Streamer channel space electric field intensity detection method considering altitude influence

Abstract

The invention relates to a streamer channel space electric field intensity detection method considering altitude influence. The method can accurately solve the space electric field intensity in a streamer channel in a high altitude environment. According to the method, the change relation of the discharge parameters in the streamer channel along with the altitude can be calculated by solving the spatial electric field intensity of the high-altitude streamer channel, so that the discharge characteristics of the streamer at the high altitude can be analyzed, and a means is provided for researching the discharge characteristics of the high-altitude streamer. The method comprehensively considers the influence of the altitude on the space charge density in the streamer channel and the interaction between the electrode surface charge density and the space electric field intensity, and has the characteristics of being simple, accurate and convenient to implement.

Description

Technical Field

[0001] The invention belongs to the field of electromagnetic environment of power transmission engineering, and in particular relates to a method for detecting the spatial electric field strength of a streamer channel taking into account the influence of altitude. Background Art

[0002] The complex geographical and climatic conditions in high-altitude areas pose greater challenges to the external insulation characteristics of the line.

[0003] Analyzing the streamer discharge characteristics of the external insulation gap at high altitude is of great significance for studying the external insulation performance of high-altitude transmission lines. However, the special environment of low pressure and low humidity in high altitude areas leads to changes in the discharge parameters in the streamer channel, which also affects the accuracy of the measurement equipment. When in a high-altitude environment, the temperature is low and the water content in the air decreases accordingly. On the one hand, water molecules in the air are more likely to collide due to their larger particle size, which increases the electron ionization coefficient. On the other hand, negative oxygen ion groups are formed due to the collision reaction, which increases the electron attachment coefficient. At the same time, the air pressure drops, the air density decreases, the mean free path of electrons in the air increases, and the ionization ability is enhanced, which is conducive to the occurrence of discharge phenomena. It can be seen that the streamer discharge characteristics at high altitudes depend on the changes in the discharge parameters in the channel, and the discharge parameters are determined by the spatial field strength of the streamer channel. Summary of the invention

[0004] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a method for detecting the electric field intensity of the streamer channel space taking into account the influence of altitude, comprising the following steps:

[0005] Step S1: Obtain the spatial electric field strength at an altitude of 0m;

[0006] Step S2: setting the initial charge density on the surface of the rod electrode;

[0007] Step S3: Calculate the space charge density at an altitude of 0 m according to the space electric field strength at an altitude of 0 m and the surface charge density of the rod electrode, and calculate the space charge density caused by the altitude change according to the space electric field strength at an altitude of 0 m and the altitude;

[0008] Step S4: Calculate the space charge density at high altitude according to the space charge density at 0 m altitude and the space charge density caused by altitude change, and calculate the space electric field intensity at high altitude according to the space charge density at 0 m altitude and the space charge density caused by altitude change by Poisson's equation;

[0009] Step S5: if it is the first iteration, the rod electrode surface charge density is updated according to the rod electrode surface charge density update formula, and step S3 is executed; if it is not the first iteration, the relative error of the spatial electric field intensity and the relative error of the spatial charge density are calculated according to the error calculation formula, and the relative error of the spatial electric field intensity and the relative error of the spatial charge density are compared with the first preset value and the second preset value respectively. If both are less than the preset values, step S6 is executed; if not, the rod electrode surface charge density is updated according to the rod electrode surface charge density update formula, and step S3 is executed;

[0010] Step S6: The calculated spatial electric field intensity at the high altitude is used as the spatial electric field intensity of the streamer channel under the influence of altitude.

[0011] Furthermore, the formula for obtaining the spatial electric field strength at an altitude of 0 m in step S1 is:

[0012]

[0013] Among them, E 平原 is the electric field strength at 0m above sea level, n e 、n p and n n are the densities of electrons, positive ions and negative ions respectively, ε0 ​​is the dielectric constant of vacuum, and e is the charge of electrons.

[0014] Furthermore, the formula for setting the initial charge density on the rod electrode surface in step S2 is:

[0015]

[0016] Among them, ρ e is the surface charge density of the rod electrode, U0 is the corona onset voltage, E eq is the background electric field strength, U is the rod electrode voltage, r eq is the equivalent radius of the rod electrode, L is the gap between the rod and the plate, E0 is the corona initiation field strength of the rod electrode,

[0017]

[0018] Where δ is the relative air density.

[0019] Furthermore, in step S3, the spatial charge density at an altitude of 0 m is calculated according to the spatial electric field intensity at an altitude of 0 m and the surface charge density of the rod electrode, and the calculation formula is:

[0020]

[0021] Among them, ρ 平原 is the space charge density at 0m altitude, A e is a scalar function greater than zero, is the electric potential at any point in space.

[0022] Furthermore, in step S3, the spatial charge density caused by the altitude change is calculated based on the spatial electric field strength at an altitude of 0 m and the altitude, and the calculation formula is:

[0023] ρ 海拔 =θE 平原

[0024] Among them, ρ 海拔 is the space charge density caused by altitude change, θ is the charge factor, and when the temperature is 20°C, the value of θ is:

[0025]

[0026] Where H is the altitude.

[0027] Furthermore, in step S4, the space charge density at a high altitude is calculated based on the space charge density at an altitude of 0 m and the space charge density caused by the altitude change, and the calculation formula is:

[0028] ρ=ρ 平原 +ρ 海拔

[0029] where ρ is the space charge density at high altitude.

[0030] Furthermore, in step S4, the spatial electric field intensity at high altitude is calculated by Poisson's equation according to the spatial charge density at 0 m altitude and the spatial charge density caused by altitude change. The calculation formula is:

[0031]

[0032] Where E is the spatial electric field strength at high altitude.

[0033] Furthermore, the update formula of the rod electrode surface charge density is:

[0034]

[0035] Among them, ρ e(n) is the surface charge density of the rod electrode at the nth iteration, ρ e(n-1) is the surface charge density of the rod electrode at the n-1th iteration, n ≥ 2, μ is the charge mobility, E max The maximum field strength on the rod motor surface when forming the streamer for each cycle iteration.

[0036] Furthermore, the error calculation formula is:

[0037]

[0038]

[0039] Among them, E n is the spatial electric field intensity at high altitude of the nth iteration, ρ n is the space charge density at the high altitude of the nth iteration, E n-1 is the spatial electric field intensity at high altitude of the n-1th iteration, ρ n-1 is the space charge density at high altitude of the n-1th iteration, δ E is the relative error of the electric field intensity in space, δ ρ is the relative error of the space charge density.

[0040] Furthermore, the first preset value is 0.5%, and the second preset value is 0.1%.

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] The main purpose of the present invention is to propose a method for detecting the spatial electric field intensity of a streamer channel taking into account the altitude, which can accurately solve the spatial electric field intensity in the streamer channel under a high altitude environment. By solving the spatial electric field intensity of the streamer channel at high altitude, the relationship between the discharge parameters in the streamer channel and the altitude can be calculated, and then the discharge characteristics of the streamer at high altitude can be analyzed, providing a means for studying the discharge characteristics of high altitude streamers. The present invention comprehensively considers the influence of altitude on the spatial charge density in the streamer channel and the interaction between the electrode surface charge density and the spatial electric field intensity, and has the characteristics of being simple, accurate and easy to implement. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a flow chart of the space electric field calculation of the present invention;

[0044] Figure 2 It is a schematic diagram of the rod plate electrode of the present invention. DETAILED DESCRIPTION

[0045] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are 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 should fall within the scope of protection of the present invention.

[0046] Embodiment 1:

[0047] In the process of calculating the electric field strength of the streamer channel considering the altitude, it is necessary to use the Poisson equation to solve it. Since the Poisson equation is a nonlinear equation, and the spatial charge density and potential and electric field strength of each point are coupled with each other, an iterative method is required for calculation. The specific solution process is as follows:

[0048] The following steps are involved:

[0049] Step S1: Calculate the spatial electric field intensity at an altitude of 0m on the plain;

[0050] The calculation formula is:

[0051]

[0052] Among them, E 平原 is the spatial electric field intensity at 0m altitude on the plain, n e 、n p and n n are the densities of electrons, positive ions and negative ions respectively, ε0 ​​is the dielectric constant of vacuum, and e is the charge of electrons.

[0053] Step S2: setting the initial charge density on the rod electrode surface; the formula for setting the initial charge density on the rod electrode surface is:

[0054]

[0055] Among them, ρ e is the surface charge density of the rod electrode, U0 is the corona onset voltage, E eq is the background electric field strength, U is the rod electrode voltage, r eq is the equivalent radius of the rod electrode, L is the gap between the rod and the plate, E0 is the corona initiation field strength of the rod electrode,

[0056]

[0057] δ is the relative air density.

[0058] Step S3: Calculate the spatial charge density at the plain according to the spatial electric field intensity at an altitude of 0 m and the surface charge density of the rod electrode. The calculation formula is:

[0059]

[0060] Among them, ρ 平原 is the space charge density in the plain, A e is a scalar function greater than zero, is the electric potential at any point in space.

[0061] The spatial charge density caused by altitude change is calculated based on the spatial electric field intensity at 0m altitude on the plain and the altitude. The calculation formula is:

[0062] ρ 海拔 =θE 平原

[0063] Among them, ρ 海拔 is the space charge density caused by altitude change, θ is the charge factor, and when the temperature is 20°C, the value of θ is:

[0064]

[0065] Where H is the altitude.

[0066] Step S4: Calculate the space charge density at high altitude based on the space charge density at the plain and the space charge density caused by altitude change. The calculation formula is:

[0067] ρ=ρ 平原 +ρ 海拔

[0068] where ρ is the space charge density at high altitude.

[0069] The spatial electric field intensity at high altitude is calculated by Poisson's equation based on the spatial charge density at the plain and the spatial charge density caused by altitude change. The calculation formula is:

[0070]

[0071] Where E is the spatial electric field strength at high altitude.

[0072] Step S5: If it is the first iteration, the surface charge density of the rod electrode is updated according to the surface charge density update formula of the rod electrode, and step S3 is executed. The surface charge density update formula of the rod electrode is:

[0073]

[0074] Among them, ρ e(n) is the surface charge density of the rod electrode at the nth iteration, ρ e(n-1) is the surface charge density of the rod electrode at the n-1th iteration, μ is the charge mobility, E max The maximum field strength on the rod motor surface when the streamer is formed for each cycle iteration;

[0075] If it is not the first iteration, the error limit formula is used to determine whether the error meets the requirements. The error limit condition is:

[0076]

[0077] Among them, E n is the spatial electric field intensity at high altitude of the nth iteration, ρ nis the space charge density at the high altitude of the nth iteration, E n-1 is the spatial electric field intensity at high altitude of the n-1th iteration, ρ n-1 is the space charge density at high altitude of the n-1th iteration, δ E is the relative error of the electric field intensity in space, δ ρ is the relative error of the space charge density.

[0078] If the error meets the requirement, step S6 is executed; if not, the surface charge density of the rod electrode is updated according to the rod electrode surface charge density update formula, and step S3 is executed;

[0079] Step S6: The calculated spatial electric field intensity at the high altitude is used as the spatial electric field intensity of the streamer channel under the influence of altitude.

[0080] Embodiment 2:

[0081] The parts not mentioned in this embodiment are the same as those in Embodiment 1.

[0082] In order to verify the accuracy of the proposed method for calculating the spatial electric field of the streamer channel considering the altitude, five altitudes of 0m, 1000m, 2000m, 3000m and 4000m were taken for analysis. Figure 2 As shown, a rod-plate electrode model is adopted, the gap distance is set to 3 mm, the rod electrode voltage is set to 3 kV, and the plate electrode is grounded.

[0083] After iterative calculation, the spatial electric field of the streamer channel considering the altitude is shown in Table 1. The change of altitude will cause the change of environmental parameters such as atmospheric pressure, humidity, and temperature. The change of air temperature affects the discharge by affecting the air density, but within the range of atmospheric ambient temperature, its effect on the gas density is not significant. Therefore, the influence of pressure and humidity on the spatial electric field is mainly considered. Compared with the existing literature [Meng Xiaobo, Hui Jianfeng, Bian Xingming, et al. Study on the characteristics of streamer discharge under low pressure [J]. Proceedings of the CSEE, 2011, 31(25): 139-149.], the maximum error does not exceed 5%, which verifies the accuracy of the method for calculating the spatial electric field intensity of the streamer channel considering the altitude proposed in the present invention.

[0084] Table 1 Spatial electric field of streamer channel at different altitudes

[0085]

[0086] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of various equivalent modifications or replacements within the technical scope disclosed by the present invention, and these modifications or replacements should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A method for detecting the electric field strength of a streamer channel space considering the influence of altitude, characterized in that: The following steps are involved: Step S1: Obtain the spatial electric field strength at an altitude of 0m; Step S2: setting the initial charge density on the surface of the rod electrode; Step S3: Calculate the space charge density at an altitude of 0 m according to the space electric field strength at an altitude of 0 m and the surface charge density of the rod electrode, and calculate the space charge density caused by the altitude change according to the space electric field strength at an altitude of 0 m and the altitude; Step S4: Calculate the space charge density at high altitude according to the space charge density at 0 m altitude and the space charge density caused by altitude change, and calculate the space electric field intensity at high altitude according to the space charge density at 0 m altitude and the space charge density caused by altitude change by Poisson's equation; Step S5: if it is the first iteration, the rod electrode surface charge density is updated according to the rod electrode surface charge density update formula, and step S3 is executed; if it is not the first iteration, the relative error of the spatial electric field intensity and the relative error of the spatial charge density are calculated according to the error calculation formula, and the relative error of the spatial electric field intensity and the relative error of the spatial charge density are compared with the first preset value and the second preset value respectively. If both are less than the preset values, step S6 is executed; if not, the rod electrode surface charge density is updated according to the rod electrode surface charge density update formula, and step S3 is executed; Step S6: The calculated spatial electric field intensity at the high altitude is used as the spatial electric field intensity of the streamer channel under the influence of altitude.

2. A method for detecting the electric field strength of a streamer channel space considering the influence of altitude according to claim 1, characterized in that: The formula for obtaining the spatial electric field strength at an altitude of 0 m in step S1 is: Among them, E 平原 is the electric field strength at 0m above sea level, n e 、n p and n n are the densities of electrons, positive ions and negative ions respectively, ε0 ​​is the dielectric constant of vacuum, and e is the charge of electrons.

3. A method for detecting the electric field strength of a streamer channel considering the influence of altitude according to claim 1, characterized in that: The formula for setting the initial charge density on the rod electrode surface in step S2 is: Among them, ρ e is the surface charge density of the rod electrode, U0 is the corona onset voltage, E eq is the background electric field strength, U is the rod electrode voltage, r eq is the equivalent radius of the rod electrode, L is the gap between the rod and the plate, E0 is the corona initiation field strength of the rod electrode, Where δ is the relative air density.

4. The method for detecting the electric field strength of the streamer channel space considering the influence of altitude according to claim 1, characterized in that: In step S3, the spatial charge density at an altitude of 0 m is calculated based on the spatial electric field intensity at an altitude of 0 m and the surface charge density of the rod electrode. The calculation formula is: Among them, ρ 平原 is the space charge density at 0m altitude, A e is a scalar function greater than zero, is the electric potential at any point in space.

5. The method for detecting the electric field intensity of the streamer channel space considering the influence of altitude according to claim 1, characterized in that: In step S3, the spatial charge density caused by the altitude change is calculated based on the spatial electric field intensity at an altitude of 0 m and the altitude. The calculation formula is: r 海拔 =θE 平原 Among them, ρ 海拔 is the space charge density caused by altitude change, θ is the charge factor, and when the temperature is 20°C, the value of θ is: Where H is the altitude.

6. The method for detecting the electric field intensity of the streamer channel space considering the influence of altitude according to claim 1, characterized in that: In step S4, the space charge density at a high altitude is calculated based on the space charge density at an altitude of 0 m and the space charge density caused by the altitude change. The calculation formula is: p=p 平原 +r 海拔 where ρ is the space charge density at high altitude.

7. The method for detecting the electric field intensity of the streamer channel space considering the influence of altitude according to claim 1, characterized in that: In step S4, the spatial electric field intensity at high altitude is calculated by Poisson's equation based on the spatial charge density at 0 m altitude and the spatial charge density caused by altitude change. The calculation formula is: Where E is the spatial electric field strength at high altitude.

8. The method for detecting the electric field strength of the streamer channel space considering the influence of altitude according to claim 1, characterized in that: The updated formula of the rod electrode surface charge density is: Among them, ρ e(n) is the surface charge density of the rod electrode at the nth iteration, ρ e(n-1) is the surface charge density of the rod electrode at the n-1th iteration, n ≥ 2, μ is the charge mobility, E max The maximum field strength on the rod motor surface when forming the streamer for each cycle iteration.

9. The method for detecting the electric field strength of the streamer channel space considering the influence of altitude according to claim 1, characterized in that: The error calculation formula is: Among them, E n is the spatial electric field intensity at high altitude of the nth iteration, ρ n is the space charge density at the high altitude of the nth iteration, E n-1 is the spatial electric field intensity at high altitude of the n-1th iteration, ρ n-1 is the space charge density at high altitude of the n-1th iteration, δ E is the relative error of the electric field intensity in space, δ ρ is the relative error of the space charge density.

10. The method for detecting the electric field strength of the streamer channel space considering the influence of altitude according to claim 1, characterized in that: The first preset value is 0.5%, and the second preset value is 0.1%.

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