Nuclear, Solar, and Wind

Chris Martz

@ChrisMartzWX

𝐍𝐔𝐂𝐋𝐄𝐀𝐑 𝐅𝐈𝐒𝐒𝐈𝐎𝐍 A standard nuclear reactor has a 1,000-megawatt (MW) rating, which means that it is installed with 1,000 MW of power capacity. On average, a 1,000 MW nuclear facility occupies just over 640 acres of land. To figure out how many homes a single 1,000 MW plant would 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 that a standard reactor operates at FULL power throughout the course of a calendar year, then it will produce 8.76 terawatt-hours (TWh) of electricity per year. 𝑬 = 1,000 MW × 24 hr (1-day) × 365 [days] (1 year) = 8.76 million MWh / year (8.76 TWh / year) However, nuclear reactors do 𝒏𝒐𝒕 operate at full power 100% of the time. They have to come offline to refuel or undergo maintenance. Therefore, we must consider capacity factor in our calculation. According to the U.S. Energy Information Administration (EIA), nuclear has the highest capacity factor out of any electricity generation source, with a capacity factor of 0.93 in 2023. https://eia.gov/electricity/annual/html/epa_04_08_b.html… What this value means is that nuclear power plants operated at full power 93.0% of the time last year. So, to figure out how much electricity that the average nuclear power plant generates in a year, we must multiply the previously calculated value of 8.76 TWh / year by 0.93. 𝑬 = (8.76 TWh / year) × 0.93 ≈ 8.15 TWh / year To determine how many homes this powers, we have to divide 𝑬 by the average amount of electricity purchased by homeowners in a year, which according to the EIA, is 10,500 kilowatt-hours (kWh), which is equivalent to 1.05 × 10⁻⁵ TWh. https://eia.gov/energyexplained/use-of-energy/electricity-use-in-homes.php… So, dividing 8.15 TWh / year by 1.05 × 10⁻⁵ TWh / year equals 776,190.4762 homes. Therefore, the average nuclear reactor occupying one square mile of land, operating with a capacity factor of 0.93, can generate enough electricity to power more than 776,190 homes throughout the course of a year. Let's now compare these results to those for solar PV and utility-scale wind. 𝐒𝐎𝐋𝐀𝐑 𝐏𝐇𝐎𝐓𝐎𝐕𝐎𝐋𝐓𝐀𝐈𝐂 (𝐏𝐕) A utility-scale solar PV array which is used to generate electricity for homes requires 1 MW of installed power. https://cleanpower.org/facts/solar-power/… A 1 MW solar PV array requires about 5-7 acres of land according to the Solar Energy Industries Association (SEIA). So, let's just go with the median of six acres for sake of ease for calculation purposes. https://seia.org/initiatives/land-use-solar-development/… And, according to the U.S. EIA, solar PV had a capacity factor of 0.232 last year. What this means is that solar farms operated at full capacity only 23.2% of the year. Using these numbers, let's now figure out roughly how many homes a 1,000 MW solar PV farm could power. Recall that, 𝑬 = 𝑷 × 𝒕 × 𝒄𝒂𝒑𝒂𝒄𝒊𝒕𝒚 𝒇𝒂𝒄𝒕𝒐𝒓 Therefore, 𝑬 = 1,000 MW × 24 hr × 365 (days) [1 year] × 0.232 = 2,032,320 MWh / year (2.032 TWh / year) Dividing 𝑬 by 1.05 × 10⁻⁵ TWh / year gives us roughly 193,523 homes. How much land would be needed? Well, recall that for 1 MW of generating capacity, solar requires about six acres of land. Therefore, a 1,000 MW solar PV array would occupy approximately 6,000 acres of land area, some 9.4 × as much land area than is required by a 1,000 MW nuclear facility, but power 582,667 fewer homes. That's not exactly practical, is it? 𝐎𝐍𝐒𝐇𝐎𝐑𝐄 𝐔𝐓𝐈𝐋𝐈𝐓𝐘 𝐒𝐂𝐀𝐋𝐄 𝐖𝐈𝐍𝐃 A typical utility-scale wind turbine occupies about 80 acres of land, with each turbine given a 2.5 MW rating. https://landgate.com/news/does-my-land-qualify-for-a-wind-farm-lease… A 1,000 MW onshore wind farm would require about 400 turbines occupying 32,000 acres of land. Also, according to the EIA, wind had a capacity factor of 0.332 in 2023, which means that wind turbines had operated at full power capacity 33.2% of the year last year in the U.S. So, how many homes would this power? Well, let's run the numbers through our handy dandy equation again, 𝑬 = 𝑷 × 𝒕 × 𝒄𝒂𝒑𝒂𝒄𝒊𝒕𝒚 𝒇𝒂𝒄𝒕𝒐𝒓 Therefore, 𝑬 = 1,000 MW × 24 hr × 365 (days) [1 year] × 0.332 =2,908,320 MWh / year (~2.91 TWh / year) Dividing 𝑬 by 1.05 × 10⁻⁵ TWh / year gives us roughly 277,143 homes. Therefore, a 1,000 MW onshore wind farm would occupy approximately 32,000 acres of land, some 50 × as much land area than is required by a 1,000 MW nuclear facility, but power 499,047 fewer homes. That's not exactly efficient either, now, is it? 𝐒𝐔𝐌𝐌𝐀𝐑𝐈𝐙𝐈𝐍𝐆 𝐈𝐓 𝐀𝐋𝐋 𝐔𝐏 In order to power the same number of homes as a typical 1,000 MW nuclear power generation station, you 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). These estimates are conservative, however, because they do 𝒏𝒐𝒕 include the land area required for battery storage because sunlight doesn't always reach the ground (e.g., on densely overcast days or at night) and the wind isn't always blowing. Based on the land requirements alone for “green” energy technologies, you should question the motives of anyone, especially climate activists, who are vehemently opposed to deploying nuclear power. They are often unserious about environmental protection and have an ulterior, more sinister political outcome that he or she is trying to achieve, using environmental concern as smoke and mirrors to meet those ends.