https://x.com/ChrisMartzWX/status/1873752918353936578
Do you like math? Do you like making climate activists cry? If so, this post is for you. 
They advertise utility-scale solar photovoltaic (PV) and wind as being “eco-friendly” energy technologies because they emit less CO₂ over their total lifecycle. Emissions is all the “greens” like to jack their sausage holsters about. But, when you point out to them just how land intensive their “green” energy technologies are, they squirm trying to justify being vehemently opposed to nuclear fission — a near-infinite, carbon-free, energy-dense electricity source — and working to destroying the landscape with massive amounts of solar cells and wind farms to save the planet.
Let’s run the numbers, shall we?
𝐍𝐔𝐂𝐋𝐄𝐀𝐑 𝐅𝐈𝐒𝐒𝐈𝐎𝐍 
The standard nuclear reactor has a 1,000-megawatt (MW) rating. This means that each plant is, on average, installed with 1,000 MW of power capacity. A 1,000-MW nuclear facility occupies, on average, just over 1 square mile (640 acres) of land.
To figure out just how many homes a single 1,000 MW plant could power, we can start by using the following equation,
𝑬 = 𝑷 × 𝒕, where,
• 𝑬 = energy (megawatt hours, MWh)
• 𝑷 = power (MW)
• 𝒕 = time (hours, hr)
If we assume a 1,000 MW nuclear reactor operates at FULL power during an entire calendar year, it will produce ~8.76 terawatt-hours (TWh) of electricity per year.
𝑬 = 1,000 MW × 24 hr (1-day) × 365 [days] (1 yr) = 8.76 million MWh / yr (8.76 TWh / yr)
However, reactors do 𝒏𝒐𝒕 operate at full power 100% of the time because they come offline for refueling or to undergo maintenance. Therefore, we must take the capacity factor into consideration in our calculation.
According to the U.S. Energy Information Administration (EIA), nuclear power has the highest capacity factor of any electricity generation source in the U.S. at 0.93 in 2023.
https://eia.gov/electricity/annual/html/epa_04_08_b.html
What this value means is that nuclear reactors in the U.S. operated at full installed power for about 93% of the calendar year in 2023.
So, to figure out how much electricity that each plant produces in a year, we must multiply the previously calculated value of 8.76 TWh by the capacity factor of 0.93. If we do that, we get,
𝑬 = (8.76 TWh / year) × 0.93 ≈ 8.15 TWh / yr
Now, to determine just how many homes this powers, we must divide 𝑬 by the average amount of electricity U.S. homeowners purchase in a year. According to the EIA, that number is ~10,500 kilowatt-hours (KWh) or 1.05 × 10⁻⁵ TWh.
https://eia.gov/energyexplained/use-of-energy/electricity-use-in-homes.php
Thus, dividing 8.15 TWh / yr by 1.05 × 10⁻⁵ TWh / yr gives us about 776,190 homes.
Therefore, a 1,000 MW nuclear electricity generation station occupying one square mile of land, operating with a capacity factor of 0.93, can power more than 775,000 homes throughout the course of a year based on U.S. data.
Now that is pretty energy-dense, eh? Why would any climate activist be opposed to that?
Let’s now compare nuclear to the greens’ preferred solar and wind technologies.
𝐒𝐎𝐋𝐀𝐑 𝐏𝐕
A utility-scale solar PV array requires at least 1 MW of installed power.
https://cleanpower.org/facts/solar-power/
A1 MW solar PV array requires about 5-7 acres of land according to the Solar Energy Industries Association (SEIA).
https://seia.org/initiatives/land-use-solar-development
And, according to the EIA, solar had a capacity factor of 0.232 last year in the U.S., by far the 𝒍𝒐𝒘𝒆𝒔𝒕 of any energy source. What this means is that solar PV arrays only operated at full power 23.2% of the year in 2023 due to variable weather conditions and sky cover.
By using the same calculations as above, a 1,000 MW solar PV array would occupy some 5,000-7,000 acres of land (mean of ~6,000 acres), all the while powering 193,523 homes, some 582,667 fewer homes than if it were nuclear power.
Yikes, that doesn’t sound very efficient. 
𝐎𝐍𝐒𝐇𝐎𝐑𝐄 𝐖𝐈𝐍𝐃 A single utility-scale wind turbine occupies ~80 acres of land, which each turbine given a 2.5 MW rating.
A 1,000 MW onshore wind farm would require about 400 2.5-MW turbines occupying some 32,000 acres of land area.
And, according to the EIA, wind had a capacity factor of 0.332 in 2023, meaning that U.S. utility-scale wind farms operated at full power capacity for 33.2% of the year last year.
If we employ the same methods as before, we’ll find that a 1,000 MW wind farm could power about 277,143 homes for one year. Therefore, a 1,000 MW wind farm would power 499,047 fewer homes than a 1,000 MW nuclear facility while occupying over 50 times as much land area.
That’s not exactly efficient either, now, is it?
𝐒𝐔𝐌𝐌𝐀𝐑𝐈𝐙𝐈𝐍𝐆 𝐈𝐓 𝐀𝐋𝐋 𝐔𝐏
In order to power the same number of homes that a 1,000 MW nuclear power plant can, it would require either:
• For 𝐬𝐨𝐥𝐚𝐫 𝐏𝐕: Approximately 4,000 MW of installed power (equivalent to four nuclear facilities) and 24,000 acres of land (some 37.5 × as much land area than a nuclear plant).
• For 𝐨𝐧𝐬𝐡𝐨𝐫𝐞 𝐰𝐢𝐧𝐝: Approximately 2,800 MW of installed power (equivalent to 2.8 nuclear facilities) and 89,600 acres of land (some 140 × as much land area than a nuclear power generation station).
But, I should caution you that these estimates are in fact conservative. Why? Because they do 𝒏𝒐𝒕 take into consideration land area required for battery storage due to their intermittency in overcast sky conditions, low wind speed and/or overnight.
Based on land requirements alone, if climate activists were serious environmentalists, they would support deployment of more nuclear power. Some of them do, but most I have interacted with don’t and find terrible excuses to support massive amounts of solar PV and onshore wind farm construction.
Nuclear power represents both continued economic growth and a clean energy future.
But, many climate activists don’t want continued economic growth. They want to abolish capitalism and overturn western culture.
https://twitter.com/ChrisMartzWX/status/1873752918353936578
Very nice Chris, this is really important. Wind and solar are a very sad joke.
Would love to see the math on bio-diesel using the concise and structured approach used in this post. I can’t imagine that they can make that much diesel without cutting down the rain forests for sugar cane, or forcing everyone on a insect diet so that current producing fields can be converted to bio-fuels, not to mention the water requirements.
Back in November of 2024, I posted an analysis describing a hypothetical 3,000 MW wind & solar capacity expansion for the US Northwest which could match the 24/7/365 performance of four AP1000 size 1,100 MW nuclear reactors.
Background
Here in the US Northwest, the regional power planning council’s 2021 long range plan calls for the addition of 3,000 MW of intermittent wind and solar capacity plus 720 MW of firming capacity. Comparatively little backup storage is projected to be needed.
The council’s 2021 plan does not come close to accounting for currently expected increases in the US Northwest’s regional power demand, as expressed in megawatt-hours consumed.
Furthermore, PacifiCorp is planning to retire its coal-fired power plants in Montana and Wyoming, replacing those plants primariy with wind and solar, including a comparatively small additional contribution of 500 MW from nuclear.
In order to account for those expected increases, and to cover the forthcoming closures of the coal-fired plants which now serve the region, suppose we simply assume that the 3000 MW expansion of intermittent wind & solar generation must now become 3,000 MW of baseload wind & solar generation operating 24/7/365.
3000 megawatts baseload delivers 72,000 megawatt-hours daily, each and every day, 365 days a year.
My November 2024 Analysis
In the analysis I posted here on WUWT in November, 2024, I estimate that in order to reliably generate 3,000 MW of renewable electricity 24/7/365 here in the US Northwest, a 6X capacity overbuild for a total of 18,000 MW of wind and solar nameplate are required, backed by a nominal 3,600,000 megawatt-hours of battery storage.
https://wattsupwiththat.com/2024/11/23/washington-state-goes-one-for-three-on-the-pragmatic-climate-scalemaybe/#comment-3998929
These two graphics form the basis of the analysis:
Note from my analysis that seasonal variability issues are much more important than are day-to-day and week-to-week variability issues in determining this huge battery storage requirement.
The hypothetical wind-solar-battery RE system described in my November 2024 analysis would cost upwards of 600 billion dollars, probably more, to acquire and install — as compared with roughly 60 billion dollars for construction of four 1,100 MW AP1000-size reactors as were installed at Vogtle 3 & 4 in Georgia.
Grid Stabilization Services
How does this 3000 MW of hypothetical wind & solar capacity deliver grid stabilization services directly comparable to what four 1,100 MW nuclear reactors could provide?
Where direct inversion isn’t capable of handling the grid’s inertia requirements, huge DC-to-AC motor-generator units employing large rotating flywheels handle the task. Motor-generator units of this size don’t currently exist, but are well within the capabilities of several grid-scale power generation equipment vendors.
Doing it this way, using huge DC-to-AC motor-generator units, is completely feasible technically. But it is also a horrifically inefficient and expensive way to supply grid stabilization services in comparison with thermal generation capacity, i.e., coal-fired, gas-fired, or nuclear.
On the other hand, if in the grand scheme of things you are already using a horrifically inefficient and expensive basic means of supplying your electricity needs — i.e., massively overbuilt wind and solar capacity backed by massive volumes of battery storage — then you really don’t care what your grid stabilization services will cost.
A 1GW plant does not need a square mile of land. Several GW could be built in a square mile.
What is missing in this analysis is Reliability. Capacity Factor covers the fact that the wind doesn’t blow all the time, same for the sun. But there are issues with the times when the wind doesn’t blow or the sun doesn’t shin over a wide area causing total blackout for days at best, and even weeks at times. For years the California Central Valley had Tule Fog so heavy that for a month you didn’t see the sun. And all the solar and wind farms were non-functional. That situation is never discussed as there is no good solution for it. Just do the math on what the battery backup requirements would be for that situation. Staggering. And unaffordable. Plus, the additional wind/solar installed capacity to power the backup system need to be included.
Great post Chris. Other interesting info in the equation would be price per megawatt after subsidies and maintenance have been factored in
The intermittent nature of solar and wind make this a best case scenario. Unless people are willing to live with about 50% of the power needs curtailed for 12-14 hours a day when the sun is not shining, and 100% loss of power when the wind is not blowing at night, we need a GW power plant burning coal or fissioning atoms to provide us with reliable power. Ask them to live like that for a year and come back and tell us how it went.
Diablo Canyon has 2 1,100 mw generators.. The actual portion of the site that produces electricity, excluding all the support facilities, is about 12 acres.. This would include the turbine building, the reactors, intake tunnels, steam piping, etc. It provides power to approximately 1,000,000 homes… Utility scale Wind and Solar is the biggest waste of time and money the human race has ever seen..