Modulated Model Predictive Control Applied to LCL-Filtered Grid-Tied Inverters: A Convex Optimization Approach

Abstract

This paper proposes a modulated model predictive strategy suitable for current control of grid-connected converters with LCL filters, allowing fast dynamic responses with a fixed switching frequency, for both strong and weak grid conditions. The duty cycles are optimized within each switching period based on the minimization of a quadratic cost function with linear constraints from the space vector modulation. Full and reduced-order models are considered for the control design, and closed-form analytical solutions for the optimization problem are derived based on the Karush-Kuhn-Tucker conditions. The closed-form expressions for the optimal solution make it possible to implement the algorithm in real time using off-the-shelf microcontrollers. Extensive evaluation illustrates good transient and steady state performances for different grid conditions. In addition, the proposed MPC takes into account the voltage synthesis capability of the inverter and copes with overmodulation in an orderly fashion even in large transients.