Detect if powered by battery or USB

[zBart]

I was wondering if there is some way to determine if the device is currently powered by a battery or via USB. For example: to show a charging indicator, or to change how often I put the device into sleep.

Also, is it possible to wake the device when USB power gets plugged in while the device is in deep sleep? For example: battery level gets below X, I show a message and put the device into sleep for a day, but when the power gets plugged in I'd like it to wake up instantly (so I can show a charging indicator).