Non-intrusive classification method for short-circuit faults of three-core cable

Abstract

The invention discloses a non-intrusive classification method for short-circuit faults of a three-core cable, and the method comprises the following steps: S1, creating an experiment platform, and measuring a tangential magnetic field on the surface of a three-core power cable through three magnetoelectric sensors in the experiment platform; three magnetoelectric sensors are placed on the surface of the three-core power cable, and the difference between the three sensors is 120 degrees; s2, performing modal transformation and dimension reduction processing on the tangential magnetic fields Btan1, Btan2 and Btan3 at the three positions according to Concordia transformation to obtain magnetic fields in an alpha mode and a beta mode, and drawing curves of the Balpha and the Bbeta in polar coordinates, namely a magnetic map; and S3, adopting a random forest algorithm to identify the type of the short-circuit fault. According to the non-intrusive classification method for the short-circuit faults of the three-core cable, the magnetic field change of the surface of the three-core cable is detected by adopting the magnetoelectric sensor with high anti-interference capability and high sensitivity, and finally, the random forest algorithm is used for the fault feature data set, so that classification of the short-circuit fault types is realized.

Description

Technical Field

[0001] The invention relates to the technical field of cable fault diagnosis, and in particular to a non-intrusive classification method for a three-core cable short-circuit fault. Background Art

[0002] Fault classification plays an important role in the protection of cables. Accurate and rapid fault classification can greatly facilitate fault location and fault isolation, thereby reducing the potential dangers of power systems. With the development of cities, underground cables are now widely used. Compared with overhead lines, underground cables are expensive to install, but compared with overhead lines, underground cables are more reliable and have a longer service life. Compared with overhead cables, fault detection in underground cables is difficult. Underground cables are less susceptible to adverse conditions such as heavy rain, snowfall and temperature changes. However, short-circuit faults still occur on distribution networks due to internal insulation breakdown or external damage. For example, a shield fault is an insulation breakdown that causes physical contact between the phase conductor and the shield. When the shield is grounded, a phase-to-ground fault occurs. The insulation between the conductors may break down due to corrosion, resulting in a phase-to-phase short-circuit fault. Accidental excavation of underground cables may cause a three-phase short circuit. Therefore, in order to minimize economic losses, significantly accelerate system improvements, and ensure the power quality of customers, it is necessary to detect it and quickly identify the fault type for subsequent relay tripping, fault location, and fault clearing.

[0003] However, many existing methods rely mainly on phase current measurement to monitor the operating status of cables or overhead lines. For encapsulated three-core cables, the total current in the steady state is zero, making the traditional inductive phase current measurement technology invalid. To overcome this limitation, the present invention proposes a non-intrusive online fault diagnosis method based on magnetic induction to provide real-time fault detection and classification capabilities for distribution cables. Magnetoelectric sensors have become excellent magnetic sensors for measuring the magnetic field generated by current, which provides a promising alternative for such applications. Summary of the invention

[0004] The purpose of the present invention is to provide a non-invasive classification method for three-core cable short-circuit faults. A magnetoelectric sensor with strong anti-interference ability and high sensitivity is used to detect the magnetic field changes on the surface of the three-core cable. Finally, a random forest algorithm is used for the fault feature data set to realize the classification of short-circuit fault types.

[0005] The present invention provides a non-intrusive classification method for a three-core cable short-circuit fault, comprising the following steps:

[0006] S1. Create an experimental platform and measure the tangential magnetic field on the surface of the three-core power cable through three magnetoelectric sensors in the experimental platform; place three magnetoelectric sensors on the surface of the three-core power cable, with the three sensors being 120 degrees apart from each other;

[0007] S2, according to the Concordia transformation, the tangential magnetic field B at the three positions tan1 , B tan2 and B tan3 Perform modal transformation and dimensionality reduction to obtain the magnetic field in α and β modes, and draw B α With B β The curves of the two in polar coordinates are called magnetic diagrams; calculate each short-circuit fault B α With B β The cosine similarity of B α The signal power of B β The signal power of and the sum of the signal powers of the two;

[0008] S3. Based on the extracted fault feature data, the random forest algorithm is used to identify the short circuit fault type.

[0009] Preferably, in step S1, the experimental platform includes a three-phase programmable AC power supply, a filtering and signal amplification module, an oscilloscope, a three-phase resistive load, a magnetoelectric sensor array and a three-core power cable;

[0010] The magnetoelectric sensor is made of two magnetostrictive layers and a piezoelectric layer in the middle, which are bonded together with epoxy resin glue, and then pressed in a hot press. Then copper wires are led out from both ends of the magnetostrictive layer.

[0011] A single magnetoelectric sensor is packaged and fixed with a 3D printed plastic shell, and a permanent magnet is added;

[0012] Three magnetoelectric sensors are installed on the surface of a three-core power cable through a 3D printed fixture. The size of the magnetoelectric sensors is 26mm×6mm×1mm.

[0013] Preferably, in step S1, O is the center point of the three-core cable, A, B, and C are three-phase conductors, and the coordinates of the center of the three-phase conductor are (r A ,θ A ), (r B ,θ B ) and (r C ,θ C ), three magnetoelectric sensors are placed on the surface of the three-core power cable, and the three magnetoelectric sensors are aligned with the line connecting the points O through the centers of the three-phase conductors A, B, and C. The magnetic flux density at any point P(R,θ) on the surface of the three-core power cable is the vector sum of the magnetic flux densities of the three-phase conductors A, B, and C at that point;

[0014] B P =B AP +B BP +B CP ;

[0015] According to the Biot-Savart law, the magnetic flux density of each phase conductor at P(R,θ) can be expressed as:

[0016]

[0017] Where μ0 is the vacuum magnetic permeability; D iP (i=A, B, C) is the distance from the center of the three-phase conductor to point P; I i (i=A, B, C) is the three-phase conductor current;

[0018] The magnetic field at point P(R,θ) is divided into the tangential magnetic field component B tan and the radial magnetic field component B rad , these two components are transformed from the X-axis magnetic field component and the Y-axis magnetic field component in the XY coordinate system as follows:

[0019]

[0020] Among them, B ix and B iy (i=A, B, C) are the magnetic flux density components in the X-axis direction and Y-axis direction of the three-phase conductor at point P respectively;

[0021] For a three-core power cable with a symmetrical structure, it is assumed that the center points of the three-phase conductors are as follows:

[0022]

[0023] Where R is the distance from point O to the center of the magnetoelectric sensor; r is the distance from point O to the center of the three-phase conductor; α is the ratio of r to R;

[0024] The tangential magnetic field at any point on the surface of a three-core cable is expressed as:

[0025]

[0026] When θ=θ i (i=A,B,C), B tan (θ) takes the maximum value, and places three magnetoelectric sensors at the three positions where the tangential magnetic field is the strongest. The magnetic field at these three positions has the following relationship with the three-phase current:

[0027]

[0028] Preferably, in step S2, the tangential magnetic field B at the three positions is converted into tan1 , B tan2 and B tan3 Perform modal transformation and dimensionality reduction to obtain the magnetic field B in α and β modes. α With B β ,

[0029]

[0030] Preferably, in step S2, the purpose of cosine similarity is to measure the directional difference between two vectors, which is independent of the length of the vectors. For two n-dimensional vectors a = {x1, x2, ..., x n} and b={y1,y2,…,y n The cosine similarity cosθ of} is defined as:

[0031]

[0032] B obtained after Concordia transformation α With B β The cosine similarity CS between is defined as:

[0033]

[0034] Preferably, in step S2, if the signal is a periodic signal, the signal power can be obtained by calculating the energy of the signal within one period and dividing it by the length N of the signal:

[0035]

[0036] Calculate the signal power P in each single cycle α With P β , and both power and P s :

[0037]

[0038] Therefore, the present invention adopts the above-mentioned non-invasive classification method for three-core cable short-circuit faults, uses a magnetoelectric sensor with strong anti-interference ability and high sensitivity to detect the magnetic field changes on the surface of the three-core cable, and finally uses the random forest algorithm for the fault feature data set to realize the classification of short-circuit fault types.

[0039] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is an overall schematic diagram of a non-intrusive classification method for a three-core cable short-circuit fault of the present invention;

[0041] Figure 2 The three-core cable surface magnetic field and the installation position of the magnetoelectric sensor array of the non-invasive classification method of the three-core cable short-circuit fault of the present invention;

[0042] Figure 3In the present invention, a non-intrusive classification method for a three-core cable short-circuit fault, when (a) is AG, B α With B β Waveform, (b) is BG B α With B β Waveform, (c) is CG B α With B β Waveforms, (d) are schematic diagrams of magnetic diagrams corresponding to three types of LG faults;

[0043] Figure 4 In the present invention, a non-intrusive classification method for a three-core cable short-circuit fault, when (a) is AG, B α With B β Waveform, (b) is AB when B α With B β Waveform, (c) is ABG B α With B β Waveform, (d) is the magnetic diagram for ABCG, (e) is the schematic diagram of the magnetic diagram corresponding to the four faults;

[0044] Figure 5 It is a schematic diagram of cosine similarity under four short-circuit faults of a non-intrusive classification method for a three-core cable short-circuit fault of the present invention;

[0045] Figure 6 The power P under four short-circuit faults of a non-intrusive classification method for a three-core cable short-circuit fault of the present invention is α , P β and P s Graphs;

[0046] Figure 7 A classification flow chart of a non-invasive classification method for a three-core cable short-circuit fault according to the present invention;

[0047] Figure 8 A schematic diagram of prediction categories of a confusion matrix reflecting prediction results of a non-invasive classification method for a three-core cable short-circuit fault of the present invention. DETAILED DESCRIPTION

[0048] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0049] Unless otherwise defined, technical or scientific terms used in the present invention shall have the common meanings understood by one having ordinary skills in the field to which the present invention belongs.

[0050] The words "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. Words such as "include" or "comprises" and similar terms mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. Words such as "connect" or "connected" and similar terms are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0051] Embodiment 1

[0052] like Figure 1-Figure 8 As shown, the present invention provides a non-invasive classification method for a three-core cable short-circuit fault, comprising the following steps: S1, creating an experimental platform, measuring the tangential magnetic field on the surface of the three-core power cable by three magnetoelectric sensors in the experimental platform; placing three magnetoelectric sensors on the surface of the three-core power cable, with the three sensors being 120 degrees apart from each other;

[0053] In step S1, the experimental platform includes a three-phase programmable AC power supply, a filtering and signal amplification module, an oscilloscope, a three-phase resistive load, a magnetoelectric sensor array, and a three-core power cable;

[0054] The magnetoelectric sensor is made of two magnetostrictive layers and a piezoelectric layer in the middle, which are bonded by epoxy resin glue and pressed in a hot press to achieve the purpose of curing. Then copper wires are used to lead out from both ends of the magnetostrictive layer.

[0055] A single magnetoelectric sensor is packaged and fixed with a 3D printed plastic shell, and a permanent magnet is added;

[0056] Three magnetoelectric sensors are installed on the surface of a three-core power cable through a 3D printed fixture. The size of the magnetoelectric sensors is 26mm×6mm×1mm.

[0057] In step S1, O is the center point of the three-core cable, A, B, and C are three-phase conductors, and the coordinates of the center of the three-phase conductor are (r A ,θ A ), (r B ,θ B ) and (r C ,θ C ), three magnetoelectric sensors are placed on the surface of the three-core power cable, and the three magnetoelectric sensors are aligned with the line connecting the points O through the centers of the three-phase conductors A, B, and C. The magnetic flux density at any point P(R,θ) on the surface of the three-core power cable is the vector sum of the magnetic flux densities of the three-phase conductors A, B, and C at that point;

[0058] B P =B AP +B BP +B CP ;

[0059] According to the Biot-Savart law, the magnetic flux density of each phase conductor at P(R,θ) can be expressed as:

[0060]

[0061] Where μ0 is the vacuum magnetic permeability; D iP (i=A, B, C) is the distance from the center of the three-phase conductor to point P; I i (i=A, B, C) is the three-phase conductor current;

[0062] The magnetic field at point P(R,θ) is divided into the tangential magnetic field component B tan and the radial magnetic field component B rad , these two components are transformed from the X-axis magnetic field component and the Y-axis magnetic field component in the XY coordinate system as follows:

[0063]

[0064] Among them, B ix and B iy (i=A, B, C) are the magnetic flux density components in the X-axis direction and Y-axis direction of the three-phase conductor at point P respectively;

[0065] For a three-core power cable with a symmetrical structure, it is assumed that the center points of the three-phase conductors are as follows:

[0066]

[0067] Where R is the distance from point O to the center of the magnetoelectric sensor; r is the distance from point O to the center of the three-phase conductor; α is the ratio of r to R;

[0068] The tangential magnetic field at any point on the surface of a three-core cable is expressed as:

[0069]

[0070] When θ=θ i (i=A,B,C), B tan (θ) takes the maximum value, and places three magnetoelectric sensors at the three positions where the tangential magnetic field is the strongest. The magnetic field at these three positions has the following relationship with the three-phase current:

[0071]

[0072] S2, according to the Concordia transformation, the tangential magnetic field B at the three positions tan1, B tan2 and B tan3 Perform modal transformation and dimensionality reduction to obtain the magnetic field in α and β modes, and draw B α With B β The curves of the two in polar coordinates are called magnetic diagrams; calculate each short-circuit fault B α With B β The cosine similarity of B α The signal power, B β The signal power of and the sum of the signal powers of the two;

[0073] In step S2, the tangential magnetic field B at the three locations is transformed according to the Concordia transformation. tan1 , B tan2 and B tan3 Perform modal transformation and dimensionality reduction to obtain the magnetic field B in α and β modes. α With B β ;

[0074]

[0075] The short-circuit fault types studied include ten short-circuit faults: single-phase ground short circuit (LG): divided into AG, BG, CG; two-phase short circuit (LL): divided into AB, BC, AC; two-phase ground short circuit (LLG): divided into ABG, BCG, ACG; and three-phase ground short circuit (ABCG), a total of ten short-circuit faults, among which A, B, C represent phase A, phase B and phase C in a three-phase circuit.

[0076] Figure 3 It is the B of LG in three short circuit situations (AG, BG, CG) α With B β Waveform and magnetic diagram.

[0077] It can be observed that after the fault occurs, after a period of transient fluctuation, the waveform stabilizes again. Therefore, the following description of the waveform characteristics and magnetic map analysis after the fault is only based on the waveform of the second cycle after the fault. It can be seen that:

[0078] B before failure α With B β The amplitude is equal, B α With B β The phase difference is 90° and the magnetic pattern is circular.

[0079] Waveform B after AG fault α Amplitude greater than B β Amplitude, B α With B β The phase difference is between 0-90°, the magnetic diagram is an ellipse, and the major axis of the ellipse is towards the first and third quadrants.

[0080] BG waveform after failure α Amplitude and B β The amplitude is similar, B α With B β The phase difference is between 90-180°, the magnetic diagram is also elliptical, and the major axis of the ellipse is oriented towards the second and fourth quadrants.

[0081] Waveform B after CG fault α Amplitude is less than B β Amplitude, B α With B β The phase difference is between 0-90°, the magnetic diagram is also elliptical, and the major axis of the ellipse is oriented towards the first and third quadrants.

[0082] The sizes of the elliptical magnetic patterns after AG, BG, and CG faults are equal.

[0083] Therefore, it can be analyzed that B α With B β The amplitude and phase difference between the two affect the shape of the magnetic pattern and the orientation of the major axis of the ellipse.

[0084] Then, we discuss different types of short-circuit faults. Considering that analyzing ten types of short-circuit faults together is easy to be confusing, we will take examples to illustrate, that is, LG takes AG as an example, LL takes AB as an example, LLG takes ABG as an example, and ABCG. Figure 4 Is B in these four short-circuit faults α With B β Waveform and magnetic diagram.

[0085] It can be seen that: waveform B after AG fault α Amplitude greater than B β Amplitude, B α With B β The phase difference is between 0-90°, the magnetic diagram is an ellipse, and the major axis of the ellipse is towards the first and third quadrants.

[0086] Waveform B after AB fault α Amplitude greater than B β Amplitude, B α With B β The phase difference is between 90-180°, the magnetic diagram is an ellipse, and the major axis of the ellipse is towards the second and fourth quadrants.

[0087] Waveform B after ABG fault α Amplitude greater than B β Amplitude, B α With B β The phase difference is between 90-180°, the magnetic diagram is an ellipse, and the major axis of the ellipse is towards the first and third quadrants.

[0088] Waveform B after ABCG faultα Amplitude equal to B β Amplitude, B α With B β The phase difference is 90° and the magnetic pattern is circular.

[0089] The sizes of magnetic maps under AG, AB, ABG, and ABCG are not equal.

[0090] from Figure 3-Figure 4 The analysis shows that B α With B β The waveform amplitude and phase difference between them will affect the shape and size of the magnetic pattern after the fault. Therefore, it is proposed to use cosine similarity to measure B α With B β The waveform phase difference between the two, and the use of signal power to calculate B α With B β The size of the waveform.

[0091] In step S2, cosine similarity measures the similarity between two vectors by measuring the cosine of the angle between them, which is between -1 and 1. The purpose of cosine similarity is to measure the directional difference between two vectors, which is independent of the length of the vectors and is defined as:

[0092]

[0093] B obtained after Concordia transformation α With B β The cosine similarity CS between is defined as:

[0094]

[0095] Taking one cycle (T = 0.02s) as the calculation basis, based on Figure 4 The waveform of B before and after the fault is calculated for each short-circuit fault. α With B β The cosine similarity is then calculated and the results are plotted as a point-line graph. Figure 5 The dot-line graphs of cosine similarity for LG (AG as an example), LL (AB as an example), LLG (ABG as an example) and ABCG faults are given.

[0096] Figure 5 It shows that the cosine similarity before the fault is equal to 0. After the short circuit fault occurs, the cosine similarity changes and reaches a steady state after a transient transition of one cycle. In the steady state, the cosine similarities of AG, AB, ABG and ABCG are different.

[0097] In step S2, for the signal power of a general signal, its calculated value is equal to the sum of the squares of the signal divided by the length of the signal. If the signal is a periodic signal, the signal power can be obtained by calculating the energy of the signal within one period and dividing it by the length N of the signal:

[0098]

[0099] Calculate the signal power P in each single cycle α With P β , and both power and P s :

[0100]

[0101] Then, based on Figure 4 The waveform of Figure 6 The signal power P from before the fault to LG (AG as an example), LL (AB as an example), LLG (ABG as an example) and ABCG faults is plotted. α , P β and P s Point-line graph.

[0102] Four types of post-fault steady-state P α The sizes are not equal, but some are close and some are quite different. β and P s The same situation exists.

[0103] Finally, based on B α With B β The waveform of the second cycle after the fault, CS and P of ten short-circuit faults are calculated. α , P β and P s , forming a fault feature data set. Then, considering the combination of different fault locations and fault resistances, 50 samples are obtained for each short-circuit fault type, and the normal state (N) is also taken into consideration for comparison.

[0104] S3. Based on the extracted fault feature data, the random forest algorithm is used to identify the short circuit fault type.

[0105] The accuracy of classification using the random forest algorithm is 99.45%, and the time used is 0.05 seconds. The confusion matrix is ​​as follows, where the values ​​on the diagonal represent correctly classified samples and the values ​​on the off-diagonal represent incorrectly classified samples.

[0106] Therefore, the present invention adopts the above-mentioned non-intrusive classification method for a three-core cable short-circuit fault, uses a magnetoelectric sensor with strong anti-interference ability and high sensitivity to detect the magnetic field changes on the surface of the three-core cable, and uses Concordia transformation to perform modal transformation on the three magnetic fields measured by the magnetoelectric sensor array to generate a magnetic field B α and B β , and draw the graphs of the two in polar coordinates, called magnetic graphs; according to the magnetic field B α and B β Based on the waveform signal and magnetic image features, four fault features are extracted based on signal power and cosine similarity, and then a feature data set is obtained; finally, the random forest algorithm is used for the fault feature data set to realize the classification of short circuit fault types.

[0107] The above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A non-intrusive classification method for three-core cable short-circuit faults, characterized in that: The following steps are involved: S1. Create an experimental platform and measure the tangential magnetic field on the surface of the three-core power cable through three magnetoelectric sensors in the experimental platform; place three magnetoelectric sensors on the surface of the three-core power cable, with the three sensors being 120 degrees apart from each other; S2, according to the Concordia transformation, the tangential magnetic field B at the three positions tan1 , B tan2 and B tan3 Perform modal transformation and dimensionality reduction to obtain the magnetic field in α and β modes, and draw B α With B β The curves of the two in polar coordinates are called magnetic diagrams; calculate each short-circuit fault B α With B β The cosine similarity of B α The signal power of B β The signal power of and the sum of the signal powers of the two; S3. Based on the extracted fault feature data, the random forest algorithm is used to identify the short circuit fault type.

2. A non-intrusive classification method for three-core cable short-circuit faults according to claim 1, characterized in that: In step S1, the experimental platform includes a three-phase programmable AC power supply, a filtering and signal amplification module, an oscilloscope, a three-phase resistive load, a magnetoelectric sensor array, and a three-core power cable; The magnetoelectric sensor is made of two magnetostrictive layers and a piezoelectric layer in the middle, which are bonded together with epoxy resin glue, and then pressed in a hot press. Then copper wires are led out from both ends of the magnetostrictive layer. A single magnetoelectric sensor is packaged and fixed with a 3D printed plastic shell, and a permanent magnet is added; Three magnetoelectric sensors are installed on the surface of a three-core power cable through a 3D printed fixture. The size of the magnetoelectric sensors is 26mm×6mm×1mm.

3. A non-intrusive classification method for three-core cable short-circuit faults according to claim 1, characterized in that: In step S1, O is the center point of the three-core cable, A, B, and C are three-phase conductors, and the coordinates of the center of the three-phase conductor are (r A ,θ A ), (r B ,θ B ) and (r C ,θ C ), three magnetoelectric sensors are placed on the surface of the three-core power cable, and the three magnetoelectric sensors are aligned with the line connecting the centers of the three-phase conductors A, B, and C at point O respectively. The magnetic flux density at any point P(R,θ) on the surface of the three-core power cable is the vector sum of the magnetic flux densities of the three-phase conductors A, B, and C at that point; B P =B AP +B BP +B CP ; According to the Biot-Savart law, the magnetic flux density of each phase conductor at P(R,θ) can be expressed as: Where μ0 is the vacuum magnetic permeability; D iP (i=A, B, C) is the distance from the center of the three-phase conductor to point P; I i (i=A, B, C) is the three-phase conductor current; The magnetic field at point P(R,θ) is divided into the tangential magnetic field component B tan and the radial magnetic field component B rad , these two components are transformed from the X-axis magnetic field component and the Y-axis magnetic field component in the XY coordinate system as follows: Among them, B ix and B iy (i=A, B, C) are the magnetic flux density components in the X-axis direction and Y-axis direction of the three-phase conductor at point P respectively; For a three-core power cable with a symmetrical structure, it is assumed that the center points of the three-phase conductors are as follows: Where R is the distance from point O to the center of the magnetoelectric sensor; r is the distance from point O to the center of the three-phase conductor; α is the ratio of r to R; The tangential magnetic field at any point on the surface of a three-core cable is expressed as: When θ=θ i (i=A,B,C), B tan (θ) takes the maximum value, and places three magnetoelectric sensors at the three positions where the tangential magnetic field is the strongest. The magnetic field at these three positions has the following relationship with the three-phase current:

4. A non-intrusive classification method for three-core cable short-circuit faults according to claim 1, characterized in that: In step S2, the tangential magnetic field B at the three locations is transformed according to the Concordia transformation. tan1 , B tan2 and B tan3 Perform modal transformation and dimensionality reduction to obtain the magnetic field B in α and β modes. α With B β :

5. A non-intrusive classification method for three-core cable short-circuit faults according to claim 1, characterized in that: In step S2, the purpose of cosine similarity is to measure the directional difference between two vectors. It is independent of the length of the vector. For two n-dimensional vectors a = {x1, x2, ..., x n } and b={y1,y2,…,y n The cosine similarity cosθ of} is defined as: B obtained after Concordia transformation α With B β The cosine similarity CS between is defined as:

6. A non-intrusive classification method for three-core cable short-circuit faults according to claim 1, characterized in that: In step S2, if the signal is a periodic signal, the signal power can be obtained by calculating the energy of the signal in one period and dividing it by the length N of the signal: Calculate the signal power P in each single cycle α With P β , and both power and P s :

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