It depends a bit on what kind of lights you are using: strobes or incandescent or LED.
And how much current you need.
Do you plan on one big power supply for three lights, or three smaller supplies—each one supplying a single light?
You may not need a pure sine wave inverter.
Most strobes take in 110 or 220 volts and change that to a higher voltage DC for the flash tube and a lower voltage for the trigger circuit. Square wave or modified sine wave can work just as well as pure sine wave. Ask the manufacturer.
I’ve run my computers, printers, and battery chargers on inexpensive (not pure sine wave) inverters in my truck and car for years. I’ve only once encountered a case where a pure sine wave inverter was actually needed to operate a delicate sound meter used for acoustic testing.
Incandescents and LEDs don’t need pure sine wave. If you want continuous light you can just buy 12 volt light bulbs, run ‘em off a car battery, and forget inverters completely. Consider LED or halogen automotive headlight bulbs.
How many watts, or amps, do your lights require? How long do you need them to run? That will determine battery size and weight.
Circuits for battery chargers: You can find plenty more on pinterest or just google them. Here is one link I’ve saved for future reference, but haven’t built yet.
https://pin.it/44bK12eEvery time I’ve started a battery charger project I have found surplus wall warts for far less money than the components. Shop at surplus electronic purveyors and you’ll find ‘em cheap, too. I paid $3 to American Science And Surplus (
www.sciplus.com) for my last 6 volt battery charger. They are up to $3.25 and $3.50 now.
https://www.sciplus.com/adapter-12vdc--17amp--55mm-female-center-positive-plug-61747-pFor 12 volts it is hard to beat the trickle chargers from Harbor Freight when they go on sale. I think my last ones were $7.
There are plenty of battery options. If you want to go with an off-the-shelf inverter, then select batteries that give you 12 volts. That could be a sealed lead acid motorcycle battery or a car battery, or a lithium battery from a 12 volt cordless drill.
Again, I frequently hit American Science and Surplus for batteries:
This is what they currently have:
https://www.sciplus.com/12-volt--8ah--ub1280--51516-x-31116-x-2916-new-47434-pBattery prices have been going up. Last time I bought, these cost half the current amount. For comparison, the same size 8 AH battery for my motorcycle would cost me $85.
Car batteries are relatively cheap, available, and easily charged. Make a nice box and bolt it to a hand truck. You can carry your lighting equipment on the same handtruck and wheel it where you need it. The car battery provides enough weight so that you might eliminate a light stand—just use a pole mounted on the handtruck to hold light, softbox, boom, or ??? whatever else you are using. This also can eliminate a cord between the battery power and the light.
If you are building your own inverter, design it around an easily obtainable battery type. Eventually you’ll need to replace it.
Circuits for inverters I’ve seen seem to use the 555 chip—probably ‘cause I’ve been reading about other uses for that timing chip.
The chip is cheap, but if you need the power equivalent of a wall outlet (1200 to 1500 watts) the transformers tend to be expensive. You might be able to salvage something from old computer power supplies.
If you want 1200 watts at 120 volts that is 10 amps output—but your input from a 12 volt battery is going to be 100 amps. That will be a big wire! Welding supply dealers sell the large gauge wire. The variety used for welding is more flexible than what is sold in hardware shops.
Cheapest option I’ve found though is jumper cables for cars. Keep, or discard, the clamp connectors that come with them, but a cheap set of jumper cables costs less than the wire alone.
Have you looked at the UPS (uninteruptible power supplies) sold for home and office computers? They typically have 12 volt, 8 amp hour, sealed lead batteries; a built in trickle charger; and a sine-wave output that is good enough for computers—which are actually pretty tolerant. They usually get trashed after 2 or three years when the battery dies, so you might get one for free.
I rewired one at my house to use a larger capacity (20 amp hour wet-cell) battery for a garden tractor. Many put out 300 to 500 watts, or more.
Good luck with your project.