Abstract
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 to the ISO problem and use it to tackle the problem of a producer. In our model, production, as well as the income of a producer, are determined based on the estimated electricity demand predicted by the ISO, which is unknown to producers.
Thus, each producer is hedging against the uncertainty of the 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.