I basically have to agree with everything MTBDOC has said.
20kW with 240AH @ 12v is just so-wrong, that's only like 8 minutes of runtime at full power (at best), and that's like a 10C rate.
It needs to be a MUCH higher voltage, and potentially more AH too.
I too am building a solar equipped HT (just the low-power equipment though: lights, projector, tv, computers, bdplayer, DSP/DACs etc)
Even though my solar system is 100% DIY and only rated for 1kW RMS it's still ending up costing me like 7 grand (to do properly).
Not even the whole house, just the HT room!
Even at this power-level it is still a 24V system, and I'll still need like untold amounts of AH and potentially another 3kW of panels just to sustain this most-basic load.
EMP hardening will cost me an extra 2-3k per 1kW, and reduce the efficiency by about 10%. (A necessary-evil IMO.)
I didn't completely cheap-out on my inverter, and I'm going for top-shelf consumer-grade Li batteries (about ~$12 per AH and electrolyte-less).
Batteries are by-far the most expensive component (if you get the good ones that last / are worth buying.)
Car and RV batteries have horrible efficiencies and lifespans
, you'd be lucky to get 5 years out of a car/rv battery when used in a off-grid install, maybe a few more years if it is only used for fallback-power rather than bill-reduction.
If you stick with cheap batteries, be prepared to replace 600lbs of lead... every 5 years, forever.
and as mentioned, you'll be buying thousands in distilled water to keep the cheap batteries topped. (You may want to run a solar powered distillery in-fact.
I figure even after 10 years use, I'll likely never break-even on my solar.
But I'm not doing it to save money... If I never break-even I'm cool with that reality.
A single space heater can be 1.5kW rms easily.
An HVAC system will be probably closer to 3-5kW rms.
Clothes dryer, dishwasher, toaster, oven, microwave... it just keeps adding up, but luckily you don't run them all at once (and if you do, you'll fry your solar system.) It has to be sized based on the load, as you know. Both RMS and burst.
Anything with a motor in it draw lots of burst power (vacuum cleaner, blender, fans, pumps etc)
Before you switch to solar you'll want to replace every incandescent, CFL and tube-lamp with 100% LED.
You want your load to be as low-as-possible before you dive in.
Energy Star appliances through-out, instant water-heater, energy-recovery HVAC, geo-thermal / heat-pump.
Better / more insulation in your house; more air-tight etc.
Everything that you CAN do, BEFORE implementing solar. (That's how inefficient and non-cost-effective solar is.)
That said / knowing all that...
FULL-STEAM ahead captain, the iceberg is awaiting for us to arrive!