Sliding-Mode-Based Direct Power Control of Grid-Connected Wind ...

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IEEE TRANSACTIONS ON ENERGY CONVERSION, VOL. 27, NO. 2, JUNE 2012

Sliding-Mode-Based Direct Power Control of Grid-Connected Wind-Turbine-Driven Doubly Fed Induction Generators Under Unbalanced Grid Voltage Conditions Lei Shang and Jiabing Hu, Member, IEEE

Abstract—This paper proposes an improved direct power control (DPC) strategy of grid-connected wind-turbine-driven doubly fed induction generators (DFIGs) when the grid voltage is unbalanced. The DPC scheme is based on the sliding mode control (SMC) approach, which directly regulates the instantaneous active and reactive powers in the stator stationary reference frame without the requirement of either synchronous coordinate transformation or phase angle tracking of grid voltage. The behavior of DFIGs by the conventional SMC–DPC, which takes no negative-sequence voltage into consideration, is analyzed under unbalanced grid voltage conditions. A novel power compensation method is proposed for the SMC-based DPC during network unbalance to achieve three selective control targets, i.e., obtaining sinusoidal and symmetrical stator current, removing stator interchanging reactive power ripples and canceling stator output active power oscillations, respectively. The active and reactive power compensation components are calculated via a simple method and the proposed three control targets can be achieved, respectively, without the need of extracting negative-sequence stator current components. Experimental results on a 2 kW DFIG prototype are presented to verify the correctness and validity of the proposed control strategy and power compensation method. Index Terms—Direct power control (DPC), doubly fed induction generator (DFIG), power compensation, sliding mode control (SMC), unbalanced grid voltage, wind turbine.

NOMENCLATURE Us, V r Is, Ir ψs , ψr ωs , ωr , ωslip Ps , Qs Te Ls , Lr

Stator (grid), rotor voltage vectors. Stator, rotor current vectors. Stator, rotor flux linkage vectors. Synchronous, rotor and slip angular frequencies. Stator output active, reactive powers. Electromagnetic torque. Stator, rotor self inductances.

Manuscript received June 29, 2011; revised October 16, 2011; accepted December 6, 2011. Date of publication January 11, 2012; date of current version May 18, 2012. This work was supported in part by the National Natural Science Foundation of China under Project 50907057. Paper no. TEC-00328-2011. L. Shang is with Nari-Relays Electric Company, Ltd., Nanjing 211100, China (e-mail: [email protected]). J. Hu (Corresponding author) is with College of Electrical and Electronic Engineering, Huazhong University of Science and Technology, and also with State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Wuhan 430074, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TEC.2011.2180389

Lls , Llr Lm Rs , Rr θr p Superscripts ∧ ∗ r j Subscripts αβ + −

Stator, rotor leakage inductances. Mutual inductance. Stator, rotor resistances. Rotor angle. Pole pairs. Conjugate complex. Reference value. Rotor reference frame. Imaginary unit. αβ-axis elements in the stator stationary reference frame. Positive-sequence components. Negative-sequence components. I. INTRODUCTION

ECENTLY, electricity production from multimegawatt (multi-MW) wind turbines arranged in wind parks has been the focus of considerable attention when it comes to the fulfillment of renewable-energy targets set by governments all over the world [1]. Despite that the focus has been shifted to the topologies utilizing direct-driven synchronous generators with either electrically excited or permanent-magnet excited, especially for off-shore wind farms, doubly fed induction generators (DFIGs) are still dominant in modern wind power generation systems due to their merits including variable speed operation, independent regulation active and reactive power capability and low converter cost [2]. Generally, there exist two big families of classic control methods for grid-connected wind-turbine-driven DFIGs, viz., vector control (VC) or field-oriented control (FOC) [2]–[5], and direct torque/power control (DTC/DPC) [6]–[10]. The VC schemes for DFIGs are usually based on either stator-voltage-orientation (SVO) [2], [3] or stator-flux-orientation (SFO) [4], [5], and are capable of controlling the instantaneous stator active and reactive powers by regulating the decoupled rotor current by using proportional-integral (PI) controllers. These control schemes can control the stator active and reactive powers accurately, but the main drawbacks are the tuning of the PI parameters, the necessity of synchronous coordinate transformations and the tracking of grid voltage phase angle. On the other hand, based on the principles of DTC for motor drives [11], [12], DPC has

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SHANG AND HU: SLIDING-MODE-BASED DIRECT POWER CONTROL OF GRID-CONNECTED WIND-TURBINE-DRIVEN DFIGs

been adopted to control DFIG systems by using either hysteresis controllers [6], [7] or predictive power model [8]–[10] to directly regulate the instantaneous stator active and reactive powers. This control method can obtain better dynamic performance and is more robust to machine parameters’ variations. IT is worth pointing out that the conventional VC and DTC/DPC strategies [2]–[10] all assume that the connected grid is ideal; however, DFIG-based wind power generation systems are usually installed far away from main power network where unbalanced faults occur frequently. The unbalanced network will seriously deteriorate the performance of wind-turbinedriven DFIGs if no negative sequence grid voltage is considered in the control system. Hence, the strategies to improve the performance of DFIGs under unbalanced network conditions have obtained a worldwide concern. More recently, quite a few efforts have been made to improve the performance of the DFIGs when the network voltage is unbalanced [13]–[15]. In [13], dual PI schemes have been illuminated with VC strategy, the one for the positive sequence rotor current component and the other one for the negative sequence rotor current component. However, this method requires the separation of the positive- and negativesequence components from the measured stator voltage, stator current and rotor current, which can acquire well steady-state performance but will result in slow transient response and poor system stability. Moreover, in [14], an auxiliary PI current controller is adopted to help conventional VC regulate negative sequence current components. It can improve the performance, but the positive- and negative- sequence current components must be extracted and regulated, which will affect dynamic performance and accurate implementation of the control system. In addition, a PI plus resonant (R) current controller is adopted in a synchronous rotating reference frame for controlling multiple current components under unbalanced network conditions in [15]. It can obtain better system dynamic but makes control system a bit complicated and requires more parameters’ tuning of the current controllers. Meanwhile, some modified DPCs have been proposed under unbalanced grid voltage conditions [16]–[18]. In [16], [17], investigation on so-called DPC+ of DFIG has been presented, which is based on conventional DPC [7]. The proposed DPC+ is capable of regulating the decoupled active and reactive power of DFIG under unbalanced grid voltage conditions, which shows that only one objective can be fully achieved, i.e., sinusoidal stator current. In addition, another modified DPC method has been presented in [18]. It can eliminate the electromagnetic torque oscillations, thus avoiding mechanical stresses and exchanging sinusoidal current with the network by using an oscillating stator active reference, which is calculated from the active/reactive power and torque estimation, thus avoids decoupling the positive- and negative-sequence voltage and current components. However, both modified DPC methods presented in [16]–[18] can only achieve single control target, which result in inadequate flexibility to fulfill the requirements of wind farm operators. As a consequence, the main contribution of this paper is to propose an improved control scheme to the standard SMC–DPC strategy [19], [20] with power compensation and

Fig. 1. frame.

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Equivalent circuit of a DFIG in the stator stationary αβ reference

three selective control targets presented, viz., obtaining sinusoidal and symmetrical grid current, removing reactive power ripples and canceling active power oscillations, in order to enhance the control flexibility and performance of the DFIGs when the network is unbalanced. The rest part of the paper is organized as follows. The behaviors of DFIGs under unbalanced network conditions are described in Section II. In Section IIIA, the analysis on instantaneous active and reactive powers is made, and the stator currents harmonics via the conventional DPC are emphasized. The power compensations method is depicted in Section III-B. The principle of SMC-based DPC is briefly described in Section III-C. The proposed control scheme with SMC–DPC and power compensations method is discussed in Section III-D. In Section IV, experimental results on a 2 kW DFIG prototype are presented to substantiate the feasibility of the proposed control scheme. Some conclusions are drawn in the final section. II. BEHAVIORS OF DFIGS UNDER UNBALANCED GRID VOLTAGE CONDITIONS The equivalent circuit of a DFIG in the stator stationary αβ reference frame is shown in Fig. 1. According to Fig. 1, the stator and rotor flux linkages can be expressed as  ψ sα β = Ls I sα β + Lm I r α β (1) ψ r α β = Lr I r α β + Lm I sα β . According to (1), the rotor flux linkages can be expressed in terms of the stator flux linkages, current, and inductances ψ r α β = σLm I sα β +

Lr ψ sα β Lm

(2)

 where, σ = 1 − Ls Lr L2m . The relationship between stator and rotor voltages and currents in the stator stationary αβ reference frame can be expressed as ⎧ dψ sα β ⎪ ⎨ U sα β = Rs I sα β + dt (3) ⎪ dψ r α β ⎩V − jωr ψ r α β . r α β = Rr I r α β + dt The stator instantaneous active and reactive powers can be represented as 3 Ps + jQs = − U sα β × Iˆ sα β 2

(4)

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where ⎧ 3 ⎪ ⎨ Ps = − (usα isα + usβ isβ ) 2 3 ⎪ ⎩ Q = − (u i − u i ) . s sβ sα sα sβ 2

(5)

dusα − dusα + = −ωs usβ + , = −ωs usβ − dt dt dusβ + dusβ − = ωs usα + , = ωs usα − . (10) dt dt Based on (7), (8), and (10), the variations of instantaneous stator voltage can be obtained as

Then, the variations of stator active and reactive powers can (11) dU s dt = jωs U s . be given as  ⎧ Equation (3) is also correct under unbalanced network condPs dusα dusβ disα disβ 3 ⎪ = − + i + u + u ⎪ i sα sβ sα sβ ditions. As a result, according to (3), the stator current variation ⎨ dt 2 dt dt dt dt can be expressed in the αβ reference frame as  ⎪ 3 du du di di dQ s sβ sα sα sβ  ⎪ ⎩ =− − isβ + usβ − usα isα . dI sα β 1 Lr dt 2 dt dt dt dt = (usα β − Rs I sα β ) V r α β − Rr I r α β − dt σLm Lm (6)  When the network is unbalanced, stator voltage and current Lr ωr ψ sα β . +j σLm I sα β + (12) can be expressed as the sum of their respective positive and σLm Lm negative sequence components Substituting (11) and (12) into (6) yields ⎧ = U + U U    sα β sα β + sα β − ⎪ ⎨ usβ usα ir α d Ps 3 Rr = I sα β = I sα β + + I sα β − (7) dt Qs 2 σLm usβ −usα ir β ⎪ ⎩ ψ sα β = ψ sα β + + ψ sα β −   usβ usα vr α 3 1 − where 2 σLm usβ −usα vr β   −usβ usα ψr α 3 1 U sα β = usα + jusβ , I sα β = isα + jisβ , ψ sα β + 2 σLm usα usβ ψr β = ψsα + jψsβ

Rs Lr  −ωsilp Ps σ L 2m U sα β + = usα + + jusβ + , I sα β + = isα + + jisβ + , ψ sα β + + Rs Lr Qs ωsilp σ L 2m = ψsα + + jψsβ +   usα usα usβ 3 Lr U sα β − = usα − + jusβ − , I sα β − = isα − + jisβ − , ψ sα β − + (13) 2 σL2m 0 0 usβ = ψsα − + jψsβ − . (8) where, ωsilp = ωs − ωr . Substituting (8) and (9) into (5), the instantaneous stator active During network unbalance, the positive and negative sequence voltage and current components in the stationary ref- and reactive powers during network unbalance can be expressed as erence frame can be expressed as  Ps = Ps0 + Ps1 + Ps2 (14) usα + = |U s+ | sin (ωs t + ϕu + ) , Qs = Qs0 + Qs1 + Qs2 usα − = |U s− | sin (−ωs t − ϕu − ) where Ps0 and Qs0 are the respective average components of



active and reactive powers, and Ps1 , Ps2 and Qs1 , Qs2 are the cos (ω usβ + = − U + t + ϕ ) , s u + s oscillating components at twice the grid frequency (100 Hz) of usβ − = |U s− | cos (−ωs t − ϕu − ) active and reactive powers, respectively. For clear illustration, they can be represented as isα + = |I s+ | sin (ωs t + ϕi+ ) , ⎤ ⎡ ⎤ ⎡ Ps0 isα − = |I s− | sin (−ωs t − ϕi− ) usα + usα − usβ + usβ − ⎥ ⎢ ⎡ ⎤ isα + ⎢ Ps1 ⎥ ⎢ isβ + = − |I s+ | cos (ωs t + ϕi+ ) , usβ + ⎥ 0 usα + ⎥ ⎢ ⎥ ⎢ 0 ⎢ Ps2 ⎥ ⎥ ⎢ isα − ⎥ 3⎢ ⎢ ⎥ ⎢ ⎥ 0 ⎥ isβ − = |I s− | cos (−ωs t − ϕi− ) (9) ⎢ 0 usβ − ⎥ = − ⎢ usα − ⎢ ⎥⎢ ⎥. ⎢Qs0 ⎥ 2 ⎢ usβ + usβ − −usα + −usα − ⎥ ⎣isβ + ⎦ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ usβ − 0 −usα − where |U s+ |, |U s− |, |I s+ |, and |I s− | are the amplitudes of ⎢ 0 ⎦ isβ − ⎣Qs1 ⎦ positive and negative sequence components of stator voltage −usα + 0 usβ + 0 Qs2 and current, respectively. ϕu + , ϕu − , ϕi+ , and ϕi− are the initial (15) phase angles of positive and negative sequence components of According to the definition of electromagnetic torque and (8), stator voltage and current, respectively. the electromagnetic torque can be represented as Based on (9), the respective variation of positive and negative Te = Te0 + Te1 + Te2 (16) sequence components of grid voltage can be obtained as

SHANG AND HU: SLIDING-MODE-BASED DIRECT POWER CONTROL OF GRID-CONNECTED WIND-TURBINE-DRIVEN DFIGs

Fig. 2. Relation between positive and negative sequence stator voltage, current vectors.

where Te0 is the average components of electromagnetic torque, and Te1 and Te2 are the oscillating components at twice the grid frequency (100 Hz) of electromagnetic torque components, respectively. They can be expressed as ⎤ ⎡ ⎤ ⎡ usα + −usα − usβ + −usβ − Te0 ⎥ 3 p ⎢ ⎥ ⎢ usα + 0 usβ + ⎦ ⎣ 0 ⎣ Te1 ⎦ = 2 ωs Te2 −usα − 0 −usβ − 0 ⎤ ⎡ isα + ⎡ ⎤ −isα + isα − −isβ + isβ − ⎥ ⎢i ⎢ sα − ⎥ 3 pRs ⎢ ⎥ ⎥ 0 0 0 ⎦ ×⎢ ⎢ isβ + ⎥ + 2 ωs ⎣ 0 ⎦ ⎣ 0 0 0 0 isβ − ⎡

isα +

⎤

⎥ ⎢i ⎢ sα − ⎥ ×⎢ ⎥. ⎣ isβ + ⎦

(17)

isβ − It is worth pointing out that the pulsating terms in stator active power and electromagnetic torque have the relationships, viz., ωs Te1 /p = Ps1 and ωs Te2 /p = −Ps2 . III. CONTROL STRATEGY BASED ON SMC–DPC DURING GRID VOLTAGE UNBALANCE A. Power Analysis During Grid Voltage Unbalance The spatial relationships of the stator voltage and current vectors are shown in Fig. 2. θu −i+ is the phase angle between positive-sequence voltage vector and current vector.θu −i− is the phase angle between negative-sequence voltage vector and current vector. U s+ , U s− , I s+ , and I s− are positive and negative sequence grid voltage and current vectors, respectively.U s and I s are the respective grid voltage and current vectors. According to (9) and (15), Ps0 , Ps1 , Ps2 and Qs0 , Qs1 , Qs2 can be expressed, respectively, as 3 Ps0 = − (usα + isα + + usβ + isβ + + usα − isα − + usβ − isβ − ) 2 3 = − (|U s+ | |I s+ | cos θu −i+ + |U s− | |I s− | cos θu −i− ) 2 (18a)

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3 Ps1 = − (usα + isα − + usβ + isβ − ) 2 3 = |U s+ | |I s− | cos (2ωs t − θu −i− ) (18b) 2 3 Ps2 = − (usα − isα + + usβ − isβ + ) 2 3 = |U s− | |I s+ | cos (2ωs t + θu −i+ ) (18c) 2 3 Qs0 = − (usβ + isα + − usα + isβ + + usβ − isα − − usα − isβ − ) 2 3 = (|U s+ | |I s+ | sin θu −i+ + |U s− | |I s− | sin θu −i− ) 2 (19a) 3 Qs1 = − (usβ + isα − − usα + isβ − ) 2 3 = − |U s+ | |I s− | sin (2ωs t − θu −i− ) 2 3 Qs2 = − (usβ − isα + − usα − isβ + ) 2 3 = |U s− | |I s+ | sin (2ωs t + θu −i+ ) . 2

(19b)

(19c)

According to (18b), (18c), (19b), and (19c), it is clearly seen that the negative sequence current generates power ripples pulsating at twice the fundamental frequency with positive sequence voltage, meanwhile the negative sequence voltage produces power oscillations with the positive sequence current. Based on the principle of the standard SMC–DPC [19], [20], active and reactive powers are directly regulated to follow their respective references, which are usually constant values when the network voltage is strictly balanced. While under unbalanced grid voltage conditions, the standard SMC–DPC also attempts to keep both active and reactive powers constant at the same time, i.e.,  Ps1 + Ps2 = 0 (20) Qs1 + Qs2 = 0. The target may lead to serious performance deterioration of DFIG generation system during network unbalance, which will be discussed in detail here. Substituting (18) and (19) into (20) yields |U s+ | |I s− | cos (2ωs t − θu −i− ) = − |U s− | |I s+ | cos (2ωs t + θu −i+ )

(21a)

|U s− | |I s+ | sin (2ωs t + θu −i+ ) = |U s+ | |I s− | sin (2ωs t − θu −i− ) .

(21b)

Equation (21) should be correct throughout the system operation with any various active and reactive power combinations once the target in (20) is selected. Thus, according to (21a), the following can be obtained  |U s+ | |I s− | = − |U s− | |I s+ | (22) cos (2ωs t − θu −i− ) = cos (2ωs t + θu −i+ ) .

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While, based on (21b), we obtain  |U s+ | |I s− | = |U s− | |I s+ | sin (2ωs t + θu −i+ ) = sin (2ωs t − θu −i− )

.

(23)

Obviously, (22) and (23) cannot be correct at the same time throughout the whole operation, as a result, the termsPs1 + Ps2 and Qs1 + Qs2 cannot be zero simultaneously. Besides, Ps1 = Ps2 = Qs1 = Qs2 = 0 is also impossible. Thus, pulsating components in the active and reactive powers cannot be eliminated simultaneously with only positive and negative sequence fundamental current components. On the other hand, if the standard SMC–DPC [19], [20] forces the active and reactive powers ripples to be null at the same time, the current harmonics will be generated. The negative-sequence third-order harmonic current component will be generated and acted with the positive-sequence fundamental grid voltage to eliminate the power ripples of twice the fundamental frequency. The power ripples of fourth fundamental frequency will then be generated by the positive-sequence fundamental voltage component and the negative sequence third-order harmonic current component. As a result, the fifth-order current harmonic must be generated, and so forth. Consequently, significant odd order current harmonics will be generated to maintain both active and reactive power constant, which is not allowed by the IEEE5191992 [21]. In order to solve the problems highlighted, different control targets are proposed and added to the standard SMC–DPC, in this paper, so as to improve the performance of the DFIG generation systems during network voltage unbalance. B. Control Targets According to the analytical results obtained in Section III-A, three selective control targets can be presented, viz., Target I: To get sinusoidal and symmetric stator current. Target II: To remove stator reactive power ripples. Target III: To cancel stator active power oscillations. Different power compensation components calculated in the stationary reference frame are injected into power references to achieve these control targets, which will be identified as follow. Target I: To get sinusoidal and symmetrical stator current. The target is to eliminate negative sequence current component to obtain sinusoidal and symmetrical stator current. As shown in (13), in order to eliminate negative sequence current, the stator output power ripples generated by the negative sequence current components should be depressed. Thus, Ps1 and Qs1 must be zero in order to achieve Target I. Meanwhile, the other oscillating power components Ps2 and Qs2 generated by the negative sequence voltage and positive sequence current will still exist in the instantaneous active and reactive powers. As a result, Ps2 and Qs2 should be injected into active and reactive power references to make Ps1 and Qs1 null. Consequently, active and reactive power compensations can be obtained as 

Pcom p = − 23 (usα − isα + + usβ − isβ + ) Qcom p = − 32 (usβ − isα + − usα − isβ + ) .

(24)

Only positive sequence stator current components are required in the power compensation calculations, obviously. Target II: To remove stator reactive power ripples. This control target is to allow the existence of negative sequence current components but eliminate the stator output reactive power ripples. In order to obtain constant reactive power, the reactive power reference must be kept constant, thus the reactive power ripples Qs1 + Qs2 must be zero. As been analyzed in Section III-A, neither reactive power ripples Qs1 + Qs2 nor active power ripples Ps1 + Ps2 can be zero simultaneously, thus the oscillating component Ps1 + Ps2 must be contained in the active power, when reactive power ripples Qs1 + Qs2 are zero. Consequently, the active power ripples Ps1 + Ps2 must be injected into the active power reference as active power compensation. Therefore, the active and reactive power compensations can be obtained as ⎧ 3 ⎪ ⎨ Pcom p = − 2 (usα − isα + + usβ − isβ + (25) + usα + isα − + usβ + isβ − ) ⎪ ⎩ Qcom p = 0. Target III: To cancel stator active power oscillations. This control target is to allow the existence of negative sequence current components but to eliminate the stator output active power oscillations. The reactive power ripples Qs1 + Qs2 cannot be eliminated when active power ripples Ps1 + Ps2 are kept at zero. Thus, oscillating components must exist in the reactive power. As a consequence, the reactive power ripples Qs1 + Qs2 are injected into reactive power reference as reactive power compensation. The active and reactive power compensations can be obtained as ⎧ ⎪ ⎨ Pcom p = 0 (26) Qcom p = − 32 (usβ + isα − − usα + isβ − ⎪ ⎩ + usβ − isα + − usα − isβ + ) . C. Standard SMC–DPC The details of the standard sliding mode control (SMC) DPC for DFIG generation systems have been presented in [19], so only a brief description is given here. For comparison, the SMC– DPC strategy without negative-sequence voltage considered is identified as the standard SMC–DPC in this paper. According to the theory of SMC, the errors of stator output active and reactive powers are selected as sliding surface  S1 = Perror (t) = Ps∗ − Ps (t) (27) S2 = Qerror (t) = Q∗s − Qs (t). When the trajectories of active and reactive powers of system coincides with the sliding surface,  1 S1 = dS dt = 0 (28) 2 S2 = dS dt = 0. Combining (13) with (27) and (28) yields dS = F + DV r dt

(29)

SHANG AND HU: SLIDING-MODE-BASED DIRECT POWER CONTROL OF GRID-CONNECTED WIND-TURBINE-DRIVEN DFIGs

where

 F =

F1

=

F2 + −



3Rr 2σLm

Lr σ L 2m



−usα usβ 3ωr Lr 2σL2m −usα −usβ   −usα −usβ ir α −usβ Rs

usα 

−ωsilp

Ps

ψ sα

Thus, Ps1 (3 (usα + isα − + usβ + isβ − ) /2) can be replaced by Ps2 (3 (usα − isα + + usβ − isβ + ) /2) in (25). Obviously, in Ps2 there are no positive sequence voltage and negative sequence current components, which do not need to be extracted. Similarly, Qs1 can also be replaced by Qs2 in Target III. Besides, as shown in (24), there are only negative sequence voltage and positive sequence current in the power compensations of Target I. As to Target II, Ps1 = Ps2 , thus



ψ sβ

ir β

Lr σ L 2m

Qs ωsilp Rs  2 3ωr Lr usα + u2sβ − 2σL2m 0  usβ T usα 3 D= 2σLm usβ −usα T  V r = v r α vr β . The following control law is selected   vr α F1 + K11 S1 + K12 sat(S1 ) −1 = −D vr β F2 + K21 S2 + K22 sat(S2 )

usα + isα − + usβ + isβ − = usα − isα + + usβ − isβ + .

Te1 + Te2 = −

(30)

λi is the width of boundary layer, i denotes 1 or 2. The proofs of stability and robustness are presented in [19].

 As known, the negative sequence current component is relatively smaller compared with the positive sequence current component. This will make the extraction of the negative sequence component less accurate and may deteriorate the performance of control system. Thus, the control method without the need of extracting negative sequence current components is preferred. Taking Target II as an example, viz., Qs1 + Qs2 = 0, we obtain

sin (2ωs t + θu −i+ ) = sin (2ωs t − θu −i− ) .

(32)

(33)

The angular relationship can be obtained as 2ωs t − θu −i− = 2ωs t + θu −i+

(34)

θu −i− = −θu −i+ .

(35)

and

Then, substituting (33) and (35) into (18) yields Ps1 = Ps2 .

(36)



(usα + isα − + usβ + isβ − ) − (usα − isα + + usβ − isβ + )

Pcom p = Ps2 = − 23 (usα − isα + + usβ − isβ + ) Qcom p = Qs2 = − 32 (usβ − isα + − usα − isβ + ) .

= 0.

(39)

Target II: 

Pcom p = 2Ps2 = −3 (usα − isα + + usβ − isβ + ) Qcom p = 0.

(40)

Target III: 

|U s− | |I s+ | sin (2ωs t + θu −i+ )

3 p 2 ωs

(38) Consequently, in Target II, it can be concluded that the ripples of reactive power and electromagnetic torque will be eliminated at the same time. This feature is good for improving the performance of wind-turbine-driven DFIG under unbalanced grid voltage conditions. Based on the results obtained earlier, only the negative sequence voltage and positive sequence current are needed to be extracted for these three selective control targets. As a result, the active and reactive power compensations for the three targets are expressed as (39), (40), and (41), respectively, viz., Target I:

D. Control System

Consequently, the following results are deduced  |U s+ | |I s− | = |U s− | |I s+ |

(37)

According to (37), the oscillation components of electromagnetic torque can be expressed as (38)

where K11 , K12 , K21 , K22 are positive control gains and ⎧ Si > λ i ⎪ ⎨ 1, (31) sat(Si ) = Si /λi , |Si | ≤ λi ⎪ ⎩ −1, Si < −λi

= |U s+ | |I s− | sin (2ωs t − θu −i− ) .

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Pcom p = 0 Qcom p = 2Qs2 = −3 (usβ − isα + − usα − isβ + ) .

(41)

Based on the proposed compensation methods for stator output active and reactive power oscillations, the schematic diagram of DFIGs operating under unbalanced grid voltage conditions is shown in Fig. 3. The notch filter method in [22] has been adopted to extract negative sequence stator voltage and positive sequence stator current. It can be seen from Fig. 3 that the improved SMC–DPC makes no change to the inner-loop structure of the standard SMC–DPC. Both the calculations of the proposed power compensations and the positive/negative extractions are implemented in the outer loop of the power controller. This will not affect the response of inner loop, and be capable of keeping well dynamic responses featured to the SMC–DPC strategy.

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Fig. 3. Schematic diagram of the proposed control system for DFIGs during network voltage unbalance. TABLE I DFIG PARAMETERS Fig. 4.

System configuration of the tested DFIG rig.

Fig. 5.

Unbalanced stator voltage (40 V/div).

IV. EXPERIMENTAL RESULTS A. Experimental System In order to verify the operational performance of the improved SMC–DPC of DFIG with the active and reactive power compensations, experimental studies were carried out on a 2-kW DFIG prototype with 20% unbalanced grid voltage conditions. The unbalanced grid voltage is shown in Fig. 4. In the tests, a sampling frequency of 5 kHz was used for the DPC strategies, which corresponds to 2.5-kHz switching frequency due to that an asymmetric SVM technique was used. The parameters of the designed converter and DFIG are shown in Table I. The experimental platform is basically composed of the elements represented in Fig. 4 schematically. In the wind turbine system, the grid side converter is enabled first, so that the converter dc-link voltage is established. The performance of RSC is only focused on in the paper, so the dc-link voltage is established by dc source, bypassing the GSC, which is represented by dash line in Fig. 4. The RSC is controlled by TI’s TMS320F2812 DSP. Unbalanced stator voltage during the tests was generated using three single-phase variacs shown in Fig. 4, but the method cannot generate transient voltage unbalance [23]. In order to make the ac voltage compatible with the stator voltage, a threephase variac is employed between the generator stator and three single-phase variacs. The unbalanced stator voltage is shown in the Fig. 5. B. Measured Results The experimental studies were carried out on the platform described in Section IV-A. For 1-kW average active power

(export of active power from the DFIG to grid) and 1 kVar reactive power (capacitive) at the speed of 1200 rpm (with synchronous speed of 1500 r/min), experimental results with a 20% voltage unbalance are shown in Fig. 6. Fig. 6(a) shows the results of the standard SMC–DPC [19] without negative voltage considered. Obviously, active and reactive powers are smooth and constant, but the stator output currents are very terrible with serious harmonic distortions. The experimental results using modified SMC–DPC with Target I, Target II, and Target III are shown in Fig. 6(b)–(d), respectively. As shown in Fig. 6(b), there are oscillating components in both active and reactive powers, but the stator current are quite sinusoidal and symmetrical. In Fig. 6(c), there are only ripples in the active power, but the reactive power is smooth and constant, and the stator currents are sinusoidal but asymmetrical. It can be seen from Fig. 6(d) that the ripples of active power are eliminated, but the oscillations still exist in the reactive power, and the stator current are also sinusoidal but asymmetrical. It can be concluded from these results that the proposed power compensation methods are capable of accomplishing the three selective control targets, respectively.

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Fig. 6. Measured results with steady-state operations under 20% unbalanced voltage conditions.  1 Electromagnetic torque (7.96 N·m/div).  2– 4 Three phase rotor currents (5 A/div).  5 Active power (1 kW/div).  6 Reactive power (1 kVar/div).  7– 9 Three phase stator currents (2 A/div). (a) Standard SMC–DPC without unbalance considered [19], (b) Target I, (c) Target II, and (d) Target III.

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Fig. 7. Measured current spectra of phase A with different control targets under 20% unbalanced voltage condition. (a) Standard SMC–DPC, (b) Target I, (c) Target II, and (d) Target III.

In addition, the ripples of electromagnetic torque and reactive power can be canceled together as shown in Fig. 6(c), which is in well accordance with the analytical results of Section III-D. It is important for wind-turbine-driven DFIG to eliminate the ripples of electromagnetic torque during network unbalance. The spectra of phase-A stator current are shown in Fig. 7(a)–(d) with different control targets when the stator voltage is 20% unbalanced. In Fig. 7(a), the stator current of standard SMC–DPC without any power compensations is very bad with prominent odd-order harmonic components, especially third order and fifth order harmonics, which is in well accordance with the analytical results of Section III-A. This can be permitted in some special situations, but is not suitable for grid-connected wind farms due to the requirement of the harmonic standard IEEE519-1992 [21]. The stator currents by using the improved SMC–DPC with three different control targets, as shown in Fig. 7(b)–(d), are all sinusoidal with few low-order harmonics. It is obvious that the modified SMC–DPC with power compensations has improved the performance of DFIG when the unbalanced supply faults occur. For clear illustrations, Fig. 8 shows the comparative results of ripples pulsating twice the grid frequency in the stator active/reactive powers and electromagnetic torque among four different control targets during network unbalance. The ripples are measured with their peak-to-peak values and normalized to their respective rated values. As shown, Target I, which aims at maintaining stator current sinusoidal and symmetrical, alleviates

Fig. 8. Comparisons of ripples in stator active/reactive powers and electromagnetic torque among different control targets.

the torque pulsations but increases the power ripples compared with the standard method. Besides, the other two control targets can effectively depress the pulsations in the reactive power and torque, and active power, respectively. It can be concluded among these targets that the proposed Target II effectively reducing the torque oscillations to a reasonable level, may be preferred by wind farm operators due to that the fatigues on the turbine shaft as well as the gear-box set are decreased when the network voltage is unbalanced. With the same unbalanced voltage conditions, the transient responses of active power, reactive power, and stator current are shown in Fig. 9 at the speed of 1200 r/min. The results of three control targets were shown in the Fig. 9, when the active power is stepped from 0 to 1 kW (export of active power from the DFIG to grid) and the reactive power is maintained zero (unity power factor). From Fig. 9, it can be seen that the modified SMC–DPC

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Fig. 9. Measured results with active power steps under stator voltage unbalance of 20%.  1 Electromagnetic torque (7.96 N·m/div).  2– 4 Three phase rotor currents (5 A/div).  5 Active power (1 kW/div).  6 Reactive power (1 kVar/div).  7– 9 Three phase stator currents (2 A/div).  7– 9 three phase stator current (2 A/div). (a) Standard SMC-DPC, (b) Target I, (c) Target II, and (d) Target III.

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with the active and reactive powers compensation method can obtain the same dynamic response as the standard SMC–DPC during various active and reactive power steps. The investigation on the control bandwidth of SMC–DPC has been implemented with the method proposed in [25] and the bandwidth of SMC–DPC is measured at around 500 Hz. The experimental tests with other various power combinations and different generator speeds were also conducted, the measured results behaved similarly to these shown in Figs. 6–9, which is not provided here due to space limitations. V. CONCLUSION An improved SMC–DPC strategy for grid-connected windturbine-driven DFIGs under unbalanced network voltage conditions has been demonstrated in this paper. The method does not require decoupling positive- and negative-sequence components of stator voltage, current, and rotor current in the inner control loop, which can improve the transient performance of the generation system. The new active and reactive power compensation method has been combined with the standard SMC–DPC to achieve three selective control targets proposed, viz., obtaining sinusoidal and symmetrical stator current, removing reactive power ripples and canceling active power oscillations. Among them, the electromagnetic torque pulsations can also be removed together with those in stator reactive power, which will reduce the fatigue of the turbine shaft. The active and reactive power compensation method can provide precise control without involving the decomposition of positive sequence grid voltage and negative sequence stator current. The nature of deteriorated performance by using the standard SMC–DPC without considering grid voltage unbalance has been analyzed when the network is unbalanced. To validate the proposed control strategies and analytical results, experimental results on a DFIG test rig have been presented, demonstrating that the modified SMC–DPC can provide pretty well steady-state and transient performance under unbalanced network conditions. REFERENCES [1] M. Liserre, R. Cardenas, M. Molinas, and J. Rodriguez, “Overview of multi-MW wind turbines and wind parks,” IEEE Trans. Ind. Electron., vol. 58, no. 4, pp. 1081–1095, Apr. 2011. [2] 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. 26–33, May/Jun. 2002. [3] A. Petersson, L. Harnefors, and T. Thiringer, “Evaluation of current control methods for wind turbines using doubly-fed induction machines,” IEEE Trans. Power Electron., vol. 20, no. 1, pp. 227–235, Jan. 2005. [4] J. Hu and Y. He, “Dynamic modeling and robust current control of windturbine used DFIG during AC voltage dip,” J. Zhejiang Univ. Sci. A, vol. 7, no. 10, pp. 1757–1764, Oct. 2006. [5] 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,” in Proc. IEE B Electr. Power Appl., May 1996, vol. 143, no. 3, pp. 231–241.

[6] R. Datta and V. T. Ranganathan, “Direct power control of grid-connected wound rotor induction machine without rotor position sensors,” IEEE Trans. Power Electron., vol. 16, no. 3, p. 390-399, May 2001. [7] L. Xu and P. Cartwright, “Direct active and reactive power control of DFIG for wind energy generation,” IEEE Trans. Energy Convers., vol. 21, no. 3, pp. 750–758, Sep. 2006. [8] G. Abad, M. A. Rodriguez, and J. Poza, “Two-level VSC-based predictive direct power control of the doubly fed induction machine with reduced power ripple at low constant switching frequency,” IEEE Trans. Energy Convers., vol. 23, no. 2, pp. 570–580, Jun. 2008. [9] G. Abad, M. A. Rodriguez, and J. Poza, “Two-level VSC based predictive direct torque control of the doubly fed induction machine with reduced torque and flux ripples at low constant switching frequency,” IEEE Trans. Power Electron., vol. 23, no. 3, pp. 1050–1061, May 2008. [10] D. Zhi and L. Xu, “Direct power control of DFIG with constant switching frequency and improved transient performance,” IEEE Trans. Energy Convers., vol. 22, no. 1, pp. 110–118, Mar. 2007. [11] M. Depenbrock, “Direct self-control (DSC) of inverter-fed induction machine,” IEEE Trans. Power Electron., vol. 3, no. 4, pp. 420–429, Oct. 1988. [12] Y. S. Lai and J. H. Chen, “A new approach to direct torque control of induction motor drives for constant inverter switching frequency and torque ripple reduction,” IEEE Trans. Energy Convers., vol. 16, no. 3, pp. 220– 227, Sep. 2001. [13] Y. S. Lai and J. H. Chen, “A new approach to direct torque control of induction motor drives for constant inverter switching frequency and torque ripple reduction,” IEEE Trans. Energy Convers., vol. 16, no. 3, pp. 220– 227, Sep. 2001. [14] L. Xu and Y. Wang, “Dynamic modeling and control of DFIG-based wind turbines under unbalanced network conditions,” IEEE Trans. Power system, vol. 22, no. 1, pp. 314–323, Feb. 2007. [15] J. Hu, Y. He, and L. Xu, “Improved rotor current control of wind turbine driven doubly fed induction generators during network voltage unbalance,” Electr. Power Syst. Res., vol. 80, no. 7, pp. 847–856, Jul. 2010. [16] J. Hu and Y. He, “DFIG wind generation systems operating with limited converter rating considered under unbalanced network conditions— Analysis and control design,” Renewable Energy, vol. 36, no. 2, pp. 829– 847, Feb. 2011. [17] D. Santos-Martin, J. L. Rodriguez-Amenedo, and S. Arnaltes, “Direct power control applied to doubly fed induction generator under unbalanced grid voltage conditions,” IEEE Trans. Power Electron., vol. 23, no. 5, pp. 2328–2336, Sep. 2008. [18] D. Santos-Martin, J. L. Rodriguez-Amenedo, and S. Arnaltes, “Providing ride-through capability to a doubly fed induction generator under unbalanced voltage dips,” IEEE Trans. Power Electron., vol. 24, no. 7, pp. 1747–1757, Jul. 2009. [19] G. Abad, M. A. Rodriguez, G. Iwanski, and J. Poza, “Direct power control of doubly fed induction generator based wind turbines under unbalanced grid voltage,” IEEE Trans. Power Electron., vol. 25, no. 2, pp. 442–452, Feb. 2010. [20] J. Hu, H. Nian, B. Hu, Y. He, and Z. Q. Zhu, “Direct active and reactive power regulation of DFIG using sliding mode control approach,” IEEE Trans. Energy Convers., vol. 25, no. 4, pp. 1028–1039, Dec. 2010. [21] J. Hu, L. Shang, Y. He, and Z. Q. Zhu, “Direct active and reactive power regulation of grid-connected DC–AC converters using sliding mode control approach,” IEEE Trans. Power Electron., vol. 26, no. 1, pp. 210–222, Jan. 2011. [22] IEEE Recommended Practices and Requirements for Harmonic Control in Electrical Power Systems, IEEE Std 519-1992, IEEE Industry Application Society, 2003. [23] G. Saccomando and J. Svensson, “Transient operation of grid-connected voltage source converter under unbalanced voltage conditions,” in Proc. IEEE 36th Ind. Appl. Conf. (IAS), Aug., 2002, vol. 4, no. 5, pp. 2419–2424. [24] J. Hu, Y. He, L. Xu, and D. Zhi, “Predictive current control of gridconnected voltage source converters during network unbalance,” IET Power Electron., vol. 3, no. 5, pp. 690–701, Aug. 2010. [25] E. Jung, H. Lee, and S. K. Sul, “FPGA-based motion controller with a high bandwidth current regulator,” in Proc. IEEE Power Electron. Specialists Conf. (PESC), 15–19 Jun., 2008, pp. 3043–3047.

SHANG AND HU: SLIDING-MODE-BASED DIRECT POWER CONTROL OF GRID-CONNECTED WIND-TURBINE-DRIVEN DFIGs

Lei Shang was born in Haicheng, Liaoning Province, China. He received the B.Sc. and M.Eng. degrees from the College of Automation, Nanjing University of Posts and Telecommunications, Nanjing, China, and the College of Electrical Engineering, Zhejiang University, Hangzhou, China, in 2008 and 2011, respectively. He is currently at Nari-Relays Electric Company, Ltd., Nanjing, China. His research interests include digital control and application of power converters in renewable energy conversion, especially the control and operation of doubly fed induction generator (DFIG) for wind-power generation using direct power control (DPC).

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Jiabing Hu (S’05–M’10) received the B.Sc. and Ph.D. degrees in College of Electrical Engineering, Zhejiang University, Hangzhou, China, in July 2004 and September 2009, respectively. From 2007 to 2008, he was a Visiting Scholar in the Department of Electronic and Electrical Engineering, University of Strathclyde, Glasgow, U.K. From April 2010 to August 2011, he was a Postdoctoral Research Associate in Sheffield Siemens Wind Power (S2WP) Research Center and the Department of Electronic and Electrical Engineering, University of Sheffield, Sheffield, U.K. Since September 2011, he has been a Professor at the College of Electrical and Electronic Engineering (CEEE), Huazhong University of Science and Technology (HUST), Wuhan, China. His current research interests include ac motor drives and the application of power electronics in renewable energy conversion, especially the control and grid integration of large-scale wind turbines based on doubly fed induction generator (DFIG) and synchronous generators with either permanent magnet (PMSG) or electrically excited (EESG).