# Fault Detection of Stator Inter-Turn Short-Circuit in PMSM on Stator Current and Vibration Signal
## 2 Materials and Methods
\tag{5}\]  
\[\widetilde{x}(n)=\frac{1}{N_{j}}\sum\limits_{n=0}^{N_{j}-1}X(k)W^{-kn} \tag{6}\]  
The formula of operator D is:  
\[\left\{ \begin{array}{ll}X(k)=\sum\limits_{n=0}^{N_{j}-1}x(n)W^{kn}&,\frac{N_ {j}}{4}\leq\frac{3N_{j}}{4}\\ X(k)=0&,\text{else}\end{array} \right. \tag{7}\]  
\[\widetilde{x}(n)=\frac{1}{N_{j}}\sum\limits_{n=0}^{N_{j}-1}X(k)W^{-kn} \tag{8}\]  
where \(x(n)\) is the wavelet packet coefficients of low frequency subbands on \(2^{j}\) scale, \(N_{j}\) is the data length, \(k\) = 0, 1,..., \(N_{j-1}\), and \(n\) = 0, 1,..., \(N_{j-1}\). The experimental platform structure diagram is shown in Figure 2. It consists of a three-phase permanent magnet synchronous motor, NI Data acquisition card (DAQ card), current sensors and a vibration sensor. The data collected by the sensors were uploaded to a computer with LabVIEW installed by DAQ card for processing and analysis. The experimental platform can be divided into hardware part and software part. The hardware of the experimental platform for PMSM fault detection is shown in Figure 3.  
Figure 2: The structure of experimental platform. Two permanent magnet low speed synchronous motors were used in the experiment. One is a normal motor and the other is a motor that is artificially placed with a 15% inter-turn fault in the stator. The motor is shown in Figure 4. This PMSM has 13 poles and 12 stator slots; its rated frequency is 50 Hz; and its rated power is 95 W.  
The stator current of these motors was collected by current sensors, which were produced by TAMURA Corporation in Tokyo, Japan in 2018. The measuring range of the sensor is 0-3 A, and the output voltage is 0-4 V. This current sensor can convert the current signals into voltage signals, which are easy for the computer to process. The vibration signal was collected by piezoelectric accelerometer, whose voltage sensitivity is 100 mV/g, frequency response range is 0.5-6000 Hz and maximum output signal is 6 V. The sensor was attached radially to the housing of the motor. A signal conditioner, YE3832, was used to condition the sensor output and send it to the computer. Both the vibration sentor and the signal conditioner were produced by Wuxi Shiao Technology Co., Ltd in Wuxi, China in 2018. Data acquisition card was installed in the computer and connected to a junction box, to facilitate the data input from the sensors. Both they were produced by National Instruments (NI) in Austin, Texas, U.S. in 2017. As for the software, LabVIEW 2017 is a program development platform developed by NI in Austin, Texas, U.S. in 2017. It has become a versatile tool with a straightforward block diagram language. In this study, LabVIEW was used to implement signal analysis algorithms, monitor the collected data, and design time-frequency transform program. Figure 4: The 90 TDY115-2B permanent magnet low speed synchronous motor. Figure 3: The experimental platform for PMSM fault detection. The fault detection system built on LabVIEW is shown in Figure 5. Data acquisition channels and sampling parameters are set on the left side of the system, and the waveform and processing results of the signal are displayed on the right side. The results of time domain analysis, frequency domain analysis, and wavelet analysis are all displayed in different modules. The improved wavelet packet algorithm was imported using the MathScript node in LabVIEW, as shown in Figure 6. The signal is decomposed, reconstructed and transformed by wavelet packet.