Dynamic modeling and analysis of coupled hydrogen-Gas-Electricity networks

In this paper, we develop a mathematical dynamic model for a coupled hydrogen-gas-electricity network, focusing on the dynamic interactions between these systems. The model incorporates hydrogen injection into the gas network and its impact on gas flow and pressure. Additionally, gas-fired power plants consume gas to generate electricity, linking the gas and electricity networks. The model includes partial differential equations (PDEs) for the gas network, differential-algebraic equations (DAEs) for the electricity network, and numerical techniques for handling slow-fast dynamics. A mathematical Theorem is introduced to describe the coupling between hydrogen injection, gas flow, and electricity generation, demonstrating how these systems interact in a stable and efficient manner. A numerical example illustrates the theory. The proposed model and Theorem provide a robust framework for understanding and optimizing the operation of coupled energy systems.