Pilot current with tap change (10 MVA)

HV is star connected, so the HV CTs are connected in delta; LV is delta connected, so the LV CTs are connected in star. The LV CT ratio is chosen so that pilot currents balance at the nominal ratio 132/33 kV. A tap change upsets this balance and a spill current flows.

Data: 10 MVA, 132/33 kV; HV CTs 75/1 (in delta); through fault = 5 × full load; tap set at 128 kV.

Step 1: LV CT ratio

For HV current I_H, the delta of HV CTs gives a pilot current √3 I_H / 75. The LV CTs (ratio N:1, star) give I_L / N, with I_L = 4 I_H (132/33).

I_L / N = √3 I_H / 75
N = 75 × (I_L/I_H) / √3 = 75 × 4 / √3 = 173.2
LV CT ratio = 173.2 : 1

Step 2: Fault currents with 128 kV tap

Full-load current on the LV (33 kV) side:

I_FL(LV) = 10 × 10⁶ / (√3 × 33 × 10³) = 174.95 A
Through-fault LV current = 5 × 174.95 = 874.77 A
HV current with tap at 128 kV = 874.77 × 33/128 = 225.53 A

Step 3: Pilot currents

From LV CTs: 874.77 / 173.2 = 5.051 A
From HV CTs: √3 × 225.53 / 75 = 5.208 A
Out-of-balance (relay) current = 5.208 − 5.051 = 0.158 A

Answer: LV CT ratio = 173.2 : 1 (star connected). For the through fault with the tap at 128 kV, the pilot currents are about 5.05 A (LV side) and 5.21 A (HV side), so an unbalanced current of 0.158 A circulates through the relay. A percentage-biased relay is needed so that this does not cause tripping. (If "5 times full load" is taken on the HV side, the corresponding values are 5.05 A, 4.90 A and 0.153 A.)