This article presents a methodology for optimizing the operation of parallel pumping stations in an open-channel water transfer system. A mathematical model was established for the minimum power with constraints on water level, flow rate and pump unit performance, and related factors. In the objective function, energy consumption of relevant equipment or facilities, such as main pump units, power transmission and transformation equipment, and auxiliary equipment, was considered comprehensively.

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... The model was decomposed to two layers for solving. In the first layer, by using discharge distribution ratio as a variable, the flow rate and water level of the two water channels could be determined by employing the dichotomy approach (DA), and were calculated according to the principle of energy conservation, considering energy loss caused by hydraulic leakage and evaporation losses. In the second layer, the number of running pumps and the flow rate of a single pump were obtained by simulated annealing–particle swarm optimization (SA–PSO). The hybrid of the two algorithms is called the dichotomy approach–simulated annealing–particle swarm optimization (DA–SA–PSO). To verify the efficiency and validity of DA–SA–PSO, SA–PSO is also applied to determine discharge distribution ratio. The results indicate that the computation time using DA–SA–PSO is 1/30 of that using double-layer SA–PSO (dSA–PSO). Compared with the original plan, the optimal solution could result in power savings of 14–35%. Thus, the DA–SA–PSO is highly efficient for optimizing system operation in real time.