Method, device and equipment for determining critical ice-melting current of iced conductor and conductor

Abstract

The application provides a method and device for determining critical ice-melting current of an iced conductor, an apparatus and a conductor. A simplified model of the iced conductor in a critical ice-melting state is established. A heat balance equation is constructed according to the simplified model of the iced conductor and a thermal circuit analysis method, and the heat balance equation includes an outer surface temperature of an ice layer and the critical ice-melting current. A mixed convection heat transfer coefficient of the heat balance equation is calculated according to a preset outer surface temperature of the ice layer. The heat balance equation is subjected to a transcendental term conversion process according to the mixed convection heat transfer coefficient, and a monomial quartic equation based on the outer surface temperature of the ice layer is obtained. The monomial quartic equation is iteratively solved until the outer surface temperature of the ice layer meets a preset convergence requirement, and a target outer surface temperature of the ice layer is obtained. The critical ice-melting current of the iced conductor is calculated by substituting the target outer surface temperature of the ice layer into the heat balance equation, and the accuracy and efficiency of the critical ice-melting current calculation are improved, thereby providing good theoretical support and engineering application scheme for iced conductor protection.

Description

Technical Field

[0001] This application relates to the field of power transmission line de-icing technology, and in particular to a method, apparatus, equipment and conductor for determining the critical de-icing current of an ice-covered conductor. Background Technology

[0002] Icing on transmission lines is one of the core challenges faced by power systems in low-temperature, high-humidity winter environments. In the field of de-icing technology, the critical de-icing current is a key parameter for determining whether de-icing can be initiated, and its calculation accuracy directly affects the formulation and execution efficiency of de-icing strategies. However, existing methods lack sufficient computational efficiency and stability under complex weather conditions, increasing the risk to power grid operation. Therefore, there is an urgent need for an efficient and stable method for calculating the critical de-icing current to meet the needs of de-icing protection and de-icing decision-making under different operating conditions, ensuring the safe operation of the power grid under extreme weather conditions.

[0003] In existing technologies, the calculation of critical melting current is mainly based on heat transfer theory, which is achieved by establishing a heat balance equation and solving it using analytical or numerical methods. Specifically, the icing conductor is simplified into a multi-layered concentric circle structure, assuming that the temperature of the inner surface of the ice layer is constant (0°C), and the equation is derived through the balance relationship between Joule heating and heat dissipation (convection and radiation).

[0004] However, the equations in the above technical solutions are highly complex, which reduces the accuracy and efficiency of solving for the ice-melting current. Summary of the Invention

[0005] This application provides a method, apparatus, equipment, and conductor for determining the critical melting current of an ice-covered conductor, in order to improve the accuracy and efficiency of solving for the melting current.

[0006] In a first aspect, this application provides a method for determining the critical de-icing current of an ice-covered conductor, comprising:

[0007] A simplified model of an ice-covered conductor under critical melting conditions was established;

[0008] Based on the simplified model of the ice-covered conductor and the thermal circuit analysis method, a heat balance equation is constructed, which includes the outer surface temperature of the ice layer and the critical melting current.

[0009] The mixing convection heat transfer coefficient of the heat balance equation is calculated based on the preset outer surface temperature of the ice layer.

[0010] The heat balance equation is transformed by the superposition term based on the mixed convective heat transfer coefficient to obtain a univariate quartic equation based on the outer surface temperature of the ice layer.

[0011] The quartic equation is solved iteratively until the outer surface temperature of the ice layer meets the preset convergence requirement, and the target outer surface temperature of the ice layer is obtained.

[0012] Substituting the outer surface temperature of the target ice layer into the heat balance equation, the critical de-icing current of the icing conductor is calculated.

[0013] Furthermore, the heat balance equation is transformed by exceeding the threshold term based on the mixed convective heat transfer coefficient, resulting in a univariate quartic equation based on the outer surface temperature of the ice layer, including:

[0014] Based on the mixed convective heat transfer coefficient, the excess term of the outer surface temperature of the ice layer is determined to be included in the heat balance equation;

[0015] Based on theoretical constraints, the transcendental term containing the outer surface temperature of the ice layer in the heat balance equation is transformed to obtain a univariate quartic equation based on the outer surface temperature of the ice layer.

[0016] The theoretical constraint is that the outer surface temperature of the ice layer is constant.

[0017] Further, the quartic equation is iteratively solved until the outer surface temperature of the ice layer meets a preset convergence requirement, thereby obtaining the target outer surface temperature of the ice layer, including:

[0018] The quartic equation in one variable is solved iteratively to obtain the updated outer surface temperature of the ice layer;

[0019] Based on the updated outer surface temperature of the ice layer, the quartic equation is updated to obtain the updated quartic equation.

[0020] When the updated outer surface temperature of the ice layer meets the preset convergence requirement, the target outer surface temperature of the ice layer is obtained;

[0021] The preset convergence requirement is that the error between two adjacent iterations is less than the preset temperature difference tolerance.

[0022] Furthermore, the simplified model of the icing conductor is a three-layer concentric circle structure;

[0023] The three-layer concentric circle structure consists of a steel core, an aluminum layer, and a circular uniform ice-coating layer, from the inside out.

[0024] Furthermore, in the simplified model of the icing conductor, under the critical melting state, the inner surface temperature of the ice layer is constant at 0°C, and the Joule heat is equal to the sum of convective and radiative heat dissipation.

[0025] The temperature of each part of the ice-covered conductor remains constant and the mass of the ice layer remains unchanged.

[0026] Furthermore, the mixed convection heat transfer coefficient is a power superposition of the forced convection Nusselt number and the natural convection Nusselt number;

[0027] The forced convection Nusselt number and the natural convection Nusselt number are calculated based on the Reynolds number, Prandtl number, and Grashof number.

[0028] Secondly, this application provides a device for determining the critical de-icing current of an ice-covered conductor, comprising:

[0029] The model building module is used to build a simplified model of the ice-covered conductor under critical melting conditions.

[0030] The heat balance equation construction module is used to construct heat balance equations based on the simplified model of the ice-covered conductor and the thermal circuit analysis method. The heat balance equations include the outer surface temperature of the ice layer and the critical melting current.

[0031] The mixed convection heat transfer coefficient calculation module is used to calculate the mixed convection heat transfer coefficient of the heat balance equation based on the preset outer surface temperature of the ice layer.

[0032] A quartic equation generation module is used to perform transcendental transformation on the heat balance equation based on the mixed convection heat transfer coefficient, thereby obtaining a quartic equation based on the outer surface temperature of the ice layer.

[0033] The ice layer outer surface temperature acquisition module is used to iteratively solve the univariate quartic equation until the ice layer outer surface temperature meets the preset convergence requirement, thereby obtaining the target ice layer outer surface temperature.

[0034] The critical melting current calculation module is used to substitute the outer surface temperature of the target ice layer into the heat balance equation to calculate the critical melting current of the ice-covered conductor.

[0035] Thirdly, this application provides a device for determining the critical melting current of an ice-covered conductor, comprising: a memory and a processor;

[0036] The memory stores computer-executed instructions;

[0037] The processor executes computer execution instructions stored in the memory, causing the processor to perform the method as described in any of the first aspects.

[0038] Fourthly, this application provides a conductor for calculating critical de-icing current, comprising:

[0039] A steel core, an aluminum layer, and a circular uniform ice coating layer are arranged concentrically in sequence to form a three-layer concentric circle structure.

[0040] The geometric parameters of the conductor are used to establish a simplified model of the icing conductor, and the thermophysical properties of the conductor are configured to support the construction of a thermal equilibrium equation to achieve the determination method described in the first aspect.

[0041] The heat balance equation satisfies the condition that the inner surface temperature of the ice layer is constant at 0°C and that Joule heat is equal to the sum of convective and radiative heat dissipation.

[0042] Furthermore, the heat conduction path of the conductor is combined with the dynamic calculation model of the mixed convection heat transfer coefficient, and the critical ice-melting current is calculated through an iterative algorithm.

[0043] The method, apparatus, equipment, and conductor provided in this application for determining the critical melting current of iced conductors are as follows: A simplified model of the iced conductor under critical melting conditions is established; based on the simplified model and thermal circuit analysis, a heat balance equation is constructed, including the outer surface temperature of the ice layer and the critical melting current; the mixed convection heat transfer coefficient of the heat balance equation is calculated based on the preset outer surface temperature of the ice layer; the heat balance equation is transformed by overriding terms based on the mixed convection heat transfer coefficient, resulting in a univariate quartic equation based on the outer surface temperature of the ice layer; the univariate quartic equation is iteratively solved until the outer surface temperature of the ice layer meets the preset convergence requirement, obtaining the target outer surface temperature of the ice layer; the target outer surface temperature of the ice layer is substituted into the heat balance equation to calculate the critical melting current of the iced conductor, improving the accuracy and efficiency of the critical melting current calculation and providing good theoretical support and engineering application solutions for icing protection of transmission lines. Attached Figure Description

[0044] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0045] Figure 1 A flowchart illustrating an embodiment of the method for determining the critical de-icing current of an ice-covered conductor provided in this application;

[0046] Figure 2 A flowchart illustrating Embodiment 2 of the method for determining the critical de-icing current of an ice-covered conductor provided in this application;

[0047] Figure 3 A flowchart illustrating Embodiment 3 of the method for determining the critical de-icing current of an ice-covered conductor provided in this application;

[0048] Figure 4 This is a simplified structural diagram of the icing conductor provided in this application;

[0049] Figure 5 A schematic diagram of the structure of the device for determining the critical de-icing current of the icing conductor provided in this application;

[0050] Figure 6 A schematic diagram of the device for determining the critical de-icing current of the icing conductor provided in this application.

[0051] The accompanying drawings have illustrated specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to specific embodiments. Detailed Implementation

[0052] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0053] This application applies to the icing protection and de-icing decision-making scenarios of high-voltage transmission lines in low-temperature and high-humidity environments during winter. Specifically, it includes: (1) real-time monitoring of the icing status of transmission lines and calculation of the critical de-icing current during power grid operation and maintenance to initiate de-icing operations; (2) dynamic adjustment of de-icing strategies for complex meteorological conditions with different wind speeds, ambient temperatures and icing thicknesses; and (3) optimization of conductor selection and de-icing system configuration by simulating the critical de-icing current under different operating conditions during the transmission line design phase.

[0054] Based on the above scenarios, it is evident that existing technologies, when calculating the critical melting current, do not comprehensively consider the mixed effect of forced convection and natural convection, leading to deviations in the calculated surface heat transfer coefficient and affecting the accuracy of the final results. Furthermore, traditional methods require directly solving complex equations containing higher-order and transcendental terms, which is difficult to solve analytically and computationally inefficient. For example, when wind speed changes cause fluctuations in the outer surface temperature of the ice layer, existing methods are prone to misjudgments due to poor convergence, delaying melting decisions. Simultaneously, some models rely on early heat transfer theories without incorporating a dynamic adjustment mechanism for the mixed convection heat transfer coefficient, resulting in discrepancies between the calculated results and actual operating conditions.

[0055] To address the aforementioned technical challenges, this application, based on heat transfer theory and a mixed convection heat transfer model, transforms complex transcendental equations into efficiently solvable quartic equations by dynamically adjusting the mixed convection heat transfer coefficient and combining iterative algorithms. This enables high-precision and high-stability calculation of the critical melting current. This technical concept simplifies the heat balance equations through theoretical constraints and gradually approximates the stable solution using the dynamic iterative mechanism of the mixed convection heat transfer coefficient. This solves the problems of low computational efficiency and poor adaptability caused by the complexity and insufficient convergence of traditional methods.

[0056] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0057] Figure 1 This is a flowchart illustrating an embodiment of the method for determining the critical de-icing current of an icing conductor provided in this application. Figure 1 As shown, the method includes:

[0058] S101. Establish a simplified model of the icing conductor under critical melting conditions.

[0059] The critical melting state refers to a dynamic thermal equilibrium limit state reached by the icing conductor, in which the temperature of the inner surface of the ice layer is just maintained at the freezing point (0℃), the Joule heat generated by the conductor is equal to the total heat lost to the environment from the outer surface of the ice layer, the temperature and mass of the ice layer at each point inside the icing conductor remain constant, and the ice layer is at the critical point where it is about to begin to melt.

[0060] The simplified model of an icing conductor refers to an idealized physical model established for theoretical analysis. In this application, it specifically refers to the abstraction of an actual icing conductor into a three-layer concentric cylindrical structure consisting of a steel core, an aluminum stranded wire layer, and a circular uniform ice layer, from the inside out.

[0061] In existing technologies, the structure of icing conductors is complex, making direct thermodynamic analysis difficult. Furthermore, the lack of a unified physical definition of the critical state leads to an unstable model foundation, affecting the accuracy of subsequent calculations. This step, however, establishes a precise and physically accurate mathematical model foundation for the entire calculation by clarifying the three core physical conditions of the "critical melting state" (0°C on the inner surface of the ice, thermal equilibrium, and steady state).

[0062] S102. Based on the simplified model of the icing conductor and the thermal circuit analysis method, construct the thermal balance equation.

[0063] Among them, the thermal circuit analysis method is a method to analyze heat conduction problems by drawing on Ohm's law and Kirchhoff's law in circuit theory, comparing temperature difference to voltage, heat flow to current, and thermal resistance to resistance.

[0064] The heat balance equation is a mathematical expression that describes the conservation relationship where the input heat (Joule heat) and output heat (convective heat dissipation and radiative heat dissipation) are equal under the critical melting state. Specifically, it includes the unknown quantities of the outer surface temperature of the ice layer and the unknown quantity of the critical melting current.

[0065] Specifically, the heat balance equation that the icing conductor model needs to satisfy (variables related to the conductor length all represent values ​​per unit length) is:

[0066]

[0067]

[0068] Where I represents the conductor current, This indicates the resistance of a wire at a specific temperature. , These represent convective heat flow and radiative heat flow, respectively. , , These represent the density, specific heat capacity, and volume of each region, respectively. This represents the latent heat absorbed per unit mass of ice melting.

[0069] In addition, the heat balance equation includes several terms such as Joule heating generated by electric current, convective and radiative heat dissipation from the ice surface, heat absorbed by temperature changes in different regions, and latent heat absorbed by ice melting. Based on the above critical melting conditions, the inner surface of the ice layer in the icing conductor model needs to maintain... Furthermore, since the model is in dynamic equilibrium, the temperature of each part remains constant, and the mass of the ice layer does not change. The heat absorbed by temperature changes in each region and the latent heat absorbed by ice melting are both zero. Therefore, the above equation can be simplified to:

[0070]

[0071] in, This represents the critical melting current. Using thermal circuit analysis, the heat flow conservation equation can be written as follows:

[0072]

[0073] in, This indicates the Joule heat flux generated by the electric current. This represents the heat transfer flux through the ice layer. Using Ohm's law applicable to thermal circuits, we obtain the following equation:

[0074]

[0075] in, , These represent the temperatures of the inner and outer surfaces of the ice layer, respectively. Indicates the thermal resistance of the ice layer. Indicates ambient temperature. This represents the equivalent thermal resistance to heat dissipation from the outer surface of the ice layer. Through heat transfer equations, the thermal resistance per unit length of ice layer can be calculated using the following formula:

[0076]

[0077] in, , These represent the radii of the inner and outer surfaces of the ice layer, respectively. This represents the thermal conductivity of the ice layer, with a value of [value missing]. Based on the above formulas and heat transfer studies, the following equations can be written under the critical melting state:

[0078]

[0079]

[0080]

[0081]

[0082] Where h represents the surface heat transfer coefficient; This represents the surface emissivity of the ice layer, with a value of 0.98. Represents the blackbody radiation constant, with a value of Combining the above formulas, we can obtain:

[0083]

[0084] in, The critical melting current, The resistance of a wire at a specific temperature. The inner surface temperature of the ice layer. The outer surface temperature of the ice layer. For ambient temperature, Thermal resistance per unit length of ice layer, The radius of the outer surface of the ice layer. The surface heat transfer coefficient, Emissivity of the ice surface is the blackbody radiation constant.

[0085] As the above analysis shows, the simplified model of the icing conductor in the critical melting state can be solved analytically through theoretical analysis. The known quantities in this problem include the model's geometric parameters and the conductor's resistance. Ambient temperature Wind speed inner surface temperature of ice layer The unknowns to be solved include the temperature of the outer surface of the ice layer. and critical de-icing current .

[0086] This step applies the thermal circuit analysis method, equating the complex heat transfer process to an intuitive series thermal resistance network (heat source from the conductor → thermal resistance of the ice layer → parallel heat dissipation from external convection and radiation). Based on the critical state assumption of S101, the complete energy equation, which includes transient heat capacity and latent heat of phase change, is successfully simplified into a clear steady-state thermal balance equation. This equation has a clear physical meaning and is directly related to the key intermediate variable of the critical melting current to be determined, the outer surface temperature of the ice layer, as well as all known environmental and geometric parameters, providing a core mathematical framework for subsequent solutions.

[0087] S103. Calculate the mixing convection heat transfer coefficient of the heat balance equation based on the preset outer surface temperature of the ice layer.

[0088] Among them, the mixed convection heat transfer coefficient is a comprehensive parameter characterizing the intensity of convective heat transfer between the outer surface of the ice layer and the surrounding air.

[0089] The preset outer surface temperature of the ice layer refers to an initial estimated value of the outer surface temperature of the ice layer assigned at the start of the iterative solution to initiate the calculation (e.g., taking the midpoint between the ambient temperature and the freezing point temperature).

[0090] Specifically, in the heat balance equation of S102, the heat transfer coefficient h of the ice surface is the key to solving it. It requires considering the mixed convection heat transfer coefficient of forced convection and natural convection, and the calculation formula is as follows:

[0091]

[0092] in, Let be the thermal conductivity of air, and x be the characteristic length. In the simplified model of the icing conductor constructed in this application, the diameter of the icing conductor is taken as . .in, To force convection Nusel numbers, The Nusselt number represents natural convection. "Forced convection" is driven by an external wind field (wind speed u), while "natural convection" is driven by the air density difference caused by the temperature difference between the ice surface and the environment.

[0093] in addition, and The calculation depends on the Reynolds number. Prandtl number P r And Grashof's number G r The calculation formula is as follows:

[0094]

[0095]

[0096] in, , For undetermined coefficients, The index is yet to be determined. , , These are the similarity feature numbers: Reynolds number, Prandtl number, and Grashof number. Reynolds number The calculation formula is as follows:

[0097]

[0098] Where u represents wind speed; v represents the air viscosity coefficient. ; Indicates air density; Represents the aerodynamic viscosity coefficient, with a value of [value missing]. .

[0099] In addition, Prandtl number The calculation formula is as follows:

[0100]

[0101] in, This represents the isobaric specific heat capacity of air, and its value is [value missing]. ; This represents the thermal conductivity of air, with a value of [value missing]. .

[0102] Glaschov number The calculation formula is as follows:

[0103]

[0104] Where g represents the acceleration due to gravity; The coefficient of volume expansion is given. Assuming the air in the model conforms to the properties of an ideal gas, then... ,in This is the qualitative temperature.

[0105] In this model, the arithmetic mean temperature of the boundary layer is taken. Among the aforementioned similar characteristic numbers, the Reynolds number... Prandtl numbers All of these can be obtained from known conditions, while the Grashof number... The unknown quantity is the outer surface temperature of the ice layer. .

[0106] Existing transmission lines are situated in a natural environment, where surface heat transfer is influenced by both forced convection (wind) and natural convection (temperature difference). Current methods often neglect one of these factors or employ simple empirical formulas, leading to inaccurate calculations of the heat transfer coefficient and becoming a major source of error in critical current calculations. This step creatively employs a hybrid convection model to calculate the combined Nusselt number, thereby obtaining the heat transfer coefficient. This model seamlessly integrates forced convection effects (via Reynolds number Re) and natural convection effects (via Grashof number Gr), where the Gr number incorporates the desired outer surface temperature of the ice layer. By pre-setting an initial value for the outer surface temperature of the ice layer, this complex nonlinear term, strongly coupled with unknowns, is transformed for the first time into a "known quantity" that can be calculated in the current iteration step. This process is a crucial prerequisite for subsequent equation transformation and iterative solutions, significantly improving the model's computational accuracy and physical realism across a wide range of wind speeds and temperature differences.

[0107] S104. Based on the mixed convection heat transfer coefficient, the heat balance equation is transformed by the transcendental term to obtain a univariate quartic equation based on the outer surface temperature of the ice layer.

[0108] The transcendental term transformation process refers to the process of using mathematical transformations to isolate or solidify the influence of transcendental function terms (here referring to Gr terms implicit in h and highly correlated with the outer surface temperature of the ice layer) that cannot be solved by a finite number of algebraic operations in the original equation, so that the equation becomes a pure algebraic equation.

[0109] Specifically, this step includes:

[0110] Based on the mixed convection heat transfer coefficient, the excess term of the ice layer outer surface temperature in the heat balance equation is determined;

[0111] Based on theoretical constraints, the transcendental term containing the outer surface temperature of the ice layer in the heat balance equation is transformed to obtain a univariate quartic equation based on the outer surface temperature of the ice layer.

[0112] The theoretical constraint is that the temperature of the outer surface of the ice layer is constant.

[0113] For example, the surface heat transfer coefficient h can be considered as a known quantity, then the unknown quantity, the outer surface temperature of the ice layer, in S103 can be considered... The transcendental equation is transformed into the following quartic equation in one variable:

[0114]

[0115] Among them, the coefficients k1, k2, and k3 can all be calculated from known quantities, and their calculation formulas are shown below:

[0116]

[0117]

[0118]

[0119] Where the unknown x represents the temperature of the outer surface of the ice layer. .

[0120] This step utilizes the technique in S103 of temporarily "solidifying" h by setting the outer surface temperature of the ice layer, compressing all the nonlinear complexity related to the outer surface temperature of the ice layer in the original transcendental equation into the coefficients k1, k2, and k3. This transformation converts the physical nonlinear solution problem into a purely mathematical algebraic equation root-finding problem, paving the way for subsequent use of stable and efficient iterative algorithms, and fundamentally overcoming the numerical difficulties of directly solving the original transcendental equation.

[0121] S105. Iterate through the quartic equation until the outer surface temperature of the ice layer meets the preset convergence requirement, and obtain the target outer surface temperature of the ice layer.

[0122] Iterative solution refers to starting from an initial guess and repeatedly applying the same calculation process (preset the outer surface temperature of the ice layer → calculate h → construct and solve a quartic equation → update the outer surface temperature of the ice layer) to generate a series of approximate values ​​that gradually approach the true solution.

[0123] The preset convergence requirement is the standard for judging whether the iteration should stop. It is usually defined as the absolute value of the difference between the outer surface temperature values ​​of the ice layer obtained from two adjacent iterations being less than a very small positive number.

[0124] Specifically, the iterative calculation method described in this step is as follows:

[0125] (1) Set the preset outer surface temperature of the ice layer Substitute Calculated (2) Transform the transcendental equation into a quartic equation in one variable; (3) Solve the quartic equation in one variable to obtain the domain. real solutions in (4) Determine the outer surface temperature of the ice layer using the following formula. Whether it converges: If convergence occurs, the temperature of the outer surface of the ice layer can be obtained. If convergence is not achieved, the newly calculated result will be... As Recalculate the surface heat transfer coefficient Repeat the above calculation process until the target ice layer outer surface problem is obtained.

[0126] This step designs a simple and robust iterative loop: 1) Calculate h using the current estimated outer surface temperature of the ice layer; 2) Substitute h into the equation to solve the quartic equation, and select the real root within a physically reasonable range as the new estimated outer surface temperature of the ice layer; 3) Check convergence. This method only requires solving one definite quartic equation in each iteration, resulting in low computational cost and high determinism. The iterative process has a clear physical meaning (continuously correcting the heat transfer coefficient h to approximate the actual thermal equilibrium), ensuring the correct convergence direction of the algorithm. Finally, it typically requires only 2-3 iterations to achieve extremely high accuracy, with extremely fast convergence speed. Its computational efficiency far exceeds that of traditional general-purpose solvers for nonlinear equations, which are sensitive to initial conditions and may diverge.

[0127] S106. Substitute the outer surface temperature of the target ice layer into the heat balance equation to calculate the critical de-icing current of the icing conductor.

[0128] The target ice surface temperature refers to the high-precision numerical solution of the ice surface temperature obtained after S105 iteration convergence, which satisfies all physical conditions and thermal balance equations.

[0129] The critical de-icing current is the minimum DC current value required to keep the iced conductor in the critical de-icing state defined by S101. It is a key parameter guiding the de-icing operation.

[0130] In this step, based on the obtained outer surface temperature of the ice layer... and the heat balance equation The critical melting current can then be obtained. .

[0131] This process, from physical modeling, equation establishment, nonlinear processing, iterative solution to final parameter acquisition, forms a logically rigorous and interconnected complete technical solution. The final output critical ice-melting current has clear physical meaning and high engineering reliability.

[0132] The method for determining the critical melting current of iced conductors provided in this application is based on heat transfer theory and a simplified iterative algorithm. It comprehensively considers heat conduction, convection, and radiation heat transfer, and uses a simplified iterative algorithm to transform complex transcendental equations into easily solvable quartic equations, thereby improving computational efficiency and stability. This method has high computational accuracy and good convergence, and can be applied to solving the critical melting current under different wind speeds, ambient temperatures, and ice thicknesses. Furthermore, it can systematically analyze the influence of environmental factors on the critical melting current, providing a theoretical basis for decision-making on ice melting of transmission lines.

[0133] Figure 2 This is a flowchart illustrating Embodiment Two of the method for determining the critical de-icing current of an icing conductor provided in this application. Figure 2 As shown, in Figure 1Based on the previous example, the quartic equation is iteratively solved until the outer surface temperature of the ice layer meets the preset convergence requirement, thus obtaining the target outer surface temperature of the ice layer. This method includes:

[0134] S201. Iteratively solve the quartic equation to obtain the updated outer surface temperature of the ice layer.

[0135] The iterative solution process refers to the process of performing a series of calculations to obtain updated values ​​based on the currently known estimated temperature of the outer surface of the ice layer within a complete iterative step. The core of this process is to re-evaluate and solidify the mixing convective heat transfer coefficient using the current temperature value, and then solve the updated quartic equation.

[0136] This step concretizes the iterative loop outlined in S105 into an executable operational unit. It specifies the input (the current estimated outer surface temperature of the ice layer) and output (the updated outer surface temperature of the ice layer) for each iteration. By executing this step, the system can utilize the current best estimate of the system state to recalculate the mixing convection heat transfer effect most significantly affected by temperature, and thereby solve an algebraic equation that more closely approximates the current physical assumptions, thus systematically advancing the solution towards the true value. This is the fundamental action that enables the entire algorithm to move from initial guesses to final convergence.

[0137] S202. Based on the updated outer surface temperature of the ice layer, the quartic equation is updated to obtain the updated quartic equation.

[0138] In this context, "updating" refers to recalculating the mixing convection heat transfer coefficient using the latest obtained ice surface temperature value during the iteration process. This generates a new set of equation coefficients, thus forming a new instance of a "univariate quartic equation" that matches the current temperature estimate. Each iteration corresponds to an equation with updated coefficients.

[0139] Specifically, during the iteration process, how can we dynamically reflect the impact of changes in the outer surface temperature of the ice layer on the heat balance equation, especially on the most nonlinear convective heat transfer term? Static equations cannot describe this coupling relationship.

[0140] This step reveals the core of the dynamic adaptability of the iterative algorithm in this application. Each time a new temperature estimate is obtained, the algorithm does not simply repeat the same equation; instead, it recalculates the mixing convection heat transfer coefficient using the new temperature value, thereby refreshing the coefficients of the quartic equation (mainly those related to the convection term). This means that the equation solved in each iteration is a more accurate mathematical description of the heat balance relationship based on the latest physical picture (the heat transfer intensity determined by the current temperature estimate). This "equation updated with solution" mechanism ensures that the iterative process can effectively track and correct the nonlinear effects caused by temperature changes, which is key to the algorithm's rapid convergence to a high-precision solution.

[0141] S203. When the updated outer surface temperature of the ice layer meets the preset convergence requirements, the target outer surface temperature of the ice layer is obtained.

[0142] Among them, the preset convergence requirement is a quantitative criterion for controlling the termination of the iteration process. It is characterized by the error of the solution results of two adjacent iterations being less than the preset temperature difference tolerance, that is, a preset, extremely small positive threshold (e.g., 0.001K or less), used to determine whether the calculation accuracy meets the requirements.

[0143] The error between two consecutive iterations usually refers to the absolute value of the difference between the ice surface temperature value obtained in the current iteration and the value obtained in the previous iteration.

[0144] This step provides a clear and quantifiable criterion for algorithm termination. By monitoring the difference between two consecutive iterations and comparing it to a preset tolerance reflecting engineering accuracy requirements, the algorithm can automatically determine whether the solution has stabilized. When the difference is less than the tolerance, it indicates that further iterations will have negligible improvement on the solution, and the current value can be used as the "target ice surface temperature" that meets the accuracy requirements. This convergence criterion is simple and effective, has low computational overhead, and has clear physical meaning (temperature changes are negligible), ensuring the reliability of the algorithm's output and avoiding unnecessary computational loops, thus optimizing overall computational efficiency.

[0145] The method for determining the critical melting current of an icing conductor provided in this application embodiment achieves stable and efficient numerical solutions to complex nonlinear thermal equilibrium problems by specifically decomposing the iterative process into standardized steps of "solving-updating-judging". The key method is to dynamically update the coefficients of the quartic equation using the new temperature value obtained in each iteration, enabling the iterative process to accurately track the strong coupling relationship between temperature and convective heat transfer in the physical model. By setting a clear convergence criterion based on the temperature difference between adjacent iterations, it is ensured that the final solution for the outer surface temperature of the ice layer meets the preset calculation accuracy requirements. This embodiment refines and improves... Figure 1The iterative solution process in the embodiment makes the entire algorithm flow clear, controllable and robust, providing a reliable computational framework for quickly and accurately obtaining key temperature parameters under critical melting conditions.

[0146] Figure 3 This is a flowchart illustrating Embodiment 3 of the method for determining the critical de-icing current of an icing conductor provided in this application. Figure 3 As shown, based on Examples 1 and 2, the specific implementation steps of the method for determining the critical de-icing current of iced conductors operating under typical conductor types and environmental parameters are described, including:

[0147] S301. Determine the model parameters and environmental parameters.

[0148] Among them, model parameters refer to physical quantities used to define the geometry and material properties of the simplified model of the icing conductor, such as conductor type, radius of each layer, and material thermal properties.

[0149] Environmental parameters refer to physical quantities that describe the external environment in which the conductor is located, such as ambient temperature and wind speed.

[0150] In this embodiment, the icing conductor model is first determined, using steel-cored aluminum stranded wire. The geometric model is simplified to a concentric circle, with the geometric dimensions referenced to LGJ-400 / 35 steel-cored aluminum stranded wire. The steel core radius is 3.3 mm, the conductor radius is 13.4 mm, the calculated cross-section of the steel core is 34.36 mm², and the calculated cross-section of the aluminum layer is 400 mm². The conductor is iced externally in a uniform circular pattern with an icing thickness of 10 mm.

[0151] Then, the environmental parameters are determined. In this embodiment, the ambient temperature is set to "-7℃", the external forced convection model adopts a fluid sweeping single-tube model, the wind direction is from left to right, and the wind speed is a uniform and constant 5m / s.

[0152] This step provides specific and clear input conditions for the entire calculation example. By selecting a widely used steel-cored aluminum stranded wire model (LGJ-400 / 35) and typical winter icing conditions (-7℃, 5m / s wind speed, 10mm icing), this example has clear engineering representativeness and reference value. Clearly distinguishing between model parameters (such as conductor size, ice thickness, and material properties) and environmental parameters (such as temperature and wind speed) ensures clear subsequent calculation logic and facilitates users in replacing corresponding parameters for new calculations based on actual working conditions, demonstrating the method's versatility and operability.

[0153] S302. Solve for the known quantities in the heat balance equation based on the known parameters.

[0154] Among them, known quantities refer to intermediate parameters or constants that can be directly calculated from the model parameters and environmental parameters determined by S301 before the iterative solution begins. These include geometric dimensions, basic physical property parameters, some similarity characteristic numbers (such as Reynolds number and Prandtl number), and coefficients in relevant empirical formulas.

[0155] Specifically, the basic parameters are determined first. The radius of the inner surface circle of the ice layer is 0.0134m, and the radius of the outer surface circle of the ice layer is 0.0234m.

[0156] The inner surface of the ice layer is considered to be in a mixed state of ice and water during the critical melting stage, with a temperature of 0℃, or 273.15K. The thermal conductivity of the ice layer is taken as 22W / (m•K), the surface emissivity of the ice layer is taken as 0.98, and the density of the ice layer is taken as 920kg / m³. 3 The latent heat of ice is taken as 335,000 J / kg. The air density is taken as 1.293 kg / m³. 3 The aerodynamic viscosity coefficient is taken as 17.2 × 10⁻⁶. -6 The calculated air viscosity coefficient is 13.28 × 10⁻⁶ Pa·s. -6 m 2 / s, the isobaric specific heat capacity of air is taken as 1.005×10 3 J / (kg•K), the thermal conductivity of air is taken as 2.44×10 -2 W / (m•K). Ambient temperature The value is 266.15K.

[0157] Then determine the feature parameters. Feature length. Qualitative temperature Coefficient of volume expansion All contain unknowns .

[0158] Finally, the number of similarity features was determined. Calculated from the known parameters, the Reynolds number was 1.762 × 10⁻⁶. 4 In this case, the fluid flow is considered to be turbulent. The Prandtl number is calculated to be 0.707.

[0159] Grashof numbers contain the unknown T out According to T out Given a value range of (266.15K, 273.15K), the maximum value of the Grashof number is 1.479 × 10⁻⁶. 5 Undetermined coefficients , Undetermined index The relationship between similarity feature number and the similarity feature number is shown in Table 1 and Table 2 below.

[0160] According to the table, The value is 0.193. The value is 0.618. The value is 0.48. The value is 0.25. Therefore, the forced convection Nusselt number is 72.344. The formula for calculating the natural convection Nusselt number is... .

[0161] Table 1 , Relationship with similarity feature number

[0162]

[0163] Table 2 , Relationship with similarity feature number

[0164]

[0165] This step systematically completed the preparatory work before the iteration. First, all basic physical and geometric parameters (such as the inner and outer radii of the ice layer, and the kinematic viscosity of air) were calculated. Second, based on the given ambient wind speed and conductor diameter, the Reynolds number Re and Prandtl number Pr were calculated, and the coefficients and exponents in the empirical formula for forced convection were determined by referring to tables, thus completely determining the forced convection Nusselt number (a constant of 72.344). This series of calculations solidified all parameters that depend on environmental conditions but are independent of the outer surface temperature of the ice layer, so that in subsequent iterations, only the part related to the outer surface temperature of the ice layer (i.e., the natural convection term) needs to be updated each time, greatly reducing the amount of calculation per iteration, improving the overall computational efficiency, and making the iteration logic more concise and clear.

[0166] S303, Iteratively solve for the outer surface temperature of the ice layer.

[0167] In this context, iterative solution specifically refers to executing the iterative algorithms described in Embodiment 1 and Embodiment 2 under the specific parameters provided by S301 and S302 until convergence, ultimately obtaining a numerical solution for the outer surface temperature of the ice layer that meets the accuracy requirements.

[0168] Specifically, the initial value of the outer surface temperature of the ice layer in the Grashof number is first set to... The iteration begins using the aforementioned iterative method, with the convergence condition set as follows: Then perform iterative calculations.

[0169] After two iterations, the results converged, and the final temperature of the outer surface of the ice layer was found to be 271.7643 K.

[0170] Finally, the critical ice-melting current was calculated and found to be 716.92A. The calculated current value is a DC current value.

[0171] This step vividly demonstrates the efficiency and robustness of the proposed method through a complete computational example. First, a reasonable initial value strategy (taking the median value between the ambient temperature and the freezing point temperature) is adopted, providing a good starting point for rapid convergence. Second, a strict relative error convergence condition (<0.000001) is set to ensure high accuracy of the final result. Most importantly, the example results show that the outer surface temperature of the ice layer converges after only two iterations, and the critical melting current is finally calculated to be 716.92 A. This strongly proves that the algorithm constructed in this application, by transforming the complex transcendental equation into a univariate quartic equation and designing a corresponding iterative process, possesses extremely fast convergence speed and excellent numerical stability. This example not only verifies the correctness of the method but also provides users with a computational paradigm and typical results that can be directly referenced.

[0172] The method for determining the critical melting current of icing conductors provided in this application embodiment concretizes the general algorithm of the aforementioned embodiment by selecting a representative conductor model (LGJ-400 / 35) and typical environmental conditions (-7℃, 5m / s wind, 10mm ice) (S301). Before calculation, all parameters independent of the temperature to be determined are systematically calculated and solidified (S302), preparing for efficient iteration. In the iterative solution stage (S303), the method demonstrates excellent performance: starting from a reasonable initial value, it quickly converges to a high-precision temperature solution in only two iterations, and calculates the specific critical melting current value (716.92A) accordingly. This embodiment fully demonstrates the entire process from parameter input to result output, not only verifying the feasibility, accuracy, and efficiency of the method proposed in this application, but also providing a clear and reliable example for engineers to apply this method to solve practical problems.

[0173] Figure 4 This is a simplified structural diagram of the icing conductor provided in this application. Figure 4 As shown, the simplified model of the icing conductor is a three-layer concentric circle structure; the three-layer concentric circle structure consists of a steel core, an aluminum layer, and a circular uniform icing layer from the inside out.

[0174] In the simplified model of the icing conductor, under the critical melting state, the inner surface temperature of the ice layer is constant at 0℃, and the Joule heat is equal to the sum of convective and radiative heat dissipation; the temperature of each part of the icing conductor remains constant and the mass of the ice layer remains unchanged.

[0175] In addition, the geometric parameters and thermophysical properties of the conductors are configured to support the construction of the thermal equilibrium equation, which satisfies that the inner surface temperature of the ice layer is constant at 0°C and that Joule heat is equal to the sum of convective and radiative heat dissipation.

[0176] The thermal conduction path of the conductor is combined with a dynamic calculation model of the mixed convection heat transfer coefficient, and the critical ice-melting current is calculated through an iterative algorithm.

[0177] This embodiment clearly describes the structural characteristics and physical constraints of the critical melting state of the simplified model of the iced conductor, providing a clear model foundation for the subsequent establishment and iterative calculation of the heat balance equation. By integrating geometric parameters, thermophysical parameters, and heat transfer conditions, and introducing a dynamic iterative mechanism for the mixed convection heat transfer coefficient, the model's adaptability to complex convection environments is enhanced, and the calculation accuracy and convergence stability of the critical melting current are improved. This provides a reliable theoretical basis and engineering applicability for transmission line icing decisions.

[0178] Figure 5 This is a schematic diagram of the device for determining the critical de-icing current of the icing conductor provided in this application. Figure 5 As shown, the device 50 for determining the critical melting current of the icing conductor provided in this embodiment includes:

[0179] Model building module 501 is used to build a simplified model of the ice-covered conductor under critical melting conditions;

[0180] The heat balance equation construction module 502 is used to construct the heat balance equation based on the simplified model of the ice-covered conductor and the thermal circuit analysis method. The heat balance equation includes the outer surface temperature of the ice layer and the critical melting current.

[0181] The mixed convection heat transfer coefficient calculation module 503 is used to calculate the mixed convection heat transfer coefficient of the heat balance equation based on the preset outer surface temperature of the ice layer.

[0182] The quartic equation is obtained by module 504, which is used to transform the heat balance equation into a transcendental term based on the mixed convection heat transfer coefficient, and obtains a quartic equation based on the outer surface temperature of the ice layer.

[0183] The outer surface temperature of the ice layer is obtained by module 505, which is used to iteratively solve the quartic equation in one variable until the outer surface temperature of the ice layer meets the preset convergence requirements, and the target outer surface temperature of the ice layer is obtained.

[0184] The critical melting current calculation module 506 is used to substitute the outer surface temperature of the target ice layer into the heat balance equation to calculate the critical melting current of the ice-covered conductor.

[0185] In one possible implementation, the module 504 for obtaining quartic equations in one variable is also specifically used for:

[0186] Based on the mixed convection heat transfer coefficient, the excess term of the ice layer outer surface temperature in the heat balance equation is determined;

[0187] Based on theoretical constraints, the transcendental term containing the outer surface temperature of the ice layer in the heat balance equation is transformed to obtain a univariate quartic equation based on the outer surface temperature of the ice layer.

[0188] The theoretical constraint is that the temperature of the outer surface of the ice layer is constant.

[0189] In one possible implementation, the ice outer surface temperature obtaining module 505 is further specifically used for:

[0190] The quartic equation in one variable is solved iteratively to obtain the updated outer surface temperature of the ice layer.

[0191] Based on the updated outer surface temperature of the ice layer, the quartic equation is updated to obtain the updated quartic equation.

[0192] When the updated outer surface temperature of the ice layer meets the preset convergence requirements, the target outer surface temperature of the ice layer is obtained.

[0193] The preset convergence requirement is that the error between two adjacent iterations is less than the preset temperature difference tolerance.

[0194] In one possible implementation, the simplified model of the icing conductor is a three-layer concentric circle structure;

[0195] The three-layer concentric circle structure consists of a steel core, an aluminum layer, and a circular, uniformly coated ice layer, arranged from the inside out.

[0196] In one possible implementation, the simplified model of the icing conductor, under the critical melting state, has a constant inner surface temperature of 0°C and Joule heat equal to the sum of convective and radiative heat dissipation.

[0197] The temperature of each part of the ice-covered conductor remains constant and the mass of the ice layer remains unchanged.

[0198] In one possible implementation, the mixed convection heat transfer coefficient is a power superposition of the forced convection Nusselt number and the natural convection Nusselt number;

[0199] The forced convection Nusselt number and the natural convection Nusselt number are calculated based on the Reynolds number, Prandtl number, and Grashof number.

[0200] The device for determining the critical melting current of the icing conductor provided in this embodiment can execute the method provided in the above-described method embodiment. Its implementation principle and technical effect are similar, and will not be described in detail here.

[0201] Figure 6 This is a schematic diagram of the device for determining the critical de-icing current of the icing conductor provided in this application. Figure 6 As shown, the device 60 for determining the critical melting current of an icing conductor provided in this embodiment includes at least one processor 601 and a memory 602. Optionally, the device 60 further includes a communication component 603. The processor 601, memory 602, and communication component 603 are connected via a bus 604.

[0202] In a specific implementation, at least one processor 601 executes computer execution instructions stored in memory 602, causing at least one processor 601 to perform the above-described method.

[0203] The specific implementation process of processor 601 can be found in the above method embodiments, and its implementation principle and technical effect are similar. It will not be repeated here.

[0204] In the above embodiments, it should be understood that the processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor.

[0205] The memory may include random access memory (RAM) and may also include non-volatile memory (NVM), such as at least one disk storage device.

[0206] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0207] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described method.

[0208] This application also provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the above-described method.

[0209] The aforementioned readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer.

[0210] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. Of course, the readable storage medium can also be a component of the processor. The processor and the readable storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and the readable storage medium can exist as discrete components in the device.

[0211] The division of units is merely a logical functional division; in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0212] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0213] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0214] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0215] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0216] Finally, it should be noted that other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein, and is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

Claims

1. A method for determining the critical de-icing current of an icy conductor, characterized in that, include: A simplified model of an ice-covered conductor under critical melting conditions was established; Based on the simplified model of the ice-covered conductor and the thermal circuit analysis method, a heat balance equation is constructed, which includes the outer surface temperature of the ice layer and the critical melting current. The mixing convection heat transfer coefficient of the heat balance equation is calculated based on the preset outer surface temperature of the ice layer. The heat balance equation is transformed by the superposition term based on the mixed convective heat transfer coefficient to obtain a univariate quartic equation based on the outer surface temperature of the ice layer. The quartic equation is solved iteratively until the outer surface temperature of the ice layer meets the preset convergence requirement, and the target outer surface temperature of the ice layer is obtained. Substituting the outer surface temperature of the target ice layer into the heat balance equation, the critical de-icing current of the icing conductor is calculated.

2. The determination method according to claim 1, characterized in that, The heat balance equation is transformed by overriding terms based on the mixed convective heat transfer coefficient, resulting in a univariate quartic equation based on the outer surface temperature of the ice layer, including: Based on the mixed convective heat transfer coefficient, the excess term of the outer surface temperature of the ice layer is determined to be included in the heat balance equation; Based on theoretical constraints, the transcendental term containing the outer surface temperature of the ice layer in the heat balance equation is transformed to obtain a univariate quartic equation based on the outer surface temperature of the ice layer. The theoretical constraint is that the outer surface temperature of the ice layer is constant.

3. The determination method according to claim 1, characterized in that, The quartic equation is iteratively solved until the outer surface temperature of the ice layer meets the preset convergence requirement, thus obtaining the target outer surface temperature of the ice layer, including: The quartic equation in one variable is solved iteratively to obtain the updated outer surface temperature of the ice layer; Based on the updated outer surface temperature of the ice layer, the quartic equation is updated to obtain the updated quartic equation. When the updated outer surface temperature of the ice layer meets the preset convergence requirement, the target outer surface temperature of the ice layer is obtained; The preset convergence requirement is that the error between two adjacent iterations is less than the preset temperature difference tolerance.

4. The determining method according to any one of claims 1 to 3, characterized in that, The simplified model of the icing conductor is a three-layer concentric circle structure; The three-layer concentric circle structure consists of a steel core, an aluminum layer, and a circular uniform ice-coating layer, from the inside out.

5. The determination method according to claim 4, characterized in that, In the simplified model of the ice-covered conductor, under the critical melting state, the inner surface temperature of the ice layer is constant at 0℃, and the Joule heat is equal to the sum of convective and radiative heat dissipation. The temperature of each part of the ice-covered conductor remains constant and the mass of the ice layer remains unchanged.

6. The determination method according to claim 2, characterized in that, The mixed convection heat transfer coefficient is a power superposition of the forced convection Nusselt number and the natural convection Nusselt number; The forced convection Nusselt number and the natural convection Nusselt number are calculated based on the Reynolds number, Prandtl number, and Grashof number.

7. A device for determining the critical melting current of an icing conductor, characterized in that, include: The model building module is used to build a simplified model of the ice-covered conductor under critical melting conditions. The heat balance equation construction module is used to construct heat balance equations based on the simplified model of the ice-covered conductor and the thermal circuit analysis method. The heat balance equations include the outer surface temperature of the ice layer and the critical melting current. The mixed convection heat transfer coefficient calculation module is used to calculate the mixed convection heat transfer coefficient of the heat balance equation based on the preset outer surface temperature of the ice layer. A quartic equation generation module is used to perform transcendental transformation on the heat balance equation based on the mixed convection heat transfer coefficient, thereby obtaining a quartic equation based on the outer surface temperature of the ice layer. The ice layer outer surface temperature acquisition module is used to iteratively solve the univariate quartic equation until the ice layer outer surface temperature meets the preset convergence requirement, thereby obtaining the target ice layer outer surface temperature. The critical melting current calculation module is used to substitute the outer surface temperature of the target ice layer into the heat balance equation to calculate the critical melting current of the ice-covered conductor.

8. A device for determining the critical de-icing current of an icing conductor, characterized in that, include: Memory, processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory, causing the processor to perform the method as described in any one of claims 1-6.

9. A conductor for calculating critical de-icing current, characterized in that, include: A steel core, an aluminum layer, and a circular uniform ice coating layer are arranged concentrically in sequence to form a three-layer concentric circle structure. The geometric parameters of the conductor are used to establish a simplified model of the icing conductor, and the thermophysical properties of the conductor are used to construct a thermal equilibrium equation to achieve the determination method described in claim 1. The heat balance equation satisfies the condition that the inner surface temperature of the ice layer is constant at 0°C and that Joule heat is equal to the sum of convective and radiative heat dissipation.

10. The conductor according to claim 9, characterized in that, The heat conduction path of the conductor is combined with the dynamic calculation model of the mixed convection heat transfer coefficient, and the critical ice-melting current is calculated through an iterative algorithm.

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