CN114994458A - Small current ground fault section positioning method based on exponential normalization Euclidean distance - Google Patents

Abstract

A small current ground fault section positioning method based on an exponential normalization Euclidean distance belongs to the technical field of power cables and overhead lines. The invention aims to represent the similarity of transient zero-mode current of a distribution line through an exponential normalized Euclidean distance, has high-order difference information and monotonicity, and further accurately identifies a fault section. The method comprises the following steps: each feeder terminal synchronously monitors the zero-mode current on the feeder in real time, and when the sudden change of the zero-mode current meets the transient wave recording starting condition, the zero-mode current is recorded and data is uploaded; the method comprises the steps that a main station receives transient zero-mode current data uploaded by a plurality of feeder terminals and determines a fault feeder; and calculating the exponential normalized Euclidean distance of the transient zero-mode current sequences at the two ends of each section on the fault feeder. The method can be suitable for accurate fault section positioning of the cable-overhead line hybrid line. In addition, the method has the characteristic of synchronization error resistance.

Description

Small current ground fault section positioning method based on exponential normalization Euclidean distance

Technical Field

The invention belongs to the technical field of power cables and overhead lines.

Background

Along with the construction of the intelligent power distribution network, the online fault positioning system of the power distribution network based on the technology of the Internet of things is popularized and applied. The main station fault positioning system obtains transient zero-mode current of each node by means of a Feeder Terminal (FTU) with a transient recording function, and is used for constructing low-current ground fault characteristics and realizing section fault positioning.

In contrast, the distribution line fault section locating principle generally uses the characteristic that the transient zero-mode current characteristics of the distribution line upstream and downstream of the fault are greatly different to distinguish the fault section from the non-fault section. The method based on the idea comprises a correlation coefficient method, a wavelet singular entropy method, a transient gravity center frequency method, a dynamic time warping method, a signal mutual distance method and the like. The correlation coefficient method only reflects the similarity of waveforms, cannot reflect amplitude difference, is easily affected by asynchronism, and causes misjudgment due to small difference between the transient zero-mode current amplitude and the frequency difference and opposite polarity. The wavelet singular entropy and transient gravity center frequency method needs to preprocess the fault signal, the complexity is relatively high, and the frequency band selection is influenced by the position of the fault point. As the structure of a power distribution network is increasingly complex, branches are increased, a large number of cables and overhead lines are mixed together, and arc suppression coils and the like influence, the shape of single-phase grounding transient zero-mode current is complex and changeable. The dynamic time warping method and the mutual distance method analyze the similarity of the signals from the signal distance angle, comprehensively reflect the relation between the amplitude and the phase of each frequency component of the signals, have moderate calculated amount and have better adaptability. The dynamic time warping method is derived from voice recognition and has strong synchronous error resistance; the law of mutual distance reflects the signal difference using manhattan distance or euclidean distance. The zero-mode current of the system changes from a few amperes to a few tens of amperes, and in order to avoid the influence of the self amplitudes of different signals on the difference degree, the dynamic time warping method and the mutual distance degree method normalize the calculated distance between the two signals by the sum of the absolute values of the two signals. Since they reflect only low-order information, a single-phase ground fault occurs in a cable-overhead line hybrid line, and there is a possibility that a zero-mode current similarity of a faulty section is higher than that of a non-faulty section, resulting in erroneous judgment.

Disclosure of Invention

The invention aims to represent the similarity of transient zero-mode current of a distribution line through an exponential normalized Euclidean distance, has high-order difference information and monotonicity, and further accurately identifies a fault section.

The method comprises the following steps:

s1, synchronously monitoring zero-mode current on the feeder line in real time by each feeder line terminal, and recording and uploading data of the zero-mode current when the sudden change of the zero-mode current meets the transient recording starting condition;

the transient zero-mode current recording starting condition is that the zero-mode current break variable is continuously satisfied twice and the following conditions are satisfied:

Δi ₀ (k)＝|i ₀ (k)-2i ₀ (k-N ₁ )+i ₀ (k-2N ₁ )|＞Δi _0set (1)

wherein, Δ i ₀ (k) Is a zero mode current abrupt change; i.e. i ₀ (k) A current sampling value of zero-sequence current; n is a radical of ₁ Sampling points for a power frequency period; delta i _0set Setting a threshold value for the abrupt change of the zero-mode current, and multiplying the maximum zero-sequence unbalanced current in normal operation by 2-3 times to obtain the maximum zero-sequence unbalanced current;

s2, the main station receives transient zero-mode current data uploaded by a plurality of feeder terminals and determines a fault feeder;

the method for determining the fault feeder line comprises the following steps:

because the transient zero-mode current of the fault line is far larger than that of the non-fault line and is not influenced by the arc suppression coil, the feeder line where the feeder line terminal with the maximum transient zero-mode current amplitude is located is found out and is judged as the fault feeder line;

s3, calculating the exponential normalization Euclidean distance d of the transient zero-mode current sequence at the two ends of each section on the fault feeder _xy Where the maximum value of distance Max { d } _xy Judging the section corresponding to the fault section;

exponential normalization Euclidean distance d of transient zero-mode current at two ends _xy The calculation is as follows:

wherein x and y are the transient zero-mode current sequence of N dimension; sigma is the bandwidth and is determined by the standard deviation of x-y; and | x-y | is the Euclidean distance between x and y.

The invention discloses a method for two-end transient zero-mode current sequence, which comprises the following steps:

the transient zero-mode current sequences of adjacent FTUp and FTUq are respectively set as

i _0p ＝{i _0p1 ,i _0p2 ,...,i _0pN }，i _0q ＝{i _0q1 ,i _0q2 ,...,i _0qN D, exponential normalization Euclidean distance d between the two _pq1 The calculation is as follows:

where σ is the bandwidth, from i _0p -i _0q Determining the standard deviation of the standard deviation; i _0p -i _0q I is i _0p And i _0q The Euclidean distance between the two adjacent pairs of the first and second pairs;

in order to avoid large signal distance difference caused by large amplitude difference of transient zero sequence currents on different circuits, the traditional method is to divide the signal distance by the sum of absolute values of two signals; i all right angle _0p And i _0q The ratio of the Euclidean distance to the sum of the absolute values of the two is recorded as d _pq2 For comparison with the metric d _pq1 Carrying out comparison;

from d _pq1 And d _pq2 Is defined by the formula i _0p And i _0q The higher the similarity between them, the higher d _pq1 And d _pq2 The closer to 0.

Compared with a normalization method of dividing the signal distance by the sum of signal absolute values, the method uses the exponential normalization Euclidean distance to represent the signal difference degree, has the properties of reflecting high-order difference information, monotonicity and the like, can eliminate the fault section identification blind area, and can be suitable for accurate fault section positioning of a cable-overhead line mixed line. In addition, the method has the characteristic of synchronization error resistance.

Drawings

FIG. 1 is a positioning process of a low current ground fault section based on an exponential normalization Euclidean distance according to the present invention;

FIG. 2 is a simplified zero-modulus equivalent circuit diagram of a faulty feeder;

FIG. 3a is d _vx1 With respect to k _A And

graph of the relationship of (1);

FIG. 3b is d _vx2 With respect to k _A And

a graph of the relationship (c);

FIG. 4a is d _vx1 With respect to k _A And k _f Graph of the relationship of (1);

FIG. 4b is d _vx2 With respect to k _A And k _f Graph of the relationship of (1);

fig. 5 is a cable-overhead line hybrid line single phase ground fault section location embodiment of the present invention;

FIG. 6a is a zero mode current waveform for FTU 7;

FIG. 6b is a waveform of zero mode current for FTU 8;

fig. 6c is a waveform of the zero mode current of FTU 9.

Detailed Description

The invention comprises the following steps:

step 1, each FTU synchronously monitors zero-mode current in real time, and when the sudden variable of the zero-mode current continuously meets the transient state wave recording starting condition twice, the transient state zero-mode current wave recording is started and zero-mode current data are uploaded.

Δi ₀ (k)＝|i ₀ (k)-2i ₀ (k-N ₁ )+i ₀ (k-2N ₁ )|＞Δi _0set (1)

Wherein, Δ i ₀ (k) Is a zero mode current abrupt change; i.e. i ₀ (k) Sampling value of zero sequence current; n is a radical of ₁ Sampling points for a power frequency period; Δ i _0set Is a zero mode current bumpAnd setting a threshold value for the variable, and multiplying the maximum zero-sequence unbalanced current in normal operation by 2-3 times to obtain the maximum zero-sequence unbalanced current.

And 2, the master station receives the transient zero-mode current data uploaded by the FTUs, and further compares the transient zero-mode current amplitudes to determine a fault feeder line.

Step 3, calculating the exponential normalization Euclidean distance d of the transient zero-mode current sequences at the two ends of each section on the fault feeder _xy Max { d } of the maximum value _xy The corresponding section is determined as a fault section.

Further, let two N-dimensional zero-mode current sequences x ═ x ₁ ,x ₂ ,...,x _N }，y＝{y ₁ ,y ₂ ,...,y _N The Euclidean distance d between the two is normalized by an index _xy The calculation is as follows:

wherein, sigma is the bandwidth and can be determined according to the standard deviation of x-y; and | x-y | is the Euclidean distance between x and y.

d _xy Not only normalizing the Euclidean distance variation range [0, + ∞) to [0, 1%]And due to an exponential function e ^x Can be decomposed into Taylor series, thus d _xy Higher order difference information for x and y is included. d _xy It also has monotonicity, increasing monotonically with increasing euclidean distance. The greater the difference between x and y, d _xy The closer to 1; otherwise, d _xy The closer to 0.

Referring to the drawings and the embodiments, the technical solution of the present invention is further described in detail with reference to fig. 1, the embodiment of the present invention provides a method for positioning a low-current ground fault section based on an exponential normalized euclidean distance,

step 1, each FTU synchronously monitors zero-mode current in real time, and when the sudden variable of the zero-mode current continuously meets the transient state wave recording starting condition twice, the transient state zero-mode current wave recording is started and zero-mode current data are uploaded.

Δi ₀ (k)＝|i ₀ (k)-2i ₀ (k-N ₁ )+i ₀ (k-2N ₁ )|＞Δi _0set (1)

Wherein, Δ i ₀ (k) Is a zero mode current abrupt change; i.e. i ₀ (k) A current sampling value of zero-sequence current; n is a radical of ₁ Sampling points for a power frequency period; Δ i _0set And setting a threshold value for the sudden change of the zero-mode current, and multiplying the maximum zero-sequence unbalanced current in normal operation by 2-3 times to obtain the maximum zero-sequence unbalanced current.

And 2, the master station receives the transient zero-mode current data uploaded by the FTUs, and further compares the transient zero-mode current amplitudes to determine a fault feeder line.

Step 3, calculating the exponential normalization Euclidean distance d of the transient zero-mode current sequences at the two ends of each section on the fault feeder _xy Max { d, maximum value _xy The corresponding section is determined as a fault section.

Setting the transient zero-mode current sequences of adjacent FTUp and FTUq as i _0p ＝{i _0p1 ,i _0p2 ,...,i _0pN }，i _0q ＝{i _0q1 ,i _0q2 ,...,i _0qN D, exponential normalization Euclidean distance d between the two _pq1 The calculation is as follows:

where σ is the bandwidth, from i _0p -i _0q Determining the standard deviation of the standard deviation; i _0p -i _0q I is i _0p And i _0q The euclidean distance between them.

In order to avoid large signal distance difference caused by large amplitude difference of transient zero-sequence currents on different lines, the traditional method is to divide the signal distance by the sum of absolute values of two signals. i.e. i _0p And i _0q The ratio of the Euclidean distance to the sum of the absolute values of the two is recorded as d _pq2 Metric d used in connection with the invention _pq1 And (6) carrying out comparison.

From d _pq1 And d _pq2 Is defined asKnown, i _0p And i _0q The higher the similarity between them, the higher d _pq1 And d _pq2 The closer to 0.

To verify the advantages of the method of the present invention, a detailed description is first performed by simulating a transient zero-mode current with a single characteristic frequency. According to the transient characteristic of the small-current ground fault, the main resonant frequency of the transient zero-mode current is generally kept at 0.3-3 kHz, the duration of the transient process is short, and the distribution of the zero-mode current in the previous 1/4 power frequency period is concentrated.

In the simplified zero-mode equivalent circuit for a faulty feeder as shown in fig. 2, the zero-mode current i at v and other detection points x on the feeder is assumed _0v And i _0x Respectively as follows:

i _0v ＝15sin(4000πt)e ^-500t A

wherein the coefficient k _A Representing the amplitude ratio and polarity relationship; k is a radical of _f Is a frequency ratio;

is a current i _0x For characterizing synchronization errors between FTUs.

In fig. 2, the zero mode current polarity is opposite upstream and downstream of the fault, and the zero mode current is larger closer to the fault point. Therefore 0<k _A <1，i _0x Can represent an upstream zero-mode current i _0u ；k _A <0，i _0x Can represent a downstream zero-mode current i _0p 。

And setting the sampling frequency to be 5kHz, and collecting data of 5ms after the fault occurs, namely the number N of sampling points is 25. To obtain i _0v And i _0x Normalized distance d between _vx1 And d _vx2 With respect to k _A 、k _f And

the rule is as follows:

(1) when k is _f When 1, σ is 40, i _0v And i _0x Normalized distance d between _vx1 And d _vx2 With respect to k _A And

the family of relationship curves of (a) is shown in fig. 3a and 3 b. As can be seen from figures 3a and 3b,

in the range of 0 to 60 DEG, d _vx1 -k _A Relationship curves remaining monotonous, d _vx1 Varying over a smaller range and d of the faulty section _vx1 Higher than normal section;

d _vx2 -k _A the relation curve becomes convex, d _vx2 Followed by

The variation is large. So d _vx1 Has the characteristic of synchronization error resistance.

(2) When in use

σ＝40，d _vx1 And d _vx2 With respect to k _A And k _f The family of relationship curves of (a) is shown in fig. 4a and 4 b. FIG. 4a shows that with k _f Decrease of d _vx1 Still varies within a small range, even when the frequency difference is large, d _vx1 -k _A The relationship curve is slightly concave, so that the probability of misjudgment is far lower than d _vx2 (ii) a Fig. 4b shows that transient zero-mode currents on both sides of a fault point have frequency difference and are influenced by time delay, and the distance of a fault section is probably smaller than that of a normal section, so that misjudgment is caused.

In conclusion, the index normalization Euclidean distance index of the invention shows stronger robustness.

One embodiment of the invention is shown in a diagram of a small current ground fault MATLAB/Simulink simulation model of a cable-overhead line hybrid power distribution line shown in FIG. 5. Wherein, the cable and the overhead line adopt a Bergeron model, and the positive sequence and the zero sequence parameters of the line are shown in the table 1. Model simulation step lengthIs 1us, and the signal sampling frequency is 5 kHz. In FIG. 5, f is set respectively ₁ ～f ₄ When the initial phase of the fault is 0 DEG, a phase A metallic grounding fault occurs, and a fault point f ₁ 、f ₂ Is the line midpoint, fault point f ₃ 1km from FTU6, failure point f ₄ 0.8km away from FTU 8. The transient zero-mode current simulation result data of 5ms after the fault occurs are taken, and σ is equal to 40, and the normalized Euclidean distance of each section of the fault feeder line and the section positioning result are calculated and shown in Table 2.

TABLE 1 distribution line Unit Length Positive and zero sequence parameters

TABLE 2 Fault zone location results

Table 2 shows that in the cable-overhead line hybrid distribution line, a single-phase metallic ground fault occurs on the trunk line and the branch line, and the calculation result of the method of the present invention is more obvious than the transient zero-mode current difference reflected by the conventional method, and the fault section can be accurately identified. Conventional method at identified failure point f ₂ ～f ₄ The zone is determined by the error. The reason for the misjudgment is that when a single-phase fault occurs in the cable-overhead line mixed line, the transient zero-mode current difference at two ends of the cable line is large, and the misjudgment is likely to be caused according to the criterion of the large zero-mode current difference. Fault with phase A earth connection f ₄ For example, as shown in fig. 6a, 6b, and 6c, transient zero-mode current waveforms of FTUs 7-9 show that amplitude differences of FTUs 8 and 9 at two ends of a non-faulty cable line are large, although amplitudes of faulty overhead wires FTUs 7 and FTUs 8 are close, characteristic frequencies are different, polarities are opposite, and calculation results of a conventional method are close, and erroneous judgment is caused.

Table 3 further shows that under the conditions of different transition resistances, different fault initial phase angles and different positions, the distance value of the fault section is obviously higher than that of the non-fault section by adopting the method, so that the fault section is accurately identified.

TABLE 3 different transition resistances and initial phase of failure vs. d _pq1 Influence of (2)

Claims (2)

1. A small current earth fault section positioning method based on an exponential normalization Euclidean distance is characterized by comprising the following steps: the method comprises the following steps:

s1, synchronously monitoring zero-mode current on the feeder line in real time by each feeder line terminal, and recording and uploading data of the zero-mode current when the sudden change of the zero-mode current meets the transient recording starting condition;

the transient zero-mode current recording starting condition is that the zero-mode current break variable is continuously satisfied twice and the following conditions are satisfied:

Δi ₀ (k)＝|i ₀ (k)-2i ₀ (k-N ₁ )+i ₀ (k-2N ₁ )|＞Δi _0set (1)

wherein, Δ i ₀ (k) Is a zero mode current abrupt change; i all right angle ₀ (k) A current sampling value of zero-sequence current; n is a radical of ₁ Sampling points for a power frequency period; Δ i _0set Setting a threshold value for the abrupt change of the zero-mode current, and multiplying the maximum zero-sequence unbalanced current in normal operation by 2-3 times to obtain the maximum zero-sequence unbalanced current;

s2, the master station receives transient zero-mode current data uploaded by the feeder terminals and determines a fault feeder;

the method for determining the fault feeder line comprises the following steps:

because the transient zero-mode current of the fault line is far larger than that of the non-fault line and is not influenced by the arc suppression coil, the feeder line where the feeder line terminal with the maximum transient zero-mode current amplitude is located is found out and is judged as the fault feeder line;

s3, calculating the exponential normalization Euclidean distance d of the transient zero-mode current sequence at the two ends of each section on the fault feeder _xy Where the maximum value of distance Max { d } _xy Judging the section corresponding to the fault section;

exponential normalization Euclidean distance d of transient zero-mode current at two ends _xy The calculation is as follows:

wherein x and y are the transient zero-mode current sequence of N dimension; sigma is the bandwidth and is determined by the standard deviation of x-y; and | x-y | is the Euclidean distance between x and y.

2. The small-current ground fault section positioning method based on exponential normalization Euclidean distance according to claim 1, characterized in that: the method for two-end transient zero-mode current sequence comprises the following steps:

setting the transient zero-mode current sequences of adjacent FTUp and FTUq as i _0p ＝{i _0p1 ,i _0p2 ,...,i _0pN }，i _0q ＝{i _0q1 ,i _0q2 ,...,i _0qN D, exponential normalization Euclidean distance d between the two _pq1 The calculation is as follows:

where σ is the bandwidth, represented by i _0p -i _0q Determining the standard deviation of the standard deviation; i _0p -i _0q I is i _0p And i _0q The Euclidean distance between the two adjacent pairs of the first and second pairs;

in order to avoid large signal distance difference caused by large amplitude difference of transient zero-sequence currents on different lines, the traditional method is to divide the signal distance by the sum of absolute values of two signals; i.e. i _0p And i _0q The ratio of the Euclidean distance to the sum of the absolute values of the two is recorded as d _pq2 For comparison with the metric d _pq1 Carrying out comparison;

from d _pq1 And d _pq2 Is defined by the formula i _0p And i _0q The higher the similarity between them, the higher d _pq1 And d _pq2 The closer to 0.

Images