CN113533913A - Cable partial discharge diagnosis method, device and medium based on AP clustering algorithm - Google Patents
Cable partial discharge diagnosis method, device and medium based on AP clustering algorithm Download PDFInfo
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Abstract
The invention discloses a cable partial discharge diagnosis method, equipment and medium based on an AP clustering algorithm, wherein the method comprises the following steps: step 1, denoising collected partial discharge signals of each cable, and then converting the signals from a time domain to a frequency domain; step 2, extracting characteristic parameters of each cable partial discharge signal from the frequency domain transformation result and constructing a characteristic vector, wherein the characteristic parameters comprise: frequency domain energy information FE, element uniformity EU, average information content AC and element offset EO; and 3, clustering the characteristic vectors of all the cable partial discharge signals by adopting an AP clustering algorithm, namely determining the type of the corresponding cable partial discharge according to the category of the characteristic vector of each cable partial discharge signal. The invention can distinguish the multi-source partial discharge of the cable line and realize the type identification of the partial discharge.
Description
Technical Field
The invention belongs to the technical field of power cables, and particularly relates to a cable partial discharge diagnosis method, equipment and medium based on an AP clustering algorithm.
Background
High-voltage cables are important components of power transmission and distribution systems as important equipment for power transmission. Partial discharge (partial discharge for short) refers to an electrical discharge in which the insulation between conductors is only partially bridged. Partial discharges are of various types, such as corona discharge, internal discharge, creeping discharge, and the like. Different types of partial discharge have different damage degrees to equipment, and different diagnosis and maintenance strategies are needed. The partial discharge monitoring can acquire partial discharge signals in real time and analyze and process the signals, so that the fault hidden danger of the cable can be found in time, and the safe and reliable operation of the cable can be guaranteed. The local discharge mode identification is one of the important links of the monitoring of the local discharge state. The partial discharge recognition difficulty is large, and the difficulty is as follows:
1) in the partial discharge monitoring, on one hand, electromagnetic interference is generated when electrical equipment is in live operation, and on the other hand, partial discharge signals generated by insulation defects are usually very weak, so that the partial discharge signals are easily submerged in serious background noise and are difficult to detect;
2) the partial discharge is of various types, the similarity of partial discharge types is high, and the difficulty of partial discharge mode identification is increased.
3) Due to the long distance of the cable, multipoint simultaneous partial discharge often exists, and the identification difficulty is large.
The partial discharge of the power cable is accompanied by physical and chemical phenomena, such as the emission of ultrasonic waves or electric pulses, electromagnetic radiation, light, temperature, and gases. The above-mentioned phenomena can be measured to indirectly monitor the partial discharge signal and to deduce therefrom the severity and possibly the location of the partial discharge. A great deal of research is also carried out on detection methods of partial discharge at home and abroad, and the detection methods can be classified into the following methods according to the classification of sensors used for collecting signals: pulse current method, high frequency current sensor detection, ultra high frequency sensor detection, ultrasonic sensor detection, and the like.
1) Pulse current method: the pulse current detection method is currently the most widely used partial discharge detection method, and the international electrotechnical commission has specifically established a measurement standard for this method in 2000 (IEC 60270). When partial discharge occurs, the sensor for detecting impedance or current can be used for detecting the apparent discharge amount of the partial discharge of the detected object, and the pulse current calculation result is the apparent discharge amount and is very close to the actual discharge amount of the partial discharge, so that the pulse current detection method is considered to be the most sensitive partial discharge detection method.
2) Ultra high frequency sensor (UHF): the ultrahigh frequency sensor detection is a method proposed in the last century, is mainly used for detecting a partial discharge signal of gas insulated switchgear equipment at first, and is gradually applied to partial discharge detection of a power cable at present. When the cable terminal and the accessories thereof generate partial discharge, the cable terminal and the accessories thereof can continuously emit ultrahigh frequency electromagnetic waves to the periphery, so that the radiated ultrahigh frequency electromagnetic waves can be detected by the ultrahigh frequency sensor and collected by the acquisition card to be used for analyzing partial discharge signals. The frequency band of high-frequency electromagnetic waves obtained by the excitation of pulse current of partial discharge of cable terminal accessories is mainly between 0.3 and 3GHz, and the frequency of field interference signals is generally less than 300MHz, so that the influence of various complex interference conditions on detection can be avoided by an ultrahigh frequency detection method, and the detection sensitivity of the method is higher. However, the structure of the cable terminal accessory is complex, the high-frequency electromagnetic wave can be refracted and reflected in the transmission process, and both the refraction and the reflection can attenuate or distort the high-frequency electromagnetic wave signal, so that great difficulty can be added to the detection of the UHF signal.
3) Ultrasonic sensor (AE): when the cable terminal and the accessory generate partial discharge, the molecules of the discharge part can generate mutual impact and the impact macroscopically generates pressure, so that ultrasonic waves can be emitted to the periphery while the partial discharge is generated. The method uses the ultrasonic sensor to measure the ultrasonic signals generated by the partial discharge and stores the ultrasonic signals so as to achieve the purposes of measuring the severity of partial discharge signals or the position of partial discharge and the like. And when the ultrasonic sensor is used for partial discharge detection, the ultrasonic sensor is not in direct contact with a defective cable sample, so that the method does not need to process the sample and has higher safety.
The existing cable partial discharge mode identification method is mainly used for identifying partial discharge types, but cannot be used for identifying partial discharge types under the working condition that a system has multi-source discharge points.
Disclosure of Invention
The invention provides a cable partial discharge diagnosis method, equipment and medium based on an AP (access point) clustering algorithm.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
a cable partial discharge diagnosis method based on an AP clustering algorithm comprises the following steps:
and 3, clustering the characteristic vectors of all the cable partial discharge signals by adopting an AP clustering algorithm, namely determining the type of the corresponding cable partial discharge according to the category of the characteristic vector of each cable partial discharge signal.
In a more preferred embodiment, step 1 uses ST transform to convertEach denoised cable partial discharge signal is transformed from a time domain to a frequency domain, and the obtained matrix is decomposed into a base matrix F ═ (F)1,f2,…,fm) And the coefficient matrix R ═ R (R)1,r2,…,rm)T(ii) a Wherein { f }qAnd { r }qAnd q is 1,2,3 … m, and m represents the column number of F and the row number of R matrix.
In a more preferred embodiment, each frequency domain basis vector { f }qCorrespondingly extracting to obtain 1 frequency domain energy information
The extraction method comprises the following steps:
for each frequency domain basis vector fqThe fourier transform is performed, expressed as:
in the formula, Fq(v) Is a basis vector fqThe result of Fourier transform; n is a basis vector { fqThe number of elements in the page;
then, for Fq(v) Performing transformation as shown in formula (14) to obtain Fq(d) Finally F is addedq(d) From n to n0Summing the absolute values of the elements to N/4 terms to obtain the frequency domain energy
As shown in formula (15);
in the formula, n0Is a positive integer less than N/4; v and d are both function factors, v represents a vector fq(n) Fourier transformFactor of the latter function, d denotes the vector fq(v) the function factor transformed by the formula (14).
In a more preferred embodiment, each frequency domain basis vector { f }qCorresponding extraction to obtain 1 element uniformity
The calculation formula is as follows:
of formula (II) to'q(n) is a basis vector { fqAdjacent element f inq(n +1) and fq(n) as in formula (17);
f′q(n)＝fq(n+1)-fq(n)n＝1,…,N-1 (17)。
in a more preferred embodiment, each frequency domain basis vector { f }qGet 1 average information quantity by corresponding extraction
Each time domain position vector rqMention of 1 average information quantity correspondingly
The calculation formula is as follows:
wherein N is a frequency domain basis vector fqLength of (d); u is a time domain position vector rqLength of (d).
In a more preferred embodiment, each time-domain position vector rq{ correspondingly mentions 1 offset
The calculation formula is as follows:
in the formula, U is a time domain position vector rqWhen vector r is equal toqWhen all the elements are equal, the element offset EO is 1.
In a more preferred technical scheme, the step 3 adopts an AP clustering algorithm to cluster the eigenvectors of all the cable partial discharge signals, specifically:
(1) initialization: taking the characteristic vector of each cable partial discharge signal as 1 data point, and forming a data set by all the data points; calculate every two data points x in the datasetiAnd xkSimilarity S (i, k) between the two, and constructing an initial similarity matrix S; assigning an initial value to the reference degree P, where P is s (k, k), and the initial value is 0; setting an attenuation coefficient lambda and a maximum iteration number T;
(2) calculate attraction values between data points:
r(i,k)＝s(i,k)-max{a(i,k′),s(i,k′)}k′≠k (6)
(3) calculating the attribution value among the sample points:
a(i,k)＝min{0,r(k,k)+∑i′≠imax[0,r(i′,k)]}i≠k (7)
a(k,k)＝∑i′≠imax[0,r(i′,k)] (8)
(4) updating the attraction degree and the attribution degree:
(5) if the current iteration time T exceeds the maximum iteration time T or when the clustering center does not change in a plurality of iterations, the calculation is terminated, anddetermining class centres by summation, i.e. calculating rt+1(i,k)+at+1(i, k), no change occurs or the change amplitude is in the reference value range, namely clustering is stable, and the corresponding data point is the clustering center; otherwise, returning to the step (2).
In a more preferred embodiment, the types of partial discharges in the cable include: internal air gap discharge, pin plate discharge, creeping discharge and floating discharge.
An apparatus comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method of any one of the preceding claims when executing the computer program.
A computer-readable storage medium, in which a computer program is stored, which, when being executed by a processor, carries out the method of any one of the preceding claims.
Advantageous effects
Compared with the traditional clustering algorithm, the method has the advantages that the AP clustering algorithm is adopted to cluster the characteristic parameters of the partial discharge signals of the fault cable, the multi-source partial discharge points caused by multi-point insulation damage can be identified, the partial discharge type pattern identification is carried out, and the like.
Drawings
FIG. 1 is a schematic illustration of a method according to an embodiment of the invention;
FIG. 2 is a flow chart of clustering using an AP clustering algorithm according to an embodiment of the present invention;
fig. 3 is a parameter diagram of partial discharge fault defects of 4 types of cables according to an embodiment of the present invention;
FIG. 4 is a partial discharge pulse signal;
FIG. 5 is a graph of the result of S transformation of partial discharge signals of 4 types of cables according to an embodiment of the present invention;
FIG. 6 shows a vector based on the basis vector f when k is equal to 1 according to an embodiment of the present inventionqExtracted parameter FEw1,EUw2,EOh1；
FIG. 7 shows a time-domain position vector { r } when k is equal to 1 according to an embodiment of the present inventionqParameter of extraction ACw1,ACh1；
Fig. 8 shows the result of the AP clustering algorithm for the 600 groups of samples of the 4-type discharges according to the embodiment of the present invention.
Detailed Description
The following describes embodiments of the present invention in detail, which are developed based on the technical solutions of the present invention, and give detailed implementation manners and specific operation procedures to further explain the technical solutions of the present invention.
The embodiment provides a cable partial discharge diagnosis method based on an AP clustering algorithm, as shown in fig. 1, including the following steps:
let the cable partial discharge signal be x (t), the present embodiment transforms each denoised cable partial discharge signal from the time domain to the frequency domain using ST transform:
wherein x (t) is a cable partial discharge time domain signal, and h (t-tau, f) is a Gaussian window; tau is a position parameter of a control Gaussian window on a time axis t; f is the cable partial discharge frequency; j is an imaginary unit;
in the formula:
the matrix resulting from the ST transformation is then decomposed into a base matrix F ═ F (F)1,f2,…,fm) And the coefficient matrix R ═ R (R)1,r2,…,rm)T(ii) a Wherein { f }qAnd { r }qAnd q is 1,2,3 … m, and m represents the column number of F and the row number of R matrix. Due to { fqAnd { r }qThe method contains most of information of the original time-frequency matrix of the high-frequency pulse of the partial discharge of the cable, so that the method is implemented from (f)qAnd { r }qAnd extracting characteristic parameters.
(1) frequency domain energy information FE
For each frequency domain basis vector fqIt is first Fourier Transformed (FT), as shown in equation (13), with q being 1,2,3 … m.
In the formula, Fq(v) is the basis vector { fqThe result of Fourier transform. N is { fqThe number of elements of the vector;
then, for Fq(v) is converted as shown in formula (14) to obtain Fq(d) Finally F is addedq(d) From n to n0Summing the absolute values of the elements to N/4 terms to obtain the frequency domain energy
As shown in formula (15). In the formula, n0Is a smaller positive integer less than N/4, the invention takes N0＝1。
(2) Elemental homogeneity EU
Frequency domain basis vector { fqThe uniformity of an element in (q ═ 1,2,3 … m) is expressed intuitively by the sum of the squares of its derivatives, as in equation (16).
Of formula (II) to'q(n) is { fqThe difference between adjacent elements in (q ═ 1,2,3 … m), as in formula (17).
f′q(n)＝fq(n+1)-fq(n)n＝1,…,N-1 (17)
(3) Average information amount AC
The average information content of the matrix sequence can be obtained by calculating the information entropy of the vector, and calculating the frequency domain basis vector { f) by using the formula (18) and the formula (19)q1,2,3 … m and a temporal position vector rqAverage information amount AC of (1, 2,3 … m).
In the formula, N is fqLength of (d); u is rqLength of (d).
(4) Element offset EO
The offset between elements is mainly reflected by sparsity, using equation (20) for { r }qCalculate the offset EO (q ═ 1,2,3 … m).
In the formula, U is rqLength of (d). As can be seen from equation (20), when all elements in the vector are equal, the element offset EO is 1.
In summary, from each fqExtract and lift
Three characteristic parameters from each rqExtract and lift
Two characteristic parameters. Therefore, with the difference of the values of m, the S transformation of the partial discharge pulse from the cableThe feature parameter set extracted from the matrix constitutes a feature vector F expressed by equation (21) and having dimensions of 5 × m.
And 3, clustering the characteristic vectors of all the cable partial discharge signals by adopting an AP clustering algorithm, namely determining the type of the corresponding cable partial discharge according to the category of the characteristic vector of each cable partial discharge signal.
In this embodiment, an AP clustering algorithm is used to cluster feature vectors of all cable partial discharge signals, as shown in fig. 2, the specific process is as follows:
(1) initialization: taking the characteristic vector of each cable partial discharge signal as 1 data point, and forming a data set by all the data points; calculate every two data points x in the datasetiAnd xkSimilarity S (i, k) between the two, and constructing an initial similarity matrix S; assigning an initial value to the reference degree P, where P is s (k, k), and the initial value is 0; setting an attenuation coefficient lambda and a maximum iteration number T;
the AP clustering algorithm adopted by the invention is a new unsupervised clustering algorithm and is used for clustering on the similarity matrix of the data points. Because the clustering aims to minimize the distance between a data point and a class representative point thereof, the Euclidean distance is used as a measure of similarity, namely, any two data points xiAnd xkThe similarity of (A) is as follows:
s(i,k)＝-d2(xi,xk)＝-‖xi-xk‖2,i≠k (1)
in the formula:
1)xiand xkData points formed by the characteristic vectors of the two cable partial discharge signals are respectively; i, k are used to distinguish two different data points;
2) s (i, k) is an arbitrary data point xiAnd xkThe similarity between them;
3)d2(xi,xk) Is a data point xiAnd xkThe euclidean distance of (c).
(2) Calculate attraction values between data points:
r(i,k)＝s(i,k)-max{a(i,k′),s(i,k′)}k′≠k (6)
wherein r (i, k) is an arbitrary data point xiAnd xkS (i, k') is: data point xiWith other arbitrary data points (divided by x)kOut of dots) similarity; k' corresponds to the data point xk‘，xk′Removing x from a data setkAny other data point.
(3) Calculating the attribution value among the sample points:
wherein a (i, k') is: data point xiWith other arbitrary data points (divided by x)kOut of point) attribution;
(4) updating the attraction degree and the attribution degree:
in order to avoid oscillation, the convergence rate of the algorithm and the stability of the iterative process are adjusted, and attenuation coefficients lambda are introduced into the update information of the attraction degree and the attribution degree; each piece of information is set to λ times its previous iteration update value plus 1- λ times this information update value. Wherein the attenuation coefficient λ is a real number between 0 and 1. Namely:
in the formula, rt(i, k) is: data point xiAnd xkCurrent attractiveness value in between;rt+1(i, k) is: data point xiAnd xkThe next iteration between attraction values;
comprises the following steps: r in last iterationt+1(ii) the value of (i, k);
(5) if the current iteration time T exceeds the maximum iteration time T, the calculation is stopped, and the class center is determined by a summation method, namely r is calculatedt+1(i,k)+at+1(i, k), no change occurs or the change amplitude is within the reference value range, i.e. the cluster is stable, and the data point x corresponding to the current data point xiAnd xkNamely the clustering center; otherwise, returning to the step (2).
Application example:
before the experiment, 4 types of cabling fault defects were set: and an internal air gap discharge model, a needle plate discharge model, a creeping discharge model and a suspension discharge model are respectively marked as P1-P4 so as to represent fault models of different cable line types.
The specific structure of each defect model, as shown with reference to fig. 3, has the following parameters:
1) internal air gap discharge model. The distance D between two copper electrodes is 5mm, and the diameter D of the air gapbIs 2 mm. And (3) pouring the spherical air gap and the two copper pole plates into the spherical air gap and the two copper pole plates by using liquid epoxy resin glue, and solidifying and shaping.
2) The needle plate discharges the model. The curvature radius of the high-pressure needle point is 0.5mm, the tip length is 15mm, the cone angle is 30 degrees, the space d between needle plates is 3.5mm, the periphery is poured by liquid epoxy resin glue, and the high-pressure needle point is solidified and shaped.
3) Creeping discharge model. The diameter D of the middle insulating plate is 45mm, and the thickness D is 3 mm. 2 copper electrodes and the insulating plate are compacted tightly and adhered by epoxy resin glue.
4) Suspension discharge model. The suspension electrode is a circular copper sheet with the thickness of 1mm and the diameter of 10mm, and is placed on an insulating plate with the thickness of 2mm, and the distance d between the surface of the insulating plate and the high-voltage electrode is 4 mm.
Firstly, acquiring a cable partial discharge signal for data preprocessing:
because the amplitude and the width of the partial discharge pulse of the cable have certain dispersibility, firstly, the acquired signal is subjected to normalization pretreatment to remove the amplitude dispersibility. Meanwhile, in order to eliminate the influence of the duration time dispersion on the feature extraction, a 1000ns cable partial discharge signal is collected to obtain a complete cable partial discharge pulse waveform. Further statistical analysis of the collected cable partial discharge signals revealed that all signals could be characterized by 1000 data points. Such as the three-phase partial discharge pulse signal shown in fig. 4.
And then carrying out coordinate transformation and characteristic parameter extraction on the cable partial discharge signal:
the results of S-transformation of four typical cable partial discharge pulse signals in fig. 3 are shown in fig. 5, and the dimension of each S-transformation matrix is 500 × 1000. As can be seen from fig. 5, the S transformation matrices of the pulse signals of different discharge sources have mutually distinct time-frequency characteristics. Fig. 6 and 7 show the cable partial discharge characteristic values of 4 types of discharge when m is 1.
And finally, clustering, separating and extracting partial discharge of the cable by adopting an AP clustering algorithm:
fig. 8 shows the clustering results of the samples of the four-class discharge model 600 of the neighbor propagation pair cable line when m is 1 to 5, wherein the ordinate represents the number of samples divided into each class for 150 groups of samples from P1 to P4. As can be seen from fig. 8, when m is 1,2,3,5 (extracted features are 5,10,15,25 dimensions, respectively), most of samples of P1 to P4 are sequentially classified into 1 st, 4 th, 3 rd, and 2 nd classes, and when m is 4 (extracted features are 20 dimensions), most of samples of P1 to P4 are sequentially classified into 4 th, 1 st, 3 rd, and 2 nd classes. Because m has different values, the detail analysis degree of the signal is different, and therefore the clustering result is different. Specifically, in an actual engineering project, the result of clustering calculation is compared with the result of actual survey, so that the optimal value of m is obtained.
The above embodiments are preferred embodiments of the present application, and those skilled in the art can make various changes or modifications without departing from the general concept of the present application, and such changes or modifications should fall within the scope of the claims of the present application.
Claims (10)
1. A cable partial discharge diagnosis method based on an AP clustering algorithm is characterized by comprising the following steps:
step 1, denoising collected partial discharge signals of each cable, and then converting the signals from a time domain to a frequency domain;
step 2, extracting characteristic parameters of each cable partial discharge signal from the frequency domain transformation result and constructing a characteristic vector, wherein the characteristic parameters comprise: frequency domain energy information FE, element uniformity EU, average information content AC and element offset EO;
and 3, clustering the characteristic vectors of all the cable partial discharge signals by adopting an AP clustering algorithm, namely determining the type of the corresponding cable partial discharge according to the category of the characteristic vector of each cable partial discharge signal.
2. The method as claimed in claim 1, wherein step 1 transforms each denoised cable partial discharge signal from time domain to frequency domain using ST transform, and decomposes the resulting matrix into a basis matrix F ═ (F ═ F)1，f2，...，fm) And the coefficient matrix R ═ R (R)1，r2，...，rm)T(ii) a Wherein { f }qAnd { r }qAnd q is 1,2, 3.. m, and m represents the column number of the F and the row number of the R matrix.
3. The method of claim 2, wherein each frequency-domain basis vector { f }qCorrespondingly extracting to obtain 1 frequency domain energy information
The extraction method comprises the following steps:
for each frequency domain basis vector fqThe fourier transform is performed, expressed as:
in the formula, Fq(v) Is a basis vector fqThe result of Fourier transform; n is a basis vector { fqThe number of elements in the page;
then, for Fq(v) Performing transformation as shown in formula (14) to obtain Fq(d) Finally F is addedq(d) From n to n0Summing the absolute values of the elements to N/4 terms to obtain the frequency domain energy
As shown in formula (15);
in the formula, n0Is a positive integer less than N/4; v and d are both function factors, v represents a vector fq(n) Fourier transformed function factor, d represents the vector fq(v) And (4) the function factor after the transformation of the formula (14).
4. The method of claim 2, wherein each frequency-domain basis vector { f }qCorresponding extraction to obtain 1 element uniformity
The calculation formula is as follows:
of formula (II) to'q(n) is a basis vector { fqAdjacent element f inq(n +1) and fq(n) as in formula (17);
f′q(n)＝fq(n+1)-fq(n)n＝1，...，N-1 (17)。
5. the method of claim 2, wherein each frequency-domain basis vector { f }qGet 1 average information quantity by corresponding extraction
Each time domain position vector rqMention of 1 average information quantity correspondingly
The calculation formula is as follows:
wherein N is a frequency domain basis vector fqLength of (d); u is a time domain position vector rqLength of (d).
6. The method of claim 2, wherein each time-domain position vector { r }qMention of 1 offset correspondingly
The calculation formula is as follows:
in the formula, U is a time domain position vector rqWhen vector r is equal toqWhen all the elements are equal, the element offset EO is 1.
7. The method according to claim 1, wherein the step 3 clusters the eigenvectors of all the cable partial discharge signals by using an AP clustering algorithm, specifically:
(1) initialization: taking the characteristic vector of each cable partial discharge signal as 1 data point, and forming a data set by all the data points; calculate every two data points x in the datasetiAnd xkSimilarity S (i, k) between the two, and constructing an initial similarity matrix S; assigning an initial value to the reference degree P, where P is s (k, k), and the initial value is 0; setting an attenuation coefficient lambda and a maximum iteration number T;
(2) calculate attraction values between data points:
r(i，k)＝s(i，k)-max{a(i，k′)，s(i，k′)} k′≠k (6)
(3) calculating the attribution value among the sample points:
a(i，k)＝min{0，r(k，k)+∑i′≠imax[0，r(i′，k)]} i≠k (7)
a(k，k)＝∑i′≠imax[0，r(i′，k)] (8)
(4) updating the attraction degree and the attribution degree:
(5) if the current iteration time T exceeds the maximum iteration time T or the calculation is stopped when the clustering center is not changed in a plurality of iterations, determining the class center by a summation method, namely calculating rt+1(i，k)+at+1(i, k), no change occurs or the change amplitude is in the reference value range, namely clustering is stable, and the corresponding data point is the clustering center; otherwise, returning to the step (2).
8. The method of claim 1, wherein the type of cable partial discharge comprises: internal air gap discharge, pin plate discharge, creeping discharge and floating discharge.
9. An apparatus comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the method of any of claims 1 to 8 when executing the computer program.
10. A computer-readable storage medium, in which a computer program is stored which, when being executed by a processor, carries out the method according to any one of claims 1 to 8.
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| CN112364704A (en) * | 2020-10-16 | 2021-02-12 | 康威通信技术股份有限公司 | Clustering method and system based on clock synchronization partial discharge |
| CN112505481A (en) * | 2020-11-20 | 2021-03-16 | 云南电网有限责任公司普洱供电局 | 35kV power line fault traveling wave extraction method based on neighbor propagation clustering |
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