Month: January 2008

Cost of coal

Let’s look at the cost of coal-fired power over the long term – aside from the environmental impact, which is worrying enough. Combustion of carbon (the main component of coal) produces 393.52 MJ/kMol – as 1 kilo-mole of carbon is 12.011 kg, that’s 32.76 MJ/kg. But coal also contains a lot of “ash” – incombustible junk – and so typically coal burns about 27 MJ/kg. Cheaper power-utilities in China dump the ash straight into the exhaust stream, which is rather nasty for everyone downwind, but in developed countries the stuff is captured and sold as a concrete ingredient, if it’s not too radioactive. Yes, radioactive, from all the uranium and thorium that naturally occurs in some coal-fields.

That aside a ton of coal typically costs $20/ton to dig up, crush and get to the furnace. Once there the stuff is burnt and the heat boils water into super-critical steam, pushing turbines. Some heat is recovered in a good coal fired plant, getting about 40% efficiency from coal lump to power-meter at the station’s transformers upping the voltage for transmission. Thus every megawatt produced means about 2.5 megawatts of heat from burning coal, about 0.0926 kg coal burnt and about 0.338 kg of carbon dioxide produced. A 500 megawatt plant thus needs to burn 46.3 kg/second or 4,000 tons of coal a day. And the plant can’t slack off because the boiler and furnaces need to burn that ALL the time. Design limitation. Thus a coal plant costs about $80,000/day in coal-mining. About $29.22 million a year. Over 30 years it burns 43.83 million tons of coal, makes 122 million tons of CO2, 7.7 million tons of ash and costs $876.6 million in coal-mining costs (non-adjusted for inflation.) Thus the $750 million dollar coal-plant costs another $876.6 million in coal-mining for 500 MW for 30 years. Throw in the costs of running the thing (about 30% extra) and, in reality, the power costs maybe $2.11 billion (non-inflation adjusted) – about $0.016 per kW.hr. So the margin of selling it for $0.05/kW.hr is quite good.

But coal isn’t always that cheap. Here in Queensland, Australia, coal is cheap – we have some of the best anthracite (high carbon coal) in the world. Our Government power companies seem to burn it for close to cost prices. If you have to buy it on the market, not just mine it, then it costs ~$US 120/ton or so. Then the costs jump to $0.0457/kW.hr and Solar Powersats look a whole lot more attractive. No wonder places like Japan are interested.

What about a “carbon tax”? If, like the nuclear industry, coal-plants had to cost-in carbon dioxide disposal things get interesting – estimates of $20/ton are bandied around as viable. That means about $60 per ton of coal burnt. Add that to the above and we get at worst a cost of $0.0657/kW.hr. Nukes start looking like the cheapest option, unless our powersats start coming down a bit more.

So how many kW.hr does a 500 MW power-source produce in 30 years? Assuming 263,000 hours in 30 years that’s 131.5 million kW.hr. If we had a solar panel on the ground only about ~ 25% of those hours would be producing energy at full strength, due to the day/night cycle and cloud-cover. Thus, to get the same power overall ground-based solar needs x4 the expected power supply, minimum. With batteries it’s more like x5 because of the inefficiency of charging/discharging batteries. Thus, if power cells cost ~ $4/W (installed with power conditioning & storage) and we want 1,000 W continual supply we need 5,000 W of cells, and it all costs $20,000. Repaid over 263,000 hours it costs $0.076/kW.hr. With interest, costs spiral to ~ $0.25/kW.hr. But solar PV cells are coming down in price all the time. Nanosolar is planning on selling for ~$1/W, thus implying eventual reduction of price to ~ $0.0625/kW.hr. But only if we’re repaying over a leisurely 30 years. Some PVs decline by ~ 10% every few years or so. If we want a 10 year repayment time we’re back up to $0.19/kW.hr.

Solar Power Satellites re-examined

Robert Zubrin’s Entering Space is a passionate defense of the idea that humanity needs to commit to colonising another planet – specifically Mars – before many other space-related concepts can become viable. One money-making venture in space that Zubrin trashes along the way is the Solar Power Satellite or Powersat a concept first proposed in the 1960s by physicist Peter Glaser, and since then extensively studied by NASA and the DoE in the US, as well JAXA and the ESA.

Zubrin’s analysis is scathing for anyone with hopes of powersats being a commercial prospect. Here’s what he assumes and computes in his argument…

(i) Insolation averages ~ 1300 W/m^2… a bit low, but not by much. References give 1368 W/m^2, averaged.
(ii) Power transmission efficiency ~ 50%… low again, typically 63% in the literature
(iii) 15% efficient PVs
(iv) PVs mass 4 kg/m^2… rather heavy.
(v) non-PV mass another 4 kg/m^2 of PV panel… even heavier.

At $40,000/kg delivery costs to GEO a 1 GW (500 MW to the ground) Powersat massing 41,000 tons would cost ~$1.65 trillion to orbit, and double that to assemble. That’s $3.3 trillion total. For some reason his quoted figures double at this point and he says $6 trillion. At 10% interest and maintenance the system annual costs go to $1 trillion (~$0.55 trillion using the corrected figures) and the cost per kilowatt.hour, for 500 MW supplied for 8,766 hours a year, is $228/kW.hr ($125/kW.hr corrected.) Some 2500 times more expensive than the $0.05/kW.hr at the time of writing (1999.)

By his analysis that means launch costs would need to drop to just $4/kg which is impossible using current techniques as that’s 4 times less than the fuel costs needed. Clearly absurd BUT let’s look at his assumptions again. We’ll grant him (i) & (ii) as the figures quoted are close to literature figures. What about (iii)-(v)?

(iii) 15% efficient PVs… well the best commercial cells are heading for 40% and techniques for increasing efficiency are being touted by various labs. One inventor is selling thermoelectric converters with 60% efficiency, while another group has developed nano-antenna collectors potentially 80% efficient. Thus the PV mass could be cut by more than 75-80%.
(iv) Mass density of 4 kg/m^2. Very heavy. The new PVs could be made much lighter by using concentrator arrays (which also cuts the costs of PV converters themselves too.) A system of inflatables could drastically cut the mass of the array – Geoff Landis designed a system massing just 800 tons (plus 500 tons structure) collecting 3 GW in space at 35% efficiency thus massing just 0.364 kg/m^2. All the old DoE/NASA studies assumed about ~ 1kg/m^2 including PVs and structure. Zubrin is wildly off-base.
(v) Double the PV mass in structure and power distribution/transmission systems. Structure can be made using self-assembling inflatables that space-cure into hard structures. Power distribution and transmission masses can be minimised by clever design – I’m doubtful they’d mass 20,500 tons for 1 GW like Zubrin imagines, but they can be heavy. Especially problematic are the heavy slip-rings and brushes needed to transfer power from the rotating collector panels to the non-rotating transmitter. A lot of mass can be saved by reducing the need for power transfer. One design uses movable mirrors focussed onto a non-moving core connected directly to the transmitter. This also reduces the heavy power-cabling needed to carry 1,000 MW to the transmitter.

Moving parts are always a potential problem, but lots of small moving mirrors reduces the impact of one or two mirrors sticking and needing repair. Conceivably those repairs could be carried out by teleoperated machinery.

Let’s call the powersat mass ~ 1 kg/m^2 – not as good as some designs, but better than Zubrin’s Strawman Argument. So where does that get us? Some 20% of 12.5% percent means the powersat now masses ~ 1025 tons. Delivery cost is still $41 billion to GEO, which is pricey. Zubrin also cuts costs even further by arguing that air-breathing rockets and ion-drive delivery systems can cut LEO then GEO by half each. Thus the powersat costs ~ $10.25 billion delivered to GEO, and double that overall. Some $20.5 billion is a lot to build a power-station supplying just 0.5 GW. Typically a coal-plant costs about $1.5 billion per gigawatt power. Thus to compete a powersat needs its costs reduced by 27-fold. GEO delivery costs need to get down to ~ $360/kg, and construction stay at twice the launch costs, to make powersats viable.

As SpaceX is aiming for $500/kg to LEO I would hazard a guess and say powersats might be a viable commercial option, assuming some reasonable improvements to the technology.

Addenda:(i) Zubrin grants a four-fold reduction in delivery costs to LEO then GEO, then a halving of that due to a mass decrease in PVs and structure. For comparison he quotes the minimum cost of LEO delivery via reusable rockets as ~ $100/kg, thus $400/kg to GEO via conventional means. Thus delivery to GEO, assuming the cost reductions and minimal rocket costs, of 20,500 tons of Powersat costs ~ $2.05 billion, and in total it costs $4.1 billion to set-up. He claims that’s still 3 times too much compared to coal. As I show in the next post that’s somewhat misleading. If we factor in carbon disposal and the cost of the coal burnt, then coal’s effectiveness goes down – especially if you’re paying $120/ton instead of $20/ton for the stuff.

For areas paying hand-over-fist for diesel powered generators, prices of $0.2/kW.hr look quite attractive. If you have no coal and no railways delivering it to your generator, then setting up a rectenna farm made of pre-fab identical components delivered via truck looks like a better deal.

(ii)He claimed a 2,000-fold (really 2,500-fold) price reduction was absurd, but with our 40-fold mass-reduction a 62.5-fold reduction in LEO rocketry prices is then acceptable – $160/kg, less stringent than the $100/kg minimum. If ion-drives can cut the delivery to GEO in half, then $320/kg to LEO is acceptable. SpaceX’s ultimate goal is not much more than that.