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What is meant by rated out-of-phase making and breaking current? When is it applicable?

Out of phase making/breaking performance is one the "special" rated characteristics for a medium voltage circuit breaker that needs to be defined only when the application requires. 
This performance is applicable when a circuit breaker is open and the conductors are not synchronous (see figure below), the voltage across the terminals can increase up to the sum of voltages in the conductors (phase opposition).

In practice, standards require the circuit breaker to break a current equal to 25% of the fault current across the terminals, at a voltage equal to twice the voltage relative to earth.
If Ur is the rated circuit breaker voltage, the power frequency recovery voltage is equal to:
• 2 / √3 Ur for networks with an effectively earthed neutral system.
• 2.5 / √3 Ur for other networks.

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