Scenario generation via moments-informed normalizing flows for stochastic optimization of local energy markets

Scenario generation is a critical step in stochastic programming for energy systems applications, where accurate representation of uncertainty directly impacts the decision quality. Normalizing flows (NFs), a class of invertible deep generative models, offer flexibility in learning complex distributions by maximizing the likelihood, but often suffer from limited accuracy in reproducing key statistical properties of real-world data. In this work we propose a moments-informed Normalizing Flows (MI-NF) framework, in which moment constraints are incorporated into the NF training process to improve the accuracy of scenario-based probabilistic forecasts. Furthermore, Gaussian Processes (GPs) are employed to adaptively determine the moment regularization weight. Case studies on the open-access dataset of the Global Energy Forecasting Competition 2014 demonstrate that scenarios generated by the MI-NF model achieve over 40% lower mean absolute error on the testing set. When applied within a stochastic programming framework for a local electricity–hydrogen market, the improved scenario accuracy leads to more cost-effective and robust operational decisions under uncertainty.