Solar Power Satellites re-examined

Robert Zubrin’s Entering Space is a passionate defense of the idea that humanity needs to commit to colonising another planet – specifically Mars – before many other space-related concepts can become viable. One money-making venture in space that Zubrin trashes along the way is the Solar Power Satellite or Powersat a concept first proposed in the 1960s by physicist Peter Glaser, and since then extensively studied by NASA and the DoE in the US, as well JAXA and the ESA.

Zubrin’s analysis is scathing for anyone with hopes of powersats being a commercial prospect. Here’s what he assumes and computes in his argument…

(i) Insolation averages ~ 1300 W/m^2… a bit low, but not by much. References give 1368 W/m^2, averaged.
(ii) Power transmission efficiency ~ 50%… low again, typically 63% in the literature
(iii) 15% efficient PVs
(iv) PVs mass 4 kg/m^2… rather heavy.
(v) non-PV mass another 4 kg/m^2 of PV panel… even heavier.

At $40,000/kg delivery costs to GEO a 1 GW (500 MW to the ground) Powersat massing 41,000 tons would cost ~$1.65 trillion to orbit, and double that to assemble. That’s $3.3 trillion total. For some reason his quoted figures double at this point and he says $6 trillion. At 10% interest and maintenance the system annual costs go to $1 trillion (~$0.55 trillion using the corrected figures) and the cost per kilowatt.hour, for 500 MW supplied for 8,766 hours a year, is $228/kW.hr ($125/kW.hr corrected.) Some 2500 times more expensive than the $0.05/kW.hr at the time of writing (1999.)

By his analysis that means launch costs would need to drop to just $4/kg which is impossible using current techniques as that’s 4 times less than the fuel costs needed. Clearly absurd BUT let’s look at his assumptions again. We’ll grant him (i) & (ii) as the figures quoted are close to literature figures. What about (iii)-(v)?

(iii) 15% efficient PVs… well the best commercial cells are heading for 40% and techniques for increasing efficiency are being touted by various labs. One inventor is selling thermoelectric converters with 60% efficiency, while another group has developed nano-antenna collectors potentially 80% efficient. Thus the PV mass could be cut by more than 75-80%.
(iv) Mass density of 4 kg/m^2. Very heavy. The new PVs could be made much lighter by using concentrator arrays (which also cuts the costs of PV converters themselves too.) A system of inflatables could drastically cut the mass of the array – Geoff Landis designed a system massing just 800 tons (plus 500 tons structure) collecting 3 GW in space at 35% efficiency thus massing just 0.364 kg/m^2. All the old DoE/NASA studies assumed about ~ 1kg/m^2 including PVs and structure. Zubrin is wildly off-base.
(v) Double the PV mass in structure and power distribution/transmission systems. Structure can be made using self-assembling inflatables that space-cure into hard structures. Power distribution and transmission masses can be minimised by clever design – I’m doubtful they’d mass 20,500 tons for 1 GW like Zubrin imagines, but they can be heavy. Especially problematic are the heavy slip-rings and brushes needed to transfer power from the rotating collector panels to the non-rotating transmitter. A lot of mass can be saved by reducing the need for power transfer. One design uses movable mirrors focussed onto a non-moving core connected directly to the transmitter. This also reduces the heavy power-cabling needed to carry 1,000 MW to the transmitter.

Moving parts are always a potential problem, but lots of small moving mirrors reduces the impact of one or two mirrors sticking and needing repair. Conceivably those repairs could be carried out by teleoperated machinery.

Let’s call the powersat mass ~ 1 kg/m^2 – not as good as some designs, but better than Zubrin’s Strawman Argument. So where does that get us? Some 20% of 12.5% percent means the powersat now masses ~ 1025 tons. Delivery cost is still $41 billion to GEO, which is pricey. Zubrin also cuts costs even further by arguing that air-breathing rockets and ion-drive delivery systems can cut LEO then GEO by half each. Thus the powersat costs ~ $10.25 billion delivered to GEO, and double that overall. Some $20.5 billion is a lot to build a power-station supplying just 0.5 GW. Typically a coal-plant costs about $1.5 billion per gigawatt power. Thus to compete a powersat needs its costs reduced by 27-fold. GEO delivery costs need to get down to ~ $360/kg, and construction stay at twice the launch costs, to make powersats viable.

As SpaceX is aiming for $500/kg to LEO I would hazard a guess and say powersats might be a viable commercial option, assuming some reasonable improvements to the technology.

Addenda:(i) Zubrin grants a four-fold reduction in delivery costs to LEO then GEO, then a halving of that due to a mass decrease in PVs and structure. For comparison he quotes the minimum cost of LEO delivery via reusable rockets as ~ $100/kg, thus $400/kg to GEO via conventional means. Thus delivery to GEO, assuming the cost reductions and minimal rocket costs, of 20,500 tons of Powersat costs ~ $2.05 billion, and in total it costs $4.1 billion to set-up. He claims that’s still 3 times too much compared to coal. As I show in the next post that’s somewhat misleading. If we factor in carbon disposal and the cost of the coal burnt, then coal’s effectiveness goes down – especially if you’re paying $120/ton instead of $20/ton for the stuff.

For areas paying hand-over-fist for diesel powered generators, prices of $0.2/kW.hr look quite attractive. If you have no coal and no railways delivering it to your generator, then setting up a rectenna farm made of pre-fab identical components delivered via truck looks like a better deal.

(ii)He claimed a 2,000-fold (really 2,500-fold) price reduction was absurd, but with our 40-fold mass-reduction a 62.5-fold reduction in LEO rocketry prices is then acceptable – $160/kg, less stringent than the $100/kg minimum. If ion-drives can cut the delivery to GEO in half, then $320/kg to LEO is acceptable. SpaceX’s ultimate goal is not much more than that.