INSULATING MEDIUM DISCHARGE STREAMER SIMULATION METHOD CONSIDERING OFFSET AND BIFURCATION

Abstract

Disclosed is a discharge streamer simulation method considering offset and bifurcation. In the method, an insulating medium is arranged in an electric field environment, the number range of discharge streamer bifurcation points in the insulating medium and the number range of effective electron avalanches generated by each bifurcation are measured, a control equation and a boundary condition for streamer simulation are constructed based on a hydrodynamic drift diffusion model and a bipolar charge carrier model, model parameters corrected based on an electron avalanche development probability theory are introduced in the equation solving process, mathematical description and simulation calculation of a streamer offset and a bifurcation phenomenon are realized, and the electric field distribution and charge distribution accompanying the discharge streamer development process considering offset and bifurcation can be finally obtained.

Description

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority from the Chinese patent application 2022101138155 filed Jan. 30, 2022, the content of which is incorporated herein in the entirety by reference.

TECHNICAL FIELD

The present disclosure belongs to the technical field of insulating medium streamer discharge, and in particular, to an insulating medium discharge streamer simulation method considering offset and bifurcation.

BACKGROUND

Oil-paper insulation is one of the most common forms of solid-liquid insulation in an electric power system. The discharge characteristics and mechanism of the oil-paper insulation have attracted much attention. In particular, the mathematical description and the simulation method of the discharge phenomenon in the oil-paper insulation have become a research hotspot. Simulation calculation not only becomes an effective supplement to experimental means, but also is the only way to explore the discharge characteristics and mechanism without the experimental conditions. However, the existing simulation model has difficulty in reflecting the randomness and dispersibility, resulting in that it is still difficult to simulate the offset and bifurcation of the discharge streamer.

In the prior art, random disturbance points (position, number and size are all random) are arranged in oil, so that bifurcation and offset phenomena are generated after the streamer arrives at the disturbance points. However, on one hand, the introduction of the random disturbance points will greatly increase the mesh generation number, increase the calculation amount and occupy the calculation resource; and on the other hand, the random disturbance points reflect the macroscopic random characteristic, for example, bubbles and impurities in the oil, oil flow disturbance and uneven local distribution, and the streamer bifurcation and offset phenomena will also occur in the pure isotropous oil. In addition, the size range and the density range of the random disturbance points are not supported by a mature theory. Therefore, it is necessary to study a method for describing streamer bifurcation and offset under the driving of microscopic mechanism based on the generation and development probability of microscopic electron avalanches.

The above information disclosed in the Background section is merely used to enhance the understanding of the background of the present disclosure; therefore, information which does not constitute the prior art known to those of ordinary skill in the art may be included.

SUMMARY

Existing streamer simulation cannot effectively and rapidly describe the streamer offset and bifurcation phenomena. An objective of the present disclosure is to provide an insulating medium streamer discharge simulation method, so as to effectively and rapidly describe streamer bifurcation and offset based on the electron avalanche development probability theory. In order to achieve the above objective, the present disclosure provides the following technical solution.

An insulating medium discharge streamer simulation method considering offset and bifurcation provided by the present disclosure includes:

First step: arranging an insulating medium in an electric field environment, measuring the number range [N_ps, N_pb] of discharge streamer bifurcation points in the insulating medium and the number range of [N_bs, N_bb] of effective electron avalanches generated by each bifurcation, randomly drawing N_bpoint∈ [N_ps, N_pb] bifurcation points from all simulation calculation time nodes and marking corresponding moments as bifurcation moments, wherein N_ps and N_pb the minimum value and the maximum value of the number of the discharge streamer bifurcation points respectively, N_bs and N_bb are the minimum value and the maximum value of the effective electron avalanches respectively, and N_bpoint is the number of the randomly drawn bifurcation points;

Second step: constructing a simulation model for discharge streamer in the insulating medium based on a hydrodynamic drift diffusion model and a bipolar charge carrier migration model, wherein the initial value a₀ of the average distance between molecules in the hydrodynamic drift diffusion model is set as a real constant greater than 0; performing calculation according to a specified simulation step length from the zero moment, if the calculation reaches the bifurcation moment, entering the third step and then continuing to perform calculation after the value of the average distance between molecules is updated, otherwise, continuing to perform calculation with the values of the original parameters, and ending after simulation calculation is performed for a specified simulation duration;

Third step: calculating the probability of bifurcation occurring at each streamer head at a certain bifurcation moment:

$P_{s-i}=\{\begin{array}{cc}\frac{{❘E_{\mathrm{smax}-i}❘}^{\eta }}{\sum _{i=1}^{n_s}{❘E_{\mathrm{smax}-i}❘}^{\eta }}& ❘E_{\mathrm{smax}-i}❘>E_c\\ 0& ❘E_{\mathrm{smax}-i}❘\le E_c\end{array}i=1,2,\dots ,n_s,$

wherein i is a serial number parameter, n_s is the total number of all streamer branches at the current moment, P_s-i, is the probability of bifurcation occurring at the i^th streamer head, E_smax-i is the maximum electric field intensity of the i^th streamer head, E_c is the threshold of the electric field for sustainable development of the streamer, the streamer with E_smax-i>E_c is a developable streamer, and η is the streamer development probability index

Fourth step: drawing a streamer bifurcation position according to the P_s-i, wherein only one bifurcation position is drawn at each bifurcation moment, the drawn streamer is referred to as a to-be-bifurcated streamer, the bifurcation position at the position of the maximum field intensity of the head is denoted as (x₀, y₀, z₀), x₀ is the X-axis coordinates of the bifurcation position, y₀ is the Y-axis coordinates of the bifurcation position, and z₀ is the Z-axis coordinates of the bifurcation position;

Fifth step making a 180° cambered surface or arc by taking the bifurcation position as a center of a circle and 1-5 times the radius r_s of the head of the streamer as a radius, wherein the r_s is a distance between the position of the maximum net charge density and the position of the maximum electric field intensity; dividing the cambered surface or arc into n_r to-be-developed points at equal grids or equal intervals, wherein n_r>(S×N_bb) is met and n_r is the number of the to-be-developed points; and calculating the probability of the effective electron avalanches moving and evolving to each to-be-developed point:

$P_{b-j}=\{\begin{array}{cc}\frac{{❘{\varphi }_{\mathrm{smax}}-{\varphi }_j❘}^{\eta }}{\sum _{j=1}^{n_r}{❘{\varphi }_{\mathrm{smax}}-{\varphi }_j❘}^{\eta }}& ❘{\varphi }_{\mathrm{smax}}-{\varphi }_j❘>{\varphi }_c\\ 0& ❘{\varphi }_{\mathrm{smax}}-{\varphi }_j❘\le {\varphi }_c\end{array}j=1,2,\dots ,n_r,$

wherein j is a serial number parameter, P_b-j is the probability of the effective avalanches moving to the j^th to-be-developed point, ϕ_smax is the electric potential at the bifurcation position, ϕ_j is the electric potential at the j^th to-be-developed point, η is the streamer development probability index, and ϕ_c is a threshold of the effective electron avalanche development electric potential;

Sixth step: randomly drawing N_branch∈[N_bs, N_bb] effective development points from the n_r to-be-developed points according to the P_b-j, wherein N_branch is the total number of the effective development points, and it is indicated that the streamer only offsets but is not bifurcated when N_branch=1; connecting (x₀, y₀, z₀) with the selected to-be-developed point (x_k, y_k, z_k) to form a vector pointing at the to-be-developed point which is regarded as the development direction of the effective electron avalanches, wherein x_k is the X-axis coordinates of the k^th effective development point, y_k is the Y-axis coordinates of the k^th effective development point, z_k is the Z-axis coordinates of the k^th effective development point, and k=1, 2, . . . , N_branch;

Seventh step: taking a plane of which the normal vector is parallel to the development direction of the to-be-bifurcated streamer and which passes through a point (x₀, y₀, z₀) as a boundary, or taking a straight line which is perpendicular to the development direction of the to-be-developed streamer and passes through a point (x₀, y₀, z₀) as a boundary, and on the to-be-developed side, calculating a distance d_k(x,y,z) from a certain point (x,y,z) in a solving domain to a ray where the development direction of each branch is located:

$d_k\left(x,y,z\right)=\{\begin{array}{cc}\begin{array}{c}a\mathrm{distance}\mathrm{to}a\mathrm{straight}\mathrm{line}\mathrm{passing}\mathrm{through}\\ \mathrm{the}\mathrm{point}\left(x_0,y_0,z_0\right)\mathrm{and}\mathrm{the}\mathrm{point}\left(x_k,y_k,z_k\right)\end{array}& \left(x_0-x_k\right)\left(x_0-x\right)+\left(y_0-y_k\right)\left(y_0-y\right)+\left(z_0-z_k\right)\left(z_0-0\right)\ge 0\\ a\mathrm{distance}\mathrm{to}\mathrm{the}\mathrm{point}\left(x_0,y_0,z_0\right)& \left(x_0-x_k\right)\left(x_0-x\right)+\left(y_0-y_k\right)\left(y_0-y\right)+\left(z_0-z_k\right)\left(z_0-0\right)<0\end{array},$

wherein the starting point of the ray is (x0, y0, z0), assuming that the minimum of dk(x,y,z) is dmin(x,y,z), a correction coefficient kcor(x,y,z) is constructed as follows:

$k_{\mathrm{cor}}\left(x,y,z\right)={\left(\frac{1}{1+d_{\min }\left(x,y,z\right)}\right)}^{\gamma },$

wherein γ is a gradient parameter for controlling the change rate of the correction coefficient; and

Eighth step: correcting the average distance between molecules in the hydrodynamic drift diffusion model in the solving domain on the to-be-developed side,

$a_{\mathrm{cor}}\left(x,y,z,t\right)=\left(1-m\times K_{\mathrm{cor}}\left(x,y,z\right)\times \frac{\Delta T_s-t}{\Delta T_s}\right)\times a_0,$

wherein a_cor is the corrected average distance between molecules and is a function related to the spatial position and time, m is a correction scaling coefficient and meets 0<m<1, K_cor is the normalized result of k_cor, a₀ is the initial value of the average distance between molecules in the hydrodynamic drift diffusion model, ΔT_s is a time interval between the moment of current bifurcation and the moment of next bifurcation and t is the streamer development time calculated from the beginning of current bifurcation; and updating the average distance between molecules of the discharge streamer simulation model in the second step to current corrected value and returning to the second step.

In the insulating medium discharge streamer simulation method considering offset and bifurcation, the positively polar streamer development probability index is 2-3, and the negatively polar streamer development probability index is 1.5-2.

In the insulating medium discharge streamer simulation method considering offset and bifurcation, the gradient parameter γ is greater than 1.

In the insulating medium discharge streamer simulation method considering offset and bifurcation, the electric field threshold E_c of the effective electron avalanche development is greater than or equal to 0, and the electric potential difference threshold of the effective electron avalanche development is greater than or equal to 0.

In the above technical solution, the insulating medium discharge streamer simulation method considering offset and bifurcation provided by the present disclosure has the following beneficial effects: the simulation description of discharge channel offset and bifurcation is realized based on the electron avalanche development probability; and the method can be used to construct and solve a two-dimensional discharge model or a three-dimensional discharge model. The present disclosure is suitable for all alternating current (power frequency, harmonic wave, square wave and the like), direct current (positive polarity and negative polarity), alternating and direct current composite electric stress and pulse electric stress. The present disclosure not only can be applied to an oil-paper insulating system, but also can be applied to any liquid-solid two-phase insulation system or liquid single-phase insulation system, and it is only necessary to set corresponding parameters according to the dielectric property. The describable discharge phenomenon not only is limited to a space streamer, but also can describe a surface streamer. The correctable parameter of the present disclosure not only is limited to the average distance of molecules, but also may be an ionized molecular density no, an ionized energy coefficient γ_e, a collision ionization coefficient A_t and a collision ionization index item coefficient B_t, and may be one or several of the above parameters. The correction method is unchanged. If the selected coefficient is positively correlated with a charge generation item, then m∈(−1, 0). If the selected coefficient is negatively correlated, m∈(0,1). The radius of the cambered surface (or arc) is 1-5 times r_s. This range is only intended to ensure the calculation accuracy. Certainly, this range may be exceeded, as long as it can be ensured that the radius of the cambered surface (or arc) is greater than 0. The solving model in the second step not only is limited to the hydrodynamic drift diffusion model and the bipolar charge carrier model, but also may be other similar streamer solving models.

BRIEF DESCRIPTION OF THE DRAWINGS

In order to describe the technical solutions in the embodiments of the present disclosure or in the prior art more clearly, the accompanying drawings required for describing the embodiments will be briefly described below. Obviously, the accompanying drawings in the following description are merely some embodiments recorded in the present disclosure, and a person of ordinary skill in the art may still derive other drawings from these accompanying drawings.

FIG. 1 is a schematic flowchart of an insulating medium discharge streamer simulation method according to the present disclosure.

FIG. 2 is a schematic diagram of a simulation calculation process of discharge streamer offset and bifurcation according to the present disclosure.

FIG. 3 shows a simulation result of space electric field distribution accompanying the streamer offset and bifurcation according to the present disclosure.

FIG. 4 shows a simulation result of space charge distribution accompanying the streamer offset and bifurcation according to the present disclosure.

DETAILED DESCRIPTION OF THE EMBODIMENTS

In order to make the objectives, technical solutions and advantages of the embodiments of the present disclosure clearer, the technical solutions in the embodiments of the present disclosure will be clearly and completely described below in conjunction with the embodiments of the present disclosure. Obviously, the described embodiments are some rather than all of the embodiments. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present disclosure without creative efforts shall fall within the protection scope of the present disclosure.

Therefore, the following detailed description of the embodiments of the present disclosure provided in the accompanying drawings are not intended to limit the protection scope of the present disclosure, but is merely representative of selected embodiments of the present disclosure. All other embodiments obtained by a person of ordinary skill in the art based on the embodiments of the present disclosure without creative efforts shall fall within the protection scope of the present disclosure.

It should be noted that similar reference numerals and letters represent similar items in the accompanying drawings below. Therefore, once an item is defined in one drawing, it does not need to be further defined and explained in subsequent drawings.

In the description of the present disclosure, the orientation or position relationship indicated by the terms “central”, “longitudinal”, “transverse”, “length”, “width”, “thickness”, “upper”, “lower”, “front”, “back”, “left”, “right”, “vertical”, “horizontal”, “top”, “bottom”, “inner”, “outer”, “clockwise”, “anticlockwise”, etc. is based on the orientation or position relationship shown in the accompanying drawings, only for the convenience of describing the present disclosure and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation or be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation to the present disclosure.

Besides, the terms “first” and “second” are used only for descriptive purposes and should not be construed as indicating or implying relative importance or implicitly indicating the number of indicated technical features. Thus, features defined with “first” and “second” may explicitly or implicitly include one or more of the features. In the description of the present disclosure, “plurality of” means two or more, unless otherwise specifically defined.

In the present disclosure, unless otherwise specified and defined, the terms such as “mounting” “connected”, “connection” and “fixing” should be understood in a broad sense. For example, connection may be fixed connection, detachable connection, or integrated connection; connection may be direct connection or indirect connection through an intermediate medium, and connection may be the internal communication between two elements or the interaction relationship between the two elements. A person of ordinary skill in the art may understand specific meanings of the foregoing terms in the present disclosure based on a specific situation.

In the present disclosure, unless otherwise specified and limited, the first feature “above” or “below” the second feature may include that the first feature and the second feature are in direct contact, and may also include that the first feature and the second feature are not in direct contact, but are in contact through another feature between the first feature and the second feature. Moreover, the first feature being “on” or “above” or “over” the second feature includes the first feature being directly above and obliquely above the second feature, or simply means that the level of the first feature is higher than that of the second feature. The first feature being “beneath” or “below” or “under” the second feature includes the first feature being directly below and obliquely below the second feature, or simply means that the level of the first feature is lower than that of the second feature.

In order to enable a person skilled in the art to better understand the technical solution of present disclosure, the present disclosure will be further described below in detail in conjunction with the accompanying drawings. An insulating medium streamer discharge simulation method considering offset and bifurcation includes:

an insulating medium discharge streamer simulation method considering offset and bifurcation, including the following steps:

First step: arranging an insulating medium in an electric field environment, measuring the number range [N_ps, N_pb] of discharge streamer bifurcation points in the insulating medium and the number range of [N_bs, N_bb] of effective electron avalanches generated by each bifurcation, randomly drawing N_bpoint∈[N_ps, N_pb] bifurcation points from all simulation calculation time nodes, and marking corresponding moments as bifurcation moments,

wherein in this embodiment, through observation and confirmation by a high-speed camera, N_ps=0, N_pb=5, N_bs=1, N_bb=3, the randomly drawn N_bpoint=2, and the corresponding bifurcation moments are the t=0.5 ns moment and the t=6.4 ns moment respectively;

Second step: constructing a simulation model for discharge streamer in the insulating medium based on a hydrodynamic drift diffusion model and a bipolar charge carrier migration model, wherein the initial value a₀ of the average distance between molecules in the hydrodynamic drift diffusion model is set as a real constant greater than 0; performing calculation according to a specified simulation step length from the zero moment, if the calculation reaches the bifurcation moment, entering the third step and then continuing to perform calculation after the value of the average distance between molecules is updated, otherwise, continuing to perform calculation with the values of the original parameters, and ending after simulation calculation is performed for a specified simulation duration, wherein the simulation time step length is set as 0.1 ns, the simulation duration is set as 200 ns, and a₀ is set as 0.3 nm;

Third step: calculating the probability of bifurcation occurring at each streamer head at the moment when t=0.5 ns or t=6.4 ns:

$P_{s-i}=\{\begin{array}{cc}\frac{{❘E_{\mathrm{smax}-i}❘}^{\eta }}{\sum _{i=1}^{n_s}{❘E_{\mathrm{smax}-i}❘}^{\eta }}& ❘E_{\mathrm{smax}-i}❘>E_c\\ 0& ❘E_{\mathrm{smax}-i}❘\le E_c\end{array}i=1,2,\dots ,n_s,$

wherein i is a serial number parameter, n_s is the total number of all streamer branches at the current moment, P_s-i is the probability of bifurcation occurring at the i^th streamer head, E_smax-i is the maximum electric field intensity of the i^th streamer head, E_c is the threshold of the electric field for sustainable development of the streamer, the streamer with E_smax-i>E_c is a developable streamer, η is the streamer development probability index, and in this embodiment, E_c is 10⁶V/m and η is 2;

Fourth step: drawing a streamer bifurcation position according to the P_s-i, wherein only one bifurcation position is drawn at each bifurcation moment, the drawn streamer is referred to as a to-be-bifurcated streamer, and the bifurcation position at the position of the maximum field intensity of the head is denoted as (x₀, y₀, z₀);

Fifth step making a 180° cambered surface or arc by taking the bifurcation position as a center of a circle and 1-5 times the radius r_s of the streamer head as a radius, wherein the r_s is a distance between the position of the maximum net charge density and the position of the maximum electric field intensity; dividing the cambered surface or arc into n_r to-be-developed points at equal grids or equal intervals, wherein n_r>(S×N_bb) is met and n_r is the number of the to-be-developed points; and calculating the probability of the effective electron avalanches moving and evolving to each to-be-developed point:

$P_{b-j}=\{\begin{array}{cc}\frac{{❘{\varphi }_{\mathrm{smax}}-{\varphi }_j❘}^{\eta }}{\sum _{j=1}^{n_r}{❘{\varphi }_{\mathrm{smax}}-{\varphi }_j❘}^{\eta }}& ❘{\varphi }_{\mathrm{smax}}-{\varphi }_j❘>{\varphi }_c\\ 0& ❘{\varphi }_{\mathrm{smax}}-{\varphi }_j❘\le {\varphi }_c\end{array}j=1,2,\dots ,n_r,$

wherein j is a serial number parameter, P_b-j is the probability of the effective avalanches moving to the j^th to-be-developed point, ϕ_smax is the electric potential at the bifurcation position, ϕ_j is the electric potential at the j^th to-be-developed point, ϕ is the streamer development probability index, ϕ_c is a threshold of the effective electron avalanche development electric potential, and in this embodiment, ϕ_c=0, n_r=20, and the arc is made by using the radius which is 3 times r_s;

Sixth step: randomly drawing N_branch ∈[N_bs, N_bb] effective development points from the n_r to-be-developed points according to the P_b-j, wherein N_branch is the total number of the effective development points, and it is indicated that the streamer only offsets but is not bifurcated when N_branch=1; connecting (x₀, y₀, z₀) with the selected to-be-developed point (x_k, y_k, z_k) to form a vector pointing at the to-be-developed point which is regarded as the development direction of the effective electron avalanches, wherein k=1, 2, . . . , N_branch and in this embodiment, the N_branch randomly drawn at each of the two bifurcation moments is 2;

Seventh step: taking a plane of which the normal vector is parallel to the development direction of the to-be-bifurcated streamer and which passes through a point (x₀, y₀, z₀) as a boundary, or taking a straight line which is perpendicular to the development direction of the to-be-developed streamer and passes through a point (x₀, y₀, z₀) as a boundary, and on the to-be-developed side, calculating a distance d_k(x,y,z) from a certain point (x,y,z) in a solving domain to a ray where the development direction of each branch is located:

$d_k\left(x,y,z\right)=\{\begin{array}{cc}\begin{array}{c}a\mathrm{distance}\mathrm{to}a\mathrm{straight}\mathrm{line}\mathrm{passing}\mathrm{through}\\ \mathrm{the}\mathrm{point}\left(x_0,y_0,z_0\right)\mathrm{and}\mathrm{the}\mathrm{point}\left(x_k,y_k,z_k\right)\end{array}& \left(x_0-x_k\right)\left(x_0-x\right)+\left(y_0-y_k\right)\left(y_0-y\right)+\left(z_0-z_k\right)\left(z_0-0\right)\ge 0\\ a\mathrm{distance}\mathrm{to}\mathrm{the}\mathrm{point}\left(x_0,y_0,z_0\right)& \left(x_0-x_k\right)\left(x_0-x\right)+\left(y_0-y_k\right)\left(y_0-y\right)+\left(z_0-z_k\right)\left(z_0-0\right)<0\end{array},$

wherein the starting point of the ray is (x₀, y₀, z₀), assuming that the minimum value in d_k(x,y,z) is d_min(x,y,z), a correction coefficient k_cor(x,y,z) is constructed as follows:

$k_{\mathrm{cor}}\left(x,y,z\right)={\left(\frac{1}{1+d_{\min }\left(x,y,z\right)}\right)}^{\gamma },$

wherein γ is a gradient parameter for controlling the change rate of the correction coefficient, and in this embodiment, γ is 3; and

Eighth step: correcting the average distance between molecules in the hydrodynamic drift diffusion model in the solving domain on the to-be-developed side,

$a_{\mathrm{cor}}\left(x,y,z,t\right)=\left(1-m\times K_{\mathrm{cor}}\left(x,y,z\right)\times \frac{\Delta T_s-t}{\Delta T_s}\right)\times a_0,$

wherein a_cor is the corrected average distance between molecules and is a function related to the spatial position and time, m is a correction scaling coefficient and meets 0<m<1, K_cor is the normalized result of k_cor, a₀ is the initial value of the average distance between molecules in the hydrodynamic drift diffusion model, ΔT_s is a time interval between the moment of current bifurcation and the moment of next bifurcation and t is the streamer development time calculated from the beginning of current bifurcation; and updating the average distance between molecules of the discharge streamer simulation model in the second step as current corrected value and returning to the second step. In this embodiment, m is 0.8, and ΔT_s=(6.4 ns−0.5 ns)=5.9 ns.

The implementation result is shown as follows:

in one embodiment, the applicant initially thought of setting the randomly distributed space charge initial condition in the solving space, which has physical significance, because the space charges in the medium are unevenly distributed under the action of external factors (such as ultraviolet rays). A Random uniform random function is set at the space charge initial condition; however, it was found that the streamer is not bifurcated, because the electric field distortion caused by the unevenly distributed initial charges gradually disappears after several time step lengths. Actually, the initial state of the space charges will rapidly change with the development of the streamer.

Although the method of the random charge distribution initial value failed, the applicant also thought of whether bifurcation will be caused if the set random space charge initial value continues to act. Therefore, the applicant set the randomly distributed background charges (not the initial value) to simulate the random factors (such as impurities and bubbles) inherent in the liquid medium. Under the action of the randomly distributed background charges, the applicant obtained the unsatisfactory simulation result. The streamer charges are intermittently distributed and not continuous, and the formed electric field channel is not obviously bifurcated. The reason is that the randomly distributed background charges do affect the electric field distortion and charge generation at the streamer head, but the development direction is not pointed for the new streamer, so the streamer is not bifurcated.

Through the above exploration, the applicant realized that in order to realize streamer bifurcation, it is necessary to start with the microscopic electron avalanche development probability, construct the development probability models in all directions and provide power for the development of new streamers. Therefore, the technical solutions of the present disclosure are put forward. The simulation result of space electric field distribution accompanying the streamer offset and bifurcation is shown in FIG. 3; and the simulation result of space charge distribution accompanying the streamer offset and bifurcation is shown in FIG. 4.

The method provided by the present disclosure has more theoretical significance because the discharge itself belongs to a probability event. Both the macroscopic random disturbance factor and the microscopic random disturbance factor are reflected in the probability change, which is more practical. However, the method for artificially setting random disturbance points (regions) can only reflect the influence of macroscopic disturbance, and it is difficult to describe a large number of discrete random disturbances by directly using mathematical formulas. Moreover, the position, number and size of the set random disturbance factors all have artificial subjective wills.

The method provided by the present disclosure has smaller calculation amount (few calculation resources and short calculation time). In the method for artificially setting random disturbance, in order to achieve considerable results, the diameter of the disturbance region needs to be controlled to 1-10 μm, and the region density is about 10¹¹ m⁻³. A large number of disturbance regions will increase the number of meshes (calculation nodes) and the calculation amount, so it is necessary to use a high-performance server for solution. The method provided by the present disclosure can be solved by using a common computer.

Finally, it should be noted that the described embodiments are merely some rather than all of the embodiments. Based on the embodiments of the present application, all the other embodiments obtained by those skilled in the art without inventive effort are within the protection scope of the present application.

Some exemplary embodiments of the present disclosure are described above only by illustration. Undoubtedly, those of ordinary skill in the art may modify the described embodiments in various ways without departing from the spirit and scope of the present disclosure. Therefore, the above drawings and descriptions are essentially illustrative and should not be construed as limiting the protection scope of the claims of the present disclosure.

Claims

1. An insulating medium discharge streamer simulation method considering offset and bifurcation, comprising the following steps: First step: arranging an insulating medium in an electric field environment, measuring the number range [Nps, Npb] of discharge streamer bifurcation points in the insulating medium and the number range of [Nbs, Nbb] of effective electron avalanches generated by each bifurcation, drawing Nbpoint∈[Nps, Npb] bifurcation points from all simulation calculation time nodes randomly and marking corresponding moments as bifurcation moments, wherein Nps and Npb are the minimum value and the maximum value of the number of the discharge streamer bifurcation points respectively, Nbs and Nbb are the minimum value and the maximum value of the effective electron avalanches respectively, and Nbpoint is the number of the randomly drawn bifurcation points;Second step: constructing a simulation model for discharge streamer in the insulating medium based on a hydrodynamic drift diffusion model and a bipolar charge carrier migration model, wherein the initial value a0 of the average distance between molecules in the hydrodynamic drift diffusion model is set as a real constant greater than 0; performing calculation according to a specified simulation step length from the zero moment, entering the third step if the calculation reaches the bifurcation moment and then continuing to perform calculation after the value of the average distance between molecules is updated, otherwise, continuing to perform calculation with the values of the original parameters, and ending after simulation calculation is performed for a specified simulation duration;Third step: calculating the probability of bifurcation occurring at each streamer head at a certain bifurcation moment:

2. The insulating medium discharge streamer simulation method considering offset and bifurcation according to claim 1, wherein the positively polar streamer development probability index is 2-3, and the negatively polar streamer development probability index is 1.5-2.

3. The insulating medium discharge streamer simulation method considering offset and bifurcation according to claim 1, wherein the gradient parameter γ is greater than 1.

4. The insulating medium discharge streamer simulation method considering offset and bifurcation according to claim 1, wherein the electric field threshold Ec of the effective electron avalanche development is greater than or equal to 0, and the electric potential difference threshold of the effective electron avalanche development is greater than or equal to 0.