How Do The Numbers Work?

Sorry, but I just can’t buy this:

PG&E is pledging to buy the power at an agreed-upon rate, comparable to the rate specified in other agreements for renewable-energy purchases, company spokesman Jonathan Marshall said. Neither PG&E nor Solaren would say what that rate was, due to the proprietary nature of the agreement. However, Marshall emphasized that PG&E would make no up-front investment in Solaren’s venture.

“We’ve been very careful not to bear risk in this,” Marshall told

Smart move.

Solaren’s chief executive officer, Gary Spirnak, said the project would be the first real-world application of space solar power, a technology that has been talked about for decades but never turned into reality.

“While a system of this scale and exact configuration has not been built, the underlying technology is very mature and is based on communications satellite technology,” he said in a Q&A posted by PG&E. A study drawn up for the Pentagon came to a similar conclusion in 2007. However, that study also said the cost of satellite-beamed power would likely be significantly higher than market rates, at least at first.

In contrast, Spirnak said Solaren’s system would be “competitive both in terms of performance and cost with other sources of baseload power generation.”

I just can’t see how. Unless there are going to be many satellites, the system has to be in GEO to provide baseload power to any given region on earth. They talk about putting up a 200 MW system with “four or five” “heavy lift” launches (where this is apparently defined as 25 tons).

Suppose the conversion efficiency of the cells is a generous 30%, the DC-MW conversion is 90%, the transmission efficiency is 90% and the MW-AC conversion efficiency is 90% (generous numbers all, I think). That gives an overall efficiency of 22% from sunlight to the grid. The solar constant in space is 1.4kW/m2, so that means you need 650,000 square meters of panels to deliver 200 MW to the grid. Suppose you can build the cells (including necessary structure to maintain stiffness) for half a kilo per square meter. That means that just for the solar panels alone, you have a payload of 325 metric tons. Generously assuming that their payload of 25 tons is to GEO (if it’s to LEO, it’s probably less than ten tons in GEO), that would require over a dozen launches for the solar panels alone.

That doesn’t include the mass of the conversion electronics, basic satellite housekeeping systems (attitude control, etc.) and the transmitting antenna, which has to be huge to get that much power that distance at a safe power density.

So even ignoring the other issues (e.g. regulatory, safety studies, etc.) that Clark mentions, I think this is completely bogus until I see their numbers. And probably even then.

40 thoughts on “How Do The Numbers Work?”

  1. Presumably, there is a time limit on this agreement. Hopefully PG&E is hoping the time runs out before they actually have to buy any of this high-priced energy. In the mean time, their only expense is the cost of employing their PR department to talk this nonsense up.

    In the real world, just how large is the earth station going to be to receive all that power?

  2. I can understand PG&E’s side in the deal. After all they are not really committing to anything. They will not pay any money upfront, only to someone if they get energy for a price similar to the one they pay today. I guess this announcement is just Solarens way of getting mindshare so someone will finance this abortive concept.

    Yeah, it does not make financial sense. All the numbers I have seen on such a business, to make it profitable, rely either on keeping launch mass down by using inflatable structures, in situ resource usage, etc, or on building some sort of magical launch vehicle which will bring launch costs down by two orders of magnitude.

    So it ain’t happening.

  3. There are ways to do this — they’re called solar concentrators. But this doesn’t reduce the overall weight of the system (and probably increases it, because the mirrors have mass as well, and have to be even more rigid than the panels to be effective). It’s hard to build an inflatable mirror that is concave, rather than convex, and the former is what you need to focus the light. All it does is save on the cost of solar panels.

  4. Also, would it not make sense to use some kind of a slow-boat, high ISP tug to push these things from LEO to GEO?

    This might improve the 10 from 25 tons ratio.

  5. I think Rand’s analysis is correct, but it seems to me that an inflatable mylar oblate spheroid with one hemisphere (centered on the short axis) aluminized on the inside could be a relatively inexpensive concentrator.

  6. Better this than sponsoring some golf tournament and yet that is all this is — publicity for PG&E.

    That said, no one else has figured out how to make an authentic profit in space, so why not embrace publicity seekers?

  7. Regarding Flighterdoc’s question, JAXA’s current plan assumes a roughly circular rectenna field 3km in diameter for 1GW beam (or is it 1GW coming out of the field, the difference is non-trivial). These numbers have to be taken under advisory, because the power density in this arrangement does not mash with their earlier announcements. They promised that it’s going to be less than 3kW/m^2 and so ships with humans onboard can safely enter the rectenna field. But my back of the envelope calculation shows 141 W/m^2 (not 141 kW). Either I lost a few zeroes or I just don’t understand something about this.

  8. Jay, such a mirror as you describe already exists and is in use in solar-thermal concentrators.

    Solar thermal power generation could be much more efficient than photovoltaic. Last January a solar thermal system tested at Sandia converted sunlight into power-delivered-to-grid at 31.25% efficiency. That efficiency would go way up if the cold sink is 3 Kelvin.

  9. How is PG&E guilty of fraud?

    It appears PG&E is promising to pay an undisclosed fixed price for solar power IF Solaren can deliver it to Earth.

    PG&E isn’t promising to do the solar power generation themselves.

  10. Oh, and I agree with those advocating solar thermal rather than photovoltaic.

    Solar thermal would also work well on the Moon, especially shaded regolith was used as the cold sink.

  11. “…why not embrace publicity seekers?

    Because we don’t want to endorse fraud, and associate it with the space movement?”

    which advice would be helpful if you followed it more

  12. How is PG&E guilty of fraud?

    I didn’t say they were.

    ,,,which advice would be helpful if you followed it more

    Another moron heard from.

  13. The outfit has a patent filed (US Patent 6936760), that talks about a foldable mirror 1 to 2 km (!) in diameter, supported by an inflatable tube. The mirror focuses sunlight onto a series of intermediate mirros until is finally strikes a solar power module (aka solar cell).

    I wonder what the practical limit for solar power density on a cell is, before it toasts?

    Fascinating read, they patent just about every permutation of the concept.

    Rand, after reading the patent, I would not be quite so quick to crush the idea. I’m still skeptical, too, but we need more details to call bs on this.

  14. If I were attempting this:

    1) I’d use a thermal generator, not solar cells – the power density (kw/kg) is much better for really big projects. (Actually, the current power density is somewhat similar – but I think the engineering R&D behind an extreme energy density thermal generator is more doable by a startup)

    2) I’d use geosync, but not geostationary. Make sure to be overhead at noon, so you get peak power pricing. The lower orbit will bring down the total cost, and simplify the transmission problems. After you have proven the concept, put up more satellites until you fill the constellation. Also, sell power to other sites around the world as convenient.

  15. If it’s an inflatable system, the mirrors could be low cost and very lightweight if aluminized on the inside of the balloon. The answer to how much concentration can be withstood by PV is about 100X. Stirling Energy Systems has had a similar PG&E agreement for over a year and they are using it to help raise the capital to provide the (ground based) hardware. See

    The photo is a six-pack of 25 KW generators at Sandia. They have overall sunlight-to-AC power efficiency above 30%

    Note the visit to the green energy site by Pres Bush. Did you see that in the MSM?

  16. If it’s an inflatable system, it will be turned into Swiss cheese by orbital debris within a year.

  17. If it’s an inflatable in GEO, orbital debris is not a problem. If they use multiple mirrors, the secondary or tertiary mirrors will presumably be smaller and can be more affordably robust for higher concentration.

  18. If it’s an inflatable in GEO, orbital debris is not a problem.

    Orbital debris is less of a problem than it is in certain LEO orbits. It still is a problem.

  19. Sean – not necessarily. The original “inflatable structures” tests against micrometeor stand-ins gave some very remarkable (positive) results so long as the structure used multiple layers of material. Furthermore, Bigelow’s habs are claimed to be able to deflect a bullet, in part due to absorbing energy from the blow instead of strictly resisting it. While debris is moving faster than a bullet, so too is the structure (presumably at no greater than 90 degrees between the orbital paths).

    Which is not to say that my first choice would be to use a thin, inflated mirror system; but it’s not completely out to lunch.

    Mr. S, would it help any if they’re trying to avoid a curved mirror outright, and simply use multiple planar mirrors at different angles with respect to a generator (PV or mechanical)? I still think they’re out of their minds if they’re trying to unfold and/or inflate mirrors measuring thousands of meters across, but breaking up the mirror should simplify the curvature issue.

  20. I’d use geosync, but not geostationary. Make sure to be overhead at noon, so you get peak power pricing. The lower orbit will bring down the total cost, and simplify the transmission problems.

    What do you mean by “geosynch, but not geostationary”? My understanding of those words is that the former has a 24-hour period, but the latter is equatorial so it’s motionless in the sky. And the latter is a subset of the former, and both have the same average altitude.

  21. Since it is a power sat. couldn’t they use some of that power to raise it’s own orbit (some kind of ion drive) even if it was a slow process? Could that lower costs?

    Then again, if power density on the surface of the Earth is about 2/3rds of space. Would an arctic or antarctic installation be competitive? Or would transmission and maintenance costs kill that idea?

  22. Geosync is used for lots of meanings ;}, but one of them is any orbit with a period that is an integer multiple or divisor of one day. So a 12 hour orbit, 8, 4, etc.

    It has the advantage of being predictably overhead, but isn’t as far away. The closer you are, the less time you spend in a position to send power to the target. But power transmission requirements go down.

  23. “I wonder what the practical limit for solar power density on a cell is, before it toasts?”

    I’ve seen photovoltaics operate at 70 sols of light intensity, and solar thermal systems operating at over 1000.

  24. Is anyone familiar with the microwave transmission part of this? What’s the energy density of the beam (can you fry an egg in it?) and how wide an area would it need to cover to deliver 200 MW? Would it be affected by weather conditions: clouds, precipitation, humidity, smog? What’s the magnitude of the heat loss at the ground-based converter, and would that have any affect on the local weather?

  25. These guys are reporting 2.5kW/kg deployed

    That would be 80 tons.

    Rather than spending a lot of money on high conversion efficiency to the grid, I’d spend it on lobbying to get the full rated capacity 24-7 to be used for renewable energy certificates (RECs).

    Not unlike other parts of the space program, this is aimed as a grab at state and federal subsidies:

    If solar on orbit is $0.22/kwh in subsidy, then that’s $385 million per year (200000*$.22*365.25*24). California has a renewable energy requirement of 20% or more coming soon. If one can get a cheap loan (5%), one can spend ($385M/.05) $7 billion+ to make that happen. That’s $90k/kg ($7B/80000kg).

    There’s an old saw that water flows up hill to money. Solar cells too can flow up hill to money.

    Gentlemen, start your engines.

  26. Some plans for super large, space based, telescope mirrors call for spinnning a minute amount of mercury on an oblate spheroid in situ. It brings the manfacturing costs of the mirror down several orders of magnitude.

  27. Some plans for super large, space based, telescope mirrors call for spinnning a minute amount of mercury on an oblate spheroid in situ. It brings the manfacturing costs of the mirror down several orders of magnitude.

    Only problem is that those mirrors weigh a lot. A “minute” amount of mercury isn’t that minute unless the oblate spheroid is actually a paraboloid. And the mirror isn’t going be able to point in a particular direction. It needs to rotate to keep the mercury on the film.

    If solar on orbit is $0.22/kwh in subsidy

    Ok, we have 2.5 kW/kg and $0.22/kWh. Assuming you can get another $0.03 in profit from selling the power on Earth, that’s $15 a day or almost $5,500 per year, which would cover launch costs in under two years.

    The only problem is that you can do a lot better on Earth due to the lower costs of an Earthside installation. The opportunity cost still makes Earthside power generation better. I’m thinking some combination of wind, nuclear, Earthside solar, or geothermal. For example, in Anartica, I gather wind power works pretty well. Nuclear would work very well with the massive heat sinks present there. Or one could go with cheap diesel generators.

  28. When I heard geosync, I was thinking more along the lines of Rand…28 degrees (for example) inclined at geosynchronous altitude. This geometry would still have an eclipse season twice a year, but the propellant cost to get there would be lower than going to zero degrees inclined. The other periods David mentions are resonant, but not really synchronous. When I worked with GPS, we always referred to its 12-hour orbit as semi-synchronous.

  29. I think the real problem is the aperture for microwave beaming doesn’t get smaller as the power level goes down. As I recall, the trades in the 1970s all came down on the side of 5 to 10GW on orbit in order to match the antenna and rectenna power densities to form the optimal spot on the ground. That means a rather large (km) dia. transmitter to have reasonable power density on the ground. Otherwise rectenna land cost and land use becomes the controlling economic factor. Such a large (even if sparsely populated) transmitter array will be the single largest mass on orbit.

  30. I don’t think so, Charles. First, the notion of free-floating elements in relation to one another has prior art, such as Ivan Bekey’s testimony to the Congress in (I believe) 1975. Others have proposed similar approaches. Second, I don’t see how you keep free floating elements of this size under control and in position without propellant expenditure. That is impractical as a number of designers have noted previously.

    Lots of people have looked at very light weight SPS alternatives, but I am regretfully still skeptical that this can be done as business proposition (vs. a technical demo funded by government) and have the case close with expendable launchers.

  31. Another approach to increasing solar cell output cheaply is to absorb unwanted wavelengths at the concentrator to reduce the cooling load at the solar cell. I’m getting good results on planet earth, patent applied for 2 years ago and still waiting. There are nanomaterials which absorb IR, for instance- or earthside, a few inches of water will do. Mylar is cheap, inexpensive, and lightweight, unlike solar cells.
    That said, I’m a skeptic, since those same solar cells and Mylar on earth are likely to produce power more economically.

  32. Economics being better on Earth is relevant to use solar for daytime load. The subsidy, though, changes things: 1) it’s just as big at night, 2) it’s adjudicated how much subsidy is paid so it may depend more on rated capacity and less on delivered energy, 3) it takes scarce goods (cells) and squeezes more subsidy out of them–the business case for terrestrial requires for their to be eight times as many cells. I’m skeptical too, but if governments are throwing billions at alternative energy, it’s possible there’s a way to drink from the gusher.

  33. Rand, I’m curious. Can you explain how you calculated the “22%” efficiency cited.
    “That gives an overall efficiency of 22% from sunlight to the grid.”
    Thank You

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