Need to upgrade circuit breaker from 20A to 30A
I have been having a problem with my heat pump unit. I live in a new house, and it worked fine for the first two years I've lived there. Lately, the circuit breaker to the outside unit has started tripping regularly during periods of extended use (i.e. hot in summer, cold in winter).
I've had an HVAC technician come out and test the unit, and everything is fine. He brought up that the panel on the heat pump itself lists 30A max, but the breaker installed is a 20A. He suggested I replace the 20A with a 30A.
I have no problem doing this, as I've already replaced the 20A breaker once (thinking the breaker was the problem.) My question is:
I have one main breaker panel, and a sub-panel. In the main panel, I have two mains (connected together) each at 200A. If I add up all the breakers in the main, I come up with 390A. One of those, of course, is a 100A to the sub-panel, which contains 80A worth of breakers. Thusly, it seems simple enough, I have 390A, if I change the 20A to a 30A I'll have 400A, and the main seems to be able to handle 400A.
It seems a little too simple. Is this an accurate way to figure this? Can I put it the 30A in place of the 20A? I also need to check the gauge of the wire, I understand, but I'm not sure exactly what it should be. There seem to be a lot of different opinions, which is odd, but my guess (or average of those) would be for a 30A, I need #10... for a 20A, #12. Is this correct? I'm hoping that (as the evidence suggests) the house builders put it the right wire but the wrong breaker.