Deciphering Convex Hull Pricing: Effective Aligning Demand With Electricity Prices Enabled By Approximated Minkowski Sum

Increasing penetration of renewable generation in power systems leads to more frequent occurrences of start-up costs, a factor not adequately characterized in conventional electricity markets. Addressing this issue, convex hull pricing has gained prominence by offering additional uplift payments to better incentivize generators to follow independent system operators' dispatch instructions. However, the interpretation and calculation of convex hull prices (CHPs) is often challenging. This stems from both non-convex generation costs and coupled optimization structures inherently involved in the convex hull pricing problem. To this end, in our paper, the CHP is deciphered as a marginal price at which the combined generation covers the targeted demand in the sense of convex hull. Drawing inspiration from this deciphering, we focus on solving the CHPs calculation issue via demand space partition, which directly builds a mapping from demands to CHPs. Following this vein, we first introduce a heuristic iterative algorithm for the individual maximum profit problem to partition the price space based on optimal generations. Then, we propose an efficient approximate method for calculating the Minkowski sum of polytopes defined by these optimal generations, thereby achieving a division of the demand space. Our results offer valuable insights into both CHP deciphering and calculation.