# Three-Phase Unbalance Analysis Method Based on Three-Phase Motor Current Instantaneous Information
## 3 Simulation Analysis and Experimental Verification
### Three-Phase Unbalance Simulation and Analysis under Amplitude Deviation and Phase Deviation
#### 3.1.2 Effect of Phase Deviation  
For Equation (11), the deviation value of the U-phase phase \(\theta_{u}\) is adjusted from \(-\pi/3\) to \(\pi/3\) with an interval of \(\pi/15\), where the three-phase current signal is shown in Figure 5 when the U-phase is \(\pi/15\) lagged and \(\pi/15\) ahead of the balanced. The instantaneous frequency and instantaneous amplitude when the U-phase phase is \(\pi/15\) ahead of the relative balance are shown in Figure 6. Phase deviation affects the transient information performance, i.e., fluctuations in instantaneous frequency and instantaneous amplitude. The U-phase phase variation corresponds to the variation in the instantaneous frequency coefficient of variation and the instantaneous amplitude coefficient of variation of the three-phase currents, as shown in Figure 7. The C.V. of the instantaneous frequency and the C.V. of the instantaneous amplitude increase with an increasing phase deviation. The deviation of amplitude and phase in the three-phase current affects the instantaneous state. From Figures 4 and 7, it can be seen that for both amplitude deviation and phase deviation, the coefficient of variation increases as the deviation increases. Comparing Figures 4 and 7, it can be seen that both amplitude distortion and phase distortion lead to changes in the instantaneous frequency variation coefficient and instantaneous amplitude variation coefficient, i.e., the instantaneous information variation coefficient increases when the deviation from the three-phase balance state increases. The unbalance of a phase current  
Figure 5: Three-phase current signals with different single-phase phase deviations: (**a**) U-phase is \(\pi/15\) lagged after the balanced; (**b**) U-phase is \(\pi/15\) ahead of the balanced. Figure 6: The phase of the U-phase current is \(\pi/15\) ahead of the balanced: (**a**) instantaneous frequency; and (**b**) instantaneous amplitude. Figure 7: Different phase deviations correspond to the following: (**a**) variation in instantaneous frequency coefficient of variation; (**b**) variation in instantaneous amplitude coefficient of variation. affects the time domain characteristics of the instantaneous amplitude and instantaneous frequency extracted from the three-phase current. The proposed method converts the three-phase signal to obtain the instantaneous information characteristics, which can analyze the unbalance situation more comprehensively and intuitively. The symmetrical components method is used to obtain the three-phase voltage/current vector through FFT, transform the amplitude and phase, and analyze the amplitude of its negative sequence component in the case of amplitude deviation and phase deviation [23]. Since this paper examines the effects of current, the equation can be expressed as Equation (12). For comparison, the coefficient is not multiplied by 100. \[\text{F}=\frac{I_{2}}{I_{1}} \tag{12}\]  
where \(I_{1}\) and \(I_{2}\) are the positive and negative vector components of the current, respectively. The results are shown in Figure 8, and it can be seen that the symmetrical components method has the same trend as the method proposed in this paper. Analyzing the main part of the algorithm proposed in this paper, the time complexity of the Park vector demodulation method is O(\(n\)), where n is the data length. For the symmetrical components method, the phase and amplitude of the three-phase current are mainly obtained by FFT. Ignoring the low-order components, the time complexity is approximately O(\(n\log n\)), where n is the data length. The simulation experiment uses Matlab R2020b, the CPU is Intel Core i5-2400 (3.1 GHz), and the memory is 8 GB (1333 MHz). The number of sampling points is N = 1000, the single calculation time for Park vector demodulation calculation amplitude analysis is 0.344 \(\pm\) 0.096 ms, and the calculation time of the phase analysis single is 0.235 \(\pm\) 0.042 ms.