CN113962171B - High-frequency coupling method for lossy ground transmission line - Google Patents
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Abstract
The invention discloses a high-frequency coupling method of a transmission line on a lossy ground, which comprises the steps of listing a transmission line model equation of a multi-conductor transmission line, and calculating a propagation constant; dividing the overhead line into three areas according to the length and the height of the overhead line, and decoupling a transmission line equation set in a second area to obtain a current expression of the area; transforming the current expression of the second region into an expression comprising a scattering coefficient matrix and a reflection coefficient matrix; performing simulation of an auxiliary stub system, and fitting simulation current by using a least square method; obtaining a line current response expression of the second area by using the fitting coefficient of the auxiliary stub; and respectively solving the line current response of the first area and the third area by using the parameters obtained by the process. The invention calculates the current response of the long wire along the line by using the current data of the auxiliary short wire in the full-wave software, the calculation cost is almost unchanged when the length is increased, and simultaneously, the response of the multi-conductor circuit system is accurately predicted.
Description
Technical Field
The invention relates to an electromagnetic field coupling algorithm of a frequency domain overhead transmission line, in particular to a high-frequency coupling method of a transmission line on a lossy ground.
Background
Overhead transmission lines are one of the important components of power systems. While high frequency electromagnetic fields, such as electromagnetic pulses (EMP) and the like, may couple to overhead transmission lines, thereby generating overvoltages and currents. These overvoltages and overcurrents can have numerous effects, such as short breaks, voltage dips, etc., and even damage electrical components, especially power distribution networks. Thus, it is very important to accurately predict the response of an overhead power line. While a multi-conductor system consisting of multiple overhead lines will become more complex in terms of current response due to the coupling involved between the lines.
Since the height of the multi-conductor will be quite a tenth of the minimum wavelength of a typical high frequency electromagnetic field or even larger in the calculation, this is beyond the application range of classical transmission line approximation, where the line response cannot be calculated by classical transmission line methods. On the other hand, while a conventional full-wave solver (e.g., a moment method) can solve the above problem, its computational cost will increase geometrically with increasing line length, so its solving efficiency is unacceptable in the case of a long length multi-conductor system.
Disclosure of Invention
The invention aims to provide a high-frequency coupling method for a power transmission line on a lossy ground, so as to solve the problems in the prior art.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a high-frequency coupling method of a power transmission line on a lossy ground comprises the following steps; the method comprises the following steps:
step one: listing a transmission line model equation set of a multi-conductor transmission line, wherein the transmission line model equation set is a 2N-element first-order differential equation set taking voltage and current on each line in the multi-conductor transmission line as variables, and N is the number of cables; calculating an impedance matrix and an admittance matrix of a unit length of a multi-conductor power transmission line according to specific parameters of the multi-conductor power transmission line, and calculating a propagation constant matrix by using the impedance matrix and the admittance matrix of the unit length of the line;
step two: dividing the multi-conductor power transmission line into three areas according to the length and the height of the multi-conductor power transmission line, marking each included partial area, wherein the first area comprises the left terminal of the multi-conductor power transmission line, the length of the first area is twice as long as the height of the multi-conductor power transmission line, the third area comprises the right terminal of the multi-conductor power transmission line, the length of the third area is twice as long as the height of the multi-conductor power transmission line, the remaining area without the terminal is divided into a second area, and decoupling the transmission line model equation set in the second area to obtain an expression of a transmission line current vector in the area;
step three: transforming the expression of the transmission line current vector of the second region into an expression comprising a scattering coefficient matrix and a reflection coefficient matrix by using a progressive method;
step four: introducing an auxiliary stub system with the same specific parameters and the length being six times of the line height, performing simulation of the auxiliary stub system in full-wave simulation software NEC-4, fitting the currents of the auxiliary stub system obtained by simulation of the full-wave simulation software NEC-4 by using a least square method, classifying the obtained fitting coefficient vectors, and combining the fitting coefficient vectors into a plurality of fitting coefficient matrixes;
step five: combining the obtained fitting coefficient vectors into a plurality of fitting coefficient matrixes, obtaining a scattering coefficient matrix and a reflection coefficient matrix by using the fitting coefficient matrixes of the auxiliary stub system, and finally solving by using the scattering coefficient matrix and the reflection coefficient matrix to obtain a line current response expression of the second area;
step six: and correspondingly solving the line current responses of the first area and the third area by using the current of the auxiliary stub system, the fitting coefficient matrix and the transmission line current vector expression of the second area.
Further, in the first step, the transmission line model equation set of the multi-conductor transmission line is the Agrawal equation:
the Agrawal equation is as follows:
wherein: x-transverse axis variable of the multi-conductor transmission line; i-response current vector; y' —line admittance matrix per unit length; v (V) S -responsive to the scatter voltage vector; z' -impedance matrix per unit length of line;——a horizontal component vector of the excitation electric field;
thus, the product of the admittance matrix and the impedance matrix in unit length of the line is diagonalized to obtain a propagation constant matrix gamma of the multi-conductor power transmission line:
γ 2 ＝T -1 Y′Z′T
wherein: t-modulus change matrix.
Further, in the second step, the transmission line model equation set is decoupled in the second area, so as to obtain an expression of the transmission line current vector in the second area, as follows:
wherein: j-imaginary units; i 0 -a current vector generated by the excitation electric field; k (k) 1 -the wave number of the excitation electric field; i 1 -right travelling wave current vector generated by reflection and scattering; i 2 -left travelling wave current vector generated by reflection and scattering;
wherein:
wherein, gamma 1 -a propagation constant of a first line of the multi-conductor transmission line; gamma ray 2 -a propagation constant of a second line of the multi-conductor transmission line; gamma ray N -propagation constant of the nth line of the multi-conductor transmission line.
Further, in the third step, assuming that all the line lengths are L, using the progressive method idea, the second area is equivalent to an infinitely long wire, the first area and the third area are equivalent to a right half infinitely long wire and a left half infinitely long wire, respectively, and then the right traveling wave current vector and the left traveling wave current vector generated by reflection and scattering are respectively:
wherein: e (E) N -an N-th order identity matrix; s is S + -left-end scattering coefficient matrix; s is S - -a right-hand scattering coefficient matrix; r is R + -a left-end reflection coefficient matrix; r is R - -a right-end reflection coefficient matrix.
Further, in the fourth step, the full-wave simulation software NEC-4 is used to solve the auxiliary stub systems, 2N auxiliary stub systems are needed to solve the reflection coefficient matrices at the left and right ends, 1 auxiliary stub system is needed to solve the scattering coefficient matrices at the left and right ends, so that a total of 2n+1 auxiliary stub systems are needed, and the lengths of 2n+1 auxiliary stub systems are all L 1 In the ith auxiliary stub system, i=1, 2, …, N, the left end of the ith wire in the auxiliary stub system is excited by a lumped source with amplitude of 1V; in the (i+N) th auxiliary stub system, exciting the right end of the (i) th lead in the auxiliary stub system by a lumped source with the amplitude of 1V; in 2N+1th auxiliary stub system, the auxiliary stub system is excited by plane waves consistent with the multi-conductor transmission line, the currents belonging to the second area in the obtained data are fitted to obtain three fitting coefficient vectors respectively, and a current equation set of the auxiliary stub system in the second area is obtained:
wherein:-the current response of the ith auxiliary stub system; i i+1 -right row current vector of the ith auxiliary stub system; i i+2 -left row current vector of the ith auxiliary stub system; />Current response of the (i+N) th auxiliary stub; />Right row current vector of the (i+N) th auxiliary stub system; />Left row current vector of the (i+N) th auxiliary stub system; i pw -the current response of 2n+1 auxiliary stub systems; i pw1 -right row current vector of 2n+1 auxiliary stub system; i pw2 -left row current vector of 2n+1 auxiliary stub system;
the vectors are classified and combined to obtain a series of current matrixes:
wherein:-a matrix of right row current vectors of the first N auxiliary stub systems; />-a matrix of left row current vectors of the first N auxiliary stub systems; />-a matrix of right row current vectors of the n+1th to 2nth auxiliary stub systems; />-a matrix of left row current vectors of the n+1th to 2nth auxiliary stub systems.
In the fifth step, the obtained fitting coefficient matrix of the auxiliary stub system is combined with the left and right current vectors of the auxiliary stub system and solved, and the scattering coefficient matrix and the reflection coefficient matrix are obtained as follows:
S + I 0 ＝TI pw1 -R + TI pw2
note that the scattering coefficient matrix is always equal to I 0 The form of multiplication occurs, so only the product of the two is solved;
and then solving to obtain a linear current response expression of the second region by using the scattering coefficient matrix and the reflection coefficient matrix.
Further, the linear current response expression of the second region obtained by solving the scattering coefficient matrix and the reflection coefficient matrix is specifically: since the scattering coefficient matrix and the reflection coefficient matrix are known, the line current response expression of the second area is obtained by solving a right traveling wave current vector and a left traveling wave current vector formula, namely:
wherein: i-the current along the second region of the multi-conductor transmission line corresponds.
In the sixth step, the current obtained by the auxiliary stub system, the fitting coefficient matrix and the line current response expression of the second area are combined, so that the line current responses of the first area and the third area can be obtained in a semi-analytic manner:
wherein:
wherein: l (L) b -a region boundary of the multi-conductor transmission line, the size of which is twice the height of the multi-conductor transmission line; i + -a matrix of current responses of the first N auxiliary stub systems; i - -a matrix of current responses of the n+1th to 2nth auxiliary stub systems;-an unknown matrix related to the left-side reflection coefficient; />-an unknown matrix related to the right-hand reflection coefficient matrix; />-an unknown matrix related to the left-hand scattering coefficient matrix; />-an unknown matrix related to the right-hand scatter coefficient matrix.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention provides a high-frequency coupling method for a power transmission line on a lossy ground, which has the following advantages: high frequency electromagnetic fields may couple to overhead transmission lines, thereby generating overvoltage and current. These overvoltages and overcurrents can have numerous effects, such as short breaks, voltage dips, etc., and even damage electrical components, especially power distribution networks. Thus, it is very important to accurately predict the response of an overhead power line. While a multi-conductor system consisting of multiple overhead lines will become more complex in terms of current response due to the coupling involved between the lines.
However, when the height of the multi-conductor is quite a tenth or more of the wavelength of the high-frequency electromagnetic field, the classical transmission line method cannot be used for solving the line current response. If a full wave algorithm is used for the solution (e.g., NEC-4), the computational cost of this approach is unacceptable when the system line length is long. The invention is based on the idea of progressive method, the current data of auxiliary stub system is used to calculate the current response along the long line in the full wave software, the half-resolution form makes the calculation cost almost unchanged relative to the full wave solving software when the length is increased, and the reflection coefficient matrix and the scattering coefficient matrix are introduced for the current in the second area, the specific values of these matrices are irrelevant to the length of the multi-conductor transmission line, so that the current expression can well adapt to the change of the length, and simultaneously, the unknown matrix related to the scattering coefficient matrix and the reflection coefficient matrix is introduced in the first area and the third area, and the relation between the current and the length is accurately found, thus the response of the multi-conductor transmission line is accurately predicted.
Drawings
FIG. 1 is a diagram of the geometry of a multi-conductor system in accordance with an embodiment of the present invention;
FIG. 2 is a cross-sectional view of a multi-conductor structure of a method of high frequency coupling of a lossy overhead transmission line of the present invention;
FIG. 3 is a block diagram of a multi-conductor system of a method of high frequency coupling of a lossy overhead transmission line according to the present invention;
FIG. 4 is a comparison of the real part of the current response of the first wire in the full-wave software with the real part of the current response of the first wire in accordance with an embodiment of the present invention;
fig. 5 is a comparison of the imaginary part of the current response of the full area of the first wire and the imaginary part of the current response of the first wire obtained by the full wave software in the embodiment of the present invention.
Detailed Description
The invention will be described in further detail with reference to the following specific examples, which are intended to illustrate the invention, but these should not be construed as limiting the scope of the invention, which is defined by the appended claims, and any changes that come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.
The invention establishes a fast algorithm of electromagnetic field coupling of frequency domain multi-conductor above the lossy ground, which is applicable to high frequency, and obtains a current expression of the multi-conductor system in a second area by utilizing a multi-conductor transmission line model equation and partitioning the multi-conductor system according to the length of the multi-conductor system. And then solving the current response along the line of the overhead transmission line in all three areas by simulation data obtained by 2N+1 auxiliary stub systems in the numerical full-wave software and fitting coefficients obtained after least square fitting.
Step one: consider an overhead transmission line structure as shown in fig. 1, in which the high frequency electromagnetic field is considered to be in the form of a uniform plane wave with polarization angle, azimuth angle and elevation angle of 0, 0 and 60 °, amplitude of 1V/m, and frequency of 200MHz, respectively. The system comprises three overhead transmission lines, the length of which is l=200m, the height of all the lines is 10m, the radius of the overhead transmission lines is 1mm, and the distance between two adjacent x lines is 0.1m. Both ends are grounded through the load, and the left end load and the right end load are both 50Ω. The dielectric constant, conductivity and permeability of air are epsilon respectively 0 0 and u 0 . The multi-conductor system is positioned above the lossy ground, and the relative dielectric constant, conductivity and permeability of the ground are respectively epsilon g ＝10、σ g =0.1s/m and u0. When the line is excited by the high frequency electromagnetic field, the voltage and current response can be represented by a multi-conductor transmission line model equation. The method is mainly expressed by adopting an Agrawal equation, and is shown as a formula (2):
wherein: i-response current vector; y' —line admittance matrix per unit length; vs—response scatter voltage vector; z' -impedance matrix per unit length of line;-a horizontal component vector of the excitation electric field.
Wherein:
Z′＝jωL′+Z g ′，Y′＝jωC′+G′ (2)
wherein: l' — inductance matrix per unit length of line; z is Z g ' ground impedance matrix; c' — a capacitance matrix per unit length of line; g' — line length conductance matrix.
Since the conductance matrix G 'is much smaller than jωc' at high frequencies, it is negligible in comparison.
Each of the parameter matrices described in equation (2) can be solved for the approximation of the sandy (Sunde) equation in the case of multiple conductors using a thin line approximation and a rahdi (radi). From the multi-conductor cross-sectional structure shown in fig. 2, the impedance and admittance matrix is known as:
wherein: h is a i -the height of the ith conductor; a, a i -radius of the ith conductor; r is (r) ij -the horizontal distance between the ith wire and the jth wire.
Obtaining a ground impedance matrix by using a Morde formula:
thereby, the product of the admittance per unit length of the line and the impedance matrix can be utilized.
Since the product of admittance per unit length of the line and the impedance matrix is not a diagonal matrix, the current and voltage of any line will be coupled to each other, and decoupling of the matrix is required. Modulus transformation is carried out on the current, and the method can obtain:
I(x)＝TI m (x) (5)
wherein: t-modulus transformation matrix; i m Modulus current vector.
Wherein T is the diagonal transformation matrix of the product matrix of admittance and impedance matrix, so that the modulus currents on the lines will be independent of each other. The propagation constant matrix γ at this time is:
when the excitation source of the line is composed of an electromagnetic field irradiated to the line, the electromagnetic field is composed of an incident wave and a reflected wave reflected by the earth. When the incoming wave is a uniform plane wave, the horizontal component of the excitation electric field of the nth line is:
wherein: e (E) 0 -an electromagnetic field waveform; psi-elevation angle of plane wave; θ—azimuth of plane wave; r is R v -fresnel reflection coefficient in the vertical direction; y is n -the y-coordinate of the nth wire; r is R h -fresnel reflection coefficient in horizontal direction; k-wavenumber in free space.
Step two: the overhead transmission line is partitioned according to line length as shown in fig. 3. Wherein L is b Taking twice the maximum height of the line. At this time, the line may be divided into three areas. Wherein the first region is a region near the left end load, referred to as the left end region; the second region can be considered as an infinitely long straight wire, which can be represented by an analytical expression; the third zone is the zone near the right end load, called the right end zone. At this time, the formula (1) is decoupled and modulus transformed, resulting in an expression of the line current response in the second region:
wherein: i 0 -a current vector generated by the excitation electric field; i 1 -right travelling wave current vector generated by reflection and scattering; i 2 -the left travelling wave current vector resulting from reflection and scattering. I 0 Values of (2)Independent of length, I 1 And I 2 The values of (2) are all related to length.
In the third step: using the progressive approach concept, the left and right end regions can be considered as right and left half-length lines, respectively, while the middle region is considered as a length line. At this time, I can be represented by the reflection matrix and the scattering matrix of the two terminals 1 And I 2 。
Consider a right semi-infinite line whose scattering current due to the external electromagnetic field in the second region is:
wherein: i s1 -scattering current generated by the right semi-infinite line in the second region; s is S + -a scattering matrix of the left terminal.
Assume that there is a current Te in the right half-infinite line γx I 2m ' from infinity to the left end, the reflected current that is generated in the second region after it flows into the left end is:
I R1 (x)＝Te γx I 2m ′+Te -γx T -1 R + TI 2m ′x≥L b (10)
wherein: i R1 -a reflected current generated by the right semi-infinite line in the second region; r is R + -a reflection matrix of the left terminal.
Then the reflected and scattered currents are superimposed and the complete current expression will be obtained:
wherein: i t1 -the complete current of the right semi-infinite line in the second region;
similarly, for the left half infinitely long line, the complete expression of the second region is:
wherein: i t2 -the complete current of the left semi-infinite line in the second region; r is R - -a reflection matrix of the right terminal; te (Te) -γx I 1m ' imaginary current flowing from an infinite distance into the right end; s is S - -a scattering matrix for the right terminal.
Since the current in the second region is uniform, the equation (11) and the equation (12) are equal, and the left current coefficient and the right current coefficient are solved by using the coefficient method to be determined as follows:
step four: in order to solve the reflection matrix and the scattering matrix, simulation of 2N+1 auxiliary stub systems with the same length is performed by using numerical full-wave software, wherein N is the number of lines in the system. The length of the auxiliary stub system is required to be larger than six times of the height of the line, and the rest parameters are consistent with the original line. The simulation cost of the auxiliary long-line system is low, and the simulation time is short. Let the length of the auxiliary stub system be L1. The simulation of the auxiliary stub system is set as follows: in the ith (i=1, 2, …, N) auxiliary stub system, the left end of the ith wire in the auxiliary stub system is excited by a lumped source with an amplitude of 1V; in the (i+n) (i=1, 2, …, N) auxiliary stub system, the right end of the i-th wire in the auxiliary stub system is excited by a lumped source with the amplitude of 1V; in 2n+1 auxiliary stub systems, the auxiliary stub system is excited by a plane wave consistent with the original system. Fitting the currents belonging to the second area in the obtained data to obtain three fitting coefficient vectors respectively, and solving a current equation set of the auxiliary stub system in the second area:
wherein:-the current response of the ith auxiliary stub system; i i+1 -right row current vector of the ith auxiliary stub system; i i+2 -left row current vector of the ith auxiliary stub system; />-the current response of the i+n auxiliary stubs; />-right row current vector of the i+n auxiliary stub system; />-left row current vector of the i+n auxiliary stub system; i pw -the current response of 2n+1 auxiliary stub systems; i pw1 -right row current vector of 2n+1 auxiliary stub system; i pw2 Left row current vector of 2n+1 auxiliary stub system.
The vectors are classified and combined to obtain a series of current matrixes:
wherein:-a matrix of right row current vectors of the first N auxiliary stub systems; />-a matrix of left row current vectors of the first N auxiliary stub systems; />-right of the auxiliary stub system from the (n+1) -th to the (2N) -th auxiliary stub systemsA matrix of row current vectors; />-a matrix of left row current vectors of the n+1th to 2nth auxiliary stub systems.
Wherein the substitution is a scattering matrix and a reflection matrix. The scattering matrix and the reflection matrix can be obtained by solving the data of each auxiliary stub system, and finally, the line current response of the second region of the system with the length L can be obtained by using the formula (13).
Step five: and combining and solving the obtained current coefficient matrix of the auxiliary line and the current coefficient expression, and obtaining a scattering coefficient and a reflection coefficient as follows:
after the scattering and reflection matrices are obtained, specific values are brought into equation (13), and I in the second region current expression can be finally obtained 1 And I 2 Vector.
Step six: the current response expressions of the first region (left end region) and the third region (right end region) can be obtained in a semi-analytic way by combining the current data obtained by the auxiliary stub system, the fitting coefficient and the linear current response expression of the second region:
wherein:
wherein: i + -a matrix of current responses of the first N auxiliary stub systems; i - -a matrix of current responses of the n+1th to 2nth auxiliary stub systems.
Thus, a system comprising all area solutions will be obtained.
In this embodiment, as shown in fig. 4 and 5, the real part and the imaginary part of the current response of the first wire in the whole area obtained by using the high frequency coupling method of the lossy ground transmission line are compared with the real part and the imaginary part of the current response of the first wire calculated by the full wave software NEC-4, respectively, so that it can be seen that the two currents are well matched, and the calculation time is only one third of the original time under the condition of 200 m. Whereas for lines longer than 200m, the calculation time of the algorithm is almost unchanged, and the calculation time required by full-wave software will increase geometrically. Therefore, the high-frequency coupling method of the power transmission line on the lossy ground can efficiently obtain the current response along the overhead multi-conductor system, the calculation efficiency of the high-frequency coupling method is almost unchanged when the line is very long, and meanwhile, the response of the overhead power line system is accurately predicted.
The invention has been described in further detail in connection with the specific embodiments of the invention, which are intended to be illustrative of the invention and are not to be construed as limiting the scope of the invention, which is defined by the appended claims, and any changes which come within the meaning and range of equivalency of the claims are therefore intended to be embraced therein.
Claims (6)
1. The high-frequency coupling method of the power transmission line on the lossy ground is characterized by comprising the following steps of; the method comprises the following steps:
step one: listing a transmission line model equation set of a multi-conductor transmission line, wherein the transmission line model equation set is a 2N-element first-order differential equation set taking voltage and current on each line in the multi-conductor transmission line as variables, and N is the number of cables; calculating an impedance matrix and an admittance matrix of a unit length of a multi-conductor power transmission line according to specific parameters of the multi-conductor power transmission line, and calculating a propagation constant matrix by using the impedance matrix and the admittance matrix of the unit length of the line;
step two: dividing the multi-conductor power transmission line into three areas according to the length and the height of the multi-conductor power transmission line, marking each included partial area, wherein the first area comprises the left terminal of the multi-conductor power transmission line, the length of the first area is twice as long as the height of the multi-conductor power transmission line, the third area comprises the right terminal of the multi-conductor power transmission line, the length of the third area is twice as long as the height of the multi-conductor power transmission line, the remaining area without the terminal is divided into a second area, and decoupling the transmission line model equation set in the second area to obtain an expression of a transmission line current vector in the area;
step three: transforming the expression of the transmission line current vector of the second region into an expression comprising a scattering coefficient matrix and a reflection coefficient matrix by using a progressive method;
in the third step, assuming that all the line lengths are L, using the progressive method idea, the second area is equivalent to an infinitely long wire, the first area and the third area are respectively equivalent to a right semi-infinitely long wire and a left semi-infinitely long wire, and then the right traveling wave current vector and the left traveling wave current vector generated by reflection and scattering are respectively:
wherein: e (E) N -an N-th order identity matrix; s is S + -left-end scattering coefficient matrix; s is S — -a right-hand scattering coefficient matrix; r is R + -a left-end reflection coefficient matrix; r is R — -a right-end reflection coefficient matrix;
step four: introducing an auxiliary stub system with the same specific parameters and the length being six times of the line height, performing simulation of the auxiliary stub system in full-wave simulation software NEC-4, fitting the currents of the auxiliary stub system obtained by simulation of the full-wave simulation software NEC-4 by using a least square method, classifying the obtained fitting coefficient vectors, and combining the fitting coefficient vectors into a plurality of fitting coefficient matrixes;
in the fourth step, the full-wave simulation software NEC-4 is used to solve the auxiliary stub systems, 2N auxiliary stub systems are needed to solve the reflection coefficient matrices of the left and right ends, 1 auxiliary stub system is needed to solve the scattering coefficient matrices of the left and right ends, and therefore 2n+1 auxiliary stub systems are needed in total, and the lengths of the 2n+1 auxiliary stub systems are all L 1 In the ith auxiliary stub system, i=1, 2, …, N, the left end of the ith wire in the auxiliary stub system is excited by a lumped source with amplitude of 1V; in the (i+N) th auxiliary stub system, exciting the right end of the (i) th lead in the auxiliary stub system by a lumped source with the amplitude of 1V; in 2N+1th auxiliary stub system, the auxiliary stub system is excited by plane waves consistent with the multi-conductor transmission line, the currents belonging to the second area in the obtained data are fitted to obtain three fitting coefficient vectors respectively, and a current equation set of the auxiliary stub system in the second area is obtained:
wherein:-the current response of the ith auxiliary stub system; />-right row current vector of the ith auxiliary stub system; />-left row current vector of the ith auxiliary stub system; />-the current response of the i+n auxiliary stubs;-right row current vector of the i+n auxiliary stub system; />-left row current vector of the i+n auxiliary stub system; i pw -the current response of 2n+1 auxiliary stub systems; i pw1 -right row current vector of 2n+1 auxiliary stub system; i pw2 -left row current vector of 2n+1 auxiliary stub system;
the vectors are classified and combined to obtain a series of current matrixes:
wherein:-a matrix of right row current vectors of the first N auxiliary stub systems; />-a matrix of left row current vectors of the first N auxiliary stub systems; />-a matrix of right row current vectors of the n+1th to 2nth auxiliary stub systems; />-a matrix of left row current vectors of the n+1th to 2nth auxiliary stub systems;
step five: combining the obtained fitting coefficient vectors into a plurality of fitting coefficient matrixes, obtaining a scattering coefficient matrix and a reflection coefficient matrix by using the fitting coefficient matrixes of the auxiliary stub system, and finally solving by using the scattering coefficient matrix and the reflection coefficient matrix to obtain a line current response expression of the second area;
step six: and correspondingly solving the line current responses of the first area and the third area by using the current of the auxiliary stub system, the fitting coefficient matrix and the transmission line current vector expression of the second area.
2. The method of claim 1, wherein in the first step, the transmission line model equation set of the multi-conductor transmission line is the Agrawal equation:
the Agrawal equation is as follows:
wherein: x-transverse axis variable of the multi-conductor transmission line; i-response current vector; y' —line admittance matrix per unit length; v (V) S -responsive to the scatter voltage vector; z' -impedance matrix per unit length of line;-a horizontal component vector of the excitation electric field;
thus, the product of the admittance matrix and the impedance matrix in unit length of the line is diagonalized to obtain a propagation constant matrix gamma of the multi-conductor power transmission line:
γ 2 ＝T -1 Y'Z'T
wherein: t-modulus change matrix.
3. The method of claim 2, wherein in the second step, the transmission line model equation set is decoupled in the second region to obtain an expression of the transmission line current vector in the second region, as follows:
wherein: j-imaginary units; i 0 -a current vector generated by the excitation electric field; k (k) 1 -the wave number of the excitation electric field; i 1 -right travelling wave current vector generated by reflection and scattering; i 2 -left travelling wave current vector generated by reflection and scattering;
wherein:
wherein, gamma 1 -a propagation constant of a first line of the multi-conductor transmission line; gamma ray 2 -Duoduo (multiple guides)A propagation constant of a second line of the bulk transmission line; gamma ray N -propagation constant of the nth line of the multi-conductor transmission line.
4. The method of claim 1, wherein in the fifth step, the obtained fitting coefficient matrix of the auxiliary stub system is combined with the left and right current vectors of the auxiliary stub system and solved, and the scattering coefficient matrix and the reflection coefficient matrix are obtained as follows:
S + I 0 ＝TI pw1 -R + TI pw2
note that the scattering coefficient matrix is always equal to I 0 The form of multiplication occurs, so only the product of the two is solved;
and then solving to obtain a linear current response expression of the second region by using the scattering coefficient matrix and the reflection coefficient matrix.
5. The method for coupling high frequencies of a lossy overhead transmission line according to claim 4, wherein the solving for the line current response expression for the second region using the scattering coefficient matrix and the reflection coefficient matrix is: since the scattering coefficient matrix and the reflection coefficient matrix are known, the line current response expression of the second area is obtained by solving a right traveling wave current vector and a left traveling wave current vector formula, namely:
wherein: i-the current along the second region of the multi-conductor transmission line corresponds.
6. The method of claim 4, wherein in the sixth step, the current obtained by the auxiliary stub system, the fitting coefficient matrix and the line current response expression of the second area are combined, so that the line current responses of the first area and the third area can be obtained in a semi-analytic manner:
wherein:
wherein: l (L) b -a region boundary of the multi-conductor transmission line, the size of which is twice the height of the multi-conductor transmission line; i + -a matrix of current responses of the first N auxiliary stub systems; i — -from the (n+1) -th to the (2N) -th auxiliary stubsA matrix of current responses of the system;-an unknown matrix related to the left-side reflection coefficient; />-an unknown matrix related to the right-hand reflection coefficient matrix; />-an unknown matrix related to the left-hand scattering coefficient matrix; />-an unknown matrix related to the right-hand scatter coefficient matrix.
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