A Plasma Dynamics-Based Method for Predicting the Lower Surface Flashover Voltage of Perfluoroisobutyronitrile Mixed Gases

Abstract

This invention provides a method for predicting surface flashover voltage in a perfluoroisobutyronitrile (PFOS) mixed gas based on plasma dynamics. It comprehensively considers the effects of gas molecule desorption and collisional ionization, surface charge accumulation at the gas-solid interface, and carrier traps in the solid medium on the solid side. A surface flashover model is constructed, and by solving the continuity governing equations, Poisson's equation, and local field approximation equations for charged particles, the spatiotemporal distribution of the electric field intensity and the transport of charged particles in space are obtained, serving as a means to predict the surface flashover voltage. This invention not only predicts surface flashover voltage but also holds promise as a data reference for the development of environmentally friendly insulating gas equipment, saving experimental costs and improving R&D efficiency.

Description

Technical Field

[0001] This invention relates to the field of electrical engineering technology. Specifically, it relates to a method for predicting surface flashover voltage in a C4F7N / CO2 mixed gas based on plasma dynamics. The method predicts surface flashover voltage under different gas mixing ratios, different gas pressure conditions, and different gas gap conditions. The prediction has been verified through experiments and can be applied to the research and development of environmentally friendly gas-insulated equipment. Background Technology

[0002] SF6 is widely used in high-voltage gas-insulated equipment due to its excellent insulation and arc-quenching properties. However, it has an extremely strong greenhouse effect (its global warming potential (GWP) is 24,300 times that of CO2) and an atmospheric lifetime of up to 3,200 years, seriously threatening global climate change. Studies have shown that the C4F7N / CO2 mixed gas exhibits excellent performance in insulation, arc-quenching characteristics, environmental friendliness, and biosafety, making it the most promising SF6 alternative gas in the high-voltage field.

[0003] According to CIGRE data, over 40% of GIS faults are caused by surface flashover of insulators, which seriously threatens the service life of high-voltage gas-insulated equipment such as GIL and GIS, as well as the safety and stability of power systems. Regarding the surface flashover characteristics of the C4F7N / CO2 mixed gas, researchers have demonstrated through multiple dimensions—power frequency withstand voltage tests, lightning impulse tests, switching impulse tests, and nanosecond pulse tests—that its insulation strength is likely to completely replace SF6. They also pointed out that during power frequency tests, the vast majority of surface flashovers occurred on the concave side of the basin insulator rather than the convex side, while under switching impulse voltage, discharges on the concave side of the basin insulator were observed to exist in two forms: breakdown along the insulator surface and breakdown along the gas gap.

[0004] Experimental methods can directly observe the discharge development path and process, and can effectively analyze insulation strength through electrical parameters such as breakdown voltage and current. However, they cannot understand the microscopic processes affecting carrier transport behavior, the electric field distortion capability of surface charge, and solid-side carrier trapping, thus limiting a deeper understanding of the surface flashover discharge mechanism and efficient improvement of surface flashover performance. Some researchers have built multiphysics discharge models, which can use numerical calculations to obtain detailed information on electric field intensity distribution and charged particle transport during the discharge process. For example, in the study of C4F7N mixed gas streamer discharge, Dmitry Levko et al. investigated the C4F7N / N2 mixed gas streamer discharge process under negative polarity DC voltage. Zang Yiming et al. used numerical calculations to obtain the distribution of electric field intensity and luminous flux density of C4F7N / CO2 mixed gas during streamer development under DC voltage. Our team studied the streamer discharge process of C4F7N / CO2 mixed gas under lightning impulse voltage and demonstrated through experiments that the model can be applied to the prediction of 50% lightning impulse voltage. However, due to the influence of factors such as gas-solid-gas-solid interface on the surface flashover, numerical calculation is quite difficult. There are few studies on the surface discharge of this mixed gas. Only Xinfeng Yan et al. constructed a surface discharge model of C4F7N / CO2 mixed gas and explored its optical phenomena on a macroscopic scale, but did not explore its discharge mechanism in depth, that is, comprehensively consider the microscopic charged particle transport process such as collisional ionization of gas molecules on the gas side, accumulation of surface charge at the gas-solid interface, and the influence of carrier traps on the solid side surface.

[0005] This invention comprehensively considers the effects of gas molecule desorption and collisional ionization on the gas side, surface charge accumulation at the gas-solid interface, and carrier traps in the solid medium on the solid side. It constructs a surface flashover model and solves the continuity governing equation, Poisson equation, and local field approximation equation for charged particles. This model can not only obtain the spatiotemporal distribution of electric field intensity and the transport of charged particles in space, but also serve as a means to predict surface flashover voltage. It is expected to serve as a data reference for the development of environmentally friendly insulating gas equipment, saving experimental costs and improving R&D efficiency.

[0006] Definitions:

[0007] C4F7N / CO2 mixed gas: Perfluoroisobutyronitrile mixed gas. Summary of the Invention

[0008] This invention discloses a method for predicting the surface flashover voltage of a C4F7N / CO2 mixed gas based on plasma dynamics to solve the aforementioned technical problems. This invention comprehensively considers the effects of desorption and collisional ionization of gas molecules on the gas side, surface charge accumulation at the gas-solid interface, and carrier traps in the solid medium on the solid side. A surface flashover model is constructed using finite element method (FE) software. By solving the continuity governing equation, Poisson's equation, and local field approximation equation for charged particles, the spatiotemporal transport behavior of charged particles is obtained, enabling the prediction of the surface flashover voltage of the C4F7N / CO2 mixed gas under different mixing ratios, electric field uniformity, gas pressures, and gas gaps.

[0009] The present invention solves its technical problem by adopting the following technical solution:

[0010] A method for predicting the lower-side flashover voltage of a perfluoroisobutyronitrile (PFOS) mixed gas based on plasma dynamics includes the following steps:

[0011] Step 1: Constructing a surface flashover test platform: The surface flashover test platform includes a solid side and a gas side. The contact surface between the solid side and the gas side forms a gas-solid interface. The gas side is filled with a C4F7N / CO2 mixed gas, and the solid side is filled with insulating material.

[0012] Step 2: Constructing a surface flashover model of the C4F7N / CO2 mixed gas: The geometry of the surface flashover model is obtained by scaling the surface flashover test platform proportionally.

[0013] In the surface flashover model, the cross-sectional data of electron collisions during the desorption and collisional ionization processes of C4F7N gas molecules and CO2 gas molecules on the gas side are obtained from the database, while the surface charge accumulation at the gas-solid interface is simulated by introducing partial differential equations.

[0014] The process of carriers being captured or escaping from carrier traps existing on the solid side is simulated using partial differential equations.

[0015] On the gas side, the Boltzmann equation is used to process the electron collision cross-sectional data of C4F7N gas and CO2 gas to obtain the average electron energy, mobility, diffusion coefficient and reaction rate; on the solid side, the medium characteristic parameters are set according to the solid medium characteristics to construct a surface flashover model of C4F7N / CO2 mixed gas.

[0016] Step 3: Using finite element method (FEM) software, solve the continuity governing equations and Poisson equations for the charged particle transport behavior in the surface flashover model. Use the local field approximation equation to simulate the potential distribution during the discharge process, and extract the voltage applied to the electrodes at the flashover moment as the predicted flashover voltage value for the surface flashover mode. ;

[0017] Step 4: Obtain the actual value of the flashover voltage using a surface flashover test platform. ;

[0018] Step 5: Establish the fitting formula:

[0019]

[0020] in, a , b These are the fitting parameters;

[0021] By inputting multiple sets and The value was obtained by fitting a and b value ；

[0022] Step 6: Using the surface flashover model of the C4F7N / CO2 mixed gas and finite element method software, the predicted flashover voltage of the C4F7N / CO2 mixed gas under test is obtained. And enter the following formula: The final predicted value of the flashover voltage of the C4F7N / CO2 mixed gas was obtained. U’ .

[0023] In a further improvement, in step two, the surface charge accumulation at the gas-solid interface is simulated by introducing partial differential equations, as shown in equations (1) to (3):

[0024] (1)

[0025] (2)

[0026] (3)

[0027] In the formula The surface charge density at the gas-solid interface; This represents the normal unit component of the solid insulating material pointing towards the gas side. This represents the solid-side volume current density. The gas-side current density; For the tangential component of the field strength at the interface; The surface conductivity of a solid dielectric. This is the electric displacement vector on the gas side; The volume conductivity of the solid medium; This represents the field strength on the solid side. This is the electric displacement vector on the solid side; e It is the elementary charge; The strength of the gas side field; , These represent the mobility of positive and negative ions, respectively. , These are the diffusion coefficients of positive and negative ions, respectively. or , or ; , These represent the densities of positive and negative ions, respectively. Boltzmann's constant; T For ambient temperature, Indicates time, in seconds.

[0028] In a further improvement, in step two, the process of carriers being captured or escaping from the carrier traps on the solid side is simulated by partial differential equations as shown in equations (4) to (8):

[0029] (4)

[0030] (5)

[0031] (6)

[0032] (7)

[0033] (8)

[0034] in, and These represent the capture and escape probabilities of charge carriers, respectively. For trap density; The initial electron-hole mobility; It is the vacuum permittivity; is the relative permittivity of epoxy resin; Et is the trap energy level; h is the escape frequency; h is Planck's constant. Boltzmann's constant; and These represent the amount of charge trapped and the amount of charge removed, respectively. The carrier capture probability; It is the elementary charge; For trap density; The probability of carrier detrapping; and These are the hole-trap recombination rate, the electron-trap recombination rate, and the electron-hole recombination rate, respectively. The charge of a free hole; The charge of the electron trap; Electron mobility; The charge of the hole trap; The charge of a free electron; This represents the hole mobility rate.

[0035] In a further improvement, in step three, the continuity equation and Poisson equation controlling the transport behavior of charged particles are solved using finite element software, as shown in equations (9) to (11):

[0036] (9)

[0037] (10)

[0038] (11)

[0039] in, These represent the number densities of electrons, positive ions, and negative ions, respectively. α m and η m These are the ionization coefficient and adhesion coefficient in the C4F7N / CO2 mixed gas, respectively. These represent the mobility coefficients of electrons, positive ions, and negative ions, respectively. The diffusion coefficients of electrons, positive ions, and negative ions; , These represent the recombination coefficients of electron-carrying and positive ions, and negative ions and positive ions, respectively. E Electric field strength; S 0 and S 1 represents electrons and positive ions generated by space photoionization; φ Let be the potential of each node in the domain; e Unit charge; ɛ 0 is the vacuum permittivity; The relative permittivity of the C4F7N / CO2 mixed gas is given.

[0040] In a further improvement, in step three, a local field approximation equation is used to simulate the potential distribution during the discharge process, as shown in equation (12):

[0041] (12);

[0042] in It represents electric potential.

[0043] Further improvements include the following dielectric characteristic parameters: relative permittivity, conductivity, carrier trapping level, and carrier capture rate.

[0044] Compared with the prior art, the present invention has the following main advantages:

[0045] a) It can obtain the transport behavior of charged particles and the distribution of electric field intensity at the microscopic level, providing an exploratory method for improving the insulation performance of gas-solid interfaces.

[0046] b) Reduce dependence on test conditions and test time, provide surface flashover data reference for the pre-development of gas-insulated equipment, and improve R&D efficiency. Attached Figure Description

[0047] Figure 1 This is a geometric diagram of the surface flashover model. In the diagram, a smoothed nanosecond-level step function is applied to boundary b1 to simulate the DC voltage applied during the experiment; boundary b2 is the gas-solid interface, with its secondary electron emission coefficient set to 0.05; boundary b3 is grounded, i.e., at potential. φ =0; while boundary b4 is set as a zero-charge boundary to isolate the outside world.

[0048] Figure 2 This is a cross-sectional view of electron collisions in a C4F7N / CO2 gas mixture.

[0049] Figure 3 This is a graph showing the basic data for the average electron energy, electron mobility, and diffusion coefficient during the discharge process.

[0050] Figure 4 This is a spatiotemporal distribution diagram of the electric field intensity during surface flashover.

[0051] Figure 5 This is a comparison chart of the predicted values ​​and actual values ​​of the model in this invention. Detailed Implementation

[0052] The method provided by the present invention will be further described below with reference to specific embodiments. This is only for illustrating the technical concept and features of the present invention, and does not constitute any limitation on the present invention.

[0053] A method for predicting the surface flashover voltage of a perfluoroisobutyronitrile (PFOS) mixed gas based on plasma dynamics is proposed, comprising: a) determining the electric field inhomogeneity, gas gap distance, and solid medium type, and constructing the geometry of the surface flashover model by scaling it proportionally to a surface flashover test platform. b) For the desorption and collisional ionization processes of gas molecules involved on the gas side, relevant electronic collision cross-sectional data of C4F7N and CO2 gas molecules are obtained from the https: / / fr.lxcat.net database, including reactions such as adhesion, ionization, elastic collision, excitation and recombination, and de-excitation. The surface charge accumulation at the gas-solid interface is simulated using a charge accumulation model. For the carrier traps existing in the solid medium on the solid side, partial differential equations are used to simulate the process of carrier capture or escape. c) On the gas side, the Boltzmann equation is used to process the cross-sectional data to obtain a series of data such as average electron energy, mobility, diffusion coefficient, and reaction rate; while on the solid side, corresponding parameters are set according to the characteristics of the solid medium. This constructs a surface flashover model for the C4F7N / CO2 mixed gas. d) The discharge process is simulated by solving the continuity control equations, Poisson equation, and local field approximation equations of charged particles in the model using finite element method software. The voltage applied to the electrode at the flashover moment is extracted as the flashover voltage of the model. e) Finally, the flashover voltage is obtained using a flashover test platform to verify the flashover voltage obtained by the model, clarify the prediction error range of the model, and obtain the fitting parameters using the fitting formula. This achieves the effect of predicting the surface flashover voltage based solely on the model flashover voltage and the fitting parameters.

[0054] In the surface flashover model, the geometry is designed using finger electrodes to simulate a slightly non-uniform field. The solid medium is epoxy resin, the mixed gas is 3.5% C4F7N / 96.5% CO2, the gas gap between the electrodes is 3 mm, and a DC voltage is applied. Figure 1 As shown.

[0055] The electron collision cross-sectional data for C4F7N / CO2 in the gaseous side are from the database at https: / / fr.lxcat.net. Figure 2 As shown in Table 1, these reactions include adhesion, ionization, elastic collision, excitation and recombination, and de-excitation.

[0056] Table 1: Electron Collision Reactions of C4F7N / CO2 Mixtures

[0057]

[0058] The accumulation of surface charge at the gas-solid interface in the surface flashover model is simulated by introducing partial differential equations, as shown in Equations 1 to 3.

[0059]

[0060] In the formula The surface charge density at the gas-solid insulation interface; This represents the normal unit component of the solid insulating material pointing towards the gas side. This represents the solid-side volume current density. The gas-side current density; For the tangential component of the field strength at the interface; The surface conductivity of a solid dielectric. This is the electric displacement vector on the gas side; The volume conductivity of the solid medium; This represents the field strength on the solid side. This is the electric displacement vector on the solid side; e It is the elementary charge; The strength of the gas side field; , The mobility of positive and negative ions; , The diffusion coefficients are for positive and negative ions; , The density of positive and negative ions. Boltzmann's constant; T The ambient temperature.

[0061] The carrier traps existing on the solid side are simulated by introducing partial differential equations, as shown in Equations 4 to 8.

[0062]

[0063] In the formula and The probability of carrier capture and escape; For trap density; For trap energy levels; Escape frequency; h It is Planck's constant; Boltzmann constant; T is temperature; and For the amount of charge trapped and the amount of charge removed; and For hole-trap, electron-trap, and electron-hole recombination rates.

[0064] On the gas side, the Boltzmann equation is used to process the cross-sectional data. Taking a 3.5% C4F7N / 96.5% CO2 mixture as an example, basic data such as average electron energy, electron mobility, and diffusion coefficient during the discharge process are obtained. Figure 3 As shown.

[0065] Some of the parameters involved in solid-side carrier traps are shown in Table 2 below.

[0066] Table 2 shows some of the parameters used in the model.

[0067]

[0068] The continuity equation and Poisson equation (as shown in Equations 9-11) controlling the transport behavior of charged particles are solved using finite element method software. The transport behavior includes the generation, migration, and recombination of different charged particles. The potential distribution during the discharge process is simulated based on the local field approximation, as shown in Equation 12.

[0069]

[0070] Numerical calculations can be used to obtain the spatiotemporal distribution of electric field intensity during surface flashover, such as... Figure 4 As shown, the example uses a 3.5%C4F7N / 96.5%CO2 mixed gas, a gas gap distance of 3mm, and a gas pressure of 0.2MPa.

[0071] Flashover voltage was obtained using a flashover test platform to verify the flashover voltage obtained by the model and to clarify the model prediction error range. Taking 0.9 MPa as an example, the error between the model prediction and the experimental value was 0.5%. Figure 5 As shown. The fitting formula is as shown in Equation 13.

[0072] (13)

[0073] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. Other modifications can be easily made by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and the illustrations shown and described herein.

Claims

1. A method for predicting the lower-side flashover voltage of a perfluoroisobutyronitrile (PFOS) mixed gas based on plasma dynamics, characterized in that, Includes the following steps: Step 1: Constructing a surface flashover test platform: The surface flashover test platform includes a solid side and a gas side. The contact surface between the solid side and the gas side forms a gas-solid interface. The gas side is filled with a C4F7N / CO2 mixed gas, and the solid side is filled with insulating material. Step 2: Constructing a surface flashover model of the C4F7N / CO2 mixed gas: The geometry of the surface flashover model is obtained by scaling the surface flashover test platform proportionally. In the surface flashover model, the cross-sectional data of electron collisions during the desorption and collisional ionization processes of C4F7N gas molecules and CO2 gas molecules on the gas side are obtained from the database, while the surface charge accumulation at the gas-solid interface is simulated by introducing partial differential equations. The process of carriers being captured or escaping from carrier traps existing on the solid side is simulated using partial differential equations. On the gas side, the Boltzmann equation is used to process the electron collision cross-sectional data of C4F7N gas and CO2 gas to obtain the average electron energy, mobility, diffusion coefficient and reaction rate; on the solid side, the medium characteristic parameters are set according to the solid medium characteristics to construct a surface flashover model of C4F7N / CO2 mixed gas. Step 3: Using finite element method (FEM) software, solve the continuity governing equations and Poisson equations for the charged particle transport behavior in the surface flashover model. Use the local field approximation equation to simulate the potential distribution during the discharge process, and extract the voltage applied to the electrodes at the flashover moment as the predicted flashover voltage value for the surface flashover mode. ; Step 4: Obtain the actual value of the flashover voltage using a surface flashover test platform. ; Step 5: Establish the fitting formula: ； in, a , b These are the fitting parameters; By inputting multiple sets and The value was obtained by fitting a and b value ； Step 6: Using the surface flashover model of the C4F7N / CO2 mixed gas and finite element method software, the predicted flashover voltage of the C4F7N / CO2 mixed gas under test is obtained. And enter the following formula: The final predicted value of the flashover voltage of the C4F7N / CO2 mixed gas was obtained. U’ .

2. The method for predicting the lower-side flashover voltage of a perfluoroisobutyronitrile mixed gas based on plasma dynamics as described in claim 1, characterized in that, In step two, the accumulation of surface charge at the gas-solid interface is simulated by introducing partial differential equations, as shown in equations (1) to (3): (1)； (2)； (3)； In the formula The surface charge density at the gas-solid interface; This represents the normal unit component of the solid insulating material pointing towards the gas side. This represents the solid-side volume current density. The gas-side current density; This represents the tangential component of the field strength at the interface. The surface conductivity of a solid dielectric. This is the electric displacement vector on the gas side; The volume conductivity of the solid medium; This represents the solid-side electric field strength. This is the electric displacement vector on the solid side; e It is the elementary charge; The strength of the gas side field; , These represent the mobility of positive and negative ions, respectively. , These are the diffusion coefficients of positive and negative ions, respectively. or , or ; , These represent the densities of positive and negative ions, respectively. Boltzmann's constant; T For ambient temperature, Indicates time, in seconds.

3. The method for predicting the lower-side flashover voltage of a perfluoroisobutyronitrile mixed gas based on plasma dynamics as described in claim 1, characterized in that, In step two, the process of carriers being captured or escaping from the carrier traps on the solid side is simulated by partial differential equations as shown in equations (4) to (8): (4)； (5)； (6)； (7)； (8)； in, and These represent the capture and escape probabilities of charge carriers, respectively. For trap density; The initial electron-hole mobility; It is the vacuum permittivity; is the relative permittivity of epoxy resin; Et is the trap energy level; h is the escape frequency; h is Planck's constant. Boltzmann's constant; and These represent the amount of charge trapped and the amount of charge removed, respectively. The carrier capture probability; It is the elementary charge; For trap density; The probability of carrier detrapping; and These are the hole-trap recombination rate, the electron-trap recombination rate, and the electron-hole recombination rate, respectively. The charge of a free hole; The charge of the electron trap; Electron mobility; The charge of the hole trap; The charge of a free electron; This represents the hole mobility rate.

4. The method for predicting the lower-side flashover voltage of a perfluoroisobutyronitrile mixed gas based on plasma dynamics as described in claim 1, characterized in that, In step three, the continuity equation and Poisson equation controlling the transport behavior of charged particles are solved using finite element software, as shown in equations (9) to (11): (9)； (10)； (11)； in, These represent the number densities of electrons, positive ions, and negative ions, respectively. α m and η m These are the ionization coefficient and adhesion coefficient in the C4F7N / CO2 mixed gas, respectively. These represent the mobility coefficients of electrons, positive ions, and negative ions, respectively. The diffusion coefficients of electrons, positive ions, and negative ions; , These represent the recombination coefficients of electron-carrying and positive ions, and negative ions and positive ions, respectively. E Electric field strength; S 0 and S 1 represents electrons and positive ions generated by space photoionization; φ Let be the potential of each node in the domain; e Unit charge; ɛ 0 is the vacuum permittivity; The relative permittivity of the C4F7N / CO2 mixed gas is given.

5. The method for predicting the lower-side flashover voltage of a perfluoroisobutyronitrile mixed gas based on plasma dynamics as described in claim 1, characterized in that, In step three, the potential distribution during the discharge process is simulated using a local field approximation equation, as shown in equation (12): (12)； in It represents electric potential.

6. The method for predicting the lower-side flashover voltage of a perfluoroisobutyronitrile mixed gas based on plasma dynamics as described in claim 1, characterized in that, The dielectric properties include relative permittivity, conductivity, carrier trapping level, and carrier capture rate.

Images