113

Control of DFIG-based Wind Farms forNetwork Unbalance Compensation

Yi Wang, Member, Lie Xu, Senior Member, and Barry W. Williams Department of Electronics & Electrical Engineering, University of Strathclyde, Glasgow, UK

Abstract—This paper investigates the control of doubly-fed induction generator (DFIG) based wind farms for compensating voltage unbalance in weak networks. A DFIG system model containing the generator and its back-to-back converters suitable for analyzing system operation under unbalanced conditions is developed. A control strategy for compensating grid voltage unbalance using DFIG systems is proposed. The negative sequence current injected into the transmission line for the rebalancing control can be provided by either the grid-side or the rotor-side converter. Various methods for coordinating these two converters and their impact on system operation are analyzed. The capabilities of the converters with a DFIG system for negative sequence current compensation are also discussed. The validity of the proposed control strategy is demonstrated by Matlab/Simulink simulations. With the proposed strategy, DFIG based wind farms can provide voltage unbalance compensation for the connected weak grid to improve the performance and stability of the whole wind energy system.

I. INTRODUCTION

Large wind farms are generally located distant from load centers due to the geographically remote wind resources. While integrating the wind farms into grids with long transmission lines, supply voltages of the wind generators are prone to becoming unbalanced because of different phase impedances, asymmetric faults and loads, etc. in the transmission network [1]. During network unbalance, wind generators may need to be disconnected from the network to avoid over-current, overheating, and extra mechanical stresses, caused by the voltage, current, power, and torque fluctuations [2]. Therefore, rebalancing control for a weak grid is necessary to improve the wind generation system stability. This issue can be resolved by the installation of an appropriately rated voltage sourced converter based Static Synchronous Compensator (STATCOM) [3]. However, the doubly fed induction generator (DFIG) system as shown schematically in Fig. 1 can also contribute to reduce network unbalance due to its control flexibility. With the increasing penetration of wind energy into the power system, the ability of the wind farms to meet grid connection requirements as well as to accurately control voltage, would have significant benefits for both generation and network operators.

Control and operation of DFIG systems during

This work was supported in part by the EPSRC (U.K.) under Grant

EP/D029775/2.

network unbalance have been studied in [4-8]. In [4-7], where they are all aimed at how to control the negative sequence current for eliminating the torque and/or power fluctuations, however, how to contribute to the network support is not considered. In [8], the grid-side converter within a DFIG is controlled as a STACOM for voltage unbalance compensation, however, any interaction between the rotor-side and grid-side converter is not considered.

This paper presents a control strategy for operating DFIG based wind farms as power conditioners which can provide compensation for network unbalance. A DFIG system dynamic model for analyzing its behavior under unbalanced conditions is developed. The principles of network voltage unbalance compensation using DFIG systems are proposed. The coordination of the rotor-side converter (RSC) and the grid-side converter (GSC) for providing the required compensation currents, is discussed. The impact of such control on DFIG torque and converter DC bus voltage oscillations is defined. The compensation capabilities of the RSC and GSC are analyzed. Finally, Matlab/Simulink simulations are used to validate the performance of the proposed control strategy using a 30 MW DFIG-based wind farm for grid unbalance compensation.

II. DFIG SYSTEM MODEL UNDER UNBALANCED CONDITIONS

A complete DFIG system model incorporating its back-to-back converters under unbalanced conditions has been developed in [6, 7, 9]. Thus only a brief summary is given.

According to the DFIG system configuration shown in Fig. 1, the complex vector equivalent circuits of the generator and its back-to-back converter in the synchronous dq reference frame in which the d-axis is orientated to the positive sequence stator voltage vector and rotates at an angular speed of e, are shown in Figs. 2 (a) and (b) respectively.

From Fig. 2, the flux, voltage, toque and power of the complete DFIG system including its back-to-back converter in the dq reference frame can be summarized as

smrrr

rmsss

IIII

LLLL

(1)

978-1-4244-1668-4/08/$25.00 ©2008 IEEE

114

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

(a) Equivalent circuit of the generator

(b) Equivalent circuit of the back-to-back converter Fig. 2. Equivalent circuits of a DFIG system in the synchronous reference frame.

dc

r

dc

gdc

gcgcegcsg

rrer

rrr

ses

sss

dd

dd

j

jd

d

jd

d

VP

VP

tV

C

tLLR

tR

tR

IIIVV

IV

IV

(2)

rsns

mssne

ˆIm23ˆIm

23 II p

LL

pT (3)

ggssoveralloverall

gsgg

resesr

rmsss

ssss

jjj

ˆ23j

ˆˆ23ˆ

23j

QPQPQP

QP

TPPPP

LL

QP

IV

IVIV

(4)

where , V and I represent the flux, voltage and current vectors respectively. Te, P and Q represent electromagnetic torque, active and reactive power respectively. Subscripts s, r and g denote the stator, rotor and grid side quantities respectively. Ls and Lr are the stator and rotor self inductances, and Lm is the mutual inductance. r is the rotor angular frequency, and r is the rotor mechanical speed. pn is the generator pole pairs.Vdc and C are the DC bus voltage and capacitor

respectively. Rc and Lc are the choke resistance and inductance of the GSC. The superscript represents conjugate complex.

Under unbalanced conditions, both positive and negative sequence components of the voltage and current need to be considered in order to accurately describe the system behavior. Considering the positive and negative sequence voltage and current, the torque, the stator, rotor and grid side power, and the DC link voltage can be expressed as [6, 7, 9]

tTtTTT ee_cos2ee_sin2e_ave 2cos2sin (5)

tQtQQQ

tPtPPP

es_cos2es_sin2s_avs

es_cos2es_sin2s_avs

2cos2sin

2cos2sin (6)

tPtPPP er_cos2er_sin2r_avr 2cos2sin (7)

tQtQQQ

tPtPPP

eg_cos2eg_sin2g_avg

eg_cos2eg_sin2g_avg

2cos2sin

2cos2sin (8)

)2cos()2sin( edc_cos2edc_sin2dc_avdc tVtVVV (9)

where e

ers is the rotor slip and

nrq

nrd

prq

prd

psq

psd

nsq

nsd

psd

psq

nsd

nsq

nsq

nsd

psq

psd

se

mn

e_cos2

e_sin2

e_av

23

IIII

VVVVVVVV

VVVV

LLp

TTT

(10)

nrq

nrd

prq

prd

psd

psq

nsd

nsq

psq

psd

nsq

nsd

psq

psd

nsq

nsd

psd

psq

nsd

nsq

nsd

nsq

psd

psq

nsq

nsd

psq

psd

s

m

nsq

psd

nsd

psd

2ns

2ps

es

s_cos2

s_sin2

s_cos2

s_sin2

s_av

s_av

23

00

22

0

23

IIII

VVVVVVVVVVVVVVVVVVVV

VVVV

LL

VVVVVV

L

QQPPQP

(11)

nsq

nsd

psq

psd

psq

psd

nsq

nsd

psd

psq

nsd

nsq

nsq

nsd

psq

psd

r_cos2

r_sin2

r_av

)2()2()2()2(

)2()2(

23

IIII

sVsVVsVssVsVVsVs

VsVssVsV

PPP

(12)

115

ngq

ngd

pgq

pgd

psd

psq

nsd

nsq

psq

psd

nsq

nsd

psq

psd

nsq

nsd

psd

psq

nsd

nsq

nsd

nsq

psd

psq

nsq

nsd

psq

psd

g_cos2

g_sin2

g_cos2

g_sin2

g_av

g_av

23

IIII

VVVVVVVVVVVVVVVVVVVV

VVVV

QQPPQP

(13)

)(2

1

)(2

1

r_sin2g_sin2dc_ave

dc_cos2

r_cos2g_cos2dc_ave

dc_sin2

PPCV

V

PPCV

V

(14)

It is clear from (5)-(14) that an unbalanced supply can result in torque, power and DC link voltage oscillations for a DFIG system.

III. DFIG CONTROL FOR NETWORK UNBALANCE COMPENSATION

A. Principle of Voltage Unbalance CompensationSimilar to positive sequence voltage regulation using

positive sequence reactive current, negative sequence voltage can also be controlled by correctly injecting negative sequence current. The equivalent circuit of the negative sequence components of a simplified transmission network in the synchronous reference frame rotating at e , is shown in Fig. 3. The voltage unbalance is represented using a negative sequence voltage source n

LV , whereas nLI and n

PCCV are the injected negative current by the DFIG based wind farm and the negative voltage at the point of common coupling (PCC) respectively. For unbalanced voltage caused by asymmetrical line impedance, single-phase loads or asymmetrical faults in the transmission network, the equivalent n

LV and LL can be obtained using Thevenin's

theorem. From Fig. 3, the voltage nPCCV is given by

tLLR

ddj

nL

LnLLe

nLL

nL

nPCC

IIIVV

(15) Under steady-state, (15) can be approximated by

nLdLe

nLq

nPCCq

nLqLe

nLd

nPCCd

ILVV

ILVV (16)

It is evident from (16) that the negative sequence voltage of the PCC can be controlled by regulating n

LI .To fully compensate the impact of the unbalanced source voltage n

LV on the voltage at the PCC, i.e., 0nPCCV , the

required d- and q- axis negative sequence compensating currents are

Le

nLdn

LqLe

nLqn

Ld LV

IL

VI (17)

Equation (17) indicates that the effect of negative

sequence voltage compensation not only depends on the compensating current but is also influenced by the network impendence. Voltage unbalance at the PCC tends to be better compensated in a weak network rather than that in a strong grid.

B. Compensation Methods Using DFIG

For a DFIG system, the compensation current nLI

consists of the RSC and GSC currents as ns

s

nr

s

mng

ns

ng

nL

1)( IIIIILL

L (18)

Depending on how the negative sequence currents ngI

and nsI from the two converters are generated, various

control options exist which result in different system performance. Four control techniques are now discussed.

Fig. 3 Equivalent circuit of a simplified transmission network in synchronous reference frame rotating at – e

Method 1 The required negative sequence current is solely

provided by the DFIG stator through the RSC, i.e.

0*ng

*nL

*ns

I

II (19)

Method 2 The required negative sequence current is solely

provided by the GSC, i.e.

*nL

*ng

*ns 0

II

I (20)

Method 3 The required negative sequence current is provided

from both the RSC and GSC, i.e.

*nL

*ns

*nL

*ng

)1( II

II (21)

where ng_max

*nL

*nL

ng_max

ng_max

*nL

for

for1

II

I

II

I and n

g_I max

is the maximum negative sequence current the GSC can produce.

Method 4 The RSC is controlled such that the DFIG’s torque

fluctuation is minimized during voltage rebalancing control. From (10), the required negative sequence currents for the RSC and GSC are

116

*ns

*nL

*ng

pr

nsp

sd

m

e

ns*n

sˆj1

III

IVVIVL

Ls (22)

Table I summarizes the respective current references for the four proposed control methods and Fig. 4 shows the schematic diagram for the generation of the negative sequence compensating currents.

nsdV

nsqV n*

LdI

n*LqI

sL

ns L

n*gI

n*sI n*

rI

+

s

Lm

n*gV

n*rV

ngI

nrICurrent

limitationVoltage

limitation

Table I

PI

PI PI

PI

Fig. 4 Schematic diagram of the negative sequence compensating current calculation

TABLE I GENERATION OF REQUIRED CURRENT REFERENCES

Method ngI n

sI

1 RSC Only 0 *nLI

2 GSC Only *nLI 0

3 both RSC and GSC

*nLI *n

L)1( I

4

RSC for removing torque ripple and GSC for unbalance compensation

*ns

*nL II p

rnsp

s

mns

s

ˆj1 IVVVL

L e

The negative sequence current of the RSC and GSC could result in oscillations in the DFIG’s torque and converter DC link voltage even if the grid voltage were to be fully rebalanced. Assuming 0n

PCCV , from (10)-(14), the torque and DC link voltage oscillations in per-unit terms are

ns_puN

ns

ps

s_pue_pu /2

3~~ II

PV

QT (23)

ns_pu

ng_pu2

dc_ave

N

ns

ng2

dc_ave

psd

dc_pu

2

43~

II

II

sCVP

sCVV

V

. (24)

where ns_puI and n

g_puI are the per-unit negative sequence stator and grid currents respectively. PN is the DFIG system rated power.

Equations (23) and (24) reveal that the negative sequence current provided by the RSC can generate both torque and DC link voltage oscillations. Therefore, for Method 3, the required negative sequence current is provided by the GSC in the first instance, and the RSC will provide the excess current once the GSC capacity limit is reached. Thus maximum voltage unbalance reduction can be achieved. If the unbalanced voltage at the PCC cannot be completely compensated, the torque

and DC link voltage ripple can be directly estimated using (10) and (14). As for Method 4, the torque ripple is eliminated by the RSC regardless of whether the grid unbalance is completely compensated.

C. Compensation capability of DFIG convertersThe maximum negative sequence currents from the

DFIG system for grid unbalance compensation are limited by the converter current and voltage capabilities. Taking into account the requirement of the positive sequence current and voltage, the maximum negative sequence currents and voltages which can be generated by the RSC and GSC are limited to

pgg_max

ng_lim

prr_max

nr_lim

I

I

II

II (25)

pgdcm

ng_lim

psdcmt

nr_lim

VVkV

VsVkkV (26)

where Ir_max and Ig_max are the maximum current capability of the RSC and GSC respectively. km is the maximum DC/AC voltage transfer ratio, e.g. for SPWM

21mk , and for space vector modulation (SVM)

31mk . kt is the DFIG’s stator/rotor turns ratio. The RSC and GSC positive sequence currents are

determined by the average active and reactive power of the system. Below rated wind speed, the turbine normally traces the optimal tip speed ratio Cp for capturing maximum power Popt, which is commonly defined as [10]

3roptopt kP or 2

rnoptopt pkT (27)

Once rated power or torque is reached, pitch control is then used to regulate the rotor speed to ensure that the tips do not exceed the design limits. Assuming that the power output becomes constant maxP when the rotor speed is above rm, according to (10) and neglecting negative sequence components in the average torque equation, the rotor d-axis positive sequence current can be expressed as

rmrr

psdm

maxse

rmr2rp

sdm

optse

prd 1

32

32

VLPLVL

kL

I (28)

In steady state, the GSC d-axis positive sequence current is p

sdpgd sII . The q-axis positive sequence

currents of the RSC and GSC are determined by the average reactive power requirements.

Apart from maximum current capability, the maximum negative sequence currents can be generated by the RSC and GSC are also limited by the DC link voltage. According to (2) and (26), as the limits are

117

(a) RSC

(b) GSC Fig. 5 Maximum negative sequence compensation currents of RSC and

GSC at different rotor speed and stator voltage unbalance

Table II SIMULATED DFIG SYSTEM PARAMETERS

Rated power 15×2MW Stator voltage/frequency 690V/50Hz Stator/ rotor turns ratio 1:3

Rs / Rr 0.0108pu / 0.012pu Lm 3.362pu

L s / L r 0.102pu / 0.11pu

DFIG

Lumped inertia constant 3s DC capacitor Cdc 15×10000μF

Choke Lg 0.25mH/15 Filter Rf / Cf 0.06 /1000μF

Transformer V1:V2 / ZT 110kV:690V/10% Network VN / SCL 110kV/400MVA

re

ns

psdcmtn

r_max )2(

)2(

Ls

ssVkkI

VV (29)

ce

ns

pgdcmn

g_max L

VkI

VV (30)

According to (25)-(30), the maximum negative sequence currents that the RSC and GSC can provide at different rotor speeds and voltage unbalance are shown in Figs. 5 (a) and (b) respectively. The parameters used are: Ir_max=1.05pu, Ig_max=0.35pu, kt=1/3, Vs=1.0pu,kmVdc=1.15pu, Lr=0.22pu, Lc=0.4pu (based on DFIG rating), and rm=1.1pu. The q-axis positive sequence currents of the RSC and GSC are assumed 33.0p

rqI and

0pgqI .

IV. SIMULATION STUDIES

In order to verify the proposed compensation strategy and compare the performance of different compensation methods, simulations were carried out using Matlab/Simulink. The wind farm is simulated as a lumped 30MW DFIG model containing 15 DFIGs each rated at 2MW. The parameters for the system simulated in Fig. 1 are given in Table II. The switching frequency for both converters is 2 kHz. The high frequency switching harmonics have been filtered from the waveforms shown for clarity. The maximum negative currents provided by the RSC and GSC are set as Fig. 5, which vary with the rotor speed. The DC bus voltage is 1100 V.

Fig. 6 and Table III compare the system performance of the four compensation methods, and the method without negative sequence voltage compensation. The source unbalance n

LV for Figs. 6 (a) and (b) are 4% and 6%, respectively. Conventional control without unbalance compensation (no negative sequence currents provided by the RSC and GSC), is used during the period 0-2s in both Figs. 6 (a) and (b). In Fig. 6(a), Method 1 is applied during 2-4s, whereas Method 2 is applied during 4-6s. In Fig. 6(b), Methods 3 and 4 are used during periods 2-4s and 4-6s, respectively. The rotor speed is fixed at 1.1pu during the simulation. Due to the large inertia of the turbine/generator system, the speed variation is much slower than the electric system time constant. From Fig. 5, the maximum negative sequence currents that the RSC and GSC can generate are 0.1pu and 0.25pu at r=1.1pu. As shown in Fig. 6 (a) and Table III, compared to the uncompensated method, Method 1 reduces the grid voltage unbalance from 3.9% to 2.4%, whereas Method 2 fully compensates the grid voltage unbalance. With the 6% voltage unbalance in Fig. 6(b), Method 3 fully compensates the network unbalance, with both RSC and GSC generating negative compensation currents. But Method 4 can only reduce the unbalance to 2% since the RSC is controlled to eliminate the torque ripple. As for the torque and DC voltage ripple shown in Fig. 6 and table III, Method 1 requires 0.1pu n

sI to compensate the voltage imbalance, which results in 10% torque ripple. A similar oscillation level is observed with Method 3, when the RSC delivers 0.1pu negative current. For Method 2, the torque ripple is small since 0n

sV and 0nsI . For

Method 4, 0.1pu ngI reduces voltage unbalance from 6%

to 2%, while the torque ripple due to the remaining 2% voltage unbalance, is minimized by the RSC’s 0.02pu correction n

sI . As can be seen, Method 3 achieves the maximum unbalance voltage reduction, while Method 4 eliminates the torque ripple during unbalance compensation. As shown in Table III, the simulated torque and DC voltage ripple are in good agreement with those calculated using the previously derived equations, which are shown in brackets in Table III.

118

The dynamic response of the system using Method 4 during transient voltage unbalance is shown in Fig. 7. The compensation control is initially enabled and voltage unbalance is introduced at 1s. The unbalanced voltage is reduced quickly while the torque ripple is simultaneously minimised. For comparison, the compensation control is disabled at 3s. This results in about 4.5% voltage unbalance and ±10% torque ripple.

Further tests with the varied rotor speed, which affects the capability of the DFIG system compensation, are performed and the results are shown in Fig. 8. Again Method 4 is used for voltage unbalance and torque ripple compensation. The equivalent unbalanced grid voltage

nLV is now 6%, and a step change of wind speed from

11m/s to 8m/s is applied at 1s. Accordingly, the DFIG’s rotor speed changes from 1.1pu to 0.84pu based on the optimal power-speed curve of the turbine system. As can be seen in Fig. 8, the GSC can provide a maximum compensation current of 0.35 pu at r=1pu, whereas its minimum compensation current is 0.18pu over the whole rotor speed range. Therefore, maximum reduction of voltage unbalance is achieved at rated rotor speed. Due to the fact that the required RSC negative sequence current for eliminating the torque ripple is less than its maximum

capability, the torque ripple is minimized through out the rotor speed range.

V. CONCLUSIONS

This paper has presented a strategy for compensating network unbalance using DFIG based wind farms. A complete DFIG system model, including both the rotor and grid side converters, has been developed that fully defines the power, torque and DC bus voltage dynamics under unbalanced conditions. The principles of network unbalance compensation using negative sequence current injection have been analyzed. The necessary negative sequence current from DFIG based wind farms for rebalancing control can be provided by the grid-side and rotor-side converters, and various coordination methods have been illustrated. The compensation capabilities of the RSC and GSC have also been discussed. Simulation results presented confirm the performance of the proposed control system. With the proposed control strategy, DFIG based wind farms can contribute to rebalancing of the network unbalance, thereby improving both wind generator stability and supply quality in weak grids.

Fig. 6 Simulation results with different control methods: (a) With 4% voltage unbalance and 0-2s: uncompensated; 2-4s: Method 1; 4-6s: Method 2; (b) With 6% voltage unbalance and 0-2s: uncompensated; 2-4s: Method 3; 4-6s: Method 4.

119

Fig. 7 Simulation results during transient unbalance with Method 4: unbalanced occurrs at 1s, and the compensation control is disabled at 4s.

Fig. 8 Simulation results during wind speed change with Method 4 and 6% source voltage unbalance.

Table III COMPARISON OF DIFFERENT COORDINATION METHODS

nLV Method n

sVngI

(pu)

nsI

(pu) e

~T dc

~V

Uncompensated 3.9% 0 0.01 ±5%(±4.9%)*

±2%(±1.5%)*

1 2.4% 0 0.1 ±10%(±12%)*

±2%(±1%)* 4%

2 0 0.24 0 ±1.5%(0)*

±8%(±7.2%)*

Uncompensated 5.9% 0 0.01 ±8%(±7%)*

±3%(±2%)*

3 0 0.25 0.1 ±10%(±10%)*

±8%(±7.6%)* 6%

4 2% 0.25 0.02 ±1.5%(1%)*

±8%(±7.7%)*

* DATA BASED ON THE ANALYTICAL EQUATIONS

VI. REFERENCES

[1] R. Piwko, N. Miller, J. S. Gasca, X. Yuan, R. Dai, J. Lyons, “Integrating large wind farms into weak power grids with long transmission lines,” in Proc. Power Electronics and Motion Control Conf., vol. 2, pp. 1-7, Aug. 2006.

[2] E. Muljadi, T. Batan, D. Yildirim, C. P. Butterfield, “Understanding the unbalanced-voltage problem in wind turbine generation,” in Proc. 34th IAS Annual Meeting, vol. 2, pp. 1359-1365, Oct. 1999.

[3] C. Hochgraf, and R. H. Lasseter, “STATCOM Controls for Operation with Unbalanced Voltage”, IEEE Trans. Power Delivery, Vol. 13, No. 2, pp. 538-544, April 1998.

[4] T. K. A. Brekken, N. Mohan, “Control of a doubly-fed induction wind generator under unbalanced grid voltage conditions,” IEEE Trans. on Energy Conversion, vol. 22, pp. 129-135, Mar. 2007.

[5] T. Brekken, and N. Mohan, “A Novel Doubly-fed Induction Wind Generator Control Scheme for Reactive Power Control and Torque Pulsation Compensation under Unbalanced grid Voltage Conditions”, Proc. of PESC 2003, Vol 2, pp. 760-764.

[6] L. Xu, and Y. Wang, “Dynamic modeling and control of DFIG-based wind turbines under unbalanced network conditions,” IEEE Trans. on Power Systems, vol. 22, pp. 314 – 323, February 2007.

[7] Y. Wang, L. Xu, “Control of DFIG-based wind generation systems under unbalanced network supply,” in Proc.2007 International Electric Machines & Drives Conf., vol. 1, pp. 430-435, May 2007.

[8] B. I. Nass, T.M. Undeland, and T. Gjengedal, “Methods for reduction of voltage unbalance in weak grids connected to wind plants,” in Proc. IEEE Workshop Wind Power Impacts Power Systems, Oslo, Norway, June 2002.

[9] L. Xu; B. R. Andersen, and P. Cartwright, “VSC transmission operating under unbalanced AC conditions-analysis and control design,” IEEE Trans. Power Delivery, vol. 20, pp. 427 – 434, Jan. 2005.

[10] R. Pena, J. C. Clare, and G. M. Asher, “Doubly fed induction generator using back-to-back PWM converters and its application to variable speed wind-energy generation,” IEE Proc.-Electr. Power Appl., Vol. 143, pp. 231-241, May 1996.