You Do Need power plug adapter while traveling from Luxembourg to Turks and Caicos Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Turks and Caicos Islands are A and B and in Luxembourg are C and F. This is how they look like.

Luxembourg

In Luxembourg, outlets of type C and F are in use.

Type C

Type F

Turks and Caicos Islands

In Turks and Caicos Islands, outlets of type A and B are in use.

Type A

Type B