Generally, motor designs have a +-10% tolerance, but generallyyou see it the other way around; a motor will be designed for 4000V and connected to a 4160V source, because the lower design voltage makes allowances for some additional voltage drop when you have a long distance from the controller and the motor. If your motor is truly designed for 4160V and you truly have only a 4000V supply, then it might be OK, but you will have very little tolerance for any additional voltage drop.
So the real answer is; it depends on other factors. The best people to ask will be the motor mfr., and give them ALL of the information, i.e. motor lead length, conductor size etc.
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It depends of the load. If your load requires 100% of the motor capacity connecting on lower voltage will pull higher than rated current. If you do not require full capacity you should not have any problem with lower voltage.
So then was your original post a dyslexic error and you have a 4000V motor and a 4160V supply then? If you do, you are golden; this is normal.
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