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Percentage differential relay: 125 MVA transformer

Short answer

At full load, HV star CT output is 328.04/80 = 4.10 A, LV delta CT line output is √3 x 546.73/240 = 3.95 A. Full-load unbalance is 0.1548 A; at 15% overload relay current is 0.178 A. Minimum setting for 25% overload is 1.25 x 0.1548 = 0.194 A.

A 125 MVA, 220/132 kV three phase power transformer is protected by percentage differential relays. The current transformers located on HV and LV sides of the power transformer are 400/5 A and 1200/5 respectively. If the HV side is delta connected and the LV side is star connected, determine: i) The output line currents of both CT at full load ii) The relay current at 15% overload iii) The minimum relay current setting to permit 25% overload.

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 of the CT output line currents.

Data: 125 MVA, 220/132 kV; HV CTs 400/5 (ratio 80); LV CTs 1200/5 (ratio 240).

i) CT output line currents at full load

I_HV = 125 × 10⁶ / (√3 × 220 × 10³) = 328.04 A
I_LV = 125 × 10⁶ / (√3 × 132 × 10³) = 546.73 A

HV CTs (star): output = 328.04 / 80 = 4.100 A
LV CTs (delta): CT secondary = 546.73 / 240 = 2.278 A
                output line = √3 × 2.278 = 3.946 A

ii) Relay current at 15% overload

Relay current at full load = 4.100 − 3.946 = 0.1548 A
At 115% load = 1.15 × 0.1548 = 0.178 A

iii) Minimum relay setting for 25% overload

The relay must not operate up to 125% load:

Setting ≥ 1.25 × 0.1548 = 0.1935 A
QuantityValue
HV CT output (FL)4.100 A
LV CT output (FL)3.946 A
Relay current at 115%0.178 A
Minimum setting (125%)0.194 A

Answer: (i) 4.10 A (HV) and 3.95 A (LV); (ii) 0.178 A; (iii) minimum relay setting ≈ 0.194 A (about 3.9% of 5 A).

✓ Answer checked by Claude Opus 5.5 (high effort)

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