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The Maury Equation June 21, 2011

Posted by Maury Markowitz in solar power satellites.
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I’m claiming my 15 microseconds of fame right… now! The Maury Equation of the Economics of Solar Power demonstrates that the price of space based power will never be competitive. I intend to prove this, below.

Some background

The price of electricity from any power system is a combination of a few basic inputs. These include:

1) capital costs
2) fixed operational costs (building maintenance, etc)
3) variable operational costs (turbine maintenance depends on delivered power)
4) fuel input costs

If you add these up for the lifetime of the system, you end up with the total cost of the power produced. Now divide that by the amount of power produced during that same lifetime, and you get the cost of that power on a per-whatever basis. I like cents per kilowatt-hour (c/kWh), because that’s what appears on people’s bills.

The result of this calculation is the “Levelised Cost of Electricity” (or Energy, depending on the source). It’s widely used when comparing power sources because it offers a simple apples-to-apples comparison.

…and how we’ll use it

In the case of solar power, the LCOE inputs for (2), (3) and (4) are vanishingly small. The cost of power is dominated entirely by the capital costs of the equipment.

As the sun’s output doesn’t change much, one can easily predict the amount of power produced on a yearly basis, multiply by the expected lifetime, and then estimate the total cost of power. For large solar farms in the US southwest, that’s somewhere in the range of 15 c/kWh assuming a 40 year life span, or 20 c/kWh if you factor in short lifetimes of the inverters and plan for two replacements over the lifetime of the panels.

In the case of space based power, there are the launch costs to consider. This is likely much more than the cost of the panels, but in effect it factors into the overall capital costs. Yet those same panels will produce more power. This makes it difficult to directly compare the two cases… well difficult until you actually try it. So let’s try it!

Go ahead and try this at home…

Lets’s start with the basic capital/construction cost calculation. Let’s define P as the cost of buying enough panels to produce 1 kW of peak power at “standard” conditions, STC. This number is the same for ground and space. But for this discussion, we also need to consider the cost of shipping those panels:

Sground is the price of shipping and installing those panels on the ground
Sspace is the price of shipping and installing those panels in space

… then the total capital cost of installing the panels, greatly simplified, we’ll define as C:

C = P + S

Now let’s look at the income side of things. Panels generate power from the “insolation”, which we’ll call I. This is normally expressed in terms of power generated over the period of a year given a set of panels that would generate 1 kW under STC. So if that’s the power it generates in a year, then we just need to multiply by the number of years the system is in operation, L. Presto, that’s the lifetime electrical generation, E. So:

E = I x L

There’s one more thing to consider in this particular case, and that’s the cost of transmission. In the case of space based power, and often for ground based as well, the systems are located at long distances from the consumption, and there will be losses on the way between the two. We’ll call this T. So then for our calculations:

E = I x L x T

Ok, so then we’re ready to go, the levelised cost of electricity from the systems we’ll be considering is simply:

LCOE = E / C

Now let’s talk numbers

So great, we have an equation, but what are we supposed to plug into it? That’s the part I’ll do for you, with a little Google-Fu

P is currently about $3000 per kWp (for comparison, hydro is about $2000, and nuclear is about $11000).

Sground is about $1 a pound, Sspace is about $12,000 a pound.

Iground is about 1600 for fixed-plate collectors in the US southwest, Ispace is about 8600 in GEO

Lground is about 40, Lspace  is roughly 12 (space is a nasty place!)

Tground is small, maybe 10% in the worst case, while around Tspace is around 50%, and then has to add Tground. Let’s leave it at 50% net for now.

So then:

Eground is 1650 * 40 * .90 ~= 60,00
Espace is 8600 * 12 * .5 ~= 52,000

So contrary to the space power boosters’ basic claim, space based power generally produces less power over the lifetime of the system.

So…

Let’s put it all together…

LCOEground = Cground / Eground = ($3000 + nothing) / 60,000 = 5 cents per kWh on capital alone

LCOEspace = Cspace / Espace = ($3000 + (100 lbs/kWp * $12,000) / 52,000 ~= 125,000 / 52,000 = $2.40 per kWh

What’s interesting about this set of equations is that it is utterly dominated by the transit costs. Doubling the efficiency of transmission, for instance, does nothing to address “the problem”. Moreover, note that the price of the panels isn’t even a factor, which means that improving the technology on the panel side does nothing — both sides improve by the same amount.

So I simply state it flat out. The numbers suggest that space based power cannot ever become competitive with ground based solar unless the cost of launch falls by three orders of magnitude. I consider this to be “effectively impossible”: although it is not specifically impossible, the chance of it happening is much lower than the chance of an entirely different invention coming along that renders the entirely argument moot (say fusion power).

Should you trust these numbers? Well, the US the DOE is in the process of driving LCOE to 6 cents by 2020, including all factors, like the cost of land, labor, everything that we ignored above. Those too are much more expensive in space, including “land” – orbital slots cost a lot more than Mohave desert.

Fight!

I ask all proponents of space solar power to attack this as hard as they can. All I ask is that you use the formulas above (or suitably modified version), present your numbers for each one, and reference why you believe that number can be supported.

The numbers used above are all fully referenced in previous posts (suddenly I wish there was a wiki-easy way of doing refs here!) but I’d be happy to present them again if anyone needs them.

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Comments»

1. bob tom - October 27, 2011

You fail at basic science. Unless your panels are installed at the equator, you will only get 8-9 hours of generation out of ground based panels. Weather / dust will reduce output even with good maintenance. Mobility of the space based systems delivery / distribution is an added value that even the military is investigating. ( reducing distribution length )

Maury Markowitz - October 27, 2011

“You fail at basic science”

This oughta be good…

“Unless your panels are installed at the equator, you will only get 8-9 hours of generation out of ground based panels. Weather / dust will reduce output even with good maintenance.”

The insolation numbers I quoted include *all* effects on yearly sunlight falling on the panels. This includes the day/night cycle, clouds, and even extra sunlight due to reflections off of snow cover (if you’re in the right area). You can trivially find these numbers on the web. Start here:

http://www.nrel.gov/gis/images/map_pv_national_hi-res.jpg

From that map you’ll find that the US southwest gets about 6.6 kWh/kWp/day, which is 2400 kWh/kWp/year. I then used the industry-standard derate factor of 0.77, which accounts for performance problems in the system itself (including 0.05 for dust), and then rounded off the result.

“Mobility of the space based systems delivery / distribution is an added value that even the military is investigating.”

As to the transmission side of things, receiver efficiencies on the order of 85 to 90% are typical, and on the broadcast side it’s 40 to 70%. So absolute best case scenario is 0.7 times 0.9 = 0.63. You can read all about it here:

http://www.sspi.gatech.edu/wptshinohara.pdf

That’s ignoring beam losses due to weather, antenna effects and DC-to-AC conversion. If we use the same industry-standard derate, you get 48% end-to-end, which I round up to 50%. This has nothing to do with path length or beam steering, these losses are inherent to any such design.

So, I don’t fail science. You might want to check your numbers next time *before* you post, especially if you’re going to name-call.

2. Paul - October 27, 2011

I assume the insolation number is raised for space having better exposure for longer periods of time.

So I’d like to talk to you about SpaceX and your launch costs.

http://en.wikipedia.org/wiki/SpaceX

The Falcon 9 is flying now, and as SpaceX has more than just Government contracts now I believe we’ll see if their kilo to orbit numbers are possible or not. Anyhow their Kilo to orbit pricing for Geostationary orbit on the Falcon 9 is cheaper than your cost to ship a Pound of solar panels to space.

When the Falcon 9 Heavy is flying we can sharpen our pencils further, but I wanted to limit myself to rockets that are flying and companies are launching payloads with.

Maury Markowitz - October 27, 2011

That’s right, the insolation is a basic figure that accounts for how much *energy* is deposited over a given time. In space you automatically get double because there’s no night, but there’s also angles and atmosphere to consider. All in all it’s about 1/4 to 1/3rd that hits the ground and gets converted into energy.

If you run the numbers, you need a factor-of-10,000 in order to get SBP to be equal to ground based. I believe Falcon 9 is a factor of 10. So, only another 1000 times reduction in price to deal with! :-)

3. Karl Hedderich - March 10, 2012

Great post! It is always nice to see a strong debate when dealing with far out things like space based solar power :)

I think that you make some pretty strong points with how unlikely SBSP is to ever be economically practical but just to play devils advocate I have a couple of counter points.

1). When comparing SBSP to other green energy generation technologies you should really include the costs of providing base load power using those technologies. SBSP provides baseload power with out requiring storage while terrestrial wind and PV would require storage to provide base load power (or they would require a global super grid to transmit power intercontinentally). Storage technologies add expense to terrestrial green energy baseload power. I acknowledge that in the real world we would just use fossil fuels to provide baseload power and just use terrestrial PV as an intermittent source rather than use a purely PV based approach to satisfying our energy needs. I also acknowledge that even if you factor in the storage costs terrestrial baseload PV power would still be 3 orders of magnitude cheaper than SBSP. But that brings me to my second point…

2). There are various reasonable proposals to bring the cost of space access three orders cheaper. A 1st gen Startram could provide access to orbit at 43$/kg to low earth orbit. A large lofstrom launch loop could drop the cost to 3$/Kg to low earth orbit. If successful a moderately reusable spacex heavy lifter could drop the cost to $500/kg to low earth orbit.

3). There might be special use cases that SBSP is especially suited to that other generation technologies are not. Providing energy to military bases in a theatre of war. Apparently gasoline can cost anywhere from 10-400$ per gallon in afghanistan for the US military! I am not sure what electricity costs but I bet that it is similarly expensive. While terrestrial solar power might be practical in this case I doubt it; it would be harder to defend a large PV array on the ground; they would require energy storage areas; large terrestrial pv arrays aren’t mobile and while neither are rectenna’s the latter are probably much cheaper and thus abandonable.

Number one Is unlikely to have any effect on the real world likelihood of developing SBSP because there are other cheap polluting baseload power solutions. Even if these were outlawed other green technologies would probably be more viable (high altitude wind power, enhanced geothermal).

Number two requires rich investors (launch loop or startram would probably cost ~50 billion dollars to build).

All in all SBSP is unlikely to become the baseload power generator for civilian use. But if spacex is successful (or we build a startram) SBSP could be a financially viable option for supplying power to forward operating bases in future conflicts.

Maury Markowitz - March 11, 2012

“When comparing SBSP to other green energy generation technologies you should really include the costs of providing base load power”

Only if you think that a particular technology has to deliver *all* forms of power. I don’t believe this. I think the right solution to practically any problem is a mix of technologies, using the ones best suited to the problem at hand.

Consider a system consisting of existing hydro, nuclear and wind for base load, new hydro and NG peakers for “fill out” and conventional PV for peak, when available. Such a system would be far less carbon intensive than the current one, while delivering the same amount of power at only slightly higher costs.

But if you want to demand PV (or wind) provide base load, the question is which is cheaper, a battery or a rocket. Do the math yourself!

“There are various reasonable proposals to bring the cost of space access three orders cheaper”

We’ve been inventing new systems to lower costs for 50 years and none of them have done so. But it doesn’t make a difference.

As you can see from the math above, a solar panel in space is likely to produce *less* power than the same panel on Earth. The cost of transport is a major concern, of course, but by no means the only one.

“Providing energy to military bases in a theatre of war”

Oh, for sure! After all, we’re all aware of the $1000 hammers, so $10 / kWh for power? Peanuts.

If this ever happens, I suspect this will be who does it. Also mineral exploration companies might be interested in any leftover power, even at very high prices (flying oil cans in on a Short Skyvan is *very* expensive)

4. Karl Hedderich - March 10, 2012
5. karl hedderich - March 11, 2012

My only complaint with your excellent article is in the wording of the thesis. As I read it the thesis presented is: “the price of space based power will never be competitive”. Competitive with what? We seem to agree that SBSP will never be a substantial portion of our energy portfolio but we also seem to agree that it might possibly be competitive in a very limited number of situations. I just think the thesis needs to be changed to: SBSP will never be a major provider of power to the earth.

As to reducing the price to orbit I agree that the government won’t fund a launch loop or startram. However, spacex has already dropped the price an order of magnitude :) I think that views on the infeasabililty of dropping costs should be moderately tempered by spacex’s success. Further, if the drop in access price can create increased demand for access to space a small private consortium could probably build the startram or launch loop. 20 billion dollars is a lot of money but if some starry eyed dotcom billionaire and his buddy’s thought they could make some profit from it they could raise that money.

Maury Markowitz - March 17, 2012

Fair comment, but “Space Based Power will never be competitive with ground based sources of grid power in the near future” didn’t fit into the headline editor ;-)

karl hedderich - March 17, 2012

Touche

6. Larry Pieniazek - May 25, 2012

The way to make space based solar effective is to not launch the panels from earth, and to not beam the power back down. Make the panels from local resources, and use the power for industrial processes up there instead of trying to beam it down here.

Maury Markowitz - March 21, 2013

WHAT industrial processes up there? The only ones anyone has ever proposed is solar power satellites.

7. Marc - April 21, 2013

The only issue I have here, is the idea of being able to predict future trends. For example this assumes that there is no space habitation or robotics being used. While I agree it is presently correct, the assumption that this will always be the case is suspect. I mention robotics specifically, while I would wish we would inhabit space, I don’t at present consider this likely. Robotics on the other hand might come into play. Bringing things up the gravity well, is a fools errand forced on us at this point due to logistics, but given our advances in robotics and technologies like ion propulsion or using mag rails, it might be possible to construct these panels and the rest of the infrastructure in space specifically. Unfortunately I don’t have numbers to work with, so I can’t say how likely or efficient it would be. BUT I mention this to illustrate why saying never, isn’t a good place to start such an argument. Otherwise I personally love how you have analysed this.

Maury Markowitz - April 21, 2013

Marc, if you want to see how *those* numbers work, try my follow-up article:

http://matter2energy.wordpress.com/2012/03/17/the-maury-equation-redux/

It’s difficult to imagine *any* case where SBSP works.


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