Conducting wire current-carrying capacity-sag coupling modeling method and system based on electro-thermal-mechanical coupling

Abstract

The invention discloses a conductor current-carrying capacity-sag coupling modeling method and system based on electro-thermal-mechanical coupling, and belongs to the technical field of transmission conductors. A thermal balance equation is established based on obtained Joule thermal power, sunlight heat absorption power, convection heat dissipation power and radiation heat dissipation power; solving the heat balance equation to obtain the surface temperature of the wire; taking the surface temperature of the wire as a boundary condition, constructing a concentric multilayer radial heat conduction model, and solving to obtain a radial temperature gradient of the wire; calculating strain of various materials in the wire based on the radial temperature gradient of the wire, and obtaining real horizontal stress through adaptive iteration; and substituting the real horizontal stress and the obtained geometric parameters of the conductor into the parabola model to obtain the maximum sag of the conductor under the current working condition. According to the method, the lead temperature evaluation precision is improved, systematic deviation caused by conductor isothermal or neglecting of irradiation / wind-induced heat exchange is avoided, and a reliable thermal boundary is provided for dynamic current-carrying capacity evaluation.

Description

Technical Field

[0001] This invention belongs to the field of power transmission conductor technology, specifically relating to a conductor current-carrying capacity-sag coupling modeling method based on electro-thermal-mechanical coupling. Background Technology

[0002] To maximize the potential current-carrying capacity of transmission conductors, power system operators often implement dynamic capacity expansion technology for conductors. Dynamic capacity expansion technology can re-plan the current-carrying capacity of conductors based on real-time monitoring status, optimizing the economy and utilization rate of existing overhead lines. However, when using dynamic conductor capacity expansion technology, various safety requirements for conductors must be fully met, such as the safe distance between conductors and ground, the distance between conductor crossings, and the maximum allowable temperature of conductors, to ensure the safe operation of the power grid under corresponding conditions. One important indicator of this safety is the sag.

[0003] When the current-carrying capacity of an overhead line is increased, i.e., the conductor current is increased, the conductor temperature will rise due to the thermal effect generated by the conductor's own resistance. This will cause thermal expansion strain, increase the conductor length, and increase the creep strain, resulting in a larger maximum sag, a closer proximity to the ground, a smaller safe distance from the ground, and a smaller conductor crossing distance. This reduces the safety margin of the line transmission and makes it more prone to grounding faults and short circuits, jeopardizing the safe operation of the line. Therefore, accurate calculation of the maximum sag is essential for improving the utilization rate of hidden capacity and enhancing both economic efficiency and safety.

[0004] A span of conductor typically refers to a conductor suspended between two towers. Under the pressure of a series of internal and external forces, such as the conductor's own weight, external wind pressure, and icing pressure, stress will be generated on any cross-section of the conductor. This stress is the internal force per unit cross-sectional area of ​​the overhead line. It is generally assumed that the load acting on the conductor is uniformly distributed along the conductor length, and the stress at each point is different, with the direction of the stress at each point being the same as the tangent to the conductor. Furthermore, geometrically, the direction of the stress at the lowest point within the span should be horizontal. In general conductor stress and sag analysis, unless otherwise specified, conductor stress refers to the horizontal stress at the lowest point of sag.

[0005] Existing techniques for calculating conductor sag still have significant shortcomings in establishing the coupling relationship between current carrying capacity and sag. First, the simplified assumption of cross-sectional isothermal treatment in the thermal model ignores the radial temperature gradient formed by the combined effects of endogenous Joule heating and surface heat dissipation. This makes it difficult to obtain the true temperature difference between the steel core and the outer aluminum stranded wire, thus introducing fundamental errors in thermal expansion and subsequent mechanical analysis, weakening the reliability of predictions under high-temperature and high-current conditions.

[0006] Secondly, in the mechanical modeling process, existing methods treat the steel-aluminum stranded conductor as a whole, which fails to characterize the stress distribution and dynamic transfer caused by thermal differences, and cannot describe the critical state transition after the aluminum stranded conductor reaches the inflection point temperature and no longer bears axial tension. This results in significant deviations between the calculated sag under high temperature and high current carrying conditions and the actual situation. At the same time, treating the steel core and aluminum stranded conductor as a single material further amplifies the aforementioned sources of error. Summary of the Invention

[0007] The purpose of this invention is to address the shortcomings of existing technologies in key aspects such as radial temperature gradient and stress switching at inflection point temperatures, which directly restrict the reliable application of existing sag calculations under safety constraints such as the safe distance between conductors and the ground, crossing distance, and maximum allowable temperature. This invention proposes a conductor current-sag coupling modeling method based on electro-thermal-mechanical coupling. Driven by the conductor current-carrying capacity and the external environment, the method first calculates the surface thermal equilibrium, then establishes a concentric multilayer radial thermal conduction model of steel-core aluminum stranded wire to obtain the average temperature of the two layers, and then calculates various strains according to material differences in the thermo-mechanical module and obtains the true horizontal stress through adaptive iteration. Finally, the maximum sag is obtained from the force-geometric relationship.

[0008] According to one aspect of the present invention, a method for modeling conductor current-carrying capacity-sag coupling based on electro-thermal-mechanical coupling is provided, comprising:

[0009] S1. Based on the obtained Joule heat power, solar heat absorption power, convective heat dissipation power and radiative heat dissipation power, establish a heat balance equation and solve the heat balance equation to obtain the surface temperature of the conductor.

[0010] S2. Using the surface temperature of the conductor as a boundary condition, construct a concentric multilayer radial thermal conduction model, and solve the concentric multilayer radial thermal conduction model to obtain the radial temperature gradient of the conductor.

[0011] S3. Calculate the strain of various materials in the conductor based on the radial temperature gradient of the conductor, and obtain the true horizontal stress through adaptive iteration;

[0012] S4. Substitute the actual horizontal stress and the obtained conductor geometric parameters into the parabolic model to obtain the maximum sag of the conductor under the current working conditions.

[0013] Furthermore, the heat balance equation is expressed as follows:

[0014] ,

[0015] in, This represents the Joule heat power generated by the resistance of the circuit itself; This indicates the AC resistance of the conductor at the maximum permissible operating temperature; This represents the solar heat absorption power per unit length of conductor under sunlight conditions. This represents the convective heat dissipation power per unit length of the conductor during operation. This represents the radiative heat dissipation power per unit length of the conductor.

[0016] Furthermore, the surface temperature of the conductor is obtained by solving the heat balance equation, including:

[0017] Construct based on conductor surface temperature Nonlinear functions with variables The expression is:

[0018] ,

[0019] in, It is Joule fever; and equal;

[0020] The Newton-Raphson method is used to iterate the nonlinear function, and the expression is:

[0021] .

[0022] Further, S2 includes:

[0023] S2.1 By solving the differential equation of heat conduction in the hollow cylindrical layer of the conductor, the radius of any part of the aluminum stranded wire layer can be obtained. Temperature distribution function at [location] , temperature distribution function Substitute the average temperature Integrating the expression yields the average temperature of the aluminum stranded wire. ;

[0024] S2.2 By solving the differential equation of heat conduction in the solid cylindrical layer of the conductor, the inner radius of the steel core can be obtained. Temperature distribution function at [location] , temperature distribution function Substitute the average temperature Integrating the expression yields the average temperature of the steel core. ;

[0025] S2.3 The average temperature of the steel core and the average temperature of the aluminum stranded wire are the radial temperature gradients of the conductor.

[0026] Furthermore, the strain of various materials in the conductor is calculated, including:

[0027] The thermal strain of the steel core and aluminum stranded wire is obtained based on the radial temperature gradient of the conductor, and the expression is:

[0028] ,

[0029] ,

[0030] Based on the thermal strain of the steel core and aluminum stranded wire, combined with the mechanical elastic strain and settlement strain of the steel core and aluminum stranded wire, as well as the creep strain caused by the service life of the overhead conductor, we obtain:

[0031] The strain expression for the steel core is: ;

[0032] The strain expression for the aluminum stranded wire is: ;

[0033] Among them, DT A and DT B Thermal strain of steel core and aluminum stranded wire, respectively, ELA A and ELA B The mechanical elastic strains of the steel core and aluminum stranded wires are respectively, ST A and ST B Settlement strains of steel core and aluminum stranded wire, respectively, CPR A and CPR B The creep strain refers to the creep strain caused by the service life of steel core and aluminum stranded wires in overhead conductors.

[0034] Furthermore, the true horizontal stress is obtained through adaptive iteration, including:

[0035] Set an initial assumed value for the horizontal stress of the conductor. The axial stress borne by the steel core and aluminum stranded wire was preliminarily calculated. and ; Axial stress on aluminum stranded wire Make a judgment:

[0036] like This indicates that the conductor is under normal stress. The Newton-Raphson method will be used to verify whether the strain of the steel core and aluminum stranded wire satisfies the conventional mechanical equilibrium conditions. ;

[0037] like This indicates that the conductor has reached or exceeded the inflection point temperature, and the aluminum stranded wire no longer bears axial tensile force; the calculation logic is automatically switched using the Newton-Raphson method: the stress of the aluminum stranded wire is... The value is forcibly set to zero, and subsequent verification is performed based on the new mechanical equilibrium conditions, namely, only the steel core is subjected to force and its strain is balanced.

[0038] Furthermore, obtaining the true horizontal stress through adaptive iteration also includes:

[0039] When the equation is not satisfied According to and The difference between them, or the assumed value of horizontal stress obtained by numerical solution based on the new equilibrium criterion after the inflection point. Make corrections to construct a system with horizontal stress. Error function of variables Then, the result is approximated using the Newton-Raphson method, expressed as:

[0040] ,

[0041] Corrected horizontal stress This will be used to initiate a new round of iterative calculations until the strain difference is less than the preset convergence accuracy, at which point the horizontal stress... This is the actual horizontal stress of the conductor under the current operating conditions.

[0042] Furthermore, the construction of the parabolic model includes:

[0043] Assuming the conductor operates in a windless state, based on the premise that the bending moment at any point on the flexible steel cable is zero, a force analysis is performed on the infinitesimal element on the conductor, yielding the force balance equations for the suspension points on both sides of the towers and any point P(x, y) on the conductor:

[0044] ,

[0045] ,

[0046] In the formula, It is the vertical stress component of the axial stress of the conductor at point A along the y-axis; assuming the connection between the lower tower and the conductor is the origin, a simplified parabolic model with respect to sag is obtained, expressed as:

[0047] ,

[0048] in, γ is the horizontal stress component on the conductor; l is the horizontal projected length between the two suspension points; h is the height difference between the towers on both sides within the conductor span. The angle between the load and the vertical direction.

[0049] Furthermore, the maximum sag of the conductor under the current operating conditions is obtained, including:

[0050] Using a mathematical analytical tree connecting the two towers, the sag at a distance x from the origin on the parabolic model is obtained as follows:

[0051] ,

[0052] By calculating the extreme value of the above formula, the maximum sag of the conductor under the current working condition is obtained. The calculation expression is:

[0053] .

[0054] According to one aspect of the present invention, a conductor current-carrying capacity-sag coupling modeling system based on electro-thermal-mechanical coupling is provided, comprising:

[0055] The conductor surface temperature calculation module is used to establish a heat balance equation based on the obtained Joule heat power, solar heat absorption power, convective heat dissipation power and radiative heat dissipation power, and solve the heat balance equation to obtain the conductor surface temperature.

[0056] The radial temperature gradient acquisition module for the conductor is used to construct a concentric multilayer radial heat conduction model by using the surface temperature of the conductor as a boundary condition, and to obtain the radial temperature gradient of the conductor by solving the concentric multilayer radial heat conduction model.

[0057] The module for obtaining the true horizontal stress is used to calculate the strain of various materials in the conductor based on the radial temperature gradient of the conductor, and to obtain the true horizontal stress through adaptive iteration.

[0058] The maximum sag acquisition module is used to substitute the actual horizontal stress and the acquired conductor geometric parameters into the parabolic model to obtain the maximum sag of the conductor under the current working conditions.

[0059] Compared with the prior art, the beneficial effects of the present invention are:

[0060] 1. This invention proposes an electro-thermal coupling surface temperature solution mechanism, which unifies Joule heating, solar heat absorption, convective heat dissipation, and radiative heat dissipation into a nonlinear thermal balance equation. The surface temperature of the conductor under given current carrying capacity and environmental conditions is obtained iteratively through the Newton-Raphson method, providing boundary conditions for subsequent radial heat conduction, improving the accuracy of conductor temperature assessment, avoiding systematic deviations caused by isothermal conduction or neglect of irradiation / wind-induced heat transfer, and providing a reliable thermal boundary for dynamic current carrying capacity assessment.

[0061] 2. This invention considers the radial steady-state thermal conductivity model and heat source distribution strategy based on the differences between the steel core and aluminum stranded wire. The total Joule heat is distributed to the steel core and aluminum stranded wire according to resistance. The radial thermal conductivity equations of the inner and outer cylindrical layers are solved separately to obtain the average temperature of the aluminum stranded wire and the average temperature of the steel core. This establishes the radial temperature gradient of the conductor cross section and reflects the influence of material property differences (thermal conductivity, temperature coefficient, resistivity, etc.) and structural differences on heat distribution. This avoids the distortion of a single equivalent material model under high current or high temperature conditions.

[0062] 3. This invention proposes a thermo-mechanical coupling inflection point temperature adaptive switching and horizontal stress solution mechanism. In each iteration step, the axial stress of the aluminum stranded wire is judged in real time. When it drops to zero, it automatically switches to a new equilibrium criterion of only the steel core being stressed. At the same time, an error function is constructed with the horizontal stress as the iteration variable, and the Newton-Raphson method is used to gradually correct it until the strain balance is satisfied. During the iteration process, the axial stress state of the aluminum stranded wire is judged in real time. When it drops to zero, it switches to a new equilibrium criterion of "only the steel core being stressed", realizing a seamless connection between the two stress calculation methods before and after the inflection point temperature. Attached Figure Description

[0063] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1 The flowchart of the conductor current-sag coupling modeling method based on electro-thermal-mechanical coupling provided by the present invention is shown. Detailed Implementation

[0065] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0066] Specifically, this invention proposes a conductor current-sag coupling modeling method based on electro-thermal-mechanical coupling. S1: Establish a thermal balance equation based on the acquired Joule heat power, solar heat absorption power, convective heat dissipation power, and radiative heat dissipation power, and solve the thermal balance equation to obtain the conductor surface temperature; S2: Use the conductor surface temperature as a boundary condition to construct a concentric multilayer radial thermal conduction model, and solve the concentric multilayer radial thermal conduction model to obtain the conductor radial temperature gradient; S3: Calculate the strain of various materials in the conductor based on the conductor radial temperature gradient, and obtain the true horizontal stress through adaptive iteration; S4: Substitute the true horizontal stress and the acquired conductor geometric parameters into a parabolic model to obtain the maximum sag of the conductor under the current operating conditions.

[0067] Specifically, this invention provides a method for calculating thermal balance and current carrying capacity. Current carrying capacity refers to the maximum current a conductor can withstand under given operating conditions, provided the conductor temperature does not exceed the maximum allowable conductor temperature. The calculation methods for each part of the thermal balance equation are given by the GB50545 standard. The steady-state thermal balance equation is a core model commonly used in electrical engineering to calculate the relationship between conductor temperature and current carrying capacity under stable operating conditions; its basic principle is based on the law of conservation of energy.

[0068] The specific equations for calculating the energy transfer relationship between the conductor and the environment are as follows:

[0069] (1)

[0070] The thermal balance of the conductor under actual operating conditions consists of four main parts. This represents the Joule heat power generated by the resistance of the circuit itself; This indicates the AC resistance of the conductor at the maximum permissible operating temperature; This represents the solar heat absorption power per unit length of conductor under sunlight conditions. This represents the convective heat dissipation power per unit length of the conductor during operation. This represents the radiative heat dissipation power per unit length of the conductor.

[0071] Specifically, this invention provides a conductor convection cooling method. Convection cooling refers to the energy transfer process in which a fluid carries heat from a high-temperature object to a low-temperature object during flow. Conductor convection cooling typically refers to the air surrounding the conductor being heated by the rising temperature of the conductor during operation. The temperature gradient change transforms from the ideal gas law to a change in air density gradient, generating airflow that carries away the heat from the conductor. Depending on the cause of the air-driven force, convection cooling is often divided into natural convection cooling and forced convection cooling. Natural convection cooling often refers to the phenomenon where, under windless conditions, the high-temperature conductor heats the air near the conductor due to the temperature difference between the conductor and the surrounding air. This temperature gradient generates a density gradient, causing airflow and heat transport. Forced convection cooling, on the other hand, originates from the mechanical disturbance of an external wind field. The increased airflow caused by external forces forms a forced convection boundary layer, carrying away the heat generated by the operating conductor. Forced convection cooling is generally more effective than natural convection cooling in dissipating heat from conductors.

[0072] Specifically, the calculation of convective heat dissipation in the GB50545 standard is mainly based on Newton's law of cooling, that is, calculating the heat dissipation through the convective heat transfer coefficient, the surface area of ​​the object, and the temperature difference. The calculation equation before simplification is:

[0073] (2)

[0074] In the formula, Re is the Reynolds number, which is calculated as follows:

[0075] (3)

[0076] In the formula, D is the diameter of the conductor, in meters (m); V is the wind speed, in meters per second (m / s). Kinematic viscosity, unit: m 2 / s; Air density, unit: kg / m³ 3 Substituting the Reynolds number expression into equation (2) yields:

[0077] (4)

[0078] In the formula, The ambient temperature during operation, in °C; The temperature of the conductor is expressed in °C. Air thermal conductivity, measured in W / (m·K). Air density. In national standards, C and p are often specified as 1, and their values ​​depend on the Reynolds number and the surface roughness of the conductor. Surface roughness is incorporated into the calculation for auxiliary judgment. In GB50545, the calculation often uses both surface roughness and Reynolds number coefficients for a comprehensive judgment, and the correlation coefficient is selected after referring to a table based on their values.

[0079] Specifically, this embodiment of the invention provides radiative heat dissipation by a conductor. Radiative heat dissipation refers to the conductor transferring its own heat to the surrounding environment through thermal radiation. Radiative heat dissipation is an inherent property of the conductor and is related to ambient temperature, conductor temperature, and circuit characteristics such as arrangement, number of splits, and conductor diameter. Under the national standard calculation model, radiative heat dissipation is derived from ideal blackbody radiation, and the calculation formula is:

[0080] (5)

[0081] In the formula, D is the outer diameter of the conductor, in meters (m). This is the emissivity of the conductor surface, which depends on the type of conductor, the aging of the conductor, and the degree of oxidation of the conductor. This is the Stefan-Boltzmann constant, with a value of 5.67 × 10⁻⁶. -8 W / (m 2 ·K 4 The calculation of radiative heat dissipation is essentially thermal radiation. Most models are based on this theory and are derived accordingly, involving only the mechanical and thermal properties in physics.

[0082] Specifically, this invention provides a method for heat absorption by a conductor during sunlight exposure. Since the core wire of a conductor is exposed during outdoor installation, it inevitably receives sunlight, causing it to absorb heat from the radiation. Generally, the amount of heat absorbed by the conductor from sunlight depends on the surface condition of the conductor, its diameter, and the intensity of the sunlight radiation. The three standard calculation methods for heat absorption by sunlight are similar. The calculation formula in the GB50545 model is as follows:

[0083] (6)

[0084] In the formula, Where is the heat absorption coefficient; D is the outer diameter of the conductor, in meters. For solar radiation intensity, 1000 W / m² is often used. 2 ; This is a regional coefficient, which is used to make regional corrections for solar radiation in different regions of my country.

[0085] Specifically, this embodiment of the invention provides the resistive heating effect of conductors. In the GB50545 calculation model, hysteresis loss and corona heat generation are ignored within the allowable error range, and the heating of AC conductors is approximated as follows:

[0086] (7)

[0087] (8)

[0088] In the formula, For the current carrying capacity of the conductor, and These represent the AC and DC resistances, respectively; k is the AC / DC resistance ratio, which can be found in the national standard calculation.

[0089] Specifically, the present invention provides a strain accumulation method, which is often used to solve physical quantities that are difficult to measure directly in the engineering field, including: cumulative deformation, fatigue life, cumulative damage, cumulative plastic strain and residual strain. These time accumulation quantities have strong statistical value and can help relevant personnel better predict the service life and residual performance of relevant conductors and towers.

[0090] Specifically, the strain accumulation method for solving the stress of overhead conductors presupposes that the steel core and aluminum strands of the conductor are considered as a whole, possessing the same coefficient of thermal expansion and tensile strength, and having the same strain along their length. Given relevant parameters such as conductor type, service life, and temperature, the horizontal tension at a specific location on the conductor is calculated, and the horizontal stress is indirectly obtained using relevant algorithms. The core of this method is to first consider the total strain of the steel core and aluminum strands separately, and then use an iterative approach to gradually increase the stress in the steel core until the inner and outer lengths of the steel core and aluminum strands are equal.

[0091] Specifically, assume that the total strains of the steel core and the aluminum stranded wire are X respectively. A and X B The thermal strain of the steel core and aluminum stranded wire caused by the temperature change of the conductor is DT. A and DT B The mechanoelastic strains produced by the two when subjected to tensile force are ELA and ELA, respectively. A and ELA B The settlement strain ST caused by the settlement of the tower foundations on both sides A and ST B And creep strain CPR caused by the service life of the conductor. A and CPR B For the above-mentioned types of strains, the following relationships should hold:

[0092] (9)

[0093] (10)

[0094] Where D represents delta, i.e., change, and S represents settlement, i.e., settling; the thermal strain of the steel core and aluminum stranded wire can be calculated using empirical formulas:

[0095] (11)

[0096] (12)

[0097] In the formula, the letter expression T A T B Here, represents the actual operating temperature of the steel core and aluminum stranded wire, respectively, in °C. It is assumed in the formula that both are equal values, equal to the surface temperature of the conductor during operation. The formula for calculating the elastic strain of the steel core and aluminum stranded wire under tensile force is:

[0098] (13)

[0099] (14)

[0100] In the formula, and E represents the axial stress on the steel core and aluminum stranded wire, respectively, in MPa; A and E B These represent the elastic moduli of the steel core and the aluminum stranded wire, respectively, in MPa. The settlement caused by the long-term operation of the towers on both sides of the conductor will induce a corresponding settlement strain in the conductor, calculated as follows:

[0101] (15)

[0102] (16)

[0103] Steel-cored and aluminum stranded wires will develop creep strain after prolonged use. Creep in steel-cored aluminum stranded wires refers to the slow and continuous deformation of the conductor over time under constant stress conditions. In real-world operating environments, it often manifests as permanent elongation deformation of the conductor. The formula for calculating creep strain is as follows:

[0104] (17)

[0105] (18)

[0106] Among them, t n This refers to the service life of the conductor to be calculated. When using the strain accumulation method, it is assumed that both ends of the steel core and aluminum stranded wire are fixed at the same point on the tower; therefore, their lengths will always be equal. This can be expressed mathematically as:

[0107] (19)

[0108] In practical calculations, the above formula is often used as a criterion to terminate iterative calculations. As can be seen from the above description, the strain accumulation method does not take into account the radial expansion and creep caused by temperature rise when applied. Therefore, it is not suitable for calculations after the inflection point temperature, and there will be a large error.

[0109] Specifically, this embodiment of the invention provides sag calculation. For a conductor spanned between two towers, the relationship between sag and stress is as follows: the smaller the stress on the conductor, the larger the sag; conversely, the larger the stress, the smaller the sag. Therefore, from the perspective of conductor tensile strength safety, the conductor sag should be maximized to reduce stress and deformation, thereby improving the safety distance factor. However, simply emphasizing increasing sag will cause the conductor to be too close to the ground, reducing the safety distance and making it prone to discharge, leading to potential faults. Therefore, to ensure the safe distance of live wires to the ground, if the line parameters are not changed, the tower height needs to be increased accordingly under the same span condition, or the span needs to be reduced under the same tower height condition. As a result, the line infrastructure investment will increase exponentially, reducing the economic efficiency of the conductor and causing economic losses.

[0110] Specifically, in engineering, a parabolic model is often chosen to solve for sag calculations. Assuming the conductor operates in a windless state, and based on the premise that the bending moment at any point on the flexible cable is zero, a force analysis of the infinitesimal elements on the conductor yields the force equilibrium equations for the suspension points on both sides of the towers and any point P(x, y) on the conductor:

[0111] (20)

[0112] (twenty one)

[0113] in, γ is the horizontal stress component on the conductor, in N / mm²; γ is the weight per unit length of the conductor, in N / m·mm²; l is the span (the horizontal projected length between two suspension points); h is the height difference between the towers on both sides within the conductor span, in m.

[0114] In the formula, It is the vertical stress component of the axial stress of the conductor at point A along the y-axis, with units of N / mm. 2 Assuming the point where the lower tower connects to the conductor is the origin, the simplified parabolic formula for sag can be obtained from the above equation:

[0115] (twenty two)

[0116] From equation (22) and the mathematical analysis tree connecting the two towers, the sag at a distance x from the origin under the parabolic model can be obtained as follows:

[0117] (twenty three)

[0118] After performing extreme value calculations on equation (23), the calculation expression for the maximum sag under the parabolic model can be obtained:

[0119] (twenty four)

[0120] Specifically, the implementation of the method of this invention first requires acquiring and inputting a comprehensive set of parameters to provide the necessary foundation for accurate calculations in subsequent electro-thermal coupling, thermo-mechanical coupling, and force-geometric coupling modules. These parameters mainly include: operating condition parameters, including the actual current carrying capacity of the conductor flowing through it. (Unit: A), Conductor surface temperature (Unit: °C); External environmental parameters, which describe the external environment in which the conductor is located, including ambient temperature. (Unit: °C), Wind Speed (Unit: m / s) and wind direction angle, and solar radiation intensity (Unit: W / m²); Line geometric parameters and loads, which define the suspension geometry of the conductor and the basic loads it is subjected to, including span. (Unit: m), Elevation difference of suspension point (Unit: m), and weight per unit length or specific load (Unit: N / m·mm²) The angle between the load and the vertical direction.

[0121] In addition, detailed physical parameters of the conductor must be entered, which define the inherent electrical, thermal, and mechanical properties of the conductor itself. These are prerequisites for accurate modeling and mainly include: the conductor's structural parameters, such as its overall outer diameter. (Unit: m), steel core radius (Unit: m), and the cross-sectional area of ​​the steel core and aluminum stranded wire respectively. and (Unit: mm²); Thermal properties of the conductor, such as the surface solar absorption coefficient. and surface emissivity And the thermal conductivity of the steel core, which is crucial for calculating the radial temperature gradient. Thermal conductivity of aluminum stranded wire (Unit: W / (m·K)); Mechanical properties of conductors, including the modulus of elasticity of steel core and aluminum stranded wire. and (Unit: MPa), coefficient of thermal expansion and (Unit: 1 / ℃), and material-specific empirical coefficients used to calculate creep and settlement strain. Finally, to ensure the accuracy of long-term effect calculations, historical parameters of the conductor, including its years of operation, must also be entered. And an initial or reference state for determining the calculation baseline.

[0122] First, the calculation of Qc and Qr in the heat balance equation of formula (1) uses the conductor temperature. Replace with conductor surface temperature The current carrying capacity can be obtained through iterative solutions such as the Newton-Raphson method. The precise temperature of the conductor surface in thermal equilibrium under environmental parameters. By rearranging terms in the heat balance equation, a new equation can be constructed using the surface temperature of the conductor. Nonlinear functions with variables Its form is as follows:

[0123] (25)

[0124] in, It is Joule fever; and equal;

[0125] The core of the Newton-Raphson method is to use the first-order Taylor expansion of the function to approximate the root of the function through the tangent line. Its iterative formula is:

[0126] (26)

[0127] After obtaining the surface temperature of the conductor, the radial temperature distribution is calculated. The conductor is precisely considered as a multi-layered concentric cylindrical structure consisting of a steel core and outer aluminum strands, and a radial steady-state heat conduction model is established from the conductor center to the surface. In this model, heat is conducted from the inner layers to the outer layers and ultimately dissipated at the conductor surface. This model is based on Fourier's law of heat conduction; for a cylindrical structure, the heat power per unit length is... With temperature gradient The relationship between them can be represented as:

[0128] (27)

[0129] in, It is the thermal power per unit length of conductor flowing radially (unit: W / m). This refers to the thermal conductivity of the material (unit: W / (m·K)). The values ​​differ for steel core and aluminum stranded wire, and are denoted as follows: and . It is the radial distance from the center of the conductor (unit: m). It is the temperature gradient along the radial direction of the conductor. Joule heating. The distribution is not uniform, but rather determined by the resistance of the steel core and aluminum strands within the conductor. Let the Joule heat distributed to the steel core be... The Joule heat distributed to the aluminum stranded wire is Then we have:

[0130] (28)

[0131] By solving the differential equation for heat conduction in the hollow cylindrical layer, the radius of any aluminum stranded wire layer can be obtained. Temperature distribution function at [location] :

[0132] (29)

[0133] in, It is the known surface temperature of the conductor. These are the heat transferred from the steel core and the heat generated by the aluminum stranded wire itself (unit: W / m). It is the equivalent thermal conductivity of the aluminum stranded wire layer (unit: W / (m·K)). It is the outer radius of the conductor. It is the radius of the steel core, which satisfies... .

[0134] Average temperature of aluminum stranded wire layer It is its internal temperature distribution function The integral average value over its cross-sectional area. The formula for calculation is:

[0135] (30)

[0136] temperature distribution function Substituting into the above formula and performing integration, we can obtain the average temperature of the aluminum stranded wire. The final calculation expression, the final result of which can be expressed as:

[0137] (31)

[0138] Among them, the average temperature rise of the aluminum stranded wire layer This is the precise value obtained from the above integral calculation. It combines the temperature rise effect caused by the combined action of heat conducted from the steel core and the heat generated by the aluminum stranded wire itself, and its value is similar to... and the geometry of the wires Directly related. Through this method, embodiments of the present invention can obtain accurate average temperatures of aluminum stranded wires, providing reliable input for subsequent thermo-mechanical coupling analysis.

[0139] Specifically, after calculating the temperature distribution of the aluminum stranded wire layer, this invention continues to calculate the temperature of the innermost steel core of the conductor. Similarly, when heat is transferred from the steel-aluminum interface to the center of the steel core, a temperature difference will also occur in the steel core layer, which has thermal resistance. The average temperature of the steel core... It can be heated by its internal heat source The temperature rise caused by its thermal resistance is calculated. The steel core is considered as a core with a radius of... A solid cylinder. Heat sources per unit length are evenly distributed within this layer. Its outer boundary The temperature, i.e., the temperature at the steel-aluminum interface. The temperature distribution function of the aluminum stranded wire layer can be obtained from equation (29). exist It was obtained from there.

[0140] By solving the differential equation for heat conduction in this solid cylindrical layer, the internal radius of the steel core can be obtained. Temperature distribution function at [location] :

[0141] (32)

[0142] Average temperature of steel core It is its internal temperature distribution function The integral average value over its cross-sectional area. The formula for calculation is:

[0143] (33)

[0144] temperature distribution function Substituting into the above formula and performing integration, we can obtain the average temperature of the steel core. The final calculation expression:

[0145] (34)

[0146] Will Substituting the expression, we can obtain... The complete calculation formula is provided. Through this method, the present invention can obtain the accurate average temperature of the steel core, ultimately completing the accurate calculation of the radial temperature gradient of the entire conductor.

[0147] Specifically, an initial assumed value for the horizontal stress of the conductor is set. Based on this, the axial stress borne by the steel core and aluminum stranded wire respectively was initially calculated. and Unlike traditional methods, this method uses the precise but variable core temperature obtained earlier when calculating various strain components. Temperature of aluminum stranded wire Substituting these into the thermal strain calculation equations (11) and (12) ensures the accuracy of subsequent calculations from the outset. Simultaneously, considering the stress in the current iteration step and the service life of the conductor... Using parameters such as elastic strain, creep strain, and settlement strain, other strain components can be accurately calculated using equation (13-18).

[0148] Specifically, after calculating the total strain of both the steel core and the aluminum stranded wire... and Afterwards, instead of making direct comparisons, the axial stress of the aluminum stranded wire is first assessed. Make a judgment. If This indicates that the conductor is under normal stress. The Newton-Raphson method will be used according to the conventional mechanical equilibrium conditions, i.e., to verify whether the total strain of the steel core and aluminum stranded wire satisfies equation (19). If This indicates that the conductor has reached or exceeded the inflection point temperature, and the aluminum stranded wire no longer bears axial tensile force. At this point, the Newton-Raphson method is used to automatically switch its calculation logic: the stress of the aluminum stranded wire is... The value is forcibly set to zero, and subsequent verification is performed based on the new mechanical equilibrium conditions, namely, only the steel core is subjected to force and its strain is balanced.

[0149] Specifically, if the mechanical equilibrium condition is not met, then according to and The difference between them (or, after the inflection point, based on the new equilibrium criterion), is obtained by numerically solving for the assumed value of horizontal stress. Perform intelligent correction to construct a system based on horizontal stress. Error function of variables Its form is:

[0150] (35)

[0151] in, and The total strain represents the horizontal stress at the current iteration step. The function.

[0152] Approximating the result using the Newton-Raphson method:

[0153] (36)

[0154] Revised This will be used to initiate a new round of iterative calculations. This process will continue until the total strain difference is less than the preset convergence accuracy, at which point the horizontal stress... This is the actual horizontal stress of the conductor under the current conditions.

[0155] Specifically, the previously calculated high-precision horizontal stress, which accurately considers radial temperature gradient, unbalanced stress distribution in steel-cored aluminum stranded wire, inflection point temperature, and creep effect, is used. Together with the input load Gear spacing and elevation difference angle Substitute the geometric parameters into the parabolic model. Using equations (20-24), the maximum sag of the conductor under the current operating conditions can be obtained. Due to the input stress of this method It has higher accuracy, thus ensuring that the final sag calculation results are highly reliable.

[0156] Specifically, this embodiment of the invention takes the real-time monitoring data of a certain 110kV high-voltage conductor as an example. The conductor section uses LGJ300 / 40 steel-cored aluminum stranded wire. Table 1 shows a series of data such as meteorological conditions, conductor current carrying capacity, and measured sag of the line section during a period in August 2020.

[0157] The current-carrying capacity of conductors under different conditions on the measured conductors was calculated using both the original method and the method proposed in this patent. The optimized sag calculation data was compared and analyzed with the data before optimization, and the percentage error of the optimized algorithm was calculated.

[0158] (37)

[0159] Table 1. Measured meteorological, flow rate and sag data

[0160] Current carrying capacity A <![CDATA[Wind speed m·s -1 > Wind direction ° Ambient temperature ℃ <![CDATA[Sunshine intensity W·m -2 > Sag m 132.8 1.1 151 30.2 850 2.33 156.5 1.1 30 32.3 223 2.09 136.4 2.0 156 30.3 364 2.04 163.5 1.3 171 33.2 375 2.15 151.9 2.4 30 28.8 137 1.97 84.1 1.5 28 24.4 125 1.88 137.5 1.7 164 30.6 502 2.08

[0161] The two are analyzed together in a table, as shown in Table 2. It can be clearly seen that after using the optimized coupled calculation model, the error in the measured sag of 2.33m working condition decreased from −8.498% to −2.575%, and other working conditions also showed systematic improvement.

[0162] Table 2 Comparison of errors before and after modeling method optimization

[0163] Actual monitoring of sag m Calculate sag m before optimization Error before optimization Optimized calculation of sag m Optimized error 2.33 2.132 -8.498% 2.27 -2.575% 2.09 2.143 2.536% 2.11 0.957% 2.04 2.134 4.608% 2.13 4.412% 1.97 2.141 8.680% 2.09 6.091% 1.88 2.116 12.553% 2.06 9.574%

[0164] The implementation of the various embodiments of the present invention is based on programmed processing by a device with processor functionality. Therefore, in practical engineering, the technical solutions and functions of the various embodiments of the present invention are encapsulated into various modules. Based on this reality, and building upon the above embodiments, the embodiments of the present invention provide a conductor current-carrying capacity-sag coupling modeling system based on electro-thermal-mechanical coupling. This system is used to execute a conductor current-carrying capacity-sag coupling modeling method based on electro-thermal-mechanical coupling from the above method embodiments.

[0165] The system includes: a conductor surface temperature calculation module, used to establish a heat balance equation based on the acquired Joule heat power, solar heat absorption power, convective heat dissipation power, and radiative heat dissipation power, and solve the heat balance equation to obtain the conductor surface temperature; a conductor radial temperature gradient acquisition module, used to construct a concentric multilayer radial heat conduction model using the conductor surface temperature as a boundary condition, and solve the concentric multilayer radial heat conduction model to obtain the conductor radial temperature gradient; a true horizontal stress acquisition module, used to calculate the strain of various materials in the conductor based on the conductor radial temperature gradient, and obtain the true horizontal stress through adaptive iteration; and a maximum sag acquisition module, used to substitute the true horizontal stress and the acquired conductor geometric parameters into a parabolic model to obtain the maximum sag of the conductor under the current operating conditions.

[0166] The conductor current-carrying capacity-sag coupling modeling system based on electro-thermal-mechanical coupling provided in this invention addresses the shortcomings of existing technologies in key aspects such as radial temperature gradient and stress switching at inflection point temperatures. These shortcomings directly restrict the reliable application of existing sag calculations under safety constraints such as conductor-to-ground safe distance, crossing distance, and maximum allowable temperature. The system employs several modules driven by conductor current-carrying capacity and the external environment. It first calculates surface thermal equilibrium, then establishes a concentric multilayer radial thermal conductivity model of steel-core aluminum stranded wire to obtain the average temperature of the two layers. Subsequently, in the thermo-mechanical module, various strains are calculated according to material differences, and the true horizontal stress is obtained through adaptive iteration. Finally, the maximum sag is obtained from the force-geometric relationship, improving the accuracy of conductor temperature assessment and avoiding systematic deviations caused by isothermal conduction of conductors or neglect of irradiation / wind-induced heat transfer. This provides a reliable thermal boundary for dynamic current-carrying capacity assessment.

[0167] Finally, it should be noted that the above specific embodiments are merely representative examples of the present invention. Obviously, the present invention is not limited to the above specific embodiments and many variations are possible. Any simple modifications, equivalent changes, and alterations made to the above specific embodiments based on the technical essence of the present invention should be considered within the protection scope of the present invention.

Claims

1. A conductor current-carrying capacity-sag coupling modeling method based on electro-thermal-mechanical coupling, characterized in that, include: S1. Based on the obtained Joule heat power, solar heat absorption power, convective heat dissipation power and radiative heat dissipation power, establish a heat balance equation and solve the heat balance equation to obtain the surface temperature of the conductor. S2. Using the surface temperature of the conductor as a boundary condition, construct a concentric multilayer radial thermal conduction model, and solve the concentric multilayer radial thermal conduction model to obtain the radial temperature gradient of the conductor. S3. Calculate the strain of various materials in the conductor based on the radial temperature gradient of the conductor, and obtain the true horizontal stress through adaptive iteration; S4. Substitute the actual horizontal stress and the obtained conductor geometric parameters into the parabolic model to obtain the maximum sag of the conductor under the current working conditions.

2. The conductor current-carrying capacity-sag coupling modeling method based on electro-thermal-mechanical coupling according to claim 1, characterized in that, The heat balance equation is expressed as follows: ， in, This represents the Joule heat power generated by the resistance of the circuit itself. I represents the AC resistance of the conductor at the maximum permissible operating temperature, and I represents the current carrying capacity of the conductor. This represents the solar heat absorption power per unit length of conductor under sunlight conditions. This represents the convective heat dissipation power per unit length of the conductor during operation. This represents the radiative heat dissipation power per unit length of the conductor.

3. The conductor current-carrying capacity-sag coupling modeling method based on electro-thermal-mechanical coupling according to claim 1, characterized in that, Solving the heat balance equation yields the conductor surface temperature, including: Construct based on conductor surface temperature Nonlinear functions with variables The expression is: ， in, It is Joule fever; and equal; The Newton-Raphson method is used to iterate the nonlinear function, and the expression is: 。 4. The conductor current-carrying capacity-sag coupling modeling method based on electro-thermal-mechanical coupling according to claim 1, characterized in that, S2 includes: S2.1 By solving the differential equation of heat conduction in the hollow cylindrical layer of the conductor, the radius of any part of the aluminum stranded wire layer can be obtained. Temperature distribution function at [location] , temperature distribution function Substitute the average temperature Integrating the expression yields the average temperature of the aluminum stranded wire. ; S2.2 By solving the differential equation of heat conduction in the solid cylindrical layer of the conductor, the inner radius of the steel core can be obtained. Temperature distribution function at [location] , temperature distribution function Substitute the average temperature Integrating the expression yields the average temperature of the steel core. ; S2.

3. Based on the average temperature of the steel core and the average temperature of the aluminum stranded wire, the radial temperature gradient of the conductor is obtained.

5. The conductor current-carrying capacity-sag coupling modeling method based on electro-thermal-mechanical coupling according to claim 1, characterized in that, Calculate the strain of various materials in the conductor, including: The thermal strain of the steel core and aluminum stranded wire is obtained based on the radial temperature gradient of the conductor, and the expression is: ， ， Based on the thermal strain of the steel core and aluminum stranded wire, combined with the mechanical elastic strain and settlement strain of the steel core and aluminum stranded wire, as well as the creep strain caused by the service life of the overhead conductor, we obtain: The strain expression for the steel core is: ; The strain expression for the aluminum stranded wire is: ; Among them, DT A and DT B Thermal strain of steel core and aluminum stranded wire, respectively, ELA A and ELA B The mechanical elastic strains of the steel core and aluminum stranded wires are respectively, ST A and ST B Settlement strains of steel core and aluminum stranded wire, respectively, CPR A and CPR B The creep strain refers to the creep strain caused by the service life of steel core and aluminum stranded wires in overhead conductors.

6. The conductor current-carrying capacity-sag coupling modeling method based on electro-thermal-mechanical coupling according to claim 5, characterized in that, The true horizontal stress is obtained through adaptive iteration, including: Set an initial assumed value for the horizontal stress of the conductor. The axial stress borne by the steel core and aluminum stranded wire was preliminarily calculated. and ; Axial stress on aluminum stranded wire Make a judgment: like This indicates that the conductor is under normal stress. The Newton-Raphson method will then be used to verify whether the strain of the steel core and aluminum stranded wire satisfies the conventional mechanical equilibrium conditions. ; like This indicates that the conductor has reached or exceeded the inflection point temperature, and the aluminum stranded wire no longer bears axial tensile force; the calculation logic is automatically switched using the Newton-Raphson method: the stress of the aluminum stranded wire is... The value is forcibly set to zero, and subsequent verification is performed based on the new mechanical equilibrium conditions, namely, only the steel core is subjected to force and its strain is balanced.

7. The conductor current-carrying capacity-sag coupling modeling method based on electro-thermal-mechanical coupling according to claim 1, characterized in that, Obtaining the true horizontal stress through adaptive iteration also includes: When the equation is not satisfied According to and The difference between them, or the assumed value of horizontal stress obtained by numerical solution based on the new equilibrium criterion after the inflection point. Make corrections to construct a system with horizontal stress. Error function of variables Then, the result is approximated using the Newton-Raphson method, expressed as: ， Corrected horizontal stress This will be used to initiate a new round of iterative calculations until the strain difference is less than the preset convergence accuracy, at which point the horizontal stress... This is the actual horizontal stress of the conductor under the current operating conditions.

8. The conductor current-carrying capacity-sag coupling modeling method based on electro-thermal-mechanical coupling according to claim 1, characterized in that, The construction of the parabolic model includes: Assuming the conductor operates in a windless state, based on the premise that the bending moment at any point on the flexible steel cable is zero, a force analysis is performed on the infinitesimal element on the conductor, yielding the force balance equations for the suspension points on both sides of the towers and any point P(x, y) on the conductor: ， ， In the formula, It is the vertical stress component of the axial stress of the conductor at point A along the y-axis; assuming the connection between the lower tower and the conductor is the origin, a simplified parabolic model with respect to sag is obtained, expressed as: ， in, γ is the horizontal stress component on the conductor; l is the horizontal projected length between the two suspension points; h is the height difference between the towers on both sides within the conductor span. The angle between the load and the vertical direction.

9. The conductor current-carrying capacity-sag coupling modeling method based on electro-thermal-mechanical coupling according to claim 1, characterized in that, To obtain the maximum sag of the conductor under the current operating conditions, including: Using a mathematical analytical tree connecting the two towers, the sag at a distance x from the origin on the parabolic model is obtained as follows: ， By calculating the extreme value of the above formula, the maximum sag of the conductor under the current working condition is obtained. The calculation expression is: 。 10. A conductor current-carrying capacity-sag coupling modeling system based on electro-thermal-mechanical coupling, characterized in that, include: The conductor surface temperature calculation module is used to establish a heat balance equation based on the obtained Joule heat power, solar heat absorption power, convective heat dissipation power and radiative heat dissipation power, and solve the heat balance equation to obtain the conductor surface temperature. The radial temperature gradient acquisition module for the conductor is used to construct a concentric multilayer radial heat conduction model by using the surface temperature of the conductor as a boundary condition, and to obtain the radial temperature gradient of the conductor by solving the concentric multilayer radial heat conduction model. The module for obtaining the true horizontal stress is used to calculate the strain of various materials in the conductor based on the radial temperature gradient of the conductor, and to obtain the true horizontal stress through adaptive iteration. The maximum sag acquisition module is used to substitute the actual horizontal stress and the acquired conductor geometric parameters into the parabolic model to obtain the maximum sag of the conductor under the current working conditions.

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