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
本发明公开了一种基于场路耦合的电弧根跳跃模型的建立方法及系统,其方法包括步骤:S1、设定材料参数,构建电弧链式模型并仿真输出电弧微元轨迹;S2、根据电弧微元轨迹提取电弧微元的位置信息,场路耦合模型对位置信息进行处理得到电弧形态信息;S3、根据步骤S2的输出结果建立电弧的二维几何模型并添加边界条件和场源,构建电场仿真模型,仿真输出电弧周围的电场强度分布情况;S4、联立电弧跳跃判据、跳跃距离计算公式及滑行距离计算公式构建跳跃判断模型,并根据场强分布判断电弧根是否跳跃并计算电弧根的跳跃距离和滑行距离。本发明能够同时得到电弧运动形态及场强分布,判断电弧根是否发生跳跃并计算电弧根的跳跃距离和滑行距离。
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
技术领域Technical field
本发明属于电弧运动仿真建模技术领域,具体地说,涉及一种基于场路耦合的电弧根跳跃模型的建立方法及系统。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.
背景技术Background technique
随着城市化进程的不断加速,城市的用电开销不断增大,因为发电主要地区和用电主要地区通常距离较远,所以在郊外的输电导线不断增多。这些导线处于旷野的高点,更容易在雷雨天受到雷击,因此避雷线的防护必不可少,对雷击原理的研究和避雷线的损伤评估也成为了保证输电安全的重要研究。电弧跳跃现象会在避雷线上造成不连续的多段损伤,可能造成多根绞线同时破坏,使避雷线有很大的断裂风险,对安全可靠的输电造成了威胁。由于关于雷电的实验不易控制变量的精确进行,故利用仿真模型进行电弧的仿真有很强的实际意义。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.
发明内容Contents of the invention
本发明的第一目的在于克服现有技术的缺点与不足,提供一种基于场路耦合的电弧根跳跃模型的建立方法,能够同时得到电弧运动形态及场强分布,判断电弧根是否发生跳跃并计算电弧根的跳跃距离和滑行距离。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.
本发明的第二目的在于提供一种基于场路耦合的电弧根跳跃模型的建立系统。The second object of the present invention is to provide a system for establishing an arc root jump model based on field-circuit coupling.
本发明的目的通过下述技术方案实现:一种基于场路耦合的电弧根跳跃模型的建立方法,包括步骤: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、设定材料参数,将电弧均分为若干电弧微元,构建电弧链式模型;基于电弧链式模型,根据预设的仿真时间及迭代的时间步长,在每个迭代的时间步长获取时间步长结束时刻各电弧微元的位置,直至迭代达到预设的迭代步数,仿真输出电弧微元轨迹;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、根据所述电弧微元轨迹提取电弧微元的位置信息、材料参数和雷电流强度,作为场路耦合模型的输入,场路耦合模型对位置信息进行处理得到电弧形态信息,通过仿真软件的命令将电弧形态信息、材料参数及雷电流强度输出;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、根据步骤S2输出的电弧形态信息、材料参数及雷电流强度建立电弧的二维几何模型,对所述二维几何模型添加边界条件和场源,构建电场仿真模型,仿真输出电弧周围的电场强度分布情况;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、联立电弧跳跃判据、跳跃距离计算公式及滑行距离计算公式,构建跳跃判断模型,其中,S4. Combine the arc jump criterion, jump distance calculation formula and sliding distance calculation formula to construct a jump judgment model, where,
所述电弧跳跃判据具体包括:所述电场仿真模型输出的电场强度的最大值大于预设的电场强度阈值,则电弧根发生跳跃;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;
所述跳跃距离计算公式如下:The jump distance calculation formula is as follows:
dj=x’m,式(1),d j =x' m , formula (1),
,式(2), , formula (2),
其中,dj为电弧根的跳跃距离,Emax为电场仿真模型输出的电场强度的最大值,(x’m,y’m)为电弧的边界上发生跳跃的位置坐标,此坐标通过电场仿真模型读取,为(x’m,y’m)点对应的电场强度;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、根据所述电场强度分布情况判断电弧根的跳跃情况,从而完成电弧根跳跃模型的建立,具体包括: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:
比较电场强度分布情况与电弧跳跃判据,判断电弧根是否发生跳跃;Compare the electric field intensity distribution with the arc jump criterion to determine whether the arc root jumps;
若是,则根据跳跃距离计算公式和滑行距离公式分别计算电弧根的跳跃距离和滑行距离;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;
若否,则根据滑行距离计算公式计算电弧根的滑行距离。If not, calculate the sliding distance of the arc root according to the sliding distance calculation formula.
优选的,步骤S1具体包括以下步骤:Preferably, step S1 specifically includes the following steps:
S11、设定仿真时间T,并将仿真时间T平均划分为H个时间步长,H为迭代步数;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、设定电流强度、空间边界、环境风速和避雷线的材料参数,将竖直雷电弧均分为若干个长度和直径相等的圆柱体电弧微元,以雷击点为坐标原点,避雷线为X轴建立平面直角坐标系,将相邻两个电弧微元连线的中点作为电弧微元的中心,各电弧微元的中心坐标沿着电弧依次表示为(x1,y1),(x2,y2)……(xn,yn),n表示电弧微元的序数;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、计算考虑边界层影响的实际风速v w :S13. Calculate the actual wind speed v w considering the influence of the boundary layer:
,式(3), , formula (3),
其中,y为电弧微元与避雷线的距离,l w 为边界层的厚度,v o 为环境风速;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、在时间步长内对电弧微元进行受力分析,根据空气阻力公式计算得到电弧微元的速度,电弧微元所受合力F及电弧微元的速度v的计算公式分别如下: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=Fc+ Fw+ F l ,式(4),F=F c + F w + F l , formula (4),
,式(5), , formula (5),
其中,Fc=BcIdl,式(6),Among them, F c =B c Id l , formula (6),
F l =B l Idl,式(7),F l =B l Id l , formula (7),
,式(8), , formula (8),
,式(9), , formula (9),
,式(10), , formula (10),
其中,Bc为流过避雷线的电流产生的磁感应强度,B l 为流过电弧微元的电流产生的磁感应强度,μ为磁导率,I为流过电弧微元的电流强度,dl为电弧微元的长度,rc为电弧微元与避雷线的距离,r l 为电弧微元相互之间的距离;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;
假定电弧微元在每个时间步长内匀速运动,计算在时间步长内电弧微元的位移,如式(11),并更新在本时间步长结束时刻电弧微元的位置,如式(12):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):
,式(11), , formula (11),
,式(12), , formula (12),
其中,,/>为第k个时间步长内电弧微元的速度,/>为第k个时间步长内电弧微元的位移,/>为k个时间步长结束时刻电弧微元的位移向量,/>为电弧微元的初始位置;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、进入下一个时间段:以步骤S14中本时间步长结束时刻电弧微元的位置作为下一个时间段起始时刻电弧微元的位置,重复步骤S14;直至迭代达到预设的迭代步数H,输出仿真时间内的电弧微元轨迹。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.
优选的,步骤S2中,所述场路耦合模型用于提取和处理所述电弧链式模型中电弧微元的位置信息,包括以下步骤: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、根据所述电弧微元轨迹提取各电弧微元的中心坐标,并对中心坐标进行处理,得到电弧微元的边界点坐标: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:
首先将相邻两个中心坐标的连线作为电弧在第n个电弧微元的中心坐标处的方向,第n个电弧微元的中心坐标处的方向角为: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:
,式(13), , formula (13),
其中,n≥2,(xn,yn)和(xn-1,yn-1)分别为第n个和第n-1个电弧微元的中心坐标;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;
确定各电弧微元的中心坐标处的方向的法向,将各电弧微元的中心坐标沿着对应的法向的两侧分别扩展,扩展距离为电弧半径r,得到电弧微元两侧的边界点,令第n个电弧微元两侧的边界点的坐标分别表示为(x’n,y’n)和(x’2N-n+1,y’2N-n+1),其中,N表示电弧微元的总个数,边界点的坐标构建公式如下: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:
当n≥2,When n≥2,
x’n=xn+rsinαn,式(14),x' n =x n +rsinα n , formula (14),
y’n=yn-rcosαn,式(15),y' n =y n -rcosα n , formula (15),
x’2N-n+1=xn-rsinαn,式(16),x' 2N-n+1 =x n -rsinα n , formula (16),
y’2N-n+1=yn+rcosαn,式(17),y' 2N-n+1 =y n +rcosα n , formula (17),
当n=1,When n=1,
x’1=x1+r,式(18),x' 1 =x 1 +r, formula (18),
x’2N=x1-r,式(19),x' 2N =x 1 -r, formula (19),
y’1= y’2N=0,式(20);y' 1 = y' 2N =0, formula (20);
S22、将计算得到的各电弧微元的边界点坐标按照顺序:(x’1,y’1)、(x’2,y’2)……(x’2N,y’2N)以矩阵的形式保存为文件,得到电弧形态信息,通过仿真软件的命令将电弧形态信息、材料参数及雷电流强度输出,所述雷电流强度为电弧链式模型仿真时间结束时刻的雷电流。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.
优选的,步骤S3具体包括以下步骤:Preferably, step S3 specifically includes the following steps:
S31、以雷击点为原点,避雷线为X轴方向建立平面直角坐标系,设置空间边界,根据所述电弧形态信息构建电弧的二维几何模型;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、根据所述材料参数对二维几何模型添加材料属性:将避雷线材料设为铜,将电弧材料设为空气等离子体,除了避雷线及电弧外的其他区域设为空气;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;
设置边界条件及场源条件:将空气边界设置为电绝缘:电荷量Q=0,避雷线设置为接地:电势U=0,将电弧的顶端设置为雷电流终端,设置雷电流为步骤S2输出的雷电流强度;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、结合二维几何模型、材料属性、边界条件及场源条件,得到电场仿真模型,运行仿真软件得到电弧周围的电场强度分布情况。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.
优选的,步骤S4中,所述滑行距离计算公式为:Preferably, in step S4, the sliding distance calculation formula is:
dc=x’1,式(21),d c =x' 1 , formula (21),
其中,dc为电弧根的滑行距离。Among them, d c is the sliding distance of the arc root.
优选的,步骤S4中,所述预设的电场强度阈值设置为5kV/cm。Preferably, in step S4, the preset electric field intensity threshold is set to 5kV/cm.
优选的,步骤S4中,所述预设的电场强度阈值根据电弧所在空间的电介质的参数进行设置。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.
一种基于场路耦合的电弧根跳跃模型的建立系统,具体包括:A system for establishing an arc root jump model based on field-circuit coupling, specifically including:
电弧链式模型建立模块,用于设定材料参数,将电弧均分为若干电弧微元,构建电弧链式模型;基于电弧链式模型,根据预设的仿真时间及迭代的时间步长,在每个迭代的时间步长获取时间步长结束时刻各电弧微元的位置,直至迭代达到预设的迭代步数,仿真输出电弧微元轨迹;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;
场路耦合模型建立模块,用于根据所述电弧微元轨迹提取电弧微元的位置信息、材料参数和雷电流强度,作为场路耦合模型的输入,场路耦合模型对位置信息进行处理得到电弧形态信息,通过仿真软件的命令将电弧形态信息、材料参数及雷电流强度输出;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;
电场仿真模型建立模块,用于根据场路耦合模型输出的电弧形态信息、材料参数及雷电流强度建立电弧的二维几何模型,对所述二维几何模型添加边界条件和场源,构建电场仿真模型,仿真输出电弧周围的电场强度分布情况;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;
跳跃判断模型建立模块,用于联立电弧跳跃判据、跳跃距离计算公式及滑行距离计算公式,构建跳跃判断模型,其中,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,
所述电弧跳跃判据具体包括:所述电场仿真模型输出的电场强度的最大值大于预设的电场强度阈值,则电弧根发生跳跃;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;
所述跳跃距离计算公式如下:The jump distance calculation formula is as follows:
dj=x’m,式(1),d j =x' m , formula (1),
,式(2), , formula (2),
其中,dj为电弧根的跳跃距离,Emax为电场仿真模型输出的电场强度的最大值,(x’m,y’m)为电弧的边界上发生跳跃的位置坐标,此坐标通过电场仿真模型读取,为(x’m,y’m)点对应的电场强度;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;
判断模块,用于根据所述电场强度分布情况判断电弧根的跳跃情况,从而完成电弧根跳跃模型的建立。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.
优选的,所述场路耦合模型用于提取和处理所述电弧链式模型中电弧微元的位置信息,包括:Preferably, the field-circuit coupling model is used to extract and process the position information of arc elements in the arc chain model, including:
第一处理模块,用于根据所述电弧微元轨迹提取各电弧微元的中心坐标,并对中心坐标进行处理,得到电弧微元的边界点坐标: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:
首先将相邻两个中心坐标的连线作为电弧在第n个电弧微元的中心坐标处的方向,第n个电弧微元的中心坐标处的方向角为: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:
,式(13), , formula (13),
其中,n≥2,(xn,yn)和(xn-1,yn-1)分别为第n个和第n-1个电弧微元的中心坐标;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;
确定各电弧微元的中心坐标处的方向的法向,将各电弧微元的中心坐标沿着对应的法向的两侧分别扩展,扩展距离为电弧半径r,得到电弧微元两侧的边界点,令第n个电弧微元两侧的边界点的坐标分别表示为(x’n,y’n)和(x’2N-n+1,y’2N-n+1),其中,N表示电弧微元的总个数,边界点的坐标构建公式如下: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:
当n≥2,When n≥2,
x’n=xn+rsinαn,式(14),x' n =x n +rsinα n , formula (14),
y’n=yn-rcosαn,式(15),y' n =y n -rcosα n , formula (15),
x’2N-n+1=xn-rsinαn,式(16),x' 2N-n+1 =x n -rsinα n , formula (16),
y’2N-n+1=yn+rcosαn,式(17),y' 2N-n+1 =y n +rcosα n , formula (17),
当n=1,When n=1,
x’1=x1+r,式(18),x' 1 =x 1 +r, formula (18),
x’2N=x1-r,式(19),x' 2N =x 1 -r, formula (19),
y’1= y’2N=0,式(20);y' 1 = y' 2N =0, formula (20);
第二处理模块,用于将计算得到的各电弧微元的边界点坐标按照顺序:(x’1,y’1)、(x’2,y’2)……(x’2N,y’2N)以矩阵的形式保存为文件,得到电弧形态信息,通过仿真软件的命令将电弧形态信息、材料参数及雷电流强度输出,所述雷电流强度为电弧链式模型仿真时间结束时刻的雷电流。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. .
优选的,跳跃判断模型建立模块中,所述滑行距离计算公式为:Preferably, in the jump judgment model building module, the sliding distance calculation formula is:
dc=x’1,式(21),d c =x' 1 , formula (21),
其中,dc为电弧根的滑行距离。Among them, d c is the sliding distance of the arc root.
本发明相对于现有技术具有如下的优点及效果:Compared with the existing technology, the present invention has the following advantages and effects:
(1)本发明的方法首先利用电弧链式模型得出对应时间下的电弧微元轨迹;根据电弧微元轨迹提取电弧微元的位置信息,将此位置信息经场路耦合模型处理后得到电弧形态信息,由场路耦合模型将电弧信息及材料参数和雷电流强度输入以作为电场仿真模型的初始条件;电场仿真模型仿真输出电弧附近空间的场强分布;最后利用跳跃判断模型,根据电场强度的分布特点和电弧跳跃判据判断电弧根在滑行过程中是否跳跃,并利用公式计算出电弧根的跳跃距离和滑行距离。利用本发明的电弧根跳跃模型进行电弧根跳跃运动的仿真研究,能够直接得出电弧附近的电场强度和电弧根跳跃距离,便于更好地对照及进行事故分析,由于雷电弧跳跃电弧跳跃会对避雷线造成多个雷击点,而雷电弧在避雷线上滑行会造成避雷线的热烧蚀损伤,此方法为进行避雷线的损伤评估提供了数据支撑。(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)本发明通过场路耦合模型实现了电弧根跳跃模型的连续运行。传统的电弧链式模型只能实现电弧形态的仿真、传统的电场仿真模型只能实现电弧附近的电场仿真,而本发明通过场路耦合模型实现两个模型的耦合,能直接在电场仿真模型中得到电弧形态和场强分布,通过在场路耦合模型进行参数设定操作,能得到两个模型的所有信息,操作十分便捷,不需要反复建模和输入,能够进行更复杂的分析判断,这是电弧链式模型或电场仿真模型仅靠自身无法实现的。(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)本发明提出了电弧根是否跳跃的电弧跳跃判据和计电弧根跳跃距离的计算方法,为进行雷电弧根跳跃现象更系统的仿真研究提供了重要的理论参考依据。(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.
附图说明Description of the drawings
图1为本发明的一种基于场路耦合的电弧根跳跃模型的建立方法的流程示意图。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.
图2为本发明的电弧链式模型的仿真流程示意图。Figure 2 is a schematic diagram of the simulation flow of the arc chain model of the present invention.
图3为本发明的场路耦合模型的仿真流程示意图。Figure 3 is a schematic diagram of the simulation flow of the field-circuit coupling model of the present invention.
图4为本发明的电场仿真模型的仿真流程示意图。Figure 4 is a schematic diagram of the simulation flow of the electric field simulation model of the present invention.
图5为本发明的避雷线附近的电弧微元的受力分析示意图。Figure 5 is a schematic diagram of the stress analysis of arc micro-elements near the lightning protection line of the present invention.
图6为本发明的电弧链式模型的仿真输出示意图。Figure 6 is a schematic diagram of the simulation output of the arc chain model of the present invention.
图7为本发明的电场仿真模型的仿真输出示意图。Figure 7 is a schematic diagram of the simulation output of the electric field simulation model of the present invention.
具体实施方式Detailed ways
下面结合实施例及附图对本发明作进一步的详细描述,但本发明的实施方式不限于此。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.
实施例1Example 1
如图1所示为一种基于场路耦合的电弧根跳跃模型的建立方法,包括步骤:Figure 1 shows a method for establishing an arc root jump model based on field-circuit coupling, including the steps:
S1、设定材料参数,将电弧均分为若干电弧微元,构建电弧链式模型;基于电弧链式模型,根据预设的仿真时间及迭代的时间步长,在每个迭代的时间步长获取时间步长结束时刻各电弧微元的位置,直至迭代达到预设的迭代步数,仿真输出电弧微元轨迹;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、根据所述电弧微元轨迹提取电弧微元的位置信息、材料参数和雷电流强度,作为场路耦合模型的输入,场路耦合模型对位置信息进行处理得到电弧形态信息,通过仿真软件的命令将电弧形态信息、材料参数及雷电流强度输出;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、根据步骤S2输出的电弧形态信息、材料参数及雷电流强度建立电弧的二维几何模型,对所述二维几何模型添加边界条件和场源,构建电场仿真模型,仿真输出电弧周围的电场强度分布情况;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、联立电弧跳跃判据、跳跃距离计算公式及滑行距离计算公式,构建跳跃判断模型,其中,S4. Combine the arc jump criterion, jump distance calculation formula and sliding distance calculation formula to construct a jump judgment model, where,
所述电弧跳跃判据具体包括:所述电场仿真模型输出的电场强度的最大值大于预设的电场强度阈值,则电弧根发生跳跃;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;
所述跳跃距离计算公式如下:The jump distance calculation formula is as follows:
dj=x’m,式(1),d j =x' m , formula (1),
,式(2), , formula (2),
其中,dj为电弧根的跳跃距离,Emax为电场仿真模型输出的电场强度的最大值,(x’m,y’m)为电弧的边界上发生跳跃的位置坐标,此坐标通过电场仿真模型读取,为(x’m,y’m)点对应的电场强度;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、根据所述电场强度分布情况判断电弧根的跳跃情况,从而完成电弧根跳跃模型的建立,具体包括: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:
比较电场强度分布情况与电弧跳跃判据,判断电弧根是否发生跳跃;Compare the electric field intensity distribution with the arc jump criterion to determine whether the arc root jumps;
若是,则根据跳跃距离计算公式和滑行距离公式分别计算电弧根的跳跃距离和滑行距离;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;
若否,则根据滑行距离计算公式计算电弧根的滑行距离。If not, calculate the sliding distance of the arc root according to the sliding distance calculation formula.
具体的,电弧链式模型采用通用的仿真软件如MATLAB进行构建,电场仿真模型采用通用的仿真软件如COMSOL进行构建,在本实例中,上述两个模型分别运用MATLAB和COMSOL仿真,场路耦合模型直接使用软件COMSOL自带的功能COMSOL with MATLAB进行仿真。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.
本发明为了判断电弧根是否发生跳跃,依次建立电弧链式模型、场路耦合模型、电场仿真模型及电弧判断模型,已完成电弧根跳跃模型的建立,利用此电弧根跳跃模型仿真时,能够得到设定时间下,电弧的运动形态以及电弧周围的场强分布;利用场强分布信息,研究电弧根滑行和跳跃运动的规律,能够判断电弧根是否跳跃以及计算电弧根跳跃的距离长度。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.
其中,电弧链式模型用于对电弧微元进行受力分析,以计算电弧微元的位移和位置,得到设定的仿真时间下的电弧微元轨迹。电弧链式模型是现有的常见用于分析电弧速度和位移的方法,通过将电弧细分为电弧微元,以电弧微元为研究对象,通过设定仿真时间和时间步长,在每个时间步长内进行获取电弧微元的位置的过程为一个迭代,当将时间步长进行叠加达到仿真时间,即达到迭代步数后,此模型的仿真结束,汇总输出由电弧微元组成的电弧轨迹,即电弧微元轨迹;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;
场路耦合模型用于提取和处理电弧链式模型中电弧微元的位置信息,得到电弧形态信息,并以该电弧形态信息作为电场仿真模型的初始条件。在电场仿真模型中,电弧形态以多边形的形式构建,因此电场仿真模型中的电弧轨迹利用场路耦合模型输出的电弧形态信息进行构建。将电弧形态信息,雷电流强度和材料信息通过COMSOL with matlab 模块中的命令的形式写入电场仿真模型。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.
电场仿真模型用于进行空间内电场模的求解,即利用COMSOL软件中自带的电流模块进行仿真,得到电弧击中避雷线后电弧附近空间的电场强度分布情况。利用场路耦合模型输入的命令,根据电弧形态信息,雷电流强度和材料信息在电弧的附近区域建立电弧的二维几何模型,二维几何模型的区域中包括电弧、雷击点附近的避雷线连同空气域,再添加各部分的材料信息、空间的场源及边界条件,利用上述条件开始仿真,电场仿真模型输出仿真时间结束时刻电弧的附近区域的电场强度分布情况。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.
最后通过跳跃判断模型根据电场强度分布情况判断电弧的跳跃情况并计算电弧的跳跃距离和滑行距离。通过将电场强度分布情况与电弧跳跃判据比较,满足电弧跳跃判据,则认定电弧发生跳跃,计算电弧根的跳跃距离和滑行距离,若不满足则认定电弧不发生跳跃,计算电弧根的滑行距离,所述跳跃距离和滑行距离均能够直接通过电场仿真模型读取。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.
具体的,如图7所示,电弧在跳跃点处会发生明显的弯曲凸起,该弯曲凸起部分的电弧附近的电场分布极不均匀,电场会集中在电弧凸起点处,且电弧凸起点距离避雷线很近,所以电弧凸起点处常常是空间中的场强最大值处。综上所述,雷电弧的跳跃点即为空间中场强最大处,并且能够通过空间中电场强度最大值是否达到跳跃阈值判断电弧是否发生跳跃。本发明的电弧跳跃判据是研究雷电弧根跳跃过程的重要结论。根据电场仿真模型的输出结果找到电场强度的最大值处,读取电场强度的最大值对应的坐标(x’m,y’m),代入公式(1)得到电弧根的跳跃距离。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.
电弧跳跃时会对避雷线造成多个雷击点,而电弧在避雷线上滑行会造成避雷线的热烧蚀损伤,本模型能够计算电弧根的跳跃距离及滑行距离,并根据研究需要将两者综合使用,实现对雷电弧根跳跃现象更复杂、更系统的研究。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.
本发明利用电弧根跳跃模型进行电弧根跳跃运动的仿真研究,能够直接得出电弧附近的电场强度和电弧根跳跃距离,便于更好地对照及进行事故分析,能一定程度上为预测电弧事故损伤情况提供参考依据,由于雷电弧跳跃电弧跳跃会对避雷线造成多个雷击点,而雷电弧在避雷线上滑行会造成避雷线的热烧蚀损伤,此方法为进行避雷线的损伤评估提供了数据支撑。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.
同时,本发明通过场路耦合模型实现了电弧根跳跃模型的连续运行。传统的电弧链式模型只能实现电弧形态的仿真,传统的电场仿真模型只能实现电弧附近的电场仿真,而本发明通过场路耦合模型实现两个模型的耦合仿真,能直接在电场仿真模型中得到电弧运动形态和场强分布,见图7,通过在场路耦合模型进行参数设定操作,能得到两个模型的所有信息,操作十分便捷,不需要反复建模和输入,能够进行更复杂的分析判断,这是电弧链式模型或电场仿真模型仅靠自身无法实现的。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.
本发明的方法除了适用于雷击时的电弧跳跃判断和跳跃距离计算,还适用非雷击的其他场合下电弧跳跃运动仿真时,电弧的跳跃判断和电弧的跳跃距离计算。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.
步骤S1具体包括以下步骤:Step S1 specifically includes the following steps:
S11、设定仿真时间T,并将仿真时间T平均划分为H个时间步长,H为迭代步数;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、设定电流强度、空间边界、环境风速和避雷线的材料参数,将竖直雷电弧均分为若干个长度和直径相等的圆柱体电弧微元,以雷击点为坐标原点,避雷线为X轴建立平面直角坐标系,将相邻两个电弧微元连线的中点作为电弧微元的中心,各电弧微元的中心坐标沿着电弧依次表示为(x1,y1),(x2,y2)……(xn,yn),n表示电弧微元的序数;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、计算考虑边界层影响的实际风速v w :S13. Calculate the actual wind speed v w considering the influence of the boundary layer:
,式(3), , formula (3),
其中,y为电弧微元与避雷线的距离,l w 为边界层的厚度,v o 为环境风速;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、在时间步长内对电弧微元进行受力分析,根据空气阻力公式计算得到电弧微元的速度,电弧微元所受合力F及电弧微元的速度v的计算公式分别如下: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=Fc+ Fw+ F l ,式(4),F=F c + F w + F l , formula (4),
,式(5), , formula (5),
其中,Fc=BcIdl,式(6),Among them, F c =B c Id l , formula (6),
F l =B l Idl,式(7),F l =B l Id l , formula (7),
,式(8), , formula (8),
,式(9), , formula (9),
,式(10), , formula (10),
其中,Bc为流过避雷线的电流产生的磁感应强度,B l 为流过电弧微元的电流产生的磁感应强度,μ为磁导率,I为流过电弧微元的电流强度,dl为电弧微元的长度,rc为电弧微元与避雷线的距离,r l 为电弧微元相互之间的距离;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;
假定电弧微元在每个时间步长内匀速运动,计算在时间步长内电弧微元的位移,如式(11),并更新在本时间步长结束时刻电弧微元的位置,如式(12):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):
,式(11), , formula (11),
,式(12), , formula (12),
其中,,/>为第k个时间步长内电弧微元的速度,/>为第k个时间步长内电弧微元的位移,/>为k个时间步长结束时刻电弧微元的位移向量,/>为电弧微元的初始位置,k∈H;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、进入下一个时间段:以步骤S14中本时间步长结束时刻电弧微元的位置作为下一个时间段起始时刻电弧微元的位置,重复步骤S14;直至迭代达到预设的迭代步数H,输出仿真时间内的电弧微元轨迹。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.
具体的,如图2和图5所示,假设雷电竖直击中避雷线,即用竖直雷电弧代表影响因素最少时的雷击,取避雷线上方4米范围内的雷电弧参与本次仿真建模,本实施例中设为1m。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.
首先将雷电弧均分为若干个长度与直径相等的刚性圆柱体的电弧微元,圆柱体微元的中心代表电弧微元的重心,圆柱体微元的轴线方向代表电弧微元中电流的方向。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. .
再进行边界层细化。紧贴避雷线的空气边界层是电弧根跳跃的重点研究对象,本实施例中设空气边界层为0.1米。根据流体力学知识,由于边界层的存在,风速在靠近避雷线时会减小,为了更精细的研究边界层对电弧形态的影响,本实施例中将边界层内的电弧微元的长度减小,数量增多:即对避雷线的边界层内的电弧微元进行进一步截取,使边界层内的电弧微元的长度相等,且小于边界层外的电弧微元的长度。将处理后的边界层内的电弧微元的坐标及边界层外的电弧微元的坐标输入电弧链式模型,作为电弧链式模型进行仿真的输入数据信息。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.
仿真前,先计算考虑边界层影响的风速,此步骤便于提高建模的准确性。然后以时间步长作为一个迭代进程进行迭代仿真,即在时间步长的循环迭代中,每次迭代对应一个时间步长。对于时间步长的设置,由于雷电的回击分量持续时间较短且电流幅值较大,在雷电流处于回击分量阶段,采用较短的时间步长以便提高仿真精度,而雷电的持续分量持续时间较长且电流幅值较小,在雷电流处于持续分量阶段,采用较长的时间步长以便减少模型的计算时间,在本实施例中,在回击发生时时间步长取10-6s,在持续分量阶段时间步长取10-3s。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.
电弧链式模型的仿真包括,在每个时间步长内,对电弧微元进行电磁力和风力的受力分析,得到电弧微元的位置,在每个时间步长的结束时刻,得到电弧微元的更新的位置后对电弧微元进行均分或者合并:即将过长的电弧微元(过长指的是长度超过初始电弧微元的1.5倍)均分为两个等长的电弧微元,过短的电弧微元(过长指的是长度小于初始电弧微元的0.5倍)与相邻的电弧微元合并,并且调整对应电弧微元的序号,此操作便于控制微元长度不会过短或过长,而是保持在初始电弧微元的0.5倍-1.5倍之间,保证仿真结果的准确性。循环迭代在达到设定的仿真时间时结束,仿真输出电弧微元轨迹,如图6所示。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.
步骤S2中,所述场路耦合模型用于提取和处理所述电弧链式模型中电弧微元的位置信息,包括以下步骤: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、根据所述电弧微元轨迹提取各电弧微元的中心坐标,并对中心坐标进行处理,得到电弧微元的边界点坐标: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:
首先将相邻两个中心坐标的连线作为电弧在第n个电弧微元的中心坐标处的方向,第n个电弧微元的中心坐标处的方向角为: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:
,式(13), , formula (13),
其中,n≥2,(xn,yn)和(xn-1,yn-1)分别为第n个和第n-1个电弧微元的中心坐标;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;
确定各电弧微元的中心坐标处的方向的法向,将各电弧微元的中心坐标沿着对应的法向的两侧分别扩展,扩展距离为电弧半径r,得到电弧微元两侧的边界点,令第n个电弧微元两侧的边界点的坐标分别表示为(x’n,y’n)和(x’2N-n+1,y’2N-n+1),其中,N表示电弧微元的总个数,边界点的坐标构建公式如下: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:
当n≥2,When n≥2,
x’n=xn+rsinαn,式(14),x' n =x n +rsinα n , formula (14),
y’n=yn-rcosαn,式(15),y' n =y n -rcosα n , formula (15),
x’2N-n+1=xn-rsinαn,式(16),x' 2N-n+1 =x n -rsinα n , formula (16),
y’2N-n+1=yn+rcosαn,式(17),y' 2N-n+1 =y n +rcosα n , formula (17),
当n=1,When n=1,
x’1=x1+r,式(18),x' 1 =x 1 +r, formula (18),
x’2N=x1-r,式(19),x' 2N =x 1 -r, formula (19),
y’1= y’2N=0,式(20);y' 1 = y' 2N =0, formula (20);
S22、将计算得到的各电弧微元的边界点坐标按照顺序:(x’1,y’1)、(x’2,y’2)……(x’2N,y’2N)以矩阵的形式保存为文件,得到电弧形态信息,通过仿真软件的命令将电弧形态信息、材料参数及雷电流强度输出,所述雷电流强度为电弧链式模型仿真时间结束时刻的雷电流。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.
具体的,如图3所示为场路耦合模型的仿真流程示意图,场路耦合模型的仿真包括使用COMSOL with MATLAB中的系列命令,提取和处理电弧链式模型的坐标数据,整合其他用于电场仿真模型的的数据。场路耦合模型对电弧微元的中心坐标进行处理得到边界点的公式,见式(14)至式(20),实际是将电弧微元处理为电弧二维模型的过程。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.
在电弧链式模型的输出中提取电弧微元的中心坐标、瞬时的电流强度和材料信息,这些中心坐标对应的是电弧链式模型仿真时间结束时刻电弧微元的中心坐标,瞬时电流强度也是该时刻的电流大小,中心坐标的表达式(xn,yn)是一个更新值,随着每个时间步长的结束,对中心坐标对应的值做更新。然后对中心坐标进行处理得到边界点,这些边界点的坐标构成电弧的边界。由于电场仿真模型中的电弧形态是以多边形的形式构建的,而多边形的边界点需要按时针方向排列,构建电弧的二维几何模型时多边形的边界才不会发生交叉。通过场路耦合模型,将各个电弧微元的中心坐标向两侧扩展出两个边界点后,使所有电弧微元的边界点的坐标按逆时针排序,根据公式(13)~公式(18)得出这些边界点按逆时针顺序排序的序列,将计算得出的(x’1,y’1)、(x’2,y’2)……(x’2N,y’2N)依次存入n行2列的二维矩阵,以xx.csv格式单独写入空文件。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.
通过仿真软件的命令将电弧形态信息、材料参数及雷电流强度输出,具体包括:The arc shape information, material parameters and lightning current intensity are output through the commands of the simulation software, including:
使用COMSOL with MATLAB中的系列命令,将上述xx.csv格式的文件Use the series of commands in COMSOL with MATLAB to convert the above xx.csv format file into
导入电场仿真模型中,作为雷电弧轨迹的几何模型的数据,使用的命令模块如下:“model.component('电弧根跳跃模型').geom('几何模型')”,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')",
使用COMSOL with MATLAB中的系列命令,将材料属性的部分参数写入电场仿真模型中,见表1,作为COMSOL系统材料库中材料数据的修改和补充。使用的命令模块如下:“model.component('电弧根跳跃模型').material('材料属性')”。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')".
表1 仿真中的材料特性Table 1 Material properties in simulation
使用COMSOL with MATLAB中的系列命令,将电弧链式模型仿真时间结束时刻的电流强度写入电场仿真模型中。使用的命令模块如下:“model.component('电弧根跳跃模型').physics('电流终端')”,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')",
以上作为场路耦合模型的输出,即对应图1中的第2输出。The above is the output of the field-circuit coupling model, which corresponds to the second output in Figure 1.
步骤S3具体包括以下步骤:Step S3 specifically includes the following steps:
S31、以雷击点为原点,避雷线为X轴方向建立平面直角坐标系,设置空间边界,根据所述电弧形态信息构建电弧的二维几何模型;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、根据所述材料参数对二维几何模型添加材料属性:将避雷线材料设为铜,将电弧材料设为空气等离子体,除了避雷线及电弧外的其他区域设为空气;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;
设置边界条件及场源条件:将空气边界设置为电绝缘:电荷量Q=0,避雷线设置为接地:电势U=0,将电弧的顶端设置为雷电流终端,设置雷电流为步骤S2输出的雷电流强度;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、结合二维几何模型、材料属性、边界条件及场源条件,得到电场仿真模型,运行仿真软件得到电弧周围的电场强度分布情况。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.
具体的,如图4所示为电场仿真模型的仿真流程示意图。利用场路耦合模型输入的命令,直接读取xx.csv文件构建雷电弧多边形的二维几何模型,其中根据电弧的边界点坐标构建电弧轨迹,在避雷线底部和空气域边缘划定空间边界,以便设置边界条件,区域中包括雷电弧、雷击点附近的避雷线及空气域。设置材料的几何参数(见表2)和场源后,通过仿真软件进行仿真,电场仿真模型输电弧附近区域的电场强度分布情况,如图7所示。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.
表2 仿真中的几何参数Table 2 Geometric parameters in simulation
步骤S4中,所述滑行距离计算公式为:In step S4, the sliding distance calculation formula is:
dc=x’1,式(21),d c =x' 1 , formula (21),
其中,dc为电弧根的滑行距离。Among them, d c is the sliding distance of the arc root.
具体的,x’1对应场路耦合模型中的x’1,见公式(18),此坐标可以直接通过电场仿真模型读取。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.
步骤S4中,所述预设的电场强度阈值设置为5kV/cm。In step S4, the preset electric field intensity threshold is set to 5kV/cm.
具体的,本实施例的研究中,设置电弧周围空间的最大电场强度达到5kV/cm,则认为雷电弧根会发生跳跃。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.
步骤S4中,所述预设的电场强度阈值根据电弧所在空间的电介质的参数进行设置。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.
具体的,电介质的参数指空气等离子体的参数,在空气潮湿和风力作用下,空气等离子体的参数有变化,对应的电场强度分布也有差异,因此根据实际的参数设置电场强度阈值,便于提高仿真准确性。同时,对于非雷击的电弧跳跃运动问题,也能够通过设置不同的电场强度阈值进行对应的跳跃判断,因此本发明的方法适用于非雷击的电弧跳跃运动问题。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.
实施例2Example 2
一种基于场路耦合的电弧根跳跃模型的建立系统,具体包括:A system for establishing an arc root jump model based on field-circuit coupling, specifically including:
电弧链式模型建立模块,用于设定材料参数,将电弧均分为若干电弧微元,构建电弧链式模型;基于电弧链式模型,根据预设的仿真时间及迭代的时间步长,在每个迭代的时间步长获取时间步长结束时刻各电弧微元的位置,直至迭代达到预设的迭代步数,仿真输出电弧微元轨迹;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;
场路耦合模型建立模块,用于根据所述电弧微元轨迹提取电弧微元的位置信息、材料参数和雷电流强度,作为场路耦合模型的输入,场路耦合模型对位置信息进行处理得到电弧形态信息,通过仿真软件的命令将电弧形态信息、材料参数及雷电流强度输出;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;
电场仿真模型建立模块,用于根据场路耦合模型输出的电弧形态信息、材料参数及雷电流强度建立电弧的二维几何模型,对所述二维几何模型添加边界条件和场源,构建电场仿真模型,仿真输出电弧周围的电场强度分布情况;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;
跳跃判断模型建立模块,用于联立电弧跳跃判据、跳跃距离计算公式及滑行距离计算公式,构建跳跃判断模型,其中,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,
所述电弧跳跃判电弧链式模型建立模块,用于设定材料参数,将电弧均分为若干电弧微元,构建电弧链式模型;基于电弧链式模型,根据预设的仿真时间及迭代的时间步长,在每个迭代的时间步长获取时间步长结束时刻各电弧微元的位置,直至迭代达到预设的迭代步数,仿真输出电弧微元轨迹;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;
场路耦合模型建立模块,用于根据所述电弧微元轨迹提取电弧微元的位置信息、材料参数和雷电流强度,作为场路耦合模型的输入,场路耦合模型对位置信息进行处理得到电弧形态信息,通过仿真软件的命令将电弧形态信息、材料参数及雷电流强度输出;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;
电场仿真模型建立模块,用于根据场路耦合模型输出的电弧形态信息、材料参数及雷电流强度建立电弧的二维几何模型,对所述二维几何模型添加边界条件和场源,构建电场仿真模型,仿真输出电弧周围的电场强度分布情况;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;
跳跃判断模型建立模块,用于联立电弧跳跃判据、跳跃距离计算公式及滑行距离计算公式,构建跳跃判断模型,其中,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,
所述电弧跳跃判据具体包括:所述电场仿真模型输出的电场强度的最大值大于预设的电场强度阈值,则电弧根发生跳跃;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;
所述跳跃距离计算公式如下:The jump distance calculation formula is as follows:
dj=x’m,式(1),d j =x' m , formula (1),
,式(2), , formula (2),
其中,dj为电弧根的跳跃距离,Emax为电场仿真模型输出的电场强度的最大值,(x’m,y’m)为电弧的边界上发生跳跃的位置坐标,此坐标通过电场仿真模型读取,为(x’m,y’m)点对应的电场强度;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;
判断模块,用于根据所述电场强度分布情况判断电弧根的跳跃情况,从而完成电弧根跳跃模型的建立,具体包括: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:
比较电场强度分布情况与电弧跳跃判据,判断电弧根是否发生跳跃;Compare the electric field intensity distribution with the arc jump criterion to determine whether the arc root jumps;
若是,则根据跳跃距离计算公式和滑行距离公式分别计算电弧根的跳跃距离和滑行距离;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;
若否,则根据滑行距离计算公式计算电弧根的滑行距离。If not, calculate the sliding distance of the arc root according to the sliding distance calculation formula.
具体的,本发明利用电弧根跳跃模型进行电弧根跳跃运动的仿真研究,能够直接得出电弧附近的电场强度和电弧根跳跃距离,便于更好地对照及进行事故分析,能一定程度上为预测电弧事故损伤情况提供参考依据,由于雷电弧跳跃电弧跳跃会对避雷线造成多个雷击点,而雷电弧在避雷线上滑行会造成避雷线的热烧蚀损伤,此方法为进行避雷线的损伤评估提供了数据支撑。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.
本发明的系统除了适用于雷击时的电弧跳跃判断和跳跃距离计算,还适用非雷击的其他场合下电弧跳跃运动仿真时,电弧根的跳跃判断和电弧根的跳跃距离计算。在本实施例中,所述预设的电场强度阈值设置为5kV/cm,预设的电场强度阈值根据电弧所在空间的电介质的参数进行设置。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.
所述场路耦合模型用于提取和处理所述电弧链式模型中电弧微元的位置信息,包括:The field-circuit coupling model is used to extract and process the position information of arc micro-elements in the arc chain model, including:
第一处理模块,用于根据所述电弧微元轨迹提取各电弧微元的中心坐标,并对中心坐标进行处理,得到电弧微元的边界点坐标: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:
首先将相邻两个中心坐标的连线作为电弧在第n个电弧微元的中心坐标处的方向,第n个电弧微元的中心坐标处的方向角为: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:
,式(13), , formula (13),
其中,n≥2,(xn,yn)和(xn-1,yn-1)分别为第n个和第n-1个电弧微元的中心坐标;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;
确定各电弧微元的中心坐标处的方向的法向,将各电弧微元的中心坐标沿着对应的法向的两侧分别扩展,扩展距离为电弧半径r,得到电弧微元两侧的边界点,令第n个电弧微元两侧的边界点的坐标分别表示为(x’n,y’n)和(x’2N-n+1,y’2N-n+1),其中,N表示电弧微元的总个数,边界点的坐标构建公式如下: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:
当n≥2,When n≥2,
x’n=xn+rsinαn,式(14),x' n =x n +rsinα n , formula (14),
y’n=yn-rcosαn,式(15),y' n =y n -rcosα n , formula (15),
x’2N-n+1=xn-rsinαn,式(16),x' 2N-n+1 =x n -rsinα n , formula (16),
y’2N-n+1=yn+rcosαn,式(17),y' 2N-n+1 =y n +rcosα n , formula (17),
当n=1,When n=1,
x’1=x1+r,式(18),x' 1 =x 1 +r, formula (18),
x’2N=x1-r,式(19),x' 2N =x 1 -r, formula (19),
y’1= y’2N=0,式(20);y' 1 = y' 2N =0, formula (20);
第二处理模块,用于将计算得到的各电弧微元的边界点坐标按照顺序:(x’1,y’1)、(x’2,y’2)……(x’2N,y’2N)以矩阵的形式保存为文件,得到电弧形态信息,通过仿真软件的命令将电弧形态信息、材料参数及雷电流强度输出,所述雷电流强度为电弧链式模型仿真时间结束时刻的雷电流。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. .
跳跃判断模型建立模块中,所述滑行距离计算公式为:In the jump judgment model building module, the sliding distance calculation formula is:
dc=x’1,式(21),d c =x' 1 , formula (21),
其中,dc为电弧根的滑行距离。具体的,x’1对应场路耦合模型中的x’1,见公式(18),此坐标可以直接通过电场仿真模型读取。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.
具体的,场路耦合模型对电弧微元的中心坐标进行处理得到边界点的公式,见式(14)至式(20),实际是将电弧微元处理为电弧二维模型的过程。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.
在电弧链式模型的输出中提取电弧微元的中心坐标、瞬时的电流强度和材料信息,这些中心坐标对应的是电弧链式模型仿真时间结束时刻电弧微元的中心坐标,瞬时电流强度也是该时刻的电流大小,中心坐标的表达式(xn,yn)是一个更新值,随着每个时间步长的结束,对中心坐标对应的值做更新。然后对中心坐标进行处理得到边界点,这些边界点的坐标构成电弧的边界。由于电场仿真模型中的电弧形态是以多边形的形式构建的,而多边形的边界点需要按时针方向排列,构建电弧的二维几何模型时多边形的边界才不会发生交叉。本发明通过场路耦合模型实现了电弧根跳跃模型的连续运行。传统的电弧链式模型只能实现电弧形态的仿真、传统的电场仿真模型只能实现电弧附近的电场仿真,而本发明通过场路耦合模型实现两个模型的耦合,能直接在电场仿真模型中得到电弧形态和场强分布,通过在场路耦合模型进行参数设定操作,能得到两个模型的所有信息,操作十分便捷,不需要反复建模和输入,能够进行更复杂的分析判断,这是电弧链式模型或电场仿真模型仅靠自身无法实现的。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.
上述实施例为本发明较佳的实施方式,并不能对本发明进行限定,其他的任何未背离本发明的技术方案而所做的改变或其它等效的置换方式,都包含在本发明的保护范围之内。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.
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