How do I start a motor in star delta connection?

If you reverse direction while running, your contactors must be AC4 rated. Not only will the mechanical load take a hammering but the coupling and the rotor too. When you buy your motor you need to state this requirement under duty cycle and chose 7, 8, 9, or 10. There would be a second timer to allow the motor to stop and then restart in the other direction. The timer on the star delta should not be changed once set. As the torque reaches maximum in star, you change to delta. Modern Motor Protection relays are able to do this from the motor data and you don't set a time but allow it to switch itself on current. ABB and WEG UMC electronic relays do this. Others will also do it.
induction motor
Please be careful when using the four contactor version that people seem keen on. Have you ever had a star delta set that sometimes trips when it changes to delta? Check the power wiring. The rule is Red in Star must connect to Blue in Delta. The first link does not show the windings but I bet that's what it does. This is because when you are running in star and the changeover takes place, during the transmission, when there is no driving force, the rotor slips back slightly. You want the phase to drop back into the delta phasor. If you do it the other way, it is required to pull up to catch up to be in phase, draws extra current and then trips. The overload is then turned up to avoid this and the protection is then compromised. With four contactors one way will have this problem. Further to this, the star and delta contactors are required to be mechanically interlocked. This is not shown on the first drawing either. This is a circuit where it is possible to weld in a contactor. Without the mechanical interlock, it is possible to electrical close the contactor while the other is in. Think to yourself, why did someone do this? Am I cleverer than these engineers? Generally there will be an answer. No one throws away money for nothing without a reason.

I tried three times to download the Eaton Book of 14.03MB and failed. TAB. That's Africa Baby. Just as I went to post this it came through (Thanks John). I don't like it. I was instrumental in the above change with Klockner Moeller and Siemens in the early 80's and I thought we have agreed. They did change the diagrams at that stage. I think read the above and make up your own mind.

Finally I see a lot of people stating use a variable frequency drive (VFD). Not required if you don't require a variable speed or a speed that is not nominal. A VFD is less efficient than DOL or Star Delta. A soft starter on the other hand has a build in by-pass contactor and thus is the same efficiency as a DOL and better than a Star Delta with better protection unless you are using an electronic protection relay. If you are using electronic overloads, the soft starter will be less expensive than a star delta.

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