  Superconductors have been being applied to a variety of large-scale power
applications, including magnets, electric machines, and fault current limiters,
because they can enable a compact, lightweight and high efficiency design. In
applications such those mentioned above, superconducting coils are always a key
component. For example, in a superconducting electric machine, the
superconducting coils are used to generate the main flux density in the air
gap, which is significantly important for the energy conversion. It is the
performance of the superconducting coils that plays an essential role in
determining the performance of the device. However, the performance of a
superconducting coil is limited by its critical current, which is determined by
temperature and the magnitude and orientation of the magnetic field inside the
superconductors. Hence, in-depth investigations to estimate the critical
current of the superconducting coils are necessary before manufacturing.
Available transient simulation models to estimate the critical current are
through the H- and T-A formulations of Maxwell's equations. Both methods
consider the same current ramp-up process occurring in experiments. Besides
these transient models, static simulations can also be used: a modified
load-line method and the so-called P-model, which is based on the asymptotic
limit of Faraday's equation when time approaches infinity. To find the best way
to calculate the critical current, the four methods are used to estimate the
critical current of a double pancake superconducting coils and results are
compared with experiments. As a conclusion, T-A formulation, P-model, and the
modified load-line methods are recommended for estimating the critical current
of the superconducting coils.
