why is it the alternator output voltage increases with capacitance loading?

Answer 1

The voltage does NOT increase with a capacitive load.
The Power output WILL increase with a capacity load. Because putting a/c power on a transmission line thru a transformer creates and inductive load, by shifting the voltage wave ahead of the current wave. And; the only way to move the voltage wave and the current wave back into synchronicity is to introduce a capacitive load. The power loss due to this wave shift is expressed in the "power factor" and measured in VARS (volt-amps reactive). So if you have more questions on this subject you should look-up "power factor" on the web or in a book.
Hope this helps,,,

Answer 2

A car alternator initally creates AC which is then recitfied into DC.

The rectified DC is not smooth and constant like the voltage from a battery. Instead the DC has peaks and valleys givin a varying unidirectional voltage. You can tink of it like a small AC component riding on a DC voltage. This AC portion of the DC is known as ripple.

The peaks and vallies of the ripple are averaged out when measured by a voltmeter. Placing a capacitor across the DC will filter out the ripple. The Capacitor will stor a charge based on the peak voltage applied to it. Then discharges this charge as the voltage starts to fall off. The net result of filtering is NOT an averaging out of the AC ripple but a Voltage support of the peak voltage supplied across the capacitor.

The voltage support is deppendant upon the charge stored on the cap and the rate at which the charge is drawn off. So adding more capacitance provide more charge storage capacity and extends the voltage support. Also minimizing current draw removes the charge more slowly extending the voltage support as well.