Superconducting current limiter simulation modeling method based on PDE and circuit module

Abstract

The invention discloses a superconductive current limiter simulation modeling method based on PDE and a circuit module, and relates to the working principle and current limiting effect analysis of a resistance type superconductive fault current limiter. The method comprises the following steps: S1, selecting a two-dimensional axial symmetry space dimension, and designing a geometric model according to a solid structure of the pie-shaped superconducting fault current limiter; s2, establishing physical attribute parameters and variables of a plurality of physical fields, and adding materials and physical field boundary conditions; s3, realizing a general form partial differential equation (PDE), solid heat transfer and circuit physical field coupling, and performing mesh generation on the geometric model; s4, setting research steps, and modifying the configuration of the solver until convergence; and S5, post-processing a simulation result, generating one-dimensional diagrams of temperature, current and the like, and drawing data by utilizing Origin. According to the method, the magnetic field and temperature changes of the pie-shaped superconducting fault current limiter under the impact of the instantaneous short-circuit current are analyzed, the current limiting performance of the pie-shaped superconducting fault current limiter is analyzed, the voltage grade and the short-circuit current can be freely set, the operation is simple, and the calculation speed is high.

Description

Technical Field

[0001] The present invention relates to the technical field of superconducting fault current limiters, and in particular to a method for simulating and modeling the current limiting capability of a resistive superconducting fault current limiter based on a general form partial differential equation (PDE) module and a circuit module. Background Art

[0002] In recent years, superconducting materials technology has developed rapidly, and its application in power equipment has become increasingly widespread and mature. In particular, technological breakthroughs, particularly in high-temperature superconducting materials, have significantly advanced the practical application of superconducting power equipment. Currently, a variety of superconducting technology-based devices, such as superconducting fault current limiters (SFCLs), superconducting current transformers (SCTs), and superconducting cables, have been demonstrated or commercialized in power systems. These devices, with their superior power transmission efficiency, low loss, and high performance, provide new technological pathways for improving the economic efficiency, stability, and reliability of power systems.

[0003] In power grids, particularly high-voltage transmission and distribution systems, growing load demands and increased network interconnectivity have led to rising short-circuit current levels. When a short-circuit fault occurs, the enormous short-circuit current poses a severe challenge to power equipment, especially high-voltage circuit breakers, testing their interrupting capacity and safety margins. Fault current limiting technology is considered an effective way to alleviate this pressure. Among existing solutions, the resistive superconducting fault current limiter (SFCL), developed based on superconducting technology, offers significant advantages due to its unique operating principle. During normal grid operation, this device maintains a superconducting state, exhibiting near-zero resistance and generating extremely low steady-state losses. Upon detecting a high short-circuit fault current, its superconducting material rapidly quenches and transforms into a high-resistance state, limiting the fault current to below a set level and significantly reducing the current amplitude required to be interrupted by the circuit breaker. Furthermore, the SFCL does not generate harmful gases during the current limiting process, operates with extremely low noise, and offers excellent environmental performance.

[0004] Previous studies have shown that superconducting fault current limiters have excellent current limiting performance and have conducted experiments on limiting a 15.7kA short-circuit current. However, so far no one has simulated the current limiting effect of R-SFCL by coupling a general form partial differential equation (PDE) module with a circuit module. Simulating its temperature rise is also necessary. Summary of the Invention

[0005] The present invention provides a simulation modeling method for the current limiting capability of a resistive superconducting fault current limiter based on PDE and circuit modules. When DC power is applied, the method can conveniently and simply simulate the fault current limiting capability of a pancake-shaped resistive superconducting fault current limiter and customize the short-circuit current size.

[0006] The present invention can be achieved through the following technical solutions:

[0007] S1: Select the two-dimensional axisymmetric space dimension and design the geometric model based on the physical structure of the pancake-shaped superconducting fault current limiter;

[0008] S2: Establish physical property parameters and variables of several physical fields, add materials and add physical field boundary conditions;

[0009] S3: Implement general form partial differential equations (PDEs), solid heat transfer, circuit physics coupling, and mesh the geometric model;

[0010] S4: Set up the study steps and modify the solver configuration until convergence;

[0011] S5: Post-process the simulation results to generate two-dimensional or one-dimensional graphs of temperature, current, etc. and plot the data using Origin.

[0012] The S1 pancake-shaped superconducting fault current limiter is a simplified model. The simulation purpose is only to observe the electrothermal conditions of the internal superconducting tape, omitting the pure nylon structure in the middle of the current limiter. The model includes the following components: 10 turns of superconducting tape (each turn is divided into 6 layers, namely a YBCO layer, two silver diversion layers, a nickel-based alloy base layer, and two stainless steel stabilization layers, omitting the buffer layer less than 1 micron thick), a nylon shell, and a liquid nitrogen domain.

[0013] The material of S2 is as described in

[0012] . The material properties of each layer are defined according to the data obtained from relevant research. The resistivity of the insulating region differs from that of the conductive region by several orders of magnitude. Therefore, for the convenience of calculation, the resistivity of the insulating liquid nitrogen domain and the nylon shell is set to 1 (Ω·m). The solid heat transfer physics field is further added.

[0014] The circuit module is independent of the actual model. By inputting the parameters calculated by the electrothermal module, the real-time current is fed back to the electrothermal module, forming a coupling between the electrothermal module and the circuit module.

[0015] Furthermore, the boundary condition settings in each physical field specifically include:

[0016] The PDE field encompasses the entire model, using point-by-point constraints to set the same current for each turn of the strip via Ampere's circuit law.

[0017] The solid heat transfer field only includes the superconducting current limiter model domain and does not include the liquid nitrogen domain. The initial temperature is set to 77K. The action time of the superconducting fault current limiter is within 10ms, so the influence of liquid nitrogen heat exchange is not considered. Therefore, the nylon shell boundary is set as thermal insulation, and the superconducting tape area is set as a heat source, which is defined as a generalized source. The power is defined by Joule's law Q = J·E in microscopic form.

[0018] Furthermore, the properties in the physics field expressions all come from the material and are not set separately.

[0019] The grid in S3 needs to be divided into regions according to the electrode shape, the sequence type is selected as user-controlled grid, the grid types include mapping and free triangle grid, and the grid size is normal.

[0020] The study step in S4 is transient, the time unit is set to ms, the output time is 0-30ms, the step size is 0.05ms, and the tolerance is set to physical field control.

[0021] Furthermore, the configuration in the transient solver 1 is selected as Fully Coupled 1, the nonlinear method is set to Automatic (Newton), the maximum number of iterations is set to 25, and the tolerance factor is set to 0.1.

[0022] In S5, select the 2D plot group, use the surface method, select Study 1 / Solution 1 as the data set, select sqrt(Hr^2+Hz^2) as the expression to analyze the magnetic field distribution, and select T as the expression to analyze the temperature distribution;

[0023] In the Derived Values ​​tree, select Maximum, then Surface Maximum. Select T in the Expression to analyze the maximum temperature and generate a table plot in the 1D Plot Group. Select Global in the 1D Plot Group tree and select cir.R1_i from the Expression to analyze the current limiting effect. Finally, import the result into Origin to generate a comparison plot.

[0024] Compared to existing technologies, the technical solution of the present invention has the following beneficial effects: It eliminates the complex three-dimensional structure of a pancake-shaped superconducting fault current limiter (SFCL). Instead, it uses the simplest two-dimensional axisymmetric superconducting fault current limiter core component—a pancake-shaped superconducting tape model—to simulate the electrothermal conditions and current-limiting capability of the SFCL during a fault. Compared to a complete model, this model offers faster calculation speed and easier data adjustment. The coupling circuit module allows for flexible adjustment of the terminal voltage level and fault current magnitude during a short circuit, effectively simulating the SFCL's fault current-limiting capability under different conditions. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 This is a flowchart of the simulation modeling method of a superconducting current limiter based on PDE and circuit modules of the present invention;

[0026] Figure 2 It is a two-dimensional axisymmetric geometric model diagram of the present invention;

[0027] Figure 3 It is a simulation circuit diagram of the circuit module;

[0028] Figure 4 A grid diagram of a two-dimensional axisymmetric geometric model of the present invention;

[0029] Figure 5 is the magnetic field distribution diagram of the superconducting fault current limiter;

[0030] Figure 6 is the temperature distribution diagram of the superconducting fault current limiter;

[0031] Figure 7 The maximum temperature trend diagram of the superconducting fault current limiter affected by the short-circuit impulse current;

[0032] Figure 8 The figure shows the comparison of short-circuit current with and without superconducting fault current limiter. DETAILED DESCRIPTION

[0033] The present invention will be described in detail below with reference to the accompanying drawings. This embodiment can be used as a basis to improve the research method and geometric model. Obviously, the described embodiment is only used to explain the present invention, and the accompanying drawings only show part of the content related to the present invention, not all of it.

[0034] A simulation modeling method for superconducting current limiter based on PDE and circuit module, such as Figure 1 As shown, the following steps are included:

[0035] S1: Select the two-dimensional axisymmetric space dimension and design the geometric model according to the physical structure of the pancake-shaped superconducting fault current limiter, such as Figure 2 As shown, the geometric parameters and physical parameters are established.

[0036] In S1, it is assumed that geometric entities are not affected by environmental factors, and the results of geometric structures and physical effects are symmetrical.

[0037] S2: Establish physical property parameters and variables of several physical fields, add materials and add physical field boundary conditions;

[0038] The electromagnetic simulation of the superconducting tape in this invention adopts the H method, in which the current flows only in the θ direction and the magnetic field has only r and z components, which is defined as H = [H r ,H z ], based on Ampere's law (1), Ohm's law (2) and Faraday's law of electromagnetic induction (3), the governing equations of the model are as follows:

[0039]

[0040] E=ρ×J (2)

[0041]

[0042] Where J is the current density, E is the electric field intensity, B is the magnetic field intensity, H is the magnetic induction intensity, μ is the magnetic permeability, ρ is the resistivity, is a vector differential operator.

[0043] Based on the above, set the global variables: J = d(Hr, z) - d(Hz, r), E = rho*J.

[0044] When the temperature of a superconducting material is lower than the critical temperature, it enters a superconducting state. At this time, the resistivity satisfies the power law formula (4):

[0045]

[0046] Where, E c is the quench judgment parameter, take 1E-4 (V / m), J c is the critical current density at the critical temperature, and n is the superconducting characteristic parameter. In the present invention, the YBCO type S8602 superconducting tape of Superconducting Power Company is used, and the parameters are shown in Table 1:

[0047] Table 1 Parameters of superconducting tape

[0048] The simulation time does not exceed 30ms, so the influence of liquid nitrogen heat transfer is not considered. The solid heat transfer module is only applied to the superconducting tape domain and the nylon shell domain. The energy conservation equation in the heat transfer field is as follows:

[0049]

[0050]

[0051] Q=J×E (7)

[0052] Where ρ is the density in the ideal gas domain, C p is the constant-pressure heat capacity, T is the temperature, q is the conductive heat flux, Q is the heat source, q is the conductive heat flux, and k is the thermal conductivity of the material. In this model, the heat source is the heat generated by the superconducting tape. Therefore, in the Heat Source interface of the Solid Heat Transfer Module, select the Superconducting Tape domain, select the Generalized Source as the Heat Source, and set the value to J*E.

[0053] S3: Implement general form partial differential equations (PDEs), solid heat transfer, circuit physics coupling, and mesh the geometric model;

[0054] The critical current density of the superconducting tape is affected by temperature and satisfies formula (8)

[0055]

[0056] Where, J cT is the critical current density of the superconducting tape at different temperatures, T cis the critical temperature of the superconducting tape, 90 K, and T0 is the ambient temperature, here the liquid nitrogen temperature is 77 K. In S2, the heat source is defined as J*E. The PDE module calculates the current density J and electric field strength E of the superconducting tape. The temperature calculated by the solid heat transfer module is then fed back to the PDE module, completing the coupling between the PDE and solid heat transfer.

[0057] Furthermore, the circuit module is an independent system, and the simulation circuit is as follows Figure 3 As shown;

[0058] R1 simulates the line impedance, R2 simulates the load impedance, the closing of switch 2 simulates the occurrence of a short-circuit fault, and the superconducting fault current limiter (SFCL) uses four resistors in parallel to simulate the current parallel situation.

[0059] By modifying the power supply voltage parameters and the resistance value of R1, different short-circuit currents can be simulated.

[0060] In this simulation, a 9-meter-long superconducting tape was used to limit a 15.7 kA fault current. The resistance of all resistors except the YBCO layer was directly calculated using the resistance calculation formula and entered into the circuit module. For the YBCO resistor, based on the parallel connection of resistors, the resistance was calculated using the metal layer voltage / YBCO layer current and entered into the circuit module. Taking the silver layer as an example, the YBCO layer resistance can be expressed as:

[0061]

[0062] Wherein, the current of each layer is calculated by integrating the current density of the corresponding layer of the model.

[0063] In the PDE module, select point-by-point constraint, set integral constraint on the strip surface, input current direction as θ, and the constraint equation is:

[0064] ∮ S J·dS=cir.R1_i (10)

[0065] Where cir.R1_i is the current flowing through R1 in the circuit module, that is, the total current in the circuit. This setting feeds the current value calculated by the circuit module back to the PDE and solid heat transfer modules, which then calculate the electromagnetic heating of the strip, thus forming a coupling between the PDE module, solid heat transfer module, and circuit module.

[0066] Further, draw Figure 4 The mesh shown uses a mapped mesh for the superconducting tape, with an average of 75 elements across the tape width. Across the tape thickness, the YBCO layer, silver layer, nickel-based alloy layer, and stainless steel layer are meshed with 1, 1, 2, and 2 elements, respectively. A free triangular mesh is used for the rest of the tape, with a normal element size.

[0067] S4: Set up the study steps and modify the solver configuration until convergence.

[0068] Add a transient step to Study 1, set the time unit to ms, set the output time step to range(0,0.05,30), and select Physics Controlled for the tolerance.

[0069] Furthermore, modify the configuration of transient solver 1, select full coupling, select automatic (Newton) for the nonlinear method, change the maximum number of iterations to 25, and change the tolerance factor to 0.1.

[0070] Next, start calculating.

[0071] S5: Post-process the simulation results to generate two-dimensional or one-dimensional graphs of magnetic field, temperature, current, etc. and plot the data using Origin;

[0072] In S5, select the 2D plot group, use the surface method, select Study 1 / Solution 1 as the data set, and use the magnetic field expression as:

[0073] H=sqrt(Hr^2+Hz^2)

[0074] like Figure 5 As shown in the figure, the magnetic field at both ends of the superconducting tape is significantly greater than that inside, indicating that the superconducting tape loses its superconductivity from both ends to the middle.

[0075] Continue to select the 2D plot group, use the surface method, select Study 1 / Solution 1 as the data set, and select T as the expression to analyze the temperature situation, such as Figure 6 As shown in Figure 3, the temperature at both ends of the superconducting tape is higher, which further indicates that the two ends of the superconducting tape are more likely to quench.

[0076] In the Derived Values ​​tree, select Maximum, then Surface Maximum. In Expression, select T to analyze the maximum temperature. Generate a table plot in the 1D Plot Group with time (ms) on the horizontal axis and maximum temperature (K) on the vertical axis. The temperature reaches a maximum of 88.55K at 21.3ms. Although the temperature has not yet reached the critical temperature of 90K, the current density has far exceeded it, indicating that the superconducting tape has actually quenched.

[0077] Select Global in the 1D Plot Group tree and select cir.R1_i from the Expressions section to analyze the current limiting effect. The horizontal axis is time (ms) and the vertical axis is the current flowing through R1 (A).

[0078] Furthermore, all data can be exported and plotted in Origin as follows Figure 7 As shown in the comparison graph, it can be seen that the superconducting fault current limiter successfully limits the 15.7kA short-circuit current to 800-1000A.

[0079] The above is a demonstration method of an embodiment of the present invention. Any calculation results obtained by simulation improvements and idea improvements based on this technical process and purpose should be included in the protection scope of the present invention.

Claims

1. A simulation modeling method for superconducting current limiters based on PDE and circuit modules S1: Select the two-dimensional axisymmetric space dimension and design the geometric model based on the physical structure of the pancake-shaped superconducting fault current limiter; S2: Establish physical property parameters and variables of several physical fields, add materials and add physical field boundary conditions; S3: Implement general form partial differential equations (PDEs), solid heat transfer, circuit physics coupling, and mesh the geometric model; S4: Set up the study steps and modify the solver configuration until convergence; S5: Post-process the simulation results to generate two-dimensional or one-dimensional graphs of magnetic field, temperature, current, etc. and plot the data using Origin.

2. The superconducting current limiter simulation modeling method based on PDE and circuit module according to claim 1, characterized in that: In S1, it is assumed that geometric entities are not affected by environmental factors, and the results of geometric structures and physical effects are symmetrical.

3. The superconducting current limiter simulation modeling method based on PDE and circuit module according to claim 1, characterized in that: The physical property parameters added in S2 include superconducting tape critical current density, critical temperature, characteristic parameters, structural dimensions of each layer, constant pressure heat capacity, thermal conductivity and electrical conductivity; All materials are custom materials with parameters set by referring to relevant literature; Each material corresponds to a different part of the superconducting fault current limiter model, and the material properties required in the calculation are related to the physical fields, including temperature and current density.

4. The superconducting current limiter simulation modeling method based on PDE and circuit module according to claim 1, characterized in that: S2 involves general form partial differential equations (PDEs), solid heat transfer (ht) and circuits (cir). The general form partial differential equations require the use of H equations to set variables and current constraints. The selected domain is the entire model. The solid heat transfer calculation domain is the superconducting fault current limiter body, that is, the superconducting tape group and nylon shell. The initial value is 77K. The circuit module is an independent system with six resistors and two switches. R1 simulates line impedance, R2 simulates load impedance, and the closure of switch 2 simulates a short-circuit fault. The superconducting fault current limiter (SFCL) uses four resistors in parallel to simulate current parallelism.

5. The superconducting current limiter simulation modeling method based on PDE and circuit module according to claim 1, characterized in that: In S3, the heat source is defined as J*E. The PDE module calculates the current density J and electric field strength E of the superconducting tape. The temperature calculated by the solid heat transfer module is then fed back to the PDE module to complete the coupling of PDE and solid heat transfer. In the PDE module, an integral constraint is set for the strip surface. The integral value of the current density is constrained to the current flowing through R1, that is, the total current in the circuit. This setting feeds the current value calculated by the circuit module back to the PDE and solid heat transfer modules. The latter then calculates the electromagnetic heating of the strip, forming a coupling between the PDE module, the solid heat transfer module, and the circuit module.

6. The superconducting current limiter simulation modeling method based on PDE and circuit module according to claim 1, characterized in that: In S3, the mesh type consists of mapped and free triangular meshes, and the element size is set to normal. The average element quality of the simulation model is 0.

85.

7. The superconducting current limiter simulation modeling method based on PDE and circuit module according to claim 1, characterized in that: In S4, a transient step is added under the study type, the time unit is set to ms, the output time step is set to range (0, 0.05, 30), and the tolerance is selected as physics field controlled.

8. The superconducting current limiter simulation modeling method based on PDE and circuit module according to claim 1, characterized in that: Modify the configuration of transient solver 1, select full coupling, select automatic (Newton) for the nonlinear method, change the maximum number of iterations to 25, and change the tolerance factor to 0.

1.

9. The superconducting current limiter simulation modeling method based on PDE and circuit module according to claim 1, characterized in that: In S5, select Global in the 1D Plot Group tree and select cir.R1_i from the Expressions section. The horizontal axis represents time (ms) and the vertical axis represents the current flowing through R1 (A). Plot a graph in Origin to analyze the current limiting effect.

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