# The LCOE is defined as the energy price (\$ per unit of energy output) for which the Net Present Value of the investment is zero.

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1 Poject Decision Metics: Levelized Cost of Enegy (LCOE) Let s etun to ou wind powe and natual gas powe plant example fom ealie in this lesson. Suppose that both powe plants wee selling electicity into the same deegulated geneation maket and both had the same expected opeational life. Which plant would be moe pofitable? Since both plants would be facing the same maket pice fo the electicity that they sell, the moe pofitable plant would be the one that had the lowe aveage cost pe Megawatt-hou of electicity ove its entie lifetime. he Levelized Cost of Enegy (LCOE) can be used to help evaluate poblems like this one, and is one of the most commonly used metics fo assessing the financial viability of enegy pojects. It is used paticulaly often in situations like the one we just discussed compaing the lifetime costs of diffeent technologies fo electic powe geneation. he LCOE can, howeve, be applied to othe enegy pojects as well (like oil and gas wells, o efineies). he LCOE is defined as the enegy pice (\$ pe unit of enegy output) fo which the Net Pesent Value of the investment is zeo. he LCOE is thus the aveage evenue pe unit of enegy output (so this would be \$/MWh fo a powe plant, o \$/bael fo an oil well, fo example) ove a poject s lifetime such that the plant beaks even. he LCOE is sometimes called the Unit echnical Cost (UC). It epesents the lifetime aveage cost of enegy fo a specific poject. We will now get into the mathematics of calculating the LCOE. We will fist pesent the most geneic LCOE fomula, and then we will discuss some simplifications of the fomula. LCOE is defined as the solution to the equation: t0 C t M t (1 ) t t0 LCOE (1 ) t LCOE, (1 ) t t0 whee C t epesents all capital costs incued in yea t (these may be zeo except duing the fist few yeas of the poject); M t epesents all opeational costs incued in yea t, and epesents the total output of the poject in yea t. he tem C t + M t epesents the annual costs of the poject (which may include payments on capital, fuel, labo, land leases and so foth). he tem epesents the annual enegy output of the plant. Note that if all capital costs ae incued in yea zeo, then the tem C t factos out of the LCOE equation. In this case you will sometimes see the capital cost tem efeed to as otal Installed Cost (IC) o Ovenight Cost (OC). In this case we wite the LCOE equation as:

2 t0 M t (1 ) t IC t0 LCOE (1 ) t LCOE t0 (1 ) t In some othe contexts (fo those of you taking AE 878 though the RESS pogam, fo example), you may see the discount ate efeed to as the Weighted Aveage Cost of Capital (WACC). We will devote an entie lesson late in the tem to the elationship between the discount ate and the WACC (sneak peview: if the entity making the poject investment is a fo-pofit entity, then the discount ate and WACC should be the same thing), and methods fo calculating what the WACC should be. We can thus solve fo LCOE as: LCOE t0 t0 C t M t (1 ) t (1 ) t. hee ae a couple of ways to make this calculation easie. Often times when evaluating pospective enegy pojects we make two assumptions: Fist, annual output of the poject is constant in each yea. Second, the vaiable cost of poduction pe unit of output is constant each yea. In this case, the Q and M tems fom the LCOE equation ae the same in each yea, and we can wite the LCOE as the sum of two tems: 1. Levelized Fixed Cost (LFC), which calculates the aveage payment equied to amotize o pay off capital costs ove yeas. 2. Levelized Vaiable Cost (LVC), which calculates the aveage payment equied to cove pe-unit opeational costs. If the vaiable cost of poduction (this would include fuel, labo and any vaiable opeations/maintenance costs) don t change, then the LVC is just equal to this total vaiable cost pe unit of output. Refeencing the LCOE equations above, LVC would just be equal to M Q. (he LVC may also just be given in the poblem statement, as in the examples below.) Calculating LFC is a little bit moe complicated. Assume that the poject involves a discount ate ; the life of the poject is yeas; and the capital costs ae paid in one lump sum IC at the beginning of the poject. LFC solves the equation: IC t1 LFC Q, (1 ) t

3 which we can ewite as: LFC t1 IC 1 (1 ) t Q. Using some mathematics of finite sums (if you ae eally cuious, Wikipedia has a detailed aticle on the geometic seies, which descibes the denominato of the LFC equation since is less than one see we 1 (1 ) can ewite the deominato as. hus, LFC IC 1 (1 ) Q IC 1 (1 ) Q and finally, we have ou expession fo LCOE: LCOE LFC LVC IC 1 (1 ) Q LVC. Along these same lines, anothe (less messy) way to wite the LCOE when output and vaiable costs ae constant ove time uses the fixed chage ate (FCR). he FCR is just the faction of the otal Installed Cost (IC) that must be set aside each yea to etie capital costs (which includes inteest on debt, etun on equity and so foth we ll discuss these in moe detail in futue lessons). hus, IC FCR is the annuity payment (the sum of pincipal plus inteest payments, like you would have with a home motgage o a college loan) needed to pay off the investment s capital cost. he FCR is calculated as: FCR ( 1) 1. (You may see o have seen the FCR equation witten with the WACC athe than the discount ate. Remembe that fo ou puposes, thee is eally no diffeence between the two.) Using the fixed chage ate, the LCOE can be witten as:

4 LCOE IC Q FCR M Q. IC In this simple vesion of the LCOE equation, note that the fist tem Q FCR is just the Levelized Fixed Cost (LFC) and the second tem (M/Q) is just the Levelized Vaiable Cost (LVC). Hee is an example: Suppose that a powe plant costs \$10 billion to build and has an expected life of 30 yeas. he vaiable cost of poducing one MWh of electicity is \$20. It will opeate 24 hous a day, 360 days a yea at a capacity of 1000 MW. (Note: to get output, multiply capacity and hous of opeation ove the plant s life). What is the levelized cost of enegy if the inteest ate is 5%? Hee is the answe: Fist, we calculate the total amount of electicity poduced annually: (360 days pe yea) (24 hous pe day) 1000 MW=8.64 million MWh pe yea. his is Q in ou LCOE fomula. LVC is equal to \$20 pe MWh. So, we calculate LCOE as: IC LCOE 1 (1 ) Q LVC \$10bil 0.05 LCOE 8.64mil (1 0.05) \$75.29 / MWh \$20 / MWh \$95.29MWh. As an execise fo youself, calculate the LCOE fo the natual gas powe plant and the wind powe plant that we laid out ealie in this lesson. As a eminde, the wind plant has a capital cost of \$1.2 million and a vaiable cost of \$5/MWh. he natual gas plant has a capital cost of \$600,000 and a vaiable cost of \$50/MWh. Each plant poduces 2,628 MWh pe yea. Assume a 10% annual discount ate and a 20-yea life fo each poject. You should find that the wind plant has LCOE = \$58.63/MWh and the gas plant has LCOE = \$76.82 pe MWh. he LCOE can be used to compae enegy pojects to pevailing maket pices. If the maket pice is highe than the LCOE, then the magin pe unit of output is positive (Maket pice LCOE is geate than zeo) and the poject should be pofitable. If the maket pice is lowe than the LCOE, then the poject will have negative magins and will not be pofitable. hee ae some pitfalls to using LCOE in this way to evaluate vaiable enewables like wind and sola, since the LCOE is often compaed to the aveage electicity pice. If you think about it, this compaison is biased against sola and biased towads wind because sola is moe likely to be poducing electicity duing the

5 daytime (when pices ae high) and wind is moe likely to be poducing electicity duing the nighttime (when pices ae usually low). A moe consistent appoach, which is just as elevant fo fossil-fied powe plants as fo enewables, would be to compae the LCOE to the aveage pice when you would expect the powe plant to be geneating electicity.

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