CN112966404B - Method for generating three-dimensional lightning leader development path - Google Patents
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Abstract
The invention discloses a method for generating a three-dimensional lightning leader development path, which comprises the following steps: step one, determining a rectangular simulation space and a development probability index; step two, performing 3D modeling on the research object, and setting a boundary condition and an uplink pilot starting point; discretizing the space potential by using a finite difference method, combining with the ultra-relaxation iteration to calculate the space potential, and determining an developed point according to the WZ model and the roulette wheel method; step four, judging whether the leader meets the end condition, if not, returning to the step three; and step five, taking the contact of the ascending and descending leaders or the contact of the descending leaders to a research object as a thunder and lightning leader development ending mark. The invention realizes the simulation of the real lightning development process by a simulation means, can simulate the lightning strike condition of each part of a target object in the lightning environment, and provides guidance and verification for the lightning protection design.
Description
Technical Field
The invention belongs to the technical field of lightning protection, and particularly relates to a method for generating a three-dimensional lightning guide development path.
Background
Lightning is a strong destructive and threatening climate phenomenon, the discharge process of the lightning is very complex, and the discharge of thunderclouds to the ground is influenced by a plurality of natural conditions such as weather, geology, terrain and the like, and has great randomness. The thundercloud discharge path tends to be unpredictable. However, the lightning development path has certain uniqueness, and the simulation of the lightning path can be realized to a certain extent by grasping some inherent characteristics of the lightning discharge path, so that the actual lightning process is truly reflected.
Many high-rise buildings and open air critical equipment are vulnerable to lightning attacks, which in turn threatens the life and property safety of nearby residents. The lightning protection of surrounding objects is usually realized by installing a lightning rod or a lightning conductor, and the method for evaluating the protection capability of the lightning rod at present mainly comprises the steps of drawing the protection range of the lightning rod, and if an object to be protected is in an envelope line of the protection range of the lightning rod, considering that the lightning rod can realize the lightning protection of the object (the probability of lightning stroke of the object is 0.1%). Therefore, the probability of lightning strike of the protected object or the lightning rod is estimated only by an empirical and theoretical method, which is obviously inconclusive, but because the occurrence of lightning is full of randomness in reality, the probability of lightning strike of an object before and after the lightning rod is installed cannot be estimated by using an actual lightning strike process.
Disclosure of Invention
In order to solve the above problems, an object of the present invention is to provide a method for generating a three-dimensional lightning leader development path, so as to simulate the threatened situation of each part of a target object in a lightning environment and provide guidance for lightning protection design.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for generating a three-dimensional lightning leader development path comprises the following steps:
the method comprises the following steps: setting a rectangular simulation space, wherein the height of the rectangular simulation space is not less than 3 times of the height of a research object, discretizing the rectangular simulation space, selecting a plurality of points on the upper surface of the rectangular simulation space as alternative points of a downlink pilot starting position, considering the randomness of the downlink pilot starting, randomly selecting an alternative point as a downlink pilot starting development point during each simulation, setting the potential of the lower surface of the rectangular simulation space to be zero, setting the potential of the upper surface to be the potential distribution generated by thundercloud on the height of the rectangular simulation space, determining the potential distribution around the rectangular simulation space according to the equal gradient attenuation from top to bottom, and determining the development probability index eta influencing the thunder development track;
step two: carrying out 3D modeling on a research object, carrying out classification labeling on each part area contained in the research object, setting different boundary conditions, writing a docking program, introducing the docking program into a rectangular simulation space, and setting an uplink pilot starting point which possibly occurs according to the research object, wherein the points are called hot points;
step three: determining a head potential of a descending pilot according to the internal field intensity distribution of the descending pilot, discretizing a space potential by using a finite difference method, calculating the space potential distribution after the development of each step of the pilot in a rectangular simulation space by combining with ultra-relaxation iteration, determining the development probability of a developed point to each point to be developed according to a pilot development WZ model, determining a final development point by using a roulette plate method, and recording the development point;
step four: taking the contact of the ascending and descending leaders or the contact of the descending leaders to a research object as a lightning leader development ending condition, if the leaders meet the ending condition, ending the development of the leader, entering the fifth step, and if not, returning to the third step;
step five: and recording the coordinates of the lightning stroke part and the lightning stroke ending mark, thus obtaining a complete lightning stroke process.
Further, in the first step, the calculation method of the surface potential distribution on the rectangular simulation space is as follows:
let the height of the original rectangular simulation space be h 0 Setting a rectangular space II with height of 2000m and length and width equal to those of original rectangular simulation space, where the potential of upper surface is equal to that of lower surface of thundercloud, i.e. -40MV, the potential of lower surface is 0, the potential of peripheral space is progressively decreased in equal gradient from top to bottom, discretizing rectangular space II, adopting ultra-relaxation iteration method to iteratively calculate potential distribution of whole space, finally deriving height h 0 The potential distribution data of (2) is used as the potential distribution of the upper surface of the original rectangular simulation space.
Further, in the step one, a method for determining the development probability index η influencing the lightning development track is as follows:
according to the WZ model, the selection of the thunder and lightning development probability index eta influences the simulated thunder and lightning development track, 30 thunder and lightning track pictures are obtained by averagely calculating each eta by continuously adjusting the value of the eta, the fractal dimension of the thunder and lightning track picture under each eta is calculated by adopting a box-dimension method and then compared with the fractal dimension of natural thunder and lightning, the fractal dimension of the natural thunder and lightning is generally between 1.1 and 1.4, and the development path of the fractal dimension accords with the fractal dimension of the natural thunder and lightning by continuously adjusting the development probability coefficient eta.
Further, the box dimension method is to use boxes without radii for covering when measuring an irregular curve or an irregular curve, and when the sizes of the small boxes are different, the required number of the small boxes is different, and now it is assumed that the radius of the small box is r, the number of the boxes is N (r), and the fractal dimension D is calculated according to the following formula:
based on a box dimension method, a fractal dimension is obtained through a FracLab tool box of MATLAB, and the process is as follows: firstly, binarization processing is carried out on a downlink pilot channel track picture simulated under different eta, the image is subjected to blocking processing by using a set size, a plurality of groups of blocks N (r) with different radiuses r and corresponding pixel values of 1 are obtained, linear fitting is carried out on a series of lnN (r) and ln (1/r) obtained, and the slope is the fractal dimension.
Further, in step three, the method for determining the potential of the descending pilot head according to the distribution of the descending pilot internal field strength is as follows:
the electric field in the pilot channel is approximate to a uniform electric field with the size of 3-10 kV/m, and after the downlink pilot undergoes the (k + 1) th iteration, the potential of the pilot head is calculated according to the following formula:
U (k+1) ＝U (k) -Ed
in the formula: u shape (k+1) The potential value of the head of the descending leader after the k +1 th iteration; u shape (k) The potential value of the kth iteration is obtained; e is the electric field size of the pilot channel, and E is more than or equal to 3kV/m and less than or equal to 10kV/m; d is the development step length; its initial iteration value U (0) The first point of the development of the descending leader corresponds to the potential value of a point on the upper surface of the rectangular simulation space.
Further, in step three, the method for calculating the spatial potential distribution by using the finite difference method and the super-relaxation iteration is as follows:
firstly, dividing a solving area into grids, and under the condition of not considering the influence of space charge, the distribution of space potential meets the Laplace equation:
for the gridded solution area, discretizing it into:
in the formula: superscript n is the nth iteration;
the potential at the (i, j, k) space coordinate after the (n + 1) th iteration;
the potentials around the point are respectively, and h is the side length of the grid;
because the simple iteration method has low convergence speed and overlong calculation time, the potential distribution is calculated by adopting an ultra-relaxation iteration method, and an iteration formula is changed into the following formula:
in the formula: w is a relaxation factor; n and n +1 are the nth and n +1 th iterations, respectively;
and (4) setting iteration precision, and stopping iteration when the (n + 1) th iteration meets the precision requirement, so that the potential distribution of the whole space is obtained.
Further, in step three, the probability of determining the lead developed point to the to-be-developed point according to the WZ model is as follows:
firstly, selecting 26 lattice points around a developed point (i, j), judging whether the 26 points to be developed have the condition of being overlapped with the previous developed point, if so, excluding the points, and setting the points to be developed which are not in conformity as the condition that a new leading section is developed back is not common in the actual observation result of natural lightning as a prohibited developing point, wherein the rest points to be developed are effective points to be considered;
the probability that the remaining valid development point becomes the next development point is shown as follows:
in the formula: p is (i,j,k)→(i′,j′,k′) The development probability from the development point (i, j, k) to the point (i ', j ', k ') to be developed is referred to; e (i,j,k)→(i′,j′,k′) Means the average electric field intensity between the point (i, j, k) to be developed (i ', j ', k '); e th A finger discharge threshold electric field; eta is a development probability coefficient;
and (3) after the probability of each effective point to be developed is solved, determining the coordinates of a new pilot development point by constructing (0-1) uniformly distributed random numbers and adopting a roulette wheel method, namely the process of selecting the pilot development point.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention provides a method for generating a three-dimensional lightning leader development path, which has the following advantages: lightning is taken as a strong destructive and threatening climate phenomenon, the discharge process of the lightning is very complex, the discharge of thunderclouds to the ground is influenced by a plurality of natural conditions such as weather, geology, terrain and the like, the lightning has great randomness, and the estimation of the lightning stroke condition of each part of an object by means of real lightning is unrealistic. Although the thundercloud discharge path is unpredictable, the lightning development path has certain uniqueness, and the simulation of the lightning path can be realized to a certain extent by mastering certain inherent characteristics of the lightning discharge path, so that the actual lightning process is truly reflected. The method establishes the thunder and lightning leading development model by taking the WZ model as the theoretical basis of the thunder and lightning leading development, so that the generated thunder and lightning leading development path is not only similar to the fractal of natural thunder and lightning, but also has the randomness of the natural thunder and lightning development, and the simulation of the real thunder and lightning development process is realized by a simulation means. Therefore, if the lightning strike condition of a certain building or equipment in the lightning environment needs to be researched, the lightning strike condition of each part of the object in the lightning environment can be simulated by only modeling the target object and placing the target object in the simulation environment set by the method, and guidance and verification are provided for the lightning protection design of the object.
Drawings
FIG. 1 is a flow chart of a method for generating a three-dimensional lightning leader development path according to the present invention;
FIG. 2 is a schematic diagram illustrating selection of points to be developed near a point to be developed in the method for generating a three-dimensional lightning leader development path according to the present invention;
FIG. 3 is a top view of the arrangement of the transformer substation and the lightning rod thereof according to the embodiment of the invention;
FIG. 4 is a schematic diagram of lightning striking equipment in a substation in accordance with an embodiment of the present invention;
fig. 5 is a schematic view of a lightning rod in a lightning strike intermediate station according to an embodiment of the present invention.
Detailed Description
The following describes the implementation of the present invention in further detail with reference to specific examples:
taking the development of thunder and lightning over a transformer substation with the length and the width of 80m as an example, the implementation process of the method for generating the three-dimensional thunder and lightning lead development path provided by the invention is described, and as shown in fig. 1, the method specifically comprises the following steps:
the method comprises the following steps: setting a rectangular simulation space, wherein the height of the rectangular simulation space is not less than 3 times of the height of a research object, discretizing the rectangular space, selecting a plurality of points on the upper surface of the rectangular space as alternative points of a downlink pilot starting position, considering the randomness of the downlink pilot starting, randomly selecting an alternative point as a downlink pilot starting development point during each simulation, setting the surface potential of the space to be zero, setting the surface potential to be the potential distribution generated by thundercloud on the height of the space, determining the potential distribution around according to the top-down equal gradient attenuation, and determining the development probability index eta influencing the thunder and lightning development track.
In the embodiment, the object to be studied is a transformer substation with the length and the width of 80m, as shown in fig. 3, a cartesian three-dimensional coordinate system is established by taking a simulation space as a cube with the length, the width and the height of 120m, the lower left corner of the space is a coordinate origin, the lower boundary potential of the space is set to be 0, and the middle above the space is taken as a lightning lead development starting point; for the boundary condition value of the boundary on the space, the boundary condition value can be determined according to the following method: as the height of the rectangular simulation space is only 120m, and the actual height of the thundercloud can reach 2000m, in order to obtain the potential boundary condition on the horizontal plane with the height of 120m, the potential distribution of 2000m high space is calculated by adopting a super-relaxation iteration method (accelerating the simulation speed) with longer step length, the potential of the thundercloud is-40 MV (namely the upper boundary potential of the simulation space with the height of 2000 m), and the potential distribution of the thundercloud on the horizontal plane with the height of 120m is obtained through multiple iterations.
Step two: the method comprises the steps of carrying out 3D modeling on a research object, carrying out classification labeling on each part area contained in the research object, setting different boundary conditions, writing a docking program, leading the docking program into a lightning leader development rectangular simulation space, and setting possible uplink leader starting points according to the research object, wherein the points are called hot points.
Step three: determining a head potential of a downlink pilot according to the internal field intensity distribution of the downlink pilot, discretizing a space potential by using a finite difference method, combining with an ultra-relaxation iteration to calculate the space potential distribution of each step of pilot development in a rectangular simulation space, determining the development probability of a developed point to each point to be developed according to a pilot development WZ model, determining the point to be developed corresponding to each developed point as shown in figure 2, determining a final developed point by using a roulette wheel method, and recording the developed point.
Discretizing the space into 120 × 120 × 120 grid points, giving the remaining grid point potentials 0 except for the grid points of the determined potentials (boundary conditions), and calculating the spatial potential distribution by combining with super-relaxation iteration, the iterative formula being:
in the formula: w is a relaxation factor; n and n +1 are the nth and n +1 iterations, respectively.
And when the (n + 1) th iteration meets the precision requirement, stopping the iteration, and obtaining the potential distribution of the full space. The probability of the developed point developing towards each point to be developed can then be determined according to the lead development WZ model specified by:
wherein the discharge threshold electric field E th Taking 75kV/m, and taking 5 as a development probability coefficient eta after continuous simulation adjustment; then, a random number of 0-1 is set, a point to be developed is determined as a final development point by using a roulette wheel method, and the development point is recorded, and then the lightning is developed one step downwards.
Step four: and (4) taking the contact of the ascending and descending pilots or the contact of the descending pilots to the research object as a thunder and lightning pilot development ending mark, if the pilots meet ending conditions, ending the development of the leaders, entering the fifth step, and if not, returning to the third step.
And if the head of the lightning leader (the latest developed point) is connected with an ascending leader generated by a certain hot point of the transformer substation or touches the ground, the development of the leader is considered to be finished, otherwise, the step three is performed again for the same operation, and the lightning leader is developed by one step downwards after each operation.
Step five: and recording the coordinates of the lightning stroke part and the lightning stroke ending mark, thus obtaining a complete lightning stroke process.
In the embodiment, as shown in fig. 4, a complete lightning lead development path is generated and strikes on a tower of a transformer substation, and in this case, a lightning rod in the transformer substation does not successfully intercept lightning, and equipment in the transformer substation is damaged by lightning. In another situation, as shown in fig. 5, a complete lightning lead development path is also successfully generated and strikes one lightning rod in the station, the lightning rod successfully intercepts the lightning, and the substation is protected. Therefore, the method for generating the three-dimensional lightning leader development path can effectively simulate the threatened condition of each part of the target object in the lightning environment, and provides guidance for the actual lightning protection design.
Claims (6)
1. A method for generating a three-dimensional lightning leader development path is characterized by comprising the following steps:
the method comprises the following steps: setting a rectangular simulation space, wherein the height of the rectangular simulation space is not less than 3 times of the height of a research object, discretizing the rectangular simulation space, selecting a plurality of points on the upper surface of the rectangular simulation space as alternative points of a downlink pilot starting position, considering the randomness of the downlink pilot starting, randomly selecting an alternative point as a downlink pilot starting development point during each simulation, setting the potential of the lower surface of the rectangular simulation space to be zero, setting the potential of the upper surface to be the potential distribution generated by thundercloud on the height of the rectangular simulation space, determining the potential distribution around the rectangular simulation space according to the equal gradient attenuation from top to bottom, and determining the development probability index eta influencing the thunder development track;
the calculation method of the surface potential distribution in the rectangular simulation space is as follows:
the height of the original rectangular simulation space is set ash 0 Setting a rectangular space II with height of 2000m and length and width identical to those of original rectangular simulation space, where the potential of upper surface of the space is equal to that of lower surface of thundercloud, i.e. -40MV, the potential of lower surface is 0, the potential of peripheral space is progressively decreased in equal gradient from top to bottom, discretizing rectangular space II, adopting ultra-relaxation iteration method to iteratively calculate potential distribution of whole space, finally deriving heighth 0 The potential distribution data of (2) is used as the potential distribution of the upper surface of the original rectangular simulation space;
step two: carrying out 3D modeling on a research object, carrying out classification labeling on each part area contained in the research object, setting different boundary conditions, writing a docking program, introducing the docking program into a rectangular simulation space, and setting an uplink pilot starting point which possibly occurs according to the research object, wherein the points are called hot points;
step three: determining a head potential of a downlink pilot according to the internal field intensity distribution of the downlink pilot, discretizing a space potential by using a finite difference method, combining with an ultra-relaxation iterative computation to calculate the space potential distribution of each step of pilot development in a rectangular simulation space, determining the development probability of a developed point to each point to be developed according to a pilot development WZ model, determining a final development point by using a roulette plate method, and recording the development point;
step four: taking the contact of the ascending and descending leaders or the contact of the descending leaders to a research object as a lightning leader development ending condition, if the leaders meet the ending condition, ending the development of the leader, entering the fifth step, and if not, returning to the third step;
step five: and recording the coordinates of the lightning stroke part and the lightning stroke end mark so as to obtain a complete lightning stroke process.
2. The method for generating a three-dimensional lightning leader development path according to claim 1, wherein: in the first step, a method for determining the development probability index eta influencing the lightning development track is as follows:
according to the WZ model, the selection of the lightning development probability index eta influences the simulated lightning development track, 30 lightning track pictures are obtained by averagely calculating each eta through continuously adjusting the value of the eta, the fractal dimension of the lightning track graph under each eta is calculated by adopting a box-dimension method and is compared with the natural lightning fractal dimension, the natural lightning fractal dimension is 1.1 to 1.4, and the development path of the natural lightning fractal dimension accords with the natural lightning fractal dimension through continuously adjusting the development probability coefficient eta.
3. The method for generating a three-dimensional lightning leader development path according to claim 2, wherein: the box dimension method is to adopt a box with different radius to cover when measuring an irregular curve or an irregular curve, when the sizes of small boxes are different, the required number of the small boxes is different, and the radius of the small box is assumed to ber，The number of the boxes is
Fractal dimensionDCalculated as follows:
based on a box dimension method, a fractal dimension is obtained through a FracLab toolbox of MATLAB, and the process is as follows: firstly, binaryzation processing is carried out on a descending pilot channel track picture simulated under different eta, and the image is subjected to blocking processing by using the set size to obtain a plurality of groups of images with different radiusesrCorresponding to the number of blocks having a pixel value of 1
For the obtained series
And
and performing linear fitting to obtain the slope of the fractal dimension, wherein the slope is the fractal dimension.
4. The method for generating a three-dimensional lightning leader development path according to claim 1, wherein: in step three, the method for determining the potential of the descending leader head according to the distribution of the internal field strength of the descending leader is as follows:
the electric field in the pilot channel is approximate to a uniform electric field with the size of 3-10kV/m, and after the downlink pilot undergoes k +1 iteration, the potential of the pilot head is calculated according to the following formula:
in the formula:
the potential value of the head of the descending leader after the k +1 th iteration;
the potential value of the kth iteration is obtained;Eis the magnitude of the electric field of the pilot channel,
；dthe step length is developed; initial iteration value thereof
The first point of the development of the descending leader corresponds to the potential value of a point on the upper surface of the rectangular simulation space.
5. The method for generating a three-dimensional lightning leader development path according to claim 1, wherein: in step three, the method for calculating the spatial potential distribution by using the finite difference method and the super-relaxation iteration is as follows:
firstly, dividing a solving area into grids, and under the condition of not considering the influence of space charge, the distribution of space potential meets the Laplace equation:
for the gridded solution area, discretizing it into:
in the formula: superscript n is the nth iteration;
for the space coordinate after the n +1 iteration is
The potential of (d);
are respectively provided withIs the potential around the point at which the potential,his the grid side length;
because the simple iteration method has low convergence speed and overlong calculation time, the potential distribution is calculated by adopting an ultra-relaxation iteration method, and an iteration formula is changed into the following formula:
in the formula:wis a relaxation factor; n and n +1 are the nth and n +1 th iterations, respectively;
and (4) setting iteration precision, and stopping iteration when the (n + 1) th iteration meets the precision requirement, so that the potential distribution of the whole space is obtained.
6. The method for generating a three-dimensional lightning leader development path according to claim 1, wherein: in step three, the probability of leading the developed point to the to-be-developed point is determined according to the WZ model as follows:
firstly, a developed point is selected
Judging whether 26 grid points around exist the situation of superposition with the previous developed point or not, if yes, removing the points, and setting the non-conforming points to be developed as the development forbidding points and the rest points to be developed as the effective points to be developed which should be considered because the situation of backward development of the newly born guide section is not common in the actual observation result of the natural lightning;
the probability that the remaining valid development point becomes the next development point is shown as follows:
in the formula:
finger developed point
To the point of development
The probability of development of (c);
point of finger development
To the point of development
Average electric field strength in between;
a finger discharge threshold electric field; eta is a development probability coefficient;
and (3) after the probability of each effective point to be developed is solved, determining the coordinates of a new pilot development point by constructing (0-1) uniformly distributed random numbers and adopting a roulette wheel method, namely the process of selecting the pilot development point.
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