Abstract:
Pumping stations are critical infrastructure in water transfer systems, yet their high energy consumption and operational inefficiencies under dynamic real-world conditions pose significant challenges. Traditional operation based on design schemes often fails to adapt to varying demands, leading to reduced efficiency and energy wastage. Optimal operation strategies can mitigate these issues, but the strong nonlinearity of constraints and the complexity of the solution space in mathematical models make it difficult for conventional intelligent algorithms to converge to feasible solutions, particularly under strict equality constraints. These challenges are addressed through the development of an optimization model aimed at minimizing the energy consumption of parallel pumping station groups, incorporating constraints such as single-unit flowrate, pump blade angles, installed unit count, and required flowrate. To solve the optimization problem, 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. The case study focused on a typical parallel pumping station group operating at a 5 m head and a 300 m
3/s flowrate demand. Results revealed that PSO, WPA, and AO could not guarantee 100% feasibility in solution generation, with PSO and WPA exhibiting high sensitivity to parameter variations. Specifically, increasing population size and iteration count improved feasibility for these algorithms, whereas AO and FA demonstrated lower parameter sensitivity. The optimal parameter combination, determined by minimizing the objective function, was a population size of 200 and 200 iterations. To enhance optimization performance, the basic algorithms were hybridized with a Simulated Annealing (SA) strategy. This integration improved the algorithms' ability to escape local optima by probabilistically perturbing the current best solution and balancing global exploration with local exploitation through temperature regulation. Compared with the basic PSO, WPA, FA and AO algorithms, the relative deviations between the energy consumption value and the mean energy consumption value of the four hybrid algorithms were reduced by 0.122%, 0.055%, 0.002% and 0.020%, respectively. 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, demonstrating superior performance in parameter sensitivity, optimization capability, and stability. This makes SA-FA particularly suitable for variable operating conditions of pumping stations. Further analysis of operational strategies revealed that under constant head conditions, pumping stations prioritize activating highly efficient units. As water demand increases, moderately efficient and less efficient units are progressively engaged. However, discrete constraints—such as blade angle settings and the number of operating units—sometimes prevent the activation of all high-efficiency units. In actual operations, fixed blade angle settings and a lack of dynamic adjustment under head variations cause operating points to deviate from high-efficiency zones. Additionally, the integer constraint on the number of operating units often results in flowrate exceeding demand. Comparative evaluation showed that the optimized operation scheme achieved energy savings ranging from 1.76% to 10.94% compared to actual operations. Assuming a CO
2 emission reduction of 0.272 kg per kW·h saved, annual operation over 200 days could reduce emissions by 898 to 4,584 tons, highlighting significant energy-saving and emission-reduction benefits. Notably, the energy-saving rate does not linearly increase with higher head and flow rate but depends on head magnitude, pump assembly efficiency, and actual pumping flowrate. To assess energy utilization efficiency, specific energy consumption was used as a metric. The optimized scheme exhibited values between 3.78 and 3.88 kW·h/(kt·m), outperforming the actual operation scheme’s range of 3.87 to 4.27 kW·h/(kt·m), confirming higher energy efficiency. This research provides both theoretical foundations and practical solutions for the energy-efficient operation of large-scale water transfer projects. The proposed hybrid algorithms, particularly SA-FA, offer robust optimization capabilities under complex constraints, ensuring feasibility while minimizing energy consumption. The findings underscore the importance of adaptive operation strategies in enhancing efficiency and reducing environmental impact, contributing to sustainable water management practices.