## 1 Introduction  
Recently, the growing capacity of the wind power generation system has led to increasing concerns about the output power quality, and operating reliability to satisfy the demand of accessing the network [1; 2]. The most widely used wind power generation system is the doubly fed induction generator (DFIG) based wind power system, in which stator windings are directly connected to the grid. Thus, the grid conditions will affect the operational performance of the DFIG system directly. According to the standard EN50160 [3], grid voltage supply may suffer from harmonics and little imbalances even during normal operation. Such disturbances may be even more frequent in remote regions, where wind power generation systems are usually located [4]. Many reports have indicated that unbalanced and harmonic grid voltages will introduce the harmonic components in the stator, rotor and grid side converter current, which finally leads to the distortion of the system's total currents and pulsations of the DFIG's electromagnetic torque [5; 6]. Thus, the unbalanced and harmonic grid voltage disturbance have to be considered in the control of the DFIG system. Up to now, many improved control strategies have been proposed under unbalanced and harmonic grid voltage conditions [7; 8; 9; 10; 11]. The most popular of them were PIR-based (proportional-integral-resonant controller,) vector control (VC). The PIR controller is comprised of the PI controller and the resonance controller, which can provide sufficiently steady-state tracking precision for corresponding AC commanded values. However, since the parameters of the controller have to be carefully tuned to provide adequate gain for both the DC component and the AC component in the synchronous reference frame, the performance of vector control depends on the accuracy of DFIG system parameters. Another drawback of PIR-based vector control is that the system stability is sensitive to system parameters [12; 13]. Thus, the performance degrades when the actual machine parameters depart from the values used in the control system. Sliding mode control (SMC), due to its insensitivity to parameter variations and disturbances [14], has been considered to be another available method in DFIG control [15; 16; 17; 18]. In [15; 16; 17; 18; 19], the SMC strategy was introduced for optimum power curve tracking, grid synchronization or power control of the DFIG system. It can be concluded that the SMC strategy can successfully deal with the random nature of wind speed, model uncertainties and external perturbations. Furthermore, in [20; 21; 22; 23], SMC strategies were adapted under less than ideal grid voltage conditions. In order to remove the pulsations of the DFIG's torque and stator active/reactive power with unbalanced grid voltage, reference [21] proposed the integral sliding mode direct torque control (ISMC-DTC). This control strategy required two controllers: (1) the integral sliding mode controller (ISMC), which could regulate the positive-sequence of torque and reactive power; (2) the integral controller, which could regulate the negative-sequence of torque and reactive power. Reference [22] proposed an ISMC-based DPC strategy for a DFIG system under unbalanced grid voltage conditions, in which both the average power and compensation power pulsating at the frequency of \(2\omega\) could be regulated by ISMC. Finally, three selective control targets, viz., sinusoidal and symmetrical stator current, steady reactive power and steady active power, and removing the electromagnetic torque pulsations can be achieved. Reference [23] proposed the ISMC-based DPC under both unbalanced and harmonically distorted grid voltage conditions, in which the pulsations of active power and reactive power were suppressed. However, the variable switching frequency in [23] may inject broadband harmonics into the grid, and complicate the design of the AC filter.