基于非支配遗传算法的小浪底水沙电联合优化调度研究

Research on joint optimization scheduling of water, sediment, and power in Xiaolangdi Reservoir based on non-dominated genetic algorithm

  • 摘要: 水库排沙调度往往需要降低水位运行,这与发电需要的高水位运行有冲突,需要制定合理的调度方案使水库能够长期运行且发挥最大效益。选取小浪底水库为研究对象,以水库减淤与发电为核心目标,结合一维水沙模型与快速非支配遗传算法(Non-dominated Sorting Genetic Algorithm III, NSGA-Ⅲ),建立了小浪底水沙电优化调度模型。该模型综合考虑了水库的泥沙调度和发电调度,且在计算水库冲淤情况时,采用了相较于经验排沙比公式更精细的一维水沙模型。结果表明:一维水沙模型能够准确地模拟各测站水位过程;通过NSGA-Ⅲ优化后得到的一系列帕累托最优解突显了调度过程中水库减淤与发电间的矛盾,且帕累托曲线上的方案明显优于原方案,在淤积量不变情况下,增加发电量11.4%,发电量不变情况下,减少淤积量48%,在发电与减淤目标函数值比值不变的情况下,两者分别增加13%和50%。研究成果可以定量分析水库发电与减淤目标间的置换关系,为多沙河流水库的水沙电联合优化调度提供了有效的技术支撑。

     

    Abstract: Sediment discharge scheduling in reservoirs often requires lowering water levels, which conflicts with the higher levels needed for power generation. Therefore, a reasonable scheduling scheme is essential to ensure long-term operation and maximize benefits. This study focuses on the Xiaolangdi Reservoir, aiming to enhance its siltation reduction and power generation benefits. By integrating a one-dimensional hydrodynamic and sediment transport model with the Non-Dominated Sorting Genetic Algorithm III (NSGA-Ⅲ), an optimization scheduling model for water, sediment, and power generation was developed. The model simultaneously considers sediment and power generation objectives, employing a refined one-dimensional hydrodynamic and sediment transport model that offers more accurate sedimentation calculations than empirical sediment discharge efficiency formulas. The Preissmann scheme discretizes the governing equations, solved via the double-sweep method. The hydro-sediment model calibration involved analyzing the effects of parameters in the sediment transport capacity formula on predicted sedimentation. In the NSGA-III algorithm, an individual represents a series of daily-averaged outflow discharges from the reservoir, which serve as outlet boundary conditions driving the hydro-sediment model. Predicted water levels and updated bed elevations at each cross-section evaluate the objective functions of power generation and siltation reduction. Initial population generation was improved by considering total released water volume. Uniform crossover and polynomial mutation are applied, with mutation amplitude constrained by reservoir discharge capacity. Results show the hydro-sediment model accurately simulates water levels at multiple stations, with Nash-Sutcliffe efficiencies from 0.77 to 0.99. Predicted outflow sediment concentration aligns well with measurements, and sedimentation volume error is within 4.3%. The proposed model optimized Xiaolangdi Reservoir outflow discharge from April 20 to October 20, 2012. Initial crossover and mutation probabilities were set at 0.4 and 0.02, respectively, dynamically reduced to 0.2 and 0.01 over iterations. The target pool level matched the actual level at the operation period's end. Population distribution in objective space was observed across generations. The Pareto optimal solutions from NSGA-Ⅲ highlight the conflict between siltation reduction and power generation, with Pareto front solutions outperforming the original plan. Holding sedimentation constant, power generation increased by 11.4%; conversely, with constant power generation, sedimentation volume reduced by 48%. Keeping the ratio of objectives constant, power generation increased by 13%, and siltation reduction by 50%. The minimum siltation plan and the turning point on the Pareto front were compared with actual operations regarding pool level processes. All optimal solutions converge to states maintaining pool levels below the flood-limited water level, satisfying flood control constraints. The minimum achievable siltation is 0.74×108 m3 and the maximum power generation is 5.82×109 kW·h. This model enables quantitative analysis of trade-offs between power generation and siltation reduction, supporting multi-objective optimal scheduling of reservoirs in heavily sediment-laden rivers.

     

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