###### Abstract  
This paper presents a novel analytical method (NAM) of inductance identification for a direct drive permanent magnet synchronous motor (DDPMSM) with a stator winding fault (SWF), which considers the spatial position of the shorted turns. First, the structure of the DDPMSM is introduced and its key parameters are reported. Second, the NAM on the inductance identification is elaborated. The inductance analytical expressions of the faulty coil are derived in detail, in which the inductances of the faulty coil and the fault branch can be quickly calculated according to the spatial position coordinates of fault turns. Then, the model of DDPMSM with SWF is established. Finally, using the NAM, finite-element method (FEM), and the simplified analytical method (SAM), the inductances of the faulty coil and the branch are calculated under different fault conditions. Additionally, the fault current of the faulty coil is also studied, where the value of the fault current reflects the fault severity. The comparisons among the FEM, NAM, and SAM show that the accuracy of the NAM is higher than that of the SAM.  
direct drive permanent magnet synchronous motor; stator winding fault; inductance identification; spatial position; analytical method, fault current +
Footnote †: journal: Applied Soft-stator winding faults need be established by the MLM, which is not universal. Based on the principle of the equivalent flux tube, the complex magnetic field in the motor is converted into an impedance network by the EMNM [7]. Then, the corresponding inductance parameters are obtained by calculating the equivalent permeability and flux of each circuit. This method can reflect the essence of the motor, but its calculation process is tedious [8]. The WFM provides an effective method to estimate inductance from windings and air gap data, in which the magnetomotive force and gap permeability of the motor are determined by the winding structure [9; 10]. However, WFT is suitable for a motor with small air gap width. It is difficult to provide accurate results for a motor with a large air-gap width, for example, the DDPMSM. All the methods mentioned above have the same shortcoming in that they cannot evaluate motor performances under the inter-turn short circuit fault (ITSCF) in different positions of the same slot. The FEM considers the influence of spatial harmonics, winding configurations, core saturation, and so on, which can accurately calculate the inductance of the motor in any fault condition. However, this method needs to perform a new simulation for every fault configuration and requires too much CPU time [11; 12]. In addition, it is also not very appropriate for parametric studies. Therefore, a novel analytical method (NAM) of inductance identification is proposed herein, which considers the spatial position of shorted turns in the stator winding fault (SWF).  
The remainder of the paper is organized as follows: The structure and some main parameters are introduced in the Section 2. In Section 3, the inductance analytical expressions of the faulty coil are derived in detail, in which the spatial position of the shorted turns in the ITSCF is considered. Then, the model of the DDPMSM with SWF is established in Section 4. In the Section 5, to verify the theoretical investigations on the inductance calculations, the inductances of the faulty coil and the branch calculated by the NAM are compared with those obtained by the FEM and simplified analytical method (SAM) for the same motor. Moreover, the fault current is also studied in this section. Finally, Section 6 presents a brief summary of this paper.