Power swords likely tap into a power source similar to what is used to power a marines armor. In Omnibus it makes mention of there being a compact fusion reactor within the confines of a marine's backpack. If that's not enough power to power up a weapon, I'm not sure what is.
"There is a cancer eating at the Imperium. With each decade it advances deeper, leaving drained, dead worlds in its wake. This horror, this abomination, has though and purpose which functions on an unimaginable, galactic scale and all we can do is try to stop the swarms of bio-engineered monsters it unleashes upon us by instinct. We have given the horror a name to salve our fears; we call it the Tyranid race, but if it is aware of us at all, it must know us only as Prey."