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CT ratio for 33/6.6 kV star/delta (400/5)

Short answer

With LV delta-side CTs 400/5 in star, pilot current is 5 A. HV line current is 400 x 6.6/33 = 80 A; HV CTs are in delta, so CT secondary is 5/√3 A. HV CT ratio is 80 : 5/√3 ≈ 138.6 : 5.

A 3-phase transformer rated for 33 kV/6.6 kV is connected star/delta and the protecting current transformer on the low voltage side have a ratio of 400/5. Determine the ratio of the current transformer on the HV side.

For differential protection of a star/delta transformer, the CTs on the star (HV) side are connected in delta and those on the delta (LV) side in star. This corrects the 30° phase shift and keeps zero-sequence current out of the relay. The CT ratios are chosen so that equal currents flow in the pilot wires.

Data: 33/6.6 kV, star/delta; LV CTs 400/5 (star connected).

Step 1: Pilot current from LV side

Take LV line current = 400 A, so the LV CT secondary (and pilot) current = 5 A.

Step 2: HV line current for the same load

I_HV = 400 × 6.6/33 = 80 A

Step 3: HV CT ratio

HV CTs are in delta; the line current from the delta is √3 × CT secondary current. For a pilot current of 5 A:

CT secondary = 5/√3 = 2.887 A
HV CT ratio = 80 : 5/√3 = 80 : 2.887
            = 138.56 : 5   (≈ 27.71 : 1)

Connection

   33 kV star ─── HV CTs (delta) ─┐
                                  ├─ pilots + relay
   6.6 kV delta ─ LV CTs (star) ──┘

Answer: HV CT ratio = 80 : 5/√3 ≈ 138.6 : 5, HV CTs connected in delta and LV CTs in star.

✓ Answer checked by Claude Opus 5.5 (high effort)

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