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Modeling Calculation and Experimental Analysis of Closed-Loop Current Based on DIgSILENT Considering Load Distribution and Three-Phase Imbalance
DOI: 10.12677/MOS.2024.131061, PDF, HTML, XML, 下载: 108  浏览: 175

Abstract: To improve the success rate of ring network switching in urban medium-voltage distribution net-works, this paper proposes a modeling and calculation method for closed-loop current that takes into account the load distribution and three-phase imbalance in medium-voltage feeders. Firstly, theoretical analysis is conducted on the steady-state and impulse currents in the medium-voltage feeders, with a formulaic analysis of the reasons for closed-loop current generation and the factors influencing it. Secondly, combining theoretical analysis, a simulation model for closed-loop current calculation is established using DIgSILENT, considering different load distributions and the three-phase unbalance of loads. Finally, simulation results are compared with on-site ring switching tests for two groups, indicating lower calculation errors when considering three-phase imbalance and varying load distributions. This research provides practical guidance for actual closed-loop current operations.

1. 引言

2. 10 kV配电网合环类型

Figure 1. Partial geographic schematic of the regional power grid

Table 1. Measured parameters of the ring network experiment

3. 合环理论分析

3.1. 合环潮流分析

Figure 2. Equivalent network considering load distribution

${\stackrel{˙}{U}}_{left}=\frac{\Delta PR+\Delta QX}{{U}_{left}}+j\frac{\Delta PX-\Delta QR}{{U}_{left}}$ (1)

${\stackrel{˙}{U}}_{left}={U}_{left}\mathrm{cos}{\delta }_{ij}+j{U}_{left}\mathrm{sin}{\delta }_{ij}$ (2)

$\begin{array}{c}\Delta P=\frac{{U}_{left}R\left({U}_{rigth}\mathrm{cos}{\delta }_{ij}-{U}_{left}\right)}{{R}^{2}+{X}^{2}}\\ +\frac{{U}_{left}{U}_{rigth}X\mathrm{sin}{\delta }_{ij}}{{R}^{2}+{X}^{2}}\end{array}$ (3)

$\begin{array}{c}\Delta Q=\frac{{U}_{left}X\left({U}_{rigth}\mathrm{cos}{\delta }_{ij}-{U}_{left}\right)}{{R}^{2}+{X}^{2}}\\ +\frac{{U}_{left}{U}_{rigth}R\mathrm{sin}{\delta }_{ij}}{{R}^{2}+{X}^{2}}\end{array}$ (4)

$\frac{\partial \Delta P}{\partial \left({U}_{left}-{U}_{rigth}\right)}\approx \frac{{U}_{rigth}R}{{R}^{2}+{X}^{2}}$ (5)

$\frac{\partial \Delta P}{\partial {\delta }_{ij}}\approx \frac{{U}_{left}{U}_{rigth}X}{{R}^{2}+{X}^{2}}$ (6)

$\frac{\partial \Delta Q}{\partial \left({U}_{left}-{U}_{rigth}\right)}\approx \frac{{U}_{rigth}X}{{R}^{2}+{X}^{2}}$ (7)

$\frac{\partial \Delta Q}{\partial {\delta }_{ij}}\approx -\frac{{U}_{left}{U}_{rigth}X{\delta }_{ij}+{U}_{left}{U}_{rigth}R}{{R}^{2}+{X}^{2}}$ (8)

3.2. 合环稳态电流分析

${{U}^{\prime }}_{a1}=\sqrt{\left[{\left({U}_{a1}-\frac{{P}_{a1}rl+{Q}_{a1}xl}{{U}_{a1}}\right)}^{2}+{\left(\frac{{P}_{a1}xl-{Q}_{a1}rl}{{U}_{a1}}\right)}^{2}\right]}$ (9)

${U}_{e}={{U}^{\prime }}_{a1}-{U}_{a1}$ (10)

${Z}_{0}={R}_{0}+{X}_{0}$ (11)

${\stackrel{˙}{U}}_{a1}=\Delta {U}_{a1}+j\Delta {u}_{a1}$ (12)

${\theta }_{a1}=-\mathrm{arctan}\left(\frac{\Delta {u}_{a1}}{\Delta {U}_{a1}}\right)$ (13)

$\Delta {U}_{i}=\frac{{P}_{i}{R}_{i}+{Q}_{i}{X}_{i}}{{U}_{i}}$ (14)

$\Delta {u}_{i}=\frac{{P}_{i}{X}_{i}-{Q}_{i}{R}_{i}}{{U}_{i}}$ (15)

$\Delta {U}_{left}=\Delta {U}_{a0}-\underset{i=1}{\overset{3}{\sum }}\Delta {U}_{i}$ (16)

$\Delta {u}_{left}=\Delta {u}_{a0}-\underset{i=1}{\overset{3}{\sum }}\Delta {u}_{i}$ (17)

${\stackrel{˙}{U}}_{left}=\Delta {U}_{left}+j\Delta {u}_{left}$ (18)

${\stackrel{˙}{U}}_{rigth}=\Delta {U}_{rigth}+j\Delta {u}_{rigth}$ (19)

$d\stackrel{˙}{U}={\stackrel{˙}{U}}_{left}-{\stackrel{˙}{U}}_{rigth}$ (20)

${\stackrel{˙}{I}}_{p}=\frac{d\stackrel{˙}{U}}{\sqrt{3}×\left({R}_{\sum }+{X}_{\sum }\right)}$ (21)

${R}_{\sum }={R}_{0}+{R}_{a1}+{R}_{a2}+{R}_{a3}+{R}_{b1}+{R}_{b2}+{R}_{b3}$ (22)

${X}_{\sum }={X}_{0}+{X}_{a1}+{X}_{a2}+{X}_{a3}+{X}_{b1}+{X}_{b2}+{X}_{b3}$ (23)

${\stackrel{˙}{I}}_{a1}={\stackrel{˙}{I}}_{a0}+{\stackrel{˙}{I}}_{p}$ (24)

${\stackrel{˙}{I}}_{b1}={\stackrel{˙}{I}}_{b0}-{\stackrel{˙}{I}}_{p}$ (25)

3.3. 合环冲击电流计算

${i}_{peak}=\sqrt{2}×{I}_{P}\left[1+{\text{e}}^{\left(-0.01/{T}_{a}\right)}\right]$ (26)

${I}_{peak}={I}_{P}×\sqrt{{\left[1+{\text{e}}^{\left(-0.01/{T}_{a}\right)}\right]}^{2}}$ (27)

${i}_{peak}=\sqrt{2}×{I}_{\text{P}}×{k}_{peak}$ (28)

${I}_{peak}={I}_{\text{P}}×\sqrt{1+2×{\left({k}_{peak}-1\right)}^{2}}$ (29)

4. 10 kV馈线负荷分布处理

4.1. 负荷分布的处理

4.2. 负荷不平衡度的处理

${\epsilon }_{s}=\frac{{S}_{\mathrm{max}}-{S}_{\mathrm{min}}}{{S}_{\mathrm{max}}}×100%$ (30)

5. 合环影响因素分析及合环条件

6. 仿真与试验对比分析

6.1. DIgSILENT简化建模

Figure 3. Specific ring network simulation using DIgSILENT in a certain location

6.2. 计算结果与试验对比分析

Figure 4. RMS value of ring current

Figure 5. Current at the head of Dusixian line

Table 2. Phase angles of ring feeder busbars

Table 3. 10 kV feeder line parameters

Table 4. Calculated results of closed-loop current for different load distributions

Table 5. Comparison of closed-loop current and actual error

Figure 6. Current at the head of Jixi line

Figure 7. Three-phase balanced ring network impulse current

Figure 8. Three-phase unbalanced ring network impulse current

7. 总结

1) 在考虑不同负荷分布情况的计算中，合环电流的有效计算能够更准确地覆盖实际负荷不确定性，提高计算结果的实用性。

2) 考虑三相不平衡情况下，当三相不平衡方向不一致时，合环后不平衡度可能会缓解，但当三相不平衡方向一致时可能会导致更大的合环电流。

3) 计算结果与实际合环试验进行对比，表明模型计算的误差相对较小，验证了模型在实际工程中的实用性。使用DlgSILENT软件有效减少了合环电流计算的工作量。

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