Q: Variable-load variable-source motor can i control induction motor theoretically that it work on -in rated conditions- 3 phase supply but also it can be adjusted automatically by means of control to work at condition of unbalance or 2 phase or 1 phase also it can work with instantaneous variable load, is that possible?

A: 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.

A: But do you intend on having a VFD on this motor? 
If not, then your theory has some merit IF you can shed load, but how much is debatable. I say a minimum of 70% load shed if the motor has one phase removed. 
The secondary problem is that this would ONLY apply if the motor was ALREADY spinning when the phase was lost. Once it stops, you would not be able to re-start the motor with a single phase source.
