Optimization Method for Measurement Points of Grounding Grids Based on a Composite Weighted Vertex Cover Model
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摘要:
为解决接地网测点优化中拓扑与电气特性脱节的问题，提升接地网故障诊断精准度与工程适用性，将接地网转化为具有节点-支路关系的无向图模型，利用节点度数衡量节点拓扑连通特性，利用节点灵敏度衡量节点电气连接特性，构建一种融合节点度数与节点灵敏度的节点复合权重确定模型，采用基于复合权重动态调优的贪婪算法对节点权重模型进行寻优，筛选出可覆盖全支路的接地网测点优化布置方案. 仿真结果表明，该方法可从7 × 7接地网的49个节点中筛选出25个测点，实现接地网所有支路的电气完全可观；在相同测点数量下，单支路腐蚀诊断平均误差较网络拓扑分层约简法降低 15.6%，多支路腐蚀诊断平均误差较网络拓扑分层约简法降低 13.4%，且在测点数量更少的情况下，多支路诊断误差仍优于凝聚层次聚类法，可实现单支路、多支路不同腐蚀程度（轻度、中度、重度）的准确诊断. 所提方法可在保证腐蚀诊断准确度的前提下减少现场测试工作量，对接地网腐蚀的精准维护具有重要实际意义.
Abstract:To address the problem of disconnection between topology and electrical characteristics in the optimization of measurement points of grounding grids and to enhance the accuracy and engineering applicability of fault diagnosis for grounding grids, grounding grids were transformed into an undirected graph model with node-branch relationships. The topological connectivity characteristics of nodes were measured using node degrees, and the electrical connection characteristics of nodes were measured using node sensitivities. A determination model of node composite weight integrating node degree and node sensitivity was constructed. A greedy algorithm based on dynamic tuning of composite weights was adopted to optimize the node weight model, and an optimized layout scheme of measurement points for grounding grids that can cover all branches was selected. Simulation results show that this method can select 25 measurement points from 49 nodes in a 7 × 7 grounding grid, achieving complete electrical observability of all branches of the grounding grid. Under the same number of measurement points, the average error of single-branch corrosion diagnosis is reduced by 15.6% compared with the network topology hierarchical reduction method, and the average error of multi-branch corrosion diagnosis is reduced by 13.4% compared with the network topology hierarchical reduction method. Furthermore, even with fewer measurement points, the multi-branch diagnosis error is still superior to that of the agglomerative hierarchical clustering method, achieving accurate diagnosis of single and multiple branches with different corrosion degrees (mild, moderate, and severe). The proposed method can reduce the on-site testing workload while ensuring the accuracy of corrosion diagnosis, and it has important practical significance for the precise maintenance of grounding grid corrosion.
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Key words:
- grounding grid /
- corrosion diagnosis /
- node coverage /
- measurement point layout
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图 3 灵敏度权重系数$ \alpha $对测点选择的影响
Figure 3. Influence of sensitivity weight coefficient $ \alpha $ on selection of measurement points
表 1 部分节点灵敏度与节点度计算结果
Table 1. Calculation results of node sensitivity and node degree for some nodes
节点编号 $ {s}_{i} $ $ {k}_{i} $ wi $ G({v}_{i}) $ $ P({v}_{i}) $ 1 0.762 2 1.000 2 2.000 21 0.450 3 2.200 3 1.363 37 0.315 4 2.664 4 1.501 
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表 2 不同优化方法的测点数量对比
Table 2. Comparison of number of measurement points for different optimization methods
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表 3 不同布置方案下单支路腐蚀诊断效果对比
Table 3. Comparison of single-branch corrosion diagnosis effectiveness under different layout schemes
测点布置方法 诊断电阻值/
$ \text{m}\Omega $腐蚀诊断
误差/%误差平均
值/%网络拓扑分层
约简法1.521 1.40
1.804.894 2.12 14.827 1.15 19.497 2.51 凝聚层次聚类法 1.477 1.53
1.125.091 1.82 15.140 0.93 19.958 0.21 本文方法 1.525 1.66
1.524.964 0.72 15.303 2.02 20.333 1.66
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表 4 不同测点布置方案下多支路腐蚀诊断效果对比
Table 4. Comparison of multi-branch corrosion diagnosis effectiveness under different measurement point layout schemes
测点布置方案 腐蚀支路诊断电阻值/$ \text{m}\Omega $ 诊断综合误差/% 误差平均值/% 网络拓扑分层约简法 场景1：2.153,8.972,13.723,20.139 2.66
3.81场景2：5.137,11.829,19.802,1.504 3.27 场景3：6.180,9.269,12.325,3.091,15.031 4.18 场景4：1.968,7.115,10.028,15.527,14.931,19.697 5.11 凝聚层聚类法 场景1：1.986,8.877,13.735,20.257 2.14
3.37场景2：5.080,12.123,20.239,1.503 2.97 场景3：5.943,9.173,11.576,3.065,14.729 3.91 场景4：2.004,6.808,10.115,15.018,14.464,20.885 4.44 本文方法 场景1：2.014,9.014,14.103,19.955 1.81
3.30场景2：5.002,12.069,19.509,1.482 2.78 场景3：6.071,8.728,11.801,2.894,15.134 3.67 场景4：1.933,7.304,10.472,14.967,15.124,19.321 4.92
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表 5 非规则网格接地网下不同测点布置方案多支路腐蚀诊断效果对比
Table 5. Comparison of multi-branch corrosion diagnosis effectiveness under different measurement point layout schemes in irregular grounding grids
测点布置方案 腐蚀支路诊断电阻值/$ \text{m}\Omega $ 诊断综合误差/% 误差平均值/% 网络拓扑分层约简法 场景1：2.161,9.025,13.816,20.215
场景2：5.152,11.937,19.916,1.512
场景3：6.214,9.352,12.417,3.126,15.108
场景4：1.975,7.182,10.116,15.613,15.022,19.7152.73
3.35
4.27
5.283.912 凝聚层聚类法 场景1：1.992,8.924,13.802,20.311
场景2：5.093,12.185,20.304,1.510
场景3：5.961,9.225,11.623,3.101,14.786
场景4：2.012,6.863,10.172,15.071,14.519,20.9422.21
3.05
4.02
4.513.448 本文方法 场景1：2.021,9.067,14.165,20.012
场景2：5.015,12.114,19.563,1.489
场景3：6.086,8.773,11.862,2.917,15.184
场景4：1.941,7.356,10.521,15.013,15.176,19.3821.87
2.84
3.74
4.983.375
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