RPI2 power supply.

Without any hardware peripheral attached to a Raspberry Pi 2 (RPI2) unit.
No display, LAN connection to WIFI router, RPI2 actually consume not much power (as comparing to normal Android phones).

I have two Samsung mobile phone travel adapter (of same model).   It is rated 5.0V @1.0A, as it is not one for those high-end phone models.  With an AC power meter and USB current/power meter, it shows that the power consumption of adapters can be around 7.5W.  With about 78% power efficiency when full loaded.  So, they have some output capability of about 5.0V @1.15A.

Usually, those phone adapters have no load self cut-off feature, so that it consumes almost no power when there is no loading.

I used this Samsung adapter for RPI2, and do some measurements.  Power is measured using my AC power meter.  Samsung 5.0V, 1.0A USB AC-DC adaptor + 1.5m switched USB cable.

1. 5.0V AC-DC adaptor powered, without connection to RPI2.  AC-DC adaptor is without LED typed.
Power = 0.00W (No load power lost)

2. Just power ON, FTDI USB-to-UART cable connected without logging in RPI2, or just logged in & stayed for a minute.
Power = 1.73W

3. "sudo init 3" command issued, X server shut down.
Power = 1.70W

4. Minutes after "sudo poweroff" command issued, and "[__timestamp__] reboot: Power down" shown.
RED power LED on RPI2 still shown.
Power = 0.55W

When I am typing text in Linux command prompt, the total power usage is only around 2.5W.

The use of 5.0V on RPI2 seems only powers the HDMI part, without HDMI output.  Other part of 3.3V & 1.8V are generated by the on-board switching power buck DC-DC, some input power variation is no problem to the system.  So, I believe a normal Li-ion battery can power the RPI2; providing 3.5V - 4.3V to micro-USB power port should be fine for RPI2's operations.