CN117332619B - Method and system for establishing arc root jump model based on field path coupling - Google Patents
Method and system for establishing arc root jump model based on field path coupling Download PDFInfo
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Abstract
The invention discloses a method and a system for establishing an arc root jump model based on field path coupling, wherein the method comprises the following steps: s1, setting material parameters, constructing an arc chained model and simulating and outputting an arc trace; s2, extracting the position information of the arc micro-element according to the arc micro-element track, and processing the position information by a field path coupling model to obtain arc form information; s3, establishing a two-dimensional geometric model of the electric arc according to the output result of the step S2, adding boundary conditions and field sources, constructing an electric field simulation model, and simulating the electric field intensity distribution situation around the output electric arc; s4, constructing a jump judgment model by using a simultaneous arc jump criterion, a jump distance calculation formula and a sliding distance calculation formula, judging whether an arc root jumps or not according to field intensity distribution, and calculating the jump distance and the sliding distance of the arc root. The invention can obtain the arc movement form and the field intensity distribution at the same time, judge whether the arc root jumps or not and calculate the jump distance and the sliding distance of the arc root.
Description
Technical Field
The invention belongs to the technical field of arc motion simulation modeling, and particularly relates to a method and a system for establishing an arc root jump model based on field path coupling.
Background
With the continuous acceleration of the urban process, the urban electricity consumption cost is increased continuously, and because the main power generation area and the main power consumption area are usually far away, the number of power transmission wires in suburbs is increased continuously. The wires are positioned at high points of the open field and are more easily struck by lightning in thunderstorm days, so that the lightning conductor is indispensable to protect, and research on the lightning strike principle and damage evaluation of the lightning conductor become important researches for ensuring the safety of power transmission. The arc jump phenomenon can cause discontinuous multistage damage on the lightning conductor, and can possibly cause simultaneous damage of a plurality of stranded wires, so that the lightning conductor has great fracture risk, and the safe and reliable power transmission is threatened. Because the experiment about thunder and lightning is not easy to control the accurate progress of the variable, the simulation of the arc by using the simulation model has strong practical significance.
Disclosure of Invention
The first object of the present invention is to overcome the drawbacks and disadvantages of the prior art, and to provide a method for establishing an arc root jump model based on field coupling, which can obtain an arc motion form and a field intensity distribution at the same time, determine whether the arc root jumps, and calculate a jump distance and a sliding distance of the arc root.
The second object of the invention is to provide a system for establishing an arc root jump model based on field path coupling.
The aim of the invention is achieved by the following technical scheme: a method for establishing an arc root jump model based on field path coupling comprises 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 edge of the arcThe position coordinates of the jump on the boundary are 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.
Preferably, the step S1 specifically includes the following steps:
s11, setting simulation time T, and dividing the simulation time T into H time steps averagelyH is the iteration step 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 vector of the arc infinitesimal at the end of k time steps +.>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.
Preferably, in step S2, the field coupling model is configured to extract and process location information of arc infinitesimal in the arc chained model, and includes 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 ) The arc shape information is obtained by storing the arc shape information in a matrix form as a file, and the arc shape information, material parameters and lightning current intensity are output through commands of simulation software, wherein the lightning current intensity is obtained when an arc chain model is simulatedLightning current at the end time of the interval.
Preferably, the step S3 specifically includes 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.
Preferably, 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.
Preferably, in step S4, the preset electric field strength threshold is set to 5kV/cm.
Preferably, in step S4, the preset electric field intensity threshold is set according to parameters of a dielectric medium in a space where the arc is located.
An arc root jump model building system based on field path coupling specifically comprises:
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.
Preferably, the field coupling model is used for extracting and processing the position information of arc microelements in the arc chain model, and comprises the following steps:
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, formula (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.
Preferably, in the jump judgment model building module, the calculation formula of the sliding distance is as follows:
d c =x’ 1 (21),
wherein d c Is the sliding distance of the arc root.
Compared with the prior art, the invention has the following advantages and effects:
(1) Firstly, obtaining an arc infinitesimal track under corresponding time by utilizing an arc chained model; extracting the position information of the arc infinitesimal according to the arc infinitesimal track, processing the position information through a field path coupling model to obtain arc form information, and inputting the arc information, material parameters and lightning current intensity through the field path coupling model to serve as initial conditions of an electric field simulation model; the electric field simulation model simulates the field intensity distribution of the space near the output arc; finally, judging whether the arc root jumps in the sliding process according to the distribution characteristics of the electric field intensity and an arc jump criterion by utilizing a jump judging model, and calculating the jump distance and the sliding distance of the arc root by utilizing a formula. The simulation research of the arc root jump movement is carried out by utilizing the arc root jump model, the electric field intensity and the arc root jump distance near the arc can be directly obtained, the accident analysis is convenient to better compare and carry out, and as the lightning arc jump and the arc jump can cause a plurality of lightning points to the lightning conductor, the lightning arc slides on the lightning conductor to cause the thermal ablation damage of the lightning conductor, the method provides data support for the damage evaluation of the lightning conductor.
(2) The invention realizes the continuous operation of the arc root jump model through the field path coupling model. The traditional arc chained model can only realize simulation of arc forms, the traditional electric field simulation model can only realize electric field simulation near the arc, the invention realizes coupling of the two models through the field path coupling model, can directly obtain arc forms and field intensity distribution in the electric field simulation model, can obtain all information of the two models through parameter setting operation of the field path coupling model, has very convenient operation, does not need repeated modeling and input, and can perform more complex analysis and judgment, which is that the arc chained model or the electric field simulation model cannot be realized only by itself.
(3) The invention provides an arc jump criterion for whether an arc root jumps or not and a calculation method for calculating the jump distance of the arc root, and provides an important theoretical reference basis for the simulation research of a lightning root jump phenomenon more system.
Drawings
Fig. 1 is a flow chart of a method for establishing an arc root jump model based on field coupling.
Fig. 2 is a schematic diagram of a simulation flow of the arc chain model of the present invention.
Fig. 3 is a schematic diagram of a simulation flow of the field coupling model of the present invention.
Fig. 4 is a schematic diagram of a simulation flow of the electric field simulation model of the present invention.
Fig. 5 is a schematic diagram of a stress analysis of arc microelements near a lightning conductor according to the present invention.
FIG. 6 is a schematic diagram of simulated output of the arc chain model of the present invention.
Fig. 7 is a schematic diagram of simulation output of the electric field simulation model of the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but embodiments of the present invention are not limited thereto.
Example 1
As shown in fig. 1, a method for establishing an arc root jump model based on field path coupling includes the 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 ) Bits for jumping on the boundary of an arcSetting coordinates, reading the coordinates through 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.
Specifically, the arc chain model is constructed by using general simulation software such as MATLAB, the electric field simulation model is constructed by using general simulation software such as COMSOL, in this example, the two models respectively simulate by using MATLAB and COMSOL, and the field coupling model directly uses the function COMSOL with MATLAB of the software COMSOL.
In order to judge whether the arc root jumps, the invention sequentially establishes an arc chain model, a field path coupling model, an electric field simulation model and an arc judgment model, and the establishment of the arc root jump model is completed, and when the arc root jump model is utilized for simulation, the movement form of the arc and the field intensity distribution around the arc can be obtained in set time; by utilizing field intensity distribution information, the law of sliding and jumping movement of the arc root is researched, whether the arc root jumps or not can be judged, and the distance length of the arc root jumping can be calculated.
The arc chained model is used for carrying out stress analysis on the arc infinitesimal to calculate the displacement and the position of the arc infinitesimal, and an arc infinitesimal track under the set simulation time is obtained. The arc chained model is a conventional method for analyzing the speed and displacement of an arc, the arc is subdivided into arc microelements, the arc microelements are used as research objects, the process of acquiring the position of the arc microelements is carried out in each time step by setting simulation time and time step as an iteration, when the time step is overlapped to reach the simulation time, namely the iteration step number is reached, the simulation of the model is finished, and the arc track formed by the arc microelements, namely the arc microelements track, is summarized and output;
The field path coupling model is used for extracting and processing the position information of the arc microelements in the arc chain model to obtain arc form information, and the arc form information is used as an initial condition of the electric field simulation model. In the electric field simulation model, the arc shape is constructed in a polygonal form, so that the arc track in the electric field simulation model is constructed by utilizing the arc shape information output by the field coupling model. Arc morphology 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 for solving an electric field mode in space, namely, simulation is carried out by utilizing a current module in COMSOL software, and the electric field intensity distribution condition of the space near the electric arc after the electric arc hits the lightning conductor is obtained. And establishing a two-dimensional geometric model of the electric arc in the vicinity of the electric arc according to the electric arc form information by utilizing a command input by the field coupling model, wherein the area of the two-dimensional geometric model comprises the electric arc, a lightning wire near a lightning stroke point and an air domain, then adding the material information of each part, a field source of the space and boundary conditions, starting simulation by utilizing the conditions, and outputting the electric field intensity distribution condition of the vicinity of the electric arc at the end time of the simulation by using the electric field simulation model.
And finally, judging the jumping situation of the electric arc according to the electric field intensity distribution situation through a jumping judgment model, and calculating the jumping distance and the sliding distance of the electric arc. By comparing the electric field intensity distribution condition with an electric arc jump criterion, the electric arc jump criterion is met, the electric arc is confirmed to jump, the jump distance and the sliding distance of an electric arc root are calculated, if not, the electric arc is confirmed to not jump, the sliding distance of the electric arc root is calculated, and the jump distance and the sliding distance can be directly read through an electric field simulation model.
Specifically, as shown in FIG. 7, an electric powerThe arc may be significantly curved at the jumping point, the electric field distribution near the arc of the curved protrusion portion is extremely uneven, the electric field may be concentrated at the arc protrusion point, and the arc protrusion point is very close to the lightning conductor, so that the arc protrusion point is often at the field intensity maximum in space. In summary, the jumping point of Lei Dianhu is the position of the maximum field strength in the space, and whether the arc jumps or not can be judged by judging whether the maximum field strength in the space reaches the jumping threshold value. The arc jump criterion of the invention is an important conclusion for researching Lei Dianhu jump processes. Finding the maximum value of the electric field intensity according to the output result of the electric field simulation model, and reading the coordinate (x 'corresponding to the maximum value of the electric field intensity' m ，y’ m ) Substituting the jump distance into the formula (1) to obtain the jump distance of the arc root.
When the electric arc jumps, a plurality of lightning strike points are caused to the lightning conductor, and the electric arc slides on the lightning conductor to cause thermal ablation damage to the lightning conductor.
According to the invention, simulation research of arc root jumping motion is carried out by utilizing an arc root jumping model, so that the electric field intensity and the arc root jumping distance near an arc can be directly obtained, better comparison and accident analysis are facilitated, a reference basis can be provided for predicting the damage condition of an arc accident to a certain extent, as Lei Dianhu jumping arc jumping can cause a plurality of lightning stroke points to a lightning conductor, and lightning arc sliding on the lightning conductor can cause thermal ablation damage to the lightning conductor, the method provides data support for carrying out damage assessment of the lightning conductor.
Meanwhile, the invention realizes the continuous operation of the arc root jump model through the field path coupling model. The traditional arc chained model can only realize simulation of arc morphology, the traditional electric field simulation model can only realize electric field simulation near the arc, the invention realizes coupling simulation of two models through the field path coupling model, can directly obtain arc motion morphology and field intensity distribution in the electric field simulation model, see fig. 7, can obtain all information of the two models through parameter setting operation of the field path coupling model, has very convenient operation, does not need repeated modeling and input, and can perform more complex analysis and judgment, which is that the arc chained model or the electric field simulation model cannot be realized only by itself.
The method is suitable for arc jump judgment and jump distance calculation in lightning stroke, and is also suitable for arc jump judgment and jump distance calculation in arc jump motion simulation under other occasions without lightning stroke.
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 the iteration step 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 microelements vThe 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 vector of the arc infinitesimal at the end of k time steps +.>K is H, which is 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.
Specifically, as shown in fig. 2 and fig. 5, it is assumed that lightning vertically hits the lightning conductor, that is, the lightning conductor with the smallest influencing factor is represented by vertical Lei Dianhu, and the lightning arc within the range of 4 meters above the lightning conductor is taken to participate in the simulation modeling, which is set to be 1m in this embodiment.
Firstly, equally dividing a lightning arc into a plurality of arc microelements of rigid cylinders with the same length and diameter, wherein the center of each cylinder microelement represents the center of gravity of the arc microelement, and the axial direction of each cylinder microelement represents the direction of current in the arc microelement.
And refining the boundary layer. The air boundary layer close to the lightning conductor is an important study object of arc root jump, and the air boundary layer is 0.1 meter in the embodiment. According to the hydrodynamic knowledge, due to the existence of the boundary layer, the wind speed is reduced when approaching the lightning conductor, and in order to more finely study the influence of the boundary layer on the arc morphology, the length of arc infinitesimal in the boundary layer is reduced, and the number is increased in the embodiment: and further intercepting the arc micro-elements in the boundary layer of the lightning conductor to ensure that the lengths of the arc micro-elements in the boundary layer are equal and smaller than the lengths of the arc micro-elements outside the boundary layer. And inputting the coordinates of the arc micro-elements in the processed boundary layer and the coordinates of the arc micro-elements outside the boundary layer into an arc chained model, and taking the coordinates and the coordinates as input data information for simulation of the arc chained model.
Before simulation, wind speed considering boundary layer influence is calculated, and modeling accuracy is improved conveniently. And then taking the time step as an iteration process to carry out iteration simulation, namely, in the loop iteration of the time step, each iteration corresponds to one time step. For the setting of the time step, since the duration of the back-striking component of the lightning is shorter and the current amplitude is larger, in the phase of the lightning current in the back-striking component, a shorter time step is adopted to improve the simulation accuracy, while the duration of the continuous component of the lightning is longer and the current amplitude is smaller, in the phase of the lightning current in the continuous component, a longer time step is adopted to reduce the calculation time of the model, in this embodiment, 10 time steps are taken when the back-striking occurs -6 s, taking 10 in duration component phase time step -3 s。
The simulation of the arc chained model comprises the steps of carrying out stress analysis of electromagnetic force and wind force on arc microelements in each time step to obtain the positions of the arc microelements, and equally dividing or merging the arc microelements after obtaining updated positions of the arc microelements at the end time of each time step: namely, an overlong arc element (overlong means that the length is 1.5 times longer than that of an initial arc element) is equally divided into two arc elements with equal length, an excessively short arc element (overlong means that the length is 0.5 times shorter than that of the initial arc element) is combined with an adjacent arc element, and the sequence numbers of the corresponding arc elements are adjusted. The loop iteration is ended when the set simulation time is reached, and the arc trace is simulated and output, as shown in fig. 6.
In step S2, the field coupling model is configured to extract and process position information of arc microelements in the arc chain model, and includes 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.
Specifically, as shown in fig. 3, a schematic diagram of a simulation flow of a field coupling model is shown, and the simulation of the field coupling model includes extracting and processing coordinate data of an arc chain model by using a series of commands in COMSOL with MATLAB, and integrating other data for an electric field simulation model. The field coupling model processes the central coordinates of the arc infinitesimal to obtain formulas of boundary points, which are shown in formulas (14) to (20), and the arc infinitesimal is actually processed into an arc two-dimensional model.
Extracting central coordinates of arc microelements, instantaneous current intensity and material information from output of an arc chained model, wherein the central coordinates correspond to central coordinates of the arc microelements at the end time of simulation of the arc chained model, the instantaneous current intensity is also the current at the moment, and the expression (x n ，y n ) Is an updated value, and the value corresponding to the center coordinates is updated as each time step ends. And then processing the central coordinates to obtain boundary points, wherein the coordinates of the boundary points form the boundary of the arc. Because the arc shape in the electric field simulation model is constructed in a polygonal form, and the boundary points of the polygons need to be arranged in a time needle direction, the boundaries of the polygons cannot be crossed when constructing a two-dimensional geometric model of the arc. After expanding the central coordinates of each arc element to two sides through a field path coupling model to obtain two boundary points, sequencing the coordinates of the boundary points of all arc elements anticlockwise, obtaining a sequence of sequencing the boundary points anticlockwise according to a formula (13) to a formula (18), and calculating (x' 1 ，y’ 1 ）、（x’ 2 ，y’ 2 ）……（x’ 2N ，y’ 2N ) Sequentially storing the n rows and 2 columns of two-dimensional matrixes, and independently writing the blank files in an xx.csv format.
Outputting arc form information, material parameters and lightning current intensity through commands of simulation software, wherein the method specifically comprises the following steps:
using the series command in COMSOL with MATLAB, the xx.csv format file is used
The command module used as the data of the geometric model of the lightning arc track is imported into the electric field simulation model as follows: "model. Component ('arc root hopping model')geom ('geometry model')",
Using the series of commands in COMSOL with MATLAB, part of the parameters of the material properties were written into the electric field simulation model, see table 1, as modifications and additions to the material data in the COMSOL system materials library. The command module used is as follows: "model. Component ('arc root hopping model'). Material ('Material Properties').
Table 1 material properties in the simulation
The current intensity at the end of the arc chain model simulation time was written into the electric field simulation model using the series of commands in COMSOL with MATLAB. The command module used is as follows: "model. Component ('arc root jump model'). Physics ('current termination')",
the above is taken as the output of the field coupling model, namely the 2 nd output in fig. 1.
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.
Specifically, fig. 4 is a schematic diagram of a simulation flow of the electric field simulation model. And directly reading xx.csv files by using a command input by a field coupling model to construct a Lei Dianhu polygonal two-dimensional geometric model, wherein an arc track is constructed according to coordinates of boundary points of an arc, and a space boundary is defined at the bottom of a lightning conductor and the edge of an air domain so as to set boundary conditions, wherein the region comprises Lei Dianhu, the lightning conductor near the lightning strike point and the air domain. After the geometrical parameters (see table 2) and the field sources of the materials are set, simulation is carried out through simulation software, and the electric field simulation model is used for simulating the electric field intensity distribution condition of the region near the transmission arc, as shown in fig. 7.
Table 2 geometric parameters in the simulation
In step S4, the sliding distance calculation formula is as follows:
d c =x’ 1 (21),
wherein d c Is the sliding distance of the arc root.
Specifically, x' 1 Corresponding to x 'in the field coupling model' 1 See equation (18), this coordinate can be read directly by the electric field simulation model.
In step S4, the preset electric field strength threshold is set to be 5kV/cm.
Specifically, in the study of this example, when the maximum electric field strength of the space around the arc was set to 5kV/cm, it was considered that Lei Dianhu pieces would jump.
In step S4, the preset electric field intensity threshold is set according to parameters of a dielectric medium in a space where the arc is located.
Specifically, the parameters of the dielectric medium refer to parameters of air plasma, the parameters of the air plasma are changed under the action of air humidity and wind power, and the corresponding electric field intensity distribution is different, so that the electric field intensity threshold value is set according to the actual parameters, and the simulation accuracy is convenient to improve. Meanwhile, for the problem of non-lightning arc jumping movement, corresponding jumping judgment can be performed by setting different electric field intensity thresholds, so that the method is suitable for the problem of non-lightning arc jumping movement.
Example 2
An arc root jump model building system based on field path coupling specifically comprises:
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 arc judging chained model building module is used for setting material parameters, equally dividing an arc into a plurality of arc microelements and building an arc chained 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 Electric field output for electric field simulation modelMaximum value of intensity, (x' 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;
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, and specifically comprises 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.
Specifically, the simulation research of the arc root jump motion is carried out by utilizing the arc root jump model, the electric field intensity and the arc root jump distance near the arc can be directly obtained, the accident analysis is convenient to better compare and carry out, a reference basis can be provided for predicting the damage condition of the arc accident to a certain extent, as Lei Dianhu jump arc jump can cause a plurality of lightning stroke points to the lightning conductor, and lightning arc slides on the lightning conductor to cause the thermal ablation damage of the lightning conductor, the method provides data support for carrying out the damage evaluation of the lightning conductor.
The system is suitable for arc jump judgment and jump distance calculation in lightning stroke, and is also suitable for arc root jump judgment and jump distance calculation in arc jump motion simulation under other occasions without lightning stroke. In this embodiment, the preset electric field intensity threshold is set to 5kV/cm, and the preset electric field intensity threshold is set according to parameters of a dielectric medium in a space where the arc is located.
The field coupling model is used for extracting and processing the position information of the arc microelements in the arc chain model, and comprises the following steps:
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, formula (18),
x’ 2N =x 1 -r, formula (19),
y’ 1 = y’ 2N =0, formula (20);
a second processing module for calculatingThe coordinates of the boundary points of each arc infinitesimal are obtained according to the sequence: (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.
In the jump judgment model building module, the calculation formula of the sliding distance is as follows:
d c =x’ 1 (21),
wherein d c Is the sliding distance of the arc root. Specifically, x' 1 Corresponding to x 'in the field coupling model' 1 See equation (18), this coordinate can be read directly by the electric field simulation model.
Specifically, the field coupling model processes the central coordinates of the arc infinitesimal to obtain formulas of boundary points, see formulas (14) to (20), and the arc infinitesimal is actually processed into an arc two-dimensional model.
Extracting central coordinates of arc microelements, instantaneous current intensity and material information from output of an arc chained model, wherein the central coordinates correspond to central coordinates of the arc microelements at the end time of simulation of the arc chained model, the instantaneous current intensity is also the current at the moment, and the expression (x n ，y n ) Is an updated value, and the value corresponding to the center coordinates is updated as each time step ends. And then processing the central coordinates to obtain boundary points, wherein the coordinates of the boundary points form the boundary of the arc. Because the arc shape in the electric field simulation model is constructed in a polygonal form, and the boundary points of the polygons need to be arranged in a time needle direction, the boundaries of the polygons cannot be crossed when constructing a two-dimensional geometric model of the arc. The invention realizes the continuous operation of the arc root jump model through the field path coupling model. The traditional arc chained model can only realize the simulation of the arc shape, and the traditional electric field simulation model can only realize the electric field near the arc The invention realizes the coupling of two models through the field path coupling model, can directly obtain the arc morphology and field intensity distribution in the electric field simulation model, can obtain all information of the two models through the parameter setting operation of the field path coupling model, has very convenient operation, does not need repeated modeling and input, and can perform more complex analysis and judgment, which is that the arc chain model or the electric field simulation model cannot be realized only by itself.
The above embodiments are preferred embodiments of the present invention, and the present invention is not limited thereto, and any other modifications or equivalent substitutions made without departing from the technical aspects of the present invention are included in the scope of the present invention.
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.
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