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. 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.

For pumping stations installed blade full-adjustable pumps with frequently varying head in a wide range, adjusting pump blade angles is an effective way to realize optimum operation. Optimal mathematical models were established aiming at the least daily operation cost for pumping station system, which includes main pump units, inlet and outlet passages and their accessories, forebay and outlet pond, auxiliary equipment, power transmission and transformation equipment, other electromechanical equipments and lightings. Also, head varying, time-varying electrical price, and blade adjusting frequency are all taken into account. Meanwhile, the influences of the blade adjusting frequency on operation cost are researched. The results indicate that the operation cost is reduced by 5.64%∼12.13% by the optimal schemes considering time-varying electrical price and adjusting pump blade angles than that of conventional schemes, taking Jiangdu Forth Pumping Station in China as a case. The more the blade adjusting frequency, the less the operation cost. Also, if the blade adjusting frequency exceeds eight times, the optimum operation cost is close to be a const. Therefore, it is advisable to adjust blade angles four to six times a day to save operation cost and guarantee the reliability of pump units.

Trash racks are set before inlet sumps of a pumping station with wet-pits in order to block trash. The flow fields before and behind the trash rack were numerically simulated and flow fields in the inlet sump were calculated using the simulated velocity distribution of the section behind the trash rack as the inlet boundary condition. Local head loss of trash-barriering increases with the increase of blockage ratio of the trash rack. When waterweeds block upper part of the trash rack, flow pattern behind the trash rack will be extremely turbulent, flow velocity of lower part of inlet section of inlet sump will increase, flow velocity of the upper part will decrease, and even backflow appears, which will deteriorate the flow pattern and increase head loss in the inlet sump. Trash-barriering has little effect on velocity distribution of impeller inlet section. Trash-barriering will not only increase head and power of the pump but also decrease the flow. For the example of the pumping station: when blockage ratios of the trash racks are 0.3, 0.5, and 0.7, operating cost will increase by 13%~43% than that of without trash racks. Therefore, the trash rack should be cleaned up timely.

To deal with the high energy consumption issue of existing pumping station operation modes, an optimization model ensuring the flow rate and safety demands of pumping station and aiming at the minimum operating power of the system, is established based on basic Particle Swarm Optimization (PSO), which can provide theoretical support for the optimal operation of pumping station. When solving high dimension problems, PSO is easy to get into local optimum and has a slow convergence rate at the later stage of iteration. In order to overcome the shortcomings mentioned above, the Halton sequence is used to generate the initial population randomly, at the same time the inertia weight reducing along the opening downward parabola and Simulated Annealing(SA) are employed, too. The Improved Hybrid Particle Swarm Optimization (IHPSO) is implemented in Matlab. And it is applied to calculate the optimization schemes of the pumping station system of the South-to-North Water Transfer Project in China. The results show that the convergence and stability of the IHPSO are better than the PSO, and IHPSO can effectively solve pumping station optimization operation with multiple variables. The power of the optimum scheme based on IHPSO is about 7.68% less than that based on PSO, and it is decreased about 11.51% compared with the designed scheme.

A water diversion system (WDS) with cascade pumping stations (CPSs) plays an important role in the application of water resources. However, high energy consumption is reported due to unreasonable scheduling schemes and long decision times. Herein, this paper presents a new method to achieve optimal scheduling schemes effectively, including the head allocation of CPSs, the number of running pumps, and pump blade angles. A double-layer mathematical model for a WDS was established with the goal of achieving minimal energy consumption, considering the constraints of flow rate, water level, and the characteristics of pump units. The inner-layer model was used to obtain scheduling schemes of single-stage pumping stations, as well as the water levels and flow rates of water channels, while the outer-layer model was used to optimize inter-stage head allocation. An improved wolf-pack algorithm (IWPA) was proposed to solve the model, using a Halton sequence to obtain the uniform initial population distribution and introducing simulated annealing (SA) to improve the global searchability. Moreover, an idea for a pre-established scheme library was suggested for inner-layer models to obtain the solutions in real time with less calculation workload. Taking an actual project as a case, in contrast with the actual schemes, the optimal scheduling method could result in energy savings of 14.37–20.39%, a CO₂ emission reduction of 13–32 tons per day, and water savings of 0.14–18.34%. Moreover, the time complexity decreased to square order, and the CPU time of the optimal method was about 1% that of the traditional method. This study provides an efficient method for the high-value utilization of energy and water resources for a WDS.