CN109490701B - Power frequency series arc fault detection method - Google Patents
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Abstract
The invention discloses a power frequency series arc fault detection method, and belongs to the field of circuit operation protection. The method comprises the steps of acquiring current data in a circuit and carrying out fast Fourier transform on the current data to obtain a spectrogram; then, counting the amplitudes of the fundamental wave and each subharmonic wave and calculating the ratio of the amplitude of each subharmonic wave to the amplitude of the fundamental wave; finally, adding the ratio of each harmonic amplitude to the fundamental amplitude into a built-in matrix, and then performing principal component analysis, namely PCA calculation; deriving the obtained principal component matrix, comparing the derived principal component matrix with a given threshold value, and determining the load type and the belonging running state; meanwhile, the length of a zero zone of the obtained original current data is calculated and compared with a threshold value, when the two conditions are met simultaneously, an arc fault can be considered to occur.
Description
Technical Field
The invention relates to a power frequency series arc fault detection method, and belongs to the field of circuit operation protection.
Background
Arcing is a self-sustaining discharge that emits intense light and heat, and an arc fault occurs when an unintended arc occurs in a live line. The arc faults include series arc faults, parallel arc faults and composite arc faults, wherein the fault currents of the parallel arc faults and the composite arc faults are large and are easy to be broken by the circuit breaker, but the currents of the series arc faults are small and are difficult to be found, and once the faults occur, great life and property losses can be caused.
According to statistics of fire departments of the Ministry of public Security, 31.2 thousands of fires are reported all over the country, 1582 people are killed, 1065 people are injured and 37.2 million yuan of direct property loss is achieved in 2016, wherein from the direct reason of fire occurrence, 30.4% of electrical fire occurrence caused by violating electrical installation and use regulations and the like accounts for the total amount, and in large-scale fires, the proportion is increased to 50%. Of these electrical fires, the fire caused by a fault arc is the most dangerous and most frequent fire.
At present, the research of the fault arc protection technology in the low-voltage distribution field in China is still blank, no fault arc database is established in China, and the market production of AFCI (arc fault circuit interrupter) is still in the starting stage, so that the low-voltage series fault arc detection technology suitable for the electric power system in China has a great application prospect.
Disclosure of Invention
The invention provides a power frequency series arc fault detection method, which comprises the steps of collecting current in a circuit through a sensor, processing waveform data by utilizing fast Fourier transform to obtain frequency spectrum information of the current, counting amplitude ratios of each subharmonic and fundamental wave, carrying out principal component analysis to reduce dimensions to obtain a new characteristic value, and adding a zero region occupation ratio as an auxiliary criterion so as to judge the type of a load and judge whether an arc fault occurs.
The invention adopts the following technical scheme for solving the technical problems:
a power frequency series arc fault detection method comprises the following steps:
step S1, collecting current data in the circuit;
step S2, calculating the harmonic amplitude and the ratio R of the harmonic amplitude and the fundamental amplitude of the collected current datan；
Step S3, obtainingHarmonic amplitude ratio R ofnAdding a built-in data set to perform PCA calculation;
step S4, derive RnComparing the corresponding principal component characteristic value with a threshold value, judging the load type and the running state, if the load type and the running state are in a fault state, carrying out the next step, and if the load type and the running state are in a normal state, returning to the step S1;
step S5, executing zero zone auxiliary criterion;
and step S6, if the zero zone auxiliary criterion is met, judging that the arc fault occurs, and giving the load type.
In step S1, current data in the circuit is collected in real time through a sensor, and the sampling frequency fs of the sensor is more than or equal to 1 kHz.
In step S2, the specific implementation steps are as follows:
s2.1, carrying out FFT calculation on the acquired current data;
step S2.2, statistics of fundamental wave amplitude Im1And amplitude of each harmonic ImnWherein n is 2-10, and n is a positive integer;
step S2.3, calculating the ratio of each harmonic amplitude to the fundamental amplitude
Wherein n is 2-10, and n is a positive integer.
In step S3, the specific implementation steps are as follows:
s3.1, adding the obtained amplitude ratio into a built-in data set to obtain a new data set D;
s3.2, carrying out PCA calculation on the obtained data set D to obtain a principal component matrix;
step S3.3, calculating a covariance matrix Y ═ cov (D) of the dataset D;
s3.4, calculating an eigenvector and an eigenvalue of the covariance matrix Y;
s3.5, arranging according to the magnitude of the characteristic values, and reserving 2-3 characteristic vectors to form a new matrix U;
step S3.6, calculate new principal component matrix C ═ YTD。
In step S4, the specific steps are as follows:
step S4.1, derive RnCorresponding principal component characteristic value Cm；
Step S4.2, compare C1-CmDetermining the load type and the operation state, if the load type and the operation state are in a fault state, executing the next step, and if the load type and the operation state are in a normal state, returning to the step S1;
in S5, the specific steps are as follows:
s5.1, calculating an absolute value of the acquired waveform data;
step S5.2, the maximum value I of the waveform is obtained from the waveform with the absolute value obtainedmax；
Step S5.3, calculating a waveform threshold IT＝Imax/10；
Step S5.4, counting all the data of the original current which are lower than the threshold value ITSum of sampling points S2；
Step S5.5, calculate K ═ S2and/S, wherein S is the total number of sampling points of the original current data.
Step S6 is carried out in the following specific process, the specific judgment condition is whether the zero zone occupation ratio K is more than or equal to 0.11, if the condition is met, the arc fault is judged to occur, and the load type is given according to the result of S4; if the condition is not satisfied, the process returns to step S1.
The invention has the following beneficial effects:
the invention analyzes and calculates the principal components of the current signals on the basis of the frequency spectrum information of the current signals to obtain new characteristic values, can distinguish different loads and different running states, simultaneously adds a zero-region ratio auxiliary criterion, analyzes and calculates the current waveforms from the angles of a frequency domain and a time domain, ensures the accuracy of the detection effect by setting different thresholds, and ensures that the arc faults can be quickly and efficiently detected.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a flow chart of harmonic and ratio calculation.
Fig. 3 is a flow chart of PCA calculation.
Fig. 4 is a flow chart of the null region assist criteria.
Fig. 5 shows a current waveform obtained by sampling a certain time under a certain load.
Fig. 6 is a current waveform FFT spectrum.
Detailed Description
The invention is described in detail below with reference to the accompanying drawings:
as shown in fig. 1, the invention provides a power frequency series arc fault detection method by performing PCA (principal component analysis) calculation on the frequency spectrum of a current signal to obtain a characteristic value and calculating the zero region proportion of a waveform, the method comprising the following steps:
step S1, collecting current data in the circuit;
in step S1, to ensure the accuracy of the fast fourier transform result in step S2, the nyquist sampling theorem may be used to obtain a sampling frequency that is 2 times or more the highest frequency, and the sampling frequency f of the sensors≥1kHz。
Step S2, calculating the harmonic amplitude and the ratio R of the harmonic amplitude and the fundamental amplitude of the collected current datan；
In step S2, the specific implementation steps are as shown in fig. 2:
step S2.1, FFT (fast Fourier transform) calculation is carried out on the collected current data;
step S2.2, statistics of fundamental wave amplitude Im1And amplitude of each harmonic Imn(n is 2-10, and n is a positive integer).
Step S2.3, calculating the ratio of each harmonic amplitude to the fundamental amplitude
(n is 2-10, and n is a positive integer).
Step S3, obtaining the harmonic amplitude ratio RnAdding a built-in data set to perform PCA calculation;
in step S3, the specific implementation steps are as shown in fig. 3:
s3.1, adding the obtained amplitude ratio into a built-in data set to obtain a new data set D;
s3.2, carrying out PCA calculation on the obtained data set D to obtain a principal component matrix;
step S3.3, calculating a covariance matrix Y ═ cov (D) of the dataset D;
s3.4, calculating an eigenvector and an eigenvalue of the covariance matrix Y;
s3.5, arranging according to the magnitude of the eigenvalue, and reserving proper M eigenvectors to form a new matrix U;
step S3.6, calculate new principal component matrix C ═ YTD, T representing transpose, i.e. YTA transposed matrix that is Y;
step S4, derive RnComparing the corresponding principal component characteristic value with a threshold value, and judging the load type and the running state;
in step S4, the specific implementation steps of the threshold comparison are as follows:
step S4.1, derive RnCorresponding principal component characteristic value Cm；
Step S4.2, compare C1-CmDetermining the load type and the operation state, if the load type and the operation state are in a fault state, executing the next step, and if the load type and the operation state are in a normal state, returning to the step S1;
step S5, executing zero zone auxiliary criterion;
in step S5, the steps of the zero zone assistance criterion performing part are shown in fig. 4:
s5.1, calculating an absolute value of the acquired waveform data;
step S5.2, the maximum value I of the waveform is obtained from the waveform with the absolute value obtainedmax；
Step S5.3, calculating a waveform threshold IT＝Imax/10；
Step S5.4, counting all the data of the original current which are lower than the threshold value ITSum of sampling points S2；
Step S5.5, calculate K ═ S2S, wherein S is the total sampling point number of the original current data;
step S6, if the zero zone auxiliary criterion is satisfied, it can be determined that an arc fault occurs, and a load type is given; (ii) a
In step S6, a specific determination condition is whether K is equal to or greater than 0.11, and if the condition is satisfied, it is determined that an arc fault has occurred and a load type is given according to the result of S4; if the condition is not satisfied, the process returns to step S1.
The method is specifically described below with reference to examples, but it should not be construed that the scope of the above-described subject matter of the present invention is limited to the following examples, and any technique realized based on the contents of the present invention falls within the scope of the present invention.
First, the current data in the circuit is collected, the sampling frequency fsThe number of sampling cycles is 5 at 1.25MHz, and the number of sampling points S is 2500, and the obtained waveform diagram is shown in fig. 5.
Next, the waveform data is subjected to fast fourier transform to obtain a spectrogram as shown in fig. 6, and the spectrogram is exported to a table as shown in table 1.
TABLE 1 post FFT spectral results of sampled waveforms
| Frequency of (Hz) | Amplitude (A) | Frequency of (Hz) | Amplitude (A) | Frequency of (Hz) | Amplitude (A) | Frequency of (Hz) | Amplitude (A) | Frequency of (Hz) | Amplitude (A) |
| 10 | 0.003168 | 110 | 0.004428 | 210 | 0.004287 | 310 | 0.004077 | 410 | 0.002127 |
| 20 | 0.002316 | 120 | 0.003433 | 220 | 0.002707 | 320 | 0.002879 | 420 | 0.001675 |
| 30 | 0.00116 | 130 | 0.002544 | 230 | 0.004547 | 330 | 0.003619 | 430 | 0.004582 |
| 40 | 0.378712 | 140 | 0.024081 | 240 | 0.026295 | 340 | 0.015104 | 440 | 0.015706 |
| 50 | 0.750856 | 150 | 0.044535 | 250 | 0.04308 | 350 | 0.024773 | 450 | 0.023847 |
| 60 | 0.372113 | 160 | 0.024322 | 260 | 0.022147 | 360 | 0.012833 | 460 | 0.011267 |
| 70 | 0.001746 | 170 | 0.002497 | 270 | 0.00218 | 370 | 0.000928 | 470 | 0.001188 |
| 80 | 0.00199 | 180 | 0.001823 | 280 | 0.001342 | 380 | 0.00092 | 480 | 0.001798 |
| 90 | 0.004317 | 190 | 0.003522 | 290 | 0.002418 | 390 | 0.002847 | 490 | 0.003321 |
| 100 | 0.004859 | 200 | 0.004194 | 300 | 0.003721 | 400 | 0.003915 | 500 | 0.003268 |
The fundamental wave amplitude and each harmonic amplitude are counted through the table, each counted harmonic and fundamental wave amplitude are calculated, and the amplitude ratio of each harmonic to the fundamental wave is calculated as shown in the following table:
TABLE 2 fundamental and subharmonic amplitudes and ratios
For simplicity of calculation and derivation, the ratio R isnAdding the last row of the built-in data set to obtain a new data set D, wherein the built-in data set is sample data of different operation states of different loads, and part of the data is shown in the following table, wherein each row is a sample, each column is an amplitude ratio of harmonic to fundamental, starting from the amplitude ratio 2/1 of the 2 nd harmonic to the fundamental, and the total number is 9:
TABLE 3 built-in data set (part)
| 2/1 | 3/1 | 4/1 | 5/1 | 6/1 | 7/1 | 8/1 | 9/1 | 10/1 |
| 0.004605 | 0.571571 | 0.000499 | 0.340038 | 0.00207 | 0.256996 | 0.001321 | 0.172801 | 0.000796 |
| 0.003671 | 0.571057 | 0.00114 | 0.339484 | 0.001544 | 0.262031 | 0.000998 | 0.172926 | 0.002288 |
| 0.003524 | 0.571288 | 0.000994 | 0.340813 | 0.002402 | 0.257808 | 0.000889 | 0.172095 | 0.003141 |
| 0.003117 | 0.576952 | 0.003047 | 0.340024 | 0.002761 | 0.258102 | 0.000527 | 0.163757 | 0.002829 |
| 0.002848 | 0.57335 | 0.001823 | 0.343117 | 0.001604 | 0.263931 | 0.002886 | 0.174907 | 0.001257 |
| 0.004722 | 0.567805 | 0.001068 | 0.345945 | 0.00287 | 0.259424 | 0.003018 | 0.177468 | 0.000514 |
| 3.15E-03 | 0.578271 | 0.001963 | 0.34479 | 0.00153 | 0.268077 | 0.001707 | 0.172359 | 0.003361 |
| 0.001736 | 0.59684 | 0.000837 | 0.32651 | 0.000723 | 0.266068 | 0.001978 | 0.145804 | 0.001597 |
Firstly, a covariance matrix Y of a data set D is calculated, and a specific calculation formula is as follows:
wherein XnThe value of the column vector of the data set D is 1-9, and the covariance matrix obtained by substituting the column vector into the data calculation is as follows:
since there are 9 column vectors in total, the resulting covariance matrix is a 9 × 9 matrix.
Next, calculating eigenvalues and eigenvectors of the covariance matrix and arranging according to the magnitudes, wherein the results are shown in the following table:
TABLE 4 eigenvalues
| Characteristic value |
| 0.30134 |
| 0.03501 |
| 0.01069 |
| 0.00899 |
| 0.00297 |
| 0.00106 |
| 0.00005 |
| 0.00028 |
| 0.00027 |
TABLE 5 feature vectors
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| -0.277 | -0.394 | 0.330 | -0.575 | -0.436 | 0.221 | 0.095 | 0.236 | 0.161 |
| -0.536 | 0.473 | 0.640 | 0.138 | 0.221 | 0.088 | -0.004 | -0.028 | -0.063 |
| -0.316 | -0.430 | 0.031 | -0.153 | 0.117 | -0.385 | -0.208 | -0.555 | -0.423 |
| -0.421 | 0.297 | -0.345 | 0.109 | -0.545 | -0.461 | -0.041 | 0.277 | -0.127 |
| -0.311 | -0.368 | -0.066 | 0.216 | 0.395 | -0.263 | -0.248 | 0.320 | 0.573 |
| -0.295 | 0.267 | -0.387 | -0.242 | -0.019 | 0.209 | 0.076 | -0.564 | 0.515 |
| -0.283 | -0.296 | -0.145 | 0.356 | 0.067 | 0.141 | 0.803 | -0.003 | -0.127 |
| -0.209 | 0.138 | -0.394 | -0.475 | 0.500 | 0.195 | -0.015 | 0.372 | -0.361 |
| -0.228 | -0.188 | -0.179 | 0.398 | -0.200 | 0.642 | -0.484 | -0.008 | -0.187 |
Next, in order to ensure the accuracy of the determination, 3 eigenvectors are reserved, i.e. the first three columns form a new matrix U, and then the principal component matrix C is equal to YTD, the calculated results are shown in the following table:
TABLE 6 principal component matrix
| C1 | C2 | C3 |
| -0.56407 | -0.46019 | -0.08109 |
| -0.5651 | -0.46124 | -0.07848 |
| -0.56471 | -0.46019 | -0.07989 |
| -0.56623 | -0.46087 | -0.08697 |
| -0.56914 | -0.46383 | -0.07683 |
| -0.5671 | -0.46041 | -0.07367 |
| -0.57342 | -0.46721 | -0.0787 |
| -0.56822 | -0.46797 | -0.10797 |
| -0.57419 | -0.46612 | -0.08546 |
| -0.57028 | -0.46293 | -0.07535 |
| … | … | … |
| -0.07987 | -0.0491 | 0.00679 |
Finally derive RnCorresponding derived feature value, i.e. feature value C of last row1＝-0.07987，C2＝-0.0491，C30.00679, the threshold table is as follows:
TABLE 7 threshold comparison Table
By comparison, it can be seen that the waveform is a fault operating condition of the resistive load, and therefore the zero zone assist criterion is implemented.
The amplitude of the original current waveform is 0.78A, so the waveform threshold IT＝Imax0.78/10-0.078A, and counting that the absolute value in the original current data is smaller than the waveform threshold ITSum of points of S2422, calculating the zero area ratio K to S2Since the value of/S is 422/2500 is 0.169 and is greater than the given threshold value of 0.11, it is determined that an arc fault has occurred and the load is a resistive load.
The foregoing is a more detailed description of the present invention that is presented in conjunction with specific embodiments, and the practice of the invention is not to be considered limited to those descriptions. It will be appreciated by those skilled in the art that a number of simple derivations or substitutions can be made without departing from the spirit of the invention and are intended to be within the scope of the invention.
Claims (5)
1. A power frequency series arc fault detection method is characterized by comprising the following steps:
step S1, collecting current data in the circuit;
step S2, calculating the harmonic amplitude and the ratio R of the harmonic amplitude and the fundamental amplitude of the collected current datan；
Step S3, obtaining the ratio R of the harmonic amplitude to the fundamental amplitudenAdding a built-in data set to perform PCA calculation; the specific implementation steps are as follows:
step S3.1, obtaining the ratio R of the harmonic amplitude to the fundamental amplitudenAdding the built-in data set to obtain a new data set D;
s3.2, carrying out PCA calculation on the obtained data set D to obtain a principal component matrix;
step S3.3, calculating a covariance matrix Y ═ cov (D) of the dataset D;
s3.4, calculating an eigenvector and an eigenvalue of the covariance matrix Y;
step S3.5, arranging according to the magnitude of the eigenvalue, and reserving M eigenvectors to form a new matrix U, wherein M is 2-3;
step S3.6, calculating a new principal component matrix C ═ UD;
step S4, derive RnComparing the corresponding principal component characteristic value with a threshold value, judging the load type and the running state, if the load type and the running state are in a fault state, carrying out the next step, and if the load type and the running state are in a normal state, returning to the step S1;
step S5, executing zero zone auxiliary criterion; the specific steps are as follows:
s5.1, calculating an absolute value of the acquired waveform data;
step S5.2, the maximum value I of the waveform is obtained from the waveform with the absolute value obtainedmax；
Step S5.3, calculating a waveform threshold IT＝Imax/10；
Step S5.4, counting all the data of the original current which are lower than the current valueThreshold value ITSum of sampling points S2；
Step S5.5, calculate the zero zone ratio K ═ S2S, wherein S is the total sampling point number of the original current data;
and step S6, if the zero zone auxiliary criterion is met, judging that the arc fault occurs, and giving the load type.
2. The power frequency series arc fault detection method according to claim 1, characterized in that: in step S1, current data in the circuit is collected in real time through a sensor, and the sampling frequency fs of the sensor is more than or equal to 1 kHz.
3. The power frequency series arc fault detection method according to claim 1, characterized in that: in step S2, the specific implementation steps are as follows:
s2.1, carrying out FFT calculation on the acquired current data;
step S2.2, statistics of fundamental wave amplitude Im1And amplitude of each harmonic ImnWherein n is 2-10, and n is a positive integer;
step S2.3, calculating the ratio of each harmonic amplitude to the fundamental amplitude
Wherein n is 2-10, and n is a positive integer.
4. The power frequency series arc fault detection method according to claim 1, characterized in that: in step S4, the specific steps are as follows:
step S4.1, derive RnCorresponding principal component characteristic value Cm，m＝1-M；
Step S4.2, compare C1-CMThe load type and the operation state are determined, and if the load type and the operation state are in the failure state, the next step is executed, and if the load type and the operation state are in the normal state, the operation returns to the step 1.
5. The power frequency series arc fault detection method according to claim 1, characterized in that: step S6 is carried out in the following specific process, the specific judgment condition is whether the zero zone occupation ratio K is more than or equal to 0.11, if the condition is met, the arc fault is judged to occur, and the load type is given according to the result of S4; if the condition is not satisfied, the process returns to step S1.
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| CN110118900A (en) * | 2019-03-27 | 2019-08-13 | 南京航空航天大学 | A kind of remained capacity and power frequency series arc faults detection method |
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| CN110174602B (en) * | 2019-05-09 | 2021-01-08 | 山东大学 | Nonlinear load series arc fault determination method and application |
| CN110488161B (en) * | 2019-07-23 | 2022-03-04 | 南京航空航天大学 | Multi-load series arc fault detection and positioning method |
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| CN113376551B (en) * | 2021-06-23 | 2022-11-08 | 北京市腾河智慧能源科技有限公司 | Method, system, device and storage medium for detecting series fault arc |
| CN113589105B (en) * | 2021-08-09 | 2022-07-26 | 山东建筑大学 | Internet of things-based building electrical fire series fault arc identification method and system |
| CN113848423B (en) * | 2021-09-18 | 2023-05-05 | 广东电网有限责任公司 | Nonlinear node detection method and system |
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