DC breaking capacity of circuit breakers - A discussion

% DC and the X/R ratio in CB

In a Circuit breaker the DC current breaking is specified in terms of % of the maximum DC present during the a fault
The maximum DC is available when the fault happens at Voltage minimum . ( The assumptions made are the circuit act as pure inductive during fault and there is no initial current through the circuit prior to the fault . This is a case where we are switching an inductive circuit . In an inductive circuit ideally , the current should lag the voltage by 90 Degree and hence when the voltage is Zero current will be lagging by 90 degree and it has maximum value . Now in actual physical circuit when the voltage is zero current is Zero ! This is a conflicting requirement ! To solve this two conflicting requirement , we assume that we have two currents at voltage zero , One steady state AC current which is equal to the circuit voltage divided by the circuit X and another DC current which is equal and opposite to the AC current . Now at instant of voltage zero ( assumed worst case fault ) , the total current is zero ( AC + DC ) . This theory satisfies our conflicting requirement ! ie ( physical current is zero as well as the AC current is lagging the voltage by 90 Degree ) .

Now what is the maximum value of the DC current possible in a network ? It must be the maximum steady state AC value possible during the fault . The maximum steady state AC value happens theoretically at zero voltage and its instantaneous value is = 1.414 RMS value Hence

The maximum value of DC current possible is 1.414 RMS Ac value ( but in opposite direction )
Now what will happen to this DC value . It decays down to zero exponentially based on the X/R ratio of the circuit

Now in case of a Circuit breaker , the circuit breaker contact starts open after some time of fault . ( contact parting time. This include relay operation time and CB contact parting time- 1.5 cycle for a 2-cycle breaker, 2 cycles for a 3-cycle breaker, 3 cycles for a 5-cycle breaker, and 3.5 cycles for an 8-cycle breaker as per IEEE C37.010.1999) Now DC current that a CB required to break is never the maximum DC ( or 100 % DC ) but a DC which is lesser based on the CB contact opening time ( start of opening) .

Now as per the standard , the X/R ratio of 14 is the standard for 50 Hz corresponding to a DC time constant of 45 msec .

Now at the time of fault the % DC is 100 % ( if the contact parting time is zero then the CB has to break the 100% DC – but as the contact parting time is never zero the % of DC that the CB required to break is always lesser )
And it decays as 100 e-^t/T as percentage
For a time constant of T= 45 msec and contact parting time of 1.5 cycles ( 30 msec )

The % DC is 100 * e^- 30/45 = 100 * 0.5134 = 51%

Hence we can find out the X/R ratio the CB manufacture has used in the calculation once we know the % DC rating of the CB and contact parting time . ( more X/R ratio please refer to IEEE C37.010.1999 - 5.10.2.2 )

But if you are interested in finding the Actual X/R ratio we have to find out from the Circuit impedance . With this basic we can discuss what X/R ratio need to be taken for our application