A Lyapunov Approach to Control Design for Grid-connected Inverters

This paper develops a Lyapunov approach to control design for grid connected inverter. The control objective is to track a reference current which is proportional to the fundamental harmonic of the grid voltage. By using the internal model principle, the grid voltage and the reference current are described as the outputs of an autonomous linear oscillatory system. The state of this oscillatory system contains all the information for the harmonics of the grid voltage and is estimated via an observer wit zero estimation error at steady state. A state space description for the whole system is obtained by combining the state of the inverter circuit and that of the oscillatory system for the grid voltage. Based on the state space description, a Lyapunov approach is developed to design a state-feedback controller for tracking a reference current with minimal tracking error. The design problem is cast into an optimization problem, which can be effectively solved with linear matrix inequality (LMI) toolbox in Matlab. The Lyapunov approach ensures internal stability and makes efficient use of the structural information, such as the total harmonic distortion (THD) of the grid voltage, and the magnitude/phase of the reference current. The effectiveness of the Lyapunov approach is validated via SimPower simulation. A real circuit is built using microcontroller ezDSP28335, the output current obtained is in phase with the grid voltage and has small THD, as we expected.