Robust Control of GTIs under wide grid impedance ranges: An approach combining metaheuristics and LMIs

Abstract

This paper provides a new design procedure for robust state feedback current controllers suitable for grid-tied inverters under wide grid impedance ranges. The proposed procedure is based on the combination of particle swarm optimization and linear matrix inequalities. The control gains, designed offline, are obtained through the minimization of a novel objective function that takes into account the grid current tracking error in the stationary reference frame, limits for the control signal, and robust stability. Linear matrix inequalities are used in the design stage to theoretically certify the closed-loop robust stability systematically and efficiently, based on a polytopic model of the grid-tied inverter, which avoids the need for exhaustive and time-consuming a posteriori tests. Real-time simulations and experimental results are presented, attesting that the closed-loop system with control gains provided by the proposed procedure is robustly stable for wide ranges in the grid inductances. Moreover, the grid currents exhibit an optimized transient performance and steady-state responses in compliance with harmonic distortion limits from IEEE 1547 Std., even encompassing operation from stiff to weak grid conditions and in the presence of distorted grid voltages. To provide a comparison, results based on other well-established state feedback design techniques are also presented, highlighting the superior performance obtained with the proposed procedure.