The math is good so far, but a 3KW system will probably disappoint. The reasons:

1. Solar panels are rated for best case scenarios, like clear, sunny days, all day, every day. At the equator.
2. Looking at my brother's solar production data, averages in the summer were about 2-3 times the averages in the winter.
3. Inverters are not 100% efficient. Mine are rated at 93% and the newer models that replaced them are less than that.
4. You have kids. ;-) Usage does vary from day to day.

Still, having said all that, if you only want to put a dent in the electric bill, then 3 KW may be just fine. Solar panels are getting cheaper all the time, and if you decide later you want more, the cost to expand should be even better than now.


Peter