HT Induction Motor

<....Will it make the motor fail?...>

If this is the <...very old plant with lot of entangled power and control cables which can not be rectified now...>, then it is likely that other causes <...Will...make the motor fail...>.

<...Any mathematical formula or calculation regarding Induction values of phase windings and their impact on the motor performance?...>

The best course of action would be to discuss the readings with the <...motor...> manufacturer. Telephone?

<...What...action plan for healthy operation of a motor?...> Proper motor protection equipment, properly set-up and properly maintained.

If in doubt, consult a local qualified Electrical Engineer.

..."The general rule regarding inductive imbalance is as follows: it should be below 7% for form wound motors and below 12% for random wound motors. However, as alluded to at the beginning, even new motors may not make the cut with these types of guidelines. When you are setting the acceptance criteria for inductive imbalance tests, there are other factors to keep in mind.

Keep in mind that power factor correction capacitors can affect the results when an inductive imbalance test is performed, as can surge and lightning arrestor circuitry. If present, they should be disconnected from the circuit before initial testing and then reconnected for comparison to see what impact they may have on the results.

To determine if the inductive imbalance is a motor issue, you can isolate the source of the imbalance to the rotor or stator by performing a RIC test with the motor energized and then, after allowing the rotor to warm up, performing that same test again. If this eliminates most of the inductive imbalance, then the problem is most likely not an issue with the motor but the after-effects of a process or test that was performed by the repair shop. In such a case, the imbalance should be recalculated minus the influence of the rotor."...

https://www.gohispeed.com/electric-motors-how-to-test-inductance-review-standards/

https://www.physicsforums.com/threads/how-to-calculate-the-inductance-of-a-stator-winding.930059/

The easy way to tell if the motor is fit for service is to measure the individual phase currents. After checking with the motor designer on the allowable temperature rise due to unbalanced phase currents, most designs trip immediately at 15%, pursue your quest with that knowledge. Unbalanced phase currents heat the rotor bars and stator windings, assuming an induction motor, and will destroy the motor in short order. Only the motor designer knows the limit, especially at that voltage.