Optimization dispatch of large pumping station units under start-stop constraints based on hybrid black-winged kite algorithm

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.