Hello rraghunath
First, I assume that you mean "reduced voltage starters"
You can apply a reduced voltage starter to almost all applications, but the limitation is that the motor must be able to develop enough torque to accelerate the motor and load to full speed before changing to full voltage.
The torque reduces with the square of the voltage reduction when a reduced voltage starter is employed.
You have nominated two reduced voltage starters and also mentioned open and closed transition starters.
Both of the starters are possible in both open and closed transition, but you should never see an open transition auto transformer starter because a closed transition can be produced for the same price.
An open transition starter has a major problem. There is an FAQ on this subject. faq237-613 The switching transient can cause significant damage electrically and mechanically over a period of time.
Cost wise, the open transition star/delta is the cheapest and has severe transients at change over. A closed transition star/delta starter is more expensive and if it is done correctly, will have lower switching transients. The start torque of the star/delta starter is one third of the full voltage starting torque of the motor and can not be altered. The closed transition star/delta starter can be effective for high inertial loads where the start toque required by the machine is purely inertial.
The auto transformer starter is almost always closed transition and so does not have the switching transient. The start torque can be set by the tapping used on the transformer. Transformers for frequent starting or high inertia loads are expensive.
I would recommend that you also consider a solid state soft starter as an option.
Best regards,
Mark Empson