The Cost of Power

In 2008 the world used about 15.04 terawatts of power, on average. That means that, at any given point in time, 15.04 terawatts of power generation was needed. This includes all the electricity, all the jet fuel in the B-52s, all the cars and trucks and trains and ships, all the firewood, all the geothermal, all the energy we require to operate planet earth in a style to which we are accustomed.

For the sake of this thought experiment, let's pretend that it's all electricity. How many kWh (1000 watts for 1 hour) does that represent?

Let's do the math:

There are about 8,766 hours in a year.

15,040,000,000,000 watts x 8766 hrs = 131,840,640,000,000,000 watts.

131,840,640,000,000,000 watts / 1000 = 131,840,640,000,000 kWh.

That's about 132 trillion kWh.

There are 6.796 billion people on earth. That means that, on average, the energy needs, per person, are about 19,400 kWh / year, or 2,210 watts per hour. That's per person, not per household. For no good reason, let's say that the average cost per kWh is $0.15. That comes to a yearly energy bill of about $2,910 per person. That includes the cost of running the tractors that plant and harvest all your food, the energy cost of manufacturing the goods you buy, the trucks that deliver them, street lights, the mall's utility bill, cooking, heat, logs for the fire, electricity, jet fuel for visiting grandma, etc. Doesn't sound so high does it? But it's an arbitrary estimate. Again, the actual number is invisibly complex. Anyone who knows the answer, please educate me.

Q: Where does this power come from?

A: 37% oil, 25% coal, 23% natural gas, 6% nuclear, 4% biomass, 3% hydroelectric, 0.5% passive solar, 0.3% wind power, 0.2% geothermal, 0.2% biofuels, 0.04% solar electric.

89.2% of that comes from fossil fuels or biomass (think firewood, ethanol, biodiesel).

The rest comes from a mix of mostly nuclear and partly renewable sources.

In the U.S. the majority of our power production comes from coal. According to this creative little breakdown (which fails to take into account the cost of environmental damage done by coal mining, CO2 production and simply makes up numbers on the nuclear side), coal production is insignificantly cheaper than nuclear. Does nuclear power produce pollution that should be included in the cost? No. It produces waste that needs to be sequestered away to avoid becoming pollution. According to that web page, 17% of the cost of nuclear energy is the cost of storage. Other than that, nuclear is clean.

Let's play a little game. Let's say that all power plants cost the same amount to build. That's obviously not true. A coal plant is much cheaper to build than nuke plant. An oil-fired plant is probably cheaper still. But let's pretend that the environmental cost of coal is measured in money and that the money has to be paid when the plant is built. There, fixed.

Let's also pretend that the only kind of power we need to concern ourselves with is electricity. Is there anything that electricity can't do that other forms of power can? Yes. Electric trucks, planes, ships- no go. Hydrogen, generated from electricity, that's another thing. But not another enough. We'll assume that at least a third of the cost of energy will be tied to the price of oil until oil is no longer for sale.

What is that price?

One barrel of oil is equivalent to 6.1 gigajoules of heat energy, which is equivalent to 1,700 kWh of heat energy. About 60% of that can be converted into electricity. That leaves about 1,000 kWh per barrel of oil.

Q: To serve the entire world's energy needs by burning oil, how much oil would you need to burn and if you were to buy it all at today's price of oil, what would it cost?

A: 132 billion barrels of oil. At $79 / barrel (1/19/10), that could cost a mere $10.4 trillion. Just for the fuel. You see, if you could get your power generation for free and just pay for the fuel, electricity would cost you about $0.08 / kWh. Oil ain't cheap.

Q: Same question, now with natural gas.

A: 6000 cubic feet of natural gas is equivalent to one barrel of oil. Natural gas costs around $5.36 / 1000 cubic feet. That means that the natural gas equivalent of oil is about $32. That's $4.21 trillion for the whole world, or $0.032 / kWh at raw generation costs.

Q: Now with coal.

A: I've got bad news. Coal plants have an actual thermal efficiency of about 30%. At that rate, they produce approximately 2 kWh per kilogram of coal. That means that one barrel of oil is equivalent to about 500 kg of coal. In 2008 a metric ton of coal in the U.S. cost about $47. In much of the world it cost 2-3 times that. *Rolls Eyes* Soooooo, about $24 per barrel of oil equivalent. That means that the total raw cost would be $3.168 trillion for the world or about $0.024 for power generation.

Q: Finally, nuclear.

A: Accord to a recent article in Wired, traditional nuclear power costs about $55 million per year to run a 1 billion watts reactor. That's a barrel of oil equivalent of $6.30, which means that the whole world's power requirements would be met for $831.6 billion. And the raw kWh cost? $0.0063.

Now, as referenced above, defenders of energy-from-coal would have you believe that the actual cost is a lot closer to that of coal. Even a little higher. They're probably right. But remember, we're assuming equal cost for building the generators. Nukes are bigger and there's an economy of scale that works in their favor. But big works against local, and local is an important part of efficient, which is an important part of cheap.

Q: Same question- only now we're talking about renewable energy- solar, wind, geothermal, hydro.

A: Remember when I said we won't count the cost of building the plant? Well, if we apply that rule here, the answer comes to zero. Obviously, plants cost money.

Now for the fun part.

In the last question, I said "traditional" nuclear power. That means enriched Uranium in carefully managed reactors with massive cooling towers and- despite being massively complex-actually trade away a huge amount of efficiency so they can be made simpler. A nuke plant is the size of a fair sized town and employs as many people (per shift). It produces weapons grade plutonium as a by-product which is great for winning Cold Wars (or destroying the planet, take your pick- or, for that matter, building nuclear propulsion starships).

Liquid thorium reactors were proposed way back in the 50s, developed through the 60s and early 70s, and thoroughly forgotten for a generation. Thorium is a superior fuel to uranium. Less radioactive, but easier to sustain. And it dissolves in flouride salts. It's possible to build a passively regulated reactor in which, if the reaction gets too hot, the molten salt expands and automatically slows the reaction. Such reactors could be built very small- as little as 3000 square feet x several stories tall. They could be used to power ships. Hell, they could be used to power large aircraft. Their nuclear by-products are relatively benign compared to uranium- becoming safe in a couple centuries instead of tens of thousands of years. And they don't help you build bombs. Which is why they were never developed. But it's also why they've become very popular with growing nations like India and China, or hyper-visionary development zones like Dubai. It's why Harry Reid and Orrin Hatch- who have never liked the idea of storing nuke waste in their back yards, have championed their development. And thorium is abundant. And cheap. There are downsides. For instance, getting the reaction started is the hard part. But once started, it can be kept going for the life of the plant. According to stats quoted in Wired, a one gigawatt reactor would take $10,000 in raw thorium fuel per year.

Q: How much would it cost to provide the entire world's energy needs using thorium reactors?

A: Try this on. A barrel of oil equivalent of less than 0.12 cents. A world cost equivalent of $151 million. A per kWh cost of less than $0.0000015.

Remember back when I mentioned the worldwide per capita cost of energy? What was it $2910? Well, if there were some way to produce all our energy needs using thorium reactors, the raw energy cost would be about $0.03. That's not per kWh. That's per year.

Q: What would it mean if all our energy needs were met for less than $3 / lifetime?

A: Well, we'd change the way we use power. We'd build maglev superhighspeed trains to replace continental air travel. Transportation costs would drop- and with it the cost of goods. Tourism would benefit. Cities would get brighter. Bright enough to grow food indoors, underground, or out in the open in the middle of the night. Astronomers would hate it. We might consider using mass drivers in place of chemical rockets to launch payload into space. All our heat would be produced electrically, virtually eliminating pollution. We'd find it more attractive to live in Alaska, northern Canada, Siberia. Cheap power would make it possible for more people to have access to education, health care, and entertainment. Energy intensive desalination would be commonplace. Your TV would probably get a lot bigger, a lot brighter (though there still wouldn't be anything on).

It would be a different world, but not so different. People would still be poor. People would still waste resources. People would still find ways to damage the environment. But in many ways it would be the world predicted back in the 50s, before the Cold War drained all the fun out of the future.

The Future of Oceanic Power Generation

Years ago I "invented" a method for harnessing sea slow-moving ocean currents.  This is a quick overview of the idea and its drawbacks.  

Ocean currents may move at only 3 kts but represent one of the most energy-dense potentials on earth.  Only fossil fuel deposits and geothermal hotspots have the potential for being denser.

A single current, such as the Gulf Stream, may represent the solar input of many thousands of square kilometers of open ocean- concentrated at the surface and transformed into motion. Currents vary in location and intensity, but to a lesser degree than wind and (except in desert areas) solar. They are far more constant than tides and waves.

I calculate that tapping a small part of the kinetic energy of contained in an area fifty-by-a hundred miles, and given a 3 kt average speed, would supply our entire planet' s energy needs.  And that assumes a sparse distribution of the generators described below.  To do the same thing with wind or solar would take up over a hundred thousand square miles of suitable territory.  

Tapping ocean currents could be done with negligible effect on the currents themselves.  How do I know this? Because the total energy available is extremely enormous. It's equivalent to somewhere in the vicinity of 1 it 1.5 million square kilometers of solar-collecting capacity. Any perturbation would be proportional to the percentage of the whole that is being tapped. Granted, this is something that would require further study. Even if extracted energy is minimal, a potentially nontrivial amount of local turbulence may be generated, which might confuse some of the less navigationally talented pelagic species. Fortunately the system described below would generate very little turbulence. Certainly no more than a bit of bad weather.

So, yes, the major problem isn't a lack of available energy. It's that you need large devices with broad cross-sections in order to tap remote current energy efficiently enough to make it pay off.  If you build a bladed turbine, you'll be forced to work with a circular cross section.  Because currents are fastest at the surface, and drop in speed with depth, it seems that ideal placement of a turbine would be close to half-in and half-out of the water- thereby allowing for its widest part to encounter the fastest speeds.  

Unfortunately, moving blades in and out of the water would cause added drag at the air-water interface.  An individual blade would only provide power half the time- unless the wind was right- and would be vulnerable to forces in directions other than the current itself- which would cause enormous stress.  Furthermore, differences in air and water properties, as well as in speeds inherent to both, would dictate a design compromise away from optimum.  

To build a bladed turbine large enough, one would have to build it incredibly strong.  Strength equates with weight.  Weight cuts into efficiency.  Weight adds to cost.  

A bladed turbine would need to be  fully submerged to remain economical in its design. Being fully submerged, it would still encounter a speed gradient that would cause significant axial stress requiring a rather robust design.  A bladed turbine would be inherrently inefficient in such a setting. It would have to be small and numerous. Again, too expensive, both in deployment and maintenance.

A bladed turbine is not the answer.

My solution doesn't use a turbine at all.  It uses paired drogue chutes designed with high-aspect-ratio shapes optimized to put the bulk of the cross-section inside the fastest part of the current (right near the surface). Each chute would very large- thousands of square meters- and be attached to one end of a long semi-buoyant cable- potentially many miles long- that would, in turn, be connected at its center to an anchored barge containing a gearbox and generator (I mix units, that's right).  While one chute is open, the second one would be closed- deflated so as to provide minimal drag as it is drawn opposite the direction of the active, open chute. If the two chutes were at the opposite ends 20-mile cable, and the current were traveling at 3 kt, and the chute was moving at 1.5 kts, it would take almost 6 hours to complete one down-current run.

When the open waterchute reaches the end of its run, it is closed- using a simple system that is nonetheless too complex to describe without the use of schematics- while its paired counterpart is opened.  The closed chute is pulled back toward the barge while the open chute goes down the current in its place.  

It's a process that would need to be actively controlled.  As the chutes pass each other, for instance, they cannot occupy the same area of the ocean.  The closed chute must be steered away, which is accomplished with a dynamically controlled rudder attached to the cable itself. 

The chute and its cable is also a hazard to deep-drafted ships.  Beacons and active navigation information would be in order. 

The greatest obstacle isn't in the design and operation of the chute system, but rather in the anchoring of the barge itself. 

I believe, however, that there will come a time when deep sea oil exploration rigs will outlive their primary use.  The setting of anchors in the sea floor is a new potential market.  As oil becames scarce, the need for alternative energy sources increases proportionally.  

What impact would these waterchutes have on sea life?  Well, for one thing, they are moving too slowly to trap anything.  They can be equipped with deterrents that would protect larger lifeforms, and holes large enough for smaller ones to escape through. 

Another obstacle is that such a system doesn't generate power constantly.  The longer the cables, the higher the duty cycle.  However, it can never reach 100%.  Running multiple systems in tandem won't solve the problem completely either.  Different units are bound to operate at different speeds, causing the down-cycle to arrive at different times.  Sometimes it would average out into smooth power.   Sometimes it would cause significant drops as multiple systems encounter simultaneous downtime.  Such factors could be managed actively by scheduling reversals at less than full extenstion. 

And then there is the huge problem of transmitting power from sea to land.  Power lines could, conceivably, be run along the bottom of the ocean, or suspended at reasonably serviceable depths.  Running power lines above the water is a special design problem but has the benefit of allowing the lines to be uninsulated.  Either system may be more practical, depending on the individual circumstances.

Another obstacle is that ocean currents rarely exist close to where the power is needed.  Fortunately, most of the world's population at least lives within a hundred miles of the ocean. Current farms could be built in many places around the world.  Industries can also locate to where power is cheapest.

Such a system may well be the cheapest, greenest power source available on a global scale.  It has an extremely high per unit cost due to the fact that it is only efficient at a large economy of scale.  That cost translates, in turn, into a huge amount of power generation.  Each one may be equivalent of an average-sized hydroelectric dam, or over a hundred wind turbines.  

Will such a system ever be built?  I doubt it.  The obstacles are too great.  The system would be too expensive to bring online.  Only if we are desperate to be able to tap ocean currents would such a system be explored.  Other sources of energy are bound to be far cheaper up front.  It's an option though.