A Stackelberg game approach for multiple energies trading in integrated energy systems

In this paper, we propose a novel game model based on the hierarchical Stackelberg game for analyzing the multiple energies trading (MET) problem in integrated energy systems (IESs). In the proposed game model, a number of distributed energy stations (DESs) lead the game deciding the unit prices of electricity and cooling energies they generated, while multiple energy users (EUs) perform as followers determining the amounts of energies to consume. In addition to maximizing the profit of each DES, the proposed hierarchical game model also considers the benefit of each EU, who actively participates in the MET. We prove that, for the first time, there exists a unique Stackelberg Equilibrium (SE) in the MET, so that the existence of an equilibrium strategy optimizing the objectives of all participants can be guaranteed. Moreover, we found that the price setting game played by DESs is a submodular game when energy dispatching is performed during their generation process, which indicates that the behaviors of DESs are strategic substitutes. Furthermore, the SE is obtained in a closed-form, by which the effects of coupling generation of multiple energies are analyzed. Finally, a best response algorithm is provided to obtain the SE in an iterative way. Numerical studies demonstrate the convergency of the proposed best response algorithm, corroborate the jointly effects of market scale and exogenous parameter on the SE and verify the practicability of the proposed game-theoretic approach.