LQR Controller with Optimal Reference Tracking for Inverter-Based Generators on Islanded-Mode Microgrids

A comprehensive method for computing a Linear Quadratic controller with Optimal Reference Tracking (LQR-ORT) for a three-phase inverter is presented in this work. The calculation of the state-feedback controller is performed by using a modified version of the classical algebraic Ricatti equation for the Linear Quadratic controller. The optimal reference signal is calculated offline by solving a trigonometric differential equation. The results of this method were compared against a known Alpha-Beta Proportional Resonant controller. Results show that the LQR-ORT controller improves harmonic rejection and minimizes tracking error.