An economic cybernetic model for electricity market operation coupled with physical system dynamics*

With the emergency of competitive markets as central operational mechanisms, the real-time market clearing results are used to determine the optimal power dispatch. It inevitably strengthens the coupling between the market update process and the physical response of the generators and networks. It necessitates the development of stability analysis for such coupled systems. Based on the primal-dual gradient method, an economic cybernetic model is established to simultaneously characterize the market operation and electromechanical power system dynamics. Inspired by modern control theory, the proposed dynamic model constructs a state space in which the actions of market participants are control signals, and the system states, such as nodal prices, bus voltages, and frequency, are treated as state variables. To promote the expandability, we also formulate the coupled dynamics in port-Hamiltonian form and provide detailed proof and sufficient conditions for its asymptotic stability by using properties of incremental passive systems. The whole transaction process implemented in a distributed manner aims at maximizing social welfare and frequency regulation when the economic-physical system reaches its equilibrium point.