Fault line selection method for coal mine power grid based on RCMDE and KFCM
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摘要: 针对普遍采用谐振接地系统的煤矿电网发生单相接地故障时难以准确选线的问题，提出一种基于精细复合多尺度散布熵( RCMDE)和核模糊C均值聚类( KFCM)的煤矿电网故障选线方法。以幅值、极性和波形相似度作为选线特征量具有以下局限性：基于幅值和极性差异的选线方法适用性有限；若线路中的零序电流互感器极性接反，基于极性的方法直接失效；采样不同步时，基于波形相似度的选线方法难以得到正确结果。为克服上述局限性，引入RCMDE来度量各线路暂态零序电流信号的复杂程度和不规则度，以RCMDE作为选线特征量。采用KFCM算法对RCMDE进行聚类分析，以实现故障线路自动识别，并通过判断轮廓系数是否超过阈值来区分母线故障和馈线故障。最后，通过聚类得到的隶属度矩阵判断馈线故障点所在线路。仿真结果表明：① 故障点所在的故障线路对应的RCMDE曲线与非故障线路间具有较大差异，可分为2类。RCMDE可作为筛选故障线路的特征指标。② 发生母线故障时聚类结果中存在平均轮廓系数小于阈值的分簇，而发生馈线故障时聚类结果各分簇的轮廓系数均大于阈值，在各类故障场景下，基于RCMDE和KFCM的煤矿电网故障选线方法均能实现正确选线，说明其准确性不受故障线路、故障位置、故障合闸角及接地电阻等因素的影响。③ 在噪声干扰情况下，基于RCMDE和KFCM的煤矿电网故障选线方法在小电阻接地或高阻接地情况下均能实现正确选线，具有较强的抗干扰能力。④ 在采样不同步及故障线路零序电流互感器极性反接等情况下，基于RCMDE和KFCM的煤矿电网故障选线方法仍可实现正确选线，选线结果具有较高的鲁棒性。Abstract: It is difficult to accurately select the fault line when the single-phase ground fault occurs in the coal mine power grid with the widely used resonant grounding system. In order to solve the above problem, a fault line selection method of the coal mine power grid based on the refined composite multiscale dispersion entropy (RCMDE) and the kernel fuzzy C-means clustering (KFCM) is proposed. The limitations of using amplitude, polarity and waveform similarity as line selection characteristic quantities: the applicability of the line selection method based on amplitude and polarity difference is limited. If the polarity of the zero sequence current transformer in the line is reversed, the method based on polarity will directly fail. When the sampling is not synchronized, the line selection method based on waveform similarity is difficult to obtain correct results. In order to overcome the above limitations, RCMDE is introduced to measure the complexity and irregularity of the transient zero sequence current signal of each line. RCMDE is used as the characteristic quantity of line selection. The KFCM algorithm is used to cluster the RCMDE to realize the automatic identification of fault lines. The bus fault and feeder fault are distinguished by judging whether the contour coefficient exceeds the threshold value. Finally, the feeder line with the fault point is judged through the membership degree matrix obtained by clustering. The simulation results show the following points. ① The RCMDE curve of the fault line is different from that of the non-fault line, and the curves can be divided into two types. RCMDE can be used as the fault characteristic index of fault line. ② When the bus fault occurs, there are clusters with an average contour coefficient less than the threshold value in the clustering results. However, when feeder fault occurs, the contour coefficients of the clustering results are all greater than the threshold value. Under various fault scenarios, the coal mine power grid fault line selection method based on RCMDE and KFCM can realize correct line selection. The results show that its accuracy is not affected by factors such as fault line, fault location, fault closing angle and grounding resistance. ③ Under the conditions of noise disturbance, the fault line selection method based on RCMDE and KFCM can realize correct line selection in the case of low resistance grounding or high resistance grounding. And the method has a strong anti-interference capability. ④ Under the conditions of asynchronous sampling and reverse polarity of zero-sequence current transformer in the fault line, the method based on RCMDE and KFCM can still realize correct line selection. And the line selection result has high robustness.
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图 1 基于RCMDE和KFCM的故障选线流程
Figure 1. Fault line selection process based on RCMDE and KFCM
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图 2 煤矿电网单相接地故障仿真模型
Figure 2. Simulation model of single phase grounding fault in coal mine power grid
表 1 电缆线路参数
Table 1 Parameter of cable line
相序 单位长度电阻/ (Ω·km−1) 单位长度电感/ (mH·km−1) 单位长度电容/ (μF·km−1) 正序 0.270 0.255 0.339 零序 2.700 1.019 0.280 
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表 2 所提方法在各类故障场景下的选线结果
Table 2 Line selection results of the proposed method in various fault scenarios
故障线路 故障位置/ km α0/ (°) Rf / Ω 隶属度矩阵U 各簇平均轮廓系数 选线结果 线路1 0.2 0 0.001 $\left[ {\begin{array}{*{20}{l}} {\bf {{{1}}{{.000\;0}}} }&{{{0}}{{.003\;0}}}&{{{0}}{{.002\;4}}}&{{{0}}{{.000\;9}}} \\[2.9pt] {{{0}}{{.000\;0}}}&{\bf {{{0}}{{.997\;0}}} }&{\bf {{{0}}{{.997\;6}}} }&{\bf {{{0}}{{.999\;1}}} } \end{array}} \right]$ $ \left[ {\begin{array}{*{20}{c}} {{1}} \\[2.9pt] {{{0}}{{.994\;7}}} \end{array}} \right] $ 线路1 0.3 60 50 $\left[ {\begin{array}{*{20}{l}} {{{0}}{{.000\;0}}}&{\bf {{{0}}{{.998\;3}}} }&{\bf {{{0}}{{.996\;9}}} }&{\bf {{{0}}{{.999\;1}}} } \\[2.9pt] {\bf {{{1}}{{.000\;0}}} }&{{{0}}{{.001\;7}}}&{{{0}}{{.003\;1}}}&{{{0}}{{.000\;9}}} \end{array}} \right]$ $ \left[ {\begin{array}{*{20}{c}} {{{0}}{{.996\;0}}} \\[2.9pt] {{1}} \end{array}} \right] $ 线路1 0.4 90 5 000 $\left[ {\begin{array}{*{20}{l}} {{{0}}{{.000\;0}}}&{\bf {{{0}}{{.999\;4}}} }&{\bf {{{0}}{{.999\;7}}} }&{\bf {{{0}}{{.999\;8}}} } \\[2.9pt] {\bf {{{1}}{{.000\;0}}} }&{{{0}}{{.000\;6}}}&{{{0}}{{.000\;3}}}&{{{0}}{{.000\;2}}} \end{array}} \right]$ $ \left[ {\begin{array}{*{20}{c}} {{{0}}{{.999\;1}}} \\[2.9pt] {{1}} \end{array}} \right] $ 线路1 线路3 0.3 75 50 $\left[ {\begin{array}{*{20}{l}} {{{0}}{{.016\;8}}}&{{{0}}{{.000\;7}}}&{\bf {{{0}}{{.998\;0}}} }&{{{0}}{{.001\;1}}} \\[2.9pt] {\bf {{{0}}{{.983\;2}}} }&{\bf {{{0}}{{.999\;3}}} }&{{{0}}{{.002\;0}}}&{\bf {{{0}}{{.998\;9}}} } \end{array}} \right]$ $ \left[ {\begin{array}{*{20}{c}} 1 \\[2.9pt] {{{0}}{{.986\;1}}} \end{array}} \right] $ 线路3 0.7 15 800 $\left[ {\begin{array}{*{20}{l}} {{{0}}{{.001\;3}}}&{{{0}}{{.001\;3}}}&{\bf {{{1}}{{.000\;0}}} }&{{{0}}{{.000\;8}}} \\[2.9pt] {\bf {{{0}}{{.998\;7}}} }&{\bf {{{0}}{{.998}}\;7} }&{{{0}}{{.000\;0}}}&{\bf {{{0}}{{.999\;2}}} } \end{array}} \right]$ $ \left[ {\begin{array}{*{20}{c}} {{1}} \\[2.9pt] {{{0}}{{.999\;6}}} \end{array}} \right] $ 线路3 1.2 45 6 000 $ \left[ {\begin{array}{*{20}{l}} {\bf {{{0}}{{.999\;3}}} }&{\bf {{{0}}{{.999\;4}}} }&{{{0}}{{.000\;0}}}&{\bf {{{0}}{{.998\;8}}} } \\[2.9pt] {{{0}}{{.000\;7}}}&{{{0}}{{.000\;6}}}&{\bf {{{1}}{{.000}} \;0} }&{{{0}}{{.001\;2}}} \end{array}} \right] $ $ \left[ {\begin{array}{*{20}{c}} {{{0}}{{.998\;2}}} \\[2.9pt] 1 \end{array}} \right] $ 线路3 母线0 — 0 5 $ \left[ {\begin{array}{*{20}{l}} {\bf {{{0}}{{.936\;0}}} }&{{{0}}{{.354\;9}}}&{{{0}}{{.045\;3}}}&{{{0}}{{.041\;3}}} \\[2.9pt] {{{0}}{{.064\;0}}}&{\bf {{{0}}{{.645\;1}}} }&{\bf {{{0}}{{.954\;7}}} }&{\bf {{{0}}{{.958\;7}}} } \end{array}} \right] $ $ \left[ {\begin{array}{*{20}{c}} {{1}} \\[2.9pt] {{{0}}{{.712\;9}}} \end{array}} \right] $ 母线0 — 45 200 $\left[ {\begin{array}{*{20}{l}} {{{0}}{{.216\;4}}}&{\bf {{{0}}{{.826\;6}}} }&{\bf {{{0}}{{.707\;4}}} }&{\bf {{{0}}{{.804\;3}}} } \\[2.9pt] {\bf {{{0}}{{.783\;6}}} }&{{{0}}{{.173\;4}}}&{{{0}}{{.292\;6}}}&{{{0}}{{.195\;7}}} \end{array}} \right]$ $ \left[ {\begin{array}{*{20}{c}} {{{0}}{{.739\;3}}} \\[2.9pt] {{1}} \end{array}} \right] $ 母线0 — 90 4 000 $ \left[ {\begin{array}{*{20}{l}} {\bf {{{0}}{{.932\;3}}} }&{{{0}}{{.426\;9}}}&{{{0}}{{.101\;7}}}&{{{0}}{{.016\;5}}} \\[2.9pt] {{{0}}{{.067\;7}}}&{\bf {{{0}}{{.573\;1}}} }&{\bf {{{0}}{{.898\;3}}} }&{\bf {{{0}}{{.983\;5}}} } \end{array}} \right] $ $ \left[ {\begin{array}{*{20}{c}} {{1}} \\[2.9pt] {{{0}}{{.640\;7}}} \end{array}} \right] $ 母线0
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表 3 噪声干扰下的选线结果
Table 3 Line selection results with noise disturbance
Rf / Ω 隶属度
矩阵U各簇平均
轮廓系数选线
结果0.001 $\left[ {\begin{array}{*{20}{l}} {\bf {{{0}}{{.984\;1}}} }&{{{0}}{{.000\;2}}}&{\bf {{{0}}{{.984\;0}}} }&{\bf {{{0}}{{.997\;7}}} } \\ {{{0}}{{.015\;9}}}&{\bf {{{0}}{{.999\;8}}} }&{{{0}}{{.016\;0}}}&{{{0}}{{.002\;3}}} \end{array}} \right]$ $ \left[ {\begin{array}{*{20}{c}} {{{0}}{{.966\;1}}} \\ {{1}} \end{array}} \right] $ 线路2 100 $\left[ {\begin{array}{*{20}{l}} {{\bf{0}}{\bf{.995\;6}}}&{{{0}}{{.022\;3}}}&{\bf {{{0}}{{.991\;5}}} }&{\bf {{{0}}{{.981\;8}}} } \\ {{{0}}{{.004\;4}}}&{\bf {{{0}}{{.977\;7}}} }&{{{0}}{{.008\;5}}}&{{{0}}{{.018\;2}}} \end{array}} \right]$ $ \left[ {\begin{array}{*{20}{c}} {{{0}}{{.985\;0}}} \\ {{1}} \end{array}} \right] $ 线路2 10000 $\left[ {\begin{array}{*{20}{l}} {{\bf{0}}{\bf{.966\;7}}}&{{{0}}{{.001\;2}}}&{\bf {{{0}}{{.989\;3}}} }&{\bf {{{0}}{{.978\;5}}} } \\ {{{0}}{{.033}}\; {3}}&{\bf {{{0}}{{.998\;8}}} }&{{{0}}{{.010\;7}}}&{{{0}}{{.021\;5}}} \end{array}} \right]$ $ \left[ {\begin{array}{*{20}{c}} {{{0}}{{.937\;8}}} \\ {{1}} \end{array}} \right] $ 线路2
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表 4 采样不同步时的选线结果
Table 4 Line selection results under asynchronous sampling
Rf / Ω 隶属度
矩阵U各簇平均
轮廓系数选线
结果5 $ \left[ {\begin{array}{*{20}{l}} {\bf {{{0}}{{.985\;6}}} }&{\bf {{{0}}{{.984\;5}}} }&{\bf {{{0}}{{.997\;7}}} }&{{{0}}{{.000\;2}}} \\ {{{0}}{{.014\;4}}}&{{{0}}{{.015\;5}}}&{{{0}}{{.002\;3}}}&{\bf {{{0}}{{.999\;8}}} } \end{array}} \right] $ $ \left[ {\begin{array}{*{20}{c}} {{{0}}{{.968\;1}}} \\ {{1}} \end{array}} \right] $ 线路4 800 $ \left[ {\begin{array}{*{20}{l}} {{{0}}{{.000\;3}}}&{{{0}}{{.000\;5}}}&{{{0}}{{.000\;6}}}&{\bf {{{1}}{{.000\;0}}} } \\ {\bf {{{0}}{{.999\;7}}} }&{\bf {{{0}}{{.999\;5}}} }&{\bf {{{0}}{{.999\;4}}} }&{{{0}}{{.000\;0}}} \end{array}} \right] $ $ \left[ {\begin{array}{*{20}{c}} {{1}} \\ {{{0}}{{.999\;6}}} \end{array}} \right] $ 线路4 5 000 $ \left[ {\begin{array}{*{20}{l}} {{{0}}{{.011\;7}}}&{{{0}}{{.013\;2}}}&{{{0}}{{.006\;7}}}&{\bf {{{0}}{{.946\;9}}} } \\ {\bf {{{0}}{{.988\;3}}} }&{\bf {{{0}}{{.986\;8}}} }&{\bf {{{0}}{{.993\;3}}} }&{{{0}}{{.053\;1}}} \end{array}} \right] $ $ \left[ {\begin{array}{*{20}{c}} 1 \\ {{{0}}{{.998\;1}}} \end{array}} \right] $ 线路4
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表 5 极性反接时的选线结果
Table 5 Line selection results with anti-polarity
Rf / Ω 隶属度
矩阵U各簇平均
轮廓系数选线
结果0.001 $ \left[ {\begin{array}{*{20}{l}} {\bf {{{0}}{{.995\;0}}} }&{\bf {{{0}}{{.994\;8}}} }&{{{0}}{{.012\;6}}}&{\bf {{{0}}{{.995\;4}}} } \\ {{{0}}{{.005\;0}}}&{{{0}}{{.005\;2}}}&{\bf {{{0}}{{.987\;4}}} }&{{{0}}{{.004\;6}}} \end{array}} \right] $ $ \left[ {\begin{array}{*{20}{c}} {{{0}}{{.999\;9}}} \\ 1 \end{array}} \right] $ 线路3 60 $ \left[ {\begin{array}{*{20}{l}} {\bf {{{0}}{{.997\;9}}} }&{\bf {{{0}}{{.999\;0}}} }&{{{0}}{{.000\;0}}}&{\bf {{{0}}{{.998\;7}}} } \\ {{{0}}{{.002\;1}}}&{{{0}}{{.001\;0}}}&{\bf {{{1}}{{.000\;0}}} }&{{{0}}{{.001\;3}}} \end{array}} \right] $ $ \left[ {\begin{array}{*{20}{c}} {{{0}}{{.998\;3}}} \\ {{1}} \end{array}} \right] $ 线路3 6 000 $ \left[ {\begin{array}{*{20}{l}} {{{0}}{{.000\;6}}}&{{{0}}{{.000\;8}}}&{\bf {{{0}}{{.999\;9}}} }&{{{0}}{{.000\;9}}} \\ {\bf {{{0}}{{.999\;4}}} }&{\bf {{{0}}{{.999\;2}}} }&{{{0}}{{.000\;1}}}&{\bf {{{0}}{{.999\;1}}} } \end{array}} \right] $ $ \left[ {\begin{array}{*{20}{c}} {{{0}}{{.999\;1}}} \\ {{1}} \end{array}} \right] $ 线路3
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