A method for predicting electromagnetic radiation from a cable

Abstract

This invention discloses a method for predicting electromagnetic radiation from cables. First, a one-dimensional conductor model of the target cable is established in a three-dimensional simulation space, and its axial direction is divided into multiple segments. Current data for each segment is solved using the finite-difference time-domain method. Then, the three-dimensional simulation space is discretized using a Yee grid, and virtual observation points corresponding to actual observation points are determined. Standard electric field and standard magnetic field update equations are established on the Yee grid based on Maxwell's equations. A field-circuit co-simulation process is established, and in each time step iteration, the current data is equivalently coupled to the standard electric field and standard magnetic field update equations to achieve synchronous updates of transmission line current and spatial electromagnetic field. Finally, this process is executed until a preset termination condition is met, and the time-domain electromagnetic field response at the virtual observation points is extracted as the time-domain electromagnetic radiation prediction result. The advantages are high prediction accuracy and high prediction efficiency.

Description

Technical Field

[0001] This invention relates to methods for predicting electromagnetic radiation, and more particularly to a method for predicting electromagnetic radiation from cables. Background Technology

[0002] In the electromagnetic compatibility (EMC) design of power electronic equipment (such as motor drives, photovoltaic inverters, and on-board chargers), cables used for power transmission are a key factor leading to excessive radiated emissions. Whether it's a DC bus, AC output phase line, or signal interface line, any cable carrying high-frequency switching noise can be considered an equivalent antenna in the complex operating environment of power electronic equipment, generating severe electromagnetic interference. Therefore, in the early design stages of power electronic equipment, to achieve effective evaluation and design guidance for the overall EMC performance, decomposing the system radiation problem and focusing on the efficient and accurate modeling of the radiation characteristics of individual cables has become a key research direction for improving the feasibility and accuracy of predictions.

[0003] Currently, techniques for predicting cable radiation mainly fall into two categories: analytical methods and numerical methods. Analytical methods, such as those based on transmission line theory, Hertzian dipoles, or multi-dipole series models, typically calculate the radiation field by simplifying equivalents or using piecewise processing, combined with measured current. These methods are computationally efficient but often rely on large amounts of measurement data and have limited accuracy when analyzing transients. Numerical methods, such as the finite-difference time-domain method, the method of moments, or the finite element method, directly solve Maxwell's equations. These methods offer high accuracy and can finely simulate complex cable bundles and three-dimensional structures, but they consume significant computational resources, require strict mesh generation, and are less efficient in broadband analysis or iterative design.

[0004] In summary, existing methods often struggle to balance efficiency and accuracy when predicting cable radiation in practical engineering applications: analytical methods are fast but lack accuracy, while full-wave numerical methods are accurate but slow. Therefore, to achieve reliable and rapid assessment of cable radiation performance in engineering design and ensure product compliance with electromagnetic compatibility standards, there is an urgent need to develop a new prediction method that significantly improves computational efficiency while maintaining acceptable accuracy for engineering applications. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for predicting electromagnetic radiation of cables with high prediction accuracy and high prediction efficiency.

[0006] The technical solution adopted by this invention to solve the above-mentioned technical problems is as follows: a method for predicting electromagnetic radiation from cables, comprising the following steps: Step S1: Establish a one-dimensional conductor model of the target cable in the three-dimensional simulation space, divide the one-dimensional conductor model into multiple segments along its axis, and solve each segment based on the finite difference method in the time domain to obtain the current data corresponding to each segment. Step S2: Discretize the three-dimensional simulation space using Yee mesh, and determine virtual observation points in the three-dimensional simulation space that correspond to the actual observation points; Step S3: Based on Maxwell's equations, establish the standard electric field update equations and the standard magnetic field update equations on the Yee grid; Step S4: Establish a field-circuit co-simulation process. In each time step iteration, the field-circuit co-simulation process achieves synchronous updates of transmission line current and spatial electromagnetic field by equivalently coupling the current data obtained in step S1 to the standard electric field update equation and standard magnetic field update equation established in step S3. Step S5: Execute the field-circuit co-simulation process until the preset termination condition is reached, and extract the time-domain electromagnetic field response at the virtual observation point as the time-domain electromagnetic radiation prediction result of the target cable.

[0007] Compared with the prior art, the advantages of the present invention are as follows: First, it has high prediction efficiency: This invention establishes a one-dimensional conductor model of the target cable, reducing the slender cable structure from three dimensions to one dimension for description. Combined with the finite-difference time-domain method, it quickly solves each segment, efficiently obtaining the current distribution along the line. At the same time, the Yee mesh is used to discretize only the surrounding space of the three-dimensional simulation space, without the need to refine the mesh to fit the target cable. This avoids the computational burden of performing high-density mesh subdivision of the entire Yee mesh to characterize the geometry of the target cable, reducing the total size of the Yee mesh in the three-dimensional solution domain, reducing mesh redundancy from the root, lowering the computational load, and significantly improving computational efficiency. Second, high prediction accuracy: This invention obtains a refined dynamic current distribution along the line by dividing the one-dimensional conductor model into multiple segments and solving for the current in each segment. This provides high-fidelity excitation source information for radiation field calculation, laying the foundation for high-precision prediction. On this basis, the constructed field-circuit co-simulation process injects current data into the established standard electric field update equation and standard magnetic field update equation in real time through an equivalent coupling mechanism. It also realizes the synchronous update of transmission line current and spatial electromagnetic field at each time step, accurately simulating the dynamic mutual coupling process between the target cable and its radiation field. This effectively overcomes the fundamental error caused by neglecting field-circuit interaction in traditional decoupling methods, significantly improving the accuracy and physical reality of time-domain electromagnetic radiation prediction results, thereby significantly improving prediction accuracy.

[0008] Furthermore, in step S1, a three-dimensional rectangular coordinate system O-XYZ is established in the three-dimensional simulation space, the axis of the one-dimensional line conductor model is along the Z-axis direction, and the Z-axis direction is consistent with the edge direction of the Yee mesh.

[0009] Furthermore, in step S1, the specific method for solving each segment based on the finite-difference time-domain method to obtain the current data corresponding to each segment is as follows: the time-domain telegraph equation of the one-dimensional conductor model is established based on transmission line theory, and the voltage nodes and current nodes are defined in an alternating manner based on each segment; the time-domain telegraph equation is solved by simulation using the finite-difference time-domain method to obtain the current data corresponding to each segment at each time point.

[0010] Furthermore, the field-path cooperative simulation process in step S4 specifically executes the following sub-steps in each time step iteration: Step S4.1: Based on the time-domain telegraph equations of the one-dimensional line conductor model, update the current data corresponding to each segment; Step S4.2: Based on the lumped element equivalent principle, each segment of the one-dimensional line conductor model is modeled as a lumped element. The lumped element is described by an equivalent circuit composed of an ideal current source, wherein the current value of the ideal current source is determined by the current data of the corresponding segment. Step S4.3: Based on the equivalent circuit, the standard electric field update equation established in step S3 is modified to obtain a modified electric field update equation that is only applicable to the edges of the Yee grid occupied by the one-dimensional line conductor model. Step S4.4: Update the electric field components of the Yee grid edges occupied by the one-dimensional line conductor model using the modified electric field update equation. At the same time, based on the standard electric field update equation and standard magnetic field update equation established in step S3, update the electric field components of the remaining edges and all magnetic field components on the Yee grid.

[0011] Furthermore, the standard electric field update equation and the standard magnetic field update equation established in step S3 are updated with "leap-frog" time-staggered updates for the electric field components and magnetic field components.

[0012] Furthermore, in step S4.2, each segment of the one-dimensional line conductor model coincides with a Yee mesh edge space in the three-dimensional simulation space.

[0013] Furthermore, each current node is located at the center of a segment, and the length of the Yee mesh edge associated with the segment is equal to the segment length.

[0014] Furthermore, the time-domain electromagnetic radiation prediction results of the target cable are subjected to a fast Fourier transform to obtain the frequency-domain electromagnetic radiation prediction results of the target cable.

[0015] Furthermore, the three-dimensional simulation space is a virtual computing domain for electromagnetic field analysis, and its boundary is provided with absorbing boundary conditions to fully accommodate the target cable and its surrounding preset electromagnetic environment. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating the cable electromagnetic radiation prediction method of the present invention. Figure 2 This is a schematic diagram illustrating the spatiotemporal evolution of voltage and current in the cable electromagnetic radiation prediction method of the present invention. Figure 3 This is a flowchart illustrating the field path collaborative simulation process architecture of the cable electromagnetic radiation prediction method of the present invention. Figure 4 This is a comparison of the near-end and far-end current results in the simulation process between the cable electromagnetic radiation prediction method of the present invention and the existing full-wave numerical method. Figure 5 This is a comparison chart of the time-domain radiation field results (i.e., time-domain electromagnetic radiation prediction results) of the cable electromagnetic radiation prediction method of the present invention and the existing full-wave numerical simulation method during the simulation process. Figure 6 This is a comparison chart showing the frequency domain results (i.e., frequency domain electromagnetic radiation prediction results) of the radiation field in the simulation process between the cable electromagnetic radiation prediction method of the present invention and the existing full-wave numerical simulation method. Detailed Implementation

[0017] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0018] Example 1: As Figure 1 As shown, a method for predicting electromagnetic radiation from cables includes the following steps: Step S1: Establish a one-dimensional conductor model of the target cable in the three-dimensional simulation space, divide the one-dimensional conductor model into multiple segments along its axis, and solve each segment based on the finite difference method in the time domain to obtain the current data corresponding to each segment. Step S2: Discretize the three-dimensional simulation space using Yee mesh, and determine the virtual observation points in the three-dimensional simulation space that correspond to the actual observation points; Step S3: Based on Maxwell's equations, establish the standard electric field update equations and the standard magnetic field update equations on the Yee grid; Step S4: Establish the field-circuit co-simulation process. In each time step iteration, the field-circuit co-simulation process achieves synchronous updates of transmission line current and spatial electromagnetic field by equivalently coupling the current data obtained in step S1 to the standard electric field update equation and standard magnetic field update equation established in step S3. Step S5: Execute the field-circuit co-simulation process until the preset termination condition is reached, and extract the time-domain electromagnetic field response at the virtual observation point as the time-domain electromagnetic radiation prediction result of the target cable.

[0019] In this embodiment, by pre-setting a virtual observation point corresponding to the actual observation point in the early stage of simulation, the electromagnetic field time-domain waveform of the virtual observation point can be recorded in real time during the simulation process. This avoids the tedious operation of post-processing and extracting massive amounts of data after the simulation ends, and improves the flexibility and efficiency of data extraction.

[0020] In this embodiment, firstly, a one-dimensional conductor model of the target cable is established to reduce the slender cable structure from three dimensions to one dimension for description. The finite-difference time-domain method is then used to quickly solve each segment, efficiently obtaining the current distribution along the cable. Simultaneously, the Yee mesh is used to discretize only the surrounding space of the three-dimensional simulation space, eliminating the need for mesh refinement to fit the target cable. This avoids the computational burden of globally high-density meshing of the entire Yee mesh to characterize the target cable's geometry, reducing the total size of the Yee mesh in the three-dimensional solution domain. This fundamentally reduces mesh redundancy, lowers the computational load, and improves computational efficiency. This hybrid strategy of "one-dimensional road domain calculation + three-dimensional field mesh" significantly reduces the total number of meshes, substantially lowers computational resource consumption and simulation time, and achieves highly efficient cable electromagnetic radiation prediction while ensuring prediction reliability, effectively meeting the needs of rapid prediction in engineering practice. Secondly, by dividing the one-dimensional conductor model into multiple segments and solving for the current in each segment, a refined dynamic current distribution along the line was obtained, providing high-fidelity excitation source information for radiation field calculation and laying the foundation for high-precision prediction. Based on this, a field-circuit co-simulation process was constructed, injecting current data into the established standard electric field update equation and standard magnetic field update equation in real time through an equivalent coupling mechanism, and achieving synchronous updates of the transmission line current and the spatial electromagnetic field at each time step. This design accurately simulates the dynamic mutual coupling process between the target cable and its radiation field, effectively overcoming the fundamental errors caused by neglecting field-circuit interactions in traditional decoupling methods, significantly improving the accuracy and physical realism of time-domain electromagnetic radiation prediction results, and effectively overcoming the shortcomings of insufficient prediction accuracy in existing technologies.

[0021] Example 2: This example is basically the same as Example 1, except that in this example, in step S1, a three-dimensional rectangular coordinate system O-XYZ is established in the three-dimensional simulation space, the axis of the one-dimensional line conductor model is along the Z-axis direction, and the Z-axis direction is consistent with the edge direction of the Yee mesh.

[0022] In this embodiment, in step S1, the specific method for solving each segment based on the finite-difference time-domain method to obtain the current data corresponding to each segment is as follows: establish the time-domain telegraph equation of a one-dimensional conductor model based on transmission line theory, and define staggered voltage nodes and current nodes based on each segment; use the finite-difference time-domain method to simulate and solve the time-domain telegraph equation to obtain the current data corresponding to each segment at each time point.

[0023] In this embodiment, the standard electric field update equation and the standard magnetic field update equation established in step S3 are updated using a "leap-frog" time-staggered update method for the electric field and magnetic field components. Based on this, each segment of the one-dimensional linear conductor model coincides with a Yee mesh edge space in the three-dimensional simulation space; each current node is located at the center of a segment, and the length of the Yee mesh edge associated with the segment is equal to the segment length.

[0024] In this embodiment, by making the segment length equal to the length of the Yee grid edge and setting the current node at the center of the segment, it is ensured that the current data of each segment can be directly mapped to the corresponding Yee grid edge without spatial interpolation, thereby avoiding numerical errors that may be introduced due to position mismatch.

[0025] In this embodiment, the three-dimensional simulation space is a virtual computing domain used for electromagnetic field analysis. Its boundary is provided with absorbing boundary conditions to fully accommodate the target cable and its surrounding preset electromagnetic environment.

[0026] Example 3: This example is basically the same as Example 2, except that: in this example, as Figure 3 As shown, the field-path co-simulation process in step S4 specifically executes the following sub-steps in each time step iteration: Step S4.1: Update the current data corresponding to each segment based on the time-domain telegraph equations of the one-dimensional line conductor model; Step S4.2: Based on the lumped element equivalent principle, each segment of the one-dimensional line conductor model is modeled as a lumped element. The lumped element is described by an equivalent circuit composed of an ideal current source, wherein the current value of the ideal current source is determined by the current data of the corresponding segment. Step S4.3: Based on the equivalent circuit, the standard electric field update equation established in step S3 is modified. The current value of the ideal current source is substituted into the standard electric field update equation, and the current excitation term is added to obtain the modified electric field update equation that is only applicable to the edges of the Yee mesh occupied by the one-dimensional line conductor model. Step S4.4: Update the electric field components of the Yee mesh edges occupied by the one-dimensional line conductor model using the modified electric field update equation. At the same time, based on the standard electric field update equation and standard magnetic field update equation established in step S3, update the electric field components of the remaining edges and all magnetic field components on the Yee mesh.

[0027] In this embodiment, the above sub-steps achieve precise coupling and iterative updating of the target cable current (path domain) and the spatial electromagnetic field (field domain) within each time step. Specifically, only the electric field component update of the Yee grid edges occupied by the target cable uses the modified electric field update equation, while the electric field component updates of the remaining edges still use the standard electric field update equation, and the magnetic field updates of all Yee grid edges still use the standard magnetic field update equation. This ensures both the accuracy of the coupling and the efficiency of the finite-difference time-domain (FDTD) algorithm.

[0028] In this embodiment, an ideal current source is used to describe each segment, which physically corresponds precisely to the electromagnetic nature of the cable segment as a secondary radiation source. According to electromagnetic field theory, time-varying current is the source of the radiation field. This embodiment directly equates each segment to an ideal current source, allowing for an intuitive and accurate acquisition of the contribution of this ideal current source when updating the electric field. This aligns with the physical constitutive relations of Maxwell's equations, making the simulation process clearly physically interpretable.

[0029] Example 4: This example is basically the same as Example 3, except that: in this example, the time-domain electromagnetic radiation prediction result of the target cable is subjected to a fast Fourier transform to obtain the frequency-domain electromagnetic radiation prediction result of the target cable.

[0030] This embodiment provides simultaneous electromagnetic radiation prediction results in both the time and frequency domains. The time-domain prediction results facilitate observation of the waveform, peak value, and time response characteristics of transient electromagnetic pulses, making it suitable for analyzing transient interferences such as lightning and electrostatic discharge. The frequency-domain prediction results facilitate examination of the radiation spectrum characteristics of the target cable under continuous wave excitation, making it suitable for radiated emission assessment in electromagnetic compatibility standard tests (such as CISPR and FCC). This combined time- and frequency-domain output capability allows this method to adapt to various application scenarios, from scientific research on mechanisms to engineering compliance testing, significantly enhancing its practical value and versatility.

[0031] Furthermore, the frequency domain electromagnetic radiation prediction results are obtained by post-processing (FFT) the results of a single time-domain simulation, eliminating the need for repeated simulations at different frequency points. Compared to the traditional frequency domain point-by-point scanning method, this significantly reduces the number of simulations and further improves prediction efficiency.

[0032] Example 5: This example is basically the same as Example 3, except that: in this example, the specific process of establishing the time-domain telegraph equations based on the one-dimensional conductor model using transmission line theory is as follows: Step S1.1: In the three-dimensional rectangular coordinate system O-XYZ, select the XOZ plane as the reference ground; the geometric trajectory of the one-dimensional line conductor model in the YOZ plane is a straight line extending along the Z-axis. Step S1.2: Denote the physical length of the one-dimensional line conductor model as... Define scalar The position coordinate variable along the Z-axis. The range of values ​​for is 0≤ ≤ Used to describe the spatial coordinates of any node on a one-dimensional line conductor model; defines a scalar. For simulation time point variables; Step S1.3: Based on transmission line theory, define the distribution parameters per unit length of the target cable: The resistance per unit length of the target cable is expressed in ohms per meter, representing the resistance of a unit length of conductor in the target cable to the flow of current. The inductance per unit length of the target cable is expressed in Henry per meter, which characterizes the property of the target cable to generate a magnetic field and store magnetic field energy when current flows through a conductor of a unit length. The capacitance per unit length of the target cable, measured in farads per meter, characterizes the energy stored in the electric field between the conductor per unit length of the target cable and the reference ground. The conductivity per unit length of the target cable, expressed in Siemens per meter, characterizes the leakage current allowed to pass through the insulation medium per unit length of the target cable.

[0033] Step S1.4: Establish the voltage equation as shown in equation (1) describing the spatiotemporal evolution of voltage, and the current equation as shown in equation (2) describing the spatiotemporal evolution of current. The voltage equation and the current equation constitute the time-domain telegraph equation set: (1) (2) in, Let the one-dimensional line conductor model be located in spatial coordinates at time point t. Voltage at the node; Let the one-dimensional line conductor model be located in spatial coordinates at time point t. The current at the node. A schematic diagram of the spatiotemporal evolution of voltage and current is shown below. Figure 2 As shown.

[0034] In this embodiment, the specific process of dividing the one-dimensional conductor model into multiple segments along its axis, and defining staggered voltage and current nodes based on each segment, is as follows: Step S1.5: Divide the one-dimensional line conductor model uniformly along the Z-axis into sections. Divide the data into segments, and record the length of each segment as... , It should not exceed one-tenth of the minimum wavelength corresponding to the highest frequency in the simulation.

[0035] Step S1.6: Arrange the items according to their Z-axis coordinates from smallest to largest. The segments are sequentially referred to as segment 1 to segment 2. The first segment is divided into segments; the starting node of the first segment is set to 0, and the second segment is divided into segments into segments. The position index of the end node of each segment is set to The position index of the intersection node of the Qth segment and the (Q+1)th segment is set to Q, where Q = 1, 2, ..., NDZ-1; Step S1.7: Define the staggered voltage and current nodes on the one-dimensional line conductor model: In the one-dimensional line conductor model, the node with position index m1 is taken as the m1th voltage node, denoted as... m1 = 0, 1, 2, ..., NDZ; In the one-dimensional line conductor model, the center node of the p-th segment is taken as the p-th current node, denoted as... p = 1, 2, ..., NDZ.

[0036] Step S1.8: Connect the source-end equivalent resistance at the starting node of the one-dimensional conductor model, introduce the load equivalent resistance at the ending node, and connect the equivalent source-end excitation source to the source-end equivalent resistance to provide a pulse voltage. The source-end equivalent resistance and the equivalent source-end excitation source are used to simulate the power input of the target cable. The resistance value of the source-end equivalent resistance... The value is set according to actual simulation requirements, generally greater than or equal to 0; the equivalent resistance of the load is... Not equal to 0, usually taken as 50 ohms, to avoid short circuit to ground in one-dimensional line conductor models; In this embodiment, the specific process of solving each segment based on the finite-difference time-domain method to obtain the current data corresponding to each segment is as follows: Step S1.9: Based on the actual simulation requirements, set the total simulation time to... The time step is , able to be Integer divisibility; define an integer time step index n, Divide the integer time step index n into voltage sampling time step indices. and current sampling time step index ,like If it is even, then , ;like If it is an odd number, then , ; Step S1.10: Discretize the voltage equations to obtain the discretized voltage equation set as shown in equations (3) to (5): (3) , (4) (5) in, For the 0th voltage node In time step index Voltage value at the corresponding time point; Index of the m-th voltage node at time step Voltage value at the corresponding time point; Index of the NDZ-th voltage node at time step Voltage value at the corresponding time point; For the equivalent source of excitation at time step index The voltage amplitude output at the corresponding time point; when n1 equals 0, , , All equal to 0 A, , , , All are equal to 0V; when n1 is greater than or equal to 2, For the first Current nodes at time step index The current value at the corresponding time point, For the first Current nodes at time step index The current value at the corresponding time point, Index of the NDZ-th current node at time step The current value at the corresponding time point, For the equivalent source of excitation at time step index -2 corresponds to the voltage amplitude output at the time point. For the 0th voltage node In time step index -2 corresponds to the voltage value at the time point. For the m-th voltage node In time step index -2 corresponds to the voltage value at the time point. For the NDZth voltage node In time step index -2 corresponds to the voltage value at the time point; Discretizing the current equation yields the discretized current equation as shown in formula (6): (6) in, The index of the p-th current node at time step The current value at the corresponding time point; For the p-th voltage node at time step index Voltage value at the corresponding time point; Index of the (p-1)th voltage node at time step The voltage value at the corresponding time point; when n2=1, The value equals 0A when n² is greater than 1. For the p-th voltage node at time step index Voltage value at the corresponding time point; Step S1.11: Define a one-dimensional linear conductor model as a lossless transmission line, where the resistance R per unit length and the conductance G per unit length are both 0; According to time step index 0 to The "leap-frog" time-interleaved iterative execution of formulas (3) to (5) and (6) is adopted, that is, the voltage and current simulations are performed alternately to calculate the voltage value of each voltage node at each voltage sampling time step and the current value of each current node at each current sampling time step. The current value of each current node at each current sampling time step is the current data of its segment at each current sampling time step.

[0037] In this embodiment, the steps for discretizing the three-dimensional simulation space using Yee mesh and determining the virtual observation points corresponding to the actual observation points in the three-dimensional simulation space are as follows: Step S2.1: Set the grid spacing of the Yee mesh in the X, Y, and Z axes of the 3D Cartesian coordinate system O-XYZ as follows: , and , , and None of them exceed one-tenth of the minimum wavelength corresponding to the highest frequency in the simulation; based on , and The 3D simulation space is divided into multiple uniform cubic Yee meshes, with each vertex of each Yee mesh being its node. Each Yee mesh contains alternating electric and magnetic field components, including an electric field component parallel to the X-axis. Electric field components in the Y-axis direction parallel to the Y-axis and Z-axis electric field components parallel to the Z-axis The magnetic field components include the magnetic field components in the X-axis direction parallel to the X-axis. Magnetic field component in the Y-axis direction parallel to the Y-axis and the magnetic field component in the Z-axis direction parallel to the Z-axis .

[0038] Step S2.2: According to the preset requirements, set an actual observation point within the geometric boundary of the three-dimensional simulation space and outside the area occupied by the one-dimensional line conductor model. The position coordinates of the actual observation point in the three-dimensional rectangular coordinate system O-XYZ are denoted as ; Step S2.3: Calculate the relationship between each node of each Yee grid and the actual observation point. The Euclidean distance between them is determined relative to the actual observation point. The node with the smallest Euclidean distance between any two Yee grids is defined as the virtual observation point; where the position coordinates of any node in the three-dimensional Cartesian coordinate system O-XYZ are denoted as... The distance between the node and the actual observation point is calculated using formula (7). Euclidean distance between : (7) In this embodiment, step S3, which involves establishing the standard electric field update equation and the standard magnetic field update equation on the Yee grid based on Maxwell's equations, is as follows: Step S3.1: Define the spatial location of any node in any Yee mesh within the 3D simulation space using discrete indices. The expression is represented as follows: where i, j, and k are all non-negative integers, and their values ​​range from 0 to 0. Nx, Ny, and Nz, respectively. Nx, Ny, and Nz are the maximum number of Yee meshes along the X-axis, Y-axis, and Z-axis directions in the three-dimensional simulation space, respectively. Step S3.2: Divide the integer time step index n into electric field sampling time step indices. and magnetic field sampling time step index ,like If it is even, then , ;like If it is an odd number, then -1, ; Step S3.3: The standard electric field update equations include standard electric field update equations along the X-axis, Y-axis, and Z-axis directions, respectively. Construct the standard electric field update equations along the X-axis, Y-axis, and Z-axis directions as shown in equations (8) to (10): (8) (9) (10) in, , , are the electric field strength components in the X-axis direction, Y-axis direction, and Z-axis direction at the node with the spatial position at the corresponding time point at the current time step index corresponding time point, and the spatial position is ; , are the dielectric constant and conductivity in the direction of the axis ( ) at the node with the spatial position of ; when is equal to 0, , , are all equal to 0; , , are all equal to 0; , are all equal to 0; , are all equal to 0; , are all equal to 0; when is greater than or equal to 2, , , are respectively the electric field strength components in the X-axis direction, Y-axis direction, and Z-axis direction at the node with the spatial position at the corresponding time point at the time step index ; , , are respectively the magnetic field strength components in the X-axis direction, Y-axis direction, and Z-axis direction at the node with the spatial position at the corresponding time point at the time step index ; when is greater than or equal to 2: if is equal to 0, then , are equal to 0; if 0 < i ≤ Nx + 1, then , are respectively the magnetic field strength components in the Y-axis direction and Z-axis direction at the node with the spatial position at the corresponding time point at the time step index ; if j is equal to 0, then , are all equal to 0; if 0 < j ≤ Ny + 1: then , are respectively the electric field strength components in the X-axis direction and Z-axis direction at the node with the spatial position at the corresponding time point at the time step index ; if k is equal to 0, then , are all equal to 0; if 0 < k ≤ Nz + 1: then , are respectively the electric field strength components in the X-axis direction and Y-axis direction at the node with the spatial position at the corresponding time point at the time step index ; if i is equal to 0, then , are all equal to 0; if 0 < i ≤ Nx + 1: then , are respectively the magnetic field strength components in the Y-axis direction and Z-axis direction at the node with the spatial position at the corresponding time point at the time step index ; if j is equal to 0, then ,

[0039] are all equal to 0; if 0 < j ≤ Ny + 1: then , are respectively the electric field strength components in the X-axis direction and Z-axis direction at the node with the spatial position at the corresponding time point at the time step index ; if k is equal to 0, then , are all equal to 0; if 0 < k ≤ Nz + 1: then , are respectively the magnetic field strength components in the X-axis direction and Y-axis direction at the node with the spatial position at the corresponding time point at the time step index ; if i is equal to 0, then , are all equal to 0; if 0 < i ≤ Nx + 1: then , are respectively the magnetic field strength components in the Y-axis direction and Z-axis direction at the node with the spatial position at the corresponding time point at the time step index ; if j is equal to 0, then , are all equal to 0; if 0 < j ≤ Ny + 1: then , are respectively the electric field strength components in the X-axis direction and Z-axis direction at the node with the spatial position at the corresponding time point at the time step index ; if k is equal to 0, then , are all equal to 0; if 0 < k ≤ Nz + 1: then , are respectively the magnetic field strength components in the X-axis direction and Y-axis direction at the node with the spatial position at the corresponding time point at the time step index ; if i is equal to 0, then , are all equal to 0; if 0 < i ≤ Nx + 1: then , are respectively the magnetic field strength components in the Y-axis direction and Z-axis direction at the node with the spatial position at the corresponding time point at the time step index ; if j is equal to 0, then , are all equal to 0; if 0 < j ≤ Ny + 1: then , are respectively the electric field strength components in the X-axis direction and Z-axis direction at the node with the spatial position at the corresponding time point at the time step index ; if k is equal to 0, then , are all equal to 0; if 0 < k ≤ Nz + 1: then , are respectively the magnetic field strength components in the X-axis direction and Y-axis direction at the node with the spatial position at the corresponding time point at the time step index ; if i is equal to 0, then , are all equal to 0; if 0 < i ≤ Nx + 1: then , are respectively the magnetic field strength components in the Y-axis direction and Z-axis direction at the node with the spatial position at the corresponding time point at the time step index ; if j is equal to 0, then , [[ID All are equal to 0; if 0 < k ≤ Nz + 1, then and are respectively the magnetic field intensity components along the X-axis and Y-axis at the node with spatial position at the corresponding time point for the time step index ; when is greater than or equal to 2, is the component of the externally applied current density source along the Z-axis at the node with spatial position at the corresponding time point for the time step index ; when is equal to 0, is equal to 0.

[0039] The standard magnetic field update equations include the standard magnetic field update equations along the X-axis, Y-axis, and Z-axis respectively; the standard magnetic field update equations along the X-axis, Y-axis, and Z-axis are constructed as shown in Equations (11) to (13): (11) (12) (13) where , , are respectively the magnetic field intensity components along the X, Y, and Z axes at the node with spatial position at the corresponding time point for the current time step index ; , , are respectively the electric field intensity components along the X, Y, and Z axes at the node with spatial position at the corresponding time point for the time step index ; , are respectively the magnetic permeability and magnetic loss coefficient along the axis at the node with spatial position ( ). If is equal to + 1, then , are equal to 0; if 0 ≤ i < Nx + 1, then , are respectively the electric field intensity components along the Y and Z axes at the node with spatial position at the corresponding time point for the time step index ; if is equal to + 1, then , The value equals 0; if 0 ≤ j < Ny+1, then , Index at time step The corresponding time point and spatial location are The electric field intensity components along the X-axis and Z-axis at the node; if equal +1, then , All are equal to 0; if 0 ≤ k < Nz+1, then , Index at time step The corresponding time point and spatial location are The electric field intensity components along the X-axis and Y-axis at the node; when When equal to 1, , , Equal to 0; when When greater than or equal to 3, , , Time step index The corresponding time point and spatial location are The magnetic field strength components along the X-axis, Y-axis, and Z-axis at the nodes; For indexing at time steps At the corresponding point in time, the spatial location is The source component of the equivalent magnetic flux density along the Z-axis at the node; when When equal to 1, It equals 0.

[0040] In this embodiment, a field-road cooperative simulation process is established. In each time step iteration, the field-road cooperative simulation process executes the following steps sequentially: Step S4.1: Based on the time-domain telegraph equations of the one-dimensional line conductor model, update the current data corresponding to each segment, where the p-th segment of the one-dimensional line conductor model is at the time step index. The current data at the corresponding time points are ; Step S4.2: Based on the lumped element equivalence principle, each segment of the one-dimensional line conductor model is modeled as a lumped element. This lumped element is described by an equivalent circuit consisting of an ideal current source. The current value of the ideal current source is determined by the current data of the corresponding segment, that is, the current value of the ideal current source corresponding to the p-th segment of the one-dimensional line conductor model is... ; Step S4.3: Based on the equivalent circuit, the standard electric field update equation established in step S3 is modified to obtain the modified electric field update equation that is only applicable to the edges of the Yee mesh occupied by the one-dimensional line conductor model. The specific method is as follows: Step S4.3.1: Based on the positions of the Yee grid nodes occupied by the one-dimensional line conductor model in the X and Y directions, set the spatial discretization indices of the one-dimensional line conductor model in the X and Y directions to known constants. and The spatial index range corresponding to the Yee mesh nodes occupied by the one-dimensional line conductor model in the Z-axis direction is set to k1 to k2. The one-dimensional line conductor model is uniformly divided into NDZ segments, and the spatial index range and the total number of segments satisfy the following relationship: When the spatial index k of the Z-axis satisfies At that time, the spatial location The edges of the Yee mesh at that location are occupied by a one-dimensional line conductor model, satisfying... ; Step S4.3.2: Based on the basic principles of electromagnetism, determine the current value of the ideal current source flowing through the edge of the Yee grid. Divide by the area of ​​the cross section containing the edge to obtain the equivalent applied current density term. ; Step S4.3.3: Substitute the equivalent applied current density term into the space node. The standard magnetic field update equation along the Z-axis is used to obtain the modified electric field update equation, as shown in equation (14), which is applicable to the edges of the Yee mesh occupied by the one-dimensional line conductor model: (14) Among them, when When equal to 0, Equal to 0; Step S4.4: Update the electric field components of the Yee grid edges occupied by the one-dimensional line conductor model using the modified electric field update equation described above. At the same time, based on the standard electric field update equation and standard magnetic field update equation established in step S3, update the electric field components of the remaining edges and all magnetic field components on the Yee grid.

[0041] In this embodiment, the specific method for executing the field-circuit co-simulation process until the preset termination condition is met, and extracting the time-domain electromagnetic field response at the virtual observation point, is as follows: Step S5.1: Convert the position coordinates of the virtual observation point in the 3D simulation space into the spatial position of the nodes of the Yee mesh, denoted as... After the electric field is updated at each time step, the spatial location is extracted as follows: The index of the electric field sampling time step at the node The electric field intensity components in the three orthogonal directions of the X, Y, and Z axes are denoted as follows: , and ; Step S5.2: Based on the extracted electric field intensity components in the three orthogonal directions, the composite electric field intensity magnitude at the virtual observation point at each time step is calculated using formula (15). : (15) Step S5.3: After obtaining the magnitude of the combined electric field intensity at all virtual observation points in all time steps, construct a time-domain sequence of the magnitudes of the combined electric field intensity at all virtual observation points in the order of the time steps. This time-domain sequence is the time-domain electromagnetic field response at the virtual observation points.

[0042] To verify the performance of the cable electromagnetic radiation prediction method of the present invention, a specific cable electromagnetic radiation test case was designed, and the cable electromagnetic radiation prediction method of the present invention was comprehensively compared with the full-wave numerical simulation method recognized in the industry as having the highest accuracy.

[0043] 1. Simulation Environment and Parameter Settings First, the model establishment and parameter settings of the cable electromagnetic radiation prediction method and the full-wave numerical simulation method of this invention are described in detail. The cable electromagnetic radiation prediction method of this invention (based on the VSC++ platform): The cable electromagnetic radiation prediction method of this invention is compiled and solved in the Visual Studio C++ (VSC++) environment. In the computational three-dimensional simulation space, the total number of spatial Yee grids is divided into 470,400, and the spatial step size is set to Δx=Δy=Δz=0.01m; in terms of time discretization, the total number of time steps is set to 3000 steps, the total time Tmax=100ns, and the single-step time step Δt=100ns / 3000. The physical parameters of the target cable are set as follows: length 1m, diameter 1mm, and height above ground 30mm. The one-dimensional conductor model is divided into NDZ=100 segments; each segment Δ l =0.01m. The spatial positions of the start and end points of the one-dimensional line conductor model are (0, 30, 0) and (0, 30, 1000), respectively. To evaluate the radiation effect, an observation point is set in the three-dimensional simulation space, with its spatial position being (1000, 30, 500). The equivalent source-end excitation source is set at the starting node (i.e., the near end) of the one-dimensional line conductor model, and a Gaussian pulse excitation with an amplitude of 5V is applied. The near end of the one-dimensional line conductor model is terminated with an equivalent source-end resistance of Rs = 50 ohms, and the far end (i.e., the tail node) is terminated with R... l =50 ohms equivalent load resistance.

[0044] Full-wave numerical simulation method (as a comparison benchmark): To provide a high-precision comparison benchmark, a full-wave numerical simulation method was used to independently model the same scenario described above. In this full-wave numerical simulation method, a three-dimensional structure of the target cable entity with parameters completely consistent with the cable electromagnetic radiation prediction method of this invention was established, namely a one-dimensional linear conductor model. The boundary conditions were set to infinite free space, and the bottom boundary condition of the one-dimensional linear conductor model was set to an infinite ground plane. The equivalent source-end excitation source was set at the near end of the one-dimensional linear conductor model, and a 5V Gaussian pulse excitation was applied. The near end of the one-dimensional linear conductor model was terminated with an equivalent source-end resistance of Rs=50 ohms, and the far end was terminated with R... l =50 ohms equivalent load resistance. The full-wave numerical simulation method uses a non-uniform mesh partitioning, where the minimum Yee mesh size is Δ. min = 4.3mm, Yee grid total is 461202.

[0045] 2. Comparison of Prediction Results and Prediction Accuracy After completing the above settings, run the cable electromagnetic radiation prediction method and the full-wave numerical simulation method of this invention respectively, and extract the corresponding terminal current and spatial electromagnetic radiation data for comparative analysis: I. Endpoint Current Comparison: Compare the near-end and far-end current responses of a one-dimensional line conductor model, such as... Figure 4 As shown. Figure 4 In this context, "full-wave numerical simulation" represents the result of the full-wave numerical simulation method, and the method represents the result of the cable electromagnetic radiation prediction method of the present invention. Figure 4 The results show that the time-domain current waveform obtained by the cable electromagnetic radiation prediction method of this invention is basically consistent with the calculation results of the full-wave numerical simulation method. The waveform trends of the two are highly consistent, and the peak error is extremely small. II. Comparison of Radiation Time-Domain Results: At the set virtual observation point, the time-domain electromagnetic field response of the radiated electromagnetic field of the cable electromagnetic radiation prediction method of this invention and the existing full-wave numerical simulation method are extracted. The comparison results of the radiation field time-domain results (i.e., the time-domain electromagnetic radiation prediction results) of the two methods are as follows: Figure 5 As shown. Figure 5 In this context, "full-wave numerical simulation" represents the result of the full-wave numerical simulation method, and the method represents the result of the cable electromagnetic radiation prediction method of the present invention. Figure 5 The results show that the radiation time-domain waveform predicted by the cable electromagnetic radiation prediction method of the present invention is in high agreement with the radiation time-domain waveform predicted by the full-wave numerical simulation method. It can accurately capture the transient jump characteristics of electromagnetic radiation with minimal error.

[0046] III. Comparison of Radiation Frequency Domain Results: The above time-domain electromagnetic field response was subjected to Fourier transform (FFT) to obtain a comparison of the radiation field frequency domain results (i.e., frequency domain electromagnetic radiation prediction results) of the cable electromagnetic radiation prediction method of this invention with existing full-wave numerical simulation methods. Figure 6As shown. Figure 6 In this context, "full-wave numerical simulation" represents the result of the full-wave numerical simulation method, and the method represents the result of the cable electromagnetic radiation prediction method of the present invention. Figure 6 The results show that, within the 0-1 GHz operating frequency band, the frequency domain radiation spectrum curves of the cable electromagnetic radiation prediction method of this invention are perfectly matched with those of existing full-wave numerical simulation methods. This proves that the method of this invention has prediction accuracy comparable to that of full-wave numerical simulation methods over a wide frequency range.

[0047] 3. Comparison of Prediction Efficiency While ensuring extremely high prediction accuracy, the cable electromagnetic radiation prediction method of this invention exhibits a significant advantage in computational efficiency. To ensure the objectivity and fairness of the comparison results, all calculation processes of the cable electromagnetic radiation prediction method and the full-wave numerical simulation method of this invention are run independently on the same desktop computer. The hardware and software configuration of this computer is: Intel Core i7-12700 2.8 GHz processor, 32 GB of running memory (RAM), and Windows 11 operating system.

[0048] Under the same test environment, the comparison of computational resources and time consumption of the two methods is shown in Table 1: Table 1

[0049] As shown in Table 1, for the above-mentioned case of target cable radiation prediction, the traditional full-wave numerical simulation method takes 85 seconds due to the need for large-scale three-dimensional spatial mesh partitioning and matrix solving; while the cable electromagnetic radiation prediction method of the present invention only takes 48 seconds, improving the computational efficiency by 43.5%.

[0050] The comparative results above show that the cable electromagnetic radiation prediction method of this invention is highly consistent with the industry's highest-precision full-wave numerical simulation method in terms of prediction accuracy, with minimal error; at the same time, it achieves a significant leap in calculation speed. This cable electromagnetic radiation prediction method of this invention balances high prediction accuracy and high prediction efficiency, breaking through the technical bottleneck of excessive computational resource consumption and long time consumption of traditional full-wave numerical simulation methods when dealing with complex cable networks. It has significant engineering application value for system-level electromagnetic compatibility (EMC) design and cable layout optimization in practical engineering.

Claims

1. A method for predicting electromagnetic radiation from cables, characterized in that, Includes the following steps: Step S1: Establish a one-dimensional conductor model of the target cable in the three-dimensional simulation space, divide the one-dimensional conductor model into multiple segments along its axis, and solve each segment based on the finite difference method in the time domain to obtain the current data corresponding to each segment. Step S2: Discretize the three-dimensional simulation space using Yee mesh, and determine virtual observation points in the three-dimensional simulation space that correspond to the actual observation points; Step S3: Based on Maxwell's equations, establish the standard electric field update equations and the standard magnetic field update equations on the Yee grid; Step S4: Establish a field-circuit co-simulation process. In each time step iteration, the field-circuit co-simulation process achieves synchronous updates of transmission line current and spatial electromagnetic field by equivalently coupling the current data obtained in step S1 to the standard electric field update equation and standard magnetic field update equation established in step S3. Step S5: Execute the field-circuit co-simulation process until the preset termination condition is reached, and extract the time-domain electromagnetic field response at the virtual observation point as the time-domain electromagnetic radiation prediction result of the target cable.

2. The method for predicting electromagnetic radiation from cables according to claim 1, characterized in that, In step S1, a three-dimensional rectangular coordinate system O-XYZ is established in the three-dimensional simulation space. The axial direction of the one-dimensional line conductor model is along the Z-axis, and the Z-axis direction is consistent with the edge direction of the Yee mesh.

3. The cable electromagnetic radiation prediction method according to claim 2, characterized in that, In step S1, the specific method for solving each segment based on the finite-difference time-domain method to obtain the current data corresponding to each segment is as follows: the time-domain telegraph equation of the one-dimensional conductor model is established based on transmission line theory, and the voltage nodes and current nodes are defined in an alternating manner based on each segment; the time-domain telegraph equation is solved by simulation using the finite-difference time-domain method to obtain the current data corresponding to each segment at each time point.

4. The method for predicting electromagnetic radiation from cables according to claim 3, characterized in that, The field-path co-simulation process in step S4 specifically executes the following sub-steps in each time step iteration: Step S4.1: Based on the time-domain telegraph equations of the one-dimensional line conductor model, update the current data corresponding to each segment; Step S4.2: Based on the lumped element equivalent principle, each segment of the one-dimensional line conductor model is modeled as a lumped element. The lumped element is described by an equivalent circuit composed of an ideal current source, wherein the current value of the ideal current source is determined by the current data of the corresponding segment. Step S4.3: Based on the equivalent circuit, the standard electric field update equation established in step S3 is modified to obtain a modified electric field update equation that is only applicable to the edges of the Yee grid occupied by the one-dimensional line conductor model. Step S4.4: Update the electric field components of the Yee grid edges occupied by the one-dimensional line conductor model using the modified electric field update equation. At the same time, based on the standard electric field update equation and standard magnetic field update equation established in step S3, update the electric field components of the remaining edges and all magnetic field components on the Yee grid.

5. The cable electromagnetic radiation prediction method according to claim 1, characterized in that, The standard electric field update equation and standard magnetic field update equation established in step S3 are updated using a "leapfrog" time-staggered update of the electric field components and magnetic field components.

6. The cable electromagnetic radiation prediction method according to claim 4, characterized in that, In step S4.2, each segment of the one-dimensional line conductor model coincides with a Yee mesh edge space in the three-dimensional simulation space.

7. The cable electromagnetic radiation prediction method according to claim 3, characterized in that, Each current node is located at the center of a segment, and the length of the Yee mesh edge associated with the segment is equal to the segment length.

8. The method for predicting electromagnetic radiation from cables according to claim 1, characterized in that, The time-domain electromagnetic radiation prediction results of the target cable are subjected to a fast Fourier transform to obtain the frequency-domain electromagnetic radiation prediction results of the target cable.

9. The method for predicting electromagnetic radiation from cables according to claim 1, characterized in that, The three-dimensional simulation space is a virtual computing domain used for electromagnetic field analysis. Its boundaries are equipped with absorbing boundary conditions to fully accommodate the target cable and its surrounding preset electromagnetic environment.

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