On the Value of Probabilistic Forecasts for the Stochastic Optimization of Local Energy Systems

The ongoing transition to renewable energy sources increases the variability and uncertainty in power systems. As a result, local energy system operations must account for uncertain energy production and prices. Two-stage stochastic programming, combined with probabilistic forecasting, provides a mathematical framework to derive optimal operation schedules under uncertainty. In the common predict-then-optimize approach, probabilistic forecasts are selected based on statistical scores, such as the continuous ranked probability score (CRPS) or the logarithmic score (LS), without considering the optimization task at hand. However, these scores do not necessarily reflect the forecasts’ performance in the optimization task. This thesis analyzes the value of probabilistic forecasts in two-stage stochastic programs for the optimal operation of local energy systems under uncertainty from three perspectives: first, in a purely theoretical examination, second, in an application to synthetic use cases, and third, in an application to a real-world university campus energy system. In the theoretical examination, we systematically analyze stochastic programming formulations of local energy systems and their market interactions to find which type of probabilistic forecast is minimally required to obtain the best mathematically possible result. The examination shows that full joint forecast distributions are required only in certain cases, such as systems with storage or bidding curve optimization. For many practical scheduling problems, univariate or bivariate forecasts are sufficient. The application to two synthetic use cases shows that while the CRPS often performs best among the considered scores, its performance in the optimization task highly depends on the specific use case and its parameters. This shows that statements about the best scores are only valid for specific cases. Finally, the application to a university campus confirms that probabilistic demand forecasts significantly improve scheduling outcomes, while expected value forecasts are sufficient for electricity prices. However, using bi- or multivariate demand forecasts in this application does not improve results over univariate demand forecasts. These insights support practitioners in selecting forecast types strategically, balancing complexity with the needs of the specific optimization problem at hand.