Dc motor has few drawbacks like
1. low voltage regulation in DC series motors
2. lower speed regulation
3. It can not be run at zero load conditions
4. Also use of permanent magnet makes the operation of motor hazardous
5. Also the armature diverter and field diverter, that can be used to control speed, need space.
6. Also speed control can not be done smoothly..
Due to these reasons DC motors can not be used in lifts. 3 phase induction motors are used in lifts. It has large starting torque and lower starting current. Also the speed control can be done smoothly by power electronics drives.
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The separately excited DC motor can be used for lift operation as it can deliver high starting torque and better speed regulation.
The Squirrel cage motor with VFD operation is best suited for lift operation.