# Three-Phase Unbalance Analysis Method Based on Three-Phase Motor Current Instantaneous Information
## 3 Simulation Analysis and Experimental Verification
### Simulation and Analysis of Three-Phase Unbalance with Continuous Change in Amplitude  
This subsection simulates the unbalance of the continuous change in amplitude, and the simulation signal is shown in Equations (13) and (14). The three-phase current amplitude is 0.5 A, the signal fundamental frequency is 50 Hz, the U-phase, V-phase, and W-phase are \(2\pi/3\), 0, and \(-2\pi/3\), respectively, \(A_{t}\) changes with time linearly from 1.1 to 1.3, and the sampling frequency is 20 kHz. \[\left\{ \begin{array}{l}I_{u}=a\cdot\cos(2\pi f_{M}t+\theta_{u})\cdot A_{t}\\ I_{v}=a\cdot\cos(2\pi f_{M}t+\theta_{v})\\ I_{w}=a\cdot\cos(2\pi f_{M}t+\theta_{w})\end{array} \right. \tag{13}\]  
\[A_{t}=g+h\cdot t \tag{14}\]  
Figure 8: Analysis of symmetrical components method coefficient changes: (**a**) symmetrical components method coefficient changes corresponding to different amplitudes deviations; (**b**) symmetrical components method coefficient changes corresponding to different phase deviations. where \(a\) is the signal amplitude, \(f_{M}\) is the signal fundamental frequency, \(\theta\) is the signal phase, \(I_{u}\), \(I_{v}\), and \(I_{w}\) are the U-phase, V-phase, and W-phase current signals, respectively, and \(\theta_{u}\), \(\theta_{v}\), and \(\theta_{w}\) are the U-phase, V-phase, and W-phase current phases, respectively; \(A_{t}\) is the amplitude time-varying signal, \(g\) is constant, and \(h\) is the rate of change. The three-phase unbalanced current signal with a continuous change in amplitude is slid, and the sliding window sizes are 100 ms and 50 ms, respectively, as shown in Figure 9.  
The coefficient of variation results for instantaneous frequencies and instantaneous amplitudes under different sliding window sizes are shown in Figures 10 and 11. As can be seen from Figures 10 and 11, for the unbalanced signal with a continuous change in amplitude, the coefficient of variation value of the instantaneous information  
Figure 11: Analysis of three-phase unbalance with continuous amplitude variation using the method of this paper when the sliding window size is 50 ms: (**a**) the C.V. of the instantaneous frequency; and (**b**) the C.V. of the instantaneous amplitude. Figure 9: Different sliding window sizes for three-phase unbalanced current signals with continuous changes in amplitude: (**a**) the sliding window size is 100 ms; (**b**) the sliding window size is 50 ms.  
increases as the unbalance increases. When reducing the sliding window size, the proposed method can still characterize the change in the unbalance. For the symmetrical components method, three-phase unbalance is analyzed as shown in Figure 12a. The results are not accurate when the sliding window size is smaller, as shown in Figure 12b. In addition, the frequency resolution of FFT will be affected by the number of sampling points. For a better test of the effect of the sliding window size (the number of sampling points) on the analysis of three-phase unbalance and the analysis of the effect of integral period sampling, the starting points of the U, V, and W phase current signals (\(t=0\)) were selected and fixed, with data of different lengths, and the FFT was calculated to obtain the phase at the maximum amplitude (fundamental frequency), with the results shown in Figure 13. Since the original simulated signal used in this section is in sine form and the FFT calculation using Matlab gives the cosine form with a difference of 90\({}^{\circ}\), the phase calculated by the FFT is obtained by subtracting 90\({}^{\circ}\) from the phase of the original signal. The signal integral period T\({}_{1}\) = 20 ms and its multiples T\({}_{n}\) (i.e., when the data point is 400 and its multiples), where n is the number of multipliers, as marked by the dashed line in Figure 13. The results of the 20 ms sliding window are shown in Figure 14, where both the proposed method and the symmetric component method can reflect the change in three-phase unbalance.