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Dynamic Modeling and Control of DFIG-Based Wind Turbines Under Unbalanced Network Conditions

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

Abstract--This paper presents an analysis and control design of a doubly-fed induction generator (DFIG)-based wind generation system operating under unbalanced network conditions. A DFIG system model in the positive and negative synchronous reference frames is presented. Variations of stator active and reactive powers and generator torque are fully defined in the presence of negative sequence voltage and current. Alternative DFIG control targets during network unbalance, such as reducing stator current unbalance, torque, and power pulsations minimization, are identified. A rotor current control strategy based on positive and negative (dq) reference frames is used to provide precise control of the rotor positive and negative sequence currents. Simulation results using EMTDC/PSCAD are presented for a 2-MW DFIG wind generation system. It shows that conventional vector control of DFIG without considering network unbalance results in excessive oscillations on the stator active/reactive power, electromagnetic torque, and stator/rotor currents even with a small stator voltage unbalance. In contrast, with the proposed control strategy, enhanced system control and operation such as minimizing oscillations in either active power, or electromagnetic torque, or stator or rotor currents can be achieved. Index Terms--Control design, converter, doubly-fed induction generator (DFIG), modeling, unbalance, wind turbine.

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

Subscripts Stationary - axis. Rotor - axis. Synchronous d-q axis. Stator, rotor. Positive, negative components.

I. INTRODUCTION NOMENCLATURE Stator, rotor voltage vectors. Stator, rotor current vectors. Stator, rotor flux linkage vectors. Stator, rotor, and slip angular frequency. Stator output active and reactive power. Mutual inductance. Stator, rotor leakage inductance. Stator, rotor self-inductance. Stator, rotor resistance. Stator flux angle. Rotor angle. Superscripts Positive, negative (dq) reference frame. Reference value for controller. Conjugate complex.

M

Manuscript received July 20, 2006; revised October 4, 2006. This work was supported in part by the EPSRC (U.K.) under Grant EP/D029775/1. Paper no. TPWRS-00474-2006. The authors are with the School of Electronics, Electrical Engineering, and Computer Science, Queen's University of Belfast, Belfast, U.K. (e-mail: [email protected]; [email protected]). Digital Object Identifier 10.1109/TPWRS.2006.889113

ANY new wind farms will employ wind turbines based on doubly-fed induction generators (DFIG), which offer several advantages when compared with fixed-speed generators [1]­[4]. These advantages, including speed control, reduced flicker, and four-quadrant active and reactive power capabilities, are primarily achieved via control of a rotor side converter, which is typically rated at around 30%­35% of the generator %. Fig. 1 rating for a given rotor speed variation range of shows the schematic diagram of a DFIG-based wind turbine. The steady-state response and performance of DFIG-based wind turbines are now well understood [1]­[5]. DFIG systems are conventionally controlled using either stator voltage-oriented [1], [2] or stator flux-oriented [3], [4] controls based on d-q decoupling. For most of the studies reported, symmetric stator voltage supply was assumed even during network disturbance. For small wind farms connected to a distribution network, it is required that they can withstand a steady-state maximum value of phase voltage unbalance of 2% without tripping [6]. Similarly to induction generators, for DFIG systems, if voltage unbalance is not taken into account by the control system, the stator current could be highly unbalanced even with a small unbalanced stator voltage. The unbalanced currents create unequal heating on the stator winding as well as torque and power pulsation in the generator. It has been found that wind farms connected to distribution networks periodically experience higher voltage unbalance of greater than 2%, and this has caused a large number of trips [7].

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Control and operation of DFIG systems during network unbalance were studied in [8]­[11]. However, in [8] and [9], the control and operation of the generator itself was not addressed, and the focus was on controlling the grid side converter to provide similar functions as a STATCOM [12]. In [10], control of DFIG for compensating torque pulsation under unbalanced supply voltage was investigated. The torque equation was expressed in the synchronous frame, and to minimize the torque pulsation at twice the supply frequency, the required rotor compensating currents were calculated. The rotor current controller had to be designed carefully to provide adequate response for both the "nominal" rotor current, which appears as dc component in the synchronous (dq) frame, and the compensating rotor current, which oscillates at twice the line frequency. The approach adopted in [11] used the observed torque pulsation as the input to a lead-lag controller to directly generate the rotor compensating voltage. Again, the controller needs to be carefully tuned to provide the required system response at double supply frequency. For all the work reported, the impact of unbalanced stator voltage on the stator and rotor currents has not been fully defined. In addition, the relationships between the pulsations of the torque, the stator active/reactive power, and the rotor currents have not been fully established. Furthermore, the analysis was carried out in the synchronous reference frame, which inevitably resulted in the control variables being at twice the line frequency. This paper investigates ways to improve the control and operation of DFIG-based wind farms under unbalanced network voltage. In the stator flux-oriented positive and negative (dq) reference frames, the mathematical model of a DFIG system under unbalanced supply is developed. Based on the developed model, the relationships between the torque, active and reactive power, and the positive and negative stator flux and rotor current are fully established. Different control targets are discussed, and the corresponding rotor positive and negative sequence currents are provided. Two rotor current controllers designed, respectively, in the positive and negative (dq) frames are illustrated. Impact of stator voltage unbalance on the voltage/power rating of the rotor side converter is discussed. Finally, simulation results on a 2-MW DFIG system are provided to demonstrate the feasibility of the proposed control strategy. II. DYNAMIC MODEL OF DFIG SYSTEMS The equivalent circuit of a DFIG can be expressed in different reference frames such as the stationary frame, the rotor frame, or the synchronous frame fixed to either the stator voltage [1], [2] or the stator flux [3], [4]. A general expression of a DFIG model in an arbitrary reference frame rotating at angular speed of is shown in Fig. 2 [13]. According to Fig. 2, the stator and and are given, respectively, by rotor flux (1) From Fig. 2, the stator and rotor voltages arbitrary reference frame can be expressed as and in the

Fig. 2. Equivalent circuit of a DFIG in an arbitrary reference frame rotating at a speed of ! .

Fig. 3. Phasor diagram of stator flux orientation.

According to (1), the rotor flux and stator current can be expressed as

(4) is the leakage factor. where Substituting (4) into (3) yields the rotor voltage in the arbitrary rotating reference frame as

(5)

A. Balanced Network Voltage A detailed model of DFIG system under balanced network supply has been studied in [1]­[5]; therefore, only a brief description is given here. If the d-axis of the reference frame is fixed to the stator flux , and , equations rotating at the synchronous speed of in the new reference frame can be derived by simply replacing with in (2), (3), and (5). Fig. 3 shows the phasor diagram of the variable , which represents voltage, current, or flux, in the , and rotor reference stator flux oriented (dq), stator frames. According to Fig. 3, the transformation between (dq), , and reference frames are given by (6) As the stator voltage is usually constant, which results in constant stator flux, (5) can be simplified as (7) where .

(2) (3)

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According to Fig. 4, the transformation between and reference frames are given by (12a) (12b) Similar to grid connected converters [14], during network unand reference frames rotating at balance, in the angular frequency of and , respectively, (8) can be expressed into two parts as

Fig. 4. Relationships between the ( ) reference frame and the (dq) (dq) reference frames.

and

Separating (7) into d-q components yields

(13a)

(8) where where Stator output active and reactive power can be calculated as (13b)

(9) Thus, the stator active and reactive powers are given by

(10)

B. Unbalanced Network Voltage Assuming no zero sequence components, the three-phase quantities such as voltage, current, and flux may be decomposed into positive and negative sequence components when reference the network is unbalanced. In the stationary frame, the voltage, current, and flux can be decomposed into positive and negative sequence components as [12], [14]

and . As defined earlier, the subscripts and refer to the positive and negative and refer to the positive components and superscripts and negative frames, respectively. Thus, (13a) defines the positive sequence components (as the subscripts frame (as the superscripts being being ) in the positive ). Similarly, (13b) defines the negative sequence components (subscripts being ) in the negative frame (superscripts being ). According to (11), (12), and Fig. 4, the stator and rotor current, voltage, and flux vectors can be expressed using their respective positive and negative sequence components as

(14) Although unbalanced, the stator voltage can still be regarded as being constant. Thus, there are (15)

(11) and are the respective phase shift for positive and where negative sequence components. reference frame, As shown in Fig. 4, for the positive -axis is fixed to the positive stator flux rotating at the the reference frames, as speed of . While for the negative -axis rotates at an angular speed can be seen from Fig. 4, its of with the phase angle to the -axis being .

Neglecting the stator resistance and taking into account (2), (4), (14), and (15), the stator voltage and current can be exreference frame as pressed in the positive

(16)

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where

(17) Similar to balanced condition, the stator output active and reactive powers can be calculated as (18) Substituting (16) and (17) into (18) and separating the active and reactive power into different oscillating components yield The electromagnetic torque of the DFIG is calculated as (23) (19) where III. SYSTEM CONTROL A. Balanced Condition Equation (10) indicates that the stator active and reactive powers can be independently controlled by controlling the rotor q- and d-axis currents, respectively. According to (8), the control system for the DFIG d- and q-axis currents in the stator flux-oriented synchronous frame can be designed. The operation of the DFIG system requires the state variables and to follow varying reference points. An auxiliary input can be defined as [14], [15] (22)

(24) where and are the proportional and integral gains of the current controller. Therefore, based on (8) and (24), the required rotor control voltages in the synchronous (dq) frame are given by (20) (25) According to Fig. 2, the electromagnetic power equals to the sum of the power outputs from the equivalent voltage source and . Thus, it is given by According to Fig. 3, the rotor control voltage in the (dq) frame frame as is then transformed to the rotor (26) B. Unbalanced Condition Under unbalanced network condition, there are four rotor current components, i.e., , and , that need to be controlled. Apart from controlling the average stator active and and shown in (19) and (20), two reactive powers, i.e., more parameters can be controlled. For instance, the system can

(21)

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TABLE I ROTOR NEGATIVE SEQUENCE CURRENT REFERENCES

(30) where the four auxiliary inputs are designed in a similar way as in (24) for balanced condition. The rotor control voltage is then transformed to the rotor frame as (31) be designed to operate according to one of the following control targets. Target 1) Balanced stator current. This ensures balanced heating on the three-phase stator winding. Target 2) Constant output active power, i.e., no active power pulsation at twice the line frequency. Target 3) Constant electromagnetic torque to reduce the mechanical stress on the turbine system. Target 4) No rotor current oscillation, i.e., no rotor negative sequence current. Other control targets, such as contributing to the rebalancing of the network voltage, can also be set, and further studies on this will be reported in the future. According to (4), the stator negative sequence current is given by (27) Thus, Target 1 requires the rotor negative sequence currents to follow as (28) For Target 2, the oscillating terms of the stator active power shown in (19) and (20) have to be zero, i.e., and . For Target 3, the oscillating terms of the electromagnetic and power shown in (22) have to be zero, i.e., . Also note that from (20), under such condition, and . both As the -axis is fixed to the positive stator flux, i.e., , the reference values for the negative sequence d-q currents for the four different targets can be simplified, and they are synthesized in Table I. Once the references of the positive and negative currents are , and determined, the control system requires to follow their respective varying reference points. According to (13a) and (13b), two current controllers can be used. frame controlling the positive One is implemented in the sequence currents, and the other is implemented in the frame controlling the negative sequence currents. Similar to balanced condition, the required rotor control voltages in the positive and negative sequence frames are given, respectively, by (33) Thus, the required voltage amplitude of the rotor positive sequence component can be calculated. Considering the small value of the leakage factor , (33) can be further simplified by neglecting the first term on the right-hand side. Thus, the required voltage amplitude of the rotor positive component can be approximated as (34) Similarly, the required negative sequence rotor voltages are given as IV. IMPACT ON CONVERTER VOLTAGE/POWER RATING As the rotor side converter needs to generate both positive and negative sequence voltages to fully control the currents, this could result in the increase of the maximum required rotor voltage and thus the power rating of the rotor side converter. According to (13a), under steady-state condition, the differentiations of the positive d-q currents are zero. Thus, the required positive sequence rotor voltage is given as

(32) Neglecting the rotor resistive voltage drop and considering the relationship between the stator flux and stator voltage, (32) can be expressed as

(35) (36) Equations (34) and (36) indicate that the required rotor voltage is mainly dependent on the rotor operating slip and the stator , to compensate the stator negative voltage. As sequence voltage, it requires a higher rotor voltage. According to (31), the positive rotor voltage appears at the rotor terminals as the fundamental component with frequency

(29)

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Fig. 6. Schematic diagram of the phase-locked loop (PLL).

Fig. 5. Variations of maximum rotor voltage for different rotor slip and stator voltage unbalance.

being . While for the negative sequence rotor voltage, it appears as harmonics superimposed on to the fundamental com. Thus, the maximum ponent with the frequency being required rotor voltage amplitude is given as

(37) Fig. 5 illustrates the impact of the stator voltage unbalance on the required rotor voltage for different rotor operating slips. The positive sequence stator voltage is assumed to be kept at 1 p.u. In reality, due to the existence of the voltage drop across the [the first term on the equivalent rotor leakage inductance right-hand side of (33) and (35)], the required maximum rotor voltage would be slightly higher than those shown in Fig. 5. Under different stator power output and control targets, which results in different rotor currents, the required rotor voltage will also be slightly different and can be calculated using (33) and (35). Nevertheless, Fig. 5 gives a clearly indication that under unbalanced supply, the voltage rating of the rotor side converter needs to be increased in order to perform the negative sequence current control with the most critical condition being at high rotor speed and voltage unbalance. The increase of the rotor current is small due to the relatively small negative sequence current compared to the nominal rotor current, as can be seen from Table I. Thus, the converter power rating only needs to be increased in proportion to the increase of the rotor voltage. V. SYSTEM IMPLEMENTATION In the stationary reference frame, the stator flux linkage is estimated using the following equation: (38) Since the stator voltage is relatively harmonic-free and its frequency is fixed, the above equation can provide an accurate estimation of the stator flux. Under unbalanced conditions, stator flux contains both positive and negative sequence components. To achieve accurate and reference frame transformation, the phaselocked loop (PLL) must lock to the positive sequence stator flux. Various strategies have been proposed in the literature, and the

method adopted here is to use a band-trap filter tuned at twice the line frequency to remove the negative sequence components as schematically shown in Fig. 6. and the position of the posOnce the rotating speed itive sequence stator flux are detected by the PLL, stator curframe can be transformed rent and flux in the stationary and frames using (12a). For the rotor current, it to is initially transformed from the rotor frame to the stator frame using (6) and then to the and frames frame, positive seusing (12a). As shown in (14), in the quence components appear as dc values while the negative sequence components are oscillating at 2 . The same applies to frame. Thus, to separate the positive and negative sethe are used to quence components, band-trap filters tuned at 2 remove the oscillating terms. Fig. 7 shows the schematic diagram of the overall control system.

VI. SIMULATION STUDIES Simulations of the proposed control strategy for a DFIGbased generation system were carried out using PSCAD/ EMTDC, and Fig. 8 shows the schematic diagram of the implemented system. The DFIG is rated at 2 MW, and its parameters are given in the Appendix. The nominal converter dc link voltage was set at 1300 V, and the switching frequencies for both converters were 2 kHz. The main objective of the grid side converter is to control the dc link voltage, and it was controlled using a similar method as for the dc voltage controller in a VSC transmission system [14]. As shown in Fig. 8, a high frequency ac filter is connected to the stator side to absorb the switching harmonics generated by the two converters. During the simulation, the grid side converter was enabled first, such that the converter dc link voltage was regulated. The DFIG stator was then energized with the rotor rotating at a fixed speed and the rotor side converter disabled. This starting process is not shown in the following results. System unbalance was created by connecting phase A to ground through a reactor on the primary side of the coupling transformer. First, the DFIG was assumed to be in speed control, i.e., the rotor speed is set externally, as the large inertia of the wind turbine results in slow change of the rotor speed. Fig. 9(A) shows the simulated results using conventional stator flux-oriented vector control without considering network unbalance. The high frequency switching harmonic components, i.e., frequencies above 2 kHz, have been removed from the waveforms for clarity. The stator voltage unbalance was around 2%, and the rotor speed was fixed at 1.1 p.u. where the synchronous speed was defined as 1 unit. Stator output active and reactive

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Fig. 7. Schematic diagram of the proposed control system.

Fig. 8. Schematic diagram of the simulated system.

power references were step-changed from 1 MW to 2 MW at 0.4 s and from MVar to MVar at 0.2 s, respectively. From Fig. 9(A), it can be seen that the stator current becomes highly unbalanced in the presence of unbalanced stator voltage. Similarly, the stator active and reactive powers, the rotor d-q currents, and the electromagnetic torque all contain significant oscillations at 100 Hz. The three-phase rotor currents, whose frequencies equal to the rotor mechanical frequency minus the stator frequencies, contain both the fundamental components of 5 Hz (55 Hz­50 Hz) and the harmonic component of 105 Hz (55 Hz 50 Hz). The measured stator current unbalance is about 8.7%, and the amplitude of the rotor 105-Hz current harmonic is about 8.0% of that of the fundamental component of 5 Hz. The oscillations of the stator active power and electromagnetic % and % of their respective rated values. torque are Since the active power exchange between the DFIG and the rotor side converter contains 100-Hz oscillation, the common % oscillation at 100 Hz. dc voltage contains Using the proposed system, Fig. 9(B) shows the simulated results with the same condition as in Fig. 9(A). For this case, Target 2, i.e., no stator active power oscillation, was selected as the control objective. For the purpose of comparison, negative sequence currents are not shown here, as will be shown later in this section. From Fig. 9(B), it can be clearly seen that the stator active power output does not contain any 100-Hz oscillations. The positive sequence rotor currents are precisely controlled, which indicates that the interaction between the positive and negative sequence current controllers is small. The 100-Hz oscillation in %. the common dc link voltage is slightly increased to

Further tests on the proposed control strategy were carried out with different control targets, and the results are shown in Fig. 10. The control target was initially set to Target 1 and changed to Target 2 at 0.2 s, to Target 3 at 0.4 s, and to Target 4 at 0.6 s, respectively. For different control targets, the measured stator current unbalance, the rotor relative amplitude of the 21st harmonic (105 Hz) to the fundamental component (5 Hz), and the pulsations of the generator torque, the stator active power, and the dc voltage at twice the line frequency (100 Hz) are compared in Table II. As can be seen from Fig. 10 and Table II, with the controller set to Target 1, the stator current unbalance becomes very low, i.e., only 0.2% compared to 8.7% with conventional control. When it is switched to Target 2 at 0.2 s, the stator active power oscillation is reduced immediately as can be seen from Fig. 10(g). Similarly, as shown in Fig. 10(h) and Table II, when Target 3 was chosen at 0.4­0.6 s, the torque pulsation disappears. According to (20) and (22), the stator reactive power oscillation also disappears when the torque pulsation terms are zero, and this is clearly indicated in Fig. 10(g). At 0.6 s, the controller switched to Target 4, the rotor current immediately becomes harmonic free (105 Hz), and this can be clearly seen from Fig. 10(c) and Table II, i.e., the relative amplitude of the 105-Hz component is reduced to 0.05%. From Fig. 10, it can be concluded that the system performance is satisfactory, and the control targets have been fully achieved. Similar tests for different rotor speed have also been carried out, and the system performances were found to be similar to those shown in Figs. 9(B) and 10. Due to space limitation, they are not shown here. As shown in Table II, under the proposed control targets, the % with condc voltage 100-Hz oscillation increases from %. The impact of such oscillaventional control to around tion on the system operation is found to be negligible as both the rotor current and the current for the grid side converter (not shown in this paper due to space limitation) are controlled precisely. If required, the dc capacitance could be increased to reduce such oscillation. As shown in Table II, Targets 1 and 4 give good attenuations of both torque and active power oscillations. For Target 2, while the active power oscillation is greatly reduced, the torque pulsation is relatively large. Similar observation can also be noticed for Target 3. The selection of the control

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Fig. 9. Simulated results with 2% stator voltage unbalance and ! : p.u. (a) Stator voltage (p.u.). (b) Stator current (kA). (c) Rotor current (kA). (d) Rotor d-axis current (kA). (e) Rotor q-axis current (kA). (f) Stator active and reactive power outputs (MVA). (g) DFIG electromagnetic torque (p.u.). (h) Converter dc voltage (p.u.). (A) Conventional control design (B) Proposed control design (Target 2).

=11

target is highly dependent on the design of the turbine system and the operation of the network. Further tests with the DFIG being in torque control, i.e., the speed is the result of stator/rotor voltage/current and the mechanical torque which is specified by external input to simulate the torque from the wind turbine. Fig. 11 shows the simulated results when the input mechanical torque step changed at p.u. to p.u. and the reactive power refer0.2 s from MVar to MVar at 0.6 s. Target ence is changed from 2 was initially chosen but switched to Target 3 at 0.8 s. The active power output reference from the DFIG is calculated from the optimal power-speed curve [1], [3]. The lumped inertia constant of the system is set to a relatively low value in the study to reduce the simulation time. As can be seen, when the mechanical torque increases, the rotor speeds up and the active power generated by the DFIG according to the optimal operation curve also increases. From Fig. 11(b), it can be seen that for the period of 0­0.8 s, the stator active power does not contain any 100-Hz pulsation. When the controller switched to Target 3 at

0.8 s, both the electromagnetic torque and reactive power pulsations quickly diminish. Fig. 11 clearly shows that the operation of the system is satisfactory during torque and rotor speed variations. VII. CONCLUSION This paper has presented an analysis of DFIG-based wind energy generation system operating under unbalanced network conditions. A DFIG system was modeled in the positive and negative synchronous reference frames. Stator active and reactive powers and generator electromagnetic torque have been fully defined under unbalance voltage supply, which indicates that significant pulsation at twice the supply frequency could exist. Methods for providing enhanced system control and operation for DFIG-based wind turbines during network unbalance i.e., power, torque, or current oscillation minimizations, are identified. A rotor current control strategy based on positive and negative (dq) reference frames was proposed to provide precise control of the rotor currents. The impact of nega-

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Fig. 11. Simulated results with variation of input torque, (a) Rotor current (kA). (b) Stator active and reactive power (MVA). (c) Electromagnetic torque (p.u.). (d) Rotor mechanical speed (p.u.). TABLE III PARAMETERS OF THE SIMULATED DFIG

Fig. 10. Simulated results with different control targets: 0­0.2 s: Target 1; 0.2 s­0.4 s: Target 2; 0.4 s­0.6 s: Target 3; 0.6 s­0.8 s: Target 4. (a) Stator voltage (p.u.). (b) Stator current (kA). (c) Rotor current (kA). (d) Rotor positive d-q axis current (kA). (e) Rotor negative d-axis current (kA). (f) Rotor negative q-axis current (kA). (g) Stator output active and reactive power (MVA). (h) DFIG electromagnetic torque (p.u.). TABLE II OF DIFFERENCE CONTROL TARGETS WITH CONVENTIONAL DESIGN

tions of the stator active and reactive powers, electromagnetic torque, and stator/rotor currents even with a small stator voltage unbalance. APPENDIX The parameters of the simulated DFIG are shown in Table III. REFERENCES

[1] S. Muller, M. Deicke, and R. W. De Doncker, "Doubly fed induction generator systems for wind turbines," IEEE Ind. Appl. Mag., vol. 8, no. 3, pp. 26­33, May/Jun. 2002. [2] H. Akagi and H. Sato, "Control and performance of a doubly-fed induction machine intended for a flywheel energy storage system," IEEE Trans. Power Electron., vol. 17, no. 1, pp. 109­116, Jan. 2002. [3] R. Pena, J. C. Clare, and G. M. Asher, "Double fed induction generator using back-to-back PWM converter and its application to variable-speed wind-energy generation," Proc. Inst. Elect. Eng. B, vol. 143, no. 3, pp. 231­241, 1996. [4] M. Yamamoto and O. Motoyoshi, "Active and reactive power control for doubly-fed wound rotor induction generator," IEEE Trans. Power Electron., vol. 6, no. 4, pp. 624­629, Oct. 1991. [5] J. B. Ekanayake, L. Holdsworth, X. G. Wu, and N. Jenkins, "Dynamic modeling of doubly fed induction generator wind turbines," IEEE Trans. Power Syst., vol. 18, no. 2, pp. 803­809, May 2003. [6] National Grid Transco, Appendix 1, Extracts from the Grid Code-- Connection Conditions, Feb. 2004. [Online]. Available: http://www. nationalgrid.com. [7] I. Codd, "Windfarm power quality monitoring and output comparison with EN50160," in Proc. 4th Int. Workshop Large-Scale Integration Wind Power Transmission Networks Offshore Wind Farm, Sweden, Oct. 20­21, 2003.

COMPARISONS

tive sequence control on the converter voltage/power rating is discussed, and it was found that the converter rating needs to be increased. Simulation results presented confirmed the effectiveness of the proposed control system. In contrast, conventional DFIG vector control system results in excessive oscilla-

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[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, Jun. 2002. [9] M. R. Rathi, P. P. Jose, and N. Mohan, "A novel H based controller for wind turbine applications operating under unbalanced voltage conditions," in Proc. 13th Int. Conf. Intelligent Systems Application Power System, 2005, pp. 355­360. [10] 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," in Proc. Power Electronics Specialist Conf., 2003, vol. 2, pp. 760­764. [11] T. Brekken, N. Mohan, and T. Undeland, "Control of a doubly-fed induction wind generator under unbalanced grid voltage conditions," in Proc. Eur. Conf. Power Electronics Applications, Sep. 2005. [12] C. Hochgraf and R. H. Lasseter, "STATCOM Controls for Operation With Unbalanced Voltage," IEEE Trans. Power Del., vol. 13, no. 2, pp. 538­544, Apr. 1998. [13] P. Vas, Vector Control of AC Machines. Oxford, U.K.: Oxford Univ. Press, 1990. [14] L. Xu, B. R. Andersen, and P. Cartwright, "VSC transmission system operating under unbalanced network conditions--Analysis and control design," IEEE Trans. Power Del., vol. 20, no. 1, pp. 427­434, Jan. 2005. [15] C. Cshauder and H. Mehta, "Vector analysis and control of advanced static VAR compensator," Proc. Inst. Elect. Eng., Elect. Power Appl., vol. 140, no. 4, pp. 299­306, Jul. 1993.

Lie Xu (M'03­SM'06) received the B.Sc. degree in electrical and electronic engineering from Zhejiang University, Hangzhou, China, in 1993 and the Ph.D. degree in electrical and electronic engineering from the University of Sheffield, Sheffield, U.K., in 1999. Currently, he is with the School of Electronic, Electrical Engineering and Computer Science, Queen's University of Belfast, Belfast, U.K. Prior to this, he was with ALSTOM T&D, Stafford, U.K., from 2001 to 2003 and with the Centre for Economic Renewable Power Delivery (CERPD), University of Glasgow, Glasgow, U.K., from 1999 to 2000. His main interests are power electronics, renewable energy, and application of power electronics to power systems.

Yi Wang (S'04­M'06) was born in Hebei, China. He received the B.Sc. and Ph.D. degrees from North China Electric Power University, Baoding, China, in 1999 and 2005, respectively, both in electrical engineering. Form 2005 to 2006, he was a Lecturer at the School of Electrical Engineering, North China Electric Power University. Currently, he is with the School of Electronics, Electrical Engineering and Computer Science, Queen's University of Belfast, Belfast, U.K. His research interests include power electronics, motor drives, and DFIG-based wind power generation.

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