CN111220879A - Method for positioning single-phase earth fault section of small current grounding system - Google Patents

Method for positioning single-phase earth fault section of small current grounding system Download PDF

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CN111220879A
CN111220879A CN202010058290.0A CN202010058290A CN111220879A CN 111220879 A CN111220879 A CN 111220879A CN 202010058290 A CN202010058290 A CN 202010058290A CN 111220879 A CN111220879 A CN 111220879A
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fault
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肖冬萍
何滔
赵文晗
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Chongqing University
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    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
    • G01R31/088—Aspects of digital computing
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R29/00—Arrangements for measuring or indicating electric quantities not covered by groups G01R19/00 - G01R27/00
    • G01R29/12—Measuring electrostatic fields or voltage-potential
    • G01R29/14—Measuring field distribution
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
    • G01R31/08—Locating faults in cables, transmission lines, or networks
    • G01R31/081—Locating faults in cables, transmission lines, or networks according to type of conductors
    • G01R31/085—Locating faults in cables, transmission lines, or networks according to type of conductors in power transmission or distribution lines, e.g. overhead

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Abstract

The invention discloses a method for positioning a single-phase earth fault section of a low-current grounding system, which belongs to the technical field of power supply and distribution line fault positioning and specifically comprises the following steps: establishing a distribution line space electric field calculation model, deducing the mathematical relation between an electric field under a line and line voltage, and determining the optimal measurement position of each measurement point along the line so that the vertical electric field at the optimal measurement point is in direct proportion to the zero sequence voltage of the line; acquiring a fault electric field of each measuring point along the line, preprocessing electric field data, intercepting fault transient data and removing singular values in the fault transient data to form a new time domain electric field waveform; and calculating the time domain electric field waveform similarity of each adjacent measuring point by adopting a dynamic time warping algorithm (DTW), and positioning the fault section by determining the measuring point with the lowest electric field waveform similarity. The method is simple and reliable and has high accuracy.

Description

Method for positioning single-phase earth fault section of small current grounding system
Technical Field
The invention belongs to the technical field of power supply and distribution, and particularly relates to a fault section positioning technology.
Background
The distribution line has long distance and complex operation environment, and is easy to have faults, wherein the single-phase earth fault accounts for about 80 percent. Due to the adoption of the low-current grounding mode, after a single-phase grounding fault occurs, the line enters a fault steady-state operation state after a short oscillation transition period, the fault current is weak, the fault characteristics are complex, and the fault positioning is difficult. The long-time fault steady-state operation may cause interphase short circuit, damage the insulation safety of the distribution line equipment, and finally cause system power supply interruption. In recent years, various intelligent devices are put into use, and higher requirements are put forward on reliable and stable power supply, so that accurate and reliable fault location is needed.
Fault section location is an important ring of distribution line fault automation technology, and fault area isolation is realized by timely and reliably determining fault sections. The fault section location method generally determines the fault section by detecting the differences in current and voltage amplitude, phase and direction of the sections upstream and downstream of the fault point after a single-phase ground fault occurs. The electric quantities of the upper and lower streams of the fault are extracted and the signal difference is analyzed, and a plurality of measuring points are required to be arranged along the line to obtain the fault signal. The traditional voltage and current transformers need to be in contact with a line for measurement, and the problems of volume structure, insulation strength, transient response speed and the like are gradually exposed. The voltage and current transformers are additionally arranged along the line, so that the installation and maintenance are inconvenient, potential safety hazards such as ferromagnetic resonance exist, in addition, a plurality of measuring devices need to be synchronized in time accurately, and the popularization and the use of the existing method are limited.
And after retrieval, the closest comparison file is 201610881840.2, and the method is a grid fault section positioning method based on fault transient traveling wave attenuation components. Under the condition that a measuring device is configured on a power grid, acquiring a wavelet coefficient modulus maximum value as a characteristic quantity for representing an initial row wave amplitude value through wavelet transformation of a signal after a fault; and the measuring point with the largest characteristic quantity corresponds to one end of the fault line, and the other end of the fault line is determined by using the attenuation characteristic of the characteristic quantity when the fault traveling wave is transmitted through the shortest path, so that the fault section is judged. The method needs to arrange a plurality of voltage measurement points along the line to extract the transient traveling wave attenuation components, and has high requirement on accurate and synchronous measurement of the voltage measurement points. In addition, line mode voltage measurement needs direct and line contact, installs voltage transformer additional in a large number and probably has the potential safety hazard to installation maintenance is inconvenient.
Given the significant positive correlation of line voltage with the electric field of the space surrounding the line, voltage differences upstream and downstream of the fault are also present in the electric field. And the electric field measurement has high insulation safety, is convenient to install and maintain and is convenient to distribute and install along the line. However, the fault transient characteristics are complex and are not easy to extract directly, so that the difference of the electric field characteristics along the line needs to be analyzed and extracted by using a recognition algorithm.
Disclosure of Invention
The present invention is directed to solving the above problems of the prior art. A method for positioning a single-phase earth fault section of a low-current grounding system is provided. The technical scheme of 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, firstly, establishing a distribution line space electric field calculation model to obtain a mathematical relation between an offline electric field and line voltage, and determining an optimal measurement position of the electric field by adopting an optimization algorithm to enable a vertical electric field at the optimal measurement position to be in direct proportion to the zero sequence voltage of the line;
step 2, after a fault is detected, synchronously acquiring electric field data at each measuring point along the line in real time, acquiring the electric field data of each measuring point along the line, and preprocessing the acquired electric field data, wherein the preprocessing comprises the steps of intercepting transient data after the fault occurs, eliminating singular values and the like, and forming a new time domain electric field waveform;
and 3, calculating the similarity of the time domain electric field waveforms of every adjacent measuring point by adopting a dynamic time warping algorithm DTW, recording the accumulated distance of the waveforms of the measuring points # i and # i +1 as Da (i), and representing the similarity of the electric field waveforms of the measuring points # i and # i +1 by using the accumulated distance Da (i). The cumulative distance of the electric field waveform along each adjacent measurement point is denoted as Da (1), Da (2) … Da (k-1) for k electric field measurement points, respectively. According to the characteristics of the DTW algorithm, when the Da is smaller, the similarity of two time domain waveforms is higher; the larger Da, the lower the similarity. When da (i) is the maximum value, the electric field waveform similarity of the measurement points # i and # i +1 is the lowest, that is, the fault point is between the measurement points # i and # i +1, and then fault section positioning is realized.
Further, the step 1 of establishing a distribution line space electric field calculation model as shown in fig. 1 to obtain a mathematical relationship between the offline electric field and the line voltage specifically includes: establishing electric fields and linesCalculation expression of the line voltage, taking into account the vertical component E of the space electric field under the lineyGreater than the horizontal component ExThus taking the vertical electric field component Ey：
Figure BDA0002373540090000031
Figure BDA0002373540090000032
Wherein G isa、Gb、GcRespectively representing the superposition coefficient of three-phase voltage to the electric field of a measuring point, x and y respectively representing the coordinate position of the measuring point, j respectively representing a, b, c and QjiRepresents the potential coefficient, ∈0Is the dielectric constant of air, Xj、YjA, B, C coordinate positions of the three-phase conductors, respectively;
according to the Karrenbauer transformation, the three-phase voltage is subjected to phase-mode transformation to obtain EyAnd a calculation expression of line mode voltage:
Figure BDA0002373540090000033
when G is satisfied1＝G 20, i.e. Ga＝Gb＝GcWhen, G0、G1、G2Respectively representing the superposition coefficient, U, after phase-mode conversion0、U1、U2Respectively representing the mode voltages after phase-mode conversion. Vertical component E of the electric field under the wireyAnd zero sequence voltage U of line0In proportion:
Ey＝G0·U0(7)
further, step 1 firstly determines the optimal measurement position of each measurement point along the line by using an optimization algorithm, and specifically includes:
from (6), when G is satisfied1＝G 20, i.e. Ga＝Gb＝GcTime, vertical component E of electric field under lineyAnd zero sequence voltage U of line0In proportion, the electric field measurement position at this time is defined as an optimal measurement position, and since an analytical expression cannot be directly given, the position needs to be optimized. Respectively combining G with the optimization algorithm of the fused particle swarm algorithm and the genetic algorithmaAnd GbAnd GcTaking the difference as an objective function, substituting the space coordinates below the three-phase wires into the solution of objective function values and selecting operators, sequencing the particle swarm according to the selected operator values, updating the historical optimal solution and the global optimal solution of each particle, selecting the first half of the particles with excellent performance in the population as parent particles, calculating child particles according to the parent particles, forming a new population by the parent particles and the child particles, updating the calculation result of the particles, and circularly calculating until the G is meta＝Gb＝GcAnd thus the best measurement position is determined. Further, step 3 calculates the time domain electric field waveform similarity of each adjacent measurement point by using a dynamic time warping algorithm DTW, and specifically includes:
setting two time sequences delta1＝{α1,α2,…,αp},δ2＝{β1,β2,…,βqWhere p and q represent the length of the respective time series, any two points α in the two seriesi、βjIs defined as the distance between
d(αi,βj)＝|αi-βj|for i＝1,…,p；j＝1,…,q (8)
Writing a distance row between each point in the two sequences into a matrix pi, wherein the matrix is provided with a plurality of accumulation paths, and accumulating along different paths to obtain different accumulation distances D;
D＝d(α1,β1)+…+d(αi,βj)+…+d(αp,βq) (9)
the DTW minimizes the accumulated distance along the path by finding an optimal path among a plurality of accumulated paths on the premise that the characteristic constraint is satisfied:
Figure BDA0002373540090000041
w (p-1, q) is pi added up (α)p,βq) The minimum accumulation distance Da is used for representing the similarity of the two time sequences, and when the Da is smaller, the similarity of the two time sequences is higher; the larger Da, the lower the similarity.
Further, the constraint conditions of the dynamic time warping algorithm DTW are:
(1) borderline, the accumulation path starts from the upper left corner of pi and ends at the lower right corner, i.e., from d (α)1,β1) Start to d (α)p,βq) Finishing;
(2) continuity, the accumulated path cannot jump, and must be continuous to ensure that all points in both sequences are matched;
(3) monotonicity, the accumulated path direction in Π remains to the right or downward, otherwise meaningless loops occur.
The invention has the following advantages and beneficial effects:
the innovation point of the method is to derive the optimal measurement position and the dynamic time warping algorithm DTW of each electric field measurement point along the line. The vertical electric field at the optimal measurement position is in direct proportion to the zero sequence voltage of the line, the vertical electric field and the zero sequence voltage of the line have the same characteristics, the optimal measurement position is determined by combining an optimization algorithm, and non-contact measurement of the zero sequence voltage of the line can be realized. The existing fault section location mainly analyzes the voltage and current characteristics of the line, so that the research on the electric field characteristics of the space around the line is less after the fault occurs.
The dynamic time warping algorithm DTW is mainly applied to the field of voice recognition, and can be used for analyzing and calculating the similarity of transient electric field waveforms of a plurality of measuring points along a line in fault section positioning. The DTW has low requirement on the accurate synchronization of multiple measuring points, the design of a measuring device is facilitated, and because the DTW is relative to the similarity of electric field waveforms, errors existing in measurement and the influence of individual singular values on an algorithm are small.
Drawings
FIG. 1 is a diagram of a preferred embodiment electric field calculation model provided by the present invention;
FIG. 2 is a graph of the distance matrix Π and the various accumulation paths;
FIG. 3 is a diagram of a single-phase earth fault model of a low-current earth system;
FIG. 4 is a fault block location flow diagram;
FIG. 5 is a schematic view of a simulation model.
FIG. 6 is a schematic diagram of a circuit configuration;
FIG. 7 shows the DTW calculation results of the outgoing feeder lines
Detailed Description
The technical solutions in the embodiments of the present invention will be described in detail and clearly with reference to the accompanying drawings. The described embodiments are only some of the embodiments of the present invention.
The technical scheme for solving the technical problems is as follows:
the basic idea of the method of the invention is as follows: establishing a distribution line space electric field calculation model, deducing the mathematical relation between an electric field under a line and line voltage, and determining the optimal measurement position of each measurement point along the line so that the vertical electric field at the optimal measurement point is in direct proportion to the zero sequence voltage of the line; acquiring fault transient electric fields of all measurement points along a line, preprocessing the acquired transient electric fields, and removing singular values to form a new time domain electric field waveform; and calculating the time domain electric field waveform similarity of each adjacent measuring point by adopting a dynamic time warping algorithm (DTW), and positioning the fault section by determining the measuring point with the lowest electric field waveform similarity.
1. Electric field calculation model and electric field optimal measurement position
After single-phase earth fault takes place, the signal frequency that transient state decay vibrates is less than 100kHz, by lambada f ═ c, transient state electric field wavelength is less than 3000m, is greater than the distance of measuring point and wire, and the electric field at this moment has quasi-static nature, and electric field can be based on voltage calculation and independent measurement under the line.
In the electric field calculation model shown in fig. 1, the three-phase line is assumed to be infinitely long and parallel to the ground. A. B, C the voltages to ground of the three-phase conductors are respectively Ua、Ub、UcEquivalent charge lambda per unit length of line by analog charge method (CSM)a,λb,λcThe calculation is as follows:
Figure BDA0002373540090000061
potential coefficient p in the formulamnCalculated from the inter-conductor geometry in fig. 1:
Figure BDA0002373540090000062
in the formula: epsilon0Is the dielectric constant of air, rmIs the radius of the wire, dmnIs the distance between the wires m and n, dm’nIs the distance between the mirror image m' of the conductor m and the conductor n.
In fig. 1, M (x, y) is an electric field measurement point, and ρ, ρ' are distances from the measurement point to the line conductor and its mirror conductor, respectively. The electric field at the measurement point M can be calculated from the superposition of A, B, C three-phase wires and their mirror conductors:
Figure BDA0002373540090000063
wherein ExAnd EyHorizontal and vertical components of the electric field, respectively, eρm,exAnd eyRespectively representing unit vectors in different directions.
In conjunction with (1) and (3), a computational expression of the electric field and line voltage can be established. Taking into account the vertical component E of the electric field in the space under the wireyGreater than the horizontal component ExThus taking the vertical electric field component EyFurther analysis was conducted
Figure BDA0002373540090000064
Figure BDA0002373540090000071
Wherein, Xj、YjRespectively representing A, B, C coordinate positions of the three-phase conductors.
According to the Karrenbauer transformation, the three-phase voltage is subjected to phase-mode transformation to obtain EyAnd a calculation expression of line mode voltage:
Figure BDA0002373540090000072
when G is satisfied1＝G 20, i.e. Ga＝Gb＝GcTime, vertical component E of electric field under lineyAnd zero sequence voltage U of line0In proportion:
Ey＝G0·U0(7)
will satisfy Ga＝Gb＝GcThe position of the measurement point of (a) is defined as the optimum measurement position, which is theoretically determined when the line configuration is determined. The optimal measurement position cannot be directly analyzed and expressed, and position optimization determination can be carried out by utilizing an optimization algorithm.
The method for determining the optimal measurement position of each measurement point along the line by adopting the optimization algorithm specifically comprises the following steps:
from (6), when G is satisfied1＝G 20, i.e. Ga＝Gb＝GcTime, vertical component E of electric field under lineyAnd zero sequence voltage U of line0In proportion, the electric field measurement position at this time is defined as an optimal measurement position, and since an analytical expression cannot be directly given, the position needs to be optimized. Respectively combining G with the optimization algorithm of the fused particle swarm algorithm and the genetic algorithmaAnd GbAnd GcTaking the difference as an objective function, substituting the space coordinates below the three-phase wires into the solution of objective function values and selecting operators, sequencing the particle swarm according to the selected operator values, updating the historical optimal solution and the global optimal solution of each particle, selecting the first half of the particles with excellent performance in the population as parent particles, calculating child particles according to the parent particles, forming a new population by the parent particles and the child particles, updating the calculation result of the particles, and circularly calculating until the G is meta＝Gb＝GcAnd thus the best measurement position is determined. Because the particle swarm algorithm and the genetic algorithm are bothIs a general algorithm and is therefore abbreviated herein.
2. Dynamic time warping algorithm (DTW)
DTW is a method for measuring the similarity of two time sequences, is mainly applied to speech recognition, and is characterized in that the speech speed of different persons and the pronunciation speed of the same word are different in the field of speech recognition, and DTW extends and compresses two sections of speech by using a dynamic normalization idea to adjust the corresponding relation between the two sequences. DTW has self-adaptability to the starting time and the length of the time sequence, so that the requirement on the accurate time synchronization of the two sequences is not high, and the DTW is suitable for the electric field analysis of a plurality of measuring points in the application.
Setting two time sequences delta1＝{α1,α2,…,αp},δ2＝{β1,β2,…,βqWherein p and q represent the length of the respective time series, any two points α in the two seriesi、βjIs defined as the distance between
d(αi,βj)＝|αi-βj|for i＝1,…,m；j＝1,…,n (8)
The distance between the points in the two sequences is written as a matrix pi in which a plurality of accumulation paths are present, as shown in fig. 2, and different accumulation distances D are obtained by accumulation along different paths.
D＝d(α1,β1)+…+d(αi,βj)+…+d(αp,βq) (9)
The DTW minimizes the accumulated distance along the path by finding an optimal path among a plurality of accumulated paths on the premise that the characteristic constraint is satisfied:
Figure BDA0002373540090000081
constraint conditions are as follows:
(1) borderline, the accumulation path starts from the upper left corner of pi and ends at the lower right corner, i.e., from d (α)1,β1) Start to d (α)p,βq) And (6) ending.
(2) Continuity, the accumulated path cannot jump, and must be continuous to ensure that all points in both sequences are matched.
(3) Monotonicity, the accumulated path direction in Π remains to the right or downward, otherwise meaningless loops occur.
Using the minimum accumulation distance Da to represent the similarity of the two time sequences, wherein the smaller the Da, the higher the similarity of the two time sequences; the larger Da, the lower the similarity.
3. Fault section positioning algorithm
The single-phase earth fault model of the low-current earth system is shown in fig. 3, and a plurality of electric field measuring points are arranged along a line.
The section positioning process of the single-phase earth fault comprises the following steps:
(1) and when the fault is detected, the electric field data are synchronously acquired by the plurality of electric field measuring devices along the line in real time.
(2) Preprocessing the electric field data acquired by each measuring point, extracting the electric field data of 1/10 power frequency period after the fault occurs, and removing singular values in the electric field data to form a new time domain waveform, wherein the singular values are defined as the electric field data sequence satisfying αi≥(αi-1+αi+1) The value of (c).
(3) The electric field time domain waveform of each adjacent measurement point is calculated by using DTW, and the cumulative distance of the waveforms is recorded as Da (i) for the measurement points # i and # i + 1.
(4) For k electric field measurement points, the electric field waveform similarity of each adjacent measurement point along the line is respectively recorded as Da (1), Da (2) … Da (k-1). When da (i) is the maximum value, the electric field waveform similarity of the measurement points # i and # i +1 is the lowest, i.e., the failure point is between the measurement points # i and # i + 1.
The fault location flow chart is shown in fig. 4.
And selecting 10kV distribution lines with 3 outgoing feeders, and constructing a simulation model shown in figure 5, wherein the distance between each measuring point is 1 km. The neutral point is grounded through an arc suppression coil and is not grounded. The arc suppression coil is set to be 10% overcompensated, and the grounding resistance is 5 omega.
When the line structure is as shown in fig. 6, the position of the measuring point M is optimized by using an optimization algorithm, and the optimal measuring position is (0, 7.72). And acquiring real-time voltage along each feeder line after single-phase grounding by using ATP-EMTP, calculating the electric field of each measuring point, and adding 10% random noise to simulate errors in electric field measurement in simulation analysis.
The preset fault occurs in the feeder line l3The calculation results of the proposed algorithm when measuring between points #7 and #8 are shown in fig. 7.
As can be obtained from the calculation results in fig. 7, the DTW result of the faulty feeder is larger, so that the faulty feeder and the healthy feeder can be effectively identified, and only the faulty feeder is targeted in the subsequent analysis; feed line l3Medium Da (7) is maximum, i.e. the fault is between measurement points #7 and #8, as in the preset condition.
For a neutral ungrounded system, the simulation results are shown in table 1 when the fault occurred in different sections along the line.
Table 1 calculation results of single-phase earth fault of ungrounded neutral system occurring in different sections along the line
Figure BDA0002373540090000091
Figure BDA0002373540090000101
Similarly, for a neutral over arc suppression coil grounding system, when the fault occurs in different sections along the line, the simulation results are shown in table 2.
TABLE 2 calculation results of single-phase earth faults of neutral point arc suppression coil earthed system occurring in different sections along the line
Figure BDA0002373540090000102
As can be seen from tables 1 and 2, for different grounding modes and fault point positions, when a preset single-phase ground fault occurs in different sections along the line, the provided method can accurately find the fault section, and the fault section is shown in bold in the table.
For a neutral over arc suppression coil grounding system, the results of calculations using the proposed method are shown in table 3 at different initial fault angles when a single phase ground fault occurs between measurement points # 7 and 8. The results of the calculations for different ground transition resistances are shown in table 4.
TABLE 3 calculation results of different initial phase angles of faults
Figure BDA0002373540090000103
Figure BDA0002373540090000111
TABLE 4 calculation results of different grounding transition resistances
Figure BDA0002373540090000112
The calculation results in tables 3 and 4 show that for different fault conditions, the algorithm can accurately find the fault section, and the reliability and the accuracy of the algorithm are verified.
The above examples are to be construed as merely illustrative and not limitative of the remainder of the disclosure. After reading the description of the invention, the skilled person can make various changes or modifications to the invention, and these equivalent changes and modifications also fall into the scope of the invention defined by the claims.

Claims (6)

1. A method for positioning a single-phase earth fault section of a low-current grounding system is characterized by comprising the following steps:
step 1, firstly, establishing a distribution line space electric field calculation model to obtain a mathematical relation between an offline electric field and line voltage, and determining an optimal measurement position of the electric field by adopting an optimization algorithm to enable a vertical electric field at the optimal measurement position to be in direct proportion to the zero sequence voltage of the line;
step 2, after a fault is detected, synchronously acquiring electric field data at each measuring point along the line in real time, acquiring the electric field data of each measuring point along the line, and preprocessing the acquired electric field data, wherein the preprocessing comprises the steps of intercepting transient data after the fault occurs, and removing singular values to form a new time domain electric field waveform;
step 3, calculating the similarity of the time domain electric field waveforms of each adjacent measuring point by adopting a dynamic time warping algorithm DTW, regarding the measuring points # i and # i +1, the accumulated distance of the waveforms is marked as Da (i), the similarity of the electric field waveforms of the measuring points # i and # i +1 is represented by using the accumulated distance Da (i), regarding k electric field measuring points, the accumulated distance of the electric field waveforms of each adjacent measuring point along the line is respectively marked as Da (1), Da (2) … Da (k-1), and when the Da is smaller, the similarity of the two time domain waveforms is higher; the larger Da, the lower the similarity, and when Da (i) is the maximum value, the electric field waveform similarity of the measurement points # i and # i +1 is the lowest, i.e. the fault point is between the measurement points # i and # i +1, and then fault section positioning is realized.
2. The method according to claim 1, wherein the step 1 of establishing a spatial electric field calculation model of the distribution line to obtain a mathematical relationship between an offline electric field and a line voltage comprises: establishing a calculation expression of the electric field and the line voltage, and considering the vertical component E of the electric field in the space under the lineyGreater than the horizontal component ExThus taking the vertical electric field component Ey：
Figure FDA0002373540080000011
Figure FDA0002373540080000012
Wherein G isa、Gb、GcRespectively representing the superposition coefficient of three-phase voltage to the electric field of a measuring point, x and y respectively representing the coordinate position of the measuring point, j respectively representing a, b, c and QjiRepresents the potential coefficient, ∈0Is the dielectric constant of air, Xj、YjA, B, C coordinate positions of the three-phase conductors, respectively;
according to the Karrenbauer conversion, the three-phase voltage is subjected to phase modeTransform to obtain EyAnd a calculation expression of line mode voltage:
Figure FDA0002373540080000021
when G is satisfied1＝G20, i.e. Ga＝Gb＝GcWhen, G0、G1、G2Respectively representing the superposition coefficient, U, after phase-mode conversion0、U1、U2Respectively representing the mode voltages after phase-mode conversion. Vertical component E of the electric field under the wireyAnd zero sequence voltage U of line0In proportion:
Ey＝G0·U0(7)。
3. the method for positioning the single-phase earth fault section of the small-current grounding system according to claim 1, wherein the step 1 firstly adopts an optimization algorithm to determine the optimal measurement position of each measurement point along the line, and specifically comprises:
from (6), when G is satisfied1＝G20, i.e. Ga＝Gb＝GcTime, vertical component E of electric field under lineyAnd zero sequence voltage U of line0In proportion, the electric field measurement position at this time is defined as an optimal measurement position, and since an analytical expression cannot be directly given, the position needs to be optimized. Respectively combining G with the optimization algorithm of the fused particle swarm algorithm and the genetic algorithmaAnd GbAnd GcTaking the difference as an objective function, substituting the space coordinates below the three-phase wires into the solution of objective function values and selecting operators, sequencing the particle swarm according to the selected operator values, updating the historical optimal solution and the global optimal solution of each particle, selecting the first half of the particles with excellent performance in the population as parent particles, calculating child particles according to the parent particles, forming a new population by the parent particles and the child particles, updating the calculation result of the particles, and circularly calculating until the G is meta＝Gb＝GcAnd thus the best measurement position is determined.
4. The method for positioning the single-phase earth fault section of the small-current grounding system according to claim 1, wherein the step 2 of acquiring the electric field data of each measurement point along the line and preprocessing the acquired electric field data specifically comprises:
the method comprises the steps that after a fault occurs, a line enters fault stable state operation after a transient attenuation oscillation process, acquired electric field data comprise transient state data and stable state data, accordingly electric field data of 1/10 power frequency periods after the fault occurs are intercepted, singular values in the electric field data are removed, a new time domain waveform is formed, and the singular values are defined to be α met in an electric field data sequencei≥(αi-1+αi+1) Value of αi、αi-1、αi+1Representing every adjacent three data in the electric field data sequence.
5. The method as claimed in claim 4, wherein the step 3 of calculating the similarity of the time domain electric field waveform of each adjacent measurement point by using a dynamic time warping algorithm DTW specifically comprises:
setting two time sequences delta1＝{α1,α2,…,αp},δ2＝{β1,β2,…,βqWhere p and q represent the length of the respective time series, any two points α in the two seriesi、βjIs defined as the distance between
d(αi,βj)＝|αi-βj|for i＝1,…,p；j＝1,…,q (8)
Writing a distance row between each point in the two sequences into a matrix pi, wherein the matrix is provided with a plurality of accumulation paths, and accumulating along different paths to obtain different accumulation distances D;
D＝d(α1,β1)+…+d(αi,βj)+…+d(αp,βq) (9)
the DTW minimizes the accumulated distance along the path by finding an optimal path among a plurality of accumulated paths on the premise that the characteristic constraint is satisfied:
Figure FDA0002373540080000031
w (p-1, q) is pi added up (α)p,βq) The minimum accumulation distance Da is used for representing the similarity of the two time sequences, and when the Da is smaller, the similarity of the two time sequences is higher; the larger Da, the lower the similarity.
6. The method for positioning the single-phase earth fault section of the small-current grounding system according to claim 5, wherein the constraint conditions of the dynamic time warping algorithm DTW are as follows:
(1) borderline, the accumulation path starts from the upper left corner of pi and ends at the lower right corner, i.e., from d (α)1,β1) Start to d (α)p,βq) Finishing;
(2) continuity, the accumulated path cannot jump, and must be continuous to ensure that all points in both sequences are matched;
(3) monotonicity, the accumulated path direction in Π remains to the right or downward, otherwise meaningless loops occur.
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