## 1 Introduction  
Due to the high power density and efficiency, permanent magnet synchronous generator based wind turbines are promising in wind conversion systems (WECSs) with variable speed operation and full-scale power delivery [1; 2]. To fulfill control demands for maximum power point tracking (MPPT) and grid codes, closed-loop feedback control is designed, relying on the mechanical, current and voltage measurements. Any inaccurate measurements caused by sensor faults will cause the controller malfunction and performance degradation. According to industrial and field statistics [3; 4; 5], current sensor faults are a type of major faults resulting from the electromagnetic interference and high power density, which causes system shutdown and fragile components. Fault diagnosis and isolation (FDI) schemes enable the control system to locate fault sensors and to compensate the fault further. For power converter systems, various diagnostic techniques are presented to handle current sensor FDI problems, including observer based, signal processing based and data-driven based methods. Model based diagnostic techniques are discussed most for power converter systems. A parallel observers based method is presented in [6] to diagnose stator and rotor current sensor faults in doubly fed induction generator (DFIG) system, but it requiresopen-loop operation while detecting the sensor fault. Similarly, a sensor FDI in [7] that a bank of observers are designed to generate residuals sensitive to sensor fault for DFIG based WECSs also requires open-loop operation until the fault is isolated. In [8], a geometric approach is presented to detect and isolate multiple sensor faults in induction motor (IM) drives. By utilizing the redundant properties of three-phase currents, two stationary frame based state space models are established to generate distinguished residuals sensitive to phase a and phase b sensor faults. In [9], the nonlinear model of DFIG is transformed into a Takagi-Sugeno (T-S) fuzzy model and a bank of observers based on the model are presented to generate residuals for sensor fault detection and isolation. To deal with both additive and multiplicative sensor faults, a generalized observer scheme is presented in [10] by combining \(\mathcal{H}\_/\mathcal{H}_{\infty}\) filter with Kalman-like observer for DFIG systems. Aforementioned schemes are presented for sensor FDI in IM drives while only a few model based sensor FDIs are proposed for permanent magnet synchronous motor (PMSM) and permanent magnet synchronous generator (PMSG) systems. In [11], a two-stage extended Kalman filter (EKF) and adaptive observer is presented to generate mechanical estimations for speed and rotor position sensor fault diagnosis. An adaptive EKF for position sensor fault diagnosis and tolerant scheme is presented in [12] for PMSM drive in electric vehicle (EV). In [13], a high-order sliding model based observer is proposed to detect and estimate rotor speed sensor fault in PMSM based EV. The authors later present a bank of observers based scheme for multiple sensor FDI [14]. However, it requires additional voltage sensors to establish the fault observers. In [15], an EKF based FDI is presented for the diagnosis of sensor fault in PMSM drives, but it can only isolate single sensor faults and does not additionally discuss about the influence of unknown disturbances on FDI performance. Furthermore, in [2], to diagnose additive and multiplicative faults for PMSG based WECSs, a two-stage model based method is proposed, in which time-varying Kalman filter (TVKF) and maximum-shift method are designed to generate robust residuals and evaluate these residuals. According to the state-of-the-art analysis, model based FDI methods are rarely reported for simultaneous multiple current sensor FDI for PMSM and PMSG based applications. Nevertheless, current sensor FDI is necessary for control system in power converters to provide further information for fault tolerant control [2; 8].