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Power Satellite Progress

This is a follow-up on my “Dollar a Gallon Gasoline” article from April 2. That article proposed power satellites as a way to solve energy, carbon, climate, water and even economic stagnation problems. The follow up is on an alternate transport system powered by microwaves rather than lasers.

Power satellites are a complicated subject. It involves economics, “rocket science,” i.e., the rocket equation, orbital mechanics, radiators, thermodynamics, microwave and laser optics, geography, geometry, radio frequency interference with communications, Skylon (rocket plane), atmospheric damage effects (from NOx), chemistry, electrochemistry, military policy, international politics, and in-space operations and assembly. It’s difficult to put enough detail in an article for it to be believable and little enough detail for it to be readable. But I will try.

The engineering has developed over the decades from 1968. It’s unusual to need an update even once a year, much less one in a few months. However, progress has recently picked up. In May, there was an article about Japanese plans for power satellites in the IEEE Spectrum by Susumu Sasaki, a senior scientist with JAXA. JAXA is Japan’s equivalent of NASA. The IEEE is the largest technical society in the world

http://spectrum.ieee.org/green-tech/solar/how-japan-plans-to-build-an-orbital-solar-farm

More recently there was a CNN article on Skylon, one of the keys to making power satellites economical.

http://www.cnn.com/2014/08/08/tech/innovation/spaceship-reinvented/index.html?hpt=hp_c3

The current schedule for Skylon is for it to fly in 2021. That means that on an ambitious schedule the first power satellite could come on line in 2023. Rapid growth could lead to displacing fossil fuels by the mid 2030s.

If you want to displace coal with cheaper power from space, the cost limit for lifting power satellite parts to GEO is around $200/kg. That depends to some extent on how many kg it takes in GEO to deliver a kW on the ground. The current consensus is 5-7 kg/kW. That’s $1000 to $1400 per kW for the transport cost. If the parts and rectenna add another $1100, the cost will be from $2100 to $2500 per kW. To get from capital cost to electric power cost you divide by 80,000, which puts the cost in the range of 2.6 to 3.2 cents per kWh. That’s far enough below coal at 4 cents to gain market share. 

Image

 

 Figure 1.

At the minimum volume (10,000 flights per year) needed to build power satellites, Reaction Engines, Ltd. estimates the cost of cargo to LEO will be $120/kg. For chemical rockets, the cost multiplier is about 2.5 from LEO to GEO (because you have to lift the fuel as well as cargo). A multiplier of 2.5 ($300/kg) is excessive if the lift cost has to stay below $200/kg.

Chemical rockets are not the only choice.  Ion engines are slower but they take much less reaction mass. At an exhaust velocity (Ve) of 20 km/s, only 21% of the mass lifted from earth is required for reaction mass.

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Figure 2.

This is not a new idea; see the 1992 paper by Brown and Eves.

http://www.utdallas.edu/~pxm017500/gap4s/Doc/Ref/Recten/00141357.pdf

The problem with ion engines is the high power consumption. To accelerate reaction mass of 1 kg per second to 20 km/s takes 200 MW. It’s a tradeoff between the cost of lifting reaction mass and the cost of supplying a lot of power.

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 Figure 3.

Microwaves are how we propose to bring power down from power satellites; they can also send power up to power ion engine rockets from LEO to GEO. However, the same microwave optics problem (focusing and scale) affects up-transmission as well as down. This sets the minimum rectenna in space at close to a km in size and the transmitter on the ground at 10 by 14 km, possibly larger. We also have to consider the effects of blasting communication satellites with the spillover that misses the rectenna on the vehicle.

If a 1000 ton rectenna and another 1000 tons of engines and structure are around 10%, the entire vehicle will mass upwards of 20,000 tons and the payload will consist of 1001 (13 layers and 91 per layer) fifteen ton Skylon cargo modules full of power satellite parts. For a dry mass of 17,000 tons, 4500 tons of reaction mass will be needed (plus a bit more to make the trip back). If the trip time is 28 days and the vehicle is in view ten percent of the time, the ground transmitter can power the vehicle for 244000 seconds. The flow rate, 4,500,000 kg/244000 seconds is 18.4 kg/s

3.7 GW would be required to accelerate 18.4 kg/s to 20 km/s. That is ~66 tons per hour, so ~4460 tons of reaction mass would flow through the engines in ~67 hours. That is in reasonable agreement with a numerical model in Excel that gave a thrust time to GEO of 73 hours. The model gave a trip time of ~28 days, close enough to the starting assumptions.

The power level at the ground is not much different for a transmitter going up compared to that from a power satellite coming down, perhaps 8 GW input to the transmitter to power ~4 GW of VASIMR thrusters. The microwave radiation level would be around 450 W/m2 at the transmitter surface. The power level will be lower if the transmitter is larger. I.e., this will not cause birds to burst into flame.

Figure 4 shows an arm putting the last layer of cargo modules on the stack.

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Figure 5 shows 15,000 tons of cargo under way using VASIMR engines making the purple glow.

 

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Artwork by Anna Nesterova 

The microwave transmitter and combustion turbines to power it will cost less than $16 B.

Written off over 5 years, the cost will be around $3.2 B/year. Using only one ion transfer vehicle and ten trips per year, the capital cost for the microwave transmitter will be $3.2 B/0.15 B kg or ~$21/kg. To that we need to add the cost of writing off the 2000 ton transfer vehicle over a number of trips and the cost of the fuel to run the turbines. If the vehicle cost in space is 3 x the lift cost, the vehicle will cost around 2 million kg x $120/kg x 3 or around $720 million. Written off in 5 years (50 trips), the cost per trip for the vehicle would be $14.4 M. The fuel cost to run the turbines per trip is around $59 M figured at 10 cents per kWh  Divided by 15 M kg payload, these two add less than five dollars per kg increasing the LEO to GEO cost to $26/kg. It will take about 3 kg of reaction mass per 15 kg delivered to GEO making the cost per 15 kG kg to GEO $120×18 for the cargo plus reaction mass plus + $26×15 for the LEO to GEO cost, ~$170/kg. We will have to watch cost carefully, but this is somewhat under $200/kg.

Laser-boosted Skylons (discussed in the previous article) are a still lower-cost approach for ground to LEO. They have a payload fraction 3 to 4 times the LOX carrying Skylon. If the cost per flight is about the same, the cost per kg to LEO using lasers would be about $40/kg plus a proportionate share of the (expensive) laser cost.

During the Strategic Defense Initiative (Star Wars) research scientists and engineers solved most of the problems with high-power lasers and tracking. This included constructing mirrors large enough to track a hydrogen heater on the wing of a Skylon from GEO. But VASIMR propulsion and microwave transmitters and receivers are at a relatively high technology readiness level (TRL) compared to big lasers and would be less risk.

Of course the combination of laser boosted Skylons and microwave propulsion (powered from GEO) would be even better, getting the cost of transport to GEO down to about $60/kg, the cost for power well under 2 cents per kWh and the cost of synthetic oil under $50/bbl.

Humans may not solve the energy and carbon problems, but it not because we lack engineering paths to do so.

Epilogue

Peter Glaser, who patented the power satellite idea in 1968, died in late May of this year.  RIP

http://www.nytimes.com/2014/06/06/us/peter-glaser-who-envisioned-space-solar-power-dies-at-90.html?_r=0

Content Discussion

Roger Arnold's picture
Roger Arnold on September 11, 2014

Nice article, well written.

One point I do question is the assertion that in just two years after first flight, Skylon could be flying with sufficient frequency to support construction of power satellites. If things go anything like I would expect for such an advanced vehicle, there will be at least two years of test launches with the first flight article before the first production Skylon rolls out of assembly.

Things might be different if development of Skylon were given the priority that of a wartime project seen as crucial to survival. I don’t think we’re quite there yet.

Keith Henson's picture
Keith Henson on September 11, 2014

Sorry, Roger, I wasn’t clear on that point.

2021 is when production at a delivery rate of one a month starts.

2023 just falls out of the financial spreadsheet since there have been enough flights to build up the mass of the first power satellite plus the infrastructure in GEO.

I should send you the spreadsheet.

Keith Henson's picture
Keith Henson on October 5, 2014

“Can you explain the reasoning behind that number?”

Sure.

You can find the formula for the levelized cost of electrcity here;  https://en.wikipedia.org/wiki/Cost_of_electricity_by_source

I am assuming $1,600,000 per MW as the initial cost and 10% per year of the cost for maintenance.  Power satellites run supplying base load, here I assume ~91% of the time; it may be higher.

The discount rate is 6.8%, same as the government uses for other sources.  It’s put into a spreadsheet here:

https://docs.google.com/spreadsheets/d/1wDvn369EudkYGsPK3jNt4FmBFpNFtt0ZwDZl_lt_SNM/edit#gid=1481425448

The ratio between the $1600/kW cost and the cost that comes out of the formula (~2 cents per kWh) is close enough to 80,000 to one.  Electric power cost is proportional to the cost of a power satellite (or any power source that has no fuel cost) in this ratio for this discount rate and years of service.

If you use the UK government discount rate of 3.5%, then the cost of power is just over 1.5 cents per kWh and the ratio is ~100,000 to one.

Keith Henson's picture
Keith Henson on October 5, 2014

Roger, the allowable cost for a power satellite is $1.6 B to $2.4 B per GW.  That gives 2-3 cent per kWh power.  The mass of one is 25-30,000 tonnes.  They come in 5 GW lumps, so the cost is $8-12 B each.

Re getting it down, mass in GEO is useful.  Old power satellites can be reprocessed into new ones when and if they ware out.  There are problems with space junk, but they are in getting parts to GEO, not satellites at GEO.  I have an analysis, if you want I can put it up as a google doc.

People have talked about reflecting sunlight on earth based solar farms.  There are problems because the sun is not a point source.  I happen to be interested in solving the big problems, not little stuff involving the ISS.

Roger Arnold's picture
Roger Arnold on October 5, 2014

The engineering parts of what you write about are sound. At least as far as I can tell. We could debate fine points, like the relative merits of ground-based launch lasers vs. microwave transmitters for delivering the energy needed for high impulse orbital transfers. That would be great fun, but I think we both know that it wouldn’t likely accomplish much.

The real problems that we face in moving the world’s energy economy away from fossil carbon and transitioning to more sustainable patterns are not primarily technical. There’s a technical dimension to them, in that technology influences economics — the amount of up-front capital investment that needs to be committed, the time period before revenue returns, the rate of payoff, etc. But even favorable economic parameters aren’t enough to make rational things happen in the absence of a favorable socio-political and investment environment. It’s the current state of that environment that’s the problem. 

There’s no real shortage of feasible engineering solutions to our current problems. A lot of different approaches could be made to work. Even the economically crazy pro-renewable / anti-nuclear agenda of the European greens could be made to work, given unlimited public willingness to pay its costs. The Strato-solar vision for high-availability PV energy with gravity storage even has the potential for making the “100% renewables / non-nuclear” path economically competetive. But like your SSP, it suffers from a perception-of-credibility issue with an investment community that, with a few notable exceptions (Go Elon!), is technically illiterate and remarkably herd-like in its behavior.

We appear to be living in a world that has lost its collective will for solving problems. The world economy has been largely taken over by wealthy parasites. When it’s easier and more rewarding to multiply one’s wealth through manipulation of the financal system, building virtual monopolies covering whole sectors of the economy, buying politicians and judges, and stirring up wars to secure lucrative “defense” contracts — when that becomes more attractive than building companies to solve real problems, then the world is in deep, deep trouble.

Perhaps I’m being overly pessimistic. Perhaps I’m too influenced by living in a declining imperial power whose people are behaving like sheep so easily herded by the media dogs of Mr. Murdoch and his ilk. Perhaps I’d see things differently if I lived in China. China has its own problems, however. The one thing it really has going for it, that I can see, is that its leaders seem to come from engineering backgrounds. It isn’t (yet) run by lawyers.

Perhaps your SSP ideas will find a future there.

Roger Arnold's picture
Roger Arnold on October 5, 2014

<blockquote>a $2B space 1GW PV plant operating at 100% CF would not be so attractive vs a $2B earth 10GWp earth plant operating at 20-30% CF.</blockquote>

Actually the 1 GWp SSP plant would still be more attractive than than the 10 GWp terrestrial plant. One GWp of SSP nameplate capacity is equivalent to 1.3 GWp of terrestrial nameplate capacity, just due to the difference in intensity of sunlight. With 50% delivery efficiency, that’s .65 GWe 24/7 power to the grid. The 10 GWp terrestrial plant might deliver for 6 full-time-equivalent hours per day in the best locations, but would need 45 GWh of storage capacity to support its 2.5 GWe average output. The cost of that much storage capacity would completely eclipse the cost of the solar plant itself. It would render the total capital cost per annual GWh delivered substantially higher for the terrestrial alternative.

Keith Henson's picture
Keith Henson on October 5, 2014

Before you talk about a “1 kw system,” you should read the Wikipedia article on space-based solar power and see why 5 GW is the minimum size for a 2.45 GHz microwave power link.

Keith Henson's picture
Keith Henson on October 5, 2014

Roger, right on there being a technical dimension.  At the moment I am stuck on the cost and mass of the VASIMR engines needed for the LEO to GEO transfer.

Otherwise, I agree with you about the reasons it is unlikely for the US to do power satellites.  At the moment, the UK is ahead because they are building Skylon.  Japan would like to do virtually anything that doesn’t need nuclear reactors.

And, as you mention, China.

Keith Henson's picture
Keith Henson on October 5, 2014

https://drive.google.com/file/d/0B5iotdmmTJQsc0xydHNPbmJPMnVPbzZmaTdpVjM1UFZUN3dZ/view?usp=sharing