Method and system for calculating closing inrush current of power transmission line based on telegraph equation

Abstract

The invention discloses a telegraph equation-based power transmission line closing inrush current calculation method and system, and belongs to the technical field of power transmission line closing inrush current calculation, and the method comprises the steps: calculating the full-frequency-domain frequency variation parameters of a cable line through the physical parameters of the cable line; based on the full-frequency-domain frequency-dependent parameters, a telegraph equation in a mode domain is obtained through mode domain decomposition analysis; and performing numerical Laplace transformation on the telegraph equation under the mode domain, solving the obtained complex frequency domain and the telegraph equation under the mode domain, obtaining a closing inrush current result under the mode domain and the complex frequency domain, and converting closing inrush current result data back to the time domain and the phase domain through numerical Laplace inverse transformation and phase-mode inverse transformation to obtain a closing inrush current calculation result. According to the method, the calculation precision of the algorithm is guaranteed, meanwhile, the limitation that transient calculation is only carried out under the dominant frequency is improved through full-frequency-domain frequency-varying parameter calculation, mode domain decomposition analysis and the like, and the calculation efficiency and precision of the algorithm are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of calculating inrush current during closing of transmission lines, and particularly relates to a method and system for calculating inrush current during closing of transmission lines based on telegraph equations. Background Art

[0002] With the rapid development of society at present, overhead lines are gradually being replaced by underground power cable lines. Compared with overhead lines, underground power cable lines have a larger capacitance. When the line circuit breaker closes, a high-level inrush current is extremely likely to be generated. The transient high-level inrush current may cause insulation aging, heating, or even direct damage to equipment such as cables and circuit breakers. Therefore, the system inrush current during closing should be simulated and calculated and evaluated before the construction of transmission projects.

[0003] At present, for simulation software for electromagnetic transient simulation calculations, such as PSCAD and ATP-EMTP, the pi model, Bergeron model, and Norda model are mostly used to model power cables. Such models often require segmenting the power cable line, and small cable segments usually require small simulation step sizes. This processing method will result in a slow calculation speed for calculating inrush current during closing. In addition, such models often calculate the frequency-varying parameters of transmission lines at the dominant frequency, and the dominant frequency needs to be set by the user. If the setting is unreasonable, it may lead to a decrease in calculation accuracy. Therefore, the current methods for calculating inrush current during closing of transmission lines are difficult to improve the calculation speed of inrush current during closing of cable transmission lines while ensuring the calculation accuracy of the algorithm. Summary of the Invention

[0004] The present invention provides a method and system for calculating inrush current during closing of transmission lines based on telegraph equations, aiming to solve the problem that the current methods for calculating inrush current during closing of transmission lines are difficult to improve the calculation speed of inrush current during closing of cable transmission lines while ensuring the calculation accuracy of the algorithm.

[0005] To achieve the above object, the present invention adopts the following technical solutions: The present invention provides a method for calculating inrush current during closing of transmission lines based on telegraph equations, including the following steps: S1. Calculate the full-frequency-domain frequency-varying parameters of the cable line through the physical parameters of the cable line; wherein, the full-frequency-domain frequency-varying parameters include a series impedance matrix and a shunt admittance matrix that are non-diagonal matrix forms in the phase domain. S2. Derive the telegraph equation of the cable transmission line based on the full-frequency-domain frequency-varying parameters, and use mode-domain decomposition analysis to convert the non-diagonal series impedance matrix and shunt admittance matrix in the phase domain into diagonal matrices in the mode domain to obtain the telegraph equation in the mode domain. S3. Numerically perform Laplace transform on the telegraph equation in the modal domain, converting the telegraph equation in the modal domain from the time domain and phase domain to the complex frequency domain and modal domain, to obtain the telegraph equation in the complex frequency domain and modal domain; S4. By solving the telegraph equation in the complex frequency domain and modal domain, obtain the inrush current result data in the modal domain and complex frequency domain, and through the inverse numerical Laplace transform and inverse phase-mode transform, convert the inrush current result data back to the time domain and phase domain to obtain the final calculated result of the inrush current.

[0006] In some embodiments, in S1, the calculation of the frequency-varying parameters of the cable in the full frequency domain includes: calculating the series impedance matrix and the shunt admittance matrix of the cable line, where the parameters of both the series impedance matrix and the shunt admittance matrix vary with frequency and are calculated in the complex frequency domain to obtain the series impedance matrix and the shunt admittance matrix that are in the form of non-diagonal matrices in the phase domain.

[0007] Further, in S1, the physical parameters of the cable line include: the resistivity of the core conductor, the resistivity of the metal sheath, and the resistivity of the earth.

[0008] Further, in S1, the calculation of the full frequency domain frequency-varying parameters takes into account the skin effect and the proximity effect.

[0009] In some embodiments, in S1, when calculating the frequency-varying series impedance matrix and the frequency-varying shunt admittance matrix, the method of eigenvalue decomposition is used to solve the product of the voltage transformation matrix and the current transformation matrix to obtain the series impedance matrix and the shunt admittance matrix of the cable in the modal domain.

[0010] In some embodiments, in S2, the modal decomposition analysis includes the construction of the voltage transformation matrix and the current transformation matrix, and the acquisition of the eigenvalue diagonal matrix. Through the modal decomposition analysis, the non-diagonal series impedance matrix and the shunt admittance matrix in the phase domain are converted into the diagonal series impedance matrix and the shunt admittance matrix in the modal domain.

[0011] Further, in S2, through the modal decomposition analysis, the telegraph equation in the modal domain is obtained as shown below: (19); Where, and are the series impedance matrix and the shunt admittance matrix in the phase domain respectively; and are the modal domain voltage and current vectors respectively; and are the voltage transformation matrix and the current transformation matrix respectively; is the diagonal matrix composed of the eigenvalues obtained after the above phase-mode decomposition analysis.

[0012] In some embodiments, in S3, the numerical Laplace transform adopts a fast Laplace transform algorithm.

[0013] In some embodiments, in S4, the numerical inverse Laplace transform adopts a numerical inversion algorithm, and the following phase-mode inverse decomposition analysis uses an inverse transform matrix corresponding to the mode-domain decomposition analysis for solution; (21); Where: and are the phase-domain voltage vector and the phase-domain current vector respectively; and are the mode-domain voltage vector and the mode-domain current vector respectively; and are the voltage transformation matrix and the current transformation matrix respectively.

[0014] The present invention also provides a transmission line closing inrush current calculation system based on the telegraph equation. The system includes a full-frequency domain frequency-varying parameter calculation module, a mode-domain decomposition analysis module, a mode-domain decomposition analysis module, a numerical Laplace transform module, and a closing inrush current calculation and inverse transform module, where: The full-frequency domain frequency-varying parameter calculation module is used to calculate the full-frequency domain frequency-varying parameters of the cable line through the physical parameters of the cable line; the full-frequency domain frequency-varying parameters include a series impedance matrix and a shunt admittance matrix that are in the form of a non-diagonal matrix in the phase domain, The full-frequency domain frequency-varying parameter calculation module is used to deduce the telegraph equation of the cable transmission line based on the full-frequency domain frequency-varying parameters, and adopt mode-domain decomposition analysis to convert the non-diagonal series impedance matrix and shunt admittance matrix in the phase domain into a diagonal matrix in the mode domain to obtain the telegraph equation in the mode domain; The mode-domain decomposition analysis module is used to perform a numerical Laplace transform on the telegraph equation in the mode domain, convert the telegraph equation in the mode domain from the time domain and the phase domain to the complex frequency domain and the mode domain, and obtain the telegraph equation in the complex frequency domain and the mode domain; The numerical Laplace transform module is used to convert the telegraph equation in the mode domain to the complex frequency domain and the mode domain; The closing inrush current calculation and inverse transform module is used to solve the telegraph equation in the complex frequency domain and the mode domain to obtain the closing inrush current result, and perform a numerical inverse Laplace transform and a phase-mode inverse decomposition analysis to obtain the final closing inrush current calculation result.

[0015] Compared with the prior art, a transmission line closing inrush current calculation method based on the telegraph equation of the present invention has the following beneficial effects: The present invention calculates the full-frequency-domain frequency-varying parameters of a cable line through the physical parameters of the cable line; derives the telegraph equation of the cable transmission line based on the full-frequency-domain frequency-varying parameters, and uses mode-domain decomposition analysis to convert the non-diagonal series impedance matrix and parallel admittance matrix in the phase domain into diagonal matrices in the mode domain to obtain the telegraph equation in the mode domain; performs a numerical Laplace transform on the telegraph equation in the mode domain to convert the telegraph equation in the mode domain from the time domain and phase domain to the complex frequency domain and mode domain, obtaining the telegraph equation in the complex frequency domain and mode domain; solves the telegraph equation in the complex frequency domain and mode domain to obtain the closing inrush current result data in the mode domain and complex frequency domain, and through the inverse numerical Laplace transform and phase-mode inverse transform, converts the closing inrush current result data back to the time domain and phase domain to obtain the final closing inrush current calculation result. The closing inrush current calculation method for a transmission line of the present invention improves the calculation speed of the closing inrush current of a cable transmission line while ensuring the calculation accuracy of the algorithm. The present invention solves the problem that the existing closing inrush current calculation algorithm for a transmission line has a slow calculation speed, overcomes the limitation that transient calculations are only carried out at the dominant frequency through methods such as full-frequency-domain frequency-varying parameter calculation and mode-domain decomposition analysis, thereby greatly improving the calculation efficiency and calculation accuracy of the algorithm, and has better practical significance. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] The accompanying drawings in the specification are used to provide a further understanding of the present invention, and constitute a part of the present invention. The schematic embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation to the present invention.

[0017] Figure 1 It is a schematic flow chart of a method for calculating the closing inrush current of a transmission line based on the telegraph equation according to the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. Usually, the components of the embodiments of the present invention described and shown in the accompanying drawings here can be arranged and designed in various different configurations.

[0019] Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed present invention, but merely represents the selected embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts fall within the scope of protection of the present invention.

[0020] It should be noted that like reference numerals and letters refer to like items in the following figures. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0021] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper", "lower", "horizontal", "inner", etc. indicate the orientation or positional relationship based on the orientation or positional relationship shown in the figures, or the orientation or positional relationship in which the invention product is usually placed during use, it is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as a limitation to the present invention. In addition, terms such as "first", "second", etc. are only used for distinguishing descriptions and cannot be understood as indicating or implying relative importance.

[0022] In addition, if the term "horizontal" appears, it does not mean that the component is required to be absolutely horizontal, but it can be slightly inclined. For example, "horizontal" only means that its direction is more horizontal relative to "vertical", and does not mean that the structure must be completely horizontal, but it can be slightly inclined.

[0023] In the description of the embodiments of the present invention, it should also be noted that unless otherwise clearly specified and limited, if terms such as "set", "installed", "connected", "connected" are understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be directly connected, or indirectly connected through an intermediate medium, and it can be the communication inside two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the present invention can be understood according to specific situations.

[0024] How to overcome the limitation that transient calculation is only carried out at the dominant frequency while ensuring the calculation accuracy of the algorithm, and improve the calculation efficiency and calculation accuracy of the algorithm.

[0025] Based on this, as Figure 1 shown, a method for calculating the closing inrush current of a transmission line based on the telegraph equation according to the present invention includes the following steps: S1. Calculate the full-frequency domain frequency-varying parameters of the cable line through the physical parameters of the cable line; wherein, the full-frequency domain frequency-varying parameters include a series impedance matrix and a shunt admittance matrix that are non-diagonal matrix forms in the phase domain. S2. Derive the telegraph equation of the cable transmission line based on the full-frequency domain frequency-varying parameters, and use modal decomposition analysis to convert the non-diagonal series impedance matrix and shunt admittance matrix in the phase domain into a diagonal matrix in the modal domain to obtain the telegraph equation in the modal domain. S3. Numerically perform Laplace transform on the telegraph equation in the modal domain, converting the telegraph equation in the modal domain from the time domain and phase domain to the complex frequency domain and modal domain, to obtain the telegraph equation in the complex frequency domain and modal domain; S4. By solving the telegraph equation in the complex frequency domain and modal domain, obtain the inrush current result data in the modal domain and complex frequency domain. Through numerical inverse Laplace transform and inverse phase-modal transform, convert the inrush current result data back to the time domain and phase domain to obtain the final calculated result of the inrush current.

[0026] By considering the full-frequency-domain frequency-varying parameters of the cable line, the present invention can more accurately reflect the actual electrical characteristics of the cable line and improve the calculation accuracy. At the same time, through modal domain decomposition analysis, the present invention converts a complex non-diagonal matrix into a diagonal matrix, simplifies the solution process of the telegraph equation, and thus simplifies the calculation process. Further, by using numerical Laplace transform and inverse transform, the present invention can quickly obtain the result data of the inrush current, improve the calculation efficiency, and improve the applicability of the method.

[0027] In some embodiments, in S1, the calculation of the full-frequency-domain frequency-varying parameters of the cable of the present invention includes: calculating the series impedance matrix and shunt admittance matrix of the cable line, where the parameters of the series impedance matrix and shunt admittance matrix vary with frequency and are calculated in the complex frequency domain to obtain the series impedance matrix and shunt admittance matrix that are in the form of non-diagonal matrices in the phase domain. By considering the influence of frequency variation on the series impedance matrix and shunt admittance matrix, the present invention can more accurately reflect the electrical characteristics of the cable line, thereby improving the calculation accuracy. The method of the present invention can be applied to the analysis of electrical characteristics in a wide frequency band range and is suitable for wide-band analysis.

[0028] Further, by considering the influence of physical parameters such as the core conductor, metal sheath, and ground on the electrical characteristics of the cable line, the present invention can more accurately calculate the full-frequency-domain frequency-varying parameters. The method of the present invention can be applied to different types of cable lines, providing certain technical support for the operation and maintenance of the power system. And when calculating the full-frequency-domain frequency-varying parameters, the present invention needs to consider the skin effect and proximity effect, which have a significant impact on the electrical characteristics of the cable line. By considering the skin effect and proximity effect, the electrical characteristics of the cable line at high frequencies can be more accurately reflected, so that the method of the present invention is applicable to the analysis and design of the power system under high-frequency conditions.

[0029] In some embodiments, when calculating the frequency-varying series impedance matrix and the frequency-varying shunt admittance matrix of the present invention, the method of eigenvalue decomposition is adopted to solve the product of the voltage transformation matrix and the current transformation matrix, so as to obtain the cable series impedance matrix and the shunt admittance matrix in the modal domain. By adopting the method of eigenvalue decomposition, the product of the voltage transformation matrix and the current transformation matrix can be solved quickly, so as to obtain the cable series impedance matrix and the shunt admittance matrix in the modal domain, effectively avoiding complex matrix operations.

[0030] In some embodiments, the modal decomposition analysis of the present invention includes: the construction of the voltage transformation matrix and the current transformation matrix, and the acquisition of the eigenvalue diagonal matrix. Through the modal decomposition analysis, the non-diagonal series impedance matrix and the shunt admittance matrix in the phase domain are converted into the diagonal series impedance matrix and the shunt admittance matrix in the modal domain. Through the modal decomposition analysis of the present invention, the complex non-diagonal matrix is converted into a diagonal matrix, simplifying the solution process of the telegraph equation, and the matrix in the phase domain can be quickly converted into the diagonal matrix in the modal domain, improving the calculation efficiency.

[0031] Furthermore, the present invention quickly completes the numerical Laplace transform by adopting the fast Laplace transform algorithm, and through the numerical inverse Laplace transform and the phase-mode inverse decomposition analysis, the closing inrush current result data in the complex frequency domain and the modal domain are converted back to the time domain and the phase domain to obtain the final closing inrush current calculation result. The present invention adopts the numerical inversion algorithm and the inverse transformation matrix for solution, and can obtain the final closing inrush current calculation result more accurately.

[0032] The present invention also provides a transmission line closing inrush current calculation system based on the telegraph equation. The system includes a full-frequency domain frequency-varying parameter calculation module, a modal decomposition analysis module, a modal decomposition analysis module, a numerical Laplace transform module, and a closing inrush current calculation and inverse transformation module, wherein: The full-frequency domain frequency-varying parameter calculation module is used to calculate the full-frequency domain frequency-varying parameters of the cable line through the physical parameters of the cable line; the full-frequency domain frequency-varying parameters include the series impedance matrix and the shunt admittance matrix in the form of a non-diagonal matrix in the phase domain. The full-frequency domain frequency-varying parameter calculation module is used to deduce the telegraph equation of the cable transmission line based on the full-frequency domain frequency-varying parameters, and adopt modal decomposition analysis to convert the non-diagonal series impedance matrix and the shunt admittance matrix in the phase domain into diagonal matrices in the modal domain to obtain the telegraph equation in the modal domain. The modal decomposition analysis module is used to perform a numerical Laplace transform on the telegraph equation in the modal domain, and convert the telegraph equation in the modal domain from the time domain and the phase domain to the complex frequency domain and the modal domain to obtain the telegraph equation in the complex frequency domain and the modal domain. The numerical Laplace transform module is used to convert the telegraph equation in the modal domain to the complex frequency domain and the modal domain. The closing inrush current calculation and inverse transformation module is used to solve the telegraph equation in the complex frequency domain and modulus domain to obtain the closing inrush current result, and perform numerical Laplace inverse transformation and phase-mode inverse decomposition analysis to obtain the final closing inrush current calculation result. Through this system, a carrier is provided for the transmission line closing inrush current calculation method based on the telegraph equation, and the calculation of the transmission line closing inrush current is realized.

[0033] The following further elaborates on a transmission line closing inrush current calculation method and system according to the present invention through specific embodiments.

[0034] As Figure 1 shown, a fast calculation method for the transmission line closing inrush current based on the telegraph equation of the present invention mainly includes: cable full-frequency domain frequency-variable parameter calculation, mode domain decomposition analysis, numerical Laplace transformation, numerical Laplace inverse transformation and mode domain inverse decomposition. The following elaborates on the four major parts involved in the algorithm in detail.

[0035] I. Cable full-frequency domain frequency-variable parameter calculation; For the fast calculation algorithm of the cable closing inrush current, it is first necessary to calculate the frequency-variable parameters of the cable line, that is, including the frequency-variable series impedance matrix and the frequency-variable shunt admittance matrix. Efficiently and accurately calculating the frequency-variable parameters of the cable line is crucial for improving the calculation speed and accuracy of the cable closing inrush current calculation.

[0036] Due to the influence of the skin / proximity effect, the parameters of the cable's series impedance matrix and shunt admittance matrix exhibit frequency-variable characteristics, that is, the calculation results of the cable parameters change with the change of the calculation frequency. Currently widely used cable models often calculate the frequency-variable parameters of the transmission line at the dominant frequency, and the dominant frequency needs to be set by the user. If the setting is unreasonable, it may lead to a decrease in calculation accuracy. Based on this, in order to improve the calculation accuracy and speed of the cable transmission line closing inrush current, the present invention calculates the frequency-variable parameters of the cable line in the entire complex frequency domain, that is, the full-frequency domain frequency-variable parameters. This processing method can significantly improve the calculation speed of the cable line closing inrush current while ensuring the calculation accuracy. The following describes the calculation method of the cable full-frequency domain frequency-variable parameters.

[0037] In this embodiment, considering the power cable as the transmission line studied in the present invention, the frequency-variable parameters of the cable line mainly include the series impedance matrix and the shunt admittance matrix. The expression of the series impedance matrix is as shown in the following formula: (1); Where: Z CC is the self-impedance of the conductor core, Z CS is the mutual impedance between the conductor core and the sheath, Z SS is the self-impedance of the sheath, Z mis the soil return impedance.

[0038] (2); Among them, The calculation method is as follows: (3); Among them, is the resistivity of the core conductor, m C is the reciprocal of the complex penetration depth of the core conductor, R1 is the outer radius of the core, J n J(x) is the modified Bessel function of the first kind of order n. m c , Z Sinner , Z Souter , Z Smutual The expressions are as follows: (4); (5); (6); (7); Among them, ρ S is the resistivity of the metal sheath, m S is the reciprocal of the complex penetration depth of the metal sheath, μ is the magnetic permeability of the core, R2 is the outer radius of the inner insulation, and R3 is the outer radius of the sheath. m s , Z CSinsul , Z SGinsul , Z earth , Z earth_mutual The expressions are as follows: (8); (9); (10); (11); (12); Among them ρ e is the resistivity of the earth, μ ins is the magnetic permeability of the inner insulation, μ out_ins is the magnetic permeability of the outer insulation,, R4 is the outer radius of the outer insulation, h is the laying depth of the cable, K0 is the modified Bessel function of the second kind, and d is the core spacing of the cable. m e is the reciprocal of the complex penetration depth of the earth, and its expression is as follows: (13); For the shunt admittance matrix of the cable , its expression is as follows: (14); where is the potential coefficient matrix, and its expression is as follows: (15); (16).

[0039] P c is the internal potential coefficient, P s is the external potential coefficient, ɛ0 is the relative permittivity of the internal insulation, and ɛ1 is the relative permittivity of the external insulation. For the calculation of the voltage conversion matrix and the current conversion matrix , the method of eigenvalue decomposition of the product of and can be used for solution. After obtaining the corresponding voltage and current conversion matrices, the series impedance matrix and the shunt admittance matrix in the modal domain can be obtained through Equation (17).

[0040] (17); Through the above calculation process, the frequency-varying parameters of the cable in the full frequency domain, namely the series impedance matrix and the shunt admittance matrix, can be obtained, laying a theoretical and computational foundation for the subsequent fast calculation algorithm of inrush current.

[0041] II. Modal decomposition analysis; In order to solve the inrush current of the cable line, it is necessary to derive the telegraph equation of the cable transmission line, as shown in the following equation: (18); In the formula: and are the series impedance matrix and the shunt admittance matrix in the phase domain, respectively; and are the phase domain voltage and current (inrush current) vectors, respectively; x is the distance of the point to be solved in the cable line from the cable head.

[0042] Due to electromagnetic coupling, the series impedance matrix and the shunt admittance matrix in the phase domain are non-diagonal matrices, which will make the solution of the above telegraph equation extremely complex. Therefore, modal decomposition analysis is used to decouple the cable loop with electromagnetic coupling relationship. The telegraph equation in the modal domain after phase-mode decomposition analysis is as shown in the following equation: (19); In the formula: and are the series impedance matrix and shunt admittance matrix in the phase domain, respectively; and are the voltage and current vectors in the modal domain, respectively; and are the voltage transformation matrix and current transformation matrix, respectively; is the diagonal matrix composed of the eigenvalues obtained from the above phase-modal decomposition analysis.

[0043] Through modal domain decomposition analysis, the non-diagonal series impedance matrix and shunt admittance matrix in the phase domain are converted into the diagonal series impedance matrix and shunt admittance matrix in the modal domain, thus greatly simplifying the difficulty of solving the telegraph differential equation and improving the calculation efficiency of the inrush current during cable line switching on.

[0044] III. Laplace Transform; The above content obtains the decoupled telegraph equation. However, the above equation is still a linear partial differential equation. Therefore, Laplace transform is used to convert it into the modal domain and complex frequency domain, so as to simplify the calculation process. The complex frequency domain and modal domain telegraph equations after Laplace transform are shown as follows: (20); R m is the equivalent resistance of the line, L m is the equivalent inductance of the line, G m is the equivalent conductance of the line, C m is the equivalent capacitance of the line.

[0045] By solving the above first-order differential equations, the inrush current results of the cable line in the modal domain and complex frequency domain can be obtained.

[0046] IV. Inverse Laplace Transform and Phase-Modal Inverse Transform; The above calculation process obtains the inrush current calculation results of the cable line in the modal domain and complex frequency domain. However, what we need is the inrush current calculation results in the phase domain and time domain. Therefore, inverse Laplace transform and phase-modal inverse decomposition analysis are required for the above calculation results. The calculation expression of the phase-modal inverse decomposition analysis is shown as follows: (21); Where: and are the phase domain voltage vector and phase domain current vector, respectively; and are the modal domain voltage vector and modal domain current vector, respectively; and are the voltage transformation matrix and current transformation matrix, respectively.

[0047] Thus, the inrush current calculation results of the cable line in the time domain and phase domain can be obtained.

[0048] A method and system for calculating inrush current during closing of transmission lines based on telegraph equations. By considering the full-frequency domain frequency-varying parameters and physical characteristics of cable lines, such as the resistivity of the core conductor, metal sheath, and ground, as well as the skin effect and proximity effect, the calculation accuracy is significantly improved. Moreover, through the application of mode-domain decomposition analysis, the complex non-diagonal matrix is converted into a diagonal matrix, simplifying the solution process of the telegraph equation. At the same time, numerical Laplace transform and inverse transform are adopted, combined with the fast Laplace transform algorithm and numerical inversion algorithm, further accelerating the calculation process, enabling the method to quickly obtain accurate inrush current results and providing effective technical support for the power system.

[0049] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and does not impose any form of limitation on the present invention. Any ordinary technical personnel in this industry can smoothly implement the present invention according to the instructions and the above description. Slight changes, modifications, and equivalent variations made by using the technical content disclosed above are all equivalent embodiments of the present invention. At the same time, any equivalent changes, modifications, and evolutions made to the above embodiments based on the essential technology of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for calculating the closing inrush current of a transmission line based on the telegraph equation, characterized in that: The steps include: S1. Calculate the full-frequency-domain frequency-variable parameters of the cable line through the physical parameters of the cable line; wherein the full-frequency-domain frequency-variable parameters include a series impedance matrix and a parallel admittance matrix in the form of a non-diagonal matrix in the phase domain; S2. Based on the full-frequency frequency-variable parameters, the telegraph equation of the cable transmission line is derived. By using the mode domain decomposition analysis, the non-diagonal series impedance matrix and the parallel admittance matrix in the phase domain are converted into the diagonal matrix in the mode domain, and the telegraph equation in the mode domain is obtained; S3, performing a numerical Laplace transform on the telegraph equation in the module domain, converting the telegraph equation in the module domain from the time domain and the phase domain to the complex frequency domain and the module domain, and obtaining the telegraph equation in the complex frequency domain and the module domain; S4. By solving the telegraph equations in the complex frequency domain and the mode domain, the closing inrush current result data in the mode domain and the complex frequency domain are obtained. By numerical inverse Laplace transform and phase mode inverse transform, the closing inrush current result data is converted back to the time domain and the phase domain to obtain the final closing inrush current calculation result.

2. The method for calculating the closing inrush current of a power transmission line based on the telegraph equation according to claim 1, characterized in that: In S1, the full-frequency domain frequency-variant parameter calculation of the cable includes: calculating the series impedance matrix and parallel admittance matrix of the cable line, where the parameters of the series impedance matrix and the parallel admittance matrix vary with frequency, and the calculation is performed in the complex frequency domain to obtain the series impedance matrix and the parallel admittance matrix in the form of non-diagonal matrices in the phase domain.

3. The method for calculating the closing inrush current of a power transmission line based on the telegraph equation according to claim 2, characterized in that: In S1, the physical parameters of the cable line include: the resistivity of the core conductor, the resistivity of the metal sheath, and the resistivity of the earth.

4. The method for calculating the closing inrush current of a power transmission line based on the telegraph equation according to claim 2, characterized in that: In S1, the calculation of frequency-variant parameters in the full frequency domain takes into account the skin effect and proximity effect.

5. The method for calculating the closing inrush current of a power transmission line based on the telegraph equation according to claim 1, characterized in that: In S1, when calculating the frequency-dependent series impedance matrix and the frequency-dependent shunt admittance matrix, the eigenvalue decomposition method is used to solve the product of the voltage conversion matrix and the current conversion matrix to obtain the cable series impedance matrix and the shunt admittance matrix in the model domain.

6. The method for calculating the closing inrush current of a power transmission line based on the telegraph equation according to claim 1, characterized in that: In S2, the modular domain decomposition analysis includes the construction of the voltage transformation matrix and the current transformation matrix, and the acquisition of the eigenvalue diagonal matrix. Through the modular domain decomposition analysis, the non-diagonal series impedance matrix and the parallel admittance matrix in the phase domain are converted into the diagonal series impedance matrix and the parallel admittance matrix in the modular domain.

7. The method for calculating the closing inrush current of a power transmission line based on the telegraph equation according to claim 6, characterized in that: In S2, through the mode domain decomposition analysis, the telegraph equation under the mode domain is obtained as follows: （19）； in, and They are the series impedance matrix and the shunt admittance matrix in the phase domain respectively; and are the module domain voltage and current vectors respectively; and They are voltage transformation matrix and current transformation matrix respectively; It is a diagonal matrix consisting of the eigenvalues ​​obtained after the above phase mode decomposition analysis.

8. The method for calculating the closing inrush current of a power transmission line based on the telegraph equation according to claim 1, characterized in that: In S3, the numerical Laplace transform uses the fast Laplace transform algorithm.

9. The method for calculating the closing inrush current of a power transmission line based on the telegraph equation according to claim 1, characterized in that: In S4, the numerical inverse Laplace transform uses a numerical inversion algorithm, and the following phase mode inverse decomposition analysis uses the inverse transformation matrix corresponding to the mode domain decomposition analysis for solution; （21）； in: and are the phase domain voltage vector and phase domain current vector respectively; and They are the module domain voltage vector and the module domain current vector respectively; and They are the voltage transformation matrix and the current transformation matrix respectively.

10. A system based on the method for calculating the closing inrush current of a power transmission line based on the telegraph equation as claimed in any one of claims 1 to 9, characterized in that: The system includes a full-frequency-domain frequency-variable parameter calculation module, a mode-domain decomposition analysis module, a mode-domain decomposition analysis module, a numerical Laplace transformation module, and a closing inrush current calculation and inverse transformation module, wherein: The full-frequency-domain frequency-variable parameter calculation module is used to calculate the full-frequency-domain frequency-variable parameters of the cable line through the physical parameters of the cable line; the full-frequency-domain frequency-variable parameters include the series impedance matrix and the parallel admittance matrix in the form of non-diagonal matrices in the phase domain, The full-frequency-domain frequency-variable parameter calculation module is used to derive the telegraph equation of the cable transmission line based on the full-frequency-domain frequency-variable parameters, and adopts the mode domain decomposition analysis to convert the non-diagonal series impedance matrix and the parallel admittance matrix in the phase domain into the diagonal matrix in the mode domain, so as to obtain the telegraph equation in the mode domain; The module domain decomposition analysis module is used to perform numerical Laplace transformation on the telegraph equation in the module domain, convert the telegraph equation in the module domain from the time domain and the phase domain to the complex frequency domain and the module domain, and obtain the telegraph equation in the complex frequency domain and the module domain; The numerical Laplace transform module is used to transform the telegraph equation in the module domain into the complex frequency domain and the module domain; The closing inrush current calculation and inverse transformation module is used to solve the telegraph equations in the complex frequency domain and the mode domain to obtain the closing inrush current results, and perform numerical Laplace inverse transformation and phase mode inverse decomposition analysis to obtain the final closing inrush current calculation results.

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