Resistance type superconducting current limiter field-circuit coupling joint simulation modeling method

Abstract

The invention discloses a field-circuit coupling joint simulation modeling method for a resistance-type superconducting current limiter, which belongs to the technical field of simulation and comprises the following steps: constructing an electromagnetic heat calculation model of the resistance-type superconducting current limiter based on COMSOL; constructing a circuit simulation model of the resistance type superconducting current limiter power system based on Simulink; and performing joint simulation according to the electromagnetic heat calculation model and the circuit simulation model to obtain the average electric field intensity of the resistance type superconducting current limiter, the average temperature of each layer of the superconducting tape and the average current density of each layer of the superconducting tape. According to the method, through joint simulation modeling of COMSOL and Simulink, current distribution, temperature field distribution, magnetic field distribution, heating and temperature rise of the resistance type superconducting current limiter can be analyzed while parameters such as voltage and current in a circuit are analyzed.

Description

Technical Field

[0001] This invention relates to the field of simulation technology, and in particular to a method for joint simulation modeling of field-circuit coupling of resistive superconducting current limiters. Background Technology

[0002] With the rapid development of the national economy, the demand for electricity has continued to rise, the power grid has expanded in scale and become increasingly complex, and the short-circuit current level of power grids at all levels has increased significantly, becoming one of the core hidden dangers threatening the safe and stable operation of the power grid. When a short-circuit fault occurs, the instantaneous surge in short-circuit current can exceed the withstand capacity of electrical equipment, easily leading to serious accidents such as circuit breaker failure, transformer damage, and even causing large-scale power outages or power grid collapse, resulting in huge losses to social production and life. Against this backdrop, fault current limiting technology has become a key support for alleviating short-circuit current pressure and ensuring the safe operation of the power grid. Among them, the resistive superconducting fault current limiter has become a research and application hotspot in the field of superconducting power equipment due to its unique working advantages.

[0003] Currently, simulation methods based on resistive superconducting current limiters have the following problems: 1) Because the resistance parameters of resistive superconducting current limiters are affected by multiple factors such as temperature, current, and magnetic field during the quenching process, the current in existing resistive superconducting current limiters simulated by COMSOL finite element methods mainly comes from preset circuits or current curves, making it difficult to achieve bidirectional coupling with the circuit. Furthermore, the built-in circuit interface in COMSOL is relatively simple and difficult to simulate the complex operating conditions of power systems. 2) Simulink-based simulations primarily perform circuit-related analyses, only obtaining average values ​​of the voltage, current, and temperature parameters of the superconducting current limiter. They struggle to accurately simulate the temperature distribution of resistive superconducting current limiters. Furthermore, under actual operating conditions, the uneven distribution of temperature and current in resistive superconducting current limiters due to winding and heat dissipation affects their current limiting and recovery performance. Summary of the Invention

[0004] The purpose of this invention is to provide a joint simulation modeling method for field-circuit coupling of resistive superconducting current limiters to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, this invention provides a method for joint simulation modeling of field-circuit coupling in resistive superconducting current limiters, comprising the following steps: S1. Construct an electromagnetic thermal calculation model of a resistive superconducting current limiter based on COMSOL; S2. Construct a circuit simulation model of a power system with a resistive superconducting current limiter based on Simulink; S3. Based on the electromagnetic thermal calculation model and the circuit simulation model, a joint simulation is performed to obtain the average electric field strength of the resistive superconducting current limiter, the average temperature of each layer of the superconducting tape, and the average current density of each layer of the superconducting tape.

[0006] Preferably, the electromagnetic heat calculation model in step S1 includes general form partial differential equations, solid and fluid heat transfer equations, and turbulence equations, wherein the general form partial differential equations are based on Maxwell's equations and employ... A - V equation, T - equation or H The equation method is used to set the voltage, current and magnetic field constraints of the resistive superconducting current limiter. The solid and fluid heat transfer equations are used to calculate the heat generation, heat dissipation and temperature of the resistive superconducting current limiter during the quench and recovery process. The turbulence equation is used to calculate the liquid nitrogen flow characteristics of the resistive superconducting current limiter during the quench and recovery process.

[0007] Preferably, the heat transfer equations for the solid and fluid are as follows: ; In the formula, Voltage of the strip; Duration of fever; For strip resistance; Thermal conductivity of the strip; For strip temperature; For heat transfer between the strip and liquid nitrogen; The density of the strip; This refers to the heat capacity of the strip.

[0008] Preferably, the turbulence equation is as follows: ; In the formula, For fluid velocity; For fluid pressure; The dynamic viscosity coefficient; It is an external force.

[0009] Preferably, in step S2, the circuit simulation model is based on a certain AC or DC system parameter, including an LC source, a pre-switch, a first thyristor, a second thyristor, a winding, a resistor, a post-switch, a Hall sensor, and a power supply. The LC source, the pre-switch, and the first thyristor are connected in sequence. The first thyristor is connected to the second thyristor and the winding, respectively. The winding is connected to the Hall sensor. The second thyristor, the winding, and the Hall sensor form a branch in parallel. The power supply, the resistor, and the post-switch are connected in sequence to form a branch two, which is connected to the branch one. The cathode of the second thyristor is connected to the ground terminal.

[0010] Preferably, the circuit simulation model further includes an oscilloscope, one end of which is connected to the winding and the other end of which is connected to the Hall sensor.

[0011] Preferably, step S3 specifically includes: S31. Set up and export the Simulink co-simulation file. Setting up the co-simulation file includes setting the input and output parameters of the COMSOL simulation. S32. Associate the circuit simulation model in Simulink with the exported co-simulation file; S33. Perform co-simulation. The simulated current obtained in Simulink is input into COMSOL, and the voltage is calculated by the average electric field strength output by COMSOL. Simulate the temperature field and flow field in COMSOL. Based on the voltage, temperature field and flow field, obtain the average electric field strength of the resistive superconducting current limiter, the average temperature of each layer of the superconducting tape, and the average current density of each layer of the superconducting tape.

[0012] Preferably, the input current parameters of the COMSOL simulation are obtained through Simulink circuit simulation, and the output parameters include the average electric field strength of the resistive superconducting current limiter, the average temperature of each layer of the superconducting tape, and the average current density of each layer of the superconducting tape.

[0013] Therefore, the above-mentioned method for joint simulation modeling of field-circuit coupling of resistive superconducting current limiter has the following beneficial effects: (1) By using Simulink and COMSOL for joint simulation, we can avoid the problem of bidirectional coupling between the partial differential equation interface and the circuit interface in COMSOL. At the same time, we can also solve the problem that the circuit interface in COMSOL is relatively simple and it is difficult to simulate complex circuits.

[0014] (2) By combining Simulink and COMSOL simulation, finite element simulation and system simulation can be combined to analyze the current distribution, temperature field distribution, magnetic field distribution, heating and temperature rise of the resistive superconducting current limiter while analyzing parameters such as voltage and current in the circuit.

[0015] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0016] Figure 1 This is a flowchart of the method in Embodiment 1 of the present invention; Figure 2 This is a flowchart of the co-simulation process in Embodiment 1 of the present invention; Figure 3 This is a schematic diagram of the co-simulation modeling of Embodiment 1 of the present invention; Figure 4 This is a schematic diagram of the circuit simulation model of Embodiment 1 of the present invention; Figure 5 This is a current-limiting current curve diagram of Embodiment 2 of the present invention; Figure 6 This is a temperature distribution cloud map of the superconducting coil during a simulation time of 10ms in Embodiment 2 of the present invention; Figure 7 This is a graph showing the average temperature curve of the superconducting coil in Embodiment 2 of the present invention; Figure Labels 1. LC source; 2. Pre-switch; 3. First thyristor; 4. Second thyristor; 5. Winding; 6. Resistor; 7. Rear switch; 8. Hall sensor; 9. Power supply; 10. Oscilloscope. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can be arranged and designed in various different configurations, and therefore should not be construed as limiting the present invention.

[0018] Example 1 Reference Figures 1-4 This invention provides a method for joint simulation modeling of field-circuit coupling in a resistive superconducting current limiter, comprising the following steps: S1. Construct an electromagnetic thermal calculation model for a resistive superconducting current limiter based on COMSOL.

[0019] The electromagnetic heat calculation model includes general form partial differential equations, solid and fluid heat transfer equations, and turbulence equations.

[0020] Electromagnetic simulation of resistive superconducting current limiters is generally based on a general form partial differential equation interface, using Maxwell's equations. A - V equation, T - equation or H Equations such as these are used to set the voltage, current, and magnetic field constraints of resistive superconducting current limiters.

[0021] A - V The equation formula is as follows: ; In the formula, It is the magnetic field vector. For electric field scalar, Permeability, Indicates electrical conductivity. For Hamiltonian operators.

[0022] T- The equation formula is as follows: ; ; In the formula, It is a current vector. For an external magnetic field, It is a magnetic field scalar. is the magnetic permeability.

[0023] H The equation formula is as follows: ; ; ; In the formula, The electric field strength of the superconducting tape, It represents the magnetic flux density. The magnetic field strength, The resistivity of the superconducting tape. This represents the current density.

[0024] The solid-fluid heat transfer equations are used to calculate the heat generation, heat dissipation, and temperature of a resistive superconducting current limiter during quench loss and recovery. The formulas for the solid-fluid heat transfer equations are as follows: ; In the formula, Voltage of the strip; Duration of fever; For strip resistance; Thermal conductivity of the strip; For strip temperature; For heat transfer between the strip and liquid nitrogen; The density of the strip; Let be the heat capacity of the strip. In solid and fluid heat transfer, the temperature change of the strip is calculated by calculating the heat generated and the heat dissipated by the strip.

[0025] During the heating and cooling process of the resistive superconducting current limiter, a large number of bubbles are generated. At this time, the boiling mode of liquid nitrogen is pool boiling turbulence. To improve simulation convergence, incompressible flow is assumed, and the turbulence equation is as follows: ; In the formula, For fluid velocity; For fluid pressure; The dynamic viscosity coefficient; It is an external force.

[0026] S2. Construct a circuit simulation model of a resistive superconducting current limiter power system based on Simulink. The circuit simulation model is based on a certain AC or DC system parameter and includes an LC source 1, a pre-switch 2, a first thyristor 3, a second thyristor 4, a winding 5, a resistor 6, a post-switch 7, a Hall sensor 8, and a power supply 9. The LC source 1, pre-switch 2, and first thyristor 3 are connected in sequence. The first thyristor 3 is connected to the second thyristor 4 and the winding 5. The winding 5 is connected to the Hall sensor 8. The second thyristor 4, the winding 5, and the Hall sensor form a branch 1 in parallel. The power supply 9, resistor 6, and post-switch 7 are connected in sequence to form a branch 2, which is connected to branch 1. The cathode of the second thyristor 4 is connected to the ground terminal.

[0027] The circuit simulation model also includes an oscilloscope 10, one end of which is connected to the winding 5 and the other end is connected to the Hall sensor 8.

[0028] S3. A joint simulation is performed based on the electromagnetic-thermal calculation model and the circuit simulation model to obtain the average electric field strength of the resistive superconducting current limiter, the average temperature of each layer of the superconducting tape, and the average current density of each layer of the superconducting tape. The specific process includes: S31. Set up and export the Simulink co-simulation file. In the Simulink co-simulation file settings, set the input and output parameters of the COMSOL simulation. The input current parameters of the COMSOL simulation are obtained through Simulink circuit simulation and input into COMSOL for multiphysics simulation. The output parameters include the average electric field strength of the resistive superconducting current limiter, the average temperature of each layer of the superconducting tape, and the average current density of each layer of the superconducting tape.

[0029] S32. Use the built-in COMSOL co-simulation module in Simulink to associate the circuit simulation model with the co-simulation file exported from the COMSOL model; S33. Perform co-simulation. The simulated current obtained in Simulink is input into COMSOL, and the voltage is calculated by the average electric field strength output by COMSOL. It runs as a controlled source in the system. Simulate the temperature field and flow field in COMSOL. Based on the voltage, temperature field and flow field, obtain the average electric field strength of the resistive superconducting current limiter, the average temperature of each layer of the superconducting tape, and the average current density of each layer of the superconducting tape.

[0030] After the simulation is complete, you can view the voltage, current and other parameters of the circuit simulation in Simulink, as well as the various physical field parameters output by the COMSOL simulation. You can also view the multi-physics parameter distribution cloud map in the saved COMSOL simulation file.

[0031] Example 2 S1. Construct an electromagnetic thermal calculation model for a resistive superconducting current limiter based on COMSOL.

[0032] In this embodiment, a two-dimensional axisymmetric dimension is selected in COMSOL. Based on the non-inductive pancake winding method of the superconducting coil of the resistive superconducting current limiter, combined with the structural parameters of the superconducting tape, a geometric model of the superconducting coil is established, and the corresponding material settings are made.

[0033] The electromagnetic properties of superconducting coils can be used to... H Taking the equation as an example, in two-dimensional axisymmetric systems, it is assumed that the current flows only along... Directional flow, can be H The equation is simplified, requiring only calculation. r and z The magnetic field strength of the axis and The formulas for the total current density, current density, and magnetic field strength in the direction of the current density can be simplified to: ; The law of electromagnetic induction can be simplified to: ; The formula for calculating electric field strength is: ; The resistivity of the superconducting layer is: ; ; In the formula, The critical electric field strength of the superconducting layer is , The current density of the superconducting layer, The critical current density of the superconducting layer. The temperature of the superconducting layer. This is the critical temperature of superconducting tapes. The operating temperature of the superconducting tape is 77.2K in this simulation. Here, represents the characteristic constant of the superconducting tape. In this example, ST-12-L superconducting tape is used, and its critical current density is... The critical temperature is 92K. It is 22.

[0034] The heat transfer module employs solid-fluid heat transfer, with the heat source set as Joule heating of the superconducting tape. .

[0035] In the fluid simulation section, the fluid flow characteristics can be obtained by solving the corresponding transport equations by combining the momentum conservation equation, continuity equation, and standard wall function of incompressible flow with gravity.

[0036] In the liquid nitrogen phase transition section, a phase transfer module is used to simulate the boiling phase transition of liquid nitrogen and to calculate the gas-liquid two-phase ratio during liquid nitrogen boiling based on the turbulence equation.

[0037] Next, mesh generation was performed. The mesh generation used both mapped mesh and free triangular mesh to draw the mesh of a single superconducting tape. Then, the mesh of the remaining tapes was drawn using a copy domain. The liquid nitrogen region was drawn using a free triangular mesh.

[0038] In the research setup, transient simulation was used, and the solver employed a direct fully coupled approach.

[0039] S2. Construct a circuit simulation model of a resistive superconducting current limiter power system based on Simulink, using a DC power supply. The circuit simulation model is the same as that in Example 1.

[0040] S3. A joint simulation is performed using the electromagnetic-thermal calculation model and the circuit simulation model to obtain the average electric field strength, average temperature of each layer of the superconducting tape, and average current density of each layer of the superconducting tape for the resistive superconducting current limiter. Specifically: S31. In COMSOL, add the Simulink co-simulation module. The output parameter of the COMSOL simulation is the average electric field strength of the superconducting coil, and the input parameter is the total current. After setting, export the Simulink co-simulation file.

[0041] S32. Start the co-simulation program of COMSOL and Simulink, and open the circuit simulation model created by Simulink. In the Simulink circuit simulation model, the capacitor C=0.1F, the inductor L=0.1mH, the capacitor pre-charge voltage is 220V, the expected peak current is 6070A, the impact time is 0.1s, the total simulation time is 1s, and the step size is set to 0.1ms.

[0042] S33. Perform co-simulation. After the simulation, obtain the current curve of the superconducting coil in Simulink, such as... Figure 5 As shown, the expected peak LC current of 6070A was limited to 1877A, and due to the current-limiting resistor of the superconducting coil, the current after current limiting changed from the expected underdamped to overdamped. A schematic diagram of the temperature distribution of the superconducting coil over 10ms and the average temperature change curve of the coil were obtained in COMSOL, as shown below. Figure 6 and Figure 7 As shown, the maximum temperature of the strip at 10ms was 209.4K, and the average temperature was 192.7K. The average temperature of the superconducting coil recovered to 77.2K at 3.15s.

[0043] Therefore, the present invention adopts the above-mentioned field-circuit coupling joint simulation modeling method for resistive superconducting current limiters. Through joint simulation modeling of COMSOL and Simulink, it is possible to analyze the current distribution, temperature field distribution, magnetic field distribution, heat generation and temperature rise of resistive superconducting current limiters while analyzing parameters such as voltage and current in the circuit.

[0044] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A method for joint simulation modeling of field-circuit coupling in a resistive superconducting current limiter, characterized in that, Includes the following steps: S1. Construct an electromagnetic thermal calculation model of a resistive superconducting current limiter based on COMSOL; S2. Construct a circuit simulation model of a power system with a resistive superconducting current limiter based on Simulink; S3. Based on the electromagnetic thermal calculation model and the circuit simulation model, a joint simulation is performed to obtain the average electric field strength of the resistive superconducting current limiter, the average temperature of each layer of the superconducting tape, and the average current density of each layer of the superconducting tape.

2. The method for joint simulation modeling of field-circuit coupling of a resistive superconducting current limiter according to claim 1, characterized in that: The electromagnetic-thermal calculation model in step S1 includes general-form partial differential equations, solid and fluid heat transfer equations, and turbulence equations. The general-form partial differential equations are based on Maxwell's equations and employ... A - V equation, T - equation or H The equation method is used to set the voltage, current and magnetic field constraints of the resistive superconducting current limiter. The solid and fluid heat transfer equations are used to calculate the heat generation, heat dissipation and temperature of the resistive superconducting current limiter during the quench and recovery process. The turbulence equation is used to calculate the liquid nitrogen flow characteristics of the resistive superconducting current limiter during the quench and recovery process.

3. The method for joint simulation modeling of field-circuit coupling in a resistive superconducting current limiter according to claim 2, characterized in that, The heat transfer equations for the solid and fluid are as follows: ； In the formula, Voltage of the strip; Duration of fever; For strip resistance; Thermal conductivity of the strip; For strip temperature; For heat transfer between the strip and liquid nitrogen; The density of the strip; This refers to the heat capacity of the strip.

4. The method for joint simulation modeling of field-circuit coupling of a resistive superconducting current limiter according to claim 2, characterized in that, The turbulence equation is as follows: ； In the formula, For fluid velocity; For fluid pressure; The dynamic viscosity coefficient; It is an external force.

5. The method for joint simulation modeling of field-circuit coupling of a resistive superconducting current limiter according to claim 1, characterized in that: In step S2, the circuit simulation model is based on a certain AC or DC system parameter, including an LC source, a pre-switch, a first thyristor, a second thyristor, a winding, a resistor, a post-switch, a Hall sensor, and a power supply. The LC source, the pre-switch, and the first thyristor are connected in sequence. The first thyristor is connected to the second thyristor and the winding, respectively. The winding is connected to the Hall sensor. The second thyristor is connected in parallel with the first branch formed by the winding and the Hall sensor. The power supply, the resistor, and the post-switch are connected in sequence to form the second branch, which is connected to the first branch. The cathode of the second thyristor is connected to the ground terminal.

6. The method for joint simulation modeling of field-circuit coupling of a resistive superconducting current limiter according to claim 5, characterized in that: The circuit simulation model also includes an oscilloscope, one end of which is connected to the winding and the other end of which is connected to the Hall sensor.

7. The method for joint simulation modeling of field-circuit coupling in a resistive superconducting current limiter according to claim 1, characterized in that, Step S3 specifically includes: S31. Set up and export the Simulink co-simulation file. Setting up the co-simulation file includes setting the input and output parameters of the COMSOL simulation. S32. Associate the circuit simulation model in Simulink with the exported co-simulation file; S33. Perform co-simulation. The simulated current obtained in Simulink is input into COMSOL, and the voltage is calculated by the average electric field strength output by COMSOL. Simulate the temperature field and flow field in COMSOL. Based on the voltage, temperature field and flow field, obtain the average electric field strength of the resistive superconducting current limiter, the average temperature of each layer of the superconducting tape, and the average current density of each layer of the superconducting tape.

8. The method for joint simulation modeling of field-circuit coupling of a resistive superconducting current limiter according to claim 7, characterized in that: The input current parameters for COMSOL simulation are obtained through Simulink circuit simulation, and the output parameters include the average electric field strength of the resistive superconducting current limiter, the average temperature of each layer of the superconducting tape, and the average current density of each layer of the superconducting tape.

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