基于DTW−Hilbert与改进K−means的谐振接地系统故障选线方法

张昭喜; 张宏乐; 黄衍法; 陈兴翔; 贾海成; 袁朋生

doi:10.13272/j.issn.1671-251x.2024090076

基于DTW−Hilbert与改进K−means的谐振接地系统故障选线方法

1.
兖矿能源集团股份有限公司东滩煤矿，山东济宁　273500
2.
江苏广识电气股份有限公司，江苏徐州　221112

基金项目: 国家自然科学基金青年基金资助项目（52307155）。

详细信息

作者简介:
张昭喜（1980—），男，山东济宁人，高级工程师，主要从事煤矿安全、机电、选煤、节能等方面的研究工作，E-mail：751761560@qq.com

通讯作者:
袁朋生（1971—），男，湖南长沙人，高级工程师，博士，主要研究方向为电力系统自动化，E-mail：yps_gushi@163.com。

中图分类号: TD60
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出版历程
- 收稿日期: 2024-09-19
- 修回日期: 2024-10-28
- 网络出版日期: 2024-10-28
- 刊出日期: 2024-11-24

Fault line selection method for resonant grounding systems based on DTW-Hilbert and improved K-means

1.
Dongtan Coal Mine, Yankuang Energy Group Company Limited, Jining 273500, China
2.
Jiangsu Guangshi Dianqi Co., Ltd., Xuzhou 221112, China

摘要

摘要:
受消弧线圈、过渡电阻、环境噪声等因素的影响，谐振接地系统故障信号特征微弱，且基于单一判据构成的故障选线方法难以保证选线结果的可靠性。针对上述问题，提出了一种基于动态时间弯曲（DTW）距离算法−Hilbert包络能量与改进K−means聚类算法的谐振接地系统故障选线方法。基于故障线路与健全线路波形相似度差距较大的原理，采用DTW距离算法定量刻画各线路电流序列之间的波形相似程度；为避免单一判据可能存在的选线盲区，基于故障线路与健全线路的能量系数区分度明显的原理，引入Hilbert包络能量衡量暂态零序电流信号中的高频分量幅值；为增强所提选线方法的数据处理能力与效率，采用改进K−means聚类算法对故障特征数据集进行分类处理，将各条线路的故障信息整理为故障数据集，作为改进K−means聚类算法的输入，聚类算法输出各条线路的聚类标签，依据聚类标签判定故障线路。仿真实验结果表明：① 该方法在面对不同过渡电阻、不同故障距离、不同故障初相角、不同线路结构等工况时，均可确保选线结果的准确性；② 相较于传统的K−means聚类算法，改进K−means聚类算法将选线准确率提升了3.4%。现场测试数据表明：该方法具有较强的抗噪声干扰能力，能够在强噪声环境下将保护的耐过渡电阻能力提升至3 000 Ω。
- 谐振接地系统 /
- 故障选线 /
- 单相接地故障 /
- 动态时间弯曲距离算法 /
- Hilbert包络能量 /
- 高频分量 /
- 聚类算法
Abstract:
Due to the influence of factors such as arc suppression coils, transition resistance, and environmental noise, the fault signal characteristics in resonant grounding systems are weak. Furthermore, fault line selection methods based on a single criterion often fail to ensure the reliability of the results. To address these issues, this paper proposed a fault line selection method for resonant grounding systems based an dynamic time warping (DTW) distance algorithm-Hilbert envelope energy, and improved K-means clustering algorithm. Based on the principle that the waveform similarity between the faulted and healthy lines differs significantly, the DTW distance algorithm was first employed to quantitatively measure the similarity between current waveforms of each line. To avoid the potential blind spots of a single criterion, Hilbert envelope energy was introduced to measure the high-frequency components in the transient zero-sequence current signals, based on the principle that the energy coefficient distinguishes faulted and healthy lines clearly. Additionally, to enhance the data processing capability and efficiency of the proposed method, the improved K-means clustering algorithm was applied to classify the fault feature dataset. The fault data from each line were organized into a fault dataset, which served as the input to the improved K-means algorithm. The clustering algorithm output the cluster labels for each line, and the fault line was determined based on the cluster labels. Simulation results showed that: ① The method ensured accurate line selection results under various conditions, such as different transition resistances, fault distances, fault initial phase angles, and line structures. ② Compared with the traditional K-means clustering algorithm, the improved K-means algorithm improved the line selection accuracy by 3.4%. Field test data demonstrated the strong noise immunity of the method, improving the protection's tolerance to transition resistance up to 3 000 Ω in a high-noise environment.
- resonant grounding system /
- fault line selection /
- single-phase grounding fault /
- DTW distance algorithm /
- Hilbert envelope energy /
- high-frequency components /
- clustering algorithm

HTML全文

图 1 改进K−means聚类算法流程

Figure 1. Improved K-means algorithm flow

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图 2 10 kV配电系统仿真结构

Figure 2. Simulation structure of 10 kV power distribution system

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图 3 不同故障工况下各线路的距离系数

Figure 3. Distance coefficients of each line under different fault cases

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图 4 不同故障工况下各线路的能量系数

Figure 4. Energy coefficients of each line under different fault cases

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图 5 聚类结果

Figure 5. Clustering results

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图 6 调整线路长度后的仿真拓扑

Figure 6. Simulation topology after adjusting line length

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图 7 线路L₁发生1 000 Ω接地故障现场录波

Figure 7. Field recording of a 1 000 Ω grounding fault on line L₁

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图 8 低压等值实验平台

Figure 8. Low-voltage equivalent experimental platform

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表 1 单位长度线路参数

Table 1 Line parameters per unit length

线路类型	相序	电阻/（Ω·km⁻¹）	电感/（mH·km⁻¹）	电容/（μF·km⁻¹）
架空线	正序	0.170	1.216	0.098
架空线	零序	0.232	5.469	0.006
电缆线	正序	0.270	0.255	0.339
电缆线	零序	2.700	1.016	0.275

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表 2 部分案例的故障特征量及选线结果

Table 2 Fault characteristics and line selection results for selected cases

故障线路/故障位置/ 过渡电阻/故障初相角	故障特征量[$ \rho_n,h_n $]				聚类标签	选线结果	是否正确
故障线路/故障位置/ 过渡电阻/故障初相角	L₁	L₂	L₃	L₄	聚类标签	选线结果	是否正确
L₁/2 km/500 Ω/90°	[1.000 0，0.693 9]	[0.662 1，0.000 1]	[0.415 3，0.096 8]	[0.413 8，0.209 3]	[2 1 1 1]	L₁	正确
L₁/5 km/500 Ω/90°	[1.000 0，0.676 9]	[0.568 6，0.000 1]	[0.398 2，0.134 5]	[0.398 8，0.188 5]	[2 1 1 1]	L₁	正确
L₁/10 km/100 Ω/0	[1.000 0，0.743 0]	[0.335 6，0.000 04]	[0.334 8，0.110 0]	[0.335 1，0.147 0]	[2 1 1 1]	L₁	正确
L₂/3 km/100 Ω/45°	[0.555 4，0.000 2]	[1.000 0，0.679 7]	[0.376 2，0.144 9]	[0.370 2，0.175 2]	[1 2 1 1]	L₂	正确
L₂/8 km/100 Ω/45°	[0.572 8，0.000 2]	[1.000 0，0.677 7]	[0.375 9，0.141 3]	[0.371 1，0.180 8]	[1 2 1 1]	L₂	正确
L₂/8 km/500 Ω/90°	[0.652 3，0.012 5]	[1.000 0，0.589 0]	[0.478 3，0.137 4]	[0.524 6，0.261 0]	[1 2 1 1]	L₂	正确
L₃/2 km/100 Ω/0	[0.348 8，0.000 05]	[0.344 5，0.000 03]	[1.000 0，0.987 7]	[0.346 8，0.012 3]	[1 1 2 1]	L₃	正确
L₃/2 km/100 Ω/45°	[0.570 2，0.021 6]	[0.791 1，0.000 2]	[1.000 0，0.553 7]	[0.521 6，0.424 5]	[1 1 2 1]	L₃	正确
L₄/4 km/150Ω/45°	[0.424 3，0.000 4]	[0.430 6，0.000 2]	[0.422 8，0.447 1]	[1.000 0，0.552 3]	[1 1 1 2]	L₄	正确
L₄/6 km/200 Ω/90°	[0.593 2，0.000 3]	[0.588 9，0.000 2]	[0.531 4，0.486 8]	[1.000 0，0.512 7]	[1 1 1 2]	L₄	正确

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表 3 不同过渡电阻时的选线结果

Table 3 Line selection results at different transition resistances

过渡电阻/Ω	故障特征量 $\left[\rho_1, \rho_2, \rho_3, \rho_4, h_1, h_2, h_3, h_4\right] $	聚类标签	选线结果
10	[1.0000,0.4124,0.3548,0.3555, 0.6117,0.0001,0.1633,0.2249]	[2 1 1 1]	L₁
100	[1.0000,0.4489,0.3539,0.3564, 0.5273,0.0001,0.2014,0.2712]	[2 1 1 1]	L₁
200	[1.0000,0.6462,0.3882,0.3868, 0.5590,0.0001,0.2163,0.2246]	[2 1 1 1]	L₁
500	[1.0000,0.7751,0.4283,0.4274, 0.5939,0.0001,0.2095,0.1966]	[2 1 1 1]	L₁
1 000	[1.0000,0.7472,0.4283,0.4271, 0.5484,0.00004,0.1894,0.2622]	[2 1 1 1]	L₁
1 500	[1.0000,0.7182,0.4250,0.4244, 0.5304,0.00003,0.1901,0.2795]	[2 1 1 1]	L₁

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表 4 不同故障距离时的选线结果

Table 4 Line selection results at different fault distances

故障位置/km	故障特征量 $\left[\rho_1, \rho_2, \rho_3, \rho_4, h_1, h_2, h_3, h_4\right] $	聚类标签	选线结果
2	[0.7171,0.6576,0.6872,1.0000, 0.0270,0.0003,0.4621,0.5106]	[1 1 1 2]	L₄
4	[0.4243,0.4306,0.4228,1.0000, 0.0004,0.0002,0.4471,0.5523]	[1 1 1 2]	L₄
6	[0.5683,0.5640,0.5107,1.0000, 0.0003,0.0002,0.4891,0.5104]	[1 1 1 2]	L₄
8	[0.5687,0.5830,0.6992,1.0000, 0.0199,0.0002,0.4734,0.5066]	[1 1 1 2]	L₄
11	[0.5340,0.5328,0.5710,1.0000, 0.0003,0.0099,0.4857,0.5041]	[1 1 1 2]	L₄

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表 5 不同故障初相角时的选线结果

Table 5 Line selection results at different fault initial phase angles

故障初相角/(°)	故障特征量 $\left[\rho_1, \rho_2, \rho_3, \rho_4, h_1, h_2, h_3, h_4\right] $	聚类标签	选线结果
0	[0.3372,1.0000,0.3356,0.3359, 0.0001,0.7453,0.1090,0.1457]	[1 2 1 1]	L₂
30	[0.5624,1.0000,0.3714,0.3705, 0.0001,0.6937,0.1327,0.1735]	[1 2 1 1]	L₂
45	[0.4416,1.0000,0.3482,0.3561, 0.0001,0.6736,0.1408,0.1854]	[1 2 1 1]	L₂
60	[0.4311,1.0000,0.3645,0.3758, 0.0002,0.6400,0.1551,0.2047]	[1 2 1 1]	L₂
90	[0.4266,1.0000,0.3804,0.3919, 0.0002,0.5730,0.1839,0.2429]	[1 2 1 1]	L₂

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表 6 不同线路长度组合下故障选线结果

Table 6 Fault line selection results for different combinations of line lengths

过渡电阻/Ω	故障特征量 [ρ₁,ρ₂,ρ₃,ρ₄,h₁,h₂,h₃,h₄]	聚类标签	选线结果
500	[0.3356,0.3355,1.0000,0.3373, 0.0411,0.0564,0.6374,0.2651]	[1 1 2 1]	L₃
1000	[0.3360,0.3359,1.0000,0.3379, 0.0448,0.0614,0.6044,0.2893]	[1 1 2 1]	L₃
1500	[0.3362,0.3361,1.0000,0.3382, 0.0451,0.0618,0.6015,0.2915]	[1 1 2 1]	L₃
2000	[0.3364,0.3363,1.0000,0.3385, 0.0452,0.0620,0.6200,0.2924]	[1 1 2 1]	L₃
3000	[0.3365,0.3364,1.0000,0.3387, 0.0454,0.0623,0.5985,0.2938]	[1 1 2 1]	L₃

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表 7 不同聚类算法评价指标对比

Table 7 Comparison of evaluation indicators for different clustering algorithms

聚类算法	选线正确率/%	轮廓系数
K−means聚类	94.8	0.81
改进K−means聚类	98.2	0.88
模糊C均值聚类	93.9	0.79
层次聚类	93.0	0.79
谱聚类	82.5	0.69

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表 8 实测数据选线结果

Table 8 Line selection results based on measured data

过渡电阻/Ω	故障特征量 [ρ₁,ρ₂,ρ₃,ρ₄,h₁,h₂,h₃,h₄]	聚类标签	是否正确
500	[1.0000,0.3963,0.3880,0.3668, 0.8528,0.1009,0.0280,0.0183]	[2 1 1 1]	正确
1 000	[1.0000,0.4800,0.4830,0.5008, 0.8587,0.0709,0.0447,0.0257]	[2 1 1 1]	正确
2 000	[1.0000,0.4583,0.4857,0.5446, 0.6308,0.1776,0.1090,0.0827]	[2 1 1 1]	正确
3 000	[1.0000,0.6025,0.5851,0.6753, 0.6340,0.0823,0.1466,0.1371]	[2 1 1 1]	正确

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