I have been asked this question many time by my friends "Can I Run My Air Conditioner on Solar". The short answer to this question is YES YOU CAN. For the longer version you would have to read rest of the article below.
Lets assume that you have a basic unit that is categorized as 1-ton. Now the way Air Conditioners work is that they draw a lot of current at the start, as much as three times the normal steady state current. So a 1-ton AC might be drawing only 1200 Watts at steady state, it may require as much as 3600 Watts at start up. Now there are two ways to solving this problem. Either you can put up 3600 Watts of Solar Panels on your roof and operate your system only when peak sunshine is available. Or, the better option is to have enough panels to run the AC at steady state and use some batteries to provide the initial peak current or power. These batteries will also provide back up after solar hours and when the electricity from the main grid is not available.
One company providing solar solutions in Pakistan recommends installing 1800 Watts of solar panels and 600 Ampere Hours of batteries. So assuming that we have 6 hours of peak sunshine available the solar panels would be able to run the AC for about 6 hours directly on solar energy (assuming an average power consumption of 1800 Watts). After the solar hours the battery would be charged by the main grid and can provide backup of at around 4 hours (12 V x 600 Ah / 1800 W =4 hours). Also one must not forget that to convert DC voltages to AC voltages you would need an inverter and for controlling the charge and discharge cycles of the batteries a charge controller would be needed. Usually the modern solar inverters have built in charge controllers which somewhat limits the costs.
After going through all this technical jargon the question that needs to be answered is "How Much Would This System Cost". The answer to this is around Rs.450,000 including transportation and installation. You might think that this is too high a cost, but think of it this way, even if you are saving Rs.5000 on your electricity bill per month you would have saved enough to offset the cost in about 8 years. And solar panels would last you much longer than 8 years (typically around 25 years).