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Respectfully, I recommend thinking twice before getting an EV for the purpose of backup power for the home. I say that as someone with now a few years of experience with an EV (2022 Hyundai Ioniq 5, with 82K miles) as well as 4 years of experience with decentralized solar as well as home battery backup (mainly to power the home through the night to usually not pull power from the grid, but I use it for backup power when the grid is down too).

My EV has the V2L (vehicle to load) that you mentioned but only as a single 120V outlet. I've played with it to test it -- good as advertised. It doesn't have the bidirectional charging to power the home (unless I ran backup power from the V2L for one extension cord to power lights or a small appliance). But for this post I'll pretend it does do bidirectional charging for whole house power.

Here's why an EV wouldn't be good in most cases for battery backup (compared to home battery storage).

1) Us EV owners are encouraged to charge the EV at night both to limit how long it holds the charge (keeping it at 50% to 60% is optimum for reducing wear, so if you come home with that much charge, don't charge it immediately to the recommended 80% to give you plenty of range for driving the next day, set the timer to charge it to 80% shortly before you leave for work). The other reason is that some power companies give you a discounted rate at night as an incentive to encourage you to shift your grid demand to when the grid is least being worked. (i.e. if you want to lower your power bill, whatever the EV charge is when you get home don't charge it until night time) End result: when the grid goes down (here that's usually during an early evening storm) your EV is probably not charged much anyway to give you backup power.

2) The other reason is the EV's battery warranty is probably not as long or as deep a discharge as home battery warranties. My EV battery is warrantied for 10 years, guaranteed to not degrade faster than a linear progression to holding 50% as much in the 10th year. My home solar batteries are guaranteed for 19 years / 50%. (Some newer home batteries have 25 year/70% warranties.) Also, the recommended top off charge for my home batteries is 100% (suggested not to drain them below 20%, though I usually cut it at 30% before I start pulling from the grid, and drain them to 20% only if the grid is down). With the EV it's usually recommended 80% to 20% (unless you're about to head out on a long trip and charge it to 100%). So even if my EV's battery capacity (77 kWh) was the same as the home battery stack (90 kWh), I can still get more regular goody out of the home batteries (100% - 20% = 80% recommended regular use) than I can from the EV battery (80% - 20% = 60% use). Unless of course you knew a storm was coming and charged the EV to 100% immediately to be ready for power outage, as long as you didn't do it regularly (don't have the EV's battery sit at 100% all day except for the few hours you're on the road driving it).

Full disclosure, for the statements above, I pretended I didn't use solar to charge my home batteries, again to save on grid pull and lower my power bill. This post is pretending I'd use grid power to keep them 100% charged all the time -- as part of the discussion for home battery vs EV battery for backup power. In real life I use my home solar batteries for both lowering my power bills (thus I drain them some at night and on heavy rain days) and for backup power. But the math is too complicated to post here on how I achieve that balance of leaving enough charge in the batteries for grid backup while draining them enough to keep my power bills averaging $65/month in my all-electric home, including charging the EV for 1,500 miles/month home charged miles, and doing most of the EV charging during sunny days and not charging it on rainy days unless I have multiple rainy days in a row with little free solar power coming in.) If you want to do what I do, it's an absolute must that you first do your homework for your particular use case to make sure solar and/or battery storage and/or EV is good for you. (We also have a gas pickup so we don't have to be fully devoted to EV tech. But it's nice driving 18K miles per year on home charged miles with a $65/month power bill and not worrying about the left's warmageddon doomsday cult raising energy prices and messing up my retirement financial planning, at least not our energy expenses.