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| Fig. 1: View of Diablo Canyon Nuclear Power Station compound. (Source: Wikimedia Commons) |
As global carbon emissions continue to rise annually, decarbonizing energy production is a goal shared by many countries. [1] There are many different non-carbon emitting energy production methods like hydroelectric, solar, wind, and nuclear power. [1]
This report will be producing a hypothetical comparison between nuclear energy and solar energy power production by utilizing data, hence it will be an entirely empirically driven comparison between energy, space, and economics. Mathematical assumptions utilized in the calculations will be specified and the reasoning behind using them will also be explained as they emerge in the report.
While the decision between using nuclear energy or renewable resources has political and ethical repercussions, those will not be discussed in this report. The scale of this report will be limited to the United States to lower assumptions needed in the rough calculations. Furthermore, focusing on the US can provide information on a global scale since the country is a significant producer of the world's municipal nuclear power generation at 16% of the world's nuclear power generation (2020) as well as 15.5% of the world's total power generation (2021). [1,2]
To simplify calculations, it will be assumed that the reactor most similar to the average of the current operating US nuclear power plant will be the standard used in the calculations going forward.
To choose this plant, the average plant capacity will be found from the operational plants being used in 2021. The average plant capacity was 3193 MWt which translates to 1031 MWe. [3,4] The closest US nuclear plant capacity in operation is 3411 MWt (1118 MWe) which is used in a few locations specifically Catawba Nuclear Station (NC), Diablo Canyon Power Plant (CA), McGuire Nuclear Station (NC), and Watts Bar Nuclear Plant (TN). [3,4] While all of these plants utilize Westinghouse PWR 4-Loop (PWR stands for Pressurized Water Reactors), the design specifications for the average nuclear power plant will be from the Diablo Canyon Power Plant because it is the only operating plant in this capacity range that also utilizes a dry, ambient pressure containment system. This is significantly more common in the US as of 2021 than the wet, ice condenser containment units in the other plants. [3,4] (See Fig. 1.)
The Diablo Canyon Power Plant is really composed of 2 nuclear power plants with their own reactors, Unit1 and Unit 2, thus the entire complex has an electrical capacity around 2250 MWe. [3-6] Since the majority of operating nuclear power plants have at least 2 reactors like Diablo Canyon, let us assume that the average nuclear power plant will also consist of two reactors with a combined electrical capacity of 2250 MWe. [3-6] The capacity factor must also be taken into account to get a proper interpretation of the actual amount of energy being produced rather than the plants max capacity. PWR nuclear power plants with a max capacity over 600 MWe have a capacity factor of 81.1%. [2] This means that the actual working capacity of the nuclear power plant is 1824.75 MWe.
The Diablo Canyon Power Plant occupies 545 acres. [5,6] The area required per Watt of nuclear power production is then
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(1) |
In October of 2008, the construction of 14 nuclear plants with the combined capacity of 28,800 MWe was calculated and submitted to the DOE as costing USD 188 billion. [7] Accounting for an average inflation rate of 2% per year from 2008 to 2022 and assuming there is a linear correlation between plant capacity and construction cost, the cost per Watt of nuclear power production in 2023 dollars is [7,8]
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(2) |
While an all-solar power system is illogical without energy storage to accompany it due to the volatility of solar power from weather and nighttime, for the sake of simplicity and due to the infancy of utility-scale deployment of energy storage, this paper is going to focus on the solar photovoltaics equipment. [9-11] The main two materials in question for solar photovoltaic (PV) module production are crystalline-silicon (c-Si) and cadmium telluride (CdTe) modules. [12] C-Si is the most common module in production with it constituting 95% of the modules sold in 2020, however CdTe is a popular module choice for large utility solar farms in the United States due to the company First Solar producing reliable, price-competitive CdTe modules. [12,13] The price difference between c-Si and CdTe are insignificant on a module scale being $0.25/W and $0.28/W, however this difference can become large with utility-scale solar farms. [12] While CdTe has begun to gain traction, c-Si is still the industry standard so c-Si will be the standard used when finding data used in this paper for solar PV modules. [13]
A solar farm that is 945 acres will produce 345 MW in direct current (DC) and 255 MW in alternating current (AC). [14] The majority of the US electrical transmission network is in AC so this is the value we shall use. Large PV facilities in the US have an average capacity factor of 27%, meaning of the 255 MW capacity possible only 68.9 MW are being produced on average. [15] The area required per average Watt of photovoltaic solar power production is then
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(3) |
The utility system capital cost was $1.01 per watt in 2020. [13,14] Thus the cost per Watt of photovoltaic power production in 2023 dollars is
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(4) |
The total US energy generation was 4406.4 terawatt-hours = 1.46 × 1018 Joules in 2021. [1] For perspective of the scale of this number, this was about 15.5% of the all the electric energy produced in the world that year. [1] The mix of this power had 819.1 terawatt-hours of nuclear power, 624.5 terawatt-hours of renewable power, and 257.7 of hydroelectric power. [1] This combines to 1701.3 terawatt-hours of energy generated from non-carbon emitting sources. Thus, the carbon-producing electricity sources are 2705.1 terawatt-hours, which is about 61% of the energy produced in the US. [1] Converting this carbon-based energy to average power we obtain
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(5) |
Let us now consider 3 hypothetical scenarios of how the energy transition away from fossil fuel energy sources might take place:
To replace the 0.309 TW of carbon-based power with nuclear power solely would require
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(6) |
To replace the 0.309 TW of carbon-based power with photovoltaic solar power solely would require
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(7) |
To replace the 0.309 TW of carbon-based power with 30% nuclear power and 70% photovoltaic solar power would require
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(8) |
To summarize, the all nuclear power scenario had an order of magnitude higher cost compared to the all solar power scenario while the all solar scenario had 2 orders of magnitude more space needed compared to the all nuclear power scenario. The nuclear/solar power mix was on the same order of magnitude of the highest values of space and cost from scenario 1 and 2.
© Annie Homer. The author warrants that the work is the author's own and that Stanford University provided no input other than typesetting and referencing guidelines. The author grants permission to copy, distribute and display this work in unaltered form, with attribution to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.
[1] "BP Statistical Review of World Energy 2022" British Petroleum, June 2022.
[2] "Nuclear Power Reactors of the World, 2021 Edition," International Atomic Energy Agency, IAEA-RDS-2/41, July 2021.
[3] "Nuclear Power Reactors of the World, 2019 Edition," International Atomic Energy Agency, IAEA-RDS-2/39, May 2019.
[4] "2022-2023" Information Digest," U.S. Nuclear Regulatory Commission, NUREG-1350 Vol. 34, February 2023.
[5] K. Mayeda and K. Reiner, "Economic Benefit of Diablo Canyon Power Plant," Pacific Gas and Electric Company, June 2013.
[6] K. Carusa, "Operations of the Diablo Canyon Power Plant," Physics 240, Stanford University, Fall 2017.
[7] "The Financing of Nuclear Power Plants," Nuclear Energy Agency, NEA No. 6360, 2009.
[8] M. Bolinger and G. Bolinger, "Land Requirements for Utility-Scale PV: An Empirical Update on Power and Energy Density," IEEE 9676427, IEEE J. Photovolt. 12, 589 (2022).
[9] D. Wald et al., "Shifting Demand: Reduction in Necessary Storage Capacity Through Tracking of Renewable Energy Generation," Adv. Appl. Energy 10, 100131 (2023).
[10] S. Lamp and M. Samano, "Large-Scale Battery Storage, Short-Term Market Outcomes, and Arbitrage," Energy Econ. 107, 105786 (2022).
[11] B. Buo et al., "Application Research on Large-Scale Battery Energy Storage System Under Global Energy Interconnection Framework," Glob. Energy Interconnect. 1, 79 (2018).
[12] B. L. Smith et al., "Photovoltaic (PV) Module Technologies: 2020 Benchmark Costs and Technology Evolution Framework Results," U.S. National Renewable Energy Laboratory, NREL/TP-7A40-78173, November 2021.
[13] M. Woodhouse et al., "Research and Development Priorities to Advance Solar Photovoltaic Lifecycle Costs and Performance," U.S. National Renewable Energy Laboratory, NREL/TP-7A40-80505, October 2021.
[14] M. Bolinger and G. Bolinger, "Land Requirements for Utility-Scale PV: An Empirical Update on Power and Energy Density," IEEE 9676427, IEEE J. Photovollt. 12, 589 (2022).
[15] A. Boretti and S. Castelletto, "Trends in Performance Factors of Large Photovoltaic Solar Plants," J. Energy Storage 30, 10506 (2020).
