Soft starters are usually less expensive than Autotransformers Keith, just so you know. At 45kW though it might be a toss up, however I don't know a lot of manufacturers who keep 45kW RVATs readily available.
Relaxjack, the type of starter you select depends on what your goal is.
Reduced Voltage Auto Transformer (RVAT) starters can provide the best bang for the buck in terms of line current to motor current because of the transformer action. Their limitation is in that they only have 3 steps of adjustment, 50, 65 or 80% voltage so if one of those doesn't work you have to take a big step to the next size up and that means more torque that you may not need. They also trade one big torque hit for two smaller ones, not as good for the motor as soft starters. Lastly they are very large and heavy and have a limited starting duty, usually much lower than the motor they are controlling. I only recommend RVATs when there is a severe problem with voltage drop or an undersized portable generator.
Reduced Voltage Solid State (RVSS) have infinite adjustability so they can be tuned to provide a very smooth transition-less acceleration, no excess torque (unless you want it). They are best for the load and motor, but motor current = line current, so they are a compromise when it comes to their effect on the incoming line voltage. Still, most people get along fine with them. They take up less space and floor weight than RVATs and typically have the same or better starting duty as the motor. They also cost less than RVATs (unless you are shopping poorly), and if you have a pump, they can be very handy for soft stopping to reduce water hammer. RVATs can't do that.
Forget Start-Delta, too many potential problems. I know that lots of people use them, but that's just because they are cheaper than RVSS. If they really knew what they are doing to the motor, power train and power supply they would run away.
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