凸包定价的共正性特征
Copositive Characterizations of Convex Hull Pricing
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中文总结 AI 辅助
针对机组组合非凸二元约束下无统一线性定价方案支持最优调度的问题，定义集中凸包价格，证明其与边际共正对偶价格在非退化时一致，并通过数值实验验证等价性及量化定价差距。
中文摘要 AI 辅助
由于机组组合（UC）的非凸二元约束，不存在统一的线性定价方案支持最优调度。凸包定价（CHP）和共正对偶定价（CDP）都解决此问题。CHP从UC凸包松弛的价值函数次梯度推导价格，CDP指可从完全正规划重新表述的对偶乘子构建的几种不同定价机制。本文在UC联合可行集上定义集中凸包价格，证明在非退化情况下它与边际共正对偶价格一致。通过数值实验验证了这种等价性并量化了半定约束引入的定价差距。
英文摘要
Due to the nonconvex binary constraints of unit commitment (UC), no uniform linear pricing scheme supports the optimal dispatch. Convex hull pricing (CHP) and copositive duality pricing (CDP) both address this problem. CHP derives the price from the subgradient of the value function of the convex hull relaxation of UC. CDP refers to several different pricing mechanisms that can be constructed from the dual multipliers of the completely positive programming reformulation. In this work, we define a centralized convex hull price over the joint feasible set of UC and prove that, under non-degeneracy, it coincides with the marginal copositive duality price. Numerical experiments on the Scarf example validate this equivalence and quantify the pricing gap introduced by the semidefinite restriction.
