Good that you are planning on building one of these systems. Given your description, I am pretty certain that a 3kw system will be sufficient. Did you get this figure by adding up the power consumption of all the devices that you plan to run? If so, great, even better if you plan to build in a little reserve.
On to more technical details. In order to get to the watts output, you first need to know the voltage and amperage. You know the voltage (12v) so the amperage will need to be 250 amps (volts x amps = Watts, or in your case, 12v x 250 amps = 3000 watts).
You can find battery inverters that can easily bump your 12v dc output to 120v ac, ignoring losses, by pumping your voltage up to 120v, your amperage will drop to 25 amps. Again, this is perfectly possible and the components are certainly easy to acquire.
But now the elephant in the room
What you have not told me is how long you want the battery bank to last. Is this for 1 hour, 10 hours, 10 days? I don’t know what exactly you need but I will run a couple of specs past you.
I am looking at building a “solar generator”, which is essentially a battery bank and hardware mounted in a case and charged by solar
panels. The build I am looking at is similar in basic respects to your needs. It is based on a 3kw inverter, so it has 3Kw output. The build I saw was powered by a 50 amp-hour 12v battery. The amp-hour (ah) is a measure of how long your battery will run on 1 amp of current output. The basic equation is similar to what we had above.
Volts x amp-hours=watt-hours output OR
V x AH = WH output
In my case, the equations looks like:
12V x 50AH = 600 WH output.
After converting to 120v a/c and ignoring losses, it looks like:
120V x 5AH = 600 WH output.
We get the same output because our increase in voltage is checked by a proportional loss in amperage.
So practically speaking, let’s make up some numbers. The above build would theoretically run 1 watt for 600 hours, 10 watts for 60 hours, 600 watts for 1 hour, or 1200 watts for 1/2 hour or 2.4 Kw for 15 minutes.
Now I personally think
that any battery build of this sort should be based on a 100AH battery at least, so one 100AH battery should double the run times listed above, 2 batteries should quadruple, and so on. I don’t know what your power load looks like or how long you need to run so I cannot give you exact numbers, but I will start with a build based on 2 100AH batteries.
Another factor that needs consideration is the exact battery chemistry. Don’t use car batteries as those are designed for huge amp output for s very short period of time—exactly what you don’t want.
The next (and cheapest) option would be a Sealed Lead Acid (SLA) battery. These are not too expensive as batteries go, but come with the hitch that they should avoid discharging over about 50% or the battery itself can be damaged and not charge properly again. This means that whatever the AH rating of the battery, cut it in half. The next cheapest (and in my opinion a good option) is the Advanced Glass Mat (AGM) deep cycle batteries. These can be discharged all the way to zero without harming the battery. Another option is Lithium Iron Phosphate which can be recharged a great many times. Avoid Lithium Ion batteries as they can only be recharged a limited number of times and confer no real advantage unless the battery pack needs to be portable. If it were me, I would go with the AGM battery because it is a reliable, mature technology.
Unfortunately I can’t go much further than this because I don’t know the run-time you need. If you can give a more specific run-time, we can talk more.
Food for though,