Running AC on [an inverter] is rich man's game – HaldorEE2)
Understood, we all would like to do that. We wish it were simple and inexpensive enough to be common. It's not common. Some folks do have A/C but the great majority of them are getting power from a generator or shore power.
Unfortunately, if you are reading this you probably haven't done the math. Prepare for some unpleasant news, because at this point you may not be familiar with:
And that's just considering running the unit in optimum solar conditions in the daytime. Running A/C at night requires a magnitude increase in battery bank. That is either $$$, heavy, or both.
One exception to this dilemma is available if you live in the desert; swamp coolers do a good job of cooling in areas of low humidity. They use very little electricity but a great deal of water.
That's right. People also make 200mph Pintos and 20ft tall bicycles.
There are people with an in-depth understanding of the issues, and the money and space to make it happen. It does not stand to reason that the average person with average resources and commitment will make the trip from idea to implementation.
If you would like to learn more about how it's been done before, start with this post by trebor then check out posts by people who have done it:
Also see this thread on DC A/C options.
RVs and travel trailers typically power their single A/C off 30A (3,600W) shore power, and sometimes can't run that and a MW at the same time depending on other loads. Dual A/C typically runs off 50A (12,000W) shore power.