Journal of Electrical and Computer Engineering

Volume 2015, Article ID 168786, 9 pages

http://dx.doi.org/10.1155/2015/168786

## Modeling and Fault Diagnosis of Interturn Short Circuit for Five-Phase Permanent Magnet Synchronous Motor

School of Automation, Northwestern Polytechnical University, Xi’an 710072, China

Received 1 June 2015; Revised 28 August 2015; Accepted 15 September 2015

Academic Editor: Ahmed F. Zobaa

Copyright © 2015 Jian-wei Yang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Taking advantage of the high reliability, multiphase permanent magnet synchronous motors (PMSMs), such as five-phase PMSM and six-phase PMSM, are widely used in fault-tolerant control applications. And one of the important fault-tolerant control problems is fault diagnosis. In most existing literatures, the fault diagnosis problem focuses on the three-phase PMSM. In this paper, compared to the most existing fault diagnosis approaches, a fault diagnosis method for Interturn short circuit (ITSC) fault of five-phase PMSM based on the trust region algorithm is presented. This paper has two contributions. (1) Analyzing the physical parameters of the motor, such as resistances and inductances, a novel mathematic model for ITSC fault of five-phase PMSM is established. (2) Introducing an object function related to the Interturn short circuit ratio, the fault parameters identification problem is reformulated as the extreme seeking problem. A trust region algorithm based parameter estimation method is proposed for tracking the actual Interturn short circuit ratio. The simulation and experimental results have validated the effectiveness of the proposed parameter estimation method.

#### 1. Introduction

Owing to high torque-to-current ratio, large power-to-weight ratio, high efficiency, high-power factor, high fault tolerance, robustness, and so forth, multiphase PMSMs have been paid more attention in high-power and high-reliability applications [1–3]. Compared with the traditional three-phase PMSM, with the added phase number, the fault tolerance of the multiphase PMSM is enhanced, and thus the reliability of the multiphase PMSM is improved. Therefore, multiphase PMSMs are widely used in fault-tolerant control systems [4, 5].

Fault diagnosis is the foundation of the fault-tolerant control of the electrical machines. In PMSMs, the usual faults include electrical faults, mechanical faults, and magnetic faults [6]. In electrical faults, short circuit faults form 21% of the faults occurring in electrical machines. The stator winding ITSC fault is the commonest short circuit fault in PMSMs. It always occurs due to insulation failures but develops into more serious faults very quickly [7]. So it is meaningful to research the effective fault diagnosis methods of stator winding interturn short circuit for PMSMs.

The current existing detection and diagnosis methods of ITSC fault can be commonly divided into off-line methods and on-line methods [8]. Compared to the off-line methods, in on-line methods, the PMSMs do not have to be taken out of service and predicting health condition and detecting faults at an incipient stage are made easier [9]. In recent years, with the application of neural network, fuzzy logic and particle swarm optimization (PSO), the artificial intelligence (AI) on-line fault detection, and diagnosis methods have drawn the attention of many authors [10]. The AI methods improve the robustness and efficiency of the fault diagnosis and have no need to interpret the collected data in relation to the occurring fault.

In some AI fault detection and diagnosis methods, such as literature [11], in order to detect and diagnose the severity of the stator winding interturn short circuit fault of PMSM, a mathematical model that can describe both healthy and fault conditions is needed first. Literature [12] built power losses model of five-phase PMSM with ITSC fault and analyzed the changes in power losses due to faults occurrence by finite elements simulations. However, this fault model is not suitable for AI fault diagnosis based on parameter optimization. Literature [13] and literature [14] proposed two mathematical models of PMSM with ITSC fault for fault diagnosis. Unfortunately, these models are all about three-phase PMSM and relatively complex. If the fault model of five-phase PMSM was built by the way shown in literature [13] and literature [14], the model would be more complex, and the calculation for the subsequent fault diagnosis based on parameter optimization would increase greatly. Thus, the efficiency of fault diagnosis would be affected. Therefore, it is meaningful to establish a relatively simple five-phase PMSM model with ITSC fault for fault diagnosis.

After the establishment of the fault model, in order to diagnose fault severity of the fault motor, the parameters associated with fault severity need to be identified. However, for the complex distribution of the parameters in the fault model, the identification problem is extremely difficult for nonlinear identification techniques. To overcome this difficulty, the fault diagnosis problem is transformed into a corresponding optimization problem and then solved by intelligent algorithm [15]. In recent years, many authors focus on PSO parameter optimization to deal with this problem, such as that shown in literature [16] and literature [17]. PSO is an evolution computation technique based on swarm intelligent methodology. PSO is initialized as a swarm of arbitrary particles (arbitrary solution), and then the optimal solution is discovered by iteration. However, the PSO algorithm creates the problems of partial convergence and precocious convergence when the particles’ diversity is decreasing. Therefore, finding a better parameter optimization algorithm for five-phase PMSM fault diagnosis is essential.

In this paper, relatively simple mathematics models of the five-phase PMSM under both healthy and ITSC fault situations are established, respectively. Furthermore, a novel fault diagnosis method of ITSC based on the trust region algorithm is proposed for five-phase PMSM. With the aid of the trust region algorithm which is global convergence, the interturn short circuit ratio is estimated with a short time transient. The simulation and experimental results have validated both the correction of the established models and the effectiveness of the proposed parameter estimation method.

#### 2. Model Analysis

##### 2.1. Five-Phase PMSM Healthy Model

In order to establish the healthy model of five-phase PMSM, without loss of generality, the following assumptions are as follows:(1)The magnetic circuit is linear. It is, in turn, that the magnetic circuit is not saturation.(2)The stator winding current is sinusoidal, symmetrical, and without harmonics. The air gap magneto motive force (MMF) is sinusoidal.(3)The rotor MMF is sinusoidal and the slot effect is neglected.(4)The five-phase PMSM is nonsalient pole structure.(5)Eddy currents and hysteresis losses are negligible.

With these assumptions, the five-phase PMSM model can be provided by

Equation (1) is the voltage balance equation, (2) is the flux equation, and (3) is the torque equation, where the stator phase voltage vector ; the stator phase current vector ; the stator winding resistance ; the stator flux vector ; the rotor flux vector ( is the rotor electrical angle and ); is the stator inductance matrix; is the differential operator; is the number of pole pairs; and is the electromagnetic torque.

Because of adding two-phase windings, compared to traditional PMSM, the stator inductance matrix of five-phase PMSM is more complex and it can be represented bywhere is the self-inductance of phase winding A (B, C, D, and E) and is the mutual- inductance between phase windings A and B (C, D, and E). Actually, the mutual-inductances can be expressed by , , , and .

##### 2.2. Five-Phase PMSM Fault Model

Without loss of generality, assume that phase winding A causes ITSC fault and the rest of the phase windings is in healthy state. The five-phase PMSM with ITSC is shown in Figure 1. Note that a short circuit loop current , which gives birth to braking torque, is produced in phase winding A. And thus the braking torque affects the motor performance seriously. Besides, the effective turns number of phase winding A is reduced, and the values of the phase winding resistance, the self-inductance, the mutual-inductance, and the flux linkage are all changed accordingly.