Bayesian Inflow Forecasting for Flexibility Quantification in Wastewater Pumping Stations

Wastewater pumping stations represent a significant and underexploited source of demand-side flexibility, which can be utilized by controlling pump energy consumption within operational constraints. Quantifying this flexibility reliably requires accurate probabilistic models of the dominant source of uncertainty: the wastewater inflow, which is driven by precipitation events and exhibits heavy-tailed, skewed dynamics that challenge standard homoskedastic modeling assumptions. This paper presents a data-driven framework for energy flexibility quantification in a wastewater pumping station in Rønne, Denmark, combining a heteroskedastic Bayesian neural network (BNN) inflow model with a sample average approximation (SAA) stochastic optimization targeting the mFRR energy activation market. The BNN substantially outperforms homoskedastic baselines in empirical calibration, which is the primary available proxy for the reliability of flexibility envelopes, as they cannot be validated against a counterfactual baseline. The computed envelopes exhibit a physically consistent diurnal pattern, with upward flexibility peaking during high-inflow events and downward flexibility dominating under dry-weather conditions, while maintaining a feasibility rate above 95% across the evaluation period.