Recently the screen of my KP57WS510 got damaged (yeah, I screwed up!) so I parted the set out. While selling the D board I found something interesting - though the service manual only shows the 57 & 65" sets using the A-1302-180-A board it seems the 51" sets did too. In fact the lady I sold my board to had 51" set. In doing some research I found the following:
KP51WS510 starting with serial number 8000001 use D board A-1302-708-A
KP51WS510 starting with serial number 8700001 use D board A-1302-180-A
KP57WS510 with serials below 9000001 use D board A-1302-708-A
KP57WS510 starting with serial number 9000001 use D board A-1302-180-A
KP65WS510 with serials below 9000001 use D board A-1302-708-A
KP65WS510 starting with serial number 9000001 use D board A-1302-180-A
Regardless of model, all other serial numbers not starting with 80 or 90 use D board A-1302-180-A
As always, it's best to confirm the board in your set before purchasing another one - consider this as a rule of thumb.
Take Care,
Steve