Temperature field and current-carrying capacity calculation method of double-circuit heterogeneous submarine cable and terminal

Abstract

The invention discloses a temperature field and current-carrying capacity calculation method and terminal for a double-circuit heterogeneous submarine cable, and the method comprises the steps: dividing the submarine cable into a deep sea section, a shoal section and a landing section according to the laying environment of the submarine cable, and remarkably reducing the geometric complexity and calculation resource occupation of a single model; and a simulation model is established for each section and a corresponding electromagnetic field, a heat transfer field and a fluid field are coupled, so that the thermal radiation and convective heat transfer mechanism of the submarine cable in the environments of ocean current, soil, concrete ditches and the like can be truly represented. An equivalent circuit is constructed for the double-circuit heterogeneous submarine cable, a circulating current value is solved in each section of the submarine cable according to sheath impedance and armored impedance of the submarine cable, and the circulating current values are injected in an electromagnetic field in an equivalent current source mode. According to the step-by-step current rising method, accurate safe current-carrying capacity judgment is realized through real-time conductor temperature feedback, and the risk of excessive design or potential temperature overrun is avoided. In this way, errors of cable temperature distribution and safe current-carrying capacity evaluation in the simulation process are effectively reduced.

Description

Technical Field

[0001] This invention relates to the technical field of submarine cable evaluation, and in particular to a method for calculating the temperature field and current carrying capacity of a double-circuit heterogeneous submarine cable, as well as a terminal. Background Technology

[0002] Traditional thermal / electromagnetic simulation methods for submarine cables mainly focus on deep-sea sections, employing a combined model of steady-state electromagnetic fields and Fourier heat conduction. However, these methods have the following drawbacks: (1) Ignoring the effect of fluids in the sea surface / soil on thermal convection leads to an underestimation of thermal coupling between the deep sea section and the shallow water section.

[0003] (2) The model used for the shallow section and the landing section is only solid heat conduction coupling, which cannot capture the convective heat transfer generated by the air flow in the cable trench.

[0004] (3) The sheath and armor of double-circuit cables will generate loop currents due to parallel operation. However, most existing technologies use single-circuit or simplified impedance methods, without solving each segment, which leads to the accumulation of loop current distribution errors.

[0005] Due to the aforementioned defects, the assessment of cable temperature distribution and safe current carrying capacity often results in significant errors, posing potential risks to system design, operation and maintenance, and safety management. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a method and terminal for calculating the temperature field and current carrying capacity of a double-circuit heterogeneous submarine cable, which can reduce the error in assessing the cable temperature distribution and safe current carrying capacity.

[0007] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows: A method for calculating the temperature field and current carrying capacity of a double-circuit heterogeneous submarine cable includes the following steps: Based on the laying environment of the submarine cable, the submarine cable is divided into deep-sea section, shallow-water section and landing section; A simulation model is established for each segment of the submarine cable, and the corresponding electromagnetic field, heat transfer field and fluid field are coupled to each segment simulation model to obtain an electromagnetic-thermal-fluid coupled model. To construct an equivalent circuit for a double-circuit heterogeneous submarine cable, the circulating current value is calculated in each segment of the submarine cable based on the sheath impedance and armor impedance of the submarine cable. The circulating current value is then injected into the electromagnetic field of the electromagnetic-thermal-fluid coupling model in the form of an equivalent current source. The temperature field distribution of the submarine cable was obtained by solving the electromagnetic-thermal-fluid coupling model. The electromagnetic-thermal-fluid coupling model is solved iteratively using the step-by-step current-increasing method, and the conductor temperature is continuously monitored. When the conductor temperature reaches a predetermined safety threshold, the current at this time is regarded as the safe current-carrying capacity of the submarine cable.

[0008] To solve the above-mentioned technical problems, another technical solution adopted by the present invention is as follows: A terminal for calculating the temperature field and current carrying capacity of a dual-circuit heterogeneous submarine cable includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it performs the various steps of calculating the temperature field and current carrying capacity of the dual-circuit heterogeneous submarine cable.

[0009] The beneficial effects of this invention are as follows: Based on the laying environment of the submarine cable, the submarine cable is divided into deep-sea, shallow-water, and landing sections, significantly reducing the geometric complexity and computational resource consumption of a single model; simulation models are established for each section and coupled with corresponding electromagnetic, heat transfer, and fluid fields, thus realistically reproducing the heat radiation and convection heat transfer mechanisms of the submarine cable in environments such as ocean currents, soil, and concrete trenches. An equivalent circuit is constructed for the double-circuit heterogeneous submarine cable, and the circulating current value is calculated in each section of the submarine cable based on the sheath impedance and armor impedance, injecting the circulating current value into the electromagnetic field as an equivalent current source. The step-by-step current-increasing method achieves accurate safe current-carrying capacity determination through real-time conductor temperature feedback, avoiding over-design or potential temperature exceedance risks. In this way, errors in cable temperature distribution and safe current-carrying capacity assessment during simulation are effectively reduced. Attached Figure Description

[0010] Figure 1 This is a flowchart illustrating a method for calculating the temperature field and current carrying capacity of a double-circuit heterogeneous submarine cable according to an embodiment of the present invention. Figure 2 This is a schematic diagram of the submarine cable laying environment structure according to an embodiment of the present invention; Figure 3 This is a schematic diagram of a simulation model of a submarine cable in different sections according to an embodiment of the present invention; Figure 4 This is a diagram illustrating the coupling relationship of multiphysics fields in an embodiment of the present invention. Figure 5 This is a mesh partition diagram of a submarine cable according to an embodiment of the present invention; Figure 6 This is the corrected equivalent circuit diagram of an embodiment of the present invention; Figure 7 This is a flowchart illustrating the calculation of the current carrying capacity of submarine cables according to an embodiment of the present invention. Figure 8 This is a schematic diagram illustrating the temperature variation of the conductor of the deep-sea submarine cable with ambient temperature according to an embodiment of the present invention. Figure 9This is a schematic diagram illustrating the temperature variation of the submarine cable conductor in the landing section with ambient temperature, according to an embodiment of the present invention. Figure 10 This is a structural diagram of a temperature field and current carrying capacity calculation terminal for a double-circuit heterogeneous submarine cable according to an embodiment of the present invention.

[0011] Label Explanation: 1. A temperature field and current carrying capacity calculation terminal for a dual-circuit heterogeneous submarine cable; 2. Memory; 3. Processor. Detailed Implementation

[0012] To explain in detail the technical content, objectives, and effects of the present invention, the following description is provided in conjunction with the embodiments and accompanying drawings.

[0013] Before detailing the embodiments of this application, some related concepts will first be explained: (1) Submarine Cables: The overall structure of submarine cables, from the inside out, includes the conductor, insulation layer, armor, and sheath. The conductor is the core for current transmission (materials include copper, aluminum, steel, etc.); the insulation layer provides electrical insulation for the conductor; the armor is a multi-strand braided structure of steel wire, aluminum wire, or composite materials, which mainly bears mechanical, pressure, and tensile strength; the sheath is the outer covering material (such as polyethylene, polyvinyl chloride, polyurethane, etc.), which provides protection against chemical, corrosive, tidal, and seawater immersion environments.

[0014] Double-circuit heterogeneous submarine cables refer to cables with two internal current loops that differ in structure, materials, and geometry. In submarine cables, the primary loop is responsible for power transmission, while the secondary loop (armor / sheath) provides mechanical support and magnetic shielding, while also generating circulating currents that significantly affect the temperature field and impedance.

[0015] (2) Armor Circulation Current: The circulating current generated by the alternating magnetic field in the armor layer mainly affects the heat loss and magnetic field distribution of mechanical components.

[0016] (3) Sheath circulating current: The circulating current generated by the same magnetic field in the outer sheath layer results in higher heat loss and affects the overall cable impedance and temperature.

[0017] (4) Armor impedance: The sum of resistance and reactance formed by the armor under alternating current, reflecting the circulating current loss, heat generation and influence on the overall impedance of the armor.

[0018] (5) Sheath impedance: The sum of resistance and reactance formed by the sheath under alternating current, reflecting the current loss, heat generation and influence on the overall impedance of the sheath in the electromagnetic field.

[0019] To at least solve the above problems, please refer to Figure 1This invention provides a method for calculating the temperature field and current carrying capacity of a double-circuit heterogeneous submarine cable, characterized by the following steps: Based on the laying environment of the submarine cable, the submarine cable is divided into deep-sea section, shallow-water section and landing section; A simulation model is established for each segment of the submarine cable, and the corresponding electromagnetic field, heat transfer field and fluid field are coupled to each segment simulation model to obtain an electromagnetic-thermal-fluid coupled model. To construct an equivalent circuit for a double-circuit heterogeneous submarine cable, the circulating current value is calculated in each segment of the submarine cable based on the sheath impedance and armor impedance of the submarine cable. The circulating current value is then injected into the electromagnetic field of the electromagnetic-thermal-fluid coupling model in the form of an equivalent current source. The temperature field distribution of the submarine cable was obtained by solving the electromagnetic-thermal-fluid coupling model. The electromagnetic-thermal-fluid coupling model is solved iteratively using the step-by-step current-increasing method, and the conductor temperature is continuously monitored. When the conductor temperature reaches a predetermined safety threshold, the current at this time is regarded as the safe current-carrying capacity of the submarine cable.

[0020] As described above, the beneficial effects of this invention are as follows: Based on the laying environment of the submarine cable, the submarine cable is divided into deep-sea, shallow-water, and landing sections, significantly reducing the geometric complexity and computational resource consumption of a single model; simulation models are established for each section and coupled with corresponding electromagnetic, heat transfer, and fluid fields, thus realistically reproducing the heat radiation and convection heat transfer mechanisms of the submarine cable in environments such as ocean currents, soil, and concrete trenches. An equivalent circuit is constructed for the double-circuit heterogeneous submarine cable, and the circulating current value is calculated in each section of the submarine cable based on the sheath impedance and armor impedance, injecting the circulating current value into the electromagnetic field as an equivalent current source. The step-by-step current-increasing method achieves accurate safe current-carrying capacity determination through real-time conductor temperature feedback, avoiding over-design or potential temperature exceedance risks. In this way, errors in cable temperature distribution and safe current-carrying capacity assessment during simulation are effectively reduced.

[0021] Furthermore, electromagnetic fields, heat transfer fields, and fluid fields are coupled into the simulation model of the deep-sea section; The simulation model of the shallow section is coupled with electromagnetic and heat transfer fields; The simulation model of the landing section is coupled with electromagnetic field, heat transfer field and fluid field; For each segment of the simulation model, establish electromagnetic-thermal coupling between the coupled electromagnetic and heat transfer fields: For the coupled heat transfer and fluid fields in the simulation models of the deep-sea section and the landing section, the fluid heat transfer control equations are established:

[0022] In the formula, Q l Indicates the heat source of the fluid material; ρ l Indicates the density of the fluid; C P2 This indicates the specific heat capacity of a fluid material at normal pressure. T Indicates the temperature of the fluid; v Represents the velocity vector of the fluid; q Indicates the heat flux by conduction; τ Represents the viscous stress tensor; P It represents the pressure of a fluid.

[0023] As described above, by coupling electromagnetic, thermal, and fluid dynamics together, the model can fully reproduce the thermal behavior of submarine cables under different environments (deep-sea currents, shallow-water calm conditions, and landing airflow), significantly improving the accuracy of temperature field prediction. Due to the bidirectional coupling between the heat source and temperature-conductivity, the model can dynamically capture the influence of circulating current loss on temperature distribution, thereby obtaining a more reliable safe current carrying capacity.

[0024] Furthermore, electromagnetic-thermal coupling is established for the coupled electromagnetic and heat transfer fields in each segment of the simulation model, including: The electromagnetic loss of the electromagnetic field is used as a heat source and applied to the core, sheath and armor of the submarine cable to obtain electromagnetic heat. The electromagnetic loss includes: Heat loss of cable core conductor:

[0025] In the formula, R This represents the effective value of the conductor resistance under actual operating conditions of the cable core. I c This indicates the current value of the conductor in the core of the submarine cable; Dielectric loss caused by insulating materials:

[0026] In the formula, f represents the voltage frequency; c represents the capacitance per unit length of cable. U 0 indicates the phase voltage during cable line operation; δ The tan θ represents the dielectric loss angle. δ Indicates the loss factor of the insulating medium; Damage to sheaths and armor:

[0027]

[0028] In the formula, W s This indicates the loss of the submarine cable sheath. I siThis represents the circulating current generated on the sheath of the i-th submarine cable. R si This represents the unit impedance of the i-th submarine cable sheath; W a Indicates cable armor loss. I ai This represents the circulating current generated on the armor of the i-th submarine cable. R ai This represents the unit impedance of the armor of the i-th submarine cable.

[0029] As described above, the heat loss of the four layers of wire core, insulation, sheath, and armor is all included in the heat source, avoiding the thermal error caused by neglecting circulating current loss in traditional methods.

[0030] Furthermore, an equivalent circuit is constructed for the double-circuit heterogeneous submarine cable. The circulating current value is calculated within each segment of the submarine cable based on the sheath impedance and armor impedance. This circulating current value is then injected into the electromagnetic field of the electromagnetic-thermal-current coupling model as an equivalent current source, including: For each segment of the submarine cable, an equivalent circuit is constructed, and the circulating current calculation equation is obtained:

[0031] In the formula, R s This indicates the total resistance of the metal sheath of the submarine cable; X s This indicates the total reactance of the metallic sheath of the submarine cable; R a This indicates the total resistance of the submarine cable armor. X a This indicates the total reactance of the submarine cable armor; R sm +j X sm Indicates the first m The impedance of the metal sheath of the submarine cable segment; R am +j X am Indicates the first m The impedance of the armor of the submarine cable segment; U n si , U n ai This represents the total induced voltage of the metal sheath and armor in state n; U n sim , U n aim Indicates the first mThe induced voltage on the metal sheath and armor of the cable segment in state n; The circulating current distribution of the sheath and the armor is dynamically calculated based on the circulating current calculation equation. The circulating current calculation equation is then introduced into the electromagnetic field in the form of an equivalent current source as the current boundary condition for the sheath and the armor.

[0032] As described above, treating the circulating current in the sheath and armor as an equivalent current source allows for the complete representation of their Joule heating in the numerical model, whereas traditional models often neglect such losses. This approach reduces subsequent temperature field prediction errors. Treating the circulating current as a current boundary condition rather than an additional heat source maintains the consistency of the coupling between the electromagnetic field, thermal field, and fluid field, avoiding multiple manual conversions and error propagation, thus improving simulation stability and maintainability.

[0033] Because the circulation calculation and electromagnetic field coupling are updated in real time during the simulation, the model can automatically adjust the circulation value according to changes in temperature, frequency, and even load. The thermal performance of different armor / sheath materials, geometries, or laying schemes can be quickly compared within the same model.

[0034] Furthermore, the electromagnetic-thermal-fluid coupling model is iteratively solved using a step-by-step current-increasing method, and the conductor temperature is continuously monitored. When the conductor temperature reaches a predetermined safety threshold, the current at this point is considered as the safe current-carrying capacity of the submarine cable, including: Starting from the initial current value, the submarine cable current is gradually increased while monitoring the conductor temperature, sheath circulating current, and armor circulating current. The current increase is stopped when the conductor temperature reaches the predetermined safety threshold. The current at this point is considered the safe current carrying capacity of the submarine cable.

[0035] As described above, by progressively increasing the flow rate and updating the temperature and circulation in real time, the additional heat loss caused by the sheath / armor circulation can be captured, avoiding overestimation or underestimation by traditional single heat estimation methods, thus obtaining a safe flow rate closer to reality.

[0036] Please refer to Figure 10 Another embodiment of the present invention provides a temperature field and current carrying capacity calculation terminal for a dual-circuit heterogeneous submarine cable, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the various steps of the above-described method for calculating the temperature field and current carrying capacity of a dual-circuit heterogeneous submarine cable.

[0037] The method for calculating the temperature field and current carrying capacity of a double-circuit heterogeneous submarine cable and the terminal thereof described above in this invention are illustrated below through specific embodiments: Please refer to Figure 1 One embodiment of the present invention is as follows: S1. Construct a double-circuit heterogeneous submarine cable laying model.

[0038] In this embodiment, when submarine cables serve as power transmission channels between two shores, their laying environments can generally be categorized into deep-sea sections, shallow-water sections, and landing sections. In the deep-sea section, due to complex seabed conditions, direct subsea laying is typically used. In the shallow-water section, to prevent damage from ship anchors, burial is typically used. In the landing section, for ease of maintenance and cable protection, cable trench laying is typically employed. Specific laying environments are as follows... Figure 2 As shown in Table 1, the environmental parameters for its installation are as follows.

[0039] Table 1 Environmental parameters for submarine cable laying

[0040] When performing finite element simulation modeling for submarine cables, it is generally believed that when the distance between cables is greater than 2m, the thermal effect between cables can be ignored. Since the distance between the deep-sea section and the shallow-water section of the cable is much greater than 2m, only a single cable needs to be built when constructing the deep-sea section and the shallow-water section.

[0041] In this embodiment, the simulation models of the three sections—deep-sea section, shallow-water section, and landing section—are as follows: Figure 3 As shown. Figure 3 (a) is a simulation model of the deep-sea section of the seabed. The cable is 2m away from the top of the seawater, 3m away from the left and right boundaries, and 3m away from the deep soil at the lower boundary. Figure 3 (b) is a simulation model of direct burial in the shallow water section, in which the submarine cable is 2 m away from the upper boundary of the soil, the seawater is a fluid domain of 0.5m×6m, and is 3m away from the deep soil. Figure 3 (c) is a simulation model of the cable trench laying in the landing section. The height of the left and right trench walls is 1.6m and the thickness is 0.1m. The width of the lower trench wall is 2.9m and the thickness is 0.1m. The width of the upper cover plate is 4m and the thickness is 0.2m. The cable trench material is concrete.

[0042] S2. Construct an electromagnetic-thermal-fluid model for a dual-circuit heterogeneous submarine cable that considers sheath circulation.

[0043] S2.1 Construct the physical field control equations.

[0044] When submarine cables are laid directly on the seabed in deep-sea sections, heat transfer mainly involves heat conduction between media and heat convection generated by seawater flow. Therefore, when establishing a finite element model, it is necessary to couple the electromagnetic field, heat transfer field, and fluid field to ensure accurate calculation of the cable temperature field. When submarine cables are buried directly on the seabed in shallow water sections, heat transfer is mainly through heat conduction between solids. The finite element model for this section only needs to couple the electromagnetic field and heat transfer field. When cable cables are laid in trenches in landing sections, since there is air in the trench in addition to the submarine cable, it is necessary to couple the electromagnetic field, heat transfer field, and fluid field when establishing a finite element model.

[0045] In the electromagnetic-thermal-fluid coupled model, Maxwell's equations are used to calculate the electromagnetic field distribution of the three-core submarine cable, the hydrodynamic equations are used to calculate the seawater flow field, and the convection-diffusion heat transfer equations for both solids and fluids are used to calculate the temperature distribution. The specific governing equations are shown below: (1) Electromagnetic field governing equations: When the conductor of a high-voltage cable is subjected to 50Hz alternating current, an electromagnetic field exists around the cable. In this embodiment, the distribution of the electromagnetic field around the cable conductor at this time is regarded as steady state. Maxwell's equations mainly consist of four laws: the current law, Faraday's law of electromagnetic induction, Gauss's law of magnetic flux, and Gauss's law of electric flux. The numerical expression is shown in equation (1), which is an important basis for the numerical calculation of electromagnetic fields.

[0046] (1) In the formula, H This represents the magnetic field strength, measured in A / m. J This represents the current density vector, with units of A / m. 2 ; D Represents the electric displacement vector, with units of C / m. 2 ; E This represents the electric field strength, measured in V / m. B Represents magnetic flux density, measured in tons (T). ρ This represents the volumetric charge density, with units of C / m³. 3 . This represents the vector differential operator.

[0047] The correspondence between the parameters is shown in equation (2): (2) In the formula, ε represents the dielectric constant, with units of F / m; μ represents the magnetic permeability of the medium, with units of H / m; γ It represents the electrical conductivity of the medium, with units of S / m.

[0048] The electromagnetic losses generated after energization act as a heat source for the heat transfer field, and then cause changes in the temperature of the submarine cable through heat conduction. Since the conductivity of some key materials in the submarine cable is affected by temperature, its conductivity also changes under temperature changes, which in turn affects the electromagnetic losses and temperature changes of the submarine cable.

[0049] (2) Control equations of the heat transfer field: There is heat transfer between the various media layers of the cable and between the cable and the surrounding environment. According to Fourier's heat transfer law and the law of conservation of energy, the mathematical model of steady-state heat transfer of submarine cables in three-dimensional space is shown in equation (3): (3) In the formula, ρ This indicates the mass density of the cable layer medium or the surrounding environment. c The t represents the specific heat capacity of the substance, and the time represents the time. T This represents the temperature variable to be determined, in Kelvin (K). λ x , λ y , λ z These represent the thermal conductivity of a material along the x, y, and z directions, respectively, with units of W / (m·K); Q v It represents the heat generated per unit volume of a substance, and its unit is W / m³. 3 The first term on the left-hand side of the formula represents the rate of change of internal energy per unit volume of the medium (temperature change over time). The second to fourth terms represent the heat transferred in the x, y, and z directions through thermal conduction (the three-dimensional form of Fourier's law). The fifth term represents the influence of internal heat sources (such as cable heating) or heat sinks (such as heat dissipation). The essence of the formula is energy conservation: the change in the internal energy of the medium equals the heat transferred in minus the heat transferred out, plus the contribution from internal heat sources.

[0050] The heat generated by submarine cables during operation mainly comes from the heat loss of the cable core conductor, the dielectric loss of the insulation material, and the loss of the sheath and armor.

[0051] The formula for calculating the heat loss of the cable core conductor is as follows: (4) In the formula, R This represents the effective value of the conductor resistance under actual operating conditions of the cable core. I c This indicates the current value of the conductor in the core of the submarine cable.

[0052] The specific method for calculating dielectric loss generated by insulating materials is as follows: The dielectric loss of the cable insulation layer mainly depends on the operating voltage, and the dielectric loss per unit length of insulation layer is: (5) In the formula, f The voltage frequency is represented; in this embodiment, the power frequency of 50Hz is used. c represents the cable capacitance per unit length, in F / m. U 0 indicates the phase voltage of the cable line during operation, in volts (V). δ The tan θ represents the dielectric loss angle. δ This indicates the loss factor of the insulating medium.

[0053] The specific method for calculating wear and tear on sheaths and armor is as follows: Traditional estimations of circulating current losses in metal-sheathed cables are typically based on the IEC-60287 standard. While this method is quick and simple, its applicability is mainly limited to cases with a small number of cable circuits. When faced with complex situations involving multiple parallel cables in phase, the calculation error increases significantly, rendering this method unsuitable. This embodiment employs the following calculation method: (6) (7) In the formula, W s This indicates the loss of the submarine cable sheath. I si This represents the circulating current generated on the sheath of the i-th submarine cable. R si This represents the unit impedance of the i-th submarine cable sheath; W a Indicates cable armor loss. I ai This represents the circulating current generated on the armor of the i-th submarine cable. R ai This represents the unit impedance of the armor of the i-th submarine cable.

[0054] (3) Fluid field governing equations The fluid field is described by the Navier-Stokes equations, which calculate the magnitude and distribution of fluid velocity in the seabed environment. The governing equations are shown in equation (8).

[0055] (8) In the formula, ρ The density of a fluid is expressed in kg / m³. 3 ; u Represents the velocity vector of the fluid, with units of m / s; p Represents fluid pressure, with units of Pa; I represents the identity matrix; μ This represents dynamic viscosity, with units of Pa. s; T This indicates the temperature of the fluid material, expressed in Kelvin (K).

[0056] (4) Multiphysics coupling equations In a heat transfer field, since electrical conductivity is a temperature-dependent function, changes in temperature affect the magnitude of the cable's conductivity, thereby altering the cable's losses. On the other hand, changes in temperature also cause changes in fluid density, inducing fluid movement and affecting the heat dissipation process and temperature distribution of the submarine cable. The coupling relationships of multiple physics fields are as follows: Figure 4 As shown.

[0057] In this embodiment, the multiphysics coupling equations include electromagnetic-thermal coupling control equations and fluid heat transfer control equations.

[0058] Among them, electromagnetic-thermal coupling uses the Joule heat generated by the electromagnetic field as the heat source of the heat transfer field for coupling. The electromagnetic-thermal coupling control equation is shown in equation (9): (9) In the formula, ρ Density indicates the density of a fluid or solid. C ρ This represents the specific heat capacity at constant pressure. u Represents the velocity vector of the fluid. q Indicates the heat flux by conduction; Q e This indicates the heat source in the material, expressed in W / m.

[0059] Submarine cables generate heat due to electromagnetic losses, which serves as the heat source for the heat transfer field. This heat causes temperature changes in the cable through thermal conduction. Since the conductivity of some key materials in the cable is affected by temperature, temperature changes alter their conductivity, thus affecting electromagnetic losses and temperature distribution. The conductivity of copper conductors... γ cu The relationship with temperature is as follows: (10) In the formula, α This represents the temperature coefficient of resistance of copper, measured in Kelvin (K). -1 ; ρ 0 represents the resistivity of copper at the reference temperature; T Indicates the actual temperature of the copper conductor; T 0 indicates the reference temperature.

[0060] The electrical conductivity of insulating materials PPLP and XLPE is related to both the electric field strength E and the temperature T. The mathematical expression for this is: (11) (12) In the formula, T represents temperature and E represents electric field strength.

[0061] The governing equation for fluid heat transfer is: (13) In the formula, Q l Indicates the heat source of the fluid material; C P2 This indicates the specific heat capacity of a fluid material at normal pressure. q Indicates the heat flux by conduction; τ Represents the viscous stress tensor; ρ l Indicates the density of the fluid. T Indicates the temperature of the fluid; v Represents the velocity vector of the fluid; P This represents the pressure of the fluid. Equation (13) is essentially the fluid energy conservation equation (thermal balance equation).

[0062] S2.2 Construct boundary conditions.

[0063] The simulation mainly involves three modules: electromagnetic field, thermal field, and flow field. The boundary conditions are as follows: (1) Electromagnetic field boundary conditions: The core, metal sheath, and armor of the submarine cable are taken as coil currents; the circulating current function that varies with the current carrying capacity is substituted into the coil current of the metal sheath and armor layer using simulation software.

[0064] (2) Heat transfer boundary conditions: Electromagnetic loss in the electromagnetic module is used as a heat source and applied to the core, metal sheath, and armor of the submarine cable to generate electromagnetic heat. For submarine cables laid or buried on the seabed, seawater is used as the fluid heat transfer medium and the remaining portion is used as the solid heat transfer medium; for submarine cables in the landing section, the air portion is used as the fluid heat transfer medium and the soil and cable trench walls are used as the solid heat transfer medium. The lower boundary is a constant temperature boundary with a temperature of 20℃; the left and right boundaries are soil boundaries with a heat flux of 0; the temperature of the upper surface of the cable trench is set at 30℃.

[0065] (3) Flow field boundary conditions: The air inside the cable trench is set as a fluid domain, and the air can flow freely.

[0066] Mesh generation: For the solution model, a denser mesh yields more accurate results, but also increases computational complexity and time required to solve the model. Therefore, simulation modeling typically aims to achieve the simplest possible mesh generation while maintaining a certain level of accuracy. Furthermore, mesh generation requires comprehensive consideration of the geometric model and boundary conditions, using different levels of mesh refinement in different regions. In this embodiment, within each segment, the core and armor layer of the cable at the source boundary of the entire submarine cable domain are meshed, such as... Figure 5As shown in (a), this makes the results, such as the heat and magnetic field information generated by the cable, more accurate. For the model of deep-sea subsea laying, since this embodiment considers the actual situation of the submarine cable being slightly embedded in the soil, the mesh at the contact point between the soil and the submarine cable is refined, as shown in (a). Figure 5 As shown in (b); for other sections, a coarser mesh is used to increase the computational speed of the model.

[0067] S2.3 Construction of the field-path coupling model for a dual-loop heterogeneous submarine cable.

[0068] Because the arrangement, phase spacing, and loop spacing of submarine cables vary in different sections, and traditional impedance calculations typically ignore the effects of different sections and only analyze the impedance of the submarine section, traditional impedance calculation methods will produce certain errors. This embodiment addresses this problem by proposing that the impedance and induced voltage in the equivalent circuit should be distributed according to the sections of the submarine cable. Taking an oil-filled submarine cable loop as an example, its impedance and induced voltage should be composed of the impedance and induced voltage of the deep-sea section, the shallow-water section, and the landing section, respectively. The equivalent circuit diagram is shown below. Figure 6 As shown.

[0069] Figure 6 middle, R sm +j X sm ( m (I, II, and III represent the deep-sea section, the shallow-water section, and the landing section, respectively) indicating the... m The impedance of the metal sheath of the submarine cable segment. R am +j X am Indicates the first m The impedance of the armor of the submarine cable segment. U n sim , U n aim ( n The superscript symbols represent, respectively U , U , U ) indicates the first m Induced voltage on the metal sheath and armor of the cable segment.

[0070] According to Figure 6 The equivalent circuit diagram is rewritten to rewrite the circulating current calculation equation, that is, the sheath and armor impedance are calculated in segments, as shown in equation (14): (14) In the formula, Rs This indicates the total resistance of the metal sheath of the submarine cable; X s This indicates the total reactance of the metallic sheath of the submarine cable; R a This indicates the total resistance of the submarine cable armor. X a This indicates the total reactance of the submarine cable armor; R sm +j X sm Indicates the first m The impedance of the metal sheath of the submarine cable segment; R am +j X am Indicates the first m The impedance of the armor of the submarine cable segment; U n si , U n ai This represents the total induced voltage of the metal sheath and armor in state n; U n sim , U n aim Indicates the first m The induced voltage on the metal sheath and armor of the cable segment in state n.

[0071] To achieve accurate calculation of circulating current across the entire submarine cable section, this embodiment, based on a modified circulating current equation, developed a function program model in mathematical modeling software with the cable current as the independent variable and circulating current as the dependent variable. This model dynamically calculates the circulating current distribution in the metal sheath and armor by analyzing cable structural parameters (such as phase spacing and loop spacing) in the deep-sea, shallow-water, and landing sections. Through the data synchronization module in the simulation software, the circulating current calculation function from the mathematical modeling software is imported into the electromagnetic physics field as the current boundary condition for the metal sheath and armor coils, thereby constructing a finite element simulation model considering circulating current across the entire section.

[0072] After the model was built, a step-by-step current increase method was used to test whether the conductor temperature reached the threshold (90℃ for XLPE and 85℃ for oil-filled submarine cables) to determine the cable's safe current carrying capacity. The specific procedure was as follows: starting from an initial current value, the submarine cable current was gradually increased while monitoring changes in conductor temperature, sheath circulating current, and armor circulating current until the conductor temperature reached the allowable upper limit. By analyzing the temperature field and circulating current distribution under different currents, the cable's current carrying capacity and its operational safety in complex environments could be accurately assessed.

[0073] This method combines current circulation calculation with multiphysics finite element simulation, overcoming the calculation errors inherent in traditional methods under complex laying environments. Through collaborative simulation using mathematical modeling and simulation software, dynamic modeling of the current circulation across the entire section and accurate prediction of the current carrying capacity are achieved. Furthermore, this method has good versatility and can be extended to cable current circulation calculation in other complex environments, providing a reliable theoretical basis and technical support for the design, laying, and operation and maintenance of submarine cables. The calculation flowchart is shown below. Figure 7 As shown.

[0074] S3, Model Validation.

[0075] To verify the accuracy of the submarine cable simulation model that takes into account the circulating current, the measured data of the Xiamen submarine cable were compared with the traditional simulation model that did not consider the influence of the circulating current throughout the entire section, and the simulation model proposed in this embodiment. Since the XLPE submarine cable loop has not yet been put into operation, only the single-loop oil-filled submarine cable model was used for comparison. When the three-phase currents of A, B, and C in actual operation were 232.15A, 252.66A, and 249.13A, respectively, the measured values ​​of the cable fiber temperature and the simulated temperatures are shown in Table 2. Among them, error 1 and error 2 are the errors between the traditional simulation, the simulation of this embodiment, and the measured temperature, respectively.

[0076] Table 2 Environmental parameters for submarine cable laying

[0077] As shown in Table 2, under the same conditions, the errors between the temperatures calculated by the traditional simulation model at the fiber optic temperature measurement points of the three-phase cables A, B, and C and the actual measured data are 6.92%, 9.47%, and 8.33%, respectively. In contrast, the errors between the temperatures calculated by the simulation model considering circulating current proposed in this embodiment and the actual measured data are 5.36%, 0.63%, and 2.25%, respectively, all smaller than the errors of the traditional simulation model. Furthermore, the model can reduce the error from 9.47% to as low as 0.63%. This demonstrates that the simulation model constructed in this embodiment has higher accuracy than the traditional simulation model, which also verifies the rationality of the structure and material parameters of the simulation model constructed in this embodiment.

[0078] S4. Temperature field and current carrying capacity results and analysis of different sections of submarine cable.

[0079] This embodiment, based on the dual-loop field-coupled submarine cable model considering sheath and armor circulation current proposed above, studies the influence of environmental factors on the current carrying capacity and temperature field of different sections of the submarine cable. It analyzes the influence and mechanism of ambient temperature on the conductor temperature and current carrying capacity of the submarine cable. This can provide a certain reference for the practical engineering design, equipment selection, and system operation and maintenance of submarine cables.

[0080] S4.1 Analyze the impact of the laying environment on the current carrying capacity of submarine cables.

[0081] S4.1.1 Analyze the influence of ambient temperature on the conductor temperature of deep-sea submarine cables.

[0082] Sea surface temperature varies significantly across seasons; therefore, the impact of different ambient temperatures on the current carrying capacity of submarine cables should be considered when calculating their safe current-carrying capacity. Assuming a seawater flow velocity of 0.5 m / s, this study investigates the temperature changes of the submarine cable conductor at surface temperatures ranging from 5 to 40°C, with temperature points taken at 5°C intervals. The results are as follows. Figure 8 As shown.

[0083] Depend on Figure 8 It is evident that the conductor temperatures of oil-filled submarine cables and XLPE submarine cables exhibit a linear positive correlation with ambient temperature. At an ambient temperature of 5℃, the conductor temperatures of the oil-filled and XLPE submarine cables are 57.8℃ and 62.7℃, respectively. When the ambient temperature rises to 40℃, the conductor temperatures increase to 95.2℃ and 100.3℃, respectively, representing increases of approximately 64.7% and 60%. This demonstrates that ambient temperature has a significant impact on the temperature of submarine cables; for every 5℃ increase in ambient temperature, the conductor temperature within the cable trench increases by approximately 5.3℃. This pattern indicates that the influence of ambient temperature on the conductor temperature of submarine cables cannot be ignored, especially in high-temperature environments, where the rise in conductor temperature may pose a threat to the safe operation of the cable.

[0084] S4.1.2 Analyze the influence of ambient temperature on the conductor temperature of the submarine cable in the shallow water section.

[0085] The ambient temperature was set to 5-40℃, and a data point was taken every 5℃. The temperature changes of the submarine cable conductor when the submarine cable was laid in the soil at depths of 0.5m and 2m are shown in Table 3.

[0086] As shown in Table 3, when the burial depth is 0.5m, as the ambient temperature increases from 5℃ to 40℃, the conductor temperatures of the oil-filled submarine cable and the XLPE submarine cable increase from 63.1℃ and 68.2℃ to 93.8℃ and 98.7℃, respectively, representing increases of approximately 48.7% and 44.7%. Furthermore, for every 5℃ increase in ambient temperature, the conductor temperature increases by approximately 4.4℃. When the burial depth is 2m, as the ambient temperature increases from 5℃ to 40℃, the conductor temperatures of the oil-filled submarine cable and the XLPE submarine cable increase from 68.7℃ and 72.8℃ to 91.7℃ and 96.9℃, respectively, representing increases of approximately 33.5% and 33.1%. Furthermore, for every 5℃ increase in ambient temperature, the conductor temperature increases by approximately 3.4℃.

[0087] Table 3. Conductor temperature of submarine cable at different burial depths and ambient temperatures

[0088] This shows that ambient temperature has a significant impact on the conductor temperature of submarine cables buried directly on the seabed. At the same time, as the burial depth increases, the influence of ambient temperature on the conductor temperature of the submarine cable gradually decreases. When the burial depth of the submarine cable increases from 0.5m to 2m, the temperature rise rate of the conductor decreases by about 10%. This conclusion provides a scientific basis for the design, laying and maintenance of submarine cables, and is of great significance for improving the reliability and economy of submarine cable projects.

[0089] S4.1.3 Analyze the influence of ambient temperature on the conductor temperature of the submarine cable in the landing section.

[0090] The air in the cable trench is controlled by natural convection, with an ambient temperature ranging from 5℃ to 40℃. The simulation temperature is set at 5℃ intervals to study the influence of the ambient temperature on the surface of the cable trench on the cables inside. The variation pattern is as follows: Figure 9 As shown.

[0091] Depend on Figure 9 It can be seen that ambient temperature has the same effect on both oil-filled submarine cables and XLPE submarine cables, with a linear positive correlation between the conductor temperature and ambient temperature. At an ambient temperature of 5℃, the conductor temperatures of the oil-filled submarine cable and the XLPE submarine cable are 69.84℃ and 64.66℃, respectively; when the ambient temperature rises to 40℃, the conductor temperatures rise to 97.79℃ and 92.95℃, respectively. This indicates that for every 5℃ increase in ambient temperature, the conductor temperature in the cable trench increases by approximately 4℃.

[0092] In summary, based on electromagnetic induction theory, this embodiment establishes a field-circuit coupling calculation model considering the overall laying environment of a dual-circuit heterogeneous submarine cable, taking into account the circulating current in the metal sheath and armor, and the cable temperature distribution. The circulating current of the three-phase circuit of the dual-circuit heterogeneous submarine cable is calculated using mathematical modeling software. A simulation model of the temperature distribution of the dual-circuit heterogeneous submarine cable, using electromagnetic-thermal-fluid multiphysics coupling, is established using finite element simulation software, with current as the coupling term. Simulation verification shows that the maximum error of the model proposed in this embodiment can be reduced from 9.47% to 0.63% compared to existing current-carrying capacity simulation models that do not consider circulating current, further improving the calculation accuracy of submarine cable temperature distribution and current-carrying capacity simulation.

[0093] This embodiment also studied the variation laws and physical mechanisms of the temperature field and steady-state current carrying capacity of submarine cables under different laying methods, and drew the following conclusions: 1. Due to differences in cable structure, the current carrying capacity of oil-filled cables is greater than that of XLPE cables under the same conditions in all sections. However, when laid in cable trenches at the landing section, the thermal effect between the cables makes the current carrying capacity and temperature difference of oil-filled cables and XLPE cables not significantly different at low flow rates.

[0094] 2. The current carrying capacity and insulation temperature difference of submarine cables in shallow water sections decrease with increasing burial depth, mainly due to the decrease in heat conduction flux with increasing burial depth.

[0095] According to another aspect of the invention, Figure 10 This is a schematic diagram illustrating a terminal for calculating the temperature field and current carrying capacity of a double-circuit heterogeneous submarine cable according to an embodiment of the present invention. It includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the various steps of the method for calculating the temperature field and current carrying capacity of a double-circuit heterogeneous submarine cable as described above.

[0096] The above description is merely an embodiment of the present invention and does not limit the patent scope of the present invention. Any equivalent modifications made based on the content of the present invention specification and drawings, or direct or indirect applications in related technical fields, are similarly included within the patent protection scope of the present invention.

Claims

1. A method for calculating the temperature field and current carrying capacity of a double-circuit heterogeneous submarine cable, characterized in that, Including the following steps: Based on the laying environment of the submarine cable, the submarine cable is divided into deep-sea section, shallow-water section and landing section; A simulation model is established for each segment of the submarine cable, and the corresponding electromagnetic field, heat transfer field and fluid field are coupled to each segment simulation model to obtain an electromagnetic-thermal-fluid coupled model. To construct an equivalent circuit for a double-circuit heterogeneous submarine cable, the circulating current value is calculated in each segment of the submarine cable based on the sheath impedance and armor impedance of the submarine cable. The circulating current value is then injected into the electromagnetic field of the electromagnetic-thermal-fluid coupling model in the form of an equivalent current source. The temperature field distribution of the submarine cable was obtained by solving the electromagnetic-thermal-fluid coupling model. The electromagnetic-thermal-fluid coupling model is solved iteratively using the step-by-step current-increasing method, and the conductor temperature is continuously monitored. When the conductor temperature reaches a predetermined safety threshold, the current at this time is regarded as the safe current-carrying capacity of the submarine cable.

2. The method for calculating the temperature field and current carrying capacity of a double-circuit heterogeneous submarine cable according to claim 1, characterized in that, For each segment of the simulation model, the corresponding electromagnetic field, heat transfer field, and fluid field are coupled, including: The simulation model of the deep-sea section is coupled with electromagnetic field, heat transfer field and fluid field; The simulation model of the shallow section is coupled with electromagnetic and heat transfer fields; The simulation model of the landing section is coupled with electromagnetic field, heat transfer field and fluid field; For each segment of the simulation model, establish electromagnetic-thermal coupling between the coupled electromagnetic and heat transfer fields: For the coupled heat transfer and fluid fields in the simulation models of the deep-sea section and the landing section, the fluid heat transfer control equations are established: In the formula, Q l Indicates the heat source of the fluid material; ρ l Indicates the density of the fluid; C P2 This indicates the specific heat capacity of a fluid material at normal pressure. T Indicates the temperature of the fluid; v Represents the velocity vector of the fluid; q Indicates the heat flux by conduction; τ Represents the viscous stress tensor; P It represents the pressure of a fluid.

3. The method for calculating the temperature field and current carrying capacity of a double-circuit heterogeneous submarine cable according to claim 2, characterized in that, For each segment of the simulation model, electromagnetic-thermal coupling is established between the coupled electromagnetic and heat transfer fields, including: The electromagnetic loss of the electromagnetic field is used as a heat source and applied to the core, sheath and armor of the submarine cable to obtain electromagnetic heat. The electromagnetic loss includes: Heat loss of cable core conductor: In the formula, R This represents the effective value of the conductor resistance under actual operating conditions of the cable core. I c This indicates the current value of the conductor in the core of the submarine cable; Dielectric loss caused by insulating materials: In the formula, f represents the voltage frequency; c represents the capacitance per unit length of cable. U 0 indicates the phase voltage during cable line operation; δ The tan θ represents the dielectric loss angle. δ Indicates the loss factor of the insulating medium; Damage to sheaths and armor: In the formula, W s This indicates the loss of the submarine cable sheath. I si This represents the circulating current generated on the sheath of the i-th submarine cable. R si This represents the unit impedance of the i-th submarine cable sheath; W a Indicates cable armor wear. I ai This represents the circulating current generated on the armor of the i-th submarine cable. R ai This represents the unit impedance of the armor of the i-th submarine cable.

4. The method for calculating the temperature field and current carrying capacity of a double-circuit heterogeneous submarine cable according to claim 2, characterized in that, To construct an equivalent circuit for a double-circuit heterogeneous submarine cable, the circulating current value is calculated in each segment of the submarine cable based on the sheath impedance and armor impedance. This circulating current value is then injected into the electromagnetic field of the electromagnetic-thermal-current coupling model as an equivalent current source, including: For each segment of the submarine cable, an equivalent circuit is constructed, and the circulating current calculation equation is obtained: In the formula, R s This indicates the total resistance of the metal sheath of the submarine cable; X s This indicates the total reactance of the metallic sheath of the submarine cable; R a This indicates the total resistance of the submarine cable armor. X a This indicates the total reactance of the submarine cable armor. R sm +j X sm Indicates the first m The impedance of the metal sheath of the submarine cable segment; R am +j X am Indicates the first m The impedance of the armor of the submarine cable segment; U n si , U n ai This represents the total induced voltage of the metal sheath and armor in state n; U n sim , U n aim Indicates the first m The induced voltage on the metal sheath and armor of the cable segment in state n; The circulating current distribution of the sheath and the armor is dynamically calculated based on the circulating current calculation equation. The circulating current calculation equation is then introduced into the electromagnetic field in the form of an equivalent current source as the current boundary condition for the sheath and the armor.

5. The method for calculating the temperature field and current carrying capacity of a double-circuit heterogeneous submarine cable according to claim 1, characterized in that, The electromagnetic-thermal-fluid coupling model is solved iteratively using a step-by-step current-increasing method while continuously monitoring the conductor temperature. When the conductor temperature reaches a predetermined safety threshold, the current at this point is considered the safe current-carrying capacity of the submarine cable, including: Starting from the initial current value, the submarine cable current is gradually increased while monitoring the conductor temperature, sheath circulating current, and armor circulating current. The current increase is stopped when the conductor temperature reaches the predetermined safety threshold. The current at this point is considered the safe current carrying capacity of the submarine cable.

6. A temperature field and current-carrying capacity calculation terminal for a dual-circuit heterogeneous submarine cable, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it performs the following steps: Based on the laying environment of the submarine cable, the submarine cable is divided into deep-sea section, shallow-water section and landing section; A simulation model is established for each segment of the submarine cable, and the corresponding electromagnetic field, heat transfer field and fluid field are coupled to each segment simulation model to obtain an electromagnetic-thermal-fluid coupled model. To construct an equivalent circuit for a double-circuit heterogeneous submarine cable, the circulating current value is calculated in each segment of the submarine cable based on the sheath impedance and armor impedance of the submarine cable. The circulating current value is then injected into the electromagnetic field of the electromagnetic-thermal-fluid coupling model in the form of an equivalent current source. The temperature field distribution of the submarine cable was obtained by solving the electromagnetic-thermal-fluid coupling model. The electromagnetic-thermal-fluid coupling model is solved iteratively using the step-by-step current-increasing method, and the conductor temperature is continuously monitored. When the conductor temperature reaches a predetermined safety threshold, the current at this time is regarded as the safe current-carrying capacity of the submarine cable.

7. The temperature field and current carrying capacity calculation terminal for a double-circuit heterogeneous submarine cable according to claim 6, characterized in that, For each segment of the simulation model, the corresponding electromagnetic field, heat transfer field, and fluid field are coupled, including: The simulation model of the deep-sea section is coupled with electromagnetic field, heat transfer field and fluid field; The simulation model of the shallow section is coupled with electromagnetic and heat transfer fields; The simulation model of the landing section is coupled with electromagnetic field, heat transfer field and fluid field; For each segment of the simulation model, establish electromagnetic-thermal coupling between the coupled electromagnetic and heat transfer fields: For the coupled heat transfer and fluid fields in the simulation models of the deep-sea section and the landing section, the fluid heat transfer control equations are established: In the formula, Q l Indicates the heat source of the fluid material; ρ l Indicates the density of the fluid; C P2 This indicates the specific heat capacity of a fluid material at normal pressure. T Indicates the temperature of the fluid; v Represents the velocity vector of the fluid; q Indicates the heat flux by conduction; τ Represents the viscous stress tensor; P It represents the pressure of a fluid.

8. The temperature field and current carrying capacity calculation terminal for a double-circuit heterogeneous submarine cable according to claim 7, characterized in that, For each segment of the simulation model, electromagnetic-thermal coupling is established between the coupled electromagnetic and heat transfer fields, including: The electromagnetic loss of the electromagnetic field is used as a heat source and applied to the core, sheath and armor of the submarine cable to obtain electromagnetic heat. The electromagnetic loss includes: Heat loss of cable core conductor: In the formula, R This represents the effective value of the conductor resistance under actual operating conditions of the cable core. I c This indicates the current value of the conductor in the core of the submarine cable; Dielectric loss caused by insulating materials: In the formula, f represents the voltage frequency; c represents the capacitance per unit length of cable. U 0 indicates the phase voltage during cable line operation; δ The tan θ represents the dielectric loss angle. δ Indicates the loss factor of the insulating medium; Damage to sheaths and armor: In the formula, W s This indicates the loss of the submarine cable sheath. I si This represents the circulating current generated on the sheath of the i-th submarine cable. R si This represents the unit impedance of the i-th submarine cable sheath; W a Indicates cable armor wear. I ai This represents the circulating current generated on the armor of the i-th submarine cable. R ai This represents the unit impedance of the armor of the i-th submarine cable.

9. The temperature field and current carrying capacity calculation terminal for a double-circuit heterogeneous submarine cable according to claim 7, characterized in that, To construct an equivalent circuit for a double-circuit heterogeneous submarine cable, the circulating current value is calculated in each segment of the submarine cable based on the sheath impedance and armor impedance. This circulating current value is then injected into the electromagnetic field of the electromagnetic-thermal-current coupling model as an equivalent current source, including: For each segment of the submarine cable, an equivalent circuit is constructed, and the circulating current calculation equation is obtained: In the formula, R s This indicates the total resistance of the metal sheath of the submarine cable; X s This indicates the total reactance of the metallic sheath of the submarine cable; R a This indicates the total resistance of the submarine cable armor. X a This indicates the total reactance of the submarine cable armor. R sm +j X sm Indicates the first m The impedance of the metal sheath of the submarine cable segment; R am +j X am Indicates the first m The impedance of the armor of the submarine cable segment; U n si , U n ai This represents the total induced voltage of the metal sheath and armor in state n; U n sim , U n aim Indicates the first m The induced voltage on the metal sheath and armor of the cable segment in state n; The circulating current distribution of the sheath and the armor is dynamically calculated based on the circulating current calculation equation. The circulating current calculation equation is then introduced into the electromagnetic field in the form of an equivalent current source as the current boundary condition for the sheath and the armor.

10. A temperature field and current carrying capacity calculation terminal for a double-circuit heterogeneous submarine cable according to claim 6, characterized in that, The electromagnetic-thermal-fluid coupling model is solved iteratively using a step-by-step current-increasing method while continuously monitoring the conductor temperature. When the conductor temperature reaches a predetermined safety threshold, the current at this point is considered the safe current-carrying capacity of the submarine cable, including: Starting from the initial current value, the submarine cable current is gradually increased while monitoring the conductor temperature, sheath circulating current, and armor circulating current. The current increase is stopped when the conductor temperature reaches the predetermined safety threshold. The current at this point is considered the safe current carrying capacity of the submarine cable.

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