A two-stage approach for a mixed-integer economic dispatch game in integrated electrical and gas distribution systems

TL;DR

This paper introduces a novel two-stage method to solve a mixed-integer game for economic dispatch in integrated electrical and gas systems, using convexification and gas flow models to approximate complex equations.

Contribution

It formulates the first game-theoretic model for integrated electrical and gas dispatch and proposes an iterative solution method leveraging convexification techniques.

Findings

The method effectively approximates the generalized Nash equilibrium.

Numerical results demonstrate the approach's computational efficiency.

The solution quality is quantitatively assessed.

Abstract

We formulate for the first time the economic dispatch problem in an integrated electrical and gas distribution system as a game equilibrium problem between distributed prosumers. Specifically, by approximating the non-linear gas-flow equations either with a mixed-integer second order cone or a piece-wise affine 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, 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.