Best Response of Producer in Pay-as-clear Electricity Market

Miroslav Pištěk, D. Aussel, R. Henrion, M. Červinka

We deal with several sources of uncertainty in electricity markets. The independent system operator (ISO) minimizes the production cost using chance constraints, thus hedging against discrepancies between estimated electricity demand and real consumption. We find an explicit solution of the ISO and use it to tackle the problem of a producer. In our model, producers face two sources of risk and uncertainty. Since producers participate in the day-ahead market, their productions, as well as revenues, are determined based on the estimate of electricity demand provided by the ISO. Thus, we consider producers to use chance constraints to hedge against the uncertainty of the ISO's prediction. Additionally, producers face uncertainty about the bid functions of their competitors. Thus each producer is maximizing his profit with respect to the worst case scenario, assuming the knowledge of the ambiguity sets in the form of intervals of bid-function coefficients of the competitors. To illustrate our results, we provide a numerical simulation of the producer's best response based on empirical data.