Reaching criterion of a three-phase voltage-source inverter operating with passive and nonlinear loads and its impact on global stability

We develop and demonstrate a technique based on composite Lyapunov functions (CLFs) to analyze the impacts of passive (RL and RC) and nonlinear (diode rectifier) loads on the reaching dynamics of a three-phase voltage-source inverter (VSI). The reaching criterion (which ensures convergences of state trajectories to an orbit) is synthesized using piecewise linear models of the VSI and the loads and conditions for switching among the various models (corresponding to the different switching states). Once orbital existence is ensured using the reaching criterion, we extend the CLF-based approach to predict the stability of the nominal (period-1) orbit of the system (comprising the three-phase VSI and the load) and compare these predictions with those obtained using a conventional impedance-criterion technique that is developed based on a linearized averaged model. Overall, we demonstrate the significance of analyzing the reaching condition from the standpoint of orbital existence and why such a criterion is necessary for analyzing global stability. On a broader note, the methodology outlined in this paper is useful for analyzing the global stability of multiphase inverters, potentially leading to advanced control design of VSI for applications including uninterrupted power supplies, telecommunication power supplies, grid-connected inverters, motor drives, and active filters.