Saturday, March 12, 2011

The Problems with Calculating the Levelized Cost of Electricity and Using it to Compare between Competing Technologies

There are major problems today with how academia & governments compare between different types of electricity generating power plants. For example, the way that the US Energy Information Administration (EIA) presents data comparing various electricity generating power plants is highly biased towards intermittent technology (like wind) and highly biased against peak-following technology (like hydro or natural gas). There is a fairly good article on this subject by Paul Joskow of MIT, which highlights the problem of comparing base-load electricity technologies (like coal, or nuclear) with intermittent technologies (like wind) or with peak-following technologies (like natural gas or hydro-electric.) However, while Joskow does a good job of points out the problem, he doesn't discuss what is the correct figure of merit that we should be using to compare technologies that generate different types of electricity.

The typical means of choosing between competing electricity power plant configurations is to compare the value of the levelized cost of electricity (LCOE). This post will highlight the problem in calculating LCOE and the problem in comparing technologies using the LCOE. And then this post will discuss how most of these problems can be solved by calculating the internal rate of return on investment.

First, I'll summarize the major problems with LCOE, and then I'll discuss each one in more detail.

Problem#1:  Electricity does not sell for the same price; it depends on what type of electricity (base-load, peak following, intermittent, etc...)

Problem#2: LCOE is incapable of handling power plants that co-produce fuels & chemicals 

Problem#3: The choice of the discount rate is often not explicitly stated

Problem#4: The units of LCOE are problematic

Problem#5:  The calculation of LCOE hides underlying self-reference

Problem#1: Electricity does not sell for the same price. Electricity that is peak-following (such as hydro & natural gas) can be sold at a higher price than the same amount of electricity that is base-load (such as nuclear or coal), and can be sold at an even higher price than the same amount of electricity that is intermittent (such as wind). The reason for this price difference is that the peak-following power plant will output more electricity when the prices of electricity are higher than when electricity prices are lower. On the other hand, a wind turbine outputs more electricity at night when wind speeds are higher, but when the prices of electricity are lower than they are on average during the day. A hydro-electric dam or a natural gas generator ends up receiving a higher revenue per unit of electricity than does a wind turbine for two main reason: a) the price of electricity is higher during the day than at night, and b) these technologies receive revenue for their spinning reserve (i.e. their ability to ramp power up or down quickly.)
The effect of this is to bias comparisons between competing technologies, as is often done by the EIA. For example, the US Energy Information Administration (EIA) only calculates the LCOE of various competing technologies. Wiki/Cost_of_electricity_by_source
The correct figure of merit to compare competing technologies must include the average price of electricity that that technology can obtain. (Note that the calculation of the rate of return on investment includes the average price of electricity at which a technology can be sold.)
Summary:  We should never compare wind turbines with hydro-electric dams using a levelized cost of electricity.

Problem#2: Power plants that co-produce fuels and chemicals, such as gasoline, natural gas, ethanol, and hydrogen, need a figure of merit that accounts for both the production of electricity and the production of fuels/chemicals. LCOE is an awkward figure of merit for co-production plants because it's supposed to give you the sale price of electricity in order to break even, but what about the sale price of the co-produced fuel? Also, LCOE does not handle the fact that there are different types of electricity, and depending on the price of electricity, a co-production plan has the capability of either increasing or decreasing the amount of electricity. LCOE does not take into the account the main advantage of a co-production power plant: producing the fuel when electricity prices are low. An example of a co-production plant would be an integrated gasification combined cycle (IGCC) power plant that co-produces synthetic gasoline (F-T fuels) or hydrogen.
(Note that the calculation of the rate of return on investment can easily account for co-production of fuels & chemicals because the rate of return does not differentiate between how the income is made.)

Problem#3: The value of the discount rate is often not explicitly stated. The discount rate is the assumed time value of money. The value of the discount rate can have a large effect on the value of LCOE. What's quite interesting, as we will see in Problem#4, is that discount rate is actually a function of the profitability of the existing power plants in society. This means that calculating the LCOE is iterative. Typically, individual researchers avoid this self-reference by assuming that the discount rate is a constant, but this approximation can not be made in the field of public policy where we are interested in the effect of mass production of certain technologies that could have a large effect on the price of electricity. (Note: that the discount rate does not appear in the rate of return on investment, so this problem doesn't occur there.)

Problem#4:The value of LCOE still has units of currency in the numerator. While converting to a currency in a different time and place is not that difficult, it does make it harder to compare between different countries or between calculations in the same country at some time in the past. Interestingly, even if the LCOE is divided by the price of electricity, the units of normalized LCOE and the rate of return are not the same. One is dimensionless, and the other has units of [per time]. As I mentioned in a previous post about how to make economics more 'physics-friendly,' (How to Train Physicists to be Energy Engineers) it would be advantageous if the units for the figure of merit that we are optimizing were solely based on fundamental units, such length, mass, or time.
It would also be preferable if the units were consistent with the underlying goal of life. As I have mentioned before (Meaning of Life), the underlying goal of life is to bring our non-equilibrium universe into equilibrium. Life does this by increasing the entropy of the universe, and it appears that the best way to increase the entropy rate of the universe is to maximize the rate of return on investment and to re-invest as much of the work generated at the power plant into building more power plants. (i.e. the goal of a power plant is to produce more power plants, just as the goal of a bacteria is to produce more bacteria.) Maximizing the internal rate of return on investment, as well as re-investing profits back into building more power plants, is the best way of growing our economy and growing life in general.
So, we see that, while the units of LCOE are convenient to compare with actual prices of electricity that we pay each month, the units of LCOE are problematic for comparing with other times/places and for understanding the basic driving more behind life.

Problem#5: The calculation of LCOE hides the underlying self-referential nature of biology and hence economics. For example, if we picked a technology with a value of LCOE higher than what we currently pay for electricity, then the actual price of electricity would have to increase. But if the actual price of electricity were to increase, this would cause the calculation of the fuel costs, the labor costs, and the maintenance cost estimates to increase. This would in turn cause the LCOE to increase, and this goes into a vicious cycle. Worse, with the new higher electricity prices, the capital costs on new power plants with this same technology would be higher. This means that the LCOE of this technology would go up even higher. If we built a second power plant with this technology, then the actual prices of electricity would go up even more. This would continue to get worse as more and more of the power plants were built.

One way to stop this vicious cycle is to calculate the internal rate of return on investment (IRR), thereby removing the units of currency from the figure of merit used to compare between competing technologies. Given the cash flow time series, the internal rate of return on investment can be easily calculated using programs like Excel { =IRR(cash flow..., guess).} The IRR is the expected rate of return on investment for an investor in the power plant who invests at the beginning of construction and who re-invests his yearly profits into an exactly similar project. The IRR is self-referential in the sense that it measures the growth rate in the capability to do work if the work (i.e. electricity) is reinvested into building exactly similar power plants. The growth rate of a society can't be any larger than the average rate of return of its power plants.

Also, it should be noted that calculating the IRR of power plants is even easier in a society with electricity-backed currency. (Energy Backed Money   Electricity backed Currency) In that case, the US would keep the average price of base-load electricity within a certain narrow range of values. This is essentially similar to operating with zero-inflation. In a society with an energy backed currency, the internal rate of return on investment measures the actual growth of money in that society. Yes, the amount of money in supply should be related to the average yearly power that can be generated.
(As noted above, this doesn't mean that the price of electricity is a's just that the Federal Reserve would print or remove currency from circulation in order to maintain the average price of electricity constant from year to year. The actual price of electricity will depend on locations and time of day/week/year.)

The goal of this post has been to detail the problems with calculating the levelized cost of electricity (LCOE) and to suggest an improved figure of merit (IRR). There are multiple problems with LCOE, mostly stemming from the fact that the price of electricity depends on the type of electricity generated. The internal rate of return on investment appears to solve most of these problems. (Although, it should be noted that the IRR of different power plants should only be compared with each other if they represent equally risky projects. The best way to compare projects is to graph the rate vs. risk and to allocate your investments so as to maximize your rate of return for a given allotment of total overall risk.)


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  2. Could you please explain what is the rationale for discounting units of electricity in the denominator while calculating the LCOE. Is it just for the sake of consistency between the numerator and the denominator or something else?

  3. Thanks for the question:
    There are at least two ways different ways of calculating the LCOE of a power plant, and the answers will be exactly the same.
    One way is assume a discount rate, and then solve for the sale price of electricity that yields the Net Present Value of the Project equal to zero.
    Another option is to add total as costs (weighted by the discount factor for the year in which the costs occur) and divide by the total electricity (weighted by the discount factor in the year that the electricity is produced.)
    We discount both the costs and the electricity because electricity generated in the future is not as valuable as electricity generated today because the electricity generated today can be invested into projects that grow our wealth. The discount rate is the interest rate that investors can achieve by investing in power plants that grow the capability to do useful work.
    A third option to calculate LCOE is to determine the fuel & variable O&M costs per unit of electricity and then add to that the levelized capital costs and levelized fixed O&M costs.

  4. Interesting discussion here! What if we assume that Initial capital costs are the only costs for the project. Is its still justified to discount the units of electricity of the project when calculating LCOE?

  5. Anonymous,
    Good question.
    If the the initial capital costs are the only costs for the project, it's probably easier to just assume a capital recovery factor in order to convert [$/kW] into [$/kWh].
    For example, you can use the following website to calculate the capital recovery factor given a choice of interest rate and leasing period. An 8%/yr interest rate and a 20 year lifetime yields a capital recovery factor of 0.1/yr.
    So, if a nuclear power plant costs $5000/kW and operates 100% of rated design and has no maintenance/fuel costs, then the LCOE would be $500/kW-yr...$57/MWh (if we assume an 8%/yr interest rate and 20 years to pay off the loan.)

  6. I believe there is an even bigger flaw with the LCOE. For me, the only way to compare different projects is to calculate the NPV. By making a graph of NPV versus interest rate then we can see that these curves can show a higher NPV for project A but project B shows a higher IRR (NPV=0). This is basic finance and is the problem with IRR. LCOE is basically the same as IRR because it calculates the price of electricity when NPV=0 and as a result it has the same flaw as IRR. I just made a case where project A was more profitable on a NPV basis compare to project B at a WACC value but yet its LCOE value was higher than project B. Meaning the project B based on LCOE would be preferable. Unless I am wrong, I haven't seen this mistake reported anywhere.

    1. (forgot to mention) the problem with IRR is the often referred as IRR between mutually exclusive projects.

      And LCOE has the same flaw.

    2. tje1,
      The problem with the NPV is exactly as you state. If Project A is a larger project (i.e. you need to invest more into it at the start), it could have a larger value NPV then Project B, even though Project B has a higher value of IRR.
      The only reason that I would invest in Project A (high NPV, but lower IRR) over Project B (lower NPV, higher IRR) is the following:
      Compare projects with the same amount of initial investment. Take the extra money being invested into Project A, and put it into some other investment so that now Project A has the same initial investment as Project B plus the extra investment. Now calculate the NPV of Project A and the NPV of Project B plus extra investment. To calculate the NPV, I'd use the average rate of return on investment your company makes each year. If the NPV of Project A is still higher than Project B plus the extra investment, then I'd invest in Project A.

      This is obviously fairly complicated, which is why I think that it's a lot easier (and wiser) to just calculate the IRR, and then invest in those projects with values of IRR above a certain value (regardless of the size of the project.)

      Let me know if you agree with my statement that "it's unwise to compare the NPV of projects with different levels of initial investment."

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  8. It's very informative and good post i ever like.