基于RCMDE和KFCM的煤矿电网故障选线方法

韩国国, 史小军, 王晖, 程卫健, 穆艳祥

韩国国,史小军,王晖,等. 基于RCMDE和KFCM的煤矿电网故障选线方法[J]. 工矿自动化,2022,48(8):92-99. DOI: 10.13272/j.issn.1671-251x.17911
引用本文: 韩国国,史小军,王晖,等. 基于RCMDE和KFCM的煤矿电网故障选线方法[J]. 工矿自动化,2022,48(8):92-99. DOI: 10.13272/j.issn.1671-251x.17911
HAN Guoguo, SHI Xiaojun, WANG Hui, et al. Fault line selection method for coal mine power grid based on RCMDE and KFCM[J]. Journal of Mine Automation,2022,48(8):92-99. DOI: 10.13272/j.issn.1671-251x.17911
Citation: HAN Guoguo, SHI Xiaojun, WANG Hui, et al. Fault line selection method for coal mine power grid based on RCMDE and KFCM[J]. Journal of Mine Automation,2022,48(8):92-99. DOI: 10.13272/j.issn.1671-251x.17911

基于RCMDE和KFCM的煤矿电网故障选线方法

基金项目: 天地(常州)自动化股份有限公司研发项目(2020GY108)。
详细信息
    作者简介:

    韩国国(1968— ),男,山西晋城人,工程师,现从事矿山机电工作,E-mail:737491540@qq.com

    通讯作者:

    程卫健(1994— ),男,浙江湖州人,硕士,主要研究方向为煤矿供配电及其自动化,E-mail:cwj8615@163.com

  • 中图分类号: TD611

Fault line selection method for coal mine power grid based on RCMDE and KFCM

  • 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.
  • 谐振接地系统又称中性点经消弧线圈接地系统,在煤矿电网中广泛应用。当发生单相接地故障时,消弧线圈将产生感应电流,可在很大程度上补偿馈线对地电容电流,减少故障电流的损害。谐振接地系统发生单相接地故障后,三相线电压仍保持对称,理论上可继续运行1~2 h,但非故障相对地电压将升高为原来的$\sqrt 3 $倍,威胁系统运行安全。煤矿电网长时间带故障运行,不仅损害线路的绝缘性能,还加大了用电设备的故障风险。此外,线路故障点产生的电火花还存在引发煤尘或瓦斯爆炸的可能[1]。因此,煤矿电网应快速、准确地筛选并切断故障线路,以满足安全供电要求。然而,消弧线圈的补偿作用使故障信号的幅值更微弱、成分更复杂,可能导致故障线路和非故障线路零序故障电流方向相同,从而加大故障选线的难度[2]

    现有的故障选线方法主要包括主动选线法和被动选线法2类。主动选线法[3]向系统注入额外的特征信号,通过检测注入信号进行选线。此方法需要额外的硬件配置,实现较为困难,成本较高,且可能危害系统的安全可靠运行,在实际工程中应用受限。被动选线法通过提取故障前后的特征变化进行故障选线,根据提取特征信息的不同又可分为稳态法和暂态法。经典的稳态法包括相位比较法[4]、五次谐波法[5]、零序导纳法[6]等。由于消弧线圈的补偿作用,线路中的稳态信号微弱,使得稳态法难以适用于谐振接地系统。线路中的暂态信号具有更丰富的故障特征,基于暂态特征的选线方法逐渐成为选线研究的热点。文献[7]将故障零模电流进行小波分解,并通过特征频带内的电流形态谱特征进行选线。该方法具有较强的抗干扰能力,但在高阻故障时若时间窗大小选择不合适,可能得到错误选线结果。文献[8]通过二次累加算法放大故障线路和非故障线路间的差异,并以综合相关系数为判据进行故障选线,但未给出母线故障时的选线依据。文献[9]通过判断各线路暂态零序电流波形极性是否一致区分母线故障和馈线故障,但当消弧线圈的补偿作用使得故障线路零序电流极性与非故障线路相同或零序电流互感器极性反接时,此方法不再可靠。文献[10-11]基于故障行波信号进行故障选线,但此方法对信号采样率要求较高,常用的信号采集装置难以满足要求。随着人工智能技术的发展,部分基于机器学习或深度学习的选线方法被提出。文献[12-14]在提取故障特征的基础上分别采用基于Adaboost算法、加扰模式卷积神经网络(Scrambling Convolutional Neural Network,S−CNN)模型及改进GoogLeNet网络实现故障线路的选择。与传统方法相比,基于人工智能的选线方法更适用于随机性、非线性逐渐增多的现代电网,但此类方法受限于实际训练样本难以获取。

    针对现有选线方法的局限性,本文提出一种基于精细复合多尺度散布熵(Refined Composite Multiscale Dispersion Entropy,RCMDE)和核模糊C均值聚类(Kernel Fuzzy C-Means Clustering,KFCM)的煤矿电网故障选线方法。RCMDE[15]是散布熵(Dispersion Entropy,DE)[16]的改进,可更好地表征信号的复杂程度,在故障诊断领域[17-18]得到广泛关注。KFCM[19]是基于核的改进模糊C均值聚类(Fuzzy C-Means Clustering,FCM)算法,将信号映射到高维空间进行聚类处理,具有较高的容错性。首先引入RCMDE度量各馈线暂态零序电流信号的复杂度,以RCMDE熵值作为选线依据;然后采用KFCM算法对RCMDE熵值进行聚类处理,并通过聚类结果的轮廓系数区分母线故障和馈线故障;最后根据隶属度矩阵确定馈线故障线路。

    无论是经小电阻接地还是高阻接地,谐振接地系统发生单相接地故障后各馈线的暂态零序电流皆具有以下特点:① 非故障线路暂态零序电流为线路本身的对地电容电流;② 故障线路暂态零序电流由母线到故障点对地电容电流之和、所有非故障线路对地电容电流之和及流经消弧线圈的电感电流3个部分组成[20]

    非故障线路暂态零序电流所含成分相同,各线路暂态零序电流在幅值、极性和波形上差异较小。故障线路暂态零序电流由3个部分组成,成分更为复杂,在幅值、极性和波形上差异较大。因此,可利用故障线路和非故障线路暂态零序电流的差异进行故障选线。

    然而,基于故障线路和非故障线路暂态零序电流差异的故障选线方法具有一定的局限性,在部分场景下难以得到正确选线结果。故障线路暂态零序电流的幅值和极性与消弧线圈的参数相关,考虑到消弧线圈电感电流的补偿作用,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,则基于极性的方法直接失效。而在采样不同步时,基于波形相似度的选线方法难以得到正确结果。

    为克服以电流幅值、极性和波形相似度作为选线特征量的局限性,本文引入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。由暂态零序电流特点可知,故障线路暂态零序电流的组成成分与非故障线路相比有很大差异,而RCMDE能很好地体现这一差异,且RCMDE的计算结果不受故障线路零序电流极性反转或采样不同步等因素的影响,以其作为故障特征可进一步扩大选线方法的适用范围。

    为实现故障线路的自动识别,在以RCMDE作为故障特征的基础上,采用KFCM聚类算法对RCMDE结果进行聚类分析。为对应故障线路和非故障线路,将KFCM聚类分簇数设为2。但当故障点位于母线处时,各馈线的特征量难以分为2类。可采用轮廓系数衡量聚类结果的性能,当故障发生在馈线时,聚类数目设置正确,轮廓系数接近1;而当故障发生在母线处,聚类性能下降,轮廓系数减小。因此,可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。通过聚类得到的隶属度矩阵U判断馈线故障点所在线路。隶属度矩阵U的行对应不同簇,列对应不同线路,U中每列最大值所在行即为该列对应线路的分簇。由于故障线路的熵值与非故障线路有很大差异,经过聚类处理后,故障线路的熵值自成一类,被单独划分为一簇,非故障线路的熵值被划分为另一簇,由隶属度矩阵U单独分为一簇的熵值所对应的线路即为故障线路。

    基于RCMDE和KFCM的煤矿电网单相接地故障选线方法流程如图1所示。当母线零序电压超过整定值(额定电压的15%)时判定故障发生,启动选线流程;采集故障后的录波数据并计算各馈线的RCMDE;采用KFCM算法对各馈线的RCMDE进行聚类处理;计算聚类结果的轮廓系数;若轮廓系数大于阈值,则判定故障为馈线故障,并根据隶属度矩阵U确定故障线路,否则判定故障为母线故障;输出选线结果。

    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

    DE的概念于2016年提出,与样本熵或排列熵相比,DE具有更好的稳定性和更快的计算速度,在度量信号复杂度时具有更优异的准确性、有效性和抗干扰性。对于一个长度为N的数据样本x={xj | j=1, 2, $ \cdots , $ N},xj为数据样本x的第j个元素,DE的计算步骤[16]如下:

    (1) 采用正态累积分布函数对x进行映射得到y={yj | j=1, 2, $\cdots , $ N},yj为映射后得到的数据,其取值范围为0~1。

    $$ {y_j} = \frac{1}{{\sigma \sqrt {2{\text{π }}} }}\int_{ - \infty }^{{x_j}} {\exp \left( {\frac{{ - \left( {\xi - \mu } \right)}}{{2{\sigma ^2}}}} \right){\text{d}}\xi } $$ (1)

    式中:σ为标准差;ξ为积分变量;μ为期望。

    (2) 采用线性变化将y映射到${{\textit{z}}}^{c} $={${\textit{z}}_j^c$ | j=1, 2, $\cdots , $ N},${\textit{z}}_j^c$为线性映射得到的数据,其取值范围为1~c的整数,c为类别个数。

    $$ {\textit{z}}_j^c = {\text{round}}\left( {c{y_j} + 0.5} \right) $$ (2)

    式中round()为四舍五入取整函数。

    (3) 计算嵌入向量${\boldsymbol{z}}_i^{m,c}$

    $$ {{{\boldsymbol{z}}}}_i^{m,c} = \left[ {{\textit{z}}_i^c,{\textit{z}}_{i + d}^c, \cdots ,\textit{z}_{i + \left( {m - 1} \right)d}^c} \right] $$ (3)

    式中:m为嵌入维数;i为嵌入向量${\boldsymbol{z}}_i^{m,c}$的个数,$ i = 1,2, \cdots ,N - \left( {m - 1} \right)d $d为时延参数。

    (4) 用λ0, λ1, $\cdots , $ λm-1表示嵌入向量中的各个元素,即${\textit{z}}_i^c = {\lambda _0}$${\textit{z}}_{i + d}^c = {\lambda _1}$$\cdots , $ ${\textit{z}}_{i + (m - 1)d}^c = {\lambda _{m - 1}}$,则嵌入向量${\boldsymbol{z}}_i^{m,c}$对应的散布模式为${a _{{\lambda _0}{\lambda _1} \cdots {\lambda _{m - 1}}}}$${\boldsymbol{z}}_i^{m,c}$对应的散步模式共有cm种。

    (5) 计算每种散布模式的概率:

    $$ p\left( {{a _{{\lambda _0}{\lambda _1} \cdots {\lambda _{m - 1}}}}} \right) = \frac{{M\left( {{a _{{\lambda _0}{\lambda _1} \cdots {\lambda _{m - 1}}}}} \right)}}{{N - \left( {m - 1} \right)d}} $$ (4)

    式中$M\left( {{a _{{\lambda _0}{\lambda _1} \cdots {\lambda _{m - 1}}}}} \right)$为嵌入向量${\boldsymbol{z}}_i^{m,c}$映射到散布模式${a _{{\lambda _0}{\lambda _1} \cdots {\lambda _{m - 1}}}}$下的个数。

    (6) 计算x的散布熵:

    $$ {E_{{\rm{DE}}}}\left( {x,m,c,d} \right) = \sum\limits_{a = 1}^{{c^m}} \left[ { {p\left( {{a _{{\lambda _0}{\lambda _1} \cdots {\lambda _{m - 1}}}}} \right)\ln p\left( {{a _{{\lambda _0}{\lambda _1} \cdots {\lambda _{m - 1}}}}} \right)} } \right]$$ (5)

    RCMDE的计算步骤[15]如下:

    (1) 将数据样本x从起始点到最后一个数据点的数据段连续分割成长度为τ的子数据段。分别求取每个子数据段的平均值并按顺序排列,得到1个粗粒化序列。分别以第1,2,$ \cdots , $τ个数据点为起始点计算粗粒化序列,共得到τ个粗粒化序列。

    (2) 计算每个粗粒化序列下散布模式${a _{{\lambda _0}{\lambda _1} \cdots {\lambda _{m - 1}}}}$的概率。

    (3) 计算所有粗粒化序列下散布模式${a _{{\lambda _0}{\lambda _1} \cdots {\lambda _{m - 1}}}}$的概率的平均值$\bar p\left( {{a _{{\lambda _0}{\lambda _1} \cdots {\lambda _{m - 1}}}}} \right)$

    (4) 计算RCMDE:

    $$ {E_{{\text{RCMDE}}}}\left( {x,m,c,d,\tau } \right) = - \sum\limits_{a = 1}^{{c^m}} \left[ { {\bar p\left( {{a _{{\lambda _0}{\lambda _1} \cdots {\lambda _{m - 1}}}}} \right)\ln \bar p\left( {{a _{{\lambda _0}{\lambda _1} \cdots {\lambda _{m - 1}}}}} \right)} } \right] $$ (6)

    FCM算法是一种经典的软聚类算法,可快速有效地实现样本无监督分类任务,但聚类结果易受噪声的干扰,鲁棒性较差。KFCM算法是基于核的改进FCM聚类算法,通过核函数进行非线性映射,将数据样本x映射到高维特征空间H$ {{\varPhi }}:{x_j} \to {{\varPhi}} ({x_j}) \in {{H}} $),$\varPhi $为映射函数,以放大不同类别样本间的差异,具有更高的容错性,可实现更为高效、准确的聚类分析。

    KFCM算法的目标函数为

    $$ \begin{split} J\left( {{\boldsymbol{U}},{\boldsymbol{V}}} \right) =& \sum\limits_{q = 1}^\gamma {\sum\limits_{j = 1}^N {\mu _{qj}^w\left\| {\varPhi \left( {{x_j}} \right) - \varPhi \left( {{v_q}} \right)} \right\|} } = \\& 2\sum\limits_{q = 1}^\gamma {\sum\limits_{j = 1}^N {\mu _{qj}^w\left( {1 - K\left( {{x_j},{v_q}} \right)} \right)} } \end{split} $$ (7)
    $$ K\left( {{x_j},{v_q}} \right) = \exp \left( { - \frac{{{{\left\| {{x_j} - {v_q}} \right\|}^2}}}{{2{\theta ^2}}}} \right) $$ (8)

    式中:V为聚类中心矩阵;γ为聚类数目;μqj为样本xj隶属于第q类的程度;w为模糊加权指数;K()为核函数;vq为第q类的聚类中心;θ为核函数的宽度参数。

    当式(7)取最小值时,μqjvq的表达式为

    $$ {\mu _{qj}} = \frac{{{{\left( {1 - K\left( {{x_j},{v_q}} \right)} \right)}^{ - 1/\left( {w - 1} \right)}}}}{{\displaystyle \sum\limits_{q = 1}^\gamma {{{\left( {1 - K\left( {{x_j},{v_q}} \right)} \right)}^{ - 1/\left( {w - 1} \right)}}} }} $$ (9)
    $$ {v_q} = \frac{{\displaystyle \sum\limits_{j = 1}^N {\mu _{qj}^wK\left( {{x_j},{v_q}} \right){x_j}} }}{{\displaystyle \sum\limits_{j = 1}^N {\mu _{qj}^wK\left( {{x_j},{v_q}} \right)} }} $$ (10)

    KFCM聚类算法的具体步骤[19]如下:

    (1) 初始化。利用FCM算法初始化隶属度矩阵U(0)、聚类中心矩阵V(0)及目标函数值J(0)

    (2) 进入下一次迭代,迭代次数t加1。根据式(9)和式(10)更新隶属度矩阵U(t)、聚类中心矩阵V(t),根据式(7)更新目标函数J(t)

    (3) 判定||J(t) J(t−1)||是否小于阈值ε或迭代次数t是否达到最大值tmax,若满足判定条件则停止迭代并输出聚类结果,否则返回步骤(2)。本文设置ε=1e−5,tmax=1 000。

    对于数据样本x中的某一点xj,其轮廓系数s(xj)为

    $$ s\left( {{x_j}} \right) = \frac{{b\left( {{x_j}} \right) - e\left( {{x_j}} \right)}}{{{{ \max \left( {b\left( {{x_j}} \right) - e\left( {{x_j}} \right)} \right)}_{ }}}} $$ (11)

    式中:b(xj)为xj与非同簇各簇数据点平均距离的最小值;e(xj)为xj与其同簇其他数据点的平均距离。

    为验证基于RCMDE和KFCM的煤矿电网故障选线方法有效性,以山西某煤矿10 kV供电网络[21]为例,在Matlab/Simulink环境中搭建煤矿电网单相接地故障仿真模型,该矿三级供电系统如图2所示,其中线路1—4为地面变电所通过井筒向井下馈出的4条线路,母线0为这4条线路所连接的母线。TV为母线0零序电压互感器,TA1—TA4为4条线路近母线端的零序电流互感器。以母线0及其馈出线路1—4发生单相接地故障为例,验证所提选线方法的有效性。其中,主变压器T0参考S11−16000/35型电力变压器进行设置。T0二次侧通过Z型变压器TZ引出中性点,该中性点经消弧线圈接地。

    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

    现代煤矿供电系统以全电缆网络为主[1],因此仿真模型所有线路均为电缆线路,其具体参数见表1

    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0.2700.2550.339
    零序2.7001.0190.280
    下载: 导出CSV 
    | 显示表格

    仿真模型采用中性点经消弧线圈接地方式,消弧线圈电感LN

    $$ \begin{split} \\ {L_{\text{N}}} = \frac{1}{{3(1 + \beta ){\omega ^2}{C_{\sum}}}} \end{split}$$ (12)

    式中:$ \; \beta $为消弧线圈过补偿度,$\; \beta $=5%;ω为工频角频率;CΣ为系统各线路零序电容总和。

    设消弧线圈有功损耗与其感性无功损耗的比值为ρρ=0.03,则消弧线圈电阻RN

    $$ {R_{\text{N}}} = \rho \omega {L_{\text{N}}} $$ (13)

    设置线路1发生单相接地故障,故障相设置为A相,故障点与母线0的距离为0.35 km,故障合闸角α0为30°,接地电阻Rf为6 000 Ω,信号采样率为10 kHz,采集得到故障后各线路的暂态零序电流值。

    首先计算各电流波形的RCMDE,设置信号长度N=2 048,嵌入维数m=3,类别个数c=6,时延参数d=1,尺度因子τ的最大值τmax=15,各馈线RCMDE的计算结果如图3所示。为了说明故障线路暂态零序电流波形复杂度与非故障线路间的差异,将不同尺度因子τ下各馈线RCMDE熵值计算结果进行归一化,如图4所示。

    图  3  RCMDE计算结果
    Figure  3.  Calculation results of RCMDE
    图  4  RCMDE归一化值
    Figure  4.  Normalized value of RCMDE

    图3图4可看出,未发生故障的线路2—4所对应的RCMDE曲线相互交叠,难以区分。而故障点所在的线路1对应的RCMDE曲线与非故障线路间具有较大的差异,故障线路和非故障线路的RCMDE曲线明显分为2类。RCMDE可充分体现各馈线暂态零序电流信号在复杂程度上的差异,可作为煤矿电网发生单相接地故障后筛选故障线路的特征指标。

    采用KFCM算法将各馈线RCMDE分为2簇,并根据聚类结果的轮廓系数判断故障位置是在母线还是馈线。经多次测试,馈线故障时2簇的平均轮廓系数均大于0.95。但直接设置阈值为0.95,可能出现某些未考虑的情况下轮廓系数略小于0.95,保留一定裕量,设定阈值为0.90。当2簇的平均轮廓系数最小值亦大于阈值时,判定为馈线故障,否则判定为母线故障。计算得到本算例2簇的平均轮廓系数分别为0.999 2和1,由此可判定本次故障点位于馈线线路。

    聚类分析后得到隶属度矩阵为${\boldsymbol{U}} = \left[ {\begin{array}{*{20}{l}} {{{0}}{{.000\;0}}}&{\bf {{{0}}{{.999\;1}}} }&{\bf {{{0}}{{.999\;3}}} }&{\bf {{{0}}{{.999\;4}}} } \\ {\bf {{{1}}{{.000\;0}}} }&{{{0}}{{.000\;9}}}&{{{0}}{{.000\;7}}}&{{{0}}{{.000\;6}}} \end{array}} \right]$,其中线路1被单独划分为一簇,而线路2—4均被划分为另一簇,由此即可判定故障线路为线路1。

    当故障发生的线路、故障距离母线0的位置、故障合闸角α0及故障接地电阻Rf不同时,基于RCMDE和KFCM的煤矿电网故障选线方法的选线结果见表2。可看出发生母线故障时聚类结果中存在平均轮廓系数小于阈值0.90的分簇,而发生馈线故障时聚类结果的轮廓系数均大于阈值0.90,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,说明选线结果对故障线路、故障位置、故障合闸角及接地电阻等因素具有较强的鲁棒性。

    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/ kmα0/ (°)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
    下载: 导出CSV 
    | 显示表格

    煤矿现场信号易受噪声的干扰,以馈线线路2发生单相接地故障为例,在采样信号中添加白噪声以验证所提方法的抗噪声干扰能力。设置故障点与母线0的距离为0.4 km,故障合闸角α0为30°,故障接地电阻Rf分别为0.001, 100, 10 000 Ω,信号信噪比为20 dB,选线结果见表3。可看出当信号有噪声干扰时,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。

    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
    下载: 导出CSV 
    | 显示表格

    在煤矿现场应用中,线路采样装置可能出现不同步的情况,以馈线线路4发生单相接地故障为例,验证基于RCMDE和KFCM的煤矿电网故障选线方法在采样不同步时的有效性。其中,故障点与母线0的距离为0.6 km,故障合闸角α0为45°,故障接地电阻Rf分别为5, 800, 5 000 Ω。此外,设置馈线线路2和线路4的采样时间滞后其他线路0.2 ms,故障选线结果见表4。可看出基于RCMDE和KFCM的煤矿电网故障选线方法适用于采样不同步时的故障选线。

    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
    下载: 导出CSV 
    | 显示表格

    消弧线圈的补偿作用使得故障线路暂态零序电流波形反向或故障线路的零序电流互感器极性反接时,无法依据故障线路暂态零序电流的极性与非故障线路不同这一特征判断故障线路。

    基于RCMDE和KFCM的煤矿电网故障选线方法利用RCMDE度量零序电流复杂度以筛选故障线路,RCMDE的计算结果与信号极性无关,因此本文所提方法的选线结果不受零序电流极性的影响。

    以线路3发生单相接地故障时零序电流互感器极性反接为例,验证所提方法对于故障线路零序电流极性的鲁棒性。设故障点与母线0的距离为1 km,故障合闸角α0为90°,故障接地电阻Rf分别0.001, 60, 6 000 Ω,选线结果见表5。可看出基于RCMDE和KFCM的煤矿电网故障选线方法在故障线路零序电流互感器极性反接时仍能实现正确选线,选线结果具有较高的鲁棒性。

    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
    下载: 导出CSV 
    | 显示表格

    (1) RCMDE可充分体现各馈线暂态零序电流信号在复杂程度上的差异,可作为筛选故障线路的特征指标。

    (2) 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,而馈线故障时聚类结果各分簇的系数均大于阈值,基于RCMDE和KFCM的煤矿电网故障选线方法不受故障线路、故障位置、故障合闸角及接地电阻等因素的影响,在各类故障场景下均能实现正确选线。

    (3) 在采样信号中添加白噪声后,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) 基于RCMDE和KFCM的煤矿电网故障选线方法在信号采样不同步或故障线路零序电流互感器极性反接时也可实现正确选线,选线结果具有较高的鲁棒性。

  • 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

    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

    图  3   RCMDE计算结果

    Figure  3.   Calculation results of RCMDE

    图  4   RCMDE归一化值

    Figure  4.   Normalized value of RCMDE

    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0.2700.2550.339
    零序2.7001.0190.280
    下载: 导出CSV

    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/ kmα0/ (°)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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV

    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
    下载: 导出CSV
  • [1] 高宏杰,赵建文,郭秀才. 煤矿电网单相漏电故障区段自动定位探索[J]. 工矿自动化,2021,47(5):106-111.

    GAO Hongjie,ZHAO Jianwen,GUO Xiucai. Research on automatic location of single-phase leakage fault zone in coal mine power network[J]. Industry and Mine Automation,2021,47(5):106-111.

    [2]

    LIU Penghui,DU Shaotong,SUN Kang,et al. Single-line-to-ground fault feeder selection considering device polarity reverse installation in resonant grounding system[J]. IEEE Transactions on Power Delivery,2021,36(4):2204-2212. DOI: 10.1109/TPWRD.2020.3022422

    [3]

    NIU Lin,WU Guiqing,XU Zhangsheng. Single-phase fault line selection in distribution network based on signal injection method[J]. IEEE Access,2021,9:21567-21578. DOI: 10.1109/ACCESS.2021.3055236

    [4] 张利,杨以涵,杨秀媛,等. 移动式比相法配电网接地故障定位研究[J]. 中国电机工程学报,2009,29(7):91-97. DOI: 10.3321/j.issn:0258-8013.2009.07.015

    ZHANG Li,YANG Yihan,YANG Xiuyuan,et al. Method of mobile phase-comparison for fault location of distribution network[J]. Proceeding of the CSEE,2009,29(7):91-97. DOI: 10.3321/j.issn:0258-8013.2009.07.015

    [5] 孙其东,张开如,刘建,等. 基于五次谐波和小波重构能量的配电网单相接地故障的选线方法研究[J]. 电测与仪表,2016,53(16):1-4. DOI: 10.3969/j.issn.1001-1390.2016.16.001

    SUN Qidong,ZHANG Kairu,LIU Jian,et al. Research on single-phase fault earth fault line selection method for the distribution network based on fifth harmonics and wavelet reconstruction[J]. Electrical Measurement & Instrumentation,2016,53(16):1-4. DOI: 10.3969/j.issn.1001-1390.2016.16.001

    [6] 栾晓明,武守远,贾春娟,等. 基于改进零序导纳法的单相接地故障选线原理[J]. 电网技术,2022,46(1):353-360. DOI: 10.13335/j.1000-3673.pst.2021.0425

    LUAN Xiaoming,WU Shouyuan,JIA Chunjuan,et al. Fault line selection principle of single-phase-to-ground fault based on improved zero-sequence admittance[J]. Power System Technology,2022,46(1):353-360. DOI: 10.13335/j.1000-3673.pst.2021.0425

    [7] 束洪春,龚振,田鑫萃,等. 基于故障特征频带及形态谱的单相接地故障选线[J]. 电网技术,2019,43(3):1041-1053.

    SHU Hongchun,GONG Zhen,TIAN Xincui,et al. Single line-to-ground fault line selection based on fault characteristic frequency band and morphological spectrum[J]. Power System Technology,2019,43(3):1041-1053.

    [8] 魏向向,温渤婴. 基于2阶累加生成相关性的谐振接地系统故障选线方法[J]. 电网技术,2017,41(5):1674-1682.

    WEI Xiangxiang,WEN Boying. A novel fault line detection method based on 2-order accumulated generating operation correlation analysis for resonant earthed system[J]. Power System Technology,2017,41(5):1674-1682.

    [9] 于群,尚雪丽. 一种矿井漏电保护选线方法[J]. 工矿自动化,2020,46(11):17-22.

    YU Qun,SHANG Xueli. A line selection method of mine leakage protection[J]. Industry and Mine Automation,2020,46(11):17-22.

    [10] 邓丰,梅龙军,唐欣,等. 基于时频域行波全景波形的配电网故障选线方法[J]. 电工技术学报,2021,36(13):2861-2870.

    DENG Feng,MEI Longjun,TANG Xin,et al. Faulty line selection method of distribution network based on time-frequency traveling wave panoramic waveform[J]. Transactions of China Electrotechnical Society,2021,36(13):2861-2870.

    [11] 王建元,朱永涛,秦思远. 基于方向行波能量的小电流接地系统故障选线方法[J]. 电工技术学报,2021,36(19):4085-4096.

    WANG Jianyuan,ZHU Yongtao,QIN Siyuan. Fault line selection method for small current grounding system based on directional traveling wave energy[J]. Transactions of China Electrotechnical Society,2021,36(19):4085-4096.

    [12] 陈奎,韦晓广,陈景波,等. 基于样本数据处理和ADABOOST的小电流接地故障选线[J]. 中国电机工程学报,2014,34(34):6228-6237.

    CHEN Kui,WEI Xiaoguang,CHEN Jingbo,et al. Fault line detection using sampled data processing and ADABOOST for small current grounding system[J]. Proceeding of the CSEE,2014,34(34):6228-6237.

    [13] 殷浩然,苗世洪,郭舒毓,等. 基于S变换相关度和深度学习的配电网单相接地故障选线新方法[J]. 电力自动化设备,2021,41(7):88-96. DOI: 10.16081/j.epae.202105028

    YIN Haoran,MIAO Shihong,GUO Shuyu,et al. Novel method for single-phase grounding fault line selection in distribution network based on S-transform correlation and deep learning[J]. Electric Power Automation Equipment,2021,41(7):88-96. DOI: 10.16081/j.epae.202105028

    [14] 郝帅,张旭,马瑞泽,等. 基于改进GoogLeNet的小电流接地系统故障选线方法[J]. 电网技术,2022,46(1):361-368.

    HAO Shuai,ZHANG Xu,MA Ruize,et al. Fault line selection method for small current grounding system based on improved GoogLeNet[J]. Power System Technology,2022,46(1):361-368.

    [15]

    HAMED A,MOSTAFA R,DANI A,et al. Refined composite multiscale dispersion entropy and its application to biomedical signals[J]. IEEE Transactions on Biomedical Engineering,2017,64(12):2872-2879. DOI: 10.1109/TBME.2017.2679136

    [16]

    ROSTAGHI M,AZAMI H. Dispersion entropy:a measure for time-series analysis[J]. IEEE Signal Processing Letters,2016,23(5):610-614. DOI: 10.1109/LSP.2016.2542881

    [17] 何玉灵,孙凯,王涛,等. 基于变分模态分解与精细复合多尺度散布熵的发电机匝间短路故障诊断[J]. 电力自动化设备,2021,41(3):164-172. DOI: 10.16081/j.epae.202101014

    HE Yuling,SUN Kai,WANG Tao,et al. Fault diagnosis of generator interturn short circuit fault based on variational mode decomposition and refined composite multiscale dispersion entropy[J]. Electric Power Automation Equipment,2021,41(3):164-172. DOI: 10.16081/j.epae.202101014

    [18] 李从志,郑近德,潘海洋,等. 基于精细复合多尺度散布熵与支持向量机的滚动轴承故障诊断方法[J]. 中国机械工程,2019,30(14):1713-1719,1726.

    LI Congzhi,ZHENG Jinde,PAN Haiyang,et al. Fault diagnosis method of rolling bearings based on refined composite multiscale dispersion entropy and support vector machine[J]. China Mechanical Engineering,2019,30(14):1713-1719,1726.

    [19]

    LIU Jingwei,XU Meizhi. Kernelized fuzzy attribute C-means clustering algorithm[J]. Fuzzy Sets and Systems,2008,159(18):2428-2445. DOI: 10.1016/j.fss.2008.03.018

    [20] 郭谋发. 配电网单相接地故障人工智能选线[M]. 北京: 中国水利水电出版社, 2020.

    GUO Moufa. Artificial intelligence line selection of single-phase grounding fault in distribution network[M]. Beijing: China Water & Power Press, 2020.

    [21] 卢丹. 基于WAMS的矿井高压电网单相接地故障选线及定位方法研究[D]. 北京: 中国矿业大学(北京), 2015.

    LU Dan. Study on single-phase earth fault line detection and fault location method of coal mine high-voltage grid base on WAMS[D]. Beijing: China University of Mining & Technology-Beijing, 2015.

  • 期刊类型引用(6)

    1. 杨战社,张程,荣相. 矿井供电系统单相接地故障选线方法现状与发展趋势. 煤矿安全. 2025(01): 212-219 . 百度学术
    2. 史鹏飞,张龙飞,何俊涛,李凯歌,刘鹏辉. 矿山供电系统单相接地故障区段定位方法. 能源与环保. 2024(04): 165-171 . 百度学术
    3. 申迎松,戴万波. 煤矿井下智能电力监控及故障诊断系统应用研究. 工矿自动化. 2024(S1): 200-204 . 本站查看
    4. 张建国. 露天煤矿供配电系统安全控制技术创新方法研究. 露天采矿技术. 2024(04): 64-68 . 百度学术
    5. 程卫健,史小军,穆艳祥. 煤矿电网的单相接地故障选线研究. 煤矿机械. 2024(09): 160-163 . 百度学术
    6. 李强. 基于RCM技术的煤矿机电设备维修. 矿业装备. 2023(12): 41-43 . 百度学术

    其他类型引用(1)

图(4)  /  表(5)
计量
  • 文章访问数:  151
  • HTML全文浏览量:  54
  • PDF下载量:  30
  • 被引次数: 7
出版历程
  • 收稿日期:  2022-03-24
  • 修回日期:  2022-07-25
  • 网络出版日期:  2022-08-14
  • 刊出日期:  2022-08-25

目录

/

返回文章
返回