Simulation and optimization of coupled gas and power networks

In this thesis, the coupling of gas and power networks is examined. The isentropic Euler equations are employed as a model for gas flow in a pipeline network, whereas the power flow equations are used as a model for an electrical grid. We find a set of conditions on pressure functions that guarantee well-posedness of the Riemann problem of the isentropic Euler equations in the sub-sonic regime. Coupling conditions for modeling gas-fired power plants and power-to-gas plants, both of which couple gas networks to power networks, are proposed and their well-posedness is shown. Solutions of the power flow equations are derived as certain time-periodic solutions to the physically more accurate Telegrapher's equations and the exponential stability of these solutions is examined. In addition, a numerical method for solving the Telegrapher's equations is introduced, which mimics the exponential stability of the analytical solution. For the power network, both deterministic and stochastic power demand is considered and the influence of the demand on the pressure (and flux) in the gas network is examined. Our findings are applied to gas and power networks of realistic size and corresponding simulation and optimization problems are solved. This also showcases the software grazer, that was written for this thesis and is capable of efficiently solving time-dependent problems that are defined on networks. It is released under the open source license MIT License to enable future use, for example in further research