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What is the meaning of "minimum breaking current" for MV fuse? How does it affect the fuse choice for a given application?

The minimum breaking current of a fuse (or I3) is the minimum current value which causes the fuse to blow and break the current. For our range of MV fuses, these values are between 3 and 5 times the In value.
For current values less than I3 , the fuse will blow, but may not break the current as arcing continues until an external event interrupts the current. It is therefore essential to avoid using a fuse in the range between In and I3. Over-currents in this range may irreversibly damage fuse elements, whilst still maintaining the risk of an arc which is not broken, and of them being destroyed.
 
The attached figure shows the operating ranges of combined type fuses.
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