Identification and positioning method for defects and short-circuit faults of power cable

Abstract

The invention discloses an identification and positioning method for power cable defects and short-circuit faults. The defect identification and positioning method comprises the following steps: establishing a power cable transmission line simulation model and a partial discharge simulation model by using electromagnetic transient simulation software; obtaining a partial discharge signal according to the power cable transmission line simulation model and the partial discharge simulation model, and identifying the partial discharge signal based on an SSA-BP algorithm; performing preliminary positioning on the power cable by adopting an ultrasonic, high-frequency and ultrahigh-frequency detection method; accurate positioning of power cable defects is realized through an infrared heat and sound wave positioning principle. According to the method, a simulation analysis method is adopted to obtain a sample, and then accurate identification of a cable fault is realized through a BP neural network (SSA-BP) optimized based on a sparrow search algorithm. And meanwhile, accurate cable fault positioning is realized aiming at different fault positions.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of cable fault detection, in particular to a method for identifying and positioning defects and short-circuit faults of power cables. BACKGROUND

[0002] With the rapid development of underground cables, the number of underground pipelines is becoming larger and larger, and the space is becoming more and more crowded, and all parties such as construction, operation and management will face great difficulties and pressure, especially the operation and maintenance need to carry out continuous insulation monitoring during normal power consumption, and the breakdown caused by cable insulation decline will cause line power failure, and in serious cases, it will cause system paralysis and heavy economic losses. The insulation state of the cable is closely related to the partial discharge of the cable, and the operation experience and data of State Grid show that the insulation performance of power equipment in China is mainly due to partial discharge, and partial discharge detection is of great significance to evaluate the degree of cable insulation deterioration. Since the cable fault position is mainly concentrated in the intermediate joint and the terminal, and most of the cables are deeply buried underground, the maintenance personnel will encounter the problems of heavy workload and low efficiency when detecting the cable. How to improve the cable operation efficiency from the detection means is the current problem to be solved, and reasonable and efficient solution to such problems needs to be adjusted and optimized from the detection means. At present, the on-line positioning technology of partial discharge of the cable still relies on the traditional time delay estimation positioning method, and the positioning accuracy is low under low signal-to-noise ratio, and the frequency characteristics of the partial discharge pulse wave speed are not considered when the partial discharge source position is estimated according to the time delay, which increases the positioning error. In addition, the complexity of the cable operation environment increases the uncertainty of the on-line positioning result. SUMMARY

[0003] To solve the above technical problems, the present application provides a method for identifying and positioning defects and short-circuit faults of power cables, which uses simulation analysis method to obtain samples, and then realizes accurate identification of cable faults through BP neural network (SSA-BP) based on sparrow search algorithm optimization; and realizes accurate positioning of cable faults for different fault positions.

[0004] The technical scheme adopted by the present application is as follows:

[0005] A method for identifying and positioning defects of power cables, comprising the following steps:

[0006] Step 1: using electromagnetic transient simulation software to establish a power cable transmission line simulation model and a partial discharge simulation model;

[0007] Step 2: obtaining a partial discharge signal according to the power cable transmission line simulation model and the partial discharge simulation model, and identifying the partial discharge signal based on the SSA-BP algorithm;

[0008] Step 3: Preliminary positioning of the power cable is performed using ultrasonic, high frequency and ultra-high frequency detection methods; precise positioning of the power cable defects is achieved through infrared thermal and acoustic positioning principles.

[0009] In step 1, the power cable model includes a core conductor, a cross-linked polyethylene (XLPE) insulation layer, a shielding layer, an inner protective layer, an armored layer, and an outer protective layer, as shown in Figure 9 The core conductor material is usually copper or aluminum alloy, and its main function is to carry current; the insulation layer serves as an electrical insulator to prevent current leakage or short circuits with other parts, while protecting the core from external environmental influences; the shielding layer suppresses the electromagnetic field generated during cable operation from interfering with the outside world, while preventing external electromagnetic interference from affecting current transmission within the cable. The main functions of the inner and outer protective layers are to protect the insulation layer and seal against moisture. The armored layer mainly provides mechanical support and grounding protection.

[0010] Because the wavelength of the pulse signal is short during cable propagation, and the cable line size is long, the cable distributed parameter model can be equivalent to a uniform transmission line model; because the resistance, inductance, capacitance, and conductance of the cable are uniformly distributed along the length of the cable, they can be represented by unit length parameters, so that the relationship between the voltage and current of the cable can be described by a differential equation. 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 length of the cable, so the parameters per unit length are R', L', G', and C', respectively. 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 during propagation 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. In the uniform transmission line model, it is assumed that the distributed parameters R', L', G', and C' of the cable are uniformly distributed along the entire length of the cable. This model is suitable for long cables and high-frequency signals. The characteristic impedance Z0 is an important parameter of the uniform transmission line, which represents the ratio of voltage to current without reflection on the transmission line. Its calculation formula is:

[0011]

[0012] In equation (1), R' is the resistance per unit length, L' is the inductance per unit length, G' is the conductance per unit length, C' is the capacitance per unit length, and ω is the angular frequency.

[0013] In high-frequency situations, R' and G' can usually be ignored because they are small relative to ωL' and ωC'. Therefore, the characteristic impedance can be simplified as:

[0014]

[0015] In summary, when the wavelength of the pulse signal is short, the size of the cable line is long, and the distributed parameters of the cable are uniformly distributed in length, the distributed parameter model of the cable can be equivalent to the uniform transmission line model. The signal experiences multiple wavelengths when propagating in the cable, and the influence of the distributed parameters of the cable on the signal needs to be described by the distributed parameter model. The uniform transmission line model can accurately describe the propagation characteristics of the signal in the cable through parameters such as characteristic impedance Z0 and propagation constant γ.

[0016] The power cable model and the power cable transmission line are the same, and both the power cable model and the power cable transmission line simulation model can be equivalent to the cable distributed parameter model.

[0017] The power cable transmission line simulation model includes: line distributed resistance, line distributed inductance, line distributed conductance and line distributed capacitance;

[0018] The voltage and current of the cable line are calculated as follows:

[0019]

[0020] In formula (3), 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, and z represents the characteristic impedance. X represents the spatial position coordinate along the transmission line.

[0021] According to the signal propagation formula U0=U i e -γl , where U0 is the output voltage of the transmission line, U i is the input voltage of the transmission line, e -γl is the attenuation factor, which describes the amplitude change after the signal propagates a distance l; and l is the length of the transmission line.

[0022] The signal propagation formula can describe the attenuation model of the signal propagating in the transmission line or the cable;

[0023] The relationship between the input and output voltages of the signal is:

[0024]

[0025] In formula (4), 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 attenuation and phase change information of the signal, 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, and e -jβlWithout changing the size of U0, only changing the phase of U0, it reflects the phase relationship between the output voltage U0 and the input voltage U i .

[0026] The above formula describes the relationship between the input voltage and the output voltage of the signal in the transmission line, considering the attenuation and phase change of the signal in the transmission process.

[0027] Cable partial discharge includes: internal discharge, surface discharge, corona discharge and suspension discharge;

[0028] 1) Air gap defect is the main reason for internal discharge of cable; The equivalent model of air gap defect inside cross-linked polyethylene insulation is established, and the equivalent circuit of the equivalent model of air gap defect inside cross-linked polyethylene insulation adopts three capacitance method, including: 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 air gap is located;

[0029] Power supply voltage u = U m sinωt acting medium, air gap voltage:

[0030]

[0031] In formula (5), u3 is the voltage of air gap, U m is the amplitude of power supply voltage, ω is the angular frequency, and t is the time.

[0032] The partial discharge simulation model adopts double exponential decay model:

[0033]

[0034] In formula (6), S(t) represents the partial discharge voltage signal; A represents the signal amplitude; t is the time; τ1 and τ2 represent the time attenuation coefficients of the signal.

[0035] 2) Regarding surface discharge, surface discharge usually occurs on the surface of insulating materials, and when the electric field strength exceeds the dielectric strength of the material, the surface may discharge. This phenomenon may be related to the unevenness of the material surface, such as impurities or defects on the surface. Surface discharge may cause gradual damage to the insulating material, which may eventually lead to insulation breakdown.

[0036] 3) Regarding corona discharge, corona discharge is a common discharge phenomenon, which usually occurs at the sharp edges of conductors or areas with small curvature radius. The generation of corona discharge is closely related to the electric field strength and the geometry of the electrode. The electric field strength is inversely proportional to the curvature radius of the conductor surface, and the formula is:

[0037]

[0038] In formula (7), Q is the charge amount of a point charge; ε0 is the vacuum dielectric constant, with a value of about 8.852 x 10 -12 F / m; and r is the radius of curvature of the electrode.

[0039] The starting field strength of corona discharge is generally calculated using an empirical formula, and the Piche formula is usually used for calculation. For engineering scenarios such as power transmission lines, the influence of conductor surface roughness, air humidity, etc. is considered, and the standard form is generally:

[0040]

[0041] In formula (8), E c is the corona starting field strength (unit: kV / cm); r is the conductor radius (unit: cm); and δ is the relative density of air.

[0042] 4) Regarding suspended discharge: Suspended discharge refers to the discharge phenomenon of a suspended conductor in insulating oil or other media under the action of an electric field. This phenomenon may be related to the potential distribution of the suspended conductor and the electric field strength of the surrounding medium. Suspended discharge can cause local damage to the medium and affect the insulation performance.

[0043] The step 2 includes the following steps:

[0044] Step 2.1: Based on the propagation characteristics of partial discharge signals under different cable lengths, the partial discharge signals are obtained according to the power cable transmission line simulation model and the partial discharge simulation model.

[0045] 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, representing the attenuation of the signal per unit length; β is the phase constant, representing the phase change of the signal per unit length; l is the distance of signal propagation in the transmission line, e -jβl reflects the relationship between the output voltage U0 and the input voltage U iThe phase relationship of the signals is considered. The effect of cable length on partial discharge signals is considered, as the cable length increases, the signals will experience more attenuation. The attenuation constant a is related to the material properties of the cable, environmental conditions, and other factors. 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. The longer the cable, the later the signal arrives at the receiving end, which may affect the timing analysis of the signal. 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.

[0046] Step 2.2: Considering the interference of the signal, denoising the partial discharge signal using empirical wavelet transform;

[0047] Empirical Wavelet Transform (EWT) is an adaptive wavelet transform method that decomposes a signal into different scale detail coefficients and approximation coefficients by iteratively decomposing and reconstructing the signal. This method is particularly suitable for the analysis of non-stationary signals, and partial discharge signals usually contain complex transient characteristics and noise, so empirical wavelet transform is used to denoise partial discharge signals.

[0048] The basic steps of empirical wavelet transform are:

[0049] Step 1: Initialization: Select a wavelet function and the number of decomposition levels;

[0050] Step 2: Decomposition: Decompose the original signal using wavelet decomposition to obtain detail coefficients and approximation coefficients at different scales;

[0051] Step 3: Threshold processing: Apply threshold processing to the detail coefficients to remove noise;

[0052] Step 4: Reconstruction: Reconstruct the signal using the processed detail coefficients and unchanged approximation coefficients;

[0053] Step 5: Iteration: Repeat steps Step 2 to Step 4 until the predetermined number of decomposition levels is reached or other stopping conditions are met.

[0054] Empirical wavelet transform can be represented by the following formula:

[0055]

[0056] In equation (9), d j is the detail coefficient of the jth layer; s jis the approximation coefficient of the jth layer; DWT denotes wavelet decomposition; IDWT denotes wavelet reconstruction.

[0057] The threshold processing can be represented as:

[0058] d' j = threshold(d j , λ) (10).

[0059] In formula (10): threshold() is threshold processing; d' j is the detail coefficient after threshold processing; λ is the threshold, which can be adaptively selected according to the characteristics of the signal and the noise level.

[0060] First, the partial discharge signal is subjected to empirical wavelet transform to obtain detail coefficients and approximation coefficients of different scales. A suitable threshold is selected according to the noise level and signal characteristics. The selection of the threshold is crucial to the denoising effect. An excessively large threshold may cause signal distortion, and an excessively small threshold may not effectively remove noise. The threshold processing is applied to the detail coefficients to remove the noise components. The processed detail coefficients and approximation coefficients are used to reconstruct the signal to obtain the denoised partial discharge signal.

[0061] Step 2.3: Based on the generative adversarial network (GAN), a data augmentation method is proposed to expand the original training sample set by synthesizing partial discharge signals;

[0062] The generative adversarial network (GAN) includes two key components: the generator G and the discriminator D. The goal of the generator G is to generate realistic data samples from random noise, while the goal of the discriminator D is to distinguish between real samples and samples generated by the generator. Both compete with each other in the training process, with the generator G constantly learning how to generate more realistic samples, while the discriminator D learns how to more accurately identify real and generated samples. The mathematical model of the generative adversarial network can be represented as:

[0063]

[0064] In formula (11): V(G, D) is the adversarial loss function, which measures the performance of the generator and the discriminator; x ~ p data (x) represents the expectation of the real data distribution; z ~ p z (z) represents the expectation of the noise distribution input to the generator; D(x) is the output of the discriminator for the real sample x; G(z) is the sample generated by the generator from the noise z.

[0065] Data enhancement process: The collected partial discharge data is preprocessed, including denoising, normalization, etc., to obtain real sample data. The real sample after preprocessing is used to train the generative adversarial network. The generator G learns to generate partial discharge signals from random noise, and the discriminator D learns to distinguish real signals and generated signals; after training, the generator G is used to synthesize new partial discharge signal samples. The synthesized samples are combined with the original training sample set to form an expanded training sample set.

[0066] The learning mechanism of the generative adversarial network GAN is as follows:

[0067] Assume that the noise z ~ N(0, 1), and m noise samples {z z ,z (1) ,z (2) ,...,z (m)} are randomly extracted from the noise prior distribution p data (x);m real samples {x (1) ,x (2) ,...,x (m)} are randomly extracted from the data generation distribution p z (x) of the small batch sample; in the training process of the 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, so the optimization problem of the generator G is as shown in the formula.

[0068]

[0069] In formula (12): represents the minimum value of the adversarial value function of the discriminator and the generator in the GAN; z ~ p z (z) represents taking the expectation of the random noise z, covering all possible noise inputs of the generator.

[0070] Update G by improving the gradient of the generator G:

[0071]

[0072] In formula (13): D(·) represents the true or false judgment of the input data by the discriminator, and the output is a probability between 0 and 1, 1 represents true data, and 0 represents false data; G(z (i) ) represents that the generator G receives random noise z (i) , and outputs fake data; θ g represents the parameters of the generator.

[0073] The optimization result of the discriminator D is D(x) = 1 and D(G(z)) = 0, so the optimization problem of the discriminator D is as shown in the formula:

[0074]

[0075] In formula (14): x~p data (x) represents taking expectation on real data x, covering all possible samples of real data; p data (x) represents the probability distribution of real data.

[0076] Similarly, according to the gradient update of promotion, the generator D is generated:

[0077]

[0078] Therefore, combined with formula (12) and formula (14), the optimization problem of GAN can be regarded as a maximum-minimum problem:

[0079]

[0080] For any And y∈[0,1], consider the following equation:

[0081]

[0082] In formula (17): α and β represent positive coefficients, are sample quantity weights, represent weighted cross-entropy loss; y represents the probability value of model output.

[0083] Therefore, given the generator G, the minimum value of the objective function formula (14) is:

[0084]

[0085] In formula (18): represents the theoretical best output that the discriminator D can achieve when the generator G is fixed; p g (x) represents the probability distribution of the data generated 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 synthesized data, and the discriminator cannot determine the ownership of the input data, the training stops; at this time, D(x) = 0.5, p data = p g , which means that the discriminator randomly outputs the prediction result, and substituting it into formula (14) gives

[0086] 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.

[0087] Step 2.4: Analyze the influence of the capacity ratio of generated samples to original training samples on pattern recognition accuracy, recognize the partial discharge signal based on the SSA-BP algorithm, as follows:

[0088] Overfitting and underfitting are common problems in machine learning, which are closely related to the number and diversity of training samples. Overfitting occurs when a model performs well on training data but poorly on new data. This is usually because the model is too complex and can remember the noise in the training data. Underfitting occurs when a model performs poorly on both training data and new data. This is usually because the model is too simple and cannot capture the complex patterns in the data. Sample size has a direct impact on the generalization ability of the model. When the sample size is insufficient, the model may not be able to fully learn the characteristics of the data, affecting the recognition accuracy. When the sample size is too large, the model may overfit, especially when the data noise is high.

[0089] In the application of recognizing partial discharge signals based on the SSA-BP algorithm, the capacity ratio of generated samples to original training samples needs to be continuously adjusted. Data augmentation techniques can be used to increase the diversity of training data, thereby improving the generalization ability of the model.

[0090] A BP neural network consists of an input layer, a hidden layer, and an output layer. The expression of the forward propagation process of the BP neural network algorithm is

[0091]

[0092] where z j is the value of the jth element of the hidden layer; f[·] is the activation function; w ij is the weight value from the ith element of the input layer to the jth element of the hidden layer; x i is the value of the ith element of the input layer; b ij is the threshold value from the ith element of the input layer to the jth element of the hidden layer; y p is the value of the pth element of the output layer; w jp is the weight value from the jth element of the hidden layer to the pth element of the output layer; b jp is the threshold value from the jth element of the input layer to the pth element of the hidden layer; n represents the number of input layers; q represents the number of hidden layers; t represents the number of output layers.

[0093] The output layer compares the calculated result with the expected result. If the output error exceeds the specified range, feedback is given to each layer, and the weights and thresholds between layers are adjusted using a nonlinear optimization algorithm until the output result meets the expected value.

[0094] SSA is a swarm intelligence-based optimization algorithm that simulates the foraging behavior of sparrows. Its core idea is to achieve a balance between global search and local search through the division of roles among discoverers, followers, and guards;

[0095] The discoverer position update strategy is as follows:

[0096]

[0097] In formula (21): t is the number of iterations; is the position of the ith sparrow at t+1 iteration; is the position of the ith sparrow at t iteration; R2 is the warning value; ST is the safety value; α is a random number between 0 and 1; Q is a random number following a normal distribution; L is a column vector with all elements being 1.

[0098] Position update formula of the alarm:

[0099]

[0100] In formula (22): γ is the step control parameter; f i is the fitness value of the current warning; f b , f w are the current optimal and worst fitness values, respectively; η is a random number between -1 and 1; ε is a constant not equal to 0; is the global optimal position of the current sparrow; is the position of the ith sparrow at t iteration; is the global worst position of the current sparrow.

[0101] The BP-SSA algorithm optimizes the initial weights and biases of the BP neural network through SSA to improve the convergence speed and recognition accuracy of the network.

[0102] The specific operations of the BP-SSA algorithm for recognizing partial discharge signals are as follows:

[0103] Initialization: Randomly generate the initial weights and biases of the BP neural network, and use them as the initial population of SSA.

[0104] Fitness function: Usually use classification accuracy or mean square error as the fitness function to evaluate the performance of the BP neural network.

[0105] Optimization process: Through the behaviors of the discoverer, follower and alarm of SSA, the weights and biases of the BP neural network are constantly adjusted to optimize the fitness function.

[0106] Train the BP neural network: Initialize the BP neural network with the optimized weights and biases, and then train it using partial discharge signal data.

[0107] Signal recognition: Input the partial discharge signal to be recognized into the trained BP neural network, and judge the type of the signal through the output of the network.

[0108] The step 3, in the preliminary detection, the cable is preliminarily positioned by using ultrasonic wave, high frequency and ultrahigh frequency detection methods, and the specific steps are as follows:

[0109] The preliminary detection includes that the surface discharge is found by ultrasonic wave partial discharge detection, the internal discharge of the insulation is found by ultrahigh frequency partial discharge detection and high frequency partial discharge detection. The cable is detected in multiple directions by the way of preliminary detection and detailed detection.

[0110] The accurate positioning of the power cable defect is realized by the infrared thermal and acoustic wave positioning principle, and the specific steps are as follows:

[0111] The fine detection includes that the approximate direction is judged by the ultrasonic wave partial discharge data, and the accurate positioning is realized by using the acoustic wave positioning principle and the infrared thermal imager. The principle of acoustic wave positioning method is that the frequency of acoustic wave positioning collection is wider than that of ultrasonic wave, environmental noise frequency band can be selectively excluded, the fault point can be accurately positioned, the maintenance work is greatly facilitated, and the acoustic wave positioning is suitable for accurate positioning. The advantages of using the infrared thermal imager are the same as those of the acoustic wave positioning, the cable fault point can be quickly found according to the temperature distribution, and the infrared thermal imager is suitable for accurate positioning.

[0112] A method for identifying and positioning a short circuit fault of a power cable, comprising the following steps:

[0113] S1: for the serious fault of the power cable, taking single-phase and three-phase short circuit faults as examples, according to the simulation model of the power cable transmission line, the currents of the single-phase short circuit and the three-phase short circuit of the cable are simulated, and the characteristics of the currents in the two faults are analyzed;

[0114] S2: through simulation of different cable lengths, short circuit types and grounding resistances, the current characteristics of the fault signals are obtained;

[0115] S3: according to the actual cable line, the currents of each phase of the cable are measured, the root mean square of the current is taken as the input value of the BP neural network under the optimization of the SSA algorithm, and the nonlinear mapping relationship between the fault current and the fault type is established;

[0116] S4: the test sample data is divided into a training set and a test set according to the proportions of 70% and 30%, the SSA-BP algorithm is combined with the actual power cable current measurement data to identify the cable fault type;

[0117] S5: the phase-mode transformation is used on the collected power cable current to obtain the line-mode component of the fault current;

[0118] S6: considering the influence of noise on the positioning of the traveling wave head, for single-phase and three-phase short circuit faults, based on the CEEMDAN and TEO algorithms, the accurate positioning of the cable fault is realized.

[0119] In the S1, when a single-phase short circuit occurs, the single-phase short circuit current is calculated according to the symmetrical component method using the following formula:

[0120]

[0121] In formula (23), I 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 system equivalent resistance; represents the system equivalent reactance.

[0122] Three-phase short circuit fault calculation formula:

[0123]

[0124] In formula (24), I represents the three-phase short circuit current; U C represents the short circuit calculation line voltage; R ∑ is the total resistance from the power supply to the short circuit point; X ∑ is the total reactance from the power supply to the short circuit point.

[0125] 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, as follows:

[0126] A single-phase short circuit fault will cause the fault phase current to increase sharply, while the other two-phase currents will decrease. A three-phase short circuit fault will cause the three-phase currents to increase sharply at the same time. In analyzing short circuit faults, the root mean square (RMS) value of the current is an important characteristic because it reflects the effective value of the current, and the root mean square calculation formula is as follows:

[0127]

[0128] In formula (25), RMS is the root mean square; n is the number of samples; x i is the i-th data in the sequence.

[0129] In S2, through simulation of different cable lengths, short circuit types and grounding resistances, the current characteristics of the fault signals are obtained, as follows:

[0130] 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 type of short circuit affects the symmetry and amplitude of the fault current. For a three-phase short circuit, the amplitude of the fault current is usually the largest, while for a single-phase ground fault, 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. The cable fault identification method based on the BP-SSA algorithm in the S3 includes the following steps:

[0131] First, the fault current of the cable monitoring points M and N is obtained;

[0132] Then, the root mean square of the current after the fault is taken as the characteristic value input to the BP-SSA algorithm, and the optimal solution is obtained by training the final algorithm iteration through the BP-SSA algorithm;

[0133] The root mean square value (RMS) of the fault current is an important quantitative indicator of the fault characteristics. The root mean square value of the fault current signal can effectively reflect the intensity and fluctuation characteristics of the fault current, and is input as a characteristic value to the BP-SSA algorithm. The BP-SSA algorithm combines the nonlinear fitting ability of the BP neural network and the global optimization ability of the SSA algorithm, and optimizes the initial weights and thresholds of the BP neural network to avoid the BP network falling into local optimization, thereby improving the training effect and prediction accuracy of the model. The specific steps are as follows:

[0134] Initialize the sparrow population, and the position of each sparrow represents a set of weights and thresholds of the BP neural network; the weights and thresholds of the BP neural network are distributed according to formula (19) and formula (20), and the position of each sparrow is updated according to formula (21).

[0135] The positions of the population are updated using the discoverer, joiner and scout behavior of SSA; the positions of the discoverer, joiner and scout population are updated according to formula (21), formula (22) and formula (26).

[0136] The updated population position is used as the initial parameter of the BP neural network for training; the optimal weights and thresholds obtained by updating the population position are used as the initial parameters of the BP neural network and substituted into formula (19) and formula (20) for training.

[0137] The weights and thresholds are adjusted through the error backpropagation of the BP neural network. According to formula (27) and formula (28), the weights and biases of the BP neural network are adjusted by the gradient descent method to minimize the error between the target value and the actual output value.

[0138] The SSA algorithm simulates the foraging and anti-predation behavior of sparrow populations in nature, with the advantages of fast convergence speed, strong optimization ability, and simple parameter setting. The specific mathematical modeling formula is as follows:

[0139] (1) When the discoverer successfully finds food, it provides search direction for the entire sparrow population. The discoverer position update strategy is shown in equation (21);

[0140]

[0141] where t is the iteration number; X t+1 i is the position of the ith sparrow at t+1 iteration; R2 is the warning value; ST is the safety value; α is a random number between 0 and 1; Q is a random number following a normal distribution; L is a column vector with all elements being 1.

[0142] (2) The joiner in the sparrow population updates its position according to equation (26) to follow the discoverer and forage.

[0143]

[0144] where: is the global optimal position of the current sparrow; X w t is the worst position of the current sparrow; k is the number of joiners; β is a random number between -1 and 1; is the position of the ith sparrow at t iteration; Q is a random number following a normal distribution.

[0145] (3) When the warning person in the sparrow population senses the presence of a predator, it will adjust its position according to equation (22) to lead the rest of the sparrows to other safe areas to continue foraging.

[0146]

[0147] where γ is the step size control parameter; f i is the fitness value of the current warning person; f b , f w are the current optimal and worst fitness values, respectively; η is a random number between -1 and 1; ε is a constant not equal to 0.

[0148] Error backpropagation is the core algorithm of BP neural network, which is used to adjust the weights and biases of the network through gradient descent method to minimize the error between the target value and the actual output value. Gradient descent is an optimization algorithm that calculates the gradient of the error function with respect to the weights and biases, and adjusts the weights and biases in the opposite direction of the gradient to minimize the error function. The update formula for weights and biases is:

[0149]

[0150] where, is the connection weight from the i-th neuron in the input layer to the j-th neuron in the hidden layer at the t+1 iteration; is the connection weight from the j-th neuron in the hidden layer to the k-th neuron in the output layer at the t+1 iteration; is the hidden layer bias at the t+1 iteration; is the output layer bias at the t+1 iteration; is the connection weight from the i-th neuron in the input layer to the j-th neuron in the hidden layer at the t iteration; is the connection weight from the j-th neuron in the hidden layer to the k-th neuron in the output layer at the t iteration; is the hidden layer bias at the t iteration; is the output layer bias at the t iteration; η is the learning rate; is the partial derivative of the loss function E with respect to the weight , reflecting the gradient of the loss with respect to the weight change; represents the gradient of the loss with respect to the weight change between the hidden layer and the output layer; represents the gradient of the loss with respect to the hidden layer bias change; represents the gradient of the loss with respect to the output layer bias change.

[0151] According to the gradient descent method, the update formula for weights and biases is:

[0152]

[0153] where, t k is the true label of the k-th output; y k is the predicted value of the k-th output; g′(z k ) is the derivative of the output layer activation function, z k is the net input of the output layer neuron; f′(u j ) is the derivative of the hidden layer activation function, u j is the net input of the hidden layer neuron; h j is the output value of the j-th neuron in the hidden layer; x i is the input value of the i-th neuron in the input layer; l represents the number of output layer neurons.

[0154] By continuously iterating this process, the weights and biases of the BP neural network will gradually adjust to the optimal value, thereby minimizing the error function and improving the training effect and prediction accuracy of the model.

[0155] Repeat the above process until the iteration condition is met, and finally obtain the optimal solution.

[0156] Finally, in order to consider the fault types under different conditions, the BP neural network model optimized based on the SSA algorithm is used to identify different fault types of the cable.

[0157] In the identification of cable fault types, the process of SSA-optimized BP neural network is as follows:

[0158] The parameters of SSA are set, including population size, maximum iteration number, etc. The population size is set to 30 and the maximum iteration number is set to 50.

[0159] And randomly initialize the weights and thresholds of BP neural network. Apply each solution of SSA to BP network and calculate its fitness value; the weights and thresholds of BP neural network are distributed according to formula (19) and formula (20), and the position of each sparrow is updated according to formula (21). Its fitness value is calculated by the following formula:

[0160]

[0161] Where E is the fitness value, representing the calculation error, Y k is the actual output value of the network, is the expected output value, and p is the number of output layer neurons.

[0162] Update the position of the solution according to the behavior of the discoverer, joiner and scout of SSA. Update the population positions of the discoverer, joiner and scout according to formula (21), formula (22) and formula (26).

[0163] Apply the updated weights and thresholds to the BP network and further optimize them by the error back propagation algorithm. Adjust the weights and biases of the BP neural network by gradient descent method according to formula (27) and formula (28) to minimize the error between the target value and the actual output value.

[0164] Repeat the above process until the iteration condition is met, and finally get the optimal weights and thresholds. Calculate its fitness value according to formula (29), and when the iteration condition is met, get the optimal weights and thresholds.

[0165] By extracting the fault current characteristic values as input, the SSA-optimized BP neural network model is used for fault type identification. The simulation results show that the SSA-BP model can quickly jump out of the local optimal solution, speed up the convergence speed, and has high fault diagnosis accuracy.

[0166] Through continuous iteration of this process, the weights and biases of the BP neural network will gradually adjust to the optimal value, thereby minimizing the error function and improving the training effect and prediction accuracy of the model.

[0167] In S5, the collected power cable current is subjected to phase-mode transformation to obtain a fault current line-mode component; specifically as follows: In a power system, a fault can cause complex inter-phase relationships. By phase-mode transformation, three-phase current can be decomposed into zero-mode, positive sequence and negative sequence components, thereby simplifying fault analysis. Phase-mode transformation can convert fault characteristics from complex three-phase space to simpler mode space.

[0168] Phase-mode transformation is a method of converting a phasor in a three-phase system into a modal quantity. A commonly used phase-mode transformation matrix is:

[0169]

[0170] Three-phase current I a , I b , and I c are converted into modal components by phase-mode transformation matrix T:

[0171]

[0172] where I0 is a zero-mode component, and I1 and I2 are line-mode components.

[0173] In S6, considering the influence of noise on traveling wave front positioning, for single-phase and three-phase short-circuit faults, the initial traveling wave arrival time of the fault current is calibrated based on CEEMDAN and TEO algorithms, which is brought into the distance calculation formula to calculate the distance of the fault point from the first and last end measurement devices, thereby realizing accurate positioning of the cable fault.

[0174] CEEMDAN is an improved EMD algorithm that improves the stability and accuracy of decomposition by adding white noise. CEEMDAN decomposes a signal into a series of IMF components. The main steps of CEEMDAN include: adding a certain amount of white noise to the original signal; EMD decomposes the signal with added white noise to obtain a series of IMF components; repeat the above process several times, each time adding different white noise; average the IMF components obtained by multiple decompositions to obtain the final IMF components.

[0175] TEO algorithm is a nonlinear operator for signal processing and feature extraction, which can quickly and accurately reflect the degree of change of signal amplitude and frequency. For discrete-time signal s(n), the definition of TEO is:

[0176]

[0177] In the formula, represents the energy operator, s(n) is the current sampling point, s(n+1) and s(n-1) are the next and previous sampling points respectively.

[0178] When the power transmission line fails, current traveling wave propagating to both ends will be generated. Double-ended traveling wave distance measurement utilizes the time difference of fault traveling wave reaching both ends of the line, combined with the traveling wave propagation speed, to calculate the fault point position. Assuming that the left and right ends of the power transmission line are denoted as M end and N end, the distance measurement formula is:

[0179]

[0180] In the formula, x is the distance of the fault point from the M end, L is the length of the power transmission line, v is the propagation speed of the traveling wave in the line, t M is the time when the fault traveling wave reaches the M end of the line, and t N is the time when the fault traveling wave reaches the N end of the line.

[0181] The present application proposes a method for identifying and locating defects and short circuit faults of power cables, and the technical effects are as follows:

[0182] 1) The present application establishes a power cable transmission line simulation model and a partial discharge simulation model. The propagation characteristics of partial discharge signals under different cable lengths are simulated, and a cable partial discharge denoising method is proposed.

[0183] 2) The present application proposes a partial discharge signal recognition method based on data enhancement and SSA-BP algorithm, adopts ultrasonic, high frequency and ultrahigh frequency detection methods to preliminarily locate the cable fault, and realizes accurate fault positioning through infrared heat and acoustic positioning principles.

[0184] 3) The present application simulates single-phase short circuit and three-phase short circuit fault current characteristics, constructs a fault recognition model based on SSA algorithm and BP neural network, and proposes a fault positioning method based on CEEMDAN and TEO algorithm, which provides a new method for accurately identifying and locating early and serious faults of power cables. BRIEF DESCRIPTION OF DRAWINGS

[0185] The present application will be further described below in conjunction with the drawings and examples:

[0186] Figure 1 The flowchart for positioning the partial discharge signal of the power cable.

[0187] Figure 2 The flowchart for identifying and positioning the short circuit fault of the power cable.

[0188] Figure 3(a) is a single-phase short circuit equivalent circuit model diagram;

[0189] Figure 3(b) is a three-phase short circuit equivalent model diagram.

[0190] Figure 4(a) is a single-phase short circuit current result;

[0191] Figure 4(b) is a three-phase short circuit current result.

[0192] Figure 5 Flow chart for partial discharge signal denoising.

[0193] Fig. 6(a) is the short circuit fault recognition result (prediction set);

[0194] Fig. 6(b) is the short circuit fault recognition result (training set).

[0195] Fig. 7(a) is the traveling wave signal CEEMDAN decomposition result (N terminal);

[0196] Fig. 7(b) is the traveling wave signal CEEMDAN decomposition result (M terminal).

[0197] Fig. 8(a) is the power cable short circuit fault positioning recognition result (N terminal);

[0198] Fig. 8(b) is the power cable short circuit fault positioning recognition result (M terminal).

[0199] Figure 9 Fig. 5 is a power cable structure model diagram;

[0200] Wherein: 1 - cable core conductor, 2 - insulation layer, 3 - shielding layer, 4 - inner protective layer, 5 - armored layer, 6 - outer protective layer. DETAILED DESCRIPTION

[0201] A method for identifying and positioning early defects and short circuit faults of power cables, comprising the following steps:

[0202] Step one, for early power cable defects, taking partial discharge as an example, according to the actual structure parameters of power cable and the characteristics of partial discharge signal, the electromagnetic transient simulation software is used to establish the power cable transmission line simulation model and the partial discharge simulation model. The power cable model includes cable core, cross-linked polyethylene (XLPE) insulation layer, metal shielding layer, inner protective layer, armored layer and outer protective layer; the partial discharge signal model adopts double exponential decay model.

[0203] Because the wavelength of the pulse signal is short during the cable propagation, and the size of the cable line is long, 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. The power cable transmission line simulation model mainly includes: line distributed resistance, line distributed inductance, line distributed conductance and line distributed capacitance.

[0204] Voltage and current of cable line:

[0205] V(x) = A1e γx + A2e -γx

[0206]

[0207] From the signal propagation formula U0=U i e -yl The input and output voltage relationship of the signal is:

[0208] U0=U i e -γl =U i e -(α+jβ)l =U i e -αl ·e -jβl

[0209] |U0|=|U i |e -αl

[0210] Cable partial discharge can be divided into internal discharge, surface discharge, corona discharge and suspension discharge, and air gap defect is the main cause of internal discharge of cable. The equivalent model of air gap defect in cross-linked polyethylene insulation is established, the equivalent circuit of XLPE insulation air gap defect is three capacitance method, 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 air gap is located.

[0211] The power voltage u=Umsinωt acts on the medium, and the voltage on the air gap is:

[0212]

[0213] The double exponential decay model is used as the partial discharge signal model

[0214]

[0215] In the formula: A represents the signal amplitude; t is time; τ1, τ2 represent the time decay coefficient of the signal.

[0216] Step two, according to the cable transmission line and partial discharge simulation model, the propagation characteristics of partial discharge signal under different cable lengths are obtained, and the partial discharge signal is obtained; considering the interference of the signal, the partial discharge denoising method of empirical wavelet transform is adopted. Based on the generative adversarial network, a data enhancement method is proposed, which expands the original training sample set by synthesizing partial discharge signals; analyze the influence of the capacity ratio of generated samples and original training samples on the pattern recognition accuracy, and propose a partial discharge signal recognition method based on SSA-BP algorithm.

[0217] The partial discharge signal is subjected to Fourier transform, the frequency spectrum of the partial discharge signal is classified by using the K-means algorithm, the signal frequency spectrum is divided by using the local maximum minimum value method, the mode component is obtained by adopting the empirical wavelet transform for adaptive filtering of the frequency segment, the mode component is selected by using the high-order statistics, i.e., the kurtosis criterion, and the useful mode component is subjected to threshold discrimination by using the 3σ criterion. The de-noising effect of the algorithm is judged according to the evaluation index, the evaluation index is the signal-to-noise ratio, the root mean square error and the waveform similarity coefficient, the signal-to-noise ratio is larger, the noise content in the partial discharge signal is smaller, the root mean square error is closer to 1, the similarity between the de-noised signal and the original signal is high, and the waveform similarity coefficient is smaller, and the waveform distortion rate of the de-noised signal is smaller.

[0218] Among them, the signal-to-noise ratio:

[0219]

[0220] The root mean square error:

[0221]

[0222] The waveform similarity coefficient:

[0223]

[0224] Based on the data enhancement technology of the generative adversarial network, the deep feature representation of the original partial discharge signal is learned by using the model, the real data distribution is restored, and a large number of partial discharge signals are synthesized to expand the original training sample set. The influence of the capacity ratio of the generated sample and the original training sample on the pattern recognition accuracy is determined, the final number of generated samples is determined, and a pattern recognition method based on the SSA-BP algorithm is proposed. The partial discharge signal caused by insulation defects shows high similarity in the mode of partial discharge, and it is difficult to distinguish by relying on expert experience. In order to solve the problem of pattern recognition, a hybrid pattern recognition method is used to detect the partial discharge mode. The field partial discharge detection data sample is relatively scarce, the sample number under each defect is often not the same, and in addition to the influence of environmental noise, the pattern recognition accuracy of the online monitoring system needs to be improved. Considering that the neural network algorithm has the defects of low stability and easy to produce multiple local minimum values, a PSO-ANN algorithm is proposed to optimize the network structure and improve the training efficiency and accuracy. The normalized test data is used as the model input, and the classification result is output, and the classification effect and network complexity of the neural network are analyzed.

[0225] Step three, two steps of preliminary detection and accurate detection are adopted, in the preliminary detection, ultrasonic wave, high frequency and ultrahigh frequency detection methods are adopted to preliminarily position the cable, and on this basis, the infrared heat and acoustic positioning principle are adopted to realize accurate positioning of the power cable defect.

[0226] The cable is preliminarily positioned by using ultrasonic, high frequency and ultra-high frequency detection methods. The preliminary detection includes finding surface discharge by ultrasonic partial discharge detection, finding internal discharge of insulation by ultra-high frequency partial discharge detection and high frequency partial discharge detection. The cable fault positions are mainly concentrated in the middle joint and the in-out line positions, and most of the cables are deeply buried underground. The maintenance personnel will encounter the problems of heavy workload and low efficiency when detecting the cable. The cable is detected in multiple directions by the way of preliminary detection and detailed detection, including ultrasonic, high frequency, ultra-high frequency, infrared, acoustic positioning and other detection methods. The preliminary detection includes finding surface discharge by ultrasonic partial discharge detection, finding internal discharge of insulation by ultra-high frequency partial discharge detection and high frequency partial discharge detection. The detailed detection includes judging the approximate direction by ultrasonic partial discharge data, and realizing accurate positioning by using acoustic positioning principle and infrared thermal imager.

[0227] The approximate direction is judged by ultrasonic partial discharge data, and the accurate positioning is realized by using acoustic positioning principle and infrared thermal imager. The ultrasonic sensor is used to detect the surface discharge of the cable or the ultrasonic signal diffracted through the insulation outer layer. The sensitivity is high, but it cannot test the discharge signal inside the insulation. The high frequency detection method is that the high frequency pulse signal generated by the partial discharge of the cable flows into the grounding system through the ground wire, and the ground partial discharge signal is collected by the high frequency mutual inductor. The high frequency method is suitable for preliminary test. The ultra-high frequency detection method uses a sensor with a frequency of 300MHz-3GHz to obtain the discharge signal, which can avoid common interference and is suitable for preliminary test. The principle of acoustic positioning method is that the frequency collected by acoustic positioning is wider than that of ultrasonic, which can selectively exclude environmental noise frequency band, and can accurately locate the fault point, which brings great convenience to the maintenance work and is suitable for accurate positioning. The advantage of using infrared thermal imager is the same as that of acoustic positioning, which can quickly find the cable fault point according to the temperature distribution, and is suitable for accurate positioning.

[0228] Step four, for the serious fault of power cable, taking single-phase and three-phase short-circuit fault as an example, according to the power cable transmission line simulation model in step one, the single-phase position is set to ground in the model, the current of single-phase short-circuit and three-phase short-circuit of the cable is simulated, 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.

[0229] For single-phase and three-phase grounding faults, according to the basic theory of circuit, the formula is:

[0230] From KVL,

[0231]

[0232] The total current after short-circuit can be represented by the following formula

[0233]

[0234] I PM is the short-circuit current periodic component amplitude;

[0235] φ k is the short-circuit impedance angle, φ k = arctg (X / R); τ is the short-circuit loop time constant, and C is the integral constant determined by the initial condition, i.e. the initial value of the non-periodic component of the short-circuit current.

[0236] When a single-phase short-circuit occurs in a large grounding current system or a three-phase four-wire system, the single-phase short-circuit current can be calculated according to the symmetrical component method as follows:

[0237]

[0238] The calculation formula in engineering is

[0239]

[0240] The calculation formula of three-phase grounding fault is:

[0241]

[0242] In the formula, R ∑ is the total resistance from the power source to the short-circuit point; X ∑ is the total reactance from the power source to the short-circuit point.

[0243] 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 source 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 position. 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 types of 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 signals are obtained by simulation of different cable lengths, short-circuit types and grounding resistances.

[0244] 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, and the current amplitude changes most. When all three-phase currents change, it can be determined that the cable has a three-phase short-circuit fault.

[0245] Step five, according to the actual cable line, the current of each phase of the cable is measured, the root mean square of the current is taken as the input value of the BP neural network under the optimization of the SSA algorithm, the nonlinear mapping relationship between the fault current and the fault type is established, and the model parameters are obtained by grid search optimization. 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 measurement data, the cable fault type is identified by algorithm.

[0246] More specifically, for the identification of cable fault type, a cable fault identification method based on BP-SSA algorithm is proposed, the specific steps are as follows: first, the fault current of the cable monitoring points M and N is obtained, the root mean square of the fault current is taken as the characteristic value input to the BP-SSA algorithm, the optimal solution is obtained through the training of the BP-SSA algorithm, and the cable fault type is identified by the BP-SSA algorithm. In order to consider the fault type under different conditions, the BP neural network model based on SSA algorithm optimization is used to identify the different fault types of the cable. Compared with single neural network algorithm, this method takes into account the advantages of sparrow algorithm and gradient descent optimization algorithm in global and local search of minimum point respectively, and avoids the risk of premature convergence to local minimum point in the training process of BP network.

[0247] The SSA algorithm simulates the foraging and anti-predation behavior of sparrow population in nature, has the advantages of fast convergence speed, strong optimization ability and simple parameter setting. The specific mathematical modeling formula is as follows:

[0248] (1) When the finder successfully finds food, it provides the search direction for the whole sparrow population, and the finder position updating strategy is as follows:

[0249]

[0250] In the formula: t is the iteration number; X t+1 i is the position of the ith sparrow at t+1 iteration; R2 is the warning value; ST is the safety value; a is a random number between 0 and 1; Q is a random number subject to normal distribution; L is a column vector and all elements are 1.

[0251] (2) The joiner in the sparrow population updates the position according to formula (13) to follow the finder foraging.

[0252]

[0253] In the formula: X b t is the global optimal position of the current sparrow; X w twhere k is the number of joiners; β is a random number between -1 and 1.

[0254] (3) When the early-warning sparrow in the sparrow population senses the presence of a predator, it will adjust its position according to the following formula to lead the rest of the sparrows to other safe areas to continue foraging.

[0255]

[0256] where γ is a step size control parameter; f i is the fitness value of the current early-warning sparrow; f b , f w are the current optimal and worst fitness values, respectively; η is a random number between -1 and 1; and ε is a constant not equal to 0.

[0257] A BP neural network is composed of an input layer, a hidden layer, and an output layer. The expression for the forward propagation process of the BP neural network algorithm is

[0258]

[0259] In the above formula, z j is the value of the jth element of the hidden layer; f[·] is the activation function; w ij is the weight value from the ith element of the input layer to the jth element of the hidden layer; x i is the value of the ith element of the input layer; b ij is the threshold value from the ith element of the input layer to the jth element of the hidden layer; y p is the value of the pth element of the output layer; w jp is the weight value from the jth element of the hidden layer to the pth element of the output layer; b jp is the threshold value from the jth element of the input layer to the pth element of the hidden layer.

[0260] The output layer compares the calculated result with the expected result. If the output error exceeds the set range, feedback is performed to each layer, and the weights and thresholds between layers are adjusted again using a nonlinear optimization algorithm until the output result meets the expected value.

[0261] Step six: The acquired power cable current is subjected to a phase-to-module transformation to obtain the fault current line module component. Considering the influence of noise on the positioning of the traveling wave front, for single-phase and three-phase short-circuit faults, a fault traveling wave front enhancement technique based on CEEMDAN and TEO algorithms is used to calibrate the initial traveling wave arrival time of the fault current, which is then brought into the distance calculation formula to calculate the distance from the fault point to the first and last end measurement devices, thereby achieving accurate positioning of the cable fault.

[0262] The phase-mode transformation is used to decouple the three-phase currents at both ends to obtain the fault current line-mode component. Without considering noise, for single-phase and three-phase short-circuit faults, the fault traveling wave head enhancement technology based on TEO algorithm is used to calibrate the arrival time of the initial traveling wave of the fault current, and the fault location distance is calculated according to the double-end current traveling wave method. When considering noise, the CEEMDAN algorithm is used to decompose the signal to obtain signal modal components of different frequencies. The current components decomposed by CEEMDAN are calculated by TEO algorithm to obtain the Teager instantaneous energy spectrum, as shown in Figs. 8(a) and 8(b). This algorithm can accurately calibrate the arrival time of the traveling wave by enhancing the characteristics of the traveling wave head signal, and the distance between the fault point and the current transformer at the first and last ends is calculated by bringing the arrival time into the distance calculation formula, so as to realize accurate positioning of the cable fault.

[0263] Figure 1 Flow chart for fault identification and positioning under early defect, taking partial discharge signal as an example.

[0264] Figure 2 For fault identification and positioning under short-circuit fault, taking single-phase short-circuit and three-phase short-circuit as examples.

[0265] Fig. 3(a) is a single-phase short-circuit equivalent circuit model diagram; Fig. 3(b) is a three-phase short-circuit equivalent model diagram. In Figs. 3(a) and 3(b), f is the fault point, and R and L are the resistance and inductance of each item in the cable.

[0266] Figs. 4(a) and 4(b) are current simulation results of single-phase short-circuit and three-phase short-circuit respectively, and the fault time is 0.02s.

[0267] As can be seen from Figs. 4(a) and 4(b), when a single-phase fault occurs, the fault-phase current amplitude and phase change suddenly, and the current amplitude after the fault is about 3kA; when a three-phase fault occurs, the three-phase current amplitude increases sharply, and the current amplitude after the fault is higher, about 15kA, which is more serious than single-phase fault.

[0268] Figure 5 The flow chart of the partial discharge denoising method using EWT based on spectral clustering is introduced.

[0269] Figs. 6(a) and 6(b) are the cable fault type identification results of BP neural network based on SSA algorithm optimization, including test set and training set results. In Figs. 6(a) and 6(b), the vertical coordinates 1 and 2 represent single-phase short-circuit and three-phase short-circuit respectively.

[0270] Figs. 7(a) and 7(b) are the results of CEEMDAN decomposition of signals at line M and N ends respectively.

[0271] It can be seen from FIG. 7(a) and FIG. 7(b) that after the signal is decomposed by CEEMDAN, IMF1 and IMF2 have more high-frequency components and contain most of the traveling wave signal characteristics, and at the same time, the noise signal content of IMF1 is higher, and the noise signal of the later IMF component is less.

[0272] FIG. 8(a) and FIG. 8(b) are simulation results of precise positioning of cable short-circuit fault by using CEEMDAN and TEO algorithms on a noisy signal.

[0273] It can be seen from FIG. 8(a) and FIG. 8(b) that there are TEO modulus maximum points, at this time the modulus maximum point is the traveling wave arrival time, the traveling wave arrival times at both ends of the line are obtained, and the precise positioning of the cable fault is realized through the double-end traveling wave distance measurement formula.

Claims

1. A method for identification and localization of defects in power cables, characterized by The method comprises the following steps: Step 1: a power cable transmission line simulation model and a partial discharge simulation model are established by using electromagnetic transient simulation software; Step 2: according to the power cable transmission line simulation model and the partial discharge simulation model, a partial discharge signal is obtained, and the partial discharge signal is identified based on an SSA-BP algorithm; Step 3: ultrasonic, high-frequency and ultrahigh-frequency detection methods are used to preliminarily position the power cable; and precise positioning of the power cable defect is realized through infrared thermal and acoustic wave positioning principles.

2. A method for identification and localization of defects in power cables according to claim 1, characterized in that: In step 1, since the wavelength of the pulse signal is short and the size of the cable line is long during cable propagation, the cable distributed parameter model can be equivalent to a uniform transmission line model, the cable distributed parameter model considers the cable resistance R, inductance L, conductance G and capacitance C along the line; the parameters per unit length are R', L', G' and C'; 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 during propagation in the cable; in the uniform transmission line model, it is assumed that the distributed parameters R', L', G' and C' of the cable are uniformly distributed over the entire cable length; the characteristic impedance Z0 represents the ratio of voltage to current on the transmission line without reflection, and the characteristic impedance can be simplified as: In summary, when the wavelength of the pulse signal is short, the size of the cable line is long, and the distributed parameters of the cable are uniformly distributed in length, the distributed parameter model of the cable can be equivalent to a uniform transmission line model; the uniform transmission line model can accurately describe the propagation characteristics of the signal in the cable through parameters such as characteristic impedance Z0 and propagation constant γ.

3. A method for identification and localization of defects in power cables according to claim 2, characterized in that: The power cable transmission line simulation model comprises: line distributed resistance, line distributed inductance, line distributed conductance and line distributed capacitance; The voltage and current of the cable line are calculated as follows: In formula (3): V(x) represents a voltage traveling wave of the uniform transmission line, I(x) represents a current traveling wave of the uniform transmission line, A1 and A2 represent traveling wave amplitude constants, A1e γx represents an incident wave propagating in the positive direction of x, A2e -γx represents a reflected wave propagating in the negative direction of x, γ represents a propagation constant, and z represents a characteristic impedance, and x represents a spatial position coordinate along the transmission line; From the signal propagation formula U0=U i e -γl Where U0 is the voltage at the output terminal of the transmission line; U i e is the voltage at the input terminal of the transmission line; -γl The attenuation factor describes the amplitude change of the signal after it has traveled a distance l; l is the length of the transmission line. The input and output voltage relationship of the signal is: In formula (4): U0 is the output voltage of the transmission line; U i is the input voltage 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 the phase of U0, which reflects the phase relationship between the output voltage U0 and the input voltage U i .

4. A method for identification and localization of defects in power cables according to claim 3, characterized in that: The cable partial discharge includes: internal discharge and corona discharge; 1) The air gap defect is the main reason for the internal discharge of the cable, an equivalent model of the air gap defect inside the cross-linked polyethylene insulation is established, the equivalent model of the air gap defect inside the cross-linked polyethylene insulation adopts a three-capacitor equivalent circuit, including: 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; Power supply voltage u = U m sin ωt acting medium, air gap upper voltage: In formula (5): 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 (6), S(t) represents the partial discharge voltage signal; A represents the signal amplitude; t is the time; τ1 and τ2 represent the time decay coefficients of the signal; 2) Regarding corona discharge, the electric field strength is inversely proportional to the curvature radius of the conductor surface, and the formula is: In formula (7), Q is the charge amount of a point charge; ε0is the vacuum dielectric constant, with a value of about 8.852 x 10 -12 F / m; r is the radius of curvature of the electrode; The starting field strength of corona discharge is generally calculated by an empirical formula, and the Pock formula is usually used for calculation; for engineering scenes such as power transmission lines, the influence of conductor surface roughness, air humidity and the like is considered, and the standard form is generally as follows: In formula (8): E c is the corona inception field strength; r is the wire radius; and δ is the relative density of air.

5. The method for identification and location of defects in power cables according to claim 3, characterized in that: Step 2 includes the following steps: Step 2.1: according to the power cable transmission line simulation model and the partial discharge simulation model, the propagation characteristics of the partial discharge signal under different cable lengths are obtained based on the partial discharge signal; 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; 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; 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 ​ Step 2.2: Considering the interference of the signal, the empirical wavelet transform is used to denoise the partial discharge signal; The empirical wavelet transform can be represented by the following formula: In formula (9): d j is the detail coefficient of the jth layer; s j is the approximation coefficient of the jth layer; DWT denotes wavelet decomposition; and IDWT denotes wavelet reconstruction. The threshold processing can be represented as: d' j = threshold(d j , λ) (10) ; In formula (10), threshold() is threshold processing; d' is the detail coefficient after threshold processing; λ is a threshold, which can be adaptively selected according to the characteristics of a signal and a noise level. j In formula (10), threshold() is threshold processing; d' is the detail coefficient after threshold processing; λ is a threshold, which can be adaptively selected according to the characteristics of a signal and a noise level. First, the empirical wavelet transform is applied to the partial discharge signal to obtain the detail coefficients and approximation coefficients at different scales; the appropriate threshold is selected based on the noise level and signal characteristics; the threshold processing is applied to the detail coefficients to remove the noise components; the processed detail coefficients and approximation coefficients are used to reconstruct the signal to obtain the denoised partial discharge signal; Step 2.3: Based on the generative adversarial network (GAN), a data augmentation method is proposed to expand the original training sample set by synthesizing partial discharge signals; Step 2.4: Analyze the influence of the capacity ratio of generated samples to original training samples on the recognition accuracy, and use the SSA-BP algorithm to recognize the partial discharge signal.

6. A method for identification and localization of defects in power cables according to claim 5, characterized in that: In step 2.3, the generative adversarial network (GAN) includes a generator G and a discriminator D, and the mathematical model of the generative adversarial network (GAN) is represented as: In Equation (11): V(G, D) is an adversarial loss function that measures the performance of the generator and discriminator; denotes the expectation over the real data distribution; denotes the expectation over the generator input noise distribution; D(x) is the output of the discriminator for a real sample x; G(z) is a sample generated by the generator from noise z; Data augmentation process: The collected partial discharge data is preprocessed, including denoising and normalization, to obtain real sample data; The preprocessed real samples are used to train the generative adversarial network, and the generator G learns to generate partial discharge signals from random noise, and the discriminator D learns to distinguish real signals and generated signals; After training, the generator G is used to synthesize new partial discharge signal samples; the synthesized samples are combined with the original training samples to form an expanded training sample set.

7. A method for identification and localization of defects in power cables according to claim 6, characterized in that: In step 2.3, the learning mechanism of the generative adversarial network (GAN) is as follows: Let the noise z ~ N(0,1), and let p be the prior distribution 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. In formula (12): denotes the minimization of the adversarial value function for the discriminator and the generator in the GAN; z ~ p z (z) denotes taking the expectation over all possible noise for the generator input; Update G by improving the gradient of the generator G: In formula (13), D(·) represents that the discriminator judges the authenticity of the input data, and the output is a probability between [0, 1], 1 represents true data, and 0 represents false data; G(z (i) ) represents that the generator G receives random noise z (i) , and outputs fake data; and θ g represents the parameters of the generator. The optimization result of the discriminator D is D(x) = 1 and D(G(z)) = 0, so the optimization problem of the discriminator D is as shown in the formula: In formula (14): x ~ p data (x) denotes the expectation taken over the true data x, covering all possible samples of the true data; p data (x) denotes the probability distribution of the true data; Similarly, update the generator D by improving the gradient: Therefore, combining formula (12) and formula (14), the optimization problem of GAN can be regarded as a maximum minimum problem: For any and y e [0, 1], consider the following equation: In formula (17): α and β represent positive coefficients, which are the weighted number of samples, and represent the weighted cross-entropy loss; y represents the probability value of the model output; Therefore, given the generator G, the minimum value of the objective function formula (14) is: In formula (18): represents the theoretical best output that the discriminator D can achieve when the generator G is fixed; p g (x) represents the probability distribution of the data generated by the generator, determined by the generator G; D and G are trained alternately to reach a Nash equilibrium; the training stops when the generator cannot improve the quality of the synthesized data, and the discriminator cannot determine the attribution of the input data; At this time, D(x) = 0.5, p data = p g , which indicates that the discriminator randomly outputs the prediction result. Substituting equation (14) can obtain 8. A method for identification and localization of defects in power cables according to claim 7, characterized in that: In step 2.4, the SSA-BP algorithm is used to recognize the partial discharge signal, as follows: The BP neural network is composed of input layer, hidden layer and output layer, and the expression of the forward propagation process of the BP neural network algorithm is where z j is the value of the jth element of the hidden layer; f[·] is the activation function; w ij is the weight from the ith element of the input layer to the jth element of the hidden layer; x i is the value of the ith element of the input layer; b ij is the threshold from the ith element of the input layer to the jth element of the hidden layer; y p is the value of the pth element of the output layer; w jp is the weight from the jth element of the hidden layer to the pth element of the output layer; b jp is the threshold from the jth element of the input layer to the pth element of the hidden layer; n represents the number of input layers; q represents the number of hidden layers; t represents the number of output layers; The output layer compares the calculated result with the expected result, if the output error exceeds the set range, feedback is performed to each layer, and the weights and thresholds between layers are adjusted again using a nonlinear optimization algorithm until the output result meets the expected value; SSA achieves a balance between global search and local search through the division of roles among discoverers, followers and sentinels; The position update strategy of the discoverer is as follows: In formula (21), t is the number of iterations; is the position of the i-th sparrow at the t+1 iteration; is the position of the i-th sparrow at the t iteration; R2 is a warning value; ST is a safety value; a is a random number between 0 and 1; Q is a random number subject to a normal distribution; and L is a column vector with all elements being 1. The position update formula of the sentinel is as follows: In formula (22): γ is a step control parameter; f i is the current warning's fitness value; f b , f w are the current best and worst fitness values, respectively; η is a random number between -1 and 1; ε is a constant not equal to 0; is the global best position of the current sparrow; is the position of the ith sparrow at the tth iteration; is the global worst position of the current sparrow; The BP-SSA algorithm optimizes the initial weights and biases of the BP neural network through SSA to improve the convergence speed and recognition accuracy of the network.

9. A method of identification and location of a short circuit fault in a power cable, characterized by The following steps are included: S1: For the serious fault of power cable, for single-phase and three-phase short-circuit fault, according to the power cable transmission line simulation model, the current of single-phase short-circuit and three-phase short-circuit of the cable is simulated, and the characteristics of the current in the two faults are analyzed; S2: Through simulation of different cable lengths, short-circuit types and grounding resistances, the current characteristics of the fault signal are obtained; S3: According to the actual cable line, the current of each phase of the cable is measured, the root mean square of the current is taken as the input value of the BP neural network optimized by the SSA algorithm, and the nonlinear mapping relationship between the fault current and the fault type is established; S4: 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 measurement data, the cable fault type is identified by SSA-BP algorithm; S5: The phase-mode transformation is used for the collected power cable current to obtain the line-mode component of the fault current; S6: Considering the influence of noise on the positioning of traveling wave front, for single-phase and three-phase short-circuit fault, based on CEEMDAN and TEO algorithm, the precise positioning of cable fault is realized.

10. A method of identification and location of a short circuit fault in a power cable according to claim 9, characterized in that: In the S3, the cable fault identification method based on BP-SSA algorithm includes the following steps: Firstly, the fault current of the cable monitoring points M and N is obtained; Then, the root mean square of the current after the fault is taken as the characteristic value input to the BP-SSA algorithm, and the optimal solution is obtained through the training of the BP-SSA algorithm; The SSA algorithm simulates the foraging and anti-predation behavior of sparrow population in nature, has the advantages of fast convergence speed, strong optimization ability and simple parameter setting; The specific mathematical modeling formula is as follows: (1) When the finder successfully finds food, it provides a search direction for the whole sparrow population, and the finder position updating strategy is shown in formula (21); where: t is the iteration number; X t+1 i is the position of the ith sparrow at iteration t + 1; R2is the warning value; STis the safety value; a is a random number between 0 and 1; Q is a random number following a normal distribution; L is a column vector with all elements being 1; (2) The joiner in the sparrow population updates the position according to formula (26) to follow the finder foraging; wherein: is the global optimum position of the current sparrow; is the worst position of the current sparrow; k is the number of joiners; β is a random number between -1 and 1; is the position of the i-th sparrow at the t-th iteration; Q is a random number subject to a normal distribution; (3) When the early warninger in the sparrow population senses the existence of the predator, it will adjust its own position according to formula (22) to lead the rest of the sparrows to other safe areas to continue foraging; where: γ is a step size control parameter; f i is the current warning's fitness value; f b , f w are the current best and worst fitness values, respectively; η is a random number between-1 and 1; ε is a constant not equal to 0; Backpropagation is the core algorithm of BP neural network, which is used to adjust the weights and biases of the network through gradient descent method to minimize the error between the target value and the actual output value; Gradient descent method adjusts the weights and biases in the opposite direction of the gradient by calculating the gradient of the error function with respect to the weights and biases, so as to minimize the error function; The update formula of weights and biases is: wherein is the connection weight from the i-th neuron in the input layer to the j-th neuron in the hidden layer at the t+1 iteration; is the connection weight from the j-th neuron in the hidden layer to the k-th neuron in the output layer at the t+1 iteration; is the hidden layer bias at the t+1 iteration; is the output layer bias at the t+1 iteration; is the connection weight from the i-th neuron in the input layer to the j-th neuron in the hidden layer at the t iteration; is the connection weight from the j-th neuron in the hidden layer to the k-th neuron in the output layer at the t iteration; is the hidden layer bias at the t iteration; is the output layer bias at the t iteration; η is a learning rate; is a partial derivative of a loss function E with respect to a weight , reflecting a gradient of a loss with respect to a weight change; represents a gradient of a loss with respect to a weight change between a hidden layer and an output layer; represents a gradient of a loss with respect to a bias change of a hidden layer; represents a gradient of a loss with respect to a bias change of an output layer; According to the gradient descent method, the update formula of weights and biases is: where t k is the true label of the kth output; y k is the predicted value of the kth output; g'(z k ) is the derivative of the output layer activation function, z k is the net input of the output layer neuron; f'(u j ) is the derivative of the hidden layer activation function, u j is the net input of the hidden layer neuron; h j is the output value of the jth neuron in the hidden layer; x i is the input value of the ith neuron in the input layer; l denotes the number of output layer neurons. Through continuous iteration of this process, the weights and biases of BP neural network will gradually adjust to the optimal value.

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