  For example in some supercondcuting generators, motors and power transmission
cables the superconductor experiences a changing magnetic field in a DC
background. Simulating the losses caused by this AC ripple field is an
important task from the application design point of view. In this work, we
compare two formulations, the $H$-formulation and the minimum magnetic energy
variation (the MMEV-formulation), based on the eddy current model (ECM) and the
critical state model (CSM), respectively, in simulating ripple field losses in
a DC biased coated conductor tape. Furthermore, we compare our simulation
results with measurements. We investigate the frequency-dependence of the
hysteresis loss predictions of the power law based ECM and verify by a
measurement, that in DC use, ECM clearly over-estimates the homogenization of
the current density profile in the coated conductor tape: the relaxation of the
local current density is not nearly as prominent in the measurement as it is in
the simulation. Hence, we suggest that the power law resistivity, used as the
\emph{local} relation between the electric field intensity ${\bf E}$ and
current density ${\bf J}$ in ECM, is not an intrinsic property of
high-temperature superconductors. The difference between the models manifests
itself as discrepancies in ripple field loss simulations in very low AC fields
with significant DC fields or currents involved. The results also show,
however, that for many practical situations, CSM and ECM are both eligible
models for ripple field loss simulations.
