电力市场中的机组组合约束纳什均衡

中文摘要 AI 辅助

电力市场的均衡建模通常假设每个参与者的优化问题具有凸性。尽管在生产调度中考虑固定发电成本和启动成本、最小发电水平以及最小运行时间和最小停机时间限制的重要性已被广泛认可，但此类建模不允许离散决策。本文考虑机组组合约束的纳什均衡。首先，我们针对自调度利润最大化生产者的联合机组组合与经济调度的混合整数凸规划问题，推导了新颖的最优性条件。接下来，我们利用这些条件将纳什均衡表述为混合整数互补问题，这有助于开发一种获取多个均衡的程序。该方法可适用于完全竞争和不完全竞争的市场环境。虽然均衡不一定总是存在，但在仿射逆需求曲线和凸发电成本的标准假设下，我们给出了通过混合整数凸规划获得古诺-纳什均衡的充分条件，并据此确立了均衡的存在性。一项案例研究证明了使用优化方法获取机组组合约束市场出清的古诺-纳什均衡的可行性。我们的结果证实，忽略机组组合会造成显著的福利损失，尽管这些损失在不同均衡之间差异很大。

英文摘要

Equilibrium modeling for power markets usually assumes convexity of each players' optimization problem. Although the importance of accounting for fixed generation costs and start-up costs, minimum generation levels and/or minimum up-time and down-time restrictions in production scheduling is widely acknowledged, such modeling does not allow for discrete decisions. This paper considers unit commitment constrained Nash equilibria. First, we derive novel optimality conditions tailored for the mixed-integer convex programming problem of joint unit commitment and economic dispatch of a self-scheduling profit-maximizing producer. Next, we use these to formulate a Nash equilibrium as a mixed-integer complementarity problem, which facilitates the development of a procedure to obtain multiple equilibria. The approach can be adapted to both perfectly and imperfectly competitive market settings. While an equilibrium may not always exist, we give sufficient conditions under which a Cournot-Nash equilibrium can be obtained by mixed-integer convex programming under the standard assumption of an affine inverse demand curve and convex generating costs, and use this to establish existence. A case study demonstrates the feasibility of using optimisation to obtain a Cournot-Nash equilibrium for unit commitment constrained market clearing. Our results confirm that ignoring unit commitment creates significant welfare losses, although these vary substantially across equilibria.

发表机构

• University of Copenhagen（哥本哈根大学）
• University College Dublin（都柏林大学学院）
• University of Edinburgh（爱丁堡大学）

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