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

Le résumé fourni par la source

The coordinated dispatch of power and gas is funda-mental for the operational security of Electricity-Gas Integrated Energy Systems (EG-IES). 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 non-linear PDE. Inaccurate modeling, such as the commonly used locally linearized model, can lead to operational limit violations in the NGS that might propagate and threaten the security of the coupled power system. To address it, we propose a globally line-arized gas network model based on the Koopman operator theo-ry. In particular, 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 em-bedded to improve generalization and accuracy. Based on this foundation, we develop an optimal dispatch model for the EG-IES. For the first time, this model explicitly incorporates the non-linear gas dynamics governed by PDEs without resorting to local linearization or spatial discretization. The case study verifies the effectiveness of this work. Simulation results reveal that the commonly used locally linearized gas network model fails to ac-curately capture the dynamic characteristics of NGS, bringing potential security threats to the system.

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