Just thought it worth mentioning that Lead-Acid rechargable batteries like a raw recharging supply. In other words, rectified but unsmoothed. The battery itself will have a smoothing effect on the supplied voltage but that is irrelevant. Look at the battery recharging circuitry in a vehicle and...
It has nothing to do with the circuit operation. A polarised capacitor needs a net voltage applied in the correct polarity to maintain the electrolytic. This circuit is AC so a non-polarised capacitor is required.
The line-to-line voltage of a three-phase system is √3 times the line to neutral voltage. This quote is taken directly from the following website.
http://en.wikipedia.org/wiki/Three-phase_electric_power
Another interesting website is...