Sobeys81 - I guess I confused you. As dpc said, the third harmonic voltages (180Hz if in US) are generated in the generator. They are superimposed on the 60 hZ waveform. The generator output is not a pure sine wave.
Assume the instantaneous generator votlage is Vgen = V1 sin(wt)+ k3 sin(3wt) + higher harmonics.
The transformer output is closer to a pure sine wave: Vtx = V2 sin(wt)
We have a circuit with two voltage sources, Vtx & Vgen, interconnected by the phase conductors and neutral conductors. The driving voltage across the circuit is (Vtx -Vgen) = k3 sin(3wt). For B and C phase the same 3rd harmonic voltage is present since sin(3wt +120) = sin(3wt)=sin(3wt - 120). (The 180hz sine wave is the same whether shited 120 degrees plus or minus).
The third harmonic cuurents in each phase have no phase shift and are all the same frequency. When combined, they add instead of combining like "normal" phase currents.
Third harmonic currents flow in each phase, circulating from the generator terminal, through the phase wires, down the transformer winding to the neutral and back to the generator neutral. The neutral wires carry all three third harmonic currents that add instead of cancelling.
If there are no neutral wires, but the transformer and generator neutrals are both grounded, the currents travel in the grounding system.
The currents are always present, fault or no fault.
As DPC said, the curents will probably not overheat the generator or the transformer, but they can create problems with ground fault sensing. If a grounding resistor is inserted in the generator's neutral to earth connection, it adds impedance to the circuit, reducing, but not eliminating the circulating currents. The resistor's continuous current rating needs to match the total circulating current.
One side note if that transformer is wye-wye, neutral currents will be induced on the primary side and can trigger the high voltage ground fault proteciton. Even if the HV is 115 kV with a 20 mile transmission line. I know.
Solutions are to buy a generator with a better waveform, increase the size and impedance of the groudning device to limit the current, use a delta transformer winding, or do not parallel the generator and transformer.
Back to your origianl quesition - Set it at 10% of the resistor rating and mesasure the 180 hZ current swhen you get on line.