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We formulate the optimal flow problem in a multi-area integrated electricaland gas system as a mixed-integer optimization problem by approximating thenon-linear gas flows with piece-wise affine functions, thus resulting in a setof mixed-integer linear constraints. For its solution, we propose a novelalgorithm that consists in one stage for solving a convexified problem and asecond stage for recovering a mixed-integer solution. The latter exploits thegas flow model and requires solving a linear program. We provide an optimalitycertificate for the computed solution and show the advantages of our algorithmcompared with respect to the state-of-the-art method via numerical simulations.

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