A multi-objective optimal control model of cascade pumping stations considering both cost and safety

It is very important to reduce the operation cost and ensure the channel safety for open-channel water diversion projects with cascade pumping stations. In this study, a multi-objective optimal control model of cascade pumping stations is coupled with the one-dimensional unsteady flow model considering both cost and safety, and a case study is performed with the section from the Tuancheng lake to the Huairou reservoir of the Miyun Reservoir Regulation and Storage Project, China, with six pumping stations. Compared with the actual scheme (M0), the average water lifting cost is reduced by 4.54–12.14% for the optimization schemes (M1-M6); the average variation of water level is reduced by 2.94–26.47% for M1-M5 but increased by 7.35% for M6. When the downstream pumping station needs to be adjusted, the larger the discharge is, the lower the average unit water lifting cost and the larger the average variation of water level will be. However, step-by-step adjustment should be used when a large adjustment (>2 m3/s) is required, because the variation of water level is higher than 30 cm/d in this case.