Sir,

I have a 4Pole,1.5 kW motor, FLC-3.4A, BMR Setting: 3A, Back up Fuse: 16A
I have faced a problem of non-tripping of motor on unbalance current.
Motor was taking unbalance current due to opening of Y-phase, but BMR didn't operate on unbalance and motor ran for more than 8 hours in this condition.
We don't have any additional single phasing supervision relay.

I think BMR should operate on unbalance. Am I right?
If yes, then please tell me what is the operating range of a BMR on unbalance in terms of % of FLC.

Sorry, don't know the term 'BMR'. Bi-metal Relay perhaps?

If that is the case, and you mean a bimetal overload relay, there is no definitive mechanism or specification that says that a bimetal overload relay must trip on unbalanced current. Some have what is called a "differential trip mechanism" wherein the pressure exerted by all 3 bimetal elements on the trip mechanism must be equal in order to counteract a compensating spring and lever. This means that technically if one phase is different, the compensating mechanism will shorten the distance any of the bimetal strips need to move in order to cause a trip. But this is highly inaccurate, rarely repeatable and subject to not functioning unless the unbalance is extreme. That is why it is usually referred to as a crude phase loss protection method, never as an unbalanced current detector. There were better ways to pick up unbalanced current with electro-mechanical devices, but the advent of inexpensive and highly reliable solid state overloads that can do this have made them all but obsolete.

Find yourself a good quality solid state overload relay or motor protection relay that has unbalanced current protection. How the solid state ones work is to track the motor thermal condition and current balancing. An algorithm in the microprocessor will calculate the heating effect that negative sequence current (caused by the unbalance current) will have on the motor's thermal profile. it is referred to as "biasing" the thermal register or image. Very effective and also helps to avoid nuisance tripping.

Amazing?
Normally motor fails after one to five minutes.

We had installed a micro controller based relay when faced with current unbalance and single phasing problems. We have far too many of such problems. We have had a bit of relief there. If you are from India you may contact me on 022 27560488 and I can give you the reference, if you wish to use these.