A Computationally Efficient Algorithm for Computing Convex Hull Prices

Bernard Knueven, James Ostrowski, Anya Castillo, Jean-Paul Watson

Research output: NRELPresentation


Electricity markets worldwide allow participants to bid non-convex production offers. While non-convex offers can more accurately reflect a resource's capabilities, they create challenges for market clearing processes. For example, system operators may execute side payments when a participant’s cost is not covered through energy sale settlements from locational marginal pricing schemes, or when a participant incurs lost opportunity costs to follow the dispatch signal. Convex hull pricing minimizes these and other types of side payments while providing uniform (i.e., locationally and temporally consistent) prices. However, computing convex hull prices involves solving either a large-scale linear program - which in turn requires explicit descriptions of market participants’ convex hulls -or the Lagrangian dual of the corresponding non-convex scheduling problem. Here, we propose a computationally feasible and industrially scalable Benders decomposition approach to computing convex hull prices at least an order of magnitude faster than the current state-of-the-art while leveraging recent advances in convex hull formulations for thermal generating units.
Original languageAmerican English
Number of pages23
StatePublished - 2020

Publication series

NamePresented at the FERC Technical Conference: Increasing Real-Time and Day-Ahead Market Efficiency and Enhancing Resilience through Improved Software, 23-25 June 2020

NREL Publication Number

  • NREL/PR-2C00-77090


  • Benders decomposition
  • convex hull pricing
  • electricity markets
  • linear programming
  • unit commitment


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