The development of energy conversion techniques enhances the coupling between the gas network and power system. However, challenges remain in the joint optimal dispatch of electricity-gas systems. The dynamic model of the gas network, described by partial differential equations, is complex and computationally demanding for power system operators. Furthermore, information privacy concerns and limited accessibility to detailed gas network models by power system operators necessitate quantifying the equivalent energy storage capacity of gas networks. This paper proposes a multi-port energy storage model with time-varying capacity to represent the dynamic gas state transformation and operational constraints in a compact and intuitive form. The model can be easily integrated into the optimal dispatch problem of the power system. Test cases demonstrate that the proposed model ensures feasible control strategies and significantly reduces the computational burden while maintaining high accuracy in the joint optimal dispatch of electricity-gas systems. In contrast, the existing static equivalent model fails to capture the full flexibility of the gas network and may yield infeasible results.

12 pages, 8 figures