Conductor Sag Research Articles

Simultaneous Structural Monitoring over Optical Ground Wire and Optical Phase Conductor via Chirped-Pulse Phase-Sensitive Optical Time-Domain Reflectometry.

Optimizing the use of existing high-voltage transmission lines demands real-time condition monitoring to ensure structural integrity and continuous service. Operating these lines at the current capacity is limited by safety margins based on worst-case weather scenarios, as exceeding these margins risks bringing conductors dangerously close to the ground. The integration of optical fibers within modern transmission lines enables the use of Distributed Fiber Optic Sensing (DFOS) technology, with Chirped-Pulse Phase-Sensitive Optical Time-Domain Reflectometry (CP-ΦOTDR) proving especially effective for this purpose. CP-ΦOTDR measures wind-induced vibrations along the conductor, allowing for an analysis of frequency-domain vibration modes that correlate with conductor length and sag across spans. This monitoring system, capable of covering distances up to 40 km from a single endpoint, enables dynamic capacity adjustments for optimized line efficiency. Beyond sag monitoring, CP-ΦOTDR provides robust detection of external threats, including environmental interference and mechanical intrusions, which could compromise cable stability. By simultaneously monitoring the Optical Phase Conductor (OPPC) and Optical Ground Wire (OPGW), this study offers the first comprehensive, real-time evaluation of both structural integrity and potential external aggressions on overhead transmission lines. The findings demonstrate that high-frequency data offer valuable insights for classifying mechanical intrusions and environmental interferences based on spectral content, while low-frequency data reveal the diurnal temperature-induced sag evolution, with distinct amplitude responses for each cable. These results affirm CP-ΦOTDR's unique capacity to enhance line safety, operational efficiency, and proactive maintenance by delivering precise, real-time assessments of both structural integrity and external threats.

Sag and Tension Calculations for High-Voltage Overhead Line Conductors

Overhead lines are used to transmit electricity from where it is generated to the receiving stations. The correct design of an overhead line affects public safety, because it should ensure the required clearances between conductors and the ground and objects located in the space under the overhead line. The temperature of conductors in overhead lines depends on the load current and weather conditions, and affects the sag and tension of the conductors. Calculations of sags and tensions of overhead conductors can be performed using simplified calculation methods that do not consider insulator sets. In some situations, this approach may cause calculation errors. This article discusses algorithms for calculating overhead conductor tensions and sags in the tensioning sections of high-voltage overhead lines, accounting for and excluding insulator sets. The analysis is carried out for different lengths of tensioning sections and various thermal and mechanical states of the conductors.

Calculation Methods of High-Voltage Direct Current (HVDC) Line Sag Considering Meteorology

Sag is one of the important indicators for judging whether a transmission line is safe. The existing sag calculation method does not consider the temperature difference between conductor strands, causing the calculated results to often deviate from the values measured with a theodolite. In this article, a sag calculation method considering the temperature difference between strands is proposed. First, finite element analysis and experiments were used to analyze the temperature differences between each area and layer of the conductor when the wind blew the conductor, and then a correction calculation model for the conductor sag was proposed. Next, a sag monitoring system based on four-point temperature measurement was designed. Finally, the method was applied to a ±400 kV transmission line in Qinghai Province, China. The results show that after considering the temperature difference in the conductor strands, the error of the sag calculation result is much smaller than that without considering the temperature difference in the conductor strands, and the maximum relative error is reduced from 7.86% to less than 2%.

Review of Technological Advances in High Temperature Overhead Line Composite Conductors

ACSR (Aluminium Conductor Steel Reinforced) conductors consisting of pure aluminum wires helically stranded around a core of high strength galvanized steel core wires are widely used in overhead transmission line applications. While the steel wires provides the required strength, the outer aluminium serves as electricity conducting member. The thermal rating or ampacity of conductors is the maximum current that a circuit can carry within the temperature limits as dictated by the allowable conductor sag or by the annealing onset temperature of the conductor, whichever is lower. On a continuous basis, ACSR may be operated at temperatures up to 100°C without any significant change in the conductor’s physical properties. Above 100°C, aluminum wires loses tensile strength over time and becomes "fully annealed" giving rise to increased thermal expansion of the conductor; this causes excessive sagging reducing the clearance between the ground and the energized conductors.
 While, the electric utilities are posed with increased challenges of production of additional capacities and building new transmission circuits to meet the ever growing demand and the high cost and environmental restrictions of constructing new lines, methods are being explored to increase their capacity with minimum changes in the existing towers. Replacement of the existing conductor with a advanced high temperature composite (HTC) conductors operating upto temperatures of 200°C with reduced sagging characteristics have been attempted and an increase in capacity of 30-80%, can be achieved through application of these composite conductors.
 The advanced HTC conductors with varied combinations of core material and outer conducting wires are being tried so as to achieve wide ranging properties. In general, HTC conductors features the combinations of either soft aluminum wires with ultra high strength steel or temperature resistant aluminium with or fiber reinforced metal/polymer matrix composites as the core. Both the alumina fiber reinforced temperature resistant aluminium metal matrix composite and the carbon fiber reinforced high temperature polymer resin composite wires as the core material appears to have favorable applications. The comparative performance of the HTC depends on the degree to which both outer aluminum strand and reinforcing core’s physical properties are stable at high temperature and on the elastic, plastic, and thermal elongation of the combined HTC.
 The summary of various developments realized in the area of composite conductors and their relative merits and demerits have been discussed in detail.

A Simplified Method of Flexible Conductors Mechanic Calculation in Switchgears without Restrictions on the Number of Taps

The purpose of the mechanical calculation of flexible conductors of switchgears and power lines is to determine the sag, tensions, and loads on support structures, minimum distances to adjacent live parts and some other parameters. Calculations should be made taking into account distributed and concentrated loads. Distributed loads directed vertically are determined by the weight of the wire, insulator strings, and possible ice deposits on them. Distributed loads in the horizontal plane should be calculated in climatic conditions with lateral wind pressure. Concentrated loads are created by such elements as taps to electrical devices, phase-to-phase insulating spacers, barrier balls, loops, etc. Concentrated loads mainly act in the vertical plane, and in the case of taps, they can have an almost arbitrary spatial direction. The most accurate methods of mechanical calculation of flexible conductors include methods based on the numerical solution of the equation of wires in the form of a flexible elastic thread. Such an algorithm is implemented in the author's computer program MR21. However, in many cases, simplified methods of mechanical calculation are preferable, as they are available to a wider range of users. The simplified method of mechanical calculation of flexible conductors proposed in the article is based on the equation of state of the wire and allows taking into account concentrated and distributed loads. Various climatic regimes and loads are taken into account using the horizontal and vertical load factors in the calculated and initial modes. Expressions are proposed for calculating the above coefficients for any number of taps in a span and with an accurate approach to taking into account their spatial arrangement. Formulas for calculating sag and horizontal deflections of conductors are given, too. The MR21 computer program, tested earlier, has been used in this work as a tool for checking the calculation results using the proposed simplified method.

Numerical Simulation of the Radar Cross Section of UHV/EHV Power Lines Illuminated by X-, C-, L-, and P-Band Spaceborne SAR

Many spaceborne synthetic aperture radars (SARs), which operate separately in the X, C, and L bands, have been employed to monitor ultra-high-voltage (UHV) and extra-high-voltage (EHV) power lines. However, a full interpretation of the scattering characteristics of these power lines in spaceborne SAR images remains a challenging task. A numerical simulation of the radar cross-section (RCS) of UHV/EHV power lines in the X, C, L, and P bands over a wide range of incidence angles is presented in this paper. A physical model of the UHV/EHV power line is first built. Here, two practical shapes of the UHV/EHV power line are considered, which include the symmetrical catenary when two suspension points have the same height and the inclined catenary when the heights of two suspension points are different. Then, the multilevel fast multipole algorithm (MLFMA) is used for the analysis of the backscatter behavior of UHV/EHV power lines in the X, C, L, and P bands. The effects of several parameters of practical importance on the backscatter RCS of UHV/EHV power lines are also studied, which include the carrier frequency, polarization type, aspect angle of illumination, span length, height difference between two suspension points, conductor sag, and cable diameter. In addition, several comparisons made between simulated and practical observation results demonstrate that the obtained theoretical results can be used to interpret the scattering characteristics of UHV/EHV power lines in spaceborne SAR images and can provide some useful suggestions for monitoring UHV/EHV power lines using spaceborne SAR images.

Transmission Line Sag Measurement and Simulation Research Based on Non-Contact Electric Field Sensing.

Sag is an important indicator of the operational health of a transmission line, and its timely measurement is of great significance to maintain the stability and reliability of power systems. However, traditional contact measurements may be affected by the electromagnetic interference of conductors. In contrast, measurement methods without direct electrical contact with the subject provide greater portability and flexibility. This paper presents a study of a transmission line sag measurement and simulation based on non-contact electric field sensing. The finite element method was used to analyze the conductor distribution, establish the coupling relationships among the electric field, transmission line, and measurement point, propose a sag inverse calculation model, and assess the impact of the transmission line parameter on the curved drooping measurement. Simultaneously, sag measurement schemes for single-round and dual-circuit lines were designed for multi-conductive lines, and measurement array studies were conducted. The vertical component of the electric field in space measured by the array was obtained, which could be used to perform conductor sag measurement simply and efficiently. The proposed method will facilitate the monitoring of the overhead transmission line status, which is conducive to the effective operation of the entire system.

Single phase to ground fault location method of overhead line based on magnetic field detection and multi-criteria fusion

The distribution network has many branches and complex structure, and the existing protection is difficult to achieve accurate fault section location. Moreover, the monitoring device based on electrical quantity has some problems, such as high cost, power failure in installation and maintenance, and the information collected can not meet the requirements of distribution network for operation monitoring. Therefore, fault location is still a difficult problem in the existing distribution network. The magnetic field (MF) under the overhead line can reflect the change of line current, locate the fault position between two pole towers, and the magnetoresistive sensor has the advantages of low cost and uninterrupted installation and maintenance. Therefore, in recent years, the non-contact fault feeder detection and location method based on MF has begun to develop rapidly. Based on the similarity analysis of MF waveform under overhead line from different aspects by using five criteria: relative entropy, Frobenius norm, maximum mean discrepancy, cosine similarity and correlation coefficient, it proposed a multi criteria fusion fault location method based on D-S evidence theory, which makes full use of the advantages of each criterion and overcomes the limitations of single criterion. Simulation results show that the method is not affected by conductor sag, galloping and data window length, and it fit for the noise interference and high impedance fault (HIF). Compared with the other MF method, the method has stronger adaptability.

Study on the sag of ultra high voltage conductor with large-tonnage tension insulator string

The aim of this paper is to establish a unified state equation of overhead line mechanics. An accurate calculation method of non-uniform load sag is proposed based on the simply supported beam theory. It is suitable for isolated span and continuous span. Meanwhile, this paper investigates the law and error influence of sag in both isolated pan and continuous span considering some sensitive factors, such as tensile force, span length, number of spans, elevation difference angle, length and weight of tension insulator string. The efficacy of the recommended algorithm for conductor sag with large-tonnage tension insulator string line is validated in the end.

Approximate Magnetic Flux Density Model of Overhead Power Lines for Conductor Sag Estimation

Monitoring and supervision of overhead power lines have become essential actions in Electrical Power Systems since the introduction of the Smart Grid concept. In order to monitor overhead power lines, simple non-invasive devices are mounted on support poles, which detect line abnormalities and faults by measuring magnetic field originating from power line conductors. Measured signals are also used to determine various electrical and non-electrical line parameters. In this paper a new approximate model for magnetic flux density vector components of the overhead power lines suitable for real-time conductor sag estimation is presented. In the proposed model, catenary-shaped power line conductors are approximated with tilted straight line conductors, and the approximate model is calibrated by tuning model coefficients to match flux density vector components as in the case of real catenary-shaped conductors. The accuracy of the proposed model is verified by measurements on three-phase overhead power line model scaled to laboratory conditions. As a conclusion, an adaptive method for possible practical implementation based on the approximate model is considered.

Contactless HVDC Overhead-Line Current Monitoring by a Magnetic Sensor Array With Sensing Parameter Correction Function

To improve the efficiency of power transmission, high-voltage direct current (HVDC) transmission systems are crucial power-related development in many countries. This study proposes a contactless DC current measurement method suitable for on-site measurements of HVDC overhead lines. In this method, a vertical magnetic field (MF) sensor array (three layers and one three-axis MF sensor installed in each layer) is designed to measure the spatial MFs on the ground. With the spatial MFs measured by the sensor array and the overhead-line specifications obtained from utilities, the core current algorithm of the proposed method can accurately calculate the current values. In addition, we design a magnetic shielding mechanism to correct a DC offset that is inevitably output from each MF sensor. The DC offset includes the quiescent voltage of the self-circuit of the MF sensor and the output voltage of the MF sensor caused by the earth’s MF. Thus, this mechanism can effectively solve the problem in which the DC offset is misjudged as an MF formed by the measured current. The simulation results indicate that under arbitrary vertical sensor array placements, the core convergence condition (geomagnetic invariance) of the proposed current algorithm can improve the algorithm convergence. Finally, the experimental results verify the feasibility of the proposed method for the measurement of overhead-line current. Without conductor sags, all the current errors are less than 2 % in both the 500-kV and 800-kV overhead-line scenarios. Moreover, even with serious conductor sags, all the current errors are still within 9 %.

Advanced Power Line Diagnostics Using Point Cloud Data—Possible Applications and Limits

The advance in remote sensing techniques, especially the development of LiDAR scanning systems, allowed the development of new methods for power line corridor surveys using a digital model of the powerline and its surroundings. The advanced diagnostic techniques based on the acquired conductor geometry recalculation to extreme operating and climatic conditions were proposed using this digital model. Although the recalculation process is relatively easy and straightforward, the uncertainties of input parameters used for the recalculation can significantly compromise such recalculation accuracy. This paper presents a systematic analysis of the accuracy of the recalculation affected by the inaccuracies of the conductor state equation input variables. The sensitivity of the recalculation to the inaccuracy of five basic input parameters was tested (initial temperature and mechanical tension, elasticity modulus, specific gravity load and tower span) by comparing the conductor sag values when input parameters were affected by a specific inaccuracy with an ideal sag-tension table. The presented tests clearly showed that the sag recalculation inaccuracy must be taken into account during the safety assessment process, as the sag deviation can, in some cases, reach values comparable to the minimal clearance distances specified in the technical standards.

Newly designed identifying method for ice thickness on high‐voltage transmission lines via machine vision

The icing of transmission lines will bring considerable challenges to the safe operation of the power grid. Therefore, a novel method combines machine vision and machine learning algorithms for identifying the ice thickness on high-voltage transmission line (HVTL) as proposed herein. First, noise and background interference in the image are filtered, and the grey image is used as input. Then, the algorithms of improved Canny edge detection, Hough transform, improved K-means clustering, and least-squares fitting are adopted in turn to locate the edges of conductors. Finally, according to the distance mapping model based on monocular vision, the ice thickness of the conductor is determined by calculating the width difference before and after icing. The experimental results show that the proposed method can accurately locate the edge of the conductor in both field and experimental environments. Moreover, it can ensure ideal effects under different illumination and hardly not be affected by distortion in both horizontal and vertical directions. Besides, the distance mapping model can map the pixel distance to the actual distance with high precision, no matter whether the background is simple or complex, and the calculated ice thickness has only a small deviation compared to the actual value. In addition, the proposed method shows high reliability and effectiveness when various interference such as different backgrounds, uneven icing, height difference changes, conductor movement, contrast changes, and conductor sag occur.

Vibration behavior of an overhead conductor under updraft winds

At present, the wind-induced response analysis of an overhead conductor is mainly based on the action of horizontal normal wind. However, for crossing hillsides or extremely strong winds, such a conductor will bear the action of updraft wind, which will change the geometry of the conductor and make its structural dynamic characteristics nonlinear to some extent. In this work, the in-plane and out-of-plane two-dimensional nonlinear equations were established under the action of self-weight and updraft wind. Furthermore, the improved equations of conductor tension and sag were obtained, and the wind-induced vibration response was further investigated. The results showed that the updraft wind caused the nonlinearity of the tension and sag of the overhead conductor, and the nonlinear geometric change significantly affected its resonance response, which exceeded 25% if the wind speed was 50 m/s. In addition, because the proportion of the resonance response in the total wind-induced response was different, the influence of the wind attack angle calculated using the gust response factor method on the gust response factor was slightly larger than that calculated using the the American society of civil engineers method.

Model of own harmonic conductor oscillations for tasks of monitoring the status of airline power transmission lines

The article substantiates the relevance of the inspection of overhead power lines by determining the mechanical loads of the conductors. The conductor sways under the action of external loads and variable internal mechanical loads. The conductor behaves in span like a pendulum. Using the inclinometric method, it is possible to determine the deviations of the conductor in space from its equilibrium position. Having restored the geometry of the conductor in the span of an overhead power line, mechanical loads can be determined. A model of the harmonic oscillations of the conductor in flight is derived to assess the mechanical loads of the conductor overhead power lines. This mathematical model is based on mathematical models of a flexible thread and a model of a physical pendulum. A conductor is a physical pendulum, where the conductor acts as the body, and in the role of the fixed axis of rotation, a straight line passing through the suspension points of the conductor. The developed model allows you to determine the arrow of its sag from the period of oscillations of the conductor in the span. The article considers algorithms for calculating the conductor sag arrows for two cases: the conductor suspension points are at the same height; conductor suspension points are at different heights. A theoretical calculation is given for a model of a span overhead power line with an estimate of the sensitivity of the developed model and its error in determining the sag of the conductor. Using the arrow of the conductor sag, you can restore its geometry, and hence the mechanical load of the conductor. Therefore, knowing the initial geometric parameters of the span of the overhead power line and the current period of the conductor’s oscillations, it is possible to examine its current state.

ASA Algorithm Combined with Current Simulation Method (CSM) for the Magnetic Induction under HV Power Lines in 3D Analysis Model

In this paper, a new hybrid approach to modeling the magnetic induction produced by HV overhead power line which combines the current simulation method (CSM) and adaptive simulated annealing algorithm (ASA) is discussed. The aim of the ASA algorithm is to find the optimal position and number of current loops used in bundles conductors for an accurate magnetic induction. Several parameters affecting the magnetic induction have been studied; it is observed that, taking into account the effect of conductor sag is much more interesting particularly at the mid-span length where the magnetic induction becomes very significant, the results also indicated that the maximum magnetic induction levels are less than the limits recommended by the ICNIRP standard for general public and occupational exposure. The calculated results are compared with those obtained from the COMSOL 4.3a Multiphysics software. A good agreement has been reached.

Numerical Algorithms for Calculating Temperature, Layered Stress, and Critical Current of Overhead Conductors

Accurate calculation of temperature, stress, sag, and critical current (corresponding to critical temperature) of operational overhead conductors is important for ensuring the strength and sag safety of overhead lines. Based on 2D steady-state heat transfer equations, this article studies the temperature fields of the cross section of typical electrified conductors and establishes numerical simulation methods for calculating the layered stress, sag, and critical temperature. Using the algorithm, the relationship between the critical temperature and characteristics of conductors (e.g., the sag and tensile force) is studied. The results are verified by a comparison with the test results for heat-resistant aluminum alloy conductors JNRLH1/G1A-400/65 and JNRLH1/G1A-630/55. Finally, the paper studies the relationship between the critical temperature of the conductor and its most sensitive factors.

Noncontact Monitoring of Overhead Transmission Lines Using Space Potential Phasor Measurements

Power system reliability requirements necessitate the development of measurement systems to monitor the operational state of critical transmission lines. In this article, a novel noncontact method for monitoring overhead transmission lines is proposed. The method is based on measuring the amplitude and relative phase of the transmission line’s space potential at two or more strategically located points in space along with the use of passive phase shifters to enhance the sensitivity of the measurements. Applications of voltage unbalance and conductor sag measurements are demonstrated along with the results of conductor sag measurements on an operating 230-kV transmission line. It is shown that using enhanced relative phase measurements can significantly improve the sensitivity of the measurements.

Characteristics of Heat Resistant Aluminum Alloy Composite Core Conductor Used in overhead Power Transmission Lines.

The heat resistant aluminum alloy wire composite material core conductor (ACCC/HW) which was used in overhead transmission lines is developed and studied in this work. The composite material core is carbon fiber/glass cloth reinforced modified epoxy resin composite. Tensile stress tests and stress-strain tests of both composite core and conductor are taken at 25 °C and 160 °C. Sag test, creep test and current carrying capacity test of composite conductor are taken. The stress of composite conductor are 425.2 MPa and 366.9 MPa at 25 °C and 160 °C, respectively. The sag of conductor of 50 m length are 95 mm, 367 mm, and 371 mm at 25 °C, 110 °C, and 160 °C, respectively. The creep strain are 271 mm/km, 522 mm/km, and 867 mm/km after 10 years under the tension of 15% RTS (Rated Tensile Strength), 25% RTS and 35% RTS at 25 °C, and 628 mm/km under 25% RTS at 160 °C, according to the test result and calculation. The carrying capacity of composite conductor is basically equivalent to ACSR (Aluminum Conductor Steel Reinforced). ACCC/HW is suitable in overhead transmission lines, and it has been used in 50 kV power grid, according to the results.

Conductor sag comparison for 132 kV overhead transmission line improvement in Malaysia

This paper presents conductor sag comparison for 132 kV overhead transmission line improvement in Malaysia. Increasing industrialization and population growth around the world demands higher electricity supply. Power generation has yet to decline but transmitting sufficient electricity to consumers is worrisome due to scarce land space occupied by rapid urbanization. Hence reconductoring method was chosen to improve existing 132 kV overhead transmission line in Malaysia. A group of selected conductors were chosen for comparison where the high temperature low sag conductor stood out the most producing up to 40% sag reduction. This paper focuses on providing conductor alternatives to improve maximum sag of lowest conductor to ground for 132 kV transmission line in Malaysia in accordance to her climate and geographical factor.