Method for determining local electric field of solid phase medium particles in an environment, medium and system

Abstract

This invention discloses a method, medium, and system for determining the local electric field of solid-phase medium particles in an environment. The method includes: applying an external electric field to the environment and obtaining medium particle parameters of a first solid-phase medium particle and a second solid-phase medium particle, as well as environmental parameters; establishing a mutual dipole model of the first and second solid-phase medium particles based on the medium particle parameters and environmental parameters; calculating the dipole moments of the first and second solid-phase medium particles based on the mutual dipole model; and calculating the actual electric field intensity on the surfaces of the first and second solid-phase medium particles based on their respective dipole moments, thereby obtaining the distribution of the local electric field on the surfaces of different solid-phase medium particles in the environment. This invention establishes a mutual dipole model to calculate the dipole moment of solid-phase medium particles considering the mutual influence of two solid-phase medium particles, thereby obtaining the local electric field on the surface of the solid-phase medium particles.

Description

Technical Field

[0001] This invention relates to the field of local electric field technology for solid media in the environment, and more particularly to a method, medium, and system for determining the local electric field of solid media particles in the environment. Background Technology

[0002] In the study of discharge in hybrid two-phase systems, the electric field distortion caused by the self-polarization and electric field coupling of particles is a significant factor affecting the discharge process. Therefore, solving for the local electric field in the mixture becomes an important aspect of analyzing its influence on the discharge process. Common research methods for this include point dipole models, multipole models, and image models, with numerical calculation methods such as the finite element method and the simulated charge method. The point dipole model is effective when the interaction force between the two particles is small; the image method, due to its complex boundary conditions, is often used when there are few particles; higher-order multipole models suffer from convergence difficulties when the dielectric constant of the dielectric particles is large. Therefore, the above methods may have limitations in their application.

[0003] Currently, among the many methods for calculating the local electric field in a hybrid, the point dipole model is used as a simple approximation. The point dipole approximation is only feasible when the difference between the dielectric constant of the particles and the environment is small, the interparticle spacing is large and much larger than the particle radius, and the interaction between particles is minimal. When two particles are close together, the local electric field is significantly affected by the interaction between the particles, leading to substantial errors in the calculation results from the point dipole model. Summary of the Invention

[0004] This invention provides a method, medium, and system for determining the local electric field of solid-phase medium particles in an environment, in order to solve the problem of large calculation errors in the local electric field of two solid-phase medium particles when they are close to each other in the prior art.

[0005] Firstly, a method for determining the local electric field of solid-phase medium particles in an environment is provided, comprising:

[0006] After applying an external electric field to the environment, the particle parameters of the first and second solid-phase media particles and the environmental parameters are obtained.

[0007] Based on the particle parameters of the first solid medium particle and the second solid medium particle and the environmental parameters, a mutual dipole model of the first solid medium particle and the second solid medium particle in the environment is established.

[0008] The dipole moments of the first solid-phase medium particles and the second solid-phase medium particles are calculated based on the mutual dipole model.

[0009] The actual electric field intensity on the surface of the first solid medium particle and the actual electric field intensity on the surface of the second solid medium particle are calculated based on the dipole moment of the first solid medium particle and the dipole moment of the second solid medium particle, respectively, so as to obtain the distribution of local electric field on the surface of different solid medium particles in the environment.

[0010] Wherein, the first solid medium particle and the second solid medium particle have the same particle radius and the same particle dielectric constant;

[0011] The dielectric particle parameters include: the particle radius, the particle dielectric constant, and the distance between the first solid-phase dielectric particle and the second solid-phase dielectric particle.

[0012] The environmental parameters include the dielectric constant of the environmental medium and the electric field strength of the applied electric field.

[0013] In a second aspect, a computer-readable storage medium is provided, wherein computer program instructions are stored thereon; when executed by a processor, the computer program instructions implement the method for determining the local electric field of solid-phase medium particles in an environment as described in the first aspect embodiment above.

[0014] Thirdly, a system for determining the local electric field of solid-phase medium particles in an environment is provided, comprising: a computer-readable storage medium as described in the second aspect embodiment above.

[0015] Thus, in this embodiment of the invention, considering two solid-phase medium particles with small spacing in a uniform field, the polarization electric field causes mutual dipole moments between the two particles, leading to the generation of new dipole moments. A mutual dipole model of the two solid-phase medium particles is established to calculate the dipole moments of the solid-phase medium particles considering the mutual influence of the two solid-phase medium particles. This allows for further vector calculation to obtain the local electric field on the surface of the solid-phase medium particles, effectively estimating the surrounding electric field distribution of a two / multiple particle system in a uniform field with small errors. It can be effectively applied to the calculation of particle electric field distribution in fields such as windy and sandy environments, transformer insulating oil, and electrostatic dust removal. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments of the present invention 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.

[0017] Figure 1 This is a flowchart of a method for determining the local electric field of solid-phase medium particles in an environment according to an embodiment of the present invention;

[0018] Figure 2 This is a schematic diagram of a mutual dipole model of two solid-phase dielectric particles in a uniform applied electric field according to an embodiment of the present invention.

[0019] Figure 3 This is a schematic diagram illustrating the selection of the electric field calculation direction for particle 1 in a specific application example of the present invention;

[0020] Figure 4 This is a schematic diagram of the local electric field results of particle 1 in a two-particle system calculated in a specific application example of the present invention. Detailed Implementation

[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0022] The existing point dipole model is applied to situations where the difference in dielectric constant between solid-phase particles and the environment is small, the particle spacing is large and much larger than the particle radius, and the interaction between particles is minimal. In this case, the point dipole model has a radius of R and a dielectric constant of ε. i The two particles have a dielectric constant of ε e The dipole moment M0 generated when a medium is polarized by an applied uniform electric field in the environment is expressed as follows:

[0023]

[0024] Where, k = (ε i -ε e ) / (ε i +2ε e ).

[0025] The electric field expression (in spherical coordinates) established by a point dipole outside a sphere is:

[0026]

[0027] Where E is the local electric field strength of the particle, M0 is the dipole moment, r is the outer radius of the sphere, r0 is the unit radial vector, θ is the horizontal angle, and θ0 is the unit angle vector.

[0028] At the poles of the sphere along the outer field direction, the actual electric field is:

[0029]

[0030] However, when the distance between the two particles is small, the influence of particle interaction forces on particle polarization must be considered. Assume that in the two-particle system, the dipole moment induced by the polarization electric field generated by particle 1 on particle 2 is the mutual dipole moment M. 12 The dipole moment induced by the polarization electric field generated by particle 2 on particle 1 is the mutual dipole moment M. 21 Therefore, the actual dipole moment of particle 1 can be considered as the self-dipole moment M caused by the external electric field. 11 The mutual dipole moment M caused by particle 2 on particle 1 21 The dipole moment of particle 2 is the self-dipole moment M induced by the external electric field. 22 The mutual dipole moment M caused by particle 1 on particle 2 12 Therefore, the dipole moment of medium particle 1 can be obtained as M1' = M 11 +M 21 The dipole moment of particle 2 is M2' = M 22 +M 12 .

[0031] Based on the above analysis, this invention discloses a method for determining the local electric field of solid-phase medium particles in an environment. This method is applied to situations where two solid-phase medium particles are close together, causing their interaction to affect the polarization of the particles and resulting in a new dipole moment. For example... Figure 1 As shown, the method includes the following steps:

[0032] Step S101: After applying an external electric field to the environment, obtain the medium particle parameters of the first solid medium particle and the second solid medium particle in the environment, as well as the environmental parameters.

[0033] The applied electric field in this embodiment of the invention is a uniform electric field.

[0034] In this invention, the first and second solid-phase medium particles are considered as spheres. In embodiments of this invention, the first and second solid-phase medium particles have the same particle radius and the same dielectric constant.

[0035] Specifically, the dielectric particle parameters involved in this embodiment of the invention include: particle radius, particle dielectric constant, and the distance between the first solid-phase dielectric particle and the second solid-phase dielectric particle. These dielectric particle parameters are measurable.

[0036] Specifically, the environmental parameters involved in the embodiments of the present invention include: the dielectric constant of the environmental medium and the electric field strength of the applied electric field. The dielectric constant of the environmental medium can be measured, and the electric field strength of the applied electric field can be calculated based on the applied voltage U using known methods.

[0037] In a preferred embodiment, the first solid medium particle and the second solid medium particle can be two sand grains in a windy and sandy environment.

[0038] In another preferred embodiment, the first solid medium particle and the second solid medium particle are two solid medium particles in transformer insulating oil.

[0039] Step S102: Based on the medium particle parameters and environmental parameters of the first solid medium particle and the second solid medium particle, establish a mutual dipole model of the first solid medium particle and the second solid medium particle in the environment.

[0040] Specifically, this step includes the following process:

[0041] (1) Select the first position on the surface of the first solid medium particle and the second position on the surface of the second solid medium particle.

[0042] Wherein, the line connecting the first position and the second position passes through the center of the first solid medium particle and the center of the second solid medium particle and is parallel to the direction of the electric field strength of the applied electric field. The first solid medium particle is not located between the first position and the second position, and the second solid medium particle is located between the first position and the second position.

[0043] by Figure 2 For example, the first position is the leftmost side of the surface of the first solid medium particle, i.e., position 1, and the second position is the leftmost side of the surface of the second solid medium particle, i.e., position 2. The direction of the applied electric field intensity is along the left-right direction.

[0044] (2) Based on the medium particle parameters and environmental parameters of the first solid medium particle and the second solid medium particle, establish the first set of calculation equations for the resultant field strength at the first position and the resultant field strength at the second position.

[0045] The combined electric field strength is obtained based on the interaction between the applied electric field and the particles in the two solid-phase media. Specifically, the first set of calculation equations is as follows:

[0046]

[0047] Where E1 represents the combined field strength at the first position, E2 represents the combined field strength at the second position, and E 21 E represents the electric field strength generated by the second solid medium particle at the first position. 12 E0 represents the electric field strength generated by the first solid medium particle at the second position, and E0 represents the electric field strength of the applied electric field.

[0048] E 21 and E 12 Based on the point dipole model, the specific details are as follows:

[0049]

[0050]

[0051] Where M1 represents the dipole moment of the first solid-phase medium particle, M2 represents the dipole moment of the second solid-phase medium particle, and ε e R represents the dielectric constant of the environmental medium, R represents the particle radius, and D represents the distance between the first solid phase medium particles and the second solid phase medium particles.

[0052] (3) Based on the medium particle parameters and environmental parameters of the first solid medium particle and the second solid medium particle, establish a second set of calculation equations for the actual electric field strength at the first position and the actual electric field strength at the second position.

[0053] Specifically, the actual electric field strength also includes the influence of the solid medium particles themselves; therefore, the second set of calculation equations is as follows:

[0054]

[0055] Where E1' represents the actual electric field strength at the first position, E2' represents the actual electric field strength at the second position, and E 11 E represents the electric field strength of the first solid-phase medium particle itself. 22 This represents the electric field strength of the particles in the second solid phase medium.

[0056] E 11 and E 22 Based on the point dipole model, the specific details are as follows:

[0057]

[0058]

[0059] (4) Establish the third set of calculation equations for the relationship between the resultant field strength at the first position and the actual electric field strength at the first position, and the relationship between the resultant field strength at the second position and the actual electric field strength at the second position.

[0060] Based on the aforementioned relationship of the actual electric field in the prior art, the third set of calculation equations is as follows:

[0061]

[0062] Where, k = (ε i -ε e ) / (ε i +2ε e ), ε i This represents the dielectric constant of the particle.

[0063] (5) By combining the first set of calculation equations, the second set of calculation equations and the third set of calculation equations, the mutual dipole model is obtained.

[0064] Specifically, the mutual dipole model is as follows:

[0065]

[0066] This step allows us to obtain a mutual dipole model that takes into account the influence of interaction forces on polarization.

[0067] Step S103: Calculate the dipole moment of the first solid medium particle and the dipole moment of the second solid medium particle according to the mutual dipole model.

[0068] By substituting the collected medium particle parameters and environmental parameters of the first and second solid medium particles into the above mutual dipole model, the dipole moments of the first and second solid medium particles can be calculated under the condition that the interaction force between the two solid medium particles affects the polarization.

[0069] Step S104: Calculate the actual electric field intensity on the surface of the first solid medium particle and the actual electric field intensity on the surface of the second solid medium particle based on the dipole moment of the first solid medium particle and the dipole moment of the second solid medium particle, respectively, so as to obtain the distribution of local electric field on the surface of different solid medium particles in the environment.

[0070] Taking the first solid-phase medium particle as an example, the actual electric field intensity at any point on the surface of the first solid-phase medium particle is the intensity E0 of the applied electric field, and the electric field intensity E generated by the first solid-phase medium particle at that point is... 1 And, the electric field intensity E generated by the second solid medium particle at this location. 2 The sum of.

[0071] As mentioned earlier, taking the direction of the applied electric field intensity as horizontal, the formula for calculating the electric field intensity generated by the first solid-phase medium particle at this location is:

[0072]

[0073] Where M1 represents the dipole moment of the first solid medium particle, r1 is the outer radius of the first solid medium particle, r0 is the unit radial vector, θ1 is the angle between the line connecting the point at this location to the center of the first solid medium particle and the horizontal x-axis, and θ0 is the unit angle vector.

[0074] The formula for calculating the electric field strength generated by the second solid medium particle at this location is:

[0075]

[0076] Where M2 represents the dipole moment of the second solid medium particle, r2 is the outer radius of the second solid medium particle, r0 is the unit radial vector, θ2 is the angle between the line connecting the point at this location to the center of the second solid medium particle and the horizontal x-axis, and θ0 is the unit angle vector.

[0077] Similarly, the actual electric field strength at any point on the surface of the second solid medium particle is the sum of the applied electric field strength, the electric field strength generated by the second solid medium particle at that point, and the electric field strength generated by the first solid medium particle at that point, which will not be elaborated here.

[0078] By obtaining the actual electric field intensity on the surface of solid medium particles, the distribution of the local electric field on the surface of solid medium particles can be obtained. This allows us to obtain the location and intensity of the maximum electric field under the mutual influence of solid medium particles, as well as the location of the weak electric field when two solid medium particles are close to each other under an applied electric field. This solves the problem of electric field calculation errors caused by the mutual influence of solid medium particles in existing technologies.

[0079] When the solid medium particles are sand particles in a sandy environment, the local electric field distribution on the surface of the sand particles can guide the design of gap insulation and coordination with external insulation of transmission lines in sandy environments, providing guidance for the external insulation protection of transmission lines in sandy environments.

[0080] When the solid dielectric particles are solid dielectric particles in transformer insulating oil, the intensity of partial discharge induced by the solid dielectric particles can be accurately assessed by observing the local electric field distribution of the solid dielectric particles in the transformer insulating oil. This can predict the partial discharge faults that may be induced by the interaction of two or more solid dielectric particles in the transformer insulating oil, and provide guidance for transformer condition monitoring and health management.

[0081] This invention also discloses a computer-readable storage medium storing computer program instructions; when executed by a processor, the computer program instructions implement the method for determining the local electric field of solid-phase medium particles in an environment as described in the above embodiments.

[0082] This invention also discloses a system for determining the local electric field of solid-phase medium particles in an environment, comprising: a computer-readable storage medium as described in the above embodiments.

[0083] The technical solution of the present invention will be further illustrated below with a specific application example.

[0084] Using the mutual dipole model of this invention, relevant parameters are set as follows: the applied uniform electric field E0 is 1 kV / cm, and the particle dielectric constant ε i =5, particle radius R = 100μm, distance between two particles D = 100μm, environmental dielectric constant ε e =1. Calculate Figure 3The dipole moments of the two particles in the model are calculated under their mutual influence, and the electric field distribution on the particle surface is further obtained. Considering the symmetry of the electric field distribution, only the upper semicircle of particle 1 is selected for calculation, that is, the arc from position 1 to position 1' of particle 1. The origin of the coordinate system is selected at the center of particle 1, with the direction of the applied electric field E0 as the x-axis and the direction perpendicular to the applied electric field E0 as the y-axis. The angle between the line connecting a point on the upper semicircle of particle 1 to the center and the direction of the applied electric field E0 is θ.

[0085] Meanwhile, to verify the effectiveness of the mutual dipole model, the electric field at the actual semicircle of particle 1 under the same electric field conditions was calculated using the finite element method, and the results obtained by the two methods were compared. The electric field variation curves of the upper semicircle of particle 1 obtained by the two methods are shown in the figure below. Figure 4 As shown, z represents the diameter distance from -R to R with the center of the sphere as the origin.

[0086] A comparison of the calculation results from the two methods shows that when D / R = 1 and the dielectric constant ε of the small ball... i With respect to the environmental dielectric constant ε e The ratio of ε i / ε e When the value is 5, the relative error of the electric field at the left endpoint 1 of sphere 1 obtained by the two calculation methods is 1.30%, and the relative error of the electric field at the right endpoint 1' is 6.02%. Comparing the electric field distribution results of the upper hemisphere of particle 1 calculated by this method with the simulation results of the finite element method, it can be seen that the change of the electric field in the upper hemisphere of particle 1 conforms to the actual electric field distribution of the sphere under the actual condition. The calculated results are similar to the actual electric field values ​​obtained by the finite element method, and the local electric field of the particles in a two-sphere system can be solved. Therefore, this invention is applicable to the calculation of the electric field distribution between solid medium particles in environments such as sandstorms and insulating oil, and provides a new scheme for calculating the electric field distribution of two or more particles.

[0087] In summary, the embodiments of the present invention consider the situation where two solid-phase medium particles with small spacing are in a uniform field, and the polarization electric field causes mutual dipole moments between the two particles, resulting in the generation of new dipole moments. A mutual dipole model of the two solid-phase medium particles is established to calculate the dipole moments of the solid-phase medium particles considering the mutual influence of the two solid-phase medium particles. Thus, the local electric field on the surface of the solid-phase medium particles can be obtained through vector operations, effectively estimating the surrounding electric field distribution of two / multiple particle systems in a uniform field with small errors. It can be effectively applied to the calculation of particle electric field distribution in fields such as wind and sand environments, transformer insulating oil, and electrostatic dust removal.

[0088] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for determining the local electric field of solid-phase medium particles in an environment, characterized in that, include: After applying an external electric field to the environment, the particle parameters of the first and second solid-phase media particles and the environmental parameters are obtained. Based on the particle parameters of the first solid medium particle and the second solid medium particle and the environmental parameters, a mutual dipole model of the first solid medium particle and the second solid medium particle in the environment is established. The dipole moments of the first solid-phase medium particles and the second solid-phase medium particles are calculated based on the mutual dipole model. The actual electric field intensity on the surface of the first solid medium particle and the actual electric field intensity on the surface of the second solid medium particle are calculated based on the dipole moment of the first solid medium particle and the dipole moment of the second solid medium particle, respectively, so as to obtain the distribution of local electric field on the surface of different solid medium particles in the environment. Wherein, the first solid medium particle and the second solid medium particle have the same particle radius and the same particle dielectric constant; The dielectric particle parameters include: the particle radius, the particle dielectric constant, and the distance between the first solid-phase dielectric particle and the second solid-phase dielectric particle. The environmental parameters include the dielectric constant of the environmental medium and the electric field strength of the applied electric field.

2. The method for determining the local electric field of a solid medium in an environment according to claim 1, characterized in that, The step of establishing mutual dipole models of the first solid-phase medium particles and the second solid-phase medium particles in the environment includes: A first position on the surface of the first solid medium particle and a second position on the surface of the second solid medium particle are selected, wherein the line connecting the first position and the second position passes through the center of the first solid medium particle and the center of the second solid medium particle and is parallel to the direction of the electric field strength of the applied electric field, the first solid medium particle is not located between the first position and the second position, and the second solid medium particle is located between the first position and the second position. Based on the particle parameters of the first and second solid medium particles and the environmental parameters, a first set of calculation equations is established for the resultant field strength at the first location and the resultant field strength at the second location. Based on the particle parameters of the first and second solid-phase media particles and the environmental parameters, a second set of calculation equations is established for the actual electric field strength at the first location and the actual electric field strength at the second location. A third set of calculation equations is established to establish the relationship between the resultant electric field strength at the first position and the actual electric field strength at the first position, and the relationship between the resultant electric field strength at the second position and the actual electric field strength at the second position. By combining the first set of computational equations, the second set of computational equations, and the third set of computational equations, the mutual dipole model is obtained.

3. The method for determining the local electric field of a solid medium in an environment according to claim 2, characterized in that, The mutual dipole model is as follows: Where M1 represents the dipole moment of the first solid medium particle, M2 represents the dipole moment of the second solid medium particle, and ε e E0 represents the dielectric constant of the environmental medium, R represents the electric field strength of the applied electric field, D represents the particle radius, and k = (ε) represents the distance between the first solid-phase medium particle and the second solid-phase medium particle. i -ε e ) / (ε i +2ε e ), ε i This represents the dielectric constant of the particle.

4. The method for determining the local electric field of a solid medium in an environment according to claim 3, characterized in that, The first set of computational equations is: Where E1 represents the combined field strength at the first position, E2 represents the combined field strength at the second position, and E 21 E represents the electric field strength generated by the second solid-phase medium particle at the first position. 12 This represents the electric field strength generated by the first solid medium particle at the second position; in, 5. The method for determining the local electric field of a solid medium in an environment according to claim 4, characterized in that, The second set of computational equations is as follows: Where E1' represents the actual electric field strength at the first position, E2' represents the actual electric field strength at the second position, and E 11 E represents the electric field strength of the first solid medium particle itself. 22 This represents the electric field strength of the first solid medium particle itself; in, 6. The method for determining the local electric field of a solid medium in an environment according to claim 5, characterized in that, The third set of computational equations is as follows:

7. The method for determining the local electric field of a solid medium in an environment according to claim 1, characterized in that: The first solid medium particle and the second solid medium particle are two sand particles in a windy and sandy environment.

8. The method for determining the local electric field of a solid medium in an environment according to claim 1, characterized in that: The first solid medium particle and the second solid medium particle are two solid medium particles in transformer insulating oil.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer program instructions; when executed by a processor, the computer program instructions implement a method for determining the local electric field of a solid medium in an environment as described in any one of claims 1 to 8.

10. A system for determining the local electric field of a solid medium in an environment, characterized in that, include: The computer-readable storage medium as described in claim 9.

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