For zero sequence current, there is zero sequence flux. This flux is all in phase and does not sum to zero in the common core sections as the pos and neg fluxes due. The zero sequence flux has a tendency to leave the core and find a return path through the air or whatever. Because of this, the inductance seen by the zero seq flux is less, hence the reactance is less. I think this is somewhat different in a five-legged core versus three-legged, but I don't have any data on this at hand.
The old information from Westinghouse T&D book and other sources indicates zero seq X is about 85% of pos seq X for a delta-wye transformer, as I recall.
Suggestion: The question appears to be linked to transformer connections, e.g. Y-Y (secondary neutral grounded only) and ground fault currents. For example, if the transformer has no magnetic phase interlinkage, e.g. shell type or three 1-phase type transformers, then there will be no zero phase sequence current on the secondary under the ground fault condition on the secondary side. However, in a core type unit the fluxes produced by zero sequence currents find a high-resistance path outside the core. Therefore, there will be a somewhat small zero phase sequence current flowing.
Because in a core type transformer almost all the zero sequence flux circulates through air (a high reluctance path), while in a shell type there is a return path through the core (low reluctance). Many textbooks treat the subject in detail. For example you can consult the book on transformers from the MIT Press.
for:
There are several transformer models available in the ATP version of EMTP [8] for an inrush study. If the ironcore
provides low reluctance path for the return of the zero-sequence flux (i.e. for 3-phase, 3-leg shell-type or 4-5
legs core type transformers) the zero sequence parameters
of the transformer are identical with the positive sequence
ones. In case of 3-phase, 3-leg core-type transformers the
zero sequence flux is forced to return through the air and
the tank, making the zero sequence magnetizing inductance high and linear. The steady-state performance of different transformer models in ATP has been compared in [9].
