A Linear Quadratic Regulator with Optimal Reference Tracking for Three-Phase Inverter-Based Islanded Microgrids

This article proposes a power sharing control method based on the linear quadratic regulator with optimal reference tracking (LQR-ORT) for three-phase inverter-based generators using inductor-capacitor-inductor (LCL) filters islanded mode. Compared to single-input single-output (SISO)-based controllers, the LQR-ORT controller increases robustness margins and reduces the quadratic value of the power error and control inputs during transient response. Supplementary loops are used to reduce frequency and voltage deviations in the ac bus without communications. The supplementary loop for voltage regulation is based on the droop controller by reducing direct and quadrature output voltages according to the active and reactive power demand. A model in a synchronous reference frame that integrates power sharing and voltage-current dynamics is also proposed. In addition, a methodology to develop an islanded microgrid model in a synchronous reference frame is proposed. Robustness analysis demonstrates stability of the LQR-ORT controller under variations in the frequency and the LCL filter components. Experimental results demonstrate accuracy of the proposed model and the effectiveness of the LQR-ORT controller on improving transient response and robustness in islanded mode.