  A better understanding of the interaction between three phases is required
when developing superconducting cables for high voltage AC systems. With a
particular focus on the energy losses of real power transmission cables, in
this paper we utilize the so-called H-formulation of Maxwell equations to
devise a 2D model for superconducting triaxial cables. The major aim of this
model is to comprehend and reproduce the experimental observations reported on
the first triaxial prototype cable developed by SuperOx and VNIIKP. The
computationally modelled and prototyped cable is made of up to 87 tapes of 4 mm
width SuperOx tape arranged across the three phases. Our computational results
are compared to the experimental measurements performed by VNIIKP with the
electrical contact method, showing a high degree of accuracy over the outer
phase of the cable, whilst revealing technical issues with the experimental
measurements at the inner phases. Thus, in consultation with VNIIKP it has been
concluded that for the actual experimental measurement of the AC losses at the
inner phases, and consequently of the overall cable, a sophisticated
calorimetric setup must be built. Still our model is capable to provide an
independent assessment of the VNIIKP-SuperOx cable design, by investigating the
magnetic profiles per phase in the time domain. In this sense, we confirm that
the unbalanced arrange of currents and distancing between the phases
affirmatively lead to no magnetic leakages, and therefore to an adequate
balance of the cabling inductance.
