We're going to need a lot of solar panels and an efficient way to transport power from a very sunny place to another location where the loads are. For instance: https://en.wikipedia.org/wiki/Pacific_DC_Intertie The pacific DC intertie right now often ends up being used to transport power from hydroelectric dams in WA/OR to California. But there's nothing to say that something couldn't function the other way if there…
>The technology now exists to theoretically cover many hundreds of square km of Libya in photovoltaics and take the electricty to Europe It really doesn't. I'm a huge fan of back-of-the-envelope maths, and this idea raises some very fun questions. How big would the power line be, if the UK (where I live) was powered entirely by solar panels in the African desert? The UK's average instantaneous power consumption is ar…
https://www.statista.com/statistics/322874/electricity-consu...
Annualized, that's an average power of 33.5 GW.
On http://gridwatch.templar.co.uk/ you can see in the yearly demand view that peak demand for the year was under 40 GW.
This initial estimate of 150 km^2 of desert solar farms is too small and your later estimate of 13,000 km^2 is too large. A conservative rule of thumb would be 10 megawatts (real power, annualized) per km^2 of solar farm, which would mean 3,350 km^2 of solar farms for 33,500 average megawatts. Note that solar farm area is larger than solar panel area because solar farms need space between racks of panels.