LMI-Based Approach for Regulating Microgrids Using Sliding Mode Control

Regulating voltage and current signals in microgrids (MG) is essential to ensure stability, optimize power quality, support grid integration, enhance operational efficiency, and promote safety within the system. This paper introduces a novel Linear Matrix Inequalities (LMI)-based approach aimed at regulating voltage and current signals within microgrids through the utilization of sliding mode control. The MG under examination in this paper is composed of a voltage source inverter (VSI) for DC to AC voltage conversion, a filter to ensure sinusoidal signal quality, and an array of loads, including those with uncertain characteristics. The objective of this study is to regulate the output voltage and current in a short period of time in the presence of diverse loads. By promptly adjusting voltage and current levels, the microgrid can effectively accommodate fluctuations in demand and maintain optimal performance under changing conditions. The presented controller consists of two parts: a state feedback gain calculated from the LMI and a sliding mode-based controller to maintain system stability. This controller is intended to reject disturbances, track reference signals, and minimize steady-state errors in a limited time. The satisfactory performance of the microgrid will have a significant impact on various parameters, such as frequency, active power, reactive power, and power factor. Simulating the voltage source inventor and presenting numerical results demonstrate the effectiveness of the proposed controller to provide high robustness against uncertainty and nonlinear loads while maintaining system stability.