A simulation method for explosion and breakdown of a three-pillar insulator of UHV GIL

Abstract

The present invention discloses a simulation method for the explosion and breakdown of a three-pillar insulator of UHV GIL: measuring and obtaining the parameters of epoxy resin / aluminum oxide composite materials; establishing a geometric model of the three-pillar insulator; establishing the electric field, stress field, phase field and their coupled control equations; iteratively solving the electric field, stress field, phase field and their coupled control equations within the region of the geometric model of the three-pillar insulator until a penetrating breakdown phase channel is formed between the high-voltage conductor and the grounded enclosure or the maximum simulation time is reached; obtaining the evolution process of explosion and breakdown, including the electric field distribution, stress distribution and breakdown channel morphology of the three-pillar insulator at different times. The present invention considers the problem of simulating the explosion and breakdown of the three-pillar insulator under electrical and mechanical loads by using the phase field model, and can more efficiently and accurately predict the explosion and breakdown morphology.

Description

Technical Field

[0001] The present invention belongs to the field of computational electro - mechanics, and more specifically, relates to a simulation method for the explosion and breakdown of three - pillar insulators in extra - high - voltage GILs. Background Art

[0002] Gas - insulated transmission lines (GILs) are metal - encapsulated power transmission equipment and are widely used in power systems due to their high reliability, strong environmental adaptability, and no secondary pollution. The three - pillar insulators widely used in GILs mainly play the roles of insulation and support, and their insulation performance largely determines the safety and stability of GILs. However, in recent years, the three - pillar insulators have frequently experienced breakdown and explosion failures during operation, seriously threatening the safety of the entire power transmission system. During operation, the three - pillars mainly bear strong electric fields and complex mechanical stresses. Under extreme electrical and mechanical loads, mechanical explosion and dielectric breakdown of the three - pillar insulators are the main forms of their failure. Existing experiments have shown that the explosion and breakdown behavior of insulating materials under electrical and mechanical stresses is very complex. Therefore, simulating the explosion and breakdown behavior of three - pillar insulators under electrical and mechanical loads has important scientific significance and engineering application value for studying their failure mechanisms, as well as for the life assessment and optimal design of three - pillar insulators. Summary of the Invention

[0003] To solve the above problems, the present invention proposes a simulation method for the explosion and breakdown of three - pillar insulators in extra - high - voltage GILs, which considers the problem of simulating the explosion and breakdown of three - pillar insulators under electrical and mechanical loads using the phase - field model and can more efficiently and accurately predict the explosion and breakdown morphology.

[0004] The object of the present invention is achieved through the following technical solutions.

[0005] The simulation method for the explosion and breakdown of three - pillar insulators in extra - high - voltage GILs of the present invention includes the following steps:

[0006] Step 1: Measure and obtain material parameters

[0007] Perform uniaxial tensile and broadband dielectric spectroscopy tests on the three - pillar insulators using epoxy resin / aluminum oxide composites to obtain epoxy resin / aluminum oxide composite material parameters, including: the elastic modulus Y of the non - breakdown phase of the epoxy resin / aluminum oxide composite p , the Poisson's ratio mu of the epoxy resin / aluminum oxide composite, the tensile strength σ of the epoxy resin / aluminum oxide composite p , the relative dielectric constant ε of the non - breakdown phase of the epoxy resin / aluminum oxide composite p ;

[0008] Step 2: Establish a geometric model of the three - pillar insulator

[0009] Based on the COMOSL finite element software, a geometric model of the 1100 kV HVAC-GIL three-pillar insulator is established, and the mesh generation of the three-pillar insulator geometric model is carried out. Among them, the three-pillar insulator geometric model includes a high-voltage conductor, three-pillar insulators, and a shell embedded coaxially from the inside out. Metal inserts are provided between the three ends of the three-pillar insulators and the shell, and initial defects are set inside the three-pillar insulators.

[0010] Step 3: Establish the control equations for the electric field, stress field, phase field, and their coupling

[0011] ① Establish the electric field control equation

[0012] The electric field intensity is solved according to the Poisson equation of the electrostatic field:

[0013]

[0014]

[0015] In the formula, ε r (r, t) is the relative permittivity of the three-pillar insulator material; E(r, t) is the electric field intensity, kV / mm; is the electric potential, kV; r is the position variable; t is the time variable;

[0016] Initial boundary conditions: The potential of the high-voltage conductor is set to 1100 kV, and the shell is grounded;

[0017] ② Establish the stress field control equation

[0018] Assume that the three-pillar insulator material is a linear elastic material, and the stress distribution is solved according to Hooke's law:

[0019] σ(r, t) = Y(r, t)·ν(r, t)

[0020] T(r, t) = G(r, t)·τ(r, t)

[0021] In the formula, σ(r, t) is the normal stress, Pa; T(r, t) is the shear stress, Pa; ν(r, t) and τ(r, t) are the elastic deformations under normal stress and shear stress respectively; Y(r, t) is the elastic modulus of the three-pillar insulator material, Pa; G(r, t) is the shear modulus of the three-pillar insulator material, Pa;

[0022] Initial boundary conditions: The high-voltage conductor is subjected to gravity, and the metal insert is set as a fixed constraint;

[0023] ③ Establish the phase field control equation

[0024]

[0025] where H(η - η c ) is the Heaviside unit step function; when η = 1, the three - pillar insulator material is regarded as the non - breakdown phase; when η = 0, the three - pillar insulator material is regarded as the breakdown phase; η c is a constant;

[0026]

[0027] where L0 is the kinetic coefficient representing the damage development rate; P is a variable, taking values 1 or 0. When breakdown occurs in the grid, P = 1, and when no breakdown occurs in the grid of the three - pillar insulator geometric model, P = 0; W t is the total energy, Pa. The phase - change process is energy - driven. Considering the influence of the electric field and mechanical stress on the breakdown process, the total energy W t in the phase - field control equation is expressed as follows:

[0028] W t = W ele + W mec

[0029] where W ele is the electrostatic energy, Pa; W mec is the strain energy, Pa;

[0030] Assuming that the three - pillar insulator material is a linear dielectric with a dielectric constant, W ele is given by the following formula:

[0031]

[0032] where ε0 is the relative dielectric constant of vacuum;

[0033] The strain energy W mec depends on the maximum value of the normal strain energy W mec1 and the shear strain energy W mec2 , which is expressed as:

[0034] W mec = max(W mec1 , W mec2 )

[0035]

[0036]

[0037] W c is the critical breakdown energy, Pa, representing the energy required for the destruction of the three - pillar insulator material, and is expressed as:

[0038]

[0039] In order to determine whether breakdown occurs within the geometric model grid of the three-pillar insulator, the following equation is proposed:

[0040] P = (R n ≥ 0.5·d)·(R n ≤ -0.5·d)

[0041] d = (1 - exp(-(W t / W c )) 2 ))

[0042] In the formula, R n is a random number between -0.5 and 0.5; d represents the failure probability and follows the Weibull distribution;

[0043]

[0044] In the formula, Δt is the time step;

[0045] When η > η c , H(η - η c ) = 1, the phase field control equation is described as:

[0046]

[0047] When η c < η < 1, H(η - η c ) = 0, the phase field control equation is described as:

[0048]

[0049] Initial boundary condition: η is set to 1 in the initial defect area of the three-pillar insulator and 0 in other complete phase areas;

[0050] ④ Establish the electric field-stress field-phase field coupling equation

[0051] ε r (r, t) = (4η 3 - 3η 4 )ε b + [(1 - (4η 3 - 3η 4 )]ε p

[0052] Among them, ε b is the relative permittivity of the breakdown phase;

[0053] Y(r, t) = Y p ·Y b / ((Y p - Y b )·η 4 + Yb )

[0054] Among them, Y b is the elastic modulus of the breakdown phase;

[0055] G(r,t) = Y(r,t) / (2×(1 + mu))

[0056] Step 4: Iterative solution of the governing equations

[0057] Set the time step and the maximum simulation time, and iteratively solve the equations in Step 3 within the geometric model region of the three - pillar insulator until a through - breakdown phase channel is formed between the high - voltage conductor and the grounded shell or the maximum simulation time is reached;

[0058] Step 5: Obtain the explosion - breakdown evolution process, including the electric field distribution, stress distribution, and breakdown channel morphology of the three - pillar insulator at different times.

[0059] Compared with the prior art, the beneficial effects brought by the technical solution of the present invention are:

[0060] The present invention modifies the existing dynamic phase - field simulation model, and for the first time proposes a simulation of the phase - field evolution process of insulator explosion - breakdown under the combined action of electrical and mechanical loads, which can effectively obtain the influence laws of electrical and mechanical loads on explosion - breakdown. Compared with the traditional phase - field model, the present invention greatly shortens the calculation time and efficiently solves the phase - field model. Moreover, the implementation process of the present invention is simple, highly practical, highly flexible, and can be widely promoted. Description of the drawings

[0061] Figure 1 is the flow chart of the simulation method for explosion - breakdown of the three - pillar insulator of UHV GIL of the present invention.

[0062] Figure 2 is the geometric structure diagram of the three - pillar insulator of the present invention.

[0063] Figure 3 is the electric field distribution diagram of the three - pillar insulator of the present invention.

[0064] Figure 4 is the stress field distribution diagram of the three - pillar insulator of the present invention.

[0065] Figure 5 is the breakdown evolution diagram of the three - pillar insulator of the present invention; among them,

[0066] (a) t = 5000s, (b) t = 10000s, (c) t = 12000s, (d) t = 13000s, (e) t = 13500s, (f) t = 14000s.

[0067] Reference numerals: 1 - three - pillar insulator, 2 - housing, 3 - high - voltage conductor, 4 - metal insert, 5 - initial defect. Detailed implementation mode

[0068] The present invention will be further described below with reference to the accompanying drawings.

[0069] The present invention proposes a simulation method for the explosion and breakdown of a three - pillar insulator of UHV GIL. Under the framework of the dielectric phase - field theory, a phase - field model is constructed to describe the evolution of the explosion and breakdown of the three - pillar insulator under the action of electrical and mechanical loads. Based on this model, the explosion and breakdown morphology of the three - pillar insulator under extreme electrical and mechanical loads is obtained, and the evolution law of the explosion and breakdown inside the three - pillar insulator under the action of electrical and mechanical loads is explored.

[0070] The simulation method for the explosion and breakdown of the three - pillar insulator of UHV GIL of the present invention, as Figure 1 shown, the specific implementation process includes the following steps:

[0071] Step 1: Measure and obtain material parameters

[0072] Perform uniaxial tensile and broadband dielectric spectroscopy tests on the three - pillar insulator with epoxy resin / aluminum oxide composite material respectively to obtain the parameters of the epoxy resin / aluminum oxide composite material, including: the elastic modulus Y of the non - breakdown phase of the epoxy resin / aluminum oxide composite material p (for example, Y p is 11290 MPa), the Poisson's ratio mu of the epoxy resin / aluminum oxide composite material (for example, mu is 0.4), the tensile strength σ of the epoxy resin / aluminum oxide composite material p (for example, σ p is 70 MPa), and the relative dielectric constant ε of the non - breakdown phase of the epoxy resin / aluminum oxide composite material p (for example, ε p is 5.5).

[0073] Step 2: Establish a geometric model of the three - pillar insulator

[0074] Based on the COMOSL finite - element software, establish a geometric model of the 1100 kV HVAC - GIL three - pillar insulator, and perform mesh division on the geometric model of the three - pillar insulator based on the COMOSL finite - element software for finite - element calculation. Among them, the geometric model of the three - pillar insulator includes a high - voltage conductor 3, a three - pillar insulator 1, and a housing 2 embedded coaxially from the inside to the outside in sequence. Metal inserts 4 are arranged between the three ends of the three - pillar insulator 1 and the housing 2, and an initial defect 5 is arranged inside the three - pillar insulator 1, as Figure 2 shown. Among them, the high - voltage conductor 3 is set as a hollow structure.

[0075] Step 3: Establish the electric field, stress field, phase field and their coupled control equations

[0076] ① Establish the electric field control equation

[0077] The electric field control equation is used to describe the electric field distribution. The electric field strength can be solved according to the Poisson equation of the electrostatic field:

[0078]

[0079]

[0080] where ε r (r, t) is the relative permittivity of the three-pillar insulator material; E(r, t) is the electric field strength, kV / mm; is the electric potential, kV; r is the position variable; t is the time variable.

[0081] Initial boundary conditions: The potential of the high-voltage conductor is set to 1100 kV, and the outer shell is grounded.

[0082] ② Establish the stress field control equation

[0083] The stress field control equation is used to describe the stress distribution. Assuming that the three-pillar insulator material is a linear elastic material, the stress distribution can be solved according to Hooke's law:

[0084] σ(r, t) = Y(r, t)·ν(r, t)

[0085] T(r, t) = G(r, t)·τ(r, t)

[0086] where σ(r, t) is the normal stress, Pa; T(r, t) is the shear stress, Pa; ν(r, t) and τ(r, t) are the elastic deformations under normal stress and shear stress respectively; Y(r, t) is the elastic modulus of the three-pillar insulator material, Pa; G(r, t) is the shear modulus of the three-pillar insulator material, Pa.

[0087] Initial boundary conditions: The high-voltage conductor is subjected to gravity, and the metal insert is set as a fixed constraint.

[0088] ③ Establish the phase field control equation, which is used to describe the breakdown phase and non-breakdown phase distributions:

[0089]

[0090] where H(η - η c ) is the Heaviside unit step function; when η = 1, the three-pillar insulator material is regarded as the non-breakdown phase; when η = 0, the three-pillar insulator material is regarded as the breakdown phase; η c is a constant, which can be 0.01.

[0091]

[0092]

[0093] In the formula, Δt is the time step and can be set to 100 s; L0 is the kinetic coefficient representing the damage development rate and can be set to 0.001 s -1 ; P is a variable with values of 1 or 0. When breakdown occurs within the grid, P = 1, and when no breakdown occurs within the grid of the three-pillar insulator geometric model, P = 0; W t is the total energy, Pa; W c is the critical breakdown energy, Pa;

[0094] The phase transition process is energy-driven. Considering the influence of the electric field and mechanical stress on the breakdown process, the total energy W in the phase field control equation t is expressed as follows:

[0095] W t = W ele + W mec

[0096] where W ele is the electrostatic energy, Pa; W mec is the strain energy, Pa.

[0097] Assume that the three-pillar insulator material is a linear dielectric with a dielectric constant. W ele is given by the following formula:

[0098]

[0099] where ε0 is the relative dielectric constant of vacuum.

[0100] The strain energy W mec depends on the maximum values of the normal strain energy W mec1 and the shear strain energy W mec2 and is expressed as:

[0101] W mec = max(W mec1 , W mec2 )

[0102]

[0103]

[0104] The critical breakdown energy W c represents the energy required for the failure of the three-pillar insulator material and can be expressed as:

[0105]

[0106] To determine whether breakdown occurs within the grid of the three-pillar insulator geometric model, the following equation is proposed:

[0107] P = (R n ≥ 0.5·d)·(R n ≤ -0.5·d)

[0108] d = (1 - exp(-(W t / W c )) 2 ))

[0109] In the formula, R n is a random number between -0.5 and 0.5; d represents the failure probability and follows the Weibull distribution.

[0110] When η > η c , H(η - η c ) = 1, the phase-field control equation is described as:

[0111]

[0112] When η c < η < 1, H(η - η c ) = 0, the phase-field control equation is described as:

[0113]

[0114] Initial boundary condition: η is set to 1 in the initial defect area of the three-pillar insulator and 0 in other complete phase areas.

[0115] ④ Establish the electric field-stress field-phase field coupling equation

[0116] ε r (r, t) = (4η 3 - 3η 4 )ε b + [(1 - (4η 3 - 3η 4 )]ε p

[0117] Among them, ε b is the relative permittivity of the breakdown phase and can be set to 1000.

[0118] Y(r, t) = Y p ·Y b / ((Y p - Y b )·η 4 + Y b )

[0119] Among them, Y bis the elastic modulus of the breakdown phase, set to 1 Mpa.

[0120] G(r,t) = Y(r,t) / (2×(1 + mu))

[0121] Step Four: Iteratively solve the governing equations

[0122] Set the time step and the maximum simulation time. Using the parameters of the epoxy resin / aluminum oxide composite material obtained in Step One, iteratively solve each equation in Step Three within the geometric model region of the three-pillar insulator until a continuous breakdown phase channel is formed between the high-voltage conductor and the grounded enclosure or the maximum simulation time is reached. The time step can be set to 100 s, and the maximum simulation time can be set to 20,000 s.

[0123] Step Five: Obtain the explosion breakdown evolution process, including the electric field distribution, stress distribution, and breakdown channel morphology of the three-pillar insulator at different times. For example Figures 3 to 5 as shown.

[0124] Although the functions and working processes of the present invention have been described above in conjunction with the accompanying drawings, the present invention is not limited to the above specific functions and working processes. The above specific embodiments are merely illustrative and not restrictive. Under the inspiration of the present invention, those of ordinary skill in the art can also make many forms without departing from the spirit of the present invention and the scope protected by the claims. These all fall within the protection scope of the present invention.

Claims

1. A simulation method for the explosion and breakdown of a three-pillar insulator of UHV GIL, characterized in that, It includes the following steps: Step 1: Measure and obtain material parameters The three-pillar insulators were respectively subjected to uniaxial tension and broadband dielectric spectroscopy tests using epoxy resin / aluminum oxide composites to obtain the parameters of the epoxy resin / aluminum oxide composites, including: the elastic modulus Y of the non-breakdown phase of the epoxy resin / aluminum oxide composites p , the Poisson's ratio mu of the epoxy resin / aluminum oxide composites, and the tensile strength σ of the epoxy resin / aluminum oxide composites p , the relative dielectric constant ε of the non-breakdown phase of the epoxy resin / aluminum oxide composites p ; Step 2: Establish a geometric model of a three-pillar insulator Based on the COMOSL finite element software, establish a geometric model of a 1100kV HVAC-GIL three-pillar insulator and perform mesh division on the geometric model of the three-pillar insulator. Among them, the geometric model of the three-pillar insulator includes a high-voltage conductor, three-pillar insulators, and a shell embedded coaxially from the inside to the outside. Metal inserts are provided between the three ends of the three-pillar insulator and the shell, and initial defects are provided inside the three-pillar insulator; Step 3: Establish electric field, stress field, phase field and their coupled control equations ① Establish the electric field control equation The electric field intensity is solved according to the Poisson equation of the electrostatic field: where ε r (r, t) is the relative permittivity of the three-pillar insulator material; E(r, t) is the electric field strength, kV / mm; is the electric potential, kV; r is the position variable; t is the time variable; Initial boundary conditions: The potential of the high-voltage conductor is set to 1100kV, and the shell is grounded; ② Establish the stress field control equation Assume that the material of the three-pillar insulator is a linear elastic material, and the stress distribution is solved according to Hooke's law: σ(r,t) = Y(r,t)·ν(r,t) T(r,t) = G(r,t)·τ(r,t) In the formula, σ(r,t) is the normal stress, Pa; T(r,t) is the shear stress, Pa; ν(r,t) and τ(r,t) are the elastic deformations under normal stress and shear stress respectively; Y(r,t) is the elastic modulus of the three-pillar insulator material, Pa; G(r,t) is the shear modulus of the three-pillar insulator material, Pa; Initial boundary conditions: The high-voltage conductor is subjected to gravity, and the metal insert is set as a fixed constraint; ③ Establish the phase field control equation where H(η - η c ) is the Heaviside unit step function; when η = 1, the three-pillar insulator material is regarded as the non-breakdown phase; when η = 0, the three-pillar insulator material is regarded as the breakdown phase; η c is a constant; In the formula, L0 is the kinetic coefficient representing the damage development rate; P is a variable with values of 1 or 0. When breakdown occurs within the grid, P = 1, and when breakdown does not occur within the geometric model grid of the three-pillar insulator, P = 0; W t is the total energy, Pa. The phase change process is energy-driven. Considering the influence of the electric field and mechanical stress on the breakdown process, the total energy W in the phase field control equation t is expressed as follows: W t = W ele + W mec Among them, W ele is the electrostatic energy, Pa; W mec is the strain energy, Pa; Assume that the material of the three-pillar insulator is a linear dielectric with a dielectric constant, W ele which is given by the following formula: Among them, ε0 is the relative permittivity of vacuum; Strain energy W mec Depends on the maximum value of the normal strain energy W mec1 and the shear strain energy W mec2 which is expressed as: W mec = max(W mec1 , W mec2 ) W c is the critical breakdown energy, in Pa, representing the energy required for the failure of the three-pillar insulator material, expressed as: In order to determine whether breakdown occurs within the mesh of the geometric model of the three-pillar insulator, the following equation is proposed: P = (R n ≥ 0.5·d)·(R n ≤ -0.5·d) d = (1 - exp(-(W t / W c ))) 2 )) where R n is a random number between -0.5 and 0.5; d represents the failure probability and follows the Weibull distribution; In the formula, Δt is the time step; When η > η c , H(η - η c ) = 1, the phase field control equation is described as: When η c <η < 1, H(η - η c ) = 0, the phase field control equation is described as: Initial boundary conditions: η is set to 1 in the initial defect area of the three-pillar insulator and 0 in other complete phase areas; ④ Establish the electric field-stress field-phase field coupling equation ε r (r,t) = (4η 3 - 3η 4 )ε b + [(1 - (4η 3 - 3η 4 )]ε p Among them, ε b is the relative permittivity of the breakdown phase; Y(r,t) = Y p ·Y b / ((Y p -Y b )·η 4 +Y b ) Among them, Y b is the elastic modulus of the breakdown phase; G(r,t) = Y(r,t) / (2×(1 + mu)) Step 4: Iteratively solve the control equations Set the time step and the maximum simulation time, and iteratively solve each equation in Step 3 within the geometric model area of the three-pillar insulator until a penetrating breakdown phase channel is formed between the high-voltage conductor and the grounded shell or the maximum simulation time is reached; Step 5: Obtain the evolution process of explosive breakdown, including the electric field distribution, stress distribution and breakdown channel morphology of the three-pillar insulator at different times.

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