Study on Optimization of Return Current Nodes in Active Return Traction Power System
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摘要:
有源回流牵引供电系统(active return traction power system，AR-TPS)通过回流节点(return current node，RCN)将走行轨电流转移至回流线缆，从而实现对城市轨道交通钢轨电位与杂散电流的治理. 为提升AR-TPS的治理性能，提出一种回流节点优化布设方法. 首先，建立两层分布参数模型与回流节点电流转移模型，揭示RCN数量与布设位置对电流转移能力的影响规律；进而基于工程约束与节点功能将节点数量精简为两个，并以治理性能最优为目标将布设位置优化于区间中点附近. 最后，基于典型列车运行曲线进行仿真验证. 结果表明：与有源阻抗变换器协同工作的外侧节点是回流电流转移至回流线缆的主要路径；AR-TPS的治理性能随RCN向区间中点靠近而持续提升. 采用传统牵引供电系统时，钢轨电位最大值为34.86 V，杂散电流最大值为2.89 A，总泄漏电荷量为134.00 C；采用优化前节点均匀布设的AR-TPS时，上述指标降低至14.84 V、0.94 A和55.70 C，相较于传统牵引供电系统的抑制率分别为57.42%、67.47%和58.43%. 采用所提方法优化后的AR-TPS时，上述指标进一步降低至8.66 V、0.66 A和38.67 C，抑制率提升至75.16%、77.16%和71.14%.
Abstract:The rail potential and stray current in urban rail transit are mitigated by the active return traction power system (AR-TPS) by transferring the running rail current to the return cables through the return current node (RCN). To improve the mitigation performance of the AR-TPS, an optimization layout method of RCNs was proposed. First, a two-layer distributed parameter model and an RCN current transfer model were established to reveal the influence laws of RCN number and layout position on the current transfer capability. Then, based on engineering constraints and node functions, the number of RCNs was simplified to two, and the layout positions were optimized near the midpoint of the section with the optimal mitigation performance as the objective. Finally, a simulation verification was conducted based on the typical train operation curve. The results indicate that the outer RCN working in coordination with the active resistance converter is the primary path for transferring the return current to the return cables. The mitigation performance of the AR-TPS continuously improves as the RCN approaches the midpoint of the section. When the conventional traction power system is adopted, the maximum rail potential is 34.86 V; the maximum stray current is 2.89 A, and the total leakage charge is 134.00 C. When the AR-TPS with uniformly distributed RCNs before optimization is adopted, the above indicators are reduced to 14.84 V, 0.94 A, and 55.70 C, and the suppression rates are 57.42%, 67.47%, and 58.43%, respectively, compared with the conventional traction power system. When the AR-TPS optimized by the proposed method is adopted, the above indicators are further reduced to 8.66 V, 0.66 A, and 38.67 C, and the suppression rates are increased to 75.16%, 77.16%, and 71.14%.
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Key words:
- power supply system /
- return current node /
- rail potential /
- stray current /
- optimization
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图 6 三节点系统中内侧节点转移电流分布
Figure 6. Distribution of transfer current of inner node in three-node system
图 9 回流节点转移电流模型验证策略
Figure 9. Verification strategy for transfer current model of return current node
图 10 回流节点转移电流仿真结果对比
Figure 10. Comparison of simulation results for transfer current of return current node
图 11 三回流节点系统各节点转移电流占比
Figure 11. Proportion of transfer current of each node in three-return current node system
图 12 两回流节点系统各节点转移电流占比
Figure 12. Proportion of transfer current of each node in two-return current node system
图 13 调整回流节点位置时的Urpm、isc及Qsum分布
Figure 13. Distribution of Urpm, isc, and Qsum when adjusting positions of return current nodes
表 1 建模参数
Table 1. Modeling parameters
变量 物理意义 iL 列车电流 UiL 列车等效电压 x 列车位置 L 区间长度 L1 外侧节点与TS的距离 L2 中间节点与外侧节点的距离 Rg 单位过渡电阻 Rr 走行轨单位电阻 Rca 回流线缆单位电阻 Rt 接触网/第三轨单位电阻 Rs 牵引所内阻 i1 ～ i6 网孔电流 $i_{{\mathrm{RCN}}_1} $ ～ $i_{{\mathrm{RCN}}_3} $ 回流节点转移电流 
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表 2 两回流节点系统各区段回流节点转移电流解析式
Table 2. Analytical expressions of transfer current of return current node for each section in two-return current node system
iRCN 区段1 区段2 区段3 ${i}_{\text{RCN}_1} $ $ \dfrac{{U}_{\text{ARC}_1} + {R}_{\text{r}}{i}_{\text{L}}x}{{L}_{1}\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} $ $ \dfrac{{U}_{\text{ARC}_1}}{{L}_{1}\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} + \dfrac{{i}_{\text{L}}{R}_{\text{r}}\left(L-{L}_{1}-x\right)}{\left(L-2{L}_{1}\right)\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} $ $ \dfrac{{U}_{\text{ARC}_1}}{{L}_{1}\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} $ ${i}_{\text{RCN}_2} $ $ \dfrac{{U}_{\text{ARC}_2}}{{L}_{1}\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} $ $ \dfrac{{U}_{\text{ARC}_2}}{{L}_{1}\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} + \dfrac{{i}_{\text{L}}{R}_{\text{r}}\left(x-{L}_{1}\right)}{\left(L-2{L}_{1}\right)\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} $ $ \dfrac{{U}_{\text{ARC}_2} + {R}_{\text{r}}{i}_{\text{L}}(L-x)}{{L}_{1}\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} $
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表 3 三回流节点系统各区段回流节点转移电流解析式
Table 3. Analytical expressions of transfer current of return current node for each section in three-return current node system
变量 区段1 区段2 区段3 区段4 $i_{{\mathrm{RCN}}_1} $ $ \dfrac{{U}_{\text{ARC}_1} + {R}_{\text{r}}{i}_{\text{L}}x}{{L}_{1}\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} $ $ \dfrac{{U}_{\text{ARC}_1}}{{L}_{1}\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} + \dfrac{{R}_{\text{r}}{i}_{\text{L}}\left(x-{L}_{2}\right)}{\left({L}_{1}-{L}_{2}\right)\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} $ $ \dfrac{{U}_{\text{ARC}_1}}{{L}_{1}\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} $ $ \dfrac{{U}_{\text{ARC}_1}}{{L}_{1}\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} $ $i_{{\mathrm{RCN}}_2} $ 0 $ \dfrac{{R}_{\text{r}}{i}_{\text{L}}\left({L}_{1}-x\right)}{\left({L}_{1}-{L}_{2}\right)\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} $ $ \dfrac{{R}_{\text{r}}{i}_{\text{L}}\left({L}_{1}-L + x\right)}{\left({L}_{1}-L + {L}_{2}\right)\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} $ 0 $i_{{\mathrm{RCN}}_3} $ $ \dfrac{{U}_{\text{ARC}_2}}{{L}_{1}\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} $ $ \dfrac{{U}_{\text{ARC}_2}}{{L}_{1}\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} $ $ \dfrac{{U}_{\text{ARC}_2}}{{L}_{1}\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} + \dfrac{{R}_{\text{r}}{i}_{\text{L}}\left({L}_{2}-x\right)}{\left({L}_{1}-L + {L}_{2}\right)\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} $ $ \dfrac{{U}_{\text{ARC}_2} + {R}_{\text{r}}{i}_{\text{L}}(L-x)}{{L}_{1}\left({R}_{\text{ca}} + {R}_{\text{r}}\right)} $
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表 4 仿真参数
Table 4. Simulation parameters
参数 取值 Rt/（mΩ·km−1） 10 Rr/（mΩ·km−1） 10 Rg/（Ω·km） 15 Rca/（mΩ·km−1） 24 L/km 5 L1/km 1.5 L2/km 1 uTS/V 750
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表 5 优化前后系统配置与治理性能对比
Table 5. Comparison of system configuration and mitigation performance before and after optimization
对比项目 CON-TPS AR-TPS AR-TPS（优化） RCN数量/个 3 2 RCN位置/km 1.5；3.5 2.4；2.6 Urpm/V 34.86 14.84 8.66 iscm/A 2.89 0.94 0.66 Qsum/C 134.00 55.70 38.67
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