CN111400957A - Computing method of ultra-fast transient radiation electromagnetic field based on time domain finite difference method - Google Patents
Computing method of ultra-fast transient radiation electromagnetic field based on time domain finite difference method Download PDFInfo
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Abstract
The invention discloses a method for calculating an ultra-fast transient radiation electromagnetic field based on a time domain finite difference method, which comprises the following steps of 1, analyzing a switch operation radiation generation mechanism and GIS shell radiation electromagnetic field characteristics, 2, establishing an antenna radiation physical model in an XFDTD, dividing a grid by adopting the time domain finite difference method, establishing a PM L boundary, and 3, introducing shell transient circulation as an excitation source, simulating and obtaining the distribution characteristics of an auxiliary electromagnetic field, wherein the prior art can not accurately evaluate the electromagnetic radiation risk of secondary side equipment when a GIS substation is switched.
Description
Technical Field
The invention belongs to the field of high-frequency electromagnetic field calculation, and particularly relates to a method for calculating an ultra-fast transient radiation electromagnetic field based on a time domain finite difference method.
Background
The GIS gas insulated substation is widely applied to high-voltage and extra-high-voltage systems due to the advantages of safety, reliability, stable operation, excellent performance and the like. In the development process of a GIS transformer substation, the problem of transient electromagnetic interference of GIS switch operation gradually draws attention, and particularly in a high-voltage and extra-high-voltage system, the problem of very fast transient electromagnetic radiation is more and more serious along with the improvement of the voltage grade. With the strong smart grid of the national grid and the proposed ubiquitous power internet of things, in order to realize the information digitization of the smart substation, the networking of the communication platform and the information sharing standard, more and more power electronic devices are required to be put into a switch field, and the characteristics of sensitivity and vulnerability of the secondary equipment to transient electromagnetic interference are generated, and the switch operation can cause a series of very fast transient phenomena, so the problem of electromagnetic interference generated by the secondary equipment cannot be ignored.
The most prominent fast transient electromagnetic radiation interference source is VFTO generated in a GIS shell, but with the continuous improvement of the voltage level of a power grid, the application of an extra-high voltage system in the power grid, and the fast transient phenomenon caused by the TEV derived from the VFTO and the shell transient circulation generated in a GIS transformer substation cannot be ignored.
The GIS external electromagnetic interference source mainly comes from high-frequency transient overcurrent on the surface of the shell and radiates to the periphery in a high-frequency electromagnetic field mode in the peripheral space. According to the antenna theory, the GIS shell is equivalent to an antenna, a Hertz dipole antenna radiation model is established, and the radiation electromagnetic field is analyzed and calculated. At present, although simulation calculation is performed on antenna radiation by methods such as finite element and finite integral, the finite element method is mainly suitable for calculating the radiation of an electrically small-sized antenna, the finite integral method can calculate the radiation of a slightly larger antenna, but the calculation precision of a large-sized model is to be considered; and the electromagnetic radiation risk of secondary side equipment of the GIS transformer substation during the switching operation can not be accurately evaluated.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the method for calculating the ultra-fast transient radiation electromagnetic field based on the time domain finite difference method is provided, and the technical problems that the electromagnetic radiation risk of secondary side equipment of a GIS substation cannot be accurately evaluated in the prior art are solved.
The technical scheme of the invention is as follows:
a method for calculating the very fast transient radiation electromagnetic field based on finite difference time domain method
The method comprises the following steps:
step 1, analyzing a switch operation radiation generation mechanism and GIS shell radiation electromagnetic field characteristics;
step 2, an antenna radiation physical model is established in XFDTD, a time domain finite difference method is adopted to divide grids, and a PM L boundary is established;
and step 3: and introducing a shell transient circulation as an excitation source, and simulating to obtain the distribution characteristics of the auxiliary electromagnetic field.
The method for analyzing the switch operation radiation generation mechanism and the GIS shell radiation electromagnetic field characteristics in the step 1 comprises the following steps: according to the method, an interference source inside a GIS shell is transmitted inside the GIS in an electromagnetic wave mode, the electromagnetic wave is lost and the energy is gradually weakened when the electromagnetic wave is transmitted in a space medium, and when the electromagnetic wave is transmitted inside the GIS shell, a transmission coefficient expression is established
Wherein α is an attenuation constant of the electromagnetic wave, which represents that the amplitude of the field attenuates with the increase of the transmission distance of the electromagnetic wave, β is a phase constant of the electromagnetic wave, which represents the phase change of the electric field strength and the magnetic field strength in the transmission process of the electromagnetic wave, and the amplitude of the electric field strength and the amplitude of the magnetic field strength can attenuate and the phase can change along the transmission direction of the wave when the electromagnetic wave propagates forwards in the GIS shell by calculating the component transmission characteristics of the electric field strength and the magnetic field strength of the electromagnetic field;
in the process of spreading, GIS internal interference sources are coupled to the outer surface of a shell through GIS shell discontinuities such as GIS sleeves and basin-type insulators, and TEV and shell transient state circulation currents are generated.
Establishing an antenna radiation physical model in the XFDTD, dividing grids by adopting a time domain finite difference method, and establishing a PM L boundary by adopting the time domain finite difference method, wherein the method comprises the steps of establishing a Hertz dipole antenna model in the XFDTD by adopting the time domain finite difference method, converting a Maxwell rotation equation with time variables into a difference equation, and gradually advancing the calculation of an electric field and a magnetic field in time and space in a jumping frog mode on a time axis.
The method for converting the Maxwell rotation equation with the time variable into a differential mode and gradually advancing the calculation of the electric field magnetic field in time and space in a frog mode on a time axis comprises the following steps:
step 2.1, expanding the Maxwell rotation equation into six scalar equations:
establishing a rectangular differential grid in space, and at the moment of n delta t:
f(x,y,z,y＝f(iΔx,jΔy,kΔz,nΔt)(3)；
step 2.2, dividing any grid in the space into six components of E and H, namely, each magnetic field component is surrounded by four electric field components, each electric field component is surrounded by four magnetic field components, the value of each grid point is the value of the previous moment of the point and the value of the time step half earlier than the adjacent point, and the value of each time step is alternately obtained through differential operation; from this principle, the difference equation is derived:
step 2.3, the difference equation set is used for replacing an electromagnetic field partial differential equation to solve, the calculation can be carried out only by the explanation convergence and the stability of the dispersed difference equation set, and the numerical stability can be maintained only by ensuring that the convergence and the stability of the solution require a time step length delta t and space step lengths delta x, delta y and delta z to meet a certain relation; the numerical stability condition is derived by mathematical derivation according to electromagnetic principles as follows:
in the formula: c is the speed of light in the medium; the time interval Δ t must not exceed the 1/3 diagonal length, 1/2 diagonal length, or the length of the cell itself, at which the wave passes through the Yee cell at the speed of light; to reduce the numerical dispersion, the requirements for the spatial dispersion Δ x and the time dispersion Δ t intervals are:
in the formula: λ is the wavelength in the dispersion-free medium, and T is the period of the wave.
When a difference equation set is used for solving instead of an electromagnetic field partial differential equation, in order to simulate an open-domain electromagnetic radiation process, an absorption boundary condition needs to be given at a truncation boundary of a calculation region, a complete matching layer PM L is a lossy medium, a transmitted wave entering a PM L layer can be rapidly attenuated, and the boundary absorption efficiency is improved by arranging PM L.
The method for acquiring the transient circulation of the shell comprises the following steps: actual measurements or simulations by modeling.
The method for obtaining the shell transient circulation by modeling and simulation comprises the following steps: establishment of SF-based assays in ATP-EMPT6The high-frequency discharge model improved by the reburning model generates transient shell potential, namely TEV, through coupling of the basin-type insulator and the sleeve, wave impedance on each path is simulated according to the propagation path of an interference source, and a GIS shell transient circulation mathematical expression is obtained according to the shell transient circulation ohm calculation law:
in the formula: and f (x) is a TEV fitting mathematical expression, the TEV is obtained according to simulation or actual measurement, and Z is the shell coupling impedance characteristic and is obtained by adopting a field-circuit coupling method.
Step 3, introducing the shell transient circulation as an excitation source, and obtaining the distribution characteristics of the auxiliary electromagnetic field in a simulation mode comprises the following steps: introducing a shell transient circulation mathematical expression as an excitation source into a large-size antenna model of an XFDTD, obtaining an electromagnetic field on a boundary surface of the near-field setting of the antenna through software simulation of the XFDTD, calculating current density J and magnetic current density M by a middle data processing module of the XFDTD according to a Huygens principle, and selecting a far-field observation point to calculate far-field radiation of the antenna through discrete Fourier transform (DTF); and obtaining the main frequency band and amplitude of the electromagnetic interference generated on the GIS shell due to the outward radiation of the shell transient circulation.
The invention has the beneficial effects that:
the invention comprehensively considers and selects the time domain finite difference method, is suitable for the calculation of large-size objects, and has the precision completely meeting the requirement of a radiation field. Therefore, the method is based on a finite difference time domain method, adopts XFDTD simulation software, and adopts non-uniform grid division and near-far field conversion technology to perform simulation calculation on the ultra-fast transient electromagnetic field aiming at large-size antenna models similar to GIS; mainly aiming at a GIS transformer substation with the characteristic of large size, a time domain finite difference method is adopted, the influence of complication of a calculation process is avoided, and broadband electromagnetic interference can be obtained through one-time calculation; the problem of the electromagnetic radiation risk assessment of secondary side equipment of GIS transformer substation when the switch of GIS transformer substation is operated is solved.
The invention has the advantages that:
1. aiming at the problem of electromagnetic calculation of a large-size GIS substation;
2. the radiation source is a shell transient circulating current;
3. the frequency domain characteristic of the antenna in the broadband can be obtained by only one calculation through the calculation method, and the nearby electromagnetic wave radiation process is given;
4. the problem of the electromagnetic radiation risk assessment of secondary side equipment of GIS transformer substation when the switch of GIS transformer substation is operated is solved.
Drawings
FIG. 1 is a block flow diagram of an embodiment of the present invention;
FIG. 2 is a schematic diagram of traveling wave coupling to a housing at a GIS bushing;
FIG. 3 is a schematic diagram of traveling wave coupling to a housing at a GIS basin insulator;
fig. 4 is a schematic diagram of a hertzian dipole antenna model.
Detailed Description
A more complete description of exemplary embodiments of the invention will be had by reference to the accompanying drawings and examples, wherein a specific embodiment is shown in figure 1, comprising the steps of:
the method comprises the following steps:
the interference source of the transient space electromagnetic field generated when the GIS switch is operated is not only VFTO and VFTC inside the GIS shell, but also TEV outside the shell and shell transient circulating current generated by coupling.
The interference source inside the GIS shell is transmitted inside the GIS in an electromagnetic wave mode, the electromagnetic wave is lost when being transmitted in a space medium, and the energy is gradually weakened. When electromagnetic waves propagate in the GIS shell, the propagation coefficient expression is as follows:
wherein, the dielectric constant is shown, mu is magnetic conductivity, sigma is electric conductivity, α is attenuation constant of electromagnetic wave, which shows that the amplitude of the field attenuates with the increase of the transmission distance of the electromagnetic wave, β is phase constant of the electromagnetic wave, which shows the phase change of the electric field intensity and the magnetic field intensity in the process of propagating the electromagnetic wave, and by calculating the propagation characteristics of the electric field intensity and the magnetic field intensity component of the electromagnetic field, the amplitude of the electric field intensity and the amplitude of the magnetic field intensity of the electromagnetic wave attenuate and the phase change along the propagation direction of the wave when the electromagnetic wave propagates forwards in the GIS shell.
In the process of spreading, GIS internal interference sources are coupled to the outer surface of a shell through GIS shell discontinuities such as GIS sleeves and basin-type insulators, and TEV and shell transient state circulation currents are generated.
The traveling wave at the GIS bushing is coupled to the housing as shown in fig. 2, and the refraction and reflection phenomena of the wave occurring at the bushing form three propagation paths: between coaxial conductors within the GIS, Z1(ii) a Between overhead line and earth, Z2(ii) a Between the outer wall of the GIS housing and the ground, Z3. When a traveling wave in the GIS is transmitted to the sleeve, one part of the traveling wave is reflected back to the inside of the GIS; a portion is refracted to the overhead line; one part is coupled to the GIS housing at the root of the casing, forming a traveling wave on the housing.
The schematic diagram of the traveling wave coupling to the shell at the GIS basin-type insulator is shown in figure 3, and 4 traveling wave paths exist at the basin-type insulator due to the discontinuous shell, between the coaxial conductors in the GIS and Z11、Z12(ii) a Between GIS housing and earth, Z21、Z22. When a traveling wave in the GIS is transmitted to one side of the basin-type insulator, one part of the traveling wave is reflected back; one part is refracted to the other side of the basin-type insulator; one part is coupled to the outer surface of the shell and respectively propagates along both sides of the basin insulator.
Step two:
a Hertz dipole antenna model is established in an XFDTD through a finite difference time domain method, the schematic diagram of the Hertz dipole antenna model is shown in figure 4, and a Hertz dipole is also called an electric dipole and a symmetrical dipole.
The core idea of the finite difference method of the time domain is to convert a Maxwell rotation equation with time variables into a difference mode and gradually advance the calculation of the electric field and the magnetic field in time and space in a frog-jumping mode on a time axis. The key points are the format of the difference equation, the stability of the solution and the setting of the absorption boundary conditions.
The Maxwell rotation equation is developed into six scalar equations:
wherein: denotes dielectric permittivity, μ denotes permeability, σ denotes conductivity, σ denotesmThe magnetic permeability is shown. Establishing a rectangular differential grid in space, wherein a time step is represented by delta t, and at the moment of n delta t:
f(x,y,z,y＝f(iΔx,jΔy,kΔz,nΔt)(3)
the difference equation can be derived from the principle of dividing any grid in space into six components, E and H, i.e., each magnetic field component is surrounded by four electric field components and each electric field component is surrounded by four magnetic field components. The value of each grid point can be obtained by the value of the previous moment of the point and the value of the adjacent point which is half time step earlier through difference operation. According to this principle, discretization is performed in time and space using the central differential pair equation (2):
in the formula:
where, the index m is a grid point coordinate corresponding to the required field amount, and the remaining definition parameters are defined in accordance with the formula (2).
The electric field and the magnetic field in other directions are obtained in the same way, and the value of the field component on each grid is calculated by the value of the previous step length of the point and the value of the half step length of the point close to the point, so that the value of each time step length of each point can be alternately calculated.
The difference equation set is used for replacing an electromagnetic field partial differential equation to solve, the calculation can be carried out only by the explanation convergence and the stability of the dispersed difference equation set, and the numerical stability can be maintained only by ensuring that the convergence and the stability of the solution require that the time step length delta t and the space step lengths delta x, delta y and delta z meet a certain relation. The numerical stability condition is derived by mathematical derivation according to electromagnetic principles as follows:
where c is the speed of light in the medium. From the above, it can be seen that the time interval Δ t must not exceed the 1/3 diagonal length (three dimensional), 1/2 diagonal length (two dimensional) or the length of the cell itself (one dimensional) of a wave passing through a Yee cell at the speed of light. To reduce the numerical dispersion, the requirements for the spatial dispersion Δ x and the time dispersion Δ t intervals are:
wherein, λ is the wavelength in the dispersion-free medium, and T is the period of the wave.
When the finite difference time domain method is used for calculation, in order to simulate the open-domain electromagnetic radiation process, an absorption boundary condition needs to be given at a truncation boundary of a calculation region, and a complete matching layer (PM L) is a lossy medium, can quickly attenuate a transmitted wave entering a PM L layer, and improves the boundary absorption efficiency by setting PM L.
Step three:
the shell transient circulating current waveform can be obtained in the following two ways: the measurement of a test base or the actual measurement of a transformer substation; the second method comprises the following steps: and (4) obtaining the product through simulation by modeling. In view of the fact that research on the transient circulation of the shell is less at the present stage and actual measurement is difficult, the method is obtained by modeling simulation.
Establishment of SF-based assays in ATP-EMPT6The high-frequency discharge model improved by the reburning model generates transient shell potential, namely TEV, through coupling of the basin-type insulator and the sleeve, wave impedance on each path is simulated according to the propagation path of the interference source in the step one, and a GIS shell transient circulation mathematical expression can be obtained according to the shell transient circulation ohm calculation law:
wherein, f (x) is a TEV fitting mathematical expression, the TEV can be obtained according to simulation or actual measurement, Z is a shell coupling impedance characteristic, and the Z can be obtained by adopting a field-circuit coupling method.
The method comprises the steps of introducing a shell transient circulation mathematical expression as an excitation source into a large-size antenna model of an XFDTD, obtaining an electromagnetic field on a boundary surface of the near-field setting of the antenna through software simulation of the XFDTD, calculating current density J and magnetic current density M through a data processing module of the XFDTD according to a Huygens principle, and selecting a far-field observation point to calculate far-field radiation of the antenna through discrete Fourier transform (DTF). And obtaining the main frequency band and amplitude of the electromagnetic interference generated on the GIS shell due to the outward radiation of the shell transient circulation.
The invention discloses a very fast transient electromagnetic radiation calculation method based on a time domain finite difference method, which is mainly based on a GIS shell and is used for solving the problem of difficult calculation of a large-size antenna radiation electromagnetic field. The above examples are merely illustrative of the technical solutions of the present invention and are not intended to be limiting, and with reference to the above examples, several additions and modifications can be made without departing from the calculation method of the present invention, and these additions and modifications should also be construed as the scope of the present invention.
Claims (8)
1. A method for calculating a very fast transient radiation electromagnetic field based on a time domain finite difference method comprises the following steps:
step 1, analyzing a switch operation radiation generation mechanism and GIS shell radiation electromagnetic field characteristics;
step 2, an antenna radiation physical model is established in XFDTD, a time domain finite difference method is adopted to divide grids, and a PM L boundary is established;
and step 3: and introducing a shell transient circulation as an excitation source, and simulating to obtain the distribution characteristics of the auxiliary electromagnetic field.
2. The method for calculating the time-domain finite difference method-based fast transient radiation electromagnetic field according to claim 1, wherein: the method for analyzing the switch operation radiation generation mechanism and the GIS shell radiation electromagnetic field characteristics in the step 1 comprises the following steps: according to the method, an interference source inside a GIS shell is transmitted inside the GIS in an electromagnetic wave mode, the electromagnetic wave is lost and the energy is gradually weakened when the electromagnetic wave is transmitted in a space medium, and when the electromagnetic wave is transmitted inside the GIS shell, a transmission coefficient expression is established
Wherein α is an attenuation constant of the electromagnetic wave, which represents that the amplitude of the field attenuates with the increase of the transmission distance of the electromagnetic wave, β is a phase constant of the electromagnetic wave, which represents the phase change of the electric field strength and the magnetic field strength in the transmission process of the electromagnetic wave, and the amplitude of the electric field strength and the amplitude of the magnetic field strength can attenuate and the phase can change along the transmission direction of the wave when the electromagnetic wave propagates forwards in the GIS shell by calculating the component transmission characteristics of the electric field strength and the magnetic field strength of the electromagnetic field;
in the process of spreading, GIS internal interference sources are coupled to the outer surface of a shell through GIS shell discontinuities such as GIS sleeves and basin-type insulators, and TEV and shell transient state circulation currents are generated.
3. The method for calculating the ultra-fast transient radiation electromagnetic field based on the time-domain finite difference method according to claim 1, wherein the method for establishing the physical model of the antenna radiation in the XFDTD and dividing the grid by the time-domain finite difference method to establish the PM L boundary comprises the steps of establishing a Hertzian dipole antenna model in the XFDTD by the time-domain finite difference method, converting a Maxwell rotation equation with a time variable into a difference equation, and gradually advancing the calculation of the electric field and the magnetic field in time and space in a frog-jumping mode on a time axis.
4. The method for calculating the time-domain finite difference method-based fast transient radiation electromagnetic field according to claim 3, wherein: the method for converting the Maxwell rotation equation with the time variable into a differential mode and gradually advancing the calculation of the electric field magnetic field in time and space in a frog mode on a time axis comprises the following steps:
step 2.1, expanding the Maxwell rotation equation into six scalar equations:
establishing a rectangular differential grid in space, and at the moment of n delta t:
f(x,y,z,y＝f(iΔx,jΔy,kΔz,nΔt) (3)；
step 2.2, dividing any grid in the space into six components of E and H, namely, each magnetic field component is surrounded by four electric field components, each electric field component is surrounded by four magnetic field components, the value of each grid point is the value of the previous moment of the point and the value of the time step half earlier than the adjacent point, and the value of each time step is alternately obtained through differential operation; from this principle, the difference equation is derived:
step 2.3, the difference equation set is used for replacing an electromagnetic field partial differential equation to solve, the calculation can be carried out only by the explanation convergence and the stability of the dispersed difference equation set, and the numerical stability can be maintained only by ensuring that the convergence and the stability of the solution require a time step length delta t and space step lengths delta x, delta y and delta z to meet a certain relation; the numerical stability condition is derived by mathematical derivation according to electromagnetic principles as follows:
in the formula: c is the speed of light in the medium; the time interval Δ t must not exceed the 1/3 diagonal length, 1/2 diagonal length, or the length of the cell itself, at which the wave passes through the Yee cell at the speed of light; to reduce the numerical dispersion, the requirements for the spatial dispersion Δ x and the time dispersion Δ t intervals are:
in the formula: λ is the wavelength in the dispersion-free medium, and T is the period of the wave.
5. The method for calculating the electromagnetic field based on the finite difference time domain method for rapid transient radiation as claimed in claim 4, wherein when the partial differential equation of the electromagnetic field is replaced by the differential equation system for solving, in order to simulate the open-domain electromagnetic radiation process, the absorption boundary condition is required to be given at the truncation boundary of the calculation region, the complete matching layer PM L is a lossy medium, the transmitted wave entering the PM L layer can be rapidly attenuated, and the boundary absorption efficiency is improved by setting the PM L.
6. The method for calculating the time-domain finite difference method-based fast transient radiation electromagnetic field according to claim 1, wherein: the method for acquiring the transient circulation of the shell comprises the following steps: actual measurements or simulations by modeling.
7. The method for calculating the time-domain finite difference method-based fast transient radiation electromagnetic field according to claim 6, wherein: the method for obtaining the shell transient circulation by modeling and simulation comprises the following steps: establishment of SF-based assays in ATP-EMPT6The high-frequency discharge model improved by the reburning model generates transient shell potential, namely TEV, through coupling of the basin-type insulator and the sleeve, wave impedance on each path is simulated according to the propagation path of an interference source, and a GIS shell transient circulation mathematical expression is obtained according to the shell transient circulation ohm calculation law:
in the formula: and f (x) is a TEV fitting mathematical expression, the TEV is obtained according to simulation or actual measurement, and Z is the shell coupling impedance characteristic and is obtained by adopting a field-circuit coupling method.
8. The method for calculating the time-domain finite difference method-based fast transient radiation electromagnetic field according to claim 1, wherein: step 3, introducing the shell transient circulation as an excitation source, and obtaining the distribution characteristics of the auxiliary electromagnetic field in a simulation mode comprises the following steps: introducing a shell transient circulation mathematical expression as an excitation source into a large-size antenna model of an XFDTD, obtaining an electromagnetic field on a boundary surface of the near-field setting of the antenna through software simulation of the XFDTD, calculating current density J and magnetic current density M by a middle data processing module of the XFDTD according to a Huygens principle, and selecting a far-field observation point to calculate far-field radiation of the antenna through discrete Fourier transform (DTF); and obtaining the main frequency band and amplitude of the electromagnetic interference generated on the GIS shell due to the outward radiation of the shell transient circulation.
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| CN112347679A (en) * | 2020-11-16 | 2021-02-09 | 北京环境特性研究所 | Metamaterial simulation method and device with electromagnetic dispersion |
| CN113076675A (en) * | 2021-04-12 | 2021-07-06 | 中国电子科技集团公司第三十三研究所 | Electromagnetic environment effect simulation design method for air cushion landing boat |
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| CN107422387A (en) * | 2017-06-27 | 2017-12-01 | 吉林大学 | A kind of transient electromagnetic emission source loading method of virtual Fdtd Method |
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN112347679A (en) * | 2020-11-16 | 2021-02-09 | 北京环境特性研究所 | Metamaterial simulation method and device with electromagnetic dispersion |
| CN113076675A (en) * | 2021-04-12 | 2021-07-06 | 中国电子科技集团公司第三十三研究所 | Electromagnetic environment effect simulation design method for air cushion landing boat |
| CN113076675B (en) * | 2021-04-12 | 2022-11-08 | 中国电子科技集团公司第三十三研究所 | Electromagnetic environment effect simulation design method for air cushion landing boat |
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