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基于模拟退火改进算法的泵站多约束优化运行

Optimal operation of a multi-constrained pumping stations using simulated annealing-enhanced algorithms

  • 摘要: 针对群体智能算法求解强等式约束下泵站运行优化模型时存在可行解搜索效率低、寻优能力不足的问题,该研究以泵站运行能耗最低为目标,以单机流量、叶片角度、装机台数和需求流量为约束条件,构建泵站优化运行数学模型。通过对比粒子群算法(particle swarm optimization,PSO)、狼群算法(wolf pack algorithm,WPA)、天鹰算法(aquila optimizer,AO)和萤火虫算法(firefly algorithm,FA)的性能,发现PSO和WPA对种群规模和迭代次数敏感性高,AO和FA的敏感性低。将模拟退火策略分别引入4种算法中,形成混合智能算法。通过模拟退火机制在局部最优解附近概率性跳出并接受劣解,搜索范围扩大,可行解出现率达100%,并且目标函数值进一步降低。其中模拟退火-萤火虫算法(simulating algorithm-firefly algorithm,SA-FA)的寻优能力与稳定性最佳。某典型泵站案例的数值计算结果表明,在恒定扬程下泵站优先启动高效机组,随需求流量增加依次启动中、低效机组,部分工况下需权衡目标抽水量与能耗选择性启停机组。相较实际运行方案,优化运行方案可节能1.76%~10.94%。研究成果可为大型调水工程节能运行方案设计提供参考。

     

    Abstract: Pumping stations have been one of the most critical infrastructures in water transfer systems. Some challenges have also been posed on the energy consumption and operational efficiencies under dynamic real-world conditions. However, conventional operation can often fail to fully meet the varying demands, leading to reduced efficiency and energy wastage. Optimal operation strategies can mitigate these issues. But there is the strong nonlinearity of constraints and the complexity of the solution space in the mathematical models. Conventional intelligent algorithms are then limited to converge into the feasible solutions, particularly under strict equality constraints. In this study, an optimal model was developed to minimize the energy consumption of the parallel pumping station groups. Some constraints were also incorporated, such as the single-unit flow rate, pump blade angles, installed unit count, and required flow rate. Four intelligent algorithms—particle swarm optimization (PSO), wolf pack algorithm (WPA), aquila optimizer (AO), and firefly algorithm (FA)—were evaluated under nine parameter combinations of population size and iteration count. A case study was carried out to focus on a typical parallel pumping station group at a 5 m head and a 300 m³/s flow rate demand. Results revealed that the PSO, WPA, and AO failed to guarantee 100% feasibility in solution generation, with the PSO and WPA with high sensitivity to parameter variations. Specifically, the population size and iteration count improved the feasibility of these algorithms. Whereas the AO and FA demonstrated the lower parameter sensitivity. The optimal combination of the parameters was determined to minimize the objective function, with a population size of 200 and 200 iterations. The basic algorithms were hybridized with a simulated annealing (SA) strategy in order to enhance the optimization performance. The improved algorithms were integrated to escape the local optima. The current best solution was obtained to avoid probabilistically perturbing. Global exploration was balanced with the local exploitation after temperature regulation. Furthermore, the relative deviations of the four hybrid algorithms were reduced by 0.122%, 0.055%, 0.002% and 0.020%, respectively, compared with the basic PSO, WPA, FA, and AO algorithms. Among the hybrid algorithms, the simulated annealing-firefly algorithm (SA-FA) achieved the smallest objective function value and the least relative deviation in 100 independent runs, indicating the superior performance in the parameter sensitivity, optimization capability, and stability. The SA-FA was particularly suitable for the variable operating conditions. Operational strategies revealed that the pumping stations were prioritized to activate the highly efficient units under constant head conditions. The moderately efficient and less efficient units were progressively engaged as the water demand increased. Nevertheless, the discrete constraints—such as blade angle settings and the number of operating units—sometimes prevented to activate all high-efficiency units. In actual operations, the fixed blade angle settings without dynamic adjustment under head variations caused the operating points and then deviated from the high-efficiency zones. Additionally, the integer constraint on the number of operating units often resulted in the flow rate exceeding demand. Comparative evaluation showed that the optimized operation scheme was achieved in the energy savings ranging from 1.76% to 10.94%, compared with the actual operations. When assuming a CO2 emission reduction of 0.272 kg per kW·h saved, the annual operation over 200 days reduced emissions by 898 to 4 584 tons, indicating the significant energy-saving and emission-reduction benefits. Notably, the energy-saving rate depended mainly on the head magnitude, pump assembly efficiency, and actual pumping flow rate, rather than the linear increase with the higher head and flow rate. Energy utilization efficiency was evaluated for the specific energy consumption as a metric. The optimal scheme exhibited the values between 3.78 and 3.88 kW·h/(kt·m), thus outperforming the actual operation scheme's range of 3.87 to 4.27 kW·h/(kt·m). The higher energy efficiency was obtained for the theoretical foundations and practical solutions in the large-scale water transfer projects. The hybrid algorithms, particularly SA-FA, can offer robust optimization under complex constraints, indicating the feasibility and minimum energy consumption. The findings can provide adaptive operation strategies to enhance the efficiency for the less environmental impacts in sustainable water practices.

     

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