工程科学与技术2026，Vol.58Issue(1)：121-132,12.DOI:10.12454/j.jsuese.202400699
梯级泵站优化调度模型参数敏感性分析及其求解算法改进
Parameter Sensitivity Analysis and Algorithm Improvement of Optimization Scheduling Model for Cascade Pumping Stations
摘要
Abstract
Objective Low operating efficiency,high energy consumption,and substantial carbon emissions are common problems in the operation of cas-cade pumping stations.To improve operational efficiency and support the"dual carbon"objective,an optimization scheduling model for cascade pumping stations is established with the goal of minimizing carbon emissions,and the Runge-Kutta algorithm(RUN)is introduced to solve the model.In addition,to address the lack of a quantitative sensitivity analysis in the optimal scheduling of cascade pumping stations,the Sobol global sensitivity method is employed to quantitatively evaluate the influence of key parameters on carbon emissions.To overcome the tendency of RUN falling into local optima due to insufficient initial population diversity and boundary stagnation,an improved Runge-Kutta(TRUN)algo-rithm based on a Tent chaotic map is proposed. Methods First,an optimal scheduling model for cascade pumping stations was developed with carbon emission minimization as the objective function.Second,the Sobol method was used to analyze the sensitivity of the head of each pumping station and the flow rate of each unit to car-bon emissions,thereby quantifying the impact of decision variables on the objective function.Third,an optimized scheduling method based on TRUN was proposed.While retaining the exploration characteristics of the RUN algorithm,Tent chaos mapping was introduced to enhance the di-versity of the initial population,accelerate convergence,and improve solution accuracy.Additionally,a Tent boundary mapping strategy was ad-opted to regenerate boundary values,further improving optimization efficiency.Six benchmark functions,including unimodal,multimodal,and fixed-dimension functions,were used to verify the performance of TRUN and the effectiveness of the improvement strategies.Finally,a three-stage pumping station was selected as a case study,in which the Sobol method was used to determine the sensitivity ranking of system param-eters,and TRUN was applied to obtain the optimal scheduling scheme. Results and Discussions The mean values and standard deviations of six benchmark functions,including unimodal(Schwefel 2.21(f1),Rosen-brock(f2)),multimodal(Schwefel(f3),Rastrigin(f4)),and fixed-dimension(Hartman(f5),Shekel(f6)),were calculated using the TRUN,RUN,TPSO,PSO,TGA,and GA algorithms.TRUN,RUN,TPSO,PSO,TGA,and GA achieved 4,2,0,0,1,and 0 optimal solutions,respectively,veri-fying the superiority of TRUN and the effectiveness of the proposed improvement strategies.Based on this,the Sobol global sensitivity analysis and TRUN-based optimization scheduling method were applied to a three-stage pumping station.The sensitivity ranking of system parameters,in descending order,was as follows:flow rate of each unit in the first-stage pumping station,flow rate of each unit in the second-stage pumping sta-tion,head of the first-stage pumping station,flow rate of each unit in the third-stage pumping station,head of the second-stage pumping station,and head of the third-stage pumping station.These results provide quantitative guidance for daily operational decision-making.In single-stage pumping station optimization,TRUN achieved 67,56,and 46 optimal solutions out of 100 comparison runs,showing a clear advantage over the other algorithms.In cascade pumping station optimization,compared with the current operating scheme,the TRUN-based scheduling scheme re-duced carbon emissions by 249 485 kg/a,outperforming RUN,TPSO,PSO,TGA,and GA,and confirming the effectiveness of the proposed algorithm. Conclusions The results demonstrate that the proposed TRUN algorithm exhibits excellent optimization performance.The TRUN-based optimal scheduling method for cascade pumping stations effectively improves system operational efficiency,and its optimization results are superior to those obtained using RUN,TPSO,PSO,TGA and GA.In addition,the Sobol global sensitivity analysis provides quantitative insights into the in-fluence key parameters on carbon emissions,offering valuable references for operational decision-making of cascade pumping station systems.关键词
改进龙格库塔算法/梯级泵站/优化调度/碳排放/敏感性分析Key words
improved Runge Kutta optimizer/cascade pumping station/optimal scheduling/carbon emissions/sensitivity analysis分类
建筑与水利引用本文复制引用
刘小莲,李贞蓉,王雪妮,翟宇,张雷克,郭维维,田雨..梯级泵站优化调度模型参数敏感性分析及其求解算法改进[J].工程科学与技术,2026,58(1):121-132,12.基金项目
国家自然科学基金面上项目(52379091) （52379091）
山西省基础研究计划项目(202203021222112) （202203021222112）
山西省水利技术研究推广补助项目(2024GM21) （2024GM21）
