have your battery tested first, then test the alternator, could be the internal voltage regulator,
but the last time this happend to me, it was the batt. and without getting into too much mechanical detail, the alternator needs voltage to work, if the batt is failing, it causes voltage drop as the alt tries to suck power from it so it can charge. i know it sounds strange, but that's how it works.
but anyway, test your battery first.
-Lance