Variable-load variable-source motor
Some variable frequency drives (VFDs) can cope with a loss of phase. Most VFDs can cope with some degree of voltage imbalance, probably to a greater extent than a than a motor could. Detailed VFD sales literature may provide sufficient information to determine what input power conditions are permissible. It may be necessary to contact a VFD sales agency or VFD factory customer support.

Loss of one phase would be single-phase not two-phase. Two phase is a special power configuration that requires three of four wires. Two-phase power service is a very archaic system that is extremely rare. It is supplied as an electronic control supply for some brushless DC motors.

Instantaneous load change within the capability of a motor will not prevent a three-phase induction motor from working. It will cause a slight speed variation, generally less than 5%. VFDs have the capability of compensating for the speed variation. To fully define the performance, it is necessary to have the exact details of the load and the variation. In some applications, a flywheel might be recommended.