Direct-current arc fault anti-interference detection method based on fractional-order cross Grubrum divergence entropy

Abstract

The invention discloses a direct current arc fault anti-interference detection method based on fractional order cross Gray divergence entropy, and the method comprises the steps: collecting a current signal of a to-be-detected branch through a current sensor, and carrying out the normalization of the current signal; calculating a cross Grubm angle field of the normalized current signal; extracting a fractional order cross Grubby divergence entropy of the normalized current signal from the cross Grubby angle field, and constructing a high-dimensional feature vector by using the fractional order cross Grubby divergence entropy; and processing the high-dimensional feature vector based on a support vector machine to obtain a detection result. Under the condition that a current signal of an adjacent normal line is interfered by arc noise, the method can overcome the defects that the traditional divergence entropy only considers correlation information between adjacent data points and information isolation between different angular fields, cannot analyze two-dimensional correlation and ignores key fault information implied in a fractional order; under the condition that an arc fault in a direct current power distribution system interferes with a normal line, the arc fault detection accuracy can be improved.

Description

Technical Field

[0001] The present invention relates to arc fault detection technology, and in particular to a DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy. Background Art

[0002] DC power distribution systems offer advantages such as zero crossover, low transmission losses, and high reliability, making them widely used in photovoltaic systems, electric vehicles, all-electric aircraft, and microgrids. However, DC power distribution systems can suffer from insulation damage or loose terminals under long-term external stress, which can easily lead to DC arc faults. Compared to AC arc faults, DC arc faults lack zero crossover. Therefore, DC arc faults are more likely to cause sustained arc ignition and fires. Traditional protection devices have difficulty detecting DC arc faults. Accurate and rapid detection of DC arc faults has attracted increasing attention.

[0003] Compared to methods based on arc physics (such as sound, light, and heat), current signal-based methods are less restricted by their detection range and have become a research focus. Currently, most researchers analyze only a single branch of the system. However, actual DC systems typically contain multiple branches, and the propagation of arc noise in the system can interfere with adjacent lines. Therefore, DC arc fault detection methods that only consider a single branch have limitations. To avoid false alarms on normal lines, it is necessary not only to determine whether a DC arc fault has occurred in the system but also to identify the faulty line.

[0004] Researchers have been investigating DC arc fault diagnosis methods (detection and location). Some researchers analyze the current in the target branch to diagnose arc faults. However, when a DC arc fault occurs in branches containing the same or similar loads, the current fluctuation patterns in the target branches will also be similar. In this case, none of the aforementioned methods can accurately identify the fault line.

[0005] To address the technical issue of accurately identifying fault lines, researchers have extracted five time-domain features (mean, median, variance, root mean square value, and the difference between the maximum and minimum values) of voltage and current signals from different branches, using a random forest algorithm to provide diagnostic results. This method offers high computational efficiency, but the time-domain features lack the ability to resist interference. Researchers have conducted a detailed analysis of the propagation of arc noise in DC microgrids and proposed an arc fault diagnosis algorithm based on an autocorrelation algorithm. By setting a threshold for the autocorrelation coefficient, this method can quickly identify fault lines. However, determining an appropriate threshold is difficult in practical applications. Accurately identifying fault lines can be achieved by extracting diverse features from current signals at different scales. However, the feature extraction process is not optimized based on the results of feature selection to accelerate DC arc fault diagnosis.

[0006] Entropy is a physical quantity that measures the regularity or complexity of a time series through the statistical probability of state. In recent years, some entropy-based methods have been applied to arc fault detection, improving the accuracy of detection results. Widely used entropy-based methods include approximate entropy, sample entropy, and fuzzy entropy. Unlike existing entropy methods, divergence entropy uses the statistical probability of pattern similarity to describe the state distribution. This definition can better reflect the changes in internal patterns and has a more accurate dynamic complexity estimate. Compared with existing entropy methods, the proposed divergence entropy has three advantages: high consistency, robustness to noise effects, and high computational efficiency. Therefore, divergence entropy has the potential to be applied to DC arc fault detection, which is beneficial to mining the subtle differences between normal line current signals and arc fault line current signals under the condition of arc interference with normal lines. However, traditional divergence entropy has the shortcomings of only considering the correlation information of adjacent data points and ignoring fault information under different fractional orders, resulting in low arc fault detection accuracy. SUMMARY

[0007] The purpose of the present application is to provide a fractional order cross gram divergence entropy-based DC arc fault anti-interference detection method that can simultaneously consider the correlation information of adjacent data points and fault information under different fractional orders, which is helpful to improve the arc fault detection accuracy in the case of arc fault interference with normal lines in a DC distribution system.

[0008] Technical solution: The fractional order cross gram divergence entropy-based DC arc fault anti-interference detection method of the present application comprises:

[0009] Collecting the current signal of the branch to be detected using a current sensor and normalizing the current signal;

[0010] Calculating the cross gram angle field of the normalized current signal;

[0011] Extracting the fractional order cross gram divergence entropy of the normalized current signal from the cross gram angle field and constructing a high-dimensional feature vector using the fractional order cross gram divergence entropy;

[0012] Processing the high-dimensional feature vector based on a support vector machine to obtain a detection result.

[0013] Further, collecting the current signal of the branch to be detected using a current sensor and normalizing the current signal comprises:

[0014] Collecting the current signal of the branch to be detected using a current sensor where I(t) is the current value at time t t∈{1,2,…,n}, n is the number of sampling points in the original current signal, and the current signal F is normalized based on the following formula: *Normalized to the interval [-1, 1]:

[0015]

[0016] wherein, is the maximum value in F * ; is the minimum value in F * ; the normalized current signal F = {x1, x2, …, xn} after normalization, wherein the normalized current value at time t is F(t) = xi, t ∈ {1, 2, …, n}. n t

[0017] Further, the calculation process of the cross Gram angle field of the normalized current signal is as follows:

[0018] Transform the normalized current signal into a polar coordinate sequence, calculate the Gram angle sum field GASF and the Gram angle difference field GADF using the polar coordinate sequence, and calculate the cross Gram angle field CGAF using the Gram angle sum field GASF and the Gram angle difference field GADF.

[0019] Further, the normalized current signal is transformed into a polar coordinate sequence using the following formula:

[0020]

[0021] wherein, δ t is the angle converted from F(t) to the polar coordinate by the inverse cosine function; λ(t) is a time stamp; and F(t) is the normalized current value at time t.

[0022] Further, the calculation formula of the Gram angle sum field GASF is as follows:

[0023]

[0024] wherein, δ n is the nth polar coordinate point, and n is the number of sampling points in the original current signal.

[0025] The calculation formula of the Gram angle difference field GADF is as follows:

[0026]

[0027] Further, the calculation formula of the cross Gram angle field CGAF is as follows:

[0028]

[0029] wherein, β is a weight factor, β ∈ [0, 1], and u n,n = β × cos(δ n + δ​​n ) + (1 - β) x sin(δ n - δ n ).

[0030] Further, the fractional order cross gram dispersion entropy of the normalized current signal is extracted from the cross gram angle field, and a high-dimensional feature vector is constructed using the fractional order cross gram dispersion entropy, including:

[0031] Based on the cross gram angle field, a plurality of phase space column matrices and a plurality of phase space row matrices are constructed;

[0032] The two-dimensional cosine correlation CRC between different phase space column matrices is calculated, and the two-dimensional cosine correlation CRR between different phase space row matrices is calculated;

[0033] A correlation value set CRG is constructed, and the elements in the CRG are composed of all the calculated CRC values and CRR values; the range [-1, 1] is evenly divided into ε intervals, and the ε intervals can be represented as {I1, I2, I3, …, I ε}, and the probability {PRO(1), PRO(2), PRO(3), …, PRO(ε)} of each interval in the ε intervals is calculated;

[0034] According to the probability {PRO(1), PRO(2), PRO(3), …, PRO(ε)} of each interval in the ε intervals in the correlation value set CRG, the fractional order cross gram dispersion entropy is calculated:

[0035]

[0036] Wherein, α is the fractional order number, and α ∈ (-1, 1); is the double gamma function of parameter 1; is the double gamma function of parameter 1-α; Γ(α+1) is the gamma function of parameter α+1; when the number of selected fractional order numbers is M, the high-dimensional feature vector FT = {FTFCD α1 , FTFCD α2 , …, FTFCD αM}, wherein FTFCD αM is the fractional order cross gram dispersion entropy value corresponding to the Mth fractional order number.

[0037] Further, based on the cross gram angle field, a plurality of phase space column matrices and a plurality of phase space row matrices are constructed, including:

[0038] Based on the cross gram angle field CGAF, a phase space column matrix phc i is constructed:

[0039]

[0040] wherein mc is the column embedding dimension; i is an integer, and 0 < i < n + 2 - mc;

[0041] The phase space row matrix phr is constructed based on the cross Gram angle field CGAF i :

[0042]

[0043] wherein mr is the row embedding dimension; i is an integer, and 0 < i < n + 2 - mr.

[0044] Further, the calculation formula of the two-dimensional cosine correlation CRC between the different phase space column matrices is as follows:

[0045]

[0046] The calculation formula of the two-dimensional cosine correlation CRR between the different phase space row matrices is as follows:

[0047]

[0048] wherein, is the two-dimensional cosine correlation value between the phase space column matrix phc r1 and the phase space column matrix phc g1 . is the two-dimensional cosine correlation value between the phase space row matrix phr r2 and the phase space row matrix phr g2 ; r1 is an integer, 0 < r1 < n + 2 - mc; g1 is an integer, 0 < g1 < n + 2 - mc; phc r1 (ic1, ie1) is the element corresponding to the ic1th row and the ie1th column in the phase space column matrix phc r1 ; phc g1 (ic1, ie1) is the element corresponding to the ic1th row and the ie1th column in the phase space column matrix phc g1 ; r2 is an integer, 0 < r2 < n + 2 - mr; g2 is an integer, 0 < g2 < n + 2 - mr; phr r2 (ic2, ie2) is the element corresponding to the ic2th row and the ie2th column in the phase space row matrix phr r2 ; phr g2 (ic2, ie2) is the element corresponding to the ic2th row and the ie2th column in the phase space row matrix phr g2 .

[0049] Further, the high-dimensional feature vector is processed based on the support vector machine to obtain a detection result, including:

[0050] Suppose a training dataset containing Q feature vectors is {FT 1 ,FT 2 ,…,FT Q}, where FT Q is the Qth feature vector; suppose a feature vector to be detected is FT # ; each training dataset contains feature vectors corresponding to normal line current signals when arc fault occurs in adjacent lines, feature vectors corresponding to normal line current signals when arc fault does not occur in adjacent lines, and feature vectors corresponding to line current signals where arc fault occurs;

[0051] The output result of the support vector machine with the kernel function K(·) is as follows:

[0052]

[0053] where FT j is the jth feature vector in the training dataset; y j is the label value corresponding to FT j ; θ j is the Lagrange multiplier corresponding to FT j ; b is a scalar threshold value; the expression of the kernel function K(·,·) is as follows:

[0054]

[0055] where exp(·) represents the power operation on the natural constant e; σ is a parameter for controlling the size of the perception domain of the kernel function; ‖·‖ 2 is an operator for calculating the 2-norm.

[0056] Beneficial effects: Compared with the prior art, the significant technical effects of the present application are as follows: (1) The present application can effectively detect arc fault in the system, and in the case that the normal line current signal is disturbed by arc noise, the present application can avoid false alarm; the present application calculates the fractional order cross Gram divergence entropy, which can overcome the shortcomings of traditional divergence entropy, i.e. only considering the correlation information between adjacent data points, isolating information between different angle fields, being unable to analyze two-dimensional correlation, and ignoring key fault information hidden in the fractional order; (2) The current data in the Cartesian coordinate system is converted into the Gram angle field in the polar coordinate system, which can effectively mine the correlation information between different data points, overcome the limitation of traditional divergence entropy which only considers the correlation information between adjacent data points, and is beneficial to improving the arc fault detection accuracy; (3) In the fractional order cross Gram divergence entropy, the present application proposes a construction method of cross Gram angle field, which can effectively fuse the Gram angle sum field and the Gram angle difference field in the subsequent two-dimensional cosine correlation calculation process, solving the defect of information isolation between the Gram angle sum field and the Gram angle difference field in the traditional Gram angle field; (4) The present application constructs a two-dimensional phase space matrix from the row and column angles, compared with the method of traditional divergence entropy which only constructs a one-dimensional phase space vector, it can introduce more levels of two-dimensional correlation information, which is beneficial to more accurately measuring the difference of current signals in different states; (5) In the fractional order cross Gram divergence entropy, the present application proposes a method for calculating the divergence entropy under different fractional orders, which can overcome the limitation of traditional divergence entropy which ignores the key fault information hidden in the fractional order. BRIEF DESCRIPTION OF DRAWINGS

[0057] Figure 1 The flowchart of the present application is shown in the figure;

[0058] Figure 2 The block diagram of the experimental platform used in the present application is shown in the figure

[0059] Figure 3 The t-SNE visualization diagram of the fractional order cross Gram divergence entropy value under normal condition and arc fault condition is shown in the figure. DETAILED DESCRIPTION

[0060] The technical solutions of the present application will be described in detail below in combination with the specific embodiments and the drawings of the specification.

[0061] As shown in the figure, Figure 1 The DC arc fault anti-interference detection method based on fractional order cross Gram divergence entropy of the present application includes the following steps:

[0062] S1, using a current sensor to collect the current signal of the branch to be detected, and normalizing the current signal.

[0063] In this embodiment, a current sensor is used to collect the current signal of the branch to be detected at a sampling rate of 200KHz. Among them, the current value at time t t∈{1,2,…,n}, n is the number of sampling points in the original current signal, and the current signal F is converted based on formula (1) * Normalized to the interval [-1,1]:

[0064]

[0065] in, F * The maximum value in ; F * The minimum value in the normalized current signal F={x1,x2,…,x n}, where the normalized current value at time t is F(t)=x t , t∈{1,2,…,n}.

[0066] S2. Calculate the cross-Gram angle field of the normalized current signal.

[0067] The specific implementation process of step S2 is as follows:

[0068] S2.1. Based on formula (2), the normalized current signal is transformed into a polar coordinate sequence:

[0069]

[0070] Among them, δ t is the angle of F(t) converted to polar coordinates by the arc cosine function; λ(t) is the timestamp; F(t) is the normalized current value at time t.

[0071] S2.2. Calculate the Gram angle sum field GASF and the Gram angle difference field GADF using the polar coordinate sequence.

[0072] The calculation formula of the Gram angle and field GASF is shown in formula (3):

[0073]

[0074] Among them, δ n is the nth polar coordinate point, and n is the number of sampling points in the original current signal;

[0075] The calculation formula of Gram angle difference field GADF is as follows:

[0076]

[0077] Among them, δ n is the nth polar coordinate point, and n is the number of sampling points in the original current signal;

[0078] S2.3, calculate the cross gram angle field CGAF using the gram angle and the field GASF and the gram angle difference field GADF.

[0079] In this embodiment, the calculation formula of the cross gram angle field CGAF is shown as formula (5):

[0080]

[0081] wherein β is a weight factor, β ∈ [0, 1], u n,n = β × cos(δ n + δ n ) + (1-β) × sin(δ n - δ n ), for example, u 2,3 = β × cos(δ2+ δ3) + (1-β) × sin(δ2- δ3).

[0082] S3, extract the fractional order cross gram dispersion entropy of the normalized current signal from the cross gram angle field, and construct a high-dimensional feature vector using the fractional order cross gram dispersion entropy.

[0083] The specific implementation process of step S3 is as follows:

[0084] S3.1, construct a plurality of phase space column matrices and a plurality of phase space row matrices based on the cross gram angle field. Specifically as follows:

[0085] Based on the cross gram angle field CGAF, construct a phase space column matrix phc i as shown in formula (6):

[0086]

[0087] wherein mc is the column embedding dimension, mc = 4; i is an integer, and 0 < i < n+2-mc;

[0088] Based on the cross gram angle field CGAF, construct a phase space row matrix phr i as shown in formula (7):

[0089]

[0090] wherein mr is the row embedding dimension, mr = 4; i is an integer, and 0 < i < n+2-mr.

[0091] S3.2, calculate the two-dimensional cosine correlation CRC between different phase space column matrices, and calculate the two-dimensional cosine correlation CRR between different phase space row matrices; specifically as follows:

[0092] The two-dimensional cosine correlation CRC between different phase space column matrices is calculated according to formula (8):

[0093]

[0094] The formula for calculating the two-dimensional cosine correlation CRR between different phase space row matrices is as follows:

[0095]

[0096] wherein, is the two-dimensional cosine correlation value between the phase space column matrix phc r1 and the phase space column matrix phc g1 . is the two-dimensional cosine correlation value between the phase space row matrix phr r2 and the phase space row matrix phr g2 ; r1 is an integer, 0 < r1 < n + 2 - mc; g1 is an integer, 0 < g1 < n + 2 - mc; and r1 and g1 are not equal; phc r1 (ic1, ie1) is the element corresponding to the ic1th row and the ie1th column in the phase space column matrix phc r1 ; phc g1 (ic1, ie1) is the element corresponding to the ic1th row and the ie1th column in the phase space column matrix phc g1 ; r2 is an integer, 0 < r2 < n + 2 - mr; g2 is an integer, 0 < g2 < n + 2 - mr; and r2 and g2 are not equal; phr r2 (ic2, ie2) is the element corresponding to the ic2th row and the ie2th column in the phase space row matrix phr r2 ; phr g2 (ic2, ie2) is the element corresponding to the ic2th row and the ie2th column in the phase space row matrix phr g2 .

[0097] S3.3, construct a correlation value set CRG, the elements in CRG are composed of all the calculated CRC values and CRR values; divide the range [-1, 1] into ε intervals on average, and the ε intervals can be represented as {I1, I2, I3, …, I ε ε}; then calculate the probability {PRO(1), PRO(2), PRO(3), …, PRO(ε)} that the elements in the correlation value set CRG fall into each interval of the ε intervals; for example, PRO(2) represents the probability that the elements in the correlation value set CRG fall into the interval I2.

[0098] S3.4, according to the probability that the elements in the correlation value set CRG fall into each of the ε intervals {PRO(1), PRO(2), PRO(3), …, PRO(ε)}, the score order cross Gram dispersion entropy can be calculated according to formula (10):

[0099]

[0100] wherein, α is the fractional order, α ∈ (-1, 1); is the double gamma function of parameter 1; is the double gamma function of parameter 1-α; Γ(α+1) is the gamma function of parameter α+1; when the number of fractional orders selected is M, the high-dimensional feature vector FT = {FTFCD α1 , FTFCD α2 , …, FTFCD αM} is obtained, wherein, FTFCD αM is the fractional order cross Gram dispersion entropy value corresponding to the Mth fractional order. For example, FTFCD α2 is the fractional order cross Gram dispersion entropy value corresponding to the 2nd fractional order.

[0101] S4, based on the support vector machine processing the high-dimensional feature vector, a detection result is obtained. Specifically as follows:

[0102] The support vector machine is trained, and it is assumed that the training data set containing Q feature vectors is {FT 1 , FT 2 , …, FT Q}, wherein, FT Q is the Qth feature vector, for example, FT 2 is the second feature vector; it is assumed that the feature vector to be detected is FT # ; each training data set contains: the feature vector corresponding to the normal line current signal when the adjacent line occurs arc fault, the feature vector corresponding to the normal line current signal when the adjacent line does not occur arc fault, and the feature vector corresponding to the line current signal where the arc fault occurs;

[0103] The output result of the support vector machine with the kernel function K(·) is shown in formula (11):

[0104]

[0105] wherein, FT j is the jth feature vector in the training data set; y j is the label value corresponding to FT j ; θ j is the Lagrange multiplier corresponding to FT j ; b is a scalar threshold; the expression of the kernel function K(·, ·) is shown in formula (12):

[0106]

[0107] wherein exp(·) represents the power operation on the natural constant e; σ is a parameter for controlling the size of the perception field of the kernel function; ‖·‖ 2 is the operator for calculating the 2-norm.

[0108] The above embodiment can realize accurate detection of the DC arc fault.

[0109] The DC arc fault anti-interference detection method based on fractional order cross Gram divergence entropy is verified through a specific embodiment.

[0110] As shown in Figure 2 Line I is taken as a to-be-detected line, and only the current signal of line I is collected in the system, and arc faults can be generated at positions A, B and C. 10000 samples are collected on the established experimental platform, of which 6000 samples are used to construct a training set, and 4000 samples are taken as a test set. Each sample contains 512 data points. The experimental conditions corresponding to the data set are shown in Table 1.

[0111] Table 1 Detailed description of the data set

[0112]

[0113] The detection results of the DC arc fault anti-interference detection method under different experimental conditions are shown in Table 2.

[0114] Table 2 Detection results of the DC arc fault detection method under different experimental conditions

[0115]

[0116] The t-SNE visualization diagram of singular values under arc fault state and normal state is shown in Figure 3 The detection accuracy is 100% under normal condition and arc fault occurs in line II. The detection accuracy is 99.1% and 99.5% respectively under arc fault occurs in line I and arc fault occurs in line III. The overall detection accuracy is 99.54%, and the overall false alarm rate is 0.16%. The experimental results show that the method can effectively detect the arc fault in the system, and effectively avoid false alarm in the case that the normal line current signal is disturbed by the arc fault of the adjacent line.

[0117] The detection accuracy of the method and two comparative methods is compared under the same experimental conditions.

[0118] Comparative method 1: This method extracts the multi-scale divergence entropy of the current signal as the fault feature, and the maximum value of the time scale is set to 10, so the dimension of the constructed feature vector is 10. The classifier used by comparative method 1 is a support vector machine.

[0119] Comparative method 2: This method extracts the peak-to-peak value, standard deviation and frequency energy of the current signal as the fault feature, so the dimension of the constructed feature vector is 3. The classifier used by comparative method 2 is a support vector machine.

[0120] Table 3 gives the detection results of different methods. The detection accuracies of the method, comparative method 1 and comparative method 2 are 99.54%, 90.18% and 96.37% respectively. The detection accuracy of the method is significantly higher than that of the two comparative methods, further proving the effectiveness and advancement of the method.

[0121] Table 3 Detection results of different detection methods

[0122]

Claims

1. A DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy, characterized in that: include: The current sensor is used to collect the current signal of the branch to be detected and normalize the current signal; Calculate the cross-Gram angle field of the normalized current signal; The fractional cross-Gram divergence entropy of the normalized current signal is extracted from the cross-Gram angle field, and a high-dimensional feature vector is constructed using the fractional cross-Gram divergence entropy. The high-dimensional feature vector is processed based on the support vector machine to obtain the detection result.

2. The DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy according to claim 1 is characterized in that: Use the current sensor to collect the current signal of the branch to be tested and normalize the current signal, including: Use current sensor to collect current signal of the branch to be tested Among them, the current value at time t n is the number of sampling points in the original current signal, and the current signal F is converted into * Normalized to the interval [-1,1]: in, F * The maximum value in ; F * The minimum value in the normalized current signal F={x1,x2,…,x n }, where the normalized current value at time t is F(t)=x t , t∈{1,2,…,n}.

3. The DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy according to claim 1 is characterized in that: The calculation process of the cross-Gram angle field of the normalized current signal is as follows: The normalized current signal is transformed into a polar coordinate sequence, and the polar coordinate sequence is used to calculate the Gram angle sum field GASF and the Gram angle difference field GADF. The Gram angle sum field GASF and the Gram angle difference field GADF are then used to calculate the cross-Gram angle field CGAF.

4. The DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy according to claim 3 is characterized in that: The normalized current signal is transformed into a polar coordinate sequence using the following formula: Among them, δ t is the angle of F(t) converted to polar coordinates by the arc cosine function; λ(t) is the timestamp; F(t) is the normalized current value at time t.

5. The DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy according to claim 3, characterized in that: The Gram angle and field GASF are calculated as follows: Among them, δ n is the nth polar coordinate point, and n is the number of sampling points in the original current signal; The calculation formula of the Gram angle difference field GADF is as follows:

6. The DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy according to claim 3, characterized in that: The calculation formula of the cross-Gram angle field CGAF is as follows: where, β is a weight factor, β ∈ [0, 1], u n,n = β × cos(δ n + δ n ) + (1 - β) × sin(δ n - δ n ).

7. The DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy according to claim 1, characterized in that: The fractional cross-Gram divergence entropy of the normalized current signal is extracted from the cross-Gram angle field, and a high-dimensional feature vector is constructed using the fractional cross-Gram divergence entropy, including: Based on the cross-Gram angle field, multiple phase space column matrices and multiple phase space row matrices are constructed; Calculate the two-dimensional cosine correlation CRC between different phase space column matrices, and calculate the two-dimensional cosine correlation CRR between different phase space row matrices; Construct a correlation value set CRG, where the elements in CRG are composed of all calculated CRC values ​​and CRR values; divide the range [-1,1] into ε intervals evenly, and the ε intervals can be expressed as {I1,I2,I3,…,I ε }, calculate the probability that an element in the correlation value set CRG falls into each of the ε intervals {PRO(1), PRO(2), PRO(3),…, PRO(ε)}; According to the probability {PRO(1), PRO(2), PRO(3), …, PRO(ε)} that an element in the correlation value set CRG falls into each of the ε intervals, the fractional cross-Gram divergence entropy is calculated: Among them, α is the fractional order, α∈(-1,1); The parameter 1 is the double gamma function; is the double gamma function with parameter 1-α; Γ(α+1) is the gamma function with parameter α+1; when the number of selected fractional orders is M, the high-dimensional eigenvector FT={FTFCD α1 ,FTFCD α2 ,…,FTFCD αM }, where FTFCD αM is the fractional cross-Gram divergence entropy value corresponding to the Mth fractional order.

8. The DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy according to claim 7, characterized in that: Based on the cross-Gram angle field, multiple phase space column matrices and multiple phase space row matrices are constructed, including: Based on the cross-Gram angle field CGAF, the phase space column matrix phc is constructed i : Where mc is the column embedding dimension; i is an integer, and 0 <i<n+2-mc; Based on the cross-Gram angle field CGAF, the phase space row matrix phr is constructed i : Where mr is the row embedding dimension; i is an integer, and 0 <i<n+2-mr。 9. The DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy according to claim 7, characterized in that: The calculation formula of the two-dimensional cosine correlation CRC between the different phase space column matrices is as follows: The calculation formula of the two-dimensional cosine correlation CRR between the different phase space row matrices is as follows: where, is the two-dimensional cosine correlation value between the phase space column matrix phc r1 and the phase space column matrix phc g1 ; is the two-dimensional cosine correlation value between the phase space row matrix phr r2 and the phase space row matrix phr g2 ; r1 is an integer, 0 < r1 < n + 2 - mc; g1 is an integer, 0 < g1 < n + 2 - mc; phc r1 (ic1, ie1) is the element corresponding to the ic1-th row and the ie1-th column in the phase space column matrix phc r1 , phc g1 (ic1, ie1) is the element corresponding to the ic1-th row and the ie1-th column in the phase space column matrix phc g1 ; r2 is an integer, 0 < r2 < n + 2 - mr; g2 is an integer, 0 < g2 < n + 2 - mr; phr r2 (ic2, ie2) is the element corresponding to the ic2-th row and the ie2-th column in the phase space row matrix phr r2 , phr g2 (ic2, ie2) is the element corresponding to the ic2-th row and the ie2-th column in the phase space row matrix phr g2 .

10. The DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy according to claim 1, characterized in that: Based on the support vector machine, high-dimensional feature vectors are processed to obtain detection results, including: Training support vector machine, let the training data set containing Q feature vectors be {FT 1 ,FT 2 ,…,FT Q }, where FT Q is the Qth eigenvector; let the eigenvector to be detected be FT # Each training data set contains the feature vector corresponding to the current signal of the normal line when an arc fault occurs in the adjacent line, the feature vector corresponding to the current signal of the normal line when no arc fault occurs in the adjacent line, and the feature vector corresponding to the current signal of the line where the arc fault occurs; The output of the support vector machine with kernel function K(·) is as follows: Among them, FT j is the jth feature vector in the training data set; y j For FT j The corresponding label value; θ j For FT j The corresponding Lagrange multiplier; b is the scalar threshold; the expression of the kernel function K(·,·) is as follows: Where exp(·) represents the exponential operation of the natural constant e; σ is the parameter that controls the size of the kernel function’s perception domain; ‖·‖ 2 is an operator for finding the 2-norm.

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