CN102788926A - Single-phase ground fault section positioning method of small-current ground system - Google Patents

Abstract

The invention provides a single-phase ground fault section positioning method of a small-current ground system. The single-phase ground fault section positioning method comprises the steps of: 1) when the small-current ground system has a single-phase ground fault, recording zero-mode current of a previous cycle and zero-mode current of a next cycle at the moment when the single-phase ground fault occurs; 2) after a pure fault component of transient zero-mode current at the moment when the single-phase ground fault occurs is decomposed through an empirical mode, selecting out a highest-frequency intrinsic mode function component; 3) according to energy spectrum entropy of the highest-frequency intrinsic mode function component of each detection point, obtaining energy spectrum entropy factor values of the highest-frequency intrinsic mode function component of each detection section; and 4) conducting cluster analysis to sample set data consisting of the energy spectrum entropy factor values through a fuzzy C-means clustering method, determining a kind of sections which occur the most as a sound kind, i.e. sound sections, and determining a kind of sections which occur the least as a fault kind, i.e. fault sections. The single-phase ground fault section positioning method of the small-current ground system has the characteristics of high detection accuracy and good universality, and can be widely used in power systems.

Description

Single-phase earth fault section positioning method for small current grounding system

Technical Field

The invention relates to a power distribution network fault diagnosis technology, in particular to a method for positioning a single-phase earth fault section of a low-current earth system.

Background

In recent years, the fault location research work of high-voltage transmission lines is greatly developed, and the developed distance measuring device is popularized and used in national power grids, so that a good effect is achieved. However, compared with the high-voltage transmission network, the small-current grounding system has many branch lines, a complex network topology structure, and is easily affected by transition resistance, and the small-current grounding system has a short transmission distance, and cannot realize high-precision fault positioning.

At present, generally, the following methods are available for the fault location problem research of a low-current grounding system: traveling wave method, signal injection method, zero sequence current method, outdoor fault point detection method, impedance method, artificial intelligence technology and the like. The traveling wave method cannot solve the problems of accurate extraction of transient traveling wave components, identification and calibration of reflected waves at fault points, determination of wave speed, calibration of arrival time of initial fault traveling wave surges and the like. The signal injection method is suitable for a system only provided with two-phase current transformers on a circuit, the injected signals are greatly influenced by factors such as the capacity of a voltage transformer, the grounding resistance, the intermittent electric arc and the like, and the fault detection effect is poor. The outdoor fault point detection method determines the fault point according to the magnitude of the magnetic field generated by the zero sequence current before and after the ground point, but the detection precision is not high. The impedance method is greatly influenced by factors such as path impedance, line load, power supply parameters and the like, is only suitable for lines with simpler structures, and cannot eliminate false fault points for lines with multiple branches. Artificial intelligence techniques, such as wavelet neural networks, fuzzy expert systems, support vector machines and the like, have complex algorithms and large calculated amount, and basically stay in a laboratory simulation stage.

Therefore, in the prior art, no matter whether the structure of the small-current grounding system is complicated or not, a universal fault detection method is available for positioning various single-phase grounding fault sections of the small-current grounding system; even if some fault detection methods can realize fault point detection of a low-current grounding system with a simpler structure, the detection accuracy is lower.

Disclosure of Invention

In view of the above, the main objective of the present invention is to provide a method for positioning a single-phase ground fault section of a low-current grounding system, which has high detection accuracy and good versatility.

In order to achieve the purpose, the technical scheme provided by the invention is as follows:

a method for positioning a single-phase earth fault section of a low-current grounding system comprises the following steps:

step 1, recording zero-mode current of a previous period and a next period of a single-phase earth fault moment when the single-phase earth fault occurs in a small-current earth system.

And 2, after the transient zero-mode current pure fault component at the moment of the single-phase grounding fault is subjected to empirical mode decomposition, selecting the highest-frequency intrinsic mode function component of the transient zero-mode current pure fault component.

And 3, acquiring the energy spectrum entropy factor value of the highest frequency intrinsic mode function component of each detection section according to the energy spectrum entropy value of the highest frequency intrinsic mode function component of each detection section.

And 4, carrying out cluster analysis on sample set data consisting of the energy spectrum entropy factor values by a fuzzy C-means clustering method, judging the type with the largest number of sections as a healthy type, namely a healthy section, and judging the type with the smallest number of sections as a fault type, namely a fault section.

In summary, the method for positioning the single-phase earth fault section of the low-current earth system adopts the transient zero-mode current pure fault component at the moment of the single-phase earth fault as the initial handling capacity of the single-phase earth fault, so that the method has higher anti-interference capability and higher detection precision; moreover, the method has no relation with the complexity of the structure of the low-current grounding system, so that the method has better universality.

Drawings

Fig. 1 is a general flow chart of a method for positioning a single-phase earth fault section of a low-current grounding system according to the present invention.

Fig. 2 is a single-phase earth fault zero-mode network equivalent circuit of the low-current grounding system.

Fig. 3 is a schematic diagram of zero mode current waveforms at each detection point when the small-current grounding system of the present invention has a single-phase ground fault. Wherein, the diagram (a1) is a schematic diagram of zero mode current waveform at detection point A; FIG. B1 is a schematic diagram of a zero mode current waveform at detection point B; FIG. C1 is a schematic diagram of zero-mode current waveform at detection point C; fig. D1 is a diagram illustrating a zero mode current waveform at the D detection point.

Fig. 4 is a schematic flow chart of empirical mode decomposition of the transient zero-mode current pure fault component according to the present invention.

Fig. 5 is a schematic diagram of the components of the transient zero-mode current high-frequency IMF1 at each detection point when the small-current grounding system is in a single-phase ground fault. Wherein, the diagram (a2) is a schematic diagram of a transient zero mode current high-frequency IMF1 component at detection point A; FIG. B2 is a diagram illustrating a transient zero-mode current high-frequency IMF1 component at point B; FIG. C2 is a diagram illustrating a high-frequency IMF1 component of the transient zero-mode current at the C detection point; the diagram (D2) is a diagram illustrating the high-frequency IMF1 component of the transient zero-mode current at the D detection point.

Fig. 6 is a schematic flow chart of the process for acquiring the highest frequency eigenmode function component energy spectrum entropy factor value of each detection region according to the present invention.

FIG. 7 is a schematic diagram of a process of clustering analysis of sample set data composed of energy spectrum entropy factor values by a fuzzy C-means clustering method according to the present invention.

Fig. 8 is a radial small current grounding system according to an embodiment of the present invention.

Fig. 9 is a global variable matrix cluster center of the neutral point ungrounded system according to the embodiment of the present invention. Wherein, the graph (a3) is a class 1 type center of a global variable matrix of the system with no ground at a neutral point; the diagram (b3) is the class 2 center of the global variable matrix of the system with ungrounded neutral points.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.

Fig. 1 is a general flow chart of a method for positioning a single-phase earth fault section of a low-current grounding system according to the present invention. As shown in fig. 1, the method for positioning a single-phase earth fault section of a low-current grounding system according to the present invention includes the following steps:

step 1, recording zero-mode current of a previous period and a next period of a single-phase earth fault moment when the single-phase earth fault occurs in a small-current earth system.

In practical application, in a low-current grounding system, one feeder line is a branch line.

And 2, after the transient zero Mode current pure fault component at the moment of the single-phase grounding fault is subjected to Empirical Mode Decomposition (EMD), selecting the component of the highest frequency Intrinsic Mode Function (IMF).

And 3, acquiring the energy spectrum entropy factor value of the highest frequency intrinsic mode function component of each detection section according to the energy spectrum entropy value of the highest frequency intrinsic mode function component of each detection section.

And 4, carrying out cluster analysis on sample set data consisting of the energy spectrum entropy factor values by a fuzzy C-means clustering method, judging the type with the largest number of sections as a healthy type, namely a healthy section, and judging the type with the smallest number of sections as a fault type, namely a fault section.

In summary, in an actual low-current grounding system, a plurality of detection devices or feeder automation terminals may be installed at intervals on each feeder. In the method for positioning the single-phase earth fault section of the small-current grounding system, firstly, when a single-phase earth fault occurs on one feeder line, a transient zero-mode current pure fault component signal is obtained according to the record of each detection device or a feeder line automatic terminal on the feeder line; secondly, decomposing the transient zero-mode current pure fault component signal by adopting an empirical mode method to obtain a highest-frequency eigenmode function component containing sufficient single-phase earth fault information; thirdly, obtaining the energy spectrum entropy value of each detection point according to the highest frequency intrinsic mode function component of the single-phase earth fault information, thereby obtaining the energy spectrum entropy factor value of each section; and finally, carrying out cluster analysis on the sample set data consisting of the energy spectrum entropy factor values by a fuzzy C-means clustering method, judging the class with the largest number of sections in the classification as a healthy class, namely a healthy section, and judging the class with the smallest number of sections in the classification as a fault class, namely a fault section. Because the final fault section judgment is carried out by adopting the fuzzy C-means clustering method, the uncertainty caused by the traditional threshold value method when the fault section judgment is carried out is abandoned, and the accuracy of the judgment result is improved. Therefore, the method has the advantages of high anti-interference capability, high detection precision and high universality. In addition, the method of the invention also has the characteristics of low cost and the like.

Fig. 2 is a single-phase earth fault zero-mode network equivalent circuit of the low-current grounding system. As shown in FIG. 2, U_0fA zero-mode virtual voltage source; c₁，C₂，C₃And C₄Respectively, the line sections AB, BF, FC, CD are grounded; the solid arrow is the reference direction of the current; the dotted arrows are the actual flow direction of the current, and the detection points A, B, C and D are four detection points respectively. The section between the point B and the point C has single-phase earth fault, and analysis shows that the zero-mode current detected by the point A and the point BIs provided with i_0B＝i_0A-i_0C1Wherein: i.e. i_0AThe sum of all non-fault line zero-mode capacitance currents to ground; i.e. i_0C1Zero mode capacitance current to ground for the AB segment. Due to the short distance of the AB section, the proportion of the earth capacitance current to the sum of the zero-mode capacitance currents of the non-fault line is small and can be ignored, so that the zero-mode currents detected at the two ends of the AB section are approximately equal, namely i_0A≈i_0B(ii) a Similarly, the zero-mode current detected across the CD is approximately equal, i_0C≈i_0D. Since a fault virtual power supply is generated at the fault point at the moment of fault occurrence, the actual direction of the zero-mode current flowing from the fault point is shown by the dotted arrow in fig. 2, and a part of the zero-mode current flows from the fault point to the upstream of the line and faces the bus (and i)₁Opposite reference direction) and another portion flows downstream from the fault point, away from the busbar (from i) and toward the line₂The same reference direction).

Fig. 3 is a schematic diagram of zero mode current waveforms at each detection point when the small-current grounding system of the present invention has a single-phase ground fault. Wherein, the diagram (a1) is a diagram of a zero mode current waveform at the point a, the diagram (B1) is a diagram of a zero mode current waveform at the point B, the diagram (C1) is a diagram of a zero mode current waveform at the point C, and the diagram (D1) is a diagram of a zero mode current waveform at the point D. As can be seen from the graphs (a1) and (B1), the zero-mode currents at the detection point a and the detection point B upstream of the fault point have similarity, regardless of the initial polarity or the amplitude; similarly, as can be seen from fig. (C1) and fig. (D1), there is also a similarity between the zero-mode currents at the C detection point and the D detection point downstream of the fault point. However, for the detection points on both sides of the fault point in fig. 3: (

In between) have opposite initial polarities, and have very different waveforms and no similarity.

In the invention, the step 1 also comprises the following steps:

step a, judging zero sequence voltage u of small current grounding system₀(t) whether or not it is more than 0.15 timesRated voltage U of bus_n: when u is₀(t)＞0.15U_nIf yes, executing step b; when u is₀(t)≤0.15U_nAnd if so, returning to the step a.

Step b, judging whether the voltage transformer is disconnected: when the voltage transformer is disconnected, sending out the disconnection warning information of the voltage transformer; and c, when the voltage transformer is not disconnected, executing the step c.

Step c, judging whether the arc suppression coil generates series resonance: when the arc suppression coil generates series resonance, the arc suppression coil is adjusted to prevent the series resonance; and when the arc suppression coil does not generate series resonance, judging that the small current grounding system has a grounding fault.

In step 2, the transient zero-mode current pure fault component at the single-phase earth fault time is a difference between a zero-mode current of a cycle after the single-phase fault time and a zero-mode current of a cycle before the single-phase fault time.

Fig. 4 is a schematic flow chart of empirical mode decomposition of the transient zero-mode current pure fault component according to the present invention. As shown in fig. 4, in step 2, the empirical mode decomposition of the transient zero-mode current pure fault component s (t) at the time of the ground fault includes the following steps:

step 21, when i is equal to 0 and p is equal to 0, taking the transient zero-mode current pure fault component x (t) as the first signal s to be decomposed₁(t), the first signal to be decomposed s₁(t) upper envelope signal l consisting of all maxima₁₁(t) lower envelope signal l formed with all its minima₁₂(t) summing to obtain a first envelope mean signal $m_1\left(t\right)=\frac{1}{2}[l_{11}\left(t\right)+l_{12}\left(t\right)].$

Step 22, obtaining the i-th decomposition average difference signal d_i(t)＝s_i(t)-m_i(t); wherein i is a natural number, s_i(t) is the ith signal to be decomposed,m_i(t) is the ith envelope mean signal, l_i1(t)、l_i2(t) i signals s to be decomposed, respectively_i(t) an upper envelope signal composed of all maxima and a lower envelope signal composed of all minima.

Step 23, judging whether i is more than 1: if not, executing step 24; if so, step 26 is performed.

Step 24, judging the first decomposed average difference signal d₁(t) whether the difference between the number of extreme points and the number of zero-crossing points is less than or equal to 1, and a first mean-square error signal d₁(t) whether the average value of the upper envelope signal composed of all the maximum values and the lower envelope signal composed of all the minimum values is 0 at any time: if the first decomposed average difference signal d₁(t) the difference between the number of extreme points and the number of zero-crossing points is less than or equal to 1, and the first mean-square error signal d₁(t) if the average value of the upper envelope signals composed of all the maximum values and the lower envelope signals composed of all the minimum values is 0 at any time, step 27 is executed; if the first decomposed average difference signal d₁(t) the difference between the number of extreme points and the number of zero-crossing points is greater than 1, and the first mean-square error signal d₁If the average value of the upper envelope composed of all the maximum values and the lower envelope composed of all the minimum values of (t) is not 0, step 25 is executed.

Step 25, get i ═ i +1, order s_i(t)＝d_(i-1)(t), return to step 22.

Step 26, judgment

Whether or not: if not, returning to the step 25; if so, step 27 is performed.

Step 27, taking p as p +1, c_p(t)＝d_i(t) and obtaining the ith remainder signal

Step 28, judging the ith remainder signal mu_i(t) whether monotonicity is present: if the ith remainder signal mu_i(t) if monotonicity exists, ending empirical mode decomposition to obtain:

if the ith remainder signal mu_i(t) if monotonicity is not present, i is taken as i +1, and s is given_i(t)＝μ_(i-1)(t), return to step 22.

In practice, the ith remainder signal mu_i(t) has monotonicity of monotonicity being monotonically increasing or monotonically decreasing.

Fig. 5 is a schematic diagram of the components of the transient zero-mode current high-frequency IMF1 at each detection point when the small-current grounding system is in a single-phase ground fault. The diagram (a2) is a diagram of a component of the transient zero mode current high-frequency IMF1 at the point a, the diagram (B2) is a diagram of a component of the transient zero mode current high-frequency IMF1 at the point B, the diagram (C2) is a diagram of a component of the transient zero mode current high-frequency IMF1 at the point C, and the diagram (D2) is a diagram of a component of the transient zero mode current high-frequency IMF1 at the point D. In practical application, the IMF1 component of the transient zero-mode current at each detection point is the highest-frequency part in the transient zero-mode current signal, and contains rich fault transient information, and at present, the IMF1 component is widely applied to power signal singularity detection, small-current grounding system line selection and traveling wave direction criterion algorithms.

In step 3 of the present invention, each of the detection points includes 1, 2, 1., j,. n, k,. n, m; j, n, k and m are natural numbers, j is less than or equal to k and less than or equal to m, n represents any one of m detection points, and n is 1, 2.

Fig. 6 is a schematic flow chart of the process for acquiring the highest frequency eigenmode function component energy spectrum entropy factor value of each detection region according to the present invention. As shown in fig. 6, in step 3, the obtaining of the energy spectrum entropy factor value of the highest frequency eigenmode mode function component of each detection region specifically includes the following steps:

step 31, according to the highest frequency eigenmode function component IMF1 of m detection points₍₁₎(N)，IMF1₍₂₎(N)，IMF1₍₃₎(N)，…IMF1_(m)(N), obtaining the highest frequency eigenmode function component energy spectrum value E of m detection points₍₁₎，E₍₂₎，…E_(m)Specifically, the following formula is calculated:

<math> <mrow> <msub> <mi>E</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msub> <mo>=</mo> <munder> <mi>&Sigma;</mi> <mi>N</mi> </munder> <msup> <mrow> <mo>|</mo> <msub> <mrow> <mi>IMF</mi> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>E</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msub> <mo>=</mo> <munder> <mi>&Sigma;</mi> <mi>N</mi> </munder> <msup> <mrow> <mo>|</mo> <msub> <mrow> <mi>IMF</mi> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>,</mo> </mrow> </math> <math> <mrow> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msub> <mi>E</mi> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> </mrow> </msub> <mo>=</mo> <munder> <mi>&Sigma;</mi> <mi>N</mi> </munder> <msup> <mrow> <mo>|</mo> <msub> <mrow> <mi>IMF</mi> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> </mrow> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> </math>

in practical application, the components of the highest-frequency eigenmode functions of all the detection points are subjected to square summation, the obtained original energy spectrum entropy value is often large, and [0, 1] normalization processing is often performed to reduce the operation scale. The normalization of [0, 1] is to regulate the original energy spectrum entropy value to the range of [0, 1 ].

Step 32, adding and summing the energy spectrum values of all the intrinsic mode function components and the decomposition remainder items of the m detection points to obtain E of the m detection points_SUM(1)，E_SUM(2)，…E_SUM(m)。

In practical application, the transient zero-mode current pure fault component of each detection point can be decomposed into a series of intrinsic mode function components and respective decomposition residuals, the intrinsic mode function components of each detection point are added with the energy spectrum values of the decomposition residuals,can obtain E of each of m detection points_SUM(1)，E_SUM(2)，…E_SUM(m)This can be used as the basis for determining the weighting factor.

Step 33, calculating the component energy spectrum value E of the highest frequency eigenmode function of the m detection points₍₁₎，E₍₂₎，…E_(m)At respective detection points E_SUM(1)，E_SUM(2)，…E_SUM(m)The weight factor q_(m)The specific calculation formula is as follows:

$q_{\left(1\right)}=\frac{E_{\left(1\right)}}{E_{\mathrm{SUM}\left(1\right)}},$ $q_{\left(2\right)}=\frac{E_{\left(2\right)}}{E_{\mathrm{SUM}\left(2\right)}},$ $...q_{\left(m\right)}=\frac{E_{\left(m\right)}}{E_{\mathrm{SUM}\left(m\right)}}$

here, the weight coefficient is necessarily less than 1.

Step 34, calculating the energy spectrum entropy value M of the component of the highest frequency eigenmode mode function of each of the M detection points according to the definition of entropy_EE(1)，M_EE(2)，…M_EE(m)The specific calculation formula is as follows:

M_EE(1)＝-∑q₍₁₎lnq₍₁₎，M_EE(2)＝-∑q₍₂₎lnq₍₂₎，…M_EE(m)＝-∑q_(m)lnq_(m)

in practical application, the narrower the power spectrum peak of the transient zero-mode current pure fault component signal is, the smaller the spectrum entropy is, the more regular the change of the signal is, and the smaller the complexity is; conversely, the flatter the power spectrum and the greater the spectral entropy, the greater the complexity of the signal.

Step 35, sequentially obtaining the energy spectrum entropy ratio of the transient zero mode current highest frequency eigenmode function components of two adjacent detection points in the m detection points, namely the energy spectrum entropy factor value, wherein the specific calculation formula is as follows:

<math> <mrow> <msub> <mi>&gamma;</mi> <mi>&alpha;&beta;</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>M</mi> <mrow> <mi>EE</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>)</mo> </mrow> </mrow> </msub> <msub> <mi>M</mi> <mrow> <mi>EE</mi> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </msub> </mfrac> </mrow> </math>

wherein, alpha and beta are two adjacent detection points.

In practical application, the energy spectrum entropy factor value can well represent the energy numerical value size characteristic of each section on the feeder line.

In the present invention, before the step 31, the method further includes:

step 30, empirical mode decompositionIn (c)₁And (t) is the highest frequency eigenmode function component IMF1 (N).

FIG. 7 is a schematic diagram of a process of clustering analysis of sample set data composed of energy spectrum entropy factor values by a fuzzy C-means clustering method according to the present invention. As shown in fig. 7, in step 4, the sample set data composed of the energy spectrum entropy factor values is subjected to cluster analysis by a fuzzy C-means clustering method, the class with the largest number of sections is determined as a healthy class, i.e., a healthy section, and the class with the smallest number of sections is determined as a fault class, i.e., a fault section. The method specifically comprises the following steps:

step 41, defining an objective function

Wherein u is_ghRepresents the h-th energy spectrum entropy factor value x_hMembership degree belonging to the g-th class, where 0. ltoreq. u_gh≤1，

U＝(u_gh)_z×lIs a membership matrix, d_gh＝||x_h-v_gL. Obviously, J (U, V) represents the spectral entropy factor values in each classification into respective clustersThe sum of weighted squared distances of class centers, the weight being the value of each spectral entropy factor x_hBelongs to the membership degree of the g-th class to the power w. The clustering criterion of the fuzzy C-means clustering method is to find U and V so that J (U and V) takes the minimum value.

Step 42, setting the number to be classified according to the actual situation, namely determining the number z of the classes; setting a fuzzy weighting index w influencing the fuzzification degree of the membership matrix, wherein w is more than 1; setting an initial membership matrix

It is common practice to take [0, 1]]Uniformly distributed random numbers on to determine an initial membership matrix U⁽⁰⁾Let λ be 1 denote step 1 iteration.

Step 43, calculating the clustering center V of the lambda step by the following formula^(λ)：

<math> <mrow> <msubsup> <mi>v</mi> <mi>g</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mfrac> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>h</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <msup> <mrow> <mo>(</mo> <msubsup> <mi>u</mi> <mi>gh</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mi>w</mi> </msup> <msub> <mi>x</mi> <mi>h</mi> </msub> </mrow> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>h</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <msup> <mrow> <mo>(</mo> <msubsup> <mi>u</mi> <mi>gh</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mi>w</mi> </msup> </mrow> </mfrac> <mo>,</mo> </mrow> </math> g＝1，2，…，z

Step 44, correcting the membership degree matrix U^(λ)Calculating an objective function value J^(λ)：

<math> <mrow> <msubsup> <mi>u</mi> <mi>gh</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mn>1</mn> <mo>/</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>z</mi> </munderover> <msup> <mrow> <mo>(</mo> <msubsup> <mi>d</mi> <mi>gh</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msubsup> <mo>/</mo> <msubsup> <mi>d</mi> <mi>jh</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mfrac> <mn>2</mn> <mrow> <mi>w</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> </msup> <mo>,</mo> </mrow> </math> g＝1，2，…z；h＝1，2，…，l

<math> <mrow> <msup> <mi>J</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msup> <mrow> <mo>(</mo> <msup> <mi>U</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msup> <mo>,</mo> <msup> <mi>V</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>h</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>g</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>z</mi> </munderover> <msup> <mrow> <mo>(</mo> <msubsup> <mi>u</mi> <mi>gh</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mi>w</mi> </msup> <msup> <mrow> <mo>(</mo> <msubsup> <mi>d</mi> <mi>gh</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </math>

Wherein, <math> <mrow> <msubsup> <mi>d</mi> <mi>gh</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>x</mi> <mi>h</mi> </msub> <mo>-</mo> <msubsup> <mi>v</mi> <mi>g</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msubsup> <mo>|</mo> <mo>|</mo> <mo>.</mo> </mrow> </math>

step 45, terminate the tolerance ε for a given membership_u> 0 (or objective function termination tolerance ε)_J> 0, or maximum iteration step lambda_max) When is coming into contact with

(or when lambda > 1, | J^(λ)-J^(λ-1)|＜ε_JOr λ ≧ λ_max) Then the iteration is stopped, otherwise λ ═ λ +1, and then go to step 43.

And step 46, after iteration of the steps, obtaining a final membership matrix U and a clustering center V of the energy spectrum entropy factor value, so that the value of the objective function J (U, V) is minimum. The attribution of all energy spectrum entropy factor values can be determined according to the value of the element in the final membership degree matrix U, and when the attribution is determined, the attribution of all energy spectrum entropy factor values

Then, the value x of the energy spectrum entropy factor can be calculated_hClassified as j.

And step 47, according to the actual operation condition of each section on the low-current grounding system line, judging the section with the largest number of sections as a healthy section, namely a healthy section, and judging the section with the smallest number of sections as a fault section, namely a fault section.

In practical application, considering the existence of the protection device in the actual system, the number of fault sections is inevitably smaller than the number of healthy sections, so after fuzzy C-means clustering is performed, the section with the largest number of sections is determined as a healthy class, and the section with the smallest number of sections is determined as a fault class. The method abandons the uncertainty caused by the traditional threshold value judgment of the fault section, and can reliably improve the accuracy of the judgment result.

Examples

Fig. 8 is a radial small current grounding system according to an embodiment of the present invention. As shown in fig. 8, in this embodiment, the line parameters are: positive sequence impedance Z₁0.17+ j0.38 Ω/km, positive sequence ground admittance b₁J3.045us/km, zero sequence impedance Z₀0.23+ j1.72 omega/km, zero order ground admittance b₀J1.884us/km, the length of each load branch line is r₁＝20km、r₂＝15km、r₃＝24km、r₄＝8km、r₅＝16km、r ₆30 km. The transformer parameters are as follows: delta/Y connection, primary side voltage 220KV, secondary side voltage 35KV and rated capacity S_N40000KVA, no-load loss of 35.63KW, and leakage impedance of primary winding of Z_1g0.4+ j12.2 Ω, and the leakage impedance of the secondary winding is Z_2gThe steady-state excitation current is 0.672A, the main flux 202.2Wb, and the excitation impedance is 400k Ω, which is 0.006+ j0.183 Ω. The parameters of the arc suppression coil of the transformer are as follows: the arc suppression coil is in an overcompensation state, the compensation degree is 8%, the series resistance value of the arc suppression coil is 10% of the inductive reactance value, and the resistance value R of the series resistance_p121.35 Ω. The load parameters are as follows: equivalent load of line 1 and line 3 is Z_{Equivalence of}＝400+j20Ω。

As shown in fig. 8, it is assumed that a single-phase ground fault occurs in the BC segment. According to the method, the maximum frequency eigenmode function component energy spectrum entropy factor values under the conditions of different grounding resistance values (5 omega, 10 omega, 20 omega, 50 omega and 100 omega) are determined when the initial voltage phase angles are respectively 0 DEG, 30 DEG, 60 DEG and 90 DEG in an ungrounded neutral point system and a grounded system through an arc suppression coil. As shown in tables 1-2 below.

Table 1 IMF1 component energy spectrum entropy factor of system without grounding neutral point

TABLE 2 IMF1 component energy spectrum entropy factor of arc suppression coil grounding system

In fig. 8, since four detection devices a, B, C, and D form 3 segments and a fault occurs in the segment BC, the segments in the line can be classified into 2 types when the analysis is performed by using the fuzzy C-means clustering: the number of clusters of healthy and failure classes, i.e., FCMs, is 2. Thus, the data in tables 1 and 2 may be constructed into a eigenvalue matrix T of 3 × σ, where σ is 1, 2, 3 … 20, respectively.

Local Variable (Local Variable) feature matrix T_{LV_σ}: when σ is 1, 2, 3 … 19, a series of feature matrices are constructed. For example, when σ is 1, 2, feature matrices of 3 × 1 and 3 × 2 are formed, respectively.

Global Variable (Global Variable) feature matrix T_GV: and when sigma is 20, forming a feature matrix. The 3 × 20 matrix formed in table 1 is referred to as a global variable feature matrix of the neutral point ungrounded system, and the 3 × 20 matrix formed in table 2 is referred to as a global variable feature matrix of the arc suppression coil grounded system.

In addition, the fuzzy weighting exponent w is set to 2 in the program calculation, the termination margin e of the objective function is set to 0.000001, the power exponent is set to 3, and the maximum number of iterations in the program is set to 200. And in the iterative process, minimizing the weighted sum of the distances from all data points to all clustering centers and the membership value as an optimization target, wherein the objective function value is continuously changed in the iterative process until convergence.

The embodiment of the invention will be derived from the local variable characteristic matrix T_{LV_σ}And a global variable feature matrix T_GVFuzzy C-means clustering analysis evaluation is carried out on two aspects, is limited to space, and only gives local variable characteristic matrix T of table 1 and table 2_{LV_1}And a global variable feature matrix T_GVCorrespondingly calculated fuzzy membership degree matrix U and respective clustering center V (wherein T)_{LV_1}The data at 0 ° and 5 Ω in tables 1 and 2, respectively). The specific calculation results are as follows:

$U_{\mathrm{LV}\_1}^{\mathrm{NG}}=\left[\begin{array}{ccc}0.0279& 1.0000& 0.0263\\ 0.9721& 0.0000& 0.9737\end{array}\right],$ $V_{\mathrm{LV}\_1}^{\mathrm{NG}}=\left[\begin{array}{c}1.1533\\ -0.5768\end{array}\right],$ $U_{\mathrm{GV}}^{\mathrm{NG}}=\left[\begin{array}{ccc}0.0739& 0.9993& 0.0683\\ 0.9261& 0.0007& 0.9317\end{array}\right]$

$V_{\mathrm{GV}}^{\mathrm{NG}}=\begin{array}{c}\left[\begin{array}{cccccccccc}1.1521& 1.1534& 1.1528& 1.1365& 1.1505& -1.0977& -1.1375& -1.1464& 1.1534& 1.1342\\ -0.5771& -0.5774& -0.5767& -0.5704& -0.5765& 0.5522& 0.5708& 0.5728& -0.5774& -0.5661\end{array}\right.\\ \left.\begin{array}{cccccccccc}1.1491& 1.1532& 1.1507& 1.1319& 1.1534& 1.1526& 1.1524& 1.1319& 1.1528& 1.1257\\ -0.5744& -0.5770& -0.5766& -0.5683& -0.5774& -0.5773& -0.5769& -0.5683& -0.5773& -0.5654\end{array}\right]\end{array}$

$U_{\mathrm{LV}\_1}^{\mathrm{AC}}=\left[\begin{array}{ccc}0.9740& 0.0000& 0.9724\\ 0.0260& 1.0000& 0.0276\end{array}\right],$ $V_{\mathrm{LV}\_1}^{\mathrm{AC}}=\left[\begin{array}{c}-0.5768\\ 1.1533\end{array}\right],$ $U_{\mathrm{GV}}^{\mathrm{AC}}=\left[\begin{array}{ccc}0.8954& 0.0021& 0.9006\\ 0.1046& 0.9979& 0.0994\end{array}\right]$

$V_{\mathrm{GV}}^{\mathrm{AC}}=\begin{array}{c}\left[\begin{array}{cccccccccc}-0.5763& -0.5695& -0.5767& -0.5752& -0.5681& 0.5732& 0.4828& 0.5755& -0.5774& -0.5728\\ 1.1497& 1.1322& 1.1504& 1.1449& 1.1292& -1.1403& -0.9528& -1.1485& 1.1507& 1.1438\end{array}\right.\\ \left.\begin{array}{cccccccccc}-0.5702& -0.5627& -0.5622& -0.5719& -0.5774& -0.5750& -0.5574& -0.5741& -0.5736& -0.5552\\ 1.1391& 1.1254& 1.1244& 1.1376& 1.1509& 1.1477& 1.1154& 1.1424& 1.1413& 1.1018\end{array}\right]\end{array}$

wherein,

respectively as a fuzzy membership matrix and a clustering center of local variables of a neutral point unconnected systemThe method comprises the following steps of (1) obtaining a matrix, a global variable fuzzy membership matrix and a global variable clustering center matrix;

the fuzzy membership matrix of local variables, the clustering center matrix of local variables, the fuzzy membership matrix of global variables and the clustering center matrix of global variables of the arc suppression coil grounding system are respectively adopted.

The embodiment of the invention takes the calculation result of a neutral point ungrounded system as an example:

1) local variable fuzzy membership matrix

Column 1 elements of 0.0279, 0.9721, respectively, indicate γ_ABThe degree of membership in the 1 st group is 0.0279, the degree of membership in the 2 nd group is 0.9721, and γ is larger than the degree of membership in the 1 st group because the degree of membership in the 2 nd group is larger than the degree of membership in the 1 st group_ABBelong to category 2; in the same way, by comparison

Column 2 data gives γ_BCBelong to class 1, comparison

Column 3 data gives_CDBelong to category 2.

2) Clustering center matrices for local variables

The elements in column 1 are 1.1533, -0.5768, respectively, indicating that the local variable feature matrix has a cluster center of 1.1533 for class 1 and a cluster center of-0.5768 for class 2, and thus it can also be seen that the two classes have different cluster centers and represent data of different sizes.

3) Fuzzy membership matrix for global variable

By the same method, gamma_ABBelong to class 2, γ_BCBelong to the class 1, γ_CDBelong to category 2.

Note that: because the fuzzy C-means clustering function determines the initial membership matrix by generating random numbers, when the fuzzy C-means clustering function is called for clustering, clustering results can have nuances each time (the whole clustering results are the same, but the sequence of the clusters can be different)

4) In addition, cluster center matrix for global variables

Observing the data in the 1 st row (or the 2 nd row), it is found that the change of the cluster centers of the respective classes can be obtained from the sign change of the data, and actually, the change reflects the change characteristics of the data in the 6 th to 8 th rows in table 1 in detail, and for the sake of intuition, the data is shown in fig. 9. By analyzing the data of Table 1 as a whole, it was found that_BCIn most cases, is compared to gamma_AB、γ_CDThe data is opposite only when the data of the 6 th to 8 th groups are data, so that the numerical value of the threshold value cannot be accurately determined by adopting the traditional threshold value discrimination method, and further the fault positioning method is invalid. In addition, when the threshold value discrimination method is adopted, the setting of the threshold value margin is often very harsh under non-failure conditions such as system oscillation, and erroneous discrimination may be caused if the threshold value margin is careless. The fuzzy C-means clustering method has the advantages that no matter how the data size changes, accurate positioning can be realized by grasping the essence that the fault section and the healthy section are necessarily inconsistent.

Analysing systems earthed via arc-suppression coils

The same conclusions as above can be drawn.

Special description: regarding the problem of how to correspond to the healthy class or the fault class in the category 1 and the category 2 in the embodiment of the present invention, considering that the number of fault sections is inevitably smaller than the number of healthy sections in the presence of a protection device in an actual system, after fuzzy C-means clustering is performed, the category with the largest number of sections is determined as the healthy class, and the category with the smallest number of sections is determined as the fault class. In the embodiment of the present invention, the 1 st class is determined as a failure class, and the 2 nd class is determined as a healthy class.

Therefore, by analyzing, fuzzy C-means clustering analysis is carried out on the IMF1 component energy spectrum entropy factors, the BC section can be accurately judged to belong to the fault class, and the AB and CD sections can be accurately judged to belong to the key class.

The embodiment of the invention adopts a local variable characteristic matrix T_{LV_σ}And a global variable feature matrix T_GVOn the two aspects, fuzzy C-means clustering analysis is carried out on IMF1 energy spectrum entropy factors of a neutral non-grounding system and an arc suppression coil grounding system, and the result shows that the fault occurring section can be accurately judged from a local variable or a global variable. In addition, experiments have been carried out, and for the energy spectrum entropy factor values in tables 1 and 2, even when the fuzzy C-means clustering analysis is carried out on the feature matrix formed by any group of data combination, the fault occurring section can be accurately judged. Furthermore, the method for positioning the single-phase earth fault section of the low-current grounding system can accurately determine the section where the single-phase earth fault occurs.

In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (7)

1. A method for positioning a single-phase earth fault section of a low-current grounding system is characterized by comprising the following steps of:

step 1, recording zero-mode current of a previous period and a next period of a single-phase earth fault moment when the single-phase earth fault occurs in a small-current earth system;

step 2, after the transient zero-mode current pure fault component at the moment of the single-phase grounding fault is subjected to empirical mode decomposition, selecting the highest-frequency intrinsic mode function component of the transient zero-mode current pure fault component;

step 3, acquiring the energy spectrum entropy factor value of the highest frequency eigenmode function component of each detection section according to the energy spectrum entropy value of the highest frequency eigenmode function component of each detection section;

and 4, carrying out cluster analysis on sample set data consisting of the energy spectrum entropy factor values by a fuzzy C-means clustering method, judging the type with the largest number of sections as a healthy type, namely a healthy section, and judging the type with the smallest number of sections as a fault type, namely a fault section.

2. The method for locating the single-phase earth fault section of the low-current grounding system according to claim 1, wherein the step 1 is preceded by the steps of:

step a, judging zero sequence voltage u of small current grounding system₀(t) whether or not it is greater than 0.15 times the rated bus voltage U_n: when u is₀(t)＞0.15U_nIf yes, executing step b; when u is₀(t)≤0.15U_nIf yes, returning to the step a;

step b, judging whether the voltage transformer is disconnected: when the voltage transformer is disconnected, sending out the disconnection warning information of the voltage transformer; when the voltage transformer is not disconnected, executing the step c;

step c, judging whether the arc suppression coil generates series resonance: when the arc suppression coil generates series resonance, the arc suppression coil is adjusted to prevent the series resonance; and when the arc suppression coil does not generate series resonance, judging that the small-current grounding system has single-phase grounding fault.

3. The method as claimed in claim 1, wherein in step 2, the transient zero-mode current pure fault component at the time of the single-phase ground fault is a difference between a zero-mode current of a cycle after the time of the single-phase ground fault and a zero-mode current of a cycle before the time of the single-phase ground fault.

4. The method for locating a single-phase earth fault section of a low-current grounding system according to claim 1, wherein in the step 2, the empirical mode decomposition of the transient zero-mode current pure fault component s (t) at the time of the earth fault includes the following steps:

step 21, when i is equal to 0 and p is equal to 0, taking the transient zero-mode current pure fault component x (t) as the first signal s to be decomposed₁(t), the first signal to be decomposed s₁(t) upper envelope signal l consisting of all maxima₁₁(t) lower envelope signal l formed with all its minima₁₂(t) summing to obtain a first envelope mean signal $m_1\left(t\right)=\frac{1}{2}[l_{11}\left(t\right)+l_{12}\left(t\right)];$

Step 22, obtaining the i-th decomposition average difference signal d_i(t)＝s_i(t)-m_i(t); wherein i is a natural number, s_i(t) is the ith signal to be decomposed,

m_i(t) is the ith envelope mean signal, l_i1(t)、l_i2(t) i signals s to be decomposed, respectively_i(t) upper envelope signals composed of all maxima and lower envelope signals composed of all minima;

step 23, judging whether i is more than 1: if not, executing step 24; if true, go to step 26;

step 24, judging the first decomposed average difference signal d₁(t) whether the difference between the number of extreme points and the number of zero-crossing points is less than or equal to 1, and a first mean-square error signal d₁(t) institute ofWhether or not the average value of the upper envelope signal having the maximum value and the lower envelope signal having all the minimum values is 0 at any time: if the first decomposed average difference signal d₁(t) the difference between the number of extreme points and the number of zero-crossing points is less than or equal to 1, and the first mean-square error signal d₁(t) if the average value of the upper envelope signals composed of all the maximum values and the lower envelope signals composed of all the minimum values is 0 at any time, step 27 is executed; if the first decomposed average difference signal d₁(t) the difference between the number of extreme points and the number of zero-crossing points is greater than 1, and the first mean-square error signal d₁(t) if the average value of the upper envelope composed of all the maximum values and the lower envelope composed of all the minimum values is not 0, executing step 25;

step 25, get i ═ i +1, order s_i(t)＝d_(i-1)(t), return to step 22;

step 26, judgment

Whether or not: if not, returning to the step 25; if true, go to step 27;

step 27, taking p as p +1, c_p(t)＝d_i(t) and obtaining the ith remainder signal

Step 28, judging the ith remainder signal mu_i(t) whether monotonicity is present: if the ith remainder signal mu_i(t) if monotonicity exists, ending empirical mode decomposition to obtain:

if the ith remainder signal mu_i(t) if monotonicity is not present, i is taken as i +1, and s is given_i(t)＝μ_(i-1)(t), return to step 22.

5. The method for locating a single-phase earth fault section of a low-current grounding system according to claim 4, wherein in step 3, each detection point comprises 1, 2, 1, j, n, k, m; j, n, k and m are natural numbers, j is not less than k and not more than m, n represents any one of m detection points, and n is 1, 2, a.

In step 3, the obtaining of the energy spectrum entropy factor value of the highest frequency eigenmode function component of each detection area specifically includes the following steps:

step 31, according to the highest frequency eigenmode function component IMF1 of m detection points₍₁₎(N)，IMF1₍₂₎(N)，IMF1₍₃₎(N)，…IMF1_(m)(N), obtaining the highest frequency eigenmode function component energy spectrum value E of m detection points₍₁₎，E₍₂₎，…E_(m)Specifically, the following formula is calculated:

<math> <mrow> <msub> <mi>E</mi> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msub> <mo>=</mo> <munder> <mi>&Sigma;</mi> <mi>N</mi> </munder> <msup> <mrow> <mo>|</mo> <msub> <mrow> <mi>IMF</mi> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>E</mi> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msub> <mo>=</mo> <munder> <mi>&Sigma;</mi> <mi>N</mi> </munder> <msup> <mrow> <mo>|</mo> <msub> <mrow> <mi>IMF</mi> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>,</mo> </mrow> </math> <math> <mrow> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msub> <mi>E</mi> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> </mrow> </msub> <mo>=</mo> <munder> <mi>&Sigma;</mi> <mi>N</mi> </munder> <msup> <mrow> <mo>|</mo> <msub> <mrow> <mi>IMF</mi> <mn>1</mn> </mrow> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> </mrow> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> </math>

step 32, adding and summing the energy spectrum values of all the intrinsic mode function components and the decomposition remainder items of the m detection points to obtain E of the m detection points_SUM(1)，E_SUM(2)，…E_SUM（m)；

Step 33, calculating the component energy spectrum value E of the highest frequency eigenmode function of the m detection points₍₁₎，E₍₂₎，…E_(m)At respective detection points E_SUM(1)，E_SUM(2)，…E_SUM(m)The weight factor q_(m)The specific calculation formula is as follows:

$q_{\left(1\right)}=\frac{E_{\left(1\right)}}{E_{\mathrm{SUM}\left(1\right)}},$ $q_{\left(2\right)}=\frac{E_{\left(2\right)}}{E_{\mathrm{SUM}\left(2\right)}},$ $...q_{\left(m\right)}=\frac{E_{\left(m\right)}}{E_{\mathrm{SUM}\left(m\right)}}$

step 34, calculating the energy spectrum entropy value M of the component of the highest frequency eigenmode mode function of each of the M detection points according to the definition of entropy_EE(1)，M_EE(2)，…M_EE(m)The specific calculation formula is as follows:

M_EE(1)＝-∑q₍₁₎lnq₍₁₎，M_EE(2)＝-∑q₍₂₎lnq₍₂₎，…M_EE(m)＝-∑q_(m)lnq_(m)

step 35, sequentially obtaining the energy spectrum entropy ratio of the transient zero mode current highest frequency eigenmode function components of two adjacent detection points in the m detection points, namely the energy spectrum entropy factor value, wherein the specific calculation formula is as follows:

<math> <mrow> <msub> <mi>&gamma;</mi> <mi>&alpha;&beta;</mi> </msub> <mo>=</mo> <mfrac> <msub> <mi>M</mi> <mrow> <mi>EE</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>)</mo> </mrow> </mrow> </msub> <msub> <mi>M</mi> <mrow> <mi>EE</mi> <mrow> <mo>(</mo> <mi>&beta;</mi> <mo>)</mo> </mrow> </mrow> </msub> </mfrac> </mrow> </math>

wherein, alpha and beta are two adjacent detection points.

6. The method for locating a single-phase ground fault section of a low-current grounding system according to claim 5, wherein before the step 31, the method further comprises:

step 30, empirical mode decomposition

c₁And (t) is the highest frequency eigenmode function component IMF1 (N).

7. The method according to claim 1, wherein in step 4, the clustering analysis is performed on the sample set data composed of the energy spectrum entropy factor values by a fuzzy C-means clustering method, the class with the highest number of the occurring segments is determined as a healthy class, i.e., a healthy segment, and the class with the lowest number of the occurring segments is determined as a fault class, i.e., a fault segment, and specifically includes the following steps:

step 41, defining an objective function

Wherein u is_ghRepresents the h-th energy spectrum entropy factor value x_hMembership degree belonging to the g-th class, where 0. ltoreq. u_gh≤1，

U＝(u_gh)_z×lIs a membership matrix, d_gh＝||x_h-v_gL. Obviously, J (U, V) represents the sum of the weighted squared distances of the spectral entropy factor values in each class to the respective cluster center, and the weight is the spectral entropy factor value x_hBelongs to the membership degree of the g-th class to the power w. The clustering criterion of the fuzzy C-means clustering method is to solve U and V so that J (U and V) obtains the minimum value;

step 42, setting the number to be classified according to the actual situation, namely determining the number z of the classes; setting a fuzzy weighting index w influencing the fuzzification degree of the membership matrix, wherein w is more than 1; setting an initial membership matrixIt is common practice to take [0, 1]]Uniformly distributed random numbers on to determine an initial membership matrix U⁽⁰⁾Let λ ═ 1 denote step 1 iteration;

step 43, calculating the clustering center V of the lambda step by the following formula^(λ)：

<math> <mrow> <msubsup> <mi>v</mi> <mi>g</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mfrac> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>h</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <msup> <mrow> <mo>(</mo> <msubsup> <mi>u</mi> <mi>gh</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mi>w</mi> </msup> <msub> <mi>x</mi> <mi>h</mi> </msub> </mrow> <mrow> <munderover> <mi>&Sigma;</mi> <mrow> <mi>h</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <msup> <mrow> <mo>(</mo> <msubsup> <mi>u</mi> <mi>gh</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mi>w</mi> </msup> </mrow> </mfrac> <mo>,</mo> </mrow> </math> g＝1，2，…，z

Step 44, correcting the membership degree matrix U^(λ)Calculating an objective function value J^(λ)：

<math> <mrow> <msubsup> <mi>u</mi> <mi>gh</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mn>1</mn> <mo>/</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>z</mi> </munderover> <msup> <mrow> <mo>(</mo> <msubsup> <mi>d</mi> <mi>gh</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msubsup> <mo>/</mo> <msubsup> <mi>d</mi> <mi>jh</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mfrac> <mn>2</mn> <mrow> <mi>w</mi> <mo>-</mo> <mn>1</mn> </mrow> </mfrac> </msup> <mo>,</mo> </mrow> </math> g＝1，2，…z；h＝1，2，…，l

<math> <mrow> <msup> <mi>J</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msup> <mrow> <mo>(</mo> <msup> <mi>U</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msup> <mo>,</mo> <msup> <mi>V</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msup> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>h</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>l</mi> </munderover> <munderover> <mi>&Sigma;</mi> <mrow> <mi>g</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>z</mi> </munderover> <msup> <mrow> <mo>(</mo> <msubsup> <mi>u</mi> <mi>gh</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mi>w</mi> </msup> <msup> <mrow> <mo>(</mo> <msubsup> <mi>d</mi> <mi>gh</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msubsup> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </math>

Wherein, <math> <mrow> <msubsup> <mi>d</mi> <mi>gh</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>x</mi> <mi>h</mi> </msub> <mo>-</mo> <msubsup> <mi>v</mi> <mi>g</mi> <mrow> <mo>(</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> </msubsup> <mo>|</mo> <mo>|</mo> <mo>;</mo> </mrow> </math>

step 45, terminate the tolerance ε for a given membership_u> 0 (or objective function termination tolerance ε)_J> 0, or maximum iteration step lambda_max) When is coming into contact with

(or when lambda > 1, | J^(λ)-J^(λ-1)|＜ε_JOr λ ≧ λ_max) Stopping iteration, otherwise, changing λ to λ +1, and then going to step 43;

and step 46, after iteration of the steps, obtaining a final membership matrix U and a clustering center V of the energy spectrum entropy factor value, so that the value of the objective function J (U, V) is minimum. The attribution of all energy spectrum entropy factor values can be determined according to the value of the element in the final membership degree matrix U, and when the attribution is determined, the attribution of all energy spectrum entropy factor values

Then, the value x of the energy spectrum entropy factor can be calculated_hClassification as jth;

and step 47, according to the actual operation condition of each section on the low-current grounding system line, judging the section with the largest number of sections as a healthy section, namely a healthy section, and judging the section with the smallest number of sections as a fault section, namely a fault section.

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