Never work on any electronic equipment while plugged in. While the ground plug in your wall may be grounded it may not have the same potential as your electronics.
What you want is the same electrical potential. Place your board on a anti-stat surface ( a motherboard bag works well) if you have a wrist strap ground clip it to the bag, if not keep skin in contact with a metal surface or the bad while working on your device, static builds constantly. If the system is in a case rest an elbow on the metal power supply.