Phone wakes when unplugged, how to keep it asleep?

I'm trying to charge my phone with an inconsistent power source. Unfortunately, the phone wakes up whenever power stops... Sometimes (often) using more power than is charged. Is there a way to stop the trigger to wake when charging ends? What is the internal name for this trigger? My workarounds so far share the same fault: I can't receive calls. It can't wake if I turn it off, and it doesn't use too much power (usually) in airplanr mode.