A transformer electric field time domain simulation method and system

Abstract

The present invention discloses a transformer electric field time-domain simulation method and system. The transformer geometric model is constructed based on the basic calculation parameters of the FDTD algorithm, and then the electric field vector and the magnetic field vector in the calculation area are updated until the calculation stop criterion is met. The final time-domain electric field vector and magnetic field vector calculation results are output, and then the output electric field vector is transformed into the time-domain frequency domain. The internal electric field distribution of the transformer at low frequency is derived by the frequency scaling technology. Compared with the traditional FDTD algorithm, the calculation time can be shortened by about 10 6 times, which can greatly improve the efficiency of transformer electric field time-domain simulation, improve the shortcomings of traditional FDTD algorithm for time-domain low-frequency simulation, and solve the technical problems of low efficiency of existing FDTD-based transformer time-domain electric field simulation methods and difficulty in providing technical support for transformer internal electric field distribution calculation, transformer insulation performance evaluation, transformer design optimization and fault cause analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of transformer electric field simulation, and in particular to a transformer electric field time domain simulation method and system. Background Art

[0002] Power transformers are devices used to transform AC voltage and current. Their main function is to increase and decrease the voltage of the power grid to meet the voltage requirements of different loads. Power transformers can realize the transmission and distribution of electric energy, so that electric energy can be transmitted and distributed within different voltage ranges. Through the voltage and current conversion function of power transformers, electric energy can reach the voltage level and current value required in different geographical locations and usage occasions, thereby realizing efficient transmission and utilization of electricity.

[0003] The time-domain electric field simulation of power transformers can help engineers predict the working conditions of transformers under different circuit conditions. The time-domain electric field simulation of transformers can predict the distribution and intensity of electric fields, evaluate the insulation performance of transformers, optimize transformer design and analyze the causes of faults. It can improve the reliability and stability of power systems and reduce the risk of equipment failure and damage. The finite-difference time-domain method (FDTD) is one of the most commonly used numerical simulation methods for calculating electromagnetic wave propagation and radiation fields. Its basic idea is to discretize the solution area into grids, use the difference equations in space and time to represent the relationship between the electromagnetic field at each discrete space-time point, and gradually calculate the time-domain evolution law of the electromagnetic field through the iterative solution method in time. The main advantages of the FDTD algorithm include its applicability to the calculation of electromagnetic wave propagation in general nonlinear, non-uniform, and anisotropic media, and the qualitative and quantitative analysis of macroscopic physical processes. The algorithm has good universality and can be used to solve various electromagnetic wave problems. Due to its simplicity, accuracy and efficiency, it has also been widely used in power transformer simulation.

[0004] The FDTD algorithm uses a step-by-step iterative solution method in time. In order to meet the stability criterion, each step-by-step time step is usually nanoseconds or even smaller. Tens of thousands of iterations are required for a microsecond time domain transient process, while more than one million iterations are required to simulate a millisecond time domain transient process. Using the FDTD algorithm to calculate the power transformer simulation, each time step takes 1 second per month. The calculation time for the microsecond time domain transient process is about several hours, while the calculation time for the millisecond time domain transient process is about several weeks. Therefore, when the time span of the time domain transient process is large, the calculation amount of the FDTD algorithm is too large to meet the requirements of engineering simulation calculations. Therefore, how to improve the efficiency of the transformer time domain electric field simulation based on FDTD and provide technical support for the calculation of the internal electric field distribution of the transformer, the evaluation of the insulation performance of the transformer, the optimization of the transformer design and the analysis of the cause of the fault is a technical problem that needs to be solved urgently by those skilled in the art. Summary of the invention

[0005] The present invention provides a transformer electric field time-domain simulation method and system, which are used to solve the technical problem that the existing FDTD-based transformer time-domain electric field simulation method is low in efficiency and difficult to provide technical support for transformer internal electric field distribution calculation, transformer insulation performance evaluation, transformer design optimization and fault cause analysis.

[0006] In view of this, a first aspect of the present invention provides a transformer electric field time domain simulation method, comprising:

[0007] S1. Construct the transformer geometric model based on the basic calculation parameters of the FDTD algorithm. The basic calculation parameters of the FDTD algorithm include the calculation area range and the grid discretization strategy;

[0008] S2. In any orthogonal direction of each grid, the electric field vector of the current time step is updated according to the electric field vector of the previous time step and the four magnetic field vectors surrounding the electric field vector of the first half of the time step;

[0009] S3, in any orthogonal direction of each grid, according to the magnetic field vector of the previous time step and the four electric field vectors surrounding the magnetic field vector of the first half time step, update the magnetic field vector of the current time step;

[0010] S4, judging whether the number of iterations has been reached or whether the electric field vector and the magnetic field vector of the current time step meet the convergence condition, if so, outputting the electric field vector and the magnetic field vector of the current time step as the target electric field vector and the target magnetic field vector, and executing step S5, otherwise, returning to step S2;

[0011] S5. Determine whether the absolute value of the electric field vector and the wavelength of the electromagnetic signal meet the application conditions of the frequency reduction mathematical model. If so, perform a time domain-frequency domain transformation on the output target electric field vector to obtain a high-frequency electric field frequency domain discrete sequence. The application conditions of the frequency reduction mathematical model are:

[0012] |σ c +jωε c |>>ωε d

[0013]

[0014] Among them, σ c is the equivalent conductivity of the transformer conductor at low frequency, ω is the discrete angular frequency at low frequency, ε c is the dielectric constant of the transformer conductor, ε d is the dielectric constant of the dielectric, λ d is the wavelength of the electromagnetic wave in the transformer dielectric, l is the geometric size of the simulated transformer, and μ is the magnetic permeability;

[0015] S6. Based on the frequency reduction mathematical model, the frequency domain discrete sequence of the electric field waveform is used to calculate the internal electric field distribution of the transformer at low frequency. The frequency reduction mathematical model is:

[0016]

[0017] Among them, E c (ω) is the electric field distribution inside the transformer at low frequency, E' c (ω) is the frequency domain discrete sequence of high-frequency electric field, ω' is the discrete angular frequency at high frequency, σ' c is the equivalent conductivity of the transformer conductor at high frequency, ε c ' is the dielectric constant of the transformer conductor at high frequency.

[0018] Optionally, step S5 includes:

[0019] The output target electric field vector is transformed from time domain to frequency domain using the discrete Fourier method to obtain a high-frequency electric field discrete sequence in the frequency domain. The time domain to frequency domain transformation formula is:

[0020]

[0021] Where E(q) is the time-domain discrete sequence of the target electric field vector, N is the total number of time steps, and q is the number of time steps.

[0022] Optionally, the equation for updating the electric field vector at the current time step is:

[0023]

[0024] Where i, j and k are the position numbers of the electric field vector based on the FDTD discrete grid, q is the number of time steps, and is the electric field vector corresponding to the position number and time step number in the three orthogonal directions of x, y, and z, Δt is the time step, Δx, Δy, and Δz are the minimum grid sizes in the three orthogonal directions of x, y, and z, and is the magnetic field vector corresponding to the position number and time step number in the three orthogonal directions of x, y, and z, σ is the equivalent conductance in the corresponding grid, and ε is the dielectric constant in the corresponding grid.

[0025] Optionally, the equation for updating the magnetic field vector for the current time step is:

[0026]

[0027] Among them, σ m is the magnetic permeability coefficient and μ is the magnetic permeability.

[0028] Optionally, basic calculation parameters of the FDTD algorithm also include space step, time step, calculation stop criterion, absorption boundary and excitation waveform.

[0029] A second aspect of the present invention provides a transformer electric field time domain simulation system, comprising:

[0030] Transformer model building module, used to build transformer geometric model based on basic calculation parameters of FDTD algorithm, including calculation area range and grid discretization strategy;

[0031] An electric field vector update module is used to update the electric field vector of the current time step in any orthogonal direction of each grid according to the electric field vector of the previous time step and the four magnetic field vectors surrounding the electric field vector of the first half of the time step;

[0032] A magnetic field vector update module is used to update the magnetic field vector of the current time step in any orthogonal direction of each grid according to the magnetic field vector of the previous time step and the four electric field vectors surrounding the magnetic field vector of the first half time step;

[0033] The first judgment module is used to judge whether the current number of iterations has been reached or whether the electric field vector and the magnetic field vector of the current time step meet the convergence condition. If so, the electric field vector and the magnetic field vector of the current time step are output as the target electric field vector and the target magnetic field vector, and jump to the second judgment module; otherwise, return to jump to the electric field vector update module;

[0034] The second judgment module is used to judge whether the absolute value of the electric field vector and the wavelength of the electromagnetic signal meet the application conditions of the frequency reduction mathematical model. If so, the output target electric field vector is transformed from time domain to frequency domain to obtain a high-frequency electric field frequency domain discrete sequence. The application conditions of the frequency reduction mathematical model are:

[0035] |σ c +jωε c |>>ωε d

[0036]

[0037] Among them, σ c is the equivalent conductivity of the transformer conductor at low frequency, ω is the discrete angular frequency at low frequency, ε c is the dielectric constant of the transformer conductor, ε d is the dielectric constant of the dielectric, λ d is the wavelength of the electromagnetic wave in the transformer dielectric, l is the geometric size of the simulated transformer, and μ is the magnetic permeability;

[0038] The low-frequency electric field distribution output module is used to perform the internal electric field distribution of the transformer at low frequency on the frequency domain discrete sequence of the electric field waveform based on the frequency reduction mathematical model. The frequency reduction mathematical model is:

[0039]

[0040] Among them, E c (ω) is the electric field distribution inside the transformer at low frequency, E' c (ω) is the frequency domain discrete sequence of high-frequency electric field, ω' is the discrete angular frequency at high frequency, σ' c is the equivalent conductivity of the transformer conductor at high frequency, ε c ' is the dielectric constant of the transformer conductor at high frequency.

[0041] Optionally, the second judgment module is specifically used to:

[0042] The output target electric field vector is transformed from time domain to frequency domain using the discrete Fourier method to obtain a high-frequency electric field discrete sequence in the frequency domain. The time domain to frequency domain transformation formula is:

[0043]

[0044] Where E(q) is the time-domain discrete sequence of the target electric field vector, N is the total number of time steps, and q is the number of time steps.

[0045] Optionally, the equation for updating the electric field vector at the current time step is:

[0046]

[0047] Where i, j and k are the position numbers of the electric field vector based on the FDTD discrete grid, q is the number of time steps, and is the electric field vector corresponding to the position number and time step number in the three orthogonal directions of x, y, and z, Δt is the time step, Δx, Δy, and Δz are the minimum grid sizes in the three orthogonal directions of x, y, and z, and is the magnetic field vector corresponding to the position number and time step number in the three orthogonal directions of x, y, and z, σ is the equivalent conductance in the corresponding grid, and ε is the dielectric constant in the corresponding grid.

[0048] Optionally, the equation for updating the magnetic field vector for the current time step is:

[0049]

[0050] Among them, σ m is the magnetic permeability coefficient and μ is the magnetic permeability.

[0051] Optionally, basic calculation parameters of the FDTD algorithm also include space step, time step, calculation stop criterion, absorption boundary and excitation waveform.

[0052] It can be seen from the above technical solutions that the transformer electric field time domain simulation method and system provided by the present invention have the following advantages:

[0053] The transformer electric field time-domain simulation method provided by the present invention builds a transformer geometric model based on the basic calculation parameters of the FDTD algorithm, then updates the electric field vector and magnetic field vector in the calculation area until the calculation stop criterion is met, outputs the final time-domain electric field vector and magnetic field vector calculation results, and then performs time-domain-frequency domain transformation on the output electric field vector, and derives the internal electric field distribution of the transformer at low frequency by frequency scaling technology. Compared with the traditional FDTD algorithm, the calculation time can be shortened by about 10 6 times, which can greatly improve the efficiency of transformer electric field time-domain simulation, improve the shortcomings of traditional FDTD algorithm for time-domain low-frequency simulation, and solve the technical problems of low efficiency of existing FDTD-based transformer time-domain electric field simulation methods and difficulty in providing technical support for transformer internal electric field distribution calculation, transformer insulation performance evaluation, transformer design optimization and fault cause analysis.

[0054] The transformer electric field time domain simulation system provided by the present invention is used to execute the transformer electric field time domain simulation method provided by the present invention. Its principle and technical effects are the same as those of the transformer electric field time domain simulation method provided by the present invention, and will not be repeated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0056] Figure 1 A schematic diagram of a flow chart of a transformer electric field time domain simulation method provided in the present invention;

[0057] Figure 2 The figure is a schematic diagram of the structure of a transformer electric field time domain simulation system provided in the present invention. DETAILED DESCRIPTION

[0058] In order to enable those skilled in the art to better understand the scheme of the present invention, the technical scheme in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0059] For easier understanding, see Figure 1 The present invention provides an embodiment of a transformer electric field time domain simulation method, comprising:

[0060] Step 101: construct a transformer geometric model based on basic calculation parameters of the FDTD algorithm. The basic calculation parameters of the FDTD algorithm include a calculation area range and a grid discretization strategy.

[0061] It should be noted that the basic calculation parameters of the FDTD algorithm include the calculation area range, grid discretization strategy, space step, time step, calculation stop criterion, absorbing boundary and excitation waveform.

[0062] The range of the calculation area is determined by the geometric dimensions of the simulated model. It is generally expanded 1.5 to 2 times based on the maximum geometric dimensions of the simulated model to fully consider the distortion effect of the electromagnetic field at the device boundary.

[0063] The grid discretization strategy is mainly determined by the calculation accuracy requirements and the computer hardware condition limitations. On the one hand, the smaller the grid size in the calculation area and the more grid discretization, the higher the calculation accuracy. On the other hand, the number of grid discretization is related to the computer memory consumption. The computer hardware conditions determine the maximum number of grids that can be discretized in the calculation area. Therefore, a non-uniform grid discretization strategy is adopted in the embodiment of the present invention. Within the number of discrete grids allowed by the hardware, the grid size of the key area is encrypted, and the number of grids is reduced in the non-key area.

[0064] The spatial step size is the grid size of the discrete grid in three orthogonal directions. Once the grid discretization strategy in the calculation area is confirmed, the spatial step size can be obtained.

[0065] The time step is the time process of each iteration cycle of the FDTD algorithm. The selection range of the time step is determined by the minimum FDTD discrete grid size and must meet the Courant-Friedrich-Levy (CFL) criterion to prevent data divergence, oscillation, non-convergence and other problems that may occur in time domain calculations, namely:

[0066]

[0067] Among them, Δt is the time step, Δx, Δy and Δz are the minimum grid sizes in the three orthogonal directions of x, y and z, and c is the propagation speed of light in the corresponding medium.

[0068] The calculation stop criterion means that when the FDTD iterative calculation meets a certain condition, the calculation is terminated. This criterion is generally that the number of electromagnetic iterations reaches a preset value, or the electromagnetic field quantity in the calculation area reaches a preset convergence condition. Convergence means that the electromagnetic field quantity reaches a steady state or periodic change.

[0069] Absorption boundary refers to a special boundary defined on the outer surface of the calculation area, so that the electromagnetic field propagating from the inside to the outside of the calculation area is absorbed at the boundary instead of being reflected, so as to simulate an infinite simulation space with a finite calculation area. Commonly used FDTD absorption boundaries include Mur boundary, LIAO boundary, PML boundary and CPML boundary. Considering the absorption effect and the additional calculation amount, the CPML absorption boundary is used in the embodiment of the present invention.

[0070] The excitation waveform refers to the waveform curve of the input current or voltage source of the FDTD electromagnetic simulation. In the embodiment of the present invention, a Gaussian pulse waveform is used, and the main frequency of the waveform is determined by the main frequency of the low-frequency band and the reduction ratio. For the time domain transient distribution of the internal electric field of the power transformer with a main frequency of 50Hz, the FDTD electromagnetic calculation can be performed by using a Gaussian pulse with a main frequency of 50MHz as the excitation waveform.

[0071] Based on the determined grid discretization strategy, a transformer geometric model is constructed in the calculation area. The model needs to include key transformer components such as windings, main insulation, longitudinal insulation, core, transformer oil, and casing. Material parameters are defined at the discrete grids corresponding to the spatial positions of the components, including conductivity σ, dielectric constant ε, and magnetic permeability μ.

[0072] Step 102: In any orthogonal direction of each grid, the electric field vector of the current time step is updated according to the electric field vector of the previous time step and the four magnetic field vectors surrounding the electric field vector of the first half time step.

[0073] It should be noted that in any orthogonal direction of each grid, the electric field vector of the current time step is updated according to the electric field vector of the previous time step and the four magnetic field vectors surrounding the electric field vector of the first half of the time step. The specific update equation is:

[0074]

[0075] Where i, j and k are the position numbers of the electric field vector based on the FDTD discrete grid, q is the number of time steps, and is the electric field vector corresponding to the position number and time step number in the three orthogonal directions of x, y, and z, Δt is the time step, Δx, Δy, and Δz are the minimum grid sizes in the three orthogonal directions of x, y, and z, and is the magnetic field vector corresponding to the position number and time step number in the three orthogonal directions of x, y, and z, σ is the equivalent conductance in the corresponding grid, and ε is the dielectric constant in the corresponding grid.

[0076] Step 103: In any orthogonal direction of each grid, the magnetic field vector of the current time step is updated according to the magnetic field vector of the previous time step and the four electric field vectors surrounding the magnetic field vector of the first half time step.

[0077] It should be noted that in any orthogonal direction of each grid, the magnetic field vector of the current time step is updated according to the magnetic field vector of the previous time step and the four electric field vectors surrounding the magnetic field vector of the first half of the time step. The specific update equation is:

[0078]

[0079] Among them, σ m is the magnetic permeability coefficient and μ is the magnetic permeability.

[0080] Step 104, determine whether the current number of iterations has been reached or whether the electric field vector and the magnetic field vector of the current time step meet the convergence conditions. If so, output the electric field vector and the magnetic field vector of the current time step as the target electric field vector and the target magnetic field vector, and execute step 105; otherwise, return to step 102.

[0081] It should be noted that the electric field and magnetic field vectors in the calculation area are repeatedly solved iteratively according to steps 103-104. Each iterative solution is equivalent to updating the electromagnetic field quantity in the calculation area in time and estimating it to the next time step Δt, thereby realizing a step-by-step solution of the electromagnetic field quantity in time. When the number of iterations or the convergence condition meets the preset conditions, the electromagnetic field calculation is terminated.

[0082] Step 105, determine whether the absolute value of the electric field vector and the wavelength of the electromagnetic signal meet the application conditions of the frequency reduction mathematical model. If so, perform a time domain-frequency domain transformation on the output target electric field vector to obtain a high-frequency electric field frequency domain discrete sequence.

[0083] It should be noted that when the absolute value of the electric field vector in the dielectric is much larger than the absolute value of the electric field vector in the conductor and the wavelength of the electromagnetic signal is ten times or more of the geometric size of the simulated object, the frequency scaling technology can be used to convert the electric field at high frequency into the electric field at low frequency.

[0084] The absolute value of the electric field vector in the dielectric is much greater than that in the conductor, which can be expressed as:

[0085] |σ c +jωε c |>>ωε d

[0086] Among them, σ c is the equivalent conductivity of the transformer conductor at low frequency, ω is the discrete angular frequency at low frequency, ε c is the dielectric constant of the transformer conductor, ε d is the dielectric constant of the dielectric.

[0087] The wavelength of the electromagnetic signal is ten times or more than the geometric size of the simulated object and can be expressed as:

[0088]

[0089] Among them, λ d is the wavelength of the electromagnetic wave in the dielectric, l is the geometric size of the simulated transformer, and μ is the magnetic permeability.

[0090] The frequency range of power transformer simulation is 30Hz~1MHz, corresponding to the wavelength of 300m~10 7 m, the geometric size of the power transformer is generally less than 10m, so the prerequisite is met The dielectric constant of the conductors and dielectrics in power transformers is on the order of 10 -11 ~10 -12 , the conductivity of the conductor in the power transformer is on the order of 10 5 ~10 7 , so the premise |σ is generally satisfied within the frequency range of interest in the power transformer simulation case c +jωε c |>>ωε d .

[0091] After the electromagnetic field calculation is terminated, the electric field calculation results and magnetic field calculation results in each discrete grid of the calculation area are derived. At this time, the electric field calculation result is the time domain electric field value under high-frequency excitation, and the low-frequency calculation electric field distribution result cannot be directly derived. Therefore, in an embodiment of the present invention, when the absolute value of the electric field vector and the wavelength of the electromagnetic signal meet the application conditions of the frequency reduction mathematical model, the discrete Fourier method (DFS) is first used to perform time domain-frequency domain transformation and then execute step 106. The time domain-frequency domain transformation formula is:

[0092]

[0093] Where E(q) is the time-domain discrete sequence of the target electric field vector, N is the total number of time steps, q is the number of time steps, and E' c (ω) is the frequency domain discrete sequence of the high-frequency electric field, and ω' is the discrete angular frequency at high frequency.

[0094] Step 106: Based on the frequency scaling mathematical model, the frequency domain discrete sequence of the electric field waveform is subjected to the transformer internal electric field distribution at low frequency.

[0095] It should be noted that the frequency scaling mathematical model is:

[0096]

[0097] Among them, E c (ω) is the electric field distribution inside the transformer at low frequency, E' c (ω) is the frequency domain discrete sequence of high-frequency electric field, ω is the discrete angular frequency at low frequency, ω' is the discrete angular frequency at high frequency, σ c is the equivalent conductivity at low frequency, σ' c is the equivalent conductivity at high frequency, ε c is the dielectric constant at low frequency, ε' c is the dielectric constant at high frequencies.

[0098] From the boundary conditions of the electromagnetic field, it can be seen that when there is no surface charge on the conductor-dielectric boundary, that is, when the conductivity of the conductor is finite, the normal electric displacement vector inside and outside the conductor-dielectric boundary is continuous, that is:

[0099]

[0100] Among them, E d and E c denote the electric field vectors in dielectrics and conductors, respectively, represents the normal component. Therefore, when and |σ c +jωε c |>>ωε d Under the condition of , if the distribution of current and electric field in dielectrics of any shape and size is known, the distribution of current and electric field in conductors of any shape and size can be obtained, that is:

[0101]

[0102] Among them, E c (ω) is the electric field distribution inside the transformer at low frequency, E' c (ω) is the frequency domain discrete sequence of high-frequency electric field, ω is the discrete angular frequency at low frequency, ω' is the discrete angular frequency at high frequency, σ c is the equivalent conductivity at low frequency, σ' c is the equivalent conductivity at high frequency, ε c is the dielectric constant at low frequency, ε' c is the dielectric constant at high frequencies.

[0103] Therefore, when the prerequisites of frequency scaling technology are met, the FDTD algorithm can be used to calculate the steady-state electric field distribution in the conductor at high frequency, and based on the formula Calculate the electric field distribution value under low frequency. It has been verified that this frequency reduction technology can obtain relatively accurate calculation results within a frequency range of 6 orders of magnitude in the application of power transformers. For example, for the time domain transient distribution of the internal electric field of a power transformer with a main frequency of 50Hz, it can be derived from the time domain transient distribution results of the broadband electric field with a main frequency of 50MHz, and the corresponding calculation time can be shortened by 10 6 times.

[0104] The transformer electric field time-domain simulation method provided by the present invention builds a transformer geometric model based on the basic calculation parameters of the FDTD algorithm, then updates the electric field vector and magnetic field vector in the calculation area until the calculation stop criterion is met, outputs the final time-domain electric field vector and magnetic field vector calculation results, and then performs time-domain-frequency domain transformation on the output electric field vector, and derives the internal electric field distribution of the transformer at low frequency by frequency scaling technology, thereby shortening the calculation time by about 10 6 times, which can greatly improve the efficiency of transformer electric field time-domain simulation, improve the shortcomings of traditional FDTD algorithm for time-domain low-frequency simulation, and solve the technical problems of low efficiency of existing FDTD-based transformer time-domain electric field simulation methods and difficulty in providing technical support for transformer internal electric field distribution calculation, transformer insulation performance evaluation, transformer design optimization and fault cause analysis.

[0105] For easier understanding, see Figure 2 The present invention provides an embodiment of a transformer electric field time domain simulation system, comprising:

[0106] Transformer model building module, used to build transformer geometric model based on basic calculation parameters of FDTD algorithm, including calculation area range and grid discretization strategy;

[0107] An electric field vector update module is used to update the electric field vector of the current time step in any orthogonal direction of each grid according to the electric field vector of the previous time step and the four magnetic field vectors surrounding the electric field vector of the first half of the time step;

[0108] A magnetic field vector update module is used to update the magnetic field vector of the current time step in any orthogonal direction of each grid according to the magnetic field vector of the previous time step and the four electric field vectors surrounding the magnetic field vector of the first half time step;

[0109] The first judgment module is used to judge whether the current number of iterations has been reached or whether the electric field vector and the magnetic field vector of the current time step meet the convergence condition. If so, the electric field vector and the magnetic field vector of the current time step are output as the target electric field vector and the target magnetic field vector, and jump to the second judgment module; otherwise, return to jump to the electric field vector update module;

[0110] The second judgment module is used to judge whether the absolute value of the electric field vector and the wavelength of the electromagnetic signal meet the application conditions of the frequency reduction mathematical model. If so, the output target electric field vector is transformed from time domain to frequency domain to obtain a high-frequency electric field frequency domain discrete sequence. The application conditions of the frequency reduction mathematical model are:

[0111] |σ c +jωε c |>>ωε d

[0112]

[0113] Among them, σ c is the equivalent conductivity of the transformer conductor at low frequency, ω is the discrete angular frequency at low frequency, ε c is the dielectric constant of the transformer conductor, ε d is the dielectric constant of the dielectric, λ d is the wavelength of the electromagnetic wave in the transformer dielectric, l is the geometric size of the simulated transformer, and μ is the magnetic permeability;

[0114] The low-frequency electric field distribution output module is used to perform the internal electric field distribution of the transformer at low frequency on the frequency domain discrete sequence of the electric field waveform based on the frequency reduction mathematical model. The frequency reduction mathematical model is:

[0115]

[0116] Among them, E c (ω) is the electric field distribution inside the transformer at low frequency, E' c (ω) is the frequency domain discrete sequence of high-frequency electric field, ω' is the discrete angular frequency at high frequency, σ' c is the equivalent conductivity of the transformer conductor at high frequency, ε' c is the dielectric constant of the transformer conductor at high frequencies.

[0117] The second judgment module is specifically used for:

[0118] The output target electric field vector is transformed from time domain to frequency domain using the discrete Fourier method to obtain a high-frequency electric field discrete sequence in the frequency domain. The time domain to frequency domain transformation formula is:

[0119]

[0120] Where E(q) is the time-domain discrete sequence of the target electric field vector, N is the total number of time steps, and q is the number of time steps.

[0121] The equation for updating the electric field vector for the current time step is:

[0122]

[0123] Where i, j and k are the position numbers of the electric field vector based on the FDTD discrete grid, q is the number of time steps, and is the electric field vector corresponding to the position number and time step number in the three orthogonal directions of x, y, and z, Δt is the time step, Δx, Δy, and Δz are the minimum grid sizes in the three orthogonal directions of x, y, and z, and is the magnetic field vector corresponding to the position number and time step number in the three orthogonal directions of x, y, and z, σ is the equivalent conductance in the corresponding grid, and ε is the dielectric constant in the corresponding grid.

[0124] Optionally, the equation for updating the magnetic field vector for the current time step is:

[0125]

[0126] Among them, σ m is the magnetic permeability coefficient and μ is the magnetic permeability.

[0127] The basic calculation parameters of the FDTD algorithm also include space step, time step, calculation stop criterion, absorbing boundary and excitation waveform.

[0128] The transformer electric field time domain simulation system provided by the present invention is used to execute the transformer electric field time domain simulation method provided by the present invention. Its principle and technical effects are the same as those of the transformer electric field time domain simulation method provided by the present invention, and will not be repeated here.

[0129] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the same. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A transformer electric field time domain simulation method, characterized in that: include: S1. Construct the transformer geometric model based on the basic calculation parameters of the FDTD algorithm. The basic calculation parameters of the FDTD algorithm include the calculation area range and the grid discretization strategy; S2. In any orthogonal direction of each grid, the electric field vector of the current time step is updated according to the electric field vector of the previous time step and the four magnetic field vectors surrounding the electric field vector of the first half of the time step; S3, in any orthogonal direction of each grid, according to the magnetic field vector of the previous time step and the four electric field vectors surrounding the magnetic field vector of the first half time step, update the magnetic field vector of the current time step; S4, judging whether the number of iterations has been reached or whether the electric field vector and the magnetic field vector of the current time step meet the convergence condition, if so, outputting the electric field vector and the magnetic field vector of the current time step as the target electric field vector and the target magnetic field vector, and executing step S5, otherwise, returning to step S2; S5. Determine whether the absolute value of the electric field vector and the wavelength of the electromagnetic signal meet the application conditions of the frequency reduction mathematical model. If so, perform a time domain-frequency domain transformation on the output target electric field vector to obtain a high-frequency electric field frequency domain discrete sequence. The application conditions of the frequency reduction mathematical model are: |s c +jωe c |>>oh d Among them, σ c is the equivalent conductivity of the transformer conductor at low frequency, ω is the discrete angular frequency at low frequency, ε c is the dielectric constant of the transformer conductor, ε d is the dielectric constant of the dielectric, λ d is the wavelength of the electromagnetic wave in the transformer dielectric, l is the geometric size of the simulated transformer, and μ is the magnetic permeability; S6. Based on the frequency reduction mathematical model, the frequency domain discrete sequence of the electric field waveform is used to calculate the internal electric field distribution of the transformer at low frequency. The frequency reduction mathematical model is: Among them, E c (ω) is the electric field distribution inside the transformer at low frequency, E′ c (ω) is the frequency domain discrete sequence of high-frequency electric field, ω' is the discrete angular frequency at high frequency, σ' c is the equivalent conductivity of the transformer conductor at high frequency, ε′ c is the dielectric constant of the transformer conductor at high frequencies.

2. The transformer electric field time domain simulation method according to claim 1, characterized in that: Step S5 includes: The output target electric field vector is transformed from time domain to frequency domain using the discrete Fourier method to obtain a high-frequency electric field discrete sequence in the frequency domain. The time domain to frequency domain transformation formula is: Where E(q) is the time-domain discrete sequence of the target electric field vector, N is the total number of time steps, and q is the number of time steps.

3. The transformer electric field time domain simulation method according to claim 1, characterized in that: The equation for updating the electric field vector for the current time step is: Where i, j and k are the position numbers of the electric field vector based on the FDTD discrete grid, q is the number of time steps, and is the electric field vector corresponding to the position number and time step number in the three orthogonal directions of x, y, and z, Δt is the time step, Δx, Δy, and Δz are the minimum grid sizes in the three orthogonal directions of x, y, and z, and is the magnetic field vector corresponding to the position number and time step number in the three orthogonal directions of x, y, and z, σ is the equivalent conductance in the corresponding grid, and ε is the dielectric constant in the corresponding grid.

4. The transformer electric field time domain simulation method according to claim 3 is characterized in that: The equation for updating the magnetic field vector for the current time step is: Among them, σ m is the magnetic permeability coefficient and μ is the magnetic permeability.

5. The transformer electric field time domain simulation method according to claim 1, characterized in that: The basic calculation parameters of the FDTD algorithm also include space step, time step, calculation stop criterion, absorbing boundary and excitation waveform.

6. A transformer electric field time domain simulation system, characterized in that: include: Transformer model building module, used to build transformer geometric model based on basic calculation parameters of FDTD algorithm, including calculation area range and grid discretization strategy; An electric field vector update module is used to update the electric field vector of the current time step in any orthogonal direction of each grid according to the electric field vector of the previous time step and the four magnetic field vectors surrounding the electric field vector of the first half of the time step; A magnetic field vector update module is used to update the magnetic field vector of the current time step in any orthogonal direction of each grid according to the magnetic field vector of the previous time step and the four electric field vectors surrounding the magnetic field vector of the first half time step; The first judgment module is used to judge whether the current number of iterations has been reached or whether the electric field vector and the magnetic field vector of the current time step meet the convergence condition. If so, the electric field vector and the magnetic field vector of the current time step are output as the target electric field vector and the target magnetic field vector, and jump to the second judgment module; otherwise, return to jump to the electric field vector update module; The second judgment module is used to judge whether the absolute value of the electric field vector and the wavelength of the electromagnetic signal meet the application conditions of the frequency reduction mathematical model. If so, the output target electric field vector is transformed from time domain to frequency domain to obtain a high-frequency electric field frequency domain discrete sequence. The application conditions of the frequency reduction mathematical model are: |s c +jωe c |>>oh d Among them, σ c is the equivalent conductivity of the transformer conductor at low frequency, ω is the discrete angular frequency at low frequency, ε c is the dielectric constant of the transformer conductor, ε d is the dielectric constant of the dielectric, λ d is the wavelength of the electromagnetic wave in the transformer dielectric, l is the geometric size of the simulated transformer, and μ is the magnetic permeability; The low-frequency electric field distribution output module is used to perform the internal electric field distribution of the transformer at low frequency on the frequency domain discrete sequence of the electric field waveform based on the frequency reduction mathematical model. The frequency reduction mathematical model is: Among them, E c (ω) is the electric field distribution inside the transformer at low frequency, E′ c (ω) is the frequency domain discrete sequence of high-frequency electric field, ω' is the discrete angular frequency at high frequency, σ' c is the equivalent conductivity of the transformer conductor at high frequency, ε′ c is the dielectric constant of the transformer conductor at high frequencies.

7. The transformer electric field time domain simulation system according to claim 6, characterized in that: The second judgment module is specifically used for: The output target electric field vector is transformed from time domain to frequency domain using the discrete Fourier method to obtain a high-frequency electric field discrete sequence in the frequency domain. The time domain to frequency domain transformation formula is: Where E(q) is the time-domain discrete sequence of the target electric field vector, N is the total number of time steps, and q is the number of time steps.

8. The transformer electric field time domain simulation system according to claim 6, characterized in that: The equation for updating the electric field vector for the current time step is: Where i, j and k are the position numbers of the electric field vector based on the FDTD discrete grid, q is the number of time steps, and is the electric field vector corresponding to the position number and time step number in the three orthogonal directions of x, y, and z, Δt is the time step, Δx, Δy, and Δz are the minimum grid sizes in the three orthogonal directions of x, y, and z, and is the magnetic field vector corresponding to the position number and time step number in the three orthogonal directions of x, y, and z, σ is the equivalent conductance in the corresponding grid, and ε is the dielectric constant in the corresponding grid.

9. The transformer electric field time domain simulation system according to claim 8, characterized in that: The equation for updating the magnetic field vector for the current time step is: Among them, σ m is the magnetic permeability coefficient and μ is the magnetic permeability.

10. The transformer electric field time domain simulation system according to claim 6, characterized in that: The basic calculation parameters of the FDTD algorithm also include space step, time step, calculation stop criterion, absorbing boundary and excitation waveform.

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