When we replace dc drive with ac drive(ac motor having same capacity as dc motor) than there is alot of saving of power why? In dc drive only rectification take place where as in ac drive rectification and then inversion take place.
The 'true power' savings will be based on power factor. The phase-controlled DC drive will have a terrible power factor at lower speeds, approaching an almost acceptable power factor at full speed. The V*A used in the motor is not that much different. The DC motor requires a magnetizing field to be energized (except PM Motors), as does the AC. The AC magnetizing current is harder to determine, but is calculated by higher end drives, such that you can see the 'loss' or 'overhead' of just turning the shaft with no load.
It depends on the size of the motor. If its a large motor, and 3-phase is available, AC wins. Small motors, where speed control is needed, DC wins (Induction motor speed control is possible too, but easier with a DC motor, just turn down the field current for more speed.). it depends on the motor/application.
I am not sure this is always true. A DC motor can be just as efficient as an AC motor. However a 3 phase induction motor as used with AC drives is likely to be a lot smaller and less costly than an equivalent DC motor. In larger DC motors it is likely they will have a field energised by DC, which is up to 10% of the motor power, and the electro-mechanical commutator is probably less efficient than electronic commutation. The speed control system used with a DC motor field may or may not be less efficient too. So the AC motor is smaller, cheaper, has less maintenance (no commutator) and does not need a field with wasted DC power. If it has a permanent magnet field, and electronic commutation/speed control, it should be just as efficient, but the distinction is becoming smaller.
Because AC slip rings are more efficient than a DC commutator
You have answered your question! AC drives are not more efficient than DC drives. AC motors has slightly better efficiency than DC motors. These margins are small, and measuring power savings is not easy. People replace DC motors + Dc drives with AC motor + AC drives mainly because 1. DC motors are getting obsolete, difficult to maintain and expensive 2. AC motors are rugged, cheap and easy to maintain With Vector controlled AC drives, its possible to get close to DC drives's speed-torque performance in an AC drive. So, power saving is not the right reason for changing to AC.