Large-span tall tower lightning current measurement and inversion method based on Gaussian integral

Abstract

The invention relates to the technical field of lightning current measurement, in particular to a large-span tall tower lightning current measurement and inversion method based on Gaussian integral. According to the technical scheme, the method comprises the steps that a rectangular plane coordinate system is established with the center O of the cross section of a platform at the middle section height of a target measurement tower as the origin of coordinates, rectangular vertexes A, B, C and D are defined, AB and CD are long sides, and AD and BC are short sides; n tunnel magnetoresistive sensors are installed on a rectangular loop path to form a rectangular sensor array Z, and n is an integer and is larger than or equal to 12 and smaller than or equal to 16. According to the lightning current measurement inversion method based on the Gaussian-Legendre integral algorithm, measurement can be carried out for different lightning currents, the influence that an external interference magnetic field and a circular array cannot be suitable for actual environment installation of a tower can be reduced, and the measurement accuracy is improved.

Description

Technical Field

[0001] The invention relates to the technical field of lightning current measurement, and in particular to a lightning current measurement and inversion method for a large-span tall pole tower based on Gaussian integration. Background Art

[0002] Lightning is a common natural disaster phenomenon in life, and lightning accidents bring great harm to people's production and life. Researching lightning current measurement methods can provide important references for the characteristics and laws of lightning protection in different scenarios. At present, there are three commonly used lightning current measurement methods: magnetic steel rod method, magnetic tape method and Rogowski coil measurement. There are also new fiber optic current sensor methods, but traditional Rogowski coils and new fiber optic current sensors have certain limitations. For example, the Rogowski coil needs to go through an integration link in the process of signal processing, and the leakage of the integrator capacitor caused by long-term use will cause baseline drift; the stability and manufacturing cost of the fiber optic current sensor make it difficult to apply it on a large scale.

[0003] At present, there are many lightning current measurement scenarios that can use several magnetic sensors to form a magnetic sensor array, and then use the corresponding integration algorithm to perform magnetic field inversion to obtain the measured lightning current. The magnetic sensor array is a new type of open-loop non-invasive linear current sensor, which has good application prospects in the field of non-invasive large current measurement. It has the advantages of high sensitivity, wide measurement range, small size, both AC and DC can be measured, and low cost. Therefore, this application proposes a large-span tall tower lightning current measurement and inversion method based on Gaussian integration. Summary of the invention

[0004] The purpose of the present invention is to address the problem that the existing lightning current measurement methods in the background technology have certain limitations, and to propose a large-span tall tower lightning current measurement and inversion method based on Gaussian integral.

[0005] The technical solution of the present invention is a method for measuring and inverting lightning current of a large-span high-rise tower based on Gaussian integral, comprising: Step 1, establish a plane rectangular coordinate system with the center O of the platform cross section at the middle height of the target measurement tower as the coordinate origin, define the rectangular vertices A, B, C, and D, where AB and CD are long sides, and AD and BC are short sides; install n tunnel magnetoresistive sensors on the rectangular loop path to form a rectangular sensor array Z, where n is an integer and 12≤n≤16; Step 2: Using the rectangular path as a closed magnetic induction intensity integration path, the position and sensitive axis direction of each sensor are determined based on the Gauss-Legendre integration algorithm, and the sensitive axis direction is consistent with the tangent of the edge where it is located; Step 3, installing sensors according to the result of step 2 to form a circular array Z surrounding the tower; Step 4: Establish an integral equation of the lightning current value I and the array Z based on the Gauss-Legendre integral theorem; Step 5, measure n magnetic field values ​​of the lightning current, integrate and sum the four sides of the rectangle piecewise, and invert to obtain the current I.

[0006] Optionally, the step 2 specifically includes: Establish a plane rectangular coordinate system with the coordinate origin O, simplify the installation position of the tunnel magnetoresistive sensor k to the installation point Pk, k=1,2…n; define n 1 is the number of integration nodes arranged on the short sides AD and BC, n 2 is the number of integration nodes arranged on the long sides AB and CD, the total number of integration nodes n satisfies 12≤n≤16, and n 1 With n 2 The distribution relationship is: When n=12, n 1 =2,n 2 =4; when n=14, n 1 =3, n 2 =4; when n=16, n 1 =3, n 2 =5; Determine the installation position of each sensor through the coordinate conversion formula, the coordinate conversion formula is: in, , are the endpoints of the integration interval, are the coordinates of the Gauss-Legendre integration nodes in the interval [-1,1], is the coordinate on the actual path.

[0007] Optionally, the Gauss-Legendre integral equation in step 4 is: in, is the lightning current value to be measured; is the distribution function of magnetic induction intensity on the path; a, b are the coordinates of the endpoints of the integration path; is the first Gauss-Legendre integration nodes; For the corresponding The weight coefficient is calculated as follows: in, is the n+1th order Legendre polynomial in The derivative at .

[0008] Optionally, the weight coefficient Node And the corresponding values ​​are determined by looking up the table, and the specific corresponding relationship is as follows: When n=4, the nodes on the long edge ±0.86, ±0.34, weight coefficient 0.35, 0.65; When n=2, the nodes on the short edge ±1.10, weight coefficient is 1.

[0009] Optionally, the length of the long sides AB and CD is 6.6 m, and the length of the short sides AD and BC is 3.8 m; the integral node position of the long side By formula: Calculate, where =-3.3m, =3.3m, The values ​​are -0.86, -0.34, 0.34, 0.86; the integration node position of the short side middle =-1.9m, =1.9m, The values ​​are -1.10 and 1.10.

[0010] Optionally, the sensitive axis direction of the tunnel magnetoresistive sensor is consistent with the tangent direction of each side of the rectangular path, and the length ratio of the long side to the short side is 1.7:1.

[0011] Optionally, the calculation formula of the inversion current I in step 5 is the algebraic sum of the four edge integral values: in, , , , They are the piecewise integration results on the long side AB, the short side BC, the long side CD, and the short side DA respectively.

[0012] Compared with the prior art, the present invention has at least one of the following beneficial technical effects: 1. The Gauss-Legendre numerical integration method used in the present invention makes up for the disadvantages that the use of a circular array structure will cause the location of individual sensors to be far away from the target to be measured and the actual conditions of a high-type pole tower cannot use a circular array structure. Therefore, this measurement method is suitable for use in scenarios where lightning current is measured on high-type pole towers.

[0013] 2. The magnetic field values ​​at the finite number of integration nodes selected by the present invention according to the Gauss-Legendre numerical integration formula can well describe the magnetic field distribution on the entire rectangular loop, so the measurement method improves the measurement precision and accuracy.

[0014] 3. In terms of application and promotion, the present invention can select the number of tunnel magnetoresistive sensors according to different accuracy levels, and select the installation position of the sensors according to the actual situation of the installation environment. It is suitable for application in various types of pole towers and has good applicability.

[0015] The present invention provides a lightning current measurement inversion method based on the Gauss-Legendre integral algorithm, which can carry out measurements for different lightning currents, reduce the influence of external interference magnetic fields and the fact that circular arrays are not suitable for installation in actual tower environments, and improve the accuracy of measurements. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 The invention discloses a method for measuring and inverting lightning current of a large-span tall tower based on Gaussian integral.

[0017] Figure 2 Schematic diagram of the arrangement of the sensor array in an embodiment of the present invention. DETAILED DESCRIPTION

[0018] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and specific embodiments.

[0019] Example like Figure 1 As shown, the Gaussian integral-based lightning current measurement and inversion method for large-span tall towers proposed in the present invention is applied to lightning current measurement, with a certain tall tower as the object. A plurality of tunnel magnetoresistive sensor probes are arranged non-uniformly around the installation platform of the target tower to be measured. The measurement inversion method uses the Gaussian-Legendre integral algorithm to determine the positions of the plurality of tunnel magnetoresistive sensors around the platform, completes the installation of the rectangular sensor array, and measures the lightning current to be measured. Each step is described in detail below.

[0020] Step 1, set the center 0 of the platform cross section at the middle height of the target measurement tower as the coordinate origin, and establish a plane rectangular coordinate system. Name the four corners of the rectangle as A, B, C, and D, where AB and CD are long sides and AD and BC are short sides, and then install n tunnel magnetoresistive sensors on the rectangular loop path to form a rectangular sensor array Z; take A as the starting point in the rectangular sensor array Z, and record the tunnel magnetoresistive sensor along A→B→C→D→A as tunnel magnetoresistive sensor k, k=1,2…n, n is a positive integer, 12≤n≤16; In the embodiment of the present invention, n=12.

[0021] Step 2: Take the rectangular path corresponding to the rectangular sensor array Z as a closed magnetic induction intensity integration path, and determine the position of each tunnel magnetoresistive sensor on the rectangular path and the sensitive axis position of the tunnel magnetoresistive sensor according to the Gauss-Legendre integration algorithm. The specific steps are as follows: A plane rectangular coordinate system is established with the center 0 of the platform cross section at the middle height of the target measurement tower as the coordinate origin, and the installation position of the tunnel magnetoresistive sensor k is simplified to the installation point Pk, k=1,2…n; The direction of the sensitive axis of the tunnel magnetoresistive sensor k is set to be tangent to the side of the rectangular loop, the lengths of the long side and the short side are determined, and n1 is defined as the number of integral nodes arranged on the short side, and n2 is defined as the number of integral nodes arranged on the long side.

[0022] The specific installation position of the sensor can be obtained through the coordinate conversion formula:

[0023] In the embodiment of the present invention, the long side is 6.6m and the short side is 3.8m. Taking the long side AB as an example, the coordinates of points A and B are (3.3, -1.9), (-3.3, -1.9), and a=-3.3 and b=3.3 are substituted into the above formula as the two endpoints of the integral interval to calculate the actual integral node position. Zi is the horizontal coordinate of the actual integral node position on the long side AB. The four magnetic sensors are placed according to the positions of the actual integral nodes shown in Table 2, and the sensitive axis direction of the sensor is tangent to AB. Similarly, the positions and integration coefficients of the three Legendre integral nodes on the short side BC can be obtained, as shown in Table 3.

[0024] Table 1 Locations of quadrature nodes and quadrature coefficients

[0025] Table 2 Locations and integration coefficients of Legendre integration nodes on long edges

[0026] Table 3 Locations and integration coefficients of Legendre integration nodes on short edges

[0027] It can be seen from Table 2 that for the long side, when n=4, t1=-0.86, t2=-0.34, t3 =0.34, t4=0.86; it can be seen from Table 3 that for the short side, when n=2, t5=-1.10, t6=1.10. The data can be used to calculate the positions of the twelve tunnel magnetoresistive sensors and the sensitive axis on the rectangular path.

[0028] like Figure 2 As shown in Figure 1, the locations of twelve tunnel magnetoresistive sensors are given. Figure 2 It can be seen that the twelve tunnel magnetoresistive sensors are not evenly distributed.

[0029] Step 3, installing n tunnel magnetoresistive sensors according to the data obtained in step 2, and forming a circular array Z around the target measurement tower measurement platform; Step 4, setting the lightning current to flow through the target measurement tower during measurement, and establishing a Gauss-Legendre integral equation between the current value I to be measured and the rectangular sensor array Z based on the Gauss-Legendre integral theorem; Step 5: The lightning current to be measured flows through the target measurement tower, and n magnetic field values ​​are measured. The n measured values ​​on the rectangular integral path are segmented and integrated. Finally, the integral values ​​on the four sides are summed to obtain the inversion current I, which is expressed as follows:

[0030]

[0031] .

[0032] in, is the lightning current value to be measured; is the distribution function of magnetic induction intensity on the path; a, b are the coordinates of the endpoints of the integration path; is the first Gauss-Legendre integration nodes; For the corresponding The weight coefficient is calculated as follows: in, is the n+1th order Legendre polynomial in The derivative at .

[0033] The present invention adopts a rectangular sensor array to replace the traditional circular array, which solves the problem of circular structure limitation in the actual installation environment of high-type pole towers, avoids individual sensors being too far away from the measured target, and significantly improves the applicability of the structure. Based on the Gauss-Legendre integral algorithm, finite integration nodes are selected to accurately characterize the magnetic field distribution on the rectangular path, and the weighted summation of the segmented integration results is performed in combination with the weight coefficient, which effectively improves the precision and accuracy of lightning current inversion. By non-uniformly arranging sensors and designing closed rectangular integral paths, the influence of external interference magnetic fields on the measurement results is suppressed, and the stability of the system is improved. It supports the selection of the number of sensors (12-16) according to actual needs, adapting to different accuracy levels and pole tower types, and the installation position is flexibly determined by the coordinate conversion formula, which has wide engineering applicability.

[0034] The above specific embodiments are only several optional embodiments of the present invention. Based on the technical solutions of the present invention and the relevant inspirations of the above embodiments, those skilled in the art can make various alternative improvements and combinations to the above specific embodiments.

Claims

1. A method for measuring and inverting lightning current of a large-span high-rise tower based on Gaussian integral, characterized in that: include: Step 1, establish a plane rectangular coordinate system with the center O of the platform cross section at the middle height of the target measurement tower as the coordinate origin, define the rectangular vertices A, B, C, and D, where AB and CD are long sides, and AD and BC are short sides; install n tunnel magnetoresistive sensors on the rectangular loop path to form a rectangular sensor array Z, where n is an integer and 12≤n≤16; Step 2: Using the rectangular path as a closed magnetic induction intensity integration path, the position and sensitive axis direction of each sensor are determined based on the Gauss-Legendre integration algorithm, and the sensitive axis direction is consistent with the tangent of the edge where it is located; Step 3, installing sensors according to the result of step 2 to form a circular array Z surrounding the tower; Step 4: Establish an integral equation of the lightning current value I and the array Z based on the Gauss-Legendre integral theorem; Step 5, measure n magnetic field values ​​of the lightning current, integrate and sum the four sides of the rectangle piecewise, and invert to obtain the current I.

2. The method for measuring and inverting lightning current of a large-span tall tower based on Gaussian integral according to claim 1 is characterized in that: The step 2 specifically includes: A plane rectangular coordinate system is established with the coordinate origin O, and the installation position of the tunnel magnetoresistance sensor k is simplified to the installation point Pk, k=1,2…n; n1 is defined as the number of integral nodes arranged on the short sides AD and BC, and n2 is defined as the number of integral nodes arranged on the long sides AB and CD. The total number of integral nodes n satisfies 12≤n≤16, and the distribution relationship between n1 and n2 is: When n=12, n1=2, n2=4; When n=14, n1=3, n2=4; When n=16, n1=3, n2=5; The installation position of each sensor is determined by the coordinate conversion formula, and the coordinate conversion formula is: in, , are the endpoints of the integration interval, are the coordinates of the Gauss-Legendre integration nodes in the interval [-1,1], are the coordinates on the actual path.

3. The method for measuring and inverting lightning current of a large-span tall tower based on Gaussian integral according to claim 1 is characterized in that: The Gauss-Legendre integral equation in step 4 is: in, is the lightning current value to be measured; is the distribution function of magnetic induction intensity on the path; a, b are the coordinates of the endpoints of the integration path; is the first Gauss-Legendre integration nodes; For the corresponding The weight coefficient is calculated as follows: in, is the n+1th order Legendre polynomial in The derivative at .

4. The method for measuring and inverting lightning current of a large-span tall tower based on Gaussian integral according to claim 3 is characterized in that: The weight coefficient Node And the corresponding values ​​are determined by looking up the table, and the specific corresponding relationship is as follows: When n=4, the nodes on the long edge ±0.86, ±0.34, weight coefficient 0.35, 0.65; When n=2, the nodes on the short edge ±1.10, weight coefficient is 1.

5. The method for measuring and inverting lightning current of a large-span tall tower based on Gaussian integral according to claim 2 is characterized in that: The length of the long sides AB and CD is 6.6 m, and the length of the short sides AD and BC is 3.8 m; the integral node position of the long side By formula: Calculate, where =-3.3m, =3.3m, The values ​​are -0.86, -0.34, 0.34, 0.86; the integration node position of the short side middle =-1.9m, =1.9m, The values ​​are -1.10 and 1.

10.

6. The method for measuring and inverting lightning current of a large-span tall tower based on Gaussian integral according to claim 1 is characterized in that: The sensitive axis direction of the tunnel magnetoresistive sensor is consistent with the tangent direction of each side of the rectangular path, and the length ratio of the long side to the short side is 1.7:

1.

7. The method for measuring and inverting lightning current of a large-span tall tower based on Gaussian integral according to claim 1 is characterized in that: The calculation formula of the inversion current I in step 5 is the algebraic sum of the four edge integral values: in, , , , They are the piecewise integration results on the long side AB, the short side BC, the long side CD, and the short side DA respectively.

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