During normal operations it should be near zero. System imbalances will result in some, but just a few percent of total current.

I’ll see your silver lining and raise you two black clouds. - Protection Operations

Thanks David, that is interesting because I have seen engineers size this as really high CT ratios compared to the phase CTs. We don't have any real intention to use it for protection so was just going to monitor zero sequence currents with it. Perhaps we should just remove this CT then or is there any value in keeping it?

In a wye/delta transformer, the zero sequence impedance is three times the positive sequence impedance.
A small imbalance on a transformer with relatively high impedance will generate a relatively low circulating current.
A large imbalance on a transformer with a relatively low impedance will generate a relatively high circulating current.
Transmission lines typically have well balanced loads and voltages and relatively high impedance transformers.
A delta tertiary winding may provide beneficial stability and balance to a transmission circuit.
Distribution circuits typically see lower impedance transformers and often unbalanced loads.
Grounded wye/delta configurations are best avoided on distribution circuits.

Bill
--------------------
Ohm's law
Not just a good idea;
It's the LAW!

Heavy current will flow inside the stabilizing tertiary winding during an LG fault on secondray side. To give an idea of current, in a typical 10 MVA 132/11 unit, Vz= 10 %, the tertiary winding will see 3 times rated current without LV feed and may increase above 7 times with LV feed.
In small transformers we eliminated stabilizing winding in India due to tertiary winding failures from the dynamic forces consequent to over currents during LG faults on secondary lines.