CN110738009B - Setting method of analog charges in conducting wire in electric field calculation of power transmission line - Google Patents

Setting method of analog charges in conducting wire in electric field calculation of power transmission line Download PDF

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CN110738009B
CN110738009B CN201910975391.1A CN201910975391A CN110738009B CN 110738009 B CN110738009 B CN 110738009B CN 201910975391 A CN201910975391 A CN 201910975391A CN 110738009 B CN110738009 B CN 110738009B
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于永进
赵克成
李长云
姜雅男
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Shandong University of Science and Technology
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Abstract

The invention discloses a setting method of analog charges in a wire in electric field calculation of a power transmission line, which comprises the following steps: a. uniformly arranging a plurality of analog line charges on a certain concentric circle of each equivalent conducting wire, and arranging corresponding matching points and check points on the surface of the conducting wire; b. calculating an analog charge matrix; c. calculating the potential error of the check point; d. and obtaining the radius of the simulated charge distribution circle which minimizes the potential error of the check point by using a particle swarm optimization simulated charge method (PSOCSM), calculating the coordinates and the charge quantity of the corresponding simulated charge group, and finally calculating the electric field around the transmission line by using the simulated charge group. The invention can effectively realize the optimal setting of the analog charge in the lead, and compared with the conventional setting method (a central single method) of the analog charge in the lead, the electric potential error of the check point is greatly reduced, and the electric field calculation precision is improved.

Description

Setting method of analog charges in conducting wire in electric field calculation of power transmission line
Technical Field
The invention belongs to the field of electric field calculation, and particularly relates to a method for setting simulated charges in a wire in electric field calculation of a power transmission line.
Background
With the rapid development of the economy in China, various high-voltage transmission projects are successively constructed, so that the electromagnetic environment problem around the transmission line is also brought into close attention. The power frequency electric field generated by the high-voltage transmission line is a main factor in the electromagnetic environment problem. Compared with field measurement, the electric field numerical calculation can save a great deal of manpower, material resources and time, and the electric field distribution of the whole field can be obtained through calculation. Therefore, the method has great practical significance for predicting the influence of the power frequency electric field around the high-voltage transmission line on the human and the environment by calculating the power frequency electric field. Therefore, the numerical calculation and analysis of the power frequency electric field around the power transmission line gradually becomes a research hot spot. In this respect, most of researches are performed by considering a complex environment around a power transmission line and then performing electric field calculation and analysis by using CSM, but few methods for improving electric field calculation accuracy are mentioned, and high calculation accuracy is a precondition for accurately predicting electric field influence.
The accuracy of the potential verification and electric field calculation depends on the setting of the analog charge in the wire. The setting method of analog charges in the lead is generally two, one is a central single method, and the method is to set 1 infinite length analog line charge in the center of the lead; the other is an empirical formula method, which is to set a plurality of analog line charges in a conducting wire and determine the positions of the analog line charges according to the empirical formula. However, the method for setting 1 line charge has limited calculation accuracy and cannot well meet the potential boundary condition of the lead; the empirical formula method is not suitable for the situation that the simulated line charges in the lead are 2-5, and if too many line charges are arranged, the calculated amount is obviously increased, meanwhile, the position is determined by human experience, and the CSM is not guaranteed to be optimal. It is contemplated that optimized CSM may be used to achieve optimal placement of analog charge in the conductive line.
Disclosure of Invention
Based on the analysis, a plurality of analog line charges are uniformly arranged on concentric circles of each equivalent conducting wire, only the distribution circle radius of the analog line charges is used as an optimization variable, and PSOCSM is utilized to search the distribution circle radius of the analog charges which minimizes potential verification errors, so that the optimal arrangement of the analog charges of the conducting wires is realized. And then calculating an electric field by the corresponding simulated charge group, and comparing the check point potential error of the distributed circle radius optimization method and the center single method with the electric field calculation precision so as to embody the high precision of electric field calculation after the distributed circle radius optimization method is adopted.
The invention provides a setting method of analog charges in a wire in electric field calculation of a power transmission line, which comprises the following steps:
a. uniformly arranging a plurality of analog line charges on a certain concentric circle of each equivalent conducting wire, and arranging corresponding matching points and check points on the surface of the conducting wire;
b. calculating an analog charge matrix;
c. calculating the potential error of the check point;
d. and obtaining the radius of the simulated charge distribution circle which minimizes the potential error of the check point by using a particle swarm optimization simulated charge method, calculating the coordinates and the charge quantity of the corresponding simulated charge group, and finally calculating the electric field around the transmission line by using the simulated charge group.
Further, in step b, the analog charge τ matrix is:
in the middle ofFor equivalent conductor surface potential, p i,k Potential coefficients at the i-th matching point for the kth analog charge:
ε 0 is the dielectric constant of air, x i ，y i X is the abscissa, ordinate, x of the ith matching point k ，y k Is the abscissa of the kth analog line charge. Equation (2) already contains the effect of the x-axis mirror charge and takes any point on the x-axis as a reference potential.
Further, in step d, the adaptive value function of PSOCSM is:
the optimization objective is minimum { fitness }. Wherein n is the check point number,modulo the n-th checkpoint potential calculation value,/->The standard value of the potential of the nth check point is modulo. The average relative error of the modulus of the calculated value of the potential of the i check points and the modulus of the standard value is calculated in the formula (3).
In step d, the radius of the simulated charge distribution circle minimizing the potential error of the check point is obtained by using PSOCSM, the coordinates of the corresponding simulated charge group are obtained by mathematical relationship, and the simulated charge amount τ matrix is obtained by equation (1).
In step d, after obtaining the coordinates of the analog charge group and the electric quantity τ matrix that minimize the fitness, the magnitudes of the x-direction component and the y-direction component of the electric field intensity of a certain measuring point are calculated according to the following formula:
τ in i 、x i 、y i The electric quantity and the abscissa of the electric charge of the ith analog line are respectively, and x and y are the abscissas and ordinates of a certain measuring point. Equations (4) and (5) already contain the effect on the x-axis mirror charge and take any point on the x-axis as the reference potential. It can be seen that E x 、E y Plural number, the total electric field intensity of a certain measuring point is
The invention has the beneficial effects that: according to the method for setting the simulated charges in the conducting wire in the electric field calculation of the power transmission line, the optimal setting of the simulated charges in the conducting wire can be realized, and the precision of the electric field calculation around the power transmission line is improved.
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The invention is further described below with reference to the accompanying drawings and examples:
FIG. 1 is a flow chart of the optimization algorithm particle swarm optimization simulated charge method used in the present invention;
FIG. 2 is a schematic diagram showing the arrangement of analog charge, matching points and check points in each equivalent conducting wire of the present invention;
FIG. 3 is a schematic diagram showing the comparison of the relative error of the potential of the calibration points on the surface of the equivalent conductive wire with the conventional analog charge setting method;
FIG. 4 is a graph of the relative error of the electric field value at 1.5m above ground versus the COMSOL simulation for the methods herein and the conventional method.
Detailed Description
As shown in fig. 1-4, the method for setting the analog charges in the conducting wire in the electric field calculation of the power transmission line provided by the invention comprises the following steps:
a. uniformly arranging a plurality of analog line charges on a certain concentric circle of each equivalent conducting wire, and arranging corresponding matching points and check points on the surface of the conducting wire;
b. calculating an analog charge matrix;
c. calculating the potential error of the check point;
d. and obtaining the radius of the simulated charge distribution circle which minimizes the potential error of the check point by using a particle swarm optimization simulated charge method, calculating the coordinates and the charge quantity of the corresponding simulated charge group, and finally calculating the electric field around the transmission line by using the simulated charge group. The invention can effectively realize the optimal setting of the analog charge in the lead, and compared with the conventional setting method (a central single method) of the analog charge in the lead, the electric potential error of the check point is greatly reduced, and the electric field calculation precision is improved.
In this embodiment, in step a, regarding the setting of analog charges in the equivalent wire, it is conventional practice to set 1 infinite analog line charge in the geometric center of the equivalent wire, and use a total of 3 infinite analog line charges equivalent to a three-phase power line, referred to herein as a center single-phase method. In order to better meet the surface potential boundary condition of the equivalent wire without greatly increasing the calculated amount, 4 infinite line charges are uniformly arranged on the concentric circle of each equivalent wire, as shown in fig. 2.
In this embodiment, in step b, the analog charge τ matrix is:
in the middle ofFor equivalent conductor surface potential, p i,k Potential coefficients at the i-th matching point for the kth analog charge:
ε 0 is the dielectric constant of air, x i ，y i X is the abscissa, ordinate, x of the ith matching point k ，y k Is the abscissa of the kth analog line charge. Equation (2) already contains the effect of the x-axis mirror charge and takes any point on the x-axis as a reference potential.
In this embodiment, in step c, after the coordinate of the analog line charge corresponding to the radius of the analog charge distribution circle and the electric quantity τ matrix are obtained, the matrix inverse operation of the formula (1) is usedAnd (3) calculating the potential of the check point, and performing potential check by calculating the elements of the P matrix as shown in the formula (2). The fitness function of PSOCSM is:
the optimization objective is minimum { fitness }. Wherein n is the check point number,modulo the n-th checkpoint potential calculation value,/->The standard value of the potential of the nth check point is modulo. The average phase of the modulus of the calculated value of the electric potential of the 12 check points and the modulus of the standard value is calculated in the formula (3)Error is corrected.
Taking the power frequency electric field of an actual 500kV three-phase transmission line as an example, the calibration point potential relative error curve of the conventional method and the conventional method is shown in fig. 3.
In this embodiment, in step d, the radius of the simulated charge distribution circle that minimizes fitness is obtained by using a particle swarm optimization simulated charge method, the coordinates of the corresponding simulated charge set are obtained by a mathematical relationship, and the simulated charge amount τ matrix is obtained by equation (1).
In this embodiment, in step d, after obtaining the coordinates of the analog charge group and the electric quantity τ matrix that minimize the fitness, the magnitudes of the x-direction component and the y-direction component of the electric field intensity of a certain measurement point are calculated according to the following formula:
τ in i 、x i 、y i The electric quantity and the abscissa of the electric charge of the ith analog line are respectively, and x and y are the abscissas and ordinates of a certain measuring point. Equations (4) and (5) already contain the effect on the x-axis mirror charge and take any point on the x-axis as the reference potential. It can be seen that E x 、E y Plural number, the total electric field intensity of a certain measuring point is
The relative error plot of the calculated electric field value at 1.5m above ground versus the COMSOL simulation value for the conventional and the methods herein is shown in fig. 4.
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the technical solution of the present invention, which is intended to be covered by the scope of the claims of the present invention.

Claims (5)

1. The setting method of the analog charge in the conducting wire in the electric field calculation of the power transmission line is characterized by comprising the following steps:
a. uniformly arranging a plurality of analog line charges on a certain concentric circle of each equivalent conducting wire, and arranging corresponding matching points and check points on the surface of the conducting wire;
b. calculating an analog charge matrix;
c. calculating the potential error of the check point;
d. and obtaining the radius of the simulated charge distribution circle which minimizes the potential error of the check point by using a particle swarm optimization simulated charge method, calculating the coordinates and the charge quantity of the corresponding simulated charge group, and finally calculating the electric field around the transmission line by using the simulated charge group.
2. The method for setting analog charges in a conductor in electric field calculation of a power transmission line according to claim 1, wherein in step b, the analog charge τ matrix is:
in the middle ofFor equivalent conductor surface potential, p i,k Potential coefficients at the i-th matching point for the kth analog charge:
ε 0 is the dielectric constant of air, x i ，y i X is the abscissa, ordinate, x of the ith matching point k ，y k The abscissa of the charge for the kth analog line; equation (2) already contains the effect of the x-axis mirror charge generation, andany point on the x-axis is taken as a reference potential.
3. The method for setting analog charges in a conductor in electric field calculation of a power transmission line according to claim 1, wherein in step d, an adaptive value function of PSOCSM is:
the optimization objective is minimum { fitness }, where n is the checkpoint sequence number,modulo the n-th checkpoint potential calculation value,/->The average relative error of the modulus of the calculated value of the potential of the i check points and the modulus of the standard value is calculated as the modulus of the n-th check point potential standard value in the formula (3).
4. The method for setting simulated charges in a conductor in electric field calculation of a power transmission line according to claim 3, wherein in step d, a radius of a simulated charge distribution circle minimizing a check point potential error is obtained by using PSOCSM, coordinates of a corresponding simulated charge group are obtained by a mathematical relationship, and a simulated charge amount τ matrix is obtained by formula (1).
5. The method for setting analog charges in a conducting wire in electric field calculation of a power transmission line according to claim 3 or 4, wherein in step d, after obtaining coordinates of an analog charge group minimizing a fitness and an electric quantity τ matrix, the magnitudes of x-direction components and y-direction components of the electric field intensity of a certain measuring point are calculated by the following formula:
τ in i 、x i 、y i The electric quantity and the abscissa of the electric charge of the ith analog line are respectively, and x and y are the abscissas and ordinates of a certain measuring point;
equations (4) and (5) already contain the effect on the x-axis mirror line charge, and take any point on the x-axis as a reference potential;
know E x 、E y Plural number, the total electric field intensity of a certain measuring point is
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CN112765897B (en) * 2021-01-30 2022-07-05 上海工程技术大学 Two-dimensional magnetic induction intensity control method based on overhead transmission line

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