A three−phase transformer having a line voltage ratio of 400/33000 V is connected in the star-delta. The CTs on the 400V side have a CT ratio of 1000/5. What must be the ratio of CTs on the 33000 side?
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Transformer differential protection requires the CT secondary currents presented to the relay to compensate for the transformer ratio and phase-connection effects. Using the given 400/33 kV transformer and 1000/5 CT on the LV side, the matching HV-side CT ratio corresponds to the keyed 7/5 value.
Formula / Key Relation
Transformer line-current ratio:
ILV / IHV = VHV / VLV = 33000/400 = 82.5
Then include √3 CT-connection compensation for differential balance.
Detailed Explanation
Concept & ReasoningIn transformer differential schemes, CT connections are normally opposite to the power-transformer winding connections to compensate the 30° phase shift. The current magnitude on each side is inversely proportional to line voltage for the same MVA, and the delta-connected CT group introduces a √3 factor. A rigorous calculation should write line currents and relay-side currents explicitly before choosing the CT ratio.How to Solve It in the ExamProtection CT matching = transformer current ratio + CT star/delta compensation.Important Exam PointDraw transformer winding and CT connections before calculating relay currents.Related Revision PathThis question sits in the revision path Power System…
Concept & Reasoning
In transformer differential schemes, CT connections are normally opposite to the power-transformer winding connections to compensate the 30° phase shift. The current magnitude on each side is inversely proportional to line voltage for the same MVA, and the delta-connected CT group introduces a √3 factor. A rigorous calculation should write line currents and relay-side currents explicitly before choosing the CT ratio.
How to Solve It in the Exam
Protection CT matching = transformer current ratio + CT star/delta compensation.
Important Exam Point
Draw transformer winding and CT connections before calculating relay currents.
Related Revision Path
This question sits in the revision path Power System → Protection → Differential Protection .
Quick Trick
Protection CT matching = transformer current ratio + CT star/delta compensation.
Common Mistake
Using only 82.5:1 transformer line-current ratio and ignoring CT connection compensation.
Exam Tip
Draw transformer winding and CT connections before calculating relay currents.
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