Differential current must exceed a pre set value to trip the associated circuit breaker(s). this value is the min value to operate the relay . In this case the expected tripping characteristic is as shown in figure (40)
If if there is a ratio mismatch in current transformers ratio, In this case there will be a small differential current in the load condition. This value is not sufficient to operate the differential relay but in the case of external fault condition this value may exceed the setting value and this leads to false operation of the relay .
To prevent the false operation of directional relays due to external false , stabilizing current is used to resist the operation of the directional relay. figure (41) shows a more stable characteristics.
This characteristics consists of two regions with two slaps .In this characteristics when , the stabilizing current increases , the differential current needed for operation will be very high .
Note :
Idiff= abs(I1+I2)
Istab= abs(I1)+abs(I2)