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基于混合黑翅鸢算法的大型泵站机组启停约束下优化调度

Optimization Dispatch of Large Pumping Station Units under Start-Stop Constraints Based on Hybrid Black-Winged Kite Algorithm

  • 摘要: 针对多数调泵站因缺乏科学运行方案导致的水能资源浪费、运行成本高的问题,该研究以引黄济青工程打渔张泵站为对象,开展降低运行电费、提升运行经济性的优化研究。在保证安全运行的前提下,考虑分时电价机制,构建了以日运行电费最小为目标的泵站系统优化调度模型,并严格约束机组启停、流量、叶片角度及开机台数,确定最优开机台数及各时段叶片角度。提出了混合黑翅鸢算法(Hybrid Black-winged Kite Algorithm,HBKA),并用经典算例测试验证了其优异的寻优能力、稳定性和收敛速度。在5.0 m运行扬程下,抽水总量约束-机组连续运行方案通过优化叶片角度实现了抽水量在不同电价时段的合理分配。该方案较抽水流量约束方案和现场实际运行方案可分别节省电费2.50%~5.15%和7.58%~21.14%,其中尖峰时段电费降低13.01%,经济效益显著。敏感性分析表明,扬程变化±10%导致电费波动−8.11%~+14.33%,模型均能保持可行性。研究成果对大型泵站机组设计选型与运行管理具有重要的理论意义和应用价值。

     

    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.

     

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