WIAS Preprint No. 2831, (2021)

Value at risk approach to producer's best response in electricity market with uncertain demand


  • Branda, Martin
  • Henrion, René
    ORCID: 0000-0001-5572-7213
  • Pištěk, Miroslav

2020 Mathematics Subject Classification

  • 91B05 91B54


  • Electricity market, multi-leader-common-follower game, stochastic demand, day-ahead bidding, chance constraints, best response




We deal with several sources of uncertainty in electricity markets. The independent system operator (ISO) maximizes the social welfare using chance constraints to hedge against discrepancies between the estimated and real electricity demand. We find an explicit solution of the ISO problem, and use it to tackle the problem of a producer. In our model, production as well as income of a producer are determined based on the estimated electricity demand predicted by the ISO, that is unknown to producers. Thus, each producer is hedging against the uncertainty of prediction of the demand using the value-at-risk approach. To illustrate our results, a numerical study of a producer's best response given a historical distribution of both estimated and real electricity demand is provided.

Appeared in

Download Documents