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• 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]