Ground electrode in time domain finite difference simulation of soil ionization effect characterization method

Abstract

The application discloses a kind of ground electrode in time domain finite difference simulation soil ionization effect characterization method, including obtaining the geometry of the ground electrode to be characterized, soil characteristics, environment and excitation source parameters, construct electrode in FTDT simulation model;The model is meshed, the absorption boundary condition and simulation total length are determined and initialized;Current density and electric field intensity around electrode are calculated, and soil resistivity is updated;The total resistance of electrode under the distribution of current soil resistivity is calculated, and the equivalent radius of electrode is calculated correspondingly;The correction factor of time domain finite difference is calculated using the equivalent radius of electrode, and then the vertical electric field component parameter of electrode is corrected;When the current simulation length reaches the simulation total length, the ground electrode top voltage, resistance, equivalent radius characterizing soil ionization effect are output;Method can accurately characterize soil ionization effect under coarse grid, greatly improve the calculation efficiency.

Description

Technical Field

[0001] This invention relates to the field of high voltage technology, and in particular to a method for characterizing the soil ionization effect of a grounding electrode in a finite-difference time-domain simulation. Background Technology

[0002] In power system lightning protection analysis, the impulse characteristics of the grounding electrode exhibit nonlinearity due to soil ionization. Accurately characterizing this nonlinearity is crucial for assessing the system's lightning backflashover tripping rate. Soil ionization occurs when large currents, such as lightning current, are injected into the soil from the grounding electrode. The electric field strength near the electrode exceeds a critical value, leading to soil breakdown. At this point, the resistivity of the ionized region decreases significantly compared to its nominal value, thereby reducing the electrode resistance and causing the impulse characteristics of the grounding electrode to exhibit nonlinearity.

[0003] In finite-difference time-domain (FDTD) simulations, existing techniques for characterizing soil ionization effects are mainly based on the element resistivity adjustment method. This method uses a dynamic soil resistivity model as its foundation. Within each simulation time step, the electric field intensity is calculated for all elements representing the soil in the FDTD grid. Then, whether ionization or deionization has occurred is determined based on whether the electric field intensity exceeds a critical value. If ionization occurs, the process is accelerated according to the formula... (in, Resistivity; The nominal resistivity of the soil; The ionization time constant; This is the time taken from the start of ionization; reducing the resistivity of the cell grid; if deionization occurs, then according to the formula... 2 (in, It has the lowest resistivity; The deionization time constant; Electric field strength; This is the critical value of the electric field strength. The time (calculated from the start of deionization) is used to restore the grid resistivity of the cell, and the above formula dynamically reflects the influence of soil ionization on electrode resistance.

[0004] However, the existing technology for characterizing soil ionization effects through unit resistivity adjustment has the following drawbacks: (1) It must rely on fine mesh discretization, which leads to a sharp increase in computational resources: In order to avoid overestimating or underestimating the ionization region, it is necessary to evaluate the electric field strength and soil ionization state with a small spatial step size. This requires the simulation working volume (including the soil region) to be discretized into a unit mesh with an extremely small size. If the unit mesh size is too large, it will lead to an increase in electric field calculation error, making it impossible to accurately determine the ionization boundary, and thus affecting the calculation accuracy of electrode resistance changes. (2) The simulation time step is forced to decrease, and the computational efficiency is greatly reduced: The decrease in the minimum unit side length corresponding to the fine mesh will directly lead to a shortening of the simulation time step. For example, when using a 0.1m fine mesh, The current method takes only 191 ps, while lightning strike simulations require tens of microseconds and millions of time step iterations. In addition, fine meshes lead to a surge in the total number of elements, and the combination of these two factors greatly increases the computation time. Under the same hardware (2.8GHz Core i7-1165G7, 32GB RAM), existing methods take 3 hours and 34 minutes to simulate a single 1m vertical grounding electrode. However, actual power system grounding analysis often involves larger working volumes or multi-electrode configurations, making the computational cost of existing methods even more prohibitive.

[0005] The root cause of the shortcomings of existing technologies lies in the inherent contradiction between their "cell-level resistivity adjustment" approach and "simulation accuracy versus computational efficiency": to ensure the computational accuracy of the ionization region, a fine mesh is necessary to achieve electric field assessment with a small spatial step size. However, a fine mesh inevitably leads to an increase in the number of cells and a decrease in the time step, resulting in excessive computational resource consumption and excessively long simulation cycles. If a coarse mesh is used to reduce computational costs, the electric field assessment error will not be able to accurately capture the ionization boundary, causing the simulation results to deviate from reality (such as overestimating electrode resistance or underestimating the ionization range). Existing technologies struggle to overcome this contradiction. For example, when FDTD simulates corona phenomena, it has also faced a similar problem of high cost for fine meshes. Although this has been alleviated by using the equivalent radius of the conductor, this approach has not been transferred to the FDTD characterization of soil ionization. Furthermore, soil ionization involves the coupled calculation of dynamic resistivity and electrode resistance, which is more complex than that of ionizer phenomena. Directly reusing this approach presents technical difficulties such as establishing the mapping relationship between electrode resistance and equivalent radius and ensuring compatibility with ionization dynamics.

[0006] In summary, existing techniques for characterizing soil ionization in FDTD simulations rely on fine-grid discretization and unit-level resistivity adjustment, which cannot balance simulation accuracy and computational efficiency. These techniques suffer from high computational costs and are not applicable to engineering grounding analysis. There is an urgent need for a method that can accurately characterize soil ionization effects with coarse grids while significantly improving computational efficiency. Summary of the Invention

[0007] To address the shortcomings of the prior art, this invention provides a method for characterizing soil ionization effects using a grounding electrode in a finite-difference time-domain simulation. This method can accurately characterize soil ionization effects under a coarse grid while significantly improving computational efficiency.

[0008] This invention provides a method for characterizing the soil ionization effect of a grounding electrode in a finite-difference time-domain simulation, comprising:

[0009] S1: Obtain the geometric parameters, soil property parameters, and environmental and excitation source parameters of the grounding electrode to be characterized, and construct a finite-difference simulation model of the grounding electrode in the time domain;

[0010] S2: Build a Yee mesh for the constructed simulation model, determine the absorbing boundary conditions and the total simulation duration, and initialize the model;

[0011] S3: Based on the preset current time step Lower ground electrode current Calculate the local current density around the grounding electrode and electric field strength Soil resistivity is obtained by combining a soil resistivity update strategy;

[0012] S4: Calculate the grounding electrode resistance under the current soil resistivity, based on the current grounding electrode grounding type. ;

[0013] S5: Grounding electrode resistance based on the current soil resistivity And the electrode type, corresponding to the calculation of the current time step. equivalent radius of the lower grounding electrode ;

[0014] S6: Calculate the correction factor for the finite-difference time-domain finite-difference ... This leads to the correction of the vertical electric field component parameters of the grounding electrode; wherein, the vertical electric field component parameters of the grounding electrode include soil conductivity and relative permittivity;

[0015] S7: Determine if the current simulation duration has reached the total simulation duration: If yes, output the voltage, resistance, and equivalent radius at the top of the grounding electrode, which characterize the soil ionization effect; if no, update the electromagnetic field components for the current time step according to the Yee grid update rules. And return to S3.

[0016] Furthermore, in S1, the geometric parameters of the grounding electrode include the radius of the grounding electrode. The burial depth of the grounding electrode Electrode types include single vertical electrodes and four parallel vertical electrodes, with the electrode spacing between the four parallel vertical electrodes; soil characteristic parameters include nominal resistivity. Critical electric field strength ionization constant Deionization constant Environmental and excitation source parameters include the size of the simulation area and the waveform of the current source, including single-peak unipolar current and double-peak bipolar current.

[0017] Furthermore, the absorption boundary condition is a Liao second-order absorption boundary condition; the model initialization includes initializing the physical dimensions of the electrodes, the nominal resistivity of the soil, the ionization / deionization time constant, the excitation source current waveform, the current of the grounding electrode, and the boundary conditions, and is initialized only once when n=0; during the simulation process, the model is initialized at each time step. Based on the results of the previous time step, the electrode current, soil resistivity, equivalent radius of the grounding electrode, soil conductivity, relative grounding constant, and correction factor are dynamically calculated.

[0018] During the simulation, the time step was set according to the finite-difference stability condition in the time domain. Conditions met:

[0019]

[0020] in, For Yee mesh in The minimum unit side length in the direction; Yee grid in The minimum unit side length in the direction; For Yee The minimum unit side length in the direction; It is the speed of light.

[0021] Furthermore, in step S4, the equipotential surface around the grounding electrode is divided into a shell of uniform thickness, and a local shell around the grounding electrode... Current density and electric field strength The specific calculation formula is as follows:

[0022]

[0023]

[0024] in, For the current shell Soil resistivity; shell Surface area.

[0025] Furthermore, in step S4, the soil resistivity update strategy specifically includes:

[0026] Determine the electric field strength Is it greater than or equal to the critical electric field strength? :

[0027] If so, it indicates that ionization has occurred, and the soil resistivity is updated according to the first update strategy. The first update strategy is as follows:

[0028]

[0029]

[0030] in, Soil resistivity; It is the critical resistivity; The nominal resistivity of the soil; The time from the start of ionization; It is the ionization constant;

[0031] If not, it indicates that deionization has occurred, and the soil resistivity is updated according to the second update strategy. The second update strategy is as follows:

[0032]

[0033] in, This represents the lowest resistivity achieved during ionization. It is the deionization constant; This represents the time since the start of ionization.

[0034] Furthermore, the resistance of the grounding electrode The calculation formula is:

[0035]

[0036] in, For time step The resistance of the lower grounding electrode; For the current shell Soil resistivity; shell Surface area.

[0037] Furthermore, when the electrode type is a single vertical electrode, the burial depth length is... From the center of the grounding electrode to the shell The distance is shell of time The formula for calculating surface area is:

[0038]

[0039] When the electrode type is four parallel and vertical electrodes, the burial depth length of all four electrodes is... The shell currently being calculated The distance to the center of the electrode is The spacing between the four parallel vertical electrodes is At that time, the shell The formula for calculating surface area is:

[0040]

[0041] in, To aid in calculating the angular parameters of the shell surface area of ​​the four parallel electrodes, and ; The radius of the grounding electrode.

[0042] Furthermore, when the electrode type is a single vertical electrode, the current time step equivalent radius of the lower grounding electrode The calculation formula is:

[0043]

[0044] in, The nominal resistivity of the soil; For time step The resistance of the lower grounding electrode; The burial depth length of a single vertical electrode;

[0045] When the electrode type is four parallel vertical electrodes, the current time step Equivalent radius of the lower electrode The calculation formula is:

[0046]

[0047] in, The burial depth length of all four electrodes is equal; The distance between the four parallel vertical electrodes.

[0048] Furthermore, the correction formula for the vertical electric field component parameters of the grounding electrode is as follows:

[0049]

[0050]

[0051] in, The conductivity before correction; This is the corrected conductivity; The relative permittivity before correction; This is the corrected relative permittivity; As a correction factor;

[0052] The correction factor The calculation formula is:

[0053]

[0054] in, This is the spatial difference step size, i.e., the grid cell size; This is the equivalent radius of the grounding electrode.

[0055] Furthermore, the Yee grid update rules are as follows:

[0056]

[0057]

[0058] in, for The magnetic field strength at the time step; For time step; The vacuum permeability; The spatial difference step size; For time step The electric field strength; It is the vacuum permittivity; This is the corrected relative permittivity; This is the corrected conductivity.

[0059] This invention proposes a method for characterizing the soil ionization effect of a grounding electrode in a finite-difference time-domain simulation, which has the following advantages:

[0060] (1) Significantly improved computational efficiency: Soil ionization characterization can be achieved by using coarse grids without relying on fine grid discretization, greatly reducing the total number of FDTD units and relaxing the time step limit, avoiding the problems of long computation time and excessive resource consumption in existing technologies, and significantly reducing simulation costs;

[0061] (2) Better simulation accuracy: The dynamic model that takes into account both ionization dynamics and local electric field strength is preferred, namely ionization dynamics + local electric field strength + dynamic model. Combined with the equipotential surface assumption and the segmented shell area calculation adapted to different electrode configurations, it is more in line with the physical nature of soil ionization. The simulation results have smaller deviations from the actual measured values, and high accuracy can be maintained in different configurations such as single rod and multi rod.

[0062] (3) Breaking the contradiction between "precision and efficiency": Existing technologies are difficult to balance the high precision of fine mesh and the high efficiency of coarse mesh. This invention transforms the resistance change into the geometric equivalence of the electrode through equivalent radius mapping. While ensuring efficiency with coarse mesh, it compensates for the precision with the help of optimization model and geometric calculation, thus achieving the unity of the two.

[0063] (4) Strong numerical stability and wide range of applicability: Only the electric field parameters perpendicular to the electrode are adjusted to ensure that the electromagnetic wave speed does not exceed the speed of light, and the equivalent radius can break through the unit size limit without numerical oscillation; there are adaptation schemes for single pole, multi-pole and different polarity current scenarios, covering the grounding electrode configuration requirements of most power systems. Attached Figure Description

[0064] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0065] Figure 1 This is a schematic diagram of the process for characterizing the soil ionization effect of a grounding electrode in a finite-difference time-domain simulation, provided by an embodiment of the present invention.

[0066] Figure 2 This is an equipotential distribution diagram of a single vertical electrode provided in an embodiment of the present invention;

[0067] Figure 3 This is an equipotential distribution diagram of four parallel vertical electrodes provided in an embodiment of the present invention;

[0068] Figure 4 This is a comparison chart of the calculated value and the measured value provided by the method in the embodiments of the present invention with the calculated value of the traditional method. Detailed Implementation

[0069] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention will be described in detail below. Obviously, the described embodiments are merely some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other implementation methods obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0070] Example 1

[0071] like Figure 1 As shown, this embodiment provides a method for characterizing the soil ionization effect of a grounding electrode in a finite-difference time-domain simulation, including:

[0072] S1: Obtain the geometric parameters, soil property parameters, and environmental and excitation source parameters of the grounding electrode to be characterized, and construct a finite-difference simulation model of the grounding electrode in the time domain;

[0073] The geometric parameters of the grounding electrode include the radius of the grounding electrode. The burial depth of the grounding electrode The electrode types include a single vertical electrode and four parallel vertical electrodes, with the electrode spacing between the four parallel vertical electrodes; the soil characteristic parameters include nominal resistivity. Critical electric field strength ionization constant Deionization constant The environmental and excitation source parameters include the size of the simulation region and the current source waveform, including single-peak unipolar current and double-peak bipolar current.

[0074] S2: Build a Yee mesh for the constructed simulation model, determine the absorbing boundary conditions and the total simulation duration, and initialize the model;

[0075] The absorption boundary condition is a Liao second-order absorption boundary condition; the model initialization includes initializing the physical dimensions of the electrodes, the nominal resistivity of the soil, the ionization / deionization time constant, the excitation source current waveform, and the boundary conditions (only in...). The model is initialized once at each time step, and the current of the ground electrode is also initialized at each time step during the simulation. Based on the results of the previous time step, the electrode current, soil resistivity, equivalent radius of the grounding electrode, soil conductivity, relative grounding constant, and correction factor are dynamically calculated. In this specific implementation, the initialization time step is included. Electrode current when =0 Soil resistivity equivalent radius of grounding electrode Soil electrical conductivity, relative contact constant, correction factor wait.

[0076] During the simulation, the time step was set according to the stability condition of the finite-difference time-domain (FDTD) model. Conditions met:

[0077]

[0078] in, For Yee mesh in The minimum unit side length in the direction; For Yee mesh in The minimum unit side length in the direction; For Yee mesh in The minimum unit side length in the direction; It is the speed of light.

[0079] S3: Based on the current at the current time step Calculate the local current density around the grounding electrode and electric field strength Soil resistivity is obtained by combining a soil resistivity update strategy.

[0080] Specifically, based on the finite-difference time-domain model at the current time step Electromagnetic field, set the current time step Total current connected to the grounding electrode To calculate the resistance of the grounding electrode, the equipotential surface surrounding the grounding electrode is considered as consisting of a cylindrical portion and a hemispherical portion. Furthermore, the equipotential surface around the grounding electrode is divided into a shell of uniform thickness, with a local shell around the grounding electrode. Current density and electric field strength The specific calculation formula is as follows:

[0081]

[0082]

[0083] in, For the current shell Soil resistivity; shell Surface area.

[0084] Specifically, the soil resistivity update strategy is as follows:

[0085] Determine the electric field strength Is it greater than or equal to the critical electric field strength? :

[0086] If so, it indicates that ionization has occurred, and the soil resistivity is updated according to the first update strategy. The first update strategy is as follows:

[0087]

[0088]

[0089] in, Soil resistivity; It is the critical resistivity; The nominal resistivity of the soil; The time from the start of ionization; It is the ionization constant;

[0090] If not, it indicates that deionization has occurred, and the soil resistivity is updated according to the second update strategy. The second update strategy is as follows:

[0091]

[0092] in, This represents the lowest resistivity achieved during ionization. It is the deionization constant; This is the time since the start of self-deionization.

[0093] S4: Based on the current grounding type of the grounding electrode, calculate the total resistance of the grounding electrode under the current soil resistivity distribution. ;

[0094] like Figure 2 The single vertical electrode shown is a cylindrical wire with a radius of [missing information]. The burial depth is To calculate the resistance of the grounding electrode, the equipotential surface around the electrode is considered to consist of a cylindrical portion and a hemispherical portion. The region around the electrode is divided into uniformly thick unit shells. Due to the unit shell Compared to the electrode length, it is very small. When current flows radially across the shell surface along the ground electrode, the unit shell... The resistance is:

[0095]

[0096] in, The resistance of the grounding electrode; shell Surface area; For the current shell The soil resistivity; among which, The calculation formula is:

[0097]

[0098] Therefore, the total resistance of the grounding electrode The calculation formula is:

[0099]

[0100] like Figure 3 The four parallel electrodes shown are inserted vertically into the ground. Each electrode is a cylindrical wire with a radius of [missing information]. The burial depth is all The spacing between the electrodes is To calculate the resistance of the grounding electrode, the equipotential surface around the electrode is considered to consist of a cylindrical portion and a hemispherical portion. The region around the electrode is divided into uniformly thick unit shells. Due to the unit shell Compared to the electrode length, it is very small. When current flows radially across the shell surface along the electrode, the shell... surface area The calculation formula is:

[0101]

[0102] in, To aid in calculating the angular parameters of the shell surface area of ​​the four parallel electrodes, and ; The spacing between the four parallel vertical electrodes; For the currently calculated shell The distance to the center of the electrode. Similarly, by measuring the distance from the electrode surface to infinity... Integrating the results yields the total resistance of the four parallel, vertical electrodes.

[0103] S5: Total resistance of the grounding electrode based on the current soil resistivity distribution And the electrode type, corresponding to the calculation of the current time step. Equivalent radius of the lower electrode .

[0104] Specifically, when the electrode type is a single vertical electrode, the current time step equivalent radius of the lower grounding electrode The calculation formula is:

[0105]

[0106] in, The nominal resistivity of the soil; For time step The resistance of the lower grounding electrode; The burial depth length of a single vertical electrode;

[0107] When the electrode type is four parallel vertical electrodes, the current time step Equivalent radius of the lower electrode The calculation formula is:

[0108]

[0109] in, This refers to the burial depth length of the four electrodes; The distance between the four parallel vertical electrodes.

[0110] S6: Calculate the correction factor for the finite-difference time-domain finite-difference ... This leads to the correction of the vertical electric field component parameters of the grounding electrode; wherein, the vertical electric field component parameters of the grounding electrode include soil conductivity and relative permittivity;

[0111] Soil ionization only alters the soil's electrical conductivity (affecting the electric field distribution) but does not change its magnetic permeability. The correction formula for the vertical electric field component parameters of the grounding electrode is as follows:

[0112]

[0113]

[0114] in, The conductivity before correction; This is the corrected conductivity; The relative permittivity before correction; This is the corrected relative permittivity; As a correction factor;

[0115] The correction factor The calculation formula is:

[0116]

[0117] in, This is the spatial difference step size, i.e., the grid cell size; This is the equivalent radius of the grounding electrode.

[0118] S8: Determine if the current simulation duration has reached the total simulation duration: If yes, output the voltage, resistance, and equivalent radius at the top of the grounding electrode, representing the soil ionization effect; if no, update the electromagnetic field components for the current time step according to the Yee grid update rules. And return to S3.

[0119] Electromagnetic field update is a standard iterative step in the FDTD method (based on the coupling relationship of Maxwell's equations, updating the magnetic field with the corrected electric field parameters, and then updating the electric field in the next time step with the magnetic field). It belongs to "field quantity iterative calculation" and is existing technology, so the electromagnetic field update will not be elaborated upon further. Specifically, the Yee mesh update rule is as follows:

[0120]

[0121]

[0122] in, for The magnetic field strength at the time step; For time step; The vacuum permeability; The spatial difference step size; Curl; For time step The electric field strength; It is the vacuum permittivity; This is the corrected relative permittivity; This is the corrected conductivity.

[0123] It should be understood that, in the embodiments of the present invention, the processor may be a Central Processing Unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor. The memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of the memory may also include non-volatile random access memory. For example, the memory may also store device type information.

[0124] The readable storage medium is a computer-readable storage medium, which can be an internal storage unit of the controller described in any of the foregoing embodiments, such as the controller's hard drive or memory. The readable storage medium can also be an external storage device of the controller, such as a plug-in hard drive, Smart Media Card (SMC), Secure Digital (SD) card, or Flash Card equipped on the controller. Further, the readable storage medium can include both the controller's internal storage unit and external storage devices. The readable storage medium is used to store the computer program and other programs and data required by the controller. The readable storage medium can also be used to temporarily store data that has been output or will be output.

[0125] Specific application example 1: A single vertical electrode, buried at a depth of 1m, with a current source waveform of bipolar current injection with double peaks.

[0126] Grounding electrode parameters: radius of the grounding electrode ; Burial depth of grounding electrode The auxiliary grounding electrode is the same size as the grounding electrode and is connected to the current source via a 15m long overhead line; the electrode type is a single vertical electrode.

[0127] Soil property parameters: homogeneous soil, nominal resistivity Critical electric field strength ionization constant Deionization constant ; hour, ;

[0128] Environmental and excitation source parameters: The working volume of the simulation area is 20×20×16m, and the current source waveform is a bipolar current with a double peak. The bipolar current is obtained by piecewise linear fitting of the measured lightning current, with a peak value of ±40A (the specific value is adjusted based on measured data), and a duration of... .

[0129] Step 1: Initialize the FDTD model and parameters:

[0130] A Yee mesh was constructed to mesh the working volume of the simulation region, uniformly discretizing it into cubic elements with a side length of 0.5m. The absorbing boundary conditions on the six faces of the cubic element were set as Liao's second-order absorbing boundary conditions. Iteration was performed using finite-difference time-domain (FDTD) time steps, with approximately 26230 time steps (25μs / 0.953 ns).

[0131] Set model initialization parameters: Initialization time step Electrode current at time Soil resistivity Equivalent radius of grounding electrode (Default value for thin conductor); Soil electrical conductivity Relative contact constant (Typical soil values), initial correction factor .

[0132] Step 2: Iterative calculation of time steps (executed every time step n). Taking the 1000th time step as an example, i.e., n=1000, the corresponding time... ;

[0133] Sub-step 2.1: Based on the FDTD current source module and the electromagnetic coupling model of the overhead line, set the current injection current. ≈25A.

[0134] Sub-step 2.2: Calculate the ionized grounding electrode resistance under the current soil resistivity distribution. :

[0135] ① Divide the soil crust: Based on the cylindrical-hemispherical equipotential surface, take the crust thickness dr = 0.01m, from the electrode surface (r = 0.025m) to infinity;

[0136] ② Calculate the shell electric field and resistivity: For each shell, the local current density Shell surface area ;electric field (Iterative calculation), according to the formula

[0137]

[0138] Calculate =523Ωm, because ;

[0139] Triggered ionization: ;

[0140] ③ Calculate resistance by integration: Note: The superscript is set to 10 instead of infinity because the infinite finite integral is approximated by a finite value, which satisfies the convergence condition of the improper integral. The results of several experiments have verified that the results are the same as those obtained when the value is set to infinity.

[0141] Sub-step 2.3: Calculate the equivalent radius ;

[0142] Substituting into the formula for the equivalent radius of the electrode:

[0143] If the cell size is less than 0.5m, the subsequent time step will increase to more than 0.5m.

[0144] Sub-step 2.4: Correct the FDTD electric field parameters

[0145] ① Calculate the correction factor ;

[0146] ② Update the vertical electric field components around the electrodes: ; ;

[0147] ③ Based on the physical property that soil ionization does not change the magnetic permeability, the magnetic field parameters and soil magnetic permeability remain unchanged. ).

[0148] Sub-step 2.5: Perform the FDTD standard iteration

[0149] Complete the current time step according to the Yee grid update rules:

[0150]

[0151]

[0152] in, for The magnetic field strength at the time step; For time step; The vacuum permeability; The spatial difference step size; Curl; For time step The electric field strength; It is the vacuum permittivity; This is the corrected relative permittivity; This is the corrected conductivity.

[0153] Step 3: Output and Verification of Results After Simulation

[0154] Output electrode tip voltage waveform: compared with measured values ​​and values ​​calculated using traditional methods, such as... Figure 4 As shown, the voltage peak error is smaller when this model is used.

[0155] Specific application example 2: A single vertical grounding rod (2.1m long), with a current source waveform of single-peak unipolar current injection.

[0156] Grounding electrode parameters: Single vertical grounding rod, radius of grounding electrode ; Burial depth of grounding electrode Overhead line height ;

[0157] Soil property parameters: nominal resistivity Critical electric field strength ionization constant ;

[0158] Environmental and excitation source parameters: The working volume of the simulation region is... The current source waveform is a single-peak unipolar current with a peak value of 6.6 kA and a duration of 50 μs.

[0159] Initialize the FDTD model and parameters:

[0160] The Yee mesh is constructed to divide the working volume of the simulation region into meshes, uniformly discretized into... Unit, time step .

[0161] The core difference from application example 1 is:

[0162] Equivalent radius calculation: Grounding electrode length l When a grounding electrode current is injected at a certain time step ,

[0163]

[0164] Note: The superscript is set to 10 instead of infinity because the infinite finite integral is approximated by a finite value, which satisfies the convergence condition of the improper integral, and the calculation result is almost the same as if the superscript were set to infinity.

[0165] but ;

[0166] Mesh and Efficiency: Total Number of Cells The computation time is approximately 32 seconds, while the traditional non-uniform fine mesh (0.04~1.0m) takes 4 hours, 38 minutes, and 46 seconds, representing a speed increase of 523 times.

[0167] Specific application example 3: Four parallel vertical grounding electrodes (3m long)

[0168] Electrode configuration: such as Figure 4 As shown, there are four parallel vertical grounding rods, one of which is a single grounding rod. burial depth of grounding electrode Overhead line height Soil parameters: , , FDTTD mesh: working volume Discretized into Unit, time step Injected current: Single-peak unipolar current, peak value... Duration The current is evenly distributed among the four rods (approximately per rod). ).

[0169] Core implementation differences (multi-electrode equivalent radius calculation) shell area calculation: piecewise calculation is used. ,like ,but

[0170]

[0171] ,but

[0172]

[0173]

[0174] Equivalent radius calculation: If the current of a single rod at a certain time step , ,but

[0175]

[0176] Result: Calculation time is approximately Traditional fine mesh requires The speed is increased by 328 times.

[0177] It is understood that the same or similar parts in the above embodiments can be referred to each other, and the contents not described in detail in some embodiments can be referred to the same or similar contents in other embodiments.

[0178] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for characterizing the soil ionization effect of a grounding electrode in a finite-difference time-domain simulation, characterized in that, include: S1: Obtain the geometric parameters, soil property parameters, and environmental and excitation source parameters of the grounding electrode to be characterized, and construct a finite-difference simulation model of the grounding electrode in the time domain; S2: Build a Yee mesh for the constructed simulation model, determine the absorbing boundary conditions and the total simulation duration, and initialize the model; S3: Based on the preset current time step Lower ground electrode current Calculate the local current density around the grounding electrode and electric field strength Soil resistivity is obtained by combining a soil resistivity update strategy; S4: Calculate the grounding electrode resistance under the current soil resistivity, based on the current grounding electrode grounding type. ; S5: Grounding electrode resistance based on the current soil resistivity And the electrode type, corresponding to the calculation of the current time step. equivalent radius of the lower grounding electrode ; S6: Calculate the correction factor for the finite-difference time-domain finite-difference ... This leads to the correction of the vertical electric field component parameters of the grounding electrode; wherein, the vertical electric field component parameters of the grounding electrode include soil conductivity and relative permittivity; S7: Determine if the current simulation duration has reached the total simulation duration: If yes, output the voltage, resistance, and equivalent radius at the top of the grounding electrode, which characterize the soil ionization effect; if no, update the electromagnetic field components for the current time step according to the Yee grid update rules. And return to S3.

2. The method according to claim 1, characterized in that, In S1, the geometric parameters of the grounding electrode include the radius of the grounding electrode. The burial depth of the grounding electrode Electrode types include single vertical electrodes and four parallel vertical electrodes, with the electrode spacing between the four parallel vertical electrodes; soil characteristic parameters include nominal resistivity. Critical electric field strength ionization constant Deionization constant Environmental and excitation source parameters include the size of the simulation area and the waveform of the current source, including single-peak unipolar current and double-peak bipolar current.

3. The method according to claim 1, characterized in that, The absorption boundary condition is a Liao second-order absorption boundary condition; the model initialization includes initializing the physical dimensions of the electrodes, the nominal resistivity of the soil, the ionization / deionization time constant, the excitation source current waveform, the current of the grounding electrode, and the boundary conditions; during the simulation process, the model initializes the physical dimensions of the electrodes, the nominal resistivity of the soil, the ionization / deionization time constant, the excitation source current waveform, the current of the grounding electrode, and the boundary conditions at each time step. Based on the results of the previous time step, the electrode current, soil resistivity, equivalent radius of the grounding electrode, soil conductivity, relative grounding constant, and correction factor are dynamically calculated. During the simulation, the time step was set according to the finite-difference stability condition in the time domain. Conditions met: ； in, For Yee mesh in The minimum unit side length in the direction; For Yee mesh in The minimum unit side length in the direction; For Yee mesh in The minimum unit side length in the direction; It is the speed of light.

4. The method according to claim 1, characterized in that, In step S4, the equipotential surface around the grounding electrode is divided into a shell of uniform thickness, and a local shell around the grounding electrode... Current density and electric field strength The specific calculation formula is as follows: ； ； in, For the current shell Soil resistivity; shell Surface area.

5. The method according to claim 1, characterized in that, In step S4, the soil resistivity update strategy is specifically as follows: Determine the electric field strength Is it greater than or equal to the critical electric field strength? : If so, it indicates that ionization has occurred, and the soil resistivity is updated according to the first update strategy. The first update strategy is as follows: ； ； in, Soil resistivity; It is the critical resistivity; The nominal resistivity of the soil; The time from the start of ionization; It is the ionization constant; If not, it indicates that deionization has occurred, and the soil resistivity is updated according to the second update strategy. The second update strategy is as follows: ； in, This represents the lowest resistivity achieved during ionization. It is the deionization constant; This represents the time since the start of ionization.

6. The method according to claim 1, characterized in that, Resistance of the grounding electrode The calculation formula is: ； in, For time steps The resistance of the lower grounding electrode; For the current shell Soil resistivity; shell Surface area.

7. The method according to claim 6, characterized in that, When the electrode type is a single vertical electrode, the burial depth length is: From the center of the grounding electrode to the shell The distance is shell of time The formula for calculating surface area is: ； When the electrode type is four parallel and vertical electrodes, the burial depth length of all four electrodes is... The shell currently being calculated The distance to the center of the electrode is The spacing between the four parallel vertical electrodes is At that time, the shell The formula for calculating surface area is: ； in, To aid in calculating the angular parameters of the shell surface area of ​​the four parallel electrodes, and ; The radius of the grounding electrode.

8. The method according to claim 1, characterized in that, When the electrode type is a single vertical electrode, the current time step equivalent radius of the lower grounding electrode The calculation formula is: ； in, The nominal resistivity of the soil; For time steps The resistance of the lower grounding electrode; The burial depth length of a single vertical electrode; When the electrode type is four parallel vertical electrodes, the current time step Equivalent radius of the lower electrode The calculation formula is: ； in, The burial depth length of all four electrodes is equal; The distance between the four parallel vertical electrodes.

9. The method according to claim 1, characterized in that, The correction formula for the vertical electric field component parameters of the grounding electrode is: ； ； in, The conductivity before correction; This is the corrected conductivity; The relative permittivity before correction; This is the corrected relative permittivity; As a correction factor; The correction factor The calculation formula is: ； in, This is the spatial difference step size, i.e., the grid cell size; This is the equivalent radius of the grounding electrode.

10. The method according to claim 9, characterized in that, The specific Yee grid update rules are as follows: ； ； in, for The magnetic field strength at the time step; For time step; Permeability of free space; The spatial difference step size; Curl; For time steps The electric field strength; It is the vacuum permittivity; This is the corrected relative permittivity; This is the corrected conductivity.

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