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For the original plans at least, the satellite will be in geostationary orbit (22,240 miles' altitude) and will only be a couple of miles in size. It will thus subtend an angle that is much smaller than the sun's disc, and thus casts no shadow. Any power plant causes heating, as it does not transfer its heating power into electricity with 100% efficiency. And it all becomes heat anyway when used by the customers.
22k miles seems a log way to transmit and energy supply but if they think they can do it ...
I take your point on the shadow, at least as far as a visible shadow might be concerned but I have in mind that there would, eventually, be quite a few of these things if they were viable. Whilst they would not evidently produce a clear shadow as we visualise such things there would still be, surely, and effective shadow for energy input values? So the trade is to try for higher capture amounts on balance.
The second aspect of increasing heat potential may not really apply provided remaining existing sources - fossil fuels for example - are removed from play. However the risk factor of geostationary collection and transmission devices 22k miles away compared to relatively readily available resources at hand looks like a challenge one would only accept as a last resort - no matter what the technical challenges might be.
I think I can be fairly sure that this idea will not be operational under any circumstances in my lifetime.
A power satellite may block some sunlight from reaching the earth's surface, but it orbits the earth once per solar day. It is only directly between the earth and the sun for a small interval on each orbit. During this time that it is between the earth and the sun it is still collecting solar energy and beaming a sizeable proportion of it back down to the surface of the earth. The remaining time, when it is not directly between the earth and the sun, it is still beaming energy down to earth, above what the earth would receive were the satellite not there.
I believe the idea is technically feasible, although it does not seem to make much economic sense. It seems to have been an attempt to spur space development. At the time the idea was first proposed, in the late 1960s, many in the space business expected that there would be people living in, or at least we would be constructing, large rotating colonies in space by now, that we would also have colonies on the moon and that humans would have at least visited Mars. And if we had the ability to do all that, we would have the ability to build power satellites too.
However, low cost orbital access was never achieved, and the rate of progress in space flight has been very slow. The global energy, and thus economic, situation seems to suggest that it will remain slow for quite a while yet. We are only just now getting to the stage that paying passengers are able to go into space for a few minutes in a parabolic flight on a private spacecraft.
I should also point out that in a geostationary orbit, the satellite is only capable of coming directly between the earth and the sun at certain times of the year--in the periods around the Spring and Autumn equinoxes. This is because geostationary orbits are in the plane of the equator, which is inclined presently at 23 degrees to the plane of the earth's orbit. At those times the satellite may also be eclipsed by the earth once per orbit.
And to correct the first sentence of my post, let me make it a lot clearer, because as stated it is wrong. The period of the geostationary orbit is the sidereal day. More accurately, the projection of the satellite's position in the plane of the earth's orbit crosses a line between the earth and the sun once per day.
I thik that the main problem here, as in the flying turbines, is the means by which the power is to be transmitted to earth. They say radio frequencies, meaning microwaves, as you can keep a fairly focused beam. However, think about this: are they going to send millions of kwh of energy on a microwave beam to earth? On how many microwave beams? I can already hear the howl of protests all over the planet. Heck, some people consider microwave ovens dangerous!