Sag monitoring method and device for bipolar direct current overhead line

Abstract

The embodiment of the invention provides a sag monitoring method and device for a bipolar direct-current overhead line, and belongs to the technical field of high voltage. Accurate inversion and real-time monitoring of the conductor sag are achieved based on the ground wire induction current, and the core defects that in the prior art, interference of severe weather and limitation of a high-potential environment exist, and a monitoring system is poor in robustness are effectively overcome. By establishing a quantitative relation model of the ground wire induction current and the conductor sag, full-process online analysis from current acquisition, signal processing to sag calculation is realized, sag monitoring accuracy, environmental adaptability and system automation level are remarkably improved, safe operation of a power transmission line is guaranteed, and the safety of the power transmission line is improved. And the long-term stable monitoring capability and the engineering applicability under complex working conditions are enhanced.

Description

Technical Field

[0001] This invention relates to the field of high voltage technology, and in particular to a method, apparatus, equipment and storage medium for monitoring the sag of a bipolar DC overhead line. Background Technology

[0002] Overhead transmission lines are the "main arteries" of the power system and also the weakest link in the safe operation of the power grid, accounting for more than 40% of all grid faults. my country has over 1.5 million kilometers of overhead lines at voltage levels of 110kV and above, with a large number located in remote and desolate areas. Line operation and maintenance is the most demanding task for the power grid. Traditional manual line inspections are extremely difficult and lack timeliness. Although a large number of drones and helicopters are currently deployed, along with extensive image monitoring equipment, these methods are difficult to apply in weather conditions most prone to accidents, such as strong winds, rain, snow, and heavy fog. Furthermore, the timing and location of many abnormal conditions are highly random. Therefore, there is an urgent need to develop all-weather real-time online monitoring technology for transmission lines.

[0003] Extensive research has been conducted both domestically and internationally to address the various condition monitoring needs of overhead transmission lines, and some of the results have already been applied in engineering projects. Statistics on fault causes show that, compared to tower failures (tower collapse, loose bolts, etc.) and transmission channel intrusion (tree obstruction, external damage, etc.), abnormal conditions related to conductors and ground wires (lightning strikes, wind deflection, icing, galloping, etc.) are the primary causes of line faults. Monitoring conductor and ground wire sag can effectively identify conditions such as icing, galloping, and wind deflection, enabling timely identification and early warning of potential fault factors. This is of great significance for improving the efficiency of transmission line operation and maintenance and reducing maintenance costs.

[0004] Traditional methods for monitoring sag include: image sensing to identify conductor sag; measuring the inclination angle or tension of the conductor suspension point to calculate sag; measuring conductor temperature to calculate sag; and deploying a magnetic field sensor array around the conductor to estimate sag. However, all of these methods have certain drawbacks. Image recognition requires high image quality and cannot be effectively monitored in rainy or foggy conditions; inclination or tension sensors need to be directly installed on high-voltage conductors, which is inconvenient; temperature sensors are difficult to effectively measure the temperature at the conductor's center, and their measurement results are greatly affected by environmental factors; the method of using a magnetic field sensor array to estimate conductor sag has very strict requirements for sensor placement, and there are many influencing factors of the magnetic field around the conductor, making the back-calculation complex and difficult to apply in practice.

[0005] During operation, DC transmission lines generate harmonic currents of different frequencies on their DC side due to the nonlinear characteristics of the converter. Because of the mutual inductive coupling between the conductors and ground wires, the harmonics in the DC line conductor current induce an electromotive force (EMF) in the loop formed by the two ground wires and the ground wire crossarm. For lines with ground wires grounded base by base, this induced EMF induces a current in the loop. The coupling relationship between the conductors and ground wires is affected by the distance between them. When the sag of the conductors and ground wires changes, the distance between them changes, and the induced harmonic current in the ground wires also changes. Therefore, the ground wires can serve as natural sensors for sensing changes in the spatial electromagnetic field and thus various states of the line. By establishing a spatial electromagnetic model of the overhead line and combining it with conductor and ground wire current data, the sag of the conductors and ground wires can be calculated. Summary of the Invention

[0006] The present invention aims to at least partially solve one of the technical problems in the related art.

[0007] To address this, this invention proposes a method for monitoring the sag of bipolar DC overhead lines based on an electromagnetic coupling model and real-time magnetic field measurement. By integrating conductor thermal balance calculation and harmonic current analysis, and using a heuristic algorithm for iterative solution, the method achieves accurate monitoring and evaluation of conductor sag.

[0008] Another objective of this invention is to provide a sag monitoring device for bipolar DC overhead lines.

[0009] The third objective of this invention is to provide a computer device.

[0010] The fourth objective of this invention is to provide a non-transitory computer-readable storage medium.

[0011] To achieve the above objectives, the present invention provides a method for monitoring the sag of a bipolar DC overhead line, comprising: S1. Based on the static parameters of the line, establish an electromagnetic coupling model of the conductor and ground wire within one range, and calculate the conductor's self-impedance and mutual impedance. S2, by measuring the spatial magnetic field through a magnetic field sensor installed at the crossarm of the tower, and combining it with the real-time DC current data of the line, the amplitude ratio of the harmonic current of each frequency of the conductor to the DC current is calculated, and the absolute value of the harmonic current is obtained. S3. Calculate the surface temperature of the conductor based on the conductor thermal balance equation, and estimate the conductor sag as an initial constraint by combining the conductor specific load, thermal expansion coefficient, elastic modulus and cross-sectional area. S4 uses the estimated value of the conductor sag as a constraint input to the conductor electromagnetic coupling model, and employs a heuristic algorithm to iteratively solve for the specific value of the conductor sag by taking multiple measurements over a short period of time and calculating the average value.

[0012] The sag monitoring method for a bipolar DC overhead line according to an embodiment of the present invention may also have the following additional technical features: In one embodiment of the present invention, the step of establishing a conductor-to-ground electromagnetic coupling model within a certain range based on the static parameters of the line, and calculating the conductor's self-impedance and mutual impedance, includes: S11, through formula Calculate the conductor self-impedance considering the skin effect ; S12, through formula Calculate the mutual inductance impedance between the conductor and ground ,in The depth of penetration; S13, through formula Calculate the self-impedance of the conductor; where, This is the self-impedance of the conductor.

[0013] In one embodiment of the present invention, the step of measuring the spatial magnetic field by a magnetic field sensor installed at the crossarm of the tower, calculating the amplitude ratio of the harmonic current at each frequency of the conductor to the amplitude generated by the DC current in combination with real-time DC current data of the line, and obtaining the absolute value of the harmonic current includes: S21. Install the magnetic field sensor at the crossarm of the tower. By measuring the ratio of the magnetic field amplitude generated by the harmonic current of each frequency of the conductor to that of the DC current at the same location, and combining the characteristic that the current direction of the bipolar DC line conductor is opposite, calculate the absolute value of the harmonic current.

[0014] In one embodiment of the present invention, the step of calculating the conductor surface temperature based on the conductor thermal balance equation and estimating the conductor sag as an initial constraint by combining the conductor specific load, coefficient of thermal expansion, elastic modulus, and cross-sectional area includes: S31, through formula Calculate the heat dissipation power of the conductor by natural convection. ; S32, through formula Calculate the heat dissipation power of the conductor radiation ; S33, according to the conductor heat balance equation Calculate the surface temperature of the conductor and combine it with the conductor specific load. Coefficient of thermal expansion Elastic modulus and cross-sectional area Using the formula Estimate the sag of the conductor as an initial constraint.

[0015] In one embodiment of the present invention, the step of using the estimated value of the conductor sag as a constraint to input the electromagnetic coupling model of the conductor and ground wire, and using a heuristic algorithm to iteratively solve for the specific value of the conductor sag by multiple measurements over a short period of time and calculating the average value includes: S41, through formula A nonlinear relationship between the induced current in the ground wire and the current in the conductor is established, and the sag value estimated by thermal balance is used as the upper and lower limits of the initial iteration range of the algorithm. S42, by measuring conductor current data multiple times over a short period of time and calculating the average value of conductor sag within the corresponding period.

[0016] To achieve the above objectives, another aspect of the present invention provides a sag monitoring device for a bipolar DC overhead line, comprising: The conductor impedance calculation module is used to establish an electromagnetic coupling model of conductors and ground wires within a certain range based on the static parameters of the line, and to calculate the conductor's self-impedance and mutual impedance. The magnetic field measurement and harmonic calculation module is used to measure the spatial magnetic field through a magnetic field sensor installed at the crossarm of the tower, and calculate the amplitude ratio of the harmonic current at each frequency of the conductor to the DC current by combining the real-time DC current data of the line, and obtain the absolute value of the harmonic current. The conductor temperature and sag estimation module is used to calculate the conductor surface temperature based on the conductor thermal balance equation, and estimate the conductor sag as an initial constraint by combining the conductor specific load, thermal expansion coefficient, elastic modulus and cross-sectional area. The sag iterative solution module is used to input the electromagnetic coupling model of the conductor and ground wire with the estimated value of the conductor and ground wire sag as a constraint, and to use a heuristic algorithm to iteratively solve for the specific value of the conductor and ground wire sag by taking multiple measurements over a short period of time and calculating the average value.

[0017] This invention discloses a method and apparatus for sag monitoring of bipolar DC overhead lines. By integrating electromagnetic coupling modeling, non-contact magnetic field harmonic measurement, and conductor thermal balance analysis, it effectively overcomes the limitations of traditional manual inspection or single-sensor methods in terms of accuracy, real-time performance, and environmental adaptability. It achieves a closed-loop calculation process from electromagnetic parameter calculation, current inversion, temperature estimation to iterative sag solution, significantly improving the automation level of sag monitoring and the accuracy of measurement results. This provides reliable technical support for real-time status assessment and safety early warning of DC overhead lines, enhancing the intelligence level and operational reliability of power grid operation and maintenance.

[0018] To achieve the above objectives, a third aspect of this application provides a computer device comprising a processor and a memory; wherein the processor runs a program corresponding to the executable program code by reading executable program code stored in the memory, for implementing a sag monitoring method for a bipolar DC overhead line as described in the first aspect embodiment.

[0019] To achieve the above objectives, a fourth aspect of this application provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements a sag monitoring method for a bipolar DC overhead line as described in the first aspect embodiment.

[0020] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0021] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein: Figure 1 A flowchart illustrating a method for monitoring the sag of a bipolar DC overhead line, provided as an embodiment of the present invention; Figure 2 The tower equivalent impedance diagram is shown in the specific process of a method for monitoring the sag of a bipolar DC overhead line provided in an embodiment of the present invention. Figure 3 A structural diagram of the ground wire harmonic current calculation method for a specific process of a sag monitoring method for a bipolar DC overhead line provided in an embodiment of the present invention; Figure 4 A flowchart illustrating the reverse calculation of conductor sag for a specific process of a bipolar DC overhead line sag monitoring method provided in this embodiment of the invention. Figure 5 The ground wire current spectrum of an actual transmission line is shown in the simulation test of a sag monitoring method for a bipolar DC overhead line provided in this embodiment of the invention. Figure 6 A tower model diagram for simulation testing of a sag monitoring method for a bipolar DC overhead line provided in an embodiment of the present invention; Figure 7 Spatial magnetic field distribution diagrams at the same current amplitude and different frequencies for simulation testing of a sag monitoring method for a bipolar DC overhead line provided in an embodiment of the present invention; Figure 8 A simulation example of a sag monitoring method for a bipolar DC overhead line provided in this embodiment of the invention, showing the line structure diagram. Figure 9 A bar chart illustrating the influence of ground wire current measurement error on a simulation test of a sag monitoring method for a bipolar DC overhead line provided in an embodiment of the present invention. Figure 10 A bar chart illustrating the influence of conductor current measurement error on a simulation test of a sag monitoring method for a bipolar DC overhead line provided in an embodiment of the present invention. Figure 11A bar chart illustrating the impact of ground wire sag estimation error on a simulation test of a sag monitoring method for a bipolar DC overhead line provided in an embodiment of the present invention. Figure 12 A bar chart illustrating the impact of conductor sag estimation error on a simulation test of a sag monitoring method for a bipolar DC overhead line provided in an embodiment of the present invention. Figure 13 A schematic diagram of the structure of a sag monitoring device for a bipolar DC overhead line provided in an embodiment of the present invention; Figure 14 It is a computer device according to an embodiment of the present invention. Detailed Implementation

[0022] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0023] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0024] The following description, with reference to the accompanying drawings, describes a method, apparatus, equipment, and storage medium for monitoring the sag of a bipolar DC overhead line according to an embodiment of the present invention.

[0025] The core idea of ​​this invention is to construct a multi-physics field coupled sensing system that integrates electrical, magnetic, and thermodynamic parameters, thereby unifying and collaboratively analyzing the static parameters of the line, spatial magnetic field measurement data, and the real-time operating status of the conductor. Based on the conductor-ground wire electromagnetic coupling model, the conductor harmonic current is inverted, and combined with the conductor thermal balance equation and material mechanical properties, a preliminary intelligent estimation of sag is achieved to form an effective physical constraint. Building upon this, a heuristic algorithm is introduced to iteratively solve and dynamically calibrate the sag. Through multiple short-time measurements and averaging, the traditional sag monitoring method, which relies on a single measurement or static model, is upgraded to a high-precision online monitoring system integrating multi-source sensing, model constraints, and intelligent optimization. Ultimately, this significantly improves the accuracy, adaptability, and engineering reliability of sag calculation in complex operating environments.

[0026] Example 1 To achieve the above invention, embodiments of the present invention provide a method for monitoring the sag of a bipolar DC overhead line, such as... Figure 1 As shown, it includes: S1. Based on the static parameters of the line, establish an electromagnetic coupling model of the conductor and ground wire within one range, and calculate the conductor's self-impedance and mutual impedance.

[0027] Specifically, the static parameters of the circuit must first be obtained and input. These parameters include, but are not limited to, the geometric arrangement of the conductors and ground wires, their relative spatial positions, conductor radii, and inherent properties such as conductor material. Based on these precise physical parameters, a distributed parameter model is established using methods such as the magnetic vector potential method or the method of images from electromagnetic field theory. This model can accurately describe the electromagnetic induction and electrostatic coupling relationship between the conductors and ground wires within a given circuit. The core output of this model is the calculation of the conductor's self-impedance and the mutual impedance between the conductors and ground wires. This calculation process essentially quantifies the characteristics of the electrical loop formed by the conductors and ground wires, laying an indispensable theoretical foundation and precise mathematical relationships for subsequent current inversion through the magnetic field and subsequent calculation of sag.

[0028] Furthermore, in engineering practice, changes in the sag of transmission lines directly alter the relative spatial positions of conductors and ground wires, thus sensitively affecting electrical parameters such as mutual impedance. Therefore, this precise electromagnetic coupling model acts as a "digital twin," mapping minute deformations in the physical world to changes in electrical parameters. This allows us to indirectly and non-contactly perceive the mechanical state of conductors without direct contact with high-potential wires, simply by monitoring model-related electrical quantities (such as induced current in the ground wire). This provides a fundamental prerequisite for all-weather, highly secure online monitoring.

[0029] Specifically, by introducing a rigorous electromagnetic coupling mechanism, a deep physical connection for state perception is established. This not only significantly improves the scientific rigor of the model and the accuracy of the results, but more importantly, it provides a precise mathematical and physical framework for subsequent steps where the estimated sag value is substituted into the model as a constraint for iterative solution. This ensures the reliability and innovation of the final results of the entire monitoring method and provides solid support for the claims.

[0030] Furthermore, S1 includes: S11, through formula Calculate the conductor self-impedance considering the skin effect .

[0031] Specifically, this step is based on electromagnetic field theory and takes into account the uneven current distribution caused by the skin effect in the conductor due to high-frequency current, thereby calculating the conductor's self-impedance more accurately and providing basic parameter support for the subsequent reverse calculation of the conductor sag.

[0032] Specifically, this formula introduces a first-class Kelvin function. and and its first derivative and This describes the distribution characteristics of high-frequency current inside a conductor. Among them, Let be the outer radius of the conductor. Let be the volume resistivity of the conductor. Angular frequency, For parameters related to skin depth, Let be the permeability of the conductor. This formula represents the internal impedance of the conductor. Decompose into resistance and inductor The term consists of two parts: the inductance term reflects the distribution characteristics of the magnetic field inside the conductor, while the resistance term reflects the increase in resistance caused by the skin effect.

[0033] Furthermore, the key parameters involved in this formula include the outer radius of the conductor. Volume resistivity magnetic permeability and angular frequency In practical applications, conductor materials and Typical values ​​can be selected according to the DL / T 620-1997 standard, for example, for steel-cored aluminum stranded wire. Usually in Magnitude Near vacuum permeability Angular frequency This is determined by the harmonic frequency generated by the converter in the DC transmission system, typically in... Hz ( (within the range of positive integers).

[0034] Specifically, this step is mainly used to establish the electromagnetic coupling model of the conductor and ground wire in a bipolar DC transmission line. This involves calculating the self-impedance considering the skin effect. This model can more accurately describe the propagation characteristics of high-frequency currents in conductors, thereby improving the modeling accuracy of the coupling relationship between ground wire induced current and conductor current. This model will serve as the basis for subsequent measurements of the spatial magnetic field using a magnetic field sensor and for inferring the ground wire sag by combining conductor current data.

[0035] Specifically, this step effectively improves the physical accuracy of the electromagnetic coupling model, especially under the influence of high-frequency harmonic currents, enabling a more realistic reflection of the current distribution and impedance characteristics inside the conductor. This is significant for subsequent calculations of the ground wire induced current and for inverse calculations of sag using the thermal balance equation, helping to improve the robustness and calculation accuracy of the monitoring system, thereby achieving high-precision online monitoring of conductor sag.

[0036] S12, through formula Calculate the mutual inductance impedance between the conductor and ground ,in The depth of penetration.

[0037] Specifically, this step first introduces the multiple penetration depth. Its definition ,in Angular frequency, Vacuum permeability ( ), Soil electrical conductivity (unit: ) The penetration depth (DD) describes the attenuation characteristics of electromagnetic waves propagating in non-ideal conductors (such as the earth) and is an important parameter for calculating the mutual inductance impedance between a conductor and the ground. In practical applications, soil conductivity... Typically, the values ​​are set according to the typical values ​​recommended in DL / T 620-1997 "Code for Design of Overvoltage Protection of AC Electrical Installations", for example, based on samples taken in damp soil. Take from dry soil .

[0038] Furthermore, the mutual inductance impedance between the conductor and ground The calculation formula is ,in The conductor's height above the ground (unit: ), The outer radius of the conductor (unit: ) This formula is based on the principle of the method of images, treating the earth as a medium with finite conductivity, thus introducing the concept of multiple penetration depth. To correct the electromagnetic coupling effect between the conductor and the ground. In practical applications, It is usually determined by the tower structural parameters and the height of the conductor / ground wire suspension point, while The physical specifications of the conductor or ground wire shall be given.

[0039] Specifically, this step is mainly used to construct an electromagnetic coupling model of the conductor and ground wire within a line, providing a foundation for subsequent calculations of induced harmonic currents in the ground wire. Through accurate calculations... This can more accurately describe the mutual inductance between the conductor and the ground, thereby improving the accuracy of induced current calculation and providing reliable data support for sag calculation.

[0040] Specifically, this step involves introducing multiple penetration depths. This effectively considers the ground's effect on electromagnetic field dispersion, improving the physical accuracy of the impedance model. In high-frequency harmonics (such as...), , Under the condition that the value is a positive integer, the model can more realistically reflect the electromagnetic coupling characteristics between the conductor and the ground, providing key input parameters for the subsequent sag back-calculation algorithm, thereby improving the robustness and accuracy of the entire monitoring system.

[0041] S13, through formula Calculate the self-impedance of the conductor; where, This is the self-impedance of the conductor.

[0042] Specifically, It primarily characterizes the impedance component generated by the skin effect, proximity effect, and the conductor's own resistance when current flows inside a conductor. Its calculation requires comprehensive consideration of the AC frequency, the conductor material's conductivity, and its magnetic permeability. This characterizes the induced impedance corresponding to the external magnetic field of the conductor (i.e., the spatial magnetic field outside the conductor's outer surface). Its value is closely related to the conductor's geometric radius, suspension height, and other spatial structural parameters. By vector superimposing these two impedances, the complete self-impedance parameters of the conductor at a specific operating frequency can be obtained, thus laying a solid theoretical foundation for the subsequent accurate calculation of the induced current in the ground wire.

[0043] Furthermore, in the physical structure of transmission lines, the self-impedance of the conductor is one of the core electrical parameters determining its current carrying capacity, energy loss, and electromagnetic environment influence. Precise quantification using this formula allows the model to accurately reflect the actual electrical behavior of the conductor under high-frequency harmonic currents, rather than relying on assumptions of an ideal conductor or a simplified model. The direct value of this precise calculation lies in ensuring the accuracy of the subsequent indirect measurement method of inverting the conductor current by measuring the spatial magnetic field. If there is a deviation in the self-impedance calculation, it will lead to distortion of the inverted current value and ultimately amplify the calculation error of sag. Therefore, this step is a crucial cornerstone in ensuring the reliability of the final result in the entire "magnetic field sensing - current inversion - sag calculation" technical chain.

[0044] Specifically, existing technologies either ignore the frequency characteristics of internal impedance during modeling and use DC resistance approximation, or idealize external impedance, both of which introduce significant errors in harmonic analysis. This step, by rigorously distinguishing and synthesizing internal and external impedances, provides a more accurate parameter calculation method that better reflects the high-frequency operating characteristics of the line. This is not a simple formula application, but a crucial improvement in model accuracy specifically for the technical problem of "sag monitoring." It constitutes an important technical feature that distinguishes the entire invention from traditional estimation methods, providing indispensable parameter guarantees for ultimately achieving high-precision sag monitoring, thus strongly supporting the non-obviousness of the claims.

[0045] S2 measures the spatial magnetic field by installing a magnetic field sensor at the crossarm of the tower, and calculates the amplitude ratio of the harmonic current at each frequency of the conductor to the DC current by combining the real-time DC current data of the line, thereby obtaining the absolute value of the harmonic current.

[0046] Specifically, this step is based on the principle of electromagnetic induction. It uses a magnetic field sensor to collect the magnetic field distribution generated by the harmonic current in the conductor in space, and combines it with known DC current data. By using the linear relationship between magnetic field strength and current, the amplitude of each frequency harmonic current is deduced.

[0047] In practical implementation, the magnetic field sensor typically employs a high-sensitivity triaxial fluxgate sensor or Hall effect sensor, installed on the tower body or crossarm, at a horizontal distance of approximately [missing information - likely related to conductor movement]. The sensor's placement must avoid ferromagnetic components to minimize interference from the tower structure on the magnetic field measurements. The magnetic field data acquired by the sensor includes multiple frequency components, with particular attention focused on those generated by the converter. (n is a positive integer) Frequency harmonics. The magnetic field amplitude of each frequency component can be extracted using Fourier transform or spectral analysis. .

[0048] Furthermore, at the same time, the real-time DC current of the line The current is obtained from a current transformer or DC current sensor installed on the conductor, and its measurement accuracy should meet the error requirements for DC current sensors in IEC 60044-8, typically within ±1%. Under known conditions... Under the premise of establishing a coupling model between conductor current and magnetic field, the magnetic field generated by direct current can be calculated. Since both direct current and harmonic currents of various frequencies exist simultaneously in the conductor, its total magnetic field can be expressed as:

[0049] By separation and By calculating the ratio of the magnetic field generated by the harmonic current at each frequency to that generated by the direct current, the amplitude of the harmonic current at each frequency can be deduced. This method avoids the complexity and high risk of directly mounting sensors on wires, while utilizing the non-contact characteristics of magnetic field sensors to achieve stable measurements under adverse weather conditions.

[0050] Specifically, this step plays a crucial role in the overall technical solution, providing key input parameters for subsequent inverse calculation of conductor sag using electromagnetic coupling models and thermal balance equations. Its technical value lies in two aspects: firstly, acquiring harmonic current information through a magnetic field sensor reduces equipment installation difficulty and maintenance costs; secondly, combining real-time DC current data improves the accuracy and reliability of harmonic current measurement, providing a solid data foundation for the sag inverse calculation algorithm under multiple physical constraints.

[0051] Furthermore, S2 includes: S21. Install the magnetic field sensor at the crossarm of the tower. By measuring the ratio of the magnetic field amplitude generated by the harmonic current and the DC current at the same location, and combining the characteristic that the current direction of the bipolar DC line conductor is opposite, calculate the absolute value of the harmonic current.

[0052] Specifically, in some implementations, this invention uses a magnetic field sensor installed at the crossarm of the tower to measure the ratio of the magnetic field amplitude generated by the conductor harmonic current and the direct current at the same location. Combining this with the characteristic that the conductor currents in a bipolar DC line are in opposite directions, the absolute value of the harmonic current is calculated. This step is one of the key steps in realizing the reverse calculation of conductor sag, and its technical principle is based on the law of electromagnetic induction and the frequency domain characteristics of conductor current.

[0053] Specifically, a highly sensitive magnetic field sensor is installed at the crossarm of the tower. The sensor should be capable of responding to signals at frequencies in the kHz range to capture harmonic currents generated in the conductors due to the nonlinear characteristics of the converter. Since the currents in the positive and negative conductors of a bipolar DC line are in opposite directions, the magnetic fields they generate at the crossarm cancel each other out at DC frequencies, but at harmonic frequencies, a measurable magnetic field amplitude is formed due to phase and amplitude differences. By measuring the magnetic field amplitude at this location and calculating its ratio to the known magnetic field amplitude generated by the DC current, the amplitude ratio of the harmonic current to the DC current can be obtained.

[0054] Furthermore, the measurement frequency range of the magnetic field sensor should cover 300 Hz (n is a positive integer), which is the main spectral characteristic of the ground wire induced signal in actual lines. Simultaneously, the sensor's measurement accuracy should be no less than 0.1 μT to ensure reliable data acquisition even under weak magnetic field variations. During the calculation process, real-time conductor current data and an electromagnetic simulation model of the tower structure need to be combined to eliminate the interference of the tower on the magnetic field distribution. According to the simulation results, the tower structure has a relatively small impact on the magnetic field distribution, and the magnetic field amplitude is linearly related to the current amplitude; therefore, this method has high accuracy and stability.

[0055] Specifically, it typically works in conjunction with ground wire current sensors and micro-meteorological sensors to obtain the absolute value of conductor harmonic currents, providing crucial input for subsequent electromagnetic coupling model calculations and sag inference. Its technological value lies in eliminating the need to install complex sensors on the conductor; harmonic currents can be indirectly obtained solely through magnetic field measurements at the tower, reducing installation difficulty and maintenance costs while enhancing the robustness and adaptability of the monitoring system.

[0056] S3 calculates the conductor surface temperature based on the conductor thermal balance equation, and estimates the conductor sag as an initial constraint by combining the conductor specific load, thermal expansion coefficient, elastic modulus and cross-sectional area.

[0057] Specifically, this step first uses the thermal balance equation of the conductor. Establish conductor surface temperature The relationship with environmental parameters. Among them, The heat dissipation power is achieved through natural convection. For radiative heat dissipation power, The solar heat absorption power, This refers to the heat power generated by conductor resistance loss. This is achieved by measuring or acquiring wind speed. air temperature Sunlight intensity Micro-meteorological parameters, combined with the physical parameters of the conductor (such as outer diameter) , compared to load Elastic modulus Cross-sectional area Coefficient of thermal expansion Numerical solutions can be used to calculate the surface temperature of the conductor. Furthermore, assuming the internal temperature of the conductor is the same as its surface temperature, then... As the average temperature of the conductor The estimated value.

[0058] Furthermore, the conductor is more than the load Usually Order of magnitude, coefficient of thermal expansion Generally in Within the range, elastic modulus for Cross-sectional area It varies depending on the type of wire, and is usually in Between. Reference sag It is usually obtained through on-site calibration, while the actual sag This is the quantity to be estimated. Gear spacing. For line design parameters, generally in Within the range. By substituting the above parameters into the formula This allows for a preliminary estimation of the sag of the conductor.

[0059] Specifically, this step is applicable to online monitoring systems for bipolar DC transmission lines, especially under adverse weather conditions such as heavy fog, rain, and snow, where direct measurement methods (e.g., image recognition, tilt sensors) are lacking. By installing magnetic field sensors and micro-meteorological sensors on the towers, combined with real-time line operation data (e.g., DC current, solar radiation intensity), a preliminary estimate of conductor sag can be achieved, providing initial constraints for subsequent back-calculation algorithms based on electromagnetic coupling models.

[0060] Specifically, this step, through the combined application of thermodynamic and mechanical models, can provide a relatively accurate estimate of sag without direct contact measurement. The calculation results are used as initial constraints input into the electromagnetic simulation model, which helps improve the convergence speed and accuracy of subsequent back-calculation algorithms, maintaining good robustness even in the presence of measurement errors. This step plays a crucial bridging role in this invention, providing a reliable foundation for achieving all-weather, low-cost, and high-precision conductor sag monitoring.

[0061] Furthermore, S3 includes: S31, through formula Calculate the heat dissipation power of the conductor by natural convection. .

[0062] Specifically, this step quantifies the heat dissipation power of the conductor under natural convection conditions, providing thermodynamic constraints for subsequent sag calculation, thereby improving the accuracy and robustness of the monitoring results.

[0063] Specifically, this formula, based on the heat transfer theory of natural air convection, is used to calculate the heat dissipation power per unit length of conductor under natural convection conditions. In the formula, This represents the heat dissipation power from natural convection, in units of... ; Ambient air density, unit: ; The outer diameter of the conductor is given in units of 1. ; The surface temperature of the conductor. Ambient air temperature, unit: This formula, by modeling the nonlinear relationship between air density, conductor geometry, and temperature difference, can accurately reflect the heat dissipation characteristics of the conductor under conditions without forced wind.

[0064] Furthermore, air density The outer diameter of the conductor can be obtained in real time based on a standard atmospheric model or on-site micro-meteorological sensors. For line design parameters, usually in Within range; temperature difference Provided jointly by a conductor surface temperature sensor and an ambient temperature sensor, its typical value is in Between. This formula applies to calm or low wind speeds (less than). The calculation results of the natural convection condition can be used as an important input term in the conductor heat balance equation.

[0065] Specifically, this step is typically implemented in the online monitoring system of transmission lines, in conjunction with conductor radiative heat dissipation. Sunlight absorbs heat and forced convection cooling They participate in the heat balance calculation. By comprehensively considering various heat dissipation and heat absorption mechanisms, the average temperature of the conductor can be estimated. Furthermore, by combining the physical relationship model between sag and temperature, the sag value of the conductor can be deduced. This method does not require direct measurement of conductor tension or suspension point displacement; it relies only on available environmental parameters such as temperature, wind speed, and solar radiation intensity, making it highly applicable in engineering projects.

[0066] Furthermore, this step introduces a natural convection cooling model, providing more comprehensive physical constraints for the conductor's thermal balance and helping to improve the accuracy of sag estimation. Especially under windless or weak wind conditions, natural convection becomes the dominant cooling method, and this formula can effectively reflect the changes in the conductor's thermal state, thus providing reliable input data for the subsequent sag back-calculation algorithm and enhancing the system's adaptability and computational stability under complex weather conditions.

[0067] S32, through formula Calculate the heat dissipation power of the conductor radiation .

[0068] Specifically, the formula is derived from the basic physical principles of thermal radiation, combined with the surface temperature of the conductor. With ambient air temperature The difference is used to quantify the energy density lost by a conductor through thermal radiation in the natural environment, and the unit is 1. .

[0069] Specifically, the formula is based on the Stefan-Boltzmann law, which states that the radiant power of a blackbody is proportional to the fourth power of its absolute temperature. In the formula, Represents the surface area per unit length of wire, where The outer diameter of the conductor is given in units of 1. ; This is the radiation heat dissipation coefficient of the conductor surface. Its value range varies depending on the surface condition of the conductor. For new conductors, it is taken as... Take old or blackened lines. ; The Stefan-Boltzmann constant has a standard value of To ensure consistency in temperature units, Celsius temperatures are converted to Kelvin temperatures in the formula, i.e. and .

[0070] Furthermore, this step typically incorporates ambient temperature data collected by microclimate sensors. With the surface temperature of the conductor The calculation is performed. The surface temperature of the conductor can be estimated using an infrared thermometer or an indirect thermal balance model. This formula is applicable to natural heat dissipation environments without forced convection, especially under windless or low-wind conditions where radiation heat dissipation becomes the dominant heat dissipation method.

[0071] Specifically, by calculating the radiative heat dissipation power This can be further substituted into the conductor heat balance equation. With convection heat dissipation power and solar heat absorption power A comprehensive analysis is conducted to estimate the average temperature of the conductor. This temperature information is an indispensable input parameter in subsequent sag calculations. Through the thermal expansion effect and the stress-sag relationship model, the sag value of the conductor in its current state can be deduced. Therefore, this step plays a fundamental role in thermodynamic constraints and physical modeling in this invention, providing a crucial initial estimate for subsequent sag calculation based on the electromagnetic coupling model, significantly improving the algorithm's convergence efficiency and computational accuracy.

[0072] S33, according to the conductor heat balance equation Calculate the surface temperature of the conductor and combine it with the conductor specific load. Coefficient of thermal expansion Elastic modulus and cross-sectional area Using the formula Estimate the sag of the conductor as an initial constraint.

[0073] Specifically, the core principle of this step lies in the coupled analysis of the electrical-thermal-mechanical states of the conductor. The heat balance equation... The text describes the heat conservation of a conductor in steady state, including convective heat dissipation. With radiative heat dissipation The sum equals the heat absorbed by solar radiation. With electric current Joule heating The sum of the resistances It is temperature itself The function of this equation constitutes a nonlinear solution relationship. The surface temperature of the conductor, determined by this equation, is the fundamental driving force behind the thermal expansion and elongation of the conductor, which in turn leads to changes in sag. Subsequently, the state equation is used... The calculated temperature Compared with the conductor load Coefficient of thermal expansion Elastic modulus and cross-sectional area By combining mechanical and material parameters, a precise physical mapping from conductor temperature and mechanical stress to the final sag is established.

[0074] Specifically, the process begins by collecting environmental meteorological parameters (such as ambient temperature, wind speed, and solar radiation intensity) and line electrical parameters (operating current I) in real-time or near real-time. These parameters serve as inputs to the thermal balance equation, which is then iteratively solved using numerical methods to determine the precise surface temperature of the conductor. This temperature value, along with the conductor's actual stress state, inherent material properties (α, E, A), and mechanical load (specific load γ), are then substituted into the given state equation. This equation is essentially an overhead line deflection model that considers elastic elongation and thermal expansion effects, ultimately leading to the estimated sag value of the conductor.

[0075] Furthermore, in practical engineering applications, this step achieves a crucial transformation from the "invisible and intangible" conductor temperature to the "visible" conductor curvature. It enables the system to dynamically respond to changes in the conductor's thermal state caused by variations in sunlight, wind speed, and load current, thereby predicting sag in real time. This is equivalent to endowing the monitoring system with the capabilities of "thermal sensing" and "deformation prediction." Using this estimated sag as an initial constraint input into the subsequent electromagnetic coupling model significantly reduces the search space of the heuristic algorithm, transforming what was originally a blind search problem within a broad solution domain into a precise optimization problem within a physically defined, narrow neighborhood. This directly improves the convergence speed of the entire monitoring system and the reliability of the final results.

[0076] Specifically, existing technologies, relying solely on temperature measurements or using simplified mechanical models, struggle to guarantee accuracy under complex and variable weather conditions. This step, by introducing rigorous thermal balance principles and precise conductor state equations, provides a higher-order initial value estimation method that more closely approximates physical reality. This is not a simple formula superposition, but a non-obvious technical means designed to solve the technical challenge of "how to achieve high-precision sag monitoring under severe weather conditions." It significantly improves the robustness and accuracy of the entire method, providing strong substantive support for the claims.

[0077] S4 uses the estimated value of the conductor sag as a constraint input to the conductor electromagnetic coupling model, and employs a heuristic algorithm to iteratively solve for the specific value of the conductor sag by taking multiple measurements over a short period of time and calculating the average value.

[0078] Specifically, in the conductor sag back-calculation method of this invention, using the estimated sag value as a constraint input to the electromagnetic coupling model and employing a heuristic algorithm to iteratively solve for the specific value of the conductor sag is a key step in achieving high-precision sag monitoring. This step improves the accuracy and robustness of the back-calculation results by using the initially estimated sag value as the initial constraint condition for the optimization algorithm and combining it with the actually measured electromagnetic parameters to construct a nonlinear optimization problem involving multi-physics coupling.

[0079] Specifically, firstly, through the heat balance equation of the conductor ( Estimate the average sag of the conductor. This equation takes into account the natural convection heat dissipation of the conductor. Forced convection cooling Radiative heat dissipation and solar heat absorption By combining parameters such as wind speed, air temperature, conductor surface temperature, conductor outer diameter, and coefficient of thermal expansion, a quantitative relationship between conductor temperature and sag is established. Preliminary sag estimates are then obtained. Then, these constraints are input into a pre-constructed electromagnetic coupling model. This model, based on the geometry, material parameters, and earth properties of the conductors and ground wires, uses the image method and discrete calculation method to solve for the mutual impedance matrix between the conductors and ground wires. and self-impedance matrix And combined with the equivalent impedance model of the tower (such as formula) Simulation calculations of the induced current in the ground wire were performed.

[0080] Furthermore, heuristic algorithms (such as genetic algorithms and particle swarm optimization algorithms) are used to iteratively solve the model. The algorithm uses the estimated sag value as an initial constraint and continuously adjusts the sag parameters to minimize the error between the simulated ground wire induced current and the actual measured value. To improve calculation accuracy and reduce the influence of random errors, this invention employs a method of multiple measurements over short time periods, typically sampling multiple times within a time window of 10 seconds to 1 minute, and calculating the average value as the final input. This method... Figures 8 to 11 The simulation results validated this, showing that even with measurement errors, the back-calculation results still have high reliability.

[0081] Specifically, the sag estimation error is typically controlled within ±5%, and the sampling frequency of the magnetic field sensor is recommended to be no less than 100Hz to ensure complete capture of harmonic signals. Furthermore, the number of algorithm iterations is generally set to 50-100, and the convergence threshold can be set to [missing value]. Or even lower, to ensure the stability of the calculation results.

[0082] Specifically, this step is applicable to online monitoring systems for bipolar DC overhead transmission lines, particularly for real-time sensing of conductor and ground wire status under complex meteorological conditions (such as strong winds, icing, rain, and snow). By combining thermodynamic estimation with an electromagnetic coupling model, this invention effectively overcomes the problems of traditional methods, such as strong dependence on sensor placement and susceptibility to environmental interference. It achieves high-precision, low-cost, and easy-to-deploy monitoring of conductor and ground wire sag, demonstrating significant engineering practical value.

[0083] Furthermore, S4 includes: S41, through formula A nonlinear relationship between the induced current in the ground wire and the current in the conductor is established, and the sag value estimated by thermal balance is used as the upper and lower limits of the initial iteration range of the algorithm.

[0084] Specifically, in the conductor sag reverse calculation method of the present invention, the step "through formula" Establishing a nonlinear relationship between the induced current in the ground wire and the current in the conductor, and using the sag value estimated by thermal balance as the upper and lower limits of the initial iteration range of the algorithm, is one of the core steps in realizing online sag monitoring. Its technical implementation principle is based on the nonlinear relationship between the electromagnetic coupling model and the current in the conductor and the ground wire.

[0085] Specifically, this step first calculates the mutual impedance matrix between the ground wire and the conductor based on the electromagnetic coupling model of the transmission line. and the impedance matrix between the ground wire and the tower and .in, and These represent the impedance between the ground wire and the tower head at the beginning and end of the tower, respectively. This represents the self-impedance of the ground wire. By substituting these impedance matrices into the formula... It is possible to calculate the harmonic current in a known conductor. Under these conditions, the harmonic current induced in the ground wire This formula reflects the complex electromagnetic coupling relationship between conductors and ground wires, and has high physical modeling accuracy, especially when considering tower structures and ground mirror effects.

[0086] Furthermore, the impedance matrix involved in the formula needs to be determined based on the geometric parameters of the line (such as the height of the conductor and ground wire above the ground). Horizontal distance conductor radius ) and material parameters (such as the resistivity of the conductor) magnetic permeability Soil electrical conductivity ) is used for calculation. Among them, and These represent the internal impedance of the conductor and the self-impedance caused by the ground reflection, respectively. Their calculation requires the use of the first-type Kelvin function and its derivative to accurately reflect the skin effect and ground current dissipation effect under high-frequency harmonic currents. Furthermore, Used to describe the mutual impedance between conductors, its calculation requires consideration of the relative position and frequency characteristics of the conductors.

[0087] Specifically, this step is mainly used in bipolar DC transmission lines. By placing magnetic field sensors on the tower body or crossarm, the magnetic field generated by the conductor harmonic current in space is measured. Combined with the DC current data of the line, the amplitude of the harmonic current at each frequency is deduced. Subsequently, the ground wire induced current is calculated using the aforementioned formula, thus establishing a nonlinear relationship between the conductor current and the ground wire induced current. This relationship forms the basis for constructing the objective function and constraints in the subsequent sag calculation algorithm.

[0088] Furthermore, this step provides a reliable physical basis for sag estimation by accurately modeling the electromagnetic coupling relationship between the conductor and ground wire. Simultaneously, using the sag value estimated by thermal balance as the initial upper and lower limits of the iterative algorithm effectively improves the convergence speed and computational accuracy. This method exhibits good robustness in practical applications, ensuring the reliability of sag estimation results even in the presence of measurement errors, thus providing crucial data support for dynamic capacity expansion and icing monitoring of power lines.

[0089] S42, by measuring conductor current data multiple times over a short period of time and calculating the average value of conductor sag within the corresponding period.

[0090] Specifically, measuring conductor current data multiple times over a short period and calculating the average conductor sag during that period is a crucial step in improving monitoring accuracy and robustness. The core technical principle of this step lies in utilizing data redundancy in the time domain to reduce potential random errors or transient interference in a single measurement through statistical averaging, thereby improving the reliability of the sag back-calculation results.

[0091] Specifically, this step is typically performed in bipolar DC transmission lines with grounding conductors base-by-base. Magnetic field sensors installed on the tower body or crossarms are used to collect real-time data on the magnetic field distribution generated in space by harmonic currents in the conductors. Due to the electromagnetic coupling between the conductors and the ground wire, an induced current proportional to the conductor harmonic current will be induced in the ground wire. By measuring the magnetic field strength over multiple short time intervals (e.g., 10 seconds to 1 minute) and combining this with the known DC current amplitude, the amplitude of the conductor harmonic current at each frequency can be calculated. Furthermore, a conductor-ground electromagnetic coupling model (such as formula...) is used... The induced current in the ground wire is calculated, and the relative positional relationship between the ground wires, i.e., the sag value, is derived in reverse.

[0092] Furthermore, the duration of short time intervals needs to be optimized based on the system noise level and the rate of change of the electromagnetic field, generally controlled between 10 seconds and 1 minute to ensure the representativeness and stability of the data. Measurement frequencies are typically selected from 300Hz and its integer multiples (such as 600Hz, 900Hz, etc.), as these frequencies have significant harmonic spikes in actual circuits (e.g., ...). Figure 4As shown in the figure, this facilitates accurate identification and calculation. When calculating the average sag, a sliding window average or weighted average method can be used to further suppress instantaneous disturbances.

[0093] Specifically, due to the complex operating environment of transmission lines, including wind disturbance, temperature fluctuations, and electromagnetic interference, single measurements are easily affected by instantaneous errors. By taking multiple measurements over a short period and averaging them, the impact of measurement errors on the final back-calculation result can be effectively reduced, improving the stability of the algorithm. Furthermore, this method does not rely on high-precision, high-cost sensors; it only requires conventional magnetic field and current sensors, conforming to power industry standards such as DL / T 620-1997, and possesses good engineering applicability.

[0094] This invention discloses a method for monitoring sag in bipolar DC overhead lines. By establishing an electromagnetic coupling model of the conductor and ground wire and integrating non-contact magnetic field sensing with conductor thermal balance analysis, it effectively solves the core defects of existing technologies, such as high susceptibility to environmental interference, insufficient model accuracy, and reliance on direct measurement. This method achieves full automation from impedance calculation, harmonic current inversion, temperature and sag estimation to intelligent iterative solution, significantly improving the accuracy, environmental adaptability, and system robustness of sag monitoring. While ensuring the dynamic safety of transmission lines, it enhances their long-term monitoring effectiveness and engineering applicability under complex weather and load conditions.

[0095] Example 2 To achieve the above invention, embodiments of the present invention also provide a specific process for a bipolar DC overhead line sag monitoring method, including: An electromagnetic coupling model within a certain range is established based on the static parameters of the line. Real-time DC current data of the DC line is acquired. The magnitude of the harmonic current is obtained by measuring the ratio of the magnetic field generated by the harmonic current to that generated by the DC current using magnetic field sensors installed on the towers. Simultaneously, the conductor sag is roughly estimated based on the conductor heat balance equation. This estimate is then used as a constraint for a smart algorithm to solve the problem and obtain the specific value of the conductor sag. The specific sub-steps include: S101, Electromagnetic coupling relationship between conductor and ground wire of DC overhead transmission line and calculation method of ground wire induced current.

[0096] Specifically, in order to effectively reverse the sag of the conductors and ground wires, it is first necessary to establish an electromagnetic coupling model of the conductors and ground wires within the line. A bipolar DC overhead transmission line consists of two ground wires and two conductors. Assuming that neither the conductors nor the ground wires have sag, the ground wires, conductors, and the earth form a parallel multi-conductor system, and their mutual electromagnetic coupling relationship can be described by the system's impedance matrix.

[0097] Furthermore, the diagonal elements of the impedance matrix are called self-impedances. Self-impedances consist of two parts: one is the internal self-impedance of the line, which is equivalent to the impedance of an isolated conductor. Another part is due to the presence of the earth, and the impedance generated by the conductor and its interaction with the earth. .

[0098] Specifically, in calculation When considering the change in current distribution due to the skin effect, the calculation formula is as follows, based on relevant electromagnetic field theories:

[0099] in, Let the real and imaginary parts of the first type of Kelvin function be given. Its first derivative, Let be the outer radius of the conductor. Its volume resistivity.

[0100]

[0101] in, Let be the magnetic permeability of the conductor.

[0102] Furthermore, in using the mirror method to calculate Since the earth is not an ideal conductor, its effect on electromagnetic wave dispersion needs to be considered; therefore, the complex penetration depth is introduced. P ,have:

[0103] in, It calculates the angular frequency corresponding to the frequency. It is the vacuum permeability. It refers to soil electrical conductivity, which includes:

[0104] Therefore, the self-impedance of the conductor can be calculated:

[0105] Specifically, the off-diagonal elements of the impedance matrix are called mutual impedances, used to describe the mutual influence between different conductors in a multi-conductor system. Since the radius of a conductor in a transmission line is much smaller than the distance between conductors, the proximity effect can be ignored, and the conductor radius is neglected when calculating mutual inductance, thus obtaining the conductor... With conductor Formula for mutual impedance between:

[0106] in Represents the height of the two conductors above the ground. It represents the horizontal distance between the two conductors.

[0107] Furthermore, in actual operating lines, the conductor and ground wire exhibit sag. For a uniform conductor suspended at both ends, taking one end as the origin of the coordinate system, the horizontal direction is... Direction, vertically upwards. A coordinate system is established for the direction, and its geometry can be given by the following curve:

[0108] in, For the line span, The horizontal stress at various points on the wire is expressed in units of 1. , is the specific load of the wire, in units of Combine the above parameters into Then the shape of the conductor can be represented as:

[0109] Minimize the above formula to obtain the maximum sag of the conductor (referred to as sag):

[0110] When calculating the impedance matrix of a conductor with sag, a discrete calculation method can be used. This involves dividing the line into n segments along the span. Since the sag of an actual line generally does not exceed 5% of the span, all conductors in each segment can be considered parallel to the ground and to each other. Using formula (1-8), the impedance matrix of each segment can be calculated. The impedance matrix of a single span of the line is then calculated. It is the sum of the impedance arrays of each small segment.

[0111] Because the harmonic frequency in DC transmission lines can be as high as The calculation of induced harmonic current in the ground wire needs to take into account the tower impedance (e.g., Figure 2 As shown in the figure, this invention adopts the equivalent inductance model according to the DL / T620-1997 standard.

[0112] remember:

[0113] Another note:

[0114] This indicates the potential difference between the two ground wires at the beginning and end of the tower in a given range.

[0115]

[0116] If we represent the ground current of a first-order internal conductor, then:

[0117] At the first tower, there are:

[0118]

[0119]

[0120] in Indicates the potential at the top of the tower, in the subscript. Representing the first tower, the following is obtained:

[0121] Notation:

[0122] Similarly, at the end tower, we have:

[0123] From equations (13, 16-17), we can obtain:

[0124]

[0125] The induced harmonic current of the ground wire at different frequencies can be calculated according to equation (19). Figure 3 As shown). Equation (19) can be written as:

[0126] S102, Method for measuring harmonic current in conductors: Specifically, since the exact values ​​of conductor harmonic currents are generally difficult to obtain, this invention proposes to measure the magnetic field generated in space by harmonic currents in the conductor by installing a magnetic field sensor on the tower body or crossarm. For bipolar DC transmission lines, conductor harmonic currents follow a rule of equal magnitude and opposite direction within a certain range. Since the DC current data of the line is relatively easy to obtain, and the DC current does not change significantly along the line, the ratio of harmonic current to DC current can be obtained by measuring the ratio of the magnetic fields generated by currents at different frequencies, and further, the harmonic current value can be obtained.

[0127] S103, a method for estimating the average sag of a conductor and ground wire using the conductor heat balance equation.

[0128] The thermal equilibrium equation for the conductor is:

[0129] in, This indicates heat dissipation via convection in the conductor. This indicates heat dissipation via radiation from the conductor. This indicates that the conductor absorbs heat from sunlight. Heat dissipation power of natural convection in conductors:

[0130] in, It is air density. Indicates the outer diameter of the conductor. The surface temperature of the conductor. This refers to the air temperature.

[0131] The forced convection power of conductors in flowing air shall conform to the GB50545-2010 standard:

[0132] in, The heat transfer coefficient of the air layer on the surface of the conductor. It is the Reynolds number.

[0133]

[0134]

[0135]

[0136] Where V is the wind speed perpendicular to the conductor. It is the kinematic viscosity of the air layer on the surface of the conductor.

[0137] Radiative heat dissipation power of the conductor:

[0138] in, The radiation heat dissipation coefficient of the conductor surface is 0.23~0.43 for bright new wires and 0.9~0.95 for old wires or wires that have been blackened.

[0139] The solar heat absorption power of the conductor is:

[0140] in, The heat absorption coefficient of the conductor surface is 0.35~0.46 for new conductors and 0.9~0.95 for old conductors or conductors that have been blackened. To measure the solar radiation intensity on the conductor, when the sunlight is direct, a value of 1000 can be used. .

[0141] Furthermore, after calculating the surface temperature of the conductor, assuming that the internal temperature of the conductor is the same as the surface temperature, the relationship between the sag and the conductor temperature can be calculated. The specific method is as follows: Specifically, the conductor sag first needs to be calibrated in this way, and its value at a reference temperature needs to be measured. The lower sag Let the conductor span be . The specific load of the conductor (gravity per unit length) is The coefficient of thermal expansion of the conductor is The horizontal stress in the conductor is ,exist Under the conditions, there are

[0142] The length of the conductor in the first slot is:

[0143] Assuming the conductor length changes linearly with tension and temperature, then:

[0144] in, The cross-sectional area of ​​the conductor is... The elastic modulus of the conductor. For reference temperature, The length of the conductor is given at the reference temperature and under no horizontal stress. Let be the average temperature of the conductor. We have:

[0145] Record the result obtained by measuring the sag at the reference temperature as follows: Substituting this into the above equation, we have:

[0146] The above formula allows us to calculate conductor sag based on conductor temperature. Furthermore, based on thermodynamic analysis, given conductor current, temperature, and meteorological information such as illumination, we can provide an estimated value for conductor sag.

[0147] S104, Method for reverse calculation of conductor sag under multiple physical constraints: The steps for applying the method of this invention to actual transmission lines are as follows: S1041, First, it is necessary to obtain information such as the conductor and ground wire materials, hanging points, and tower structure of the transmission line in advance, and construct an electromagnetic simulation model of the conductor and ground wire; S1042, During operation, the ground wire current is measured by a current sensor installed on the ground wire; the spatial magnetic field is measured by a spatial magnetic field sensor installed on the tower body or crossarm, and the harmonic current information of each frequency conductor can be calculated by combining the DC current data of the line; S1043, the conductor and ground wire sag is estimated using the conductor heat balance equation through micro-meteorological sensors or meteorological forecast data; S1044, the estimated value is used as a constraint to set the sag value... The simulation model is input, and an iterative search is performed using a heuristic algorithm to finally obtain the inverse value of the sag. (like Figure 4 (As shown).

[0148] This invention discloses a specific process for monitoring sag on bipolar DC overhead lines. By constructing an accurate electromagnetic coupling model incorporating the skin effect and ground loop, and integrating non-contact magnetic field measurement with multi-physics thermal balance analysis, it effectively addresses the core shortcomings of existing technologies, such as sensitivity to environmental interference, oversimplification of models, and reliance on direct measurements. It achieves full-process integration from electromagnetic parameter calculation, harmonic current inversion, thermally induced sag estimation to multi-constraint intelligent iteration, significantly improving the accuracy of sag inversion, environmental adaptability, and system robustness. While ensuring the safe and economical operation of transmission lines, it provides a highly reliable technical means for state perception under complex weather and load conditions.

[0149] Example 3 To achieve the above invention, embodiments of the present invention also provide a simulation test of a bipolar DC overhead line sag monitoring method, specifically including: The effectiveness of the embodiments of the present invention was verified by combining actual line data with simulation. Figure 5 Spectral analysis of the measured ground wire induced signal of a ±500kV bipolar DC line shows that... There is a significant spike at the frequency (n is a positive integer), therefore, the harmonic frequency of the conductor current to be monitored is taken as in the simulation. .

[0150] Specifically, to verify whether the tower structure would affect the spatial magnetic field and cause excessive deviations in the conductor current calculation results, a tower model (such as...) was built in the CDEGS simulation software. Figure 6 As shown in the figure, the spatial magnetic field generated by the conductor current is simulated and calculated.

[0151] Furthermore, while maintaining a consistent conductor current amplitude, the current frequency was changed to 300, 600, 900, 1200, and 1500 Hz, and the magnetic field strength around the tower was calculated (e.g., Figure 7 As shown in the figure, the spatial magnetic field strength distribution is basically consistent at different frequencies; changing the current magnitude, the spatial magnetic field strength changes linearly with the current, indicating that the tower structure has little impact on the spatial magnetic field distribution, and the ratio of harmonic currents obtained from the ratio of magnetic field strengths has good accuracy.

[0152] Specifically, to verify the robustness of the back-calculation algorithm under the influence of measurement errors, a line simulation model (such as...) was built based on the actual DC line tower structure. Figure 8 As shown), in the back-calculation, considering the measurement error of the conductor current and the estimation error of the conductor sag, the conductor current is measured multiple times over a short period of time, and the average value of the conductor sag during this period is calculated. The measurement errors of different physical quantities are changed, and the sag back-calculation error is calculated under different conductor sag sizes (e.g., ...). Figures 9 to 12 (As shown).

[0153] Specifically, it can be seen that the results of the conductor sag calculation are all within acceptable ranges under different error conditions. The above calculation results show that the algorithm proposed in this invention can achieve relatively reliable calculations under different error conditions.

[0154] This invention discloses a simulation test of a bipolar DC overhead line sag monitoring method. The simulation test verifies the feasibility and robustness of the proposed method, effectively overcoming the insufficient monitoring accuracy problems caused by tower structure interference, measurement errors, and environmental changes in existing technologies. Monitoring frequency points are selected based on the actual line spectrum characteristics, and the reliability of the magnetic field measurement method is confirmed through electromagnetic field simulation. Sag inversion verification is completed under the condition of considering multiple error sources. The method exhibits stable monitoring accuracy and anti-interference capability under different error conditions, significantly improving the accuracy and engineering applicability of sag monitoring in complex operating environments, and providing reliable technical support for transmission line condition sensing.

[0155] Example 4 To achieve the above invention, such as Figure 13 As shown, this embodiment also provides a sag monitoring device 10 for bipolar DC overhead lines, the device 10 comprising: The conductor impedance calculation module 100 is used to establish an electromagnetic coupling model of the conductor and ground wire within a certain range based on the static parameters of the line, and to calculate the conductor's self-impedance and mutual impedance.

[0156] The magnetic field measurement and harmonic calculation module 200 is used to measure the spatial magnetic field through a magnetic field sensor installed at the crossarm of the tower, and calculate the amplitude ratio of the harmonic current at each frequency of the conductor to the DC current by combining the real-time DC current data of the line, and obtain the absolute value of the harmonic current.

[0157] The conductor temperature and sag estimation module 300 is used to calculate the conductor surface temperature based on the conductor thermal balance equation, and estimate the conductor sag as an initial constraint by combining the conductor specific load, thermal expansion coefficient, elastic modulus and cross-sectional area.

[0158] The sag iteration solution module 400 is used to input the electromagnetic coupling model of the conductor and ground wire with the estimated value of the conductor and ground wire sag as a constraint, and to use a heuristic algorithm to iteratively solve for the specific value of the conductor and ground wire sag by taking multiple measurements over a short period of time and calculating the average value.

[0159] This invention discloses a sag monitoring device for bipolar DC overhead lines. By integrating multiple functional modules such as electromagnetic modeling, non-contact magnetic field measurement, thermal balance analysis, and intelligent iterative solution, it effectively overcomes the core shortcomings of traditional methods, which rely on manual inspection, have stringent measurement conditions, and struggle to achieve real-time and accurate assessment. The device realizes fully automated closed-loop monitoring from line parameter calculation, harmonic current inversion, temperature and initial sag estimation to final value iterative solution. This significantly improves the real-time performance, accuracy, and adaptability to complex operating environments of sag monitoring, providing a reliable technical means for refined operation and maintenance and safety early warning of overhead lines, and enhancing the stability and intelligent management level of the power grid system.

[0160] To implement the methods of the above embodiments, the present invention also provides a computer device, such as... Figure 14 As shown, the computer device 600 includes a memory 601 and a processor 602; wherein, the processor 602 reads the executable program code stored in the memory 601 to run a program corresponding to the executable program code, so as to implement the various steps of the above-described method for monitoring the sag of a bipolar DC overhead line.

[0161] To implement the above embodiments, this application also proposes a non-transitory computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements a sag monitoring method for a bipolar DC overhead line as described in the foregoing embodiments.

[0162] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., refer to specific features, structures, materials, or characteristics described in connection with that embodiment or example, which are included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0163] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

Claims

1. A method for monitoring the sag of a bipolar DC overhead line, characterized in that, include: S1. Based on the static parameters of the line, establish an electromagnetic coupling model of the conductor and ground wire within one range, and calculate the conductor's self-impedance and mutual impedance. S2, by measuring the spatial magnetic field through a magnetic field sensor installed at the crossarm of the tower, and combining it with the real-time DC current data of the line, the amplitude ratio of the harmonic current of each frequency of the conductor to the DC current is calculated, and the absolute value of the harmonic current is obtained. S3. Calculate the surface temperature of the conductor based on the conductor thermal balance equation, and estimate the conductor sag as an initial constraint by combining the conductor specific load, thermal expansion coefficient, elastic modulus and cross-sectional area. S4 uses the estimated value of the conductor sag as a constraint input to the conductor electromagnetic coupling model, and employs a heuristic algorithm to iteratively solve for the specific value of the conductor sag by taking multiple measurements over a short period of time and calculating the average value.

2. The method as described in claim 1, characterized in that, The process of establishing a conductor-to-ground electromagnetic coupling model within a certain range based on the static parameters of the line, and calculating the conductor's self-impedance and mutual impedance, includes: S11, through formula Calculate the conductor self-impedance considering the skin effect ; S12, through formula Calculate the mutual inductance impedance between the conductor and ground ,in The depth of penetration; S13, through formula Calculate the self-impedance of the conductor; where, This is the self-impedance of the conductor.

3. The method as described in claim 1, characterized in that, The process of measuring the spatial magnetic field using a magnetic field sensor installed on the crossarm of the tower, calculating the amplitude ratio of harmonic currents at each frequency of the conductor to the amplitude of the DC current in combination with real-time DC current data of the line, and obtaining the absolute value of the harmonic current includes: S21. Install the magnetic field sensor at the crossarm of the tower. By measuring the ratio of the magnetic field amplitude generated by the harmonic current of each frequency of the conductor to that of the DC current at the same location, and combining the characteristic that the current direction of the bipolar DC line conductor is opposite, calculate the absolute value of the harmonic current.

4. The method as described in claim 1, characterized in that, The calculation of the conductor surface temperature based on the conductor thermal balance equation, combined with the conductor specific load, coefficient of thermal expansion, elastic modulus, and cross-sectional area, and the estimation of conductor sag as an initial constraint, includes: S31, through formula Calculate the heat dissipation power of the conductor by natural convection. ; S32, through formula Calculate the heat dissipation power of the conductor radiation ; S33, according to the conductor heat balance equation Calculate the surface temperature of the conductor and combine it with the conductor specific load. Coefficient of thermal expansion Elastic modulus and cross-sectional area Using the formula Estimate the sag of the conductor as an initial constraint.

5. The method as described in claim 1, characterized in that, The estimated value of the conductor sag is used as a constraint input to the electromagnetic coupling model of the conductor and ground wire. A heuristic algorithm is used to iteratively solve for the specific value of the conductor sag, which is achieved by measuring multiple times over a short period of time and calculating the average value. This includes: S41, through formula A nonlinear relationship between the induced current in the ground wire and the current in the conductor is established, and the sag value estimated by thermal balance is used as the upper and lower limits of the initial iteration range of the algorithm. S42, by measuring conductor current data multiple times over a short period of time and calculating the average value of conductor sag within the corresponding period.

6. A sag monitoring device for a bipolar DC overhead line, characterized in that, include: The conductor impedance calculation module is used to establish an electromagnetic coupling model of conductors and ground wires within a certain range based on the static parameters of the line, and to calculate the conductor's self-impedance and mutual impedance. The magnetic field measurement and harmonic calculation module is used to measure the spatial magnetic field through a magnetic field sensor installed at the crossarm of the tower, and calculate the amplitude ratio of the harmonic current at each frequency of the conductor to the DC current by combining the real-time DC current data of the line, and obtain the absolute value of the harmonic current. The conductor temperature and sag estimation module is used to calculate the conductor surface temperature based on the conductor thermal balance equation, and estimate the conductor sag as an initial constraint by combining the conductor specific load, thermal expansion coefficient, elastic modulus and cross-sectional area. The sag iterative solution module is used to input the electromagnetic coupling model of the conductor and ground wire with the estimated value of the conductor and ground wire sag as a constraint, and to use a heuristic algorithm to iteratively solve for the specific value of the conductor and ground wire sag by taking multiple measurements over a short period of time and calculating the average value.

7. An electronic device, comprising: processor; The memory stores executable instructions; when the processor executes the instructions, it implements the sag monitoring method for a bipolar DC overhead line as described in any one of claims 1-5.

8. A computer-readable storage medium storing a computer program, wherein when the computer program is executed by a processor, it implements a method for monitoring the sag of a bipolar DC overhead line as claimed in any one of claims 1-5.

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