With the increasing demand of energy and the growing intensity of energy crisis, various smart energy systems are developed on the distribution level, such as integrated energy system (IES). In this article, a trading mechanism among various energy retailers and consumers is designed under the open market environment. The trading problem is formulated as a multi‐leader and multi‐follower Stackelberg game, which is built with the strategy set of energy bidding price and purchasing pattern. In particular, consumer's demand is described with the price elasticity property of demand, and non‐cooperative competition behavior among retailers is analyzed mathematically. To implement the proposed game approach, a distributed algorithm is presented by combining particle swarm optimization (PSO) and interior point method (IPM). Finally, simulation results show that the proposed trading mechanism will contribute to the development of heterogeneous energy market and the overall profit of retailers in the traditional trading mechanism is 37.8% lower than the profit in the proposed mechanism.

中文翻译：

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综合能源系统中异构能源市场的Stackelberg博弈方法

随着能源需求的增加和能源危机的加剧，各种智能能源系统都在配电领域得到发展，例如综合能源系统（IES）。本文在公开市场环境下设计了各种能源零售商和消费者之间的交易机制。贸易问题被公式化为一个多领导者和跟随者的Stackelberg游戏，它是根据能源投标价格和购买模式的策略集构建的。特别是，用需求的价格弹性特性描述了消费者的需求，并对零售商之间的非合作竞争行为进行了数学分析。为了实现所提出的博弈方法，结合粒子群算法（PSO）和内点法（IPM）提出了一种分布式算法。最后，