Multi-Stage Modeling With Recourse Decisions for Solving Stochastic Complementarity Problems With an Application in Energy

Pattanun Chanpiwat, Steven Gabriel, Maxwell Brown

Research output: Contribution to journalArticlepeer-review


This paper presents a multi-stage model with recourse decisions for solving complementarity problems in a competitive electricity market under uncertainty, while also considering renewable energy technologies and battery storage utilization. The model is based on a Nash-Cournot formulation of imperfect competition among power producers. We analyze the value of variable renewable energy (VRE) and battery storage under different uncertainties, such as demand level and VRE availability. To illustrate the proposed model, we apply it to three- bus five-player model and analyze different cases varying costs, including a user-optimal perspective (with market power) and a system-optimal perspective (with central planning). We also consider the potential for congestion in the system by restricting the transmission capacity between a single interface that connects two buses. Our findings show that increasing the battery storage capacity results in a decrease in the need for perfect information about future uncertainties. Additionally, as the model allows for more uncertainty, it becomes more apparent that the stochastic mixed complementarity problem (MCP) has an advantage over a deterministic equivalent. We propose the use of the Value of the Stochastic Equilibrium Solution (VSES) as a quality metric to compare the stochastic MCP with its deterministic equivalent. Overall, expanding battery storage capacity can lower the maximum, mean, and variance values of delivered prices, but there are diminishing returns to this approach.
Original languageAmerican English
Pages (from-to)4935-4948
Number of pages14
JournalIEEE Transactions on Power Systems
Issue number3
StatePublished - 2024

NREL Publication Number

  • NREL/JA-6A20-84918


  • battery storage
  • energy modeling
  • game theory
  • market power
  • mixed complementarity problem


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