Numerical calculation method of electromagnetic transients in high-voltage transmission lines based on increased-dimensional precise integration

Abstract

A numerical calculation method for electromagnetic transients of a high-voltage transmission line based on dimensionality-increased fine integration includes the following steps: S100, obtaining high-voltage transmission line information data, wherein the high-voltage transmission line information data includes size information and feature information, and the feature information includes insulator position information, ground wire position information, and line material information; S200, performing calculation processing based on the size information and line material information to obtain line resistance data, line capacitance data, and line inductance data; S300, modeling the high-voltage transmission line based on the high-voltage transmission line information data, line resistance data, line capacitance data, and line inductance data to obtain an electromagnetic transient mathematical model of the high-voltage transmission line; S400, performing analysis processing based on the electromagnetic transient mathematical model of the high-voltage transmission line to obtain current data, charge distribution data, and electromagnetic characteristics.

Description

Technical Field

[0001] The present invention relates to the technical field of electromagnetic transient calculation of power systems, in particular to a numerical calculation method of electromagnetic transient of high-voltage transmission lines based on dimension-increased precise integration. Background Art

[0002] High-voltage transmission lines are a crucial component of power systems. Analyzing their electromagnetic transients using numerical methods can address numerous power system challenges. These include simulating transmission line faults to determine short-circuit currents and harmonic components, researching transmission line fault location algorithms, and calculating overvoltages during no-load closing.

[0003] The existing numerical calculation method of electromagnetic transients of high-voltage transmission lines does not deal with singular integrals in electromagnetic transients. Since high-voltage transmission lines are slender structures, the accuracy of the numerical calculation results of electromagnetic transients of high-voltage transmission lines does not meet the requirements. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a numerical calculation method for electromagnetic transients of high-voltage transmission lines based on dimensionality-increasing fine integration, which solves the problem that the existing numerical calculation method for electromagnetic transients of high-voltage transmission lines does not process singular integrals in electromagnetic transients. Since high-voltage transmission lines are slender structures, the accuracy of the numerical calculation results of electromagnetic transients of high-voltage transmission lines does not meet the requirements.

[0005] To solve the above technical problems, the technical solution adopted by the present invention is: a numerical calculation method of electromagnetic transient of high-voltage transmission lines based on dimensionality-increased precise integration, comprising the following steps:

[0006] S100: Acquire high-voltage transmission line information data, wherein the high-voltage transmission line information data includes size information and feature information, and the feature information includes insulator position information, ground wire position information, and line material information;

[0007] S200, performing calculations based on the size information and the line material information to obtain line resistance data, line capacitance data, and line inductance data;

[0008] S300, modeling the high-voltage transmission line based on the high-voltage transmission line information data, line resistance data, line capacitance data, and line inductance data to obtain an electromagnetic transient mathematical model of the high-voltage transmission line;

[0009] S400: Analyze and process the electromagnetic transient mathematical model of the high-voltage transmission line to obtain current data, charge distribution data, and electromagnetic characteristics.

[0010] Preferably, the steps of performing calculations and processing based on the size information and the line material information in step S200 to obtain line resistance data, line capacitance data, and line inductance data are as follows:

[0011] S201, analyzing and processing the dimension information to obtain the transmission line length data, the transmission line cross-sectional area, and the number of turns of the transmission line;

[0012] S202, analyzing and processing the line material information to obtain the resistivity, dielectric constant, and relative permeability of the transmission line;

[0013] S203, performing correction calculation based on the transmission line length data, the transmission line cross-sectional area, and the resistivity of the transmission line to obtain transmission line resistance data;

[0014] S204, performing correction calculation based on the transmission line length data, the transmission line cross-sectional area, and the dielectric constant of the transmission line to obtain transmission line capacitance data;

[0015] S205 , performing correction calculation based on the transmission line length data, the transmission line cross-sectional area, the number of turns of the transmission line, and the relative magnetic permeability of the transmission line to obtain the transmission line inductance data.

[0016] Preferably, the calculation formula for transmission line resistance data is:

[0017] ;

[0018] Where R is the resistance data of the transmission line; is the resistivity of the transmission line; D is the length of the transmission line; S is the cross-sectional area of ​​the transmission line; A is the resistance compensation parameter of the transmission line;

[0019] The calculation formula for transmission line capacitance data is:

[0020] ;

[0021] Where C is the capacitance data of the transmission circuit, is the dielectric constant of the transmission line; D is the length of the transmission line; S is the cross-sectional area of ​​the transmission line; B is the capacitance compensation parameter of the transmission line;

[0022] The calculation formula for transmission line inductance data is:

[0023] ;

[0024] Where, L is the inductance data of the transmission line; is the magnetic permeability of the transmission line in vacuum; is the relative magnetic permeability of the transmission line; is the number of turns of the transmission line; D is the length of the transmission line; S is the cross-sectional area of ​​the transmission line; and E is the inductance compensation parameter of the transmission line.

[0025] Preferably, in step S300, modeling the high-voltage transmission line according to the high-voltage transmission line information data, line resistance data, line capacitance data, and line inductance data to obtain the electromagnetic transient mathematical model of the high-voltage transmission line specifically includes the following steps:

[0026] S301, obtaining geographic information of high-voltage transmission lines;

[0027] S302: Perform data modeling operations on the high-voltage transmission line and its geographic information based on the high-voltage transmission line information data, line resistance data, line capacitance data, and line inductance data to obtain an electromagnetic transient mathematical model of the high-voltage transmission line.

[0028] Preferably, the step S400 of analyzing and processing the electromagnetic transient mathematical model of the high-voltage transmission line to obtain current data, charge distribution data and electromagnetic characteristics specifically includes the following steps:

[0029] S401, discretizing the electromagnetic transient mathematical model of the high-voltage transmission line to obtain a minimum unit, wherein the minimum unit includes an insulator minimum unit and a transmission line minimum unit;

[0030] S402, analyzing the minimum unit through Maxwell's equations to obtain an electromagnetic field equation model corresponding to the minimum unit;

[0031] S403. Calculate and process the electromagnetic field equation model through dimensionality-increasing precise integration to obtain current data, charge distribution data, and electromagnetic characteristics.

[0032] Preferably, the step S401 of discretizing the electromagnetic transient mathematical model of the high-voltage transmission line to obtain the minimum unit, wherein the minimum unit includes the minimum insulator unit and the minimum transmission line unit, specifically includes the following steps:

[0033] S4011. Divide the transmission line in the electromagnetic transient mathematical model of the high-voltage transmission line by using the finite element method to obtain the minimum unit of the transmission line;

[0034] S4012. Divide the insulators in the electromagnetic transient mathematical model of the high-voltage transmission line by the finite element method to obtain the minimum unit of the insulator.

[0035] Preferably, the step S403 of calculating and processing the electromagnetic field equation model by dimensionality-increasing precise integration to obtain current data, charge distribution data and electromagnetic characteristics specifically includes the following steps:

[0036] S4031. Calculate and process the electromagnetic field equation model in the time domain to obtain the time domain integral of the transmission line and the insulator;

[0037] S4032. Calculate and process the electromagnetic field equation model in the spatial domain to obtain spatial integrals of the transmission line and the insulator;

[0038] S4033. Calculate and process the time domain integral and the space domain integral through dimensionality-increased fine integration to obtain current data, charge distribution data, and electromagnetic characteristics.

[0039] Preferably, the step S4033 of calculating and processing the time domain integral and the space domain integral by means of dimensionality-increasing fine integration to obtain current data, charge distribution data, and electromagnetic characteristics specifically includes the following steps:

[0040] S40331. Analyze and process the time domain integral and the space domain integral to determine the time domain singular integral and the space domain singular integral;

[0041] S40332. Performing a transformation operation on the time domain singular integral and the space domain singular integral by dimensionality-increasing fine integration to obtain the time domain regularized integral and the space domain regularized integral;

[0042] S40333. Analyze and process the time domain canonical integral and the space domain canonical integral to obtain current data, charge distribution data, and electromagnetic characteristics.

[0043] The present invention provides a method for numerically calculating electromagnetic transients of high-voltage transmission lines based on dimensionality-increased precise integration. The method analyzes the high-voltage transmission line to determine the capacitance data, resistance data, and inductance data of the transmission line. The method then combines the size information and characteristic information of the high-voltage transmission line to perform modeling, obtains an electromagnetic field equation model of the high-voltage transmission line, performs time domain and space domain analysis on the electromagnetic field equation model, and converts singular integrals in the electromagnetic field equation model into regular integrals using dimensionality-increased precise integration, thereby making the results of electromagnetic transient numerical calculations more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] The present invention will be further described below with reference to the accompanying drawings and examples:

[0045] Figure 1 is a flow chart of the method of the present invention;

[0046] Figure 2 Schematic diagram of the flow of steps S201-S205 in the numerical calculation method for electromagnetic transient of high-voltage transmission lines based on dimensional-increased precise integration proposed by the present invention;

[0047] Figure 3 This is a flow chart of steps S301-S302 in the numerical calculation method for electromagnetic transient of high-voltage transmission lines based on dimensional-increased precise integration proposed by the present invention;

[0048] Figure 4 This is a flow chart of steps S401-S403 in the numerical calculation method for electromagnetic transient of high-voltage transmission lines based on dimensional-increased precise integration proposed by the present invention;

[0049] Figure 5 This is a flow chart of steps S4011-S4012 in the numerical calculation method for electromagnetic transient of high-voltage transmission lines based on dimensional-increased precise integration proposed by the present invention;

[0050] Figure 6 This is a flow chart of steps S4031-S4033 in the numerical calculation method for electromagnetic transient of high-voltage transmission lines based on dimensional-increased precise integration proposed by the present invention;

[0051] Figure 7 This is a flow chart of steps S40331-S40333 in the numerical calculation method for electromagnetic transient of high-voltage transmission lines based on dimensional-increased precise integration proposed by the present invention;

[0052] Figure 8 The electromagnetic transient calculation results (initial phase angle) of the high-voltage transmission line under the dimensional precision integration );

[0053] Figure 9 The electromagnetic transient calculation results of the high-voltage transmission line under the CDA method (initial phase angle ). DETAILED DESCRIPTION

[0054] like Figure 1 As shown in Figure 1, the numerical calculation method of electromagnetic transient of high-voltage transmission line based on dimensionality-increased precise integration includes:

[0055] S100: Acquire high-voltage transmission line information data, wherein the high-voltage transmission line information data includes size information and feature information, and the feature information includes insulator position information, ground wire position information, and line material information;

[0056] S200, performing calculations based on the size information and the line material information to obtain line resistance data, line capacitance data, and line inductance data;

[0057] S300, modeling the high-voltage transmission line based on the high-voltage transmission line information data, line resistance data, line capacitance data, and line inductance data to obtain an electromagnetic transient mathematical model of the high-voltage transmission line;

[0058] S400, performing analysis and processing based on an electromagnetic transient mathematical model of a high-voltage transmission line to obtain current data, charge distribution data, and electromagnetic characteristics;

[0059] It will be understood by those skilled in the art that to perform numerical calculations of electromagnetic transients on high-voltage transmission lines, it is necessary to establish an electromagnetic field equation model of the high-voltage transmission line, integrate the electromagnetic field equation model in the time domain and space domain, determine the time domain singular integrals and space domain singular integrals, convert the time domain singular integrals and space domain singular integrals through dimensionality-increased fine integration, convert the singular integrals into regular integrals, and then process the regular integrals to obtain circuit data, charge distribution, and electromagnetic characteristics of the high-voltage transmission line.

[0060] Reference Figure 2 As shown, the calculation and processing based on the size information and line material information to obtain the transmission line resistance data, transmission line capacitance data, and transmission line inductance data specifically includes the following steps:

[0061] S201, analyzing and processing the dimension information to obtain the transmission line length data, the transmission line cross-sectional area, and the number of turns of the transmission line;

[0062] S202, analyzing and processing the line material information to obtain the resistivity, dielectric constant, and relative permeability of the transmission line;

[0063] S203, performing correction calculation based on the transmission line length data, the transmission line cross-sectional area, and the resistivity of the transmission line to obtain transmission line resistance data;

[0064] The calculation formula for transmission line resistance data is:

[0065] ;

[0066] Where R is the resistance data of the transmission line; is the resistivity of the transmission line; D is the length of the transmission line; S is the cross-sectional area of ​​the transmission line; A is the resistance compensation parameter of the transmission line;

[0067] S204, performing correction calculation based on the transmission line length data, the transmission line cross-sectional area, and the dielectric constant of the transmission line to obtain transmission line capacitance data;

[0068] The calculation formula for transmission line capacitance data is:

[0069] ;

[0070] Where C is the capacitance data of the transmission line, is the dielectric constant of the transmission line; D is the length of the transmission line; S is the cross-sectional area of ​​the transmission line; B is the capacitance compensation parameter of the transmission line;

[0071] S205, performing correction calculation based on the transmission line length data, the cross-sectional area of ​​the transmission line, the number of turns of the transmission line, and the relative magnetic permeability of the transmission line to obtain the transmission line inductance data;

[0072] The calculation formula for transmission line inductance data is:

[0073] ;

[0074] Where, L is the inductance data of the transmission line; is the magnetic permeability of the transmission line in vacuum; is the relative magnetic permeability of the transmission line; is the number of turns of the transmission line; D is the length of the transmission line; S is the cross-sectional area of ​​the transmission line; E is the inductance compensation parameter of the transmission line;

[0075] It will be understood by those skilled in the art that the size and material of the high-voltage transmission line are analyzed to determine the resistance data, capacitance data and inductance data of the high-voltage transmission line. However, due to the different operating environments of the high-voltage transmission line and the external environment affecting the resistance data, inductance data and capacitance data of the high-voltage transmission line, the transmission line resistance compensation parameter A, the transmission line capacitance compensation parameter B, and the transmission line inductance compensation parameter E are introduced to correct the resistance data, inductance data and capacitance data, so that the subsequent electromagnetic transient calculation results are more accurate.

[0076] Reference Figure 3 As shown, the high-voltage transmission line is modeled based on the high-voltage transmission line information data, line resistance data, line capacitance data, and line inductance data to obtain the electromagnetic transient mathematical model of the high-voltage transmission line, which specifically includes the following steps:

[0077] S301, obtaining geographic information of high-voltage transmission lines;

[0078] S302: Perform data modeling operations on the high-voltage transmission line and its geographic information based on the high-voltage transmission line information data, line resistance data, line capacitance data, and line inductance data to obtain an electromagnetic transient mathematical model of the high-voltage transmission line.

[0079] Reference Figure 4 As shown, the analysis and processing based on the electromagnetic transient mathematical model of the high-voltage transmission line to obtain current data, charge distribution data and electromagnetic characteristics specifically includes the following steps:

[0080] S401, discretizing the electromagnetic transient mathematical model of the high-voltage transmission line to obtain a minimum unit, wherein the minimum unit includes an insulator minimum unit and a transmission line minimum unit;

[0081] The transmission lines and insulators are divided into units through the finite element method, the structure of the transmission lines, and the insulator structure. Each unit is analyzed through Maxwell's equations to determine the electromagnetic field equation model corresponding to each unit. The electromagnetic field equation model is then transformed based on the dimensionality-increasing fine integration to determine the current data, charge distribution data, and electromagnetic characteristics.

[0082] S402, analyzing the minimum unit through Maxwell's equations to obtain an electromagnetic field equation model corresponding to the minimum unit;

[0083] S403. Calculate and process the electromagnetic field equation model through dimensionality-increasing precise integration to obtain current data, charge distribution data, and electromagnetic characteristics.

[0084] Reference Figure 5 As shown in FIG, the electromagnetic transient mathematical model of the high-voltage transmission line is discretized to obtain the minimum unit of the transmission line, which specifically includes the following steps:

[0085] S4011. Divide the transmission line in the electromagnetic transient mathematical model of the high-voltage transmission line by using the finite element method to obtain the minimum unit of the transmission line;

[0086] S4012. Divide the insulators in the electromagnetic transient mathematical model of the high-voltage transmission line by the finite element method to obtain the minimum unit of the insulator.

[0087] Reference Figure 6 As shown, the electromagnetic field equation model is calculated and processed by dimensionality-increased precise integration to obtain current data, charge distribution data and electromagnetic characteristics, which specifically includes the following steps:

[0088] S4031. Calculate and process the electromagnetic field equation model in the time domain to obtain the time domain integral of the transmission line and the insulator;

[0089] S4032. Calculate and process the electromagnetic field equation model in the spatial domain to obtain spatial integrals of the transmission line and the insulator;

[0090] S4033. Calculate and process the time domain integral and the space domain integral through dimensionality-increased fine integration to obtain current data, charge distribution data, and electromagnetic characteristics.

[0091] Reference Figure 7 As shown, the time domain integral and the space domain integral are calculated and processed by the dimensionality-increased fine integration to obtain the current data, charge distribution data, and electromagnetic characteristics. Specifically, the steps include:

[0092] S40331. Analyze and process the time domain integral and the space domain integral to determine the time domain singular integral and the space domain singular integral;

[0093] S40332. Performing a transformation operation on the time domain singular integral and the space domain singular integral by dimensionality-increasing fine integration to obtain the time domain regularized integral and the space domain regularized integral;

[0094] S40333. Analyze and process the time domain canonical integral and the space domain canonical integral to obtain current data, charge distribution data, and electromagnetic characteristics;

[0095] Those skilled in the art will understand that the electromagnetic field equation model is integrated in the time domain and space domain because the current in the high-voltage transmission line is a conduction process, which changes with time and space. Therefore, the electromagnetic field at different positions of different high-voltage transmission lines also changes with time. Therefore, the electromagnetic field equation model is integrated in the time domain and space domain, and then the time domain integral and the space domain integral are analyzed to determine the singular integrals in the time domain integral and the space domain integral. The singular integrals are then converted through dimensionality-increasing fine integration to convert the singular integrals into regular integrals. The time domain integral and the space domain integral that do not contain singular integrals are then differentiated and restored to the electromagnetic field equation model. The current data, charge distribution and electromagnetic characteristics are determined based on the electromagnetic field equation model.

[0096] Reference Figure 8 、 9 As shown in the figure, taking the sinusoidal signal as the input of the high-voltage transmission line as an example, the calculation formula is:

[0097] ;

[0098] Where, ; a is a constant; is the phase angle, which is a known quantity;

[0099] according to For sinusoidal information, new variables are introduced to increase the dimension of the state variables. The dimension increase formula is:

[0100] ;

[0101] Using the dimension-increasing precise integration method, when When the voltage at the end of the high-voltage transmission line changes with time, the curve is as follows: Figure 8 ;

[0102] Using the CDA method, when When the voltage at the end of the high-voltage transmission line changes with time, the curve is as follows: Figure 9 ;

[0103] In summary, compared with the CDA method, the increased-dimensional precise integration method is better at suppressing numerical oscillation problems.

[0104] The above embodiments are merely preferred technical solutions of the present invention and should not be construed as limiting the present invention. The scope of protection of the present invention shall be the technical solutions set forth in the claims, including equivalent alternatives to the technical features of the technical solutions set forth in the claims. In other words, equivalent alternatives and improvements within this scope are also within the scope of protection of the present invention.

Claims

1. A numerical calculation method for electromagnetic transients of high-voltage transmission lines based on dimensionality-increased precise integration, characterized in that: The following steps are involved: S100: Acquire high-voltage transmission line information data, wherein the high-voltage transmission line information data includes size information and feature information, and the feature information includes insulator position information, ground wire position information, and line material information; S200, performing calculations based on the size information and the line material information to obtain line resistance data, line capacitance data, and line inductance data; S300, modeling the high-voltage transmission line based on the high-voltage transmission line information data, line resistance data, line capacitance data, and line inductance data to obtain an electromagnetic transient mathematical model of the high-voltage transmission line; S400, performing analysis and processing based on an electromagnetic transient mathematical model of a high-voltage transmission line to obtain current data, charge distribution data, and electromagnetic characteristics; Obtain the electromagnetic field equation model corresponding to the smallest unit of the insulator and the smallest unit of the transmission line; The electromagnetic field equation model is calculated and processed in the time domain to obtain the time domain integral of the transmission line and insulator; the electromagnetic field equation model is calculated and processed in the space domain to obtain the space domain integral of the transmission line and insulator; Analyze and process the time domain integral and the space domain integral to determine the time domain singular integral and the space domain singular integral; By performing transformation operations on the time domain singular integral and the space domain singular integral through dimensionality-increasing fine integration, the time domain regular integral and the space domain regular integral are obtained; The time domain canonical integral and the space domain canonical integral are analyzed and processed to obtain current data, charge distribution data, and electromagnetic characteristics.

2. The numerical calculation method for electromagnetic transient of high-voltage transmission line based on dimension-increased precise integration according to claim 1 is characterized in that: The steps of performing calculations and processing in step S200 based on the size information and the line material information to obtain line resistance data, line capacitance data, and line inductance data are as follows: S201, analyzing and processing the dimension information to obtain the transmission line length data, the transmission line cross-sectional area, and the number of turns of the transmission line; S202, analyzing and processing the line material information to obtain the resistivity, dielectric constant, and relative permeability of the transmission line; S203, performing correction calculation based on the transmission line length data, the transmission line cross-sectional area, and the resistivity of the transmission line to obtain transmission line resistance data; S204, performing correction calculation based on the transmission line length data, the transmission line cross-sectional area, and the dielectric constant of the transmission line to obtain transmission line capacitance data; S205 , performing correction calculation based on the transmission line length data, the transmission line cross-sectional area, the number of turns of the transmission line, and the relative magnetic permeability of the transmission line to obtain the transmission line inductance data.

3. The numerical calculation method for electromagnetic transient of high-voltage transmission line based on dimension-increased precise integration according to claim 2 is characterized in that: The calculation formula for transmission line resistance data is: Where R is the resistance data of the transmission line; is the resistivity of the transmission line; D is the length of the transmission line; S is the cross-sectional area of ​​the transmission line; A is the resistance compensation parameter of the transmission line; The calculation formula for transmission line capacitance data is: Where C is the capacitance data of the transmission circuit, is the dielectric constant of the transmission line; D is the length of the transmission line; S is the cross-sectional area of ​​the transmission line; B is the capacitance compensation parameter of the transmission line; The calculation formula for transmission line inductance data is: Where, L is the inductance data of the transmission line; is the magnetic permeability of the transmission line in vacuum; is the relative magnetic permeability of the transmission line; is the number of turns of the transmission line; D is the length of the transmission line; S is the cross-sectional area of ​​the transmission line; and E is the inductance compensation parameter of the transmission line.

4. The numerical calculation method for electromagnetic transient of high-voltage transmission line based on dimension-increased precise integration according to claim 1 is characterized in that: In step S300, modeling the high-voltage transmission line according to the high-voltage transmission line information data, line resistance data, line capacitance data, and line inductance data to obtain the electromagnetic transient mathematical model of the high-voltage transmission line specifically includes the following steps: S301, obtaining geographic information of high-voltage transmission lines; S302: Perform data modeling operations on the high-voltage transmission line and its geographic information based on the high-voltage transmission line information data, line resistance data, line capacitance data, and line inductance data to obtain an electromagnetic transient mathematical model of the high-voltage transmission line.

5. The numerical calculation method for electromagnetic transient of high-voltage transmission line based on dimension-increased precise integration according to claim 1 is characterized in that: The analysis and processing in step S400 based on the electromagnetic transient mathematical model of the high-voltage transmission line to obtain current data, charge distribution data and electromagnetic characteristics specifically includes the following steps: S401, discretizing the electromagnetic transient mathematical model of the high-voltage transmission line to obtain a minimum unit, wherein the minimum unit includes an insulator minimum unit and a transmission line minimum unit; S402. Analyze the minimum unit through Maxwell's equations to obtain an electromagnetic field equation model corresponding to the minimum unit.

6. The numerical calculation method for electromagnetic transient of high-voltage transmission line based on dimension-increased precise integration according to claim 5 is characterized in that: The step S401 is to discretize the electromagnetic transient mathematical model of the high-voltage transmission line to obtain the minimum unit, wherein the minimum unit includes the minimum insulator unit and the minimum transmission line unit. Specifically, the steps include: S4011. Divide the transmission line in the electromagnetic transient mathematical model of the high-voltage transmission line by using the finite element method to obtain the minimum unit of the transmission line; S4012. Divide the insulators in the electromagnetic transient mathematical model of the high-voltage transmission line by the finite element method to obtain the minimum unit of the insulator.

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