A direct current arc fault anti-interference detection method based on fractional order cross gram divergence entropy

Abstract

The application discloses a DC arc fault anti-interference detection method based on a fractional order cross Gram divergence entropy, which comprises the following steps: collecting a current signal of a branch to be detected by using a current sensor and normalizing the current signal; calculating a cross Gram angle field of the normalized current signal; extracting a fractional order cross Gram divergence entropy of the normalized current signal from the cross Gram angle field, and constructing a high-dimensional feature vector by using the fractional order cross Gram divergence entropy; and processing the high-dimensional feature vector based on a support vector machine to obtain a detection result. In the case that the current signal of a normal line close to the branch to be detected is disturbed by arc noise, the method can overcome the shortcomings of traditional divergence entropy, i.e., only considering the correlation information between adjacent data points, isolating the information between different angle fields, being unable to analyze two-dimensional correlation and ignoring the key fault information hidden in the fractional order. In the case that the arc fault disturbs the normal line in a DC distribution system, the method is helpful to improve the arc fault detection accuracy.

Description

Technical Field

[0001] This invention relates to arc fault detection technology, specifically to a DC arc fault anti-interference detection method based on fractional-order cross-gram divergence entropy. Background Technology

[0002] DC power distribution systems offer advantages such as no zero-point ride-through, low transmission loss, and high reliability, making them widely used in photovoltaic systems, electric vehicles, all-electric aircraft, and microgrids. However, under long-term external stress, DC power distribution systems may experience insulation damage or loose terminals, which can easily lead to DC arcing faults. Compared to AC arcing faults, DC arcing faults do not involve zero-point current ride-through. Therefore, DC arcing faults are more likely to generate a sustained arc and ignite a fire. Traditional protection devices struggle to detect DC arcing faults. Accurate and rapid detection of DC arcing faults has attracted increasing attention from researchers.

[0003] Compared to methods based on arc physics phenomena (such as sound, light, and heat), current-signal-based methods are less limited by detection range and are a focus of research. Currently, most researchers only analyze single branches of the system, but real-world DC systems typically contain multiple branches, and the propagation of arc noise 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] Currently, scholars have studied methods for diagnosing DC arc faults (detection and location). Some researchers have achieved arc fault diagnosis by analyzing the current in the target branch. However, when a DC arc fault occurs in a branch containing the same or similar loads, the current fluctuation pattern of the target branch will also be similar. In this case, none of the above methods can accurately identify the faulty line.

[0005] To address the technical problem of inaccurate fault line identification, some researchers extracted five time-domain features (mean, median, variance, root mean square value, and difference between maximum and minimum values) of voltage and current signals from different branches, and used random forests to provide diagnostic results. This method has high computational efficiency, but the anti-interference capability of the time-domain features is insufficient. Other researchers have analyzed the propagation law of arc noise in DC microgrids and proposed an arc fault diagnosis algorithm based on autocorrelation. By setting a threshold for the autocorrelation coefficient, this method can quickly identify faulty lines. However, it is difficult to determine a suitable threshold in practical applications. Extracting diverse features of current signals at different scales can accurately identify faulty lines; however, the feature extraction process itself is not optimized based on the feature selection results to accelerate DC arc fault diagnosis.

[0006] Entropy is a physical quantity that measures the regularity or complexity of a time series through state statistical probabilities. In recent years, some entropy-based methods have been applied to the field of 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 estimate of dynamic complexity. Compared with existing entropy methods, the proposed divergence entropy has three advantages: high consistency, robustness to noise, and high computational efficiency. Therefore, divergence entropy has the potential to be applied to DC arc faults and is beneficial for uncovering the subtle differences between the current signals of normal lines and arc-faulted lines under arc interference. However, traditional divergence entropy has the disadvantage of only considering the correlation information of adjacent data points and ignoring fault information at different fractional orders, resulting in low accuracy in arc fault detection. Summary of the Invention

[0007] Purpose of the invention: The purpose of this invention is to provide a DC arc fault anti-interference detection method based on fractional-order cross-gram divergence entropy, which can simultaneously consider the correlation information of adjacent data points and the fault information under different fractional orders. In the case of arc faults interfering with normal lines in DC power distribution systems, this method helps to improve the accuracy of arc fault detection.

[0008] Technical solution: The present invention provides a DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy, comprising:

[0009] The current signal of the branch to be tested is collected using a current sensor and then normalized.

[0010] Calculate the cross-Gram angle field of the normalized current signal;

[0011] The fractional-order 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-order cross-Gram divergence entropy.

[0012] The detection results are obtained by processing high-dimensional feature vectors using support vector machines.

[0013] Furthermore, a current sensor is used to acquire the current signal of the branch under test, and the current signal is normalized, including:

[0014] The current signal of the branch under test is collected using a current sensor. Wherein, the current value at time t t∈{1,2,…,n}, where n is the number of sampling points in the original current signal, and the current signal F is based on the following formula. *Normalize to the interval [-1, 1]:

[0015]

[0016] in, For F * The maximum value in; For F * The minimum value in the range; 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}.

[0017] Furthermore, the calculation process for the cross-gram angle field of the normalized current signal is as follows:

[0018] The normalized current signal is transformed into a polar coordinate sequence. The Gram angle sum field (GASF) and Gram angle difference field (GADF) are calculated using the polar coordinate sequence. The cross Gram angle field (CGAF) is calculated using the Gram angle sum field (GASF) and Gram angle difference field (GADF).

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

[0020]

[0021] Where, δ t F(t) is the angle converted to polar coordinates by the inverse cosine function; λ(t) is the timestamp; F(t) is the normalized current value at time t.

[0022] Furthermore, the formulas for calculating the Gram angle and the field GASF are as follows:

[0023]

[0024] Where, δ n Let n be the nth polar coordinate point, where n is the number of sampling points in the original current signal;

[0025] The formula for calculating the Gram angle difference field GADF is as follows:

[0026]

[0027] Furthermore, the calculation formula for the cross-gram angle field CGAF is as follows:

[0028]

[0029] Where β is the weighting factor, β∈[0,1], u n,n =β×cos(δ n +δn )+(1-β)×sin(δ n -δ n ).

[0030] Furthermore, the fractional-order 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-order cross-Gram divergence entropy, including:

[0031] Multiple phase space column matrices and multiple phase space row matrices are constructed based on the cross-Gram angle field;

[0032] Calculate the two-dimensional cosine correlation (CRC) between column matrices of different phase spaces, and calculate the two-dimensional cosine correlation (CRR) between row matrices of different phase spaces;

[0033] Construct a correlation value set CRG, where each element of the CRG consists of all calculated CRC and CRR values; divide the range [-1, 1] into ε intervals, which can be represented as {I1, I2, I3, ..., I...} ε}, calculate the probability {PRO(1),PRO(2),PRO(3),…,PRO(ε)} of each of the ε intervals in the correlation value set CRG;

[0034] Based on 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, calculate the fractional cross-Gram divergence entropy:

[0035]

[0036] Where α is the fractional order, α∈(-1,1); For the double gamma function with parameter 1; Γ(α+1) is the double gamma function with parameter 1-α; Γ(α+1) is the gamma function with parameter α+1; when the number of fractional orders selected is M, the high-dimensional feature vector FT = {FTFCD} α1 ,FTFCD α2 ,…,FTFCD αM}, where FTFCD αM This is the fractional cross-gram divergence entropy value corresponding to the Mth fractional order.

[0037] Furthermore, multiple phase space column matrices and multiple phase space row matrices are constructed based on the cross-gram angle field, including:

[0038] The phase space column matrix phc is constructed based on the cross-Gram angle field CGAF. i :

[0039]

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

[0041] Construct the phase space row matrix phr based on the cross Gram angular field CGAF i :

[0042]

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

[0044] Furthermore, 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] Among them, 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 .

[0049] Furthermore, process the high-dimensional feature vectors based on the support vector machine to obtain the detection results, including:

[0050] For training a support vector machine, let the training dataset contain Q feature vectors be {FT}. 1 FT 2 ,…,FT Q}, where FT Q Let be the Q-th feature vector; let the feature vector to be detected be FT. # Each training dataset contains the feature vectors corresponding to the normal line current signal when an arc fault occurs on a nearby line, the feature vectors corresponding to the normal line current signal when no arc fault occurs on a nearby line, and the feature vectors corresponding to the line current signal where the arc fault occurs.

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

[0052]

[0053] Among them, FT j For the j-th feature vector in the training dataset; y j For FT j The corresponding label value; θ j For FT j The corresponding Lagrange multipliers; b is the scalar threshold; the expression for the kernel function K(·,·) is as follows;

[0054]

[0055] Where exp(·) represents exponentiation of the natural constant e; σ is a parameter controlling the size of the receptive field of the kernel function; ‖·‖ 2 To find the operator for the 2-norm.

[0056] Beneficial effects: Compared with the prior art, the significant technical effects of the present invention are as follows: (1) The present invention can effectively detect arc faults in the system, and can avoid false alarms when the current signal of the adjacent normal line is interfered with by arc noise; the present invention can overcome the shortcomings of traditional divergence which only considers the correlation information between adjacent data points, the information isolation between different angle fields, the inability to analyze two-dimensional correlation, and ignores the key fault information hidden in the fractional order by calculating the fractional order cross-Gram divergence entropy; (2) Converting the current data in the Cartesian coordinate system into the Gram angle field in polar coordinates can effectively mine the correlation information between different data points, overcome the limitation of traditional divergence which only considers the correlation information between adjacent data points, and is conducive to improving the accuracy of arc fault detection; (3) The present invention In the fractional-order cross-Gram divergence entropy, the invention proposes a method for constructing a cross-Gram angle field, which can effectively integrate the Gram angle sum field and the Gram angle difference field in the subsequent two-dimensional cosine correlation calculation process, and solves 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 invention constructs a two-dimensional phase space matrix from the perspectives of rows and columns. Compared with the traditional divergence entropy method of constructing only a one-dimensional phase space vector, it can introduce more levels of two-dimensional correlation information, which is conducive to more accurately measuring the difference of current signal under different states; (5) In the fractional-order cross-Gram divergence entropy, the invention proposes a method for calculating divergence entropy under different fractional orders, which can overcome the limitation of the traditional divergence entropy ignoring the key fault information implicit in the fractional order. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the process of the present invention;

[0058] Figure 2 This is a block diagram of the experimental platform used in this invention.

[0059] Figure 3 t-SNE visualization of fractional-order cross-gram divergence entropy values ​​under normal and arc fault conditions. Detailed Implementation

[0060] The technical solution of the present invention will now be described in detail with reference to specific embodiments and accompanying drawings.

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

[0062] S1. Use a current sensor to collect the current signal of the branch to be tested and normalize the current signal.

[0063] In this embodiment, a current sensor is used to acquire the current signal of the branch under test at a sampling rate of 200 kHz. Wherein, the current value at time t t∈{1,2,…,n}, where n is the number of sampling points in the original current signal, and the current signal F is processed based on formula (1). * Normalize to the interval [-1, 1]:

[0064]

[0065] in, For F * The maximum value in; For F * The minimum value in the range; 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 equation (2), the normalized current signal is transformed into a polar coordinate sequence:

[0069]

[0070] Where, δ t F(t) is the angle converted to polar coordinates by the inverse 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 polar coordinate sequences.

[0072] The formulas for calculating Gram angle and field GASF are shown in equation (3):

[0073]

[0074] Where, δ n Let n be the nth polar coordinate point, where n is the number of sampling points in the original current signal;

[0075] The formula for calculating the Gram angle difference field GADF is shown in equation (4):

[0076]

[0077] Where, δ n Let n be the nth polar coordinate point, where 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 sum field GASF and the Gram angle difference field GADF.

[0079] In this embodiment, the calculation formula for the cross-gram angle field CGAF is shown in equation (5):

[0080]

[0081] Where β is the weighting 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 divergence 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 divergence entropy.

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

[0084] S3.1. Construct multiple phase space column matrices and multiple phase space row matrices based on the cross-Gram angle field. Details are as follows:

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

[0086]

[0087] Where 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, the phase space row matrix phr is constructed as shown in formula (7). i :

[0089]

[0090] Where 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 column matrices of different phase spaces, and calculate the two-dimensional cosine correlation (CRR) between row matrices of different phase spaces; details are as follows:

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

[0093]

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

[0095]

[0096] Where, is the two-dimensional cosine correlation value between the phase space column matrix phr 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 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; and r2 and g2 are not equal; 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

[0097] S3.3. Construct the correlation value set CRG, and the elements in CRG are composed of all calculated CRC values and CRR values; evenly divide the range [-1, 1] into ε intervals, and the ε intervals can be expressed as {I1, I2, I3, …, I ε}, and then calculate the probability {PRO(1), PRO(2), PRO(3), …, PRO(ε)} that the elements in the correlation value set CRG fall into each 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. Based on the probability {PRO(1),PRO(2),PRO(3),…,PRO(ε)} of each of the ε intervals in the correlation value set CRG, the fractional cross-Gram divergence entropy can be calculated according to formula (10):

[0099]

[0100] Where α is the fractional order, α∈(-1,1); For the double gamma function with parameter 1; Γ(α+1) is the double gamma function with parameter 1-α; Γ(α+1) is the gamma function with parameter α+1; when the number of fractional orders selected is M, the high-dimensional feature vector FT = {FTFCD} α1 ,FTFCD α2 ,…,FTFCD αM}, where FTFCD αM This is the fractional-order cross-gram divergence entropy value corresponding to the Mth fractional order. For example, FTFCD. α2 This is the fractional cross-gram divergence entropy value corresponding to the second fractional order.

[0101] S4. The high-dimensional feature vectors are processed using a support vector machine to obtain the detection results. Details are as follows:

[0102] For training a support vector machine, let the training dataset contain Q feature vectors be {FT}. 1 FT 2 ,…,FT Q}, where FT Q For the Q-th feature vector, e.g., FT 2 Let be the second feature vector; let the feature vector to be detected be FT. # Each training dataset contains: the feature vector corresponding to the normal line current signal when an arc fault occurs on a nearby line, the feature vector corresponding to the normal line current signal when no arc fault occurs on a nearby line, and the feature vector corresponding to the line current signal where the arc fault occurs.

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

[0104]

[0105] Among them, FT j For the j-th feature vector in the training dataset; y j For FT j The corresponding label value; θ j For FT j The corresponding Lagrange multipliers; b is the scalar threshold; the expression for the kernel function K(·,·) is shown in equation (12):

[0106]

[0107] Where exp(·) represents exponentiation of the natural constant e; σ is a parameter controlling the size of the receptive field of the kernel function; ‖·‖ 2 To find the operator for the 2-norm.

[0108] The above embodiments can achieve accurate detection of DC arc faults.

[0109] The following specific embodiment verifies the DC arc fault anti-interference detection method based on fractional-order cross-gram divergence entropy proposed in this invention.

[0110] like Figure 2 As shown, line I is the line to be tested. The system only collects the current signal of line I, and can generate arc faults at three locations: A, B, and C. 10,000 samples were collected on the established experimental platform, of which 6,000 samples were used to construct the training set and 4,000 samples were used as the test set. Each sample contains 512 data points. The experimental conditions corresponding to the dataset are shown in Table 1.

[0111] Table 1. Detailed description of the dataset

[0112]

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

[0114] Table 2 shows the detection results of the DC arc fault detection method proposed in this invention under different experimental conditions.

[0115]

[0116] The t-SNE visualization of singular values ​​under arc fault and normal conditions is shown below. Figure 3 As shown, the detection accuracy is 100% under both normal conditions and when the arc fault occurs on line II. The detection accuracy is 99.1% when the arc fault occurs on line I and 99.5% when the arc fault occurs on line III. The overall detection accuracy is 99.54%, and the overall false alarm rate is 0.16%. Experimental results demonstrate that the method proposed in this invention can effectively detect arc faults in the system and effectively avoid false alarms when the normal line current signal is interfered with by an arc fault on a nearby line.

[0117] This invention also compares the detection accuracy of the proposed method with two comparative methods under the same experimental conditions.

[0118] Comparison with Method 1: This method extracts the multi-scale divergence entropy of the current signal as a fault feature, with the maximum time scale set to 10, thus the constructed feature vector has a dimension of 10. Method 1 uses a support vector machine as its classifier.

[0119] Comparison Method 2: This method extracts the peak-to-peak value, standard deviation, and frequency domain energy of the current signal as fault features, thus constructing a feature vector with a dimension of 3. Comparison Method 2 uses a support vector machine as its classifier.

[0120] Table 3 shows the detection results of different methods. The detection accuracies of the proposed method, comparative method 1, and comparative method 2 are 99.54%, 90.18%, and 96.37%, respectively. The detection accuracy of the proposed method is significantly higher than that of the two comparative methods, further demonstrating the effectiveness and advancement of the proposed 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 signal of the branch to be tested is collected using a current sensor and then normalized. Calculate the cross-Gram angle field of the normalized current signal; The fractional-order cross-Gram divergence entropy of the normalized current signal is extracted from the cross-Gram angle field. A high-dimensional feature vector is constructed using this fractional-order cross-Gram divergence entropy, including: Multiple phase space column matrices and multiple phase space row matrices are constructed based on the cross-Gram angle field; Calculate the two-dimensional cosine correlation between different phase space column matrices Calculate the two-dimensional cosine correlation between row matrices in different phase spaces. ; Construct a correlation value set CRG, where the elements of the CRG are all calculated values. value and Value composition; will This range is divided into ε intervals on average. The interval can be represented as Calculate the elements falling into the correlation value set CRG. The probability of each interval in the given intervals ; where PRO(2) indicates that an element in the correlation value set CRG falls into the interval The probability of; Based on the elements falling into the correlation value set CRG The probability of each interval in the given intervals Calculate the fractional-order cross-gram divergence entropy: ； in, For fractional order, ; For the double gamma function with parameter 1; For parameters The double gamma function; For parameters The gamma function; when the number of fractional orders selected is M, the high-dimensional eigenvectors ,in, This is the fractional cross-gram divergence entropy value corresponding to the Mth fractional order; The detection results are obtained by processing high-dimensional feature vectors using support vector machines.

2. The DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy according to claim 1, characterized in that, The current signal of the branch under test is acquired using a current sensor, and the current signal is normalized, including: The current signal of the branch under test is collected using a current sensor. ,in, Current value at time , , The number of sampling points in the original current signal is given, and the current signal is converted based on the following formula. Normalization to interval : ; in, for The maximum value in; for The minimum value in the normalized current signal; Among them, after normalization The current value at time is , .

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

4. The DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy according to claim 3, characterized in that, The normalized current signal can be transformed into a polar coordinate sequence using the following formula: ； in, for The angle is converted to polar coordinates using the inverse cosine function. For timestamps; After normalization Current value at any given time.

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 formulas for calculating the Gram angle and the field GASF are as follows: ； in, For the first A polar coordinate point, The number of sampling points in the original current signal; The formula for calculating 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 formula for calculating the Cross-Gram Field (CGAF) is as follows: ； in, As a weighting factor, , .

7. The DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy according to claim 1, characterized in that, Multiple phase space column matrices and multiple phase space row matrices are constructed based on the cross-Gram angle field, including: Based on the cross-gram corner field Construct the phase space column matrix : ； in, The column embedding dimension; It is an integer, and ; Based on the cross-gram corner field Construct the phase space row matrix : ； in, Let the row embedding dimension be denoted as 'Row Embedding Dimension'. It is an integer, and .

8. The DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy according to claim 1, characterized in that, The two-dimensional cosine correlation between the different phase space column matrices The calculation formula is as follows: ； The two-dimensional cosine correlation between different phase space row matrices The calculation formula is as follows: ； in, Phase space column matrix With phase space column matrix The two-dimensional cosine correlation value between them; A row matrix in phase space With phase space row matrix The two-dimensional cosine correlation value between them; It is an integer. ; It is an integer. ; Phase space column matrix The Middle line, number The elements corresponding to the column, Phase space column matrix The Middle line, number The element corresponding to the column; It is an integer. ; It is an integer. ; A row matrix in phase space The Middle line, number The elements corresponding to the column, A row matrix in phase space The Middle line, number The elements corresponding to the column.

9. The DC arc fault anti-interference detection method based on fractional-order cross-Gram divergence entropy according to claim 1, characterized in that, The detection results are obtained by processing high-dimensional feature vectors using support vector machines, including: Train a support vector machine, assuming it contains The training dataset for each feature vector is ,in, For the first There are feature vectors; let the feature vector to be detected be... Each training dataset contains the feature vectors corresponding to the normal line current signal when an arc fault occurs on a nearby line, the feature vectors corresponding to the normal line current signal when no arc fault occurs on a nearby line, and the feature vectors corresponding to the line current signal where the arc fault occurs. Kernel function is The output of the support vector machine is as follows: ； in, For the training dataset, the first 1 eigenvector; for The corresponding tag value; for The corresponding Lagrange multipliers; Scalar threshold; kernel function The expression is as follows: ； in, This indicates exponentiation of the natural constant e; Parameters that control the size of the receptive field of the kernel function; To find the operator for the 2-norm.

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