Drives can reduce inrush current. They can manage speed, torque, and up and down ramping at start and stop to suit your application. More options are out there if you look around. Classic motor starters supply current directly to the motor all at once and provide overload protection. That's about it.
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They are not really comparable. Both start an AC motor
DOL is the most basic form. Fewest parts, highest MTBF, smallest package. No other advantages whatsoever. Biggest disadvantage is highest starting current, highest torque shock to the load, uncontrolled deceleration (coasting).
VFD is the most expensive way to control a motor but changes speed, controls acceleration and deceleration infinitely, something virtually impossible to do any other way. If you do not need to change speed, a VFD is a waste of money (unless you have an extreme starting power limitation to deal with).
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Modulating the speed of a motor using a VVVFD can give energy savings that qualify for capital grants under the Carbon Trust's scheme. Such grants can greatly enhance the payback rate on the investment as well as reducing carbon footprint compared to DOL.
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