CN118296980A - SF (sulfur hexafluoride)6Evaluation method for arc extinguishing characteristics of substitute gas - Google Patents
SF (sulfur hexafluoride)6Evaluation method for arc extinguishing characteristics of substitute gas Download PDFInfo
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- 238000000034 method Methods 0.000 title claims abstract description 44
- 229910018503 SF6 Inorganic materials 0.000 title description 3
- SFZCNBIFKDRMGX-UHFFFAOYSA-N sulfur hexafluoride Chemical compound FS(F)(F)(F)(F)F SFZCNBIFKDRMGX-UHFFFAOYSA-N 0.000 title description 3
- 229960000909 sulfur hexafluoride Drugs 0.000 title description 3
- 239000002245 particle Substances 0.000 claims abstract description 27
- 238000005315 distribution function Methods 0.000 claims abstract description 24
- 238000001179 sorption measurement Methods 0.000 claims abstract description 17
- 238000004364 calculation method Methods 0.000 claims abstract description 13
- 230000015556 catabolic process Effects 0.000 claims abstract description 13
- 238000009413 insulation Methods 0.000 claims abstract description 9
- 239000000203 mixture Substances 0.000 claims abstract description 8
- 238000010891 electric arc Methods 0.000 claims abstract description 5
- 230000005684 electric field Effects 0.000 claims description 15
- 238000006243 chemical reaction Methods 0.000 claims description 9
- 230000008569 process Effects 0.000 claims description 7
- 239000000126 substance Substances 0.000 claims description 6
- 230000008859 change Effects 0.000 claims description 4
- 238000004134 energy conservation Methods 0.000 claims description 4
- 230000006698 induction Effects 0.000 claims description 4
- 238000004422 calculation algorithm Methods 0.000 claims description 3
- 230000005672 electromagnetic field Effects 0.000 claims description 3
- 238000002924 energy minimization method Methods 0.000 claims description 3
- 230000005855 radiation Effects 0.000 claims description 3
- 230000008033 biological extinction Effects 0.000 claims description 2
- 230000015572 biosynthetic process Effects 0.000 claims description 2
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- 230000007935 neutral effect Effects 0.000 claims description 2
- 230000035699 permeability Effects 0.000 claims description 2
- 239000007789 gas Substances 0.000 description 73
- 238000004088 simulation Methods 0.000 description 6
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Abstract
The invention discloses an assessment method for arc extinguishing characteristics of SF 6 substituted gas, which belongs to the application research field of gas insulated switchgear and SF 6 substituted gas, and comprises the following steps: determining a control equation and establishing a two-dimensional arc magnetohydrodynamic model; setting a calculation area, determining boundary conditions, and further solving a control equation to obtain the temperature distribution condition of the electric arc; calculating a gas plasma particle composition based on the temperature distribution spatial information; two approximate simplifications are carried out on the Boltzmann equation, and then the Boltzmann equation is solved, so that an electron energy distribution function of the gas after the arc is obtained; further, calculating a reduced ionization coefficient and a reduced electron adsorption coefficient of the gas after the arc based on the electron energy distribution function; and finally, calculating the reduced critical breakdown field intensity, and evaluating the insulation property of the gas according to the result.
Description
Technical Field
The invention relates to the technical field of substitute gas, in particular to a method for evaluating arc extinguishing characteristics of SF 6 (sulfur hexafluoride) substitute gas.
Background
SF 6 (sulfur hexafluoride) is an insulating and arc extinguishing medium in commonly used high-voltage power equipment, and is widely used because of its excellent insulating property, high thermal stability, chemical corrosion resistance and other advantages. However, since it is a powerful greenhouse gas, the effect on global warming is remarkable and is classified as one of the most serious greenhouse gases in the world due to its extremely high greenhouse effect. Therefore, the international society has begun to take measures to limit its use and actively seek more environmentally friendly alternative gases. In the search for SF 6 replacement gas, the arc extinction characteristics of the candidate gas need to be evaluated. The arc extinguishing characteristics refer to the ability of a gas to rapidly extinguish an arc and prevent its re-ignition when the gas generates an arc at high pressure. Therefore, the evaluation of the arc extinguishing characteristics of the substitute gas is of great importance.
Currently, the commonly used evaluation methods mainly comprise two types of laboratory tests and numerical simulation. Laboratory tests evaluate their arc extinguishing characteristics by performing a gas arc extinguishing test under specific conditions, but this method requires a lot of time, labor and materials, and has many limitations such as difficulty in repetition of test results, difficulty in control of test conditions, and the like. The numerical simulation is to simulate and analyze the gas arc extinguishing process by a computer to evaluate the arc extinguishing characteristics of the gas by establishing a gas arc extinguishing model, and has the advantages of high efficiency, accuracy, strong repeatability and the like, so that the numerical simulation becomes one of the main methods for researching and replacing the gas arc extinguishing characteristics at present.
However, the current numerical simulation method still has some problems, such as insufficient simulation accuracy, slower calculation speed, and the like, which affect the application of the numerical simulation method in actual engineering. Therefore, there is a need to develop a new method and system that can more accurately and rapidly evaluate the arc extinguishing characteristics of SF 6 replacement gas to support the development of more environmentally friendly high voltage power equipment.
Disclosure of Invention
Aiming at the defects of the prior art, the invention aims to provide an assessment method for the arc extinguishing characteristics of SF 6 instead of gas.
The aim of the invention can be achieved by the following technical scheme:
an assessment method for arc extinguishing characteristics of SF 6 substituted gas comprises the following steps:
s1, determining a control equation, and establishing a two-dimensional arc magnetohydrodynamic model;
s2, setting a calculation area and determining boundary conditions;
S3, solving a control equation to obtain the temperature distribution condition of the electric arc;
S4, calculating gas plasma particle components based on the temperature distribution space information obtained in the step S3;
s5, in order to evaluate the insulation characteristic number of the gas under study, the Boltzmann equation needs to be introduced to calculate the energy distribution function of electrons in the gas plasma. To simplify the calculation process, two approximations are made to the boltzmann equation;
s6, solving a Boltzmann equation to obtain an electron energy distribution function of the gas after the arc;
s7, calculating a reduced ionization coefficient and a reduced electron adsorption coefficient of the gas after the arc based on the electron energy distribution function;
s8, calculating the reduced critical breakdown field intensity;
and S9, evaluating the insulation property of the gas according to the result.
Further, in S1, the control equation to be determined includes: mass conservation equation, energy conservation equation and momentum conservation equation, and electromagnetic field equation and gas state equation; unlike conventional fluids, the arc is subject to lorentz forces under the action of an electromagnetic field, so j rBθ and j xBθ source terms characterizing the lorentz forces are considered in the momentum conservation equation; the energy conservation equation of the arc model is different from the traditional hydrodynamic equation in that: the joule heating term σe 2, which characterizes the arc heat source, is added to the radiation term u, which represents the energy transfer between the arc and the surrounding gas flow, and the specific form of the control equation is as follows:
(1) Conservation of mass equation
Wherein t is time; r is the radial distance; x is the axial distance; ρ is the mass density of the environment-friendly SF 6 instead of the gas arc plasma; v x is the axial velocity; v r is the radial velocity.
(2) Conservation of momentum equation
Wherein, p is environmental protection type gas pressure; τ ij is the viscous stress tensor of environment-friendly SF 6 substituted gas arc plasma; j x and j r are axial and radial current densities, respectively; b θ is the circumferential magnetic induction intensity.
(3) Conservation of energy equation
Wherein e is the total internal energy of the environment-friendly SF 6 substituted gas of unit mass; k is the turbulent thermal conductivity; t is the gas temperature; sigma is conductivity; e is the electric field strength; u is the radiation term.
(4) Equation of electric field
Solving the electric field in the arc plasma by using a Maxwell equation set can obtain the following potential equation:
In the method, in the process of the invention, Is an electric potential.
Electric field strength is available from electric potential:
Wherein E x is the axial electric field strength; e r is the radial electric field strength.
The current density is obtainable according to the simplified ohm's law:
jx＝σEx (13)
jr＝σEr (14)
(5) Equation of magnetic field
The magnetic field equations include an axial magnetic vector conservation equation and a radial magnetic vector conservation equation.
The circumferential magnetic induction intensity B θ can be obtained according to the magnetic vector:
Wherein A x is an axial magnetic vector; a r is radial magnetic vector; mu 0 is vacuum permeability.
(6) Equation of gas state
Wherein Z is a gas correction coefficient; r 0 is a gas constant; m w is the molecular mass of the gas.
Further, in S2, the calculation area needs to be set according to the structural characteristics of the gas switch, and the boundary condition needs to be set according to the actual physical environment. For example: assuming that the current density is uniformly distributed over the anode contact surface, the current density is determined by the arc current per unit area, and the potential boundary condition for the cathode surface is set to 0. The remaining boundary conditions such as temperature, pressure, magnetic vector, etc. are treated as default.
Further, in S3, a control equation set is solved by adopting a finite volume method and a simple algorithm
Further, in S4, the plasma particle composition is calculated according to the gibbs free energy minimization method. The gibbs free energy G of a plasma system consisting of N particles can be expressed as:
Where n i is the number density of the particles and μ i is the chemical potential of the particles; And Is the translational and internal component of the overall chemical potential; Is the enthalpy of formation of the particles.
According to thermodynamic theory, any spontaneously occurring process in the system under constant temperature and pressure conditions will result in a decrease in the gibbs free energy of the system until the system reaches equilibrium, i.e. dg=0. Thus, the composition of the plasma can be obtained by searching the minimum gibbs free energy of the plasma system, the specific steps of the method are as follows: first, the initial state components of the system are defined and mathematical relationships between gibbs free energy and components are established using conservation of material and thermodynamic equilibrium conditions. Then, the equation about the component is obtained by deriving the gibbs free energy, and then the derivative of the equation is made to be equal to zero, so that the value of the component is solved. Based on this new component state, the system Gibbs free energy is recalculated and taken as the new initial state. The above steps are repeated until the gibbs free energy of the system is no longer significantly changed, i.e. a minimum value is reached, and the composition of the system is determined.
Further, in S5, the boltzmann equation is processed using two approximate simplified methods, which may include linearization of the boltzmann equation and assuming that collisions between plasma particles are elastic collisions. The boltzmann equation is in the form:
Wherein f is an Electron Energy Distribution Function (EEDF), v is an electron velocity, E is an electron charge amount, m is an electron mass, E is an electric field strength, For the velocity gradient operator, C is the rate of change of the electron energy distribution function f during particle collisions.
Further, in S6, the component parameters of the plasma and the collision cross section parameters of the particles are required to be used as inputs, and the boltzmann equation is solved by iterative calculation by adopting a numerical solution method, so as to obtain the electron energy distribution function of the gas after the arc.
Further, in S7, it is necessary to calculate the approximated ionization coefficient α/N and the approximated adsorption coefficient η/N of the gas after the arc based on the electron energy distribution function. The specific calculation formula is as follows:
the microscopic parameters corresponding to the variables in the formula are as follows: n is neutral particle number density, W is electron drift velocity, Q i is ionization reaction collision section, Q a is electron adsorption reaction collision section, F0 is electron energy distribution function which is obtained by performing two approximate expansions and keeps constant in time and space, epsilon i is electron ionization reaction critical energy, epsilon a is electron adsorption reaction critical energy, and epsilon is electron energy.
Further, in S8, it is necessary to calculate the reduced critical breakdown field strength according to the condition that the reduced ionization coefficient is equal to the reduced electron adsorption coefficient.
Further, in S9, the insulation properties of the gas are evaluated by means of a controlled variable method.
The invention has the beneficial effects that:
1. The invention provides a novel SF 6 substituted gas arc extinguishing characteristic evaluation method, which can evaluate the insulating characteristic of SF 6 substituted gas more accurately by establishing a two-dimensional arc magnetohydrodynamic model, calculating the components of gas plasma particles, simplifying the Boltzmann equation and the like.
2. The invention adopts a finite volume method and a simple algorithm to solve the control equation set, and simultaneously introduces a Gibbs free energy minimization method to calculate the components of the plasma particles, so that the technical means enable the evaluation result to be more accurate.
3. The method calculates the reduced ionization coefficient and the reduced electron adsorption coefficient of the gas after the arc based on the electron energy distribution function, and calculates the reduced critical breakdown field intensity according to the condition that the reduced ionization coefficient is equal to the reduced electron adsorption coefficient, thereby further improving the accuracy and the reliability of the evaluation.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described, and it will be obvious to those skilled in the art that other drawings can be obtained according to these drawings without inventive effort.
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph of transient temperature profiles of a C 4F7N-CO2 (1:1) gas two-dimensional arc under different current conditions;
FIG. 3 is a graph showing the ionization coefficient and adsorption coefficient results of a C 4F7N-CO2 (1:1) gas mixture at different pressures;
FIG. 4 is a graph showing the calculated critical breakdown electric field of C 4F7N-CO2 (1:1) gas at various pressures;
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
As shown in fig. 1, a new method for evaluating arc extinguishing characteristics of SF 6 instead of gas includes the following steps:
s1, determining a control equation, and establishing a two-dimensional arc magnetohydrodynamic model;
s2, setting a calculation area and determining boundary conditions;
S3, solving a control equation to obtain the temperature distribution condition of the electric arc;
S4, calculating gas plasma particle components based on the temperature distribution space information obtained in the step S3;
S5, performing two approximate simplifications on the Boltzmann equation;
s6, solving a Boltzmann equation to obtain an electron energy distribution function of the gas after the arc;
s7, calculating a reduced ionization coefficient and a reduced electron adsorption coefficient of the gas after the arc based on the electron energy distribution function;
s8, calculating the reduced critical breakdown field intensity;
and S9, evaluating the insulation property of the gas according to the result.
Examples:
In the embodiment, C 4F7N-CO2 (1:1) gas is taken as an object, and gas arc extinguishing characteristics are evaluated; the method comprises the following specific steps:
s1, determining a control equation, and establishing a two-dimensional arc magnetohydrodynamic model;
S2, setting a calculation area again, and determining boundary conditions;
S3, solving a control equation to obtain the temperature distribution condition of the electric arc;
S4, calculating gas plasma particle components based on the temperature distribution space information obtained in the step S3;
S5, performing two approximate simplifications on the Boltzmann equation;
s6, solving a Boltzmann equation to obtain an electron energy distribution function of the gas after the arc;
s7, calculating a reduced ionization coefficient and a reduced electron adsorption coefficient of the gas after the arc based on the electron energy distribution function;
s8, calculating the reduced critical breakdown field intensity;
and S9, evaluating the insulation property of the gas according to the result.
The temperature distribution structure of the two-dimensional magnetohydrodynamic modeling solution of the embodiment is shown in fig. 3, and then an electron energy distribution function is solved based on two approximate boltzmann equations, and the calculated critical breakdown electric field calculation result of the C 4F7N-CO2 (1:1) gas under different pressures is shown in fig. 4.
FIG. 4 shows the effect of pressure on the variation of the reduced ionization coefficient α/N and the reduced adsorption coefficient η/N of a C 4F7N-CO2 (1:1) ratio gas at a temperature of 2000K with reduced electric field strength E/N. It can be observed that at the same E/N, alpha/N and eta/N increase with increasing pressure, which can be explained by increasing the pressure resulting in an increase in the molecular density of the gas. Under high pressure environment, gas molecules are more dense, thereby increasing the collision frequency between electrons and gas molecules. More collision events provide more opportunities for electrons to transfer energy to the gas molecules, which in turn results in a general increase in the efficiency of the ionization and excitation process. The effect of pressure on critical breakdown field (E/N) cr in 50% C 4F7N-CO2 (1:1) proportioning gas at 300-3500K. It can be seen that in the temperature range of 300-500K, the (E/N) cr of the C 4F7N-CO2 (1:1) ratio gas has little dependence on the gas pressure, since at low temperatures the mole fraction of the main component remains relatively stable in this temperature range. thus, even with increasing pressure, the interactions between the gas molecules do not change significantly, resulting in no significant change in the value of (E/N) cr. However, when the temperature is raised to between 1000-2700K, increasing the pressure can increase (E/N) cr, thereby improving the breakdown performance of the C 4F7N-CO2 (1:1) proportioning gas. This is because in this temperature range, interactions between gas molecules are more pronounced, and as the pressure increases, the collision frequency between gas molecules increases, and ionization and dissociation processes occur more easily, thereby increasing the value of (E/N) cr. In the high temperature range between 2700 and 3500K, no obvious rule exists between the pressure and (E/N) cr. this may be due to other factors (such as chemical reactions, energy transfer, etc.) beginning to dominate the breakdown performance of the C 4F7N-CO2 (1:1) proportioning gas over this temperature range, not just the pressure. This causes the value of (E/N) cr to no longer have a linear relationship with respect to pressure changes, and thus irregularities occur.
This shows that the method of the present invention can be used for adjusting the conditions of gas proportion, gas pressure, etc. to evaluate the insulation property and find out the substitute gas meeting the requirements.
The foregoing has shown and described the basic principles, principal features and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, and that the above embodiments and descriptions are merely illustrative of the principles of the present invention, and various changes and modifications may be made without departing from the spirit and scope of the invention, which is defined in the appended claims.
Claims (9)
1. The assessment method of the SF 6 alternative gas arc extinguishing characteristics is characterized by comprising the following steps:
s1, determining a control equation, and establishing a two-dimensional arc magnetohydrodynamic model;
s2, setting a calculation area and determining boundary conditions;
S3, solving a control equation to obtain the temperature distribution condition of the electric arc;
S4, calculating the components of the gas plasma particles based on the temperature distribution space information obtained in the step S3;
s5, introducing a Boltzmann equation to calculate an energy distribution function of electrons in the gas plasma to evaluate the insulation characteristic number of the gas under study;
s6, performing two approximate simplifications on the Boltzmann equation, and then solving the equation to obtain an electron energy distribution function of the gas after the arc;
s7, calculating a reduced ionization coefficient and a reduced electron adsorption coefficient of the gas after the arc based on the electron energy distribution function;
s8, calculating the reduced critical breakdown field intensity;
and S9, evaluating the insulation property of the gas according to the result.
2. The method for evaluating the arc extinguishing characteristics of SF 6 instead of gas according to claim 1, wherein the control equation to be determined in step S1 includes: mass conservation equation, energy conservation equation and momentum conservation equation, and electromagnetic field equation and gas state equation;
The mass conservation equation is:
Wherein t is time; r is the radial distance; x is the axial distance; r is the mass density of environment-friendly SF 6 substituted gas arc plasma; v x is the axial velocity; v r is the radial velocity;
The momentum conservation equation is:
Wherein, p is environmental protection type gas pressure; τ ij is the viscous stress tensor of environment-friendly SF 6 substituted gas arc plasma; j x and j r are axial and radial current densities, respectively; b θ is the circumferential magnetic induction intensity;
the energy conservation equation is:
Wherein e is the total internal energy of the environment-friendly SF 6 substituted gas of unit mass; k is the turbulent thermal conductivity; t is the gas temperature; sigma is conductivity; e is the electric field strength; u is a radiation term;
The potential equation is as follows:
In the method, in the process of the invention, Is at an electrical potential;
from the potential available electric field strength equation:
wherein E x is the axial electric field strength; e r is the radial electric field strength;
the current density equation is derived from the simplified ohm's law:
jx＝σEx
jr＝σEr
the magnetic field equation comprises an axial magnetic vector conservation equation and a radial magnetic vector conservation equation, namely:
The circumferential magnetic induction intensity B θ can be obtained according to the magnetic vector:
Wherein A x is an axial magnetic vector; a r is radial magnetic vector; mu 0 is vacuum permeability.
The gas state equation is as follows:
Wherein Z is a gas correction coefficient; r 0 is a gas constant; m w is the molecular mass of the gas.
3. The method for evaluating the arc extinguishing characteristics of SF 6 instead of gas according to claim 1, wherein in step S3, a finite volume method is used in combination with a simple algorithm to solve a control equation set.
4. The method for evaluating the arc extinguishing characteristics of SF 6 instead of gas according to claim 1, wherein in step S4, the composition of the plasma particles is calculated according to the gibbs free energy minimization method, and the gibbs free energy G of a plasma system consisting of N particles is expressed as:
Where n i is the number density of the particles and μ i is the chemical potential of the particles; And Is the translational and internal component of the overall chemical potential; Is the enthalpy of formation of the particles;
The plasma particle composition is obtained by searching the minimum gibbs free energy of the plasma system, and the method comprises the following specific steps:
Firstly, defining an initial state component of a system, and establishing a mathematical relationship between gibbs free energy and the component by utilizing a conservation of substances relationship and thermodynamic equilibrium conditions;
Then, obtaining an equation about the component by deriving the Gibbs free energy, enabling the derivative of the equation to be equal to zero, solving the value of the component, and recalculating the Gibbs free energy of the system according to the new component state and taking the new initial state;
The above steps are repeated until the gibbs free energy of the system is no longer significantly changed, i.e. a minimum value is reached, and the plasma particle composition is obtained.
5. The method of evaluating the arc extinguishing characteristics of SF 6 instead of gas according to claim 1, characterized in that in step S5, the boltzmann equation is processed using two approximate simplified methods, including linearization of the boltzmann equation and defining the collisions between plasma particles as elastic collisions, the boltzmann equation being of the form:
Wherein f is an Electron Energy Distribution Function (EEDF), v is an electron velocity, E is an electron charge amount, m is an electron mass, E is an electric field strength, For the velocity gradient operator, C is the rate of change of the electron energy distribution function f during particle collisions.
6. The method for evaluating the arc extinguishing characteristics of SF 6 instead of gas according to claim 1, wherein in step S6, component parameters of plasma and collision cross section parameters of particles are used as input, a numerical solution method is adopted, and Boltzmann equation is solved through iterative calculation, so that an electron energy distribution function of gas after arc is obtained.
7. The method for evaluating arc extinction characteristics of SF 6 as defined in claim 1, wherein in step S7, the approximate ionization coefficient α/N and the approximate adsorption coefficient η/N of the gas after arc are calculated based on the electron energy distribution function, and the specific calculation formula is as follows:
the microscopic parameters corresponding to the variables in the formula are as follows: n is neutral particle number density, W is electron drift velocity, Q i is ionization reaction collision section, Q a is electron adsorption reaction collision section, F0 is electron energy distribution function which is obtained by performing two approximate expansions and keeps constant in time and space, epsilon i is electron ionization reaction critical energy, epsilon a is electron adsorption reaction critical energy, and epsilon is electron energy.
8. The method according to claim 1, wherein the reduced critical breakdown field strength is calculated in step S8 based on the condition that the reduced ionization coefficient is equal to the reduced electron adsorption coefficient.
9. The method for evaluating the arc extinguishing characteristics of SF 6 instead of gas according to claim 1, characterized in that the insulating characteristics of the gas are evaluated by means of a controlled variable method in step S9.
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