On the optimal game control in the DC microgrid systems

Abstract

This paper introduces static and dynamic competitive optimal control of DC/DC converters in DC microgrids based on game theory considering mutual effects. Using static and dynamic game theories, the conditions for competitive optimal control of DC/DC converters in Nash equilibrium with static and dynamic states are determined. Also, to reduce the complexity in the design of competitive optimal control of DC/DC converters due to the bilinear dynamic model of the system, generalized objective functions are considered. The competitive optimal controls using the Lyapunov and Riccati equations are determined to track the system trajectory to Nash equilibrium. Also, the numerical and experimental results are presented and compared in several cases. The results show that the competitive optimal control of the DC/DC converters in the DC microgrids can effectively improve the performance of the system.