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

This article deals with accelerating three 3-D optimization scenarios for bulk superconductor-based electromechanical systems. For this objective, distributed equivalent-permeability models for high-temperature-superconducting (HTS) 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. The optimization of a 3-D zero-field-cooled levitation system is presented to demonstrate the models' applicability. To validate the equivalent-permeability model, the 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 multiobjective optimization using the nondominated sorting genetic algorithm II tool is performed to maximize levitation force while minimizing the HTS bulk volume. Hence, using the equivalent-permeability models, stationary and linear finite-element model simulations provide highly accurate results and significantly reduce computational time, mainly in the 3-D optimization scenarios.