I have always looked at it this way:
When the transformer is sized for the load as well as the secondary conductors size correctly and secondary protection is properly sized to protect the conductors then the transformer is protected from overload.
Should you size the pri. OCPD to also protect the transformer from overload it is redundant OL protection. If the pri. OCPD is viewed as short circuit protection because the transformer already has OL protection then the pri. OCPD is viewed as taking the transformers off line should the transformer short circuit internally and fail.
I believe that we agree that transformer overload protection of a delta-delta transformer can be done from the primary only as the secondary doesn't have a neutral. Currents seen at the secondary are seen proportionately on the primary.
But with a Delta-wye that has a neutral the L-L currents seen on the primary don't necessarily reflect those L-N currents on the secondary so a pri. only OCPD can not adequately protect the transformer from OL.
And, as such, pri. and sec. OCPD are provided and one could opt for the 250% pri. OCPD but you must pay attention to that 25' tap rule.
In summary the sec. OCPD protects the transformer from OL and the pri. OCPD protects the distribution system from a transformer failure.
Dave T
