Feasibility verification of a MILP model by outer approximation for the optimal operation of natural gas networks

The power system and the natural gas network are becoming increasingly interconnected due to the rising number of gas-fired power plants and the emergence of power-to-gas technology. The coordinated operation of power and gas systems is a promising solution to add flexibility to future energy systems, facilitating renewable integration. The optimal operation of the power system is commonly modeled as a mixed-integer linear problem (MILP). Conversely, the natural gas network optimization is a mixed-integer nonlinear problem (MINLP), due to the highly nonlinear and nonconvex Weymouth equation modeling the gas flow in pipelines. Different linearization and convexification approaches have been investigated in the literature for the gas optimization problem, but few authors have verified the quality of the solution. In this paper, a MILP model for the gas problem is developed using an outer approximation technique, and the feasibility of the solution is assessed. A sensitivity analysis on the number of linearization breakpoints is conducted to show the impact on the solution quality and computational time.