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浙江大学学报(工学版)
Journal of ZheJiang University (Engineering Science)  2023, Vol. 57 Issue (12): 2501-2512    DOI: 10.3785/j.issn.1008-973X.2023.12.017
    
Optimal scheduling of cascade pumping stations based on improved Harris hawks optimization algorithm
Lei-ke ZHANG1(),Xiao-peng HOU1,Xiao-lian LIU1,*(),Yu TIAN2
1. College of Water Resources Science and Engineering, Taiyuan University of Technology, Taiyuan 030024, China
2. State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, China
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Abstract  

The optimal operation model of cascade pumping stations was established with the objective function of maximizing the total operation efficiency. An optimized scheduling method based on improved Harris hawks optimization (HUHHO) was proposed to raise the operation efficiency of the system and save the cost. Firstly, the starvation rate was introduced in order to control the balance between exploration and exploitation. Secondly, considering the effect of hunger intensity on prey hunting ability, an offset item was added in the exploration stage to enhance the search capability and avoid falling into the local optimum. Then, the superior performance of HUHHO was demonstrated by the benchmark functions. In addition, the proposed method was applied to the optimal operation of a three-stage pumping station in Beijing. Finally, the feasibility and effectiveness of HUHHO for solving the optimal scheduling problem in cascade pumping stations were verified. Results show that compared with the current scheme, the optimization scheme based on HUHHO can increase the operation efficiency of the system by 0.11 percentage points and save 42 187 yuan in annual operating costs, which are better than those obtained by using particle swarm optimization (PSO), genetic algorithm (GA) and Harris hawks optimization (HHO).

Key words： cascade pumping station      optimal scheduling      economic operation      improved Harris hawks optimization algorithm (HUHHO)      large-scale system      decomposition-coordination model     
Received: 06 February 2023      Published: 27 December 2023
CLC:  TV 675  
Fund:  国家重点研发计划项目(2021YFC3001000)；国家自然科学基金资助项目(51879273)
Corresponding Authors: Xiao-lian LIU     E-mail: zhangleike@tyut.edu.cn;liuxiaolian@tyut.edu.cn
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Lei-ke ZHANG
Xiao-peng HOU
Xiao-lian LIU
Yu TIAN
Cite this article:

Lei-ke ZHANG,Xiao-peng HOU,Xiao-lian LIU,Yu TIAN. Optimal scheduling of cascade pumping stations based on improved Harris hawks optimization algorithm. Journal of ZheJiang University (Engineering Science), 2023, 57(12): 2501-2512.

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https://www.zjujournals.com/eng/10.3785/j.issn.1008-973X.2023.12.017     OR     https://www.zjujournals.com/eng/Y2023/V57/I12/2501


基于改进哈里斯鹰算法的梯级泵站优化调度

为了提高梯级泵站系统运行效率，节约工程运行成本，以梯级泵站运行效率最大化为目标，建立梯级泵站优化调度模型，提出基于改进哈里斯鹰算法（HUHHO）的梯级泵站优化调度方法. 将饥饿率引入哈里斯鹰算法（HHO）以更好地实现探索与开发之间的平衡；在探索阶段添加1个偏移项以考虑哈里斯鹰饥饿感强弱对搜寻猎物能力的影响，提高算法的寻优能力、避免陷入局部最优. 通过基准测试函数验证HUHHO寻优性能的优越性. 将HUHHO应用于北京市某三级泵站优化调度中，对HUHHO求解梯级泵站优化调度问题的可行性与有效性进行验证. 结果表明：相较于现状方案，基于HUHHO的优化方案可使梯级泵站运行效率提高0.11个百分点，年运行成本节约42 187元，优于利用粒子群优化算法（PSO）、遗传算法（GA）、HHO得到的运行效率及节约成本.


关键词： 梯级泵站,  优化调度,  经济运行,  改进哈里斯鹰算法（HUHHO）,  大系统,  分解协调模型 
Fig.1 Structure diagram of optimal dispatching model for cascade pumping station
Fig.2 Flow chart of improved Harris hawks optimization algorithm
算法 Rastrigin Ackley Foxholes Kowalik
Mean Std Mean Std Mean Std Mean Std
PSO 4.014×10 9.711 4.856 9.542×10?1 1.950 1.495 8.020×10?4 3.957×10?4
GA 1.098×10 2.267 2.942 2.046×10?1 1.576 1.526 1.631×10?2 1.988×10?2
GWO 2.802 3.459 1.053×10?13 1.658×10?14 3.935 4.106 3.730×10?3 7.568×10?3
HHO 0 0 1.007×10?15 6.486×10?16 1.164 3.768×10?1 4.138×10?4 2.468×10?4
HUHHO 0 0 8.882×10?16 0 1.031 1.815×10?1 4.048×10?4 2.035×10?4
Tab.1 Optimization performance test of different algorithms
Fig.3 Convergence curves of different algorithms with different test functions
Fig.4 Flow chart of optimal scheduling of cascade pumping stations based on improved Harris hawks optimization algorithm
Fig.5 Schematic diagram of cascade pumping station in three-stage pumping station
泵站 Ht/m h/m Qj，k/（m3·s?1） ηj, k Hn h/Hn ηj,max/% ηc,max/%
k=1 k=2 k=3 k=1 k=2 k=3
1 1.03 6.47 6.47 6.47 0.37 0.37 0.37 37.04
0.51
2 1.60 6.47 6.47 6.47 0.51 0.51 0.51 4.84 0.33 51.00 34.09
0.11
3 2.21 6.47 6.47 6.47 0.63 0.63 0.63 62.66
Tab.2 Current situation scheme for water transfer system of three-stage pumping station
Fig.6 Comparison of optimization effects for different algorithm
优化方案 泵站 Ht/m h/m Qj，k/（m3·s?1） ηj, k Hn/m h/Hn ηj,max/% ηc,max/%
k=1 k=2 k=3 k=1 k=2 k=3
基于PSO 1 1.04 6.30 6.80 6.30 0.36 0.39 0.36 4.84 0.334 5 37.31 34.11
0.56
2 1.62 6.80 6.80 5.80 0.54 0.54 0.46 51.64
1.06
3 2.18 6.50 6.40 6.50 0.62 0.61 0.62 61.92
基于GA 1 1.14 6.30 6.58 6.52 0.40 0.42 0.41 4.79 0.327 3 41.17 34.12
0.52
2 1.45 6.80 6.37 6.23 0.49 0.46 0.45 46.29
1.05
3 2.19 6.49 6.49 6.41 0.62 0.62 0.62 62.20
基于HHO 1 1.12 6.98 6.34 6.08 0.43 0.40 0.38 4.80 0.328 6 40.29 34.15
0.56
2 1.50 6.30 6.58 6.52 0.47 0.49 0.49 48.24
1.02
3 2.17 6.60 6.40 6.40 0.63 0.61 0.61 61.50
基于HUHHO 1 1.23 6.47 6.47 6.7 0.45 0.45 0.45 4.74 0.320 8 44.71 34.20
0.44
2 1.31 6.43 6.47 6.50 0.41 0.42 0.42 41.70
1.08
3 2.20 6.50 6.41 6.49 0.63 0.62 0.63 62.47
Tab.3 Optimization results of cascade pumping station based on different algorithms
Fig.7 Comparison of convergence process based on Harris hawks optimization algorithm before and after improved
N ηc,max
Th=50、Tq=50 Th=100、Tq=50 Th=50、Tq=100 Th=100、Tq=100 Th=100、Tq=150 Th=150、Tq=150
30 0.341 6 0.342 0 0.342 0 0.342 0 0.342 1 0.342 2
50 0.341 6 0.342 1 0.342 1 0.342 1 0.342 3 0.342 3
100 0.341 8 0.342 2 0.342 2 0.342 2 0.342 4 0.342 4
150 0.342 0 0.342 4 0.342 4 0.342 5 0.342 5 0.342 5
Tab.4 Optimization results by improved Harris hawks optimization algorithm in different population sizes and maximum iterations
[1]   仇锦先. 南水北调东线水源泵站优化运行理论及其应用研究[D]. 武汉: 武汉大学, 2010.
QIU Jin-xian. Study on the theory and application of the water-source pumping station optimal operation of South-to-North Eastern Route Water Diversion Project [D]. Wuhan: Wuhan University, 2010.
[2]   付辉, 郭新蕾, 杨开林, 等 南水北调中线工程典型倒虹吸进口上游垂向流速分布[J]. 水科学进展, 2017, 28 (6): 922- 929
FU Hui, GUO Xin-lei, YANG Kai-lin, et al Distribution of vertical flow velocity upstream of an inverted siphon in the Middle Route of South-to-North Water Diversion Project[J]. Advances in Water Science, 2017, 28 (6): 922- 929
doi: 10.14042/j.cnki.32.1309.2017.06.013
[3]   龚懿, 程吉林, 张仁田 淮安-淮阴段梯级泵站群运行优化[J]. 农业工程学报, 2013, 29 (22): 59- 67
GONG Yi, CHENG Ji-lin, ZHANG Ren-tian Operation optimization of Huai’an-Huaiyin multistage pumping stations[J]. Transactions of the Chinese Society of Agricultural Engineering, 2013, 29 (22): 59- 67
doi: 10.3969/j.issn.1002-6819.2013.22.007
[4]   鄢碧鹏, 杜晓雷, 刘超, 等 基于遗传算法和神经网络的泵站经济运行研究[J]. 农业机械学报, 2007, 38 (1): 80- 82
YAN Bi-peng, DU Xiao-lei, LIU Chao, et al optimal operation of pumping stations based on genetic algorithms and artificial neural networks[J]. Transactions of the Chinese Society for Agricultural Machinery, 2007, 38 (1): 80- 82
doi: 10.3969/j.issn.1000-1298.2007.01.020
[5]   GUO W, XU P, DAI F, et al Improved Harris hawks optimization algorithm based on random unscented sigma point mutation strategy[J]. Applied Soft Computing, 2021, 113: 108012
doi: 10.1016/j.asoc.2021.108012
[6]   杨建军, 刘扬, 魏立新, 等 多源注水系统泵站优化调度的双重编码混合遗传算法[J]. 自动化学报, 2006, 32 (1): 154- 160
YANG Jian-jun, LIU Yang, WEI Li-xin, et al Dual coding hybrid genetic algorithm for optimal schedule of pumping stations in multi-sources water injection system[J]. Acta Automatica Sinica, 2006, 32 (1): 154- 160
doi: 10.16383/j.aas.2006.01.024
[7]   LÓPEZ-IBÁÑEZ M, PRASAD T D, PAECHTER B Ant colony optimization for optimal control of pumps in water distribution networks[J]. Journal of Water Resources Planning and Management, 2008, 134 (4): 337- 346
doi: 10.1061/(ASCE)0733-9496(2008)134:4(337)
[8]   MCCORMICK G, POWELL R S Derivation of near-optimal pump schedules for water distribution by simulated annealing[J]. Journal of the Operational Research Society, 2004, 55: 728- 736
doi: 10.1057/palgrave.jors.2601718
[9]   SEDKI A, OUAZAR D Hybrid particle swarm optimization and differential evolution for optimal design of water distribution systems[J]. Advanced Engineering Informatics, 2012, 26 (3): 582- 591
doi: 10.1016/j.aei.2012.03.007
[10]   冯晓莉, 王永兴, 仇宝云 基于混合狼群算法参数优选的泵站群运行优化[J]. 农业工程学报, 2020, 36 (3): 30- 36
FENG Xiao-li, WANG Yong-xing, QIU Bao-yun Operation of pumping station group based on optimized parameters using hybrid wolf pack algorithm[J]. Transactions of the Chinese Society of Agricultural Engineering, 2020, 36 (3): 30- 36
doi: 10.11975/j.issn.1002-6819.2020.03.004
[11]   张俊涛, 申建建, 程春田, 等 耦合目标接近度和边际分析原理的梯级水电站多目标优化调度方法[J]. 中国电机工程学报, 2019, 39 (5): 1268- 1277
ZHANG Jun-tao, SHEN Jian-jian, CHENG Chun-tian, et al Multi-objective optimal operation of cascade hydropower stations based on objective adjacent scale and marginal analysis principle[J]. Proceedings of the CSEE, 2019, 39 (5): 1268- 1277
doi: 10.13334/J.0258-8013.PCSEE.172296
[12]   冯仲恺, 廖胜利, 牛文静, 等 改进量子粒子群算法在水电站群优化调度中的应用[J]. 水科学进展, 2015, 26 (3): 413- 422
FENG Zhong-kai, LIAO Sheng-li, NIU Wen-jing, et al Improved quantum-behaved particle swarm optimization and its application in optimal operation of hydropower stations[J]. Advances in Water Science, 2015, 26 (3): 413- 422
doi: 10.14042/j.cnki.32.1309.2015.03.012
[13]   HEIDARI A A, MIRJALILI S, FARIS H, et al Harris hawks optimization: algorithm and applications[J]. Future Generation Computer Systems, 2019, 97: 849- 872
doi: 10.1016/j.future.2019.02.028
[14]   BEDNARZ J C Cooperative hunting Harris’ hawks (Parabuteo unicinctus) [J]. Science, 1988, 239 (4847): 1525- 1527
doi: 10.1126/science.239.4847.1525
[15]   谢渊, 高玮, 汪义伟, 等 基于哈里斯鹰优化遗传规划的钢筋混凝土地下结构硫酸盐腐蚀寿命预测[J]. 土木工程学报, 2022, 55 (4): 33- 41
XIE Yuan, GAO Wei, WANG Yi-wei, et al Life prediction of RC underground structure by sulfate attack based on Harris hawks optimizing genetic programming[J]. China Civil Engineering Journal, 2022, 55 (4): 33- 41
doi: 10.15951/j.tmgcxb.2022.04.001
[16]   MOUASSA S, BOUKTIR T, JURADO F Scheduling of smart home appliances for optimal energy management in smart grid using Harris-hawks optimization algorithm[J]. Optimization and Engineering, 2021, 22: 1625- 1652
doi: 10.1007/s11081-020-09572-1
[17]   苏佳, 杨志华, 刘彦明. 基于改进哈里斯鹰算法的系统能效优化[EB/OL]. [2023-01-01]. https://kns.cnki.net/kcms/detail/42.1658.n.20221108.1255.002.html.
[18]   CHAKRABORTY S, VERMA S, SALGOTRA A, et al Solar-based DG allocation using Harris hawks optimization while considering practical aspects[J]. Energies, 2021, 14 (16): 5206
doi: 10.3390/en14165206
[19]   ARYA AZAR N, GHORDOYEE MILAN S, KAYHOMAYOON Z Predicting monthly evaporation from dam reservoirs using LS-SVR and ANFIS optimized by Harris hawks optimization algorithm[J]. Environmental Monitoring and Assessment, 2021, 193: 695
doi: 10.1007/s10661-021-09495-z
[20]   LONG W, JIAO J, LIANG X, et al A velocity-guided Harris hawks optimizer for function optimization and fault diagnosis of wind turbine[J]. Artificial Intelligence Review, 2023, 56: 2563- 2605
doi: 10.1007/s10462-022-10233-1
[21]   SUN W, PENG T, LUO Y, et al Hybrid short-term runoff prediction model based on optimal variational mode decomposition, improved Harris hawks algorithm and long short-term memory network[J]. Environmental Research Communications, 2022, 4 (4): 045001
doi: 10.1088/2515-7620/ac5feb
[22]   LIU J, LIU X, WU Y, et al Dynamic multi-swarm differential learning Harris hawks optimizer and its application to optimal dispatch problem of cascade hydropower stations[J]. Knowledge-Based Systems, 2022, 242: 108281
doi: 10.1016/j.knosys.2022.108281
[23]   赵世杰, 高雷阜, 于冬梅, 等 融合能量周期性递减与牛顿局部增强的改进HHO算法[J]. 控制与决策, 2021, 36 (3): 629- 636
ZHANG Shi-jie, GAO Lei-fu, YU Dong-mei, et al Improved harris hawks optimization coupling energy cycle decline mechanism and Newton local enhancement strategy[J]. Control and Decision, 2021, 36 (3): 629- 636
doi: 10.13195/j.kzyjc.2019.0810
[24]   ALABOOL H M, ALARABIAT D, ABUALIGAH L, et al Harris hawks optimization: a comprehensive review of recent variants and applications[J]. Neural Computing and Applications, 2021, 33: 8939- 8980
doi: 10.1007/s00521-021-05720-5
[25]   QU C, HE W, PENG X, et al Harris hawks optimization with information exchange[J]. Applied Mathematical Modelling, 2020, 84: 52- 75
doi: 10.1016/j.apm.2020.03.024
[26]   LIU X, TIAN Y, LEI X, et al An improved self-adaptive grey wolf optimizer for the daily optimal operation of cascade pumping stations[J]. Applied Soft Computing, 2019, 75: 473- 493
doi: 10.1016/j.asoc.2018.11.039
[27]   郑和震, 张召, 吴辉明, 等 梯级泵站输水系统日优化调度及经济运行研究[J]. 水利学报, 2016, 47 (12): 1558- 1565
ZHENG He-zhen, ZHANG Zhao, WU Hui-ming, et al Study on the daily optimized dispatching and economic operation of cascade pumping stations in water conveyance system[J]. Journal of Hydraulic Engineering, 2016, 47 (12): 1558- 1565
doi: 10.13243/j.cnki.slxb.20151350
[28]   ABDOLLAHZADEH B, GHAREHCHOPOGH F S, MIRJALILI S African vultures optimization algorithm: a new nature-inspired metaheuristic algorithm for global optimization problems[J]. Computers and Industrial Engineering, 2021, 158: 107408
doi: 10.1016/j.cie.2021.107408
[29]   JIA H, LANG C, OLIVA D, et al Dynamic Harris hawks optimization with mutation mechanism for satellite image segmentation[J]. Remote Sensing, 2019, 11 (12): 1421
doi: 10.3390/rs11121421
[30]   YAO X, LIU Y, LIN G Evolutionary programming made faster[J]. IEEE Transactions on Evolutionary Computation, 1999, 3 (2): 82- 102
doi: 10.1109/4235.771163
[31]   TIAN H, YUAN X, JI B, et al Multi-objective optimization of short-term hydrothermal scheduling using non-dominated sorting gravitational search algorithm with chaotic mutation[J]. Energy Conversion and Management, 2014, 81: 504- 519
doi: 10.1016/j.enconman.2014.02.053
[32]   桑国庆. 基于动态平衡的梯级泵站输水系统优化运行及控制研究[D]. 济南: 山东大学, 2012.
SANG Guo-qing. Research on operation and control optimization of cascade pumping station water-delivery system based on dynamic balance [D]. Jinan: Shandong university, 2012.
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