The major considerations driving solar power satellite design decisions are:
- location (geostationary, LEO, other)
- energy delivery method to Earth
- solar panel photovoltaic versus turbine generator (efficiency/cost tradeoff)
- size of an SPS (dimensions, mass, power)
Most studies recommend a geostationary orbit for Solar Power Satellites. This choice simplifies designs, and is the only choice that can deliver continuous power from a single SPS – the others require a constellation of satellites with any given ground station receiving power from a sequence of satellites. The disadvantages are that a relatively large transmitting antenna is required, and it takes more energy to reach those geostationary orbits.
Another disadvantage is that it is inefficient to deliver power to high latitudes; multiple satellites with Molniya orbits are one possible alternative.
An SPS constellation in medium Earth orbit has been proposed, because of the lower cost to launch from Earth and the smaller size of the transmitting antenna. The disadvantages are that both the transmitting and receiving antennas may need to be dynamically aimed, plus the “dark” time due to passing through the Earth’s shadow is much greater, requiring still more satellites to deliver continuous power.
The remainder of this post will focus on geostationary locations, which have been studied more thoroughly.
MICROWAVE ENERGY DELIVERY TO EARTH
The minimum size of an SPS is driven by the size of the energy transmitter and the Earthside receiving station. While several alternatives have been considered, the best option appears to be beaming microwaves to Earth receiving stations from geosynchronous orbit. To achieve sufficiently narrow beams that arrive at sufficiently low energy densities (so as not to cook anything in their path), we’ll need a transmitting antenna one kilometer wide.
The receiving station is larger at 10 kilometers east-to-west and as long north-to-south as necessary to appear circular from the SPS (a 10 kilometer circle at the equator, a 10 by 15 kilometer oval at 30 degrees latitude, 10 by 20 kilometers at 45 degrees latitude, perhaps 10 by 30 kilometers at 60 degrees). Note that 60 degrees latitude is approximately the limit of feasibility due to both the size of the receiving array and the amount of atmosphere that must be traversed. Luckily, this supports serving the vast majority of the global population, excluding only the Artic regions, Alaska (U.S.A.), northern Canada, and the European Nordic countries and northern Russia. Note that St. Petersburg (Russia), Helsinki (Finland), Stockholm (Sweden), and Oslo (Norway) are near the limits of servable destinations.
An Earth-side energy density of 23 mW/cm² (chosen as safe for all life forms) equates to 5 gigawatts as a minimum power limit near the equator and proportionally more at higher latitudes. Building smaller SPS systems can be done, but the antenna arrays would not be smaller (or cheaper), and thus would be less cost-effective. Note that some sources suggest a minimum size of 4 gigawatts. In any event, at 2.45 Ghz (the highest frequency with negligible absorption by rain, snow, clouds, and people), a one-kilometer transmitter could not possibly focus higher intensities upon the Earth, making this a safe and non-military technology.
The likely technology for the receiving station is a rectenna array, a network of many simple wires with diodes. It can be deployed above cropland (and herds of cattle, even forests) with only minor loss of productivity of the farm. Receiver losses will be of the order of 10%, much less than typical long distance power transmission.
A side point: direct-to-home power transmission is perfectly feasible. A home rooftop rectenna could easily capture 5 or 10 kilowatts of power, several times the average household demand. The problem is all the power wasted between rooftops, including undesirable electric currents induced in most metals and wiring. But perhaps this is not a problem in a military environment, where an energy beam could be directed to the conflict zone, not as a weapon, but for providing electrical power wherever needed. This also has direct military applications: SPS powered drones could fly indefinitely.
HOW BIG IS A SOLAR POWER SATELLITE?
So how big is the SPS itself? That depends critically on the efficiency of solar energy capture and thus the technology used. There are two likely technologies: solar cells (photovoltaic) and solar dynamic (mirrors and gas or steam turbine powered generators). Both methods take advantage of the near-constant sunlight (only shadowed by the Earth for a few total hours near midnight twice a year, and never for more than 75 minutes at a time) – a net 99% availability. Also, the intensity of solar energy in space is greater than on the Earth’s surface due to the lack of air to absorb energy. About 950w/m2 strikes the Earth’s surface at noon on the equator on a clear day, while in orbit the solar energy density is 1367w/m2 all of the time.
Solar Photovoltaic versus Solar Dynamic
Solar cells vary hugely in cost and efficiency. Common cells convert about 10% of the incoming energy to electricity. But modern cells convert 20% (thin film) to 40% (optimized) of the incoming energy. Caltech claimed to achieve 85% in a highly experimental demonstration in March of 2010. We don’t know what technology will be the most cost-efficient. Note that 25% efficiency implies a 4km by 4km photovoltaic array would generate 5 gigawatts in orbit, although it would take a 4.25km square array to deliver 5 gigawatts to the Earth assuming an 80% efficiency in the transmitter / receiver.
Solar dynamic may be more efficient, as large, low-cost mirror arrays focus the sun’s heat on a boiler driving a turbine electric generator. The mirrors are relatively inexpensive, and the cost will be dominated by the need to remove the waste heat using large cooling arrays. But the efficiencies are quite high, typically 40% to 50% (potentially even higher, depending upon the fluid used). Ordinary steam turbines can achieve 40% efficiency. Hybrid designs with a gas turbine followed by a steam turbine can achieve 60% or higher efficiency. The problem with solar dynamic is that moving parts imply mechanical failures. These units would likely require a nearby crew for maintenance – something easily provided from a space-based habitat. Note that at 60% efficiency, a circular mirror of 2.8 km diameter (or a 2.5 km square array) is sufficient for a 5 gigawatt SPS.
Solar dynamic has other advantages: lightweight flexible mirrors (such as ordinary aluminum foil) are not significantly affected by radiation, ultraviolet light, or micrometeor punctures. Disadvantages include that the turbines and generators are heavy, high-tech components that may have to be launched from the Earth. Also, the working fluid in the gas/steam turbines may not be cheaply available. The only gas available in large quantities is oxygen, which is very corrosive to many metal surfaces, at least until we capture the resources of a live or extinct comet which is likely to contain enormous quantities of water and ammonia.
PHYSICAL SIZE OF A SOLAR POWER SATELLITE
Using assumptions listed above, the width of an SPS might range from 2.5km to 4.25km, or as large as 6.75km if we use the cheapest solar cell technologies. But 4.25km looks like a reasonable target. Note that at geosync orbital distances, these would be as visible as the larger planets, and easily resolved with binoculars. Once hundreds were in orbit, they would appear as an arc of lights to anyone who looked up on a clear night.
There is also a nearby 1.0km microwave transmitting antenna, visible using binoculars. One problem is that the solar cells must always point at the sun while the transmitting antenna must always point to the Earth side receiving station. Proposed solutions include:
- use the same structure with phased array techniques to steer the beam (always pointed at the sun), difficult for certain orientations;
- use separate structures with some connecting mechanism that rotates one or both arrays;
- use a smaller integrated array of a 1km transmitter (always pointing to the Earth) backed by a (fixed) 1km photovoltaic array, and a separate large mirror to track the sun and focus its light on the back of the transmitter. While appealing in several respects, this does have its own problems: dissipating roughly 15kw of waste heat per square meter, which implies a blackbody temperature of 240oC if there is no additional radiating surface (it couldn’t be a manned structure, and would have to cool off prior to maintenance). The mirror and the transceiver would have different orbits – one would require constant adjustments. Lastly, it would be difficult to focus sufficient light on the transceiver near local noon each day. But some clever engineer may find a solution to all these problems.
MASS OF A SOLAR POWER SATELLITE
Using modestly optimistic assumptions for solar photovoltaic panels, supporting structure, power collection, and for the microwave transmitter and its own antenna, I estimate a total mass of 25,000 tons for a five-gigawatt SPS. Early estimates were closer to five times higher, and some optimists currently estimate that thin film panels would weigh one-fifth as much, although a supporting structure and the transmitter must also be considered. Note that if the solar panel array is 4km on a side, then 1.0 kg/m2 of panels, structure, and wiring results in a total mass of 16,000 tons, leaving the remainder of my mass allowance for the transmitter, its antenna, and other support structures.
A 1.0kg/m2 mass allowance solar cells, wiring, and structure seems like a significant challenge, requiring a substrate similar to a sheet of paper in thickness. Note that a silicon wafer sliced 1.0mm thick weighs 2.3kg/m2. However, the typical thickness of photovoltaic silicon wafers today is only a tenth that, and thus weighs 0.23kg/m2, leaving adequate allowance for structural components and wiring.
When using the resources of an asteroid to build the Solar Power Satellite, the mass of the photovoltaic panels is only a minor concern, as there is more than enough silicon and iron in even a small asteroid to build them as crudely as desired. Indeed, using a convenient asteroid allows the construction of large and inefficient but presumably simple and reliable solar power satellites. The final technology choice may be one of minimum labor costs or total time-to-market. Those tradeoffs are not simple, because using a less efficient technology (that is simpler to produce) implies a significantly larger structure with more materials and thus more time and effort to build.
But by using an asteroid for raw materials, we at least have choices to make beyond “is it even feasible?” Launch costs of people and tools to bootstrap the process will be high enough as it is, but having the cheap and convenient asteroidal resources in orbit where we need them gives us the flexibility to try not just one approach, but several approaches and learn which is the best way to deliver clean and cheap energy to the inhabitants of Earth.
It appears to me that this would result in 230 w/m2 at the earth. Given a 60% aperture efficiency this would be ~140 w/m2. Solar can be much higher, even if it has lower availability.
Can you comment on whether the SPS is competitive?
Your math is correct.
A minor point: microwave rectennas can achieve much higher conversion efficiencies than 60%; even 90%.
More importantly, however, is that the 230 w/m2 is a design point that allows people (and wildlife) to thrive even when in the beam. If we don't care about cooking them, we can use much higher energy densities.
Most importantly, that energy is available 24x7, while ground-based solar power doesn't work at night, when it's cloudy, or in early morning or late afternoon when the sun angle is too low, and the fraction of time of high sun angles varies by season. On average, ground solar is available perhaps 8 hours per day (more in dry deserts where you don't need it, less in high-latitude cloudy areas like the mid-west and north-eastern states where you need it most).
A last point: solar radiance in space is 1367 w/m2, while on the ground is only about 1000 w/m2 even when the sun is shining directly overhead.
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