Nonlinear PDE Constrained Optimal Dispatch of Gas and Power: A Global Linearization Approach

The coordinated dispatch of power and gas in the electricity-gas integrated energy system (EG-IES) is fundamental for ensuring operational security. However, the gas dynamics in the natural gas system (NGS) are governed by the nonlinear partial differential equations (PDE), making the dispatch problem of the EG-IES a complicated optimization model constrained by nonlinear PDE. To address it, we propose a globally linearized gas network model based on the Koopman operator theory, avoiding the commonly used local linearization and spatial discretization. Particularly, we propose a data-driven Koopman operator approximation approach for the globally linearized gas network model based on the extended dynamic mode decomposition, in which a physics-informed stability constraint is derived and embedded to improve the generalization ability and accuracy of the model. Based on this, we develop an optimal dispatch model for the EG-IES that first considers the nonlinear gas dynamics in the NGS. The case study verifies the effectiveness of this work. Simulation results reveal that the commonly used locally linearized gas network model fails to accurately capture the dynamic characteristics of NGS, bringing potential security threats to the system.