Grounding grid electric heating power multi-field coupling modeling method and system considering soil nonlinear breakdown

Abstract

The invention discloses a grounding grid electric heating power multi-field coupling modeling method and system considering soil nonlinear breakdown, and belongs to the technical field of power system grounding grids. The method comprises the following steps: establishing a three-dimensional geometric model containing a soil domain and a grounding grid conductor; defining non-linear conductivity characteristics of the soil; setting multi-physical field parameters and corresponding boundary conditions of the three-dimensional geometric model; and establishing a multi-physical field coupling control equation set including an electric field equation, a heat conduction equation and a thermal stress equation, and solving by adopting a finite element method to obtain three-dimensional space distribution data of the grounding grid under lightning current impact. According to the invention, on the basis of fully considering the nonlinear breakdown characteristic of the soil, the accurate simulation of the electric heating power multi-physical field behavior of the grounding grid under the impact current effect is realized, and the accuracy of impact impedance, potential distribution and temperature rise prediction is obviously improved.

Description

Technical Field

[0001] This invention belongs to the field of power system grounding grid safety assessment technology. Specifically, it is a grounding grid electrothermal multi-field coupling modeling method and system that considers the nonlinear breakdown characteristics of soil. It is applicable to the analysis of the electrical performance, thermal stability and mechanical stress of grounding grids under lightning current impact. Background Technology

[0002] The grounding grid is a crucial facility in power systems for ensuring equipment and personnel safety. Its performance directly affects the stable operation of electrical equipment and the effectiveness of lightning and electric shock protection. When subjected to lightning impulse current or short-circuit fault current, the grounding grid must rapidly dissipate the current into the ground through the soil. However, due to the large amplitude and steep rise of the impulse current, the soil around the grounding grid conductor experiences significant electric field enhancement and temperature rise effects, thereby triggering a complex coupling process involving multiple physical fields such as electrothermal and mechanical fields.

[0003] Most existing grounding grid modeling and analysis methods are based on the linear soil assumption, which assumes that the soil's conductivity and dielectric constant remain constant under the influence of an electric field. While this approach simplifies calculations, it neglects the nonlinear breakdown effect of soil under strong impact electric fields and high temperatures. Numerous studies and experiments have shown that: 1. Under high electric fields, soil conductivity exhibits exponential or power-law-like nonlinear growth, leading to significant differences in the discharge current distribution compared to linear models; 2. Joule heating is generated during current dissipation in the soil, causing a rapid increase in local temperature, further exacerbating soil breakdown and vaporization effects, and creating an electro-thermal positive feedback mechanism; 3. The strong current caused by lightning strikes can also cause soil expansion, contraction, and cracking, resulting in stress concentration and local discharge, exhibiting electro-thermal-mechanical coupling characteristics. Therefore, traditional grounding grid modeling methods based on equivalent resistance or simplified electromagnetic fields cannot accurately reflect the actual operating characteristics of the grounding grid under nonlinear soil breakdown conditions, leading to large deviations in impact impedance calculations and unreliable grounding safety assessment results. Summary of the Invention

[0004] To address the problem that traditional modeling methods for grounding grids under lightning current impact cannot accurately characterize the nonlinear breakdown behavior of soil and the electro-thermal-mechanical multi-field coupling effect, this invention provides a grounding grid electro-thermal-mechanical multi-field coupling modeling method and system that considers the nonlinear breakdown characteristics of soil. By constructing a three-dimensional geometric model, defining the nonlinear conductivity characteristics of soil, setting multi-physics parameters and boundary conditions, and constructing and solving the electro-thermal-mechanical multi-physics coupling control equation set, it is possible to achieve accurate simulation and visualization analysis of the electric field, temperature field, and stress field of the grounding grid under lightning current impact.

[0005] This invention adopts the following technical solution: a multi-field coupled electrothermal modeling method for grounding grids considering soil nonlinear breakdown, comprising the following steps:

[0006] 1) Establish a three-dimensional geometric model including the soil domain and the grounding grid conductor;

[0007] 2) Define the nonlinear electrical conductivity characteristics of soil;

[0008] 3) Set the multiphysics parameters and corresponding boundary conditions for the 3D geometric model;

[0009] 4) Based on steps 1) to 3), establish a set of multi-physics field coupled control equations including electric field equations, heat conduction equations and thermal stress equations, and solve them using the finite element method to obtain the three-dimensional spatial distribution data of the grounding grid under lightning current impact.

[0010] Furthermore, in step 2), the expression for the nonlinear conductivity characteristics of the soil is:

[0011]

[0012] Where σ is the nonlinear conductivity of the soil, σ0 is the initial conductivity of the soil, A is the nonlinear coefficient, and |E| represents the absolute value of the soil breakdown field strength; E b Let H() be the soil breakdown field strength threshold, and H() be the unit step function. The nonlinear conductivity characteristics of soil are described by a piecewise exponential function, which accurately characterizes soil conductivity in the low field strength region (|E|≤E). b The gradual change in conductivity and in the high field strength region (|E|>E) b The breakdown saturation characteristics of ).

[0013] Furthermore, in step 2), the nonlinear electrical conductivity characteristics of the soil are loaded using the material properties module of the COMSOL Multiphysics software.

[0014] Furthermore, in step 2), the nonlinear electrical conductivity characteristics of the soil are embedded as a key input parameter into the material library of the COMSOL Multiphysics software for dynamic invocation during the calculation process to dynamically respond to changes in the electric field.

[0015] Furthermore, in step 3), the multi-physics parameters include the soil nonlinear conductivity of the grounding grid conductor, the relative permittivity of the soil, and the constant-pressure heat capacity.

[0016] Furthermore, in step 3), the boundary conditions include:

[0017] The current injection point is selected at the end of the grounding grid conductor;

[0018] Lightning current excitation involves injecting lightning current into a section of the grounding grid conductor;

[0019] The volumetric heat source Q1, according to the Joule heat power formula Q1 = J2 ·ρ is generated, where J is the current density and ρ is the soil resistivity;

[0020] Mechanical fixed constraint points are applied at the four corners of the grounding grid to suppress rigid displacement;

[0021] The spatial coordinates of the current injection point and the mechanically fixed constraint point are correlated through parametric modeling.

[0022] Further, in step 4), the process of establishing the multi-physics field coupled control equation set is as follows: introduce the nonlinear function of soil conductivity-electric field strength to construct the electric field control equation; combine the Joule heating effect and the heat conduction equation to describe the temperature rise distribution under the impact of lightning current; further couple thermal expansion with mechanical stress to form the electrothermal multi-physics field coupled control equation set.

[0023] Furthermore, in step 4), the set of electrothermal-mechanical multiphysics coupling control equations is as follows:

[0024] Electric field governing equations:

[0025]

[0026] In the formula, J is the curl operator, H is the magnetic field strength; c =σ(T)E is the current density, σ(T)=σ0[1+β σ ΔT] represents the temperature-dependent nonlinear conductivity of the soil, σ0 represents the initial conductivity of the soil, and β σ The temperature coefficient representing electrical conductivity; ε(T)=ε0[1+β ε ΔT] is the temperature-dependent dielectric constant, ε0 represents the vacuum dielectric constant, and β ε The temperature coefficient represents the dielectric constant; ΔT is the temperature rise.

[0027] Heat conduction equation:

[0028]

[0029] In the formula, Here, T is the gradient operator, E is the temperature, and E is the electric field strength; the heat source term Q2 = σ(T)|E| 2 Indicates Joule heating; ρ a (T), c p (T) and k(T) are temperature-dependent material property parameters, namely material density, specific heat capacity and thermal conductivity, respectively;

[0030] Thermal stress equation:

[0031] σ th =Y(T)·α(T)·ΔT

[0032] In the formula, Y(T)=E0[1+β E ΔT] is the temperature-dependent elastic modulus, E0 represents the initial elastic modulus, and β E The temperature coefficient representing the elastic modulus; α(T)=α0[1+β α ΔT] is the temperature-dependent coefficient of thermal expansion, α0 represents the initial coefficient of thermal expansion, and β α The temperature coefficient represents the coefficient of thermal expansion.

[0033] Further, in step 4), the three-dimensional spatial distribution data includes: the potential gradient cloud map and current density vector field output by the electric field control equation; the location of the highest temperature rise output by the heat conduction equation and its evolution curve over time; and the coordinates and stress values ​​of the Von Mises stress concentration region output by the thermal stress equation.

[0034] The present invention also employs another technical solution: a grounding grid electrothermal multi-field coupling modeling system considering soil nonlinear breakdown, comprising:

[0035] The three-dimensional geometric model building unit is used to build a three-dimensional geometric model that includes the soil domain and the grounding grid conductor;

[0036] Electrical conductivity characteristic definition unit: used to define the nonlinear electrical conductivity characteristics of soil;

[0037] Parameter and boundary bar setting unit: used to set the multiphysics parameters and corresponding boundary conditions of the 3D geometric model;

[0038] Establishment of Coupled Control Equations Unit: Based on the aforementioned unit, a multi-physics field coupled control equation set including electric field equation, heat conduction equation and thermal stress equation is established, and solved using the finite element method to obtain the three-dimensional spatial distribution data of the grounding grid under lightning current impact.

[0039] Through the above-mentioned technical solution, this invention, based on fully considering the nonlinear breakdown characteristics of soil, achieves accurate simulation of the electro-thermal-mechanical multi-physics behavior of grounding grids under the action of impulse current (lightning current or short-circuit current), significantly improving the accuracy of impulse impedance, potential distribution and temperature rise prediction. At the same time, it reveals the influence mechanism of multi-field coupling effect on grounding grid performance, providing reliable theoretical support and data support for its optimized design and safe operation. Attached Figure Description

[0040] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0041] Figure 1 This is a flowchart of a multi-field coupling modeling method for grounding grids considering nonlinear soil breakdown, according to the present invention.

[0042] Figure 2 This is a nonlinear curve of soil electrical conductivity according to the present invention;

[0043] Figure 3 This is a temperature distribution diagram of the grounding grid conductor according to the present invention;

[0044] Figure 4 This is a potential distribution diagram of the grounding grid conductors according to the present invention;

[0045] Figure 5 This is a current density distribution diagram of the grounding grid conductor according to the present invention;

[0046] Figure 6 This is a Von Mises stress distribution diagram of the grounding grid conductor of the present invention;

[0047] Figure 7 This is a diagram illustrating the composition of a grounding grid electrothermal multi-field coupling modeling system that considers soil nonlinear breakdown according to the present invention. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, 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. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0049] Example 1

[0050] This embodiment presents a multi-field coupled electro-thermal modeling method for grounding grids that considers soil nonlinear breakdown. Figure 1 As shown, the steps are as follows:

[0051] 1) Establish a three-dimensional geometric model including the soil domain and the grounding grid conductor;

[0052] 2) Define the nonlinear electrical conductivity characteristics of soil;

[0053] 3) Set the multiphysics parameters and corresponding boundary conditions for the 3D geometric model;

[0054] 4) Based on steps 1) to 3), establish a set of multi-physics field coupled control equations including electric field equations, heat conduction equations and thermal stress equations, and solve them using the finite element method to obtain the three-dimensional spatial distribution data of the grounding grid under lightning current impact.

[0055] Specifically, in step 1, the soil zone has dimensions of 16m × 16m × 0.2m; the grounding grid conductor has a grid structure with dimensions of 10m × 10m × 0.3m and is made of galvanized Q235 steel, in order to fully reflect the geometric characteristics of the actual grounding grid and ensure the integrity of the calculation area.

[0056] Specifically, in step 2), the expression for the nonlinear electrical conductivity characteristics of the soil is:

[0057]

[0058] Where σ is the nonlinear conductivity of the soil, σ0 = 0.01 S / m is the initial conductivity of the soil, and A = 1 × 10⁻⁶. -4 E is a nonlinear coefficient. b =300000V / m is the soil breakdown field strength threshold, |E| represents the absolute value of the soil breakdown field strength; H() is the unit step function.

[0059] The nonlinear electrical conductivity characteristics of the soil are described by a piecewise exponential function, which accurately characterizes the soil in the low field strength region (|E|≤E). b The gradual change in conductivity and in the high field strength region (|E|>E) b The breakdown saturation characteristics of ).

[0060] The nonlinear electrical conductivity characteristics of the soil were loaded using the material properties module of COMSOL Multiphysics software, and the nonlinear electrical conductivity characteristic curve of the soil is shown below. Figure 2 As shown, the nonlinear electrical conductivity of soil is embedded as a key input parameter into the material library of the COMSOL Multiphysics software for dynamic invocation during the calculation process, in order to dynamically respond to changes in the electric field.

[0061] Specifically, in step 3), the multi-physics parameters include the soil nonlinear conductivity of the grounding grid conductor, the relative permittivity of the soil, and the constant-pressure heat capacity.

[0062] The boundary conditions include:

[0063] The current injection point is selected at the end of the grounding grid conductor;

[0064] Lightning current excitation involves injecting a lightning current with an amplitude of 2000A into a section of the grounding grid conductor.

[0065] The volumetric heat source Q1, according to the Joule heat power formula Q1 = J 2 ·ρ is generated, where J is the current density and ρ is the soil resistivity;

[0066] Mechanical fixed constraint points are applied at the four corners of the grounding grid to suppress rigid displacement;

[0067] The spatial coordinates of the current injection point and the mechanically fixed constraint point are correlated through parametric modeling.

[0068] Specifically, in step 4), the process of establishing the multi-physics field coupled control equation set is as follows: introduce the nonlinear function of soil conductivity-electric field strength to construct the electric field control equation; combine the Joule heating effect and the heat conduction equation to describe the temperature rise distribution under the action of lightning current impact; further couple thermal expansion with mechanical stress to form the electrothermal multi-physics field coupled control equation set.

[0069] The aforementioned set of electrothermal-mechanical multiphysics coupling control equations is as follows:

[0070] Electric field governing equations:

[0071]

[0072] In the formula, J is the curl operator, H is the magnetic field strength; c =σ(T)E is the current density, σ(T)=σ0[1+β σ ΔT] represents the temperature-dependent nonlinear conductivity of the soil, σ0 represents the initial conductivity of the soil, and β σ The temperature coefficient representing electrical conductivity; ε(T)=ε0[1+β ε ΔT] is the temperature-dependent dielectric constant, ε0 represents the vacuum dielectric constant, and β ε The temperature coefficient represents the dielectric constant; ΔT is the temperature rise.

[0073] Heat conduction equation:

[0074]

[0075] In the formula, Here, T is the gradient operator, E is the temperature, and E is the electric field strength; the heat source term Q2 = σ(T)|E| 2 Indicates Joule heating; ρ a (T), c p (T) and k(T) are temperature-dependent material property parameters, namely material density, specific heat capacity and thermal conductivity, respectively;

[0076] Thermal stress equation:

[0077] σ th =Y(T)·α(T)·ΔT

[0078] In the formula, Y(T)=E0[1+β E ΔT] is the temperature-dependent elastic modulus, E0 represents the initial elastic modulus, and β E The temperature coefficient representing the elastic modulus; α(T)=α0[1+β α ΔT] is the temperature-dependent coefficient of thermal expansion, α0 represents the initial coefficient of thermal expansion, and β α The temperature coefficient represents the coefficient of thermal expansion.

[0079] The aforementioned three-dimensional spatial distribution data includes: the potential gradient cloud map and current density vector field output by the electric field control equation, and the potential distribution of the grounding grid conductor, as shown in the figure. Figure 4 As shown, the current density distribution of the grounding grid conductor is as follows: Figure 5 As shown; the location of the highest temperature rise output by the heat conduction equation and its evolution curve over time; the temperature distribution of the grounding grid conductor is shown in the figure. Figure 3 As shown; the coordinates and stress values ​​of the Von Mises stress concentration region output by the thermal stress equation; the Von Mises stress distribution is as follows. Figure 6 As shown.

[0080] All output data are used to generate visualization reports with grid-level precision of less than 0.1m resolution, providing quantitative basis for the design and safety assessment of grounding grids.

[0081] Example 2

[0082] This embodiment presents a multi-field coupled electrothermal modeling system for grounding grids that considers soil nonlinear breakdown. Figure 7 As shown, it includes:

[0083] The three-dimensional geometric model building unit is used to build a three-dimensional geometric model that includes the soil domain and the grounding grid conductor;

[0084] Electrical conductivity characteristic definition unit: used to define the nonlinear electrical conductivity characteristics of soil;

[0085] Parameter and boundary bar setting unit: used to set the multiphysics parameters and corresponding boundary conditions of the 3D geometric model;

[0086] Establishment of Coupled Control Equations Unit: Based on the aforementioned unit, a multi-physics field coupled control equation set including electric field equation, heat conduction equation and thermal stress equation is established, and solved using the finite element method to obtain the three-dimensional spatial distribution data of the grounding grid under lightning current impact.

[0087] The specific functions and examples of each unit in the grounding grid electrothermal multi-field coupling modeling system of the present invention can be found in the relevant descriptions of the corresponding steps in the above method embodiments, and will not be repeated here.

[0088] As described above, these are merely preferred embodiments of the present invention and are not intended to limit the present invention in any way. Any simple modifications, alterations, or equivalent structural changes made to the above embodiments based on the technical essence of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A multi-field coupled electro-thermal modeling method for grounding grids considering nonlinear soil breakdown, characterized in that, Including the following steps: 1) Establish a three-dimensional geometric model including the soil domain and the grounding grid conductor; 2) Define the nonlinear electrical conductivity characteristics of soil; 3) Set the multiphysics parameters and corresponding boundary conditions for the 3D geometric model; 4) Based on steps 1) to 3), establish a set of multi-physics field coupled control equations including electric field equations, heat conduction equations and thermal stress equations, and solve them using the finite element method to obtain the three-dimensional spatial distribution data of the grounding grid under lightning current impact.

2. The grounding grid electrothermal multiphysics coupling modeling method according to claim 1, characterized in that, In step 2), the expression for the nonlinear conductivity characteristics of soil is: Where σ is the nonlinear conductivity of the soil, σ0 is the initial conductivity of the soil, A is the nonlinear coefficient, and |E| represents the absolute value of the soil breakdown field strength; E b H is the soil breakdown field strength threshold, and H() is the unit step function.

3. The grounding grid electrothermal multiphysics coupling modeling method according to claim 2, characterized in that, In step 2), the nonlinear electrical conductivity characteristics of the soil are loaded using the material properties module of the COMSOL Multiphysics software.

4. The grounding grid electrothermal multiphysics coupling modeling method according to claim 3, characterized in that, In step 2), the nonlinear electrical conductivity characteristics of the soil are embedded as a key input parameter into the material library of the COMSOL Multiphysics software for dynamic calling during the calculation process.

5. The method for coupled electro-thermal-physical multi-physics modeling of grounding grids according to claim 1, characterized in that, In step 3), the multi-physics parameters include the soil nonlinear conductivity of the grounding grid conductor, the relative permittivity of the soil, and the constant-pressure heat capacity.

6. The method for coupled electro-thermal-physical multi-physics modeling of grounding grids according to claim 1, characterized in that, In step 3), the boundary conditions include: The current injection point is selected at the end of the grounding grid conductor; Lightning current excitation involves injecting lightning current into a section of the grounding grid conductor; The volumetric heat source Q1, according to the Joule heat power formula Q1 = J 2 ·ρ is generated, where J is the current density and ρ is the soil resistivity; The mechanical fixed constraint points are the fixed constraint points applied at the four corners of the grounding grid; The spatial coordinates of the current injection point and the mechanically fixed constraint point are correlated through parametric modeling.

7. The grounding grid electrothermal multiphysics coupling modeling method according to claim 1, characterized in that, In step 4), the process of establishing the multi-physics field coupled control equation set is as follows: introduce the nonlinear function of soil conductivity-electric field strength to construct the electric field control equation; combine the Joule heating effect and the heat conduction equation to describe the temperature rise distribution under the action of lightning current impact; further couple thermal expansion with mechanical stress to form the electrothermal multi-physics field coupled control equation set.

8. The method for coupled electro-thermal-physical multi-physics modeling of grounding grids according to claim 7, characterized in that, In step 4), the set of electrothermal-mechanical multiphysics coupling control equations is as follows: Electric field governing equations: In the formula, J is the curl operator, H is the magnetic field strength; c =σ(T)E is the current density, σ(T)=σ0[1+β σ ΔT] represents the temperature-dependent nonlinear conductivity of the soil, σ0 represents the initial conductivity of the soil, and β σ The temperature coefficient representing electrical conductivity; ε(T)=ε0[1+β ε ΔT] is the temperature-dependent dielectric constant, ε0 represents the vacuum dielectric constant, and β ε The temperature coefficient represents the dielectric constant; ΔT is the temperature rise. Heat conduction equation: In the formula, Here, T is the gradient operator, E is the temperature, and E is the electric field strength; the heat source term Q2 = σ(T)|E| 2 Indicates Joule heating; ρ a (T), c p (T) and k(T) are temperature-dependent material property parameters, namely material density, specific heat capacity and thermal conductivity, respectively; Thermal stress equation: s th =Y(T)·α(T)·ΔT In the formula, Y(T)=E0[1+β E ΔT] represents the temperature-dependent elastic modulus, E0 represents the initial elastic modulus, and β E The temperature coefficient representing the elastic modulus; α(T)=α0[1+β α ΔT] is the temperature-dependent coefficient of thermal expansion, α0 represents the initial coefficient of thermal expansion, and β α The temperature coefficient represents the coefficient of thermal expansion.

9. The method for coupled electro-thermal-physical multi-physics modeling of grounding grids according to claim 1, characterized in that, In step 4), the three-dimensional spatial distribution data includes: the potential gradient cloud map and current density vector field output by the electric field equation; the location of the highest temperature rise output by the heat conduction equation and its evolution curve over time; and the coordinates and stress values ​​of the Von Mises stress concentration region output by the thermal stress equation.

10. A multi-field coupled electrothermal-electrical modeling system for grounding grids considering nonlinear soil breakdown, characterized in that, include: The three-dimensional geometric model building unit is used to build a three-dimensional geometric model that includes the soil domain and the grounding grid conductor; Electrical conductivity characteristic definition unit: used to define the nonlinear electrical conductivity characteristics of soil; Parameter and boundary condition setting unit: used to set the multiphysics parameters and corresponding boundary conditions of the 3D geometric model; The coupled control equation set establishment unit: Based on the aforementioned three-dimensional geometric model establishment unit, conductivity characteristic definition unit, and parameter and boundary condition setting unit, a multi-physics field coupled control equation set including electric field equation, heat conduction equation, and thermal stress equation is established and solved using the finite element method to obtain the three-dimensional spatial distribution data of the grounding grid under lightning current impact.

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