Study: Solar power is cheaper than nuclear

[ivanm]

Ivan, I think it all boils down to whether we're smart enough as a species to do what we need to do. If we don't I don't think we survive.

I wish I didn't have come down on the side of us being stupid enough to destroy ourselves but I see little evidence that we're not. I would love nothing more than if you were to prove me wrong.

I can agree with the apparent ignorance of many.  Perhaps we have the brains to do what is right in principle but lack the motivation.  Financial greed and the cornering of the market in the energy industry is a major roadblock to progress IMO.  Down thru the years a number of novel inventions have been suppressed and kept off the market by Detroit auto and by "big oil".  I think that at one time GM fought the introduction of a commuter bus and in time ended up making the darned things.  Supposedly carbuerators that would improve our mileage immensely have been bought up (the rights to them) and held off the market by those that might stand to lose because of using them.

When it comes to changing a huge economy with millions of drivers that is a major undertaking that will probably take decades unless we are slapped with a major outage of crude oil.  People are reluctant to change, to trade something new and untried for something old and familiar. It amazes me to still hear folks objecting to using E10 in their cars when I have been using it for the past 30 years and have had no engine problems with doing so. The gas mileage has been only minimally less than when using straight unleaded gasoline.  E10 helps the engine to burn cleaner and should therefore help to prolong the life of the engine. Ethanol is also an oxygenator and is being used in place of the old tetraethy to combat pre-ignition knock, or pinging.  Most of all, it is domestic in origin and it is renewable.

[Velleity]

I can agree with the apparent ignorance of many.  Perhaps we have the brains to do what is right in principle but lack the motivation.

What could be more motivating than the survival of our species?

 Financial greed and the cornering of the market in the energy industry is a major roadblock to progress IMO.

So you're saying that lassaize faire capitalism isn't the end all and be all. I guess you're a "socialist" after all?

Sometimes profit motive is a very good thing. Sometimes not so much.

It's relative. Isn't it?

 Down thru the years a number of novel inventions have been suppressed and kept off the market by Detroit auto and by "big oil".  I think that at one time GM fought the introduction of a commuter bus and in time ended up making the darned things.  Supposedly carbuerators that would improve our mileage immensely have been bought up (the rights to them) and held off the market by those that might stand to lose because of using them.

I'm sure that's true but it's nothing compared to the power and influence that businesses buy.

I am a big fan of the University of Illinois. U of I had the best accounting program in the nation primarily because they were a bought and paid for subsidiary of Arthur Anderson. They used that platform to influence FASB and other accounting standards, and look at what happened?

Even academia can be bought, under the right circumstances.

[johnhp]

I hadn't noticed the premise to biofuels not being able to fill our needs on this site.  Did you get that from somewhere else?  I once read that we have enough biomass, if converted to methanol, that would serve as an alternative to our gasolie consumption and have some left to apply to the diesel needs.  And the biomass would be domestic and renewable, which are two pluses for that fuel source.

i think i was responding to your biomass statement you made earlier.  Growing algae, i think, eliminates the problem you were discussing there.

I think that one thing that stands in the way is our mindset that only one or two motor fuels can be used and should be used nationwide.  How about a situation where the prevailing fuel in a given area be used there and some other prevailing source be used elsewhere?  Is it really necessary to have a motor vehicle that will operate across the nation?  Most of the driving is done relatively close to home for the typical private auto owner, so having one that is tailored to a given fuel type in the area where it is being used shouldn't be a major hindrance.  

i would not disagree, there, but the problem with that is infrastructure for production.  Car companies would not go for it if it means different power plants.  The other direction to go would be regional biofuel production facilities, especially if algae is viable.

[johnhp]

Neither Solow nor I are invoking that paradox. Solow is not saying that you can never get to a point and that isn't what the math is about.

Actually, Zeno's paradox is precisely the model of what you are talking about when you claim that if you reduce use less energy each year because you become more efficient, that you will never run out.  i took it to mean that by energy we are referring to fossil fuels in the discussion.

In fact I'm talking about reaching the smaller and smaller units. The real problem with the model is whether or not the kinds of increases in efficiency that are required can actually be achieved.

The other problem in the model is a finite energy resource.  If, however, you are going to discuss substitution, it has to be a viable substitution.  In terms of fuel, algae and in terms of delivering electricity to the grid, i say a Tokomak reactor.

[ivanm]

Actually, Zeno's paradox is precisely the model of what you are talking about when you claim that if you reduce use less energy each year because you become more efficient, that you will never run out.  i took it to mean that by energy we are referring to fossil fuels in the discussion.



The other problem in the model is a finite energy resource.  If, however, you are going to discuss substitution, it has to be a viable substitution.  In terms of fuel, algae and in terms of delivering electricity to the grid, i say a Tokomak reactor.

No doubt that algae would be a fine source of biofuel but we also need to utilize other resources in areas where
the algae may not do so well.

[johnhp]

No doubt that algae would be a fine source of biofuel but we also need to utilize other resources in areas where
the algae may not do so well.

Algae can be grown anywhere.  It produces more oil that any other bio-source per acre adn it has a harvesting cyclwe of a week adn a half.

[Velleity]

Actually, Zeno's paradox is precisely the model of what you are talking about when you claim that if you reduce use less energy each year because you become more efficient, that you will never run out.  i took it to mean that by energy we are referring to fossil fuels in the discussion.

No it isn't. If you can do the math here let me know.

SOLOW GROWTH MODEL

Start with a Constant Returns to Scale (CRTS) production function: Y = f (K,L). CRTS implies that by multiplying each input by some factor “z”, output changes by a multiple of that same factor: zY  = f ( zK, zL)

In this case, let z = 1/L. That means:

Y * 1/L = f (K * 1/L, L * 1/L)

or

Y/L = f (K/L, 1)

define y = Y/L and k = K/L, so that the production function can now be written as

y = f (k),

where y is output per worker and k is capital per worker.

A graphical depiction of the production relation is:

The production function shows the production of goods. We now look at the demand for goods. The demand for goods, in this simple model, consists of consumption plus investment:

y = c + i

where y = Y/L; c = C/L; and i = I/L.

Investment, as always, creates additions to the capital stock.

The consumption function in this simple model is: C = (1 – s) Y,

which can be rewritten as c = (1 – s) y, where “s” is the savings rate and 0 < s < 1.

Going back to the demand for goods, y = c + i, we can rewrite this as

y = (1 – s) y + i

y = y – sy + i

so, y – y – sy = i

which means that sy = i: savings equals investment.

We can now put our knowledge to use by looking at a simple model of growth.

Investment adds to the capital stock (investment is created through savings):

i = sy = s f(k)

The higher the level of output, the greater the amount of investment:

Assume that a certain amount of capital stock is consumed each period: depreciation takes away from the capital stock. Let “d“be the depreciation rate. That means that each period d*k is the amount of capital that is “consumed” (i.e., used up):

We can now look at the effect of both investment and depreciation on the capital stock:

Dk = i – dk, which is stating that the stock of capital increases due to additions (created by investment) and decreases due to subtractions (caused by depreciation). This can be rewritten as Dk =s* f(k) – dk.

The steady state level of capital stock is the stock of capital at which investment and depreciation just offset each other: Dk = 0:

if k < k* then i > dk , so k increases towards k*

if k > k* then i <dk , so k decreases towards k*

Once the economy gets to k*, the capital stock does not change.

The Golden Rule level of capital accumulation is the steady state with the highest level of consumption. The idea behind the Golden Rule is that if the government could move the economy to a new steady state, where would they move? The answer is that they would choose the steady state at which consumption is maximized. To alter the steady state, the government must change the savings rate.

Since y = c + i,

then c = y – i

which can be rewritten as c = f(k) – s f(k)

which, in the steady state, means c = f(k) – dk. This indicates that to maximize consumption, we want to have the greatest difference between y and depreciation.

Since we want to maximize  c = f(k) – dk, we take the first derivative and set it equal to zero:

 

Since we are looking at incremental changes in k, dk = 1, which leaves us with

the result that at the Golden Rule, the marginal product of capital must equal the rate of depreciation: MPK =d.

Introducing Population Growth

Let “n” represent growth in the labor force. As this growth occurs, k = K/L declines (due to the increase in L) and y = Y/L also decines (also due to the increase in L).

Thus, as L grows­, the change in k is now:

Dk = s*f(k) – d*k – n*k,

where n*k represents the decrease in the capital stock per unit of labor from having more labor. The steady state condition is now that s*f(k) = (d+n) * k:

In the steady state, there’s no change in k so there’s no change in y. That means that output per worker and capital per worker are both constant. Since, however, the labor force is growing at the rate n (i.e., L increases at the rate “n”), Y (not y) is also increasing at the rate “n”. Similarly, K (not k) is increasing at the rate n.

Introducing Technological Progress

We shall assume that technological progress occurs because of increased efficiency of labor.  That idea can be incorporated into the production function by simply assuming that  each period, labor is able to produce more output than the previous period:

Y = f (K, L*E)

where E represents the efficiency of labor. We will assume that E grows at the rate “g”. Still assuming constant returns to scale, the production function can now be written as:

y = Y / L*E = f ( K/L*E , L/L*E ) = f (k), where k = K/L*E

We are now looking at output per efficiency unit of labor and capital per efficiency unit of labor.

Since k = K / L *E, we can see how k changes over time:

where, the sign of the first term on the right, kdis negative because capital is being consumed by depreciation (dK/K <0).

The steady state condition is modified to reflect the technological progress:

Dk = s*f(k) – (d+g+n)*k,

when Dk = 0 (i.e., at the steady state), s*f(k) =  (d+g+n)*k.

At the steady state, y and k are constant. Since y = Y/L*E, and L grows at the rate n while E grows at the rate g, then Y must grow at the rate n+g. Similarly since k = K/L*E, K must grow at the rate of n+g.

The Golden Rule level of capital accumulation with this more complicated model is found by maximizing consumption at a steady state, which yields the following relation:

,

which simply indicates that the marginal product of capital net of depreciation must equal the sum of population and technological progress.

Example:

Let Y = K1/3(LE)2/3

with s = .25, n = .01, d=.1, and g = .015

The production function, because it exhibits CRTS, can be rewritten as

To find the steady state, recall that DΔk = 0, so s*f(k) = (d+n+g) k

which can be rewritten as:

s/ (d+n+g) = k / f(k)

Since f(k) = k1/3, this can be rewritten as:

With this value for k*, we can find y* = (k*)1/3 = 1.41, and c* = y* - s y* = 1.06.

To find the Golden Rule level of capital accumulation, recall that at the GR,

MPK =(d+n+g).

Since Y = K1/3(LE)2/3 then

Since, at the Golden Rule, the above calculated MPK must equal (d+n+g),

Since k** = 4.35,

y** = k1/3 = 1.63

c** = y** - .125k** = 1.088

s** = 1 – (c**/y**) = .333

The graph depicting this would be:




The other problem in the model is a finite energy resource.  If, however, you are going to discuss substitution, it has to be a viable substitution.  In terms of fuel, algae and in terms of delivering electricity to the grid, i say a Tokomak reactor.
[/quote]

[johnhp]

No it isn't. If you can do the math here let me know.

SOLOW GROWTH MODEL

That is exactly how i would express the paradox mathematically.


i am responding specifically to your application, not to production but to efficiency and energy.

[nraforlife]

My guess is conservative types will still insist that nuclear plants must be built - because solar does not generate enough hazardous waste 

Study: Solar power is cheaper than nuclear

The Holy Grail of the solar industry — reaching grid parity — may no longer be a distant dream. Solar may have already reached that point, at least when compared to nuclear power, according to a new study by two researchers at Duke University.

It’s no secret that the cost of producing photovoltaic cells (PV) has been dropping for years. A PV system today costs just 50 percent of what it did in 1998. Breakthroughs in technology and manufacturing combined with an increase in demand and production have caused the price of solar power to decline steadily. At the same time, estimated costs for building new nuclear power plants have ballooned.

The result of these trends: “In the past year, the lines have crossed in North Carolina,” say study authors John Blackburn and Sam Cunningham. “Electricity from new solar installations is now cheaper than electricity from proposed new nuclear plants.”

http://theenergycollective.com/oshadavidson/40559/study-solar-power-cheaper-nuclear

The NYT has issued the following statement about their report on the study "Historic Crossover," a statement which I believe calls into question the validity of the claims:


An article published July 27 in an Energy Special Report analyzed the costs of nuclear energy production. It quoted a study that found that electricity from solar photovoltaic systems could now be produced less expensively than electricity from new nuclear power plants.

In raising several questions about this issue and the economics of nuclear power, the article failed to point out, as it should have, that the study was prepared for an environmental advocacy group, which, according to its Web site, is committed to ‘‘tackling the accelerating crisis posed by climate change — along with the various risks of nuclear power.’’ The article also failed to take account of other studies that have come to contrasting conclusions, or to include in the mix of authorities quoted any who elaborated on differing analyses of the economics of energy production.

Although the article did quote extensively from the Web site of the Nuclear Energy Institute, an industry group, representatives of the institute were not given an opportunity to respond to the claims of the study. This further contributed to an imbalance in the presentation of this issue.

[Velleity]

That is exactly how i would express the paradox mathematically.

Show me.

[johnhp]

Show me.

You know i am kidding.

[ivanm]

The NYT has issued the following statement about their report on the study "Historic Crossover," a statement which I believe calls into question the validity of the claims:


An article published July 27 in an Energy Special Report analyzed the costs of nuclear energy production. It quoted a study that found that electricity from solar photovoltaic systems could now be produced less expensively than electricity from new nuclear power plants.

In raising several questions about this issue and the economics of nuclear power, the article failed to point out, as it should have, that the study was prepared for an environmental advocacy group, which, according to its Web site, is committed to ‘‘tackling the accelerating crisis posed by climate change — along with the various risks of nuclear power.’’ The article also failed to take account of other studies that have come to contrasting conclusions, or to include in the mix of authorities quoted any who elaborated on differing analyses of the economics of energy production.

Although the article did quote extensively from the Web site of the Nuclear Energy Institute, an industry group, representatives of the institute were not given an opportunity to respond to the claims of the study. This further contributed to an imbalance in the presentation of this issue.

I think that a nuclear plant, like a fossil fuel plant, can develop a whopping amount of power to be targeted to a heavy use regioin, if necessary.  Can PV systems do this?  So what is my point or points? The Wolf Creek Station can deliver 1200 MW of power, which is enough to power about 800,000 homes.  Can anyone visualize the acreage of PV cells that would be needed to do the same thing? There may be plenty of land available out in the SW but not here in Ks or in other states where it is being put to use already.  To me that is a consideration I haven't seen any attention being given to when arguing for PV power.  PV power may be ok for powering your wristwatch or some other toy but let's leave the heavy loads to the big boys.

A system that depends on sunlight tends to be intermittent, what with cloudy days and nightfall, where the nuke can keep on cranking it out 24/7.  I am not in favor of more nuclear plants because of the risks associated with
disposing of the spent fuels and the fact that nuclear fuel is essentially nonrenewable.  And I will bet a cookie that we will be importing nuclear fuel just like we are now importing petro fuels and crude oil. From the standpoint of national security neither practice is a good deal.

So why is it important that a large power plant can feed a concentrated load?  If electrical power is transmitted over 300 miles the line losses become significant and I can see this being the case with PV systems because the sunny areas are not usually the concentrated user areas.  For example, the industrial areas are in the north around the lakes and on into the eastern parts of the country but the areas with lots of sunshine are out here in the sticks, so it is a long haul to transmit the energy from the sticks to the industrial users.

Traditionally people followed the water supplies and the wood supplies as they moved west, and small towns sprang up along the river valleys.  Heavy industry tended to  develop near the sources of iron ore, as another example of why people located or congregated where they did.  For the past several decades there seems to have been a population shift from the industrial north to the sunny south, but did the heavy industry go with them?  I doubt it. Who wants a smelly smelter in their backyard anyway.

Electrical power also developed close to the demand, and coal burning power plants were developed long ago.  Turbines weren't invented yet so the early plants used big steam driven piston engines to turn the generators.  Now most plants use steam turbines and gulp a whopping amount of coal.  I think I had already mentioned the Jeffries plant in NE Ks using 3 million pounds per hour when it was really working out. Yesterday I went down that way, some 20 miles south of the plant, and the plumes of steam coming off the boilers and the excess being
exhausted into the air was awesome.  No doubt the amount of  particulates and the CO2 gas being pumped out by that plant was awesome too.   

Now I am not a tree hugger by any means but I do see the need to reduce emissions and to develop a lifestyle that requires less energy to get the same results, the same satisfaction out of life. And if we are too blind or too lazy or too stubborn to see the need to make changes, then like Vel says, we may in time do ourselves in.

[johnhp]

I think that a nuclear plant, like a fossil fuel plant, can develop a whopping amount of power to be targeted to a heavy use regioin, if necessary. 

What do you think about a tokamak reactor?

[ivanm]

What do you think about a tokamak reactor?

I looked that up yesterday after you had mentioned it in a post.  If I remember correctly the reactor uses the fission principle rather than the fusion principle.  Very potent but the major problem seems to be containing the terrific amount of heat or energy developed by the nuclear process.  I think they have been working on this for decades now. 

I may be wrong, but it seems that fission is a cleaner process than fusion in that less radiation is generated, which is a very important safety consideration.  Sorry but I know next to nothing about this type of device but I will agree, it is a very awesome source of heat energy.

[ivanm]

There is a plus to using nuclear energy in that doing so doesn't emit CO2 or other substances but we still are faced with the inefficiencies of driving a turbine with steam.  The nuke simply heats water, so to speak, and the steam drives the turbine and the generator.

There are forms of power that avoid the combustion process, which is a source of emissions, and they include solar, wind, and hydroelectric. Fuel cells are also a relatively clean type of generator, or so it seems.  At least they don't oxidize fuel to create the usual emissions.  It seems that a fuel cell's waste is essentially water and heat.  They aren't overly efficient and the output voltage level of one cell is pitifully small, but at least they can be stacked to increase the voltage output.

Hydrogen gas is a nice fuel for the fuel cells but there have been experiments with using methane gas, or NG as we usually know it.  Somehow the hydrogen ions in the methane can easily be knocked loose to be fed on into the plates that convert hydrogen into electrical power. From what I have read methanol, which is normally in liquid form, is also a ready source of hydrogen and that could also be used as a feedstock for a fuel cell generating plant, providing the creation of the methanol is cost effective.  Meth can also be burned in an internal combustion engine or in a turbine. 

When I was in the AF back in the 60s I was stationed at Offutt AFB, and we had tankers that took off during all hours.  The early KC-135s, calle the A models, did not have fan jets so the thrust was boosted if needed for taking off with a heavy load of fuel.  Appro. 600 gallons of a water-alcohol mixture was injected into the four engines in just over a minute's time, and that old bird would really haul ass. It was terribly noisy and smoky, but the birds got up and away. 

This little anectode is intended to illustrate the power of alcohol fuels. It is there and all we have to do is to grow it and to harness it efficiently. Methanol, once called wood alcohol, is usually made from woody plants and from wood, where ethanol is usually made from grains or sugary substances such as suger cane stalks.  Natural gas is a source of methanol and, much to my disappointment, this seems to be the favored method of making methanol.  The conversion process certainly is not 100% efficient, so we are giving up valuable energy in doing so as well as using up a very convenient and relatively clean fuel for home heating.

I gotta to drive some clunkers for the dealership now, so take care.