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Energy system integration enables raising operational synergies by coupling the energy infrastructures for electricity, methane, and hydrogen. However, this coupling reinforces the infrastructure interdependencies, increasing the need for integrated modeling of these infrastructures. To analyze the cost-efficient, sustainable, and secure dispatch of applied, large-scale energy infrastructures, an extensive and non-linear optimization problem needs to be solved. This paper introduces a nested decomposition approach with three stages. The method enables an integrated and full-year consideration of large-scale multi-energy systems in hourly resolution, taking into account physical laws of power flows in electricity and gas transmission systems as boundary conditions. For this purpose, a zooming technique successively reduces the temporal scope while first increasing the spatial and last the technical resolution. A use case proves the applicability of the presented approach to large-scale energy systems. To this end, the model is applied to an integrated European energy system model with a detailed focus on Germany in a challenging transport situation. The use case demonstrates the temporal, regional, and cross-sectoral interdependencies in the dispatch of integrated energy infrastructures and thus the benefits of the introduced approach. [ABSTRACT FROM AUTHOR]

• Optimal power and gas flow problem considering power-to-gas. • Quasi-stationary modeling considering DC power flow and gas dynamics. • Scalable approach using successive linear programming. • Use case analyzing dispatch of renewable energy systems. The integrated modeling of power and gas systems gains importance as a result of increasing interdependencies due to bidirectional coupling in renewable energy systems through power-to-gas and gas-fired power plants. The optimal power and gas flow problem (OPGF) aiming to minimize system dispatch costs is mostly applied to small test systems. However, to investigate system-wide effects of sector coupling, large-scale transmission grids must be considered. Due to nonlinearities especially in the pressure loss equation, a nonlinear optimization problem results. This paper aims to demonstrate that successive linear programming, in contrast to other discussed approaches, is suitable for solving large-scale and multi-period OPGF-problems. The presented approach shows high solution quality despite short computing time even for large-scale systems such as the German power and gas transmission grid. [ABSTRACT FROM AUTHOR]