(8)

where subscript 1 corresponds to bus 3.

. Design of voltage-source-converter controller

An important part of the WT is the VSC controller shown in Fig. 2.more detailed block diagram of the VSC controller depicting the

espective input and output variables is shown in Fig. 4. The VSController module includes the rotor-side converter controller, therid-side converter controller, and the DC-link controller.

Here, Psett is the set-value for the active power for the WT ter-

inal (see Fig. 2). The value of Psett is determined from the WT

nergy-harvesting characteristic [19] as shown in Fig. 5, which isepresented here as a look-up table Pset

t (ωr) defined in terms of

enerator rotor speed ωr.

When the PFC-mode is used, the reactive power set-points, Q setr

nd Q setg , are set to zero. When the LVC mode is used, Q set

r and/orsetg can be adjusted by the local controller to maintain the voltaget the WT terminal (Table 1).

Fig. 5. WT maximum energy-harvesting curve.

Proportional-integral (PI) controllers for the rotor-side convert,he DC-link, and the grid-side converter, are designed. In this paper,hese PI controllers are tuned using the Nyquist constraint tech-ique to deal with uncertainties [22]. The design of the VSC controlan be found in [21] and is depicted in Fig. 6.

. Reactive power control

When controlling WT, it is important that the operating limit ofT is not exceeded. The reactive power required from an individual

onverter of back-to-back VSC can be computed as

setj = min

{Qmaxj ,

Qmaxj

Qmaxr + Qmax

g�Qpcc

}, (9)

Fig. 6. The block diagram of VSC control.

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1844 H.-S. Ko et al. / Electric Power Systems Research 78 (2008) 1841–1849

Table 1Operating conditions in the operation of Mode 1

BUS V (pu) P (pu) Q (pu)

Load3(PCC) 0.9879

Grid 0.5391 −0.03873Cable 0.3408 0.11870Total 0.8799 0.07998Load 1.1a 0.1b

WT 1 0.9927 0.3415 0TR 2 0.9926 0.3415 −0.001206

a Resistance.b Reactance.

Fig. 7. VSC active- and reactive-power operating limits.

Fig. 8. Comparison between the full-order (42nd) and the reduced-order (6th)transfer function from the injected reactive power to the voltage at PCC.

Fig. 9. Implementation of PI controller with the distributed anti-windup.

wsheaQ

so

v

Q

wctBmb

Fig. 10. Wind speed (m/s).

Fig. 7 shows the active- and the reactive-power operating limits,herein it is assumed that a converter (rotor-side or the grid-

ide) should not exceed its apparent power limit depicted by thealf-circle. Suppose that at a given time each converter is deliv-ring active power denoted herein by Pj. Then, in addition to thective power, the converter can supply or absorb a maximum ofmaxj

of reactive power. So, the reactive power available from aingle converter lies within the limits [−Qmax

j; +Qmax

j], which are

perating-condition dependent.Thus, the maximum available reactive power from the each con-

erter can be expressed as

maxj =

√(Smax

c )2 − P2j

(10)

here it is assumed that the nominal apparent power of the each

onverter is Smax

c , defined here as 1/3 of the WT rating [22], and Qp ishe reactive power, which has been produced from each converter.ased on Fig. 7, it also follows that −Smax

c ≤ Pj ≤ Smaxc . Thus, the

aximum reactive power set-point of Q setr and Q set

g (see Fig. 3) cane determined by (9).

Fig. 11. Voltage observed at the PCC due to the wind speed variation.

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H.-S. Ko et al. / Electric Power Systems Research 78 (2008) 1841–1849 1845

he 40%

5

stat

csttw

ats

oiio

Fig. 12. Voltage observed at the PCC due to t

. Proportional-plus-integral controller design

To enable a systematic selection of controller gains, it is neces-ary to find a plant model that represents the relationship betweenhe input and the output with regard to the control objective. Thus,transfer function from the reactive power injected by the WT to

he change in voltage observed at the PCC is needed.Although differential and algebraic equations describing all

omponents of the system of Fig. 1 are known and available,traightforward analytical derivation of the required transfer func-ion is not practical due to the very large size and complexity ofhe overall system. Instead, the full 42nd-order transfer functionas extracted from the overall model using numerical linearization

iTwcr

Fig. 13. Active and reactive power observed at the PCC du

(left) and 50% (right) impedance decrease.

vailable in Simulink [23]. The resulting transfer function magni-ude and phase for a considered operating point of interest arehown in Fig. 8.

Since the order of the linearized model is very high, a model-rder reduction technique [24] is used to find a lower order approx-mate transfer function that is more suitable for the purpose of tun-ng the controller gains. In this paper, a balanced realization model-rder reduction technique was considered as it preserves the dom-

nant states of the system in terms of the input/output behaviour.he reduced-order model is then obtained by neglecting modesith the smallest Hankel singular values. The model reduction is

arried out using the Control System Toolbox [25]. Fig. 8 shows theeduced 6th-order transfer function for the same operating point.

e to 40% (left) and 50% (right) impedance decrease.

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1846 H.-S. Ko et al. / Electric Power Systems Research 78 (2008) 1841–1849

drop

caoo[fAwit[

6

t

sbwwvzcisP

6

F

Fig. 14. Voltage observed at the PCC due to voltage

In wind power generation systems, operating conditions areontinually changing due to wind speed fluctuations and load vari-tions. Thus, to ensure that the proposed PI controller can robustlyperate under the changing conditions, a design technique basedn the Nyquist constraint is used here to tune the controller gains22]. The PI gain and its tuning parameters including the transferunction of the reduced-order model are summarized in Appendix. Since limiting control action should be implemented togetherith the integrator-anti-windup scheme that would stop integrat-

ng the error when the limit is being reached, a PI controller withhe proposed distributed anti-windup is implemented in Simulink23] as shown in Fig. 9 for case studies.

. Case studies

The system depicted in Fig. 1 was implemented in detail usinghe Matlab/Simulink [23]. Computer studies considering the wind

fmv

ig. 15. Active and reactive power observed at the stator (Ps, Qs), the rotor (Pr, Qr), and the

at infinite-bus (left) and fault at the bus 3 (right).

peed variations, the local-load variations, and large-signal distur-ances such as the three-phase symmetrical fault and voltage sagere conducted to compare the dynamic responses of the systemith different controls. In comparison, Mode 1 indicates the con-

entional PFC-mode operation of WT, whichQ setr andQ set

g are set toero. As another conventional operation, Mode 2 implies that theonventional local voltage control at the terminal of WT whereQ set

rs actively utilized while Q set

g is set to zero. Mode 3 is the proposedcheme when both converters are used for voltage control at theCC; thus, both Q set

r and Q setg can be instantly utilized.

.1. Wind-speed variation

In this study, the wind speeds shown in Fig. 10 was consideredor the WT. Fig. 11 shows the voltage at the PCC, predicted by the

odel with different controls. As seen in Fig. 11, the wind speedariations did not represent a problem.

grid-side converter (Pg, Qg) in Mode 1 (left), Mode 2 (middle), and Mode 3 (right).

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H.-S. Ko et al. / Electric Power Systems Research 78 (2008) 1841–1849 1847

t the

6

divbs

vdi(

Fig. 16. DC-voltage observed at the DC-link and the AC-current observed a

.2. Local-load variation

Two cases were conducted: the local-load impedance by 40%ecrease and by 50% decrease. For the case when the local-load

mpedance is decreased by 40% and 50%, the comparison of theoltage transients observed at the PCC was showed in Fig. 12. As cane noticed, in the case of 40% decrease, the performance has beenignificantly improved at the PCC from Mode 1 operation. Also, the

wsPf

Fig. 17. AC-voltage observed at the stator and the rotor winding

grid-side converter in Mode 1 (left), Mode 2 (middle), and Mode 3 (right).

oltage has been recovered to its predefined value. In the case of 50%ecrease of the local-load impedance, when in the Mode 1, the load

mpedance changes resulted in noticeable drop of the bus voltageby 8%). When the WT operated in Mode 2 and 3, the voltage drop

as significantly reduced (to 2%). However, the proposed control

cheme, Mode 3, performed faster in the bus-voltage recovery at theCC. Since the maximally available instantaneous reactive-powerrom both converters was fully utilized, the steady-state errors from

s in Mode 1 (left), Mode 2 (middle), and Mode 3 (right).

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1848 H.-S. Ko et al. / Electric Power Systems Research 78 (2008) 1841–1849

indin

Mri

6

afv2s

stsAitvDMr

stroswi

7

ss

wiawodi

A

Fig. 18. AC-current observed at the stator and the rotor w

ode 2 and Mode 3 were noticed. Fig. 13 showed the active andeactive power observed at the PCC in the case of the 40% and 50%mpedance decrease, respectively.

.3. Fault ride-through study

To consider a large-signal disturbance, voltage sag was assumedt the infinite-bus whose voltage was assumed by 20% decreaserom its initial value. As shown in the left-hand side in Fig. 14, theoltage deviation by 20% has been noticed in Mode 1 while Modeand 3 resulted in the voltage deviation by 12%. However, Mode 3

howed faster voltage recovery than others.To implement another large-signal disturbance, a three-phase

ymmetrical fault was assumed in the middle of TL. To emulatehis fault scenario, the fault was assumed at t = 0.2 s and was sub-equently cleared at t = 0.7 s by restoring the initial TL impedance.s can be noted in the right-hand side in Fig. 14, the fault resulted

n significant voltage swings that can undesirably interfere withhe protection circuitry and possibly trip the WT. From this point ofiew, it is desirable to minimize and/or suppress the voltage swings.uring the fault, the voltage drop has been slightly improved inode 2 and 3. After the fault was cleared, faster voltage recovery to

each to its predefined voltage at the PCC was noticed in Mode 3.In the case of the fault at the bus 3, Figs. 15–18 showed more

ystem responses according to different mode operations such thathe active and the reactive power observed at the stator (Ps, Qs), theotor (Pr, Qr), and the grid-side converter (Pg, Qg), the DC-voltagebserved at the DC-link and the AC-current observed at the grid-ide converter, the AC-voltage observed at the stator and the rotorindings, and AC-current observed at the stator and the rotor wind-

ngs.

. Conclusion

This paper presented the modeling of DFIG-based variable-peed wind-turbine and demonstrated an advanced voltage controlcheme. The goal of investigation was to make use of available

gs in Mode 1 (left), Mode 2 (middle), and Mode 3 (right).

ind-turbine technology, namely the variable-speed doubly fednduction generator with power electronic converters, to take anctive part in improving the voltage control at a remote locationhere the wind turbines are connected to a grid. To ensure reliable

peration of the proposed control scheme, the operating-point-ependent reactive power limit of each wind turbine was taken

nto account.

ppendix A

Base values

Sb = 2 MVA, Vb = 690 V,ωb = 2�f (rad/s), f = 60 Hz, Zdc = Vdc/idc,ib = 1900 A, Vdc = 1200 V, Zb = (Vb/

√3)/ib, Lb = Zb/ωb, Ldc = Zdc/ωb,

Cb = 1/(Zbωb), Tb = Sb/ωb, jb = Sb/(ω2b), idc = Sb/Ydc, Cdc = 1/(Zdcωb)

Infinite-bus voltage (pu)

vdq,inf = [ 0.989 0.15 ]

Line parameter (pu)

RTL = 0.012, LTL = 0.12, Rca = 0.0049, Lca = 0.0251, Cca = 0.2502Rfilt = 0.0012, Lfilt = 0.0209, Rtr = 0.000366, Ltr = 0.0103

DFIG (pu)

Rs = 0.0092, Rr = 0.0076, Ls = 0.19, Lr = 0.0792, Lm = 4.5926

Maximum operating limit of VSC (pu) and cut-in and cut-out windspeed

Smax = 0.3, cut-in wind speed: 4 m/s, cut-out wind speed: 22 m/sController gains (pu)- Rotor-side converter:

Controllers PI1 and PI3: kp = 0.0252, kl = 10.4832Controllers PI2 and PI4: kp = 0.9995, kl = 20

Page 9: Modeling and Control of DFIG-based Variable-speed Wind-turbine

stems

G2.18

9.6e

R

[

[

[

[

[

[

[

[

[

[[

[

[[[[

HUsciRve

GHrpzlIpa

NUfr

Wvfrom Seoul National University, Seoul, Korea, in 1980 and 1989 respectively. He

H.-S. Ko et al. / Electric Power Sy

- Grid-side converter: controllers PI5 and PI6: kp = 0.7147,ki = 7.1515

- DC-link module: vrefdc = 1, Cdc = 12.7227, kp = 0.9544, ki = 3.8175

- Reactive power controllers

Transfer function of the 6th-order reduced model:

(s) = 0.000324s6 − 1.75s5 − 2366s4 + 7.9e6s3 + 7.5e9s2 + 5e12s+s6 + 2340s5 + 8.67e6s4 + 4.79e9s3 + 2.7e12s2 + 1.27e14s+

Tuning parameter: Ms = 1.75, phase margin �m = 70◦

Rotor-side converter: kp = 1.5525, ki = 68.0599Grid-side converter: kp = 0.0868, ki = 50.9005

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ee-Sang Ko received his B.S. degree in electrical engineering from Cheju Nationalniversity, Jeju, Korea, in 1996, his M.Sc. degree in electrical engineering from Penn-ylvania State University, University Park, USA, in 2000, and his Ph.D. in electrical andomputer engineering from the University of British Columbia, Vancouver, Canada,n 2006. He is a researcher in Wind Energy Research Center, Korea Institute of Energyesearch. His research interests include wind power generation, power systemsoltage and transient stability, data processing for power systems security analysis,lectricity market analysis, and system identification.

i-Gab Yoon received his B.S., M.Sc., and Ph.D. degree in electrical engineering fromanyang University, Seoul, Korea, in 1983, 1988, and 1999. He has over 20 years of

esearch experience in the field of power systems. He has published a number ofapers and provided the technical advices and consultations for industrial organi-ations and consulting firms. He is presently a senior researcher in power systemaboratory and advanced distribution system group at Korea Electric Power Researchnstitute (Kepri). He manages and executes a number of key projects including windower generation system, distribution power system, intelligent power networkrchitecture, and modeling and control of power system.

am-Ho Kyung received his B.S. degree in electrical engineering from Seoul Nationalniversity, Seoul, Korea, in 1978, his M.Sc. and Ph.D. degree in electrical engineering

rom Korea Advanced Institute of Science and Technology, Korea, in 1980 and 1987,espectively. From 2006, he is the header of Wind Energy Research Group.

on-Pyo Hong received his B.S degree in Electrical Engineering from Sungsil Uni-ersity, Seoul, Korea, in 1978, his M.Sc. and Ph.D. degree in Electrical Engineering

s a professor of the Department of Building Services Engineering at the Han-at National University. His research activities are in the areas of the buildingnd industrial application of field-bus, energy management, building automationnd control, intelligent networked control, and control and planning of distributednergy resource.