I believe Tim is correct -- the last para of the TS' original post says it. Put together a (commercially-made) inverter & sealed-acid battery (will need a charger as well), not design and build it from the ground up.
Here's one guy who did just this (all-in-one casing, circuit breakers and all) :
I suppose Sim Lim Tower (there was an earlier reference for inverters from there) is still the best place to look for the component parts you'll need. Don't really know how much you'll save though, and it probably won't be worth the time you spend on putting things together. Also, it would probably be a good idea to ask a friend who knows about these things to look over your plans and make recommendations (pref an electrical engineer)