Is a VFD cost effective , I have no idea ?
Don
If you don't already own the motor and are designing new so that you can use a 3 phase motor from the get go, then yes, a VFD is often a cost effective way to do this at 3HP 230V and below. Single phase submersible pump motors are not as simplistic as surface mounted motors; the capacitors for starting it are usually too big to go down the hole with the motor. So what they do is put the caps up on top in the "control box" and use a voltage relay that looks at the motor back EMF to determine when to switch the starting cap out of the circuit with a contactor. All that added apparatus helps offset the added cost of a VFD and a much simpler motor arrangement.
But to use a VFD, he would have to buy a new submersible motor as well as arrange to have it pulled and replaced (not easy or cheap on a 400' deep well), and he already owns the single phase submersible motor that is already at the bottom of the hole. So I don't think the VFD option is as viable now as just getting a better generator.
Most likely, as I think about this to write that answer, the TYPE of submersible and type of genset might be the culprits here. Some smaller inexpensive portable generators now use a relatively inexpensive engine with a crappy little governor (if any) and an inverter to create the regulated AC output at a constant frequency. But those don't do as well with motor starting loads, that's why they use the marketing term "surge capacity" rather than specifically SAY "motor starting capacity", because it kind of hedges their bets. So it might work OK starting a regular single phase motor with an old fashioned centrifugal switch, but might be troublesome for some types of submersibles. There are two types; "2 wire" and "3 wire", referring to the number of wires (NOT including the ground) that are going down the hole to the motor. In basic "3 wire" motors, there are 3 hot lines going down the hole; two for windings and one from the capacitor. What happens, as kwired already said, is that there is a potential relay in a "control box" at the top of the well. The voltage relay reacts to the back EMF of the motor and when it gets to speed, the relay drops out, removing the start capacitor from the circuit. From my experience those work fine on all types of generators and solar inverters, etc.
But on some submersibles sold as "2 wire" where the caps and controls are on the motor (and even some 3 wire versions with "solid state" controls), the relay is not a simple electromagnetic device, it is a solid state device with sensors etc. With the inverter output from the generator, it may be interacting with the solid state sensors and the device fails to respond correctly, therefore never taking out the starting cap. I know that I have seen that kind of warning on solar inverter based systems for submersible well pumps, telling you that you must get rid of the solid state controls and put in old fashioned voltage relay based controls. Look for info on the pump and if anything says "solid state", I'd be very suspicious.
