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... for running in motor mode it needs 36 Volts power supply.
14 x sqrt(2) x 2 = 39.6 Volts, 36 Volts is not equal but it approaches good enough.
You would normally drive a 14 V RMS motor with DC of about 14 * 1.414 = 20 VDC; you get the factor of 2 by using a push-pull circuit. You could probably use a 24 V battery for this, and maybe overvoltage the alternator a little (if it overheats, just don't use the full voltage available). By using a 6 transistor circuit (you need three drivers, one for each phase), you can regen into the battery without changing the battery configuration (leave it as 24 V).

But remember that the alternator is designed for a voltage such that 14 V is a diode drop over about 87% (from poor memory) of the peak of the waveform. So it would be running at just over 10 V RMS. Three 12 V batteries would be about 2.5x what it is designed for, and being not very efficient, it could well overheat very quickly.

At such low voltages, three single ended drivers might be more efficient, but then you have the hassle of switching the batteries for regen.

I assume that the point of running the alternator as a motor is in a mild hybrid setup. Alas, even 4 kW is so mild that I doubt you'd be able to measure the effect, i.e. it could well be way too mild!
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