A Distributed Equivalent-Permeability Model for the 3D Design Optimization of Bulk Superconducting Electromechanical Systems

This paper deals with accelerating 3D optimization scenarios for bulk superconductor-based electromechanical systems. For this objective, distributed equivalent-permeability models for High-Temperature-Superconducting bulks are first developed. These are stationary models capable of replicating the distribution of electromagnetic forces in bulks when subjected to external magnetic fields, minimizing the need for time-dependent simulations using the E-J power law. After introducing these models, their initialization phases are proposed to minimize their computational time requirements while still providing good accuracy. Optimization of a 3D Zero-Field-Cooled levitation system is presented to demonstrate the models' applicability. To validate the equivalent-permeability model, experimental tests are carried out. The measured experimental levitation forces resulting close to the ones obtained using the proposed equivalent-permeability model and the time-dependent H-formulation with the E-J power law. After validation, a multi-objective optimization using the NSGA-II tool is performed to maximize levitation force while minimizing the HTS bulk volume. Hence, using the equivalent-permeability models, stationary and linear FEM simulations provide highly accurate results and significantly reduce computational time, mainly in 3D optimization scenarios.