Design of LQR for Three-Phase Grid-Tied Inverter System

The increasing penetration of renewable energy sources in modern power systems necessitates advanced control strategies for grid-tied inverters to ensure reliable power quality and efficient operation. This paper presents a comprehensive study on the design and implementation of a Linear Quadratic Regulator (LQR) for a three-phase grid-tied inverter system, and compares its performance with conventional Proportional-Integral-Derivative (PID) control. The proposed LQR controller, derived from a detailed state-space model, minimizes a quadratic cost function that effectively balances state deviations and control effort, resulting in enhanced transient response, improved voltage regulation, and reduced harmonic distortion. A key advantage of the LQR approach is its ability to access full state feedback, enabling it to utilize all available data of the system state, in contrast to the PID controller that relies solely on the measured output to track the reference signal. Simulation and experimental results validate the superior dynamic performance and robustness of the LQR-based design under varying load conditions and grid disturbances. This work provides significant insights into state-space control methodologies, demonstrating that LQR-based controllers offer a reliable and computationally efficient alternative for managing grid-tied inverter systems in renewable energy applications. Results contribute to advancing future smart grid integration strategies in modern applications.