There's also some other advantages when dealing with the rectification of the AC power to DC, which is of particular importance to EV's. Single phase AC has a point 120 times per second where the voltage is zero and so is the useable power output, this requires capacitors to store energy to produce a smooth DC output. 3 phase by nature doesn't have this problem, if you look at the chart below the sum of the power output at any time is always the same, this produces a smooth DC output.
3 phase when wired in the delta configuration also doesn't require a ground as the 3 phases cancel each other perfectly. Our welders at work operate this way, 3 power wires and a safety earth ground, they also produce an extremely smooth DC output.
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To answer your question, 3 phase is often supplied to farms for a couple reasons. Farms often pull significantly more power than a standard house, well pumps, septic, grain dryers, milking equipment, pumps, etc. 3 phases systems simply supply more energy to power all these loads. The other is many loads require 3 phase power to operate, particularly motors.
For small lower output electric motors single phase works fine, although it does require a start winding in the motor and a starting circuit to get the motor spinning. (think bicycle with one pedal up and the other down, how do get moving if you can only push down on the pedals?). The starter circuit acts 90 degrees to this to get the rotor moving and inertia takes care of the rest. 3 phase motors don't have this problem, they are self starting. The other is vibration, as talked about before single phase goes to zero power 120 times per second, which requires inertia in the motor and whatever it's turning to absorb the rotational vibration. 3 phase doesn't have this issue either, its a smooth output, (think single cylinder engine vs 3 or 4 cylinder).
