A Little Simple Math

With all the news about how VPIRG wants to increase Entergy’s taxes, I can’t help but suspect that whatever it is they are claiming about taxes, their true motives are to put Yankee out of business.  My suspicions were
first raised at the Progressive Party Caucus when I repeatedly heard people saying “we want to put Yankee out of business.” As I left the meeting and walked past the “Close Yankee Now!” signs I started wondering what, exactly, they might have meant. Then, it struck while reading the “Stop Vermont Yankee” bumper sticker on the car in front of me.   These people want to close Yankee.
    And this revelation got me thinking about what Vermont would look like if these people are ever successful in replacing the high power density nuclear facility with a myriad of renewables.
    So walk with me here.

According to Entergy spokesman Rob Williams the Yankee plant sits on 127 Acres of land, (most of which is undeveloped). From this lot, the plant produces 650 Megawatts of power per hour which equates to 15,600,000,000 Watts of power per day. On a per square foot basis this means that Yankee produces 2,820 Watts of power each day for each square foot of land used. Let’s see how this compares to some alternatives.

Solar

The total average daily total solar radiation in Burlington in 1990 was 336 Watts per square foot.  Using the most efficient solar panels available today that operate at 22% efficiency this equates to an energy density of 74 Watts of electricity per square foot per day or 38 times less than Yankee. (Field studies suggest actual output is 20% - 30% less than panels rating, thus reducing output to as low as 54 Watts/foot). At an energy density of 74 watts per square foot, it would take 4840 acres of land paved with solar cells to equal the output of Yankee. I wonder if anyone at VPIRG has asked the ACT 250 guys how they feel about this?

Even if it were possible (which it isn’t) to convert sunlight to electricity at 100% efficiency it would still take over 1000 acres of land to replace Yankee. Clear cutting a 1000 acres anywhere in the state sounds like a bad idea to me. Obviously, large scale land-based solar is not a realistic option for Vermont – not without sacrificing huge tracts of land which is in conflict with many of our other goals.

There is the option of installing small-scale solar on the rooftops of homes. But, how many homes would it take? A typical footprint for a modest home is 32’ x 48’ Assuming the roof pitch is 45 degrees the roof would have a run of 22 feet. So, to keep the math simple, let's assume the average home has a 20’ x 50’ (i.e. 1000 ft^2) flat roof that articulates to track the sun and that the entire surface is covered with solar panels (also unrealistic). Even with these generous assumptions it would require 210,831 solar powered homes to produce the energy of Yankee.

Now let’s see how much this would cost. Using panels of the highest available rating 1000 ft^2 equates to a system rated at approximately 16 kilowatts (remember actual output is a function of the suns energy which is 336 Watts/ft/day in Burlington). This system would cost approximately $168,000 each or a total of $35,419,608,000. Obviously this is not a viable option. Even if the cost decreases by a factor of ten it would still be excessive. This is what Adam Smith meant by ‘economies of scale’. You simply cannot compete with the high energy density of nuclear using the diluted power of the sun. If you build the solar arrays in one area, you need to clear-cut lots of land. If you disperse them, you lose the economies of scale and the cost skyrocket.

Wind

Wind, like solar, is "low density" energy. This means you need a large collector to capture a large amount of energy. The worlds largest and most powerful wind turbines produce 6 megawatts at peak performance. Actual performance is a function of the wind. In Vermont, the Searsburg plant averages 21%. Thus it would take about 500 of the largest turbines in the world to produce 650 megawatt hours of power. And this power would only be produced when the wind blows, which is not necessarily when you need it. This might explain why Denmark has been unable to shut down any of its conventional power plants despite having over 6,000 wind turbines that produced electricity equal to 19% of what the country used in 2002.  But this is a diversion, what I’m interested in knowing is what our natural landscape will look like if we install 650 megawatts of wind power.

The big question is – how much land is required? The proposed 45-square-mile facility on the Scottish island of Lewis represents 50 acres for each megawatt of rated capacity. FPL Energy says it requires 40 acres per installed megawatt, and the U.S. Environmental Protection Agency (EPA) says 60 acres is likely. Facilities worldwide generally use 30-70 acres per megawatt, i.e., about 120-280 acres for every megawatt of likely average output (25% capacity factor). Therefore we're talking about clearing between 40 and sixty acres for each of the 500 turbines for a total of  between 20,000 to 30,000 acres .

Here is a rundown of Mw per acre for US sites. However, forested ridgeline development is usually much more land- efficient, requiring perhaps as little as 4-6 acres of clearance per tower. Thus, it’s possible to match the output of Yankee with wind at the lower cost of between 2000 – 3000 acres of pristine forested ridgeline. Although, based on the comparables linked abov,e the reality is probably much higher than 4-6 acre per Mw. 

And, for all this ruined land ... we still wouldn’t be able to shut down Yankee.

Comments

[Lazarus Long]

Oh No! Don't confuse me with facts! Clasps hands over ears while running away.

I would love to see all of the pants wetting that would occur if VY did open the switch. Let's see, we would need federal/state aid for the poor so they could pay their electrical bills - that's a sound bite for Bernie.

[pwapvt]

Do your number take into consideration the additional costs to build transmission lines etc to get transport the energy?

[Ye Old Vermonter]

Your invention of a new unit measure of efficiency, watts per square foot, is surely creative; however, I fail to find the science behind the development of such a measurement. I wonder how you would calculate the watts per square foot for hydro generation? Would you go all the way back to the headwaters and compute the surface area of the river? How would you deal with multiple dams on the same river? Or, maybe you would take the whole watershed as the base for computations? TVA and Hoover would end up with interesting numbers, I suspect. Even the long history of power production on the Connecticut River would yield funny numbers.

It would appear that your new measure has only one purpose, one more crazy attempt to discredit wind and solar energy projects. Good try, but no brass ring.

[Gordon Smith]

It is hardly a crazy attempt to discredit wind and solar. I think Mr. Decker is just pointing out that it is no magic bullet, and would take years, many dollars, and many undesirable effects to replace Yankee. Hydro is similar. Although more efficient, you are now going to have to build MANY dams - good luck with the enviros ion that one. I think watts/sf is an excellent measure.

[Greg Decker]

Ye Old Vermonter, the unit of measurement watt/area/time IS used in the engineering community. Its a measure of energy density. Its used to measure the energy of the sun for example. Solar engineering texts define it as: Gsc (the solar constant) which is the energy from the sun, per unit of time, received on a unit area of surface perpendicular to the direction of prorogation, at mean earth-sun distance, outside the atmosphere. The internationally accepted value of the Solar Constant is approximately 1367 W/m^2 +- 1% (note the absence of a unit of time in the constant - this is because a watt is kg*M^2/s^3 thus it has a measure of time as part of the watt unit. Also note, factoring a watt by an hour is still consistent with the formula and is a traditional unit of measure used for power generation calculations).

My calculations used watts/foot/day based on actual observed 'available radiation' that was collected by a US government installation in Burlington. The data was provided in the format W/M^2/day. I converted the units to W/ft^2/day using my trusty HP 48GX. I used the data from 1990 because it was the most current year available.

Likewise the energy available in a column of wind is also measured using watts/area/time, (and yes, a 'column' of wind is also an engineering term). However, for the purposes of calculating the efficiency of wind power the preferred unit of measure is the W/acre because people are usually most interested in knowing the power generated as a function of the land required to produce it. This is because wind power consumes large tracks of land because each mill interacts with its neighbors unless they're spaced far enough apart. Thus, the sources I cited gave numbers using this unit. Again, my trusty old HP came in handy converting the units.

As for hydro, I can say for sure what units are typically used to measure the potential energy on a body of water. Although, I do know that the power of a hydro electric generation facility is a function of the head pressure which is a function of depth of the water. Or, more precisely, the difference in height between the water surface and the turbine. Thus, piping the water down the side of a mountain is equivalent to having a pond as deep as the mountain. The power generated by hydro is not a function of the area of a the body of water. Thus, when a dam creates large bodies of standing water the land consumed by the water is not a contributing to the power of the facility.

This hydro discussion has nothing to do with my post but since you brought it up I would take a wild guess and say that hydro has a relatively high energy density. This is because unlike wind, water itself is dense and can use gravity to move fast in a short time. Obviously, the actual area required for a hydro facility is more a function of topography than anything else. Therefore, hydro can be high density but not necessarily so. My guess is that facilities are only built when the density/area ratio is high.

All of this is basic physics that anyone who studied engineering would remember from their freshman year. I assume by your response that your not an engineer. Might I suggest you follow a few of the links provided in the post and do a little research to help you better understand my argument?

[anonymous]

I wonder how many acres of Russia are unusable around Chernobyl? I think that is the worry of Windham County.

[Ye Old Vermonter]

"the unit of measurement watt/area/time IS used in the engineering community." Interesting, a google of "watt/area/time" yields nothing. Must be a term not used frequently by the scientific community. Or, at least seldom written about.

[Greg Decker]

I wonder if Chernobyl ruined more land than the 47.75 million acres consumed by China's Three Gorges Dam project?

[Greg Decker]

Ye Old Vermonter, try looking at any of the solar panel company web sites. They provide efficiency information of their products in the form W/ft^2. This unit is a measure of efficiency for an instant in time. To calculate actual predicted output of their product over time you'll need to tell them where you live so they can factor in the estimated daily solar hours which differs from latitude, region, and time of year. Rather than using estimates, I used actual observed data for solar radiation in Burlington which was 336 W/ft^2/day.

Also, the Solar Constant I referred to earlier is the most fundamental of measurements. Essentially all of the calculation used in solar engineering rely on this constant which of course is given in the form energy/area/time.

The solar constant is:
1376 W/m^2 = (kg*m^2/s^3)/m^2
1.960 cal/cm^2/min = (kg*m^2/s^2)/m^2/min
433 Btu/ft^2/h = (kg*m^2/s^2)/m^2/h
4.921 MJ/m^2/h = (kg*m^2/s^2)/m^2/h

Where you may be getting confused is that a W contains a unit of time thus by reduction of the equation the unit of time is combined into the watt. (note the first equation contains a s^3 instead of a S^2) In the last two example of G time cannot be combined to make other units so it is shown. But, even then you might not find these number displayed in this way. for example, MJ/m^2/h can also be written MJ/(m^2*h). You'll find if you play around with the equations enough solar energy is ALWAYS represented in the form energy/area/time. But, the units used can vary depending on who/why the calculation is being done.

Also, its common for people to leave off the trailing unit of time when talking about electricity. For example, a 100W light bulb will consume 100W of electricity in an hour but nobody ever states the hour. This is because a W/hour is a standard measure of electricity. thus, Yankee is called a 650 Mw generator because it makes 650 Mw of electricity per hour. For the purposes of my argument I used watts per day because its the way solar energy is calculated. It wouldn't make any sense to use watt hours because the suns output changes every instant. Thus we have to use daily averages. If I used w/h for solar the radiation available for conversion to electricity in Burlington, on average, is 14 watts per square foot per hour.

As for your claims about me trying to discredit solar. This is all there is to it. There is absolutely nothing anybody can ever do to overcome the simple fact that in our region the yearly average daily watts radiated by the sun over the course of an entire day is 336 per square foot.

The sun, like the wind, is a dilute energy source. The only way to scale its power generation is to scale the land area used to capture the energy. And, the scaling is linear meaning there's no economies of scale. The more power you want the bigger you have to go.

[pwapvt]

I know you are all big fans of personal responsibility around here so hows about you mandate that IBM & other major manufacturers put solar panels on their roofs. I'm sure some bright spot out there could calculate the sq-ft of power they could generate for that area. Bonus for the rest of us is that we don't have to pay for the power line upgrades to bring the power to them.

[Greg Decker]

pwapvt, IBM uses 8% of all the power consumed in the state which amount to about 60 Mw. Roughly 1/10th of the power of Yankee. They would need 480 acres of solar panels (using todays technology) to produce enough power to meet their needs.

To answer your earlier question, my calculations do not include transmission lines. I simply calculated the area needed to generate the power. I did not deal with the land used for the lines because using today's technology the lines will be necessary even with solar or wind because these sources do not provide steady base-load power. However, in the future when storage systems do exist to hold the power until its needed then the high-power lines may not be so important. In fact, its my opinion that a distributed generation network is in our national interest. The system we have now is susceptible to cascading failures and has many critical weak links that could be easily exploited by no-gooders whereas as distributed network would be more resilient.

[pwaptvt]

How much would they need to run their light & computers? Take out the machinery and what's the demand?

[Greg Decker]

Unfortunately I don't have those numbers. Although, I suspect the lights and computers only amount to a small part of the power they use. From what I understand making microchips requires lots of power.

Perhaps Jack Harding has something to say about this?

[T. Shea]

Ye Olde Vermonter:

Frist of all, I find your screen ID to be a little incongruous. I haven't met any old Vermonters who share your reasoning.

google this:
watt per area per time
There are hudreds of hits for it.

Wind power is inefficient and sporadic. Google won't fix that. Nor will misinformation and sniping at other posters.

[Jack Harding]

Greg,

The definitive answer to your question about the power consumption of semiconductor foundries is, "A lot".

Check out this link to an abstract of a paper adressing this topic for Taiwanese foundries (that lead the world in power efficiency):

http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V2S-482YVX1-3&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=cc43eeba84b99dc09257f97b0b9d7b8d

[Greg Decker]

From what I can find the National Electrical Code (NEC)calls for 4.5 watts per square foot for office lighting and receptacle power. Although, there are people advocating for new a standard of 2.5 watts per sqft because modern lighting and computers are much more efficient. However, I also found references to tenants that demand as much as 8-10 watt/sqft. How much is really used I can't say but I can assume it's somewhere between 2.5 and 10 w/sqft at peak times. Estimates I've read suggest actual loads can be as much as 90% during business hours but much lower during nights and weekends.

I assume the w/sqft figures are for w/hours similar to the rating of most consumer devices. Thus, an office building should use somewhere between 60-240 w/sqft/day max. I don't have enough information to calculate actual daily watts but can assume it is something less than the max.

This is very interesting because according to my earlier calculations of 74 w/day available solar energy in the Burlington region (using today's technologies) it would seem a typical single story office building could in fact substantially support its energy needs with solar providing they covered their entire roof surface with panels. I think you already knew this didn't you pwaptvt?

Of course right now the cost of doing this is prohibitively expensive. And, there are practical problems related to the unpredictable and uneven levels of solar power production. For example, in 1990 total daily watts (at 22% conversion efficiency) ranged from 20w in December to 123w in July. So while it might seem you could supply an offices entire needs with solar I suspect in practice its much harder to do than it sounds. You'll still need the full base load capacity of existing plant to supply power on days when the solar gain is near zero. And, you'll need something to do with the excess power on bright sunny days. What can you do with excess power? Do like the Danes and sell it at a low wholesale rates so that you can buy it back at high market rates when you need it? Or, wait for storage technologies that may never exist? Or use clean, safe, and inexpensive nuclear?

[PwapVt]

And, you'll need something to do with the excess power on bright sunny days. That's being done already isn't it? I believe that the utilities have to buy it.

Batteries?

I agree they can't run the whole thing on solar, but they could generate some & when not using sell renewable power into the grid. That increases the available power in the grid, and cuts their cost over time. It doesn't cost other ratepayers in Chittenden Cty to upgrade lines etc.

Of course right now the cost of doing this is prohibitively expensive.

More expensive than the power line up the Champlain valley?
More expensive than a million a mile in an existing ROW into Stowe?

I think you already knew this didn't you pwaptvt?

Nope.

...story office building could in fact substantially support its energy needs with solar... That, windows & skylights, and motion switches for office lights. Lots of things that can be done now to use less.

clean, safe, and inexpensive nuclear? So sorry. Until you tell me where the waste is going to go for the next 10,000 years, and prove that once someone starts building one it'll be cheaper than some light switches and solar panels, I just don't buy that line.

Not safe, not clean, not inexpensive, nuclear power.

[Greg Decker]

In Vermont the utilities maintain a moving average (30 days I think) of your power production. On any given day if you have net draw from the grid you're only charged for the amount in excess of your moving average assuming your average is more than your usage. You never get paid for your excess energy - unused credits expire as the moving average moves along. But, getting paid for the power is only half the problem. Selling power to the power company still requires a power company. Even if every business in the state put up solar panels we wouldn't be able to shut down a single power plant.

The key point to understand is that the grid is not a storage system. The power in the grid needs to be maintained at a steady level even when intermittent sources are putting in power at their discretion. This generally requires running existing power plants at full capacity and dumping the excess into the national grid – if somewhere else needs it that is. In Denmark, they’ve been known to shut down wind mills during peak production periods because nobody wanted the excess.

You can’t just start and stop a huge power plant whenever you want. If you need a 650 Mw base-load capacity during low solar production times you will need to keep that plant running all the time – even if you don’t need the power when the sun is shining – unless you install quick reacting 'Peakers" and scale back the production of the big plants. The problem is the Peakers are filthy polluters. So Solar can produce a bunch of electricity but rarely when you need it. New storage technologies are the only real solution to the problem.

To your next point - Existing batter technology is inadequate. Google it if you don't believe me.

Power lines – will not be going away even with Solar. Not in the short term anyways. Again, storage is the key. Unless there’s a viable storage system you’ll still need the grid to maintain stable base-load power.

As for the cost of the power lines - how many million dollar miles are they planning on building? More than 35,000 miles? With the current cost of solar it will cost 35 billions dollars (by my rudimentary estimates that are probably conservative) to match the capacity of Yankee and most solar cells only last 20-30 years.

I’m no fan of power lines either and have personally investigated solar year in and year out waiting for the day I can ask the power company to come and get their utility pole. Unfortunately, the numbers simply don’t work out yet.

Lastly, how many people have been killed in the US by nuclear accidents? None.

[Ye Old Vermonter]

"Ye Olde Vermonter:
"Frist (sic)of all, I find your screen ID to be a little incongruous. I haven't met any old Vermonters who share your reasoning."

We must travel in different circles. I know a number of individuals who share many of my views who fit into this definition: Born, raised and educated in Vermont; live in the state full time and have been collecting social security for a number of years. We are all old Vermonters.

I do wonder sometimes how many of the posters on this site meet the definition above? But at the same time want you all to know, we Old Vermonters are glad to have you here and appreciate your contributions to our state.

[James Ehlers]

The most encouraging aspect of nuclear power is the role it can play in the Hydrogen Economy. Solar and wind cannot provide us with this opportunity to forever alter our transportation system to the clean and efficient one provided by the hydrogen fuel cell-based system.

Geopolitical and national security issues will look very different in a nuclear/hydrogen US economy.

Of course, some people do not apply reason in their own lives so there should be very little expectation they would do so in the discussion of matters regarding public policy. Difficult to reason with the unreasonable.

Perhaps focus on the vast majority who are just uninformed but who are eager to move away from our foreign oil dependence and the other negative issues we have learned that are associated with hydrocarbon fuels.

Sincerely,
James Ehlers

[Edward Charles Ponzi Jr.]

"A Little Simple Math"

TOO simple -- you have left out RISK.

We are a broken pump or 2 away from NO MORE VT. Nuclear power might be safe in theory -- but Al-Entergy is willing to take insane risks such as a 20% power uprate of a very old plant -- turning an un-pressurized system into a pressurized one.

The aging and hot-rodded US nuke fleet is certainly a greater danger than any "terrorists".

If you want to be for some sort of nuclear power generation -- fine. If you support Al-Entergy in their current plan -- then you support UNSAFE NUCLEAR POWER -- PERIOD. Of course if you are an ideologue -- then it is more important to support your point than actually be for something safe.

See:

http://www.ucsusa.org/clean_energy/nuclear_safety/snap-crackle-pop-experimental-power-uprates-at-boiling-water-reactors.html

[James Ehlers]

Dear Mr. Ponzi,
Please explain the engineering behind your assertion that "we are a broken pump ir 2 away from NO MORE VT."

Do you support the construction of new nuclear generating facilities in Vermont?

Thank you.

Sincerely,
James Ehlers

[Mister Guy]

Close VT Yankee? Sounds good to me...it's a permanent nuclear waste dump that's only going to get bigger the longer that's operating. It's also one of the most unsafe and unsecure nuclear facilities in the nation. That land that it sits on will *never* be developed, ever. Close it now before we all end up "glowing in the dark"!

Just about every single family dwelling in the USA can generate it's own power...right now. I had a co-worker that built a house in NY state up along the Canadian border about 10 years ago. He well-insulated his house, added some solar panels to his roof, added a small wind turbine to another structure that he had on his property, and he's been generating *all* of his own power ever since then. The govt. needs to get behind people generating their own power and selling their excess power (and there will be a *lot* of it) back to the electrical grid. How many homes are there in VT again? The more this technology is used and encouraged...the cheaper and more efficient it will get over time. The faster we start...the faster this will happen.

Only 3% of the land in VT is currently suitable for wind power generation. Half of that is owned by the federal govt. and the other half is divided equally between the state of VT and the private sector. Anyone that knows anything about wind power knows that we could generate roughly 10% (sometimes more when it's windier...sometimes less when it's not so windy) of our needed power over an entire year thru wind alone. Some people say that one huge wind farm out along the eastern slopes of the Rockies (where it's apparently very windy a lot) would generate enough power for the whole country.

Hydrogen fuel cells are a carrot being held at the end of a stick by the car and oil companies IMO. I don't think it's ever really going to happen. Stop being a stick in the mud...