|Fig. 1: Levelized cost of electricity production (P0), reported by the US EIA, adjusted for inflation (to 2015 dollars) using Eq. (2). [1-6] (Source: E. Kountz)|
Civilization runs on energy. One of the largest uses of energy is in the production of electricity for industrial, commercial, and residential use. When generating electricity, the most pressing concerns are cost and reliability. The purpose of this report is to compare the cost of electricity production from the most common sources and to illustrate how the cost of electricity would change for each source if a carbon tax existed.
The costs to generate electricity can be direct costs or external costs. Direct costs include the cost to mine a ton of coal or the cost to enrich uranium to the proper grade. These costs are included in the cost of electricity. External costs, such as the cost of adding carbon dioxide (CO2) to the atmosphere, are not included in the cost of electricity. A tax on CO2 emissions would change the external cost into a direct cost as it would change the price of electricity based on the amount of CO2 emitted.
Throughout this article, all costs will be stated in or converted to 2015 dollars. Energies will be stated in gigajoules (1 GJ = 109 J = 278 kWh). The amount of CO2 emitted will be stated in kilograms (1000 kg = 1 Mg = 1 metric ton). The price of electricity will be stated in dollars per gigajoule where $1/GJ = $0.0036/kWh. A carbon tax t will be stated in dollars per kilogram CO2 emitted.
A carbon tax has the simple linear effect on the cost of producting electricity P of
where P0 is the pre-tax dollar cost of producing 1 GJ of energy, t is the carbon tax in dollars per kilogram of CO2 emitted, and (dM/dE) is the number of kilograms of CO2 emitted per GJ of energy produced.
Adjustment to 2015 dollars is made using the Consumer Price Index (CPI) according to
A simple but inaccurate way to find the cost of producing electricity is to calculate the cost to buy a fuel to be converted into electricity. The method of only including fuel cost is not the most accurate way to measure costs because measuring only the cost of obtaining fuel ignores capital costs. For example, capital costs are significant for nuclear power while fuel costs are low, and the only costs for wind, solar, and hydropower are capital costs. Therefore, in order to better quantify the cost of electricity from different sources, it important to include the cost of the power plant itself. This is done with the levelized cost of electricity (LCOE).
The levelized cost of electricity includes the capital costs of building the power plant and maintenance and labor costs over the course of the plant's life in addition to the cost of fuel. The LCOE is the total discounted cost of the power plant over the plant's lifetime divided by the total discounted amount of electricity that the source will provide over its lifetime. The LCOE can be interpreted as the minimum average cost the electricity needs to be sold at for the power plant to break even. As such, calculated values of LCOE are given for many different power sources and LOCE values can be used to compare the cost of producing electricity from different sources. Values for LOCE in the United States by source are shown in Fig. 1. [1-6]
|Fig. 2: A graph showing amount of CO2 emissions per GJ of energy produced (dM/dE) from various power sources.  (Source: E. Kountz)|
The second part of the cost of electricity is calculating the external costs of a power source. The most important external cost in generating electricity is the amount of CO2 emitted; therefore, CO2 emissions and methane equivalents will be included as the external cost of generating electricity. Carbon dioxide emissions can be direct emissions and indirect emissions. Only coal and natural gas plants have direct emissions. Biomass, the other type of power generated from combustion, is currently legally defined as "carbon neutral."  Indirect sources of CO2 include processing fuel, decommissioning, and fuel transportation (infrastructure and supply chain), CO2 equivalents for methane production, and emissions from biomass (since biomass emissions are not counted in the direct emissions). These direct and external CO2 emissions can then be added together for a total amount of CO2 emissions for each type of electricity as shown in Fig. 2. 
Fig. 2 shows the amount of CO2 emissions from coal in GJ of energy produced is much greater than that from natural gas. Both of these sources have much larger emissions than any of the others. Carbon capture and storage (CCS) reduces the coal and natural gas CO2 emissions to a value comparable to that of biomass. However, both biomass and the various carbon capture and storage technologies have emissions much greater than renewable or nuclear power.
Finally, it is possible to combine the cost of generating electricity from different sources with the CO2 emissions and a carbon tax to find a new cost of electricity, per Eq. (1). For example, a carbon tax of t = $1 per Mg = $0.001 per kg would increase the cost of a gallon of gasoline or a gallon of diesel by around $0.01. Table 1 lists the pre-tax costs of generating electricity and the CO2 emissions for various fuels.
|Table 1: Pre-tax costs for producing electricity from various power sources (from Fig. 1) and CO2 emissions from each power source (Fig. 2). [1-6,8]|
|Fig. 3: Plot of Eq. (1) showing the cost of electricity from various power sources as a function a carbon tax t, assuming the parameters of Table 1. (Source: E. Kountz)|
While any carbon tax might vary from this first order study, and technology improvements and more precise measurements of cost and CO2 emissions might cause slightly different results, the broad results will not significantly change. Fig. 3 shows a carbon tax ranging from $0/kg to $1/kg. At a tax between $0.1/kg and $0.2/kg, coal becomes the most expensive power source. At $0.2/kg, all sources of power that involve combustion are more expensive than non-combustion-based power, except for offshore wind. This includes biomass and carbon capture and storage technologies. At prices above $0.4/kg, all combustion based power is at least twice as expensive as any alternative power, save for offshore wind. Likewise, any tax below $0.1/kg would probably not have a large impact on the cost of any source of power.
Fig. 3 thus shows that any carbon tax could be divided into three categories. A low carbon tax would not significantly change the resulting cost of electricity for any power source and so would not result in a large change in use of renewable power or fossil fuels. A very large carbon tax would result in all types of fossil fuels being replaced with nuclear and renewable power. However, a carbon dioxide emission tax between the two (in this analysis between $0.1/kg and $0.2/kg, or an equivalent increase in the price of gasoline by around $1/gal to $2/gal), would result in only coal based power becoming priced out of competition. This should not be a surprise since coal is made of carbon and will have the highest carbon dioxide emissions per unit power while other fossil fuels including natural gas (and oil) contain carbon and hydrogen.
© Erik Kountz. 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.
 "Levelized Cost and Levelized Avoided Cost of New Generation Resources in the Annual Energy Outlook 2016," U.S. Energy Information Administration, August 2016.
 "Annual Energy Outlook 2016 with Projections to 2040," U.S. Energy Information Administration, 0383(2016), August 2016.
 "Levelized Cost and Levelized Avoided Cost of New Generation Resources in the Annual Energy Outlook 2015," U. S. Energy Information Administration, June 2015.
 "Annual Energy Outlook 2015 with Projections to 2040," U.S. Energy Information Administration, 0383(2015), April 2015.
 "Consumer Price Index - December 2013," U.S. Bureau of Labor Statistics, USDL-14-0037, 16 Jan 14.
 "Consumer Price Index - December 2015," U.S. Bureau of Labor Statistics, USDL-16-0109, 20 Jan 16
 K. Bracmort, "Is Biopower Carbon Neutral?," Congressional Research Services, R41603, February 2016.
 Climate Change 2014: Mitigation of Climate Change: Working Group III Contribution to the IPCC Fifth Assessment Report, 1st Ed. (Cambridge University Press, 2015).