This paper introduces a new strategy for controlling electric water heaters (EWH) using mixed-integer linear programming (MILP). It has two major contributions: 1) To balance between cost savings and the discomfort (cold water) that Demand Response (DR) could bring, the discomfort is modeled as undelivered energy in the objective of the problem rather than a thermal constraint. This improves both sides of the cost-saving Vs. User-comfort trade-ff. 2) in EWH control, many previous works only rely on electricity prices for scheduling. However, this work is among the very few works that also consider consumption for scheduling. Further, by treating the hot water withdrawal pattern as a random variable, the algorithm finds the best setpoints for EWH via stochastic optimization over a range of possible hot water withdrawal patterns, rather than requiring perfect foresight of withdrawal. The result of these changes is an algorithm that can let the temperature fall below minimum when probability of energy usage is low without affecting user comfort while other methods always keep the temperature above minimum. The effectiveness of this approach on improving both sides of the cost Vs. discomfort trade-off and the effectiveness of stochastic approach is confirmed by compassion with two other methods.

本文介绍了一种使用混合整数线性规划（MILP）控制电热水器（EWH）的新策略。它有两个主要贡献：1）为了在节省成本和需求响应（DR）可能带来的不舒适感（冷水）之间取得平衡，该不舒适感被建模为问题的目标，而不是热约束。这改善了节省成本的双方。用户舒适度-ff。2）在EWH控制中，许多以前的工作仅依靠电价进行调度。但是，这项工作是为数不多的也考虑了计划消耗的工作之一。此外，通过将热水抽取模式视为随机变量，该算法通过在一系列可能的热水抽取模式上进行随机优化来找到EWH的最佳设定点，而不是要求完美的预见力。这些变化的结果是一种算法，当能量使用的可能性较低时，可以使温度降至最低以下，而不会影响用户的舒适度，而其他方法则始终将温度保持在最低以上。这种方法在改善成本Vs双方的有效性。不适感的折衷和随机方法的有效性已通过同情其他两种方法得到了证实。