CN106874565B - Method for calculating three-dimensional electric field below power transmission line in rainy days - Google Patents

Method for calculating three-dimensional electric field below power transmission line in rainy days Download PDF

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CN106874565B
CN106874565B CN201710034706.3A CN201710034706A CN106874565B CN 106874565 B CN106874565 B CN 106874565B CN 201710034706 A CN201710034706 A CN 201710034706A CN 106874565 B CN106874565 B CN 106874565B
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马爱清
陈健
赵天成
林鹏远
梁家凡
徐捷立
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Shanghai University of Electric Power
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Abstract

The invention relates to a method for calculating a three-dimensional electric field below a power transmission line in rainy days, which comprises the following steps: (1) establishing a three-dimensional coordinate system, and establishing a three-dimensional model of the power transmission line and the tower in the three-dimensional coordinate system by adopting a three-dimensional line unit simulation charge method according to the distribution condition of the power transmission line and the tower; (2) establishing a raindrop model in a three-dimensional coordinate system by adopting a three-dimensional point charge simulation charge method according to the rainfall condition; (3) and calculating the electric field intensity distribution of the electric field intensity area to be calculated according to the coordinate of the electric field intensity area to be calculated and the field intensity calculation formula and the superposition principle. Compared with the prior art, the method has the advantages that the calculation result is more real and reliable, the electric field distribution under various power transmission lines in rainy days can be calculated, and the method has higher applicability.

Description

Method for calculating three-dimensional electric field below power transmission line in rainy days
Technical Field
The invention relates to a method for calculating a three-dimensional electric field below a power transmission line, in particular to a method for calculating a three-dimensional electric field below a power transmission line in a rainy day.
Background
With the rapid development of ultrahigh voltage and extra-high voltage power transmission in China, the electromagnetic environment problem caused by the ultrahigh voltage and extra-high voltage power transmission has been more and more concerned by the society and the nation. For an actual power transmission line, the influence of a conductor sag and a tower needs to be considered, and the calculation of an electric field of the actual power transmission line is a complex three-dimensional field problem. Meanwhile, the line actually runs in a complex weather environment, mainly rainy days and sunny days, the difference between the electric field in the rainy days and the electric field in the sunny days is not clear, and the calculation of the electric field in the rainy days is little at present, so that the three-dimensional electric field analysis under the complex weather condition is necessary.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for calculating a three-dimensional electric field below a power transmission line in rainy days.
The purpose of the invention can be realized by the following technical scheme:
a method for calculating a three-dimensional electric field below a power transmission line in a rainy day comprises the following steps:
(1) establishing a three-dimensional coordinate system, and establishing a three-dimensional model of the power transmission line and the tower in the three-dimensional coordinate system by adopting a three-dimensional line unit simulation charge method according to the distribution condition of the power transmission line and the tower;
(2) establishing a raindrop model in a three-dimensional coordinate system by adopting a three-dimensional point charge simulation charge method according to the rainfall condition;
(3) and calculating the electric field intensity distribution of the electric field intensity area to be calculated according to the coordinate of the electric field intensity area to be calculated and the field intensity calculation formula and the superposition principle.
The step (1) of establishing the three-dimensional models of the transmission line and the tower by the three-dimensional line unit charge simulation method specifically comprises the following steps: the method comprises the steps of respectively and equivalently connecting leads or pole pieces of the power transmission line into a plurality of sections of three-dimensional line unit charges end to end, wherein the charges are located in the centers of the three-dimensional line units, matching points and check points are arranged on the surfaces of the three-dimensional line units, and the line charge density of the three-dimensional line units is determined by performing charge matching and checking according to the matching points and the check points.
The three-dimensional point charge simulation charge method for establishing the raindrop model in the step (2) specifically comprises the following steps: determining the distance between two adjacent raindrops to be d meters according to the rainfall condition, determining the positions of the raindrops on the boundary of the region, setting the adjacent raindrops at intervals of d meters in the directions of an x axis, a y axis and a z axis of a three-dimensional coordinate system, finishing distribution setting of the positions of the raindrops in the set region according to the rule, correspondingly setting a three-dimensional point charge for each raindrop in the region, locating the charge at the center of the raindrop, setting a matching point and a check point on the surface of the raindrop, and performing charge matching and checking according to the matching point and the check point to determine the charge quantity of the three-dimensional point charge.
The line charge density of the three-dimensional line unit is obtained by the following method:
(a1) assuming that the charge quantity of the head and the tail of the three-dimensional line unit charge is tau1And τ2And obtaining the electric potential V of the matching points corresponding to the head and the tail1And V2And the potential V of the check point corresponding to the head and the tail3And V4；
(a2) Calculating the potential coefficient of the head and the tail points to the corresponding matching points as P1And P2Through τ1＝V1/P1，τ2＝V2/P2Obtaining the electric charge quantity tau of the first and the last points1And τ2；
(a3) Respectively calculating the potential coefficients of the head and the tail of the two points to the corresponding check points to be P3And P4The potential V of the verify point is calculated by the following formula31And V41：V31＝P3*τ1，V41＝P4*τ2；
(a4) Respectively obtain V31And V3Difference of (D) and V41And V4When the difference is smaller than the set value, executing the step (a5), otherwise returning to the step (a 1);
(a5) the charges in the charges of the three-dimensional line unit are linearly distributed and pass through the charge amount tau of the head and the tail1And τ2And calculating to obtain the line charge density of the three-dimensional line unit.
The charge amount of the three-dimensional point charge is obtained by the following method:
(b1) assuming that the charge amount of the three-dimensional point charge is q, and acquiring the potential V of the matching point on the three-dimensional point charge5；
(b2) Calculating the potential coefficient of the three-dimensional point charge to the matching point to be P5By q ═ V5/P5Obtaining the charge quantity of the three-dimensional point charge;
(b3) calculating the potential coefficient of the three-dimensional point charge to the check point to be P6Through V61＝P6Q calculating to obtain potential V of check point51；
(b4) Finding V61And V6Difference of (V)6And (c) determining the charge amount of the three-dimensional point charge as q when the difference value is smaller than the set value, and otherwise, returning to the step (b 1).
Step (3) respectively calculating the electric field intensity of each point in the electric field intensity area to be calculated so as to obtain electric field intensity distribution, setting the point of the electric field intensity to be calculated as a point P, wherein the calculation formula of the electric field intensity of the point P is as follows:
EPx＝Epx line+EPx point
EPy＝EPy wire+EPy point
EPz＝EPz line+EPz point，
EPx、EPyAnd EPzCorresponding to the components of the electric field strength of the point P in the x, y and z directions, EPx line、EPy wireAnd EPz lineCorresponding to the sum of the components of the electric field intensity of all three-dimensional line unit charges at the point P in space in the x direction, the y direction and the z direction, EPx point、EPy pointAnd EPz pointThe component sum of the electric field intensity of all three-dimensional point charges in the space at the point P in the x direction, the y direction and the z direction is corresponded.
The distance d between adjacent raindrops is obtained by the following formula:
Figure GDA0002436756810000031
Figure GDA0002436756810000032
Figure GDA0002436756810000033
where D is the known diameter of the raindrop and vbFor ending speed, r is the total amount of rainfall, ρ, over a period of tWater (W)Is the density of water, pAir conditionerThe density of air, g is the gravity acceleration, T is the total time of one rainfall, R is the total rainfall amount in the T time period, and T is a certain time period in the T time period.
The components E 'of the electric field intensity of a certain three-dimensional line unit charge at point P in the x direction, the y direction and the z direction'Pxxian、E′PyxianAnd E'PzxianCalculated by the following method:
let the starting point of the three-dimensional line unit charge be P1(x1,y1,z1) End point is P2(x2,y2,z2) Assuming that the length of the line unit is L, the line charge density of the three-dimensional line unit is tau (u) au + b, a and b are constants, u is Lt, t is more than or equal to 0 and less than or equal to 1, and the coordinate of the point P is P (x, y, z), the potential generated by the charge of the three-dimensional line unit at the point P is determined
Figure GDA0002436756810000034
Comprises the following steps:
Figure GDA0002436756810000035
wherein epsilon0Is a vacuum dielectric constant, DlThe distance from the field source point to the point P in the three-dimensional line unit,
Figure GDA0002436756810000036
Figure GDA0002436756810000037
Figure GDA0002436756810000041
τ(0)＝τ1，τ(L)＝τ2，b＝τ1，a＝(τ2-τ1)/L。
component E 'of electric field intensity of certain three-dimensional point charge at point P in x direction, y direction and z direction'Pxdian、E′PydianAnd E'PzdianCalculated by the following method:
let the three-dimensional point charge coordinate be Q (x)1,y1,z1) And the coordinate of the point P is P (x, y, z), the electric potential generated by the three-dimensional point charge at the point P is
Figure GDA0002436756810000042
Comprises the following steps:
Figure GDA0002436756810000043
wherein d is the distance from the three-dimensional point charge coordinate to the point P, Q is the charge quantity of the three-dimensional point charge, and epsilon is the dielectric constant of air;
further, it is possible to prevent the occurrence of,
Figure GDA0002436756810000044
compared with the prior art, the invention has the following advantages:
(1) the invention combines a three-dimensional line unit simulation charge method and a three-dimensional point charge simulation charge method, and simultaneously utilizes the field intensity superposition principle to provide a calculation method for calculating a near-earth three-dimensional electric field below a power transmission line in rainy days, so that the near-earth electric field below the power transmission line in rainy days is calculated, the factors of conductor sag, pole tower and rainy days are comprehensively considered, the calculation result is more real and reliable, the electric field distribution in rainy days below various power transmission lines can be calculated, and the method has higher applicability;
(2) according to the invention, different weather conditions such as heavy rain, medium rain and light rain can be simulated by changing the distance d between adjacent raindrops, so that the calculation result is more fit with the actual working condition, and the result is more reliable.
Drawings
FIG. 1 is a flow chart of a method for calculating a three-dimensional electric field below a power transmission line in a rainy day according to the present invention;
FIG. 2 is a three-dimensional line cell simulation charge model;
FIG. 3 is a three-dimensional point charge model;
FIG. 4 is a three-dimensional model of a tower;
FIG. 5 is a schematic view of a sag wire;
FIG. 6 is a three-dimensional electric field distribution diagram at a position 1.5m away from the center of a tower in sunny weather;
FIG. 7 is a three-dimensional electric field distribution diagram at a position 1.5m away from the center of a tower in light rain;
FIG. 8 is a diagram comparing the electric field distribution in sunny days and rainy days at a distance of 1.5m from the center of the tower;
FIG. 9 is a diagram comparing electric field distribution in rainy days at a distance of 1.5m from the center of the tower at different rainfall levels;
FIG. 10 is a graph comparing the electric field distribution under different weather strips at a distance of 1.5m below the edge phase.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Examples
As shown in fig. 1, a method for calculating a three-dimensional electric field below a power transmission line in a rainy day includes the following steps:
(1) establishing a three-dimensional coordinate system, and establishing a three-dimensional model of the power transmission line and the tower in the three-dimensional coordinate system by adopting a three-dimensional line unit simulation charge method according to the distribution condition of the power transmission line and the tower;
(2) establishing a raindrop model in a three-dimensional coordinate system by adopting a three-dimensional point charge simulation charge method according to the rainfall condition;
(3) and calculating the electric field intensity distribution of the electric field intensity area to be calculated according to the coordinate of the electric field intensity area to be calculated and the field intensity calculation formula and the superposition principle.
The step (1) of establishing the three-dimensional models of the transmission line and the tower by the three-dimensional line unit charge simulation method specifically comprises the following steps: the method comprises the steps of respectively and equivalently connecting leads or pole pieces of the power transmission line into a plurality of sections of three-dimensional line unit charges end to end, wherein the charges are located in the centers of the three-dimensional line units, matching points and check points are arranged on the surfaces of the three-dimensional line units, and the line charge density of the three-dimensional line units is determined by performing charge matching and checking according to the matching points and the check points.
The three-dimensional point charge simulation charge method for establishing the raindrop model in the step (2) specifically comprises the following steps: determining the distance between two adjacent raindrops to be d meters according to the rainfall condition, determining the positions of the raindrops on the boundary of the region, setting the adjacent raindrops at intervals of d meters in the directions of an x axis, a y axis and a z axis of a three-dimensional coordinate system, finishing distribution setting of the positions of the raindrops in the set region according to the rule, correspondingly setting a three-dimensional point charge for each raindrop in the region, locating the charge at the center of the raindrop, setting a matching point and a check point on the surface of the raindrop, and performing charge matching and checking according to the matching point and the check point to determine the charge quantity of the three-dimensional point charge.
Let the length of the transmission line be LlAnd rice, performing numerical modeling setting by using three-dimensional line unit simulation charges, wherein the length of the line unit is L meters, and the line is formed by Llthe/L section line unit is formed by connecting end to end, the electric charge is positioned in the center of the lead, and the matching point and the check point are arranged on the surface of the lead. The tower is composed of a plurality of steel columns, one section of the steel columns is taken for modeling description, the steel columns are in column shapes, three-dimensional line unit simulation charges are used for carrying out numerical modeling, and the length of the section of the steel column is set to be LTm, a length of the wire unit of lTm, it is composed of L connected end to endT/lTThe section line unit is formed, the electric charge is located in the center of the steel column, and the matching point and the check point are arranged on the surface of the steel column. The length of a raindrop space distribution region is x m, the width is y m, the height is z m, the distance between two adjacent raindrops is d m, the position of one raindrop on the boundary of the region is determined, then the adjacent raindrops are arranged in d m directions of an x axis, a y axis and a z axis, the raindrop position distribution arrangement is completed in the region according to the rule, each raindrop in the region is correspondingly provided with a three-dimensional point charge, the charge is located at the center of the raindrop, and a matching point and a check point are arranged on the surface of the raindrop. Firstly, obtaining a potential coefficient matrix [ P ] of all matching points through a related calculation formula of three-dimensional line unit analog charges and three-dimensional point charges]Due to the potential matrix [ V ] of each matching point]Known as being represented by [ V ]]＝[P]·[Q]Left multiplication [ P]-1Determining a quantity matrix [ Q ] of each charge]. In order to determine whether the charge quantity is set reasonably or not and whether the charge electricity quantity calculation is correct or not, verification is required to be carried out, and a potential coefficient matrix [ P 'of a verification point is obtained']Through [ V']＝[P’]·[Q]，[V’]And calculating a potential matrix for the check points, calculating to obtain the calculated potential of each check point, performing error calculation on the calculated potential of each check point and the corresponding actual potential of each check point, and if the calculated potential of each check point meets the requirement, setting the quantity of charges reasonably and calculating the electric quantity of the charges correctly. Finally, the field intensity components and the combined field intensity of any point P in the space on the x axis, the y axis and the z axis can be obtained through a field intensity calculation formula of the three-dimensional line unit simulation charges and the three-dimensional point charges, and the field intensity formed by all the charges in the space at the point P is superposed according to the vector by combining the field intensity superposition theorem to obtain the total field intensity.
Specifically, the method comprises the following steps: the line charge density of the three-dimensional line unit is specifically obtained by:
(a1) assuming that the charge quantity of the head and the tail of the three-dimensional line unit charge is tau1And τ2And obtaining the electric potential V of the matching points corresponding to the head and the tail1And V2And the potential V of the check point corresponding to the head and the tail3And V4；
(a2) Calculating the potential coefficient of the head and the tail points to the corresponding matching points as P1And P2Through τ1＝V1/P1，τ2＝V2/P2Obtaining the electric charge quantity tau of the first and the last points1And τ2；
(a3) Respectively calculating the potential coefficients of the head and the tail of the two points to the corresponding check points to be P3And P4The potential V of the verify point is calculated by the following formula31And V41：V31＝P3*τ1，V41＝P4*τ2；
(a4) Respectively obtain V31And V3Difference of (D) and V41And V4When the difference is smaller than the set value, executing the step (a5), otherwise returning to the step (a 1);
(a5) the charges in the charges of the three-dimensional line unit are linearly distributed and pass through the charge amount tau of the head and the tail1And τ2And calculating to obtain the line charge density of the three-dimensional line unit.
The charge amount of the three-dimensional point charge is obtained by the following method:
(b1) assuming that the charge amount of the three-dimensional point charge is q, and acquiring the potential V of the matching point on the three-dimensional point charge5；
(b2) Calculating the potential coefficient of the three-dimensional point charge to the matching point to be P5By q ═ V5/P5Obtaining the charge quantity of the three-dimensional point charge;
(b3) calculating the potential coefficient of the three-dimensional point charge to the check point to be P6Through V61＝P6Q calculating to obtain potential V of check point51；
(b4) Finding V61And V6Difference of (V)6Is the potential real of the check pointAnd measuring, when the difference value is smaller than the set value, determining the charge quantity of the three-dimensional point charge as q, otherwise, returning to the step (b 1).
Step (3) respectively calculating the electric field intensity of each point in the electric field intensity area to be calculated so as to obtain electric field intensity distribution, setting the point of the electric field intensity to be calculated as a point P, wherein the calculation formula of the electric field intensity of the point P is as follows:
EPx＝Epx line+EPx point
EPy＝EPy wire+EPy point
EPz＝EPz line+EPz point，
EPx、EPyAnd EPzCorresponding to the components of the electric field strength of the point P in the x, y and z directions, EPx line、EPy wireAnd EPz lineCorresponding to the sum of the components of the electric field intensity of all three-dimensional line unit charges at the point P in space in the x direction, the y direction and the z direction, EPx point、EPy pointAnd EPz pointThe component sum of the electric field intensity of all three-dimensional point charges in the space at the point P in the x direction, the y direction and the z direction is corresponded.
The distance d between adjacent raindrops is obtained by the following formula:
Figure GDA0002436756810000071
Figure GDA0002436756810000072
Figure GDA0002436756810000073
where D is the known diameter of the raindrop and vbFor ending speed, r is the total amount of rainfall, ρ, over a period of tWater (W)Is the density of water, pAir conditionerThe density of air, g is the gravity acceleration, T is the total time of one rainfall, R is the total rainfall amount in the T time period, and T is a certain time period in the T time period.
One thirdComponent E 'of dimension line unit charge at point P in x direction, y direction and z direction'Pxxian、E′PyxianAnd E'PzxianCalculated by the following method:
let the starting point of the three-dimensional line unit charge be P1(x1,y1,z1) End point is P2(x2,y2,z2) Assuming that the length of the wire unit is L, the line charge density of the three-dimensional wire unit is tau (u) ═ au + b, a and b are constants, u ═ Lt (0 ≦ t ≦ 1), and the coordinate of the point P is P (x, y, z), the potential generated at the point P by the charges of the three-dimensional wire unit is determined
Figure GDA0002436756810000081
Comprises the following steps:
Figure GDA0002436756810000082
wherein epsilon0Is a vacuum dielectric constant, DlThe distance from the field source point to the point P in the three-dimensional line unit,
Figure GDA0002436756810000083
Figure GDA0002436756810000084
Figure GDA0002436756810000085
τ(0)＝τ1，τ(L)＝τ2，b＝τ1，a＝(τ2-τ1)/L。
component E 'of electric field intensity of certain three-dimensional point charge at point P in x direction, y direction and z direction'Pxdian、E′PydianAnd E'PzdianCalculated by the following method:
let the three-dimensional point charge coordinate be Q (x)1,y1,z1) And the coordinate of the point P is P (x, y, z), the charge of the three-dimensional point is PPotential generated by a point
Figure GDA0002436756810000086
Comprises the following steps:
Figure GDA0002436756810000087
wherein d is the distance from the three-dimensional point charge coordinate to the point P, Q is the charge quantity of the three-dimensional point charge, and epsilon is the dielectric constant of air;
further, it is possible to prevent the occurrence of,
Figure GDA0002436756810000091
and (3) calculating a three-dimensional electric field close to the ground below the power transmission line, wherein the traditional two-dimensional calculation method cannot meet the requirement. Therefore, based on the theoretical basis of the charge simulation method, the three-dimensional point charge simulation charge method is deduced, the three-dimensional models of the tower, the sag wire and the raindrops are established by combining the three-dimensional line unit charge simulation method, the raindrop is orderly distributed in the space to simulate the rainy day environment, and the near-earth electric field of the rainy day under different rainfall intensities is calculated. When modeling of a tower and a sag conductor, a three-dimensional line unit simulation charge is needed, a three-dimensional point charge is used for building a raindrop model, and a field intensity formula of a three-dimensional point charge and three-dimensional line unit hybrid simulation charge method is obtained by combining the superposition principle of field intensity.
Three-dimensional line cell analog charge model as shown in FIG. 2, assuming P1Is the starting point of the line unit, edge P1P2Establishing a local coordinate u in the direction, and setting the length of the line unit as L, then any point Q (x) in the unit3,y3,z3) The coordinates of (c) can be found by:
Figure GDA0002436756810000092
where L is the length of the line unit, u ∈ [0, L ], the line charge density (i.e. charge capacity), τ is linearly distributed within the unit:
τ(u)＝au+b (2)
wherein a and b are undetermined, the potential generated by any point P (x, y, z) in the field
Figure GDA0002436756810000093
Comprises the following steps:
Figure GDA0002436756810000094
Dlis the distance from the field source point to the point P in the three-dimensional line unit, epsilon0Is the dielectric constant in vacuum. By substituting the integration limit with a variable, let u be Lt (0 ≦ t ≦ 1), equation (3) may be expressed as:
Figure GDA0002436756810000101
let τ (0) be τ1，τ(L)＝τ2，b＝τ1，a＝(τ2-τ1) L, the integral found potential coefficient is:
Figure GDA0002436756810000102
Figure GDA0002436756810000103
p is a potential coefficient. P1Charge and P2The potential coefficient of the charge is:
Figure GDA0002436756810000104
due to the fact that
Figure GDA0002436756810000105
Generally of known quantity, combined
Figure GDA0002436756810000106
Thus, τ can be determined1And τ2Further, the values of a and b are obtained.
To satisfy the boundary strip with zero earth potentialElement, requiring the addition of a mirror charge, P1Corresponding mirror charge and P2The potential coefficient of the corresponding image charge is:
Figure GDA0002436756810000107
Figure GDA0002436756810000108
l'＝x2-x1
m'＝y2-y1
n'＝(-z2)-(-z1)＝z1-z2
E'＝l'2+m'2+n'2
F'＝-2[l(x-x1)+m(y-y1)+n(z-(-z1))]
G'＝(x-x1)2+(y-y1)2+(z-(-z1))2(9)
according to the principle of electric field superposition, the actual electric field intensity of any point P in space is the sum of non-mirror image and mirror image, and the expression is as follows:
Figure GDA0002436756810000111
in the invention, a three-dimensional point charge simulation charge method is deduced according to the modeling requirement in rainy days, wherein Q is one point charge in a space, P is any point in the space, and coordinates of the two points are shown in figure 3.
The distance of the point charge Q to the space point P can be calculated by the following equation,
Figure GDA0002436756810000112
the potential at point P is:
Figure GDA0002436756810000113
wherein q is the charge capacity.
The potential coefficient of the charge at the Q-point is known as:
Figure GDA0002436756810000114
due to the fact that
Figure GDA0002436756810000115
Generally of known quantity, combined
Figure GDA0002436756810000116
Q can be obtained.
The electric field calculation formula for the point P is as follows:
Figure GDA0002436756810000117
in order to make the calculation result have general significance, the embodiment models a 500kV power transmission line model which is common in China, a wine glass type tower is adopted as a tower model, the type of a lead is 4 XLGJ-400/35, the distance between sub-leads is 0.45m, the distance between phases is 12m, and the suspension height of a phase lead is 31 m. The line phase voltage is set to change according to a three-phase symmetrical sine rule, an effective value is adopted for calculation, the rated line voltage is 500kV, and the calculated voltage is 1.05 times of the rated voltage in consideration of actual operation, namely UA＝303.1kV，UB＝1.5×102-j2.6×102kV，UC＝-1.5×102+j2.6×102kV. The three-dimensional model of the transmission tower is shown in fig. 4, and the schematic view of the sag conductors is shown in fig. 5.
Meanwhile, in order to avoid the particularity of a calculation result caused by the real-time change of the parameters such as the size of raindrops and the distance between raindrops in the actual rainy day, three-dimensional point charge models with different radiuses are orderly distributed in the space to simulate the rainy day environment with different rainfall intensities. In rainy days with different rainfall intensities, the size, the quantity and the spacing of raindrops can influence the space electric field to different degrees.
Figure GDA0002436756810000121
Figure GDA0002436756810000122
Figure GDA0002436756810000123
Wherein T is the total time of one rainfall; r is the total rainfall amount in the T time period; t is a certain time period in the T time period; r is the total rainfall in the time period t; rhoWater (W)Is the density of water; rhoAir conditionerIs the density of air; g is the acceleration of gravity; d is the diameter of the raindrop; d is the raindrop spacing distance; v. ofbThe ending velocity.
The raindrop adopts a three-dimensional point charge model, the charge is concentrated in the center of a sphere, and a potential matching point and a potential check point are arranged on the surface of the sphere. The data in table 1 and equations (15) - (17) are combined, and the calculated parameters related to raindrops at different rainfall intensity levels are shown in table 2.
TABLE 1 average raindrop size at different rainfall levels
Figure GDA0002436756810000124
TABLE 2 raindrop correlation parameters for different rainfall classes
Figure GDA0002436756810000125
FIG. 6 is the electric field distribution of a square region [ x (-1.5,1.5), y (-1.5,1.5) ] at the center of the tower and 1.5m from the ground under a sunny weather. FIG. 7 is the electric field distribution of a square region [ x (-1.5,1.5), y (-1.5,1.5) ] at the center of the tower and 1.5m from the ground in light rain. From fig. 7 it can be seen that there are many small spikes in the electric field, illustrating that the presence of raindrops distorts the electric field.
Fig. 8 is a comparison of electric field distribution in sunny days and rainy days at a distance of 1.5m below the edge phase, and it can be found from the figure that the electric field intensity curve in rainy days is lower than that in sunny days, which indicates that the phenomenon is caused by the existence of rainy days, and the existence of rainy days has a shielding effect on the electric field in the rainy days. According to the electrostatic shielding principle, due to the existence of a small rain space area and the fact that rain water serves as a conductor, the interior of the space area can be approximately regarded as the interior of the conductor, but due to the existence of gaps among rain drops, the interior of the space is not the interior of a completely closed conductor, so that the space has a certain shielding effect on an electric field, but the electric field cannot be completely shielded.
Fig. 9 is a comparison of electric field distribution in rainy days of different rainfall levels at a position 1.5m away from the center of the tower, and fig. 10 is a comparison of electric field distribution in rainy days of different rainfall levels at a position 1.5m away from the lower side of the side phase under different meteorological conditions, from which it can be seen that the electric field distribution curve corresponding to small rain is higher than that corresponding to medium rain and that corresponding to large rain, which indicates that the shielding effect of large rain on the electric field is strongest, and then medium rain, and finally small rain. The density of the large rain, the medium rain and the small rain in the space is different, the density of the large rain in the space is greater than that of the medium rain and the small rain, and the raindrop space formed by the large rain is closer to a whole, so that the shielding effect on an electric field is more obvious.
TABLE 3 comparison of field strengths of model without ground wire, with tower and with sag under different meteorological conditions
Figure GDA0002436756810000131
The data are shown in Table 3 by numerical calculations on sunny and rainy days, and referring to the guidelines and standards set by the International non-ionizing radiation protection Commission (ICNIRP) on the electromagnetic field exposure limits. As can be seen from Table 3, the maximum field strengths in sunny and rainy days are both less than the requirements of professional exposure field strength and public exposure field strength in China.

Claims (5)

1. A method for calculating a three-dimensional electric field below a power transmission line in a rainy day is characterized by comprising the following steps:
(1) establishing a three-dimensional coordinate system, and establishing a three-dimensional model of the power transmission line and the tower in the three-dimensional coordinate system by adopting a three-dimensional line unit simulation charge method according to the distribution condition of the power transmission line and the tower;
(2) establishing a raindrop model in a three-dimensional coordinate system by adopting a three-dimensional point charge simulation charge method according to the rainfall condition;
(3) calculating the electric field intensity distribution of the electric field intensity area to be calculated according to the coordinate of the electric field intensity area to be calculated and a field intensity calculation formula and a superposition principle;
the step (1) of establishing the three-dimensional models of the transmission line and the tower by the three-dimensional line unit charge simulation method specifically comprises the following steps: respectively and equivalently connecting the leads or the pole pieces of the power transmission line into a plurality of sections of three-dimensional line unit charges in an end-to-end manner to form the power transmission line, wherein the charges are positioned in the centers of the three-dimensional line units, matching points and check points are arranged on the surfaces of the three-dimensional line units, and the line charge density of the three-dimensional line units is determined by performing charge matching and checking according to the matching points and the check points;
the three-dimensional point charge simulation charge method for establishing the raindrop model in the step (2) specifically comprises the following steps: determining the distance between two adjacent raindrops to be d meters according to the rainfall condition, determining the positions of the raindrops on the boundary of the region, setting the adjacent raindrops at intervals of d meters in the directions of an x axis, a y axis and a z axis of a three-dimensional coordinate system, finishing distribution setting of the positions of the raindrops in the set region according to the rule, correspondingly setting a three-dimensional point charge for each raindrop in the region, locating the charge at the center of the raindrop, setting a matching point and a check point on the surface of the raindrop, and performing charge matching and checking according to the matching point and the check point to determine the charge quantity of the three-dimensional point charge;
the line charge density of the three-dimensional line unit is obtained by the following method:
(a1) assuming that the charge quantity of the head and the tail of the three-dimensional line unit charge is tau1And τ2And obtaining the electric potential V of the matching points corresponding to the head and the tail1And V2And the potential V of the check point corresponding to the head and the tail3And V4；
(a2) Calculating the potential coefficient of the head and the tail points to the corresponding matching points as P1And P2Through τ1＝V1/P1，τ2＝V2/P2Obtaining the electric charge quantity tau of the first and the last points1And τ2；
(a3) Respectively calculating the potential coefficients of the head and the tail of the two points to the corresponding check points to be P3And P4The potential V of the verify point is calculated by the following formula31And V41：V31＝P3*τ1，V41＝P4*τ2；
(a4) Respectively obtain V31And V3Difference of (D) and V41And V4When the difference is smaller than the set value, executing the step (a5), otherwise returning to the step (a 1);
(a5) the charges in the charges of the three-dimensional line unit are linearly distributed and pass through the charge amount tau of the head and the tail1And τ2Calculating to obtain the line charge density of the three-dimensional line unit;
the charge amount of the three-dimensional point charge is obtained by the following method:
(b1) assuming that the charge amount of the three-dimensional point charge is q, and acquiring the potential V of the matching point on the three-dimensional point charge5；
(b2) Calculating the potential coefficient of the three-dimensional point charge to the matching point to be P5By q ═ V5/P5Obtaining the charge quantity of the three-dimensional point charge;
(b3) calculating the potential coefficient of the three-dimensional point charge to the check point to be P6Through V61＝P6Q calculating to obtain potential V of check point6 1；
(b4) Finding V61And V6Difference of (V)6And (c) determining the charge amount of the three-dimensional point charge as q when the difference value is smaller than the set value, and otherwise, returning to the step (b 1).
2. The method for calculating the three-dimensional electric field below the power transmission line in the rainy day according to claim 1, wherein the step (3) is that the electric field intensity of each point in the area of the electric field intensity to be calculated is calculated respectively so as to obtain the electric field intensity distribution, the point of the electric field intensity is set as a point P, and the calculation formula of the electric field intensity of the point P is as follows:
EPx＝Epx line+EPx point
EPy＝EPy wire+EPy point
EPz＝EPz line+EPz point，
EPx、EPyAnd EPzCorresponding to the components of the electric field strength of the point P in the x, y and z directions, EPx line、EPy wireAnd EPz lineCorresponding to the sum of the components of the electric field intensity of all three-dimensional line unit charges at the point P in space in the x direction, the y direction and the z direction, EPx point、EPy pointAnd EPz pointThe component sum of the electric field intensity of all three-dimensional point charges in the space at the point P in the x direction, the y direction and the z direction is corresponded.
3. The method for calculating the three-dimensional electric field below the power transmission line in the rainy day according to claim 1, wherein the distance d between adjacent raindrops is obtained by the following formula:
Figure FDA0002436756800000021
Figure FDA0002436756800000022
Figure FDA0002436756800000023
where D is the known diameter of the raindrop and vbFor ending speed, r is the total amount of rainfall, ρ, over a period of tWater (W)Is the density of water, pAir conditionerThe density of air, g is the gravity acceleration, T is the total time of one rainfall, R is the total rainfall amount in the T time period, and T is a certain time period in the T time period.
4. The method for calculating the three-dimensional electric field below the power transmission line in the rainy day according to claim 2, wherein the electric field intensity of a certain three-dimensional line unit charge at a point P is in the x direction,Component E 'in the y-and z-directions'Pxxian、E′PyxianAnd E'PzxianCalculated by the following method:
let the starting point of the three-dimensional line unit charge be P1(x1,y1,z1) End point is P2(x2,y2,z2) Assuming that the length of the line unit is L, the line charge density of the three-dimensional line unit is tau (u) au + b, a and b are constants, u is Lt, t is more than or equal to 0 and less than or equal to 1, and the coordinate of the point P is P (x, y, z), the potential generated by the charge of the three-dimensional line unit at the point P is determined
Figure FDA0002436756800000039
Comprises the following steps:
Figure FDA0002436756800000031
wherein epsilon0Is a vacuum dielectric constant, DlThe distance from the field source point to the point P in the three-dimensional line unit,
Figure FDA0002436756800000032
Figure FDA0002436756800000033
Figure FDA0002436756800000034
Figure FDA0002436756800000035
Figure FDA0002436756800000036
A'＝a'L＝(-τ2+τ1)L
B'＝b'＝-τ1
τ(0)＝τ1，τ(L)＝τ2，b＝τ1，a＝(τ2-τ1)/L。
5. the method of claim 2, wherein the electric field intensity of a certain three-dimensional point charge at point P is the component E 'in the x direction, y direction and z direction'Pxdian、E′PydianAnd E'PzdianCalculated by the following method:
let the three-dimensional point charge coordinate be Q (x)1,y1,z1) And the coordinate of the point P is P (x, y, z), the electric potential generated by the three-dimensional point charge at the point P is
Figure FDA0002436756800000037
Comprises the following steps:
Figure FDA0002436756800000038
wherein d is the distance from the three-dimensional point charge coordinate to the point P, Q is the charge quantity of the three-dimensional point charge, and epsilon is the dielectric constant of air;
further, it is possible to prevent the occurrence of,
Figure FDA0002436756800000041
Figure FDA0002436756800000042
Figure FDA0002436756800000043
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