AI 中文总结
该研究针对供水系统水泵调度的不确定性问题，整合需水量与电价概率预测构建风险感知随机优化框架，发现其核心益处为提升运行鲁棒性，最优策略可实现最高9%的成本节约。
AI 中文摘要
饮用水公用事业面临需水量和电价的不确定性，以及可靠且成本高效的运行要求。本文研究了参与日前拍卖并后续不平衡市场结算的饮用水供应商在不确定性下的序贯多阶段水泵调度问题。我们将需水量和电价的概率预测整合到风险感知随机优化框架中。可靠性和经济风险偏好通过结合条件风险价值（CVaR）和超额风险（Exceedance Risk）测度的词典式目标来表示，该框架可明确考虑不平衡市场结算。数值研究表明，预测性能的提升通常会转化为策略性能的改善。此外，我们发现随机优化的主要益处在于提高运行鲁棒性，而非降低预期成本。需水量被发现是策略质量的主导驱动因素，电价预测进一步改进的边际价值相对有限，表明价格信息中可经济利用的部分已在很大程度上被捕捉。与价格不变基准相比，最优随机策略实现了高达9%的成本节约，表明通过接受精心控制的不平衡暴露和运行风险增加，可实现显著的经济效益。
英文摘要
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.
