Risk-Aware Pump Control in Water Supply Systems Using Probabilistic Water Demand and Electricity Price Forecasts

Abstract

Drinking water utilities face uncertain water demand and electricity prices, as well as requirements for reliable and cost-efficient operation. This paper investigates a sequential multi-stage pump scheduling problem under uncertainty for a drinking water supplier participating in the day-ahead auction with subsequent imbalance market settlement. We integrate probabilistic forecasts of water demand and electricity prices into a risk-aware stochastic optimization framework. Reliability and economic risk preferences are represented through a lexicographic objective incorporating Conditional Value-at-Risk and Exceedance Risk measures, where the framework allows to explicitly account for the imbalance market settlement. A numerical study demonstrates that improvements in forecasting performance generally translate into improved policy performance. Furthermore, we found that the primary benefit of stochastic optimization lies in improved operational robustness rather than lower expected costs. The water demand is found to be a dominant driver of policy quality, the marginal value of further improvements in electricity price forecasts appears comparatively limited, indicating that the economically exploitable component of the price information is already captured to a large extent. Compared with a price-invariant benchmark, the best stochastic policy achieves cost savings of up to $9\%$, indicating that substantial economic benefits can be realized by accepting a carefully controlled increase in imbalance exposure and operational risk.