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To maintain the system's real-time balance, mature electricity markets generally tend to raise the frequency of market clearing. Given the shrinking time lag between the price update process and underlying electromechanical dynamics, it inevitably considers the two in a unified, dynamical framework. However, the relationship between market activities and the evolution of electricity networks has received scant attention in pertinent research. Inspired by the primal-dual gradient method and modern control theory, we propose a novel multi-rate hybrid model that simultaneously accounts for the continuous nature of physical system dynamics and the discrete nature of market clearing. To maintain the asymptotical convergence of the proposed model, we derive the explicit constraints on the upper bounds of market clearing and bidding intervals. These bounds can be determined without prior knowledge of the Nash equilibrium, and even the time schedules don't have to be periodic, which dramatically improves the applicability of the proposed model in practical market operation. The whole model provides a new perspective to study economic-physical problems, which can be readily implemented in a distributed way and achieve social welfare maximization along with frequency regulation. • A novel economic-physical model is established for the market operation coupled with the power networks' dynamics. • The proposed hybrid model considers frequency evolution's continuous nature and bidding's discrete nature. • We derive the upper bounds on the time lengths of consecutive bidding and market clearing. • The multi-rate hybrid system can maximize social welfare and regulate frequency. [ABSTRACT FROM AUTHOR]

• Provide a new perspective to study the market operation based on control theory. • Establish a dynamic economic-physical model for the market operation. • The game action is described by state equations derived from the primal-dual method. • The whole trading process can be executed in a distributed way. • The stability analysis relies on the Lyapunov function and incremental passivity. 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. [ABSTRACT FROM AUTHOR]