CN117332619B - Method and system for establishing arc root jump model based on field path coupling - Google Patents

Abstract

The invention discloses a method and system for establishing an arc root jump model based on field-circuit coupling. The method includes the steps: S1. Set material parameters, construct an arc chain model and simulate and output arc micro-element trajectories; S2. According to the arc The micro-element trajectory extracts the position information of the arc micro-element, and the field-circuit coupling model processes the position information to obtain the arc shape information; S3. Establish a two-dimensional geometric model of the arc based on the output result of step S2 and add boundary conditions and field sources to construct the electric field. Simulation model, simulates and outputs the electric field intensity distribution around the arc; S4, combines the arc jump criterion, jump distance calculation formula and sliding distance calculation formula to build a jump judgment model, and determines whether the arc root jumps based on the field strength distribution and calculates the arc root jumping distance and sliding distance. The invention can simultaneously obtain the arc motion shape and field intensity distribution, determine whether the arc root jumps and calculate the jumping distance and sliding distance of the arc root.

Description

A method and system for establishing an arc root jump model based on field-circuit coupling

Technical field

The invention belongs to the technical field of arc motion simulation modeling, and specifically relates to a method and system for establishing an arc root jump model based on field-circuit coupling.

Background technique

With the continuous acceleration of urbanization, the cost of electricity in cities continues to increase. Because the main power generation areas and the main power consumption areas are usually far away, the number of transmission conductors in the suburbs continues to increase. These wires are located at high points in the wilderness and are more likely to be struck by lightning during thunderstorms. Therefore, the protection of lightning protection wires is essential. Research on the principles of lightning strikes and damage assessment of lightning protection wires have also become important research to ensure the safety of power transmission. The arc jumping phenomenon will cause discontinuous multi-segment damage on the lightning protection wire, which may cause multiple stranded wires to be damaged at the same time, putting the lightning protection wire at great risk of breakage and posing a threat to safe and reliable power transmission. Since it is difficult to accurately control variables in lightning experiments, it is of great practical significance to use simulation models to simulate arcs.

Contents of the invention

The first object of the present invention is to overcome the shortcomings and deficiencies of the existing technology and provide a method for establishing an arc root jumping model based on field-circuit coupling, which can simultaneously obtain the arc motion shape and field intensity distribution, determine whether the arc root jumps and Calculate the arc root jump distance and sliding distance.

The second object of the present invention is to provide a system for establishing an arc root jump model based on field-circuit coupling.

The object of the present invention is achieved through the following technical solution: a method for establishing an arc root jump model based on field-circuit coupling, including the steps:

S1. Set material parameters, divide the arc into several arc elements, and construct an arc chain model; based on the arc chain model, according to the preset simulation time and iteration time step, at each iteration time step Obtain the position of each arc element at the end of the time step until the iteration reaches the preset number of iteration steps, and simulate the trajectory of the arc element;

S2. Extract the position information, material parameters and lightning current intensity of the arc micro-element according to the trajectory of the arc micro-element as input to the field-circuit coupling model. The field-circuit coupling model processes the position information to obtain the arc shape information, which is processed by the simulation software. The command outputs arc shape information, material parameters and lightning current intensity;

S3. Establish a two-dimensional geometric model of the arc based on the arc shape information, material parameters and lightning current intensity output in step S2, add boundary conditions and field sources to the two-dimensional geometric model, build an electric field simulation model, and simulate and output the electric field around the arc. Intensity distribution;

S4. Combine the arc jump criterion, jump distance calculation formula and sliding distance calculation formula to construct a jump judgment model, where,

The arc jump criterion specifically includes: the maximum value of the electric field intensity output by the electric field simulation model is greater than the preset electric field intensity threshold, then the arc root jumps;

The jump distance calculation formula is as follows:

d _j =x' _m , formula (1),

, formula (2),

Among them, d _j is the jumping distance of the arc root, E _max is the maximum value of the electric field intensity output by the electric field simulation model, (x' _m , y' _m ) is the coordinate of the position where the jump occurs on the boundary of the arc. This coordinate is passed through the electric field simulation model reading, is the electric field intensity corresponding to the (x' _m , y' _m ) point;

S5. Determine the arc root jumping situation according to the electric field intensity distribution, thereby completing the establishment of the arc root jumping model, which specifically includes:

Compare the electric field intensity distribution with the arc jump criterion to determine whether the arc root jumps;

If so, calculate the jumping distance and sliding distance of the arc root according to the jumping distance calculation formula and the sliding distance formula respectively;

If not, calculate the sliding distance of the arc root according to the sliding distance calculation formula.

Preferably, step S1 specifically includes the following steps:

S11. Set the simulation time T and divide the simulation time T into H time steps evenly. , H is the number of iteration steps;

S12. Set the current intensity, space boundary, environmental wind speed and the material parameters of the lightning protection line. Divide the vertical lightning arc into several cylindrical arc elements with equal lengths and diameters. With the lightning strike point as the origin of the coordinates, the lightning protection line is _A plane rectangular coordinate system is established on _the x ₂ , y ₂ )... (x _n , y _n ), n represents the number of arc elements;

S13. Calculate the actual wind speed v _w considering the influence of the boundary layer:

, formula (3),

Among them, y is the distance between the arc element and the lightning protection line, l _w is the thickness of the boundary layer, v _o is the ambient wind speed;

S14. Perform stress analysis on the arc element within the time step, and calculate the speed of the arc element according to the air resistance formula. The calculation formulas of the resultant force F on the arc element and the speed v of the arc element are as follows:

F=F _c + F _w + F _l , formula (4),

, formula (5),

Among them, F _c =B _c Id l , formula (6),

F _l =B _l Id l , formula (7),

, formula (8),

, formula (9),

, formula (10),

Among them, B _c is the magnetic induction intensity generated by the current flowing through the lightning protection wire, B _l is the magnetic induction intensity generated by the current flowing through the arc element, μ is the magnetic permeability, I is the current intensity flowing through the arc element, d l is the length of the arc element, r _c is the distance between the arc element and the lightning protection line, r _l is the distance between the arc elements;

Assuming that the arc element moves at a uniform speed in each time step, calculate the displacement of the arc element within the time step, as shown in Equation (11), and update the position of the arc element at the end of this time step, as shown in Equation (11) 12):

, formula (11),

, formula (12),

in, ,/> is the velocity of the arc element in the kth time step,/> is the displacement of the arc element in the kth time step,/> is the displacement vector of the arc micro-element at the end of k time steps,/> is the initial position of the arc element;

S15. Enter the next time period: use the position of the arc element at the end of this time step in step S14 as the position of the arc element at the beginning of the next time period, repeat step S14; until the iteration reaches the preset number of iteration steps H, output the arc micro-element trajectory within the simulation time.

Preferably, in step S2, the field-circuit coupling model is used to extract and process the position information of the arc elements in the arc chain model, including the following steps:

S21. Extract the center coordinates of each arc element according to the arc element trajectory, and process the center coordinates to obtain the boundary point coordinates of the arc element:

First, the line connecting two adjacent center coordinates is taken as the direction of the arc at the center coordinate of the n-th arc element. The direction angle at the center coordinate of the n-th arc element is:

, formula (13),

Among them, n≥2, (x _n , y _n ) and (x _n-1 , y _n-1 ) are the center coordinates of the n-th and n-1 arc elements respectively;

Determine the normal direction of the direction at the center coordinate of each arc element, and extend the center coordinate of each arc element along both sides of the corresponding normal direction. The extension distance is the arc radius r, and the boundaries on both sides of the arc element are obtained. point, let the coordinates of the boundary points on both sides of the nth arc element be expressed as (x' _n , y' _n ) and (x' _2N-n+1 , y' _2N-n+1 ) respectively, where, N Represents the total number of arc micro-elements, and the coordinate construction formula of the boundary point is as follows:

When n≥2,

x' _n =x _n +rsinα _n , formula (14),

y' _n =y _n -rcosα _n , formula (15),

x' _2N-n+1 =x _n -rsinα _n , formula (16),

y' _2N-n+1 =y _n +rcosα _n , formula (17),

When n=1,

x' ₁ =x ₁ +r, formula (18),

x' _2N =x ₁ -r, formula (19),

y' ₁ = y' _2N =0, formula (20);

S22. Calculate the calculated boundary point coordinates of each arc element in the order: (x' ₁ , y' ₁ ), (x' ₂ , y' ₂ )... (x' _2N , y' _2N ) in the matrix The form is saved as a file to obtain the arc shape information, and the arc shape information, material parameters and lightning current intensity are output through the commands of the simulation software. The lightning current intensity is the lightning current at the end of the arc chain model simulation time.

Preferably, step S3 specifically includes the following steps:

S31. Establish a plane rectangular coordinate system with the lightning strike point as the origin and the lightning protection line as the X-axis direction, set the spatial boundary, and construct a two-dimensional geometric model of the arc based on the arc shape information;

S32. Add material attributes to the two-dimensional geometric model according to the material parameters: set the lightning protection line material to copper, set the arc material to air plasma, and set other areas except the lightning protection line and arc to air;

Set the boundary conditions and field source conditions: set the air boundary to electrical insulation: charge quantity Q=0, lightning protection line to ground: potential U=0, set the top of the arc to the lightning current terminal, and set the lightning current to the output of step S2 The lightning current intensity;

S33. Combine the two-dimensional geometric model, material properties, boundary conditions and field source conditions to obtain the electric field simulation model, and run the simulation software to obtain the electric field intensity distribution around the arc.

Preferably, in step S4, the sliding distance calculation formula is:

d _c =x' ₁ , formula (21),

Among them, d _c is the sliding distance of the arc root.

Preferably, in step S4, the preset electric field intensity threshold is set to 5kV/cm.

Preferably, in step S4, the preset electric field intensity threshold is set according to parameters of the dielectric in the space where the arc is located.

A system for establishing an arc root jump model based on field-circuit coupling, specifically including:

The arc chain model building module is used to set material parameters, divide the arc into several arc micro-elements, and construct an arc chain model; based on the arc chain model, according to the preset simulation time and iteration time step, in The time step of each iteration obtains the position of each arc element at the end of the time step, until the iteration reaches the preset number of iteration steps, and the arc element trajectory is simulated and output;

The field-circuit coupling model establishment module is used to extract the position information, material parameters and lightning current intensity of the arc micro-element according to the arc micro-element trajectory, as input to the field-circuit coupling model. The field-circuit coupling model processes the position information to obtain the arc Shape information, arc shape information, material parameters and lightning current intensity are output through the commands of the simulation software;

The electric field simulation model building module is used to establish a two-dimensional geometric model of the arc based on the arc shape information, material parameters and lightning current intensity output by the field-circuit coupling model, add boundary conditions and field sources to the two-dimensional geometric model, and construct an electric field simulation. Model, simulate and output the electric field intensity distribution around the arc;

The jump judgment model building module is used to combine the arc jump criterion, jump distance calculation formula and sliding distance calculation formula to build a jump judgment model, where,

The arc jump criterion specifically includes: the maximum value of the electric field intensity output by the electric field simulation model is greater than the preset electric field intensity threshold, then the arc root jumps;

The jump distance calculation formula is as follows:

d _j =x' _m , formula (1),

, formula (2),

Among them, d _j is the jumping distance of the arc root, E _max is the maximum value of the electric field intensity output by the electric field simulation model, (x' _m , y' _m ) is the coordinate of the position where the jump occurs on the boundary of the arc. This coordinate is passed through the electric field simulation model reading, is the electric field intensity corresponding to the (x' _m , y' _m ) point;

The judgment module is used to judge the jumping situation of the arc root according to the electric field intensity distribution, thereby completing the establishment of the arc root jumping model.

Preferably, the field-circuit coupling model is used to extract and process the position information of arc elements in the arc chain model, including:

The first processing module is used to extract the center coordinates of each arc element according to the arc element trajectory, and process the center coordinates to obtain the boundary point coordinates of the arc element:

First, the line connecting two adjacent center coordinates is taken as the direction of the arc at the center coordinate of the n-th arc element. The direction angle at the center coordinate of the n-th arc element is:

, formula (13),

Among them, n≥2, (x _n , y _n ) and (x _n-1 , y _n-1 ) are the center coordinates of the n-th and n-1 arc elements respectively;

Determine the normal direction of the direction at the center coordinate of each arc element, and extend the center coordinate of each arc element along both sides of the corresponding normal direction. The extension distance is the arc radius r, and the boundaries on both sides of the arc element are obtained. point, let the coordinates of the boundary points on both sides of the nth arc element be expressed as (x' _n , y' _n ) and (x' _2N-n+1 , y' _2N-n+1 ) respectively, where, N Represents the total number of arc micro-elements, and the coordinate construction formula of the boundary point is as follows:

When n≥2,

x' _n =x _n +rsinα _n , formula (14),

y' _n =y _n -rcosα _n , formula (15),

x' _2N-n+1 =x _n -rsinα _n , formula (16),

y' _2N-n+1 =y _n +rcosα _n , formula (17),

When n=1,

x' ₁ =x ₁ +r, formula (18),

x' _2N =x ₁ -r, formula (19),

y' ₁ = y' _2N =0, formula (20);

The second processing module is used to put the calculated boundary point coordinates of each arc element in order: (x' ₁ , y' ₁ ), (x' ₂ , y' ₂ )... (x' _2N , y' _2N ) is saved as a file in the form of a matrix to obtain the arc shape information, and the arc shape information, material parameters and lightning current intensity are output through the commands of the simulation software. The lightning current intensity is the lightning current at the end of the arc chain model simulation time. .

Preferably, in the jump judgment model building module, the sliding distance calculation formula is:

d _c =x' ₁ , formula (21),

Among them, d _c is the sliding distance of the arc root.

Compared with the existing technology, the present invention has the following advantages and effects:

(1) The method of the present invention first uses the arc chain model to obtain the arc micro-element trajectory at the corresponding time; extracts the position information of the arc micro-element according to the arc micro-element trajectory, and processes this position information through the field-path coupling model to obtain the arc For morphological information, the field-circuit coupling model inputs arc information, material parameters, and lightning current intensity as the initial conditions of the electric field simulation model; the electric field simulation model simulates and outputs the field intensity distribution in the space near the arc; finally, the jump judgment model is used to determine the electric field intensity based on the electric field intensity. The distribution characteristics and arc jumping criteria are used to determine whether the arc root jumps during the sliding process, and the jumping distance and sliding distance of the arc root are calculated using formulas. Using the arc root jump model of the present invention to conduct simulation research on the arc root jump motion can directly obtain the electric field intensity near the arc and the arc root jump distance, which facilitates better comparison and accident analysis. Since lightning arc jump and arc jump will cause The lightning protection wire causes multiple lightning strike points, and the lightning arc sliding on the lightning protection wire will cause thermal ablation damage to the lightning protection wire. This method provides data support for the damage assessment of the lightning protection wire.

(2) The present invention realizes the continuous operation of the arc root jump model through the field-circuit coupling model. The traditional arc chain model can only realize the simulation of the arc shape, and the traditional electric field simulation model can only realize the electric field simulation near the arc. However, the present invention realizes the coupling of the two models through the field circuit coupling model, which can directly simulate the electric field in the electric field simulation model. Obtain the arc shape and field strength distribution, and perform parameter setting operations through the field-circuit coupling model. All information of the two models can be obtained. The operation is very convenient. There is no need to repeatedly model and input, and more complex analysis and judgment can be made. This is The arc chain model or electric field simulation model cannot be realized by itself.

(3) The present invention proposes arc jumping criteria for whether arc roots jump and a calculation method for arc root jumping distance, which provides an important theoretical reference for more systematic simulation research on lightning arc root jumping phenomena.

Description of the drawings

Figure 1 is a schematic flow chart of a method for establishing an arc root jump model based on field-circuit coupling in the present invention.

Figure 2 is a schematic diagram of the simulation flow of the arc chain model of the present invention.

Figure 3 is a schematic diagram of the simulation flow of the field-circuit coupling model of the present invention.

Figure 4 is a schematic diagram of the simulation flow of the electric field simulation model of the present invention.

Figure 5 is a schematic diagram of the stress analysis of arc micro-elements near the lightning protection line of the present invention.

Figure 6 is a schematic diagram of the simulation output of the arc chain model of the present invention.

Figure 7 is a schematic diagram of the simulation output of the electric field simulation model of the present invention.

Detailed ways

The present invention will be described in further detail below with reference to the examples and drawings, but the implementation of the present invention is not limited thereto.

Example 1

Figure 1 shows a method for establishing an arc root jump model based on field-circuit coupling, including the steps:

S1. Set material parameters, divide the arc into several arc elements, and construct an arc chain model; based on the arc chain model, according to the preset simulation time and iteration time step, at each iteration time step Obtain the position of each arc element at the end of the time step until the iteration reaches the preset number of iteration steps, and simulate the trajectory of the arc element;

S2. Extract the position information, material parameters and lightning current intensity of the arc micro-element according to the trajectory of the arc micro-element as input to the field-circuit coupling model. The field-circuit coupling model processes the position information to obtain the arc shape information, which is processed by the simulation software. The command outputs arc shape information, material parameters and lightning current intensity;

S3. Establish a two-dimensional geometric model of the arc based on the arc shape information, material parameters and lightning current intensity output in step S2, add boundary conditions and field sources to the two-dimensional geometric model, build an electric field simulation model, and simulate and output the electric field around the arc. Intensity distribution;

S4. Combine the arc jump criterion, jump distance calculation formula and sliding distance calculation formula to construct a jump judgment model, where,

The arc jump criterion specifically includes: the maximum value of the electric field intensity output by the electric field simulation model is greater than the preset electric field intensity threshold, then the arc root jumps;

The jump distance calculation formula is as follows:

d _j =x' _m , formula (1),

, formula (2),

Among them, d _j is the jumping distance of the arc root, E _max is the maximum value of the electric field intensity output by the electric field simulation model, (x' _m , y' _m ) is the coordinate of the position where the jump occurs on the boundary of the arc. This coordinate is passed through the electric field simulation model reading, is the electric field intensity corresponding to the (x' _m , y' _m ) point;

S5. Determine the arc root jumping situation according to the electric field intensity distribution, thereby completing the establishment of the arc root jumping model, which specifically includes:

Compare the electric field intensity distribution with the arc jump criterion to determine whether the arc root jumps;

If so, calculate the jumping distance and sliding distance of the arc root according to the jumping distance calculation formula and the sliding distance formula respectively;

If not, calculate the sliding distance of the arc root according to the sliding distance calculation formula.

Specifically, the arc chain model is constructed using general simulation software such as MATLAB, and the electric field simulation model is constructed using general simulation software such as COMSOL. In this example, the above two models are simulated using MATLAB and COMSOL respectively, and the field-circuit coupling model Directly use the function COMSOL with MATLAB that comes with the software COMSOL for simulation.

In order to determine whether the arc root jumps, the present invention successively establishes an arc chain model, a field-circuit coupling model, an electric field simulation model and an arc judgment model. The establishment of the arc root jump model has been completed. When simulating using this arc root jump model, it can be obtained Under the set time, the movement shape of the arc and the field intensity distribution around the arc; using the field intensity distribution information to study the rules of arc root sliding and jumping motion, it can determine whether the arc root jumps and calculate the distance length of the arc root jump.

Among them, the arc chain model is used to perform force analysis on the arc micro-elements to calculate the displacement and position of the arc micro-elements and obtain the arc micro-element trajectory under the set simulation time. The arc chain model is a common existing method used to analyze arc speed and displacement. By subdividing the arc into arc micro-elements, taking the arc micro-elements as the research object, and setting the simulation time and time step, in each The process of obtaining the position of the arc elements within the time step is an iteration. When the time steps are superimposed to reach the simulation time, that is, after the number of iteration steps is reached, the simulation of this model ends, and the arc composed of arc elements is summarized and output. Trajectory, that is, arc micro-element trajectory;

The field-circuit coupling model is used to extract and process the position information of the arc elements in the arc chain model to obtain the arc shape information, and use the arc shape information as the initial conditions of the electric field simulation model. In the electric field simulation model, the arc shape is constructed in the form of polygons, so the arc trajectory in the electric field simulation model is constructed using the arc shape information output by the field-circuit coupling model. The arc shape information, lightning current intensity and material information are written into the electric field simulation model in the form of commands in the COMSOL with matlab module.

The electric field simulation model is used to solve the electric field mode in space. That is, the built-in current module in COMSOL software is used for simulation to obtain the electric field intensity distribution in the space near the arc after the arc hits the lightning protection line. Using the commands input by the field-circuit coupling model, a two-dimensional geometric model of the arc is established in the area near the arc based on the arc shape information, lightning current intensity and material information. The area of the two-dimensional geometric model includes the arc, lightning protection lines near the lightning strike point, and In the air domain, add the material information of each part, the field source and boundary conditions of the space, and start the simulation using the above conditions. The electric field simulation model outputs the electric field intensity distribution in the area near the arc at the end of the simulation time.

Finally, the jumping judgment model is used to judge the jumping situation of the arc according to the electric field intensity distribution and calculate the jumping distance and sliding distance of the arc. By comparing the electric field intensity distribution with the arc jumping criterion, if the arc jumping criterion is met, it is deemed that the arc has jumped, and the jumping distance and sliding distance of the arc root are calculated. If it is not satisfied, it is deemed that the arc has not jumped, and the sliding distance of the arc root is calculated. The distance, the jumping distance and the sliding distance can all be read directly through the electric field simulation model.

Specifically, as shown in Figure 7, the arc will have an obvious bending bulge at the jumping point. The electric field distribution near the arc in this curved bulging part is extremely uneven. The electric field will be concentrated at the arc bulging point, and the arc bulging point will It is very close to the lightning protection line, so the arc convex point is often the maximum field strength in space. To sum up, the jumping point of a lightning arc is the place where the field intensity in space is maximum, and whether the arc jumps can be judged by whether the maximum electric field intensity in space reaches the jumping threshold. The arc jump criterion of the present invention is an important conclusion for studying the lightning arc root jump process. Find the maximum value of the electric field intensity according to the output result of the electric field simulation model, read the coordinates (x' _m , y' _m ) corresponding to the maximum value of the electric field intensity, and substitute it into formula (1) to obtain the jumping distance of the arc root.

When the arc jumps, it will cause multiple lightning strike points on the lightning protection wire, and the arc sliding on the lightning protection wire will cause thermal ablation damage to the lightning protection wire. This model can calculate the jumping distance and sliding distance of the arc root, and combine the two according to research needs. Comprehensive use enables more complex and systematic research on lightning arc root jumping phenomena.

The present invention uses the arc root jump model to conduct simulation research on the arc root jump motion, which can directly obtain the electric field strength near the arc and the arc root jump distance, facilitate better comparison and accident analysis, and can predict arc accident damage to a certain extent. The situation provides a reference basis. Since lightning arc jumping and arc jumping will cause multiple lightning strike points on the lightning protection wire, and the lightning arc sliding on the lightning protection wire will cause thermal ablation damage to the lightning protection wire, this method provides a basis for the damage assessment of the lightning protection wire. Data support.

At the same time, the present invention realizes the continuous operation of the arc root jump model through the field-circuit coupling model. The traditional arc chain model can only realize the simulation of the arc shape, and the traditional electric field simulation model can only realize the electric field simulation near the arc. However, the present invention realizes the coupled simulation of the two models through the field-circuit coupling model, which can directly simulate the electric field simulation model. The arc motion shape and field strength distribution are obtained in Figure 7. Through the parameter setting operation of the field-circuit coupling model, all the information of the two models can be obtained. The operation is very convenient. There is no need to repeatedly model and input, and more complex operations can be performed. According to the analysis and judgment, this is something that the arc chain model or the electric field simulation model cannot achieve by itself.

The method of the present invention is not only suitable for arc jump judgment and jump distance calculation during lightning strikes, but also applicable for arc jump judgment and arc jump distance calculation during arc jump motion simulation in other situations other than lightning strikes.

Step S1 specifically includes the following steps:

S11. Set the simulation time T and divide the simulation time T into H time steps evenly. , H is the number of iteration steps;

S12. Set the current intensity, space boundary, environmental wind speed and the material parameters of the lightning protection line. Divide the vertical lightning arc into several cylindrical arc elements with equal lengths and diameters. With the lightning strike point as the origin of the coordinates, the lightning protection line is _A plane rectangular coordinate system is established on _the x ₂ , y ₂ )... (x _n , y _n ), n represents the number of arc elements;

S13. Calculate the actual wind speed v _w considering the influence of the boundary layer:

, formula (3),

Among them, y is the distance between the arc element and the lightning protection line, l _w is the thickness of the boundary layer, v _o is the ambient wind speed;

S14. Perform stress analysis on the arc element within the time step, and calculate the speed of the arc element according to the air resistance formula. The calculation formulas of the resultant force F on the arc element and the speed v of the arc element are as follows:

F=F _c + F _w + F _l , formula (4),

, formula (5),

Among them, F _c =B _c Id l , formula (6),

F _l =B _l Id l , formula (7),

, formula (8),

, formula (9),

, formula (10),

Among them, B _c is the magnetic induction intensity generated by the current flowing through the lightning protection wire, B _l is the magnetic induction intensity generated by the current flowing through the arc element, μ is the magnetic permeability, I is the current intensity flowing through the arc element, d l is the length of the arc element, r _c is the distance between the arc element and the lightning protection line, r _l is the distance between the arc elements;

Assuming that the arc element moves at a uniform speed in each time step, calculate the displacement of the arc element within the time step, as shown in Equation (11), and update the position of the arc element at the end of this time step, as shown in Equation (11) 12):

, formula (11),

, formula (12),

in, ,/> is the velocity of the arc element in the kth time step,/> is the displacement of the arc element in the kth time step,/> is the displacement vector of the arc micro-element at the end of k time steps,/> is the initial position of the arc element, k∈H;

S15. Enter the next time period: use the position of the arc element at the end of this time step in step S14 as the position of the arc element at the beginning of the next time period, repeat step S14; until the iteration reaches the preset number of iteration steps H, output the arc micro-element trajectory within the simulation time.

Specifically, as shown in Figures 2 and 5, it is assumed that lightning hits the lightning protection line vertically, that is, the vertical lightning arc represents the lightning strike when the influencing factors are the least. The lightning arc within 4 meters above the lightning protection line is used in this simulation. For modeling, it is set to 1m in this example.

First, the lightning arc is divided into several rigid cylinder arc elements with equal length and diameter. The center of the cylinder element represents the center of gravity of the arc element, and the axis direction of the cylinder element represents the direction of the current in the arc element. .

Then perform boundary layer refinement. The air boundary layer close to the lightning protection line is the key research object of arc root jump. In this embodiment, the air boundary layer is set to 0.1 meters. According to the knowledge of fluid mechanics, due to the existence of the boundary layer, the wind speed will decrease when approaching the lightning protection line. In order to study the influence of the boundary layer on the arc shape more carefully, in this embodiment, the length of the arc elements in the boundary layer is reduced. , the number increases: that is, the arc elements in the boundary layer of the lightning protection line are further intercepted, so that the lengths of the arc elements in the boundary layer are equal and smaller than the length of the arc elements outside the boundary layer. The processed coordinates of the arc micro-elements within the boundary layer and the coordinates of the arc micro-elements outside the boundary layer are input into the arc chain model as input data information for simulation of the arc chain model.

Before simulation, calculate the wind speed taking into account the influence of the boundary layer. This step can improve the accuracy of modeling. Then iterative simulation is performed using the time step as an iterative process, that is, in the loop iteration of the time step, each iteration corresponds to a time step. Regarding the setting of the time step, due to the short duration of the lightning return component and the large current amplitude, when the lightning current is in the return component stage, a shorter time step is used to improve the simulation accuracy, while the duration of the lightning continuous component is is longer and the current amplitude is smaller. When the lightning current is in the sustained component stage, a longer time step is used to reduce the calculation time of the model. In this embodiment, the time step is 10 ^-6 s when a return stroke occurs. In the sustained component stage, the time step is taken to be 10 ^-3 s.

The simulation of the arc chain model includes analyzing the electromagnetic force and wind force of the arc micro-element in each time step to obtain the position of the arc micro-element. At the end of each time step, the arc micro-element is obtained. After the updated position of the element, the arc elements are equally divided or merged: that is, the arc elements that are too long (overlong refers to the length exceeding 1.5 times of the initial arc elements) are equally divided into two arc elements of equal length. , the arc element that is too short (too long means the length is less than 0.5 times the initial arc element) is merged with the adjacent arc element, and the serial number of the corresponding arc element is adjusted. This operation facilitates the control of the length of the arc element. If it is too short or too long, it should be kept between 0.5 times and 1.5 times of the initial arc microelement to ensure the accuracy of the simulation results. The loop iteration ends when the set simulation time is reached, and the simulation outputs the arc micro-element trajectory, as shown in Figure 6.

In step S2, the field-circuit coupling model is used to extract and process the position information of the arc elements in the arc chain model, including the following steps:

S21. Extract the center coordinates of each arc element according to the arc element trajectory, and process the center coordinates to obtain the boundary point coordinates of the arc element:

First, the line connecting two adjacent center coordinates is taken as the direction of the arc at the center coordinate of the n-th arc element. The direction angle at the center coordinate of the n-th arc element is:

, formula (13),

Among them, n≥2, (x _n , y _n ) and (x _n-1 , y _n-1 ) are the center coordinates of the n-th and n-1 arc elements respectively;

Determine the normal direction of the direction at the center coordinate of each arc element, and extend the center coordinate of each arc element along both sides of the corresponding normal direction. The extension distance is the arc radius r, and the boundaries on both sides of the arc element are obtained. point, let the coordinates of the boundary points on both sides of the nth arc element be expressed as (x' _n , y' _n ) and (x' _2N-n+1 , y' _2N-n+1 ) respectively, where, N Represents the total number of arc micro-elements, and the coordinate construction formula of the boundary point is as follows:

When n≥2,

x' _n =x _n +rsinα _n , formula (14),

y' _n =y _n -rcosα _n , formula (15),

x' _2N-n+1 =x _n -rsinα _n , formula (16),

y' _2N-n+1 =y _n +rcosα _n , formula (17),

When n=1,

x' ₁ =x ₁ +r, formula (18),

x' _2N =x ₁ -r, formula (19),

y' ₁ = y' _2N =0, formula (20);

S22. Calculate the calculated boundary point coordinates of each arc element in the order: (x' ₁ , y' ₁ ), (x' ₂ , y' ₂ )... (x' _2N , y' _2N ) in the matrix The form is saved as a file to obtain the arc shape information, and the arc shape information, material parameters and lightning current intensity are output through the commands of the simulation software. The lightning current intensity is the lightning current at the end of the arc chain model simulation time.

Specifically, Figure 3 is a schematic diagram of the simulation process of the field-circuit coupling model. The simulation of the field-circuit coupling model includes using a series of commands in COMSOL with MATLAB to extract and process the coordinate data of the arc chain model, and integrate other components used for electric fields. Simulation model data. The field-circuit coupling model processes the center coordinates of the arc element to obtain the formula for the boundary point, see equation (14) to equation (20). It is actually a process of processing the arc element into a two-dimensional arc model.

Extract the center coordinates, instantaneous current intensity and material information of the arc element from the output of the arc chain model. These center coordinates correspond to the center coordinates of the arc element at the end of the arc chain model simulation time, and the instantaneous current intensity is also the same. The current size at the moment, the expression of the center coordinate (x _n , y _n ) is an update value. With the end of each time step, the value corresponding to the center coordinate is updated. Then the center coordinates are processed to obtain boundary points, and the coordinates of these boundary points constitute the boundaries of the arc. Since the arc shape in the electric field simulation model is constructed in the form of polygons, and the boundary points of the polygons need to be arranged in the clockwise direction, the boundaries of the polygons will not cross when constructing the two-dimensional geometric model of the arc. Through the field-circuit coupling model, after extending the center coordinates of each arc micro-element to two boundary points on both sides, the coordinates of the boundary points of all arc micro-elements are sorted counterclockwise, according to formula (13) to formula (18) Get the sequence of these boundary points sorted in counterclockwise order, and store the calculated (x' ₁ , y' ₁ ), (x' ₂ , y' ₂ )...(x' _2N , y' _2N ) in sequence Enter a two-dimensional matrix with n rows and 2 columns, and write an empty file separately in xx.csv format.

The arc shape information, material parameters and lightning current intensity are output through the commands of the simulation software, including:

Use the series of commands in COMSOL with MATLAB to convert the above xx.csv format file into

Import the data of the geometric model of the lightning arc trajectory into the electric field simulation model. The command module used is as follows: "model.component('Arc Root Jump Model').geom('Geometry Model')",

Use a series of commands in COMSOL with MATLAB to write some parameters of the material properties into the electric field simulation model, as shown in Table 1, as a modification and supplement to the material data in the COMSOL system material library. The command module used is as follows: "model.component('Arc root jump model').material('Material properties')".

Table 1 Material properties in simulation

Use a series of commands in COMSOL with MATLAB to write the current intensity at the end of the arc chain model simulation time into the electric field simulation model. The command module used is as follows: "model.component('Arc root jump model').physics('Current terminal')",

The above is the output of the field-circuit coupling model, which corresponds to the second output in Figure 1.

Step S3 specifically includes the following steps:

S31. Establish a plane rectangular coordinate system with the lightning strike point as the origin and the lightning protection line as the X-axis direction, set the spatial boundary, and construct a two-dimensional geometric model of the arc based on the arc shape information;

S32. Add material attributes to the two-dimensional geometric model according to the material parameters: set the lightning protection line material to copper, set the arc material to air plasma, and set other areas except the lightning protection line and arc to air;

Set the boundary conditions and field source conditions: set the air boundary to electrical insulation: charge quantity Q=0, lightning protection line to ground: potential U=0, set the top of the arc to the lightning current terminal, and set the lightning current to the output of step S2 The lightning current intensity;

S33. Combine the two-dimensional geometric model, material properties, boundary conditions and field source conditions to obtain the electric field simulation model, and run the simulation software to obtain the electric field intensity distribution around the arc.

Specifically, Figure 4 is a schematic diagram of the simulation flow of the electric field simulation model. Using the command input from the field-circuit coupling model, directly read the xx.csv file to construct a two-dimensional geometric model of the lightning arc polygon. The arc trajectory is constructed based on the boundary point coordinates of the arc, and the spatial boundary is delineated at the bottom of the lightning protection line and the edge of the air domain. In order to set boundary conditions, the area includes lightning arcs, lightning protection lines near the lightning strike point, and air areas. After setting the geometric parameters of the material (see Table 2) and the field source, the simulation is carried out through the simulation software. The electric field intensity distribution in the area near the electric field simulation model of the transmission arc is shown in Figure 7.

Table 2 Geometric parameters in simulation

In step S4, the sliding distance calculation formula is:

d _c =x' ₁ , formula (21),

Among them, d _c is the sliding distance of the arc root.

Specifically, x' ₁ corresponds to x' ₁ in the field-circuit coupling model, see formula (18). This coordinate can be read directly through the electric field simulation model.

In step S4, the preset electric field intensity threshold is set to 5kV/cm.

Specifically, in the study of this embodiment, if the maximum electric field intensity in the space around the arc reaches 5kV/cm, it is considered that the lightning arc root will jump.

In step S4, the preset electric field intensity threshold is set according to parameters of the dielectric in the space where the arc is located.

Specifically, the parameters of the dielectric refer to the parameters of air plasma. Under the action of air humidity and wind, the parameters of air plasma change, and the corresponding electric field intensity distribution is also different. Therefore, the electric field intensity threshold is set according to the actual parameters to facilitate improved simulation. accuracy. At the same time, for non-lightning arc jumping motion problems, corresponding jump judgments can also be made by setting different electric field intensity thresholds. Therefore, the method of the present invention is suitable for non-lightning arc jumping motion problems.

Example 2

A system for establishing an arc root jump model based on field-circuit coupling, specifically including:

The arc chain model building module is used to set material parameters, divide the arc into several arc micro-elements, and construct an arc chain model; based on the arc chain model, according to the preset simulation time and iteration time step, in The time step of each iteration obtains the position of each arc element at the end of the time step, until the iteration reaches the preset number of iteration steps, and the arc element trajectory is simulated and output;

The field-circuit coupling model establishment module is used to extract the position information, material parameters and lightning current intensity of the arc micro-element according to the arc micro-element trajectory, as input to the field-circuit coupling model. The field-circuit coupling model processes the position information to obtain the arc Shape information, arc shape information, material parameters and lightning current intensity are output through the commands of the simulation software;

The electric field simulation model building module is used to establish a two-dimensional geometric model of the arc based on the arc shape information, material parameters and lightning current intensity output by the field-circuit coupling model, add boundary conditions and field sources to the two-dimensional geometric model, and construct an electric field simulation. Model, simulate and output the electric field intensity distribution around the arc;

The jump judgment model building module is used to combine the arc jump criterion, jump distance calculation formula and sliding distance calculation formula to build a jump judgment model, where,

The arc jump judgment arc chain model building module is used to set material parameters, divide the arc into a number of arc micro-elements, and construct an arc chain model; based on the arc chain model, according to the preset simulation time and iterative Time step, at the time step of each iteration, the position of each arc element is obtained at the end of the time step, until the iteration reaches the preset number of iteration steps, and the arc element trajectory is simulated and output;

The field-circuit coupling model establishment module is used to extract the position information, material parameters and lightning current intensity of the arc micro-element according to the arc micro-element trajectory, as input to the field-circuit coupling model. The field-circuit coupling model processes the position information to obtain the arc Shape information, arc shape information, material parameters and lightning current intensity are output through the commands of the simulation software;

The electric field simulation model building module is used to establish a two-dimensional geometric model of the arc based on the arc shape information, material parameters and lightning current intensity output by the field-circuit coupling model, add boundary conditions and field sources to the two-dimensional geometric model, and construct an electric field simulation. Model, simulate and output the electric field intensity distribution around the arc;

The jump judgment model building module is used to combine the arc jump criterion, jump distance calculation formula and sliding distance calculation formula to build a jump judgment model, where,

The arc jump criterion specifically includes: the maximum value of the electric field intensity output by the electric field simulation model is greater than the preset electric field intensity threshold, then the arc root jumps;

The jump distance calculation formula is as follows:

d _j =x' _m , formula (1),

, formula (2),

Among them, d _j is the jumping distance of the arc root, E _max is the maximum value of the electric field intensity output by the electric field simulation model, (x' _m , y' _m ) is the coordinate of the position where the jump occurs on the boundary of the arc. This coordinate is passed through the electric field simulation model reading, is the electric field intensity corresponding to the (x' _m , y' _m ) point;

The judgment module is used to judge the jumping situation of the arc root according to the electric field intensity distribution, thereby completing the establishment of the arc root jumping model, which specifically includes:

Compare the electric field intensity distribution with the arc jump criterion to determine whether the arc root jumps;

If so, calculate the jumping distance and sliding distance of the arc root according to the jumping distance calculation formula and the sliding distance formula respectively;

If not, calculate the sliding distance of the arc root according to the sliding distance calculation formula.

Specifically, the present invention uses the arc root jump model to conduct simulation research on the arc root jump motion, which can directly obtain the electric field strength near the arc and the arc root jump distance, which facilitates better comparison and accident analysis, and can provide prediction to a certain extent. Arc accident damage conditions provide a reference basis. Since lightning arc jumps, arc jumps will cause multiple lightning strike points on the lightning protection wires, and the lightning arc sliding on the lightning protection wires will cause thermal ablation damage to the lightning protection wires. This method is to damage the lightning protection wires. The assessment provides data support.

In addition to being suitable for arc jump judgment and jump distance calculation during lightning strikes, the system of the present invention is also suitable for arc root jump judgment and arc root jump distance calculation during arc jump motion simulation in other situations other than lightning strikes. In this embodiment, the preset electric field intensity threshold is set to 5 kV/cm, and the preset electric field intensity threshold is set according to the parameters of the dielectric in the space where the arc is located.

The field-circuit coupling model is used to extract and process the position information of arc micro-elements in the arc chain model, including:

The first processing module is used to extract the center coordinates of each arc element according to the arc element trajectory, and process the center coordinates to obtain the boundary point coordinates of the arc element:

First, the line connecting two adjacent center coordinates is taken as the direction of the arc at the center coordinate of the n-th arc element. The direction angle at the center coordinate of the n-th arc element is:

, formula (13),

Among them, n≥2, (x _n , y _n ) and (x _n-1 , y _n-1 ) are the center coordinates of the n-th and n-1 arc elements respectively;

Determine the normal direction of the direction at the center coordinate of each arc element, and extend the center coordinate of each arc element along both sides of the corresponding normal direction. The extension distance is the arc radius r, and the boundaries on both sides of the arc element are obtained. point, let the coordinates of the boundary points on both sides of the nth arc element be expressed as (x' _n , y' _n ) and (x' _2N-n+1 , y' _2N-n+1 ) respectively, where, N Represents the total number of arc micro-elements, and the coordinate construction formula of the boundary point is as follows:

When n≥2,

x' _n =x _n +rsinα _n , formula (14),

y' _n =y _n -rcosα _n , formula (15),

x' _2N-n+1 =x _n -rsinα _n , formula (16),

y' _2N-n+1 =y _n +rcosα _n , formula (17),

When n=1,

x' ₁ =x ₁ +r, formula (18),

x' _2N =x ₁ -r, formula (19),

y' ₁ = y' _2N =0, formula (20);

The second processing module is used to put the calculated boundary point coordinates of each arc element in order: (x' ₁ , y' ₁ ), (x' ₂ , y' ₂ )... (x' _2N , y' _2N ) is saved as a file in the form of a matrix to obtain the arc shape information, and the arc shape information, material parameters and lightning current intensity are output through the commands of the simulation software. The lightning current intensity is the lightning current at the end of the arc chain model simulation time. .

In the jump judgment model building module, the sliding distance calculation formula is:

d _c =x' ₁ , formula (21),

Among them, d _c is the sliding distance of the arc root. Specifically, x' ₁ corresponds to x' ₁ in the field-circuit coupling model, see formula (18). This coordinate can be read directly through the electric field simulation model.

Specifically, the field-circuit coupling model processes the center coordinates of the arc micro-element to obtain the formula of the boundary point, see equation (14) to equation (20). It is actually a process of processing the arc micro-element into a two-dimensional arc model.

Extract the center coordinates, instantaneous current intensity and material information of the arc element from the output of the arc chain model. These center coordinates correspond to the center coordinates of the arc element at the end of the arc chain model simulation time, and the instantaneous current intensity is also the same. The current size at the moment, the expression of the center coordinate (x _n , y _n ) is an update value. With the end of each time step, the value corresponding to the center coordinate is updated. Then the center coordinates are processed to obtain boundary points, and the coordinates of these boundary points constitute the boundaries of the arc. Since the arc shape in the electric field simulation model is constructed in the form of polygons, and the boundary points of the polygons need to be arranged in the clockwise direction, the boundaries of the polygons will not cross when constructing the two-dimensional geometric model of the arc. The present invention realizes the continuous operation of the arc root jump model through the field-circuit coupling model. The traditional arc chain model can only realize the simulation of the arc shape, and the traditional electric field simulation model can only realize the electric field simulation near the arc. However, the present invention realizes the coupling of the two models through the field circuit coupling model, which can directly simulate the electric field in the electric field simulation model. Obtain the arc shape and field strength distribution, and perform parameter setting operations through the field-circuit coupling model. All information of the two models can be obtained. The operation is very convenient. There is no need to repeatedly model and input, and more complex analysis and judgment can be made. This is The arc chain model or electric field simulation model cannot be realized by itself.

The above embodiments are preferred implementations of the present invention and do not limit the present invention. Any other changes or other equivalent substitutions that do not deviate from the technical solution of the present invention are included in the protection scope of the present invention. within.

Claims (10)

1. The method for establishing the arc root jump model based on field path coupling is characterized by comprising the following steps:

s1, setting material parameters, equally dividing an electric arc into a plurality of electric arc microelements, and constructing an electric arc chain model; based on an arc chained model, according to preset simulation time and iterative time steps, acquiring the position of each arc micro element at the end time of each iterative time step until the iteration reaches the preset iterative step number, and simulating and outputting an arc micro element track;

S2, extracting position information, material parameters and lightning current intensity of an arc micro element according to the arc micro element track, and taking the position information, the material parameters and the lightning current intensity as input of a field coupling model, processing the position information by the field coupling model to obtain arc form information, and outputting the arc form information, the material parameters and the lightning current intensity through commands of simulation software;

s3, establishing a two-dimensional geometric model of the electric arc according to the arc form information, the material parameters and the lightning current intensity output in the step S2, adding boundary conditions and field sources to the two-dimensional geometric model, constructing an electric field simulation model, and simulating and outputting the electric field intensity distribution situation around the electric arc;

s4, constructing a jump judgment model by combining an arc jump criterion, a jump distance calculation formula and a sliding distance calculation formula,

the arc jump criterion specifically comprises: the maximum value of the electric field intensity output by the electric field simulation model is larger than a preset electric field intensity threshold value, and then an arc root jumps;

the jump distance calculation formula is as follows:

d _j =x’ _m (1),

(2),

wherein d _j For the jump distance of the arc root, E _max Maximum value of electric field intensity (x 'for electric field simulation model output)' _m ，y’ _m ) Is the position coordinate of jump on the boundary of the arc, the coordinate is read by an electric field simulation model, Is (x' _m ，y’ _m ) The electric field strength corresponding to the point;

s5, judging the jumping situation of the arc root according to the electric field intensity distribution situation, thereby completing the establishment of an arc root jumping model, and specifically comprising the following steps:

comparing the electric field intensity distribution condition with an electric arc jump criterion to judge whether the electric arc root jumps or not;

if yes, respectively calculating the jump distance and the sliding distance of the arc root according to the jump distance calculation formula and the sliding distance formula;

if not, calculating the sliding distance of the arc root according to the sliding distance calculation formula.

2. The method for establishing an arc root jump model based on field coupling according to claim 1, wherein the step S1 specifically comprises the following steps:

s11, setting simulation time T, and dividing the simulation time T into H time steps averagelyH is iterationStep number;

s12, setting current intensity, space boundary, ambient wind speed and material parameters of a lightning conductor, equally dividing a vertical lightning arc into a plurality of cylindrical arc microelements with equal length and diameter, taking a lightning stroke point as a coordinate origin, and taking the lightning conductor as an X axis to establish a plane rectangular coordinate system, taking the midpoint of a connecting line of two adjacent arc microelements as the center of the arc microelements, wherein the center coordinates of each arc microelements are sequentially expressed as (X) along the arc ₁ ，y ₁ ），（x ₂ ，y ₂ ）……（x _n ，y _n ) N represents the ordinal number of the arc infinitesimal;

s13, calculating actual wind speed considering boundary layer influencev _w ：

(3),

wherein,yis the distance between the arc infinitesimal and the lightning conductor,l _w for the thickness of the boundary layer,v _o is the ambient wind speed;

s14, carrying out stress analysis on the arc microelements in the time step, and calculating to obtain the speed of the arc microelements according to an air resistance formula, wherein the resultant force F of the arc microelements and the speed of the arc microelementsvThe calculation formulas of (a) are respectively as follows:

F=F _c + F _w + F _l (4),

(5),

wherein F is _c =B _c Idl(6),

F _l =B _l Idl(7),

(8),

(9),

(10),

wherein B is _c For the magnetic induction intensity generated by the current flowing through the lightning conductor, B _l For the magnetic induction intensity generated by the current flowing through the arc microelements, mu is magnetic permeability, I is the current intensity flowing through the arc microelements, and dlIs the length of arc infinitesimal, r _c Is the distance between the arc infinitesimal and the lightning conductor, r _l Is the distance between the arc microelements;

assuming that the arc element moves at a uniform speed in each time step, calculating the displacement of the arc element in the time step as shown in formula (11), and updating the position of the arc element at the end of the time step as shown in formula (12):

(11),

(12),

wherein,，/>for the speed of the arc infinitesimal in the kth time step,/for the arc infinitesimal>For the displacement of arc infinitesimal in the kth time step,/>For the displacement direction of arc infinitesimal at the end of k time stepsQuantity (S)>The initial position of the arc infinitesimal;

s15, entering the next time period: taking the position of the arc element at the ending time of the step S14 as the position of the arc element at the starting time of the next time period, and repeating the step S14; and outputting an arc trace element track in simulation time until iteration reaches a preset iteration step number H.

3. The method for establishing the arc root jump model based on field coupling according to claim 1, wherein in step S2, the field coupling model is used for extracting and processing the position information of the arc micro-element in the arc chain model, and the method comprises the following steps:

s21, extracting the central coordinates of each arc micro-element according to the arc micro-element track, and processing the central coordinates to obtain the boundary point coordinates of the arc micro-elements:

firstly, taking a connecting line of two adjacent central coordinates as the direction of an electric arc at the central coordinate of an nth electric arc micro-element, wherein the direction angle at the central coordinate of the nth electric arc micro-element is as follows:

(13),

wherein n is greater than or equal to 2, (x) _n ，y _n ) And (x) _n-1 ，y _n-1 ) The central coordinates of the nth and the (n-1) th arc microelements are respectively;

determining the normal direction of the direction at the central coordinates of each arc element, respectively expanding the central coordinates of each arc element along the two sides of the corresponding normal direction by the arc radius r to obtain boundary points at the two sides of the arc element, and respectively expressing the coordinates of the boundary points at the two sides of the nth arc element as (x '' _n ，y’ _n ) And (x' _2N-n+1 ，y’ _2N-n+1 ) Wherein N represents the total number of arc infinitesimal, and the coordinate construction formula of the boundary point is as follows:

when n is more than or equal to 2,

x’ _n =x _n +rsinα _n (14),

y’ _n =y _n -rcosα _n (15),

x’ _2N-n+1 =x _n -rsinα _n (16),

y’ _2N-n+1 =y _n +rcosα _n (17),

when n=1,

x’ ₁ =x ₁ +r, formula (18),

x’ _2N =x ₁ -r, formula (19),

y’ ₁ = y’ _2N =0, formula (20);

s22, the calculated boundary point coordinates of each arc infinitesimal are sequentially: (x' ₁ ，y’ ₁ ）、（x’ ₂ ，y’ ₂ ）……（x’ _2N ，y’ _2N ) And storing the arc form information in a matrix form as a file to obtain arc form information, and outputting the arc form information, material parameters and lightning current intensity which is the lightning current at the end time of the simulation time of the arc chained model through commands of simulation software.

4. The method for establishing an arc root jump model based on field coupling according to claim 1, wherein the step S3 specifically comprises the following steps:

S31, establishing a plane rectangular coordinate system by taking a lightning stroke point as an origin and a lightning wire as an X-axis direction, setting a space boundary, and constructing a two-dimensional geometric model of an electric arc according to the electric arc morphological information;

s32, adding material properties to the two-dimensional geometric model according to the material parameters: the lightning conductor material is copper, the arc material is air plasma, and other areas except the lightning conductor and the arc are air;

setting boundary conditions and field source conditions: the air boundary is set to be electrically insulating: the charge amount q=0, and the lightning conductor is set to ground: setting the top end of the electric arc as a lightning current terminal, and setting the lightning current as the lightning current intensity output in the step S2;

s33, combining the two-dimensional geometric model, the material attribute, the boundary condition and the field source condition to obtain an electric field simulation model, and operating simulation software to obtain the electric field intensity distribution condition around the arc.

5. The method for building an arc root jump model based on field coupling according to claim 3, wherein in step S4, the sliding distance calculation formula is:

d _c =x’ ₁ (21),

wherein d _c Is the sliding distance of the arc root.

6. The method for establishing an arc root jump model based on field coupling according to claim 1, wherein in step S4, the preset electric field intensity threshold is set to 5kV/cm.

7. The method for establishing an arc root jump model based on field coupling according to claim 1, wherein in step S4, the preset electric field intensity threshold is set according to parameters of a dielectric medium in a space where an arc is located.

8. The system for establishing the arc root jump model based on field path coupling is characterized by comprising the following specific steps:

the arc chain model building module is used for setting material parameters, equally dividing an arc into a plurality of arc infinitesimal units and building an arc chain model; based on an arc chained model, according to preset simulation time and iterative time steps, acquiring the position of each arc micro element at the end time of each iterative time step until the iteration reaches the preset iterative step number, and simulating and outputting an arc micro element track;

the field coupling model building module is used for extracting the position information, the material parameters and the lightning current intensity of the arc micro-element according to the arc micro-element track, and as the input of the field coupling model, the field coupling model processes the position information to obtain arc form information, and the arc form information, the material parameters and the lightning current intensity are output through commands of simulation software;

The electric field simulation model building module is used for building a two-dimensional geometric model of the electric arc according to the electric arc morphological information, the material parameters and the lightning current intensity output by the field path coupling model, adding boundary conditions and field sources to the two-dimensional geometric model, building an electric field simulation model and simulating the electric field intensity distribution situation around the output electric arc;

the jump judgment model building module is used for building a jump judgment model by combining an arc jump criterion, a jump distance calculation formula and a sliding distance calculation formula,

the arc jump criterion specifically comprises: the maximum value of the electric field intensity output by the electric field simulation model is larger than a preset electric field intensity threshold value, and then an arc root jumps;

the jump distance calculation formula is as follows:

d _j =x’ _m (1),

(2),

wherein d _j For the jump distance of the arc root, E _max Maximum value of electric field intensity (x 'for electric field simulation model output)' _m ，y’ _m ) Is the position coordinate of jump on the boundary of the arc, the coordinate is read by an electric field simulation model,is (x' _m ，y’ _m ) The electric field strength corresponding to the point;

and the judging module is used for judging the jumping situation of the arc root according to the electric field intensity distribution situation so as to complete the establishment of an arc root jumping model.

9. The system for building an arc root jump model based on field coupling according to claim 8, wherein the field coupling model is used for extracting and processing the position information of arc infinitesimal in the arc chain model, and comprises:

the first processing module is used for extracting the center coordinates of each arc element according to the arc element track and processing the center coordinates to obtain the boundary point coordinates of the arc elements:

firstly, taking a connecting line of two adjacent central coordinates as the direction of an electric arc at the central coordinate of an nth electric arc micro-element, wherein the direction angle at the central coordinate of the nth electric arc micro-element is as follows:

(13),

wherein n is greater than or equal to 2, (x) _n ，y _n ) And (x) _n-1 ，y _n-1 ) The central coordinates of the nth and the (n-1) th arc microelements are respectively;

determining the normal direction of the direction at the central coordinates of each arc element, respectively expanding the central coordinates of each arc element along the two sides of the corresponding normal direction by the arc radius r to obtain boundary points at the two sides of the arc element, and respectively expressing the coordinates of the boundary points at the two sides of the nth arc element as (x '' _n ，y’ _n ) And (x' _2N-n+1 ，y’ _2N-n+1 ) Wherein N represents the total number of arc infinitesimal, and the coordinate construction formula of the boundary point is as follows:

When n is more than or equal to 2,

x’ _n =x _n +rsinα _n (14),

y’ _n =y _n -rcosα _n (15),

x’ _2N-n+1 =x _n -rsinα _n (16),

y’ _2N-n+1 =y _n +rcosα _n (17),

when n=1,

x’ ₁ =x ₁ +r（18），

x’ _2N =x ₁ -r, formula (19),

y’ ₁ = y’ _2N =0, formula (20);

the second processing module is used for sequentially calculating the coordinates of the boundary points of each electric arc micro element: (x' ₁ ，y’ ₁ ）、（x’ ₂ ，y’ ₂ ）……（x’ _2N ，y’ _2N ) And storing the arc form information in a matrix form as a file to obtain arc form information, and outputting the arc form information, material parameters and lightning current intensity which is the lightning current at the end time of the simulation time of the arc chained model through commands of simulation software.

10. The system for building an arc root jump model based on field coupling according to claim 9, wherein in the jump judgment model building module, the sliding distance calculation formula is:

d _c =x’ ₁ (21),

wherein d _c Is the sliding distance of the arc root.