Power cable fault diagnosis method based on multi-feature fusion

Abstract

According to the power cable fault diagnosis method based on multi-feature fusion, accurate diagnosis of partial discharge, an early fault and a short-circuit fault of a power cable is realized by comprehensively considering feature parameters such as partial discharge, temperature, current and voltage. Samples are obtained by adopting a simulation analysis method, cable fault identification is realized through an artificial intelligence algorithm, and a rapid and accurate method is provided for cable fault identification and positioning. For cable fault type identification, the CNN-BiLSTM-based cable fault identification method is provided, and the method comprises the following specific steps: firstly, obtaining fault current of cable monitoring points M and N, taking the root mean square of the current after the fault as a feature value, inputting the feature value into an artificial intelligence algorithm, training through the artificial intelligence algorithm, and finally carrying out algorithm iteration to obtain an optimal solution; and a cable fault type is obtained through algorithm identification. In order to consider fault types under different conditions, different fault types of the cable are identified by using an artificial intelligence algorithm.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of power cable fault diagnosis, and particularly relates to a power cable fault diagnosis method based on multi-feature fusion. BACKGROUND

[0002] As a key equipment for power transmission, the operation state of power cable is directly related to the stability and reliability of the entire power system. During long-term operation, power cable may be affected by various factors such as insulation aging, mechanical damage, environmental corrosion, etc., thereby causing partial discharge and short-circuit fault. Partial discharge is an important manifestation of cable insulation aging, and if not discovered and handled in time, it may further develop into a short-circuit fault, leading to large-area power outage accidents and causing huge losses to society and economy. Traditional power cable fault diagnosis methods mainly rely on a single characteristic parameter such as current or temperature, and these methods have certain limitations in actual application and cannot accurately and timely diagnose the fault type of the cable. The low-voltage pulse method cannot produce obvious reflection waveforms at high-resistance fault points, and this method cannot be used for high-resistance measurement. The patent "Cable fault identification method, device and medium based on improved MVMD-KSD-PEPM" (application number: 202411370355.X) points out that the cable fault current is collected and the characteristic vector is selected for cable fault identification. In this paper, only the cable current is analyzed, and the influence of other factors is not considered comprehensively, which may make the cable fault diagnosis not accurate enough.

[0003] Therefore, it is of great significance to develop a power cable fault diagnosis method based on feature fusion for improving the safety and reliability of the power system. SUMMARY

[0004] The present application proposes a power cable fault diagnosis method based on multi-feature fusion, which realizes accurate diagnosis of power cable partial discharge, early fault and short-circuit fault by comprehensively considering characteristic parameters such as partial discharge, temperature, current and voltage.

[0005] The technical scheme adopted by the present application is as follows:

[0006] Scheme (one): a power cable partial discharge fault diagnosis method based on multi-feature fusion, comprising the following steps:

[0007] Step a1: for power cable partial discharge defects, according to the actual structure parameters of power cable and the characteristic of partial discharge signal, a power cable partial discharge simulation model is established;

[0008] Step a2: according to the power cable partial discharge simulation model, the propagation characteristics of the partial discharge signal under different cable lengths are obtained, and the partial discharge signal is obtained;

[0009] Step a3: local discharge denoising is performed by synchronous squeezed wavelet transform (SSWT) based on spectrum clustering K-Medoids.

[0010] Step a4: power cable partial discharge identification is performed based on a CNN-BiLSTM model.

[0011] In the step a1, the power cable partial discharge simulation model is as follows:

[0012] The cable partial discharge includes internal discharge, surface discharge, corona discharge and suspension discharge, and the air gap defect is the main cause of internal discharge of the cable; an air gap defect equivalent model in the cross-linked polyethylene insulation is established, and the air gap defect equivalent model in the cross-linked polyethylene insulation adopts a three-capacitance method equivalent circuit: C1 is the equivalent capacitance of normal XLPE insulation medium, C2 is the equivalent capacitance of insulation medium in series with the air gap defect, and C3 is the equivalent capacitance of insulation where the air gap is located; the equivalent circuit diagram is as shown in Figure 1 .

[0013] The power supply voltage u = U m sinωt acts on the medium, and the voltage on the air gap is:

[0014]

[0015] In formula (1), u3 is the voltage divided by the air gap, U m is the amplitude of the power supply voltage, ω is the angular frequency, and t is the time.

[0016] The partial discharge simulation model adopts a double exponential decay model:

[0017]

[0018] In formula (2), S(t) represents the partial discharge voltage signal; A represents the signal amplitude; τ1 and τ2 represent the time decay coefficients of the signal; and represent typical exponential decay functions, which gradually tend to 0 as t increases.

[0019] In the step a2, the propagation characteristics of the partial discharge signal under different cable lengths are obtained, and the partial discharge signal is obtained.

[0020] According to the signal propagation formula U0 = U i e -yl , the input and output voltage relationship of the signal is:

[0021]

[0022] In formula (3), U0 is the output voltage of the transmission line; U iis the input voltage of the transmission line; γ is the propagation constant, which contains the attenuation and phase change information of the signal; α is the attenuation constant, which represents the degree of signal attenuation per unit length; β is the phase constant, which represents the phase change of the signal per unit length; e -jβl Without changing the size of U0, only the phase of U0 is changed, which reflects the phase relationship between the output voltage U0 and the input voltage U i .

[0023] The relationship between the input voltage and the output voltage of the partial discharge signal in the transmission line is U0=U i e -αl ·e -jβl , which takes into account the attenuation and phase change of the signal during transmission. U0 is the output voltage; U i is the input voltage; α is the attenuation constant, which represents the degree of signal attenuation per unit length; β is the phase constant, which represents the phase change of the signal per unit length; l is the distance of signal propagation in the transmission line, e -jβl reflects the phase relationship between the output voltage U0 and the input voltage U i . Considering the influence of cable length on partial discharge signal, as the cable length increases, the signal will experience more attenuation. The attenuation constant α is related to the material properties of the cable, environmental conditions, etc. Longer cables will result in further reduction of signal amplitude. There will be a certain delay when the signal propagates in the cable, which is described by the phase constant β. In long cables, the signal may experience more frequency-selective attenuation, leading to signal distortion. This distortion may affect the feature extraction and diagnosis of partial discharge signals. A known partial discharge signal is injected at one end of the cable, and the propagation characteristics of the signal are measured at the other end to obtain the propagation characteristics of the partial discharge signal under different cable lengths.

[0024] In the step a3,

[0025] a3.1: Fourier transform of partial discharge, as follows:

[0026]

[0027] In formula (4): I[n] represents the frequency domain output; i[k] represents the time domain input signal; N represents the total number of signal sampling points; represents the complex exponential base function, which controls the frequency decomposition; n, k represent the indexes of frequency domain and time domain respectively.

[0028] a3.2: The frequency spectrum of partial discharge signal is classified by K-Medoids algorithm, which is divided by local maximum and minimum method, as follows:

[0029] The partial discharge signal is subjected to Fourier transform to obtain the spectrum data S(f), where f is the frequency and S(f) is the amplitude at the corresponding frequency. To reduce noise interference, the spectrum needs to be smoothed using a moving average method to obtain the preprocessed spectrum S′(f).

[0030] The dynamic averaging method smooths signals by calculating the average value of data within a certain window around a point. The formula is:

[0031]

[0032] In equation (5): S(f i ) represents the original spectrum at frequency point f i The amplitude; S′(f i ) represents the smoothed value; 2N+1 represents the sliding window size; k represents the offset index within the window; S(f i+k ) represents the original signal S at frequency point f. i+k The value at that location.

[0033] The local maximum and minimum method divides a continuous spectrum into several characteristic intervals by identifying the maxima and minima in the spectrum, with each interval corresponding to a characteristic frequency segment of partial discharge;

[0034] Local maxima identification: for frequency point f i If the following condition is met: S'(f) i )>S'(f i-1 And S'(f) i )>S'(f i+1 ), S'(f i ) represents the smoothed value; S'(f i-1 ) represents the frequency point f i The previous adjacent frequency point f i-1 Processed signal value; S'(f i+1 ) represents the frequency point f i The next adjacent frequency point f i+1 The processed signal value. Then f i For a local maximum point, the corresponding amplitude S'(f) i () represents the peak value.

[0035] Local minimum identification: for frequency point f j If the following condition is met: S'(f) j ) <S'(f j-1 And S'(f) j ) <S'(f j+1 ), then f j For a local minimum point, the corresponding amplitude S'(f) j () represents the valley value.

[0036] By dividing the spectrum interval, taking two adjacent minima f j1 and f j2 as the boundaries, j1<j2; the interval [f j1 , f j2 ] containing one or more peaks in the middle is taken as a feature sub-spectrum, denoted as S k (f), k = 1, 2,..., m, m is the number of divided intervals.

[0037] K-Medoids is a prototype-based clustering algorithm, whose clustering centers are actual samples in the data set rather than means, and is more robust to noise and outliers, and is suitable for classification of partial discharge spectrum. K-Medoids uses distance to measure the similarity between samples and clustering centers, and uses Manhattan distance:

[0038]

[0039] In formula (6), d(x i , m j ) represents the Manhattan distance between sample x i and clustering center m j ; x i = [x i,1 , x i,2 ,..., x i,d ] is the feature vector of the i-th sample; m j = [m j,1 , m j,2 ,..., m j,d ] is the center sample of the j-th cluster; t is the feature index; x i,t represents the value of sample x i in the t-th feature dimension; m j,t represents the value of clustering center m j in the t-th feature dimension; a represents the number of feature dimensions.

[0040] The sample assignment rule assigns each sample to the cluster where the nearest medoid is located:

[0041]

[0042] In formula (7), C j represents the j-th cluster, j = 1, 2,..., K, K is the preset number of clusters; x i represents the sample to be classified; d(x i , x j ) represents the distance between sample x i and the j-th cluster center; d(x i , x k ) represents the distance between sample x iDistance of the reference point corresponding to the kth cluster.

[0043] Generate a clustering objective function, and optimize by minimizing the total clustering cost, which is defined as the sum of distances from all samples to their corresponding cluster medoids:

[0044]

[0045] In equation (8), Total Cost represents the total cost of clustering, K represents the number of clusters of clustering; j represents the index of the cluster, j = 1, 2, …, K, which is used to traverse each cluster.

[0046] Medoid update formula, for each cluster C j , traverse all samples x in it, and calculate the intra-cluster cost when x is the temporary medoid:

[0047]

[0048] In equation (9), Cost(x) represents the cost of the distance between the intra-cluster sample and the reference point; d(x, x') represents the distance measure between sample x and sample x'.

[0049] Select the sample that minimizes the cost as the new medoid:

[0050]

[0051] In equation (10), m' j represents the updated center of the jth cluster, and argmin represents the value of the independent variable x that makes the following function minimum.

[0052] When one of the following conditions is met, the algorithm stops iteration:

[0053] ①. The new medoid is completely consistent with the old medoid or the distance is less than the preset threshold ∈: represents the distance function of the jth element pair, which measures the difference between m' j and m j .

[0054] ②. The change of the total clustering cost is less than the threshold: |Total Cost new - Total Cost old | < ε, Total Cost new represents the new total cost; Total Cost old represents the old total cost.

[0055] ③. Reach the maximum number of iterations.

[0056] a3.3: Adopting synchronous squeeze wavelet transform to filter frequency segment adaptively, obtaining modal component;

[0057] Synchronous squeeze wavelet transform (SWT) is a time-frequency analysis method, which improves the time-frequency resolution by rearranging the time-frequency coefficients of traditional wavelet transform, and can realize adaptive filtering and extraction of modal components of partial discharge signals.

[0058] The continuous wavelet transform is performed on the signal x(t) to obtain the time-frequency coefficients:

[0059]

[0060] In formula (11), W x (a,b) represents the coefficients of the signal x(t) after continuous wavelet transform; ψ(t) is the mother wavelet, ψ * is its complex conjugate; a is the scale parameter, which is inversely proportional to the frequency; b is the translation parameter; x(t) is the original signal to be analyzed; t is the time.

[0061] The continuous wavelet transform decomposes the signal into components of different scales, but the time-frequency concentration is limited and frequency dispersion is easy to occur. In order to improve the time-frequency resolution, the CWT coefficients are squeezed and rearranged, and the core is to calculate the instantaneous frequency and map the coefficients to the corresponding frequency axis. For each time-frequency point (a,b), the instantaneous frequency is estimated by the phase derivative of the wavelet coefficient:

[0062]

[0063] In formula (12), ω x (a,b) represents the instantaneous frequency of the signal x(t) after continuous wavelet transform at scale a and translation b; represents the partial derivative of the translation factor b; represents the frequency conversion coefficient; arg{·} represents the phase of the complex coefficient.

[0064] The original scale-time domain coefficient W x (a,b) is mapped to the frequency-time domain T x (ω,b):

[0065]

[0066] In formula (13), C ψ is the wavelet normalization constant; δ is the frequency resolution threshold, which controls the squeezing accuracy; is the weighted wavelet coefficient, a 3 / 2 is the scale weighting of the wavelet transform coefficient; the summation only retains the coefficients with instantaneous frequency close to the target frequency ω, realizing time-frequency concentration.

[0067] The high-resolution time-frequency distribution T x (ω, b) obtained by using the synchronous squeeze wavelet transform (SWT) can be used to divide the frequency interval Ω of interest in the time-frequency domain according to the spectral characteristics of the partial discharge signal k k1 , ω k2 ], k = 1, 2, …, K, K representing the total number of divided frequency intervals.

[0068] Adaptive filtering is performed on each frequency interval to retain the time-frequency coefficients within the interval and filter out noise and interference outside the interval:

[0069]

[0070] In formula (14), T x,k (ω, b) represents the time-frequency of the kth characteristic mode of the signal x.

[0071] Inverse synchronous squeeze transformation is performed on the filtered time-frequency coefficients T x,k (ω, b) to reconstruct the kth modal component x k (t):

[0072]

[0073] In formula (15), x k (t) represents the output reconstructed signal; ω k1 represents the starting frequency of the interval; ω k2 represents the ending frequency of the interval; T x,k (ω, b) is the time-frequency representation of the kth characteristic mode of the signal x; is the wavelet basis function; a(ω) is the frequency-scale conversion relationship, which is determined by the center frequency ω0 of the mother wavelet, a = ω0 / ω; finally, the original signal can be decomposed into the sum of multiple modal components: where ∈(t) is the residual noise.

[0074] The synchronous squeeze wavelet transform realizes high-resolution time-frequency analysis through instantaneous frequency estimation and time-frequency coefficient rearrangement, accurately extracts the modal components of the partial discharge signal by combining adaptive filtering of frequency segmentation, and realizes adaptive filtering of frequency segmentation to obtain appropriate modal components.

[0075] a3.4: Use high-order statistics, i.e., kurtosis criterion, to select useful modal components, and use 3σ criterion to perform threshold discrimination on the useful modal components.

[0076] The kurtosis value K is defined by formula:

[0077]

[0078] In formula (16), K i ​denotes kurtosis value; x i denotes the i-th modal component sequence, μ i , σ i denotes the mean and standard deviation of the i-th modal component sequence, respectively, and E denotes the expectation of the signal;

[0079] When the modal component only contains white noise, since the amplitude obeys normal distribution, the distribution curve has normal kurtosis, and the kurtosis value is 3; when the modal component contains non-Gaussian partial discharge signal, since the impact component content increases, the pulse amplitude significantly deviates from the normal distribution, the kurtosis value significantly increases, and accordingly the useful modal component is selected.

[0080] a3.5: According to the evaluation index to judge the denoising effect, the evaluation index is signal-to-noise ratio, root mean square error, and waveform similarity coefficient;

[0081] Among them: signal-to-noise ratio:

[0082]

[0083] In formula (17), s(n) represents the original signal; denotes the reconstructed signal; N denotes the total number of signal sampling points; n denotes the n-th sampling point of the signal sequence for traversal calculation.

[0084] Root mean square error:

[0085]

[0086] Waveform similarity coefficient:

[0087]

[0088] The larger the signal-to-noise ratio, the smaller the noise content in the partial discharge signal; the closer the root mean square to 1, the higher the similarity between the denoised signal and the original signal; the smaller the waveform similarity coefficient, the smaller the waveform distortion rate of the denoised signal.

[0089] Scheme (two): A power cable early fault diagnosis method based on multi-feature fusion, comprising the following steps:

[0090] Step b1: For the early fault of the power cable, according to the actual structure parameters of the power cable, a 10kV power cable temperature field simulation model is established;

[0091] Step b2: Analyze the cable body heat loss and heat transfer, the heat loss includes the core heat loss and the cable insulation interface loss, and the heat transfer includes heat conduction, heat convection and heat radiation;

[0092] Step b3: According to the 10kV power cable temperature field simulation model, analyze the transient temperature distribution results of the power cable body, consider the temperature distribution of the power cable body under different defects, and measure the temperature change rate and temperature peak value;

[0093] Step b4: Early fault identification of power cable based on CNN-BiLSTM model.

[0094] In step b1, a 10kV power cable temperature field simulation model is established;

[0095] The typical structure of 10kV power cable is taken as an example, and the single-core cable with cross-linked polyethylene insulation is taken as an example. From inside to outside, it is conductor: the core part of conducting current, which is the main heat source; Shielding layer: semi-conductive material, used for uniform electric field; Insulation layer: usually cross-linked polyethylene, which plays the role of electrical insulation.

[0096] In step b2,

[0097] (1) Cable body heat loss:

[0098] 1) Wire core heat loss:

[0099] The heat loss generated by the wire core conductor is the main source of heat of the cable body. The Joule heat generated by the thermoelectric effect causes the temperature of the cable to rise, and the calculation expression of the Joule heat is:

[0100] Q c =I 2 R (20);

[0101] In formula (20), Q c represents the heat loss of the cable wire core conductor; I represents the effective value of the alternating current flowing through the wire core conductor; R represents the alternating resistance value.

[0102] 2) Cable insulation interface loss:

[0103] In addition to the wire core, the insulation loss of each medium layer inside the cable is generated under the action of a strong electric field, and its expression is:

[0104] W d =2πfCU c tanδ (21);

[0105] In formula (21), W d represents the insulation loss generated by the medium layer; f represents the 50Hz voltage frequency; C represents the medium capacitance; U c represents the operating voltage of the cable; tanδ represents the loss factor of the cable insulation medium, and δ is the medium loss angle.

[0106] (2) Heat transfer:

[0107] 1) Thermal conduction heat transfer mode is caused by the thermal motion of micro-particles in the cable medium, and the mathematical expression of the conduction is:

[0108]

[0109] In formula (22), q represents the heat flow density; Φ represents the total heat flowing through per unit area S; K represents the thermal conductivity; T represents the temperature; n represents the normal direction of heat conduction; it can be seen from formula (22) that the heat flow density is proportional to the temperature gradient.

[0110] 2) Thermal conduction and thermal radiation are both a way of heat transfer, and the expression is:

[0111]

[0112] In formula (23), q c is the heat convection; q r is the heat radiation; h represents the natural convection heat transfer coefficient; σ0 represents the Stefan-Boltzmann constant; △t represents the temperature difference between the solid surface and the fluid; △T represents the absolute temperature difference between the object surface and the environment. In step b3, the transient temperature distribution result of the power cable body is analyzed, and it can be known from the cable body temperature field simulation result that, Figure 6 The red small circle corresponds to the most concentrated part of the cable conductor and the surrounding heat, the yellow area is the intermediate area of heat transfer from the core to the environment, and the blue-green area is the peripheral area close to the ambient temperature. The heat diffusion between the cores will affect each other due to the short distance, so that the temperature distribution of the transition heat dissipation area presents a certain correlation, which embodies the characteristics of thermal coupling of multi-core cables.

[0113] Considering the temperature distribution of the power cable body under different defects, the temperature change rate and the temperature peak value are measured; it can be known from the cable body temperature field simulation result that when the conductor contact is poor, an abnormally high temperature core will appear at the corresponding core position, which is brighter and larger than the red area of the normal core. In terms of temperature change rate, due to the rapid accumulation of heat, the temperature rising slope in the transient stage is much larger than that of the normal core. When the insulation layer is locally deteriorated, temperature abnormal patches appear in the corresponding area of the insulation layer. In terms of temperature peak value, the temperature at the center of the patch is higher than that in the normal insulation area; due to the influence of thermal resistance, the heat transfer is blocked, and the temperature rises slowly at first and then quickly in the transient state, which is different from the stable temperature change rate of the normal insulation area.

[0114] Scheme (three): a power cable short circuit fault diagnosis method based on multi-feature fusion, comprising the following steps:

[0115] Step c1: for power cable short circuit fault, taking single-phase and three-phase short circuit fault as an example, a power cable transmission line simulation model is established;

[0116] Step c2: simulate the current of single-phase short circuit and three-phase short circuit of the cable by setting the single-phase position to ground in the power cable transmission line simulation model;

[0117] Step c3: analyze the characteristics of the current in the two faults in step c2, and simulate the current characteristics of the fault signal through different cable lengths, short circuit types and grounding resistances.

[0118] Step c4: power cable short circuit fault identification based on CNN-BiLSTM model.

[0119] In step c1, single-phase and three-phase short circuit faults are taken as examples to establish a power cable transmission line simulation model:

[0120] The power cable transmission line simulation model can be equivalent to a distributed parameter model. The cable distributed parameter model considers the resistance R, inductance L, conductance G and capacitance C along the cable. These parameters are uniformly distributed along the cable length. When the wavelength λ of the pulse signal is short and the length l of the cable line is long, the signal will experience multiple wavelengths when propagating in the cable. At this time, the influence of the distributed parameters of the cable on the signal cannot be simply described by a lumped parameter model, and the influence of the distributed parameters needs to be considered.

[0121] In step c2,

[0122] When a single-phase short circuit occurs, the single-phase short circuit current can be calculated according to the symmetrical component method as follows:

[0123]

[0124] In equation (24): I represents the single-phase short circuit current; U represents the phase voltage; R T R represents the resistance of the transformer; X T X represents the reactance of the transformer; R represents the equivalent resistance of the system; X represents the equivalent reactance of the system.

[0125] Three-phase short circuit fault calculation formula:

[0126]

[0127] In equation (25): I represents the three-phase short circuit current; U C U represents the short circuit calculation line voltage; R ∑ R is the total resistance from the power source to the short circuit point; X ∑ X is the total reactance from the power source to the short circuit point.

[0128] In step c3, the characteristics of the current in the two faults in step c2 are analyzed, and the current characteristics of the fault signal are simulated by different cable lengths, short circuit types and grounding resistances.

[0129] The cable length affects the amplitude and waveform of the fault current, and the resistance and inductance of the cable increase with the length. The short circuit type affects the symmetry and amplitude of the fault current. For three-phase short circuit, the amplitude of the fault current is usually the largest, while for single-phase ground short circuit, the amplitude of the fault current is usually the smallest. The grounding resistance directly affects the size of the ground fault current. The larger the grounding resistance, the smaller the fault current. In power systems, by simulating the effects of different cable lengths, short circuit types and grounding resistances on the current characteristics of the fault signal, the fault behavior that may occur in the actual system can be better understood and predicted.

[0130] The present application proposes a power cable fault diagnosis method based on multi-feature fusion, and the technical effects are as follows:

[0131] 1) The present application establishes a power cable transmission line simulation model and a partial discharge simulation model. The propagation characteristics of the partial discharge signal under different cable lengths are simulated. A temperature field simulation model is established to analyze the heat loss and heat transfer of the power cable.

[0132] 2) A cable partial discharge denoising method and data enhancement method are proposed. The original training sample set is expanded by synthesizing partial discharge signals, and the temperature, current and voltage signal feature quantities collected are combined and input into the cable fault recognition model based on CNN-BiLSTM model. BRIEF DESCRIPTION OF DRAWINGS

[0133] The present application will be further described below in combination with the drawings and examples:

[0134] Figure 1 The equivalent circuit diagram of air gap defect.

[0135] Figure 2 The structure diagram of 10kV cable.

[0136] Wherein: 1-conductor, 2-metal shielding layer, 3-insulating layer.

[0137] Figure 3 The overall flowchart of power cable fault diagnosis.

[0138] Figure 4 The flowchart of partial discharge signal fault recognition and positioning.

[0139] Figure 5 The partial discharge denoising method flowchart using EWT based on frequency spectrum clustering is introduced.

[0140] Figure 6The simulation results of the temperature field of the cable body based on the simulation software.

[0141] Figure 7 The circuit model diagrams of single-phase short circuit and three-phase short circuit. Figure 7 In the formula, f is the fault point, and R and L are the resistance and inductance of each phase in the cable.

[0142] Figure 8 The simulation results of the current of single-phase short circuit and three-phase short circuit, and the fault time is 0.02s.

[0143] Figure 9 The simulation results of the voltage of single-phase short circuit and three-phase short circuit.

[0144] Figure 10 The bidirectional long short-term memory network model diagram, which consists of an input layer, a forward layer, a reverse layer, and an output layer. Figure 11 The neural network-based cable fault type identification results; including test set (a) and training set (b) two results, Figure 11 In the formula, the ordinate 1 and 2 represent single-phase short circuit and three-phase short circuit, respectively. DETAILED DESCRIPTION

[0145] The power cable fault diagnosis method based on multi-feature fusion includes the following steps:

[0146] Step 1: For early power cable defects, taking partial discharge as an example, according to the actual structure parameters of the power cable and the characteristics of the partial discharge signal, an electromagnetic transient simulation software is used to establish a power cable partial discharge simulation model. The power cable model includes the cable core, the cross-linked polyethylene (XLPE) insulation layer, the metal shielding layer, the inner protective layer, the armored layer, and the outer protective layer; the partial discharge signal model adopts a double exponential decay model.

[0147] More specifically, for partial discharge, there is a close relationship between early cable defects and partial discharge, and the insulation state of medium-voltage distribution cable is closely related to cable partial discharge. The insulation performance of most medium and high voltage power equipment is attributed to partial discharge. Due to factors such as equipment aging or external damage, voids, impurities, bubbles, and other defects are generated in the XLPE insulation layer of the cable. During actual operation, when the field strength on these local defects reaches the insulation breakdown field strength, partial discharge occurs. This discharge phenomenon is an early sign of cable insulation deterioration, and if not addressed, partial discharge will gradually expand, eventually leading to cable insulation breakdown and causing early failure.

[0148] Because the wavelength of the pulse signal is short and the size of the cable line is long during the cable propagation, the cable transmission line simulation model is regarded as a distributed parameter model. In order to simplify the equivalent model and facilitate theoretical analysis, the cable distributed parameter model can be equivalent to a uniform transmission line model, and the power cable transmission line simulation model mainly includes: line distributed resistance, line distributed inductance, line distributed conductance and line distributed capacitance.

[0149] Voltage and current of the cable line:

[0150]

[0151] In the formula, V(x) represents the voltage traveling wave of the uniform transmission line; I(x) represents the current traveling wave of the uniform transmission line; A1 and A2 represent the traveling wave amplitude constant; A1e γx represents the incident wave propagating in the positive direction of x; A2e -γx represents the reflected wave propagating in the negative direction of x; γ represents the propagation constant; z represents the characteristic impedance; and x represents the spatial position coordinate along the transmission line. According to the signal propagation formula U0=U i e -yl The input and output voltage relationship of the signal can be obtained as follows:

[0152]

[0153] In the formula, U0 is the output voltage of the transmission line; U i is the input voltage of the transmission line; γ is the propagation constant, which contains the signal attenuation and phase change information; α is the attenuation constant, which represents the attenuation degree of the signal per unit length; β is the phase constant, which represents the phase change of the signal per unit length; e -jβl does not change the size of U0, but only changes the phase of U0, which reflects the phase relationship between the output voltage U0 and the input voltage U i ; e -αl represents the exponential attenuation factor, which describes the attenuation proportion of the signal with the propagation distance l.

[0154] More specifically, the cable partial discharge can be divided into internal discharge, surface discharge, corona discharge and suspension discharge, and the air gap defect is the main cause of the internal discharge of the cable. The equivalent model of the air gap defect in the cross-linked polyethylene insulation is established, the equivalent circuit of the air gap defect in the XLPE insulation adopts the three-capacitor method, C1 is the equivalent capacitance of the normal XLPE insulation medium, C2 is the equivalent capacitance of the insulation medium in series with the air gap defect, and C3 is the equivalent capacitance of the insulation where the air gap is located.

[0155] The power voltage u=U m sinωt acts on the medium, and the voltage on the air gap:

[0156]

[0157] wherein: u3 is the voltage divided by the air gap, U m is the power supply voltage amplitude, ω is the angular frequency, and t is time.

[0158] The partial discharge simulation model adopts a double exponential decay model:

[0159]

[0160] wherein: S(t) represents the partial discharge voltage signal; A represents the signal amplitude; t is time; τ1 and τ2 represent the time decay coefficients of the signal.

[0161] Step two: According to the above power cable partial discharge simulation model, the propagation characteristics of the partial discharge signal under different cable lengths are obtained, and the partial discharge signal is obtained; considering the interference of the signal, a partial discharge denoising method based on the synchronous squeezed wavelet transform (SSWT) of the K-Medoids frequency spectrum clustering is adopted. Based on the generative adversarial network, a data enhancement method is proposed, which expands the original training sample set by synthesizing the partial discharge signal; the influence of the capacity ratio of the generated sample and the original training sample on the pattern recognition accuracy is analyzed, and a partial discharge signal recognition method based on the CNN-BiLSTM model is proposed.

[0162] More specifically, the partial discharge signal is subjected to Fourier transform, the frequency spectrum of the partial discharge signal is classified using the K-Medoids algorithm, the signal frequency spectrum is divided using the local maximum and minimum value method, the frequency segments are adaptively filtered using the synchronous squeezed wavelet transform, the modal components are obtained, the useful modal components are selected using the high-order statistics, i.e., the kurtosis criterion, and the useful modal components are subjected to threshold discrimination using the 3σ criterion.

[0163] The denoising effect of the algorithm is judged according to the evaluation index, and the evaluation index is the signal-to-noise ratio, the root mean square error, and the waveform similarity coefficient. The larger the signal-to-noise ratio, the smaller the noise content in the partial discharge signal; the closer the root mean square error to 1, the higher the similarity between the denoised signal and the original signal; the smaller the waveform similarity coefficient, the smaller the distortion rate of the denoised signal waveform.

[0164] The signal-to-noise ratio is:

[0165]

[0166] The root mean square error is:

[0167]

[0168] The waveform similarity coefficient is:

[0169]

[0170] More specifically, based on generative adversarial networks (GANs), this paper employs a model to learn the deep feature representation of the original partial discharge signals, recovers the true data distribution, and expands the original training sample set by synthesizing a large number of partial discharge signals. The impact of the ratio of generated samples to original training samples on pattern recognition accuracy is determined, the final number of generated samples is determined, and a pattern recognition method based on a CNN-BiLSTM model is proposed. Partial discharge signals caused by insulation defects exhibit high similarity in partial discharge patterns, making them difficult to distinguish using expert experience alone.

[0171] To address the challenge of pattern recognition, a hybrid pattern recognition method is employed to detect partial discharge patterns. However, on-site partial discharge detection data samples are scarce, and the number of samples varies across different defects. Furthermore, the influence of environmental noise further complicates the pattern recognition accuracy of online monitoring systems. Considering the limitations of neural network algorithms, such as low stability and the tendency to generate multiple local minima, a CNN-BiLSTM algorithm is proposed to optimize the network structure, improving training efficiency and accuracy. The optimized network is trained using a data-augmented training set, with normalized test data used as model input. The output classification results are then analyzed, highlighting the classification performance and network complexity of the neural network.

[0172] Data augmentation process:

[0173] The collected partial discharge data is preprocessed, including denoising and normalization, to obtain real sample data. The preprocessed real samples are then used to train a generative adversarial network (GAN), including a generator and a discriminator. The generator learns to generate partial discharge signals from random noise, and the discriminator learns to distinguish between real and generated signals. After training, the generator synthesizes new partial discharge signal samples. The synthesized samples are then merged with the original training sample set to form an expanded training sample set. The learning mechanism of the GAN is as follows:

[0174] Assuming the noise z ~ N(0,1), from the prior distribution p of the noise z m noise samples are randomly selected from (z) {z} (1) ,z (2) ,...,z (m)}; Generate distribution p from small batch sample data data m real samples are randomly selected from (x) {x} (1) ,x (2) ,...,x (m) During the training of generator G, the optimization result of G is D(G(z)) = 1, which means that the discriminator D cannot distinguish all generated samples from real samples. Therefore, the optimization problem of generator G is as shown in the equation.

[0175]

[0176] wherein V(D, G) represents an adversarial loss function measuring the performance of the generator and the discriminator; D(G(z)) represents the discrimination result of the discriminator D on the generated data G(z) after the generator G inputs the noise z; and G(z) represents the sample generated by the generator from the noise z. represents the expectation on the noise distribution input to the generator.

[0177] The generator G is updated by the gradient boost as follows:

[0178]

[0179] wherein D(G(z (i) )) represents the true-false judgment of the discriminator on the generated data G(z (i) ) output by the generator G receiving the random noise z (i) ; G(z (i) ) represents the output of the fake data by the generator G receiving the random noise z g ; and m represents the batch size; and θ

[0180] The optimization result of the discriminator D is D(x) = 1 and D(G(z)) = 0, and thus the optimization problem of the discriminator D is as shown in the formula.

[0181] wherein: represents the expectation on the real data x, covering all possible samples of the real data.

[0182] Similarly, the generator D is updated according to the gradient boost as follows:

[0183]

[0184] Therefore, in combination with formula (27) and formula (29), the optimization problem of the GAN can be regarded as a maximum-minimum problem:

[0185] For any and y ∈ [0, 1], the following equation is considered:

[0186]

[0187] Therefore, given the generator G, the minimum value of the objective function formula (29) is:

[0188]

[0189] wherein: represents the theoretical best output that the discriminator D can achieve when the generator G is fixed; and p g(x) represents the probability distribution of the generated data by the generator, which is determined by the generator G. D and G are trained alternately to reach a Nash equilibrium. When the generator cannot improve the quality of the synthetic data, and the discriminator cannot determine the attribution of the input data, the training stops. At this time, D(x) = 0.5, p data = p g , which indicates that the discriminator randomly outputs the prediction result. Substituting into equation (29) can obtain In summary, once D and G establish a dynamic balance, the global optimal solution is obtained as -log4. Through the data enhancement method based on the generative adversarial network, the original training sample set of partial discharge signals can be effectively expanded, and the recognition accuracy of the model for partial discharge signals can be improved.

[0190] Step three: for early cable faults, based on the actual structure parameters of power cables, a 10kV power cable temperature field simulation model is established based on COMSOL simulation software, and the cable body heat loss and heat transfer are analyzed. The heat loss includes the core heat loss and the cable insulation interface loss, and the heat transfer includes heat conduction, heat convection and heat radiation.

[0191] More specifically, a 10kV power cable temperature field simulation model is established based on COMSOL simulation software, and the cable body heat loss and heat transfer are analyzed. The heat loss includes the core heat loss and the cable insulation interface loss, and the heat transfer includes heat conduction, heat convection and heat radiation.

[0192] Under normal circumstances, the cable temperature is within a certain range, and if early failure or short circuit failure occurs, it will cause local temperature to abnormally rise. The surface temperature of the cable is measured using an infrared thermometer, and the optical fiber temperature sensor is installed inside or on the surface of the cable to monitor the temperature change in real time. By monitoring the cable operating temperature for a long time, the temperature change trend is analyzed. If the temperature gradually rises and exceeds the normal range, and local discharge signals are detected, the power cable may have early failure. If the temperature of a certain part of the cable rises sharply in a short time, and the current abnormally increases, it can be judged as a short circuit fault. By combining temperature, short circuit current and partial discharge data, the fault type is comprehensively judged.

[0193] The main heat source of the cable in actual operation is the heat loss generated by the core conductor and the dielectric loss generated at the interface of the insulation material. The heat radiation generated by the cable surface contacting the outside world and the heat convection with the air. The heat loss and heat transfer of the cable body will be analyzed as follows.

[0194] (1) Cable body heat loss:

[0195] 1) Core heat loss:

[0196] The heat loss generated by the core conductor is the main source of heat of the cable body. It makes the cable temperature rise through the Joule heat generated by the thermoelectric effect. The calculation expression of the Joule heat is:

[0197] Q c = I 2 R (20) ;

[0198] wherein: Q c represents the heat loss of the cable core conductor; I represents the effective value of the alternating current flowing through the core conductor; and R represents the alternating resistance value, in Ω / m.

[0199] 2) Cable insulation interface loss:

[0200] In the cable operation, in addition to the core, the insulation loss of each medium layer inside the cable is generated under the action of a strong electric field, and its expression is:

[0201] W d = 2πfCU c tanδ (21) ;

[0202] wherein: f represents the frequency of the 50Hz voltage; C represents the medium capacitance, in F / m; U c represents the cable operating voltage; and tanδ represents the loss factor of the cable insulation medium, and δ is the medium loss angle.

[0203] (2) Heat transfer:

[0204] 1) Heat conduction is caused by the thermal motion of micro-particles in the cable medium. Micro-particles cause heat energy to be conducted from a high-temperature medium to a low-temperature medium, and the mathematical expression of the conduction is:

[0205]

[0206] wherein: q represents the heat flux density; Φ represents the total heat flowing through the unit area S; and K represents the thermal conductivity; it can be seen from equation (22) that the heat flux density is proportional to the temperature gradient.

[0207] 2) Heat convection and heat radiation Heat convection and heat radiation are both a way of heat transfer, involving the physical movement of fluid and the heat radiation generated by resistance loss, medium loss, etc. in the cable operation, and its expression is:

[0208]

[0209] wherein: q c is the heat convection; q r is the heat radiation; h represents the natural convection heat transfer coefficient, in W / (m 2 ·K); σ0 represents the Stefan-Boltzmann constant; and generally takes the value of 5.67×10 -8 .

[0210] Step four: According to the above-mentioned power cable temperature field simulation model, the transient temperature distribution results of the power cable body are analyzed, the temperature distribution of the power cable body under different defects is considered, and the temperature change rate and temperature peak value and other data are measured. An early fault identification method based on artificial intelligence algorithm is proposed.

[0211] More specifically, normal operation data and fault data of the power cable are collected as training samples. The normal operation data includes the measured values of ground current, temperature and short-circuit current under normal state; the fault data includes the measured values of each characteristic parameter under partial discharge and short-circuit fault state.

[0212] For current and voltage, time domain features such as mean, variance and peak value, as well as frequency domain features such as spectral energy and power spectral density are extracted;

[0213] For temperature, time domain features such as average temperature and temperature change rate are extracted; for short-circuit current, time domain features such as amplitude and phase are extracted. These characteristic quantities are used as the input values of the mixed model of convolutional neural network (CNN) and bidirectional long short-term memory network (BiLSTM), to establish the nonlinear mapping relationship between the characteristic quantities and the fault types. According to the simulation calculation data, combined with the actual power cable partial discharge, temperature, current and voltage measurement data, the early fault of the cable is identified by algorithm.

[0214] More specifically, an early fault identification method based on CNN-BiLSTM is proposed. Convolutional neural network CNN is a deep learning model, mainly composed of data input layer, convolutional layer, excitation layer, pooling layer and full connection layer 5 parts. The convolutional layer is responsible for extracting the features of the input data, which is nonlinearly mapped into the pooling layer through the excitation layer, and the pooling layer further screens these features, and finally the full connection layer is converted into a vector output, and its main structure is shown in Figure 10 The LeNet model commonly used in CNN is selected as the feature extraction model to process the fault signal data. After feature extraction, the obtained data results are transmitted into the CNN-BiLSTM model for fault identification.

[0215] LSTM is a neural network algorithm that can extract complex feature relationships in long and short time series. The structure of LSTM is composed of input gate, output gate and forget gate. Through the control of the "gate", LSTM can update the time state information of the storage unit. The update process is as follows.

[0216] (1) The forget gate determines the information that needs to be forgotten from the storage unit according to time, and the state f t of the forget gate is equal to 1 when all is saved, and equal to 0 when all is forgotten, and the expression is:

[0217] ft = σ(W f h t-1 + U f x t + b f ) (33).

[0218] In formula (33), σ is an activation function; W f is a weight matrix for linear transformation of a previous hidden state h t-1 ; h t-1 is an output at time (t-1); x t is an input at time t; b f is a forget gate bias; U f represents an input x t at the current time and W t is a weight matrix for linear transformation of the input.

[0219] (2) The input gate determines new input information in the storage unit, and the expression is:

[0220] i t = σ(W f h t-1 + U f x t + b i ) (34).

[0221] g t = tanh(W f h t-1 + U f x t + b g ) (35).

[0222] C t = C t-1 f t + i t g t (36).

[0223] In formulas (34) to (36), i t is an input gate state; b i is an input gate bias; g t is a temporary transformation unit state; b g is a temporary transformation unit bias; C t is a storage unit state at time t; and C t-1 is a storage unit state at time (t-1).

[0224] (3) The output gate updates the current state and obtains a final output, and the expression is:

[0225] o t = σ(W f ht-1 +U f x t +b o (37);

[0226] h t =o t tanh(C t (38);

[0227] In the formula: o t b represents the result of the output gate at time t; o The offset of the output gate; σ(i) represents the Sigmoid activation function; h t Let be the load value at time t; tanh(C) t ) indicates the cell state C t Perform hyperbolic tangent activation.

[0228] The limitation of LSTM is that it can only utilize information from the past and present moments, and cannot utilize information from future moments. Long Short-Term Memory (LSTM) networks are a special type of recursive neural network (RNN) that can solve the gradient vanishing or exploding problems that RNNs often encounter when processing long sequences of data, effectively capturing long-term dependencies. Bidirectional Long Short-Term Memory (BiLSTM) networks build upon LSTM by connecting two LSTM units in reverse parallel, forming a bidirectional recurrent structure that combines forward and backward connections. By optimizing the model structure by introducing elements from the time direction, it can further integrate forward and backward information from the current moment and uncover the correlation features of time-series data. This characteristic allows BiLSTM to focus on both forward and backward dependencies in feature extraction. Its network structure is as follows: Figure 10 As shown, it mainly consists of an input layer, a forward layer, a reverse layer, and an output layer. The calculation formula is as follows:

[0229]

[0230] In the formula, x t Input features at time t; y t This is the output vector; The output of the LSTM hidden state of the feedforward layer at time t; t represents the hidden state output of the LSTM inverse layer at time t; w1, w2, ..., w6 are the weights of each layer.

[0231] Step five: For the serious fault of power cable, taking single-phase and three-phase short-circuit fault as an example, according to the simulation model of power cable transmission line, the current of single-phase and three-phase short-circuit fault of the cable is simulated by setting the single-phase position to ground in the model, and the characteristics of the current in the two faults are analyzed. The current characteristics of the fault signal are simulated by different cable lengths, short-circuit types and grounding resistances.

[0232] More specifically, for single-phase and three-phase ground fault, according to the basic theory of circuit, formula

[0233] From KVL:

[0234]

[0235] In the formula: R represents resistance; i k represents the current in the circuit; U m represents the amplitude of the sinusoidal voltage; ω represents the angular frequency of the sinusoidal voltage; t represents time; θ represents the initial phase of the sinusoidal voltage.

[0236] The total current after short-circuit can be represented by the following formula:

[0237]

[0238] In the formula: i z represents the steady-state component of the current; i fi represents the transient component of the current; I PM represents the amplitude of the steady-state sinusoidal current R and X and are the resistance and inductance, respectively; represents an exponential decay function; φ k is the impedance angle of short-circuit after short-circuit, φ k = arctg (X / R); τ is the short-circuit loop time constant, and C is the integral constant, which is determined by the initial condition, i.e. the initial value of the non-periodic component of the short-circuit current.

[0239] When single-phase short-circuit occurs, the single-phase short-circuit current can be calculated by the following formula according to the symmetrical component method:

[0240]

[0241] In the formula, represents the single-phase short-circuit current; represents the phase voltage; R T represents the resistance of the transformer; X T represents the reactance of the transformer; represents the equivalent resistance of the system; represents the equivalent reactance of the system.

[0242] The calculation formula of three-phase ground fault is:

[0243]

[0244] wherein, denotes the three-phase short-circuit current; U C denotes the short-circuit calculation line voltage; R ∑ is the total resistance of the power supply to the short-circuit point; X ∑ is the total reactance of the power supply to the short-circuit point.

[0245] For the simulation model, in the electromagnetic transient calculation program (ATP-EMTP) software, a cable distribution line system is established by using the JMARTI cable model, the power supply is an ideal voltage source, and the voltage is reduced to the cable feeder through a transformer. Two sections of cables are connected to form a power cable with adjustable fault location. The ground resistance in the power cable line simulation is set, the distance from the fault point to the head end is set, the signal sampling rate is 10 MHz, the simulation time is set to 0.04 s, and the fault time is set to 0.02 s. The currents of single-phase short-circuit and three-phase short-circuit of the cable are obtained by simulation, and the characteristics of the currents in the two faults are analyzed, including the root mean square of the three-phase currents at the beginning and end of the cable. The current characteristics of the fault signal are obtained by simulation of different cable lengths, short-circuit types and ground resistances.

[0246] According to the basic theory of circuit, when a single-phase short-circuit fault occurs, the amplitude and phase of the fault phase current change abruptly, and the non-fault phase has a slight fluctuation due to electromagnetic induction at the fault moment, and returns to normal operation after the fault. When the amplitude of the current of a certain phase changes abruptly, the phase can be identified as the fault phase. When a three-phase short-circuit fault occurs, the amplitude and phase of the fault phase current change abruptly at the moment of short-circuit fault, and the three-phase short-circuit fault current changes most severely, with the largest change in current amplitude. When all three-phase currents change, it can be determined that the cable has a three-phase short-circuit fault.

[0247] Step six, according to the actual cable line, measure the current and voltage of each phase of the cable, take the current and voltage size and change rate as the input value of the neural network, and establish the nonlinear mapping relationship between the fault current and voltage and the fault type. According to the simulation calculation data above, the test sample data is divided into training set and test set according to the proportion of 70% and 30%, combined with the actual power cable current and voltage measurement data, the cable fault type is identified by artificial intelligence algorithm.

[0248] More specifically, for the recognition of cable fault type, a cable fault recognition method based on CNN-BiLSTM is proposed, and the specific steps are as follows:

[0249] First, the fault current of the cable monitoring points M and N is obtained, the root mean square of the current after the fault is taken as the characteristic value, which is input into the CNN-BiLSTM model, and the optimal solution is obtained through the training of the artificial intelligence algorithm. The algorithm identification obtains the cable fault type. In order to consider the fault type under different conditions, the CNN-BiLSTM model is used to identify the different fault types of the cable.

Claims

1. A power cable partial discharge fault diagnosis method based on multi-feature fusion, characterized by The method comprises the following steps: Step a1: for power cable partial discharge defects, according to the actual structure parameters of power cable and the characteristics of partial discharge signal, a power cable partial discharge simulation model is established; Step a2: according to the power cable partial discharge simulation model, the propagation characteristics of the partial discharge signal under different cable lengths are obtained, and the partial discharge signal is obtained; Step a3: the synchronous extrusion wavelet transform SSWT based on frequency spectrum clustering K-Medoids is used for partial discharge denoising; Step a4: the CNN-BiLSTM model is used for power cable partial discharge identification.

2. The method according to claim 1, characterized in that: In step a1, the power cable partial discharge simulation model is as follows: An equivalent model of air gap defect inside cross-linked polyethylene insulation is established, and the equivalent model of air gap defect inside cross-linked polyethylene insulation adopts a three-capacitance equivalent circuit: C1 is the equivalent capacitance of normal XLPE insulation medium, C2 is the equivalent capacitance of insulation medium in series with air gap defect, and C3 is the equivalent capacitance of insulation where the air gap is located; Power supply voltage u = U m sin ωt acting medium, air gap voltage: In formula (1): u3 is the voltage divided by the air gap, U m is the power supply voltage amplitude, ω is the angular frequency, and t is time. The partial discharge simulation model adopts a double exponential decay model: In formula (2), S(t) represents a partial discharge voltage signal; A represents a signal amplitude; τ1 and τ2 represent time attenuation coefficients of the signal; and represents a typical exponential decay function, which gradually approaches 0 as t increases.

3. The method according to claim 1, characterized in that: In step a2, the propagation characteristics of the partial discharge signal under different cable lengths are obtained, and the partial discharge signal is obtained; From the signal propagation equation U0= U i e -yl , the input and output voltage relationship of the signal is: In formula (3): U0 is the voltage at the output end of the transmission line; U i is the voltage at the input end of the transmission line; γ is the propagation constant, containing the attenuation and phase change information of the signal; α is the attenuation constant, representing the attenuation degree of the signal per unit length; β is the phase constant, representing the phase change of the signal per unit length; e -jβl does not change the size of U0, only changes the phase of U0, reflecting the phase relationship between the output voltage U0 and the input voltage U i ​ The relationship between the input voltage and the output voltage of the partial discharge signal in the transmission line is U0=U i e -αl ·e -jβl , which takes into account the attenuation and phase change of the signal in the transmission process; U0 is the output voltage; U i is the input voltage; and a is an attenuation constant, representing the attenuation degree of the signal per unit length. β is a phase constant, representing the phase change of the signal per unit length; l is the distance travelled by the signal in the transmission line, e -jβl reflects the phase relationship of the output voltage U0 and the input voltage U i .

4. The method according to claim 1, characterized in that: The step a3 comprises: Fourier transform is performed on the partial discharge, and the specific steps are as follows: In formula (4), I[n] represents a frequency domain output; i[k] represents a time domain input signal; and N represents a total number of sampling points of the signal. represents a complex exponential base function, controls frequency resolution; and n and k represent indexes of the frequency domain and the time domain, respectively. The frequency spectrum of the partial discharge signal is classified by using the K-Medoids algorithm, and the local maximum and minimum value method is used to divide the signal frequency spectrum; the specific steps are as follows: The frequency spectrum data S(f) of the partial discharge signal is obtained by Fourier transform, wherein f is the frequency, and S(f) is the amplitude corresponding to the frequency; the frequency spectrum is smoothed by using the moving average method to obtain the preprocessed frequency spectrum S'(f); the moving average method smoothes the signal by calculating the average value of the data in a certain window around a certain point, and the formula is as follows: In formula (5): S(f i ) is the amplitude of the original spectrum at frequency point f i ; S'(f i ) is the smoothed value; 2N+1 is the size of the sliding window; k is the offset index within the window; S(f i+k ) represents the value of the original signal S at frequency point f i+k . The local maximum and minimum value method divides the continuous frequency spectrum into several characteristic intervals by identifying the maximum and minimum values in the frequency spectrum, and each interval corresponds to a characteristic frequency band of partial discharge; Local maxima identification: for frequency point f i If the following condition is met: S'(f) i )>S'(f i-1 And S'(f) i )>S'(f i+1 ), S'(f i ) represents the smoothed value; S'(f i-1 ) represents the frequency point f i The previous adjacent frequency point f i-1 Processed signal value; S'(f i+1 ) represents the frequency point f i The next adjacent frequency point f i+1 The processed signal value; then f i For a local maximum point, the corresponding amplitude S'(f) i () represents the peak value; Local minimum identification: for frequency point f j , if the following conditions are satisfied: S'(f j )<S'(f j-1 ) and S'(f j )<S'(f j+1 ), then f j is a local minimum point, and the corresponding amplitude S'(f j ) is a valley value; By dividing the spectrum interval, taking the adjacent two minima f j1 and f j2 as boundaries, j1<j2; the interval [f j1 , f j2 ] containing one or more peaks in the middle is taken as a characteristic sub-spectrum, denoted as S k (f), k=1, 2,..., m, m is the number of divided intervals; K-Medoids uses the similarity between samples and cluster centers to measure the distance: In formula (6): d(x i ,m j ) represents the Manhattan distance between sample x i and cluster center m j ; x i = [x i,1 , x i,2 , …, x i,d ] is a feature vector of the i-th sample; m j = [m j,1 , m j,2 , …, m j,d ] is a center sample of the j-th cluster; t is a feature index; x i,t represents the value of sample x i in the t-th feature dimension; m j,t represents the value of cluster center m j in the t-th feature dimension; a represents the number of feature dimensions; The sample assignment rule assigns each sample to the cluster where the nearest medoid is located: In formula (7), C j represents the jth cluster, j = 1, 2, …, K, K is a preset cluster number; x i represents a sample to be classified; d(x i ,x j ) represents a distance between the sample x i and the jth cluster center; d(x i ,x k ) represents a distance between the sample x i and the kth cluster corresponding reference point; The clustering objective function is generated, and optimization is realized by minimizing the total clustering cost, and the cost is defined as the sum of the distances from all samples to the medoids of their own clusters: In formula (8), Total Cost represents the total cost of clustering, K represents the number of clusters, j represents the index of the cluster, j=1, 2, …, K, and is used to traverse each cluster; Medoid update formula, for each cluster C j , iterate over all samples x in C, compute the intra-cluster cost with x as temporary medoid: In formula (9), Cost(x) represents the cost caused by the distance between the samples in the cluster and the reference point; d(x,x') represents the distance measure between sample x and sample x'; The sample with the minimum cost is selected as the new medoid: In formula (10): m' j denotes the center of the updated jthcluster, argmin denotes finding the value of the argument x that makes the following function take its minimum value; The algorithm stops iterating when one of the following conditions is met: ①. The new medoid is identical to the old medoid or the distance is less than a preset threshold represents a distance function of the jth element pair, measuring the difference between m j and m j ; ii. The change in the total clustering cost is less than a threshold: |Total Cost new - Total Cost old | < ε, Total Cost new denotes the new total cost; Total Cost old denotes the old total cost; ③. Reach the maximum number of iterations.

5. The method according to claim 4, characterized in that: Adaptive filtering is performed on the frequency segments by using synchronous extrusion wavelet transform to obtain modal components; The synchronous extrusion wavelet transform SWT realizes adaptive filtering and extracts modal components of the partial discharge signal; Continuous wavelet transform is performed on the signal x(t) to obtain time-frequency coefficients: In formula (11): W x (a, b) represents the coefficients of the signal x(t) after continuous wavelet transform; ψ(t) is the mother wavelet, ψ * is its complex conjugate; a is the scale parameter, which is inversely proportional to the frequency; b is the translation parameter; x(t) is the original signal to be analyzed; t is the time; The continuous wavelet transform decomposes the signal into components of different scales, rearranges the CWT coefficients, calculates the instantaneous frequency and maps the coefficients to the corresponding frequency axis; for each time-frequency point (a, b), the instantaneous frequency is estimated by the phase derivative of the wavelet coefficient: In formula (12): ω x (a, b) represents the instantaneous frequency of the signal x(t) after continuous wavelet transform at scale a and translation b; represents the partial derivative with respect to the translation factor b; represents the frequency conversion factor; arg{•} represents the phase of the complex coefficient; The original scale-time domain coefficients W x (a,b) are mapped to the frequency-time domain T x (ω,b): In formula (13): C ψ is a wavelet normalization constant; δ is a frequency resolution threshold, controlling the squeezing precision; is the weighted wavelet coefficient, a 3 / 2 is the scale weighting of the wavelet transform coefficient; the summation only retains the coefficients with instantaneous frequencies close to the target frequency ω, realizing time-frequency concentration; The high-resolution time-frequency distribution T obtained by using the synchronous extrusion wavelet transform SWT x (ω, b), which can divide the frequency interval Ω of interest in the time-frequency domain according to the spectral characteristics of the partial discharge signal k = [ω k1 , ω k2 ], k = 1, 2, …, K, K represents the total number of divided frequency intervals Adaptive filtering is performed on each frequency interval to retain the time-frequency coefficients within the interval and filter out noise and interference outside the interval: In formula (14): T x,k (ω, b) represents the time-frequency of the kth feature mode of the signal x; The filtered time-frequency coefficients T x,k The kth modal component x k (t) is reconstructed by inverse synchrosqueezing transform of In formula (15): x k (t) represents the reconstructed signal output; ω k1 represents the starting frequency of the interval; ω k2 represents the ending frequency of the interval; T x,k (ω, b) is the time-frequency representation of the kth characteristic mode of the signal x; is a wavelet base function; a(ω) is a frequency-scale conversion relationship determined by the center frequency ω0 of the mother wavelet, a = ω0 / ω; finally, the original signal can be decomposed into the sum of multiple modal components: where ∈(t) is the residual noise.

6. The method according to claim 5, wherein the method further comprises: Use high-order statistics, i.e. kurtosis criterion, to select useful modal components, and use 3σ criterion to threshold the useful modal components; The kurtosis value K is defined by the formula: In formula (16): K i denotes the kurtosis value; x i denotes the i-th modal component sequence, μ i , σ i denote the mean and standard deviation of the i-th modal component sequence, respectively, and E denotes the expectation of the signal; When the modal component contains only white noise, since its amplitude follows a normal distribution, the distribution curve has a normal kurtosis, and the kurtosis value is 3; when the modal component contains non-Gaussian partial discharge signals, since the impact component content increases, the pulse amplitude significantly deviates from the normal distribution, and the kurtosis value significantly increases, thereby selecting useful modal components.

7. The method according to claim 6, characterized in that: The de-noising effect is judged according to the evaluation index, and the evaluation index is signal-to-noise ratio, root mean square error and waveform similarity coefficient; Among them: signal-to-noise ratio: In Equation (17), s(n) represents the original signal. represents the reconstructed signal; N represents the total number of sampling points of the signal; and n represents the calculation of the nth sampling point of the signal sequence. Root mean square error: Waveform similarity coefficient: The larger the signal-to-noise ratio, the smaller the noise content in the partial discharge signal; the closer the root mean square is to 1, the higher the similarity between the de-noised signal and the original signal; the smaller the waveform similarity coefficient, the smaller the waveform distortion rate of the de-noised signal.

8. A power cable early fault diagnosis method based on multi-feature fusion, characterized in that Comprising the following steps: Step b1: for early fault of power cable, according to actual structure parameters of power cable, 10kV power cable temperature field simulation model is established; Step b2: analyze cable body heat loss and heat transfer, heat loss includes core heat loss and cable insulation interface loss, heat transfer includes heat conduction, heat convection and heat radiation; Step b3: according to 10kV power cable temperature field simulation model, analyze power cable body transient temperature distribution result, consider power cable body temperature distribution under different defects, measure temperature change rate and temperature peak value; Step b4: early fault identification of power cable is carried out based on CNN-BiLSTM model.

9. The method according to claim 8, characterized in that: In the step b2, (1) cable body heat loss: 1) core heat loss: The heat loss generated by the core conductor is the main source of heat in the cable body. It causes the cable temperature to rise through the joule heat generated by the thermoelectric effect. The calculation expression of joule heat is: Q c = I 2 R (20); In formula (20): Q c represents the cable core conductor heat loss; I represents the effective value of the alternating current flowing through the core conductor; R represents the alternating resistance value; 2) cable insulation interface loss: In addition to the core, the insulation loss of each medium layer in the cable is generated under the action of strong electric field. Its expression is: W d = 2πfCU c tan δ (21); In formula (21): W d represents the dielectric loss generated by the medium layer; f represents the frequency of the 50 Hz voltage; C represents the dielectric capacity; U c represents the cable operating voltage; tanδ represents the loss factor of the cable insulation medium, and δ is the dielectric loss angle; (2) heat transfer: 1) heat conduction is caused by the thermal motion of micro-particles in the cable medium. The mathematical expression of conduction is: In formula (22), q represents heat flux, Φ represents the total heat flowing through unit area S, K represents thermal conductivity, T represents temperature, and n represents the normal direction of heat conduction. It can be seen from formula (22) that the heat flux is proportional to the temperature gradient; 2) heat convection and heat radiation are both ways of heat transfer. Their expressions are: In formula (23): q c is the heat convection; q r is the heat radiation; h represents the natural convection heat transfer coefficient; σ0represents the Stefan-Boltzmann constant; Δt represents the temperature difference between the solid surface and the fluid; and ΔT represents the absolute temperature difference between the object surface and the environment.

10. The method according to claim 9, characterized in that: In the step b3, the power cable body transient temperature distribution result is analyzed, The temperature distribution of the power cable body under different defects is considered, and the temperature change rate and the temperature peak value are measured. From the simulation results of the cable body temperature field, when the conductor contact is poor, an abnormally high temperature core will appear at the corresponding core line position, which is brighter and larger than the normal core line red area. In terms of temperature change rate, due to rapid heat accumulation, the temperature rising slope in the transient stage is much larger than that of the normal core line. When the insulation layer is locally deteriorated, temperature abnormal patches appear in the corresponding area of the insulation layer. In terms of temperature peak value, the temperature at the center of the patch is higher than that in the normal insulation area. Due to the influence of thermal resistance, heat transfer is blocked, and the temperature rises slowly at first and then quickly in the transient state, which is different from the smooth temperature change rate of the normal insulation area.

11. A power cable short-circuit fault diagnosis method based on multi-feature fusion, characterized by The method comprises the following steps: Step c1: for power cable short circuit fault, taking single-phase and three-phase short circuit fault as an example, a power cable transmission line simulation model is established; Step c2: by setting the single-phase position to ground in the power cable transmission line simulation model, the current of single-phase short circuit and three-phase short circuit of the cable is simulated; Step c3: analyze the characteristics of the current in the two faults in step c2, and simulate the current characteristics of the fault signal by different cable lengths, short circuit types and grounding resistances; Step c4: based on the CNN-BiLSTM model, the power cable short circuit fault is identified.

12. The method according to claim 11, wherein the method further comprises: In step c1, for single-phase and three-phase short circuit fault, a power cable transmission line simulation model is established; the power cable transmission line simulation model can be equivalent to a distributed parameter model, which considers the resistance R, inductance L, conductance G and capacitance C along the cable; these parameters are uniformly distributed along the cable length; when the wavelength λ of the pulse signal is short and the length l of the cable line is long, the signal will experience multiple wavelengths when propagating in the cable.

13. The method according to claim 11, wherein the method further comprises: In step c2, When single-phase short circuit occurs, the single-phase short circuit current can be calculated according to the symmetrical component method as follows: In formula (24): denotes the single-phase short-circuit current; denotes the phase voltage; R T denotes the resistance of the transformer; X T denotes the reactance of the transformer; denotes the system equivalent resistance; denotes the system equivalent reactance; The three-phase short circuit fault calculation formula is: In formula (25): denotes the three-phase short-circuit current; U C denotes the short-circuit calculation line voltage; R ∑ is the total resistance of the power supply to the short-circuit point; X ∑ is the total reactance of the power supply to the short-circuit point.

14. The method according to claim 11, wherein the method is characterized by: In step c3, analyze the characteristics of the current in the two faults in step c2, and simulate the current characteristics of the fault signal by different cable lengths, short circuit types and grounding resistances; The cable length will affect the amplitude and waveform of the fault current, and the resistance and inductance of the cable will increase with the increase of the length; The short circuit type affects the symmetry and amplitude of the fault current; for three-phase short circuit, the amplitude of the fault current is usually the largest, and for single-phase ground short circuit, the amplitude of the fault current is usually the smallest; the grounding resistance will directly affect the size of the grounding fault current; The greater the grounding resistance, the smaller the fault current.

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