I am having a problem I believe with voltage drop .
i have a 4160 volt service supplying a 7000 hp vfd, on that same service I have a 4160 to 480 volt transformer providing power to several cnc machines . When I rack the breaker in for the vfd I get a low voltage alarm and the lights dim for a split second . I am considering a capacitor bank on the 480 volt side. Any thoughts if this will cure my problem
You likely have a Voltage Source Inverter (VSI) MV drive. All VSI drives have a system referred to as a "pre-charge circuit" that limits the capacitor charging current, otherwise that can damage the front-end rectifier components, as well as the capacitors themselves. It's remotely possible that your drive has a failure in that system that is taking place, so you might want to call the VFD mfr for a PM service call to be sure.
But also, a lot of modern MV VSI drives are built to mitigate the severe harmonics that are caused by them and will do so by using a "multi-pulse" front end rectifier design. That system uses a specially wound transformer arrangement to take the incoming 3 phases 4160V and create 9 phase (aka "18 pulse") or 12 phase (aka "24 pulse") output, with each set of 3 phases separated by a 20 or 15 degree phase shift from one to the next. Each set of 3 phases then goes into separate rectifiers and converted to DC, which are all then combined (in various ways) to recreate the 4160V 3 phase output to the motor. So in this case, even though there is a pre-charge circuit for each rectifier, it doesn't actually help with this issue.
There is still the magnetic inrush current of the big main transformer input itself when you close that breaker (assuming that you rack it in, THEN close it).
Bottom line, unless there is a problem in the VFD pre-charge circuit(s), there isn't much you are going to be able to do about it now. If the dip is brief, I wouldn't worry about it, it just comes with the territory. If on the other hand is is causing shutdowns and lost production, then someone might want to consider a alternative type of VFD that will not cause that.
PS: Do not add the cap bank, you are asking for more troubles and it likely won't help anyway.