A method for obtaining electrothermal parameters of a superconducting cable

Abstract

The present invention relates to a method for obtaining electrothermal parameters of a superconducting cable, comprising: S1: obtaining structural parameters, material properties and laying conditions of a superconducting cable; S2: obtaining boundary conditions according to the laying conditions, and obtaining constitutive equations according to structural parameters and material properties; S3: establishing a two-dimensional finite element model according to the constitutive equation, boundary conditions and equivalent resistivity of a partial differential equation; S4: performing transient solution of the two-dimensional finite element model according to the current size of the superconducting cable to obtain an AC loss characteristic curve of the superconducting cable; S5: performing steady-state solution of the two-dimensional finite element model according to the AC loss characteristics of the superconducting cable to obtain the temperature field distribution during the steady-state operation of the superconducting cable. Compared with the prior art, the method reduces the complexity of calculation and improves the convergence of the model.

Description

Technical Field

[0001] The invention relates to the field of high-temperature superconducting cables, and in particular to a method for obtaining electrothermal parameters of superconducting cables. Background Art

[0002] In recent years, with the rapid development of urbanization and industrialization, high temperature superconducting (HTS) technology, as a strategically significant leading technology, has shown broad application prospects in the fields of urban power grid transformation, magnetic levitation transportation, and large scientific facilities. High temperature superconducting power transmission, known as a revolution in the power industry of this century, has the advantages of low loss, large capacity, small size, and no pollution. At present, there are many superconducting cables in operation around the world, such as the Albany superconducting cable project in the United States, the Yokohama superconducting cable project in Japan, and the AmpaCity superconducting cable project in Germany. However, according to their cable structure and operating environment, the specific parameter analysis and test methods are different, and no unified standards or guidelines have been formed.

[0003] The three-phase cold-insulated high-temperature superconducting cable adopts a turnkey layer structure, in which the conductor layer and the shielding layer are both wound at a certain angle by the second-generation high-temperature superconducting tape YBCO. In the actual operation process, the current through the conductor layer and the shielding layer is equal in magnitude and opposite in direction. The electromagnetic heat accumulation generated causes the temperature inside the cable to rise. Therefore, in order to prevent the cable from quenching due to excessive temperature and ensure the safety margin of the superconducting cable line, it is necessary to combine the thermal conductivity of the cooling medium liquid nitrogen and the current characteristics of the superconducting cable layer structure, and perform multi-field coupled simulation analysis on the electromagnetic characteristics, AC loss, temperature field distribution, maximum current flow and other electrothermal parameters of the superconducting cable.

[0004] Due to the zero resistance characteristic of superconducting materials within a certain range, traditional analysis methods often treat the circuit structure of superconducting cables as equivalent to pure inductance elements in parallel without considering their dynamic change characteristics. However, due to the highly nonlinear resistivity of superconducting materials, the fluid characteristics of the cooling medium liquid nitrogen, and the relatively complex geometric structure, the solution requires a lot of calculations.

[0005] At present, how to reduce the amount of calculation for obtaining electrothermal parameters is an urgent problem to be solved. Summary of the invention

[0006] The purpose of the present invention is to provide a method for obtaining the electrothermal parameters of a superconducting cable in order to overcome the defects of the prior art.

[0007] The purpose of the present invention can be achieved by the following technical solutions:

[0008] A method for obtaining electrothermal parameters of a superconducting cable, the method comprising:

[0009] S1: Obtain the structural parameters, material properties and line laying conditions of the superconducting cable;

[0010] S2: Obtain boundary conditions based on laying conditions, and obtain constitutive equations based on structural parameters and material properties;

[0011] S3: Establish a two-dimensional finite element model based on the constitutive equation, boundary conditions and equivalent resistivity of the partial differential equation;

[0012] S4: Perform transient solution of the two-dimensional finite element model according to the current size of the superconducting cable to obtain the AC loss characteristic curve of the superconducting cable;

[0013] S5: A steady-state solution of a two-dimensional finite element model is performed according to the AC loss characteristics of the superconducting cable to obtain the temperature field distribution during the steady-state operation of the superconducting cable.

[0014] The structural parameters of the superconducting cable include the relative positions of the three-phase cable cores of the superconducting cable, the thickness and outer diameter of the copper core, conductor layer, insulation layer, shielding layer and outer stabilizing layer of each phase of the superconducting cable, and the thickness and outer diameter of the liquid nitrogen channel and constant temperature insulation layer of the superconducting cable.

[0015] The material properties include density, resistivity, magnetic permeability, thermal conductivity and constant-pressure heat capacity of the copper core, conductor layer, insulation layer, shielding layer, outer stabilization layer, liquid nitrogen and constant-temperature insulation layer of the superconducting cable.

[0016] The constitutive equation includes an electromagnetic module and a heat conduction module. The expression of the electromagnetic module is:

[0017] E=ρJ,B=μH

[0018] Wherein, μ0 is the vacuum magnetic permeability, E is the electric field intensity, B is the magnetic induction intensity, J is the current density, H is the magnetic field intensity, ρ is the equivalent resistivity of the layer containing the superconducting material, and μ is the magnetic permeability of the material;

[0019] The expression of the heat conduction module is:

[0020]

[0021] Where λ is the thermal conductivity of liquid nitrogen, C th is the constant pressure specific heat capacity of each layer inside the superconducting cable, T is the internal temperature of the superconducting cable, q is the local heat flux density, h is the average convection heat transfer coefficient, T LN2 is the temperature of the cooling medium liquid nitrogen.

[0022] The calculation formula of the equivalent resistivity ρ is:

[0023]

[0024] Among them, |J| is the actual current passing through the layer, norm(J) is the corrected current passing through the layer, and J c is the critical current density of the layer, E0 and n are constants reflecting the nonlinear characteristics of the superconducting material of the layer transforming to a conventional conductor, E0 = 0.1 V / cm, n = 21.

[0025] The actual current magnitude norm(J) passing through the layer after correction is expressed as:

[0026] norm(J)=|J|+eps

[0027] Among them, eps is an infinitesimal quantity.

[0028] The transient solution process in S4 includes: setting the excitation of the electromagnetic module by the AC electric field of the superconducting cable, obtaining the equivalent resistivity of each layer of material according to the calculation formula of the equivalent resistivity ρ, and then obtaining the current density J and electric field intensity E based on the expression of the electromagnetic module, and then using the area integral The AC loss time-varying curve of the superconducting cable is obtained.

[0029] The process of steady-state solution in S5 includes: setting the excitation of the heat conduction module according to the periodic mean of the AC loss of the superconducting cable, and obtaining the temperature field distribution of steady-state operation according to the expression of the heat conduction module.

[0030] Compared with the prior art, the present invention has the following advantages:

[0031] (1) The nonlinear EJ characteristics of superconducting materials are defined in the form of partial differential equations, and a two-dimensional electromagnetic-thermal multi-field coupling model of superconducting cables is established, which reduces the complexity of the calculation and improves the convergence of the model.

[0032] (2) By combining transient solution with steady-state solution, the interaction between the electromagnetic module and the heat conduction module of the superconducting cable is reflected. The model has strong adaptability and can obtain richer information than existing calculation methods, which is helpful for evaluating the operation of superconducting cable lines. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 is a flow chart of the present invention;

[0034] Figure 2 It is a two-dimensional structural schematic diagram of a 35kV three-phase turnkey cold-insulated high-temperature superconducting cable according to an embodiment of the present invention;

[0035] Figure 3 The electric field distribution of the superconducting cable according to the embodiment of the present invention;

[0036] Figure 4The magnetic field distribution of the superconducting cable according to the embodiment of the present invention;

[0037] Figure 5 is a periodically changing AC loss characteristic curve of a superconducting cable according to an embodiment of the present invention;

[0038] Figure 6 The temperature field distribution of a two-dimensional cross section of a superconducting cable according to an embodiment of the present invention under steady-state operation conditions;

[0039] Figure 7 The temperature distribution curve along the radial direction of the cross section of the superconducting cable in the steady-state operation condition according to the embodiment of the present invention is shown. DETAILED DESCRIPTION

[0040] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0041] Example

[0042] This embodiment provides a method for obtaining electrothermal parameters of a superconducting cable. Figure 1 As shown, including:

[0043] S1: Obtain the structural parameters, material properties and line laying conditions of the superconducting cable;

[0044] S2: Obtain boundary conditions based on laying conditions, and obtain constitutive equations based on structural parameters and material properties;

[0045] S3: Establish a two-dimensional finite element model based on the constitutive equation, boundary conditions and equivalent resistivity of the partial differential equation;

[0046] S4: Perform transient solution of the two-dimensional finite element model according to the current size of the superconducting cable to obtain the AC loss characteristic curve of the superconducting cable;

[0047] S5: A steady-state solution of a two-dimensional finite element model is performed according to the AC loss characteristics of the superconducting cable to obtain the temperature field distribution during the steady-state operation of the superconducting cable.

[0048] like Figure 2 As shown, this embodiment takes the operating characteristics of a 35kV cold-insulated three-phase turnkey superconducting cable line under alternating current excitation as an example:

[0049] 1. Determine the structural parameters of the superconducting cable, the material properties of each layer and the laying conditions of the line.

[0050] The structural parameters of superconducting cables include: the relative position of the three-phase cable cores of the superconducting cable, the thickness and outer diameter of the copper core, conductor layer, insulation layer, shielding layer and outer stabilizing layer of each phase of the superconducting cable, and the thickness and outer diameter of the liquid nitrogen channel and constant temperature insulation layer of the superconducting cable.

[0051] The material properties of superconducting cables include: density, resistivity, magnetic permeability, thermal conductivity and constant-pressure heat capacity of the copper core, conductor layer, insulation layer, shielding layer, outer stabilization layer, liquid nitrogen and constant-temperature insulation layer of the superconducting cable.

[0052] Since the equivalent resistivity ρ of high-temperature superconducting materials has obvious anisotropy, it is defined as follows:

[0053]

[0054] Among them, J c is the critical current density of the superconducting material, E0 and n are constants, reflecting the nonlinear characteristics of the superconductor transition to a conventional conductor, E0 = 0.1 V / cm, n = 21. In addition, to avoid zero division, an infinitesimal parameter eps is introduced to define the parameter norm(J), ensuring the correctness of the equation without introducing errors:

[0055] norm(J)=|J|+eps

[0056] Among them, |J| is the actual current passing through the superconducting material.

[0057] The line laying conditions adopt the method of direct burial in the soil.

[0058] Based on the above conditions, a two-dimensional finite element model of the superconducting cable cross section is established, and the grid is divided from the inside to the outside and from the regular to the irregular. Starting from the superconducting layer, the grid is refined layer by layer to the outer layer to ensure that the number of division units of the boundary circle exceeds 50. The internal area of ​​the superconducting cable is divided into triangular grids to ensure the solution accuracy of the model. This embodiment is implemented by COMSOL Multiphysics simulation software, and the complete grid of the model contains 6832 domain units and 1108 boundary elements.

[0059] 2. Rewrite the control equation of the model's physical field according to the partial differential equation form of the finite element simulation software, and determine the boundary conditions of the model according to the line operation environment. The constitutive equation mainly includes two physical field modules: electromagnetic module and heat conduction module.

[0060] The physical field control equations of the electromagnetic module include Maxwell's equations and Faraday's law, as well as the inherent relationship between the physical parameters of the electromagnetic field. Based on the two-dimensional model plane of this method, they are organized in three-dimensional form:

[0061]

[0062]

[0063] E=ρJ,B=μH (3)

[0064] Among them, E is the electric field intensity (V / m), B is the magnetic induction intensity (T), and J is the current density (A / m 2 ), H is the magnetic field intensity (A / m), ρ is the equivalent resistivity of the layer containing the superconducting material (Ω·m), and μ is the magnetic permeability of the material (T·m / A).

[0065] This embodiment is implemented by COMSOL Multiphysics simulation software, in the form of a generalized partial differential equation:

[0066]

[0067] Among them, e a Denotes the quality coefficient, d a represents the damping coefficient, Γ is the conserved flux, f is the source term, and inΩ represents the interior of the boundary defined by the model. The Maxwell equations in equation (1) are rewritten as follows, where μ0 is the vacuum permeability:

[0068]

[0069] The physics equations governing the Heat Transfer Module include:

[0070]

[0071] h(TT LN2 )=q

[0072] Where, λ is the thermal conductivity of liquid nitrogen (W / (m·K)), C th is the constant pressure specific heat capacity of each layer of material inside the superconducting cable (J / (kg·K)), T is the internal temperature of the superconducting cable (K), q is the local heat flux density (W / m 2 ), h is the average convective heat transfer coefficient (W / (m 2 K)), T LN2 is the temperature of the cooling medium liquid nitrogen (K).

[0073] The average convective heat transfer coefficient h characterizes the cooling effect of liquid nitrogen on the phase conductor of the superconducting cable. It is related to the temperature field, thermal conductivity, and temperature difference between the liquid nitrogen and the wall. Existing studies have fitted and analyzed the measured results of the convective heat transfer coefficient of liquid nitrogen. When ΔT = 10K, the convective heat transfer coefficient h of liquid nitrogen is 1.5W / (cm 2 ·K).

[0074] 3. According to the current of the superconducting cable, set the excitation of the electromagnetic module of the superconducting cable model. In this embodiment, the power frequency current is 2.2kA and the voltage is 35kV to perform transient solution of the model. The calculation step size of the model is set to 10. -6 -10 -5 s, with a tolerance of 1×10 -5 s, and obtain the current density J and electric field strength E( Figure 3 ), magnetic field strength B( Figure 4 ).

[0075] According to the area integral, the periodic AC loss characteristic Q( Figure 5 ):

[0076]

[0077] 4. Based on the periodic mean Q of the AC loss characteristics of superconducting cables ave = 20.64W / m, set the excitation of the superconducting cable heat conduction module, perform steady-state solution of the model, and obtain the temperature field distribution of the superconducting cable during steady-state operation ( Figure 6 ), the copper core temperature of the single-phase cable core is T former =76.96K, the conductor layer temperature is T con =77.29K( Figure 7 ), according to the critical temperature of the superconducting material and the safety margin of the line operation, the maximum temperature rise ΔT in steady-state operation is obtained max =12K, repeat step 3 to obtain the maximum current I allowed to pass through the superconducting cable line max =2.76kA.

Claims

1. A method for obtaining electrothermal parameters of a superconducting cable, characterized in that: The method includes: S1: Obtain the structural parameters, material properties and line laying conditions of the superconducting cable; S2: Obtain boundary conditions based on laying conditions, and obtain constitutive equations based on structural parameters and material properties; S3: Establish a two-dimensional finite element model based on the constitutive equation, boundary conditions and equivalent resistivity of the partial differential equation; S4: Perform transient solution of the two-dimensional finite element model according to the current size of the superconducting cable to obtain the AC loss characteristic curve of the superconducting cable; S5: Perform steady-state solution of the two-dimensional finite element model according to the AC loss characteristics of the superconducting cable to obtain the temperature field distribution during the steady-state operation of the superconducting cable; The constitutive equation includes an electromagnetic module and a heat conduction module. The expression of the electromagnetic module is: Wherein, μ0 is the vacuum magnetic permeability, E is the electric field intensity, B is the magnetic induction intensity, J is the current density, H is the magnetic field intensity, ρ is the equivalent resistivity of the layer containing the superconducting material, and μ is the magnetic permeability of the material; The expression of the heat conduction module is: Where λ is the thermal conductivity of liquid nitrogen, C th is the constant pressure specific heat capacity of each layer inside the superconducting cable, T is the internal temperature of the superconducting cable, q is the local heat flux density, h is the average convection heat transfer coefficient, T LN2 is the temperature of the cooling medium liquid nitrogen.

2. The method for obtaining electrothermal parameters of a superconducting cable according to claim 1, characterized in that: The structural parameters of the superconducting cable include the relative positions of the three-phase cable cores of the superconducting cable, the thickness and outer diameter of the copper core, conductor layer, insulation layer, shielding layer and outer stabilizing layer of each phase of the superconducting cable, and the thickness and outer diameter of the liquid nitrogen channel and constant temperature insulation layer of the superconducting cable.

3. The method for obtaining electrothermal parameters of a superconducting cable according to claim 1, characterized in that: The material properties include density, resistivity, magnetic permeability, thermal conductivity and constant-pressure heat capacity of the copper core, conductor layer, insulation layer, shielding layer, outer stabilization layer, liquid nitrogen and constant-temperature insulation layer of the superconducting cable.

4. The method for obtaining electrothermal parameters of a superconducting cable according to claim 1, characterized in that: The calculation formula of the equivalent resistivity ρ is: Among them, |J| is the actual current passing through the layer, norm(J) is the corrected current passing through the layer, and J c is the critical current density of the layer, E0 and n are constants reflecting the nonlinear characteristics of the superconducting material of the layer transforming to a conventional conductor, E0 = 0.1 V / cm, n = 21.

5. The method for obtaining electrothermal parameters of a superconducting cable according to claim 4, characterized in that: The actual current magnitude norm(J) passing through the layer after correction is expressed as: norm(J)=|J|+eps Among them, eps is an infinitesimal quantity.

6. The method for obtaining electrothermal parameters of a superconducting cable according to claim 4, characterized in that: The transient solution process in S4 includes: setting the excitation of the electromagnetic module by the AC electric field of the superconducting cable, obtaining the equivalent resistivity of each layer of material according to the calculation formula of the equivalent resistivity ρ, and then obtaining the current density J and electric field intensity E based on the expression of the electromagnetic module, and then using the area integral The AC loss time-varying curve of the superconducting cable is obtained.

7. The method for obtaining electrothermal parameters of a superconducting cable according to claim 1, characterized in that: The process of steady-state solution in S5 includes: setting the excitation of the heat conduction module according to the periodic mean of the AC loss of the superconducting cable, and obtaining the temperature field distribution of steady-state operation according to the expression of the heat conduction module.

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