If you are running a 1390 or smaller laser, you have a few options, depending on what else you have going at the same time. If you don't want to be spending money on petrol or diesel, you will need an inverter, batteries, and possibly a couple of solar panels to keep the batteries charged during longer outages.
For the purposes of this exercise, I will assume you have a 100W tube, a 5200 chiller, a PC with a screen, and a few 8W LED lights to see what you are doing. Obviously, a smaller setup will use less power. I will also assume a 50% cutting and 50% engraving time, and an 80% duty cycle (you need to stop to change material, have a drink, and maybe take a comfort break).
You can also keep your fibre internet ONT and your WiFi router going at the same time. This will only consume about 100W maximum.
The laser tube and power supply will use about 400W when running at around 60% power
The electronics and mechanicals (display, stepper motors, etc.) will use about 100W
The air assist pump will use about 50W
The extractor fan (inline) will use about 150W
The chiller will use about 100W in idle mode, and about 300W when the compressor is running. (This will momentarily spike up to about 1500W when the compressor switches on, so we need to account for that so your inverter does not trip.)
The PC will use between 150 and 350W – depending on monitor size etc.
8W LED lights will obviously use 8W each, so 24W for 3
Total around 1474W (2174W for very short periods when the compressor switches on).
To continue running a 100W laser through a 2 or 3 hour loadshedding period, a 3KW inverter with 2 x 100Ah gel batteries should be more than adequate in most cases, although LiFePo4 (Lithium Ferrous Phosphate) batteries will be more efficient (but more expensive in initial outlay).
Gel batteries should not be run down to less than 60 – 70% power, and are rated for around 300 charging cycles, while the LiFePo4 batteries should be good for around 2000 – 3000 cycles – even if you run them down to 10% power. This is a whole other discussion though.
Of course, you can also power other things with this setup – if your laser is not being used. Your fridge for example, or a coffee machine, DSTV decoder, large LCD TV and more.
Do your research – there are lots of 3KW inverter options available.