A modeling method of insulating oil streamer discharge impurity particles considering medium inhomogeneity and electron trap effect

Abstract

The application discloses a kind of insulating oil stream injection discharge impurity particle modeling method considering medium non-uniformity and electron trap effect, belong to liquid dielectric discharge simulation and power equipment insulation state evaluation technical field.This method is based on the three-carrier hydrodynamics model of insulating oil, typical oil impurities such as cellulose particles and aging clusters are uniformly represented as local non-uniform regions;Through the continuous mapping of local relative dielectric constant and conductivity by smoothing the impurity region function, introduce the number density of trapped electrons, electron capture term and electron release term in the impurity region, and feedback the captured electrons to the Poisson equation as fixed negative charge;To describe the surface induced charge of particle and local electric field distortion.This method can calculate the influence of impurities on stream injection electric field, carrier distribution, propagation path and branch morphology under the same hydrodynamics framework, and can be used for environmental ester insulating oil lightning impulse insulation design and oil impurity risk assessment.

Description

Technical Field

[0001] This invention belongs to the technical field of liquid dielectric discharge simulation and power equipment insulation status assessment. Specifically, it relates to a method for modeling impurity particles in insulating oil streamer discharge that considers dielectric non-uniformity and electron trapping effects. It is applicable to the numerical analysis of the influence of typical impurities in natural ester insulating oil, synthetic ester insulating oil, mineral insulating oil and their oil-paper insulation systems on lightning impulse streamer discharge. Background Technology

[0002] Oil-immersed power equipment is widely used in power transmission and transformation systems. The insulating oil in this equipment not only serves as an insulating medium but also provides heat dissipation and arc extinguishing functions. During long-term operation, various types of impurity particles inevitably accumulate or are introduced into the insulating oil. These include cellulose particles from the aging and shedding of insulating paper, aging agglomerates formed during the aging process of the oil paper, and metal particles generated during equipment manufacturing and operational wear. These impurity particles, due to their different physical structures and electrical properties, significantly affect the internal electric field distribution, carrier migration, space charge accumulation, and streamer development process of the insulating oil. However, existing simulation methods for insulating oil streamer discharge are typically based on the assumption of a homogeneous insulating medium, considering only the transport processes of electrons, positive ions, and negative ions, and have the following main shortcomings:

[0003] (1) It cannot describe the local dielectric non-uniformity caused by impurity particles. Existing models usually regard insulating oil as a uniform and continuous medium and ignore the local dielectric constant and conductivity changes caused by impurity particles during actual operation, which makes the calculated electric field distribution deviate from the actual situation.

[0004] (2) It cannot reflect the influence of non-metallic impurities on the electron migration process. Cellulose particles and aged clusters contain a large number of polar groups, defect structures and interface states, which can form electron traps and capture and release free electrons. Traditional models only simulate non-metallic impurities by changing material parameters, which cannot describe the dynamic process of electrons being captured and forming fixed negative charges, and further affecting the space charge distribution and local electric field evolution.

[0005] (3) The conductive polarization effect of metal particles cannot be accurately described. Metal particles have high electrical conductivity and will generate induced charge redistribution under the action of external impact electric field, so that the particle interior maintains an equipotential state and a local electric field enhancement is generated at the particle edge. Traditional dielectric region modeling methods cannot reflect the floating conductor characteristics of suspended metal particles, which makes it impossible to accurately evaluate the influence of metal particles on the initiation and propagation process of streamers.

[0006] (4) There is a lack of a unified method for evaluating the impact of impurities. Existing studies usually judge the impact of impurities by observing the stream morphology, and lack quantitative evaluation indicators for different types, sizes and spatial locations of impurities. Therefore, this invention proposes a modeling method and system for impurity particles in oil based on electrohydrodynamic stream discharge simulation. By establishing an impurity geometric model, a region function continuous mapping model, an electron trap coupling model and a floating conductor model, the invention achieves accurate simulation and quantitative evaluation of the impact of different types of impurity particles on the stream discharge process of insulating oil.

[0007] Cellulose-based nonmetallic impurities possess high dielectric constants and abundant surface defect structures, enabling them to form electron trapping centers. This leads to electron accumulation within the impurity region, altering the local space charge distribution. Existing models typically describe nonmetallic impurities by simply altering local dielectric parameters, failing to capture the dynamic impact of electron traps on streamer development. For metallic particle impurities, their high conductivity causes charge redistribution under an external electric field, creating equipotential regions within the particles and exhibiting significant electric field enhancement at the particle edges. Traditional insulating dielectric region modeling methods cannot describe the induced polarization behavior on the surface of metallic particles, resulting in discrepancies between simulation results and actual discharge processes.

[0008] The development process of the stream determines the final breakdown strength of the insulating oil. Therefore, to accurately describe the influence of impurity particles on the stream propagation process, it is necessary to establish a modeling method for oil impurity particles that can simultaneously describe the non-uniformity effect of non-metallic impurity media, the electron trap effect, and the floating conductor effect of metallic particles. This is of great significance for improving the accuracy of insulating oil stream discharge simulation and enhancing the insulation reliability of oil-immersed equipment. Summary of the Invention

[0009] This invention aims to address the problem that existing simulation methods for insulating oil streamer discharge cannot accurately describe the influence of impurity particles in the oil. It proposes a method and system for modeling impurity particles in oil based on electrohydrodynamic streamer discharge simulation. The invention employs the following technical solution: This invention provides a method for modeling impurity particles in oil based on electrohydrodynamic streamer discharge simulation, comprising the following steps:

[0010] Step 1: Establish the basic model of insulating oil streamer discharge. First, establish the calculation region for insulating oil streamer discharge, including: high-voltage needle electrode; ground plane electrode; and the insulating oil region located between the needle electrode and the ground plane electrode. A three-carrier hydrodynamic model is used to describe the development process of the insulating oil streamer, where the carriers include: electrons; positive ions; and negative ions. Solve the following equations through coupling: potential control equation; Poisson equation; electron transport equation; positive ion transport equation; and negative ion transport equation. Describe the following under the action of the impact electric field: electric field spatial distribution; electron collision ionization process; ion migration process; space charge formation process; and streamer channel development process. The potential satisfies:

[0011]

[0012] Space charge density is expressed as:

[0013]

[0014] The carrier transport equation is expressed as:

[0015]

[0016] in: Indicates the concentration of electrons, positive ions, or negative ions; This represents the carrier drift diffusion flux; This indicates ionization, recombination, and adhesion reactions.

[0017] Step Two: Establish a geometric description model of impurity particles in the oil. For different types of impurity particles in actual insulating oil, this invention establishes equivalent geometric models based on their structural characteristics. The impurity particle establishment steps include:

[0018] S21. Cellulose Impurity Particle Model: Since cellulose particles produced by the aging of insulating paper typically have a slender structure, an elliptical region is used for equivalent description. Let the coordinates of the cellulose particle center be: Major half-axis: Short half-shaft: Establish the elliptic level set function:

[0019]

[0020] Used to describe the spatial location and size of cellulose particles.

[0021] S22. Aging Cluster Particle Model: This model addresses clustered impurities formed during the aging process of oiled paper, employing a combination of multiple round or elliptical sub-particles. The j-th sub-particle is represented as:

[0022]

[0023] pass:

[0024]

[0025] The overall cluster region is obtained. This method can describe the structure of aging clusters of different sizes and degrees of aggregation.

[0026] S23. Metal Particle Model: Based on the high conductivity of metal particles, they are defined as independent conductor regions, rather than ordinary dielectric regions. Metal particles satisfy:

[0027]

[0028] Make its interior: That is, the metal particles maintain an equipotential state.

[0029] Step 3: Construct a continuous mapping model of non-metallic impurity region function and material parameters. In actual operation, non-metallic impurities such as cellulose particles and aging clusters inside the insulating oil usually have complex spatial morphology. Their size, shape and distribution location will affect the local electric field distribution and carrier migration process.

[0030] To describe the local dielectric parameter variations and dielectric inhomogeneity caused by impurity particles, this invention proposes a non-metallic impurity modeling method based on level set functions and continuous material parameter mapping. The non-metallic impurity region is converted into a continuous distribution function, and the spatial variation of insulating oil material parameters is realized using this regional function, thereby establishing a non-uniform insulating dielectric model containing non-metallic impurities.

[0031] Step three includes the following steps:

[0032] S31. Establish the geometric level set function for nonmetallic impurities.

[0033] First, a corresponding geometric description function is established based on the actual morphological characteristics of the non-metallic impurity particles. For the first... For each non-metallic impurity particle, define its geometric level set function:

[0034]

[0035] in: Represents the spatial coordinates within the calculation area; This represents the positional relationship of a spatial point relative to the impurity boundary. The positional relationship between a spatial point and the impurity region is determined using a level set function, when: This indicates that the location is inside the impurity particle; when: This indicates that the location is at the boundary of the impurity particle; when: This indicates that the location is within the insulating oil region. Using the above method, non-metallic impurity particles of different shapes can be described using a unified mathematical form.

[0036] S32. Constructing a function to smooth the impurity region

[0037] In the finite element method (FEM) solution, directly using a hard boundary between the impurity region and the insulating oil region can lead to abrupt changes in material parameters at the interface, increasing mesh dependence and potentially causing numerical instability. Therefore, this invention further constructs a smoothing domain function based on the level set function. For the first... The region function of an impurity particle is defined as:

[0038]

[0039] in: Indicates the first A function for the region of each impurity particle; This parameter represents the transition width of the impurity boundary. When the spatial point is located inside the impurity: ,therefore: This indicates that the area is completely occupied by impurity material; when the space point is located in the insulating oil area... ,therefore: This indicates that the region is pure insulating oil, when the spatial point is near the impurity boundary:

[0040]

[0041] This creates a continuous transition region. In this way, the traditional binarized material distribution is transformed:

[0042]

[0043] Converting it to a continuously varying form improves the stability of finite element calculations.

[0044] S33. A continuous mapping model for non-metallic impurity material parameters is established. After obtaining the overall impurity region function, this invention further utilizes this function to achieve continuous conversion between insulating oil and impurity material parameters. The material parameters include: relative permittivity; conductivity. The relative permittivity at any location in the calculation region is defined as:

[0045]

[0046] in: Indicates the relative permittivity of insulating oil; This represents the equivalent relative permittivity of nonmetallic impurity particles. When: At that time, That is, the pure oil region, when: At that time, we obtained: This refers to the impurity region.

[0047] therefore: It can continuously describe the changes in dielectric properties from insulating oil to impurity regions.

[0048] Similarly, local conductivity is expressed as:

[0049]

[0050] in: Indicates the electrical conductivity of insulating oil; This indicates the electrical conductivity of non-metallic impurity particles. Because cellulose particles and aged aggregates have different electrical conductivity properties than insulating oil, therefore:

[0051]

[0052] This causes a localized change in current density near the impurities.

[0053] S34. Material parameter mapping and streamer model coupling

[0054] Obtaining spatial changes: and Then, it was introduced into the electrohydrodynamic streamer model, in the Poisson equation:

[0055]

[0056] in The local electric field distribution is determined, and the local conductivity also has an impact on the charge transport equation: This, in turn, alters electron migration speed, ion movement processes, and space charge accumulation. Therefore, non-metallic impurities influence the entire stream development process through continuous changes in material parameters.

[0057] Step 4: Establish a coupling model for electron traps of non-metallic impurities. Since non-metallic impurities such as cellulose particles and aging clusters in insulating oil are usually composed of cellulose fragments, polar oxidation products, carbonization products and oil paper aging by-products, they contain a large number of polar groups, structural defects and interface states.

[0058] When insulating oil is subjected to a high-intensity impact electric field, a large number of high-energy electrons are generated in the stream head region. These electrons interact with non-metallic impurities during migration, and some are captured by defects and polar groups on the impurity surface, forming bound electrons. These captured electrons cannot participate in free electron migration but act as fixed negative charges, affecting the local space charge distribution and further altering the electric field intensity distribution and stream propagation path. This invention introduces electron trap state variables within the non-metallic impurity region, establishing a coupling relationship between the electron transport process and impurity trap dynamics. Step four includes the following specific steps:

[0059] S41. Define the electron trapping region for nonmetallic impurities, based on the aforementioned nonmetallic impurity region function: Define the effective area of ​​the electronic trap. When When, it indicates the region of non-metallic impurities; when At this point, the region represents pure insulating oil. Therefore, the trap density is limited to the impurity region:

[0060]

[0061] in: Indicates the effective trap density at a spatial location; This indicates the maximum equivalent trap density of non-metallic impurities. In this way, the electron trapping process occurs only in the non-metallic impurity region and does not affect the pure insulating oil region.

[0062] S42. Establish an electron capture kinetic model. Under high field strength, free electrons migrate at high speed towards the anode. When electrons enter the region near a nonmetallic impurity, they interact with the internal traps of the impurity. The electron capture rate of the impurity is expressed as:

[0063]

[0064] in: This indicates the number of electrons captured per unit time. Indicates the electron capture coefficient Indicates the maximum trap density; This indicates that the trap electron density has been occupied; This represents the free electron number density. The formula involves two physical processes: as the free electron concentration increases, the probability of electrons colliding with traps increases, thus increasing the number of captured electrons; when... As the number of available traps decreases, the electron capture rate decreases, and this model can describe the process of trap saturation.

[0065] S43. Establish an electron release kinetic model. Trapped electrons are not permanently fixed; under the influence of an external electric field, thermal excitation, and space charge, some trapped electrons may be released back to the free electron state. The electron release process is represented as:

[0066]

[0067] in: Indicates the rate of electron release; This represents the electron release coefficient. The electron release coefficient is related to the trap energy level and can be expressed as:

[0068] in: Indicates the frequency of electron attempts; Indicates the trap energy level; Represents the Boltzmann constant; It represents absolute temperature and describes the characteristic that the ability of trapped electrons to be released increases with increasing temperature.

[0069] S44. Establish the dynamic evolution equation for trapped electrons. Combining the electron capture and release processes, trapped electrons satisfy the following:

[0070]

[0071] Right now:

[0072]

[0073] This equation describes the entire process of a free electron entering an impurity region, being trapped by a trap, the trap gradually filling, and the trapped electron being released again.

[0074] S45. Perform coupling corrections to the electron transport equations. In the traditional three-carrier model, the electron transport equations are expressed as:

[0075] in This includes: impact ionization; electron recombination; and electron attachment. Since non-metallic impurities consume free electrons, electron capture and release terms are added. The revised electron source term is:

[0076]

[0077] Therefore, the electron transport equation becomes:

[0078]

[0079] in: This indicates that the electrons were lost due to being trapped in a trap; This indicates that the release of trapped electrons leads to electron replenishment. A spatial confinement model for trapped electrons is further constructed. Since trapped electrons have lost their ability to migrate freely, they cannot participate in drift-diffusion motion like free electrons. Therefore, this invention sets a trap electron diffusion coefficient for trapped electrons.

[0080]

[0081] at the same time:

[0082]

[0083] This indicates that the trapped electron mobility is zero, therefore the trapped electron density is already occupied. This setting, which changes only over time and does not involve spatial migration, conforms to actual physical processes.

[0084] S46. Correction of the space charge equation for trapped electron pairs, conventional space charge density:

[0085]

[0086] Impurity-trapped electrons are not considered; since trapped electrons are negatively charged, they are included in the space charge calculation.

[0087]

[0088] in: Indicates the density of positive ions; Represents the density of free electrons; Indicates the density of negative ions; The density of trapped electrons is represented, therefore the Poisson equation is modified to:

[0089]

[0090] Step 5: Establish a floating conductor model of metal particles. In the actual operation of oil-immersed power equipment, the insulating oil may contain metal particle impurities caused by manufacturing residues, mechanical wear, electrode corrosion, and aging of metal materials. Since metal particles have a much higher conductivity than insulating oil, under the influence of an external electric field, their internal free electrons can migrate and redistribute rapidly, generating induced charges on the surface of the metal particles. This process leads to: a consistent internal potential within the metal particles; the formation of positive and negative induced charge regions on the surface of the metal particles; localized electric field enhancement at the particle tips or edges; alteration of nearby electron migration paths; and promotion of streamer initiation and propagation. However, existing insulating oil streamer simulation models typically employ a homogeneous medium assumption or simply set the metal particles as ordinary dielectric regions with high dielectric constants and high conductivity, failing to reflect the conductor polarization behavior of suspended metal particles under the influence of an electric field.

[0091] Therefore, this invention proposes a metal particle modeling method based on the floating conductor theory, which equates suspended metal particles in oil to independent conductor regions that are not electrically connected to external electrodes. By using floating potential boundary conditions and overall charge conservation constraints, the redistribution process of induced charge on the surface of metal particles is simulated, thereby achieving an accurate description of the influence of metal particles on the streamer discharge process.

[0092] To address the impact of suspended metal particle impurities in insulating oil on the streamer discharge process, this invention proposes an equivalent modeling method for metal particle impurities based on a floating conductor model. Due to the high conductivity of metal particles, their internal free electrons can migrate rapidly. Under the influence of an external electric field, the interior of the metal particles can be approximated as being in an equipotential state. Simultaneously, induced charges redistribute on the particle surface, thereby altering the local electric field distribution and affecting the streamer development process. Therefore, this invention does not artificially increase the dielectric constant to simulate metal particles, but instead treats the metal particles as equivalent to suspended conductors in the insulating oil, describing the conductivity characteristics of the metal particles by setting floating potential boundary conditions.

[0093] Specifically, an independent geometric region of metal particles is established within the insulating oil calculation area, while preserving the internal boundary between the metal particles and the insulating oil, allowing the metal particles to participate in model coupling as an independent calculation region. Based on the size range of metal shavings particles in actual transformer insulating oil, the metal particles are set as circular structures and arranged near the streamer propagation path. The coordinates of the center of the circle are set. This setting places the metal particles in the rapid expansion region of the streamer, thereby enabling the analysis of their influence on the streamer propagation path, electric field strength, and branch structure.

[0094] Furthermore, the established metal particle region is endowed with metallic material properties. The conductor characteristics of the metal particles are mainly achieved through floating potential boundary conditions. The material conductivity is used to characterize the physical properties of the metal particles, rather than replacing the actual conductor behavior by setting an extremely large dielectric constant. In the electrostatic field calculation module, only the insulating oil region is set as the electric field solution region; the interior of the metal particles does not participate in the Poisson equation solution. Floating potential boundary conditions are applied to the outer surface of the metal particles, and the initial total charge of the particles is set as follows:

[0095]

[0096] This setting indicates that the metal particles are not electrically connected to the external electrodes and remain electrically neutral in the initial state. Under the influence of an external impact electric field, the free charges on the surface of the metal particles can redistribute, maintaining equipotential within the particles, while simultaneously generating opposite induced charges at the two ends of the particles, thus producing a local electric field enhancement effect. In the streamer transport model, the continuity equations for electrons, positive ions, and negative ions are solved only within the insulating oil region; carrier concentration, mobility, diffusion coefficient, and reaction source terms are not set for the metal particle region. The application of flux-free boundary conditions for electrons and ions on the surface of the metal particles indicates that charge carriers will not directly enter the interior of the metal particles, avoiding the incorrect treatment of the metal particles as a medium region with charge carrier transport processes.

[0097] For the space charge distribution, the three-carrier coupling model is still used in the insulating oil region, and its space charge density is expressed as:

[0098]

[0099] in, , and These represent the number densities of electrons, positive ions, and negative ions, respectively. This represents the amount of electron charge. Since the surface induced charge of metal particles can be automatically solved using the floating potential condition, no additional volume charge term for metal particles is required, avoiding redundant calculations of the charge effect generated by metal particle polarization. The metal particle impurity model established using the above method can simultaneously consider the high conductivity, equipotential characteristics, and surface induced charge effect of metal particles, realizing the electric field coupling between suspended metal particles and the discharge process of insulating oil streamers. This provides a model basis for subsequent analysis of the influence of metal particles of different sizes, positions, and numbers on the initiation, propagation, and branching evolution of streamers.

[0100] Compared with existing methods for simulating the discharge of insulating oil streamers, the oil impurity particle modeling method and system based on electrohydrodynamic streamer discharge simulation provided by this invention has the following advantages:

[0101] (1) This invention improves the modeling accuracy of complex impurity structures in insulating oil and enhances the realism of streamer simulation. For typical non-uniform structures present in insulating oil during actual operation, such as cellulose impurities, aged paper agglomerates, and metal wear particles, corresponding mathematical description models are established, achieving accurate characterization of impurity particles with different morphologies and electrical properties. Compared to traditional simulation methods that treat insulating oil as a homogeneous medium, this invention can more realistically reflect the influence of impurities on the local electric field distribution and streamer development process, improving the consistency between simulation results and the actual operating state of the insulation system.

[0102] (2) A continuous mapping method for material parameters in the impurity region is proposed to improve the stability of finite element calculations and the ability to describe interfaces. This invention utilizes continuous region functions to achieve a smooth transition of material parameters such as dielectric constant and conductivity between the insulating oil and the impurity region, avoiding the mesh sensitivity and numerical error problems caused by abrupt changes in material parameters in traditional region replacement methods. This method can more accurately describe the local electric field changes at the impurity-insulating oil interface and improve the stability and reliability of the multiphysics coupling solution process.

[0103] (3) A coupling model of electron trapping in non-metallic impurities was established to realize the dynamic correlation analysis between impurities and carrier transport processes. This invention introduces parameters such as electron trapping density, electron capture coefficient, and electron release coefficient into the non-metallic impurity region to establish a dynamic conversion relationship between free electrons and trapped electrons, and incorporates trapped electrons into space charge calculations, thereby simulating processes such as electron capture, negative space charge accumulation, electric field redistribution, and streamer path changes. Compared with traditional methods that only change material parameters, this invention can reveal more deeply the microscopic physical mechanism by which non-metallic impurities affect streamer development.

[0104] (4) A floating metal particle conductor model was established to improve the simulation accuracy of the local electric field enhancement effect induced by metal impurities. This invention equates suspended metal particles in insulating oil to floating conductors not connected to external electrodes. The migration of free charges inside the metal particles and the accumulation of surface induced charges are described by floating potential constraints and charge conservation conditions, thus achieving accurate simulation of the equipotential characteristics of the metal particle conductor and the edge field enhancement effect. This method can more realistically reflect the promoting effect of metal wear particles on the rapid development of flow streams and the increased risk of insulation breakdown.

[0105] (5) This invention achieves multi-physics field coupling analysis of impurity particles, electric field distribution, space charge evolution, and streamer development. It directly embeds the impurity model into the streamer discharge control equation system, enabling full-process coupling analysis of impurity structure changes, material parameter modulation, electric field distortion, carrier transport, space charge accumulation, and streamer expansion. By establishing a complete physical interaction chain, the influence of different types of impurities on the discharge behavior and breakdown risk of insulating oil can be revealed more comprehensively.

[0106] (6) This invention improves the predictive ability and engineering application value of the insulating oil flow simulation model. By comprehensively considering the geometric characteristics, electrical parameters, and dynamic charge behavior of different impurity types, the simulation model can more accurately predict the internal discharge evolution process of insulating oil under complex operating conditions. This method can provide a more reliable theoretical basis for the insulation status assessment, fault risk analysis, and operation and maintenance strategy formulation of oil-immersed power equipment.

[0107] (7) The model has been enhanced in terms of versatility and scalability. It is applicable to a variety of insulating media and operating conditions. The impurity particle modeling method established by this invention has good adaptability. By adjusting the impurity geometric parameters, material parameters, electron trap parameters and metal particle size, it can be extended to different insulating media such as mineral insulating oil, natural ester insulating oil and synthetic ester insulating oil. It can also be applied to a variety of electrical scenarios such as lightning strike, switching impact, AC breakdown and partial discharge development, and has high engineering application value. Attached Figure Description

[0108] Figure 1 Flowchart of a method for modeling multiple types of impurity particles in insulating oil based on electrodynamic streamer discharge simulation

[0109] Figure 2 Figure 1 shows the simulation results of pure oil jet discharge.

[0110] Figure 3 Simulation results of cellulose impurity particles interfering with the flow stream.

[0111] Figure 4 Simulation results of flow stream interference from aging clusters.

[0112] Figure 5 Simulation results of metal particle interference in the streamer

[0113] Figure 6 Flowmeter discharge experiment diagram Detailed Implementation

[0114] The following detailed description, in conjunction with specific embodiments, illustrates a method for modeling multiple types of impurity particles in insulating oil based on electrodynamic jet discharge simulation, as proposed in this invention.

[0115] This embodiment uses the finite element method (FEM) to establish a discharge model of insulating oil streamers containing typical impurity particles. By introducing three types of impurities commonly encountered in actual operation—cellulose particles, aged agglomerates, and metal particles—it simulates and analyzes the impact of different types of impurities on the initiation, propagation, and space charge evolution of insulating oil streamers. The specific process is as follows: Figure 1 As shown.

[0116] First, a two-dimensional axisymmetric needle-plate electrode flowstream discharge calculation model is established. The model includes a high-voltage needle electrode, a grounding plate electrode, and an insulating oil region located between the two electrodes. The radius of curvature at the tip of the needle electrode is set to 50 μm, the needle-plate spacing is set to 20 mm, a high-voltage negative polarity lightning impulse voltage is applied to the needle electrode, and the plate electrode is grounded.

[0117] The jet discharge process of insulating oil is described using a three-carrier hydrodynamic model, which treats electrons, positive ions, and negative ions as the main charged particles. By coupling and solving the potential equation, Poisson's equation, and the drift-diffusion-reaction equations for electrons, positive ions, and negative ions, the model describes the changes in the internal electric field, carrier migration, space charge formation, and jet channel development under impulse voltage. This model is based on the MIT three-carrier hydrodynamic model, and its governing equations are as follows: The electric field satisfies:

[0118]

[0119] As shown in Table 1, E represents the electric field strength, and V represents the electric potential. Space charge satisfies the Poisson equation:

[0120]

[0121] Where ε0 is the vacuum permittivity, εr is the relative permittivity of the insulating oil, and q is the electron charge. , and These represent positive ions, negative ions, and electron number density, respectively. The transport process of each charge carrier is represented as follows:

[0122]

[0123] As shown in Table 1, Indicates the first carrier concentration, Represents the carrier drift diffusion flux. This represents the terms related to ionization, recombination, and adhesion reactions. During the model solution process, corresponding dielectric parameters, conductivity, carrier mobility, diffusion coefficient, ionization parameters, and electron adhesion parameters are set according to different insulating oil types. The finite element method is used to obtain the jet development process under pure insulating oil conditions. Based on this, an impurity particle region is further introduced, and by changing the local material parameters and carrier reaction process, the jet discharge process of insulating oil containing impurities is simulated.

[0124] During long-term operation of oil-immersed power equipment, the aging of insulating paper produces cellulose fragments. These particles typically have a slender fibrous structure and possess a high dielectric constant and a certain electron trapping ability. Therefore, in this embodiment, the cellulose impurity is equivalent to an elliptical non-metallic dielectric region within the insulating oil region. First, the center position of the cellulose particles is defined:

[0125]

[0126] The major and minor semi-axles are as follows: Among them, the long half-axis Indicates the dimension along the fiber length direction, short semi-axis This represents the dimension along the fiber width direction. Establish the elliptical horizontal set function:

[0127]

[0128] when: This indicates that the computational region is located inside the cellulose particle; when: This indicates that the computational domain is located in the insulating oil region. To avoid abrupt changes in material parameters at the interface between cellulose particles and insulating oil, a smooth step function is used in the finite element model to establish the impurity region function:

[0129]

[0130] in: Indicates the first A function for the region of each impurity particle; This parameter represents the transition width of the impurity boundary. When the spatial point is located inside the impurity: ,therefore: This indicates that the area is completely occupied by impurity material; when the space point is located in the insulating oil area... ,therefore: This indicates that the region is pure insulating oil, when the spatial point is near the impurity boundary: A continuous transition region is formed. This indicates the width of the interface transition; in this embodiment, it is set to 5 μm.

[0131] Continuous mapping of local material parameters based on domain functions:

[0132]

[0133]

[0134] in: , These represent the relative permittivity and conductivity of the insulating oil, respectively. , These represent the equivalent dielectric constant and conductivity of cellulose particles, respectively.

[0135] Furthermore, considering the surface defect structure of cellulose particles and the electron-trapping effect of polar groups, an electron trapping model is introduced within the cellulose region. The trap electron density is defined as follows:

[0136]

[0137] in This represents the maximum electron trap density of cellulose particles.

[0138] The electron capture process is represented as:

[0139]

[0140] The electron release process is represented as:

[0141]

[0142] As shown in Table 2: The electron capture coefficient; The electron release coefficient; The density of trapped electrons.

[0143] At the same time, the captured electron is added as a fixed negative charge to the space charge term:

[0144]

[0145] The above method enables the simulation of the comprehensive influence of cellulose particles on local dielectric parameters, electric field distribution, and electron migration processes.

[0146] During the long-term thermo-oxidative aging process of oil-paper insulation systems, clustered impurities composed of cellulose degradation products, polar oxides, and carbides are generated. Since these impurities typically have irregular aggregate structures, this embodiment uses a combination of multiple sub-particles for equivalent modeling.

[0147] Suppose that the aging cluster consists of N sub-particles, and the center coordinates of the j-th sub-particle are: The radius is: Its regional function is expressed as:

[0148]

[0149] pass: Obtain the overall cluster region. The overall aging cluster region is obtained by combining multiple sub-particle region functions:

[0150]

[0151] This method can describe the structure of aged clusters of different sizes and degrees of aggregation. Then, using the same method as with cellulose particles, the aged cluster regions are mapped to non-uniform material regions:

[0152]

[0153]

[0154] Simultaneously, the electron trap density is set within the aging cluster region:

[0155]

[0156] The influence of aging products on the free electron migration process is described using electron capture and release equations. Compared with the single cellulose particle model, the aging cluster model, through the combined action of multiple interface regions, can simulate the multi-point electric field disturbances and space charge accumulation effects caused by complex aggregated impurities in actual operating oil.

[0157] Because metal wear particles such as copper and iron filings may be generated during the operation of oil-immersed equipment, and these impurities have high electrical conductivity, they will exhibit induced polarization under the influence of an external impact electric field. Therefore, this embodiment does not use a conventional dielectric region description, but instead uses a floating conductor model for simulation.

[0158] First, establish independent conducting regions based on the size and spatial location of the metal particles. Let the radius of the metal particles be: The center coordinates are: The region of metal particles is defined as an independent conductor domain.

[0159] In the electrostatic field module, a floating potential boundary condition is applied to the metal particles:

[0160]

[0161] in This represents the floating potential of the metal particle. Simultaneously, it satisfies the overall charge conservation:

[0162]

[0163] As shown in Table 3: Indicates the boundary of metal particles; Represents the outward normal unit vector; This represents the electric displacement vector. This condition ensures that the metal particles remain electrically neutral as a whole, while allowing for the redistribution of surface induced charges under the influence of an external electric field.

[0164] In the process of carrier transport calculation:

[0165] (1) Electrons, positive ions and negative ions are solved only in the insulating oil region;

[0166] (2) The interior of the metal particles does not participate in the carrier migration process;

[0167] (3) The surface of the metal particles is provided with flux-free boundary conditions for electrons, positive ions and negative ions.

[0168] By using the above settings, the equipotential properties inside metal particles and the enhanced electric field effect at the particle edges can be simulated, thereby analyzing the influence of metal particles on stream initiation, propagation speed, and branching development.

[0169] To verify that the oil impurity particle modeling method proposed in this invention can accurately describe the influence of different types of impurities on the jet discharge process of insulating oil during actual operation, a pure insulating oil model, a cellulose impurity particle model, an aged cluster model, and a metal particle model were established, and jet discharge simulation calculations were carried out under negative polarity lightning impulse conditions.

[0170] In contrast, a pure oil streamer discharge model was first established using the traditional homogeneous insulating oil dielectric assumption. This model only considers the migration, diffusion, ionization, and recombination processes of electrons, positive ions, and negative ions, without considering the local dielectric parameter changes and electron trapping effects caused by impurity particles in the oil. The simulation results are as follows: Figure 2 As shown.

[0171] Depend on Figure 2 As can be seen, in the pure oil model, the streamers mainly originate from the high-field region near the tip of the needle electrode and extend towards the grounding electrode along the direction of the applied electric field, exhibiting a relatively regular axial propagation characteristic. However, since the traditional model assumes that the insulating oil is a homogeneous medium and ignores impurities such as cellulose fragments, aging products, and metal wear particles present inside the insulating oil during actual operation, the simulated streamer path is more idealized and differs somewhat from the complex propagation process inside the actual insulating oil. Furthermore, based on the above streamer model, the impurity particle modeling method proposed in this invention is introduced to perform equivalent modeling for different types of impurities.

[0172] For cellulose impurity particles, an elliptical non-uniform dielectric region is used for description. The local dielectric constant and conductivity are continuously mapped using an impurity region function. Simultaneously, an electron trap model is introduced to describe the influence of surface defect structures on the electron trapping and release processes of the cellulose particles. The streamer simulation results are as follows: Figure 3 As shown.

[0173] Depend on Figure 3It is evident that when the stream propagates near the cellulose particles, the electric field distribution at the stream head changes due to the difference in dielectric parameters between the impurity region and the insulating oil, causing a certain deflection of the propagation path. Simultaneously, because electrons are trapped in the cellulose region, the local electron concentration and space charge distribution change, leading to branching and expansion of the stream channel. This result is consistent with the phenomenon of stream path disturbance caused by cellulose debris generated from the aging and shedding of insulating paper during actual operation.

[0174] For the clustered polar products formed during the aging process of oiled paper, this invention uses a model of aging clusters formed by combining multiple sub-particles, and describes the complex aggregation structure through a global region function. The simulation results are as follows: Figure 4 As shown.

[0175] Depend on Figure 4 It is known that, due to the multiple interface regions of aged clusters, the stream propagation process is subject to continuous non-uniform disturbances in the medium, forming multiple local high-field regions near the clusters, causing the streams to exhibit significant bending and bifurcation. Simultaneously, the electron traps within the aged clusters further enhance the space charge accumulation effect, making the stream propagation morphology more closely resemble the irregular development characteristics observed in actual aged oil.

[0176] For metal particle impurities, this invention differs from traditional dielectric region treatment methods by treating them as equivalent to a floating conductor region unconnected to external electrodes. The equipotential characteristics inside the metal particles and the redistribution of surface induced charges are described using floating potential boundary conditions. The simulation results are as follows: Figure 5 As shown.

[0177] Depend on Figure 5 It is evident that under the influence of an external impact electric field, significant charge polarization occurs on the surface of the metal particles, forming a localized area of ​​enhanced electric field at the particle edges. When the stream propagates to the vicinity of the metal particles, the enhanced electric field promotes electron multiplication and local ionization, resulting in significant acceleration and directional deflection of the stream. Compared to cellulose particles and aging clusters, metal particles have a stronger promoting effect on the stream propagation process. This result aligns with the physical law that metal wear particles easily induce partial discharge and insulation degradation during the actual operation of oil-immersed equipment.

[0178] To further verify the effectiveness of the model of this invention, the simulation results were compared with the streamer images obtained from actual lightning impulse experiments on insulating oil. The experiment employed a needle-plate electrode structure, and under the action of a negative polarity lightning impulse voltage, the streamer development process was recorded using a high-speed camera system. The experimental streamer images are shown below. Figure 6 As shown.

[0179] Depend on Figures 2-6The comparison shows that the traditional pure oil model produces a relatively regular stream channel, mainly characterized by continuous expansion along the electric field direction, which differs from the complex branching structure observed in experiments. However, by using the impurity particle modeling method proposed in this invention, the simulation results can reflect phenomena such as stream path deflection, branching, local field strength enhancement, and space charge redistribution caused by different impurity types, which are more consistent with the non-uniform propagation characteristics shown in the experimental stream images.

[0180] Among them, the cellulose impurity model can reflect the local obstruction and path disturbance caused by solid fiber particles; the aging cluster model can describe the complex electric field distortion effect caused by multi-interface structure; and the metal particle model can accurately reflect the local field strength enhancement phenomenon caused by conductor polarization. Therefore, compared with the traditional uniform insulating oil streamer model, this invention improves the realism and accuracy of insulating oil streamer discharge simulation by introducing impurity region functions, electron trap coupling mechanisms, and floating conductor models.

[0181] The above embodiments only describe the preferred implementation process of the present invention and do not limit the scope of protection of the present invention. Adjustments to the size, quantity, material parameters, and spatial distribution of impurity particles without departing from the core idea of ​​the technical solution of the present invention are all within the scope of protection of the present invention.

[0182] Table 1: Geometric Model Symbols and Their Meanings

[0183] Table 2: Impurity Model Symbols and Their Meanings

[0184] Table 3: Model Parameter Symbols and Their Meanings

Claims

1. A method for modeling impurity particles in insulating oil streamer discharge considering dielectric inhomogeneity and electron trapping effects, characterized in that, Includes the following steps: S1. Establish a calculation model for the flow discharge of insulating oil, establish a flow discharge calculation domain including needle electrode, plate electrode and the insulating oil region located between the needle electrode and the plate electrode, and establish a three-carrier current-hydrodynamic flow discharge model to describe the flow development process in insulating oil. S2. Establish a geometric description model of impurity particles in oil, based on the type, size parameters and spatial location of the impurity particles to be simulated, where the impurity particles include non-metallic impurity particles and metallic impurity particles. S3. Construct a non-metallic impurity region function and a continuous mapping model for material parameters. For non-metallic impurities such as cellulose particles and aged agglomerates, construct a smooth impurity region function to continuously map the local material parameters in the calculation domain of insulating oil, so as to form a non-uniform medium model containing non-metallic impurities. S4. Construct a coupling model of electron traps for non-metallic impurities, introduce the trap electron number density variable into the non-metallic impurity region, and introduce the trap electron number density as a fixed negative charge into the space charge density term in the Poisson equation to describe the influence of non-metallic impurities on the simulation results. S5. Construct a floating conductor model of metal impurity particles. For the metal impurity particles, set floating potential boundary conditions at the boundaries of the metal particles, and set carrier flux-free boundary conditions on the surface of the metal particles to simulate the influence of metal particles on the simulation results. S6. Solve the streamer discharge model containing impurity particles and evaluate its impact. Solve the electrohydrodynamic streamer discharge model in the time domain after non-metallic impurity parameter mapping, electron trap coupling and metal particle boundary treatment, and evaluate the results.

2. The method for modeling impurity particles in insulating oil streamer discharge considering dielectric inhomogeneity and electron trapping effects according to claim 1, characterized in that, The impurity particles include one or more of cellulose particles, aged agglomerate particles, and metal particles; wherein, the cellulose particles are equivalent to elliptical dielectric particles with major and minor axis dimensional characteristics; the aged agglomerate particles are equivalent to a combination structure of multiple overlapping circular or elliptical dielectric sub-particles; and the metal particles are equivalent to floating conductor particles that are not directly electrically connected to external electrodes.

3. The method for modeling impurity particles in insulating oil streamer discharge considering dielectric inhomogeneity and electron trapping effects according to claim 1, characterized in that, The impurity region function is constructed using a smooth step function, forming a continuous transition at the boundary of the impurity particles; for the i-th impurity particle, a geometric level set function is first established: Through: Obtain the corresponding impurity region function, where, For having transition width A smooth step function.

4. The method for modeling impurity particles in insulating oil streamer discharge considering dielectric inhomogeneity and electron trapping effects according to claim 3, characterized in that, For cellulose particles distributed along the direction of the applied electric field, their geometric level set function is: in: Indicates the coordinates of the center of the cellulose particle; Indicates the length of the minor semi-axis; Represents the length of the major semi-axis; and satisfies: To describe the elongated structural features of cellulose impurities along the direction of the electric field.

5. The method for modeling impurity particles in insulating oil streamer discharge considering dielectric inhomogeneity and electron trapping effects according to claim 3, characterized in that, When multiple impurity particles exist simultaneously within the computational region, the total impurity distribution function is obtained by combining multiple impurity region functions: Make the total impurity region function satisfy: To avoid the non-physical superposition of material parameters when multiple impurity regions overlap.

6. The method for modeling impurity particles in insulating oil streamer discharge considering dielectric inhomogeneity and electron trapping effects according to claim 1, characterized in that, The local material parameters are continuously mapped in the following manner: in: , These represent the relative permittivity and conductivity of pure insulating oil, respectively. , These represent the equivalent relative permittivity and conductivity of the impurity region, respectively.

7. The method for modeling impurity particles in insulating oil streamer discharge considering dielectric inhomogeneity and electron trapping effects according to claim 1, characterized in that, The trap electron number density variable It does not participate in the electric field-driven migration process, and its diffusion coefficient is set to zero or much smaller than the free electron diffusion coefficient, so that the captured electrons are confined to the interior of the impurity region.

8. The method for modeling impurity particles in insulating oil streamer discharge considering dielectric inhomogeneity and electron trapping effects according to claim 1, characterized in that, The electron capture term and the electron release term are represented as follows: in: The free electron number density; The density of traps in the impurity region; The maximum equivalent trap density; and These are the electron capture coefficient and release coefficient, respectively. The electron reaction source term is corrected as follows: Trapped electrons satisfy: The method for modeling impurity particles in insulating oil streamer discharge considering dielectric inhomogeneity and electron trapping effects according to claim 1 is characterized in that the space charge density in the Poisson equation is corrected as follows: in: It is the elementary charge; It is the positive ion number density; It is the electron number density; The negative ion number density; This represents the trap electron number density.

9. The method for modeling impurity particles in insulating oil streamer discharge considering dielectric inhomogeneity and electron trapping effects according to claim 2, characterized in that, The metal particle impurities are modeled using a floating conductor model, where the metal particles are equivalent to highly conductive particles with no electrical connection to the external electrodes. In the electrostatic field model, the metal particles are defined as independent conductor regions, and floating potential boundary conditions are applied to the boundaries of the metal particles to maintain a consistent internal potential, simulating the characteristic that the internal electric field of highly conductive particles is approximately zero. Under the action of an applied impact electric field, the floating conductor model allows for the redistribution of induced charges on the surface of the metal particles, thereby characterizing the influence of the metal particles on the local electric field distribution of the insulating oil and the stream propagation path. The transport equations for electrons, positive ions, and negative ions are solved only in the insulating oil region, and flux-free boundary conditions are set on the surface of the metal particles. The boundaries of the metal particles satisfy the overall electroneutrality constraint condition, which is expressed as: in, Indicates the boundary of metal particles. Represents the unit normal vector outside the boundary of the metal particle. The electric displacement vector is represented; the constraint condition is used to limit the initial total charge of the metal particles to zero, while allowing charge polarization and spatial redistribution to occur on the surface of the metal particles under the action of an applied electric field. The transport equations of electrons, positive ions and negative ions are solved only in the insulating oil region. The interior of the metal particles does not participate in the carrier migration process, and no-flux boundary conditions are set on the surface of the metal particles for electrons, positive ions and negative ions to prevent carriers from entering the interior of the metal particles.

10. The method for modeling impurity particles in insulating oil streamer discharge considering dielectric inhomogeneity and electron trapping effects according to claim 1, characterized in that, By changing the number, size parameters, and spatial distribution of impurity particles, different impurity particle distribution models were established, and the time-domain solution of the streamer discharge process under different impurity particle conditions was performed. Based on the solution results, the influence parameters of impurity particles on the streamer discharge process were extracted. The influence parameters include at least one of the following: streamer starting position, streamer propagation velocity, streamer propagation length, streamer stopping distance, number of streamer branches, and degree of local electric field enhancement, in order to evaluate the promoting or inhibiting effect of impurity particles on the development of insulating oil streamers.

Images