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

Here is Why You Need An Adapter

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

Turks and Caicos Islands

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

Type A

Type B

Luxembourg

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

Type C

Type F