Approximate solutions to the optimal flow problem of multi-area integrated electrical and gas systems

We formulate the optimal flow problem in a multi-area integrated electrical and gas system as a mixed-integer optimization problem by approximating the non-linear gas flows with piece-wise affine functions, thus resulting in a set of mixed-integer linear constraints. For its solution, we propose a novel algorithm that consists in one stage for solving a convexified problem and a second stage for recovering a mixed-integer solution. The latter exploits the gas flow model and requires solving a linear program. We provide an optimality certificate for the computed solution and show the advantages of our algorithm compared with respect to the state-of-the-art method via numerical simulations.