Method for optimizing landing section cable load flow based on convective heat flux saturation characteristics

Abstract

The application discloses a landing section submarine cable current-carrying capacity optimization method based on convection heat flux saturation characteristics, and the method comprises the following steps: firstly, collecting the submarine cable body structure, thermal physical properties and landing section marine environment thermal parameters to generate comprehensive thermal parameter sets; secondly, establishing a submarine cable multi-layer structure equivalent thermal circuit model, and deducing a mathematical correlation formula of the convection heat flux, heat exchange coefficient and environmental temperature difference; thirdly, solving the convection heat flux sequence under different current-carrying capacities, identifying a saturation inflection point to determine a saturation threshold; and finally, taking the threshold and the highest allowable working temperature of the conductor as constraints, constructing an optimization objective function, and solving the optimal current-carrying capacity by using a Newton iteration algorithm. The application quantifies the saturation characteristics of the convection heat flux, realizes the closed-loop coupling of the submarine cable and the environmental parameters, improves the precision and engineering applicability of the current-carrying capacity optimization, and takes into account the submarine cable power transmission potential release and operation safety.

Description

Technical Field

[0001] This invention relates to the field of power transmission technology, and in particular to a method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux. Background Technology

[0002] As a core connecting component between offshore wind farms and onshore power grids, the thermal management performance of the landing section submarine cable directly restricts the upper limit of transmission capacity and long-term operational safety. In marine engineering practice, the landing section submarine cable needs to traverse the transition zone between dynamic seawater and static seabed sediment, forming a highly non-uniform heat exchange environment. Traditional current-carrying capacity calculation methods mainly rely on IEC standards or empirical formulas. These methods generally employ idealized assumptions in the modeling process and fail to incorporate the unique influence mechanism of the seawater-sediment composite medium in the landing section. The key drawback is that when the current-carrying capacity of the submarine cable increases to a critical point, the convective heat transfer process on the cable surface will enter a saturated state due to the limitation of the thermal boundary layer of the environmental medium: at this point, the convective heat flux no longer increases linearly with the increase of current-carrying capacity, but tends to the physical limit value, reflecting the inherent upper limit of heat transfer capacity. Under the current technological framework, this saturation characteristic has neither been systematically quantified nor integrated into the optimization process, leading to three prominent problems. First, the overly conservative current-carrying capacity calculation, which ignores the saturation threshold, prevents the full release of the actual power transmission potential of the submarine cable, resulting in low equipment utilization and economic losses. Second, in designs without saturation constraints, it is easy to set current-carrying capacity that exceeds the thermal equilibrium capacity, causing the conductor temperature to accumulate continuously, accelerating the thermal degradation of the insulation layer and increasing the risk of failure. Third, there is a disconnect between the thermal circuit model and marine environmental parameters. For example, dynamic data such as seawater temperature field and flow velocity distribution fail to form a closed loop with the structural thermal parameters, causing logical disconnect between optimization steps and ultimately weakening the engineering applicability of the calculation results.

[0003] Therefore, it is necessary to propose a solution to improve one or more problems existing in the above-mentioned related technical solutions.

[0004] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0005] The purpose of this disclosure is to provide a method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux, thereby overcoming, to at least some extent, one or more problems caused by the limitations and defects of related technologies.

[0006] A method for optimizing the current carrying capacity of a submarine cable in its landing section based on the saturation characteristics of convective heat flux, according to an embodiment of this disclosure, includes the following steps: Collect structural parameters, thermal properties, and marine environmental thermal parameters of the submarine cable in the landing section to generate a comprehensive thermal parameter set of the submarine cable and environment. Based on the comprehensive thermal parameter set of the submarine cable-environment, an equivalent thermal path model of the multi-layer structure of the submarine cable in the landing section is established, and the mathematical correlation formula between the convective heat flux on the surface of the submarine cable and the heat transfer coefficient and the ambient temperature difference is derived. Substitute the actual operating parameters of the landing section into the equivalent thermal circuit model and mathematical correlation formula to obtain the numerical sequence of convective heat flux on the surface of the submarine cable under different current carrying capacity. Based on the numerical sequence, identify the inflection point of convective heat flux saturation characteristics and determine the convective heat flux saturation threshold. Using the aforementioned convective heat flux saturation threshold as a constraint, and combined with the boundary condition of the maximum allowable operating temperature of the submarine cable conductor, an optimization objective function for the current carrying capacity of the submarine cable in the landing section is constructed. The objective function for optimizing the carrying capacity is solved using a pre-defined numerical iterative algorithm, and the optimal carrying capacity of the submarine cable in the landing section is output, thus completing the carrying capacity optimization.

[0007] In an exemplary embodiment of this application, the step of collecting structural parameters, thermal property parameters, and marine environmental thermal parameters of the landing section of the submarine cable to generate a comprehensive thermal parameter set of the submarine cable and the environment includes: The structural parameters of the submarine cable and the thermophysical parameters of each layer are obtained based on the multi-layer structure of the submarine cable. Marine environmental thermal parameters were collected from discrete points along the landing section and spatially interpolated to form a continuous environmental thermal parameter field. The body parameters are normalized and integrated with the continuous environmental thermal parameter field to form a standardized submarine cable-environment integrated thermal parameter set.

[0008] In an exemplary embodiment of this application, the structural parameters of the submarine cable body in the landing section include the diameter of the cable conductor, the thickness of the insulation layer, the thickness of the sheath layer, and the size of the armor layer; the thermal property parameters include the thermal conductivity and specific heat capacity of the conductor, insulation layer, sheath layer, and armor layer; and the marine environmental thermal parameters of the landing section include the seawater temperature of the landing section, the thermal conductivity of the seabed sediment, the seawater flow velocity, and the convective heat transfer coefficient of the seabed sediment.

[0009] In an exemplary embodiment of this application, the step of establishing an equivalent thermal path model of the multi-layer structure of the submarine cable in the landing section based on the integrated thermal parameter set of the submarine cable and the environment, and deriving the mathematical correlation formula between the convective heat flux on the surface of the submarine cable and the heat transfer coefficient and the ambient temperature difference, includes: Based on the comprehensive thermal parameter set of the submarine cable-environment, the thermal resistance of the submarine cable conductor, the thermal resistance of the insulation layer, the thermal resistance of the armor layer, the thermal resistance of the outer sheath, and the convective heat transfer thermal resistance of the submarine cable surface are calculated in sequence. By connecting the thermal resistances of each layer in series, a radial one-dimensional equivalent thermal path model of the submarine cable in the landing section is constructed, and conductor Joule loss and dielectric loss are introduced at the thermal path input end as the total heat source term. Based on the equivalent thermal circuit model, a thermal balance equation was established, and the mapping relationship between the outer surface temperature of the submarine cable and the current carrying capacity and the thermal resistance of each layer was derived. Based on Newton's law of cooling and the temperature difference between the outer surface of the submarine cable and the ambient medium, a mathematical formula for the convective heat flux on the surface of the submarine cable is derived.

[0010] In an exemplary embodiment of this application, the mathematical formula relating the convective heat flux on the surface of the submarine cable is expressed as follows: in, For the convective heat flux on the surface of the submarine cable, The convective heat transfer coefficient of the submarine cable surface. The outer surface temperature of the submarine cable. The temperature of the ambient medium during the landing segment.

[0011] In an exemplary embodiment of this application, the step of substituting the actual operating parameters of the landing section into the equivalent thermal circuit model and the mathematical correlation formula to obtain the numerical sequence of convective heat flux on the surface of the submarine cable under different current carrying capacities, identifying the inflection point of convective heat flux saturation characteristics based on the numerical sequence, and determining the convective heat flux saturation threshold includes: Set the traversal interval of the carrying capacity and the equal interval of the carrying capacity step size, and substitute the operating condition parameters of the landing section ambient temperature and seawater flow velocity into the equivalent thermal circuit model. Substitute each current carrying capacity value into the equation one by one, and solve for the conductor temperature and outer surface temperature of the submarine cable under the corresponding working conditions. Then, calculate the corresponding convective heat flux using the mathematical correlation formula of the convective heat flux. All carrying capacity and their corresponding convective heat flux are organized to generate a discrete numerical sequence of carrying capacity-convective heat flux.

[0012] In an exemplary embodiment of this application, the step of substituting the actual operating parameters of the landing section into the equivalent thermal circuit model and the mathematical correlation formula to obtain the numerical sequence of convective heat flux on the surface of the submarine cable under different current carrying capacities, identifying the inflection point of convective heat flux saturation characteristics based on the numerical sequence, and determining the convective heat flux saturation threshold further includes: By performing the first-order numerical derivative of the smoothed flow-convection heat flux sequence, the rate of change of convective heat flux with flow rate is obtained. A preset threshold for judging the rate of change of convective heat flux is set. When the value in the rate of change sequence is less than the threshold for the first time, the operating point corresponding to the value is judged as the inflection point of convective heat flux saturation characteristics. The convective heat flux value at this inflection point is determined as the saturation threshold for convective heat flux of the submarine cable in the landing section.

[0013] In an exemplary embodiment of this application, the step of constructing the objective function for optimizing the current carrying capacity of the submarine cable in the landing section, using the convective heat flux saturation threshold as a constraint and combining it with the boundary condition of the maximum allowable operating temperature of the submarine cable conductor, includes: The saturation threshold of convective heat flux is used as a constraint parameter, and the maximum allowable operating temperature of the conductor is determined based on the submarine cable as a boundary constraint parameter. The optimization objective is to minimize the absolute difference between the actual convective heat flux of the submarine cable and the saturation threshold, so that the convective heat flux of the submarine cable during operation is as close as possible to the saturation threshold and does not exceed the threshold. The explicit constraints are that the temperature of the submarine cable conductor does not exceed the maximum allowable operating temperature, and the convective heat flux on the surface of the submarine cable does not exceed the convective heat flux saturation threshold. By integrating the optimization objective and constraints, an optimization objective function for the current carrying capacity of the submarine cable in the landing section is constructed, where the current carrying capacity is the independent variable for optimization.

[0014] In an exemplary embodiment of this application, the constructed load-carrying capacity optimization objective function expression is: in, For submarine cable current carrying capacity, The saturation threshold for convective heat flux. For carrying capacity The corresponding conductor temperature, The maximum permissible operating temperature for the conductor.

[0015] In an exemplary embodiment of this application, the step of solving the load-carrying capacity optimization objective function using a preset numerical iteration algorithm to output the optimal load-carrying capacity of the submarine cable in the landing segment and completing the load-carrying capacity optimization includes: Initialize the iterative calculation parameters, including setting the initial iterative carrying capacity, convergence accuracy threshold, and maximum number of iterations; Substitute the aforementioned load capacity optimization objective function and corresponding constraints into the Newton iteration algorithm, and calculate the objective function value and constraint verification value using the current iteration load capacity. The iterative value of the current carrying capacity is corrected according to the iterative update rule, and the conductor temperature and convective heat flux are recalculated for constraint compliance verification. Determine if the objective function value is less than the convergence accuracy threshold. If it is, determine the current iteration carrying capacity as the optimal carrying capacity of the submarine cable in the landing segment and output it. If it is not, continue iterating until the maximum number of iterations is reached to complete the carrying capacity optimization.

[0016] This application proposes a method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux. On the one hand, by constructing an equivalent thermal path model of the submarine cable, deriving the convective heat flux formula, identifying and quantifying the saturation threshold of convective heat flux, and incorporating it into the optimization constraints, it solves the problem that traditional methods ignore saturation characteristics, leading to conservative current carrying capacity calculations or causing over-temperature faults. On the other hand, by combining the saturation threshold with the conductor's maximum operating temperature to construct an optimization objective function, and using a numerical iterative algorithm to solve for the optimal current carrying capacity, it achieves closed-loop coupling between the submarine cable and environmental parameters, compensates for the defect of parameter coupling discontinuity in traditional models, and improves the accuracy and engineering applicability of current carrying capacity optimization. Attached Figure Description

[0017] 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. It is obvious that the drawings described below are merely some embodiments of this application, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0018] Figure 1 This diagram illustrates the steps of the method for optimizing the current carrying capacity of a submarine cable in the landing section based on the saturation characteristics of convective heat flux in an exemplary embodiment of this application. Figure 2 This diagram illustrates a flowchart of a method for optimizing the current carrying capacity of a submarine cable in the landing section based on the saturation characteristics of convective heat flux, as shown in an exemplary embodiment of this application. Detailed Implementation

[0019] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0020] Furthermore, the accompanying drawings are merely illustrative of this disclosure and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities may be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0021] This example implementation first provides a method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux. This method can be applied to a terminal device, such as a mobile terminal like a mobile phone, desktop computer, personal digital assistant, laptop, tablet, or smartwatch. (Reference) Figure 1 , Figure 2 As shown, the method may include the following steps: Step S101: Collect the structural parameters, thermal properties, and marine environmental thermal parameters of the landing section of the submarine cable, and generate a comprehensive thermal parameter set of the submarine cable and environment. Step S102: Based on the integrated thermal parameter set of the submarine cable-environment, establish an equivalent thermal path model of the multi-layer structure of the submarine cable in the landing section, and derive the mathematical correlation formula between the convective heat flux on the surface of the submarine cable and the heat transfer coefficient and the ambient temperature difference. Step S103: Substitute the actual operating parameters of the landing section into the equivalent thermal circuit model and mathematical correlation formula to obtain the numerical sequence of convective heat flux on the surface of the submarine cable under different current carrying capacity. Based on the numerical sequence, identify the inflection point of convective heat flux saturation characteristics and determine the convective heat flux saturation threshold. Step S104: Using the convective heat flux saturation threshold as a constraint and combining it with the boundary condition of the maximum allowable operating temperature of the submarine cable conductor, construct the objective function for optimizing the current carrying capacity of the submarine cable in the landing section. Step S105: Solve the objective function of the load-carrying capacity optimization using a preset numerical iterative algorithm, output the optimal load-carrying capacity of the submarine cable in the landing section, and complete the load-carrying capacity optimization.

[0022] This application proposes a method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux. On the one hand, by constructing an equivalent thermal path model of the submarine cable, deriving the convective heat flux formula, identifying and quantifying the saturation threshold of convective heat flux, and incorporating it into the optimization constraints, it solves the problem that traditional methods ignore saturation characteristics, leading to conservative current carrying capacity calculations or causing over-temperature faults. On the other hand, by combining the saturation threshold with the conductor's maximum operating temperature to construct an optimization objective function, and using a numerical iterative algorithm to solve for the optimal current carrying capacity, it achieves closed-loop coupling between the submarine cable and environmental parameters, compensates for the defect of parameter coupling discontinuity in traditional models, and improves the accuracy and engineering applicability of current carrying capacity optimization.

[0023] Below, as Figures 1-2 As shown, a more detailed explanation will be given of the method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux proposed in this example embodiment.

[0024] It is important to understand that in traditional optimization methods for the current carrying capacity of submarine cables in the landing section, the saturation characteristics of convective heat flux in the seawater-sediment composite environment are not quantified, leading to deviations in current carrying capacity calculations. When the current carrying capacity of the submarine cable increases to a certain threshold, the surface convective heat transfer capacity reaches its upper limit, and the convective heat flux no longer increases linearly with the increase in current carrying capacity, exhibiting a saturation trend. Existing technologies use IEC standards or empirical formulas, failing to incorporate this saturation characteristic, resulting in current carrying capacity calculations that are lower than the actual capacity or higher than the safety limit. Lower than the actual capacity leads to underutilization of the submarine cable's power transmission capacity, while higher than the safety limit introduces the risk of overheating and aging of the submarine cable. Furthermore, the thermal circuit model has low coupling with environmental parameters, the parameter transfer logic is inconsistent, and the optimization accuracy is insufficient.

[0025] For example, in the operation of submarine cables in the landing section of offshore wind farms, the cables are buried in the intertidal zone, where seawater and sediment alternately cover the area. During high-load operation in summer, as the cable's current carrying capacity gradually increases, traditional calculation methods predict that the convective heat flux will continue to increase linearly. However, actual monitoring data shows that when the current carrying capacity reaches a certain level, the rate of increase in convective heat flux slows down, indicating that saturation characteristics have emerged. Because this saturation threshold was not identified, maintenance personnel set the current carrying capacity too high based on traditional methods, causing the local temperature of the submarine cable to exceed the allowable limit, accelerating the aging of the insulation material. At the same time, during low-load periods, because the calculated results are lower than the actual capacity, the potential transmission capacity is not released, affecting the flexibility of grid dispatch.

[0026] The long-term use of current-carrying capacity optimization methods that do not consider the saturation characteristics of convective heat flux will lead to suboptimal operation of submarine cables. Overheating aging risks may shorten cable lifespan and increase the probability of failure; wasted transmission capacity reduces system efficiency. Furthermore, the disconnect between the thermal circuit model and environmental parameters makes the optimization process inaccurate and difficult to adapt to changes in the complex marine environment, ultimately affecting the economic viability and reliability of renewable energy projects such as offshore wind power.

[0027] In this example embodiment, a method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux is proposed: Step S101: Collect the structural parameters, thermal properties, and marine environmental thermal parameters of the landing section of the submarine cable, and generate a comprehensive thermal parameter set of the submarine cable and environment.

[0028] Specifically, the structural parameters of the submarine cable and the thermal properties of each layer are obtained based on the multi-layer structure of the submarine cable; marine environmental thermal parameters at discrete points along the landing section are collected and spatially interpolated to form a continuous environmental thermal parameter field; the structural parameters and the continuous environmental thermal parameter field are normalized and integrated to form a standardized submarine cable-environment integrated thermal parameter set.

[0029] Based on the multi-layered structure of the submarine cable, the structural parameters of the cable body and the thermophysical parameters of each layer are obtained, comprehensively collecting the physical dimensions and thermal properties of the cable itself. The structural parameters refer to the geometric dimensions of each component of the cable, such as conductor diameter, insulation thickness, sheath thickness, and armor dimensions. The thermophysical parameters refer to the thermal properties of each layer of material, such as the thermal conductivity and specific heat capacity of the conductor, insulation layer, sheath layer, and armor layer. These parameters can be obtained by consulting the cable design drawings, product specifications, or technical manuals provided by the manufacturer, or by conducting precise physical measurements and laboratory thermophysical tests on cable samples, such as differential scanning calorimetry and hot wire methods.

[0030] Marine environmental thermal parameters are collected from discrete points along the landing section and spatially interpolated to form a continuous environmental thermal parameter field, transforming discrete measurement data into continuous environmental information covering the entire landing section. Marine environmental thermal parameters include seawater temperature, seabed sediment thermal conductivity, seawater flow velocity, and seabed sediment convective heat transfer coefficient. To obtain these parameters, multiple discrete monitoring points can be deployed along the landing section, and real-time or periodic data can be collected using sensors such as temperature sensors, current meters, and heat flow meters. Subsequently, spatial interpolation techniques, such as Kriging interpolation, inverse distance weighted (IDW) interpolation, spline interpolation, or nearest neighbor interpolation algorithms, are used to infer the distribution field of continuous environmental parameters covering the entire landing section from these discrete measurement data.

[0031] The cable's intrinsic parameters are normalized and integrated with the continuous environmental thermal parameter field to form a standardized set of integrated thermal parameters of the submarine cable and the environment. This unifies the representation of parameters from different sources and with different dimensions, ensuring data consistency and comparability. Normalization and integration can employ various methods, such as min-max normalization, scaling the data to a specific interval, such as [0,1], or Z-score normalization, converting the data into a distribution with a mean of 0 and a standard deviation of 1. During integration, the cable's intrinsic parameters, such as thermal resistance and thermal capacity of each layer, can be associated and stored with the continuous environmental thermal parameter field, such as temperature, velocity, and thermal conductivity, by constructing a unified data structure, such as a multidimensional array, database table, or a data file in a specific format. This ensures that all parameters can be efficiently and accurately accessed in subsequent model calculations.

[0032] In one specific implementation, optimizing the current carrying capacity of the submarine cable in the landing section first requires obtaining detailed parameters of the cable. For the structural parameters of the cable itself in the landing section, dimensional information such as conductor diameter, insulation thickness, sheath thickness, and the diameter and number of armor wires can be directly obtained from the technical specifications provided by the cable manufacturer. For thermal properties, relevant material standards or material data sheets provided by the manufacturer can be consulted to obtain the thermal conductivity and specific heat capacity of the conductor (e.g., copper or aluminum), insulation (e.g., cross-linked polyethylene XLPE), sheath (e.g., polyethylene PE), and armor (e.g., galvanized steel wire) within the operating temperature range. When collecting marine environmental thermal parameters for the landing section, historical data from marine environmental monitoring stations or by deploying sensors in the field can be used to obtain the average seawater temperature and seasonal variation range of the cable laying area. The thermal conductivity of seabed sediment can be measured in a laboratory using thermal probe methods by sampling seabed sediment. Seawater flow velocity can be monitored in real time or long-term average data can be obtained by deploying acoustic Doppler current profilers (ADCPs) along the cable path. The convective heat transfer coefficient of seabed sediment can be estimated based on factors such as the type and porosity of the seabed sediment, as well as the seawater flow velocity, using empirical formulas or numerical simulation results. Ensuring that all key parameters are collected comprehensively and accurately provides a solid data foundation for subsequent flow capacity optimization.

[0033] Step S102: Based on the integrated thermal parameter set of the submarine cable-environment, establish an equivalent thermal path model of the multi-layer structure of the submarine cable in the landing section, and derive the mathematical correlation formula between the convective heat flux on the surface of the submarine cable and the heat transfer coefficient and the ambient temperature difference.

[0034] Specifically, based on the comprehensive thermal parameter set of the submarine cable-environment, the thermal resistance of the cable conductor, insulation layer, armor layer, outer sheath, and surface convective heat transfer are calculated sequentially. The thermal resistances of each layer are connected in series to construct a radial one-dimensional equivalent thermal path model of the landing section of the submarine cable, and conductor Joule loss and dielectric loss are introduced as total heat source terms at the thermal path input end. A heat balance equation is established based on the equivalent thermal path model, and the mapping relationship between the cable's outer surface temperature and current carrying capacity, as well as the thermal resistance of each layer, is derived. Based on Newton's law of cooling and the temperature difference between the cable's outer surface temperature and the ambient medium, a mathematical formula for the convective heat flux on the cable surface is derived.

[0035] The heat transfer of the submarine cable in the landing section is mainly radial one-dimensional heat conduction. The thermal resistance of its multi-layer structure follows the series superposition law. Fourier's law is used to calculate the thermal resistance of each layer, including the conductor, insulation layer, armor layer, and outer sheath. The calculation of convective heat transfer resistance relies on the convective heat transfer formula. The Joule loss of the conductor and the dielectric loss generated during the operation of the submarine cable are the total heat source terms in the thermal circuit model. The principle of heat balance requires that the total heat source terms equal the total heat flow rate transferred through the thermal resistance of each layer and dissipated through surface convective heat transfer. The heat balance equation is established to derive the mapping relationship between the outer surface temperature of the submarine cable and the current carrying capacity and the thermal resistance of each layer. Newton's law of cooling connects the radial heat conduction and surface convective heat transfer of the submarine cable. Its formula is directly derived from Newton's law of cooling to quantify the surface convective heat transfer capacity of the submarine cable.

[0036] First, based on the existing standardized set of integrated thermal parameters of submarine cable and environment, the thermal resistance of the annular multilayer structure is calculated according to Fourier's law: ; in, For the inner radius of each layer, For the outer radius of each layer, For the thermal conductivity of each layer, To calculate the length of the submarine cable, the thermal resistance of the cable conductor is precisely calculated by combining structural parameters such as conductor diameter, insulation thickness, sheath thickness, and armor dimensions with thermal properties such as thermal conductivity of the conductor, insulation, sheath, and armor. Thermal resistance of insulation layer thermal resistance of the armor layer outer sheath thermal resistance .

[0037] Then, by combining the seabed sediment convective heat transfer coefficient and the seawater convective heat transfer coefficient in the marine environmental thermal parameters of the landing section, appropriate values ​​are selected. As the convective heat transfer coefficient of the submarine cable surface, it is calculated based on the convective heat transfer thermal resistance formula: ,in, The convective heat transfer coefficient of the submarine cable surface is determined by factors such as seawater velocity, fluid properties, and cable surface morphology, reflecting the strength of convective heat transfer. The larger the size, the stronger the heat exchange capacity. The heat transfer area of ​​the submarine cable's outer surface refers to the cylindrical lateral surface area of ​​the cable's outer surface that participates in convective heat transfer. A = πDL, where D is the cable's outer diameter and L is its calculated length. A larger area means a greater effective heat transfer zone and lower thermal resistance. The calculated convective heat transfer thermal resistance of the submarine cable surface is then obtained. To ensure that all parameters used in the thermal resistance calculations are derived from the integrated thermal parameter set of the submarine cable and the environment and are matched with the actual structure of the submarine cable and the marine environmental conditions, the calculated thermal resistance of the submarine cable conductor is then superimposed according to the principle of series superposition of thermal resistance. Thermal resistance of insulation layer thermal resistance of the armor layer outer sheath thermal resistance thermal resistance of convective heat transfer with the surface of the submarine cable By sequentially connecting the components, a one-dimensional equivalent thermal path model of the submarine cable in the landing section is constructed. At the same time, the total heat source term generated during the operation of the submarine cable is introduced into the input of this thermal path model. Total heat source item Based on Joule's law and the formula for calculating dielectric loss, it is determined as follows: ;in, Total heat source term, For submarine cable current carrying capacity, Submarine cable conductor resistance This refers to the dielectric loss of the submarine cable.

[0038] Based on the complete path of heat source input and thermal resistance transfer in the thermal circuit model, the thermal balance equation is established according to the principle of thermal balance: ,in The difference between the conductor temperature of the submarine cable and the ambient temperature of the landing section. The total thermal resistance after connecting all layers in series is given. By rearranging and simplifying the heat balance equation and eliminating intermediate variables, the outer surface temperature of the submarine cable can be derived. The expression was used to establish the outer surface temperature of the submarine cable. With carrying capacity The quantitative mapping relationship between the thermal resistances of each layer is used to accurately express the influence of current-carrying capacity changes on the outer surface temperature of the submarine cable. Finally, based on Newton's law of cooling, its expression is: ; in, For the convective heat transfer on the surface of the submarine cable, This refers to the heat exchange area of ​​the outer surface of the submarine cable. The convective heat transfer coefficient of the submarine cable surface. The outer surface temperature of the submarine cable. The ambient temperature of the landing section, combined with the definition of convective heat flux, which is the convective heat transfer per unit area. Divide both sides of Newton's law of cooling by the heat transfer area. The mathematical correlation formula for the convective heat flux on the surface of the submarine cable was derived. The formula for the convective heat flux on the surface of the submarine cable Convection heat transfer coefficient with submarine cable surface It is directly proportional to, and also related to, the temperature of the outer surface of the submarine cable. and the temperature of the ambient medium in the landing segment The difference is proportional; in practical implementation, the convective heat transfer coefficient in this formula... From Integrated values ​​of marine environmental thermal parameters, submarine cable outer surface temperature The ambient medium temperature is obtained by solving the heat balance equation and the current carrying capacity. The marine environmental thermal parameters from the landing segment allow for the accurate determination of various physical quantities through prior parameter acquisition, thermal resistance calculations at each layer, and thermal path model solutions. This ensures the accurate calculation of the convective heat flux based on the formula. The results can accurately reflect the actual convective heat transfer on the surface of the submarine cable, providing a direct and accurate mathematical basis for subsequent calculations of the numerical sequence of convective heat flux under different loads and identification of the inflection point of convective heat flux saturation characteristics.

[0039] Step S103: Substitute the actual operating parameters of the landing section into the equivalent thermal circuit model and mathematical correlation formula to obtain the numerical sequence of convective heat flux on the surface of the submarine cable under different current carrying capacity. Based on the numerical sequence, identify the inflection point of convective heat flux saturation characteristics and determine the convective heat flux saturation threshold.

[0040] It is important to understand that by substituting the actual operating parameters of the landing section into the aforementioned equivalent thermal circuit model and mathematical correlation formula, a numerical sequence of convective heat flux on the submarine cable surface under different load capacities is obtained. Based on this numerical sequence, the inflection point of convective heat flux saturation characteristics is identified, and the convective heat flux saturation threshold is determined. This step aims to quantify the convective heat flux saturation characteristics of the submarine cable by simulating different operating conditions. Specifically, a series of discrete load capacities can be manually set, for example, increasing from low to high in fixed steps. For each set load capacities, they are substituted into the simplified equivalent thermal circuit model and mathematical correlation formula to manually calculate the corresponding convective heat flux on the submarine cable surface. These load capacities and their corresponding convective heat flux values ​​are recorded to form a numerical list. Subsequently, by manually observing this numerical list or drawing a simple scatter plot, when it is found that the rate of increase of convective heat flux with increasing load capacities slows down significantly, this point is manually judged as the inflection point of convective heat flux saturation characteristics, and the convective heat flux value at this inflection point is taken as the saturation threshold.

[0041] Specifically, the flow rate traversal interval and the equal interval flow rate step size are set, and the operating condition parameters of the landing section ambient temperature and seawater flow velocity are substituted into the equivalent thermal circuit model. Substitute each current carrying capacity value into the equation one by one, and solve for the conductor temperature and outer surface temperature of the submarine cable under the corresponding working conditions. Then, calculate the corresponding convective heat flux using the mathematical correlation formula of the convective heat flux. All the carrying capacity and its corresponding convective heat flux are organized to generate a discrete numerical sequence of carrying capacity-convective heat flux. By performing the first-order numerical derivative of the smoothed flow-convection heat flux sequence, the rate of change of convective heat flux with flow rate is obtained. A preset threshold for judging the rate of change of convective heat flux is set. When the value in the rate of change sequence is less than the threshold for the first time, the operating point corresponding to the value is judged as the inflection point of convective heat flux saturation characteristics. The convective heat flux value at this inflection point is determined as the saturation threshold for convective heat flux of the submarine cable in the landing section.

[0042] Formula for convective heat flux on the surface of a submarine cable ,in Based on the equivalent thermal circuit model combined with current carrying capacity The solution shows that the current carrying capacity traversal uses an equal interval step size setting. n is the number of iterations. To traverse the initial load capacity, Given the current carrying capacity step size, the first-order numerical difference derivative formula for the discrete sequence is: in, For the nth traversal of the load capacity The corresponding convective heat flux, the rate of change is determined by a threshold comparison, i.e., when... This is determined to be the saturation inflection point. The preset threshold for determining the rate of change of convective heat flux is... The saturation threshold, For the first time to meet The corresponding number of traversals is determined by first setting the current carrying capacity traversal interval reasonably based on the actual operating conditions and design parameters of the submarine cable in the landing section. The lower limit of the interval is the minimum operating current carrying capacity of the submarine cable, and the upper limit is the maximum design current carrying capacity of the submarine cable. At the same time, an evenly spaced current carrying capacity step size is set. The step size setting needs to balance computational accuracy and efficiency, and then take into account the ambient medium temperature under the actual operating conditions of the landing segment. Convective heat transfer coefficient corresponding to seawater flow velocity Substituting marine environmental thermal parameters into the constructed radial one-dimensional equivalent thermal path model of the landing section submarine cable ensures that the model's operating parameters closely match the actual operating conditions. Then, the model is traversed according to the set current carrying capacity sequence. Substitute each value into the equivalent thermal circuit model and apply the thermal balance equation. Solve for each current carrying capacity in sequence Corresponding submarine cable conductor temperature and the outer surface temperature of submarine cables To ensure that the numerical accuracy of the temperature solution matches the model requirements, the obtained solution is then... Substituting into the core formula for convective heat flux Calculate each current carrying capacity one by one Corresponding convective heat flux After completing the calculations for all current carrying capacity traversal conditions, all current carrying capacity values ​​will be... and the corresponding convective heat flux values Arrange the data in traversal order to generate a discrete numerical sequence of current carrying capacity and convective heat flux. N represents the total number of iterations. The generated discrete numerical sequence of current carrying capacity and convective heat flux is then smoothed using a moving average method to eliminate random calculation errors and parameter acquisition errors, ensuring the smoothness of the sequence's trend. The smoothed discrete sequence is then processed using the first-order numerical difference derivative formula. Calculations were performed to obtain the rate of change of convective heat flux with respect to the flow rate for each flow-carrying node, and these values ​​were then compiled into a rate of change sequence. Based on the heat exchange characteristics of the submarine cable in the landing section and practical engineering experience, a reasonable threshold ε for judging the rate of change of convective heat flux is preset. This threshold needs to be calibrated in conjunction with the type of submarine cable and marine environmental conditions to ensure accurate identification of the saturation inflection point. Then, the rate of change sequence is verified point by point, and the rate of change values ​​are compared in order of increasing current carrying capacity. With the judgment threshold The magnitude of the rate of change when it first appears. Less than the judgment threshold When that value is determined, the corresponding operating point is identified. This represents the inflection point of the convective heat flux saturation characteristic, where The number of iterations required to first satisfy the condition is given, and the final value is the convective heat flux corresponding to the inflection point of the saturation characteristic. The saturation threshold for convective heat flux of the submarine cable in the landing section was determined. Throughout the process, all formula parameters are derived from the previous integrated thermal parameter set of submarine cable-environment and actual operating condition parameters, ensuring that the determination of the saturation threshold is highly consistent with the actual operating state of the submarine cable, and providing accurate constraint parameters for the subsequent construction of the current carrying capacity optimization objective function.

[0043] Step S104: Using the convective heat flux saturation threshold as a constraint and combining it with the boundary condition of the maximum allowable operating temperature of the submarine cable conductor, construct the objective function for optimizing the current carrying capacity of the submarine cable in the landing section.

[0044] It's important to understand that, using the convective heat flux saturation threshold as a constraint, combined with the boundary condition of the maximum allowable operating temperature of the submarine cable conductor, an objective function for optimizing the current carrying capacity of the landing section of the submarine cable is constructed. This step aims to incorporate the convective heat flux saturation characteristics into the consideration of current carrying capacity optimization, in order to achieve a more accurate current carrying capacity assessment. For example, the convective heat flux saturation threshold can be set as a hard upper limit, requiring that the convective heat flux of the submarine cable during actual operation must not exceed this value under any circumstances. Simultaneously, the maximum allowable operating temperature of the submarine cable conductor is set as another key boundary condition, ensuring that the conductor temperature is always below this limit. The optimization objective can be simply set as maximizing the current carrying capacity of the submarine cable while satisfying these two constraints.

[0045] Specifically, optimizing the current carrying capacity of the submarine cable in the landing section is an engineering optimization problem with a single independent variable and dual hard constraints. It aims to maximize the utilization of convective heat transfer capacity under the insurmountable constraint of ensuring the safe operation of the submarine cable, and to achieve the saturation threshold of convective heat flux. The physical limit of the heat transfer capacity of the submarine cable surface is determined by the characteristics of the thermal boundary layer and cannot be exceeded; this is the maximum allowable operating temperature of the submarine cable conductor. These are the safety limits of the submarine cable's materials and structure; exceeding these temperatures will accelerate the thermal degradation of the insulation layer and cause failures. Both are hard constraints in the optimization process, while the optimization objective is set to minimize the actual convective heat flux. and The absolute difference is to fully release the heat exchange potential of the submarine cable without exceeding the limits, thereby achieving the optimal configuration of the current carrying capacity. It is the only optimization independent variable, the actual convective heat flux. and conductor temperature All single-valued functions, External surface temperature derived from heat flux formula and thermal circuit model get, The solution obtained from the heat balance equation has a clear quantitative mapping relationship. The objective function for optimizing the current carrying capacity is a constrained single-objective optimization form, and the objective function is: in, For submarine cable current carrying capacity, The saturation threshold for convective heat flux. For carrying capacity The corresponding conductor temperature, The maximum allowable operating temperature for the conductor. First, determine the saturation threshold for convective heat flux in the landing section of the submarine cable. As a core constraint parameter, this parameter is a determined value obtained through numerical sequence solving and inflection point identification in the early stage. It is highly consistent with the actual heat transfer characteristics of the submarine cable. Then, based on the characteristics of the submarine cable's main material, the type of insulation layer, and the submarine cable design and operation standards of the power engineering industry, the maximum allowable operating temperature of the submarine cable conductor is determined. As a boundary constraint parameter, this parameter must strictly adhere to the technical specifications of the submarine cable product to ensure it matches the actual temperature resistance of the cable's insulation and armor layers, without any empirical adjustments. Therefore, the core objective of this current-carrying capacity optimization is to minimize the actual convective heat flux of the submarine cable. With saturation threshold The absolute difference, that is, to make the actual convective heat flux during the operation of the submarine cable as close as possible to... Furthermore, the heat transfer capacity of the submarine cable surface should not exceed this threshold, thereby maximizing its utilization while ensuring that the heat transfer process does not exceed the physical limits imposed by the thermal boundary layer of the environmental medium. The optimization process also involves two hard constraints: the first constraint is the actual convective heat flux on the submarine cable surface. Not exceeding the saturation threshold of convective heat flux The second constraint is the actual operating temperature of the submarine cable conductor. Not exceeding the conductor's maximum allowable operating temperature Both types of constraints are insurmountable engineering safety constraints, and constraint compliance verification must be performed throughout the subsequent optimization process.

[0046] Step S105: Solve the objective function of the load-carrying capacity optimization using a preset numerical iterative algorithm, output the optimal load-carrying capacity of the submarine cable in the landing section, and complete the load-carrying capacity optimization.

[0047] It is important to understand that a pre-defined numerical iterative algorithm is used to solve the objective function for optimizing the current carrying capacity, outputting the optimal current carrying capacity for the landing section of the submarine cable, thus completing the current carrying capacity optimization. This step aims to find the optimal current carrying capacity that satisfies all conditions through computational methods. A reasonable current carrying capacity search range is set. Within this range, each current carrying capacity value is tested one by one with a pre-defined step size. For each tested value, its corresponding convective heat flux and conductor temperature are calculated, and it is checked whether the constraints of the above-mentioned saturation threshold and the maximum operating temperature of the conductor are met. Among all current carrying capacities that meet the constraints, the one with the largest value is selected as the optimal current carrying capacity and output.

[0048] Specifically, initialize the iterative calculation parameters, including setting the initial iterative carrying capacity, convergence accuracy threshold, and maximum number of iterations; Substitute the aforementioned load capacity optimization objective function and corresponding constraints into the Newton iteration algorithm, and calculate the objective function value and constraint verification value using the current iteration load capacity. The iterative value of the current carrying capacity is corrected according to the iterative update rule, and the conductor temperature and convective heat flux are recalculated for constraint compliance verification. Determine if the objective function value is less than the convergence accuracy threshold. If it is, determine the current iteration carrying capacity as the optimal carrying capacity of the submarine cable in the landing segment and output it. If it is not, continue iterating until the maximum number of iterations is reached to complete the carrying capacity optimization.

[0049] First, the initialization of iterative calculation parameters is carried out. Based on the design carrying capacity of the submarine cable in the landing section, the actual operating carrying capacity range, and the previously generated carrying capacity-convective heat flux numerical sequence, the initial iterative carrying capacity is reasonably set. This value is selected from the median of the commonly used operating current carrying capacity of submarine cables or the current carrying capacity traversal range. Then, based on the accuracy requirements of submarine cable current carrying capacity calculation in power engineering, a convergence accuracy threshold is set. This threshold needs to be calibrated based on actual engineering needs. The smaller the value, the higher the solution accuracy. At the same time, to avoid infinite iteration, a reasonable maximum number of iterations should be set according to the characteristics of the objective function and the processing power of the computing device. After setting all initial parameters for the iterations, the constructed load capacity optimization objective function is substituted into the Newton-Raphson iteration algorithm, with the load capacity of the current iteration as the starting point. Based on this, combined with the previous derivation and , and The quantization mapping relationship is used to calculate the objective function value corresponding to the k-th iteration. and constraint verification values and After completing the basic numerical calculations for this iteration, the formula is updated based on Newton's iterations: Calculate the objective function in The first derivative at Then, the carrying capacity value for the (k+1)th iteration is obtained using the formula. After correcting the calculation and obtaining the new iterative current carrying capacity, it is combined again. and , and The quantization mapping relationship is recalculated. Corresponding conductor temperature and convective heat flux And according to the constraint compliance check formula ,and Perform constraint compliance checks; if the check results meet the constraint conditions, retain the results. As the base value for the next iteration, if the verification result exceeds any constraint, then... Make reasonable corrections, adjusting the values ​​by approximating them within the constraints, until the corrected current carrying capacity value satisfies the dual constraints. Then, use this value as the effective current carrying capacity value for the (k+1)th iteration, and finally apply the convergence criterion formula. The convergence of the objective function value obtained in the current iteration is judged. If the objective function value is less than the preset convergence accuracy threshold... This indicates that the current iteration's carrying capacity is close to the optimal solution. At this point, the carrying capacity for this iteration can be directly increased. The optimal current carrying capacity of the submarine cable for the landing segment is determined and the numerical value is output. If the objective function value does not meet the convergence accuracy requirement, it is then determined whether the current iteration number k has reached the preset maximum iteration number. If the target is not reached, increment the value of k by 1 to adjust the result. For the new iterative carrying capacity, repeat the above steps of calculating the objective function value, constraint verification, and iterative update. If the number of iterations reaches... Then the iteration stops, and the last iteration carrying capacity that satisfies the constraints is determined as the optimal carrying capacity and output. This completes the solution of the entire carrying capacity optimization objective function and the determination of the optimal carrying capacity. Throughout the implementation process, all formula parameters are derived from the precisely determined values ​​obtained in the previous steps. The principle of constraint priority is always followed during the iteration process to ensure that the optimal carrying capacity obtained not only meets the optimization requirements of the objective function, but also strictly complies with the thermal safety constraints of submarine cable operation. At the same time, the efficiency of the Newton iteration algorithm ensures the engineering practicality of the solution process, allowing the calculation results of the optimal carrying capacity to be directly applied to the actual operation and scheduling of the submarine cable in the landing section. Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of the embodiments of this application, "multiple" means two or more, unless otherwise explicitly specified.

[0050] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0051] Other embodiments of this application will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this application that follow the general principles of this application and include common knowledge or customary techniques in the art not disclosed herein.

Claims

1. A method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux, characterized in that, Includes the following steps: Collect structural parameters, thermal properties, and marine environmental thermal parameters of the submarine cable in the landing section to generate a comprehensive thermal parameter set of the submarine cable and environment. Based on the aforementioned integrated thermal parameter set of submarine cable and environment, an equivalent thermal path model of the multi-layer structure of the submarine cable in the landing section is established, and mathematical correlation formulas between the convective heat flux on the surface of the submarine cable and the heat transfer coefficient and the ambient temperature difference are derived. Substitute the actual operating parameters of the landing section into the equivalent thermal circuit model and mathematical correlation formula to obtain the numerical sequence of convective heat flux on the surface of the submarine cable under different current carrying capacity. Based on the numerical sequence, identify the inflection point of convective heat flux saturation characteristics and determine the convective heat flux saturation threshold. Using the aforementioned convective heat flux saturation threshold as a constraint, and combined with the boundary condition of the maximum allowable operating temperature of the submarine cable conductor, an objective function for optimizing the current carrying capacity of the submarine cable in the landing section is constructed. The objective function for optimizing the carrying capacity is solved using a pre-defined numerical iterative algorithm, and the optimal carrying capacity of the submarine cable in the landing section is output, thus completing the carrying capacity optimization.

2. The method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux according to claim 1, characterized in that, The step of collecting structural parameters, thermal properties, and marine environmental thermal parameters of the submarine cable in the landing section to generate a comprehensive thermal parameter set for the submarine cable and environment includes: The structural parameters of the submarine cable and the thermophysical parameters of each layer are obtained based on the multi-layer structure of the submarine cable. Marine environmental thermal parameters were collected from discrete points along the landing section and spatially interpolated to form a continuous environmental thermal parameter field. The body parameters are normalized and integrated with the continuous environmental thermal parameter field to form a standardized submarine cable-environment integrated thermal parameter set.

3. The method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux according to claim 2, characterized in that, The structural parameters of the submarine cable body in the landing section include the diameter of the cable conductor, the thickness of the insulation layer, the thickness of the sheath layer, and the size of the armor layer; the thermal properties include the thermal conductivity and specific heat capacity of the conductor, insulation layer, sheath layer, and armor layer; and the marine environmental thermal parameters of the landing section include the seawater temperature of the landing section, the thermal conductivity of the seabed sediment, the seawater flow velocity, and the convective heat transfer coefficient of the seabed sediment.

4. The method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux according to claim 1, characterized in that, The steps of establishing an equivalent thermal path model of the multi-layer structure of the submarine cable in the landing section based on the integrated thermal parameter set of the submarine cable and the environment, and deriving the mathematical correlation formula between the convective heat flux on the surface of the submarine cable and the heat transfer coefficient and the ambient temperature difference, include: Based on the aforementioned integrated thermal parameter set of submarine cable and environment, the thermal resistance of the submarine cable conductor, insulation layer, armor layer, outer sheath, and convective heat transfer thermal resistance of the submarine cable surface are calculated sequentially. By connecting the thermal resistances of each layer in series, a radial one-dimensional equivalent thermal path model of the submarine cable in the landing section is constructed, and conductor Joule loss and dielectric loss are introduced at the thermal path input end as the total heat source term. Based on the equivalent thermal circuit model, a thermal balance equation was established, and the mapping relationship between the outer surface temperature of the submarine cable and the current carrying capacity and the thermal resistance of each layer was derived. Based on Newton's law of cooling and the temperature difference between the outer surface of the submarine cable and the ambient medium, a mathematical formula for the convective heat flux on the surface of the submarine cable is derived.

5. The method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux according to claim 4, characterized in that, The mathematical formula relating the convective heat flux on the surface of the submarine cable is expressed as follows: in, For the convective heat flux on the surface of the submarine cable, The convective heat transfer coefficient of the submarine cable surface. The outer surface temperature of the submarine cable. The temperature of the ambient medium during the landing segment.

6. The method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux according to claim 1, characterized in that, The step of substituting the actual operating parameters of the landing section into the equivalent thermal circuit model and mathematical correlation formula to obtain the numerical sequence of convective heat flux on the surface of the submarine cable under different current carrying capacities, identifying the inflection point of convective heat flux saturation characteristics based on the numerical sequence, and determining the convective heat flux saturation threshold includes: Set the traversal interval of the carrying capacity and the equal interval of the carrying capacity step size, and substitute the operating condition parameters of the landing section ambient temperature and seawater flow velocity into the equivalent thermal circuit model. Substitute each current carrying capacity value into the equation one by one, and solve for the conductor temperature and outer surface temperature of the submarine cable under the corresponding working conditions. Then, calculate the corresponding convective heat flux using the mathematical correlation formula of the convective heat flux. All carrying capacity and their corresponding convective heat flux are organized to generate a discrete numerical sequence of carrying capacity-convective heat flux.

7. The method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux according to claim 6, characterized in that, The step of substituting the actual operating parameters of the landing section into the equivalent thermal circuit model and mathematical correlation formula to obtain the numerical sequence of convective heat flux on the surface of the submarine cable under different current carrying capacities, identifying the inflection point of convective heat flux saturation characteristics based on the numerical sequence, and determining the convective heat flux saturation threshold further includes: By performing the first-order numerical derivative of the smoothed flow-convection heat flux sequence, the rate of change of convective heat flux with flow rate is obtained. A preset threshold for judging the rate of change of convective heat flux is set. When the value in the rate of change sequence is less than the threshold for the first time, the operating point corresponding to the value is judged as the inflection point of convective heat flux saturation characteristics. The convective heat flux value at this inflection point is determined as the saturation threshold for convective heat flux of the submarine cable in the landing section.

8. The method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux according to claim 1, characterized in that, The steps for constructing the objective function for optimizing the current carrying capacity of the submarine cable in the landing section, using the aforementioned convective heat flux saturation threshold as a constraint and combining it with the boundary condition of the maximum allowable operating temperature of the submarine cable conductor, include: The saturation threshold of convective heat flux is used as a constraint parameter, and the maximum allowable operating temperature of the conductor is determined based on the submarine cable as a boundary constraint parameter. The optimization objective is to minimize the absolute difference between the actual convective heat flux of the submarine cable and the saturation threshold, so that the convective heat flux of the submarine cable during operation is as close as possible to the saturation threshold and does not exceed the threshold. The explicit constraints are that the temperature of the submarine cable conductor does not exceed the maximum allowable operating temperature, and the convective heat flux on the surface of the submarine cable does not exceed the convective heat flux saturation threshold. By integrating the optimization objective and constraints, an optimization objective function for the current carrying capacity of the submarine cable in the landing section is constructed, where the current carrying capacity is the independent variable for optimization.

9. The method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux according to claim 8, characterized in that, The constructed objective function expression for the load capacity optimization is as follows: in, For submarine cable current carrying capacity, This represents the actual convective heat flux over the surface of the submarine cable. The saturation threshold for convective heat flux. For carrying capacity The corresponding conductor temperature, The maximum permissible operating temperature for the conductor.

10. The method for optimizing the current carrying capacity of submarine cables in the landing section based on the saturation characteristics of convective heat flux according to claim 1, characterized in that, The step of solving the objective function for optimizing the carrying capacity using a preset numerical iterative algorithm and outputting the optimal carrying capacity of the submarine cable in the landing section to complete the carrying capacity optimization includes: Initialize the iterative calculation parameters, including setting the initial iterative carrying capacity, convergence accuracy threshold, and maximum number of iterations; Substitute the aforementioned load capacity optimization objective function and corresponding constraints into the Newton iteration algorithm, and calculate the objective function value and constraint verification value using the current iteration load capacity. The iterative value of the current carrying capacity is corrected according to the iterative update rule, and the conductor temperature and convective heat flux are recalculated for constraint compliance verification. Determine if the objective function value is less than the convergence accuracy threshold. If it is, determine the current iteration carrying capacity as the optimal carrying capacity of the submarine cable in the landing section and output it. If it is not, continue iterating until the maximum number of iterations is reached to complete the carrying capacity optimization.

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