# Power beaming

Power beaming is clearly central to space-based solar power concepts. Here I will provide a quick overview of my understanding of power beaming, the various equations involved, typical example calculations.

If power beaming were efficient and cheap, I believe space-based solar power would be quite viable even for grid power. However it’s not, and that largely has to do with the distances involved AND the fact that you need to convert energy multiple times, with losses along the way. The distances involved aren’t a complete show-stopper, since you can solve that problem just by operating at a large enough scale. However, the conversion inefficiencies (and the need to dump waste heat, etc) is not going to go away simply by operating at greater scale (although it helps).

The first equation we need is the diffraction limit. Roughly speaking, the spot size of a transmitted beam (microwave or laser) is:

Spot size = distance-to-spot * wavelength/(aperture diameter).

This is close enough for an order-of-magnitude estimate. More detailed work to follow.

But if we have a satellite out in Geosynchronous orbit (36000km altitude) transmitting power at roughly 10GHz (3cm wavelength, the shortest wavelength that still penetrates readily through the atmosphere) with an antenna 300m in diameter (NRO SIGINT/ELINT satellites are rumored to be that big, but maybe only around 100m in diameter), you’d have a spot size on the order of:

3.6E7m*3E-2m/(3E2m) = 3.6E3m or 3.6km in diameter…

…turns out that not all the energy of your beam is contained in this diameter (“Where’s that factor of 1.22,” you cry), but that’s a halfway decent start (and you’d need an infinitely wide aperture to collect all the energy in the beam…). 3.6km is obviously huge. The biggest full-aperture dish ever built is the half-way finished Chinese Arecibo clone at 500m. Still, there are ways to tweak this.

With a laser operating at 1micron, in medium-Earth-orbit (10000km) with 1 meter diameter optics needs only a:

1E7m*1E-6m/1m=10m diameter receiver to receive the vast majority of the beam’s energy. This is much, much better, obviously. You could put a 10m diameter receiver on top of a tethered airship or drone or something that allows you to transmit it to the ground without interference from clouds.

Or heck, use it to power high-altitude aircraft… but that’s a whole ‘nother blog post! (And suffice it to say, there are lots of caveats about laser transmission of energy, too.)

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### 13 Responses to Power beaming

1. gbaikie says:

It seems that if going to beam energy to earth surface, one has to have electrical power at about 1 cent per kW hour in space. Which essential true of any power generation if
it’s on Earth. Or electrical power at a hydro dam before considering the cost distributing this power. So to make the power is about 1 cent, and getting to the customer tacks on another 10 cents per Kw/hour.
So if someone can buy power at GEO at 1 cent per kw hour can sell it at the earth surface [invest whatever money for the infrastructure to be able to get it to customers].

Of course at moment GEO satellite are paying about \$20 per kw hour for their electrical power. And before one consider sending electrical power to earth, the cost of GEO would *have to* lower to at least \$1 kw/hour. And could extend to say that electrical power anywhere in Earth orbit, the Moon, or Mars would be somewhere around \$1 or less per Kw hour. And if you have water available this means one could have cheap rocket fuel in space.
It also means that if one could just buy \$1 kw/hour that one cost cost of doing anything
does not require hauling up from Earth some kind of powerplant- rather you connect to the grid, as one does on Earth. Or if Home Depot had to provide it’s own power, Home Depot would cost more to establish it’s stores. But Manufacturing anything is more critical in this aspect than a retail store.

So I think as metric lunar rocket fuel would have be about \$100 per lb or less, before considering producing electrical power from Space to Earth. And expect that lunar rocket fuel to start at around \$2000 per lb, and require decades to lower to \$100 per lb.
One important aspect of making electrical power in space [whenever it occurs] is you will get *better electrical power* and cheaper electrical power. And will be better because you get only get the amount you want, where and when you want.

But anyhow having massive antennas in space doesn’t seem to be a problem. Or if want big, one could have nuclear Orion lifting things from the Lunar surface- if made economic sense. It’s also possible Space elevators carry a wire. Or carry a wire from GEO to a lower orbit and those point distribute it globally.

But first one needs to be able to buy rocket fuel in space for about \$2000 per lb- it’s not so much the cost as the availability, and a competitive market which will lower it’s and other thing’s cost/price.

2. Peterh says:

A transmitter antenna a kilometer across doesn’t seem prohibitive if you’re using solar collector arrays that scale. But this does not appear to be a technology that does well at small scale. A 1 km square collector array at less than 10% can generate 100MW. And efficiency, of the whole or any single step, is not the bottom line: cost of delivered electricity is.

3. Chris Stelter says:

Efficiency may not be the bottom line, but every loss increases the cost of all the other components above that component, since they must be increased in capability to compensate. This is pretty brutal for any attempt to use lasers to transmit electricity to the grid from space, and even microwaves struggle. For lasers, the brutal part is finding a way to dump all that waste heat into the vacuum of space (because the sort of efficient, solid-state lasers we’re talking about HATE operating at high temperatures!).

I mean, from what I can tell, you’re only going to get about 55% of the power that is available on your in-orbit array onto the grid with microwaves (and getting that much efficiency requires a very large array), and with lasers, the efficiency is down in the 15-20% range if you’re lucky. Which still might be enough for niche applications. The advantage the lasers have is FAR greater power density (and, um, dual-use if you’re in the military) and the fact that you can get useful power even at small scales, starting in the Megawatt range versus the Gigawatt range you basically need for microwaves.

So, roughly speaking, you need 2 Gigawatts per satellite for a microwave system to be worth pursing at all (multiple square kilometers of solar array in space… dozens of launches), but probably around 5-10 Megawatts for a laser system (which actually isn’t too bad, about twice the footprint of the ISS… with a fancy-enough solar array tech, you could package this in a single launch, and the optics are in the range of current state-of-the-art experimental laser weapon optics and smaller than some optics that have already been launched into space). And the laser system could be modular, i.e. you start with smaller 1Megawatt laser satellites (150-200kW on the receiver side) and develop a fleet of them that can allow you to aggregate power where it’s needed. With microwaves, that’s not worth doing because the transmitter antenna needs to be so dang big to begin with (and no, you can’t use a distributed array with power transmission to act as a single large aperture! It works for radiotelescope imaging of radiobright objects, but not for power transmission since the losses eat up all the gain) compared to the ~1meter laser optics.

….and this is another comment that should probably be turned into a blog post.

4. George Turner says:

A simpler method might be to simply avoid conversions and leave the incoming solar energy unmodified, so you’re still in the visual part of the spectrum, and reflect it down to where it’s needed at night, such as a sports complex, or perhaps every outdoor baseball, football , and soccer field in the northern hemisphere. The shafts of light coming down might drive everyone nuts, though.

5. john hare says:

I think the answer is inherent in your post and I am having trouble collecting it.

What about distributed collectors well below geosync just above the radiation hazards with steering antennas? It would seem to me that cutting the distance by two thirds would cut the rectenna dimensions by two thirds. The downside is the constant antenna aiming and the requirements for multiple collectors in similar orbits.

The other thought is lower altitude relay sats that accept and send beams optimized for efficiency in the particular regime in question. I know I’ve read of these concepts before, but I can’t recall particulars at the moment.

6. Chris Stelter says:

Yeah, operating at 6000km would give you microwave transmitters that only need to be 300m in diameter, which may be on order of what SIGINT satellites are. HOWEVER, now you have to deal with significant shadowing from the Earth, which severely impacts your capacity factor (although you could deal with this in a few different ways… Heck, storing the energy for a few hours with batteries would probably be the simplest! It’d be perfectly predictable, and wouldn’t be that expensive, all things considered).

…also, anytime you’re not in GSO, you now have to justify either a huge loss when the satellites aren’t visible or you have to establish multiple sites scattered around the world to collect energy. A big fat satellite in GSO, without the major shadowing problem, starts to sound pretty attractive. And really, we know we can build a receiving array about 500m in diameter. Heck, we have solar farms that are multiple square kilometers, such as this one, the largest solar farm in the world at over 550MW (over 700MW if you count DC capacity, but nowadays, they often install to lower AC output since the very peak output only occurs for a very short time, which would be a waste of inverter equipment… in essence, this allows higher capacity factor): https://goo.gl/oUOnQG

So a couple kilometer diameter receiver is NOT out-of-the-question, although I would avoid it as I tend to think space-based solar power’s strength is to provide higher power density (and, of course, a capacity factor approaching 1).

7. Chris Stelter says:

Hmmm… You know, solar power is now a major thing, with multiple projects in the US (in the southwest) already built or under construction that are around 500MW in size, many square miles each. I think we can build a large receiving array, then. 2km in diameter, with a 500meter transmitting antenna, 2 Gigawatts input power, 1 GW power to the grid. That should be launchable in one go (for the antenna), with, say, 40 Falcon Heavy launches for the solar array, each tugged into position by SEP (solar array being 1kW/kg thin film solar which is lightweight, cheap, and perhaps intrinsically radiation-tolerant at least if you anneal it occasionally), a couple launches for structure, BUT… here’s the kicker… You’re going to need very high efficiency for the magnetron or very high operating temperature because at 90% efficiency, you’ll have to reject 100MW of heat! With a radiator near room temperature! For that sort of thing, the specific heat rejection is only like 50-150W/kg, so you’re looking at just as many Falcon Heavy launches needed for the heat rejection system!

…so the transmitter will need to be VERY high efficiency or will need to operate at elevated temperature or the heat rejection system will dominate the system mass! (This is worse for lasers, by the way… solid state lasers can’t really operate at high temperatures, and they’re much less efficient than magnetrons, so they put out just as much heat as they output light, and that heat must be rejected at near room temperature or the efficiency is even worse!)

Anyway, 100 Falcon Heavy Launches will set you back maybe \$5 billion if you cut a deal with SpaceX. Also need to tug that into place and assemble it. Solar arrays may cost, say, \$1/Watt (\$2B), power conversion cost about \$1/Watt-output (\$1B), heat rejection may cost another \$2billion, and the receiving antenna structure about \$200 million, based on China’s radio telescope. So a bit more than \$10 billion for 1 Gigawatt. Not too bad. That works out to (given a life of ~15 years) about \$0.09/kWh. Not stupendous, but not ridiculous, either. But notice that launch is only half of the cost! And that’s assuming only a 50% cut from typical SpaceX pricing. With a few of these puppies in orbit, you could cut a deal on a fully reusable launch vehicle for probably 20% of that cost, bringing the total down to about \$0.05/kWh. Very optimistic assumptions, but let’s leave it there for now.

…I should collect my thoughts, here, and make a proper blog post.

8. Andrew_W says:

Yeah, operating at 6000km would give you microwave transmitters that only need to be 300m in diameter, which may be on order of what SIGINT satellites are. HOWEVER, now you have to deal with significant shadowing from the Earth, which severely impacts your capacity factor (although you could deal with this in a few different ways… Heck, storing the energy for a few hours with batteries would probably be the simplest! It’d be perfectly predictable, and wouldn’t be that expensive, all things considered).

http://www.earthspaceagency.org/space-opinions/the-space-grid-sun-synchronous-orbiting-sbsp-satellites-with-equatorial-orbiting-reflector-satellites-for-earth-and-space-energy.html

This paper presents a new architecture option for low Earth orbit (LEO) Space-based Solar Power (SBSP) using wireless power transmission (WPT) and a space power relay (SPR) for Earth and Space energy. The goal is to determine the technical viability of this new space power concept to provide energy to the Earth and to a variety of space architectures and determine the possible reductions in mass to orbit.

A Sun-synchronous orbit (SS-O) is a special case of the polar orbit. Like a polar orbit, the satellite travels from the north to the south poles as the Earth turns below it. The orbital plane of a sun-synchronous orbit must also precess (rotate) approximately one degree each day, eastward, to keep pace with the Earth’s revolution around the sun. Sun-synchronous orbits are typically low Earth orbits (LEO) with altitudes of 550 to 850 km. There is a special kind of sun-synchronous orbit called a dawn-to-dusk orbit. In a dawn-to-dusk orbit, the satellite trails the Earth’s shadow. When the sun shines on one side of the Earth, it casts a shadow on the opposite side of the Earth. Because the satellite never moves into this shadow, the sun’s light is always on it.

9. Chris Stelter says:

I was aware of the idea of using SSO, I just don’t think it’s viable due to the reasons specified in your link. Reflectors are one solution, but that’s very complicated. Additionally, inflatable structures in space are not long for this world, IMO, as large, very thin inflatable structures are susceptible to MMOD. It’s clever, but not doable, IMO.

10. Andrew_W says:

While I’m not married to the ideas in the link, I suspect the use of relay satellites sounds more complicated than it actually is, in much the same way that cell phone networks (the cell phones switching between towers as the phone moves, and even managing to do these changeovers for millions of phones – unnoticed, during an uncountable number of conversations) sounds an unbelievably ambitious system.

Using inflatable structures for the relay reflectors is one option, quite possibly other lightweight construction methods could be used.

11. If solar thermal converters are used than AC current can be generated directly.

12. Chris Stelter says:

Andrew W: And the important difference is that cell towers are relaying information, not energy. Information integrity can be boosted through amplification and error-correction at each stage, while energy transmission just has losses compounding upon losses. I know you’re just using it as an analogy, but it’s an important distinction.

…but your statement that just because something is ambitious doesn’t mean it won’t work is true. But a system which ONLY works at an ambitious scale means the barrier to entry is VERY high, especially for things that haven’t been done before which means getting enough capital to build it is incredibly challenging, to say the least. If you can make this work at the scale of a city (like early cellular networks, ala the one in Tokyo or the even earlier one in St. Louis), then you’ll have proven the concept and be able to raise capital through both debt and equity and be able to have enough credibility to get traction with the regulatory bodies, etc, for a much larger system.

So… I suppose it’s worth asking what the smallest viable system would look like.

13. George Turner says: