Insulation powder coating dielectric breakdown simulation method based on phase field method

Abstract

The invention provides an insulating powder coating dielectric breakdown simulation method based on a phase field method, and belongs to the technical field of phase field methods and materials. The method comprises the following steps: constructing an insulating powder coating dielectric breakdown phase field calculation model, constructing a main breakdown phase field variable, constructing a relative dielectric constant distribution function changing along with space coordinates, and solving to obtain a total electric field intensity component; the total free energy F of the model is introduced, a unit step function is introduced to correct the Allen-Cahn equation, and a phase field control equation is obtained; weak forms of phase field and electrostatic field control equations are determined, and dielectric breakdown simulation is completed through mutual coupling of the phase field and the electrostatic field. The model constructed by the invention not only can accurately simulate the whole breakdown starting process of the insulating coating in a strong electric field, but also can effectively predict the critical breakdown voltage and the possible breakdown path of the insulating coating, and provides a direct and quantitative tool for accurate optimization and performance improvement of an insulating powder formula.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of phase field method and material technology, in particular to an insulating powder coating dielectric breakdown simulation method based on the phase field method. BACKGROUND

[0002] Insulating powder is widely used in busbars, copper bars, circuit breakers, switch cabinets, insulators, bus ducts, and bus insulations in switch cabinets, which require high-voltage-resistant electrical component insulation. By spraying or electrostatically depositing insulating powder on the surface of a metal conductor and forming a coating through solidification, the dielectric strength and environmental resistance of electrical equipment can be effectively improved. Due to its simple process and low cost, powder coating has become an important technology for electrical equipment insulation.

[0003] However, current research on the breakdown characteristics of insulating powder coating relies heavily on high-voltage testing methods, which involve applying an external voltage until the coating fails to obtain the breakdown strength. Although this method is intuitive, it is complex, time-consuming, and greatly affected by sample preparation conditions, test environment, and operation methods, making it difficult to accurately reveal the breakdown mechanism. Meanwhile, existing research mostly focuses on macroscopic electrical performance testing, and lacks effective theoretical modeling and prediction methods for microscopic processes such as internal electric field distribution, defect evolution, charge accumulation, and electric tree expansion.

[0004] To solve the above problems, some scholars have proposed corresponding technical solutions, such as the invention patent CN120493480A published in August 2025, which proposes a composite material dielectric breakdown multi-scale simulation method and device. This method mainly calculates the target breakdown probability of the grid based on the material parameters and structural parameters of the composite material, and uses the electric field strength and molecular interaction energy to generate target state parameters. Finally, the target breakdown strength value is obtained, and the breakdown strength simulation method of the composite material is obtained by fitting the Weibull distribution. Although this method can predict the macroscopic breakdown strength of the material to some extent, its core idea has inherent limitations and cannot deeply reveal the physical nature of breakdown. It still has the following shortcomings: (1) This method simplifies the complex physical and chemical process of dielectric breakdown into a probability model. The calculation of the "breakdown probability" relies on empirical or semi-empirical parameters, and cannot fundamentally describe the initiation and expansion mechanism of the breakdown channel.

[0005] (2) The final output of this method is a macroscopic statistical breakdown strength value. Although it can be used for preliminary screening, it is difficult to quantitatively reveal how microscopic parameters such as filler shape, size, and interface characteristics specifically affect the selection and evolution of the breakdown path.

[0006] (3) The probability model is usually calculated based on the initial static structure of the material. It is difficult to dynamically and continuously simulate the real-time evolution process of the internal micro-defects (such as the branching growth of electrical tree) of the material under the action of the electric field. SUMMARY

[0007] The technical problem to be solved by the present application is that it is difficult to dynamically and continuously simulate the real-time evolution process of the internal micro-defects of the material under the action of the electric field in the prior art, and it is difficult to solve the influence of the micro-parameters such as the shape, size and interface characteristics of the filler on the simulation model, so that the simulation is inaccurate.

[0008] The present application provides an insulating powder coating dielectric breakdown simulation method based on a phase field method, comprising the following steps: Step 1, constructing an insulating powder coating dielectric breakdown phase field calculation model; in the insulating powder coating dielectric breakdown phase field calculation model, the insulating powder coating dielectric breakdown includes three states, which are a breakdown phase, a continuous evolution transition phase and an unbroken phase; Step 2, constructing a main breakdown phase field variable related to time and space η ( r , t ), r is a spatial coordinate, t is time; Step 3, measuring the relative permittivity ε p of the unbroken phase of the insulating powder coating material, and giving the relative permittivity of the breakdown phase ε b ; based on the spatial distribution of the main breakdown phase field variable η ( r , t ), a relative permittivity distribution function ε r ( r ) varying with the spatial coordinate is constructed, which is ε r ( r ) connected to the unbroken phase and the breakdown phase through a diffusion interface smoothing; Step 4, substituting the relative permittivity distribution function ε r ( r ) into the electrostatic field control equation to obtain the total electric field strength component; Step 5, introducing the total free energy of the model F , F=F sep + F grad + F elec , wherein F sepis the free energy of phase separation, F grad is the free energy of interface, F elec is the free energy of electrostatic field; Step 6, introducing a unit step function to modify the Allen-Cahn equation, and taking it as the phase field control equation; Step 7, given the basic parameters of the phase field and electrostatic field control equation, constructing the boundary conditions of the phase field and electrostatic field control equation, setting the initial value, and determining the weak form of the phase field and electrostatic field control equation, completing the dielectric breakdown simulation through the mutual coupling of the phase field and electrostatic field.

[0009] Preferably, the insulating powder coating in the dielectric breakdown phase field calculation model of the insulating powder coating in step 1 is a solid cube, and the solid cube is composed of a matrix and a plurality of fillers randomly distributed in the matrix; the space occupied by the plurality of fillers is combined as a filler calculation domain, and the space other than the filler calculation domain is combined as a matrix calculation domain.

[0010] Preferably, the main breakdown phase field variable η (r,t) in step 2 has the expression: .

[0011] Preferably, in step 3, the measurement is performed as follows: first, a sample is taken from the insulating powder coating, which is composed of a matrix containing fillers, and then the sample is measured by a broadband dielectric spectrometer; The diffuse interface is represented by introducing a smooth interpolation function L ( r ) and has the expression: ; In the formula, η ( r ) is a sub-breakdown phase field variable considering only the spatial coordinates; The expression of the relative permittivity distribution function ε r ( r ) is: .

[0012] Preferably, the expression of the electrostatic field control equation in step 4 is: ; In the formula, ε 0 is the vacuum permittivity, is the gradient operator, is the electric potential, ρ is the volume charge density, and "·" is the dot product symbol. the total electric field intensity component E ( r ) is given by: .

[0013] Preferably, the phase separation free energy F sep is given by: ;

[0014] wherein V is the computational domain, f sep is the phase separation free energy density given by: ;

[0015] wherein α is the phase separation coefficient; the interfacial free energy F grad is given by: ;

[0016] wherein γ is the gradient energy coefficient under the isotropic approximation; the electrostatic field free energy F elec is given by: ;

[0017] wherein f elec is the electrostatic energy density.

[0018] Preferably, the unit step function of step 6 is given by: ;

[0019] wherein H( f elec －f critical ) is the unit step function, f critical is the critical energy density of the insulating powder coating material given by: ;

[0020] wherein E B is the critical breakdown field strength of the insulating powder coating material; the phase field control equation is: ;

[0021] wherein, L is a kinetic coefficient related to the interfacial mobility.

[0022] Preferably, the basic parameters in step 7 include: critical breakdown field strength of the insulating powder coating material E B , vacuum dielectric constant ε 0 , relative dielectric constant of the breakdown phase ε b , phase separation coefficient α , kinetic coefficient related to the interfacial mobility L , gradient energy coefficient under the isotropic approximation γ ; The boundary conditions are Dirichlet boundary conditions and Neumann boundary conditions. The Dirichlet boundary conditions are: in the electrostatic field, the upper surface of the matrix calculation domain is a fixed potential, and the lower surface is grounded; in the phase field, the center positions of the upper and lower surfaces of the matrix calculation domain are set to the breakdown phase. The Neumann boundary conditions are: the boundaries of the matrix calculation domain are zero flux. The set initial values are: the potential in the matrix calculation domain is zero, and the breakdown phase field variable is zero. The weak form expression of the phase field control equation is: ;

[0023] wherein, η is a breakdown phase field variable, v is a test function, n is a normal component, ε p is a relative dielectric constant of the non-breakdown phase, S is an outer boundary of the matrix calculation domain. The weak form expression of the electrostatic field control equation is: ;

[0024] The expression of the mutual coupling of the phase field and the electrostatic field is: ;

[0025] The dielectric breakdown simulation is completed by the mutual coupling of the phase field and the electrostatic field.

[0026] Preferably, the material of the filler is spherical silica, and the material of the matrix is epoxy resin.

[0027] The application further provides a device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the dielectric breakdown simulation method of the insulating powder coating based on the phase field method when executing the computer program.

[0028] Compared with the prior art, the application has the following beneficial effects: (1) The application describes the initiation and expansion mechanism of the breakdown channel by constructing the total free energy model comprising the phase separation energy, the gradient energy and the electrostatic energy from the physical nature of the dielectric breakdown.

[0029] (2) The application can clearly and quantitatively reveal the specific influence mechanism of the micro-parameters such as the shape, size and interface characteristics of the filler on the breakdown behavior, and can intuitively display how different microstructures distort the electric field, hinder or guide the expansion of the breakdown path, thereby providing a direct and quantitative theoretical basis for the precise optimization and performance improvement of the insulating powder formulation.

[0030] (3) The application has the ability of dynamic continuous simulation, and can simulate the whole space-time evolution process of the internal micro-defects (such as the electrical tree) from initiation, branching to final penetration under the action of a strong electric field in real time, and realize the precise capture and visual presentation of the overall development of the breakdown. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 The flowchart of the method of the application.

[0032] Figure 2 The structural diagram of the insulating powder coating in the phase field calculation model of the dielectric breakdown of the insulating powder coating in the embodiment of the application.

[0033] Figure 3 The measurement curve of the relative dielectric constant of the epoxy resin at 25 DEG C.

[0034] Figure 4 The simulation result of the dielectric breakdown of the insulating powder coating in the embodiment of the application. DETAILED DESCRIPTION

[0035] The application will be further described below in combination with the drawings and embodiments.

[0036] Figure 1 The flowchart of the method of the application, which comprises the following steps: Figure 1 It can be seen that the dielectric breakdown simulation method of the insulating powder coating based on the phase field method comprises the following steps: Step 1, constructing a dielectric breakdown phase field calculation model of the insulating powder coating; in the dielectric breakdown phase field calculation model of the insulating powder coating, the dielectric breakdown of the insulating powder coating comprises three states, namely the breakdown phase, the continuous evolution transition phase and the unbroken phase.

[0037] In the embodiment, the insulating powder coating in the calculation model is a solid cube, the body of which is composed of a matrix and a plurality of fillers randomly distributed in the matrix; the space occupied by the plurality of fillers is combined and recorded as a filler calculation domain, and the space other than the filler calculation domain is recorded as a matrix calculation domain.

[0038] In the embodiment, the material of the fillers is spherical silica, and the material of the matrix is epoxy resin.

[0039] Figure 2 FIG. 1 is a structural schematic diagram of an insulating powder coating in an insulating powder coating dielectric breakdown phase field calculation model in an embodiment of the present application. As shown in FIG. 1, the insulating powder coating is a solid cube, the body of which is composed of a matrix and a plurality of fillers randomly distributed in the matrix, that is, the microstructure of the insulating powder coating is described through this structure. Figure 2 As shown in FIG. 1, the insulating powder coating is a solid cube, the body of which is composed of a matrix and a plurality of fillers randomly distributed in the matrix, that is, the microstructure of the insulating powder coating is described through this structure.

[0040] In the embodiment, the solid cube is a square cube with a side length of 100 μm. The fillers are spherical silica with a diameter of 5 μm.

[0041] Step 2, constructing a main breakdown phase field variable related to time and space η (r, t), r is a spatial coordinate, t and t is time.

[0042] In the embodiment, the expression of the main breakdown phase field variable η (r, t) is: .

[0043] Step 3, measuring the relative dielectric constant ε of the unbroken phase of the insulating powder coating material p , and giving the relative dielectric constant ε of the breakdown phase ε b ; based on the spatial distribution of the main breakdown phase field variable η ( r , t ), a relative dielectric constant distribution function ε r ( r ) varying with the spatial coordinate is constructed, and the function ε r ( r ) smoothly connects the unbroken phase and the breakdown phase through a diffusion interface.

[0044] In the embodiment, the measurement is performed as follows: firstly, a sample is taken from the insulating powder coating, which is composed of a matrix containing fillers, and then the sample is measured by a Novocontrol concept80 broadband dielectric spectrometer. Specifically, the sample is a circular sheet with a diameter of 40 mm and a thickness of 1 mm, the loading voltage during the test is 1 V, the measurement frequency is from 0.1 Hz to 10 6 Hz, and the measurement temperature is from -25℃ to 150℃. Figure 3 The measured curve of the relative dielectric constant of the epoxy resin at 25℃ is shown in Fig. 1.

[0045] The diffusion interface is represented by introducing a smooth interpolation function L ( r ) whose expression is as follows: ; wherein, η ( r ) is a secondary breakdown phase field variable considering only the spatial coordinates.

[0046] The expression of the relative dielectric constant distribution function ε r ( r ) is as follows: .

[0047] Step 4: substituting the relative dielectric constant distribution function ε r ( r ) into the electrostatic field control equation to obtain the total electric field intensity component.

[0048] In the embodiment, the expression of the electrostatic field control equation is as follows: ; wherein, ε 0 is the vacuum dielectric constant, is the gradient operator, is the electric potential, ρ is the volume charge density, and “·” is the dot product symbol; The expression of the total electric field intensity component E ( r ) is as follows: ; Step 5: introducing the model total free energy F , F=F sep + F grad + F elec wherein, Fsep is the free energy of phase separation, F grad is the free energy of interface, F elec is the free energy of electrostatic field.

[0049] In the present embodiment, the free energy of phase separation F sep is expressed as: ; wherein, V is the calculation domain, f sep is the free energy density of phase separation, which is expressed as: ; wherein, α is the phase separation coefficient.

[0050] The free energy of interface F grad is expressed as: ; wherein, γ is the gradient energy coefficient under the isotropic approximation.

[0051] The free energy of electrostatic field F elec is expressed as: ; wherein, f elec is the electrostatic energy density.

[0052] The free energy of phase separation F sep is used to drive phase separation, the free energy of interface F grad is used to adjust the transition of phase boundary, and the free energy of electrostatic field F elec is used for the synergistic contribution of electric field.

[0053] Step 6, introducing a unit step function to modify the Allen-Cahn equation and taking it as a phase field control equation.

[0054] In the present embodiment, the expression of the unit step function is: ; wherein, H( f elec - f critical ) is a unit step function, fcritical The critical energy density of the insulating powder coating material is expressed as: ; In the formula, E B The critical breakdown field strength of the insulating powder coating material is expressed as:

[0055] The phase field control equation is expressed as: ; In the formula, L The kinetic coefficient related to the interface mobility is expressed as:

[0056] The Allen-Cahn equation is expressed as: .

[0057] Step 7, given the basic parameters of the phase field and electrostatic field control equation, the boundary conditions of the phase field and electrostatic field control equation are constructed, the initial value is set, and the weak form of the phase field and electrostatic field control equation is determined, and the dielectric breakdown simulation is completed through the mutual coupling of the phase field and electrostatic field.

[0058] In this embodiment, the basic parameters include: the critical breakdown field strength of the insulating powder coating material E B , the vacuum dielectric constant ε 0 , the relative dielectric constant of the breakdown phase ε b , the phase separation coefficient α , the kinetic coefficient related to the interface mobility L , the gradient energy coefficient under the isotropic approximation γ .

[0059] The boundary condition is the Dirichlet boundary condition and the Neumann boundary condition; The Dirichlet boundary condition is that in the electrostatic field, the upper surface of the matrix calculation domain is a fixed potential, and the lower surface is grounded; in the phase field, the center positions of the upper and lower surfaces of the matrix calculation domain are set to the breakdown phase; The Neumann boundary condition is that the boundary of the matrix calculation domain is zero flux.

[0060] The set initial value is that the potential in the matrix calculation domain is zero, and the breakdown phase variable is zero.

[0061] The weak form of the phase field control equation is expressed as: ; In the formula, η is the breakdown phase variable, v is the test function, and n is the normal component.ε p the relative dielectric constant of the non-breakdown phase, S the outer boundary of the matrix calculation domain.

[0062] The weak form expression of the electrostatic field control equation is: ; The expression of the phase field and electrostatic field mutual coupling is: ; The dielectric breakdown simulation is completed by the mutual coupling of the phase field and the electrostatic field.

[0063] In the embodiment of the present application, the critical breakdown field strength E B 25kV / mm, the relative dielectric constant of the breakdown phase ε b 10 4 , the phase separation coefficient α 10 6 J / m 3 , the interface mobility related kinetic coefficient L 10 -7 m 2 / (s·N), the gradient energy coefficient γ 10 -10 J / m.

[0064] The boundary condition setting: the center position of the upper and lower boundaries of the matrix calculation domain is set as the needle-type breakdown phase, that is, η =1; the area electric field is set to increase at a speed of 1kV / mm·s, that is, the upper surface of the matrix calculation domain is applied with a potential of 100V / s, and the lower surface of the matrix calculation domain is grounded. By solving by the finite element method, the dielectric breakdown process of the epoxy powder coating can be obtained.

[0065] Figure 4 The dielectric breakdown simulation result of the insulating powder coating in the embodiment of the present application.

[0066] The present application also provides a device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the steps of the insulating powder coating dielectric breakdown simulation method based on the phase field method when executing the computer program.

Claims

1. A simulation method for dielectric breakdown of insulating powder coatings based on the phase-field method, characterized in that, Includes the following steps: Step 1: Construct a phase-field calculation model for dielectric breakdown of insulating powder coating; In the phase-field calculation model for dielectric breakdown of insulating powder coating, dielectric breakdown of insulating powder coating includes three states, namely breakdown phase, continuous evolution transition phase and non-breakdown phase; Step 2: Construct the principal breakdown phase field variables related to time and space. η ( r , t ), r For spatial coordinates, t For time; Step 3: Measure the relative permittivity ε of the non-breakdown phase of the insulating powder coating material. p And given the relative permittivity of the breakdown phase. ε b Based on the main breakdown phase field variables η ( r , t The spatial distribution of the relative permittivity is used to construct a distribution function that varies with spatial coordinates. ε r ( r ), the function ε r ( r The non-breakdown phase and the breakdown phase are smoothly connected through a diffusion interface; Step 4, the relative permittivity distribution function ε r ( r Substituting into the electrostatic field control equation, we obtain the components of the total electric field intensity; Step 5, introduce the total free energy of the model. F , F=F sep + F grad + F elec ,in, F sep For phase separation free energy, F grad For interface free energy, F elec It is the free energy of the electrostatic field; Step 6: The Allen-Cahn equation is modified by introducing a unit step function, which is then used as the phase field control equation. Step 7: Given the basic parameters of the phase field and electrostatic field control equations, construct boundary conditions for the phase field and electrostatic field control equations, set initial values, and determine the weak form of the phase field and electrostatic field control equations. The dielectric breakdown simulation is completed through the mutual coupling of the phase field and electrostatic field.

2. The method for simulating dielectric breakdown of insulating powder coatings based on the phase-field method according to claim 1, characterized in that, In the dielectric breakdown phase field calculation model of the insulating powder coating described in step 1, the insulating powder coating is a solid cube. The body of the solid cube is composed of a matrix and several fillers randomly distributed in the matrix. The space occupied by the several fillers is denoted as the filler calculation domain, and the space other than the filler calculation domain is denoted as the matrix calculation domain.

3. The method for simulating dielectric breakdown of insulating powder coatings based on the phase-field method according to claim 2, characterized in that, Step 2 describes the main breakdown phase field variables. η The expression for (r,t) is: 。 4. The method for simulating dielectric breakdown of insulating powder coatings based on the phase-field method according to claim 3, characterized in that, In step 3, the measurement method is as follows: first, a sample is taken from the insulating powder coating. The sample is composed of a matrix containing filler. Then, the sample is measured by a broadband dielectric spectrometer. The diffusion interface is achieved by introducing a smooth interpolation function. L ( r ) indicates that its expression is: In the formula, η ( r () represents the secondary breakdown phase field variable considering only spatial coordinates; The relative permittivity distribution function ε r ( r The expression for ) is: 。 5. The method for simulating dielectric breakdown of insulating powder coatings based on the phase-field method according to claim 4, characterized in that, The expression for the electrostatic field control equation in step 4 is as follows: In the formula, ε 0 The vacuum permittivity, For gradient operators, For electric potential, ρ is the volume charge density, and "·" is the dot product symbol; The total electric field intensity components E ( r The expression for ) is: 。 6. The method for simulating dielectric breakdown of insulating powder coatings based on the phase-field method according to claim 5, characterized in that, The phase separation free energy described in step 5 F sep The expression is: In the formula, V For the computational domain, f sep The phase separation free energy density is expressed as follows: In the formula, α The phase separation coefficient; The interface free energy F grad The expression is: In the formula, γ The gradient energy coefficient under the isotropic approximation; The electrostatic free energy F elec The expression is: In the formula, f elec It represents the electrostatic energy density.

7. The method for simulating dielectric breakdown of insulating powder coatings based on the phase-field method according to claim 6, characterized in that, The expression for the unit step function mentioned in step 6 is: In the formula, H( f elec －f critical () is a unit step function. f critical The critical energy density of the insulating powder coating material is expressed as follows: In the formula, E B This represents the critical breakdown field strength of the insulating powder coating material. The phase field control equation is as follows: In the formula, L This is a kinetic coefficient related to the interface mobility.

8. The method for simulating dielectric breakdown of insulating powder coatings based on the phase-field method according to claim 7, characterized in that, The basic parameters mentioned in step 7 include: the critical breakdown field strength of the insulating powder coating material. E B vacuum permittivity ε 0 The relative permittivity of the breakdown phase ε b Phase separation coefficient α Kinetic coefficients related to interface mobility L Gradient energy coefficient under isotropic approximation γ ; The boundary conditions mentioned are the Dirichlet boundary conditions and the Newman boundary conditions; The Dirichlet boundary conditions are as follows: in the electrostatic field, the upper surface of the matrix computational domain is at a fixed potential, and the lower surface is grounded; in the phase field, the center positions of the upper and lower surfaces of the matrix computational domain are set as the breakdown phase. The Newman boundary condition is: the matrix computational domain boundary has zero flux; The initial values ​​set are: zero potential in the matrix calculation domain and zero breakdown phase field variable; The weak form of the phase field control equation is expressed as follows: In the formula, η To break down the phase field variable, v For the test function, n For the normal component, ε p The relative permittivity of the unbroken phase. S The outer boundary of the matrix is ​​calculated; The weak form of the electrostatic field control equation is as follows: The expression for the mutual coupling of the phase field and the electrostatic field is: Dielectric breakdown simulation is achieved by coupling phase field and electrostatic field.

9. The method for simulating dielectric breakdown of insulating powder coatings based on the phase-field method according to claim 2, characterized in that, The filler is made of spherical silica, and the matrix is ​​made of epoxy resin.

10. A device, characterized in that, The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the dielectric breakdown simulation method for insulating powder coating based on the phase field method as described in any one of claims 1 to 9.

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