单水库汛期分段线性调度的在线策略与分析

An Online Strategy for Piecewise Linear Scheduling of Hydroelectric Station

针对汛期内洪峰到达水库时刻不确定情形下如何调度水电站库容以最小化水电站汛期内总损失的问题,设计了放水速率可变的多时段水电站在线调度策略。该策略基于在线竞争分析的方法,平衡了水电站低水位发电与弃水两方面的损失,使得洪峰在任意时段内到达水库造成的水电站汛期内总损失上限相等且最小;给出该策略相对于离线最优策略的竞争比并证明策略最优性。实际水库的仿真实验结果表明,竞争比的大小只与在线损失有关,当且仅当库容均匀变化的区间长度相等且洪峰在各个调度区间的端点处到来造成的损失相等时,水电站汛期在线总损失上限最小。与传统调度策略相比,在线调度策略有效降低了损失及损失上限值,损失平均降低了7.09%。

A multi-period online strategy is proposed to deal with the hydroelectric station scheduling problem during the flood season when arrival time of flood peak is uncertain. The purpose of the strategy is to minimize the total loss. The strategy bases on the online competitive analysis, and makes a trade-off between the losses caused by low water head and by surplus water. The strategy equalizes and minimizes all the upper bounds of total losses brought by the arrival of the flood peak at different periods. The competitive ratio of the online strategy is given and the optimality of the strategy is proved. The competitive ratio is only related to the online loss, and the upper bound of total loss gets its minimum if and only if all the lengths of periods are equal and losses brought by the arrival of flood peak at all the endpoints of the periods are equal. Numerical tests and comparisons with the traditional strategy show that the total loss using the proposed strategy decreases by 7.09%.