Multi-scale Model Method For Ac Loss Calculation Of Large-Scale High-temperature-Superconducting Coils

In recent years,electromagnetic numerical models of high-temperature-superconducting(HTS)conductors have been well developed.But most of the models are focused on the simulation of small-size superconductors.As for the large-scale coils involving large numbers of tapes,modeling by conventional methods will produce massive meshes and degrees of freedom to be solved.The homogenization model can simplify coils significantly by building bulks,but it is only applicable to the 2nd generation superconducting flat tapes,while not to the 1 st generation round wires.In order to solve the difficult problem of ac loss calculation of large-scale HTS coils,the thesis developed the simulation method of multi-scale model,which can be widely applied to different types of conductors.Different from the conventional models imposing currents on the superconducting coils directly,the main idea behind multi-scale model is to estimate coils' magnetic field using a conventional magnetic field module,and then compute tapes' ac losses with the magnetic field.AC loss calculation of a coil will be broken up to the calculation of single-turn tapes.The loss of the whole coil can be obtained by interpolation of a few tapes' results.The thesis proposed the approximation of infinite-turn coils to obtain accurate current density to calculate magnetic field.By adding appropriate periodic boundary conditions on a simplified model,the whole coil can be characterized.And the current density distributions of the superconducting coil can be approximated by the results from that simplified model.Firstly,the high accuracy and efficiency of multi-scale model on ac loss calculation was validated through experimental measurements and numerical calculations.Based on a double-pancake and a four-pancake coil,several imposing currents were measured and calculated.The results showed that multi-scale model based on the approximation of infinite-turn coils maintains high accuracy on the calculation of current density,magnetic field and ac loss.And the calculations will be more accurate,if the coil contains more tapes.Due to the application of parallel computation,the computing efficiency of multi-scale model is higher than the conventional model by 2 orders of magnitudes.The full-size structure of coils needs to be modeled in the multi-scale model to calculate magnetic field.Although the calculation is implemented in the conventional magnetic field module with no consideration of highly nonlinear E-J power law,modeling a large-scale coil with thousands of tapes is not practicable.To solve the problem,the thesis proposed to optimize the calculation of multi-scale model with homogenization model.Since the calculation of single-turn tapes is kept,the employment of homogenization model is applicable to the simulation of the 1st generation round wires.The optimized multi-scale model was applied to simulate prototype coils from a reference.After optimization,1464 current domains in the original model can be reduced to 270 ones,and the error of ac loss compared with results from the reference is around 10%.The research of the thesis presented that the multi-scale model can also be applied to the simulation of inner-outer double coils.The magnetic field of the outer coils gets stronger,the error of ac loss calculation on the inserted HTS coils with uniform current density will be smaller.Based on the study and optimization of the method,the thesis calculated the ac loss of HTS central solenoid magnets designed for tokamak.The HTS magnet contains 1120 conductors,and each conductor contains 525 Bi-2212 wires.Uniform current density is applied to estimate the losses of a single conductor and the whole magnet.Good self-consistency and reliability of the computational models are validated through the analyses of the results.And some suggestions of magnets design are proposed based on the results.The study demonstrates that the multi-scale model developed in the thesis is an approach for ac loss calculation of large-scale HTS magnets with reliable accuracy and high computing efficiency.It can be a powerful tool to estimate ac loss of HTS central solenoid magnets in tokamak,and guide the design and optimization of magnets.