Global asymptotic stability assessment of three‐phase inverters with saturation

Abstract

Saturation is reported to have a significant influence on the stability of the inverter. In this study, a direct Lyapunov function method to analyse the stability of a three-phase inverter with saturation is presented. The overall model of the three-phase inverter is established and the order of the original model is reduced based on the singular perturbation theory. Then the global asymptotic stability assessments of inverters are transformed into linear matrix inequalities problems that are easy to be solved numerically. Through the analysis of this study, it can be proved that the three-phase inverter based on conventional proportional-integral modulation can achieve global stabilisation. The proportional coefficients of the voltage loop have the greatest influence on the stability of the three-phase inverter. Besides, the saturation also has an important effect on the stability of the inverter. The proposed method has some advantages compared with the small-signal analysis. It can quantify the stability degree of the inverter and explain some non-linear phenomena caused by saturation. Simulation developed in PSCAD demonstrates the effectiveness of this method and the results are compared with the real-time digital simulation results implemented in RT-LAB and hardware results.