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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]