Balanced Linear Quadratic Gaussian Model Reduction for Islanded Microgrid Control Applications

Abstract

This study addresses the challenge of reducing the dynamic order of islanded microgrid (ISMG) systems, which are increasingly deployed to enhance power system stability and facilitate the integration of distributed energy resources such as photovoltaic arrays and battery storage. The main objective is to alleviate the computational complexities associated with high-order dynamic models in real-world microgrid control and optimization, thereby enabling more efficient and reliable controller design for practical applications. The contribution of this research is the development and implementation of a Balanced Linear-Quadratic Gaussian Model Reduction (BLQGMR) approach, which systematically integrates LQG control theory with state-space balancing techniques to generate reduced-order models that preserve essential controllability and observability properties. The BLQGMR method involves solving coupled Riccati equations to quantify the importance of system states, followed by a balanced truncation process that eliminates states with negligible influence on system input–output behavior. Numerical experiments on a representative ninth-order ISMG model demonstrate that the BLQGMR algorithm can effectively reduce the system order to between one and eight, with rigorous performance evaluation based on H∞ and H₂ error norms. Results show that fourth- and fifth-order reduced models achieve a favorable trade-off between model accuracy and computational efficiency, with H∞ errors of approximately 6.90×10-1 and 1.99×10-1, and H2 errors of 1.53×10-1 and 5.28×10-2, respectively. These reduced models successfully reproduce the dynamic response of the original system across both time and frequency domains, as evidenced by Nyquist, Nichols, and step response analyses. The research demonstrates that BLQGMR provides a robust and practical solution for order reduction in ISMGs, supporting advanced control strategies while significantly reducing computational costs. Opening avenues to extend the approach to nonlinear and multivariable systems, as well as to address high-frequency limitations and cybersecurity challenges in intelligent microgrid control.