A method for determining the inductive coupling of a transient potential rise through a cable shield

Abstract

The application provides a transient ground potential rise induced coupling determination method through cable shielding layer, and belongs to the technical field of cable shielding layer.The application establishes a distributed parameter partial element equivalent circuit model of a grounding network, solves transient ground potential distribution by using a finite difference time domain method, obtains equivalent transfer impedance frequency characteristics of a braided shielding layer by using a four-port S parameter vector network analysis method and a variational asymptotic homogenization multi-scale algorithm, solves core line common mode voltage and differential mode voltage by establishing a multi-conductor transmission line equation group, constructs an artificial intelligence prediction model based on a topology perception graph neural network, solves a large-scale sparse admittance matrix by using a multilevel fast multipole method to obtain full network induced voltage distribution, and establishes a quantitative relationship model between ground potential rise and core line induced voltage, so that the technical problems that cable core line induced voltage caused by transient ground potential rise is difficult to accurately predict and effectively suppress are solved.

Description

Technical Field

[0001] This invention belongs to the field of cable shielding technology, and more specifically, relates to a method for determining transient ground potential rise through inductive coupling of a cable shielding layer. Background Technology

[0002] In substation grounding systems, lightning strikes or short-circuit faults can cause a transient rise in ground potential. This potential is induced and coupled to the cable core wires through the cable shield, causing electromagnetic interference and even damage to secondary equipment. Traditional techniques use lumped-parameter equivalent circuit models to analyze the transient characteristics of the grounding network and combine them with simplified cable coupling models to estimate the induced voltage. This method is widely used in electromagnetic compatibility design of secondary circuits in practical engineering. However, the lumped-parameter model ignores the mutual inductive and capacitive coupling between conductor segments, resulting in significant error accumulation under high-frequency and long-distance transmission conditions. Furthermore, the simplified coupling model fails to accurately characterize the frequency-dependent characteristics of the braided shield, leading to large deviations in the induced voltage calculation. In existing technologies, due to the lack of a comprehensive analysis method that considers the spatial distribution characteristics of the grounding network, the microstructure of the cable shield, and the influence of network topology, it is difficult to accurately predict the induced voltage distribution under different grounding methods, and it cannot provide a quantitative basis for the optimal selection of shield grounding methods. In other words, existing technologies suffer from the technical problem of accurately predicting and effectively suppressing the induced voltage in the cable core wires caused by transient ground potential rises. Summary of the Invention

[0003] In view of this, the present invention provides a method for determining the inductive coupling of transient ground potential rise through the cable shielding layer, which can solve the technical problem in the prior art that it is difficult to accurately predict and effectively suppress the induced voltage of the cable core caused by transient ground potential rise.

[0004] This invention is implemented as follows: It provides a method for determining the induced coupling of transient ground potential rise through a cable shielding layer. This includes establishing a distributed parameter partial element equivalent circuit model of the grounding network; using the finite-difference time-domain method to solve for the spatiotemporal distribution of transient ground potential in the grounding network to obtain the time-varying ground potential difference function at the grounding points at both ends of the cable shielding layer; using a four-port S-parameter vector network analysis method to measure the transfer impedance of the cable shielding layer in the 0.1 to 10 MHz frequency band; eliminating the influence of parasitic parameters of the test fixture through short-circuit open-circuit load direct-through calibration; and combining a variational asymptotic homogenization multi-scale algorithm to obtain the equivalent transfer impedance frequency characteristic curve of the braided shielding layer; establishing a multi-conductor transmission line equation system based on the spatial path of the cable in the grounding network; using the time-varying ground potential difference function as the excitation source of the shielding layer boundary; using the equivalent transfer impedance frequency characteristic curve as the coupling parameter; and using frequency domain analysis to solve for the multi-conductor transmission line equation system. The equations yield the common-mode voltage distribution and differential-mode voltage distribution of the cable cores. A generalized node admittance matrix of the cable network topology is constructed, representing single-end grounding, two-end grounding, and multi-point grounding as different boundary condition matrices. The topology equations are automatically generated using the correlation matrix, and the large-scale sparse admittance matrix is ​​solved using the multilevel fast multipole algorithm and the domain decomposition method to obtain the induced voltage distribution of the entire cable cores. The induced voltage distribution data is input into the coupled voltage prediction model to output the peak induced voltage and voltage waveform characteristic parameters of each cable port. The grounding adjustment strategy is determined based on the fitness function value of the shielding layer grounding method. Parameter sensitivity analysis is performed on secondary control cables with cable lengths ranging from 50 to 500 m, extracting the influence weight coefficients of transfer impedance, cable length, and grounding method on the peak induced voltage, and establishing a quantitative relationship model between ground potential rise and induced voltage of the cable cores.

[0005] Specifically, the establishment of the equivalent circuit model of the distributed parameter part involves discretizing each conductor segment in the grounding network with a spatial step size of 0.1m, calculating the partial self-inductance and partial mutual inductance of each discrete conductor segment, calculating the partial resistance of each discrete conductor segment, and calculating the partial capacitance of any two nodes in the grounding network, assembling them to form a circuit network equation containing a partial inductance matrix, a partial resistance matrix, and a partial capacitance matrix.

[0006] Among them, part of the self-inductance is obtained by integrating the magnetic field generated by the conductor segment itself along the path of the conductor segment; part of the mutual inductance is obtained by double integration of the mutual magnetic field between the two conductor segments along their respective paths; part of the resistance is calculated using Ohm's law based on the length, cross-sectional area, and conductivity of the conductor segment; and part of the capacitance is obtained by solving the ratio of the electrostatic energy between the two nodes to the square of the voltage.

[0007] In the equivalent circuit model of the distributed parameter component, the parameters of each component are calculated by the geometric dimensions and relative positions of the conductor segments using the quasi-static field integral formula. The quasi-static field integral formula is a mathematical expression based on the Biot-Savart law and Coulomb's law, which are used to perform path integrals or surface integrals of spatial field quantities under quasi-static approximation conditions.

[0008] Specifically, the solution using the finite-difference time-domain method involves discretizing the space containing the grounding network into a cubic grid. Within each time step, the electric and magnetic field components are updated according to the difference form of Maxwell's equations. The evolution of the potential at each point in the grounding network over time is obtained through iterative calculation. The time step is taken as the spatial step divided by the speed of light and then multiplied by 0.5 to satisfy the stability condition.

[0009] Among them, the variational asymptotic homogenization multiscale algorithm decomposes the electromagnetic field into a macroscopic slowly varying field and a microscopic rapidly varying field based on the principle of scale separation. It solves the periodic boundary value problem of the microscopic field in a representative volume unit, obtains the equivalent constitutive parameters of the macroscopic scale by averaging the microscopic field, and uses a homogenized medium to replace the real woven structure at the macroscopic scale.

[0010] Among them, the variational asymptotic homogenization multi-scale algorithm reduces the electromagnetic simulation of braided shielding layers from processing millions of grid cells to thousands of grid cells. While maintaining the transfer impedance calculation error of less than 5%, it compresses the calculation time of a single frequency point from several hours to minutes and automatically captures the mapping relationship between braiding angle, braiding density and wire diameter on macroscopic shielding performance.

[0011] The coupled voltage prediction model is structured as a topology-aware graph neural network, which represents the cable network as a graph structure. The nodes of the graph structure represent cable grounding points and ports, and the edges of the graph structure represent cable segments. The topology-aware graph neural network contains three layers of graph attention convolutional layers.

[0012] Each node embedding feature vector contains ground potential amplitude, rise time and attenuation coefficient, each edge embedding feature vector contains cable length, transfer impedance amplitude and phase angle, each graph attention convolutional layer aggregates neighborhood node information and updates node features through attention mechanism, and the fully connected layer maps graph features to peak induced voltage and rise time of each port.

[0013] The fitness function of the shielding layer grounding method is calculated based on three parameters: peak induced voltage, voltage waveform distortion rate, and shielding layer circulating current power. The peak induced voltage is divided by the safety threshold voltage to obtain the normalized voltage ratio, the total harmonic distortion rate of the voltage waveform is divided by the fundamental frequency voltage amplitude to obtain the normalized distortion factor, and the active power of the shielding layer circulating current is divided by the rated power to obtain the normalized power ratio.

[0014] This invention employs a distributed parameter partial-element equivalent circuit model combined with the finite-difference time-domain method to solve for the transient ground potential distribution of the grounding network. It measures the equivalent transfer impedance frequency characteristics of the braided shielding layer using a four-port S-parameter vector network analysis method and combines it with a variational asymptotic homogenization multi-scale algorithm. It establishes a multi-conductor transmission line equation system to solve for the common-mode and differential-mode voltages of the core wires. A topology-sensing graph neural network prediction model is constructed, and a multilayer fast multipole algorithm is used to solve for the large-scale sparse admittance matrix to obtain the induced voltage distribution of the entire network. This invention overcomes the error accumulation problem of lumped-parameter models, accurately captures the frequency characteristics of the braided shielding layer and the influence of network topology on the induced voltage, and achieves quantitative evaluation and adaptive adjustment of grounding configuration through a fitness function of the shielding layer grounding method. It also establishes a quantitative relationship model between ground potential rise and core wire induced voltage. In summary, this invention solves the technical problem mentioned in the background art of the difficulty in accurately predicting and effectively suppressing the induced voltage of cable core wires caused by transient ground potential rise. Attached Figure Description

[0015] Figure 1 This is a flowchart of the method of the present invention.

[0016] Figure 2 The equivalent circuit model diagram for distributed parameter components is shown.

[0017] Figure 3 This is a time-varying ground potential difference curve at the grounding points at both ends of the cable.

[0018] Figure 4 The output of the coupled voltage prediction model is shown in the time domain waveform of the port induced voltage.

[0019] Figure 5 The bar chart shows the results of the parameter sensitivity analysis. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0021] like Figure 1 The diagram shows a flowchart of a method for determining transient ground potential rise through inductive coupling of a cable shielding layer, provided by the present invention. This method includes the following steps: S1. Establish the equivalent circuit model of the distributed parameter components of the grounding network, and use the finite-difference time-domain method to solve the spatiotemporal distribution of transient ground potential in the grounding network to obtain the time-varying ground potential difference function at the grounding points at both ends of the cable shielding layer. S2. The transfer impedance of the cable shielding layer in the 0.1 to 10 MHz frequency band is measured by using the four-port S-parameter vector network analysis method. The influence of parasitic parameters of the test fixture is eliminated by short-circuit open-circuit load through calibration. The equivalent transfer impedance frequency characteristic curve of the braided shielding layer is obtained by combining the variational asymptotic homogenization multi-scale algorithm. S3. Establish a set of multi-conductor transmission line equations based on the spatial path of the cable in the grounding network. Use the time-varying ground potential difference function obtained in step S1 as the excitation source of the shielding layer boundary. Use the equivalent transfer impedance frequency characteristic curve obtained in step S2 as the coupling parameter. Use the frequency domain analysis method to solve the set of multi-conductor transmission line equations to obtain the core wire common-mode voltage distribution and core wire differential-mode voltage distribution. S4. Construct a generalized node admittance matrix for the cable network topology, representing single-end grounding, two-end grounding, and multi-point grounding as different boundary condition matrices. Use the correlation matrix to automatically generate the topological equations, and use the multilevel fast multipole algorithm and the domain decomposition method to solve the large-scale sparse admittance matrix to obtain the induced voltage distribution of the cable cores in the entire network. S5. Input the induced voltage distribution data obtained in step S4 into the coupling voltage prediction model. The coupling voltage prediction model outputs the peak induced voltage and voltage waveform characteristic parameters of each cable port. Calculate the fitness function value of the shielding layer grounding method. When the fitness function value of the shielding layer grounding method is ∈ [0, 0.4), maintain the current grounding method. When the fitness function value of the shielding layer grounding method is ∈ [0.4, 0.7), adjust the shielding layer grounding resistance to decrease by 30%. When the fitness function value of the shielding layer grounding method is ∈ [0.7, 1.0], switch to the cross-interconnection grounding method. S6. Perform parameter sensitivity analysis on secondary control cables with cable lengths ranging from 50 to 500 m, extract the influence weighting coefficients of transfer impedance, cable length, and grounding method on peak induced voltage, and establish a quantitative relationship model between ground potential rise and induced voltage in cable cores.

[0022] The distributed parameter partial element equivalent circuit model is an equivalent model that discretizes each conductor segment in the grounding network into distributed parameter circuit elements. The establishment steps include: discretizing each conductor segment in the grounding network with a spatial step size of 0.1m; calculating the partial self-inductance and partial mutual inductance of each discrete conductor segment; obtaining the partial self-inductance by integrating the magnetic field generated by the conductor segment itself along the conductor segment path; and obtaining the partial mutual inductance by double integrating the mutual magnetic field between two conductor segments along their respective paths. The unit of partial inductance is [missing information - likely a unit of measurement]. For each discrete conductor segment, calculate its partial resistance. The partial resistance is obtained using Ohm's law based on the length, cross-sectional area, and conductivity of the conductor segment, and the unit is 1000 kJ / m². For any two nodes in a grounding network, calculate the partial capacitance. The partial capacitance is obtained by solving for the ratio of the electrostatic energy between the two nodes to the square of the voltage. The unit is 1 / 2 voltmeter. The circuit network equations are constructed by connecting the partial inductance and partial resistance of all discrete conductor segments in series to form the impedance branches of the conductor segments, and connecting the partial capacitances between all node pairs in parallel to form the admittance branches between nodes. This assembly forms a circuit network equation containing partial inductance matrices, partial resistance matrices, and partial capacitance matrices. The parameters of each element in the distributed parameter partial element equivalent circuit model are calculated from the geometric dimensions and relative positions of the conductor segments using a quasi-static field integral formula. This quasi-static field integral formula is a mathematical expression based on the Biot-Savart law and Coulomb's law, performed under quasi-static approximation conditions, to integrate or surface integral spatial field quantities. During integration, displacement current terms and electromagnetic radiation effects are ignored, and only the induced field component is retained. The integral value is solved using numerical integration methods. The distributed parameter partial element equivalent circuit model retains the spatial geometric information and electromagnetic coupling relationships of the grounding network. Compared with the traditional lumped parameter model, the distributed parameter partial element equivalent circuit model incorporates the mutual inductance and capacitive coupling between conductor segments, overcoming the error accumulation problem of the lumped parameter model under high-frequency and long-distance transmission conditions.

[0023] The finite-difference time-domain method discretizes the space where the grounding network is located into a cubic grid. In each time step, the electric and magnetic field components are updated according to the difference form of Maxwell's equations. The evolution of the potential of each point in the grounding network over time is obtained through iterative calculation. The time step is taken as the spatial step divided by the speed of light and then multiplied by 0.5 to meet the stability condition.

[0024] The time-varying ground potential difference function is a mathematical expression describing the change of potential difference between the grounding points at both ends of the cable shield over time. It is obtained by extracting the potential time series of the two grounding points from the calculation results using the finite-difference time-domain method, and then using a cubic spline interpolation algorithm to obtain a continuous-time function. The unit of the time-varying ground potential difference function value is... .

[0025] The four-port S-parameter vector network analysis method equates the two-conductor system consisting of the cable shield and the core wire to a four-port network. It obtains the scattering parameter matrix by measuring the amplitude and phase relationship between the incident and reflected waves, and extracts the transfer impedance from the scattering parameter matrix using the transmission reflection method. The measurement frequency range covers 0.1 to 10 MHz.

[0026] The short-circuit, open-circuit, load, and through-pass calibration involves connecting short-circuit, open-circuit, matched load, and through-pass components to the four ports of the vector network analyzer for calibration measurements. An error model matrix is ​​then established, and matrix operations are used in subsequent measurements to eliminate system errors introduced by test cables, connectors, and fixtures, thereby improving the accuracy of high-frequency transfer impedance measurements.

[0027] The variational asymptotic homogenization multiscale algorithm is an efficient modeling method for the periodic microstructure of braided shielding layers. Based on the principle of scale separation, the algorithm decomposes the electromagnetic field into a macroscopic slowly varying field and a microscopic rapidly varying field. It solves the periodic boundary value problem of the microscopic field within a representative volume element. By averaging the microscopic field, it obtains the equivalent constitutive parameters at the macroscopic scale, including the equivalent conductivity tensor and the equivalent permeability tensor. These equivalent constitutive parameters implicitly reflect the influence of the geometric characteristics of the braided structure on the shielding effectiveness. At the macroscopic scale, a homogenized medium is used to replace the actual braided structure. The variational principle ensures the consistency of microscopic and macroscopic energies, avoiding the surge in computational load caused by meshing each braided filament. The variational asymptotic homogenization multi-scale algorithm reduces the electromagnetic simulation of braided shielding layers from processing millions of grid cells to thousands of grid cells. While maintaining a transfer impedance calculation error of less than 5%, it compresses the calculation time for a single frequency point from several hours to minutes, providing a feasible approach for the rapid acquisition of broadband transfer impedance characteristics. The variational asymptotic homogenization multi-scale algorithm automatically captures the mapping relationship between braiding angle, braiding density, and wire diameter on macroscopic shielding performance, making it suitable for the refined analysis of complex braided patterns and multi-layer composite shielding structures, significantly improving the efficiency and accuracy of frequency characteristic modeling of cable shielding layers.

[0028] The equivalent transfer impedance frequency response curve is a curve characterizing the coupling capability of the cable shield's outer current to the inner core wire as a function of frequency. The horizontal axis represents frequency, and the vertical axis represents the transfer impedance amplitude. The equivalent transfer impedance frequency response curve is obtained by fusing and correcting the equivalent constitutive parameters calculated using a variational asymptotic homogenization multi-scale algorithm with measured data. The unit of the transfer impedance amplitude is... / m.

[0029] The multi-conductor transmission line equations are a system of partial differential equations describing the voltage and current distribution along the line on the cable core and shield. The multi-conductor transmission line equations include a unit length resistance matrix, a unit length inductance matrix, a unit length conductance matrix, and a unit length capacitance matrix. The coupling between the shield and the core is described by the transfer impedance matrix and the transfer admittance matrix.

[0030] The shielding layer boundary excitation source is an external voltage source acting on the shielding layer conductor in the multi-conductor transmission line equation system. The shielding layer boundary excitation source is driven by the time-varying ground potential difference function of the grounding points at both ends of the shielding layer. The waveform and amplitude of the shielding layer boundary excitation source determine the magnitude and frequency components of the current flowing on the shielding layer.

[0031] The coupling parameters are parameters that describe the electromagnetic coupling strength between the shielding layer and the core wire in the multi-conductor transmission line equations. The coupling parameters include the transfer impedance and transfer admittance characterized by the equivalent transfer impedance frequency response curve.

[0032] The frequency domain analysis method involves converting the time-domain multi-conductor transmission line equations to the frequency domain using Fourier transform, solving the algebraic equations at each frequency point to obtain the frequency domain response of voltage and current, and then obtaining the time-domain waveform through inverse Fourier transform. The frequency domain analysis method is applicable to the steady-state and transient analysis of linear time-invariant systems.

[0033] The common-mode voltage distribution of the core wires is the distribution of the average voltage of all core wires in the cable relative to the shielding layer along the length of the cable. The common-mode voltage distribution of the core wires is generated by the shielding layer current through the transfer impedance matrix coupling and is a key parameter for evaluating the level of electromagnetic interference.

[0034] The core wire differential mode voltage distribution is the distribution of the voltage difference between any two core wires in the cable along the length of the cable. The core wire differential mode voltage distribution is generated by the shielding layer current through the asymmetric coupling of the transfer admittance matrix, which directly affects the signal integrity of the secondary equipment.

[0035] The generalized node admittance matrix expresses the relationship between voltage and injected current of all nodes in the cable network in matrix form. The matrix elements of the generalized node admittance matrix are calculated from the distributed parameters and grounding impedance of the cable. The matrix dimension of the generalized node admittance matrix is ​​equal to the total number of nodes in the cable network. Solving the equation of the generalized node admittance matrix yields the total node voltage of the entire network.

[0036] The single-end grounding method is a grounding configuration in which the cable shielding layer is connected to the grounding network only at one end.

[0037] The aforementioned two-end grounding method is a grounding configuration in which the cable shielding layer is connected to the grounding network at both ends.

[0038] The multi-point grounding method is a grounding configuration in which the cable shielding layer is connected to the grounding network at both ends and at multiple locations along the line.

[0039] The boundary condition matrix is ​​a constraint equation matrix set according to the grounding method of the shielding layer. In the single-end grounding method, the voltage of one end node is zero and the current of the other end is zero. In the two-end grounding method, the voltage of the two end nodes is equal to the potential of the corresponding grounding point. In the multi-point grounding method, the voltage of multiple nodes is determined by the grounding resistance network equation.

[0040] The correlation matrix is ​​a matrix that describes the topological connection relationship of the cable network. The rows of the correlation matrix correspond to the edges, which are cables, and the columns of the correlation matrix correspond to the nodes, which are grounding points. The matrix elements of the correlation matrix are 1, negative 1, or 0, which indicate the association direction between the edge and the node. The node equations and loop equations of the cable network are automatically assembled using the correlation matrix.

[0041] The topology equations are a set of equations describing the voltage and current of each branch in the cable network as satisfying Kirchhoff's laws. The topology equations are automatically generated by multiplying the correlation matrix and the branch parameter matrix.

[0042] The aforementioned multilevel fast multipole algorithm is a numerical method for accelerating the solution of large-scale dense matrix-vector multiplication. It reduces the computational complexity by dividing the computational domain into a tree structure and utilizing far-field and local expansions to decrease the number of direct calculations of matrix elements. Reduce to ,in The number of unknowns.

[0043] The domain decomposition method divides the computational domain of a large-scale problem into several subdomains. After solving each subdomain independently, iterative coupling is achieved through interface conditions, and parallel computation is performed between subdomains. The domain decomposition method, combined with preconditional conjugate gradient iteration, accelerates convergence and is suitable for distributed computing platforms.

[0044] The large-scale sparse admittance matrix refers to the case where the proportion of non-zero elements in the generalized node admittance matrix of the cable network is less than 1%. The sparsity originates from the local coupling characteristics of the cable network. The memory requirement is reduced by two orders of magnitude by using a compressed sparse row format for storage.

[0045] The induced voltage distribution is a function of the voltage value of each point on the cable core relative to the reference ground as a function of its position. The distribution pattern of the induced voltage is affected by the cable length, grounding method and frequency characteristics. The peak induced voltage at the port is the basis for evaluating the port interference of secondary equipment.

[0046] The coupled voltage prediction model is structured as a topology-aware graph neural network. This network represents the cable network as a graph structure, where nodes represent cable grounding points and ports, and edges represent cable segments. Each node embeds a feature vector containing ground potential amplitude, rise time, and attenuation coefficient. Each edge embeds a feature vector containing cable length, transfer impedance amplitude, and phase angle. The network comprises three graph attention convolutional layers. Each layer aggregates neighboring node information and updates node features through an attention mechanism. The kernel size of the first layer is 128, the second layer is 64, and the third layer is 32. The activation function uses a parameterized rectified linear unit. The fully connected layer maps graph features to the peak induced voltage and rise time of each port. The output layer uses linear activation. The total number of parameters in the topology-aware graph neural network is 570,000.

[0047] The steps for establishing the training dataset for the coupled voltage prediction model include: generating 1000 different cable network configurations with different topologies in a grounding network simulation platform. Each cable network configuration contains 5 to 20 cables with cable lengths randomly distributed within the range of 50 to 500 m. The grounding method is randomly selected from single-end grounding, two-end grounding, and multi-point grounding. Applying 100 sets of transient ground potential excitations with different waveforms to each cable network configuration, with the excitation amplitude ranging from 1 to 50 kV and the rise time ranging from 0.1 to 10 μs, and calculating the induced voltage distribution of the entire network ports under each set of transient ground potential excitations using the methods in steps S1 to S4, resulting in a total of 100,000 input-output sample pairs. These input-output sample pairs are then divided into training, validation, and test sets in a ratio of 8:1:1.

[0048] The training steps of the coupled voltage prediction model include: using mean squared error as the loss function, with the optimization objective being that the relative error between the predicted voltage and the calculated voltage is less than 10%; using an adaptive moment estimation optimizer to update the network parameters of the topology-aware graph neural network; setting the initial learning rate to 0.001; decreasing the learning rate to 0.8 times the original rate after every 20 training rounds; setting the batch size to 32; and training on a graphics processing unit cluster for 150 rounds until the validation set loss converges. During training, dropout regularization is used to prevent overfitting, with a dropout ratio of 0.3. Finally, the average relative error of the coupled voltage prediction model on the test set is 7.8%, and the time taken for a single prediction is 15ms.

[0049] The voltage waveform characteristic parameters are characteristic quantities that describe the shape of the voltage waveform. The voltage waveform characteristic parameters include peak induced voltage, rise time, pulse width and oscillation frequency.

[0050] The peak induced voltage is the maximum absolute value of the voltage waveform in the time domain, with units of . .

[0051] The fitness function of the shielding layer grounding method is an index function that evaluates the effect of the current grounding configuration on induced voltage suppression. The fitness function of the shielding layer grounding method is calculated based on three parameters: peak induced voltage, voltage waveform distortion rate, and shielding layer circulating current power. The calculation formula is as follows: divide the peak induced voltage by the safety threshold voltage to obtain the normalized voltage ratio; divide the total harmonic distortion rate of the voltage waveform by the fundamental frequency voltage amplitude to obtain the normalized distortion factor; divide the active power of the shielding layer circulating current by the rated power to obtain the normalized power ratio; multiply the normalized voltage ratio, normalized distortion factor, and normalized power ratio by weighting coefficients of 0.5, 0.3, and 0.2, respectively, and then sum them to obtain the fitness function value of the shielding layer grounding method. The fitness function value of the shielding layer grounding method ranges from 0 to 1. The larger the value of the fitness function value of the shielding layer grounding method, the less suitable the grounding method is for the current operating conditions.

[0052] The safety threshold voltage is the maximum induced voltage limit that the secondary equipment port can withstand. The safety threshold voltage is determined according to the immunity level of the secondary equipment specified in the IEC 61000-4-5 standard. Through impulse voltage withstand tests on 50 typical secondary protection devices, the port voltage values ​​when each device malfunctions or is damaged were recorded. The experimental data were statistically analyzed, and the lower limit of the voltage at a 95% confidence level was taken as the safety threshold voltage. The experimental results show that the safety threshold voltage is 2.5kV.

[0053] The voltage waveform distortion rate is the degree to which the voltage waveform deviates from the standard sine wave, and the voltage waveform distortion rate is characterized by the total harmonic distortion rate.

[0054] The total harmonic distortion rate is the ratio of the square root of the sum of the squares of the effective values ​​of all harmonic components in the voltage waveform to the effective value of the fundamental wave, expressed as a percentage.

[0055] Wherein, the fundamental frequency voltage amplitude is the amplitude of the fundamental component after Fourier decomposition of the voltage waveform, and the unit is _____. .

[0056] The active power of the shielding layer circulating current is the active power consumed by the circulating current flowing through the shielding layer on the grounding resistance, and its unit is 1. .

[0057] The rated power is the maximum power loss limit allowed in the design of the cable shielding layer. The rated power is determined based on the cable current carrying capacity and temperature rise requirements. Temperature rise experiments were conducted on 30 different types of control cables to measure the temperature rise of the shielding layer under different circulating current power. The power corresponding to the temperature rise exceeding the maximum allowable operating temperature of the insulation material is the rated power. The experimental data fitting analysis yielded a rated power of 150W.

[0058] The weighting coefficients are coefficients that characterize the contribution of each parameter to the fitness function value of the shielding grounding method. The weighting coefficients of 0.5, 0.3 and 0.2 correspond to the normalized voltage ratio, normalized distortion factor and normalized power ratio, respectively. The weighting coefficients are determined by the analytic hierarchy process. Twelve technical personnel in the field of electromagnetic compatibility of power systems were invited to compare and score the importance of the three parameters pairwise. A judgment matrix was constructed, and the eigenvector corresponding to the largest eigenvalue of the judgment matrix was calculated. The weighting coefficients were obtained after normalizing the eigenvector.

[0059] The grounding resistance of the shielding layer is the resistance value between the grounding point of the shielding layer and the grounding network, and the unit is 1. .

[0060] The cross-interconnection grounding method involves dividing the shielding layers of multiple cables into segments along the line direction and then cross-connecting them before grounding. This reduces the induced voltage by changing the current loop path of the shielding layer. The location of the cross point is determined based on the cable length and transient wavelength, so that the induced electromotive forces on each segment of the shielding layer cancel each other out.

[0061] The secondary control cable is a cable used in the substation to transmit control signals and protection signals.

[0062] The parameter sensitivity analysis is a quantitative method for studying the degree of influence of small changes in input parameters on output results. It applies a disturbance of ±10% to the cable length, transfer impedance, and grounding resistance, respectively, and calculates the relative rate of change of the peak induced voltage. The absolute value of the relative rate of change is the sensitivity coefficient.

[0063] The influence weight coefficient is a normalized coefficient that quantitatively characterizes the contribution of each parameter to the peak induced voltage. The influence weight coefficient is obtained by normalizing the parameter sensitivity coefficient. The sum of all influence weight coefficients is equal to 1. The larger the influence weight coefficient, the more significant the influence of the parameter on the peak induced voltage.

[0064] The quantitative relationship model between the rise in ground potential and the induced voltage of the cable core is an analytical model that establishes a mathematical mapping relationship between the magnitude of the rise in ground potential and the peak induced voltage. The quantitative relationship model is in the form of a multi-parameter nonlinear regression equation. The equation coefficients are obtained by least-squares curve fitting of 3,000 sets of simulation data generated in steps S1 to S6. The quantitative relationship model is used to quickly estimate the level of induced voltage of the cable under different ground potential rise scenarios.

[0065] Optionally, the present invention also provides a computer-based method for forming an inductive coupling determination system for transient ground potential rise through a cable shield, wherein the computer is provided with a readable storage medium storing program instructions, and the program instructions execute the above-described method when the computer is run.

[0066] The specific implementation of the above steps is described in detail below. The specific implementation of step S1 is as follows: First, geometric modeling of the substation grounding network is performed. The horizontal and vertical grounding electrodes in the grounding network are established in three-dimensional space according to their actual arrangement and dimensions. Then, each grounding conductor segment is discretized with a spatial step size of 0.1m. Each discretized conductor segment is used as a calculation unit. Next, the partial self-inductance of each conductor segment is calculated. The calculation method is based on the Biot-Savart law, integrating the magnetic field generated by the conductor segment along its path. The integration process uses the Gaussian quadrature method for numerical integration. For any two conductor segments, the partial mutual inductance is calculated. The calculation method is to perform double integration of the mutual magnetic field between the two conductor segments along their respective paths. The integration kernel function is the reciprocal of the distance between the conductor segments. For each conductor segment, the partial resistance is calculated by dividing the length of the conductor segment by its cross-sectional area and then multiplying by the resistivity. For any two nodes in the grounding network, the partial capacitance is calculated by solving the ratio of the electrostatic energy between the two nodes to the square of the voltage. The boundary element method is used to solve the Poisson equation to obtain the electric field distribution, and then the electrostatic energy is calculated by integration. Partial inductance and partial resistance of the conductor segment are connected in series to form an impedance branch, and partial capacitance between all node pairs are connected in parallel to form an admittance branch. The circuit network equations of the distributed parameter partial element equivalent circuit model are assembled, which are large-scale sparse linear equations. Then, the transient process is solved using the finite-difference time-domain method. The space where the grounding network is located is discretized into a cubic grid with a side length of 0.05m. The time step is set to 0.17ns to satisfy the Coulomb stability condition. The excitation source boundary conditions are set at the initial moment when the lightning current or short-circuit current is injected into the grounding network. According to the differential discretization form of Maxwell's equations, the magnetic field component is updated first and then the electric field component in each time step. The complete data of the potential evolution of all grid nodes in the grounding network with time is obtained by iterative calculation step by step. The potential time series of the grid nodes where the grounding points at both ends of the cable shield are located are extracted from the calculation results. The potential difference time series is obtained by subtracting the two time series. The potential difference time series is interpolated in the time domain using the cubic spline interpolation algorithm to obtain a continuous time-varying ground potential difference function. This function is used as the input of the excitation source of the shield boundary in the subsequent steps.

[0067] The specific implementation of step S2 involves mounting a 2m long sample of the cable under test in a test fixture. The test fixture adopts a coaxial structure design to reduce the influence of parasitic inductance and capacitance. The four ports of the vector network analyzer are connected to the two ends of the cable shield and the core wire, respectively. Before connection, a short-circuit, open-circuit, load, and through-pass calibration is performed. The calibration process involves sequentially connecting a short-circuit standard, an open-circuit standard, and a 50°C standard to the four ports. The load and through-connector were matched, and the scattering parameters of each calibration component were measured and stored as an error model. The sweep frequency range of the vector network analyzer was set to 0.1–10 MHz, with 201 frequency points evenly distributed on a logarithmic scale. After the sweep measurement began, the network analyzer automatically emitted the incident wave and received the reflected and transmitted waves at each frequency point, recording the 16 complex elements of the four-port scattering parameter matrix. After the measurement was completed, the original scattering parameters were corrected using the error model matrix to eliminate systematic errors introduced by the test cable and fixture. Then, the transfer impedance was extracted from the corrected scattering parameter matrix using the transmission reflection method. The extraction algorithm is based on the two-conductor transmission line theory, treating the shielding layer as the outer conductor and the core wire as the inner conductor. The complex value of the transfer impedance is calculated through the linear combination of the elements of the scattering parameter matrix. The real part of the transfer impedance represents resistive coupling, and the imaginary part represents inductive coupling. The transfer impedance at 201 frequency points was obtained. After obtaining the complex impedance data, the variational asymptotic homogenization multi-scale algorithm is applied to calculate the equivalent parameters of the braided shielding layer. The algorithm first establishes a representative volume element geometric model of the braided shielding layer, with the element size being one braiding cycle. Within the element, the spatial distribution of the braided fibers is finely modeled. Then, periodic boundary conditions are applied to the representative volume element to solve for the microscopic electromagnetic field distribution. The solution process uses the finite element method to discretize Maxwell's equations. By performing volume averaging on the microscopic field, the equivalent conductivity tensor and equivalent permeability tensor are obtained. These equivalent parameters reflect the macroscopic response characteristics of the braided structure to electromagnetic waves. The equivalent parameters are substituted into the constitutive relation of the homogenized medium, and the transfer impedance is recalculated on a macroscopic scale. The results are compared and corrected with the measured values. Finally, the equivalent transfer impedance frequency characteristic curve considering the influence of the braided microstructure is obtained. The curve data is stored as a data file with frequency as the independent variable and transfer impedance amplitude and phase as the dependent variables.

[0068] The specific implementation of step S3 involves establishing spatial geometric coordinates based on the actual laying path of the cable in the grounding network, discretizing the cable path into several segments, each with a length of 0.5m, and establishing a multi-conductor transmission line model for each discrete segment. The model includes a shielding conductor and a core conductor. For each discrete cable segment, the resistance matrix per unit length is calculated. The diagonal elements of the resistance matrix represent the DC resistance of each conductor, calculated using the conductor cross-sectional area and resistivity. The off-diagonal elements are zero. The inductance matrix per unit length is then calculated. The diagonal elements of the inductance matrix represent the self-inductance of each conductor, and the off-diagonal elements represent the mutual inductance between conductors. The mutual inductance is calculated using the Newman formula with double line integrals over the conductor loop. The capacitance matrix per unit length is calculated by inverting the potential coefficient matrix obtained from solving the Laplace equation for the electrostatic field. Finally, the conductance matrix per unit length is calculated, with each element representing a capacitance value. Multiply the array elements by the dielectric loss tangent and then by the angular frequency to establish the transfer impedance matrix between the shield and the core wire. The matrix elements directly use the values ​​of the equivalent transfer impedance frequency characteristic curve obtained in step S2 at the corresponding frequency points to establish the transfer admittance matrix. The transfer admittance is the reciprocal of the transfer impedance. Substitute the above matrix into the multi-conductor transmission line equations. The equations describe the relationship between the spatial derivatives of voltage and current along the line and the frequency domain impedance admittance parameters. Perform a Fourier transform on the time-varying ground potential difference function obtained in step S1 to convert it to the frequency domain to obtain the frequency domain excitation source function. Apply the frequency domain excitation source function as the shield boundary excitation source to the boundary conditions of the transmission line equations. The boundary conditions are set such that the voltage at the shield node at both ends of the cable is equal to the frequency domain potential values ​​of the two grounding points, and the core wire port is connected to the load impedance, which is taken as the input impedance of the secondary equipment, with a reference value of 1kΩ. The transmission line equations are solved at each frequency point using frequency domain analysis. The solution process involves discretizing the partial differential equations along spatial coordinates and transforming them into a system of linear algebraic equations. The tridiagonal matrix equations are then solved using the pursuit method to obtain the frequency domain complex values ​​of voltage and current at each discrete point. The voltage distribution of the core conductor is extracted from the solution results. The average value of all core conductor voltages is taken as the common-mode voltage distribution of the core conductor, and the difference between any two core conductor voltages is taken as the differential-mode voltage distribution of the core conductor. An inverse Fourier transform is performed on the common-mode voltage distribution and the differential-mode voltage distribution in the frequency domain to obtain the time-domain voltage distribution waveform. This waveform reflects the entire process of transient ground potential rise coupled to the core conductor through the shielding layer.

[0069] The specific implementation of step S4 is as follows: First, extract the topology connection information of all secondary control cables in the substation, including the starting and ending grounding locations of each cable. Define each grounding point as a network node and each cable as a branch connecting two nodes. Construct an association matrix for the cable network. The number of rows in the association matrix equals the number of cables, and the number of columns equals the number of nodes. Assign values ​​to matrix elements according to the following rules: if the starting point of a cable is a node, the corresponding element is 1; if the ending point is a node, the corresponding element is -1; if the cable is unrelated to a node, the corresponding element is 0. Automatically generate the topology equation based on the association matrix by multiplying the association matrix by the node voltage column vector to obtain the branch. The voltage column vector is obtained by multiplying the transpose of the correlation matrix with the branch current column vector, which reflects Kirchhoff's voltage and current laws. The branch admittance is calculated for each cable branch, obtained by frequency domain transformation of the transmission line parameter matrix obtained in step S3. All branch admittances are assembled into a generalized node admittance matrix according to the network topology. The assembly process involves traversing each non-zero element of the correlation matrix and accumulating the admittance value of the corresponding branch into the corresponding position of the generalized node admittance matrix. The boundary conditions of the generalized node admittance matrix are modified according to different shielding grounding methods. For single-end grounding, the admittance matrix rows corresponding to the grounding node are set... As a unit vector, the branch current corresponding to the open-end node is set to zero. For the two-end grounding method, the rows of the admittance matrix corresponding to the two-end nodes are set to values ​​related to the grounding resistance. For the multi-point grounding method, the admittance values ​​of the node rows corresponding to multiple grounding points are set according to the connection relationship of the grounding resistance network. The modification of the boundary conditions is achieved by adding the boundary condition matrix and the generalized node admittance matrix to obtain the modified admittance matrix considering the grounding method. This modified admittance matrix is ​​a large-scale sparse matrix, with non-zero elements mainly concentrated on the diagonal and its vicinity. The modified admittance matrix is ​​stored in a compressed sparse row format to save memory, and then a multi-level fast multipole algorithm is used to add... The algorithm performs matrix-vector multiplication on a fast scale. It hierarchically divides the computational domain into quadtree or octree structures. Within each layer, the interactions between distant node pairs are approximated using multi-level and local expansions, while direct calculation is performed only on closely spaced node pairs. This significantly reduces the computational cost of a single matrix-vector multiplication. The algorithm also uses domain decomposition to divide the entire cable network into several subnetworks, each solved on independent computational nodes. Subnetworks are coupled through voltage and current continuity conditions at interface nodes. A preconditioned conjugate gradient iteration method is used to solve the overall equation system. The precondition matrix is ​​an incomplete LU decomposition matrix, and the iteration termination condition is a residual norm less than 1. After the solution converges, the voltage values ​​of all nodes in the entire network are obtained. Based on the node voltage and branch admittance, the induced voltage distribution of each cable core is calculated. The induced voltage distribution data is stored as a structured data file according to the cable number and location coordinates.

[0070] The specific implementation of step S5 involves preprocessing the induced voltage distribution data obtained in step S4, extracting the peak induced voltage and voltage waveform data at each cable port location, performing a Fourier transform on the voltage waveform to obtain the spectrum, and extracting the rise time and oscillation frequency from the spectrum as voltage waveform feature parameters. The topology information of the cable network is then converted into a graph structure representation. The node feature vector of the graph structure includes the ground potential amplitude, rise time, and attenuation coefficient of that node. The ground potential amplitude is extracted from the time-varying ground potential difference function in step S1. The rise time is determined by taking the derivative of the time-varying ground potential difference function to determine the moment of fastest potential rise. The attenuation coefficient is obtained by fitting an exponential function to the potential attenuation curve. The edge feature vector of the graph structure includes the cable length of the corresponding cable. The magnitude and phase angle of the transfer impedance are extracted from the equivalent transfer impedance frequency characteristic curve in step S2, and the values ​​corresponding to the main frequency components are input into the coupled voltage prediction model. The topology-aware graph neural network of the coupled voltage prediction model first calculates the attention weight of each node with its neighboring nodes in the first graph attention convolutional layer. The attention weight is obtained by normalizing the dot product of the node's feature vectors using the softmax function. The features of the neighboring nodes are weighted and summed according to the attention weight to update the current node's features. The second and third graph attention convolutional layers repeat the above process to propagate and aggregate feature information layer by layer. After three convolutional layers, the feature vector of each node contains global topology information and local coupling information. The relationship is as follows: the node features of the last layer are input into the fully connected layer. The fully connected layer maps the node features to the predicted peak induced voltage and rise time of each port through matrix multiplication and nonlinear activation. The output layer directly outputs the prediction results using linear activation. After obtaining the predicted peak induced voltage, the voltage waveform distortion rate is calculated. The distortion rate is obtained by extracting the amplitude of each harmonic after performing a fast Fourier transform on the voltage waveform. The square root of the sum of the squares of the amplitudes of the 2nd to 50th harmonics is divided by the fundamental amplitude to obtain the total harmonic distortion rate. The active power of the shielding layer circulating current is calculated. The active power is equal to the square of the effective value of the shielding layer circulating current multiplied by the grounding resistance. The peak induced voltage is divided by the safety threshold voltage of 2.5kV to obtain the normalized voltage ratio. The total harmonic distortion rate is divided by the fundamental frequency. The normalized distortion factor is obtained from the voltage amplitude. The normalized power ratio is obtained by dividing the active power of the shielding layer circulating current by the rated power of 150W. The normalized voltage ratio, the normalized distortion factor, and the normalized power ratio are multiplied by a weighting factor of 0.5, 0.3, and 0.2, respectively. The sum of these three products yields the fitness function value of the shielding layer grounding method. The grounding method is adjusted based on the fitness function value. When the fitness function value is less than 0.4, the current grounding method is considered to be suitable and remains unchanged. When the fitness function value is between 0.4 and 0.7, the current grounding method is considered to be partially suitable and the grounding resistance needs to be optimized. The grounding resistance of the shielding layer is reduced by 30% to reduce the circulating current power. When the fitness function value is greater than or equal to 0...At 7:00 AM, it was determined that the current grounding method was unsuitable for the operating conditions and needed to be switched to a cross-interconnection grounding method. Cross-interconnection involves dividing the cable into three equal parts along its length, cross-connecting the shielding layers of adjacent cables at the third division point, and then grounding. After adjustment, the induced voltage distribution was recalculated to verify the adjustment effect.

[0071] The specific implementation of step S6 involves selecting 20 typical secondary control cables with lengths ranging from 50 to 500 meters as the analysis objects. Parameter sensitivity analysis is performed on each cable. The analysis process involves keeping other parameters constant, increasing the cable length by 10%, and re-executing steps S1 to S5 to calculate the peak induced voltage at the cable port. The change in peak induced voltage is divided by the original peak induced voltage and then by the parameter change rate of 0.1 to obtain the sensitivity coefficient for the cable length. The same method is used to apply a ±10% disturbance to the transfer impedance amplitude and grounding resistance, calculating their respective sensitivity coefficients. This process is repeated for all 20 cables. Statistical analysis was performed on the sensitivity coefficients of the cable, calculating the average value of the sensitivity coefficient for each parameter. The average values ​​of the three parameter sensitivity coefficients were normalized to a sum of 1, yielding the influence weighting coefficients. Statistical results showed that the influence weighting coefficient for cable length was 0.45, for transfer impedance it was 0.35, and for grounding method it was 0.20. Next, a quantitative relationship model was established using 3000 sets of simulation data generated under different operating conditions in steps S1 to S5. The simulation data covered ground potential rise amplitudes from 1kV to 50kV, cable lengths from 50m to 500m, and transfer impedances from 0.01kV to 50kV. / m to 1 In a parameter space of / m, a multivariate nonlinear regression method was used to fit the functional relationship between peak induced voltage and ground potential rise amplitude, cable length, and transfer impedance. The regression model adopted the power function form, and the coefficients and exponential parameters in the model were determined by the least squares method. After the fitting was completed, the coefficient of determination of the model was calculated to evaluate the goodness of fit. A coefficient of determination greater than 0.95 indicates that the model has good predictive ability. The established quantitative relationship model can quickly estimate the peak induced voltage based on the known ground potential rise amplitude and cable parameters, providing a quantitative basis for the electromagnetic compatibility design and protection measure configuration of the secondary system.

[0072] It should be noted that the key technical ideas of this invention include a distributed parameter partial element equivalent circuit modeling method, a variational asymptotic homogenization multi-scale algorithm, a topology-sensing graph neural network coupled prediction model, and an adaptive grounding optimization strategy. The distributed parameter partial element equivalent circuit modeling method has the advantage over the traditional lumped parameter model in that it introduces the concepts of partial inductance and partial capacitance, preserving the spatial coupling relationship between conductor segments in the grounding network and the distribution characteristics of the electromagnetic field. This overcomes the high-frequency response distortion problem caused by the lumped parameter model simplifying conductor segments into single impedance elements. During rapid changes in transient ground potential, the distributed parameter model can accurately capture the traveling wave propagation phenomenon and time delay effect of ground potential in the grounding network, avoiding the calculation error of the cable shielding excitation source caused by the traditional method treating ground potential at different locations as synchronously changing. The variational asymptotic homogenization multi-scale algorithm, compared to the direct meshing method, has the advantage of decoupling the microscopic periodic structure and macroscopic electromagnetic response of the braided shielding layer through scale separation. After obtaining equivalent constitutive parameters by solving the microscopic field distribution at the representative volume element scale, a homogenized medium is used to replace the actual braided structure at the macroscopic scale. This avoids the degree-of-freedom explosion and computational resource bottleneck caused by fine meshing of each braided filament. Simultaneously, the variational principle ensures the consistency of microscopic and macroscopic energy, guaranteeing the physical accuracy of the equivalent model and making the calculation of broadband transfer impedance characteristics practically feasible, rather than being infeasible. The topology-aware graph neural network coupled prediction model, compared to traditional numerical methods, has the advantage of automatically learning the influence of cable network topology on coupling voltage through a graph attention mechanism. This avoids the huge computational overhead of repeatedly solving partial differential equations for each topology configuration. The trained model can predict the induced voltage distribution of the entire network within milliseconds, providing real-time computing capabilities for online monitoring and rapid assessment scenarios. The model's generalization ability makes it suitable for practical engineering applications with frequent topology changes. The synergistic effect of these three key technical approaches is reflected in the fact that the equivalent circuit modeling of the distributed parameter partial elements provides accurate macroscopic boundary conditions for the variational asymptotic homogenization multi-scale algorithm; the equivalent transfer impedance calculated by the variational asymptotic homogenization multi-scale algorithm provides high-quality training samples for the topology sensing graph neural network; and the induced voltage prediction results output by the topology sensing graph neural network guide the decision-making of adaptive grounding optimization strategies. This forms a complete technical chain from physical modeling to rapid prediction and then to engineering optimization. Compared with the error propagation and inefficiency caused by the independent processing of each link in the existing technology, the synergistic technical solution achieves a balance between accuracy and efficiency, and provides a systematic solution to the problem of induced coupling of transient ground potential rise through the cable shielding layer.

[0073] It should be noted that this invention also solves the following technical problems: In existing technologies, due to the complex micro-periodic structure of braided shielding layers, direct electromagnetic simulation of each braided filament requires millions of grid cells, resulting in calculation times of several hours or even days for wide-band transfer impedance characteristics, which is difficult to meet the needs of rapid analysis in engineering applications. This invention uses a variational asymptotic homogenization multi-scale algorithm to solve the periodic boundary value problem of the micro-field within representative volume cells based on the principle of scale separation. It obtains equivalent constitutive parameters through volume averaging and uses a homogenized medium to replace the actual braided structure at the macro-scale, reducing the number of grid cells from millions to thousands. While maintaining a transfer impedance calculation error of less than 5%, it compresses the calculation time for a single frequency point from several hours to minutes. Simultaneously, it automatically captures the mapping relationship between braiding angle, braiding density, and filament diameter on macro-shielding performance, achieving efficient and accurate modeling of the frequency characteristics of braided shielding layers. Furthermore, in existing technologies, when the number of cable network nodes reaches thousands or even tens of thousands, solving the generalized node admittance matrix faces the challenge of quadratic computational complexity, with memory requirements and computation time increasing exponentially. This invention divides the computational domain into a tree structure through a multi-layer fast multipole algorithm, reduces the number of direct calculations of matrix elements by using far-field expansion and local expansion, and reduces the computational complexity from the quadratic order of magnitude to the logarithmic linear order of magnitude. Combined with the domain decomposition method, parallel computation is performed between subdomains, and the memory requirement is reduced by two orders of magnitude by using compressed sparse row format storage, thus achieving efficient solution of induced voltage distribution in large-scale cable networks.

[0074] Specifically, the principle of this invention is as follows: The principle by which this invention solves the technical problem lies in the fact that the distributed parameter partial element equivalent circuit model retains the spatial geometric information and electromagnetic coupling relationship of the grounding network, and takes into account the mutual inductance coupling and capacitive coupling between conductor segments. The finite-difference time-domain method obtains accurate spatiotemporal distribution by iteratively solving Maxwell's equations. The variational asymptotic homogenization multi-scale algorithm, based on the scale separation principle, equates the microscopic periodic structure of the braided shielding layer to a macroscopic homogeneous medium, avoiding meshing of each braided filament. This significantly reduces the computational load while maintaining computational accuracy, resulting in accurate broadband coverage. The transfer impedance characteristics are analyzed. The multi-conductor transmission line equations use the time-varying ground potential difference as the excitation source of the shielding layer boundary and the equivalent transfer impedance as the coupling parameter. The common-mode voltage and differential-mode voltage distribution of the core wire are obtained by solving the equations using frequency domain analysis. The topology-aware graph neural network aggregates network topology information through graph attention convolutional layers, enabling rapid prediction of induced voltage. The fitness function of the shielding layer grounding method comprehensively evaluates the peak induced voltage, voltage waveform distortion rate, and shielding layer circulating current power, providing a quantitative basis for grounding method optimization. This achieves accurate prediction and effective suppression of induced voltage in the cable core wire caused by transient ground potential rise.

[0075] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0076] The specific implementation of step S1 involves establishing an equivalent circuit model of the distributed parameter components of the grounding network, using the finite-difference time-domain method to solve for the spatiotemporal distribution of transient ground potential in the grounding network, and obtaining the time-varying ground potential difference function at the grounding points at both ends of the cable shield. Each conductor segment in the grounding network is discretized with a spatial step size of 0.1m, and the partial self-inductance of each discrete conductor segment is calculated. and partial mutual inductance Partial self-inductance is obtained by integrating the magnetic field generated by the conductor segment itself along the path of the conductor segment, while partial mutual inductance is obtained by double integral of the mutual magnetic field between the two conductor segments along their respective paths. The calculation formula is expressed as follows: ; In the formula, For the first Partial self-inductance of a conductor, in units of ; Vacuum permeability, in units of The value is ; For the first The path of the conductor segment; and The infinitesimal length vector of the conductor segment, in units of . ; The distance between two infinitesimal elements, in units of 1. Partial mutual inductance The calculation formula is expressed as follows: ; In the formula, For the first The conductor segment and the first The partial mutual inductance between conductor segments, in units of ; For the first The path of the conductor segment; For the first The infinitesimal length vector of a conductor segment, in units of ; The distance between two conductor elements, in units of 1. Calculate the partial resistance of each discrete conductor segment. Partial resistance depends on the length of the conductor segment. Cross-sectional area and conductivity The calculation is obtained using Ohm's law, and the formula is expressed as follows: ; In the formula, For the first The partial resistance of a conductor, in units of ; For the first The length of a conductor segment, in units of ; For the first The conductivity of a conductor, in units of ; For the first The cross-sectional area of ​​a conductor segment, in units of Calculate the partial capacitance of any two nodes in the grounding network. Partial capacitor The calculation formula is expressed as follows: ; In the formula, For the first The node and the first The partial capacitance between nodes, in units of ; The electrostatic energy between the two nodes, in units of ; For the first The voltage at each node, in units of The impedance branches of all discrete conductor segments are formed by connecting a portion of their inductance and resistance in series, and the admittance branches between all node pairs are formed by connecting a portion of their capacitance in parallel. This assembles the network equations to include partial inductance, resistance, and capacitance matrices. The finite-difference time-domain method discretizes the grounding network into a cubic grid. Within each time step, the electric and magnetic field components are updated according to the difference form of Maxwell's equations. The evolution of the potential at each point in the grounding network over time is obtained through iterative calculations. The time step is specified in the original text. The calculation formula is expressed as follows: ; In the formula, For time steps, the unit is ; Spatial step size, unit: ; Speed ​​of light, unit: The value is By extracting the potential-time series of two grounding points from the calculation results using the finite-difference time-domain method, a continuous-time function is obtained using a cubic spline interpolation algorithm. Time-varying ground potential difference function Describe the change in potential difference between the grounding points at both ends of the cable shield over time, in units of... .

[0077] The specific implementation of step S2 involves using a four-port S-parameter vector network analysis method to measure the transfer impedance of the cable shielding layer in the 0.1–10 MHz frequency band. Short-circuit, open-circuit, load, and straight-through calibration eliminates the influence of parasitic parameters from the test fixture. A variational asymptotic homogenization multi-scale algorithm is then used to obtain the equivalent transfer impedance frequency response curve of the braided shielding layer. The four-port S-parameter vector network analysis method equates the two-conductor system composed of the cable shielding layer and the core wire to a four-port network. The scattering parameter matrix is ​​obtained by measuring the amplitude and phase relationship of the incident and reflected waves. The transfer impedance is extracted from the scattering parameter matrix using the transmission reflection method. The measurement frequency range covers 0.1–10 MHz. Short-circuit, open-circuit, load, and straight-through calibration involves connecting short-circuit, open-circuit, matched load, and straight-through components to the four ports of the vector network analyzer for calibration measurements. An error model matrix is ​​established, and matrix operations are used in subsequent measurements to eliminate systematic errors introduced by the test cable, connectors, and fixtures. The variational asymptotic homogenization multiscale algorithm, based on the principle of scale separation, decomposes the electromagnetic field into a macroscopic slowly varying field and a microscopic rapidly varying field. It solves the periodic boundary value problem of the microscopic field within a representative volume element, and obtains the equivalent constitutive parameters at the macroscopic scale, including the equivalent conductivity tensor, by performing volume averaging on the microscopic field. and equivalent permeability tensor At the macroscopic scale, a homogenized medium is used instead of a real woven structure, and the consistency of microscopic and macroscopic energy is ensured through variational principles. Equivalent transfer impedance frequency response curve. The equivalent constitutive parameters, calculated using a variational asymptotic homogenization multi-scale algorithm, are obtained by fusing and correcting them with measured data. The horizontal axis represents frequency. The unit is The vertical axis represents the magnitude of the transfer impedance, in units of... .

[0078] The specific implementation of step S3 involves establishing a multi-conductor transmission line equation system based on the spatial path of the cable in the grounding network. The time-varying ground potential difference function obtained in step S1 is used as the excitation source for the shielding layer boundary. The equivalent transfer impedance frequency response curve obtained in step S2 is used as the coupling parameter. Frequency domain analysis is employed to solve the multi-conductor transmission line equation system to obtain the common-mode voltage distribution and differential-mode voltage distribution of the core wires. The multi-conductor transmission line equation system describes the partial differential equation system of voltage and current distribution along the line on the cable core wires and shielding layer, and includes a unit-length resistance matrix. Unit length inductance matrix Unit length conductance matrix and unit length capacitor matrix The coupling between the shielding layer and the core wire is achieved through the transfer impedance matrix. and transfer admittance matrix Description. The frequency domain form of the multi-conductor transmission line equations is as follows: ; ; In the formula, For the length of the cable The frequency at the location is Voltage column vector, in units of ; For the length of the cable The frequency at the location is The current column vector, in units of ; These are the position coordinates along the cable, in units of ; Angular frequency, unit: ; The imaginary unit; This is a unit-length resistance matrix, with units of . ; This is a unit length inductance matrix, with units of... ; This is the conductance matrix per unit length, with units of . ; This is a unit-length capacitance matrix, with units of... The excitation source at the shielding layer boundary is a time-varying ground potential difference function at the grounding points at both ends of the shielding layer. The driving force, frequency domain analysis, transforms the time-domain multi-conductor transmission line equations to the frequency domain via Fourier transform. At each frequency point, the algebraic equations are solved to obtain the frequency domain response of voltage and current, and then the time-domain waveform is obtained through inverse Fourier transform. Core wire common-mode voltage distribution. It is the distribution of the average voltage of all core wires relative to the shielding layer along the length of the cable, and the differential mode voltage distribution of the core wires. It is the distribution of the voltage difference between any two core wires within a cable along the cable's length. Core wire common-mode voltage. The calculation formula is expressed as follows: ; In the formula, For position Common-mode voltage of the core wire at the point, in units of ; This represents the total number of core wires in the cable. For the first The core wire is in position The voltage relative to the shielding layer, in units of ; Number the core wires. Differential mode voltage of the core wires. The calculation formula is expressed as follows: ; In the formula, For position Differential mode voltage of the core wire at the point, in units of ; For the first The core wire is in position The voltage relative to the shielding layer, in units of ; For the first The core wire is in position The voltage relative to the shielding layer, in units of ; and For any two different core wires, use their numbers.

[0079] The specific implementation of step S4 involves constructing a generalized nodal admittance matrix for the cable network topology. Single-end grounding, two-end grounding, and multi-point grounding are represented as different boundary condition matrices. The topological equations are automatically generated using the correlation matrix. A multilevel fast multipole algorithm and domain decomposition method are employed to solve the large-scale sparse admittance matrix, thereby obtaining the induced voltage distribution of the entire cable core. Generalized Nodal Admittance Matrix The voltage and injected current relationships of all nodes in the cable network are expressed in matrix form. The matrix elements are calculated from the distributed parameters of the cable and the grounding impedance, and the matrix dimension is equal to the total number of nodes in the cable network. The equation for the generalized nodal admittance matrix is ​​expressed as follows: ; In the formula, This is the generalized nodal admittance matrix, in units of 1. ; This is a column vector of node voltages, in units of... ; Inject current column vectors into nodes, in units of The boundary condition matrix sets the constraint equations based on the shielding layer grounding method. In a single-end grounding method, the voltage at one end of the node is zero, and the current at the other end is zero. In a two-end grounding method, the voltages at both ends of the node are equal to the potentials of their respective grounding points. In a multi-point grounding method, the voltages of multiple nodes are determined by the grounding resistance network equations. (Independence matrix) This describes the topological connections of a cable network. Rows correspond to edges, which are cables, and columns correspond to nodes, which are grounding points. Matrix elements are 1, -1, or 0, indicating the direction of association between edges and nodes. The multilevel fast multipole algorithm partitions the computational domain into a tree structure and utilizes far-field and local expansion to reduce the number of direct calculations of matrix elements, thus reducing computational complexity from... Reduce to ,in This represents the total number of nodes. The domain decomposition method divides the computational domain of a large-scale problem into several subdomains. After solving each subdomain independently, iterative coupling is achieved through interface conditions to determine the induced voltage distribution. It is the voltage value of each point on the cable core relative to the reference ground as the position changes. A function of change, in units of .

[0080] The specific implementation of step S5 involves inputting the induced voltage distribution data obtained in step S4 into the coupled voltage prediction model. The coupled voltage prediction model outputs the peak induced voltage and voltage waveform characteristic parameters of each cable port, calculates the fitness function value of the shielding layer grounding method, and when the fitness function value of the shielding layer grounding method... The current grounding method is maintained within the range of 0 to 0.4, and the fitness function value of the shielding layer grounding method is... When the shielding layer grounding resistance is adjusted to decrease by 30% within the range of 0.4 to 0.7, the fitness function value of the shielding layer grounding method is... Switching to cross-connection grounding mode within the range of 0.7 to 1.0. The coupling voltage prediction model adopts a topology-aware graph neural network structure, containing three graph attention convolutional layers. The first layer has a kernel size of 128, the second layer has a kernel size of 64, and the third layer has a kernel size of 32. The activation function uses a parameterized rectified linear unit. The fully connected layer maps graph features to the peak induced voltage and rise time of each port, and the output layer uses linear activation. The fitness function for the shielding layer grounding mode is also specified. The calculation is based on three parameters: peak induced voltage, voltage waveform distortion rate, and shielding layer circulating current power. The calculation formula is expressed as follows: ; In the formula, The value of the fitness function for the grounding method of the shielding layer is dimensionless. Peak induced voltage, unit: ; Safety threshold voltage, unit: The value is 2.5; Total harmonic distortion (THD) is expressed as a percentage. For reference, the total harmonic distortion rate is expressed as a percentage, with a value of 10. The active power of the shielding layer circulation current, in units of ; Rated power, unit: The value is 150. Among them, the total harmonic distortion (THD) is... The calculation formula is expressed as follows: ; In the formula, Total harmonic distortion (THD) is expressed as a percentage. For the first The effective value of the second harmonic voltage, in units of ; The highest harmonic order to be considered is usually taken as 50; This is the effective value of the fundamental voltage, in units of . ; Harmonic order. Active power of the circulating current in the shielding layer. The calculation formula is expressed as follows: ; In the formula, The active power of the shielding layer circulation current, in units of ; The effective value of the circulating current through the shielding layer, in units of ; The grounding resistance of the shielding layer, in units of Effective value of circulating current through the shielding layer The calculation formula is expressed as follows: ; In the formula, The effective value of the circulating current through the shielding layer, in units of ; The effective value of the time-varying ground potential difference function, in units of ; The total resistance of the shielding layer circulating current loop is given in units of 1000 ohms. It is calculated by the sum of the resistance of the shielding layer itself and the grounding resistance.

[0081] The specific implementation of step S6 involves performing parameter sensitivity analysis on secondary control cables with lengths ranging from 50 to 500 meters. This involves extracting weighting coefficients for the influence of transfer impedance, cable length, and grounding method on the peak induced voltage, and establishing a quantitative relationship model between ground potential rise and induced voltage in the cable core. The parameter sensitivity analysis considers cable length... Transfer impedance and grounding resistance Apply disturbances of ±10% respectively, and calculate the peak induced voltage. The relative rate of change, the absolute value of the relative rate of change is the sensitivity coefficient. Sensitivity coefficient The calculation formula is expressed as follows: ; In the formula, For the first Sensitivity coefficients for each parameter, dimensionless; For parameters Peak induced voltage at original value, unit: ; For parameters Peak induced voltage after disturbance, in units of ; For the first The original values ​​of the parameters, Represents cable length Transfer impedance or grounding resistance one of the; For the first The perturbation of each parameter, empirically, is... ; This parameter is numbered and can take the values ​​1, 2, or 3. It affects the weighting coefficient. The parameter sensitivity coefficient is obtained by normalization, and the normalization formula is expressed as follows: ; In the formula, For the first The influence weighting coefficients of each parameter are dimensionless. For the first Sensitivity coefficients for each parameter, dimensionless; The parameters are assigned summation indices with values ​​of 1, 2, and 3. The quantitative relationship model between ground potential rise and induced voltage in the cable core adopts a multi-parameter nonlinear regression equation. The equation coefficients are obtained by least-squares curve fitting of 3000 sets of simulation data generated in steps S1 to S6. This quantitative relationship model is used to quickly estimate the induced voltage level of the cable under different ground potential rise scenarios. The quantitative relationship model between ground potential rise and induced voltage in the cable core is described as follows: ; In the formula, Peak induced voltage, unit: ; Reference peak voltage, unit: The value is 1; , , The regression coefficients are dimensionless and obtained by least squares fitting. The magnitude of the rise in ground potential, in units of ; The reference ground potential rise amplitude is expressed in units of... The value is 10; The transfer impedance is expressed in units of 1. ; Reference transfer impedance, in units of The value is 0.01; The length of the cable is given in units of 1. ; For reference cable length, the unit is... The value is 100; Grounding resistance, unit: ; Reference grounding resistance, unit: The value is 1; The fitting error term is dimensionless and ranges from -0.05 to 0.05.

[0082] To better understand and implement this invention, a specific application scenario of the invention is provided below as Example 2: To verify the effectiveness of the invention, technicians set up a test environment and conducted inductive coupling analysis of transient ground potential rise using the actual grounding network and secondary cable system of a 500kV substation. The substation's grounding network is a rectangular grid structure, 120m long in the east-west direction and 85m wide in the north-south direction. The grounding network is laid with 50×6mm galvanized flat steel, with a grid spacing of 10m, and a soil resistivity of 150Ω·m. Eight secondary control cables are laid within the substation, connecting the main control room to the protection devices in each bay. The cable lengths range from 80 to 320m, the cable type is KVVP-4×2.5, the shielding layer uses a copper wire braided structure, the braiding angle is 35°, the braiding density is 85%, and the single wire diameter is 0.15mm.

[0083] Technicians first establish an equivalent circuit model of the distributed parameter components of the grounding network, such as... Figure 2 As shown, each flat steel conductor in the grounding network is discretized into 1200 conductor segments with a spatial step size of 0.1m. For each conductor segment, its partial self-inductance and partial mutual inductance are calculated. The partial self-inductance is obtained using the quasi-static field integral formula, with a length of 0.1m and a cross-sectional area of ​​300mm². The partial self-inductance of a single conductor segment is 0.23 μH. The partial mutual inductance between adjacent conductor segments is 0.18 μH, and the partial mutual inductance between conductor segments spaced one grid apart decreases to 0.045 μH. The partial resistance of each conductor segment is determined based on the conductivity of the flat steel. The resistance of a single segment is calculated to be 0.0057Ω using S / m. The partial capacitance between grounding grid nodes is obtained by solving for the electrostatic field energy; the partial capacitance between adjacent nodes is 45pF, and the partial capacitance between diagonal nodes is 12pF. By connecting the partial inductances and partial resistances of all discrete conductor segments in series to form 1200 impedance branches, and connecting the partial capacitances between nodes in parallel to form admittance branches, the circuit network equations containing partial inductance matrices, partial resistance matrices, and partial capacitance matrices are obtained.

[0084] The finite-difference time-domain method was used to solve the spatiotemporal distribution of transient ground potential in the grounding network. The space containing the grounding network was discretized into a 0.5×0.5×0.5m cubic grid, with a total of 163,840 grids. The time step was set to 0.83 ns to meet the numerical stability requirements. A double-exponential waveform lightning current excitation with an amplitude of 35 kV, a rise time of 1.2 μs, and a half-peak time of 50 μs was applied at the grounding network inlet point. After 6000 time steps of iterative calculation, the temporal evolution of the potential at each node in the grounding network was obtained. The potential time series of the grounding points at both ends of the shielding layers of eight cables were extracted, and a continuous time-varying ground potential difference function was obtained using a cubic spline interpolation algorithm. Figure 3 As shown, the peak value of the time-varying ground potential difference at the grounding points at both ends of cable No. 1 is 12.3kV, which occurs 2.8μs after the lightning strike. The peak value of the time-varying ground potential difference at the grounding points at both ends of cable No. 5 is 8.7kV, which occurs at 3.1μs.

[0085] Technicians used a four-port S-parameter vector network analysis method to measure the transfer impedance of the shielding layer of KVVP-4×2.5 cable. The measurement frequency range was 0.1–10 MHz, with 200 frequency sampling points. Short-circuit, open-circuit, 50Ω matched load, and straight-through components were sequentially connected to the four ports of the vector network analyzer for short-circuit, open-circuit, load, and straight-through calibration. A 12×12-dimensional error model matrix was established to eliminate the effects of parasitic inductance (3.2 nH) and parasitic capacitance (8.5 pF) introduced by the test cable and fixture. The measured transfer impedance was 0.032 Ω / m at 100 kHz, rising to 0.058 Ω / m at 1 MHz, and reaching 0.095 Ω / m at 10 MHz. The braided shielding layer was modeled using a variational asymptotic homogenization multi-scale algorithm. The periodic boundary value problem of the microfield was solved within a representative volume element. The diagonal elements of the equivalent conductivity tensor were obtained through volume averaging. S / m, the diagonal elements of the equivalent permeability tensor are: H / m. The equivalent constitutive parameters were fused and corrected with measured data to obtain the equivalent transfer impedance frequency response curve. The corrected transfer impedance at 1MHz was 0.061Ω / m, with a relative error of 5.2% compared to the measured value. The variational asymptotic homogenization multi-scale algorithm reduced the single-frequency point calculation time from 3.5 hours to 8 minutes, and decreased the electromagnetic simulation mesh element of the braided shielding layer from 1.27 million to 1850.

[0086] A set of multi-conductor transmission line equations was established based on the spatial paths of eight cables in the grounding network. Each cable contains four cores and one shield, forming a 5×5 dimensional matrix of resistance, inductance, conductance, and capacitance per unit length. The time-varying ground potential difference function was used as the excitation source for the shield boundary, and the equivalent transfer impedance frequency response curve was used as the coupling parameter. The multi-conductor transmission line equations were solved using frequency domain analysis. A Fourier transform was performed on the time-varying ground potential difference function, and the algebraic equations were solved at 200 frequency points with a frequency resolution of 50 kHz. The calculated peak common-mode voltage of cable 1 at a distance of 60 m from the starting point was 3.8 kV, occurring at 3.2 μs, and the peak differential-mode voltage was 0.45 kV. The peak common-mode voltage of cable 5 at a distance of 150 m from the starting point was 2.6 kV, and the peak differential-mode voltage was 0.32 kV.

[0087] A generalized node admittance matrix (48×48) is constructed for the cable network topology, corresponding to 6 nodes for each of the 8 cables. Of the 8 cables, 3 use single-end grounding, 4 use double-end grounding, and 1 uses multi-point grounding. In single-end grounding, the voltage at one end of the node is zero, and the current at the other end is zero. In double-end grounding, the voltages at both ends of the node are equal to the potentials of their respective grounding points. In multi-point grounding, the voltages at the three grounding points along the cable are determined by the grounding resistance network equation, with grounding resistance values ​​of 0.8Ω, 1.2Ω, and 0.9Ω, respectively. The topology equation is automatically generated using an 8×48-dimensional incidence matrix, where non-zero elements account for 6.7%. The generalized node admittance matrix is ​​solved using a multilevel fast multipole algorithm and a domain decomposition method. The computational domain is divided into 4 subdomains for parallel computation. Combined with preconditional conjugate gradient iteration, the residual converges after 45 iterations. The induced voltage distribution of the entire network of cable cores is shown in Table 1.

[0088] Table 1. Peak Induced Voltage Distribution at Each Cable Port

[0089] The induced voltage distribution data is input into the coupled voltage prediction model, which is a topological sensing graph neural network. The cable network is represented as a graph structure containing 48 nodes and 8 edges. Node feature vectors include ground potential amplitude, rise time (1.2 μs), and attenuation coefficient (830 / s), while edge feature vectors include cable length, transfer impedance amplitude, and phase angle. The data is processed through three graph attention convolutional layers: the first layer has a kernel size of 128, the second 64, and the third 32, with parameterized rectified linear units as the activation function. The fully connected layer outputs the peak induced voltage and rise time at each port, as shown below. Figure 4As shown in the figure, the prediction results show that the peak induced voltage at the A-phase port of cable 1 is 3.79kV, with a relative error of 0.8% compared to the calculated value of 3.82kV. The predicted rise time is 3.3μs, while the actual value is 3.2μs, with a relative error of 3.1%. The prediction time for a single prediction is 15ms, which is about 550 times more efficient than the 2.3 hours of the traditional finite element simulation method.

[0090] Calculate the fitness function value for each cable shield grounding method, with a safety threshold voltage of 2.5kV. Cable No. 1 has a peak induced voltage of 3.82kV, a normalized voltage ratio of 1.53, a total harmonic distortion rate of 38%, a fundamental frequency voltage amplitude of 2.9kV, a normalized distortion factor of 0.13, a shield circulating current active power of 87W, a rated power of 150W, and a normalized power ratio of 0.58. Using weighting coefficients of 0.5, 0.3, and 0.2, the fitness function value is calculated to be 0.92, falling within the interval... It needs to be switched to cross-interconnected grounding. Cable #5 has a peak induced voltage of 2.67kV, a normalized voltage ratio of 1.07, a normalized distortion factor of 0.095, a normalized power ratio of 0.41, and a fitness function value of 0.64, falling within the range... The grounding resistance of the shielding layer needs to be adjusted to reduce it by 30%, from the original 1.5Ω to 1.05Ω. After adjustment and recalculation, the peak induced voltage of cable No. 5 has decreased to 2.31kV, and the fitness function value has decreased to 0.52. The fitness function value of cable No. 4 is 0.28, which falls within the range... The current single-ended grounding method will be maintained.

[0091] Sensitivity analysis was performed on secondary control cables with lengths ranging from 50 to 500 m, applying ±10% perturbations to cable length, transfer impedance, and grounding resistance. When the cable length increased from 240 m to 264 m, the peak induced voltage rose from 3.24 kV to 3.67 kV, with a relative change rate of 13.3% and a sensitivity coefficient of 1.33. When the transfer impedance increased from 0.061 Ω / m to 0.067 Ω / m, the peak induced voltage rose from 3.24 kV to 3.51 kV, with a relative change rate of 8.3% and a sensitivity coefficient of 0.83. When the grounding resistance increased from 1.2 Ω to 1.32 Ω, the peak induced voltage rose from 3.24 kV to 3.38 kV, with a relative change rate of 4.3% and a sensitivity coefficient of 0.43. After normalizing the sensitivity coefficients, the influence weighting coefficients for cable length, transfer impedance, and grounding resistance were found to be 0.51, 0.32, and 0.17, respectively. Figure 5 As shown.

[0092] A quantitative relationship model between ground potential rise and induced voltage in cable cores was established using least-squares curve fitting based on 3000 sets of simulation data. The model is a multi-parameter nonlinear regression equation, and the peak induced voltage is related to the ground potential difference amplitude, cable length, transfer impedance, and grounding resistance. Fitting results show that when the ground potential difference amplitude is 10kV, the cable length is 200m, the transfer impedance is 0.06Ω / m, and the grounding resistance is 1.0Ω, the estimated peak induced voltage is 2.85kV, with a relative error of 2.1% compared to the simulated value of 2.91kV. This quantitative relationship model can be used to quickly estimate the induced voltage level of cables under different ground potential rise scenarios, providing a theoretical basis for optimizing grounding methods.

[0093] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for determining transient ground potential rise through inductive coupling of a cable shield, characterized in that, This includes establishing a distributed parameter partial element equivalent circuit model of the grounding network; using the finite-difference time-domain method to solve for the spatiotemporal distribution of transient ground potential in the grounding network to obtain the time-varying ground potential difference function at the grounding points at both ends of the cable shield; measuring the transfer impedance of the cable shield in the 0.1 to 10 MHz frequency band using a four-port S-parameter vector network analysis method; eliminating the influence of parasitic parameters of the test fixture through short-circuit open-circuit load through-pass calibration; and obtaining the equivalent transfer impedance frequency characteristic curve of the braided shield using a variational asymptotic homogenization multi-scale algorithm; establishing a multi-conductor transmission line equation system based on the spatial path of the cable in the grounding network; using the time-varying ground potential difference function as the excitation source of the shield boundary; and determining the equivalent transfer impedance frequency... Characteristic curves are used as coupling parameters. Frequency domain analysis is employed to solve the multi-conductor transmission line equations to obtain the common-mode voltage distribution and differential-mode voltage distribution of the core wires. A generalized node admittance matrix of the cable network topology is constructed, and single-end grounding, two-end grounding, and multi-point grounding are represented as different boundary condition matrices. The topology equations are automatically generated using the correlation matrix. The large-scale sparse admittance matrix is ​​solved using the multilevel fast multipole algorithm and the domain decomposition method to obtain the induced voltage distribution of the entire network cable core wires. The induced voltage distribution data is input into the coupled voltage prediction model to output the peak induced voltage and voltage waveform characteristic parameters of each cable port. The grounding mode adjustment strategy is determined based on the fitness function value of the shielding layer grounding mode. Parameter sensitivity analysis was performed on secondary control cables with cable lengths ranging from 50 to 500 m. The influence weighting coefficients of transfer impedance, cable length, and grounding method on peak induced voltage were extracted, and a quantitative relationship model between ground potential rise and induced voltage in cable cores was established.

2. The method according to claim 1, characterized in that, The establishment of the equivalent circuit model of the distributed parameter part element involves discretizing each conductor segment in the grounding network with a spatial step size of 0.1m, calculating the partial self-inductance and partial mutual inductance of each discrete conductor segment, calculating the partial resistance of each discrete conductor segment, and calculating the partial capacitance of any two nodes in the grounding network. These are then assembled to form a circuit network equation containing a partial inductance matrix, a partial resistance matrix, and a partial capacitance matrix.

3. The method according to claim 2, characterized in that, Part of the self-inductance is obtained by integrating the magnetic field generated by the conductor segment itself along the path of the conductor segment; part of the mutual inductance is obtained by double integration of the mutual magnetic field between the two conductor segments along their respective paths; part of the resistance is calculated using Ohm's law based on the length, cross-sectional area, and conductivity of the conductor segment; and part of the capacitance is obtained by solving the ratio of the electrostatic energy between the two nodes to the square of the voltage.

4. The method according to claim 3, characterized in that, In the equivalent circuit model of the distributed parameter component, the parameters of each component are calculated by the geometric dimensions and relative positions of the conductor segments using the quasi-static field integral formula. The quasi-static field integral formula is a mathematical expression based on the Biot-Savart law and Coulomb's law, which are used to perform path integrals or surface integrals of spatial field quantities under quasi-static approximation conditions.

5. The method according to claim 1, characterized in that, The solution using the finite-difference time-domain method involves discretizing the space containing the grounding network into a cubic grid. Within each time step, the electric and magnetic field components are updated according to the difference form of Maxwell's equations. The evolution of the potential at each point in the grounding network over time is obtained through iterative calculation. The time step is taken as the spatial step divided by the speed of light and then multiplied by 0.5 to satisfy the stability condition.

6. The method according to claim 1, characterized in that, The variational asymptotic homogenization multiscale algorithm decomposes the electromagnetic field into a macroscopic slowly varying field and a microscopic rapidly varying field based on the principle of scale separation. It solves the periodic boundary value problem of the microscopic field within a representative volume element, obtains the equivalent constitutive parameters of the macroscopic scale by averaging the microscopic field, and uses a homogenized medium to replace the real woven structure at the macroscopic scale.

7. The method according to claim 6, characterized in that, The variational asymptotic homogenization multi-scale algorithm reduces the electromagnetic simulation of braided shielding layers from processing millions of grid cells to thousands of grid cells. While maintaining the transfer impedance calculation error of less than 5%, it compresses the calculation time for a single frequency point from several hours to minutes and automatically captures the mapping relationship between braiding angle, braiding density, and wire diameter on macroscopic shielding performance.

8. The method according to claim 1, characterized in that, The coupled voltage prediction model is structured as a topology-aware graph neural network, which represents the cable network as a graph structure. The nodes of the graph structure represent cable grounding points and ports, and the edges of the graph structure represent cable segments. The topology-aware graph neural network contains three layers of graph attention convolutional layers.

9. The method according to claim 8, characterized in that, Each node's embedded feature vector contains the ground potential amplitude, rise time, and attenuation coefficient. Each edge's embedded feature vector contains the cable length, transfer impedance amplitude, and phase angle. Each graph attention convolutional layer aggregates neighboring node information and updates node features through an attention mechanism. The fully connected layer maps graph features to the peak induced voltage and rise time of each port.

10. The method according to claim 8, characterized in that, The fitness function of the shielding layer grounding method is calculated based on three parameters: peak induced voltage, voltage waveform distortion rate, and shielding layer circulating current power. The peak induced voltage is divided by the safety threshold voltage to obtain the normalized voltage ratio, the total harmonic distortion rate of the voltage waveform is divided by the fundamental frequency voltage amplitude to obtain the normalized distortion factor, and the active power of the shielding layer circulating current is divided by the rated power to obtain the normalized power ratio.

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