An insulating powder coating dielectric breakdown simulation method based on phase field method

Abstract

The application provides a dielectric breakdown simulation method for insulating powder coating based on a phase field method, and belongs to the field of phase field method and material technology. The method comprises the following steps: constructing a dielectric breakdown phase field calculation model of the insulating powder coating, constructing a main breakdown phase field variable, constructing a relative dielectric constant distribution function changing with a spatial coordinate, and solving to obtain a total electric field intensity component; introducing a model total free energy F , introducing a unit step function to modify an Allen-Cahn equation, and obtaining a phase field control equation; determining a weak form of the phase field and electrostatic field control equation, and completing dielectric breakdown simulation through mutual coupling of the phase field and electrostatic field. The model constructed by the application can not only accurately simulate the whole process of breakdown of the insulating coating under a strong electric field, but also effectively predict a critical breakdown voltage and a possible breakdown path, thereby providing a direct and quantitative tool for precise optimization and performance improvement of the 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, the experimental process is complex, time-consuming, and greatly influenced 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, lacking 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 address 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 calculates the target breakdown probability of the grid based on the material parameters and structural parameters of the composite material, uses the electric field strength and molecular interaction energy to generate target state parameters, and finally obtains the target breakdown strength value to perform Weibull distribution fitting to obtain the breakdown strength simulation method of the composite material. 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:

[0005] (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.

[0006] (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.

[0007] (3) This probabilistic 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 of micro-defects (such as the branching growth of electric trees) inside the material under the action of an electric field. Summary of the Invention

[0008] The technical problem to be solved by the present invention is that it is difficult to dynamically and continuously simulate the real-time evolution process of microscopic defects inside materials under the action of an electric field in the prior art, and it is difficult to solve the problem of the influence of microscopic parameters such as filler shape, size, and interface characteristics on the simulation model, resulting in simulation distortion.

[0009] This invention proposes a simulation method for dielectric breakdown of insulating powder coatings based on the phase-field method, comprising the following steps:

[0010] 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;

[0011] Step 2: Construct the principal breakdown phase field variables related to time and space. η ( r , t ), r For spatial coordinates, t For time;

[0012] 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;

[0013] Step 4, the relative permittivity distribution function ε r ( r Substituting these components into the electrostatic field control equation, we obtain the total electric field intensity components.

[0014] Step 5, introduce the total free energy of the model. F , F=F sep + Fgrad + F elec wherein, F sep is the free energy of phase separation, F grad is the free energy of interface, F elec is the free energy of electrostatic field;

[0015] Step 6, introducing a unit step function to modify the Allen-Cahn equation, and taking it as a phase field control equation;

[0016] 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, and completing the dielectric breakdown simulation through the mutual coupling of the phase field and electrostatic field.

[0017] 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 and recorded as a filler calculation domain, and the space other than the filler calculation domain is recorded as a matrix calculation domain.

[0018] Preferably, the expression of the main breakdown phase field variable η (r,t) in step 2 is:

[0019] .

[0020] Preferably, in step 3, the measurement is performed by first taking a sample from the insulating powder coating, which is composed of a matrix containing fillers, and then measuring the sample by a broadband dielectric spectrometer.

[0021] The diffuse interface is represented by introducing a smooth interpolation function L ( r ) whose expression is:

[0022] ;

[0023] In the formula, η ( r ) is a sub-breakdown phase field variable considering only the spatial coordinates;

[0024] The expression of the relative permittivity distribution function ε r ( r ) is:

[0025] .

[0026] Preferably, the expression of the electrostatic field control equation of step 4 is:

[0027] ;

[0028] wherein, 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;

[0029] the expression of the total electric field intensity component E ( r ) is:

[0030] .

[0031] Preferably, the expression of the phase separation free energy F sep of step 5 is:

[0032] ;

[0033] wherein, V is the computational domain, f sep is the phase separation free energy density, whose expression is:

[0034] ;

[0035] wherein, α is the phase separation coefficient;

[0036] the expression of the interfacial free energy F grad is:

[0037] ;

[0038] wherein, γ is the gradient energy coefficient under the isotropic approximation;

[0039] the expression of the electrostatic field free energy F elec is:

[0040] ;

[0041] wherein, f elec is the electrostatic energy density.

[0042] Preferably, the expression of the unit step function of step 6 is:

[0043] ;

[0044] H( f elec －f critical ) is a unit step function, f critical is the critical energy density of the insulating powder coating material, and its expression is:

[0045] ;

[0046] wherein, E B is the critical breakdown field strength of the insulating powder coating material;

[0047] The phase field control equation is:

[0048] ;

[0049] wherein, L is the dynamic coefficient related to the interfacial mobility.

[0050] Preferably, the basic parameters in step 7 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 dynamic coefficient related to the interfacial mobility L , the gradient energy coefficient under the isotropic approximation γ ;

[0051] The boundary condition is the Dirichlet boundary condition and the Neumann boundary condition;

[0052] The Dirichlet boundary condition is: in the electrostatic field, the upper surface of the matrix calculation domain is 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;

[0053] The Neumann boundary condition is: the boundary of the matrix calculation domain is zero flux;

[0054] The set initial value is: the potential in the matrix calculation domain is zero, and the breakdown phase field variable is zero;

[0055] The expression of the weak form of the phase field control equation is:

[0056] ;

[0057] wherein, ηfor the breakdown phase variable, v for the test function, n for the normal component, ε p for the relative permittivity of the unbroken phase, S for the outer boundary of the base matrix calculation domain;

[0058] The weak form expression of the electrostatic field control equation is:

[0059] ;

[0060] The expression of the phase field and the electrostatic field mutual coupling is:

[0061] ;

[0062] The dielectric breakdown simulation is completed by the phase field and the electrostatic field mutual coupling.

[0063] Preferably, the material of the filler is spherical silica, and the material of the base matrix is epoxy resin.

[0064] 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 based on the phase field method of the insulating powder coating when the computer program is executed.

[0065] Compared with the prior art, the application has the following beneficial effects:

[0066] (1) The application describes the initiation and expansion mechanism of the breakdown channel by constructing a total free energy model comprising phase separation energy, gradient energy and electrostatic energy, from the physical nature of dielectric breakdown.

[0067] (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 direct and quantitative theoretical basis for precise optimization and performance improvement of the insulating powder formulation.

[0068] (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 electrical treeing) from initiation, branching to final penetration under the action of strong electric field in real time, and realize accurate capture and visual presentation of the whole picture of the dynamic development of breakdown. BRIEF DESCRIPTION OF DRAWINGS

[0069] Figure 1 The figure is a flowchart of the method of the application.

[0070] Figure 2A structural schematic diagram of the insulating powder coating in the insulating powder coating dielectric breakdown phase field calculation model in the embodiment of the present application.

[0071] Figure 3 A curve of the relative dielectric constant of the epoxy resin at 25 DEG C.

[0072] Figure 4 A dielectric breakdown simulation result of the insulating powder coating in the embodiment of the present application. DETAILED DESCRIPTION

[0073] The present application is further described below in conjunction with the accompanying drawings and embodiments.

[0074] Figure 1 A flow chart of the method of the present application, comprising Figure 1 It can be seen that the insulating powder coating dielectric breakdown simulation method based on the phase field method comprises the following steps:

[0075] 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.

[0076] In the embodiment, the insulating powder coating in the calculation model is a solid cube, the body of 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.

[0077] In the embodiment, the material of the filler is spherical silica, and the material of the matrix is epoxy resin.

[0078] Figure 2 A structural schematic diagram of the insulating powder coating in the insulating powder coating dielectric breakdown phase field calculation model in the embodiment of the present application. By Figure 2 It can be seen that the insulating powder coating is a solid cube, the body of the solid cube 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 by this structure.

[0079] In the embodiment, the solid cube is a square cube with a side length of 100 microns. The filler is spherical silica with a diameter of 5 microns.

[0080] Step 2, constructing a main breakdown phase field variable related to time and space η (r,t), r as a spatial coordinate, t as time.

[0081] In the embodiment, the main breakdown phase field variableη The expression of (r, t) is:

[0082] .

[0083] 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 of the broken phase ε b ; based on the spatial distribution of the main broken phase field variable η ( r , t ), a relative dielectric constant distribution function ε r ( r ) varying with spatial coordinates is constructed, which is smoothly connected with the unbroken phase and the broken phase by a diffusion interface ε r ( r ).

[0084] In this embodiment, the measurement is 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 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 testing 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 phase at 25℃.

[0085] The diffusion interface is represented by introducing a smooth interpolation function L ( r ), and its expression is:

[0086] ;

[0087] In the formula, φ η ( r ) is the secondary broken phase field variable considering only the spatial coordinates.

[0088] The expression of the relative dielectric constant distribution function ε r ( r ) is:

[0089] .

[0090] Step 4, constructing the relative dielectric constant distribution function ε r ( rSubstitute the electrostatic field control equation, and get the total electric field intensity component.

[0091] In this embodiment, the expression of the electrostatic field control equation is:

[0092] ;

[0093] 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.

[0094] The expression of the total electric field intensity component E ( r ) is:

[0095] ;

[0096] Step 5, introduce the model total free energy F , F=F sep + F grad + F elec , wherein F sep is the phase separation free energy, F grad is the interface free energy, F elec is the electrostatic field free energy.

[0097] In this embodiment, the expression of the phase separation free energy F sep is:

[0098] ;

[0099] In the formula, V is the calculation domain, f sep is the phase separation free energy density, and the expression is:

[0100] ;

[0101] In the formula, α is the phase separation coefficient.

[0102] The expression of the interface free energy F grad is:

[0103] ;

[0104] γ is the gradient energy coefficient under isotropic approximation.

[0105] The free energy of the electrostatic field F elec The expression is:

[0106] ;

[0107] f elec is the electrostatic energy density.

[0108] The free energy of the phase separation F sep for driving the phase separation, the interfacial free energy F grad for adjusting the transition of the phase boundary, the free energy of the electrostatic field F elec for the electric field synergistic contribution.

[0109] Step 6, introduce the unit step function to modify the Allen-Cahn equation, and take it as the phase field control equation.

[0110] In this embodiment, the expression of the unit step function is:

[0111] ;

[0112] f elec - f critical is the unit step function, f critical is the critical energy density of the insulating powder coating material, and the expression is:

[0113] ;

[0114] E B is the critical breakdown field strength of the insulating powder coating material.

[0115] The phase field control equation is:

[0116] ;

[0117] L is the dynamic coefficient related to the interfacial mobility.

[0118] The expression of the Allen-Cahn equation is:

[0119] .​​​​​

[0120] Step 7, given the basic parameters of phase field and electrostatic field control equation, boundary conditions are constructed for phase field and electrostatic field control equation, initial values are set, and weak forms of phase field and electrostatic field control equation are determined, and dielectric breakdown simulation is completed through mutual coupling of phase field and electrostatic field.

[0121] In the embodiment, the basic parameters include: critical breakdown field strength of insulating powder coating material E B , vacuum dielectric constant ε 0 , relative dielectric constant of breakdown phase ε b , phase separation coefficient α , dynamics coefficient related to interface mobility L , gradient energy coefficient under isotropic approximation γ .

[0122] The boundary condition is a Dirichlet boundary condition and a Neumann boundary condition;

[0123] 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 be the breakdown phase;

[0124] The Neumann boundary condition is that the boundary of the matrix calculation domain is zero flux.

[0125] The set initial value is that the potential in the matrix calculation domain is zero, and the breakdown phase variable is zero.

[0126] The expression of the weak form of the phase field control equation is:

[0127] ;

[0128] In the formula, η is the breakdown phase variable, v is a test function, n is a normal component, ε p is the relative dielectric constant of the unbroken phase, S is the outer boundary of the matrix calculation domain.

[0129] The expression of the weak form of the electrostatic field control equation is:

[0130] ;

[0131] The expression of the mutual coupling of the phase field and the electrostatic field is:

[0132] ;

[0133] The dielectric breakdown simulation is completed by phase field and electrostatic field mutual coupling.

[0134] In the embodiment of the present application, the critical breakdown field strength E B Taking 25kV / mm, the relative dielectric constant of the breakdown phase ε b Taking 10 4 , the phase separation coefficient α Taking 10 6 J / m 3 , the interface mobility related kinetic coefficient L Taking 10 -7 m 2 / (s·N), the gradient energy coefficient γ Taking 10 -10 J / m.

[0135] 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, i.e. η =1; the area electric field is set to increase at a speed of 1kV / mm·s, i.e. the potential of the upper surface of the matrix calculation domain is applied at a speed of 100V / s, and the lower surface of the matrix calculation domain is grounded. The dielectric breakdown process of the epoxy powder coating can be obtained by solving by the finite element method.

[0136] Figure 4 The simulation result of the dielectric breakdown of the insulating powder coating in the embodiment of the present application.

[0137] 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 dielectric breakdown simulation method of the insulating powder coating based on the phase field method.

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 these components into the electrostatic field control equation, we obtain the total electric field intensity components. 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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