A typical solar panel electrical package will include a series of solar panels (rating and quantity based on expected load), a charge controller, a battery bank (rating and quantity based on expected load) and an inverter (yes, rating based on expected load).
If you are confident that you will need 1000 watts of power, you should be configuring your system for at least twenty percent more than that, as one does not achieve one hundred percent efficiency from solar panels. If one is in an area of less than ideal weather conditions, one should increase the size proportionally. For the sake of this answer, I'll stick with the 1200 watt value.
In the USA, The Home Depot sells a 1200 watt system with 4 panels of 77 inches by 14 inches (1.9m x .35m) which is quite a large array. These panels include micro-inverters, one m-inverter per panel and provide AC voltage directly to the included controller and sub-panel.
This is not the type of system you would want if your intention is to run the computer continuously, but is provided as an example of the size of panels and general configuration.
A company called Armory Survival(!) sells an 1100 watt system, also with 4 panels of similar size, but has an off-grid configuration that permits battery connection. Very expensive bundles that do not include batteries means additional expense to have continuous (night) electrical power.
A frequent discussion in the electric vehicle world is the concept of a motor vehicle powered by solar panels exclusively. It's a different type of portability, but the numbers are equally challenging.
I'm not confident that you'll find a system to meet your requirements, especially considering the balcony constraint. Additionally, if your balcony does not point toward geographic south, the efficiency deteriorates for lack of solar energy.