A numerical verification method for the initiation criterion of a lightning rod corona discharge
Patent Information
- Application Number
- CN202210744099.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-06-28
- Publication Date
- 2026-10-30
- Estimated Expiration
- 2042-06-28
AI Technical Summary
但在数值模拟中，把空间分割成离散的网格，无法直接获取尖端表面的电场值，只能取距离尖端表面最近的一个格点上的电场值作为尖端表面的电场值，这将使得尖端表面电场值的计算结果受网格大小影响明显，这会使得我们在电晕放电数值模拟计算中因网格大小不同而引入不可避免的计算误差
[0049]本发明首先求解接闪杆周围的电场，基于有限差分法求解泊松方程，建立了三维变网格数值模型；然后，设置参数(接闪杆形状，半径以及空间分辨率等)；紧接着，计算在各种空间分辨率下，空间内的各点电场；然后，利用计算的电场，分别计算出达到两种判据条件时的背景电场；接着，利用背景电场计算相对误差；最后，比较相对误差，证实本发明的判据更适用于数值模拟研究；本发明针对现有大于Ecor值这一判据，在不同数值仿真时因采用的空间分辨率不同而导致计算结果存在较大差异的不足进行改进，提供了一种新的等效判据，减少了空间分辨率粗细对电晕始发模拟结果的影响。
Smart Images
Figure CN115270545B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of high voltage technology and lightning science and technology, and more specifically, to a numerical verification method for the initiation criterion of corona discharge on a lightning rod. Background Technology
[0002] Corona discharge, an air breakdown phenomenon occurring at sharp surfaces, is extremely common. In the early stages of thunderstorm cloud formation, as cloud electrification continues, corona discharge can occur at the tips of ground structures or lightning rods when the ground electric field reaches a certain threshold. During the mature stage of a thunderstorm, the electric field recovery time between two lightning strikes typically ranges from a few seconds to several minutes, during which time corona discharge at ground-level sharp points (such as lightning rods) continues. Therefore, corona discharge is prevalent throughout the entire thunderstorm cloud process. The released corona charge forms a corona charge layer tens or even hundreds of meters high in the air, altering the electric field distribution characteristics near the ground, which may affect the lightning protection characteristics of lightning rods and consequently their lightning protection effectiveness. Essentially, tip corona discharge, macroscopically speaking, is a discharge phenomenon where the local electric field strength near the tip exceeds the corona breakdown threshold. Based on numerous laboratory simulations, Peek has summarized formulas for calculating the corona initiation threshold for lightning rods of different shapes, which have been widely applied.
[0003] Due to variations in conductor surface roughness and the influence of temperature, humidity, and atmospheric pressure, the corona threshold is affected. The calculation formula (Peek formula) is as follows:
[0004]
[0005] Where m is the surface roughness coefficient of the conductor, ranging from 0 to 1. E0 is an empirical value, taken as 27.2 kV / m for a hemispherical lightning rod and 30 kV / m for a cylindrical lightning rod. R is the radius of curvature of the hemispherical tip, and δ is the relative air density. The calculation formula is as follows:
[0006]
[0007] P is the actual atmospheric pressure (Pa), and P0 is the reference atmospheric pressure, taken as 101.3 × 10⁻⁶. 3 Pa; t is the actual temperature, t0 is the reference temperature, taken as 25℃. In the numerical simulation, the conductor surface is smoothed, the conductor surface roughness coefficient is taken as 1, and the actual atmospheric pressure is taken as standard atmospheric pressure 101.3 × 10⁻⁶. 3 Pa, the actual temperature is taken as 20℃, and the value of δ is taken as 1.
[0008] However, since the electric field on the tip surface is difficult to measure effectively using existing observation methods, the development of computer technology has led to the widespread use of discretized grids for numerical calculations to solve for the electric field on the tip surface, compensating to some extent for the shortcomings of actual observations. In numerical simulations, the Peek formula is commonly used as the criterion for the initiation of corona discharge at a known radius tip; that is, corona discharge begins when the electric field on the tip surface is greater than the Eco calculated by the formula. This criterion is widely used in existing numerical simulation studies of corona discharge on lightning arresters. However, in numerical simulations, dividing the space into discrete grids makes it impossible to directly obtain the electric field value of the tip surface. Only the electric field value at the grid point closest to the tip surface can be taken as the electric field value of the tip surface. This makes the calculation result of the electric field value of the tip surface significantly affected by the grid size, which introduces unavoidable calculation errors in the numerical simulation calculation of corona discharge due to different grid sizes. It is generally believed that the finer the resolution, the more accurate the calculation result, but it introduces a lot of time consumption, which is impractical for applying numerical verification to engineering calculations. Summary of the Invention
[0009] This invention provides a numerical verification method for the initiation criterion of corona discharge on a lightning rod, which can reduce the influence of spatial resolution on the simulation results of corona initiation.
[0010] To achieve the above-mentioned technical effects, the technical solution of the present invention is as follows:
[0011] A numerical verification method for the initiation criterion of corona discharge on a lightning rod includes the following steps:
[0012] S1: Solve for the electric field around the lightning rod and establish a three-dimensional variable mesh numerical model;
[0013] S2: Set the parameters of the model;
[0014] S3: Calculate the electric field at various spatial resolutions at each point in space;
[0015] S4: Using the calculated electric field, calculate the background electric field when the two criteria conditions are met respectively;
[0016] S5: Calculate the relative error using the background electric field, compare the relative error, and obtain a more criterion.
[0017] Furthermore, the process of step S1 is as follows:
[0018] The relationship between the corona discharge electric fields of two spherical electrodes is calculated as follows:
[0019]
[0020]
[0021] Among them, E cor U is the corona initiation threshold; U is the voltage across the electrodes; f is a constant; X is the distance between the two spherical electrodes; and R is the radius of the spherical electrodes.
[0022] Furthermore, the process of step S3 is as follows:
[0023] According to formula (1), we can obtain:
[0024]
[0025] The electric field at a distance a from the spherical electrode is approximately:
[0026]
[0027] Furthermore, the process of step S4 is as follows:
[0028] The empirical formula for the local electric field threshold of corona discharge at a hemispherical tip is as follows:
[0029]
[0030] From formulas (1) and (5):
[0031]
[0032] Therefore, we get:
[0033]
[0034] According to formulas (4) and (7), we can obtain:
[0035]
[0036] That is, E0 is the distance from the spherical electrode. The electric field value at that location.
[0037] Furthermore, under the same conditions, the magnitude of E0 does not change with the tip radius; it is a fixed value. That is, when the electric field on the surface of the spherical tip reaches the corona induction field, the value at a distance from the tip surface... The electric field value at the tip surface all reaches E0; thus, it can be seen that the electric field value at the tip surface is E0. The electric field reaching E0 at a given point is equivalent to the Peek criterion as the corona initiation criterion.
[0038] Furthermore, the process of step S5 is as follows:
[0039] The following two criteria will be compared in numerical simulation:
[0040] Criterion 1:
[0041]
[0042]
[0043] Criterion 2:
[0044]
[0045]
[0046] E(surface) represents the electric field at the tip surface, η1 represents the relative error of the background electric field under criterion 1, and η2 represents the relative error of the background electric field under criterion 2. b1 To determine the background electric field at each spatial resolution for halo formation under criterion 1, E b2 The background electric field for halo formation at each spatial resolution under criterion 2.
[0047] Furthermore, in step S2, the tip is a hemisphere with a tip radius R = 0.3cm, 0.6cm, and 0.9cm; the area above the ground is 250m × 250m × 250m, the background electric field is -10kV / m, and the spatial resolution h is... min = 0.05cm, 0.06cm, 0.075cm, 0.1cm, 0.15cm; E0 is an empirical value of 27.2kV / cm.
[0048] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:
[0049] This invention first solves for the electric field around the lightning arrestor, and establishes a three-dimensional variable mesh numerical model by solving the Poisson equation using the finite difference method. Then, parameters (lightning arrestor shape, radius, and spatial resolution, etc.) are set. Next, the electric field at various points in space is calculated under different spatial resolutions. Then, using the calculated electric field, the background electric field is calculated when two criteria are met. Next, the relative error is calculated using the background electric field. Finally, the relative errors are compared, confirming that the criterion of this invention is more suitable for numerical simulation research. This invention improves upon the existing criterion of values greater than Eco, which suffers from significant differences in calculation results due to different spatial resolutions in different numerical simulations, providing a new equivalent criterion that reduces the influence of spatial resolution on the simulation results of corona initiation. Attached Figure Description
[0050] Figure 1 Verification steps flowchart;
[0051] Figure 2 Cross-sectional view of the lightning rod;
[0052] Figure 3 Background electric field for halo formation under two criteria;
[0053] Figure 4Relative error under the two criteria. Detailed Implementation
[0054] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent.
[0055] To better illustrate this embodiment, some parts in the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions.
[0056] It will be understood by those skilled in the art that certain well-known structures and their descriptions may be omitted in the accompanying drawings.
[0057] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.
[0058] Example 1
[0059] like Figure 1 As shown, a numerical verification method for the initiation criterion of corona discharge on a lightning rod includes the following steps:
[0060] S1: Solve for the electric field around the lightning rod and establish a three-dimensional variable mesh numerical model;
[0061] S2: Set the parameters of the model;
[0062] S3: Calculate the electric field at various spatial resolutions at each point in space;
[0063] S4: Using the calculated electric field, calculate the background electric field when the two criteria conditions are met respectively;
[0064] S5: Calculate the relative error using the background electric field, compare the relative error, and obtain a more criterion.
[0065] The process of step S1 is as follows:
[0066] The relationship between the corona discharge electric fields of two spherical electrodes is calculated as follows:
[0067]
[0068]
[0069] Among them, E cor U is the corona initiation threshold; U is the voltage across the electrodes; f is a constant; X is the distance between the two spherical electrodes; and R is the radius of the spherical electrodes.
[0070] The process of step S3 is as follows:
[0071] According to formula (1), we can obtain:
[0072]
[0073] The electric field at a distance a from the spherical electrode is approximately:
[0074]
[0075] The process of step S4 is as follows:
[0076] The empirical formula for the local electric field threshold of corona discharge at a hemispherical tip is as follows:
[0077]
[0078] From formulas (1) and (5):
[0079]
[0080] Therefore, we get:
[0081]
[0082] According to formulas (4) and (7), we can obtain:
[0083]
[0084] That is, E0 is the distance from the spherical electrode. The electric field value at that location.
[0085] Under the same conditions, the magnitude of E0 does not change with the tip radius; it is a fixed value. That is, when the electric field on the surface of the spherical tip reaches the corona induction field, the value of E0 is constant at a distance from the tip surface. The electric field value at the tip surface all reaches E0; thus, it can be seen that the electric field value at the tip surface is E0. The electric field reaching E0 at a given point is equivalent to the Peek criterion as the corona initiation criterion.
[0086] The process of step S5 is as follows:
[0087] The following two criteria will be compared in numerical simulation:
[0088] Criterion 1:
[0089]
[0090]
[0091] Criterion 2:
[0092]
[0093]
[0094] E(surface) represents the electric field at the tip surface, η1 represents the relative error of the background electric field under criterion 1, and η2 represents the relative error of the background electric field under criterion 2.b1 To determine the background electric field at each spatial resolution for halo formation under criterion 1, E b2 The background electric field for halo formation at each spatial resolution under criterion 2.
[0095] Example 2
[0096] like Figure 1 As shown, a numerical verification method for the initiation criterion of corona discharge on a lightning rod includes the following steps:
[0097] S1: Solve for the electric field around the lightning rod and establish a three-dimensional variable mesh numerical model;
[0098] S2: Set the parameters of the model;
[0099] S3: Calculate the electric field at various spatial resolutions at each point in space;
[0100] S4: Using the calculated electric field, calculate the background electric field when the two criteria conditions are met respectively;
[0101] S5: Calculate the relative error using the background electric field, compare the relative error, and obtain a more criterion.
[0102] Accurate calculation of the electric field at the tip is essential for corona initiation. This invention establishes a three-dimensional variable mesh numerical model based on the finite difference method to solve the electric field around the lightning arrester. After establishing the model, its parameters were set: the lightning arrester is cylindrical with a height of 30m; the tip is hemispherical with radii R = 0.3cm, 0.6cm, and 0.9cm, as shown in the cross-sectional diagram. Figure 2 As shown. The simulation domain is a 250m×250m×250m area above the ground, with a background electric field of -10kV / m and spatial resolutions hmin = 0.05cm, 0.06cm, 0.075cm, 0.1cm, and 0.15cm.
[0103] The process of step S1 is as follows:
[0104] The relationship between the corona discharge electric fields of two spherical electrodes is calculated as follows:
[0105]
[0106]
[0107] Among them, E cor U is the corona initiation threshold; U is the voltage across the electrodes; f is a constant; X is the distance between the two spherical electrodes; and R is the radius of the spherical electrodes.
[0108] The process of step S3 is as follows:
[0109] According to formula (1), we can obtain:
[0110]
[0111] The electric field at a distance a from the spherical electrode is approximately:
[0112]
[0113] The process of step S4 is as follows:
[0114] The empirical formula for the local electric field threshold of corona discharge at a hemispherical tip is as follows:
[0115]
[0116] From formulas (1) and (5):
[0117]
[0118] Therefore, we get:
[0119]
[0120] According to formulas (4) and (7), we can obtain:
[0121]
[0122] That is, E0 is the distance from the spherical electrode. The electric field value at that location.
[0123] Under the same conditions, the magnitude of E0 does not change with the tip radius; it is a fixed value. That is, when the electric field on the surface of the spherical tip reaches the corona induction field, the value of E0 is constant at a distance from the tip surface. The electric field value at the tip surface all reaches E0; thus, it can be seen that the electric field value at the tip surface is E0. The electric field reaching E0 at a given point is equivalent to the Peek criterion as the corona initiation criterion.
[0124] The process of step S5 is as follows:
[0125] The following two criteria will be compared in numerical simulation:
[0126] Criterion 1:
[0127]
[0128]
[0129] Criterion 2:
[0130]
[0131]
[0132] E(surface) represents the electric field at the tip surface, η1 represents the relative error of the background electric field under criterion 1, and η2 represents the relative error of the background electric field under criterion 2. b1 To determine the background electric field at each spatial resolution for halo formation under criterion 1, E b2 The background electric field for halo formation at each spatial resolution under criterion 2.
[0133] Example 3
[0134] like Figure 1 As shown, a numerical verification method for the initiation criterion of corona discharge on a lightning rod includes the following steps:
[0135] S1: Solve for the electric field around the lightning rod and establish a three-dimensional variable mesh numerical model;
[0136] S2: Set the parameters of the model;
[0137] S3: Calculate the electric field at various spatial resolutions at each point in space;
[0138] S4: Using the calculated electric field, calculate the background electric field when the two criteria conditions are met respectively;
[0139] S5: Calculate the relative error using the background electric field, compare the relative error, and obtain a more criterion.
[0140] The process of step S1 is as follows:
[0141] The relationship between the corona discharge electric fields of two spherical electrodes is calculated as follows:
[0142]
[0143]
[0144] Among them, E cor U is the corona initiation threshold; U is the voltage across the electrodes; f is a constant; X is the distance between the two spherical electrodes; and R is the radius of the spherical electrodes.
[0145] The process of step S3 is as follows:
[0146] According to formula (1), we can obtain:
[0147]
[0148] The electric field at a distance a from the spherical electrode is approximately:
[0149]
[0150] The process of step S4 is as follows:
[0151] The empirical formula for the local electric field threshold of corona discharge at a hemispherical tip is as follows:
[0152]
[0153] From formulas (1) and (5):
[0154]
[0155] Therefore, we get:
[0156]
[0157] According to formulas (4) and (7), we can obtain:
[0158]
[0159] That is, E0 is the distance from the spherical electrode. The electric field value at that location.
[0160] Under the same conditions, the magnitude of E0 does not change with the tip radius; it is a fixed value. That is, when the electric field on the surface of the spherical tip reaches the corona induction field, the value of E0 is constant at a distance from the tip surface. The electric field value at the tip surface all reaches E0; thus, it can be seen that the electric field value at the tip surface is E0. The electric field reaching E0 at a given point is equivalent to the Peek criterion as the corona initiation criterion.
[0161] The process of step S5 is as follows:
[0162] The following two criteria will be compared in numerical simulation:
[0163] Criterion 1:
[0164]
[0165]
[0166] Criterion 2:
[0167]
[0168]
[0169] E(surface) represents the electric field at the tip surface, η1 represents the relative error of the background electric field under criterion 1, and η2 represents the relative error of the background electric field under criterion 2. b1 To determine the background electric field at each spatial resolution for halo formation under criterion 1, E b2 The background electric field for halo formation at each spatial resolution under criterion 2.
[0170] Accurate calculation of the electric field at the tip is essential for corona initiation. This invention establishes a three-dimensional variable mesh numerical model based on the finite difference method to solve the electric field around the lightning arrester. After establishing the model, its parameters were set: the lightning arrester is cylindrical with a height of 30m; the tip is hemispherical with radii R = 0.3cm, 0.6cm, and 0.9cm, as shown in the cross-sectional diagram. Figure 2 As shown. The simulation domain is a 250m×250m×250m area above the ground, with a background electric field of -10kV / m and spatial resolutions hmin = 0.05cm, 0.06cm, 0.075cm, 0.1cm, and 0.15cm.
[0171] After setting the parameters, the electric field around the three specifications of lightning rods was calculated, using the five spatial resolutions mentioned above. Using the calculated electric field, the background electric field for halo formation under the two criteria mentioned above can be calculated at these five spatial resolutions, such as... Figure 3 As shown, E b1 E is the background electric field value for halo initiation under criterion 1. b2 The value of the background electric field for halo initiation under criterion 2 is given. As shown in the figure, E... b The value is linearly correlated with resolution, and then the two broken lines in the figure are linearly fitted. At R = 0.3 cm, E... b1 The slope of the linear fit is 5.43, E b2 The slope of the linear fit is 1.67. E b1 The slope is greater than E b2 The slope of E can be seen. b1 The value of E changes more significantly with increasing spatial resolution, meaning criterion 1 is more affected by resolution. The same pattern applies to lightning rods with tip radii R = 0.6 cm and R = 0.9 cm. b1 The slope is greater than E b2 The slope of the criterion shows that criterion 1 is more affected by spatial resolution.
[0172] This invention uses the background electric field value calculated at a resolution of 0.05 cm as the most accurate value, and calculates the relative error relative to this value. For example... Figure 1 As shown, η1 is E under criterion 1 b1 The relative error, η2 is E under criterion 2 b2 The relative error is shown in the figure. It is clear from the figure that the relative error of the required background electric field value using criterion 2 is always smaller than that of criterion 1. That is, criterion 2 of this invention is more suitable for numerical simulation studies.
[0173] Using the criteria of this invention, errors caused by the coarseness of spatial resolution in numerical simulations can be significantly reduced. For example... Figure 4 As shown, Figure 4Three types of lightning rods with different tip radii and at different spatial resolutions h min The relative errors of the electric field at 0.05cm, 0.06cm, 0.075cm, 0.1cm, and 0.15cm are given, where η1 is the relative error of the background electric field under criterion 1, and η2 is the relative error of the background electric field under criterion 2. (From...) Figure 4 It can be concluded that Criterion 1 and Criterion 2 follow similar patterns: the coarser the spatial resolution, the greater the relative error of the background electric field. Furthermore, the η2 curve is consistently below the η1 curve, indicating that at different resolutions, the relative error of the required background electric field value using Criterion 2 is always smaller than that of Criterion 1. This suggests that the influence of spatial resolution on Criterion 2 is always smaller than its influence on Criterion 1, meaning that Criterion 2 of this invention is more suitable for numerical simulation research. Especially for cases with fine, pointed edges in large spaces, such as calculating the corona discharge initiation threshold on a lightning rod on a building under a thunderstorm cloud, a relatively coarse resolution is needed to simulate a large area as accurately as possible. However, the radius of the lightning rod tip is relatively small in such cases. Using Criterion 2 is more beneficial for shortening engineering calculation time while achieving a certain level of calculation accuracy.
[0174] The same or similar labels correspond to the same or similar parts;
[0175] The positional relationships depicted in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent.
[0176] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.
Claims
1. A numerical verification method for the initiation criterion of corona discharge on a lightning rod, characterized in that, Includes the following steps: S1: Solving for the electric field around the lightning rod, a three-dimensional variable mesh numerical model was established; the relationship between the corona discharge electric fields of the two spherical electrodes was calculated: in, This is the corona initiation threshold; The voltage across the electrodes; It is a constant; The distance between the two spherical electrodes is denoted as . The radius of the spherical electrode; S2: Set the parameters of the model; S3: Calculate the electric field at various spatial resolutions at each point in space; the process of step S3 is as follows: According to formula (1), we can obtain: The electric field at a distance a from the spherical electrode is approximately: S4: Using the calculated electric field, calculate the background electric field when the two criteria conditions are met respectively; the process of step S4 is as follows: The empirical formula for the local electric field threshold of corona discharge at a hemispherical tip is as follows: From formulas (1) and (5): Therefore, we get: According to formulas (4) and (7), we can obtain: Right now For distance spherical electrode The electric field value at that location; S5: Calculate the relative error using the background electric field, compare the relative errors, and obtain more criterion; The process of step S5 is as follows: The following two criteria will be compared in numerical simulation: Criterion 1: Criterion 2: For the electric field on the tip surface, The relative error of the background electric field under criterion 1, The relative error of the background electric field under criterion 2, To determine the spatial resolution under criterion 1 The background electric field that causes haloing. To determine the spatial resolution under criterion 2 The background electric field that causes haloing.
2. The numerical verification method for the initiation criterion of corona discharge on a lightning rod according to claim 1, characterized in that, Under the same environment, The magnitude of the electric field does not change with the radius of the tip; it is a fixed value. That is, when the electric field on the surface of the spherical tip reaches the corona induction field, the electric field at a distance from the tip surface... The electric field values at all points reached .
3. The numerical verification method for the initiation criterion of corona discharge on a lightning rod according to claim 2, characterized in that, In step S2, the tip is a hemisphere with a tip radius R = 0.3 cm, 0.6 cm, and 0.9 cm.
4. The numerical verification method for the initiation criterion of corona discharge on a lightning rod according to claim 3, characterized in that, In step S2, the background electric field is -10 kV / m over a 250 m × 250 m × 250 m area above the ground, with a spatial resolution of [missing information]. =0.05cm, 0.06 cm, 0.075 cm, 0.1 cm, 0.15cm.
5. The numerical verification method for the initiation criterion of corona discharge on a lightning rod according to any one of claims 1-4, characterized in that, The empirical value is 27.2 kV / cm.
6. The numerical verification method for the initiation criterion of corona discharge on a lightning rod according to claim 5, characterized in that, With the tip surface The electric field at that location reaches As a criterion for the initiation of corona discharge, it is equivalent to the Peek criterion.