When I have my MacBook Pro 10.10 connected to the AC Power my external display connected through HDMI works fine.
As soon I disconnect the MacBook from the AC Power and start running on battery, my external display turns off, even the MacBook is not sleeping.
How to avoid external display go off after I unplug my MacBook from the AC Power?
I unplug the power connector and external display goes off immediately if I have the lid closed.
The laptop is still awake, I can test that because it responded to the ping.
I plug in the power connector and the external display turns on immediately, but the screen is locked, so I have to type my password.