Convex Hull Pricing for Unit Commitment: Survey, Insights, and Discussions

Energy prices are usually determined by the marginal costs obtained by solving economic dispatch problems without considering commitment costs. Hence, generating units are compensated through uplift payments. However, uplift payments may undermine market transparency as they are not publicly disclosed. Alternatively, energy prices can be obtained from the unit commitment problem which considers commitment costs. But, due to non-convexity, prices may not monotonically increase with demand. To resolve this issue, convex hull pricing has been introduced. It is defined as the slope of the convex envelope of the total cost function over the convex hull of a unit commitment (UC) problem. Although several approaches have been developed, a relevant survey has not been found to aid the understanding of convex hull pricing from the current limited literature. This paper provides a systematic survey of convex hull pricing. It reviews, compares, and links various existing approaches, focusing on the modeling and computation of convex hull prices. Furthermore, this paper explores potential areas of improvement and future challenges due to the ongoing efforts for power system decarbonization.