Control of Three-Phase Two-Level Inverters: A Stochastic LPV Model Approach

Abstract

This paper proposes a stochastic linear parameter-varying (LPV) model approach to design a state feedback controller for three-phase, two-level inverters. To deal with the parameter changes, stochastic noise, and delays faced by the inverter, it is modeled as a stochastic LPV system with time delay. Stability analysis and control synthesis are conducted for the LPV system. With parameter-dependent Lyapunov functionals, a condition of sufficient stability for asymptotical mean-square stability is obtained. In addition, the slack matrix technique is employed to improve the feasibility and reduce the conservatism of the conditions. The obtained theoretical results are applied to the three-phase, two-level inverter, whose currents are treated as state variables and are controlled to reach the equilibrium point. The simulation results validate the effectiveness of the proposed theories and demonstrate the advantages of using the slack matrix.

Keywords

• three-phase two-level inverter
• linear parameter-varying (LPV) system
• stochastic system
• time delay
• mean square stability