Transmission line network transient response calculation method

Abstract

The invention relates to a method for calculating transient response of a transmission line network, which mainly comprises the following steps of: providing a hybrid method combining an adaptive frequency sampling algorithm based on local rational modeling and modeling based on an electromagnetic topology theory; according to the self-adaptive frequency sampling method based on local rational modeling, an accurate electromagnetic topology network can be established in a complex electromagnetic environment according to the electromagnetic topology theory, and field line coupling, multi-conductor crosstalk and tree-shaped transmission line network conducted interference are considered at the same time. And the non-uniform external field calculation process can be obviously accelerated by reducing frequency domain sampling points. Based on the method, the transient response of the underground cable comprehensive pipe gallery under the action of direct thunder and inductive thunder is calculated and compared with calculation results of other calculation methods, so that the effectiveness of the method is explained. The invention aims to provide a transient response rapid calculation method which provides technical support for electromagnetic interference calculation and protection design of a complex transmission line network.

Description

Technical Field

[0001] The invention relates to a method for calculating transient response of a transmission line network, which is suitable for fast calculation of transient response of a large-scale complex transmission line network. Background Art

[0002] Transmission line networks are carriers of energy and information. Transmission line networks such as underground pipeline water tunnels, aircraft / ship independent electrical systems, overhead power networks, and transmitting / receiving antenna array networks are extremely susceptible to natural and man-made electromagnetic interference, which interferes with the normal operation of power and communication systems and even causes large-scale system failures. In the fields of power supply compatibility and electromagnetic compatibility, it has become a pressing issue to quickly and accurately calculate the transient response of large transmission line networks. For typical complex transmission line networks such as underground cable integrated pipe corridors, electromagnetic transient calculations must simultaneously consider field line coupling, multi-conductor transmission line crosstalk, and tree-like transmission line network conduction interference, which brings difficulties to electromagnetic modeling. At present, most of the existing electromagnetic models are overly simplified and only consider a single form of electromagnetic coupling, which is difficult to reflect actual working conditions. In addition to various forms of electromagnetic interference, various electromagnetic environments such as soil, tunnel body, and tunnel protective layer must also be considered, making the electromagnetic model of typical complex transmission line networks such as underground cable integrated pipe corridors more complex. The electromagnetic topology method decomposes complex electromagnetic systems into a series of simpler subsystems, which can be used to solve system-level electromagnetic interference modeling problems in complex environments. When the subsystems are exposed to external fields, they can be analyzed by field line coupling, and the interactions between the subsystems can be studied by matrix equations based on transmission line theory.

[0003] When the transmission line network is large, although the existing full-wave methods (such as FDTD, MoM, IETD) can theoretically realize the transient calculation of large-scale transmission line networks under non-uniform external field excitation, as the network size increases, the computing resources and computing speed required by the full-wave method are unbearable. The frequency domain BLT equation regards the transmission line as a pipeline, the excitation source and the load as nodes, and represents the node response in matrix form. Most importantly, the node response is independent of the transmission line length, which means that the calculation time is no longer limited by the transmission line length.

[0004] When a system is subjected to non-uniform external fields such as lightning electromagnetic fields, obtaining a clear analytical expression of the non-uniform field can be a difficult task. For the traditional linear frequency sweeping (LFS) method, a large number of samples need to be collected over the entire frequency range to obtain accurate results, which significantly increases the complexity of the calculation. In addition, when the non-uniform external field is coupled with the cable, it is necessary to obtain the field values ​​of multiple observation points on the cable and perform further numerical integration along the line. As the cable length increases, more observation points are required, resulting in longer calculation time. The adaptive frequency sampling (AFS) algorithm based on local rational modeling (LRM) can effectively reduce the model complexity of rational modeling on the one hand, and on the other hand, it can effectively reduce the number of sampling points. Therefore, it is suitable for calculating the transient response of transmission line networks under non-uniform external field excitation. The patents (invention patent: CN107608931B, invention patent: CN112507647B) respectively propose to use Chebyshev pseudo-spectrum and FDTD methods to discretize the transmission line equations, and calculate the coupling process of the external field and the transmission line in the form of distributed sources. It is essentially a full-wave method. When the transmission line is very long, the number of grids will increase rapidly, and the calculation speed is limited. The present invention proposes to use electromagnetic topology to model complex networks, and then use the BLT equation to calculate the transient response of the transmission line network. It is not limited by the length of the transmission line. The local rational modeling adaptive frequency domain sampling calculation is used for non-uniform external fields, which can effectively reduce the number of sampling points. The complex network modeling, transient response calculation, and non-uniform external field processing methods proposed in the present invention are of great significance to the transient calculation of large-scale transmission line networks in complex environments, and can provide technical support for electromagnetic interference calculation and protection design of transmission line networks. Summary of the invention

[0005] The technical problem to be solved by the present invention is to propose a hybrid method combining electromagnetic topology theory and an adaptive frequency sampling algorithm based on local rational modeling to achieve rapid calculation of transient responses of large-scale complex transmission line networks, in view of the shortcomings of over-simplification of traditional electromagnetic models, slow calculation of transient responses by full-wave methods, and slow calculation of non-uniform spatial electromagnetic fields by traditional linear frequency scanning.

[0006] The present invention solves the above technical problems, adopts electromagnetic topology theory to realize transmission line network modeling in complex environment, adopts BLT super matrix equation in electromagnetic topology to calculate node transient response, and adopts local rational modeling adaptive frequency domain sampling algorithm to calculate non-uniform external field, including the following steps:

[0007] The first step is to establish the electromagnetic topology network diagram of the transmission line network in a complex environment based on electromagnetic topology theory, which is used for the subsequent quantitative solution and calculation of electromagnetic transient response.

[0008] Electromagnetic topology modeling needs to follow the following sequence:

[0009] (1) Establish a complete electromagnetic topology map based on the actual structure and coupling path of the pipeline tunnel;

[0010] (2) Based on the principle of good shielding approximation, draw an electromagnetic topology equivalent diagram, including interference source, shielding layer and interference path;

[0011] (3) Draw an electromagnetic coupling sequence diagram based on the interference path to analyze the electromagnetic interference coupling sequence;

[0012] (4) Draw the electromagnetic topology network diagram based on the electromagnetic coupling timing diagram and further conduct pipeline energy analysis.

[0013] In the second step, the BLT super-matrix equation in electromagnetic theory is used to quantitatively describe the transient response solution process, and by rewriting the matrix elements in the BLT super-matrix equation, the three effects of field line coupling, multi-conductor transmission line crosstalk, and tree-like transmission line network conduction are considered simultaneously.

[0014] According to the transmission line theory, the BLT supermatrix equation is

[0015] V=(U+S)(Γ-S) -1 ×V S

[0016] I=Y c (US)(Γ-S) -1 ×V S

[0017] Where V and I represent the node voltage and current responses, U represents the unit diagonal matrix, S represents the scattering matrix, Γ represents the propagation matrix, and V s represents the excitation source vector, Y c Represents the characteristic admittance matrix.

[0018] (1) Node voltage vector

[0019] Use V mnk Represents the voltage of the node, where m represents the node number, n represents the number of the connected pipeline, and k represents the number of the wire in the pipeline connected to the node. Where m is the first priority, n is the second priority, and k is the third priority. The total voltage supervector V of the nodes arranged in ascending order is expressed as:

[0020]

[0021] (2) Propagation Matrix

[0022] For pipeline T n , the transfer matrix can be expressed as

[0023]

[0024] Among them, K n represents the number of transmission lines in n pipelines, N represents the number of pipelines in the topology, and M k It is pipe T k The number of transmission lines in . It is a K n ×K n Diagonal matrix, γ i is the propagation constant of the ith transmission line, L i is the length of the i-th transmission line, and the matrix O is a K n ×K n The propagation matrix Γ of the entire topology is composed of the propagation matrices of each pipeline

[0025] Γ=diag(Γ 1 …Γ k …Γ N )

[0026] (3) Scattering matrix

[0027] The transmission matrix is ​​related to the pipeline, while the scattering matrix is ​​related to the node. The scattering matrix of the entire topology can be regarded as the combination of the scattering matrices at each node.

[0028] For physical nodes, the scattering matrix consists of the reflection coefficients caused by the node load,

[0029] S j =(Z L,j -Z c,j )(Z L,j +Z c,j ) -1

[0030] Among them, Z L,j represents the load matrix of node j, Z c,j is the pipeline T associated with node j k After assembling the node scattering matrix diagonally, and adjusting the order according to the order of the node voltage vectors, the correct scattering matrix of the entire topology can be obtained.

[0031] (4) Excitation source vector

[0032] For the excitation source supervector, the excitation can be divided into two forms: lumped excitation and distributed excitation. In the case of lumped excitation,

[0033]

[0034] In the case of distributed incentives

[0035]

[0036] Among them, P is the eigenvector matrix, V 0 ,I 0 Represents the lumped voltage source and lumped current source vector, V x (x) is the voltage source vector along the line in Agrawal form, V 1 、V 2 is the equivalent lumped voltage source vector in Agrawal form.

[0037] According to the two excitation source vectors, the excitation source vector of the total transmission line network is obtained by arranging the pipelines as follows:

[0038] V S =[V S1 V S2 …V Sn …V SN ] T

[0039] Field line coupling occurs at the entrance of the tunnel. Field line coupling can be achieved by the excitation source vector V s This can be achieved by rewriting the elements at the entrance of the tunnel. When there is crosstalk in a multi-conductor transmission line, the propagation constant γ will change. By rewriting the propagation constant γ in the propagation matrix Γ, the multi-conductor crosstalk can be taken into account in the BLT equation. The tree-shaped transmission line network is connected by ideal nodes, and the ideal nodes only play the role of electrical connection. For ideal nodes, since they are not connected to the load, the load matrix and characteristic impedance matrix cannot be defined. The role of ideal nodes can be considered quantitatively using Kirchhoff.

[0040] In the third step, the lumped source and distributed source are calculated respectively to fill the excitation source vector in the BLT supermatrix equation. When calculating the distributed source, the proposed local rational modeling adaptive frequency domain sampling is used to accelerate the calculation of the non-uniform external field.

[0041] The lightning current under lumped excitation can be expressed by the double Heilder function

[0042]

[0043] The distributed source is represented by the non-uniform spatial electromagnetic field of the double Heilder function base current and the MTLE lightning channel model. According to the dipole radiation field formula, the lightning spatial radiation field under frequency domain conditions can be expressed as

[0044]

[0045] The LRM AFS algorithm is used to divide the entire frequency range of the lightning spatial radiation field into several sub-bands. Then reasonable modeling is performed using the frequency points obtained by adaptive sampling within each sub-band, allowing the data of the entire frequency range to be approximated with fewer frequency points.

[0046] Adaptive frequency domain sampling on each sub-band can effectively reduce the number of sampling points. Chebyshev polynomial zero-point interpolation has high numerical accuracy and stable error, and can effectively reduce the Runge phenomenon in high-dimensional interpolation. Therefore, this paper uses Chebyshev polynomial zero-point to perform adaptive frequency sampling on each sub-band. i} is denoted as [f l ,f h ].

[0047] The N zeros of the N-degree Chebyshev polynomial in the interval [0,1] are

[0048]

[0049] Therefore, in the frequency band [f l ,f h ], the zero point of the N-order Chebyshev polynomial, that is, the N sampling frequency points are

[0050]

[0051] The sample data corresponding to N sampling frequency points can be obtained through interpolation.

[0052] After obtaining the zero points of the N-order Chebyshev polynomial and the corresponding sample data, we can further analyze f i The sub-bands are rationally modeled, and the general rational model can be written as

[0053]

[0054] Among them, f k is the ith sub-band (f i -0.5Δf,f i +0.5Δf). The complex matrix numerator and the complex matrix denominator polynomial D i and P i Expressed as

[0055]

[0056] Among them, d in and p in are the unknown rational model coefficients used to capture the dynamic changes in each local model. D 、N Pis the model order of the numerator and denominator.

[0057] The numerator and denominator coefficients of formula (3) are obtained by solving the least squares estimation, thus establishing a local rational model.

[0058]

[0059] In order to evaluate the computational accuracy of the proposed local rational modeling adaptive frequency domain sampling, an error estimation function based on the vector 1 norm is defined. N ) is the data obtained by sampling at N points, then the relative error estimation function error(N) can be defined as

[0060]

[0061] In the algorithm, the error threshold can be set as the basis for the convergence of the adaptive algorithm, that is,

[0062] error(N)≤ε,3≤N≤8

[0063] When the zero-point order of the Chebyshev polynomial of the local frequency band reaches 8 and has not converged, the frequency band is further divided by bisection, that is,

[0064]

[0065] The fourth step is to solve the BLT super-matrix equation to obtain the transient response of the node, and apply IFFT to further transform the frequency domain response into the time domain response. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] In order to more clearly illustrate the implementation process of the present invention, the drawings involved in the embodiments are briefly introduced below.

[0067] Figure 1 It is a calculation flow chart of the present invention;

[0068] Figure 2 This is a schematic diagram of a certain underground cable integrated pipeline corridor;

[0069] Figure 3 It is a simplified modeling flow chart of electromagnetic topology;

[0070] Figure 4 It is the electrical connection diagram of the electromagnetic topology network;

[0071] Figure 5 is node J 2 Pipeline connection diagram;

[0072] Figure 6 It is T 2 and T 4 Schematic diagram of the arrangement of multiple conductors in a pipeline;

[0073] Figure 7 This is a schematic diagram of lightning electromagnetic field coupling at the entrance of the tunnel;

[0074] Figure 8 It is the pseudo code of the adaptive frequency domain sampling algorithm for local rational modeling;

[0075] Fig. 9 is the transient voltage response of the node under lumped excitation;

[0076] Fig.10 It uses local rational modeling and adaptive frequency domain sampling to calculate node J 1 Lightning electromagnetic field;

[0077] Fig.11 It is a comparison of the calculation errors of lightning electromagnetic fields using local rational modeling and global rational modeling;

[0078] Fig.12 is the transient voltage response of the node under distributed excitation. DETAILED DESCRIPTION

[0079] The technical solution and steps of the present invention are described in detail below in conjunction with the accompanying drawings and embodiments.

[0080] This embodiment takes an underground cable integrated pipeline corridor as an example to calculate the transient response of the cable terminal under the action of direct lightning and induced lightning.

[0081] Step 1: According to the electromagnetic topology modeling steps, Figure 2 Perform electromagnetic topology modeling. The electromagnetic topology modeling process is as follows: Figure 3 The electromagnetic topology is shown in Figure 3 (a) shows the main structure of the underground pipeline tunnel (including protective layer, pipeline tunnel body, internal buildings) and possible electromagnetic coupling paths (transmission coupling, aperture coupling, cable radiation and conduction coupling). The electromagnetic topology equivalent diagram is shown in Figure 3 (b) where V 0 、V 1 and V 2 Represents atmosphere, protective layer and pipeline gallery respectively. 3,1 ,V 3,2 and V 3,3 They represent the individual buildings in the underground cable corridor. 0,1 Indicates V 0 and V 1 The contact surface of the pipe gallery is shown in Figure 1, and the hole indicates the entrance of the pipe gallery. 1,2 Indicates V 1 and V 2 The contact surface, S 2,31 and S 2,32 ,S 2,33 Respectively represent V 2 and V3,1 ,V 3,2 ,V 3,3 Usually, S 0,1 and S 1,2 The thick reinforced concrete structure can be approximated as an effective shielding surface, and the projection coupling can be ignored. The electromagnetic coupling timing diagram is shown in Figure 3 (c) shows that the solid line represents a path and the dotted line represents an open circuit. Due to the existence of the shielding surface, the path passing through the shielding surface can be regarded as an open circuit. Therefore, only the cables at the entrance of the corridor extending into the building constitute an effective electromagnetic path. The electromagnetic topology network is shown in Figure 3 (d) In the figure, J is a node, T is a tube, the dotted tube is a radiation path, and the solid tube is a conduction path. The incident wave and the reflected wave propagate along the tube gallery, and the reflection occurs at the node. The combined effect of the incident wave and the reflected wave determines the actual response at the node.

[0082] The second step is based on Figure 4 The electrical connection of the electromagnetic topology network shown in the figure shows that there are 9 nodes in the electromagnetic topology network diagram, represented by J. 1 It is the load node of the transmission line at the far end of the pit, connected to the ground load, J 2 For the pit, J 3 , J 、5 is the ideal node in the pipeline, J 4 , J 6 , J 7 , J 8 , J 9 is the load node inside the building, and each load node is connected to the ground load. In addition, there are 8 pipelines, represented by T, where T 1 The pipeline is the transmission line from the remote load node to the pipeline pit, and is the main structure for external electromagnetic field coupling; T 2 There are 5 horizontally arranged transmission lines inside the pipeline, T 4 There are three horizontally arranged transmission lines inside the pipeline, T 3 , T 5 , T 6 , T 7 , T 8 The pipelines each have a transmission line for connecting to the load.

[0083] Figure 5 The node connection diagram shown can obtain the scattering matrix at the node, which is further assembled into the scattering matrix of the entire topology. The node scattering matrix of the ideal node can be defined by Kirchhoff's current law and voltage law of the node

[0084]

[0085] Where C V，J and CI，J are the voltage coefficient matrix and current coefficient matrix of node J, Y c，J is the characteristic admittance matrix of node J. In this way, the propagation matrix and scattering matrix of the BLT supermatrix equation considering multiple effects can be completely filled.

[0086] Figure 6 The arrangement of multi-conductor transmission lines shown can calculate the propagation constant, thus obtaining the propagation matrix of the pipeline, which is further assembled into the propagation matrix of the entire topology. The multi-conductor transmission line equation satisfies

[0087]

[0088] where γ is the propagation constant, satisfying

[0089]

[0090] Among them, Z′ and Y′ can be calculated through the unit length parameters of the multi-conductor transmission line.

[0091] The third step is to determine the relative position of the lightning channel and the cable. Figure 7 As shown in the figure, the lightning channel is located at the midpoint of the cable at the entrance of the tunnel, 50m (y 0 =50m), the lightning channel height is 7500m (H=7500m). The cable height from the ground is h=1m, and the length is L 1 = 200m. The node load is 50Ω. In order to calculate the lightning electromagnetic field distribution source along the entrance of the tunnel more quickly, the Figure 8 The LFS AFS algorithm shown accelerates the lightning electromagnetic field calculation process. The LFSAFS algorithm is used to calculate each observation point of the cable. Adaptive sampling is performed based on Chebyshev polynomials at each observation point. The number of points is between (3, 8). When the maximum sampling point 8 is reached and the accuracy is still not met, the current segment is dichotomized, and then the Chebyshev polynomial adaptive sampling is repeated for each sub-band.

[0092] The fourth step is to calculate the transient response of the underground cable gallery according to the proposed method. Fig. 9 The calculation results under lumped excitation are shown in Table 1, which is the relative error between the calculation results of this paper and the CST calculation results. Fig. 9 From the waveform shown, the proposed method has good calculation accuracy.

[0093] Table 1

[0094]

[0095] Fig.10 Node J calculated for Locally Reasonable Modeling (LRM) and Globally Rational Modeling (GRM) 1The horizontal electric field component E at r (f) and the vertical electric field component E z (f) The result is Fig.11 is the relative error between local favorable modeling (LRM) and global rational modeling (GRM). It can be seen that global rational modeling cannot accurately simulate ( Fig.10 (a)), local rational modeling can still accurately simulate, which shows that local favorable modeling has better robustness.

[0096] Fig.12 The calculation results under distributed excitation, the 1 norm relative error is shown in Table 2, which is the relative error of the LRM AFS algorithm in this paper relative to the linear sweep calculation results. Fig.12 From the waveform shown, the proposed method has good calculation accuracy.

[0097] Table 2

[0098]

[0099] In addition, we counted the calculation time in Table 3, where "total time" is the sum of "field time" and "response time". "CST" is the control group under lumped excitation, and "LFS" + "BLT-IFFT" is the control group under distributed excitation. As can be seen from Table 3, the BLT-IFFT method is very fast, completing the calculation in only 4.5 seconds, which is particularly advantageous compared to 4 hours and 1 minute for CST. For distributed excitation, the calculation time is mainly affected by the non-uniform external field. The LRM AFS algorithm takes 7 minutes and 9 seconds, and the LFS algorithm takes 46 minutes and 27 seconds. Compared with the "field time", the "response time" (3 seconds) is almost negligible, and the efficiency of the proposed method ("LRM AFS" + "BLT-IFFT") is 85% faster than that of the control group.

[0100] Table 3

[0101]

Claims

1. A method for calculating the transient response of a transmission line network, characterized in that: The method comprises the following steps: Based on electromagnetic topology theory, the electromagnetic topology network diagram of the transmission line network in complex environment is established to quantitatively solve the electromagnetic transient response; The transient response of the node is calculated by using the BLT super-matrix equation, which comprehensively considers the field line coupling, the crosstalk of the multi-conductor transmission line, and the conducted interference of the tree-like transmission line network by expressing the node response as a matrix form of voltage and current; Adopting local rational modeling adaptive frequency domain sampling algorithm to accelerate the calculation of external non-uniform electromagnetic field by reducing sampling points; The transient response of the underground cable integrated pipeline corridor under the action of direct lightning and induced lightning is calculated, and the frequency domain response is converted into time domain response through inverse Fourier transform (IFFT).

2. The calculation method according to claim 1, characterized in that: The steps of establishing the electromagnetic topology map include: According to the actual structure and coupling path of the pipeline tunnel, a complete electromagnetic topology map is established; Draw an electromagnetic topology equivalent diagram, taking into account interference sources, shielding layers and interference paths; Draw the electromagnetic topology network diagram based on the electromagnetic interference sequence diagram of the coupling path.

3. The calculation method according to claim 1 or 2, characterized in that: The BLT supermatrix equation based on electromagnetic topology theory can simultaneously consider field line coupling, crosstalk of multi-conductor transmission lines and conduction interference effects of tree-like transmission line networks by rewriting matrix elements.

4. The calculation method according to claim 3, characterized in that: The local rational modeling adaptive frequency sampling algorithm performs adaptive sampling in each frequency band through Chebyshev polynomials to reduce the number of sampling points. When the accuracy does not meet the requirements, the current frequency band is further divided by binary division.

5. The calculation method according to claim 4, characterized in that: The method is suitable for calculating the electromagnetic transient response of an underground cable integrated pipeline corridor, and can quickly and accurately calculate the transient response under the action of a lightning electromagnetic field.

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