As surprising as it was to most experienced scientists and engineers, there was renewed interest a few years back in the notion of placing large arrays of PV cells in orbit around the earth and beaming microwave or optical power back to receiving stations on earth. The chorus from space enthusiasts grew to the point that congressional hearings were held and a small amount of DOD funding was appropriated to support a conference and a preliminary report. The report that came from the conference of advocates in the fall of 2007 was full of generalities and claims but devoid of serious analysis.

The closest the conference report came to anything physics-based was to note that in the three decades that have elapsed since the last serious study was carried out on SBSP there have been a number of technical advances: (1) a factor-of-three increase in PV efficiencies; (2) a factor-of-four increase in the efficiency of solid-state high-power microwave transmitters (but that is actually irrelevant, as the klystron transmitters considered in the earlier study, though not solid state, were only slightly less efficient and slightly more massive than today’s state-of-the-art solid-state transmitters); (3) improved beam steering technologies; (4) vastly improved robotics (to better handle assembly in space); and (5) significantly reduced PV cell thickness. Of course, they failed to note that launch fuel costs have increased by a factor of four in the last decade. They noted that the US no longer has heavy-lift capability.

The NASA-supported engineering studies from the mid-1970s clearly showed that the SBSP concepts were at least two orders of magnitude away from being cost effective (though that is never acknowledged by SBSP advocates). That study estimated in-space system mass of 30 kg per kilowatt of power (kW_E) actually generated in the earth receiving stations. Launch costs for geosynchronous orbit (GEO) over the past two decades have averaged over $30,000 per kilogram of payload – and the recent trend is rapidly upward. Moreover, it is the nature of system cost optimizations that no single cost component will likely be a major fraction of the total system cost. It is quite uncommon for any single cost component to exceed 30% of the total system cost. On this basis alone, assuming that an order-of-magnitude reduction in orbiting mass can be achieved compared to the optimistic and forward-thinking assumptions from the mid-1970s, one estimates a system cost of $100,000/kW_E.

Even after correcting for the difference between continuous power from SBSP and variable power from wind, SBSP energy is still over 40 times the cost of wind energy – assuming similar system lifetimes. But a lifetime of even 10 years seems like an unrealistic stretch for paper-thin PV arrays (of many square miles) in the harsh environment of outer space. Hence, an optimistic estimate of the cost of SBSP energy is about 100 times the cost of wind energy – but 1000 times the cost of wind energy if the SBSP system fails after one year of operation.

The primary response of the SBSP advocates to the above “back-of-the-envelop” analysis is that the launch costs should be able to be reduced by more than an order of magnitude at the scale required by SBSP, and the quick rebuttal to this is that multi-billion-dollar space programs in several countries have been unsuccessfully trying to achieve launch-cost reductions for decades. Moreover, it seems highly implausible that order-of-magnitude launch-cost reductions would now be possible in an era of hyperinflation of energy and material costs. The next response by the SBSP advocates is that placing satellites in low earth orbit (LEO) costs only one-third as much as in GEO, and it may be possible to devise lower-cost methods (many have been proposed) for boosting satellites from LEO to GEO. Unfortunately, a factor of two reduction in costs of GEO is but a very small step.

The best real reference case for SBSP is the International Space Station (ISS), which is supposed to be completed in 2011. Its solar power generation capacity is about 80 kW. The cost of this power plant (not the entire station) was about $3,000,000/kW_E – and it doesn't include conversion to microwave and beaming to earth, which loses about half the initial power. The 10-m robot arm alone for servicing the ISS cost about $1B. Perhaps the robot arms for positioning and servicing PV and transmitter modules in PV arrays 20,000 times larger than on the ISS (as would be needed to generate 500 MW_E on earth) would cost $100B. If so, that alone would contribute $200,000/kW_E to the cost of SBSP. The point here is that components in outer space are often 1000 times as expensive as similar components on earth.

Finally, there is another showstopper argument against SBSP today – that was not an issue even 10 years ago. To have any chance of succeeding, there must be a plausible path toward high-efficiency, high-power microwave transmitters at a frequency where atmospheric absorption is relatively low and not already committed to communications or other purpose. There are no remaining microwave or millimeter-wave windows available of sufficient width that meet the requirements

References:

http://en.wikipedia.org/wiki/Space-based_solar_power

http://en.wikipedia.org/wiki/International_Space_Station

http://www.nasa.gov/mission_pages/station/main/onthestation/facts_and_figures.html

Footnote: We also should point out that many of the enthusiasts have cited some crude analyses by an early advocate of SBSP, David Criswell, that contained a factor of 30 error in the antenna sizes required to achieve the needed focusing of the microwave radiation.

The diffraction limit for 1/e² beam width is 1.22*lambda/diameter. Assuming perfect phasing accuracy, ideal antennas, and 6 GHz (4 cm) radiation from 35,000 km up, the diffraction limit requires that the product of the diameters of the two antennas must be 4 km² for 95% beam energy focusing/reception. So a 1 km transmitter array requires a 4 km receiving array. Criswell believes the product is smaller by a factor of 30. He's flatly wrong. Apparently, not very many physicists have taken the time to check his calculations.