We're using ballpark figures for a large amount of these numbers, we're assuming we're only taking up the solar arrays, and that the supporting microwave transmission hardware is present, but negligible in comparison to the solar arrays themselves. we are also assuming that the solar arrays are the same ones as on the ISS (international space station) as data on their outputs was readily available. Another assumption is that everything works properly on the arrays, and that volume of the load is not an issue. It is important to note that these are factors to consider, and are important, but this isn't a detailed account of exactly what goes into orbit, more of an estimate to provide an inkling of an idea of what would be required to do such a thing. The last thing we assume is a 90% (which is generous) loss in power due to the microwave transmission.
Let's look at our facts and figures (all values will be approximated to the nearest whole number to provide ease of reading and calculations).
ISS solar array
Power output: 31kW
Mass: 963kg
delta-V: 3066 m/s
Estimated output of Solar array: 2000kW
Now let's start doing some math.
Power loss: 200kW
Generation required to recoup:2200kW
Number of arrays required: 2200/31=71 arrays
Mass of arrays 71*963= 68341kg
Now we have our mass we want to get into orbit. We need to also select a rocket that can actually get this hunk of arrays up there. The rocket pictured on the right is the Delta-IV rocket, probably the most powerful rocket being used today to lift things into orbit.
It's payload capacity is 14,220kg to geostationary orbit, even the discontinued Saturn V rocket didn't have the payload capacity for a single launch like this (47,000kg). We would need 5 launches to get all of our solar arrays up into the orbit we wanted them at. The cost of launching anything with this is roughly $3870/kg. If we do some more multiplication, we end up with a launch cost (of all 5 launches) $264,479,670. This doesn't seem too terrible, there have been more costly launches before, but it's not an inconsiderable sum for something being put into orbit.
But hold on, we are only generating 2000kW from this one array. A ballpark number for the price of energy is $0.15/kWhr. If we do a little math, we find that if this array wishes to pay itself off, you would have to wait 9,051,520 years before it paid for its own launch in power costs.
Clearly this is the dooming fact about orbital solar power. Even though these numbers are perhaps very very rough estimates, it still does not negate the fact that there would be a lot of work required to actually make this a cost effective power solution. Unless you happened to be extremely patient.
This whole website has really only been devoted to giving a brief introduction to the ideas of orbital mechanics and wireless power transmission. There are completely legitimate ideas being proposed to do this, with many facts and figures having been taken from ideas that were proposed. Perhaps in the future when space travel becomes far cheaper will orbital solar arrays be a more viable option, but for now? It is likely that it will be stuck in the math until someone is crazy enough to make it.
http://media3.s-nbcnews.com/i/newscms/2014_44/739341/141028-antares-rocket-explosion-jms-1825_c6574a8e67fd20cddbc518bebd937bd4.jpg
http://en.wikipedia.org/wiki/Delta_IV#mediaviewer/File:Delta_IV_Medium_Rocket_DSCS.jpg