Optimal Siting and Sizing forInverter Feedback Devices Applied in Urban Rail Transit
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摘要:
以节省逆变回馈装置投资成本和提高再生制动能量利用率为目标，建立了城轨牵引供电系统逆变回馈装置定容选址优化模型. 将考虑逆变回馈装置周期性间歇工作制的城轨牵引供电系统交直流混合潮流算法与带精英策略的快速非支配排序遗传算法（fast non-dominated sorting genetic algorithm Ⅱ，fast NSGA-Ⅱ）相结合，求解多目标函数的Pareto解集；并采用基于信息熵的序数偏好法（technique for order preference by similarity to ideal solution，TOPSIS）筛选逆变回馈装置定容选址的最优方案. 以广州地铁某线路为算例进行仿真验证，结果表明：优化方案相对该地铁工程实际逆变回馈装置配置方案，其装置投资成本节省70万元，系统级节能率提高3.25%，投资回报周期相应缩短.
Abstract:A multi-objective optimization model of siting and sizing of inverter feedback devices is established with an objective of saving the investment cost of inverter feedback devices and improving the utilization rate of regenerative braking energy. The AC-DC hybrid power flow algorithm that involves the intermittent work cycle of the inverter feedback device and the fast non-dominated sorting genetic algorithm Ⅱ (fast NSGA-Ⅱ) are combined to solve the Pareto solution set. The entropy-based technique for order preference by similarity to ideal solution (TOPSIS) is adopted to select the optimal site of the inverter feedback device. Cases with a metro line in Guangzhou were studied to compare the optimal solution with the actual configuration scheme of the inverter feedback device, showing that the optimal solution saved 700, 000 yuan of investment cost, increased the system level energy saving rate by 3.25%, and shortened the investment return period.
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Key words:
- traction power supply system /
- inverter feedback device /
- optimal design /
- genetic algorithm /
- entropy
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图 2 安装逆变回馈装置的系统能量流向示意
Figure 2. Energy flow direction for installation of inverter feedback devices
图 4 基于NSGA-Ⅱ求解逆变回馈装置容量配置优化流程
Figure 4. Optimization process of siting and sizing for inverter feedback devices based on NSGA-Ⅱ algorithm
图 6 逆变回馈装置价格与容量关系
Figure 6. Relationship between price and capacity of inverter feedback devices
图 7 目标函数Pareto解集的最优方案变化过程
Figure 7. Change process of optimal scheme of Pareto solution set
图 10 区间所2逆变回馈装置工作占空比
Figure 10. Operating duty ratio of inverter feedback devices in section traction station 2
表 1 牵引所位置信息
Table 1. Traction station position information
牵引所 位置/km 牵引所 位置/km Sub1 0.243 Sub6 13.900 Sub2 2.456 区间所 1 16.287 Sub3 4.568 区间所 2 20.527 Sub4 7.804 Sub8 23.322 Sub5 10.670 Sub9 25.685 
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表 2 仿真参数设置
Table 2. Simulation parameter setting
仿真参数 取值 仿真参数 取值 N 20 Z/MW 2×2.5 J 0.9 Ud0/V 1680 B 0.1 xmax/MW 3 G/次 100 Ui/V 1720 WT1/（kW•h） 3954.17 Ubr/V 1830
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表 3 Pareto解集收敛结果
Table 3. Convergence results of Pareto solution set
V(j) f1(X)/
（×102 万元）f2(X)/% V(j) f1(X)/
（×102 万元）f2(X)/% 1 −3.30 9.54 11 −7.30 19.81 2 −3.60 9.55 12 −8.60 20.28 3 −4.00 14.03 13 −10.10 20.46 4 −4.20 14.53 14 −10.70 20.86 5 −5.30 16.15 15 −11.10 21.48 6 −5.40 16.66 16 −14.90 21.68 7 −5.80 17.94 17 −16.80 21.7 8 −6.70 17.79 18 −6.90 17.61 9 −6.90 17.95 19 −6.20 18.05 10 −7.10 18.85 20 −5.80 17.39
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表 5 逆变回馈装置方案对比
Table 5. Scheme comparison of inverter feedback devices
MW 牵引所 V(7)，Va 牵引所 V(7)，Va Sub1 0，2.0 Sub6 0，0 Sub2 2.0，0 区间所 1 0，0 Sub3 0，0 区间所 2 2.0，0 Sub4 1.5，0 Sub8 0，2.0 Sub5 0，0 Sub9 0，3.0
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表 6 不同优化方案目标函数值对比
Table 6. Comparison of objective function values of different optimization schemes
优化方案 f1(X)/（×102万元） f2(X)/% V(7) 5.80 17.94 Va 6.50 14.69
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表 4 最优方案V(7)每小时潮流计算结果
Table 4. Hourly power flow calculated by optimal scheme V(7)
kW•h 牵引所 WT2 WF WR Sub1 275.97 0 45.66 Sub2 459.14 270.84 Sub3 499.08 0 Sub4 501.06 238.75 Sub5 473.03 0 Sub6 292.77 0 区间所 1 321.41 0 区间所 2 462.30 273.07 Sub8 416.51 0 Sub9 280.59 0 合计 3981.86 782.66 45.66
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