A non-intrusive voltage measurement method based on near-end integral inversion

Abstract

This invention discloses a non-invasive voltage measurement method based on near-end integration inversion, comprising: selecting a reference point around the device under test (DUT); using the vertical line between the DUT and the reference point as the integration interval [0, H] of the measured electric field; normalizing the upper limit H and lower limit 0 of the integration interval [0, H] to obtain normalized integration node positions; based on the normalized integration node positions, dividing the integration interval [0, H] into a weak field region [0, kH] and a strong field region [kH, H]; selecting the strong field region and discarding the weak field region, and using the strong field region as the effective integration interval; arranging an electric field sensor array on the effective integration interval; acquiring the electric field intensity of the sensor array on the effective integration interval; and determining the voltage of the DUT using the electric field integration method. This invention improves the validity of the data during the measurement process, significantly reduces the influence of other adverse factors, and thus enables accurate measurement of the voltage value of the DUT.

Description

Technical Field

[0001] This invention relates to the field of voltage sensor measurement technology, and more specifically, to a non-invasive voltage measurement method based on near-end integral inversion. Background Technology

[0002] Currently, the method for obtaining voltage data in actual power grid applications is generally through contact-type voltage transformers, mainly divided into capacitive and electromagnetic types. This contact-type measurement method has problems such as large size, inconvenient installation, low measurement accuracy, and small response range, which cannot meet the actual needs of current power grid intelligence and automation.

[0003] Non-contact measurement methods utilize sensors to obtain electric field data around the device, and then use the electric field integration method to calculate the potential value at the measured point, thereby achieving the measurement of the voltage value of the device under test. No current is generated during the measurement process, and no energy transfer or conversion occurs between the sensor and the device under test, eliminating energy loss. Therefore, non-contact voltage sensor measurement has advantages such as low insulation requirements, small size, and ease of integration, making it a current development direction for smart and automated power grids.

[0004] However, existing non-contact measurement methods are insufficient for utilizing and analyzing online monitoring data. After large amounts of data are uploaded, there is a lack of methods for analyzing and processing the data. Voltage measurement and calculation still rely on experience, lacking effective and timely automatic analysis functions, resulting in poor performance. Summary of the Invention

[0005] To address the aforementioned problems, the present invention aims to provide a non-invasive voltage measurement method based on near-end integral inversion. This method can effectively utilize and analyze online monitoring data from existing non-contact measurement methods, and employs appropriate electric field sensor arrays for different devices under test. The voltage of the device under test can be determined in real time based on the measurement results of the electric field sensor array, providing effective support for defect analysis and fault prediction of the device under test.

[0006] This invention provides a non-invasive voltage measurement method based on near-end integral inversion, the method comprising:

[0007] S1. Select a reference point around the device under test, and use the vertical line between the device under test and the reference point as the integration interval [0, H] of the electric field under test. Normalize the upper limit H and lower limit 0 of the integration interval [0, H] to obtain the position of the normalized integration node. The upper limit H and lower limit 0 of the integration interval are the vertical distances from the device under test and the reference point to the ground, respectively.

[0008] S2, based on the position of the normalized integration node, the integration interval [0, H] is divided into a weak field region [0, kH] and a strong field region [kH, H]. The strong field region is selected and the weak field region is discarded. The strong field region is taken as the effective integration interval. The strong field region represents the integration area close to the device under test, and the weak field region represents the integration area far from the device under test. k represents the division factor.

[0009] S3, An electric field sensor array is arranged on the effective integration interval. Each electric field sensor in the electric field sensor array is arranged on the vertical line between the device under test and the reference point. One electric field sensor measures the electric field intensity at an integration node in the effective integration interval.

[0010] S4, acquire the electric field strength of the sensor array over the effective integration interval, and determine the voltage V of the device under test using the electric field integration method. H =∫E(x)dx, where E(x) represents the electric field strength measured at the integration node at a distance x from the ground.

[0011] As a further improvement of the present invention, in S1,

[0012] Normalize the upper bound H and lower bound 0 of the integration interval [0, H] to transform the integration interval [0, H] into the interval [-1, 1], and obtain the positions of the normalized integration nodes, including:

[0013] S11, the magnitude of the electric field intensity within the integration interval [0, H] is expressed as a function f(x) with respect to the position x of the integration node, and the voltage of the device under test is determined.

[0014]

[0015] In the formula, n represents the number of integration nodes in the integration interval [0, H], and x j A represents the position of the j-th integration node within the integration interval [0, H]. j Let represent the weight coefficient of the j-th integration node within the integration interval [0, H], where 1 ≤ j ≤ n;

[0016] S12, normalize the integration interval [0, H]:

[0017]

[0018] in,

[0019]

[0020] S13, based on the Chebyshev integral principle, taking the zeros of the nth-degree Chebyshev polynomial as Gaussian points, the above equation (2) is transformed into:

[0021]

[0022] In the formula, t = 0.5H(t′+1), n ​​represents the number of integration nodes in the integration interval [0, H], j represents the j-th integration node in the integration interval [0, H], 1 ≤ j ≤ n, and π / (n+1) is the weight coefficient corresponding to the normalized integration node during integration. This indicates the position of the normalized integral node.

[0023] As a further improvement of the present invention, the electric field sensors in the electric field sensor array are arranged at non-equidistant intervals on the effective integration interval within the strong field region.

[0024] As a further improvement of the present invention, the arrangement density of electric field sensors gradually increases from the reference point to the device under test.

[0025] As a further improvement to the present invention, in S4,

[0026]

[0027] In the formula, L1 and L2 represent the weak field region and the strong field region, respectively;

[0028] Based on the position of the normalized integral node, the above equation (5) is transformed as follows:

[0029]

[0030] Wherein, the position x of the integrator node within the strong field region i =0.5(1-k)Ht i +0.5(1+k)H, i=1,2,…,m, m represents the number of integration nodes in the strong field region, and i represents the i-th integration node in the strong field region;

[0031] In the formula,

[0032] Among them, A i t represents the weight coefficient of the i-th integration node within the strong field region. i This indicates the position of the i-th integration node within the strong field region.

[0033] The beneficial effects of this invention are as follows: The non-invasive voltage measurement method based on near-end integral inversion of this invention can effectively utilize and analyze the online monitoring data of existing non-contact measurement methods, and involves appropriate electric field sensor arrays for different devices under test, so as to determine the voltage of the device under test in real time based on the measurement results of the electric field sensor array. During the measurement process, it can improve the validity of the data, effectively reduce the influence of adverse factors such as strong electromagnetic interference in weak field regions, and thus accurately measure the voltage value of the device under test, providing effective support for defect analysis and fault prediction of the device under test. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0035] Figure 1 This is a schematic diagram illustrating the principle of a non-invasive voltage measurement method based on near-end integral inversion according to an exemplary embodiment of the present invention;

[0036] Figure 2 This is a schematic diagram of the electric field distribution of the device under test according to an exemplary embodiment of the present invention;

[0037] Figure 3 This is a schematic diagram of the arrangement of an electric field sensor array according to an exemplary embodiment of the present invention;

[0038] Figure 4 shows the electric field variation curves in the Z direction of each integration node on the vertical line below the three-phase line in a horizontal arrangement of the 10kV voltage level line according to an exemplary embodiment of the present invention. In Figure 4(a), phase A is represented, phase B is represented, and phase C is represented.

[0039] Figure 5 is a schematic diagram of the three-phase voltage inversion calculation waveform of a 10kV voltage level line arranged in a horizontal manner according to an exemplary embodiment of the present invention, wherein Figure 5(a) represents phase A, Figure 5(b) represents phase B, and Figure 5(c) represents phase C;

[0040] Figure 6 shows the electric field variation curves in the Z direction of each integration node on the vertical line below the three-phase line in a triangular arrangement according to an exemplary embodiment of the present invention. In Figure 6(a), phase A is represented, phase B is represented, and phase C is represented.

[0041] Figure 7 is a schematic diagram of the three-phase voltage inversion calculation waveform of a 10kV voltage level line arranged in a triangular configuration according to an exemplary embodiment of the present invention. In the figure, Figure 7(a) represents phase A, Figure 7(b) represents phase B, and Figure 7(c) represents phase C. Detailed Implementation

[0042] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0043] It should be noted that if the embodiments of the present invention involve directional indicators (such as up, down, left, right, front, back, etc.), the directional indicators are only used to explain the relative positional relationship and movement of the components in a certain specific posture (as shown in the figure). If the specific posture changes, the directional indicators will also change accordingly.

[0044] Furthermore, the terminology used in the description of this invention is for illustrative purposes only and is not intended to limit the scope of the invention. The terms "comprising" and / or "including" are used to specify the presence of said elements, steps, operations, and / or components, but do not exclude the presence or addition of one or more other elements, steps, operations, and / or components. The terms "first," "second," etc., may be used to describe various elements, do not represent an order, and do not limit these elements. Moreover, in the description of this invention, unless otherwise stated, "a plurality of" means two or more. These terms are used only to distinguish one element from another. These and / or other aspects become apparent in conjunction with the following drawings, and those skilled in the art will more readily understand the description of the embodiments of the invention. The drawings are used for illustrative purposes only to depict the embodiments of the invention. Those skilled in the art will readily recognize from the following description that alternative embodiments of the structures and methods shown in the invention can be employed without departing from the principles of the invention.

[0045] The present invention provides a non-invasive voltage measurement method based on near-end integral inversion, the method comprising:

[0046] S1. Select a reference point around the device under test, and use the vertical line between the device under test and the reference point as the integration interval [0, H] of the electric field under test. Normalize the upper limit H and lower limit 0 of the integration interval [0, H] to obtain the position of the normalized integration node. The upper limit H and lower limit 0 of the integration interval are the vertical distances from the device under test and the reference point to the ground, respectively.

[0047] S2, based on the position of the normalized integration node, the integration interval [0, H] is divided into a weak field region [0, kH] and a strong field region [kH, H]. The strong field region is selected and the weak field region is discarded. The strong field region is taken as the effective integration interval. The strong field region represents the integration area close to the device under test, and the weak field region represents the integration area far from the device under test. k represents the division factor.

[0048] S3, An electric field sensor array is arranged on the effective integration interval. Each electric field sensor in the electric field sensor array is arranged on the vertical line between the device under test and the reference point. One electric field sensor measures the electric field intensity at an integration node in the effective integration interval.

[0049] S4, acquire the electric field strength of the sensor array over the effective integration interval, and determine the voltage V of the device under test using the electric field integration method. H =∫E(x)dx, where E(x) represents the electric field strength measured at the integration node at a distance x from the ground.

[0050] like Figure 1 As shown, the method of this invention selects a suitable reference point around the device under test (DUT), simplifies the electric field calculation process by defining strong and weak field regions and discarding the integration interval of the weak field region, selects an effective integration interval within the strong field region, and chooses a suitable sensor array arrangement within this effective integration interval. Based on the arranged sensor array, it acquires the electric field data values ​​within the effective integration interval, and finally calculates the voltage of the DUT based on the measured electric field data values. This method is a non-invasive voltage measurement method based on near-end integration inversion. During the measurement process, suitable electric field sensor arrays can be designed for different DUTs, and the voltage of the DUT can be calculated in real time based on the electric field sensor measurement results, improving the validity of the data and providing effective support for defect analysis and fault prediction of the DUT. Simultaneously, it can effectively reduce the influence of adverse factors such as strong electromagnetic interference in weak field regions and insufficient measurement effect due to fewer electric field lines, thereby enabling accurate measurement of the voltage value of the DUT.

[0051] In step S1, the ground directly below the device under test is taken as the reference point, and the vertical line between the device under test and the ground is taken as the integration interval. The upper and lower limits of the integration interval are taken from the device under test and the ground, respectively.

[0052] In one embodiment, in step S1, the upper limit H and lower limit 0 of the integration interval [0, H] are normalized to transform the integration interval [0, H] into the interval [-1, 1], thereby obtaining the normalized integration node positions, including:

[0053] S11, the magnitude of the electric field intensity within the integration interval [0, H] is expressed as a function f(x) with respect to the position x of the integration node, and the voltage of the device under test is determined.

[0054]

[0055] In the formula, n represents the number of integration nodes in the integration interval [0, H], and x j A represents the position of the j-th integration node within the integration interval [0, H]. j Let represent the weight coefficient of the j-th integration node within the integration interval [0, H], where 1 ≤ j ≤ n;

[0056] S12, normalize the integration interval [0, H]:

[0057]

[0058] in,

[0059]

[0060] S13, based on the Chebyshev integral principle, taking the zeros of the nth-degree Chebyshev polynomial as Gaussian points, the above equation (2) is transformed into:

[0061]

[0062] In the formula, t = 0.5H(t′+1), n ​​represents the number of integration nodes in the integration interval [0, H], j represents the j-th integration node in the integration interval [0, H], 1 ≤ j ≤ n, and π / (n+1) is the weight coefficient corresponding to the normalized integration node during integration. This indicates the position of the normalized integral node.

[0063] It can be understood that S1 normalizes and optimizes the upper and lower limits of the integration interval. The magnitude of the electric field intensity on the integration interval (i.e., the integration path) is a function of the distance x from the ground, denoted as f(x). A linear combination of the function values ​​at multiple integration nodes can approximate the definite integral of f(x) over the integration interval. The solution is to find the vertical distance H from the tested equipment (the conductor position of the transmission line) to the ground.

[0064] Assuming there are n electric field intensity measurement points (i.e., n integration nodes) within the integration interval, the formula for calculating the voltage of the transmission line is:

[0065]

[0066] Where, x j ∈[0, H] represents the position of the integration node within the integration interval, Aj It represents the weight coefficient corresponding to the j-th integration node within the integration interval during integration.

[0067] Based on Chebyshev's integral principle, the upper and lower limits of the integration interval [0, H] are normalized.

[0068] make: t' is a variable introduced for normalization calculation.

[0069] Transform the integration interval [0, H] to [-1, 1]:

[0070] Let t = 0.5H(t′+1), where t is a variable introduced during normalization. Using the zeros of the nth-degree Chebyshev polynomial as Gaussian points, the above equation can be transformed as follows:

[0071]

[0072] Where π / (n+1) is the weight corresponding to the normalized integration node during integration, and the position of the normalized integration node corresponds to the right-hand side equal to... By changing the number of integration points, normalized integration node information can be obtained. The method described in this invention can measure different voltage levels, normalize for different voltage levels, and transform the continuous electric field integral into a discrete sum of the product of the electric field intensity and the integration weight.

[0073] according to As can be seen, with the increase of the number of integration nodes, the highest and lowest nodes are closer to the upper and lower limits respectively, and the overall distribution shows a symmetrical pattern. The normalized integration interval is shown in Table 1.

[0074] Table 1 shows the positions of some normalized integration nodes within the integration interval [0, H].

[0075] n <![CDATA[A j ]]> <![CDATA[x1]]> <![CDATA[x2]]> <![CDATA[x3]]> <![CDATA[x4]]> <![CDATA[x5]]> 2 1.571H 0.8533H 0.1465H / / / 3 1.047H 0.9330H 0.5000H 0.0670H / / 4 0.785H 0.9620H 0.6914H 0.3087H 0.0381H / 5 0.628H 0.9878H 0.7939H 0.5000H 0.2061H 0.0245H

[0076] In Table 1, A jLet x1 represent the weighting coefficient corresponding to the j-th integration node within the integration interval [0, H] during integration, x2 represent the position of the first integration node within the integration interval [0, H], x3 represent the position of the third integration node within the integration interval [0, H], x4 represent the position of the fourth integration node within the integration interval [0, H], and x5 represent the position of the fifth integration node within the integration interval [0, H]. Table 1 reveals that a large number of integration node positions are too close to the reference point. For example, with two integration nodes, the second integration node is close to the reference point; with three integration nodes, the third integration node is close to the reference point; with four integration nodes, the fourth integration node is close to the reference point; and with five integration nodes, the fifth integration node is close to the reference point. Because the electric field signal measured by these nodes is singular and relatively weak, and easily affected by other interference sources such as ground potential, the measurement accuracy cannot meet the actual requirements. Therefore, the position of the normalized integration node needs to be optimized by moving the low integration node upwards. This results in a stronger electric field signal measured by the optimized integration node, avoiding interference from sources such as ground potential and improving measurement accuracy. The weighting coefficient A... j The specific value is not specifically limited in this invention, and can be adaptively adjusted according to specific instances.

[0077] Step S2 above can be understood as optimizing the positions of the normalized integration nodes, that is, retaining only the positions of the normalized integration nodes in the strong field region. For example... Figure 2 The figure shows the electric field distribution of the device under test (DUT). It can be observed that the electric field between the DUT and the reference point decreases significantly with distance from the DUT. The region closer to the DUT has a denser electric field distribution and higher electric field strength; the integrated voltage value is closer to the true value, therefore this region is considered a strong field region. Conversely, with increasing distance from the DUT, the electric field strength decreases and the electric field distribution becomes sparser; the integrated voltage value is very small, therefore this region is considered a weak field region.

[0078] At this point, based on the principle of additivity of definite integrals, the original normalized integration interval can be piecewise integrated, resulting in the sum of the integrals from the strong field region and the weak field region. Further quantization of the strong and weak field regions is performed, using a scaling factor to segment the integration interval. Through a reliable partitioning factor k, the integration interval [0, H] is divided into two sub-intervals: a weak field region [0, kH] and a strong field region [kH, H], labeled L1 and L2 respectively, where L1 and L2 represent the weak field region and the strong field region, respectively. The partitioning factor k is influenced by factors such as the voltage level and height of the device under test. The rate of change of the electric field below the device under test provides a direct visual representation of the interval division. Figure 2It can be seen that the electric field strength below the tested device generally exhibits a steep drop followed by a stable change. In the weak field region, the electric field information is relatively simple and stable; while in the strong field region, the electric field gradient information is larger. Comparing the electric field changes at multiple data points along the integration path, and considering the spatial position sensitivity requirements of the electric field sensor, a sensor can be selected where the rate of change of the electric field with position first exceeds 3kV / m. 2 The lower limit of the interval is used as the dividing position.

[0079] Based on the above analysis, when calculating the voltage of the device under test in S4, the integral part far from the device under test can be omitted, that is, only the sub-interval of the strong field region is retained as the effective integration interval. Therefore, the line voltage calculation formula is:

[0080]

[0081] Based on the positions of the normalized integral nodes, the above equation (5) is transformed as follows:

[0082]

[0083] Wherein, the position x of the integrator node within the strong field region i =0.5(1-k)Ht i +0.5(1+k)H, i=1,2,…,m, m represents the number of integration nodes in the strong field region, which can be understood as m being less than or equal to n, and i represents the i-th integration node in the strong field region;

[0084] In the formula,

[0085] Among them, A i t represents the weight coefficient corresponding to the i-th integrator node during integration within the strong field region. i This represents the position of the i-th integration node within the strong field region. It can be understood that, after normalization, a strong field region was selected to calculate the line voltage, and this position t... i This represents the position of the normalized integral node. The weight coefficient A is... i The specific value is not specifically limited in this invention, and can be adaptively adjusted according to specific instances.

[0086] In one embodiment, the electric field sensors in the electric field sensor array are arranged at non-equidistant intervals on the effective integration interval within the strong field region.

[0087] It is understandable that after optimizing S2, the effective integration interval for the final voltage calculation is selected, such as... Figure 3As shown, the electric field sensor is arranged within the effective range, i.e., it is not placed in the weak field region but is placed in the strong field region. This arrangement can reduce the number of electric field sensors and avoid the distortion of the electric field distribution caused by multiple electric field sensors. MEMS electric field sensors can be used as an example.

[0088] In one embodiment, the density of the electric field sensors gradually increases from the reference point to the device under test. Installing the multiple electric field sensors with spacing determined by the magnitude of the electric field strength in a strong field region, rather than with equal spacing, ensures measurement accuracy.

[0089] The method described in this invention will now be simulated and verified. During the verification process, simulations were performed on 10kV voltage level lines arranged horizontally and in a triangular configuration.

[0090] 1. Divide the space into strong field zones by arranging the 10kV voltage level lines horizontally, and calculate the positions of different measuring points (i.e., electric field sensors) within the strong field zones. Taking an actual 10kV line as an example, the line height is 6.5m, i.e., H = 6.5m. The actual positions of each integration node within the strong field zone can be obtained, as shown in Table 2.

[0091] Table 2 shows the actual locations of each integration node calculated when different measuring points are selected within the strong field region.

[0092]

[0093] The actual positions of each integration node in Table 2 above can also be understood as the actual installation positions of each electric field sensor. i This represents the weighting coefficient corresponding to the i-th integration node within the strong field region during integration. Taking one measurement point in Table 2 as an example, the weighting coefficient A... i =0.9425, then the actual installation location of the electric field sensor is x1 = 0.9425 × 6.5m = 6.1264. The above is an illustrative example; the calculations for other measuring points in Table 2 are similar.

[0094] Taking the three measuring points in Table 2 as examples, the electric field intensity at the corresponding locations (i.e., at each integration node) in the electric field simulation of the 10kV voltage level line is extracted based on the calculation results of the location of the integration node in the strong field region. The electric field variation curves in the vertical direction of each integration node on the vertical line below the three-phase line are shown in Figure 4. In the figure, the horizontal axis represents time, and the vertical axis represents electric field intensity.

[0095] Using the calculation results in Table 2 above, we substitute them into calculation formula (6) and obtain the calculation results shown in Figure 5 through Maltlab. In the figure, the horizontal axis represents time and the vertical axis represents voltage. As shown in Figure 5, after inversion based on the near-end electric field integral, the fitted waveform is basically consistent with the actual voltage waveform, with a small phase error. The phase errors of phases A and C are larger, while the phase error of phase B is smaller.

[0096] Next, the inversion calculation errors were compared when different numbers of measuring points were selected in the strong field region during the verification process. The phase error situation when selecting 2-5 measuring points is the same as when selecting 3 measuring points, and will not be repeated here. Table 3 shows the inversion calculation amplitude error when different measuring points are selected in the strong field region.

[0097] Table 3. Inversion calculation amplitude error when selecting different measuring points in the strong field region.

[0098]

[0099] As shown in Table 3, when three measuring points are arranged in the strong field area, the measurement voltage errors of the three phases of the 10kV voltage level line are relatively small. Furthermore, based on actual engineering conditions, the fewer the number of sensor nodes, the better. Therefore, it is recommended to choose a three-sensor arrangement for actual measurements.

[0100] Second, divide the space into strong field zones by arranging the 10kV voltage level line in a triangular manner, and calculate the positions of different measuring points (electric field sensors) in the strong field zones, that is, the positions of each integration node in the strong field zones.

[0101] Taking three measuring points as an example, the electric field intensity at the corresponding locations (i.e., at each integration node) in the electric field simulation of the 10kV voltage level line is extracted based on the calculation results of the integration node positions in the strong field region. The electric field variation curves in the Z direction of each integration node on the vertical line below the three-phase line are shown in Figure 6. In the figure, the horizontal axis represents time, and the vertical axis represents electric field intensity.

[0102] As shown in Figure 7, after inversion based on near-end electric field integration, the fitted waveform is basically consistent with the actual voltage waveform, with a small phase error. The phase errors of phases A and C are larger, while the phase error of phase B is smaller. In the figure, the horizontal axis represents time and the vertical axis represents voltage.

[0103] Numerous specific details are set forth in the specification provided herein. However, it will be understood that embodiments of the invention may be practiced without these specific details. In some instances, well-known methods, structures, and techniques have not been shown in detail so as not to obscure the understanding of this specification.

[0104] Furthermore, those skilled in the art will understand that although some embodiments described herein include certain features but not others included in other embodiments, combinations of features from different embodiments are intended to be within the scope of the invention and form different embodiments. For example, in the claims, any of the claimed embodiments can be used in any combination.

[0105] Those skilled in the art will understand that although the invention has been described with reference to exemplary embodiments, various changes may be made and its elements may be substituted with equivalents without departing from the scope of the invention. Furthermore, many modifications may be made to adapt particular situations or materials to the teachings of the invention without departing from the essential scope of the invention. Therefore, the invention is not limited to the specific embodiments disclosed, but rather the invention will include all embodiments falling within the scope of the appended claims.

Claims

1. A non-invasive voltage measurement method based on near-end integral inversion, characterized in that, The method includes: S1. Select a reference point around the device under test, and use the vertical line between the device under test and the reference point as the integration interval [0, H] of the electric field under test. Normalize the upper limit H and lower limit 0 of the integration interval [0, H] to obtain the position of the normalized integration node. The upper limit H and lower limit 0 of the integration interval are the vertical distances from the device under test and the reference point to the ground, respectively. S2, based on the position of the normalized integration node, the integration interval [0, H] is divided into a weak field region [0, kH] and a strong field region [kH, H]. The strong field region is selected and the weak field region is discarded. The strong field region is taken as the effective integration interval. The strong field region represents the integration area close to the device under test, and the weak field region represents the integration area far away from the device under test. k represents the division factor. S3, An electric field sensor array is arranged on the effective integration interval. Each electric field sensor in the electric field sensor array is arranged on the vertical line between the device under test and the reference point. One electric field sensor measures the electric field intensity at an integration node in the effective integration interval. S4, acquire the electric field strength of the sensor array over the effective integration interval, and determine the voltage V of the device under test using the electric field integration method. H =∫E( x )d x , where E ( x () indicates the measured distance from the ground is x The electric field intensity at the integration node; where, （5） In the formula, L1 and L2 represent the weak field region and the strong field region, respectively; Based on the position of the normalized integral node, the above equation (5) is transformed as follows: （6） The location of the integration node within the strong field region. , , m This indicates the number of integration nodes within the strong field region. i Indicates the first term within the strong field region i One integration node; In the formula, , ; Among them, A i Indicates the first term within the strong field region i The weight coefficients of each integration node. Indicates the first term within the strong field region i The position of each integration node.

2. The method as described in claim 1, wherein, In S1, Normalize the upper bound H and lower bound 0 of the integration interval [0, H] to transform the integration interval [0, H] into the interval [-1, 1], and obtain the positions of the normalized integration nodes, including: S11, the magnitude of the electric field intensity within the integration interval [0, H] is expressed as a function of the position of the integration node. x function f ( x ), determine the voltage of the device under test : （1） In the formula, n This represents the number of integration nodes within the integration interval [0, H]. x j This indicates the first integer in the integral interval [0, H]. j The position of each integration node. A j This indicates the first integer in the integral interval [0, H]. j The weight coefficients of each integration node, 1 ≤ j ≤ n ; S12, normalize the integration interval [0, H]: （2） in, （3） S13, based on the Chebyshev integral principle, taking the zeros of the nth-degree Chebyshev polynomial as Gaussian points, the above equation (2) is transformed into: （4） In the formula, , n This represents the number of integration nodes within the integration interval [0, H]. j This indicates the first integer in the integral interval [0, H]. j There are n integration nodes, 1 ≤ j ≤ n π / (n+1) is the weighting coefficient corresponding to the integration of the normalized integration nodes. This indicates the position of the normalized integral node.

3. The method as described in claim 1, wherein, The electric field sensors in the electric field sensor array are arranged at non-equidistant intervals on the effective integration interval within the strong field region.

4. The method of claim 1, wherein, The density of electric field sensors gradually increases from the reference point to the device under test.

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