Long-run optimal pricing in electricity markets with non-convex costs

Abstract

Determining optimal prices in non-convex markets remains an unsolved challenge. Non-convex costs are critical in electricity markets, as startup costs and minimum operating levels yield a non-convex optimal value function over demand levels. While past research largely focuses on the performance of different non-convex pricing frameworks in the short-run or uses convex approximations, we determine long-run adapted resource mixes associated with each pricing framework while preserving the full extent of the non-convex operations. We frame optimal pricing in terms of social surplus achieved and transfer of consumer to producer surplus in adapted long-run market equilibria. We find that convex hull pricing achieves the highest social surplus and is also associated with the lowest transfer of consumer to producer surplus. Marginal prices determined by fixing integer variables to their optimal values in the pricing run are also associated with high social surplus and high consumer surplus when the optimality gap in the original mixed integer linear program is very small. Other pricing frameworks tend to over-compensate inframarginal units, leading to resource mixes with lower social surplus and a greater transfer of consumer surplus to producer surplus in the long-run.