Convex hull pricing has been introduced recently to increase transparency and reduce uplift payments for the U.S. wholesale markets. A convex primal formulation approach is one of the most efficient methods to obtain a high-quality convex hull price. Even though significant progress has been made, the co-optimization of energy and ancillary services is much more challenging due to the discrete nature in formulating ancillary services, for example, the regulating reserve commitment variables, which are binary introduced by some Independent System Operators (ISOs), such as Midcontinent ISO (MISO), to capture the special characteristics of certain generators, such as combined-cycle units. In this paper, we propose convex primal formulations for convex hull pricing considering regulating, spinning, and online/offline-supplemental reserves, in which the regulating reserve commitment variables are considered. Accordingly, we can solve a linear program, instead of a mixed-integer program, which is much harder to solve, to derive the minimum uplift payments and exact convex hull price for the case without general ramping constraints. For the case with general ramping constraints, an upper bound of the minimum uplift payment can also be derived. The final computational experiments on MISO cases verify the effectiveness of our approach in solution quality and computational time.

中文翻译：

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具有储备承诺的凸包定价的凸原始公式

最近引入了凸包价格，以提高透明度，并减少美国批发市场的运费。凸原始公式化方法是获得高质量凸船体价格的最有效方法之一。尽管已经取得了重大进展，但是由于制定辅助服务的离散性，例如，调节储备承诺变量（由一些独立系统运营商二进制引入），能源和辅助服务的共同优化更具挑战性。 ISO，例如中陆ISO（MISO），以捕获某些发电机（例如联合循环机组）的特殊特性。在本文中，我们针对凸包定价提出了凸原始公式，其中考虑了调节，自旋以及在线/离线补充储备，其中考虑了调节准备金承诺变量。因此，我们可以求解一个线性程序，而不是求解更难求解的混合整数程序，以得出在没有通用坡度约束的情况下的最小抬升费用和确切的凸包价格。对于具有一般斜坡约束的情况，也可以得出最小隆起支付的上限。MISO案例的最终计算实验证明了我们的方法在解决方案质量和计算时间方面的有效性。对于具有一般斜坡约束的情况，也可以得出最小隆起支付的上限。MISO案例的最终计算实验证明了我们的方法在解决方案质量和计算时间方面的有效性。对于具有一般斜坡约束的情况，也可以得出最小隆起支付的上限。MISO案例的最终计算实验证明了我们的方法在解决方案质量和计算时间方面的有效性。