A method and system for detecting transmission line sag based on non-contact electric field sensing

Abstract

The application discloses a kind of transmission line sag detection method and system based on non-contact electric field sensing, and relates to the field of power transmission, for the non-contact sag detection of the transmission line formed by multiple conductors.The vertical electric field component is collected on the ground directly below the lowest point of the transmission line.For the case of consistent sag, only the vertical electric field component of one point located in the center needs to be collected.For the case of inconsistent sag, the vertical electric field components of points equal in number to the conductors need to be collected.The points are arranged in a straight line at equal intervals, and are as close as possible to the transmission line below.After determining the arrangement of the conductors and the consistency of the sag, the relationship between the vertical electric field components of the points and the sag of the conductors can be determined.Furthermore, by measuring the electric field intensity of each point, the sag of each conductor can be calculated.The application only needs to collect electric field data at several points on the ground to calculate the sag of each conductor, which is simple to operate, has minimal environmental impact, and has high detection accuracy.

Description

Technical Field

[0001] This invention relates to the field of power, and in particular to a method and system for detecting the sag of transmission lines based on non-contact electric field sensing. Background Technology

[0002] With continuous technological advancements and rapid economic development, informatization, digitalization, and automation have become core trends in societal development. New power systems, through technologies such as multi-sensoring, big data, and intelligent control, integrate energy entities with modern information technology. The stability of power systems is a critical concern. Overhead transmission lines, as reliable power carriers, play a vital role in long-distance power transmission and distribution, connecting power sources to distributed networks and users. Real-time monitoring of the status of overhead transmission lines is crucial for maintaining the stability and reliability of the entire system.

[0003] Most transmission lines are exposed to harsh conditions in the field. Harsh weather conditions pose direct and indirect threats to the safety of these lines, which in turn threaten the power grid. For example, high temperatures in hot weather can cause transmission lines to elongate, increasing sag. The greater the sag and the smaller the clearance, the greater the likelihood of a short circuit with the surrounding environment. In severe cases, this can lead to the collapse of a portion of the transmission network, ultimately resulting in a power outage. Therefore, sag is a crucial indicator for the operation and maintenance of transmission lines, and timely measurement is essential for developing preventative and remedial measures.

[0004] Traditional sag measurement methods are primarily based on contact principles, including tension measurement, tilt measurement, and temperature measurement. In addition, some methods install GPS receivers on the line to determine the conductor's geographical location using the Global Positioning System (GPS); others utilize simple optical mechanisms to convert variations in sag into changes in grating optical parameters; still others employ inspection robots on power lines for remote control and data transmission. These contact devices are expensive, need to be installed on live conductors of transmission lines, and, because the equipment must be located very close to the phase conductors, their performance may be affected by electromagnetic interference from conductor corona discharge.

[0005] Non-contact measurement allows for direct electrical contact between the measuring device and the object being measured, without affecting system operation. It offers portability, flexibility, and the ability to perform high-frequency measurements. Non-contact sag measurement methods for transmission systems are primarily based on electromagnetic sensing principles. Magnetic field-based measurement schemes require multiple magnetic field sensors and iterative fitting algorithms for estimation. For example, a biaxial magnetic field sensor array equal to the number of conductors can be used vertically on the support tower to estimate line current and sag. However, convergence may fail when tower tilt reduces sag. To address this issue, the paper "Magnetic-Field-Sensing-Based Approach for Current Reconstruction, Sag Detection, and Inclination Detection for Overhead Transmission System" discloses a method for detecting sag, tower tilt, and current in transmission systems based on an artificial immune system. This method avoids the inconvenience of installation on support towers by detecting the magnetic field distribution along the ground centerline. However, transmission line current varies significantly with load, complicating magnetic field-based measurement techniques and making it impossible to use consistent iterative fitting algorithms for estimation. In contrast, transmission line voltage is relatively constant and less affected by surrounding environmental and meteorological conditions; therefore, electric field-based measurement schemes are more accurate. Electric field-based measurement schemes primarily utilize voltage monitoring and require multiple electric field sensors and inversion algorithms for estimation. The paper "Nonontact Monitoring of Overhead Transmission Lines using Space Potential Phaser Measurements" introduces the application of voltage imbalance and conductor sag measurement, enabling the measurement of the amplitude and relative phase of the transmission line's spatial potential at two or more strategically located points in space. The paper "Overhead Transmission Lines Sag and Voltage Monitoring Method Based on Electrostatic Inverse Calculation" proposes a novel contactless sag and voltage monitoring method for overhead transmission lines. This method requires only a simple potential measurement array and can be applied to dynamic conductor measurements; its drawback is that it only considers simple single-circuit lines. Summary of the Invention

[0006] The purpose of this invention is to provide a non-contact electric field sensing-based transmission line sag detection scheme to address the aforementioned problems, thereby enabling high-precision inspection of the sag of various multi-conductor transmission lines in a low-complexity manner.

[0007] The technical solution adopted in this invention is as follows:

[0008] This invention provides a method for detecting sag of transmission lines based on non-contact electric field sensing, the method comprising:

[0009] The arrangement of each conductor is determined, including horizontal arrangement and triangular arrangement for single-circuit lines, and vertical arrangement of double-circuit lines.

[0010] Ensure the consistency of sag for each conductor;

[0011] When the sag of each conductor is consistent, a test point is determined below the transmission line, and the vertical electric field component of the test point is measured; when the sag of each conductor is inconsistent, multiple test points are determined below the transmission line, and the vertical electric field component of each test point is measured. The number of test points is the same as the number of conductors.

[0012] Based on the determined arrangement of each conductor and the consistency of sag, the relationship between the vertical component of the electric field at each measured point and the sag of each conductor is determined. Based on the measured vertical component of the electric field at each measured point, the sag of each conductor is calculated.

[0013] To address all or part of the above-mentioned problems, the present invention also provides a transmission line sag detection system based on non-contact electric field sensing, the system comprising:

[0014] The arrangement determination unit is configured to determine the arrangement of each conductor, including horizontal arrangement and triangular arrangement of single-circuit lines, and vertical arrangement of double-circuit lines.

[0015] The sag consistency determination unit is configured to determine the consistency of the sag of each conductor;

[0016] An electric field sensor is configured at a defined measurement point to measure the vertical electric field component at that point. When the sag of each conductor is consistent, a measurement point is determined below the transmission line. When the sag of each conductor is inconsistent, the same number of measurement points as the number of conductors are determined below the transmission line.

[0017] The sag calculation unit is configured to determine the relationship between the vertical component of the electric field at the measured point and the sag of each conductor based on the determination results of the arrangement method determination unit and the sag consistency discrimination unit. It determines the relationship between the vertical component of the electric field at the measured point and the sag of each conductor from the pre-configured relationship between the vertical component of the electric field at the measured point and the sag of each conductor under different arrangement methods and different sag consistency. Based on the vertical electric field component measured by each electric field sensor, it calculates the sag of each conductor.

[0018] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are:

[0019] 1. Based on the distribution of electric fields in multiple conductors, this invention establishes the relationship between conductor sag and spatial electric field distribution. It only requires collecting electric field data generated during the operation of transmission lines on the ground to calculate the sag of each conductor. The operation process is extremely simple, and the designed detection (solution) method is minimally affected by the environment, resulting in high accuracy of the detection results.

[0020] 2. This invention comprehensively considers the influence of multiple parameters—including tower height, span, and tower height difference—on the electric field strength, and finally determines the principle of calculating sag based on the electric field of the lowest point of the conductor relative to the ground, which is more consistent with the theory, that is, the accuracy of the calculation results is high.

[0021] 3. The location of the measured point determined by the present invention (including the setting of the line and the spacing) can greatly simplify the complexity of the calculation process, that is, the complexity of the calculation formula, making the detection of sag more efficient. Attached Figure Description

[0022] The present invention will be described by way of example and with reference to the accompanying drawings, wherein:

[0023] Figure 1 This is a simplified schematic diagram of a single conductor.

[0024] Figure 2 This is a schematic diagram of the circuit parameters for a single conductor.

[0025] Figure 3 This is a schematic diagram comparing the electric fields of a horizontal conductor and a catenary.

[0026] Figure 4 This is a schematic diagram of the circuit parameters for a single-conductor catenary.

[0027] Figure 5 This is a schematic diagram of a single conductor and its mirror image.

[0028] Figure 6 This is a schematic diagram showing the relationship between sag and electric field strength.

[0029] Figure 7 These are schematic diagrams of conductors with different spans but the same sag.

[0030] Figure 8 It corresponds to Figure 7 A schematic diagram showing the effect of the span length on the electric field at the mid-span.

[0031] Figure 9 These are schematic diagrams of conductors with different span lengths and different sags.

[0032] Figure 10 It corresponds to Figure 9 A schematic diagram showing the effect of the span length on the electric field at the mid-span.

[0033] Figure 11This is a schematic diagram showing the effect of span length on parameters A, B, and C.

[0034] Figure 12 This is a schematic diagram of conductors with different tower heights but the same sag.

[0035] Figure 13 It corresponds to Figure 12 A schematic diagram showing the effect of the span length on the electric field at the mid-span.

[0036] Figure 14 This is a schematic diagram showing the effect of tower height on parameters A, B, and C.

[0037] Figure 15 This is a schematic diagram of a conductor erection with a tower height difference at both ends.

[0038] Figure 16 This is a schematic diagram illustrating the effect of the tower height difference on the electric field at the mid-span.

[0039] Figure 17 This is a schematic diagram illustrating the effect of the tower height difference on the electric field below the tower.

[0040] Figure 18 This is a schematic diagram illustrating the effect of the tower height difference on parameters A, B, and C.

[0041] Figure 19 This is a schematic diagram of three ways to arrange power transmission lines.

[0042] Figure 20 This is a schematic diagram illustrating the change of conductor voltage over time.

[0043] Figure 21 It corresponds Figure 19 A schematic diagram of the electric field of the conductors in three different arrangements.

[0044] Figure 22 This is a schematic diagram of the electric field acting on the measured points in a horizontal arrangement.

[0045] Figure 23 This is a schematic diagram of the electric field acting on the measured point in a triangular arrangement.

[0046] Figure 24 This is a schematic diagram of the electric field effect of a double-circuit vertically arranged single-sided three-phase conductor on the point being measured.

[0047] Figure 25 This is a schematic diagram of the electric field acting on the measured point under a double-loop vertical arrangement.

[0048] Figure 26 This is a flowchart for sag detection of multi-conductor transmission lines. Detailed Implementation

[0049] All features disclosed in this specification, or all steps in all disclosed methods or processes, may be combined in any way, except for mutually exclusive features and / or steps.

[0050] Any feature disclosed in this specification (including any appended claims and abstract) may be replaced by other equivalent or similar features, unless specifically stated otherwise. That is, unless specifically stated otherwise, each feature is merely one example of a series of equivalent or similar features.

[0051] The non-contact electric field sensing-based sag detection method for transmission lines of the present invention is an adaptive extension of sag detection for single-conductor lines. The method for sag detection of single-conductor lines includes:

[0052] The electric field strength of the ground beneath the mid-span of the power transmission line (catenback) is collected. This electric field strength can be acquired by placing an electric field sensor on the ground. In addition, the electric field strength collected by the electric field sensor includes the induced electric field of the power transmission line and the mirror electric field of the ground.

[0053] Based on the relationship between sag and electric field strength, the sag value is calculated using the collected electric field strength. In the calculation, the effective height of the conductor is first calculated based on the relationship between the effective height of the conductor and the electric field strength. The relationship is: Sag S = Tower Height H - Effective Height h. Since the tower height H is known, the conductor sag S can then be calculated based on the effective height h.

[0054] The finite element numerical instability of space charge propagation is caused by the detailed description of the wire structure, such as... Figure 1 As shown in (a); to avoid such numerical instability and modeling complexity, a simple circular conductor with radius r was used in the finite element model of the transmission line with sag, as shown in (a). Figure 1 As shown in (b).

[0055] When analyzing the electric field of overhead transmission lines, it is generally assumed that the line is horizontal and parallel to the flat ground. The sag caused by the weight of the line is ignored by taking the "average" height between the maximum and minimum height of the line.

[0056]

[0057] Where H is the maximum height of the conductor, S is the sag, and H ave This represents the average height of the conductor.

[0058] The effective height of the transmission line is determined by selecting the distance from the lowest point of the conductor to the ground. An ideal horizontal conductor is constructed by plotting the surface electric field at the lowest point of the catenary for visual comparison. Figure 2 As shown (h = HS).

[0059] The surface charge distributed on the conductor's surface is simulated by the line charge located inside the equivalent conductor. The electric field produced by the horizontal conductor at point P on the ground can be derived as follows:

[0060]

[0061] In the formula, ε0 is the free space constant, with a value of 8.85 * 10⁻⁶. -12 F / m, λ0 is the linear charge density, and d is the span length of the conductor. λ0 can be obtained from the relationship between the electric field strength and the conductor voltage U0:

[0062]

[0063] When a conductor is placed on a uniform, flat surface, considering the mirror principle, the electric field above the surface is equal to the superposition of the field generated by the actual conductor and the field generated by the mirrored underground conductor. Therefore, the equivalent electric field at point P is:

[0064]

[0065] Assuming the conductors have the same span, simulate and calculate the electric field at point P for a single catenary, a horizontal conductor at its highest point, and a horizontal conductor at its lowest point, respectively. Figure 3 As shown, the difference between the electric fields is illustrated. It can be seen that the electric field of the horizontal conductor at point P, the lowest point, is approximately equal to the electric field produced by a single catenary.

[0066] In fact, transmission lines are periodic catenaries, and sometimes the influence of the catenary on the electric field amplitude is significant. Therefore, the sag caused by the weight of the line can be used to derive the basic contact network geometry of a single-conductor catenary, such as... Figure 4 As shown in the figure. Where H is the maximum height of the line, h is the minimum height at mid-span, the sag is S = Hh, and d represents the length of the line span.

[0067] Construct a coordinate axis, with the transmission lines located in the XZ plane and symmetrically distributed with respect to the Z-axis, then we have:

[0068]

[0069] In the formula, S is the sag of the arc, d is the span length, and h is the minimum height.

[0070] The transmission line is divided into several small segments using a segmented equivalence method. Each segment is approximated by a short straight line connecting two points, and the charge density in each segment is approximately assumed to be equal. The electric field can then be calculated by superimposing the values ​​of these straight segments. The electric field of a single-conductor catenary can be obtained using the following formula:

[0071]

[0072] In the formula, ε0 is the free space constant, with a value of 8.85 * 10⁻⁶. -12 F / m; λ(r′) is the linear charge density, which depends on the voltage across the conductor. M=|R|=|rr′|, r′ refers to the position of any point on the curve, and r is the position of the point to be measured in space.

[0073] Considering the influence of electric field and current in a conductive ground, we introduce a mirror line between the air and the ground, such as... Figure 5 As shown. Then the electric field above the ground is equal to the superposition of the field generated by the actual contact wire C1(r') and the field generated by the mirrored underground wire C2(r'), and formula (6) becomes:

[0074]

[0075]

[0076]

[0077] In the formula, (x, y, z) are the spatial coordinates of the point to be measured on the ground, and (x′, y′, z′) are the coordinates of any point on the traverse. y'0 is the constant position of the single traverse on the y-axis. Here, y'0 = 0.

[0078] Since point P is located on the ground and at the midpoint of the span, the electric field produced by the catenary at point P has only a vertical component. The electric field at point P is:

[0079]

[0080]

[0081] In summary, the electric field strength is related to the contact network equation. Combining equation (5), the electric field at point P becomes:

[0082]

[0083] As can be seen from equation (12), the electric field strength has a monotonically increasing relationship with the sag of the arc. When the sag of the arc increases, the electric field strength also increases.

[0084] The above process reveals the relationship between the electric field strength at the detection point and the sag S. Using inversion calculations, the sag S of the transmission line is calculated by reverse calculation of the electric field strength measured at the detection point:

[0085]

[0086] Furthermore, the derivation of the electric field strength at point P in equation (12) and above was obtained through numerical calculation. In this embodiment, the finite element method was used to derive the electric field strength. However, in practical applications, methods such as finite difference and charge simulation (CSM) can also be used for calculation. By calculation, the corresponding values ​​between the electric field strength and the sag can be obtained. By simulating and fitting the values, an approximate functional relationship between the sag and the electric field strength can be obtained, such as... Figure 6 The figure shows the calculated values ​​and fitted curves of sag and electric field strength. This curve was obtained through simulation with a span length d = 300m, tower height H = 20m, and conductor voltage of 110kV. Based on the fitted curve, the functional relationship between sag and electric field strength is obtained:

[0087]

[0088] In the formula, S is the sag of the arc, and E0 is the electric field intensity at point P. At this time, a = 20.4, b = -1.81 * 10⁻⁶. 4 c = 1125.

[0089] Through the analysis of the electric field, it can be seen that the line charge density λ(r′) in the formula depends on the voltage of the conductor, that is, the electric field strength is proportional to the conductor voltage. Based on this, the line charge density is normalized, and the line charge density per unit conductor voltage is λ0(r′). Formula (14) is then simplified as follows:

[0090]

[0091] In the formula, y represents the sag of the arc, and x represents the electric field strength per unit conductor voltage.

[0092] It can be noted that the sag of a transmission line is not only related to the electric field strength, but also affected by parameters A, B, and C, with coefficient A having the greatest impact. Parameters A, B, and C are related to the line configuration parameters. If the line configuration remains unchanged, the greater the electric field strength, the greater the sag value. Therefore, the sag measurement of transmission lines is also affected by the line parameters to varying degrees.

[0093] The impact of different line configurations on sag measurement will be analyzed below. The line configuration includes the design of span length, tower height, and tower height difference.

[0094] First, consider the impact of span length on sag measurement.

[0095] Without considering the variation of conductor sag with span, such as Figure 7 As shown, it is assumed that the conductor sag remains constant as the span length increases (L1>L2>L3, S1=S2=S3=S). Through simulation measurements, the electric field strength at point P1 (i.e., the ground position below the mid-span) with different span lengths and the same sag is obtained, as shown below. Figure 8As shown. Figure 8 This shows the position of the conductor mid-span without considering the variation of conductor sag with span. Figure 7 The influence of the span length (at position P1) on the electric field on both sides of the conductor along its longitudinal distance is shown. It can be seen that the smaller the longitudinal distance from the conductor, the larger the electric field value. Most importantly, the span length has a very small impact on the electric field at the mid-span; conductors of different lengths produce very similar, almost identical, electric fields. This is because the conductor length is much greater than the distance from the measuring point to the conductor, resulting in a smaller contribution of the conductor to the electric field.

[0096] When considering the variation of conductor sag with span, such as Figure 9 As shown, it is assumed that the conductor sag decreases as the span decreases (L1>L2>L3, S1>S2>S3). Through simulation measurements, the electric field strength at position P1 under different sags and span lengths is obtained, as shown below. Figure 10 As shown. Figure 10 This shows the effect of the span length on the electric field at position P1 when the conductor sag varies with the span. It can be observed that, in this case, the span length has a greater impact on the electric field at mid-span, and the electric fields generated by conductors of different lengths have significant differences. The larger the span length, the larger the peak value of the electric field generated by the conductor. Figure 9 Implementation methods and Figure 7 The difference between the implementation methods lies in the different conductor sag, therefore, Figure 10 and Figure 8 In comparison, we can conclude that the influence of conductor sag is greater than that of span.

[0097] According to equation (15), the influence of sag measurement is mainly reflected in the influence of parameters A, B, and C. Assuming that the tower height remains constant (H = 20m), we simulate spans of different lengths and obtain the values ​​of each parameter by calculating the electric field under different sags of the conductor, so as to analyze the relationship between the span length and the parameters. Figure 11 Neutron plots (a), (b), and (c) show the simulated sizes of parameters A, B, and C for different span lengths, respectively.

[0098] according to Figure 11 Analyzing the results, when the conductor span varies within the range of [100m, 500m], the maximum rate of change for parameter A is approximately 6.2%, for parameter B approximately 6.8%, and for parameter C approximately 13%. This indicates that parameters A, B, and C are relatively unaffected by the span length, exhibiting minimal changes in value, and there is no clear functional relationship between each parameter and the span length. Therefore, when the electric field strength is constant, the larger the conductor span, the smaller the corresponding sag change, which can be considered constant.

[0099] In the second scenario, we consider the impact of tower height on sag measurement.

[0100] like Figure 12 As shown, it is assumed that the span length of a single conductor remains the same as the tower height (maximum line height) decreases, and the conductor sag remains constant (H1>H2>H3). Through simulation measurements, the electric field strength at position P1 under different tower heights with the same sag and span length is obtained, as shown below. Figure 13 As shown. Figure 13 The effect of the tower height of a single conductor on the electric field amplitude at point P1 is shown. It can be found that the smaller the tower height, the greater the electric field strength in its vicinity. This is because the maximum height of the line decreases, the distance between the line and the ground decreases, resulting in a smaller gap between the line and point P1, thus increasing the electric field amplitude.

[0101] Furthermore, this invention analyzes the influence of tower height on parameters A, B, and C. Assuming a constant conductor span of d = 300m, simulations were performed at different tower heights. By calculating the electric field of the conductor at different tower heights, the values ​​of each parameter were obtained to analyze the relationship between tower height and the parameters. Figure 14 Neutron plots (a), (b), and (c) show the simulated values ​​of parameters A, B, and C for different tower heights, respectively. Furthermore, the values ​​of parameters A, B, and C can be fitted with variation curves.

[0102] according to Figure 14 It can be seen that when the tower height varies within the range of [12m, 28m], parameters A, B, and C all gradually increase with the increase of tower height. By fitting an approximate functional relationship between the parameters and the tower height through simulation, we obtained... Figure 14 Fitted curve in:

[0103] A(H)=2.942*e 0.09947*H (16)

[0104] B(H) = 958.3 * H - 3.762 * 10 4 (17)

[0105] C(H)=0.8533*e 0.2871*H +862.4 (18)

[0106] In the formula, H is the tower height, which is the maximum height of the line.

[0107] Among these factors, the tower height has the greatest impact on the values ​​of parameters A and B, which increase with the tower height. Based on the relationship between electric field strength and sag described earlier, we can conclude that when the electric field strength remains constant, the greater the tower height, the greater the corresponding sag.

[0108] The third scenario considers the impact of tower height difference on sag measurement.

[0109] Generally, it is assumed that adjacent towers of transmission lines are of equal height, and the lowest point of the catenary is located at the mid-span. However, in reality, many lines have towers of unequal height, such as... Figure 15 In the single-conductor catenary, there is a height difference m between adjacent towers (m = H). m2 -H m1 At this point, the lowest point of the catenary deviates from the mid-span. Assume that the conductor sag remains constant despite changes in tower height. Through simulation measurements, the electric field strength at the mid-span and tower base positions is obtained, as shown below. Figure 16 , Figure 17 As shown. Figure 16 and Figure 17 This shows the difference in tower height at different tower locations. Figure 15 The electric field at points P1 and P2 (in the middle of the span) and the longitudinal distance between the conductors on both sides is affected. It can be seen that as the tower height difference increases, the electric field value at point P1 gradually decreases, while the electric field value at point P2 gradually increases. This is because the lowest point of the catenary shifts to the right as the height difference increases, gradually deviating from the mid-span position, thus reducing the electric field at P1; simultaneously, the gap between the line and point P2 on the ground decreases, thus increasing the electric field value generated by the conductor on the ground. It is worth noting that the tower height difference has a greater impact on the electric field at the lower position below the tower, i.e., point P2, compared to the electric field below the mid-span.

[0110] Furthermore, this invention analyzes the influence of the tower height difference on parameters A, B, and C to explore the impact of the tower height difference on sag measurement. It is assumed that the conductor span and the maximum tower height remain constant (d = 300m, H...). m1 =20m), by simulating the electric field at point P1 under different tower height differences and calculating the magnitudes of the parameters, namely the values ​​of A, B, and C, the relationship between the tower height difference and each parameter is further analyzed. Figure 18 Neutron plots (a), (b), and (c) show the simulated values ​​of parameters A, B, and C corresponding to different tower height differences, respectively.

[0111] according to Figure 18 It can be seen that when the tower height difference varies within the range of [0m, 5m], the maximum rate of change for parameter A is approximately 11.6%, for parameter B it is approximately 7.3%, and for parameter C it is approximately 62.5%. This indicates that the tower height difference has a greater impact on parameters A and C, and a smaller impact on parameter B. Specifically, the values ​​of parameters A and C increase with the increase of the tower height difference, showing a clear functional relationship between the parameters and the tower height. By fitting their approximate functions through simulation, we can obtain... Figure 18 Fitted curves in (a) and (c):

[0112] A(m)=19.19*e 0.0199*m (19)

[0113] C(m)=903.4*e 0.06198*m (20)

[0114] In the formula, m is the height difference between adjacent towers.

[0115] According to the principle of equation (15), parameter A has a greater influence on sag than parameter C. Therefore, when the field strength remains constant, the greater the difference in tower height, the greater the corresponding sag.

[0116] The preceding text explained the theory of sag measurement for single-conductor lines and analyzed the influence of transmission line parameters (span, tower height, and tower height difference) on sag measurement. Based on this, this embodiment provides a detailed explanation of sag measurement for multi-conductor catenary lines.

[0117] As high-voltage overhead lines, transmission lines typically have three distribution patterns: horizontal arrangement, triangular arrangement, and double-circuit vertical arrangement, in that order. Figure 19 As shown in (a), (b), and (c) in the figure. In the calculation model of this embodiment, the three distribution methods are divided into single-circuit lines and double-circuit lines, wherein... Figure 19 (a) and Figure 19 (b) is a single-circuit line. Figure 19 (c) is a double-circuit line on the same tower.

[0118] When a transmission line consists of multiple conductors, the induced charge on each conductor is calculated using the potential coefficient. For three contour points located on the equivalent conductor surface, the potential will be equal to the conductor surface voltage. Generally, the voltage amplitudes of each phase conductor in a transmission line are equal, with the phase angles laging by 120° sequentially. Therefore, the conductor voltage changes periodically with time, such as... Figure 20 As shown.

[0119] To simplify the problem, the catenary is equivalent to an infinitely long conductor, whose height is the distance from the lowest point to the ground, such as... Figure 2 The horizontal straight conductor in the line is used. Therefore, a two-dimensional cross-section at this point can be selected for calculation. Furthermore, this paper only considers the effective voltage amplitude of the transmission line. Since the effective voltage amplitude of each phase conductor is equal, the linear charge density of the conductors can be considered to be the same.

[0120] Figure 21 The simulation shows the electric fields of three-phase conductors under different arrangements. The simulation reveals that the electric fields of multi-conductor transmission lines are mutually coupled, and the electric field on the ground is formed by the combined effects of the multiple conductors.

[0121] Based on the electric field calculation of an infinitely long straight conductor, the electric field generated by the single-conductor catenary on the ground is as follows:

[0122]

[0123]

[0124] In the formula, U e R is the effective amplitude of the conductor voltage, r is the equivalent conductor radius, and h is the distance from the lowest point of the conductor to the ground. i It is the distance from a point on the ground to the center point of the equivalent conductor profile.

[0125] By using superposition techniques, the electric field generated by a multi-conductor catenary on the ground can be calculated:

[0126]

[0127] In the formula, n represents the number of catenary conductors.

[0128] When performing sag inversion calculations using an infinitely long model, it is necessary to determine the unknown variables based on the number of multi-conductor catenaries, thereby further determining the number of measurement points and their location distribution. The calculation methods differ depending on the arrangement of the multi-conductor catenaries.

[0129] Example 1

[0130] The sag detection method in this embodiment is for single-circuit lines, which include two methods: horizontal arrangement and triangular arrangement.

[0131] First, let's analyze the horizontal arrangement. Since the transmission line is composed of multi-conductor catenary conductors, the arrangement of each phase conductor may differ from the other phase conductors. This results in two possibilities: the sag of each phase conductor may be consistent or inconsistent.

[0132] If the sag of each phase conductor is consistent, the sag calculation includes one unknown variable; if the sag of each phase conductor is inconsistent, the sag calculation includes three unknown variables. For example... Figure 20 and Figure 21 As shown, sensors are placed parallel to each other at different positions on the horizontal ground below each phase conductor to measure the spatial electric field. The three measurement points form a measurement array. From this, three equations can be obtained to solve for the sag of a single-circuit line.

[0133] Since existing electric field sensors can only detect one-dimensional or two-dimensional electric field strength, and the detection direction is generally parallel or perpendicular to the sensor's main axis, for simplicity and convenience, the electric field measured in this invention refers to the perpendicular component of the electric field.

[0134] like Figure 22 The diagram shows a spatial electric field detection diagram of three horizontally arranged three-phase conductors. An electric field sensor is placed directly below the midpoint of each conductor: point P1 below conductor A, point P below conductor B, and point P2 below conductor C. D represents the horizontal distance between each conductor, and h represents the distance from the lowest point of each conductor to the ground. The electric fields generated by each conductor on the ground are E0 and E1 respectively. AE B and E C .

[0135] If the sag of the three-phase conductors is equal, that is, the equivalent conductors are at the same height from the ground, h = HS, the electric field at point P is:

[0136]

[0137]

[0138] Due to symmetry, E A =E C The electric field at point P is the perpendicular component of the electric field:

[0139]

[0140] In the second scenario, the sag of the three-phase conductors is not equal. Assume the distances (i.e., effective heights) from the lowest points of the three-phase conductors to the ground are h, respectively. A h B h C h A =HS A h B =HS B h C =HS C At this moment, the perpendicular component of the electric field at point P is:

[0141]

[0142]

[0143]

[0144] Similarly, the perpendicular components of the electric field at points P1 and P2 are:

[0145]

[0146]

[0147] A measurement array is obtained by measuring the electric field intensity at three points P, P1, and P2 respectively, and the sag of each phase conductor is calculated by inversion according to the above equations (29), (30), and (31).

[0148] Another arrangement for a single-circuit line is a triangular arrangement. For example... Figure 23As shown, similar to the horizontal arrangement, an electric field sensor is installed directly below the midpoint of each of the three phase conductors: point P1 below conductor A, point P below conductor B, and point P2 below conductor C. h is the effective height of the taller conductor, D1 is the horizontal distance between the conductors, and D2 is the vertical distance between the conductors. The electric fields generated on the ground by each phase conductor are E... A E B and E C .

[0149] Using the same method as for horizontal arrangement testing, if the sag of the three phase conductors is equal, the electric field at point P is:

[0150]

[0151]

[0152] R X Let X be the distance from the conductor X to point P.

[0153] If the sag of the three-phase conductors is not equal, the vertical components of the electric field at points P, P1, and P2 are respectively:

[0154]

[0155]

[0156]

[0157] h A h B h C These represent the distances from the lowest point of the three-phase conductors to the ground.

[0158] Let E be the perpendicular component of the spatial electric field measured at the nth measurement point. n F n It is a measurement matrix relating n measurement points and the sag values ​​of each phase conductor. After obtaining data such as conductor voltage, the sag of each conductor can be further calculated by measuring the electric field components. Therefore, by setting up a measurement array to measure the spatial electric field, the inverse calculation of the sag of three-phase conductors can be achieved.

[0159]

[0160] For a single-circuit line, n = 3. Fn is the inversion matrix, which can be derived from equations (34)-(36) and S = Hh. The sag of each conductor can be solved by arranging equations based on the detected electric field strength and the relationship between sag and tower height and effective conductor height.

[0161] Example 2

[0162] The sag detection method in this embodiment is for double-circuit lines. Similarly, for double-circuit lines, the sag between the phase conductors may be the same or different.

[0163] When the voltage and conductors are fixed, if the sag of each phase conductor is considered to be consistent, the sag calculation includes one unknown variable; if the sag of each phase conductor is considered to be inconsistent, the sag calculation includes six unknown variables. For example... Figure 24 The diagram shows three-phase conductors A1, B1, and C1 arranged vertically on one side. Figure 25 As shown, three other phase conductors, A2, B2, and C2, are symmetrically arranged on the other side of the Z-axis. Electric field sensors are placed parallel to the horizontal tangent at different positions on the ground below the conductors to measure the spatial electric field. Three measurement points constitute a measurement unit, and two measurement units (i.e., the data from the six electric field sensors) form a measurement array. From this, six equations can be obtained to solve for the sag of the double-circuit line.

[0164] like Figure 24 As shown, D3 is the vertical distance between adjacent conductors, 2*D4 is the horizontal distance between the two conductors, Y0 is the distance between adjacent electric field sensors, and h is the distance from the lowest point of the lowest conductor to the ground. Point P is located at the intersection of the midline of the two conductors and the ground. Therefore, the horizontal distance from the conductor to point P is D4, to point P1 is D4+Y0, and to point P2 is D4+2Y0. The electric fields generated by each phase conductor on the ground are E... A E B and E C .

[0165] Similar to the measurement method for a single-circuit line, if the sag of the three-phase conductors is equal, the electric field strength at point P is:

[0166]

[0167] If the sags of the three-phase conductors are not equal, then the vertical electric field components at points P, P1, and P2 are:

[0168]

[0169]

[0170]

[0171] h A h B h C These represent the distances from the lowest point of the three-phase conductors to the ground.

[0172] The above are the vertical electric field components at points P, P1, and P2 for a three-phase conductor arranged vertically on one side. The vertical electric field components at points P, P1, and P2 for a three-phase conductor arranged vertically on the other side can be calculated similarly. The vertical electric field components at points P, P1, and P2 for the three-phase conductors on both sides can be obtained by superimposing them. Based on this principle, the vertical electric field components at each determined point (P, P1, P2...Pn) for the three-phase conductors on both sides can be determined according to equation (23). Furthermore, the vertical electric field components at that point can be determined. The vertical electric field components at each point are E0, E1, E2...E n .

[0173] For a three-phase conductor arranged in a double-circuit perpendicular arrangement, the electric field at the measuring point on the ground is equal to the superposition of the electric fields generated by the three-phase conductors arranged perpendicularly on both sides, such as... Figure 25 As shown, the horizontal distance between the two conductors is 2*D4, and the effective voltage amplitude is the same.

[0174] If we consider the case where the sag of the conductors in each phase of a double-circuit line is inconsistent, six measurement points are selected at different locations on a horizontal surface. The electric field measurement at each point is approximately the same as the calculation method described above for a single-sided vertical arrangement. These six measurement points form a measurement array, which is as follows:

[0175]

[0176]

[0177] For a double-circuit line, n = 6. The relationship between E0 to E5 and the effective height of each conductor can be determined according to equation (23), F n The inversion matrix is ​​derived from equations (39)-(41), (44) and S = Hh.

[0178] If we consider the case where the sag of each phase conductor in a double-circuit line is uniform, then we only need to measure the electric field at one point to solve for the sag, such as point P. Due to symmetry, the electric field strength at point P is:

[0179]

[0180] h is the distance from the lowest point of the conductor to the ground. h is calculated by inversion based on the detected electric field strength, and then the conductor sag is calculated according to the sag S = Hh.

[0181] In general, regardless of the arrangement of the multi-conductor transmission line, such as Figure 26As shown, the methods for determining sag are as follows: If the sag of each conductor is considered to be uniform, a location point can be selected on the ground, and the vertical component of its electric field can be measured. Based on the relationship between the vertical component of the electric field and the effective height of the conductor, the effective height of the conductor can be obtained, and thus the sag can be calculated. If the sag of each conductor is considered to be inconsistent, a corresponding number of location points can be selected on the ground according to the number of conductors. The vertical component of the electric field at each point can be measured, and based on the relationship between the vertical component of the electric field at each point and the effective height of each conductor, the effective height of each conductor can be solved, and thus the corresponding sag value of each conductor can be calculated.

[0182] In terms of implementation process or logic, it includes: firstly, determining whether the sag values ​​of each conductor are consistent (including consistent, partially consistent, and completely inconsistent, with the latter two cases classified as inconsistent). When performing calculations on a computer using a transmission line sag detection system based on non-contact electric field sensing (hereinafter referred to as the sag detection system), the sag consistency discrimination unit receives external input to determine whether the sag values ​​of each conductor are consistent.

[0183] When consistent, only one unknown variable h needs to be determined; therefore, only the electric field strength at a single point is needed to solve for S. A point on the ground is selected, and the electric field strength at that point is measured to obtain the perpendicular electric field component. The electric field strength can be obtained by placing an electric field sensor at that point to detect the spatial electric field. In some preferred embodiments, the selected point is the foot of the perpendicular bisector of the lowest point of each of the two side conductors to the horizontal ground. Typically, both single-circuit and double-circuit lines are symmetrically distributed; therefore, this point can also be understood as the foot of the perpendicular bisector of the axis of symmetry of the lowest point of each conductor to the ground, i.e., point P in the above embodiment.

[0184] If there is inconsistency, the effective height h of each conductor needs to be determined separately. x (x = A, B, or C), meaning the number of parameters to be determined is the same as the number of conductors. Then, n points are selected on the ground (n is the number of conductors; for example, n = 3 for a single-circuit line and n = 6 for a double-circuit line in the previous embodiment), and the electric field intensity at each point is measured to obtain the vertical electric field component of each point. A plane perpendicular to the horizontal ground is determined through the lowest point of each conductor, and all selected points lie on the intersection of this plane and the horizontal ground (i.e., the first straight line). For ease of calculation, the spacing between adjacent points is designed to be equal.

[0185] Regardless of whether the sag of each conductor is consistent, at least one parameter to be determined is included, meaning at least one measurement point will be set. Preferably, one measurement point is determined to be the perpendicular position (i.e., the first position) of the perpendicular bisector of the lowest point of the conductors on both sides of the transmission line and the aforementioned first straight line, i.e., the projection of the midpoint of the line connecting the lowest points of the two conductors onto the horizontal ground. For cases where the sag is consistent, only this measurement point exists. For cases where the sag is inconsistent, one of the multiple measurement points is set at this point. For the other measurement points, preferably, they are arranged on both sides of this point, and the difference in the number of measurement points on both sides does not exceed one. For example, see Appendix. Figure 23 As shown, point P is set at the first position, and two measurement points P1 and P2 are set on the left and right sides of point P, respectively. (The last sentence appears to be incomplete and possibly refers to a different context.) Figure 25 As shown, point P is set at the first position, with two test points set to the left of point P and three test points set to the right of point P.

[0186] The vertical component of the electric field can be obtained by installing an electric field sensor at a specific point.

[0187] After measuring the vertical component of the electric field at the determined points and determining the arrangement of the multiple conductors, the effective height of each conductor is calculated by inversion based on the relationship between the electric field strength and the effective height of the conductors under the determined arrangement. The sag of each conductor is then calculated using S = Hh, or S can be directly calculated by substituting h = SH into the aforementioned relationship. In the sag detection system, the arrangement determination unit receives external input to determine the arrangement of the multiple conductors, i.e., whether it is a horizontal arrangement of a single-circuit line, a triangular arrangement, or a double-circuit vertical arrangement (symmetrical arrangement) of a double-circuit line, to further determine the calculation formula used for inversion. The sag calculation unit, based on the arrangement of the multiple conductors determined by the arrangement determination unit and the consistency of the sag of each conductor determined by the sag consistency judgment unit, determines the calculation method for sag calculation from the pre-configured sag calculation algorithm. This involves determining the relationship between the vertical component of the electric field at the measured point and the sag of each conductor under the current arrangement and sag consistency, then acquiring the vertical component of the electric field detected by each electric field sensor, and calculating the effective height / sag of each conductor. Specifically, for horizontal arrangement, when the sag values ​​of each conductor are consistent, h is calculated based on equation (26), and the sag S is further calculated. In the sag detection system, the sag calculation unit is configured to calculate h using the inversion calculation method of equation (26) for this situation, and then calculate the sag S. When the sag values ​​of each conductor are inconsistent, h is calculated based on equations (29), (30), and (31). x (x = A, B, or C), further calculate S respectively. x In the sag detection system, the sag calculation unit is configured to calculate h using the inversion calculation methods of equations (29), (30), and (31) in this case. x S was further calculated separately.x For the triangular arrangement, when the sag values ​​of each conductor are consistent, h is calculated based on the inversion of equation (33), and the sag S is further calculated. In the sag detection system, the sag calculation unit is configured to calculate h using the inversion calculation method of equation (33) in this case, and then calculate the sag S. When the sag values ​​of each conductor are inconsistent, h is calculated based on the inversion of equations (34), (35), and (36). x S was further calculated separately. x In the sag detection system, the sag calculation unit is configured to calculate h using the inversion calculation methods of equations (34), (35), and (36) in this case. x S was further calculated separately. x For the double-channel arrangement, when the sag values ​​of each conductor are consistent, h is calculated based on the inversion of equation (44), and the sag S is further calculated. In the sag detection system, the sag calculation unit is configured to calculate h using the inversion calculation method of equation (44) according to this situation, and then calculate the sag S. When the sag values ​​of each conductor are inconsistent, S is calculated based on the inversion of equation (42). i (i = A1, A2, B1, B2, C1 or C2), the specific process is to first calculate the effective height of each conductor, and then according to S i =H i -h i The sags are calculated, and in the sag detection system, the sag calculation unit is configured to calculate S using the inversion calculation method of equation (42) according to the corresponding situation. i .

[0188] This invention is not limited to the specific embodiments described above. The invention extends to any new feature or combination disclosed in this specification, as well as any new method or process step or combination disclosed herein.

Claims

1. A method for detecting sag in transmission lines based on non-contact electric field sensing, the method being designed for transmission lines composed of multiple conductors, characterized in that... include: The arrangement of each conductor is determined, including horizontal arrangement and triangular arrangement for single-circuit lines, and vertical arrangement of double-circuit lines. Ensure the consistency of sag for each conductor; When the sag of all conductors is consistent, a test point is determined below the transmission line, and the vertical component of the electric field at the test point is measured. When the sag of each conductor is inconsistent, multiple test points are determined below the transmission line, and the vertical component of the electric field at each test point is measured. The number of test points is the same as the number of conductors. Based on the determined arrangement of each conductor and the consistency of the sag, the relationship between the vertical component of the electric field at each measured point and the height of the lowest point of each conductor from the ground is determined. Based on the measured vertical component of the electric field at each measured point, the height of the lowest point of each conductor from the ground is calculated. Then, based on the mathematical relationship between conductor sag, tower height, and the height of the lowest point of the conductor from the ground, the sag of each conductor is calculated separately.

2. The method for detecting sag of transmission lines based on non-contact electric field sensing as described in claim 1, characterized in that, All measured points are located on the first straight line; a plane perpendicular to the horizontal ground is determined through the lowest point of each traverse, and the intersection of this plane and the horizontal ground is the first straight line.

3. The method for detecting sag of transmission lines based on non-contact electric field sensing as described in claim 2, characterized in that, When determining multiple measurement points, the distance between adjacent measurement points is equal.

4. The method for detecting sag of transmission lines based on non-contact electric field sensing as described in claim 2, characterized in that, Of all the measured points, one is located at the first position; the foot of the perpendicular line from the lowest point of the conductors on both sides of the transmission line to the first straight line is the first position.

5. The method for detecting sag of transmission lines based on non-contact electric field sensing as described in claim 4, characterized in that, When determining multiple test points, the difference in the number of test points on both sides of the first position shall not exceed 1.

6. A sag detection system for transmission lines based on non-contact electric field sensing, the system being designed for transmission lines composed of multiple conductors, characterized in that... include: The arrangement determination unit is configured to determine the arrangement of each conductor, including horizontal arrangement and triangular arrangement of single-circuit lines, and vertical arrangement of double-circuit lines. The sag consistency determination unit is configured to determine the consistency of the sag of each conductor; An electric field sensor is configured at a defined measurement point to measure the vertical component of the electric field at that point. When the sag of each conductor is consistent, a measurement point is determined below the transmission line. When the sag of each conductor is inconsistent, the same number of measurement points as the number of conductors are determined below the transmission line. The sag calculation unit is configured to determine the relationship between the vertical component of the electric field at the measured point and the height of the lowest point of each conductor from the pre-configured relationship between the vertical component of the electric field at the measured point and the height of the lowest point of each conductor from the ground under different arrangement methods and different sag consistency. Based on the vertical component of the electric field measured by each electric field sensor, the height of the lowest point of each conductor from the ground is calculated. Then, based on the mathematical relationship between conductor sag, tower height, and the height of the lowest point of the conductor from the ground, the sag of each conductor is calculated separately.

7. The transmission line sag detection system based on non-contact electric field sensing as described in claim 6, characterized in that, All measured points are located on the first straight line; a plane perpendicular to the horizontal ground is determined through the lowest point of each traverse, and the intersection of this plane and the horizontal ground is the first straight line.

8. The transmission line sag detection system based on non-contact electric field sensing as described in claim 7, characterized in that, When determining multiple measurement points, the distance between adjacent measurement points is equal.

9. The transmission line sag detection system based on non-contact electric field sensing as described in claim 7, characterized in that, Of all the measured points, one is located at the first position; the foot of the perpendicular between the perpendicular bisector of the conductors on both sides of the transmission line and the first straight line is the first position.

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