They quoted a 2 battery installed system at $22K (before the 26% (credit). depending on what you want to power during an outage and for how long, 1 battery could be sufficient, so that about $16K for 2 batteries totaling 32KW of power after the tax credit.

You know this but make sure you're using the right units! Battery storage has two measurements, current (instantaneous power) and energy (average power).

If you have a 100 amp service from Xcel then you have roughly 12 kW of potential capacity for your loads but you actually don't consume that much constantly. Say you actually consume perhaps 2 kW on average which means over a day you consume 2,000 watts * 24 hours = 48,000 watt-hours = 48 kW-hr. Xcel charges you by the kW-hr, about a nickel to a dime per kW-hr, so that would have cost a couple of Dollars.

You and/or your installer probably already went through the calcs but for people not electrically-minded when I look at my house our furnace consumes 10.5 amps, so roughly 10.5A * 120V = 1,260 watts. Our deep freeze about 2 amps running, so roughly 240 watts. Our swamp cooler draws 14.9 amps, so about 1,788 watts.

You go through all your loads this way to get your total load. Whatever you think might be running at the same time needs to be accommodated. So you'd want the fridge, freezer and HVAC to be able to run at the same time. But if your clothes dryer or TV puts you over the limit that's inconvenient but not critical. You could wait to do laundry at night when the swamp cooler isn't running, for example.

So in my pared down example I'd want at least the freezer and the swamp cooler to be supported, so 2 + 14.9 amps = 16.9 amps * 120V = 2,028 watts = 2 kW minimum load capacity.

If the maximum load is 32kW then I'm well within that limit.

But that's only half the story. You have to figure out duty cycle, e.g. how long something's expected to run. Our swamp cooler runs constantly most of the day so 100% duty cycle for about 10 hours over a 24 hour period. The freezer runs about 10 minutes every half hour or so, thus 33% duty cycle or 8 hours in every 24. The furnace might run for 15 minutes at 50% of the time when it's cold, so 12 hours every 24.

So to know how much storage you need add them up. Just doing the math for summer.

Swamp cooler is 1788 * 10 hours = 17,888 watt-hours = 17.9 kW-hr

Freezer is 240 * 8 hours = 1,920 watt-hours = 1.9 kW-hr

That means every day I need 17.9 + 1.9 = 19.8 kW-hr for these two things and therefore a 32 kW-hr battery bank will run me for 1.6 days without sun.

So when getting quotes make sure to ask for clarification whether it's 32 kW load it can support (there is a maximum current any battery can safely discharge, which you must fuse to protect against) or 32 kW-hr of energy stored.

If it's both that means it can supply its full load capacity of 32 kW for one hour or any combination otherwise, such as 1 kW load for 32 hours. I assume it's 32 kW-hr they mean because 32 kW at 120V means 266 amps. If your inverter is converting perhaps 48V DC that would require around 665 amps from the batteries, which is patently ridiculous for a residence, but could be the case if you're running an off-grid welding shop or something like that. At which point you'd step up to a completely different class probably using 96V up to perhaps 192V DC battery buses and a 10 kW inverter the size of a kitchen fridge.

Bottom line is knowing your instantaneous load (

*especially* surge currents) is crucial for sizing the inverter. Knowing your average load is crucial for sizing the battery bank.