# Three-Phase Unbalance Analysis Method Based on Three-Phase Motor Current Instantaneous Information
###### Abstract
[20] proposed a technique based on the symmetrical component positions of the three-phase rotor currents to form a \"wing shape\" and investigated the effects of unbalanced stator voltages and structural imbalances, etc. on rotor current measurements. The existing methods, such as Fast Fourier Transform (FFT), the symmetrical components method, etc. are widely used. FFT is suitable for processing steady-state and periodic signals. For unsteady, aperiodic signals, FFT analysis can produce spectral aliasing and leakage. The symmetrical components method is used to decompose the three-phase voltage/current into positive-sequence, negative-sequence, and zero-sequence components [21]. Moreover, the negative-sequence component and zero-sequence component is obtained for the calculation of unbalance through a vector calculation. The symmetrical components method is only suitable for circuits with linear parameters according to the principle of superposition. Although the methods mentioned above had been widely used, quick analysis can be further investigated. In this study, to verify the effectiveness of the method, the three-phase unbalanced state caused by amplitude deviation and phase deviation was analyzed by analyzing the instantaneous information characteristics and compared with the symmetrical components method. To analyze the unbalance in the unsteady signal state, the sliding window size is changed and the transient information characteristics performance is analyzed. This paper proposes a three-phase unbalance analysis method based on three-phase current instantaneous information, by calculating the instantaneous amplitude and instantaneous frequency of three-phase currents and calculating their coefficients of variation to analyze three-phase unbalance. Then, the coefficient of variation of the instantaneous amplitude and instantaneous frequency is calculated to evaluate the three-phase unbalance. Key highlights:  
1. The method of the calculation of the instantaneous frequency coefficient of variation and the instantaneous amplitude coefficient of variation to analyze the three-phase unbalance is proposed. 2. Simulations of the amplitude deviation and phase deviation are carried out, as well as the continuous amplitude change, the effectiveness of the method is verified, and the effects of switching noise and harmonics are analyzed. 3. Experiment results verify the effectiveness of the method. Advantages: The instantaneous information of the three-phase current is obtained through Park vector demodulation, the calculation result is similar to the trend of the symmetrical components method, the time complexity of this method is smaller than that of the symmetrical components method, and a smaller sliding window size is required. Novelty: The instantaneous state change of the measured system is analyzed from the perspective of instantaneous information, and continuous unbalances can also be analyzed. Compared with the symmetrical components method, the proposed method has lower time complexity and a shorter calculation time. There is no requirement for the integer period and its multiple for sliding window selection, and a smaller number of sampling points can be used for analysis. The remaining sections of this paper are organized as follows. Section 2 illustrates the Park vector demodulation method and the calculation of the coefficient of variation. In Section 3, the simulation verification analyzes the effect of amplitude deviation and phase deviation on three-phase unbalance and its instantaneous information performance. The unbalance of continuous change in amplitude is analyzed, the switching noise addition is carried out, and the effect is analyzed. Simulation of three-phase unbalance using Simulink is realized, and the harmonic effect is analyzed. The experimental verification is carried out to compare and analyze the differences in current instantaneous information of three-phase unbalanced motors at different speeds. The last section is the conclusion.