You can throw mathematics around all day long, I know my own experience, my battery and inverter lasts for at least 5 hours
I believe you.
The issue with some of the responses here, the way I see it, is that:
1) They may talking about recreating the same levels of bass that you'd get at a 'proper' gig.
2) They see a 200W amplifier and are looking for ways to power the amplifier at max output, when in reality you are unlikely to be using anything close to that number.
Years ago I needed battery-operated amplification. My band wanted to busk at the beach, at a couple of parks and on several spots around town. We've got a busy annual festival here and the regulations about street playing are relaxed somewhat and it's a lot of fun plus we actually get a few gig offers while we're at it, sell CDs etc. It's a nice experience.
I considered going the inverter+battery route and use my little MarkBass CMD121P, as the battery opeated amplifiers I could find were either too small, or too expensive for what might have been a one-off thing (it didn't, we did it a lot over the years, but it could have well turned out that we do it once and never again). I found the info very confusing... some argued I needed huge batteries and it just became too big and heavy, and I just didn't have enough experience to judge what I really needed.
I ended up trying a cheap solution. One of those 'portable PA' units. A QTX QR10PA. It's less than 10Kg, reasonably small, various inputs including USB. The wireless mic was quickly discarded, but the unit itself is not bad, and the box made of some kind of plastic that takes bumps and scratches pretty well. It's rated at 100W with a built-in rechargeable battery of some sort.
I presume the 100W rating is very optimistic... but the truth is, in practice, this thing is more than loud enough, and I don't turn volume to max either. However, see point #1 above: no, it's not the level you'll expect at a festival or an indoor gig. Of course not. But it's a very good volume to play outside with the band in a city environment. People can stand a good 10m-20m away and hear what we do very well.
The band? It's a ska/funk originals type of band. Not exactly coffee-house chilled quiet.
* 3 guitarists with a Roland MicroCube each.
* 1 drummer, using just hi-hats and snare for portability. Sometimes he'd use a small bass drum. Or sometimes he'd use a cajon and we'd mic it and put it through my 'portable PA' thingy (I bought a battery operated 4 channel stereo mixer for around £30 too).
* myself on bass
* 2 trumpets and 1 sax, no amplification
* 1 main vocalist (sometimes 2) who either used his own little vocal amp, or put his mic through mi miniPA unit too.
That was good enough for several hours. Definitely 3-4 hours. Guitar amps tended to run out of juice after 3h. Sometimes I noticed my amp started to distort a bit when pushed, indicating battery was starting to suffer, but turning down bass EQ would sort that.
So, judging from that experience, I imagine your solution is a pretty good one for the stated purpose.
If you want 'proper' outdoor gig type of levels, then yeah you're going to need a lot more power but it didn't seem to me like the OP was talking about that kind of situations.