Pumping stations have been one of the most critical infrastructures in water transfer systems. Some challenges have also been posed on the energy consumption and operational efficiencies under dynamic real-world conditions. However, conventional operation can often fail to fully meet the varying demands, leading to reduced efficiency and energy wastage. Optimal operation strategies can mitigate these issues. But there is the strong nonlinearity of constraints and the complexity of the solution space in the mathematical models. Conventional intelligent algorithms are then limited to converge into the feasible solutions, particularly under strict equality constraints. In this study, an optimal model was developed to minimize the energy consumption of the parallel pumping station groups. Some constraints were also incorporated, such as the single-unit flow rate, pump blade angles, installed unit count, and required flow rate. Four intelligent algorithms—particle swarm optimization (PSO), wolf pack algorithm (WPA), aquila optimizer (AO), and firefly algorithm (FA)—were evaluated under nine parameter combinations of population size and iteration count. A case study was carried out to focus on a typical parallel pumping station group at a 5 m head and a 300 m³/s flow rate demand. Results revealed that the PSO, WPA, and AO failed to guarantee 100% feasibility in solution generation, with the PSO and WPA with high sensitivity to parameter variations. Specifically, the population size and iteration count improved the feasibility of these algorithms. Whereas the AO and FA demonstrated the lower parameter sensitivity. The optimal combination of the parameters was determined to minimize the objective function, with a population size of 200 and 200 iterations. The basic algorithms were hybridized with a simulated annealing (SA) strategy in order to enhance the optimization performance. The improved algorithms were integrated to escape the local optima. The current best solution was obtained to avoid probabilistically perturbing. Global exploration was balanced with the local exploitation after temperature regulation. Furthermore, the relative deviations of the four hybrid algorithms were reduced by 0.122%, 0.055%, 0.002% and 0.020%, respectively, compared with the basic PSO, WPA, FA, and AO algorithms. Among the hybrid algorithms, the simulated annealing-firefly algorithm (SA-FA) achieved the smallest objective function value and the least relative deviation in 100 independent runs, indicating the superior performance in the parameter sensitivity, optimization capability, and stability. The SA-FA was particularly suitable for the variable operating conditions. Operational strategies revealed that the pumping stations were prioritized to activate the highly efficient units under constant head conditions. The moderately efficient and less efficient units were progressively engaged as the water demand increased. Nevertheless, the discrete constraints—such as blade angle settings and the number of operating units—sometimes prevented to activate all high-efficiency units. In actual operations, the fixed blade angle settings without dynamic adjustment under head variations caused the operating points and then deviated from the high-efficiency zones. Additionally, the integer constraint on the number of operating units often resulted in the flow rate exceeding demand. Comparative evaluation showed that the optimized operation scheme was achieved in the energy savings ranging from 1.76% to 10.94%, compared with the actual operations. When assuming a CO₂ emission reduction of 0.272 kg/(kW·h) saved, the annual operation over 200 days reduced emissions by 898 to 4 584 tons, indicating the significant energy-saving and emission-reduction benefits. Notably, the energy-saving rate depended mainly on the head magnitude, pump assembly efficiency, and actual pumping flow rate, rather than the linear increase with the higher head and flow rate. Energy utilization efficiency was evaluated for the specific energy consumption as a metric. The optimal scheme exhibited the values between 3.78 and 3.88 kW·h/(kt·m), thus outperforming the actual operation scheme's range of 3.87 to 4.27 kW·h/(kt·m). The higher energy efficiency was obtained for the theoretical foundations and practical solutions in the large-scale water transfer projects. The hybrid algorithms, particularly SA-FA, can offer robust optimization under complex constraints, indicating the feasibility and minimum energy consumption. The findings can provide adaptive operation strategies to enhance the efficiency for the less environmental impacts in sustainable water practices.

Most large pumping stations have suffered from substantial water and energy resource wastage with high operational costs, due mainly to the absence of scientific operation strategies. This study aims to reduce the cost of secure and reliable operations in large pumping stations. A case study was employed at the Dayuzhang Pumping Station within the Yellow River-to-Qingdao Water Diversion Project. An optimal model was formulated to minimize the total cost of daily electricity. A systematic investigation was implemented to reduce the energy consumption of primary pump units, auxiliary equipment, and substation facilities under a time-of-use (TOU) electricity pricing mechanism. Safety and reliability were realized to constrain the unit start-stop operations within short-duration cycles. While the critical hydraulic and engineering constraints were simultaneously incorporated, including flow rate, adjustable blade angles, and the permissible number of operating units. A mathematical model was constructed to determine the optimal unit commitment and blade angles for each period. An enhanced Hybrid Black-winged Kite Algorithm (HBKA) was proposed to simulate the annealing mechanism using Black Kite Algorithm (BKA). The feasible global optima were then obtained after optimization. According to parameter sensitivity tests, the population sizes and maximum iterations were configured as 300 and 200, respectively. Benchmark tests against a classic optimization model confirmed that the superior efficacy of HBKA was achieved with a 23.2% reduction in relative standard deviation and a 28% decrease in computational time, compared with the Hybrid Particle Swarm Optimization (HPSO) algorithm. A strong suitability was found for this class of nonlinear and constrained pump station. A case study from the target pumping station revealed that the blade angles were adjusted to optimally allocate the pumping volume under an operating head of 5.0 m in the different TOU price periods. The continuous units were used under total pumping volume constraints. There was an inverse correlation between the optimal blade angle and the prevailing electricity price after optimization: A smaller blade angle reduced the hourly averaged pumping volume, as the TOU price escalated. The blade angle reached its operational lower bound to stabilize at the minimum; Consequently, the hourly averaged electricity cost increased linearly with the tariff, directly taking the electricity price as the dominant factor in the operational cost function. Comparative analysis revealed that one of the alternative unit commitment was taken as the lowest theoretical electricity cost, which was required for approximately 10 start-stop cycles daily, leading to significant mechanical stress and long-term reliability. In contrast, the daily electricity costs were reduced by 2.50% to 5.15%, and 7.58% to 21.14%, compared with the constant flow constraints and the on-site actual operation, respectively. Crucially, the 13.01% cost was significantly reduced during on-peak hours, while the start-stop cycles were reduced to prioritize the operational safety and equipment longevity. Sensitivity analysis further revealed that there was the ±10% variation in the operating head, leading to an electricity cost from -8.11% to +14.33%. Yet the optimization model maintained feasibility over this range, indicating its practical robustness against parameter fluctuations. This finding can provide a theoretical and practical contribution to the optimal design, unit selection, and advanced operation of large-scale pumping stations. The HBKA optimization can offer a viable pathway towards a sustainable water-energy nexus in critical water infrastructure. Future work can tackle operational uncertainties in head, electricity price, and equipment efficiency. Robust optimization was integrated to enhance disturbance-resistant dispatch. Hydraulic model experiments were then validated to predict the real-time command adjustment and system integration.