Fast calculation method of submarine cable current carrying capacity based on compactly supported radial basis function

Abstract

The present invention discloses a method for rapidly calculating the current carrying capacity of submarine cables based on compactly supported radial basis functions, comprising the following steps: S1, obtaining submarine cable parameters and their value ranges; S2, constructing an adaptive surface response model based on compactly supported radial basis functions and electromagnetic-thermal-fluid coupling; S3, using the constructed adaptive surface response model to rapidly calculate the current carrying capacity of cables under arbitrary submarine cable parameters. The present invention can rapidly calculate the current carrying capacity under arbitrary cable parameters, while ensuring the accuracy of the calculation results, and can also greatly reduce the calculation time and reduce the calculation cost.

Description

Technical Field

[0001] The invention relates to the technical field of cables, and in particular to a method for quickly calculating the current carrying capacity of a submarine cable. Background Art

[0002] With the global development of marine renewable energy and the increasing demand for energy on some islands and offshore oil platforms, more and more submarine cable projects are being built or planned. Submarine cables can only maintain long-term safe and stable operation when the operating current is lower than its rated current carrying capacity. The current carrying capacity of the cable is mainly determined by the long-term maximum temperature of the insulating material used. For example, for the widely used cross-linked polyethylene (XLPE) cable, the long-term maximum operating temperature of the cable core conductor cannot exceed 90 degrees Celsius.

[0003] Accurately evaluating the temperature field and current carrying capacity of submarine cables is related to their safe and stable operation, efficient operation and cost saving. Figure 1 There are two ways to lay the submarine cable: laying and burying. Laying means directly placing the submarine cable on the seabed, which is generally used in deep sea; burying means using a cable plow to dig a trench, placing the submarine cable in the trench and then covering it, which is often used in shallow sea. Whether it is buried or laid, it belongs to the problem of heat transfer and fluid flow of a constant electromagnetic heat source in a free fluid (seawater) or a porous medium (seabed sediment). Therefore, analyzing the interaction mechanism between the submarine cable and the surrounding medium is a necessary prerequisite for accurately calculating the current carrying capacity of the submarine cable.

[0004] The coupling mechanism of the interaction between submarine cables and the surrounding medium is as follows: When current is passed through the submarine cable, an electromagnetic field is generated, which causes corresponding losses in the conductor and insulation. The losses cause the cable temperature to rise and cause changes in the temperature field of the cable and the surrounding medium. Since the conductivity of the conductor of the submarine cable is a function related to temperature, changes in the temperature field in turn affect the conductivity, which in turn affects the electromagnetic field and cable losses. In addition, changes in the temperature field of the medium around the cable cause changes in the density of the seawater around it. The buoyancy generated by the density change causes the seawater to flow, and the convective heat transfer generated by the seawater flow will affect the change in the temperature field. Therefore, the submarine cable needs to couple the electromagnetic field, thermal field, and fluid field to calculate the current carrying capacity of the submarine cable.

[0005] In the calculation of the current carrying capacity of submarine cables, the parameters of the submarine cables are input variables and the current carrying capacity is the output variable. Therefore, the functional relationship between the cable parameters and the current carrying capacity can be reconstructed by using the surface response model, thereby improving the calculation efficiency and reducing the calculation cost.

[0006] The response surface model (RSM) is a method that uses mathematical statistics knowledge to establish the input-output relationship of a system (device). The core of this method is to construct an analytical solution to the input-output relationship based on the response of the system at a series of sampling points using certain basis functions. Therefore, the key problem to be solved in constructing the RSM model is to determine the appropriate basis function to construct the relationship between the output variable and the input variable.

[0007] At present, the most commonly used basis function of the RSM model in engineering is the radial basis function (RBF). The advantages of RBF are that the interpolation function constructed is very simple for discrete sampling points of any dimension and does not require too much calculation. However, the surface response model constructed based on the full-support radial function has the following problems: (1) the constructed function is not an "optimal" function in a "certain" sense; (2) it is difficult for this model to handle irregular sampling points; (3) it cannot automatically achieve the best matching of algorithm parameters; (4) when there are many sampling points, the calculation of the reconstruction function still requires a lot of computing resources. Furthermore, when the surface response model reconstructs the input-output relationship, the more and denser the sampling points selected, the higher the accuracy of the reconstruction function, but the computational burden also increases accordingly. Summary of the invention

[0008] The purpose of the present invention is to provide a method for quickly calculating the current carrying capacity of submarine cables based on compactly supported radial basis functions. The present invention can quickly calculate the current carrying capacity under any cable parameters, while ensuring the accuracy of the calculation results, and can also greatly reduce the calculation time and reduce the calculation cost.

[0009] In order to solve the above technical problems, the present invention provides the following technical solutions: A method for quickly calculating the current carrying capacity of submarine cables based on compactly supported radial basis functions, comprising the following steps:

[0010] S1. Obtaining submarine cable parameters and their value ranges;

[0011] S2. Construct an adaptive surface response model based on compactly supported radial basis functions and electromagnetic-thermal-fluid coupling;

[0012] S3. Use the constructed adaptive surface response model to quickly calculate the cable current carrying capacity under any submarine cable parameters.

[0013] The above-mentioned method for quickly calculating the current carrying capacity of submarine cables based on compactly supported radial basis functions, the construction of the adaptive surface response model is to first establish a response model based on compactly supported radial basis functions, then couple the electromagnetic field, thermal field and fluid field to obtain a multi-physical field model, solve the cable current carrying capacity according to the multi-physical field model, and finally combine the adaptive strategy to obtain an adaptive surface response model that meets the error control.

[0014] The aforementioned method for rapid calculation of submarine cable current carrying capacity based on compactly supported radial basis function, the establishment of the response model based on compactly supported radial basis function is:

[0015] Construct a compactly supported radial basis function, whose general expression is:

[0016]

[0017] In the formula, p(r) is a given polynomial, The specific meaning is:

[0018]

[0019] For k = 0, 1, 2, 3, φ with 2k-order continuous derivatives l,k The analytical expression of (r)) is as follows:

[0020]

[0021]

[0022]

[0023]

[0024] Where: l = [d / 2+k+1], d is the dimension of the function space;

[0025] For any f(X):R n →R, if it is known that at a series of sampling points x i ∈R D The function value on (i=1,2,…,N) is f i , then the surface response model is:

[0026]

[0027] By adding the derivative function interpolation term to the interpolation formula of the above equation, we can obtain the response model based on the compactly supported radial basis function:

[0028]

[0029] Where N B is the number of sampling points on the boundary, c j and d k are coefficients respectively, where:

[0030]

[0031] f k ′ is the function f at the boundary sampling point X kThe first derivative value of the radial variable r;

[0032] (φ 11 ) ij =φ(||X i -X j ||)(i,j=1,2,…,N)

[0033] (φ 12 ) ij =φ′(||X i -X j ||)(i=1,2,…,N; j=1,2,…,N B )

[0034] (φ 21 ) ij =φ′(||X i -X j ||)(j=1,2,…,N; i=1,2,…,N B )

[0035] (φ 22 ) ij =φ″(||X i -X j ||)(i,j=1,2,…,N B ).

[0036] In the aforementioned fast calculation method of submarine cable current carrying capacity based on compactly supported radial basis functions, in the multi-physics field model, the processes of current loading in the conductor, water flow, heat transfer in the fluid, heat transfer in the solid, and electrothermal coupling are described by the following control equations:

[0037] The governing equation of the eddy current field is:

[0038]

[0039] In the eddy current zone:

[0040] In the non-eddy zone

[0041] Where: A is the vector magnetic potential, V is the scalar potential, ν is the magnetic resistivity, σ is the conductivity, J s is the source current density; is the vector differential operator, i.e. the gradient operator;

[0042] The temperature field control equation is:

[0043]

[0044] Where: ρ is density, C pis the heat capacity at normal pressure, u is the velocity vector, k is the thermal conductivity, Q e is the heat source's heating power per unit volume, q is the heat flux density; is the temperature gradient, J is the current density vector, and E is the electric field intensity vector;

[0045] The fluid field satisfies the laws of conservation of mass, momentum, and energy:

[0046]

[0047] Where: I is the unit matrix, μ is the dynamic viscosity, T is the temperature of the fluid material, and F is the volume force.

[0048] The aforementioned fast calculation method of submarine cable current carrying capacity based on compactly supported radial basis function uses the chord intercept method to solve the current carrying capacity, that is, when the maximum temperature of the cable conductor reaches 90 degrees Celsius, the current at this moment is defined as the current carrying capacity of the cable; the corresponding conductor temperature is calculated by solving the temperature field, and the chord intercept method is used to calculate the cable current carrying capacity. In the iterative calculation, when |T k When the value of -90| is less than 0.01℃, the cable conductor temperature is considered to be stable at the maximum allowable temperature. At this time, the current flowing through the cable is the cable current carrying capacity.

[0049] The aforementioned fast calculation method of submarine cable current carrying capacity based on compactly supported radial basis function is combined with the adaptive strategy to obtain an adaptive surface response model that meets the error control requirements. The specific process is as follows:

[0050] First, determine the parameter range of the submarine cable core conductor as x∈[x min ,x max ], calculate the sampling point x min and x max The current carrying capacity of the submarine cable at the position is then constructed based on the surface response model of the compactly supported radial basis function, denoted as M 1 , then in x min ~x max Take a certain number of parameters (t 1 ,t 2 ,…t n ) are test points, and the constructed surface response model M is applied respectively. 1 And the multi-physics field model calculates the current carrying capacity of the submarine cable at the test point; if the relative error ε i <tol,i=1,2,···,n, then output the surface response model, otherwise min ~x max Take new sampling points s 1 =0.5×(x min +x max ), and use the electromagnetic field, thermal field and fluid field coupling model to calculate the new sampling point s1 The current carrying capacity of the submarine cable is then calculated, and a new surface response model based on compactly supported radial basis functions is constructed, denoted as M 2 , respectively applying the newly constructed surface response model M 2 The multi-physics model is used to calculate the current carrying capacity of the submarine cable at the test point; if the relative error ε i <tol,i=1,2,···,n, then output the surface response model, otherwise min ~s 1 、s 1 ~x max Take sampling points s 21 ,s 22 As the new sampling point, s 21 For x min and 1 The arithmetic midpoint, s 22 For 1 and x max The arithmetic midpoint of the new sampling point s is then calculated using the multiphysics model. 21 、s 22 The current carrying capacity of the submarine cable is then calculated, and a new surface response model based on compactly supported radial basis functions is constructed, denoted as M 3 , respectively applying the constructed surface response model M 3 The multi-physics model is used to calculate the current carrying capacity of the submarine cable at the test point; if the relative error ε i <tol,i=1,2,···,n, then output the surface response model, otherwise start a new round at x min ~s 21 、s 21 ~s 1 、s 1 ~s 22 、s 22 ~x max Sampling is performed within the range and the above operation is repeated until an adaptive surface response model that meets the error control requirements is obtained.

[0051] Compared with the prior art, the present invention is based on the calculation data (capacity) of the known submarine cable magnetic-fluid-thermal coupling model, and by constructing an adaptive surface response model based on compact support radial basis functions and magnetic-thermal-fluid coupling, the input-output relationship between the submarine cable parameters and the current carrying capacity is reconstructed, and then the submarine cable current carrying capacity under any submarine cable parameters is obtained. Compared with the existing cable current carrying capacity calculation method, the present invention can quickly calculate the current carrying capacity under any cable parameters, while ensuring the accuracy of the calculation results, it can also greatly reduce the calculation time and reduce the calculation cost. The present invention overcomes the shortcomings of the existing methods that cannot calculate the cable current carrying capacity under any submarine cable parameters. The adaptive surface response model based on compact support radial basis functions and electromagnetic-thermal-fluid multi-field coupling model of the present invention obtains a reconstruction function that meets the error control requirements at the lowest possible calculation cost, effectively balancing the calculation accuracy and calculation simplicity. The present invention has good calculation numerical accuracy for any parameter within the feasible interval of parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a schematic diagram of the process of the present invention;

[0053] Figure 2 It is a flow chart for calculating the current carrying capacity of cables. DETAILED DESCRIPTION

[0054] The present invention is further described below in conjunction with the embodiments and drawings, but they are not intended to limit the present invention.

[0055] Embodiment: A method for rapidly calculating the current carrying capacity of a submarine cable based on a compactly supported radial basis function, characterized in that it comprises the following steps:

[0056] S1. Obtaining submarine cable parameters and their value ranges;

[0057] The cable selected in this embodiment is a HYJQ71-F127 / 220kV-1600mm2 single-core optoelectronic composite submarine cable, and the parameters of each part are shown in Table 1. In this embodiment, the radius of the submarine cable core conductor is selected as a variable parameter, and the value range is: x∈[20,28], in millimeters.

[0058] Serial number name Material Nominal thickness mm 1 Core conductor Copper conductor x(radius) 2 Conductor shielding Semi-conductive tape + semi-conductive shield 2.0 3 insulation XLPE insulation material 24.0 4 Insulation shielding Semi-conductive shielding material 1.2 5 Water blocking buffer layer Semi-conductive water hose 0.8 6 Metal sleeve Lead Alloy 4.1 7 Inner sheath Polyethylene insulation sheath material 3.9 8 Asphalt layer asphalt 1.65 9 Optical cable protection filling layer Polyethylene fill strips 6.3 10 Armor layer Galvanized Steel Diameter 6.0 11 Outer layer Polyethylene insulation sheath material 4.0

[0059] Table 1

[0060] S2. Construct an adaptive surface response model based on compactly supported radial basis functions and electromagnetic-thermal-fluid coupling; the construction of the adaptive surface response model is to first establish a response model based on compactly supported radial basis functions, then couple the electromagnetic field, thermal field and fluid field to obtain a multi-physics field model, solve the cable current carrying capacity according to the multi-physics field model, and finally combine the adaptive strategy to obtain an adaptive surface response model that meets the error control requirements.

[0061] The establishment of the response model based on compactly supported radial basis function is:

[0062] Construct compactly supported radial basis functions (compactly supported radial basis functions are positive definite radial basis functions with compact support proposed by Wu and Wendland in the mid-1990s. For R n (1≤n≤d), any C can be constructed 2k Continuous, strictly positive definite compactly supported radial function φ d,k (r). This embodiment uses the compactly supported radial basis function constructed by Wendland), whose general expression is:

[0063]

[0064] In the formula, p(r) is a given polynomial, The specific meaning is:

[0065]

[0066] For k = 0, 1, 2, 3, φ with 2k-order continuous derivatives l,k The analytical expression of (r)) is as follows:

[0067]

[0068]

[0069]

[0070]

[0071] Where: l = [d / 2+k+1], d is the dimension of the function space;

[0072] For any f(X):R n →R, if it is known that at a series of sampling points x i ∈R D The function value on (i=1,2,…,N) is f i , then the surface response model is:

[0073]

[0074] When the above formula is used for interpolation, although the interpolation accuracy is very high within the interval, there is a large error in the derivative of the reconstructed function on the boundary. For this reason, the derivative function interpolation term is added to the interpolation formula of the above formula, and the response model based on the compact support radial basis function is obtained:

[0075]

[0076] Where N B is the number of sampling points on the boundary, c j and d k are coefficients respectively, where:

[0077]

[0078] f k ′ is the function f at the boundary sampling point X k The first derivative value of the radial variable r;

[0079] (φ 11 ) ij =φ(||X i -X j ||)(i,j=1,2,…,N)

[0080] (φ 12 ) ij =φ′(||X i -X j ||)(i=1,2,…,N; j=1,2,…,N B )

[0081] (φ 21 ) ij =φ′(||X i -X j ||)(j=1,2,…,N; i=1,2,…,N B )

[0082] (φ 22 ) ij =φ″(||X i -X j ||)(i,j=1,2,…,N B ).

[0083] As described in the background technology, the submarine cable needs to couple the electromagnetic field, thermal field, and fluid field to complete the calculation of the current carrying capacity of the submarine cable. In the multi-physics field model of this embodiment, the process of loading current in the conductor, water flow, heat transfer in the fluid, heat transfer in the solid, and electrothermal coupling is described by the following control equation:

[0084] The governing equation of the eddy current field is:

[0085]

[0086] In the eddy current zone:

[0087] In the non-eddy zone

[0088] Where: A is the vector magnetic potential, V is the scalar potential, ν is the magnetic resistivity, σ is the conductivity, J s is the source current density; is the vector differential operator, that is, the gradient operator;

[0089] The temperature field control equation is:

[0090]

[0091] Where: ρ is density, C p is the heat capacity at normal pressure, u is the velocity vector, k is the thermal conductivity, Q e is the heat source's heating power per unit volume, q is the heat flux density; is the temperature gradient, J is the current density vector, and E is the electric field intensity vector;

[0092] The fluid field satisfies the laws of conservation of mass, momentum, and energy:

[0093]

[0094] Where: I is the unit matrix, μ is the dynamic viscosity, T is the temperature of the fluid material, and F is the volume force (the default is 0).

[0095] Based on the above multi-physics field model, the chord intercept method is used to solve the current carrying capacity (the calculation of the current carrying capacity of the submarine cable is based on the calculation of the temperature field, which is the inverse process of the calculation of the electromagnetic field and the temperature field), such as Figure 2 As shown in the figure, when the maximum temperature of the cable conductor reaches 90 degrees Celsius, the current at this moment is defined as the current carrying capacity of the cable; the initial value of the current can be calculated according to the IEC60287 standard. The corresponding conductor temperature is calculated by solving the temperature field, and the chord intercept method is used to calculate the cable current carrying capacity. In the iterative calculation, when |T k When the value of -90| is less than 0.01℃, the cable conductor temperature is considered to be stable at the maximum allowable temperature. At this time, the current flowing through the cable is the cable current carrying capacity.

[0096] S3. Use the constructed adaptive surface response model to quickly calculate the cable current carrying capacity under any submarine cable parameters. As mentioned above, the input-output relationship between the submarine cable parameters and the current carrying capacity based on the sampling points within the submarine cable parameter interval can be constructed through the compact support radial basis function and the multi-physics field model. It is worth noting that the more sampling points are selected, the higher the accuracy of the reconstruction function, but the calculation burden also increases accordingly. Therefore, the construction of the surface response model requires a balance between accuracy and simplicity. To this end, the present invention adopts an adaptive strategy to adaptively select sampling points and adaptively determine the number of sampling points finally adopted.

[0097] First, determine the parameter range of the submarine cable core conductor as x∈[x min ,xmax ], calculate the sampling point x min and x max The current carrying capacity of the submarine cable at the position is then constructed based on the surface response model of the compactly supported radial basis function, denoted as M 1 , then in x min ~x max Take a certain number of parameters (t 1 ,t 2 ,…t n ) are test points, and the constructed surface response model M is applied respectively. 1 And the multi-physics field model calculates the current carrying capacity of the submarine cable at the test point; if the relative error ε i <tol,i=1,2,···,n, then output the surface response model, otherwise min ~x max Take new sampling points s 1 =0.5×(x min +x max ), and use the electromagnetic field, thermal field and fluid field coupling model to calculate the new sampling point s 1 The current carrying capacity of the submarine cable is then calculated, and a new surface response model based on compactly supported radial basis functions is constructed, denoted as M 2 , respectively applying the newly constructed surface response model M 2 The multi-physics model is used to calculate the current carrying capacity of the submarine cable at the test point; if the relative error ε i <tol,i=1,2,···,n, then output the surface response model, otherwise min ~s 1 、s 1 ~x max Take sampling points s 21 ,s 22 As the new sampling point, s 21 For x min and 1 The arithmetic midpoint, s 22 For 1 and x max The arithmetic midpoint of the new sampling point s is then calculated using the multiphysics model. 21、 s 22 The current carrying capacity of the submarine cable is then calculated, and a new surface response model based on compactly supported radial basis functions is constructed, denoted as M 3 , respectively applying the constructed surface response model M 3 The multi-physics model is used to calculate the current carrying capacity of the submarine cable at the test point; if the relative error ε i <tol,i=1,2,···,n, then output the surface response model, otherwise start a new round at x min ~s 21 、s 21 ~s1 、s 1 ~s 22 、s 22 ~x max Sampling is performed within the range and the above operation is repeated until an adaptive surface response model that meets the error control requirements is obtained.

[0098] Therefore, the present invention adopts the above-mentioned adaptive surface response model to obtain a reconstruction function that meets the error control requirements at the lowest possible computational cost, effectively balances the computational accuracy and computational simplicity, and utilizes the surface response model constructed by the present invention to input any submarine cable parameters within the feasible interval, and calculates and outputs the cable current carrying capacity. In summary, the present invention is based on the calculation data (current carrying capacity) of the known submarine cable magnetic-fluid-thermal coupling model, and by constructing an adaptive surface response model based on compactly supported radial basis functions and magnetic-thermal-fluid coupling, the input-output relationship between the submarine cable parameters and the current carrying capacity is reconstructed, and the submarine cable current carrying capacity under any submarine cable parameters is obtained. Compared with the existing cable current carrying capacity calculation method, the present invention can quickly calculate the current carrying capacity under any cable parameters, while ensuring the accuracy of the calculation results, it can also greatly reduce the calculation time and reduce the calculation cost.

Claims

1. A fast calculation method for the current carrying capacity of submarine cables based on compactly supported radial basis functions, characterized in that: The steps include: S1. Obtaining submarine cable parameters and their value ranges; S2. Construct an adaptive surface response model based on compactly supported radial basis functions and electromagnetic-thermal-fluid coupling; S3, using the constructed adaptive surface response model to quickly calculate the cable current carrying capacity under any submarine cable parameters; The construction of the adaptive surface response model is to first establish a response model based on a compactly supported radial basis function, then couple the electromagnetic field, thermal field and fluid field to obtain a multi-physics field model, solve the cable current carrying capacity according to the multi-physics field model, and finally combine the adaptive strategy to obtain an adaptive surface response model that meets the error control requirements; Combined with the adaptive strategy, an adaptive surface response model that meets the error control requirements is obtained. The specific process is: First, determine the parameter range of the submarine cable core conductor as x∈[x min ,x max ], calculate the sampling point x min and x max The current carrying capacity of the submarine cable at the location; Then, a surface response model based on compactly supported radial basis functions is constructed, denoted as M1, and then min ~x max Take a certain number of parameters t1, t2, ···t n The constructed surface response model M1 and multi-physics field model are used to calculate the current carrying capacity of the submarine cable at the test point. If the relative error ε i <tol,i=1,2,···,n, then output the surface response model, otherwise min ~x max Take a new sampling point s1=0.5×(x min +x max ), and use the electromagnetic field, thermal field and fluid field coupling model to calculate the current carrying capacity of the submarine cable at the new sampling point s1, and then construct a new surface response model based on the compact support radial basis function, denoted as M2, and use the newly constructed surface response model M2 and the multi-physics field model to calculate the current carrying capacity of the submarine cable at the test point; if the relative error ε i <tol,i=1,2,···,n, then output the surface response model, otherwise min ~s1、s1~x max Take sampling points s 21 ,s 22 As the new sampling point, s 21 For x min and s1, s 22 For s1 and x max The arithmetic midpoint of the new sampling point s is then calculated using the multiphysics model. 21 、s 22 The current carrying capacity of the submarine cable is then calculated by constructing a new surface response model based on compactly supported radial basis functions, denoted as M3. The constructed surface response model M3 and the multi-physics field model are used to calculate the current carrying capacity of the submarine cable at the test point. If the relative error ε i <tol,i=1,2,···,n, then output the surface response model, otherwise start a new round at x min ~s 21 、s 21 ~s1、s1~s 22 、s 22 ~x max Sampling is performed within the range and the above operation is repeated until an adaptive surface response model that meets the error control requirements is obtained.

2. The method for rapidly calculating the current carrying capacity of submarine cables based on compactly supported radial basis functions according to claim 1 is characterized in that: The establishment of the response model based on compactly supported radial basis function is: Construct a compactly supported radial basis function, whose general expression is: In the formula, p(r) is a given polynomial, The specific meaning is: For k = 0, 1, 2, 3, φ with 2k-order continuous derivatives l,k The analytical expression of (r) is as follows: C 0 ∩PD d ; C 2 ∩PD d ; C 4 ∩PD d ; C 6 ∩PD d ; Where: l = [d / 2+k+1], d is the dimension of the function space; For any f(X):R n →R, if it is known that at a series of sampling points x i ∈R D , the function value on i=1,2,···N is f i , then the surface response model is: By adding the derivative function interpolation term to the interpolation formula of the above equation, we can obtain the response model based on the compactly supported radial basis function: Where N B is the number of sampling points on the boundary, c j and d k are coefficients respectively, where: f k ′ is the function f at the boundary sampling point X k The first derivative value of the radial variable r; 3. The method for rapidly calculating the current carrying capacity of submarine cables based on compactly supported radial basis functions according to claim 1, characterized in that: In the multiphysics model, the processes of current loading in conductors, water flow, heat transfer in fluids, heat transfer in solids, and electrothermal coupling are described by the following governing equations: The governing equation of the eddy current field is: In the eddy current zone: In the non-eddy zone Where: A is the vector magnetic potential, V is the scalar potential, ν is the magnetic resistivity, σ is the conductivity, J s is the source current density; is the vector differential operator, i.e. the gradient operator; The temperature field control equation is: Where: ρ is density, C p is the heat capacity at normal pressure, u is the velocity vector, k is the thermal conductivity, Q e is the heat source's heating power per unit volume, q is the heat flux density; is the temperature gradient, J is the current density vector, and E is the electric field intensity vector; The fluid field satisfies the laws of conservation of mass, momentum, and energy: Where: I is the unit matrix, μ is the dynamic viscosity, T is the temperature of the fluid material, and F is the volume force.

4. The method for rapidly calculating the current carrying capacity of submarine cables based on compactly supported radial basis functions according to claim 3 is characterized in that: The chord intercept method is used to solve the current carrying capacity, that is, when the maximum temperature of the cable conductor reaches 90 degrees Celsius, the current at this moment is defined as the current carrying capacity of the cable; the corresponding conductor temperature is calculated by solving the temperature field, and the chord intercept method is used to calculate the cable current carrying capacity. In the iterative calculation, when |T k When the value of -90| is less than 0.01℃, the cable conductor temperature is considered to be stable at the maximum allowable temperature. At this time, the current flowing through the cable is the cable current carrying capacity.

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