I had to check the numbers myself. Instead I just used 20 million barrels per day of oil to see how well it would do to replace US energy usage. The energy stored in the oil used in one day is 1.22 * 10^17 J. The energy incident on a square array (in a place where it won’t be eclipsed by the Earth often such as a geostationary orbit) is 1.17 * 10^14 J.
To be fair, the article only said a single kilometer-wide array. It *could* be 1000 km long! I also didn’t take into account the efficiencies of transmission or thermodynamics. I’m just drawing a rough conclusion to within an order of magnitude.
Of course when you look at worldwide energy usage of 15 TW, this idea is laughable. Overall 1.3 * 10^18 J are used per day. So now we have a 100 km by 100 km array (or perhaps 1 km by 10,000 km to meet this article’s requirements).
It would have to be close to 187,000 km long to reach the available power of their claim. Although I suspect there are some significant difficulties keeping an object in orbit that is 15 times larger than the diameter of the earth.