I have been using an old iPhone 4S as a navigation system for the last year. Just wired up one of those cig lighter USB supplies to power it. No problems keeping it charged.
Smartphones use all manner of information for navigation--cell towers, publicly known wi-fi networks, and GPS satellites. Satellites are more power consuming, but when I was in some pretty remote areas where there was no other source of location info, the phone still stayed charged as long as it was plugged in.
Haven't had much luck finding an app that meets my needs and wants, though. Rever is nice when it works (especially with offline maps), but it still seems like it's unfinished and needs further debugging before it's a product. InRoute (highly recommended by a BMW magazine a couple years ago) is limited, is completely dependent on having a cell signal, and seems to use the magnetic compass in the phone for direction info... which means oddly tilted displays at times. Maps.me is free and self-contained, but too limited to do much more than show me where I am so I can navigate with paper maps. I wish they made MapFactor Navigator for the iPhone, as it would be about perfect for my needs. I'm getting close to the point of buying a cheap Android phone and using it as a dedicated GPS.