Analytical calculation method of low-frequency near-field region magnetic field of finite-length energized straight wire in conductive medium

Abstract

The analytic calculation method of the magnetic field in the low-frequency near field area of the finite-length energized straight conductor in the conductive medium comprises the following steps: taking the center of the energized straight conductor as the origin, taking the length of the energized straight conductor as the X axis, taking the length perpendicular to the energized straight conductor as the Y axis, and taking the plane perpendicular to the X axis and the Y axis as the Z axis to establish a coordinate system, and the coordinates of two end points A and B of the energized straight conductor in the above coordinate system are (0.5L, 0, 0) and (-0.5L, 0, 0) respectively, and the real part and the imaginary part of the magnetic field induction intensity of an arbitrary point P (x, y, z) in the coordinate system are obtained through the formula.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic fields. It is applied to a method for analytically calculating the low-frequency near-field of a finite-length current-carrying straight conductor in a conductive medium, such as underwater. Background Technology

[0002] In existing technologies, a finite-length current-carrying straight conductor is a fundamental way to generate a magnetic field, and the magnetic field calculation method can be derived from Maxwell's equations.

[0003] A finite-length current-carrying straight conductor along the x-axis, such as Figure 1 As shown, the time-domain expression of Maxwell's equations in a conductive medium is:

[0004]

[0005]

[0006]

[0007]

[0008] because Therefore, the magnetic field can be It is expressed as a vector curl, i.e.:

[0009]

[0010] Substituting the above equation into... have to:

[0011]

[0012] Transforming the above equation, we get:

[0013]

[0014] Since the curl of divergence is always equal to 0, It can be expressed as the divergence of a scalar, i.e.

[0015]

[0016] therefore, and It can be represented using a vector function and a scalar function as follows:

[0017]

[0018] Based on knowledge of vectors, to define a vector, its divergence and curl must be specified simultaneously. To ensure the uniqueness of the expression, the vector field...

[0019] Lorentz specification:

[0020]

[0021] Therefore, under the Lorentz gauge condition...

[0022] and destruction The satisfied d'Alembert equation is:

[0023]

[0024] When the electromagnetic field is a time-harmonic field, it can be written as:

[0025]

[0026] in

[0027]

[0028]

[0029]

[0030] The solution to the above equation is:

[0031]

[0032]

[0033] A current element is the basic radiating unit of a current-carrying straight conductor. Assuming the current element has a length of L, its center is located at the origin, and it is placed along the x-axis, the vector magnetic potential on the current element can be expressed as:

[0034]

[0035] Because it is a line current, therefore lr, The current in the line is in phase. Therefore, the above formula can be written as:

[0036] In spherical coordinates, this can be represented as:

[0037]

[0038] The spatial distribution of the magnetic field of the line current can be obtained as follows:

[0039]

[0040] The magnetic field of a current-carrying straight conductor in a lossy medium is obtained as follows:

[0041]

[0042] In a rectangular coordinate system, it is represented as

[0043] B x =0,

[0044] Where L is the length of the current-carrying straight conductor, and K is the complex wave number.

[0045]

[0046]

[0047] Obviously, for the near-field magnetic field, integration is required, but the original function expression cannot be obtained. Therefore, numerical integration can only be used in software design, which involves a large amount of computation and is not conducive to real-time processing.

[0048] In the actual operation of underwater active electromagnetic detection, the detector can detect the low-frequency magnetic field near a finite-length straight conductor towed by an underwater vehicle or surface vessel. This magnetic field includes the low-frequency magnetic field generated by the finite-length straight conductor and the low-frequency magnetic field generated by nearby metal. In order to find out whether there is metal near the finite-length straight conductor, it is necessary to quickly calculate the low-frequency magnetic field of the space around the finite-length straight conductor in real time. The calculated low-frequency magnetic field of the space around the finite-length straight conductor is compared with the low-frequency magnetic field detected by the detector to determine whether there are other metallic substances near the finite-length straight conductor. Summary of the Invention

[0049] This invention proposes an analytical method for calculating the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium, which avoids computationally intensive numerical integration calculations and significantly improves calculation speed.

[0050] To achieve the purpose of this invention, the following technical solution is adopted:

[0051] This invention discloses an analytical calculation method for the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium. A coordinate system is established with the center of the current-carrying straight conductor as the origin, the length of the conductor as the X-axis, the length perpendicular to the conductor as the Y-axis, and the plane perpendicular to both the X and Y axes as the Z-axis. The coordinates of the two endpoints A and B of the current-carrying straight conductor in this coordinate system are (0.5L, 0, 0) and (-0.5L, 0, 0), respectively. The real and imaginary parts of the magnetic field induction intensity at any point P (x, y, z) in the coordinate system are obtained using the following formula:

[0052]

[0053]

[0054] in:

[0055]

[0056]

[0057] B0 represents the magnetic field induction intensity in the air, r1 and r2 are the distances between the two endpoints A and B of the current-carrying straight conductor and point P, respectively, r0 is the perpendicular distance from point P to the current-carrying straight conductor, I is the peak value of the alternating current in the current-carrying straight conductor, ω is the angular frequency of the alternating current, σ is the conductivity of the medium, and μ is the magnetic permeability of the medium. for The integer rounded to the nearest whole number; The application range of formulas (1) and (2) is: the vertical distance r0 from point P to the current-carrying straight conductor (1) is within the range of 0.1λ < r0 < 0.22λ.

[0058] The present invention provides an analytical calculation method for the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium, wherein:

[0059] The present invention provides an analytical calculation method for the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium, wherein:

[0060] The present invention provides an analytical calculation method for the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium, wherein:

[0061] The present invention provides an analytical calculation method for the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium, wherein: θ1 = arcsin(r0 / r1).

[0062] The present invention provides an analytical calculation method for the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium, wherein: θ2=arcsin(r0 / r2)

[0063] The present invention provides an analytical calculation method for the magnetic field in the low-frequency near-field region of a finite-length current-carrying straight conductor in a conductive medium, wherein the length of the current-carrying straight conductor (1) is less than 1000 meters.

[0064] The present invention relates to an analytical calculation method for the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium, wherein the conductive medium is water, oil, alcohol, or a mixture thereof.

[0065] Through extensive practical experience, the applicant of this invention has discovered a formula for calculating the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium. This formula directly calculates the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor using analytical expressions, avoiding tedious numerical integration calculations, significantly improving calculation speed, adapting to the real-time calculation requirements of embedded systems, and achieving the required accuracy for practical calculations. Attached Figure Description

[0066] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0067] Figure 1 A schematic diagram of a finite-length current-carrying straight conductor;

[0068] Figure 2 Calculation results for a 1080Hz alternating magnetic field on a 70m long current-carrying straight conductor;

[0069] Figure 3 Calculation results for a 580Hz alternating magnetic field on a 70m long current-carrying straight conductor;

[0070] Figure 4 Calculation results for a 200Hz alternating magnetic field on a 70m long current-carrying straight conductor;

[0071] Figure 5 Calculation results for a 1080Hz alternating magnetic field on a 50m long current-carrying straight conductor;

[0072] Figure 6 Calculation results for a 580Hz alternating magnetic field on a 50m long current-carrying straight conductor;

[0073] Figure 7 Calculation results for a 200Hz alternating magnetic field on a 50m long current-carrying straight conductor;

[0074] Figure 8 Calculation results for a 1080Hz alternating magnetic field on a 30m long current-carrying straight conductor;

[0075] Figure 9 Calculation results for a 580Hz alternating magnetic field on a 30m long current-carrying straight conductor;

[0076] Figure 10 The calculation results are for a 200Hz alternating magnetic field on a 30m long current-carrying straight conductor.

[0077] exist Figure 1 In the diagram, number 1 represents a straight, energized conductor. Detailed Implementation

[0078] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0079] like Figure 1 As shown, the analytical calculation method for the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium according to this application includes: establishing a coordinate system with the center of the current-carrying straight conductor 1 as the origin, the length of the current-carrying straight conductor 1 as the X-axis, the length perpendicular to the length of the current-carrying straight conductor 1 as the Y-axis, and the plane perpendicular to the X-axis and Y-axis as the Z-axis. The coordinates of the two endpoints A and B of the current-carrying straight conductor 1 in the above coordinate system are (0.5L,0,0) and (-0.5L,0,0) respectively. The real and imaginary parts of the magnetic field induction intensity at any point P (x,y,z) in the coordinate system are obtained by formula:

[0080]

[0081]

[0082] in:

[0083]

[0084]

[0085] B0 is the magnetic field induction intensity in the air, r1 and r2 are the distances between the two endpoints A and B of the current-carrying straight conductor (1) and point P, respectively, r0 is the perpendicular distance from point P to the current-carrying straight conductor (1), I is the peak value of the alternating current of the current-carrying straight conductor, ω is the angular frequency of the alternating current, σ is the conductivity of the medium, and μ is the magnetic permeability of the medium. for The integer rounded to the nearest whole number; The application range of formulas (1) and (2) is: the vertical distance r0 from point P to the current-carrying straight conductor (1) is within the range of 0.1λ < r0 < 0.22λ.

[0086] according to Figure 1 The geometric relationships, and the formulas for calculating r1, r2, r0, θ1, and θ2 are as follows:

[0087]

[0088]

[0089]

[0090] θ1 = arcsin(r0 / r1)

[0091] θ2=arcsin(r0 / r2)

[0092] The length of the current-carrying straight conductor is less than 1000 meters. The conductive medium is water, oil, alcohol, or a mixture thereof.

[0093] The applicant simulated the magnetic field of current-carrying straight conductors 1 of different lengths, and used numerical integration and fitted analytical formulas to calculate the results for example... Figures 2-10 As shown.

[0094] The wavelength of alternating electromagnetic waves in a conductive medium is

[0095]

[0096] Then a = 2πr0 / λ. Simulation results show that the analytical formula proposed in this invention is relatively accurate in the range of a∈(0.6,1.4), with an error within 10%. The corresponding range of the side distance of the current-carrying straight conductor 1 is 0.1λ<r0<0.22λ.

[0097] Figures 2-10 In this context, the dielectric parameters are: electrical conductivity σ = 3.5 S / m, magnetic permeability μ = 4π × 10⁻⁶. -7 H / m, the three graphs on the left are the existing numerical integration results of the real part of the magnetic field, the calculation results of the real part of the magnetic field of the present invention, and the difference between the calculation results of the real part of the magnetic field by the two methods. The three graphs on the right are the existing numerical integration results of the imaginary part of the magnetic field, the calculation results of the imaginary part of the magnetic field of the present invention, and the difference between the calculation results of the imaginary part of the magnetic field by the two methods.

[0098] from Figures 2 to 10 As can be clearly seen, the analytical calculation method for the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium in this application has an error of less than 10% compared with the existing integral method. However, the analytical calculation method for the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium in this application can conveniently and quickly calculate the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium, and its accuracy is acceptable in practical use.

[0099] This invention may have other various embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these changes and modifications should all fall within the protection scope of the claims of this invention.

Claims

1. An analytical calculation method for the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium, wherein a coordinate system is established with the center of the current-carrying straight conductor (1) as the origin, the direction of the current-carrying straight conductor (1) as the X-axis, the direction perpendicular to the current-carrying straight conductor (1) as the Y-axis, and the plane perpendicular to the X-axis and Y-axis as the Z-axis, and the coordinates of the two endpoints A and B of the current-carrying straight conductor (1) in the above coordinate system are (0.5L,0,0) and (-0.5L,0,0) respectively, characterized in that: The real and imaginary parts of the magnetic field strength at any point P (x, y, z) in the coordinate system can be obtained using the following formula: ； ； in: ； ； B0 is the magnetic field induction intensity in the air, and r1 and r2 are the distances between point P and the two endpoints A and B of the current-carrying straight conductor (1). r 0 is the perpendicular distance from point P to the current-carrying straight conductor (1). I Let ω be the peak value of the alternating current in the current-carrying straight conductor, ω be the angular frequency of the alternating current, σ be the conductivity of the medium, and μ be the permeability of the medium. The integer rounded to the nearest whole number; The application range of formulas (1) and (2) is: the vertical distance from point P to the current-carrying straight conductor (1) r 0 in Within the range; θ1 = arcsin(r0 / r1); θ2 = arcsin(r0 / r2); L is the length of the current-carrying straight conductor (1).

2. The analytical calculation method for the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium as described in claim 1, characterized in that: The .

3. The analytical calculation method for the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium as described in claim 2, characterized in that: The .

4. The analytical calculation method for the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium as described in claim 3, characterized in that: The .

5. The analytical calculation method for the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium as described in claim 4, characterized in that: The length of the energized straight conductor (1) is less than 1000 meters.

6. The analytical calculation method for the low-frequency near-field magnetic field of a finite-length current-carrying straight conductor in a conductive medium as described in claim 5, characterized in that: The conductive medium is water, oil, alcohol, or a mixture thereof.

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