Abstract:
The majority of large pumping stations suffer from substantial water and energy resource wastage coupled with elevated operational costs, primarily attributable to the absence of scientific operation strategies. To achieve the objectives of cost reduction while ensuring secure and reliable operation, this study employs the Dayuzhang Pumping Station within the Yellow River-to-Qingdao Water Diversion Project as a representative case. A comprehensive optimization model was formulated with the explicit objective of minimizing total daily operational electricity cost. The model systematically considers the energy consumption of primary pump units, auxiliary equipment, and substation facilities under a time-of-use (TOU) electricity pricing mechanism. The model rigorously constrains unit start-stop operations within short-duration cycles to guarantee safety and reliability, while simultaneously incorporating constraints critical hydraulic and engineering constraints including flow rate, adjustable blade angles, and the permissible number of operating units, aiming to determine the optimal unit commitment and blade angles for each period. To address the computational challenges inherent in solving this complex mathematical optimization model, particularly the difficulty of the basic Black Kite Algorithm (BKA) in locating feasible global optima, an enhanced Hybrid Black-winged Kite Algorithm (HBKA) incorporating a simulated annealing mechanism is proposed. Based on parameter sensitivity tests, the population size and maximum iterations are configured as 300 and 200, respectively. Benchmark tests against a classic pump station optimization model confirm the superior efficacy of HBKA, which achieves a 23.2% reduction in relative standard deviation and a 28% decrease in computational time compared to the Hybrid Particle Swarm Optimization (HPSO) algorithm, demonstrating its strong suitability for this class of nonlinear, constrained problems. Case study results from the target pumping station reveal that under an operating head of 5.0 m, the proposed operation scheme with continuous units under total pumping volume constraint achieves optimal allocation of pumping volume across different TOU price periods by adjusting blade angles. The optimization results reveal a distinct inverse correlation between the optimal blade angle and the prevailing electricity price: as the TOU price escalates, the algorithm prescribes a smaller blade angle to reduce the hourly averaged pumping volume. Once the blade angle reaches its operational lower bound, it stabilizes at this minimum value; consequently, during peak pricing periods, the hourly averaged electricity cost increases linearly with the tariff, directly establishing electricity price as the dominant factor in the operational cost function. Comparative analysis reveals that while an alternative scheme permitting unit commitment yields the lowest theoretical electricity cost, it necessitates approximately 10 start-stop cycles daily, which may induce significant mechanical stress and compromise long-term reliability. In contrast, the proposed scheme offers a balanced solution. It reduces daily electricity costs by 2.50% to 5.15% compared to the constant flow constraint scheme, and by 7.58% to 21.14% compared to the on-site actual operation scheme. Crucially, it delivers a significant 13.01% cost reduction specifically during on-peak hours while completely eliminating start-stop cycles, thereby prioritizing operational safety and equipment longevity. Sensitivity analysis further reveals that a ±10% variation in operating head leads to electricity cost changes of -8.11% to +14.33%, yet the optimization model maintains feasibility across this range, demonstrating its practical robustness against parameter fluctuations. This research provides substantive theoretical contributions and practical methodologies for the optimal design, unit selection, and advanced operation management of large-scale pumping stations. The developed HBKA-based optimization methodology offers a viable pathway towards sustainable water-energy nexus management in critical water infrastructure systems. Future work will tackle operational uncertainties in head, electricity price, and equipment efficiency by integrating robust optimization methods to enhance disturbance-resistant dispatch, validating the strategies via hydraulic model experiments, and applying model predictive control for real-time command adjustment and system integration.