CN110738009A - Method for setting analog charges in conductor in electric field calculation of power transmission line - Google Patents

Method for setting analog charges in conductor in electric field calculation of power transmission line Download PDF

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CN110738009A
CN110738009A CN201910975391.1A CN201910975391A CN110738009A CN 110738009 A CN110738009 A CN 110738009A CN 201910975391 A CN201910975391 A CN 201910975391A CN 110738009 A CN110738009 A CN 110738009A
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transmission line
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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 method for setting analog charges in wires in electric field calculation of a power transmission line, which comprises the following steps of a, uniformly setting a plurality of analog line charges on a certain concentric circle of each equivalent wire, setting a corresponding matching point and a check point on the surface of the wire, b, calculating an analog charge matrix, c, calculating the potential error of the check point, d, obtaining the radius of an analog charge distribution circle which enables the potential error of the check point to be minimum by utilizing a particle swarm optimization analog charge method (PSOCSM), then calculating the coordinates and the charge amount of a corresponding analog charge group, and finally calculating the electric field around the power transmission line by utilizing the analog charge group.

Description

Method for setting analog charges in conductor 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 analog charges in a lead in electric field calculation of a power transmission line.
Background
With the rapid development of economy in China, various high-voltage transmission projects are built successively, so that the electromagnetic environment problem around the transmission line also begins to be closely concerned. Wherein, the power frequency electric field generated by the high-voltage transmission line is the main factor in the electromagnetic environment problem. Compared with field measurement, the electric field numerical calculation can save a large amount 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 human and 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 become a research hotspot. In the research in this respect, the complex environment around the transmission line is mostly considered, and then the electric field calculation and analysis are performed by using CSM, but a method for improving the electric field calculation accuracy, which is a prerequisite for accurately predicting the electric field influence, is rarely mentioned.
The precision of potential check and electric field calculation depends on the setting of analog charges in the wire, methods for setting the analog charges in the wire are two, methods are center single method, the method is to set 1 infinite length analog line charge in the center of the wire, and methods are empirical formula methods, the method is to set a plurality of analog line charges in the wire and determine the position of the analog line charges according to an empirical formula, however, the method for setting 1 line charge has limited calculation precision and cannot well meet the potential boundary condition of the wire, the empirical formula method is not suitable for the condition that the number of the analog line charges in the wire is 2-5, if too many line charges are set, the calculated amount is obviously increased, and the position determination is based on human experience, and CSM optimization is considered, so the optimal setting of the analog charges in the wire is realized.
Disclosure of Invention
Based on the above analysis, a plurality of analog line charges are uniformly arranged on the concentric circle of each equivalent wire, only the radius of the distribution circle of the analog line charges is used as an optimization variable, and the radius of the distribution circle of the analog charges, which enables the potential verification error to be minimum, is searched by using the PSOCSM, so that the optimal setting of the analog charges of the wires is realized. And then calculating the electric field by the corresponding analog charge group, and comparing the potential error of the check point of the distributed circle radius optimization method and the single center method with the electric field calculation precision to embody the high precision of the electric field calculation after the distributed circle radius optimization method is adopted.
The invention provides a method for setting analog charges in wires in electric field calculations 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 surfaces of the conducting wires;
b. calculating an analog charge matrix;
c. calculating a potential error of the check point;
d. and obtaining the radius of a simulated charge distribution circle which enables the potential error of the check point to be minimum by utilizing a particle swarm optimization simulated charge method, then calculating the coordinates and the charge quantity of the corresponding simulated charge group, and finally calculating the electric field around the power transmission line by the simulated charge group.
Step , in step b, the analog charge τ matrix is:
Figure BDA0002233444360000021
in the formulaIs equivalent to the surface potential of the conductor, pi,kPotential coefficient acting on the ith matching point for the kth analog charge:
Figure BDA0002233444360000023
ε0is the dielectric constant of air, xi，yiIs the abscissa, x, of the ith matching pointk，ykEquation (2) already includes the effects of x-axis mirror line charge, with any points on the x-axis being used as reference potentials.
Step , in step d, the adaptive value function of PSOCSM is:
Figure BDA0002233444360000031
the optimization goal is minimize { fixness }. In the formula, n is the serial number of the check point,
Figure BDA0002233444360000032
the modulus of the calculated value for the nth checkpoint potential,
Figure BDA0002233444360000033
is the modulus of the standard value of the potential of the nth check point. Equation (3) calculates the average relative error between the modulus of the calculated value of the potential of i calibration points and the modulus of the standard value.
In step , in step d, the radius of the simulated charge distribution circle that minimizes the error in the potential of the checkpoint is obtained using PSOCSM, the coordinates of the corresponding simulated charge group are obtained from a mathematical relationship, and the matrix of the simulated charge amount τ is obtained from equation (1).
Step , in step d, after obtaining the coordinate of the analog charge group and the electric quantity τ matrix for minimizing the fitness, calculating the magnitude of the x-direction component and the y-direction component of the electric field intensity at a certain measuring point according to the following formula:
Figure BDA0002233444360000034
Figure BDA0002233444360000035
in the formula taui、xi、yiThe electric quantity and the horizontal and vertical coordinates of the ith analog line charge respectively, and x and y are the horizontal and vertical coordinates of a certain measuring point, the expressions (4) and (5) already contain the effect generated on the x-axis mirror image line charge, and any points on the x-axis are taken as reference potentialsx、EyThe total electric field intensity of a certain measuring point is a plurality
The method for setting the simulation charges in the conducting wire in the electric field calculations of the power transmission line has the advantages that the optimal setting of the simulation charges in the conducting wire can be realized, and the calculation precision of the electric field around the power transmission line is improved.
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The invention is further described with reference to the following figures and examples:
FIG. 1 is a flow chart of a particle swarm optimization simulation charge method used in the optimization algorithm of the present invention;
FIG. 2 is a schematic diagram of the placement of analog charges, matching points and verification points within each equivalent lead of the present invention;
FIG. 3 is a schematic diagram of the comparison of the relative error of the checkpoint potential on the surface of the equivalent conductive line of the present invention 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 for the present and conventional methods versus a simulated value of COMSOL.
Detailed Description
As shown in fig. 1 to 4, the method for setting the analog charge in the conductor in the calculation of the electric field of power transmission lines 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 surfaces of the conducting wires;
b. calculating an analog charge matrix;
c. calculating a potential error of the check point;
d. and obtaining the radius of a simulated charge distribution circle which enables the potential error of the check point to be minimum by utilizing a particle swarm optimization simulated charge method, then calculating the coordinates and the charge quantity of the corresponding simulated charge group, and finally calculating the electric field around the power transmission line by the simulated charge group. The invention can effectively realize the optimal setting of the analog charges in the conducting wire, and compared with the conventional method (a central single-wire method) for setting the analog charges in the conducting wire, the potential error of the check point is greatly reduced, and the calculation precision of the electric field is improved.
In this embodiment, regarding the setting of the analog charge in the equivalent conductor in step a, it is a conventional practice to set 1 infinite length analog line charge at the geometric center of the equivalent conductor, and to use a total of 3 infinite length analog line charges to make the equivalent three-phase transmission line, which is referred to as a center single method herein. In order to better satisfy the boundary condition of the equivalent conductor surface potential without greatly increasing the calculation amount, 4 infinite long line charges are uniformly arranged on the concentric circles of each equivalent conductor, as shown in fig. 2.
In this embodiment, in step b, the analog charge τ matrix is:
Figure BDA0002233444360000051
in the formula
Figure BDA0002233444360000052
Is equivalent to the surface potential of the conductor, pi,kPotential coefficient acting on the ith matching point for the kth analog charge:
Figure BDA0002233444360000053
ε0is the dielectric constant of air, xi，yiIs the abscissa, x, of the ith matching pointk，ykEquation (2) already includes the effects of x-axis mirror line charge, with any points on the x-axis being used as reference potentials.
In this embodiment, after obtaining the coordinates of the analog line charge and the electric quantity τ matrix corresponding to the radius of the analog charge distribution circle in step c, the matrix inversion operation of equation (1) is used
Figure BDA0002233444360000054
And (3) calculating the potential of the check point, and calculating the elements of the P matrix according to the same formula (2) to check the potential. The fitness function of PSOCSM is:
Figure BDA0002233444360000055
the optimization goal is minimize { fixness }. In the formula, n is the serial number of the check point,
Figure BDA0002233444360000056
for the nth check pointThe modulo of the value of the bit calculation,
Figure BDA0002233444360000057
is the modulus of the standard value of the potential of the nth check point. Equation (3) calculates the average relative error between the modulus of the calculated values of the potentials of the 12 calibration points and the modulus of the standard value.
Taking the power frequency electric field of an actual 500kV three-phase transmission line as an example, the relative error curve of the check point potentials of the conventional method and the method is shown in FIG. 3.
In this embodiment, in step d, the particle swarm optimization simulation charge method is used to obtain the radius of the simulation charge distribution circle that minimizes the fitness, the coordinates of the corresponding simulation charge group are obtained from a mathematical relationship, and the matrix of the simulation charge amount τ is obtained from equation (1).
In this embodiment, after obtaining the coordinate of the analog charge group and the electric quantity τ matrix that minimizes the fitness in step d, the magnitudes of the x and y directional components of the electric field strength at a certain measurement point are calculated by the following equation:
Figure BDA0002233444360000061
Figure BDA0002233444360000062
in the formula taui、xi、yiThe electric quantity and the horizontal and vertical coordinates of the ith analog line charge respectively, and x and y are the horizontal and vertical coordinates of a certain measuring point, the expressions (4) and (5) already contain the effect generated on the x-axis mirror image line charge, and any points on the x-axis are taken as reference potentialsx、EyThe total electric field intensity of a certain measuring point is a plurality
Figure BDA0002233444360000063
The relative error plots of the calculated electric field at 1.5m above ground for the conventional method and the method herein versus the simulated COMSOL value are shown in fig. 4.
Finally, the above embodiments are only for illustrating the technical solutions of the present invention and not for limiting, 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 or equivalent substitutions may be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all of them should be covered in the claims of the present invention.

Claims (5)

1, method for setting analog charge in wire in electric field calculation of power transmission line, 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 surfaces of the conducting wires;
b. calculating an analog charge matrix;
c. calculating a potential error of the check point;
d. and obtaining the radius of a simulated charge distribution circle which enables the potential error of the check point to be minimum by utilizing a particle swarm optimization simulated charge method, then calculating the coordinates and the charge quantity of the corresponding simulated charge group, and finally calculating the electric field around the power transmission line by the simulated charge group.
2. The method for setting the analog charges in the wires in the electric field calculation of the power transmission line according to claim 1, wherein in the step b, the analog charge τ matrix is:
Figure FDA0002233444350000011
in the formula
Figure FDA0002233444350000012
Is equivalent to the surface potential of the conductor, pi,kPotential coefficient acting on the ith matching point for the kth analog charge:
ε0is the dielectric constant of air, xi，yiIs the abscissa, x, of the ith matching pointk，ykIs the abscissa and ordinate of the k-th analog line charge, equation (2) already includes the effect of x-axis mirror line charge, and takes any point on the x-axis as the reference potential.
3. The method for setting the analog charge in the conducting wire in the electric field calculation of the power transmission line according to claim 1, wherein in the step d, the adaptive value function of the PSOCSM is as follows:
the optimization target is minimize { fixness }, wherein n is the check point sequence number,
Figure FDA0002233444350000021
the modulus of the calculated value for the nth checkpoint potential,
Figure FDA0002233444350000022
equation (3) calculates the average relative error between the modulus of the calculated value of the potential of i calibration points and the modulus of the standard value, which is the modulus of the standard value of the potential of the nth calibration point.
4. The method according to claim 3, wherein in step d, PSOCSM is used to obtain the radius of the simulated charge distribution circle that minimizes the potential error of the checkpoint, the coordinates of the corresponding simulated charge group are obtained from a mathematical relationship, and the matrix of the simulated charge amount τ is obtained from equation (1).
5. The method for setting the simulation charges in the conducting wire in the calculation of the electric field of the power transmission line according to claim 3 or 4, wherein in step d, after the coordinates of the simulation charge group and the electric quantity τ matrix for minimizing the fitness are obtained, the magnitude of the x-direction component and the y-direction component of the electric field strength at a certain measuring point is calculated by the following formula:
Figure FDA0002233444350000023
Figure FDA0002233444350000024
in the formula taui、xi、yiThe electric quantity and the horizontal and vertical coordinates of the charge of the ith analog line are respectively, and x and y are the horizontal and vertical coordinates of a certain measuring point;
equations (4) and (5) already include the effect on the x-axis mirror line charge, and any point on the x-axis is used as the reference potential;
to know Ex、EyThe total electric field intensity of a certain measuring point is a plurality
Figure FDA0002233444350000025
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CN111859713A (en) * 2020-08-03 2020-10-30 国网重庆市电力公司电力科学研究院 Indoor transformer substation power frequency electric field optimizing device
CN112765897A (en) * 2021-01-30 2021-05-07 上海工程技术大学 Two-dimensional magnetic induction intensity control method based on overhead transmission line

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CN111859713A (en) * 2020-08-03 2020-10-30 国网重庆市电力公司电力科学研究院 Indoor transformer substation power frequency electric field optimizing device
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CN112765897A (en) * 2021-01-30 2021-05-07 上海工程技术大学 Two-dimensional magnetic induction intensity control method based on overhead transmission line
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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