coordinated control of dfig and fsig-based wind farms under unbalanced grid conditions-xy9

7/29/2019 Coordinated Control of DFIG and FSIG-Based Wind Farms Under Unbalanced Grid Conditions-XY9

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IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 1, JANUARY 2010 367

Coordinated Control of DFIG and FSIG-Based WindFarms Under Unbalanced Grid Conditions

Yi Wang, Member, IEEE, and Lie Xu, Senior Member, IEEE

AbstractThis paper investigates the control and operation ofdoubly-fed induction generator (DFIG) and fixed-speed inductiongenerator (FSIG) based wind farms under unbalanced grid con-ditions. A DFIG system model suitable for analyzing unbalancedoperation is developed, and used to assess the impact of an unbal-anced supply on DFIG and FSIG operation. Unbalanced voltageat DFIG and FSIG terminals can cause unequal heating on thestator windings, extra mechanical stresses and output power fluc-tuations. These problems are particularly serious for the FSIG-based wind farm without a power electronic interface to the grid.To improve the stability of a wind energy system containing bothDFIG and FSIG based wind farms during network unbalance, acontrol strategy of unbalanced voltage compensation by the DFIG

systems is proposed. The DFIG system compensation ability andthe impact of transmission network impedance are illustrated. Thesimulation results implemented in Matlab/Simulink show that theproposed DFIG control system improves not only its own perfor-mance, but also the stability of the FSIG system with the same gridconnection point during network unbalance.

Index TermsDoubly fed induction generator (DFIG), fixedspeed induction generator (FSIG), stability, unbalance, windpower generation.

NOMENCLATURE

, , Flux, voltage and current vectors.

, , Mutual, stator, and rotor inductances.

, Stator and rotor leakage inductances.

, Stator and rotor phase resistances.

, , Stator, rotor and slip angular frequencies.

, Active and reactive power.

Electromagnetic torque.

DC bus voltage.

DC bus capacitance.

, Choke resistance and inductance.

, Stator voltage and rotor angles.

Manuscript received May 18, 2009; revised May 18, 2009. First publishedDecember 04, 2009; current version published December 23, 2009. This workwas supported in part by the EPSRC (U.K.) under Grant EP/D029775/2. Paperno. TPWRD00415-2008.

Y. Wang is with the School of Electrical and Electronic Engineering,North China Electric Power University, Baoding 071003, China (e-mail:[email protected]).

L. Xu is with the School of Electronics, Electrical Engineering and Com-puter Science, Queens University of Belfast, Belfast, BT9 5AH, U.K. (email:[email protected]).

Digital Object Identifier 10.1109/TPWRD.2009.2033966

Generator pole pairs.

Rotor mechanical speed.

A. Superscripts

conjugate complex;

, positive- and negative-sequence components;

reference value;

ripple amplitude.

B. Subscripts

, , stator, rotor, and grid quantities;

, DFIG and FSIG quantities;

, synchronous - and -axis.

I. INTRODUCTION

W

ITH increased penetration of wind generation into

power systems over the years, there are requirementsfor power sources to contribute to network support rather than

being disconnected from the network when abnormal grid

voltage is detected [1][4]. For wind farms connected with

long transmission lines to the ac grid, voltage unbalance may

arise due to a number of reasons, such as asymmetric line

impedances and loads [5]. The unbalanced voltage can have a

significant effect on the performance and stability of connected

equipment (e.g., induction machines [6][8]). Rebalancing

control using a static synchronous compensator (STATCOM)

was proposed in [9].

Most early wind farms use wind turbines based on the fixed-

speed induction generator (FSIG) whereas many recent wind

farms use doubly-fed induction generator (DFIG) based windturbines. It has been shown for the FSIG, that its stator current

can be highly unbalanced even with a small voltage imbalance

[10]. This also results in unequal heating of the stator winding

and significant torque oscillation which could have detrimental

effect on the mechanical system [10], [11]. It has been found

that for those wind farms connected by a long distance transmis-

sion line, voltage unbalance of up to 2% can appear regularly.

In some distribution networks, voltage unbalance can periodi-

cally exceed 2% and this has resulted in a large number of trips

as wind turbines have to be protected from the detrimental ef-

fects caused by unbalanced voltage [12], [13]. Unlike the FSIG,

the DFIG system provides more control flexibility due to its

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368 IEEE TRANSACTIONS ON POWER DELIVERY, VOL. 25, NO. 1, JANUARY 2010

Fig. 1. Closely coupled FSIG and DFIG based wind farms with the same PCC.

power-electronic interface with the grid. The control and oper-

ation of DFIG systems during network unbalance were studied

in [13][17]. In [13][16], the negative-sequence current is used

to eliminate the torque and/or power fluctuations of the DFIG

system, but how such DFIG based wind farms can make contri-

butions to the network operation, e.g., network voltage unbal-

ance reduction, is not considered. In [17], the grid side converter(GSC) within a DFIG is controlled as a STATCOM for voltage

unbalance compensation. However, the operations of the rotor

side converter (RSC) and the generator under voltage unbalance,

and their impacts on GSC operation, are not considered in the

paper.

Sometimes, DFIG based wind turbines are installed along

side wind turbines based on FSIG as schematically shown in

Fig. 1. Use of the DFIG as a power conditioner to improve

system operation of the FSIG based wind turbines, would have

significant benefit for the wind farms and network operators.

The aim of this paper is to investigate DFIG control and op-

eration during network unbalance, to enhance the operation ofFSIG based wind farms which are located at relatively short dis-

tances from wind farms using DFIGs. This paper first summa-

rizes a developed DFIG system model incorporating the RSC

and GSC under unbalanced conditions. The impact of an un-

balanced supply on DFIG and FSIG operations is illustrated.

A rebalancing control strategy for improving the operation of

the wind farms containing both DFIGs and FSIGs is proposed.

The ability of unbalanced voltage compensation by DFIG sys-

tems, and the impact of transmission network impedance on

such compensation are discussed. Finally, simulations of a 20

MW FSIG plus 30 MW DFIG based wind generation system

are implemented using Matlab/Simulink to validate the perfor-

mance of the proposed control strategy.

II. SYSTEM MODELS FOR DFIG AND FSIG UNDER

UNBALANCED CONDITIONS

Under unbalanced conditions, both positive and negative-se-

quence components of the voltage and current need to be consid-

ered in order to accurately describe system behavior. The DFIG

system model developed in [15], [16] will be briefly summa-

rized first and the behavior of FSIG under network unbalance

will then be extended.

A. DFIG Model

According to the DFIG system configuration, the complexvector equivalent circuits of the generator and its back-to-back

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

converter in the reference frame in which the -axis is ori-

entated to the positive-sequence stator voltage and rotates at an

angular speed of , are shown in Fig. 2(a) and (b) respectively.

According to Figs. 1 and 2, the flux, voltage, torque and power

of the DFIG system incorporating its back-to-back converter in

the reference frame are summarized as

(1)

(2)

(3)

(4)

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 [15], [16]

(5)

(6)

(7)

(8)



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WANG AND XU: COORDINATED CONTROL OF DFIG AND FSIG-BASED WIND FARMS 369

(9)

where is the rotor slip and (10)(14), shown

at the bottom of the page.

It is clear from (5)(14) that the unbalanced supply can gen-

erate torque, power, and dc-link voltage oscillations for a DFIG

system.

B. FSIG Model

The developed DFIG model can also be applied to FSIG by

assuming a zero rotor-side voltage . According to (1) and (2)

and , under steady state, the negative-sequence components in

the negative-sequence reference frame rotating at are

given as

(15)

where is the generators leakage factor.

Under stead-state and neglect, the rotor resistive voltage drop,

(15) can be simplified to

(16)

Thus, in per unit terms where the rated voltage and current are

defined as the respective 1 unit, the amplitude of the negative-

sequence stator current can be estimated as

(17)

where , are the rated voltage and current of the DFIG,

respectively. is the FSIGs current ratio between zero speed

(starting) and at rated speed (rated current) and typically, it is in

the range of 48 [18].

Thus, (17) indicates that a small negative-sequence voltage

can result in a large negative-sequence current for a FSIG.

Substituting (16) into (10) results in the average and ripple

torque at double supply frequency as

(18)

Equation (18) shows that negative-sequence components

have little impact on the average torque. However, for a FSIG,

they can produce significant torque oscillation at double the

supply frequency of . The output power oscillations from

the FSIG can also be calculated using (11).

(10)

(11)

(12)

(13)

(14)



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III. COORDINATION OF DFIG AND FSIG

UNDER UNBALANCED CONDITIONS

The system shown in Fig. 1 is considered where a FSIG-based

and a DFIG-based wind farms are closely coupled to a grid at

the same point of common connection (PCC).

A. DFIG Control Without Considering FSIG

For DFIG systems, the negative-sequence currents of both the

GSC and RSC can be regulated to control the torque, output

power, and DC voltage oscillations under unbalanced conditions

[13][16]. To eliminate the torque ripple, i.e., , according

to (10), the required negative-sequence current provided by the

RSC is

(19)

According to (4) and (11)(13), the ripple in the DFIG total

output active power ( ) can be eliminated by regulating

the GSC negative-sequence current as

(20)

Therefore, by combined control of the RSC and GSC, the os-

cillations in DFIG systems torque and total active power output

can be eliminated.

B. DFIG Control for Unbalanced Voltage Compensation

The use of a DFIG system as a power conditioner for compen-

sating network unbalance can benefit the network and improve

the operation of any FSIG based wind farms connected nearby.

Similar to positive-sequence voltage regulation using posi-tive-sequence reactive current, the negative-sequence voltage

can also be controlled by injecting a correct negative-sequence

current. For the system shown in Fig. 1, the simplified equiva-

lent circuit for the negative-sequence components of the FSIG,

the DFIG, and the transmission network in the stationary frame

are shown in Fig. 3. As shown in Fig. 3, based on (16), the FSIG

is represented by an equivalent inductance of . The

DFIG is represented using a negative-sequence current source

since the DFIG is able to control its negative-sequence cur-

rent output. The unbalanced grid voltage is represented by a

negative-sequence voltage source , whereas and are

the negative-sequence voltages at the FSIG and DFIG termi-nals respectively. For a linear system, the unbalanced voltage

caused by asymmetric line impedance, loads or faults in the

transmission network can also be represented as an equivalent

negative-sequence voltage source and a balanced three-phase

impedance, i.e., and shown in Fig. 3. The details of the

derivation of such an equivalent circuit for a simplified case con-

taining a balanced voltage and asymmetric line impedance are

shown in the Appendix . , and are the respective cur-

rents of the transmission line, the DFIG and the FSIG, and

represent the impedances seen from the wind farm terminals

to the PCC. From Fig. 3, in steady state, the negative-sequence

voltage at the DFIG terminal is given by

Fig. 3. Negative sequence equivalent circuit in the stationary reference frame.

(21)

Thus, the negative-sequence voltage at the DFIG-based wind

farm terminal can be reduced by regulating its negative-se-

quence current . According to Fig. 3, the FSIG terminal

negative-sequence voltage can be estimated as

(22)

Thus, for a closely coupled system, the reduction of atthe

DFIG terminal can significantly reduce at the FSIG terminal

and consequently, the operation of the FSIG-based wind farm

can be improved.

For a DFIG-based wind farm, the required negative-\se-

quence compensating current can be provided by the RSC

through the DFIG stator and the GSC as

(23)

Depending on how the negative-sequence currents for the two

converters are generated, namely and , various optionsexist, resulting in different system performances.

If both the GSC and RSC contribute to the negative-sequence

compensating current, maximum reduction of voltage unbal-

ance could be achieved. However, such control might result in

large DFIG torque oscillations. If the DFIG terminal voltage

unbalance is completely compensated, according to (10), the

DFIGs double-frequency torque ripple due to the interaction

between the positive voltage and negative current is given in

per-unit term as

(24)

where is the rated electromagnetic torque, is the per-

unit negative rotor current.

For minimizing the DFIG torque ripple, the RSC can be con-

trolled to regulate the negative-sequence current according to

(19), whereas the GSC is used to compensate the voltage unbal-

ance. For such coordinated control, the required negative cur-

rents for the GSC are given by

(25)

Fig. 4 shows the schematic diagram of the proposed negative-sequence voltage compensation using a DFIG based wind farm



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Fig. 4. Schematic diagram of the negative-sequence voltage compensation.

where is the number of operating wind turbines in the wind

farm. The negative-sequence voltage controller based on (21) is

implemented in the same way as for positive-sequence voltage

control [1], [19], [20] (e.g., the negative-sequence voltage at thewind farm point of coupling is measured and used to generate

the required total negative-sequence compensating currents

for the whole wind farm). This current is then divided by the

number to yield the negative-sequence compensating current

order for each turbine where DFIG torque ripple elimination

using the RSC and voltage unbalance compensation using the

GSC are implemented. Once the negative-sequence current or-

ders for the GSC and RSC of each wind turbine have been gen-

erated, separate negative-sequence current controllers are then

used to regulate the respective negative-sequence current of the

GSC and RSC [15], [21], [22].

C. Compensation Capabilities of the RSC and GSC

The coordinated control of the RSC and GSC minimizes

the DFIG torque ripple and reduces voltage unbalance. Con-

sequently, the FSIG torque ripple and current unbalance are

reduced. However, the maximum negative-sequence currents of

the DFIG system used for voltage unbalance and torque ripple

compensation are limited by the converter current and voltage

capabilities. Taking into account the requirement of the positive

current and voltage, the maximum negative-sequence currents

and voltages which can be generated by the RSC and GSC are

limited to

(26a)

(26b)

where and are the maximum current capability

of the RSC and GSC respectively. is the maximum DC/AC

voltage transfer ratio of the converter, e.g., for SPWM

, and for space vector modulation (SVM) . is

the stator/rotor turns ratio of the DFIG.

The positive-sequence currents of the RSC and GSC are de-

termined by the average active and reactive power of the system.Below rated wind speed, turbines trace the optimum tip speed

ratio for capturing maximum power , which is commonly

defined as [23]

(27)

where is the coefficient representing the power conversion

efficiency of a wind turbine, and is defined as a function of the

tip-speed ratio and blade pitch angle in a pitch controlled

wind turbine. is the air density, is the turbine radius, and

is the wind speed. For each wind speed, there exists a turbine

optimal speed resulting in the highest captured power, and the

subscript denotes the values at this optimal speed.

Once rated power or torque is reached at the rotor speed of

, pitch control is then used to regulate the turbine to en-

sure constant power operation, e.g., the turbine maintains rated

power of for rotor speed above . The generator torquecan be expressed as

(28)

According to (10) and (28), and neglecting negative-sequence

components in the average torque equation, the rotor -axis pos-

itive-sequence current can be expressed as

(29)

In steady state, the grid -axis positive-sequence current canbe expressed as

(30)

The -axis positive-sequence currents of the RSC and GSC

are determined by the average reactive power requirements.

Apart from maximum current capability, the maximum neg-

ative-sequence currents that can be generated by the RSC and

GSC are also limited by the DC link voltage. According to (2)

and (26a), these limits are

(31a)

(31b)

According to (26)(31), the maximum negative-sequence

currents that the RSC and GSC can provide at different rotor

speeds and voltage unbalance are shown in Fig. 5(a) and (b) re-

spectively, where the parameters are set as: ,

, , ,

, ,

(based on the DFIG rating), and . The -axis

positive-sequence currents of the RSC and GSC are assumed tobe and . As can be seen from Fig. 5, both the



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Fig. 5. Maximum negative-sequence compensation currents of RSC and GSCat different rotor speed and stator voltage unbalance. (a) RSC. (b) GSC.

RSC and GSC have capabilities for providing extra negative-se-

quence compensating current though they are affected by the

voltage unbalance and active /reactive power conditions. Theproposed method is most suitable for small voltage unbalance,

e.g., a few percent. During an asymmetric fault which results in

large voltage unbalance, the DFIG is likely to go into protection

mode using a rotor crowbar and the RSC is usually blocked.

Under such condition, it is not possible to perform the proposed

strategy.

If and , the stator voltage

and torque oscillation can be fully compensated. Under such

condition, the double supply frequency oscillations for the total

output active power and DC bus voltage of the DFIG system are

given as

(32)

where is the average DC voltage.

Equation (32) indicates that in the presence of negative-se-

quence current, substantial DC voltage oscillation at double

supply frequency can exist. Such DC voltage fluctuations can

cause unwanted coupling between the DC and AC sides, e.g.,

low order harmonics in the converter output. Excessive ripple

can also induce DC over- or under-voltage protection, etc. Thus,

in order to limit the DC voltage ripple, bigger DC capacitorsmight be required.

If which can occur during large voltage un-

balance, and/or high positive-sequence current due to large ac-

tive/reactive power requirement, the unbalanced voltage cannot

be fully compensated. However, due to voltage unbalance re-

duction, operation and stability of both the DFIG and FSIG sys-

tems can still be improved.

D. Impact of Transmission Network Impedance

As the DFIG system is controlled to reduce its terminal

voltage unbalance, according to (22), voltage unbalance at the

FSIG terminal is affected by the impedances of various trans-

mission networks. If the DFIG terminal voltage is completely

rebalanced, i.e., , from (22), the relationship of the

FSIG terminal and grid negative-sequence voltages is

(33)

Equation (33) indicates that and have a positive effect,

whereas has a negative effect on the reduction of voltageunbalance at the FSIG terminal.

Fig. 6 illustrates the impact of the transmission line imped-

ances on the FSIG voltage unbalance assuming the DFIG ter-

minal unbalanced voltage being completely compensated. The

transmission network impedances including the transformers

and lines in per-unit terms (based on 33 kV/50 MVA) are:

, , ,

, where and are the lengths of Line 1 (FSIG

based wind farm to PCC) and Line 2 (DFIG based wind farm

to PCC) respectively, and SCR is the negative-sequence short

circuit ratio at the PCC. Fig. 6(a))shows the impact of , where

, ; Fig. 6(b) shows the impact of , where, ; Fig. 6(c) shows the impact of SCR,

where . Fig. 6(b) indicates that the closer the

DFIG based farm is located to the PCC, the more significant the

control will have on the FSIG. In addition, as shown in Fig. 6(c),

the bigger the negative-sequence source impedance is, i.e., the

smaller the equivalent negative-sequence SCR is, the better the

unbalance voltage compensation at the FSIG terminal.

IV. SIMULATION STUDIES

The performance of the proposed control system was evalu-

ated with Matlab/Simulink simulation for a wind energy system

containing a 30 MW DFIG-based wind farm and a 20 MWFSIG-based wind farm. Although the exact proportion of the

two wind farms does not represent a real installation, there are

a number of existing wind farms which have both FSIG and

DFIG in the range of around tens MW. The simulated system

has the same configuration as the one shown in Fig. 1, and the

system parameters are given in Table I. The DFIG based wind

farm consists of 15 2 MW turbines, whereas the FSIG based

wind farm consists of 40 500 kW turbines. Each wind farm

is connected directly to their respective 33 kV lines. The two

33 kV lines are then connected together at the PCC which is

connected to the source through a long 110 kV transmission

line. The switching frequencies for the DFIG converters are 2

kHz. Thehigh frequency switching harmonics have been filteredfrom the waveforms shown for clarity. A simple pitch control,



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Fig. 6. Impact of the transmission line impedances on compensation controlbased on (33).

TABLE IPARAMETERS OF THE SIMULATED SYSTEM

which effectively reduces the mechanical torque output from the

turbine when the rated power is reached, is modeled in the simu-

lated control system. As the dynamics of the mechanical system

does not influence the electrical compensation proposed here, a

simple lumped-mass system with the lumped inertia constantcombining the turbine and generator rotors is implemented.

Fig. 7. Simulated results with various control methods, 00.4 s: Conventionalcontrol; 0.40.8 s: Control without considering FSIGs; 0.81.2 s, Coordinatedcontrol.

To separate the positive and negative-sequence components

from the measured voltage, current, etc, notch filters tuned at

double-supply frequency and phase-lock-loop (PLL) which

tracks the positive-sequence voltage, are used [15].

In order to illustrate the effect of the proposed control scheme

on the operation of the FSIG and DFIG based wind farms under

unbalanced conditions, three control schemes are considered inthe simulations:

1) DFIG with conventional control without negative-se-

quence controller for either the RSC or the GSC;

2) DFIGs negative-sequence currents are controlled to elim-

inate the torque and total output active power oscillations;

3) Proposed control scheme, which is, the RSC eliminates the

torque ripple and the GSC compensates voltage unbalance.

Fig. 7 and Table II compare the simulation results for the three

control schemes. The equivalent unbalanced grid voltage is

set to 5%, and the wind speed is fixed at 11 m/s. The conven-

tional control method is applied initially and switched to the

second method at 0.4 s. The coordinated control method is ap-

plied at 0.8 s. For the conventional control in 00.4 s as shownin Fig. 7, the unbalanced grid voltage results in 3% and 3.4%



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TABLE IICOMPARISON OF DIFFERENT CONTROL METHODS

negative-sequence voltages at the FSIG and DFIG terminals re-

spectively. They generate 0.11 p.u. negative-sequence current

and torquerippleto the FSIGsystem, and 0.03 p.u.stator

negative-sequence current and torque ripple to the DFIG

system.

For the second control method without compensating voltage

unbalance as shown in 0.40.8 s, the torque and DC link voltage

oscillations of the DFIG system are reduced to . How-

ever, the voltage unbalance at the FSIG system continues to pro-

duce significant torque oscillation. After the coordinated con-

trol is enabled at 0.08 s, the negative-sequence voltages at the

DFIG and FSIG terminals are quickly reduced. Consequently,the FSIGs negative current and torque ripple are reduced from

0.11 p.u. and to 0.035 p.u. and , respectively. On the

other hand, the ripple of the DFIGs DC link voltage increases,

which indicates that a slightly larger DC capacitor might be

needed. Fig. 7 and Table II clearly show that the proposed co-

ordinated control method significantly reduces the torque oscil-

lation and network voltage unbalance and therefore, improves

system operation of both the DFIG and FSIG based wind farms.

In Fig. 8, the unbalanced voltage is generated by connecting a

three-phase asymmetric load at the PCC at 1 s, which results in

the same unbalanced currents and torque oscillations as in Fig. 7

without compensation. The coordinated control of the RSC andGSC for voltage unbalance and torque ripple compensation is

initially enabled. As seen, the unbalanced voltages are quickly

limited at 1 s, and consequently the unbalanced generator cur-

rents and torque oscillations of both the FSIG and DFIG-based

wind farms are well restrained. For comparison, the compensa-

tion control is disabled at 2 s. As seen in Fig. 8, the unbalanced

voltages, currents and torque oscillations, all increase signifi-

cantly without compensation.

Further studies on the variations of compensation capability

of the proposed control strategy during wind speed and power

variation were carried out and the results are shown in Fig. 9.

Coordinated RSC and GSC control is used for both voltage un-

balance and torque ripple compensation. The equivalent unbal-anced grid voltage is set to 6%. The wind speed is step

Fig. 8. Simulated results when asymmetric fault occurring at 1 s, and applyingthe coordinated control in 12 s.

changed from 11 m/s to 8 m/s at 1 s for the DFIG system and at

4 s for the FISG system respectively. For capturing maximum

wind energy, the DFIG rotor speed is adjusted from 1.1 p.u.

to 0.84 p.u.. As can be seen, the DFIG system compensation

ability varies with the variations of the rotor speed and power

output. The GSC maximum compensation ability is achieved at

with a maximum compensation current of 0.35 p.u.

compared to that of 0.25 p.u. at . Thus from Fig. 9,maximum reduction of negative-sequence voltages at the DFIG

and FSIG terminals is achieved when operating near the syn-

chronous speed at around 2 s. As the required RSC negative-se-

quence current is less than its limit, the DFIG torque ripple is

minimized across the whole speed range. For the FSIG system,

the torque ripple is about to with the negative-se-

quence voltage and current variation.

Fig. 10 illustrates the impact of the transmission line imped-

ances on FSIG unbalanced terminal voltage compensation. The

conditions are identical to the analytical study shown in Fig. 6.

The equivalent grid voltage unbalance is 4%, and the DFIG

terminal unbalanced voltage is completely compensated. The

simulated results are in good agreement with Fig. 6 based onthe analytical equations using (33). Figs. 6 and 10 show that the



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Fig. 9. Variations of compensation capability when the wind speed is step changed from 11 m/s to 8 m/s at 1 s for the DFIG system and at 4 s for the FSIG system.

Fig. 10. Simulated results of the impact of the transmission line impedanceson compensation control.

ratio of FSIG terminal voltage unbalance to grid voltage unbal-

ance is mainly dependant on the grid SCR and the distance of

the DFIG based wind farm to the PCC.

V. CONCLUSION

This paper has presented a control strategy for improvingthe performance and stability of closely coupled wind farms

based on DFIG and FSIG systems. The behaviors of the DFIG

and FSIG systems under unbalanced supplies have been de-

scribed using a mathematical model. The performance of DFIG

based wind farms can be improved by regulating the negative-

sequence current to eliminate torque, output power, and DC

voltage oscillations. However, operation of a FSIG system canonly be improved by reducing network voltage unbalance. The

use of the DFIG systems to provide rebalancing control has

been proposed by injecting the correct negative-sequence cur-

rent into the transmission network. The coordinated control of

the DFIGs RSC and GSC, for compensating voltage unbalance

and torque ripple, has been presented. The DFIG compensation

ability varying with its rotor speed, output power, and the impact

of transmission network impedance on FSIG terminal unbal-

anced voltage reduction, have been illustrated. The simulation

studies show that the DFIG system can contribute to network

unbalance compensation, thereby improving the performance of

FSIG wind farms with reduced negative-sequence currents and

torque oscillation.

APPENDIX

A simple three-phase three-wire system which contains a bal-

anced source and asymmetric line impendence is shown in Fig.

11(a) where , , are the source voltages, , , are the

line currents, and , , are the voltages at the point of cou-

pling. Using space vector representation, the relationship be-

tween the three-phase source voltage , the line current and

the voltage on the coupling point are given in the stationary

reference frame as [24], [25]

(A1)



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Fig. 11. (a) Simple three-phase circuit with asymmetric line impedance. (b)Negative-sequence equivalent circuit.

where

(A2)

Under steady state, voltage and current can be represented

by using their respective positive and negative-sequence com-

ponents as

(A3)

Substituting (A3) into (A1) yields

(A4)

Thus, the system equations for the positive and negative-se-

quence components can be derived from (A4) as

(A5)

(A6)

Based on (A6), the negative-sequence equivalent circuit

for the simple system shown in Fig. 11(a) can be repre-sented by using an equivalent negative-sequence voltage of

and a balanced impedance of as

shown in Fig. 11(b).

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[22] L. Xu, Coordinated control of DFIGs rotor and grid side convertersduring network unbalance, IEEE Trans. Power Electron., vol. 23, no.3, pp. 10411049, May 2008.

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Yi Wang (S04M06) received the B.Sc. and Ph.D.degrees in electrical engineering from North ChinaElectric Power University, Baoding, China, in 1999and 2005, respectively .

Currently, he is an Associate Professor in theSchool of Electrical and Electronic Engineering,North China Electric Power University. He wasa Postdoctoral Research Fellow at Queens Uni-versity, Belfast, U.K., from 2006 to 2007, andwith the University of Strathclyde, Glasgow, U.K.,from 2007 to 2009. His research interests include

power-electronics applications in power system and motor drives, and windpower generation.

Lie Xu (M03SM06) received the B.Sc. degreein electrical engineering from Zhejiang University,Hangzhou, China, in 1993, and the Ph.D. degreein electrical engineering from the University ofSheffield, Sheffield, U.K., in 1999.

He joined Queens University, Belfast, U.K., in2004 where he is currently a Senior Lecturer. Hismain interests are power electronics, wind energy

generation, and grid integration, and application ofpower electronics to power systems.

coordinated control of dfig and fsig-based wind farms under unbalanced grid conditions-xy9

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