A Two-Stage Approach for a Mixed-Integer Economic Dispatch Game in Integrated Electrical and Gas Distribution Systems

We formulate for the first time the economic dispatch problem among prosumers in an integrated electrical and gas distribution system (IEGDS) as a game equilibrium problem. Specifically, by approximating the nonlinear gas-flow equations either with a mixed-integer second-order cone (MISOC) or a piecewise affine (PWA) model and by assuming that electricity and gas prices depend linearly on the total consumption, we obtain a potential mixed-integer game. To compute an approximate generalized Nash equilibrium (GNE), we propose an iterative two-stage method that exploits a problem convexification and the gas-flow models. We quantify the quality of the computed solution and perform a numerical study to evaluate the performance of our method.