# 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
The results of the 10 ms sliding window are shown in Figure 15, where the length of the sliding window is less than the integral period T\({}_{1}\), and the FFT calculation results required by the symmetrical components method have spectral leakage, and the amplitude and frequency obtained are inaccurate, making the results of the symmetrical components method inaccurate. Similarly, as shown in Figure 12b, the 50 ms sliding window (2.5 times T\({}_{1}\)) is not a multiple of the integral period of the signal, and there is a difference between the calculated phase and the phase calculated at the integral period, so the results of the symmetrical components method cannot truly reflect the change in the three-phase unbalance. For the method proposed in this paper, the change in three-phase unbalance can still be reflected under the sliding window of 10 ms.  
Figure 12: Analysis of three-phase unbalances with continuous amplitude variation using the symmetrical components method when the sliding window size is as follows: (**a**) 100 ms; (**b**) 50 ms.  
Figure 13: The phase corresponding to the fundamental frequency is obtained using FFT for different data points: (**a**) U-phase, (**b**) V-phase, (**c**) W-phase. For the choice of window width, it can be no less than the integral period, i.e., the inverse of the instantaneous frequency of the signal. The method proposed in this paper does not require the window length to be chosen as a multiple of the integral period and has better window length adaptability. In summary, compared with the symmetrical components method, the proposed method can still analyze the three-phase unbalance with fewer data points (smaller sliding window size). The switching frequency of the converter generates noise [24; 25]. Based on Equations (13) and (14), the analysis of the effect of switching noise is simplified by using the switching frequency superimposed on random noise, as shown in the following equation. The high-frequency signal amplitude is set to 0.02 times the fundamental frequency signal amplitude, the switching frequency is 1 kHz, the initial phase is 0 rad, and the random noise amplitude is 0.01 times the fundamental frequency signal amplitude. \[\left\{ \begin{array}{l}I_{u}=a\cdot\cos(2\pi f_{M}t+\theta_{u})\cdot A_{t}+b \cdot\cos(2\pi f_{N}t+\theta_{uN})+c\cdot noise_{u}\\ I_{v}=a\cdot\cos(2\pi f_{M}t+\theta_{v})+b\cdot\cos(2\pi f_{N}t+\theta_{vN})+ c\cdot noise_{v}\\ I_{w}=a\cdot\cos(2\pi f_{M}t+\theta_{w})+b\cdot\cos(2\pi f_{N}t+\theta_{wN})+ c\cdot noise_{w}\end{array} \right. \tag{15}\]  
where \(b\) is the high-frequency signal amplitude, \(f_{N}\) is the switching frequency, \(\theta_{uN}\), \(\theta_{vN}\), and \(\theta_{wN}\) are the switching frequency phases, \(c\) is the random noise amplitude, and \(noise_{u}\), \(noise_{v}\), and \(noise_{w}\) are the random noise. The simulation signal is shown in Figure 16, with the sliding window set to 50 ms. The FFT values and the total harmonic distortion (THD) of the U, V, and W phase current signals are calculated separately, and the results are shown in Figure 17 (the fundamental frequency amplitude is 100%). For three-phase current signals, high-frequency signals can be seen on the spectrum, as well as many noise frequencies. For U-phase currents, many side frequencies are present near the fundamental frequency on the spectrum. Figure 14: The sliding window is 0.02 s: (**a**) the C.V. of the instantaneous frequency; (**b**) the C.V. of the instantaneous amplitude; (**c**) the symmetrical components method. Figure 15: The sliding window is 0.01 s: (**a**) the C.V. of the instantaneous frequency; (**b**) the C.V. of the instantaneous amplitude; (**c**) the symmetrical components method. The analysis results of the proposed method are shown in the Figure 18.  
Figure 16: Three-phase unbalanced current signals with continuous changes in amplitude after adding switching noise: (**a**) 0 to 500 ms signal, (**b**) 0 to 50 ms signal, (**c**) 450 ms to 500 ms signal.