Archive for the ‘Solar power’ Category

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Comparison of Arizona Nuclear and Solar Energy

December 9, 2015

Let’s compare and contrast solar energy and nuclear energy in Arizona. There is only one nuclear power plant in the state, the Palo Verde Nuclear Generating Station in Tonopah. There are several solar energy sites, so we will pick the Aqua Caliente Solar Project because it won the Renewable Energy World Solar Project of the Year category in their 2012 Excellence in Renewable Energy Awards.

Palo Verde Nuclear Generating Station

This nuclear plant consists of three reactors with with a total nameplate capacity of 3,937 MW. If these reactors ran for 24 hours day for 365 days a year they would yield 34,500 GWh (gigawatt hours) per year. The actual output is about 31,300 GWh per year (2010). This means they have a capacity factor of about 90%. Averaged over time Palo Verde yields 3,543 MW.

Palo Verde became operational in 1988 and is currently approved to operate until 2047, giving a lifetime of nearly 60 years.

Palo Verde’s construction cost was $5.9 billion in 1988 ($11.86 billion in 2015 dollars). Its operating costs for fuel and maintenance were about 1.33 cents per kWh in 2004 (1.67 cents in 2015 dollars.)

Based on an average power yield of 3,543 W and a cost of $11.86 billion (in 2015 dollars), the construction cost per watt for Palo Verde was $3.34 per Watt (in 2015 dollars).

Agua Caliente Solar Project

This 9.7 square kilometer solar energy farm has a nameplate capacity of 290 MW peak.  Its first year of full operation was 2014. If it were able to produce its nameplate capacity of 290 MW continuously for one year the energy output would be 2540 GWh. The energy output was 741 GWh in 2014, which means a capacity factor of 29%, an excellent result for solar energy. Averaged over time, this solar farm yields 84.6 MW.

Construction cost for Aqua Caliente was $1.8 billion.

Based on an average yield of 84 MW and a construction cost of $1.8 billion, the construction cost per watt for Aqua Caliente was $21.43 per Watt.

Comparison

The cost per kilowatt hour of energy for either of these sources is combination of the construction cost and the operation, fuel and maintenance cost.  The longer the facilities are in operation the lower the fraction of construction cost per kilowatt hour.

The operation, fuel and maintenance cost for the Palo Verde Nuclear plant were about 1.33 cents per kWh in 2004 (1.67 cents in 2015 dollars.)  The great advantage of the Agua Caliente solar farm is that its fuel cost is zero, and we will assume for the sake of argument that its other operation and maintenance costs are also zero.

The following chart shows various costs per kilowatt hour for each of the facilities for various lifetimes.

spreadsheet

1.  $0.0133 per kilowatt hour in 2004.  Converted to 2015 dollars.
2. 2013 energy output.
3. $5.9 million construction cost in 1988 dollars.  Converted to 2015 dollars.
4. 2014 energy output
5. $1.8 billion construction cost in 2014.
6. (GWh/year) x (number of years) x (1,000,000)
7. (Construction cost) / (kilowatt hours produced over lifetime)
8. (Construction cost per kWh) + (operating cost per kWh)

Two blocks of data are highlighted in yellow.  These are the most likely lifetime scenarios for each of the power generating plants.  The Palo Verde nuclear plant has had its license extended to 60 years.  Aqua Caliente solar farm is made from First Solar CdTe modules that have a 10 year material and workmanship warranty and a  warranty of 80% of the nominal output power rating during twenty-five (25) years.  It is reasonable to hope that it will last 40 years

There is one more thing to be considered.  We have assumed so far that the yearly output of each of these power generating stations it the same year after year.  That is not entirely correct.  Historically, the Palo Verde nuclear plant has increased its capacity factor through time as operations have become more efficient.  Whether that trend will continue is unknown.

Solar modules tend to slowly degrade with time.  The First Solar CdTe modules that are used at Aqua Caliente will likely decay at about 0.5% per year. The chart above gives a best case estimate for Agua Caliente and does not compensate for this degradation.

Based on the highlighted sections of the above chart, Aqua Caliente Solar Farm will likely cost about 2.5 times more per kilowatt hour than the Palo Verde Nuclear Plant over the course of their lifetimes.

One more point.  Aqua Caliente requires 9.7 square kilometers to generate an average of 84.6 MW.  Palo Verde Nuclear Plant generates and average of 3,543 MW.  So it would take 41 Agua Calientes to equal the power of Palo Verde.  That would require about 400 square kilometers.

Energy is the lifeblood of civilization.  The pursuit of energy abundance is the pursuit of healthier and more fulfilling lifestyle for greater numbers of people.  I present this data to help inform the choices that need to be made in that pursuit.

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Scientific American’s “A Path to Sustainable Energy by 2030:” the Cost

November 13, 2009

091111 November 09 SA coverThe cover story of the November issue of Scientific American, A Path to Sustainable Energy by 2030,” by Mark Z. Jacobson and Mark A. Delucchi  promises a path to a “sustainable future” for the whole world in just 20 years. They define “sustainable” as a world where all energy sources are derived from water, wind and solar. Nuclear need not apply.

The article had a few words about the cost, but much was left out.  Jacobson and Delucchi conclude that their grand plan will cost about $100 trillion dollars.  I found this ridiculously large sum to be too low!  My rough calculations yields a cost of $200 trillion!

This post is an attempt to fill in a few blanks.

I will accept the authors’ mix of energy sources, apply some capacity factor estimates for each source, throw in an estimate of the land required for some sources, and estimate the installation cost per Watt for each source. Since all of these numbers are debatable, I provide references for most of them. But some of the numbers are simply my estimates. Also, I consider only installation costs.  I do not consider the additional costs of operation and maintainance, which may considerable.

Another point, the authors say that the US Energy Information Administration projects the world power requirement for 2030 would be 16.9 TW to accomodate population increase and rising living standards. By my reading, the Energy Information Administration’s estimate is actually 22.6 TW by 203013.  Nevertheless, Jacobson and Delucchi base their plan on only 11.5 TW, with an assumption that a power system based entirely on electrification would be much more efficient.  I will go along with their estimate of 11.5 TW for the sake of argument.

Here are my numbers

(click on image to get larger view)…

Total energy cost calculation

 

The numbers that I have placed in the blue columns are open to debate, but I am fairly confident of the capacity factors.  The capacity factor for concentrated solar power, with energy storage, such as molten salt, can vary depending on interpretation.  If energy is drawn from storage at night, then the capacity factor could be argued to be higher.  On the other hand, it would result in greater collection area, collection equipment and expense.   Note that using my estimates for capacity factors, the “total real power” works out to 12.03 TW, close to Jacobson’s and Delucchi’s 11.5 TW.

PV installation costThe dollars per installed watt is where I would expect the greatest argument.  For example, Jacobson and Delucchi call for 1.7 billion 3000 watt rooftop PV systems.  That is residential size, on the order of 300 square feet.  You can find offers for residential systems at much lower rates than $8 per watt installed.  But this is because of rebates and incentives.  Rebates and incentives only work when a small fraction of the population takes advantage of them.  If every residence must install a photovoltaic system, there is no way to pass the cost on to your neighbors.  Click on the chart on the left, from Lawrence Berkeley National Laboratory: of all the states listed, only one comes in at under $8 per installed watt for systems under 10 kilowatts, and half of the remaining come in at over $9.

Turbine transaction priceWouldn’t prices fall as technology advances?  Not necessarily.  Look at the cost to install wind facilities – it has been increasing since the early 2000s. A large part of the installed price for wind is the cost of the wind turbine itself.  Click on this graph showing the price of wind turbines per kilowatt capacity.  This increasing trend will likely continue if demand is artificially pushed up by a grandiose plan to install millions more wind turbines beyond what are called for by the free-market.

Expect to see the same effect for photovoltaic prices.  While the cost of photovoltaic power has been slowly falling, the demand (as a fraction of the total energy market) has been miniscule.  Jacobson and Delucchi call for 17 TW of photovoltaic power (5 TW from rooftop PV and 12 TW from PV power plants) by 2030.  Compare that to the what is already installed in Europe, the world’s biggest marked for PV: 0.0095 TW.  Achieving Jacobson’s and Delucchi’s desired level would require an orders or magnitude demand increase.  This is likely to lead to higher prices, not lower.  For my calculations I am staying with today’s costs for photovoltaics.

Some perspective

We have started using the word “trillion” when talking about government expenditures.  Soon we may become numb to that word, as we have already become numb to “million” and “billion.”  My estimate for the cost of Jacobson’s and Delucchi’s system comes out to about $210 trillion.  So how much is $210 trillion dollars?

It is approximately 100 times the $2.157 trillion of the total United States government receipts of 2009 (see documentation from the Government Printing Office) . 

It is about 15 times the GDP of the United States.

$210 trillion dollars is about 11 times the yearly revenue of all the national government budgets in the world!  You can confirm this by adding all the entries in the revenue column in the Wikipedia “Government Budget by Country.”

What about just the United States?

Jacobson and Delucchi calculate that with their system the US energy demand with be 1.8 TW 2030.  Keep in mind that the demand today is already 2.8 TW.  If we accept their estimate of 1.8 TW, then that  is about 16% of their estimated world demand of 11.5 TW for 2030.  So roughly speaking, the US share of the cost would be 16% of $210 trillion, or about $34 trillion.  That is 16 times the total United States government receipts of 2009. 

Doesn’t seem to likely to work, does it?

I know that Jacobson and Delucchi don’t like nukes.  But the Advanced Boiling Water Reactor price of under $2 per installed watt sure sounds attractive to me now.  Just a thought.

Update 11/14/2009

Jacobson and Delucchi compared their scheme to the building of the interstate highway system.  See here for are realistic comparison.

Notes

1) Capacity factor of wind power realized values vs. estimates, Nicolas Boccard, Energy Policy 37(2009)2679–2688
2)  http://www.oceanrenewable.com/wp-content/uploads/2009/05/power-and-energy-from-the-ocean-waves-and-tides.pdf
3)  Fridleifsson,, Ingvar B.,  et. al.,  The possible role and contribution of geothermal energy to the mitigation of climate change. (get copy here)
4)  http://en.wikipedia.org/wiki/Hydroelectricity
5)  Tracking the Sun II, page 19 , Lawrence Berkeley National Laboratory, http://eetd.lbl.gov/ea/emp/reports/lbnl-2674e.pdf
6)  Projecting the Impact of State Portfolio Standards on Solar installations, California Energy commission, http://www.cleanenergystates.org/library/ca/CEC_wiser_solar_estimates_0205.pdf
7)  David MacKay – “Sustainable Energy – Without the Hot Air” http://www.withouthotair.com/download.html
8).  64MW/400acres = 40MW/km2 http://www.chiefengineer.org/content/content_display.cfm/seqnumber_content/3070.htm
9)  http://www.windustry.org/how-much-do-wind-turbines-cost
10)  I have chosen a low cost because most hydroelectric has already been developed.
11) 280 MW for $1 billion, http://www.tucsoncitizen.com/ss/related/77596
12) Based on my personal experience as a Scientist working on photovoltaics for 14 years at the National Renewable Energy Laboratory.  This number varies according to insolaton, latitude, temperature, etc.
13)  The EIA predicts a need for 678 quadrillion (6.78 x 1017) BTUs of yearly world energy use by 2030.  One BTU is the same as 2.9307 x 10-4  kiloWatt hours.   So, (6.78 x 1017 BTU) x (2.9307 x 10-4  kWhr / BTU) = 1.98 x 1014 kWhr.    One year is 8.76 x 103 hours.  So the required world power would be given by:  (1.98 x 1014 kWhr) / (8.76 x 103 hr) = 2.26 x 1010 kW = 22.6  TW.

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Funny numbers from Palm Desert, California

March 20, 2009
Rick and Wendy Clark (NYT photo)

Rick and Wendy Clark (NYT photo)

This New York Times story tells us the tale of Rick Clark and the financial backing he is getting from the Palm Desert, California city government to pay for a home solar PV installation.    Applying some back of the envelope calculations based on this NYT piece leaves me scratching my head.  Mr Clark, who the Times takes pains to assure us is not some global warming fearing greeny, borrowed $62,000 on a twenty year loan from a municipal financing program to pay for his new PV array.  Clark’s monthly payment would be about $400 per month at 4% interest.  This is probably not a great hardship for guy who has “a buggy for racing on sand dunes, and two sleek power boats for pulling water skiers” in his garage.  Clark won’t have to worry about any financial pinch because, as the article explains…

“California residents receive a straight rebate for about 20 percent of the cost of a solar power system. In addition, a federal income tax credit for 30 percent of the cost of installing solar panels was extended to participants in the municipal loan programs as part of the economic stimulus bill passed by Congress.”

 The article doesn’t say, but by my calculations this $62,000 of city money bought about 8,000 watts of installed PV at $8/Watt.  A generous estimate would be that this array will yield about 50 kilowatt-hours per day, or about 1500 kilowatt-hours per month in sunny southern California.  (Insolation at Palm Desert is about 6000 Watt-hours per square meter per day.  Roughly speaking, each installed watt will then yield about 6 Watt-hours per day. So, 8000 installed watts X 6 watt-hours per installed watt per day gives 48,000 watt hours per day or 48 kilowatt-hours per day.) This is important to Clark because

“His monthly energy bill for a 3,400-square-foot home and a guest house routinely surpassed $1,400 in summer months when the air conditioning ran all the time.”

I am forced to conclude one of two things.  Either Mr. Clark is a colossal energy hog, or the cost of electricity is way too high in California.  The average residential cost for electricity in the United States was 11.47 cents per kilowatt-hour in November of 2008.  At that rate Clark’s monthly $1400 would buy 12,000 kilowatt-hours of energy.  That’s more than amount of electrical energy I use in my house every two years!!!!  We’re told by the Energy Information Administration that the average cost per kilowatt-hour in California is 14.76 cents per kilowatt-hour.  In this case Mr. Clark must have been paying for 9500 kilowatt-hours per month.  Still a colossal amount.  But wait a minute, we calculated above that Clark’s PV system would yield about 1500 kilowatt-hours per month, nowhere near 9500.  If 1500 kilowatt-hours is worth $1400, that’s almost $1 per kilowatt-hour!!!  Even the vaunted tiered utility pricing doesn’t come close to this (…yet).

Neither one of these conclusions seems possible.  So maybe the claim that “his monthly energy bill…routinely surpassed $1,400 in summer months” was a wee bit of an exageration to make the story in the NYT more compelling.  The storyline goes something like this:

“See how expensive electricity is in California.  It will soon be that expensive for you to.  But don’t worry, solar PV is a great investment.”

City provided $7.5 million for loans

Mr Clark’s $62,000 came from a $7.5 million pool of city money provided these solar PV loans.  The money is almost tapped out with about 100 borrowers.  With an estimated 2.5 people per household those 100 borrowers represent about 0.5% or Palm Desert’s total population of 50,000.  I would be willing to bet that Mr. Clark (with his house, guest house, dune buggy, two speed boats and $1400 monthly summer electric bill)  and the other 100 borrowers live off incomes far above the average Palm Desert household income of $65,505. 

There is something funny about these numbers. This is just one more gear in the elaborate political/economic/eco-religious Rube Goldberg machine that delivers energy to consumers in California.

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Controversy over a proposal build a new electricity generation plant

July 1, 2008

The Rocky Mountain News reported on a supposed controversy over a proposal by Xcel Energy to build a new electricity generation plant powered by natural gas in Denver.  This plant would cost under $650 million dollars and have a generating capacity of 480 megawatts.  The RMN points out that critics…

“question the need for the plant, whose estimated cost today is more than $600 million, up from initial estimates of $436 million in November, due in part to escalating costs for labor, steel and equipment.

Opponents argue that renewable sources of energy, such as solar and wind, or energy conservation can substitute for an expensive new plant.”

Really? 

Solar

I wonder if the opponents have checked the cost of solar energy lately.  According to the June 2008 survey results for the Solar Electricity Global Benchmark Price Indices, the cost per watt for industrial sized solar electricity installations is $4.94 per watt.  At that rate it would cost about $2.4 billion to build a 480 megawatt solar plant, four times the cost of the natural gas plant.  But, of course, the gas powered facility can operate near maximum capacity for 24 hours a day, yielding over 11,000 megawatt-hours of energy per day.  The solar powered plant can realisticly operate at its maximum power for about four or five hours a day on the average (in Colorado), and if lucky would yield maybe 3,000 megawatt-hours of energy per day.  To equal the the daily maximum energy output of the gas powered plant, the solar powered plant would actually need to have about four times the installed wattage, and would cost closer to $10 billion!  With typical silicon solar technology of today, such a solar facility would have a footprint of about 15 square kilometers, or roughly 200 times the size of Coors Field, as illustrated in figure 1, below.

15 square kilometers over downtown Denver

Figure 1.  Click on image to enlarge.  About 15 square kilometers of solar arrays would be needed to yield the same energy as a 480 kilowatt natural gas power plant averaged over a typical day.  That is approximately 200 times the size of Coors Field.  This image shows 15 square kilometers compared to downtown Denver with Coors field near the top.  Image is from Google Earth with annotation added by Tom Moriarty.

Wind

 Wind is a better bet than solar at this time, and in the long run is cheaper than gas per kilowatt-hour generated.  It would still be very expensive to install enough wind turbines to be able to match the continuous output of a gas fired plant.  480 megawatts worth of wind turbines would put out 480 megawatts of power if the wind is blowing fast enough.  But when the wind is not blowing fast enough, the the output will be lower.  A multiplicative number, called the “capacity factor” is used to calculate the amount of energy that is produced over time, versus the amount that would have been produced if the turbine had been running at its maximum output 100% of the time.   Roughly speaking, the capacity factor for wind power in Eastern Colorado is about 35%.  The capacity factor for modern gas fired electricity generation would be better than 85%.  So, in order to get the same energy as a 480 megawatt gas fired plant, you would have to install twice as much wind capacity, or about 1000 megawatts.  The realistic installation cost of wind power (with the required transmission lines, etc.) is about $3 per watt, as seen here.  So it would cost about $3 billion dollars worth of wind generation facilities to replace the $600 million natural gas powered plant.

However, even with the high construction cost, wind energy would still be cheaper per kilowatt-hour than gas in the long run.  Gas is expensive and going up, while wind is still free.  But wind has another problem.  When the wind is slow or zero, the power is low or zero.  It doesn’t make any difference how many watts of wind power have been installed when the wind isn’t blowing.  There is no power.  There must always be enough non-wind (and non-solar) power generation capacity to cover the load when the wind isn’t blowing (and the sun isn’t shining).

The folks at Xcel Energy figured this out a long time ago.  That is why our lights are not going out.  They know that wind turbines are a great asset for reducing the load on the more traditional types of power generation, but only when the wind is blowing.  That is why they are already the leading wind power provider in the United States, with over 2500 megawatts of installed wind capacity and plans for more in the future.  But they still must maintain the non-fickle conventional power sources, like gas, or the lights will start going out when the wind stops blowing.

Conservation.

Who can argue with conservation, if it means not being wasteful.  But be careful when some environmental activists says “conservation.”  The Rocky Mountain News article quotes the environmental activist, Leslie Glustrom expressing her reservations about moving from coal to gas.  In another recent opinion piece in the Boulder Daily Camera Glustom wrote:

“The alternative to building gas turbines to meet the summer peak is to begin using modern internet-based tools to manage the demand by cycling non-essential motors, lights, air conditioning and HVAC systems. There are a growing number of firms that develop these high-tech “demand response” systems, but, despite repeated efforts from citizen interveners, Xcel repeatedly refused to explore this powerful form of demand management.”

In other words, “citizen interveners,” (like Glustrom herself, no doubt) would like to use tools to control your use of pesky wasteful things like motors and lights.  Don’t worry, I’m sure they have your best interest in mind.

Conclusion

I am all for solar and wind energy.  Really.  Just click on the “ClimateSanity by Tom Moriarty” tab at the top of this page if you doubt me.  But I believe the market, rather than demands by “activists”  will ultimately lead to a better mix of renewables and non-renewables, with renewables gaining share as they become more cost effective.  As for Ms. Glustrom’s idea to “manage the demand,” I suggest a better alternative would be to have plenty of generating capacity and a varying rate scale for consumers based on the cost of generation by Xcel or the time of day.  That way, as the cost of generation varies with demand consumers can adjust their own practices and manage their own demand, without any help by Ms. Glustrom.