A Finite-Element Method Framework for Modeling Rotating Machines With Superconducting Windings

Abstract

Electrical machines employing superconductors are attractive solutions in a variety of application domains. Numerical models are powerful and necessary tools to optimize their design and predict their performance. The electromagnetic modeling of superconductors by finite-element method (FEM) is usually based on a power-law resistivity for their electrical behavior. The implementation of such constitutive law in conventional models of electrical machines is quite problematic: the magnetic vector potential directly gives the electric field and requires using a power-law depending on it. This power-law is a non-bounded function that can generate enormous uneven values in low electric field regions that can destroy the reliability of solutions.The method proposed here consists in separating the model of an electrical machine in two parts, where the magnetic field is calculated with the most appropriate formulation: the H-formulation in the part containing the superconductors and the A-formulation in the part containing conventional conductors (and possibly permanent magnets). The main goal of this work is to determine and to correctly apply the continuity conditions on the boundary separating the two regions. Depending on the location of such boundary -in the fixed or rotating part of the machine -the conditions that one needs to apply are different. In addition, the application of those conditions requires the use of Lagrange multipliers satisfying the field transforms of the electromagnetic quantities in the two reference systems, the fixed and the rotating one. In this article, several exemplary cases for the possible configurations are presented. In order to emphasize and capture the essential point of this modeling strategy, the discussed examples are rather simple. Nevertheless, they constitute a solid starting point for modeling more complex and realistic devices. F ( ) = constant along Γ L ( ). Therefore, along this boundary part there is only the tangential component of the magnetic field B t = Q Q , R R , 0 .

A Coupled A–H Formulation for Magneto-Thermal Transients in High-Temperature Superconducting Magnets

“…The Dirichlet boundary conditions (6) and (7) are assumed to be incorporated into the function spaces. The third integral in (13) and the fourth integral in (14) provide the natural coupling interface exploited by the coupled field formulation. It is worth noting that following [20], the constraint condition for the current in (5) can be reformulated as…”

“…The discrete field problem is derived from the general weak formulation in (13), (14) and (15). The slab approximation is enforced by defining a set of edge functions v r q which encode the field constraints (33) and (34).…”

Analytical Model for the Magnetic Field Distribution in a Flux Modulation Superconducting Machine

“…So from (5) to (10), the boundary condition can be re-written in terms of the magnetic scalar potential in order to find the eigenvalue of the problem defined in the r-direction. 3) General solution in each region By using the separation of variable method, a general solution of (4) is obtained by satisfying the boundary conditions (11). The general solution is the same for regions I and II and can be written as 00 ( , )…”

“…2. Numerical methods as finite elements using a variety of formulation [11]- [16]. These methods can deal with complex geometries of superconductors but need more computational time than analytical methods.…”

Field Cooling Magnetization and Losses of an Improved Architecture of Trapped-Field Superconducting Rotor for Aircraft Applications

“…These conflicting requirements were identified early in the project [14] and in this work the solution devised is presented with the assistance of a 2D finite element model, developed by KIT also within ASuMED [15], weakly coupling two formulations. The model allows a superconducting machine to be treated roughly as a conventional one during this stage of its development and yields numerical results both about its performance (torque) and the expected losses in the stacks, providing insight about its demagnetization rate.…”