Disable power nap when not plugged in

Power nap is a good idea when my laptop is plugged in at night.

However I notice that it also happens when it is not plugged in.

When I wake up in the morning I will immediately notice some emails in Mail.app which are from 2am. Then after a few more moments it will connect to Wifi then I will get all my emails.

I am not sleep walking. The computer is not plugged in. Is this behavior documented? Can I turn it off?