Hello Harry,
Check the voltage of the curtain opener, many of them are 12v and have an in-line converter to change domestic current to DC. (Just like your laptop, tablet, mobile telephone and probably your WIFI box have too). So you may not need an inverter, which wastes a lot of
energy just by being switched on.
While you're designing the system, why not use a slightly larger solar panel than you need and run a few
LED lights, charge your telephone and do all sorts of other things with the spare energy? After all you only open and close curtains once a day.
Solar panels are relatively cheap but batteries and reliable inverters are not. Am I being cheeky asking why you want to spend time and money on stuff when you already have a system that works on your domestic circuit?