The Value of Probabilistic Forecasts for Electricity Market Bidding and Scheduling Under Uncertainty

This work examines the value of probabilistic forecasts for optimizing the interaction of local energy systems with electricity markets, namely bid or schedule optimization by the responsible market agent. We aim to understand what type and quality of forecast is needed in the optimization task. First, we theoretically examine typical stochastic programming formulations to find which forecast type, namely expected values, marginal distributions, or joint distributions, is required to achieve the mathematically best possible result. We find that only few specific problem settings require full multivariate joint forecast distributions. In many other common cases, marginal distributions or expected values only are sufficient. Second, we experimentally analyze the influence of forecast errors on the performance of the stochastic program's solution for two important variations of the scheduling problem and compare this to common statistical loss functions used for training forecasts. The evaluation is made computationally feasible by a formal analysis of the stochastic programs. We find that the continuous ranked probability score (CRPS) better matches the true performance of the probabilistic forecast than the logarithmic score in our setups, being less prone to overestimating the predicted variance. Nevertheless, solutions with similar CRPS may still perform very differently in the optimization task.