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My understanding is that on most (if not all) differential relays, there are currents coming in from both sides of the operating coil. These currents should cancel out, or in reality, nearly cancel out. Therefore, the effective current in the operating coil is zero. When the net current in the operating coil is not zero, the relay trips.

There are instances when you don't want the relay to trip though. Therefore, the operating coil works together with a restraint coil. (Well probably 2 restraint coils.) The relay will trip if the operating coil's current must exceed the restraint coil's current by a certain amount.

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Q: What is operating coil of differential relay?
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