Coordinated Control of DFIG's Rotor and Grid Side Converters During Network Unbalance

IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 23, NO. 3, MAY 2008 1041

Coordinated Control of DFIG’s Rotor and GridSide Converters During Network Unbalance

Lie Xu, Senior Member, IEEE

Abstract—This paper proposes a coordinated control of therotor side converters (RSCs) and grid side converters (GSCs) ofdoubly-fed induction generator (DFIG) based wind generationsystems under unbalanced voltage conditions. System behaviorsand operations of the RSC and GSC under unbalanced voltage areillustrated. To provide enhanced operation, the RSC is controlledto eliminate the torque oscillations at double supply frequencyunder unbalanced stator supply. The oscillation of the statoroutput active power is then cancelled by the active power outputfrom the GSC, to ensure constant active power output fromthe overall DFIG generation system. To provide the requiredpositive and negative sequence currents control for the RSC andGSC, a current control strategy containing a main controllerand an auxiliary controller is analyzed. The main controlleris implemented in the positive ( )+ frame without involvingpositive/negative sequence decomposition whereas the auxiliarycontroller is implemented in the negative sequence ( ) framewith negative sequence current extracted. Simulation results usingEMTDC/PSCAD are presented for a 2 MW DFIG wind generationsystem to validate the proposed control scheme and to show theenhanced system operation during unbalanced voltage supply.

Index Terms—Control design, converter, doubly-fed inductiongenerator (DFIG), modeling, unbalance, wind turbine.

NOMENCLATURE

, , Stator and rotor voltages.

, Stator and rotor currents.

, GSC output voltage and current.

, Stator and rotor flux linkage.

, , Stator, rotor, and slip angular frequencies.

, Stator output active and reactive powers.

, GSC output active and reactive powers.

Total active power generated by thesystem.Common dc link voltage.

Coupling inductance for the GSC.

Mutual inductance.

, Stator and rotor leakage inductance.

, Stator and rotor self inductance.

Manuscript received February 8, 2007. This work was supported in part bythe EPSRC (U.K.) under Grant EP/D029775/1. Recommended for publicationby Associate Editor Z. Chen.

The author is with the Department of Electronic and Electrical Engi-neering, University of Strathclyde, Glasgow G1 1XW, U.K. (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TPEL.2008.921157

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

, Stator and rotor resistance.

, Stator flux angle and rotor angle.

Superscripts:

, Positive , negative referenceframes.Reference value for controller.

Conjugate complex.

Subscripts:

, Stationary - axis.

, Rotor - axis.

, Synchronous - axis.

, Stator, rotor.

, Positive, negative components.

I. INTRODUCTION

DOUBLY-FED induction generators (DFIGs) as schemat-ically shown in Fig. 1, have been widely used for large

scale wind generation systems and their control and operationshave been the subject of intense research during the last fewyears. The response and performance of DFIG based wind tur-bines during steady state and transient conditions under sym-metrical stator voltage supply are now well understood [1]–[7].However, both transmission and distribution networks can havesteady state and transient voltage unbalances and it is importantthat DFIG systems can operate satisfactory under such condi-tions. If voltage unbalance is not taken into account by the DFIGcontrol system, a small unbalanced stator voltage could result inlarge oscillations of torque and output power. It has been foundthat wind farms connected to distribution networks periodicallyexperience higher voltage unbalance of greater than 2%, and thishas caused a large number of trips [8]. Therefore, it is vital thatDFIG control systems are designed to minimise the impact ofsuch unbalance on wind farm operation.

Control of stand alone DFIG systems for supplying un-balanced load was briefly investigated in [9] whereas DFIG

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1042 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 23, NO. 3, MAY 2008

system protection under asymmetric network disturbance wasaddressed in [10]. Control and operation of DFIG systemsduring network unbalance were studied in [11]–[15]. However,in [11], [12], the studies were purely on controlling the grid sideconverter (GSC) to provide similar functions as a STATCOM[16]. In [13], [14], control of the rotor side converter (RSC) forcompensating DFIG torque pulsation under unbalanced supplyvoltage was investigated. The required rotor compensatingvoltage was generated from the doubly-frequency oscillatingterms of either compensating currents [13] or torque pulsation[14]. Thus the controllers had to be carefully tuned to providethe required system response at double supply frequency. In[15], the authors provided a detailed investigation of the impactof unbalanced stator voltage on the pulsations of DFIG statorand rotor currents, torque, and stator active and reactive powers.Various control targets including minimising the stator/rotorcurrents unbalance, or stator active/reactive powers and torqueoscillations, were proposed. However, due to the limited controlvariables of the RSC, it is not possible to achieve simultaneouselimination of both power and torque oscillations.

Taking into account the two converters within a DFIG system,this paper proposes a coordinated control strategy for the RSCand GSC to provide enhanced control and operation under un-balanced supply. The paper is organized as follows. Section IIdescribes the system behavior and operation of the RSC andGSC under unbalanced condition. Coordinated control of theRSC and GSC is proposed in Section III whereas the designsof the current controllers for the RSC and GSC are illustrated inSection IV. Simulation results on a 2 MW DFIG system are pro-vided in Section V and finally Section VI draws the conclusions.

II. OPERATIONS OF RSC AND GSC OF DFIG SYSTEMS

The main objective of the RSC is to control the DFIG statoractive power/torque/speed and reactive power. While for theGSC, it mainly controls the common dc link voltage but alsoprovides limited reactive power support to the network.

A. RSC (DFIG) Operation

Under unbalanced stator voltage supply, the stator and rotorvoltage, current, and flux may all contain both positive and nega-tive sequence components. Fig. 2 shows the generalized equiva-lent circuit of a DFIG represented in an arbitrary reference framerotating at angular speed of . According to Fig. 2, the stator androtor voltage and flux are given, respectively, by

(1)

(2)

According to (2), the rotor flux and stator current can be ex-pressed using the stator flux and rotor current as

(3)

where is the leakage factor.

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

Fig. 3. Relationships between the (��), (� � ), and the (dq) and (dq)reference frames.

Substituting (3) into (1) yields the rotor voltage as

(4)

Under unbalanced supply, a convenient way to model a DFIGis to use a positive reference frame rotating at the speed ofand a negative reference frame rotating at the speed of [15].The spatial relationships of various reference frames are shownin Fig. 3. As shown, the -axis is fixed to the positive statorflux and rotates at the speed of whereas the -axis rotatesat an angular speed of with the phase angle to the -axisbeing .

According to Fig. 3, the transformation of vector between, , and reference frames are given by

(5)

where and .Thus the system expressed in (4) can be separated into two

subsystems, i.e., positive sequence components in the positivereference frame and negative sequence components in the

negative reference frame. Taking into account the con-stant stator positive and negative sequence voltages, a two-partDFIG model is given as

(6a)

(6b)

where , ,and .

In the frame, the stator and rotor current, voltage, andflux vectors can be expressed using their respective positiveand negative sequence components as

(7)

XU: COORDINATED CONTROL OF DFIG’S ROTOR AND GRID SIDE CONVERTERS 1043

As shown in [15], under unbalanced conditions, the statoroutput active and reactive powers are given as

(8)

(9)

where

(10a)

(10b)

According to Fig. 2, the total power imported from the rotorshaft equals to the sum of the power outputs from the equivalentvoltage source and . Thus, it is given by [15]

(11)

where

(12)

The electromagnetic torque of the DFIG is calculated as

(13)

where is the number of pole pairs.The active power output from the rotor to the RSC can also

be calculated based on the stator output active power and thepower imported from the rotor shaft as

(14)where

(15)

Fig. 4. AC and dc equivalent circuits of the GSC. (a) AC. (b) DC.

B. GSC Operation

Similar to a grid connected VSC system [17], [18], GSC canbe defined in the synchronous reference frame where the

-axis is fixed to the grid ac voltage. Fig. 4 shows the ac and dcequivalent circuits of the GSC. According to Fig. 4(a), the GSCac system model can be represented as

(16)

Under unbalanced supply, similar to the RSC, separating (16)into positive sequence components in the reference framewhose -axis is fixed to the positive grid voltage and negativesequence components in the reference frame, yields atwo-part model for the GSC as

(17a)

(17b)

where , .Neglect the , the active and reactive power outputs from

the GSC to the network can be expressed as [17]

(18)

where is the angle between the - and the -axis, and

(19)

As shown in Fig. 4(b), the common dc link voltage is givenas

(20)


Fig. 5. Relationship between the stator flux and voltage oriented synchronousreference frames.

III. COORDINATED CONTROL OF RSC AND GSC

Under unbalanced network conditions, the RSC controls thefour rotor current components, i.e., , , , and .Apart from controlling the average stator active and reactivepowers, i.e., and shown in (9) and (10), two more param-eters can be controlled. Depending on the design of the turbinesystem and the network operation, the oscillations of the torqueand active power output at double supply frequency are likely tobe the main concerns. According to (10) the stator active powerpulsation can be eliminated by making 0 and0. Alternatively, the torque oscillation can be eliminated byensuring 0 and 0. However, it is not possibleto eliminate both the stator active power and torque oscillationsusing the RSC due to limited control variables.

As shown in Fig. 1, the total active power generated by thewind generation system is the sum of the active power outputsfrom the DFIG stator and the GSC as

(21)

Due to the different orientations of the RSC (DFIG), i.e., statorflux, and the GSC, i.e., grid/stator voltage, the oscillating termsdefined in (9) and (18) appear to be different. Under steady stateconditions and neglecting the stator resistance, the positive statorflux lags the voltage by 90 . Fig. 5 illustrates the relationship be-tween the two reference frames where and refer to the fluxoriented positive synchronous frame used for the RSC whileand refer to the voltage oriented positive synchronous frameused for the GSC. Thus, according to Fig. 5, there is

(22)

Thus, according to (9), (18), (21) and (22), the total activepower generated by the system can be expressed as

(23)

Similarly, based on (9), (11), (20), and (22) the dc link voltageis given as

(24)

Thus, to provide enhanced operation of the DFIG generationsystem, the RSC and GSC can be controlled as follows.

1) To reduce the turbine mechanical stress, the RSC iscontrolled to minimize the DFIG torque oscillation, i.e.,

0 and 0. According to (12) and takinginto account 0, the references for the negativesequence rotor currents are given as

(25)where , .

2) The GSC is controlled such that the pulsation of the totalactive power generated by the DFIG system is zero. Ac-cording to (23), the GSC active power oscillations must becontrolled as

(26)

According to (19) and (26) and taking into account0, the references for the GSC negative sequence currentsare given as

(27)

where , ,and are calculated according to (10b).

Thus, both the electromagnetic torque and the total activepower output contain no double-frequency oscillations evenwith unbalanced voltage supply. In addition, under such con-ditions, the oscillating terms of the dc voltage equation shownin (24) also become zero. This indicates that there will be nodouble-frequency oscillation on the dc link voltage either.

IV. CURRENT CONTROLLER DESIGN

Both the RSC and GSC have to control their respectivepositive and negative sequence currents. Typical control designwould use a dual-current controller, i.e., a positive sequencecurrent controller in the frame and a negative sequencecurrent controller in the frame [15], [19]. Both positiveand negative sequence components have to be decomposedfrom the voltages, flux, and currents. As the process of ex-tracting positive and negative sequence components involvesconsiderable time delay and adds considerable amplitude andphase errors to the signals, the system cannot achieve accuratedecoupling under transient conditions. Therefore, the systemperformance is degraded and stability of the system is reduced.Furthermore, even when the network is perfectly balanced,the control system still has to decompose the current, voltage,and flux and perform positive and negative sequence currentscontrol. This unnecessarily affects the dynamic performance ofthe overall system.

In order to overcome the problems highlighted, the strategyadopted here is to have a main controller and an auxiliary con-troller as used in a VSC Transmission system [17]. The maincontroller is implemented in the frame without involvingpositive and negative sequence separation, i.e., it is designed


in the same way as the conventional method without consid-ering network unbalance. The auxiliary controller is speciallydesigned for controlling the negative sequence current and isimplemented in the frame with negative sequence com-ponents extracted.

A. RSC

Based on the requirement of , and (25), the four rotorcurrent references, i.e., , , , and , can be de-termined.

According to (4), under unbalanced conditions, a DFIGsystem can be represented in the frame as

(28)where and refer to the rotor control voltages from themain and auxiliary controllers, respectively.

Using conventional decoupling control and without involvingany positive and negative sequence decomposition, of themain controller is designed as

(29)

where

(30)

Substituting (7) and (29) into (28) and splitting into positiveand negative sequence subsystems yield

(31a)

(31b)

Equation (31a) represents the dynamics of the positive se-quence currents and appropriate selection of the proportionaland integral gains of and of the main controller can pro-vide the required response. Alternatively, (31b) gives the dy-namics of the negative sequence current with the auxiliary con-troller. Without causing significant impact on the system dy-namic performance (31b) can be simplified by neglecting theintegral term as

(32)

where .Based on (32), the control system for the auxiliary controller

can then be designed using decoupling control in the similar wayas for the main controller. Thus, in the reference frame,extracting the negative sequence components and is thengiven by

(33)

Fig. 6. Structure for the top-level controller.

where

(34)The overall rotor control voltage is the combination of the

outputs from the main and the auxiliary controllers. Accordingto Fig. 3 and (5), in the rotor frame it is given as

(35)

B. GSC

The GSC controls the average dc link voltage which deter-mines and provides limited reactive power support to thegrid, i.e., . Similar to the RSC, the four current referencesfor the GSC, i.e., , , , and can be generatedbased on , , and (27). The design of the current controllerfor the GSC uses the same principles as for the RSC.

Based on (16), under unbalanced conditions, the GSC can beexpressed in the frame as

(36)

where and refer to the control voltages from the mainand auxiliary controllers, respectively.

Without involving any positive and negative sequence decom-position, of the main controller is designed as

(37)

where

(38)

Similarly, substituting (37) into (36) yields the positive andnegative sequence components as

(39a)

(39b)

where .


Fig. 7. Schematic diagram of the current controllers.

Thus, in the reference frame, extracting the negativesequence components and is then given by

(40)

where

(41)The overall GSC control voltage is the combination of the

outputs from the main and the auxiliary controllers. Thus in thestationary frame, it is given as

(42)

C. System Implementation

Fig. 6 shows the structure of the top-level control system.A voltage unbalance detector (VUD) which monitors the per-centage of the negative sequence voltage with reference to thepositive one is used to detect the network unbalance. Undernormal conditions with very small voltage unbalance, the aux-iliary controllers for both the RSC and GSC are disabled andthe system is controlled in the same way as with conventionaldesign. When voltage unbalanced is detected, the auxiliary con-troller is immediately switched on and the positive and negativesequence current references are generated according to the ac-tive power/dc voltage, reactive power, and (25) and (27).

The proposed current controllers for the RSC and GSC areshown in Fig. 7. As shown, the generated current references arepassed to the main and the auxiliary controllers (only switchedon when voltage unbalance is detected by the VUD) to generatethe required rotor and grid control voltages. Space vector mod-ulation (SVM) [20] is used to produce the switching patterns forboth converters.

If SVM is used, the maximum modulation index is 1.15 be-fore over-modulation occurs [20]. Thus the maximum ampli-tude of the phase voltages can be produced for both convertersis 0.575 . As shown in [15], the RSC requires higher rotorvoltage to control the negative sequence rotor current during net-work unbalance. If the required rotor control voltage exceeds thecapability of the RSC, the full control of the negative sequencerotor currents will not be achieved.

TABLE IPARAMETERS OF THE DFIG SIMULATED

V. SIMULATION STUDIES

Simulations of the proposed control strategy for a 2 MWDFIG based generation system were carried out using PSCAD/EMTDC. The DFIG parameters are given in Table I while Fig. 8shows the schematic diagram of the implemented system. Thenominal converter dc link voltage is 1200 V and SVM with aswitching frequency of 2 kHz is used for both the RSC and GSC.As shown in Fig. 8, a single-phase resistive load is used to gen-erate the voltage unbalance.

Initial tests with constant rotor speed were conducted as thelarge inertia of a turbine/generator system results in much largermechanical time constant compared to electrical one. Fig. 9shows the simulation results with a 3.5% voltage unbalancewhere three different control modes are compared, i.e.,

1) Mode 1 (0–0.3 s): conventional vector control withouttaking into account voltage unbalance is used for both theRSC and GSC, i.e., the auxiliary controllers for the RSCand GSC are disabled.

2) Mode 2 (0.3–0.6 s): the auxiliary controller for the RSC isenabled with the control target set at torque oscillation min-imization. However, the auxiliary controller for the GSC isdisabled.

3) Mode 3 (0.6–0.9 s): the auxiliary controllers for both theRSC and GSC are enabled, i.e., using the proposed coor-dinated control strategy.

As can be seen from Fig. 9(a) and (b), under Mode 1, thestator currents contain significant negative sequence component(around 10%) while the rotor current contains both the 5 Hzfundamental component (positive slip 55 Hz 50 Hz) and the105 Hz harmonic component (negative slip 55 Hz 50 Hz).The stator active, reactive powers, the total active power, andthe torque all have significant 100 Hz oscillations. In addition,


Fig. 8. Schematic diagram of the simulated system.

Fig. 9. Simulation results with various control methods under 3.5% voltage unbalance and 1.1 pu rotor speed; 0–0.3 s: Mode 1; 0.3–0.6 s: Mode 2; 0.6–0.9 s:Mode 3.

100 Hz oscillation also appears in the common dc link voltage.As shown in Fig. 9(d) and (e), when the auxiliary controller forthe RSC is enabled at 0.3 s the rotor negative sequence currentsare immediately controlled according to the requirement ofminimizing torque oscillation. Consequently, the torque andstator reactive power oscillations immediately diminish asshown in Fig. 9(f)and (n), respectively. However, the stator andtotal active power outputs, and the common dc voltage stillcontain significant 100 Hz oscillations during Mode 2 control.At 0.6 s, the control method is switched to Mode 3 and asshown in Fig. 9(i) and (j), the negative sequence currents of theGSC are immediately regulated. As shown in Fig. 9(k)–(m), theoscillation of the GSC output active power compensates that of

the stator active power and consequently, 100 Hz oscillation iseliminated from the generated total active power of the system.In addition, as shown in Fig. 9(g), the dc voltage oscillation isdisappeared under the proposed control strategy. From Fig. 9,it is evident that the proposed control method can significantlyenhance the control and operation of DFIG system under un-balanced supply with zero torque, active power, and commondc link voltage oscillation.

Further tests on system control and operation during a largertransient voltage unbalance of 9.5% were carried out and theresults are shown in Fig. 10. The voltage unbalance was intro-duced by switching in a single-phase load between 0.1–0.3 s.As shown, Fig. 10(a) and (b) compare the system responses be-


Fig. 10. Simulation results during transient unbalance of 9.5% between 0.1–0.3s (! = 1.1 pu). (A) Conventional design. (B) Coordinated design.

tween the conventional control and the proposed method. Withthe proposed control, when the unbalance occurred at 0.1 s, it isimmediately detected by the VUD. Consequently, the auxiliarycontrollers for the RSC and GSC are automatically switched on.From Fig. 10(a) and (b), it can be seen that compared to con-ventional design, the proposed control system results in a muchsmoother operation during such transient network unbalancewith oscillations of the torque, current, power and dc voltageall being significantly reduced. After the removal of the voltageunbalance at 0.3 s, the auxiliary controllers are automaticallyswitched off and the system back to the normal control mode.

As indicated in [10], compensating the impact of statorvoltage unbalance requires a large rotor voltage which couldexceed the capability of the RSC. Under such condition, itwould not be able to precisely control the rotor negative se-quence currents. Thus, the larger the voltage unbalance is, theless significant the proposed control becomes due to the RSCvoltage limit.

The proposed control strategy during variations of DFIGspeed and torque were also studied and the results are shownin Fig. 11. The input mechanical torque and reactive powerreference were step changed from 0.3 pu to 1 pu at 0.3 s andfrom 0.5 MVar (lagging) to 0.5 MVar (leading) at 0.5 s,respectively. The voltage unbalance was 3.5%. The reference ofthe DFIG active power output was calculated from the optimal

Fig. 11. Simulation results with torque and speed variations under proposedcoordinated control strategy (voltage unbalance: 3.5%).

power-speed curve [1]. The lumped inertia constant of thesystem was set to a relatively small value of 0.5 s in the studyfor a better illustration. Fig. 11 clearly shows the satisfactoryoperation of the system with no oscillation in the torque andthe generated total active power.

VI. CONCLUSION

This paper has presented coordinated control strategies forthe RSC and GSC of a DFIG system to provide enhanced systemcontrol and operation during network unbalance. The behaviorsof a complete DFIG system including the generator, RSC andGSC have been analyzed. A new coordinated control strategyfor the RSC and GSC has been proposed. The RSC controlsthe rotor negative sequence currents to eliminate any torque os-cillation while the GSC compensates the DFIG stator activepower oscillation to ensure zero oscillation in the total gener-ated active power of the DFIG system. Positive and negativesequence current control strategy for both the RSC and GSCbased on a main and an auxiliary controller has been illustrated.The main controller is designed in the same way as for the con-ventional control without involving into positive and negativesequence decomposition. While for the auxiliary controller, itis designed specifically for the negative sequence components.Simulation results confirmed the effectiveness of the proposedcontrol system with reduced oscillations for the stator/rotor cur-rents, torque, and total active power generation.

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Lie Xu (M’03–SM’06) received the B.Sc. degree inelectrical and electronic engineering from ZhejiangUniversity, Hangzhou, China, in 1993 and the Ph.D.degree in electrical and electronic engineering fromthe University of Sheffield, Sheffield, U.K., in 1999.

Currently, he is with the Department of Electronicand Electrical Engineering, University of Glasgow,Glasgow, U.K. He was with Queen’s University ofBelfast, Belfast, U.K., from 2004 to 2007, ALSTOMT&D, Stafford, U.K., from 2001 to 2003, and theUniversity of Glasgow, from 1999 to 2000. His main

interests are power electronics, wind energy generation and grid integration,and application of power electronics to power systems.

Documents

Coordinated Control of DFIG's Rotor and Grid Side Converters During Network Unbalance