Discussion
If I1 and I2 are currents flowing from the secondary of CT1 and CT2 in pilot wires respectively and n0 and N are number of turns of operating coil and restraining coil respectively in differential protection scheme, then which of the following is correct ?
Answer: D
The correct relation is \(\frac{n_{0}}{N} = \frac{(I_{1} + I_{2})/2}{I_{1} - I_{2}}\).
In a biased (percentage) differential relay, the operating coil carries the difference current \(I_{1} - I_{2}\), and the restraining coil, connected at the midpoint of the pilot wires, carries the average current \(\frac{I_{1} + I_{2}}{2}\). At the operating threshold the two sets of ampere-turns balance:
\[ \begin{aligned} n_{0}(I_{1} - I_{2}) &= N\,\frac{I_{1} + I_{2}}{2} \\ \frac{n_{0}}{N} &= \frac{(I_{1} + I_{2})/2}{I_{1} - I_{2}} \end{aligned} \]
The first option is this ratio turned upside down. The two options with \(n_{0} \times N\) multiply the turns, which does not come from balancing ampere-turns.
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