  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.
