Your question makes it sound like a couple things are going on at the same time. First, I'm assuming the differential relays are electromechanical otherwise you'd be able to program the relay to handle any issues. Second, given the electromechanical relay assumption any phase shift across the transformer has to be corrected for in the connections of the ct's supplying the relays. Third, the ct ratios have to match reasonably well with the available taps on the differential relays so the relay does not trip on through faults. I'll speculate given the transformer turns ratio and the ct taps available (or maybe you have single-ratio ct's) that the ct's don't provide the required currents with the relay taps available to meet the relay's sensitivity and mismatch characteristics so someone retrofitted aux ct's to get the correct ratio and then made the required phase shift correction via the aux ct's as well.
Depending on the relay, web sites such as ABB's discusses the calculations, settings and issues - look at their instruction leaflet 41-347.12C for the type HU and HU-1.
thanks for the explanation. i think all 3 of your assumptions are correct about my setup. we are installing a new set of 5kV aux swgr (typical gen plant arrangement)and will certainly be using solid state relaying to cover the diffs.
There is another issue: blocking of zero sequence current from the star (Y) side. Probably the CTs delta connected are on the star side of the power transformer.
If you don't do it, the relay may trip unwanted for external faults, necause the delta side of the power transformer blocks zero sequence fault current, but not the star side, so you have to compensate at aux. CT's level.
For numerical relays, this is also done automatically in the algorithm, or it is settable.
Is there a a restricted earth fault relay involved? For differential protection a delta / wye transformer requires CTs connected delta on the wye side of the transformer. This is at odds with the REF requirement of wye connected CTs. Auxilliary CTs can be use to get both connections.
