Interesting link but wow - good thing I was not on her thesis committee because with a claim like that she would fail (either than or they are reporting it wrongly).
The total solar radiation at the Earth, outside the atmosphere, is 1.36 kW/m^2. Multiply that by the area given and the number of hours in a year and you get 762,470 TWh. However this would be the power for a solar satellite always pointing at the sun - so not even in orbit around the earth but say at one of the Lagrange points.
However things are not so simple because the panels on the ground rotate with the Earth. This means that for half the time they get no power and for the daylight period their angle is only optimal at midday. Note that even tracking panels will not help here because they would have to be spaced out so that their shadows did not meet another panel and so you would have less power collected at midday. The day-night cycle reduces the total power to 381,235 TWh and the angle of the sun throughout the day - I'll assume an RMS average here - drops it further to 269,573 TWh.
Now this assumes that the station in on the equator. If it actually was in West Virginia the power would drop further to 209,498 TWh due to the latitude (39 degrees) of the land. Now we need to look at the solar cell efficiency. The
best that has ever been achieved in a lab is 46% so this leaves a total energy generating capacity of 96,369 TWh.
Unfortunately in 2008 world energy consumption was 143,851 TWh. Hence there is absolutely no way whatsoever that a solar plant of 25,000 square miles can supply the energy needs of the world. Even if it was located on the equator, there were never any cloudy days, we could mass produce solar cells which have only ever been available in a lab AND world energy needs have not increased since 2008 we still could not power the world from such an area! If the thesis in question makes those claims as reported it is just plain wrong.