Optimal transient control of microgrids using a game theoretic approach

Small scale power systems (SSPS) are collections of interconnected electrical energy sources and loads. However, the analysis and control of SSPS are different from the more traditional large scale power system techniques because in SSPS the generation has minimal inertia with little if any spinning reserve. A differential game-theoretic framework is helpful in designing the control structures for SSPS for efficient and reliable operation with simultaneous player movement. Defining both loads and sources as players in a SSPS and forming a game between them is the key to modeling in this framework. This paper presents a modeling approach to find the optimum trajectory for the load players to reach a desirable operating point from an arbitrary initial condition given a transient system event. The players follow the optimum trajectory in the movement. In addition, the load modeling is proposed for the power electronic converter end load during transient. Further, this paper defines the suitable modifications needed to drive the optimum trajectory to an unknown static set point. This modification is important while system moves from nominal equilibrium to a new equilibrium due to sudden load or source changes. Example cases are presented with nine bus dc power system with load players.