You Do Need power plug adapter while traveling from Libya to Abu Dhabi.

Here is Why You Need An Adapter

The outlet and plug type used in Abu Dhabi is G and in Libya are C and L. This is how they look like.

Libya

In Libya, outlets of type C and L are in use.

Type C

Type L

Abu Dhabi

In Abu Dhabi, outlets of type G are in use.

Type G