Percentage differential relay: 150 MVA transformer

HV is delta connected, so its CTs are connected in star; LV is star connected, so its CTs are connected in delta. The relay current is the difference between the CT output line currents caused by the CT ratio mismatch.

Data: 150 MVA, 220/110 kV; HV (delta) CTs 400/5 (ratio 80); LV (star) CTs 1600/5 (ratio 320).

(i) CT secondary currents at full load

I_HV = 150 × 10⁶ / (√3 × 220 × 10³) = 393.65 A
I_LV = 150 × 10⁶ / (√3 × 110 × 10³) = 787.30 A

HV CTs (star): secondary = 393.65 / 80 = 4.921 A
LV CTs (delta): secondary (phase) = 787.30 / 320 = 2.460 A
                output line current = √3 × 2.460 = 4.261 A

(ii) Relay current at full load

I_relay = 4.921 − 4.261 = 0.659 A

(iii) Relay current setting for 90% loading

At 90% load all currents scale by 0.9:

I_relay = 0.9 × 0.659 = 0.593 A

The relay setting must therefore be above 0.593 A so that it does not operate at this loading (in practice a percentage bias is used to cover this mismatch).

Answer: (i) HV CT secondary 4.92 A, LV CT secondary 2.46 A (line output 4.26 A); (ii) relay current 0.659 A; (iii) 0.593 A at 90% load, so the setting must exceed this value.