(2018 Editor’s note: The sudden interest in this article led to a review that uncovered a couple errors and hence their corrections. In that effort, we have learned that the article provides one way among several to get a handle on the cost of producing power by wind-turned generators, and a few other related costs.
We also learned that Financial calculations are not for lovers of certainty or for the faint of heart. This is because, in part, financial terms are unfamiliar to the average reader and the discipline’s ideas change with time and technology. )
By Taylor Johnson | September 14, 2009
I have become increasingly tired of comments and discussion around the web in which random people make even unfounded claims regarding the profit and cost aspects of wind power generation. Due to this annoyance, I have researched and so provide here links to several equations and figures for costs and calculating costs for a few figures that surround the generation of power by wind. Most all data provided is sourced from national and government resources.
For example, according to EIA (Electricity Information Administration), the average wholesale cost to generate electricity for 2007 was 5.72 cents per kilowatt-hour (¢/kWh) (2007 is their most recent data). And according to PacifiCorp annual reports (a Mid-American Subsidiary) the average revenue (cost to buyers) is 7.2 ¢/kWh. This value is necessary for calculations, not the wholesale value. The costs for transmission are extra and not addressed here.
These figures vary by region, state, regulated versus non-regulated, and a number of other things. People in some areas of the country pay an average as high as 25 ¢/kWh for their power. However, for the calculations here, I will use 7.2 ¢/kWh because it is a good national average.
A few equations
According to NREL (National Renewable Energy Laboratories), the formula for calculating profitability or the cost to generate power (Pcost to gen ) with a wind turbine or farm is:
Pcost to gen = [(FCR x IC) / AEP] + [(LRC + O&M + LLC) / AEP ] (1)
FCR = fixed charge rate. For the interested reader, https://www.e-education.psu.edu/eme801/node/560 has a good discussion on the rate, and says this of the variable: It’s the fraction of the Total Installed Cost that must be set aside each year to retire capital costs which include interest on debt, return on equity, and so forth.
For our purposes, we use 7% or 0.07.
IC = initial capital or CapEx, the capital expenditure, in $.
AEP = net annual energy production, kWh.
LRC = levelized replacement cost (yearly sinking fund for overhauls and replacements), $
O&M = cost for operations and maintenance (turbine maintenance, cost/yr), $
LLC = land lease cost, $/year
Finding values for the terms in Equation 1
FCR Assume we are a utility company building a 1-MW wind power plant rather than building another coal-powered plant. Because we are a utility, we expect to sell power for 7.2 ¢/kWh (or $0.072 /kWh), as per above.
IC The initial capital investment or Capex is the total cost of the entire installation, which according to AWEA (American Wind Energy Association) is about $1.3 million for a 1-MW (1,000 kW) turbine.
AEP For the annual energy production, assume a 39% capacity factor. That is, a turbine will generate on average 39% of its nameplate rating. Hence:
AEP =1,000 kW x 24 hr/day x 365 day/yr x 0.39,
AEP = 3,416,400 kWh per year.
Note to those who are checking the math here: Always include units because they will hint at a correct or meaningful figure. If a unit such as $2 comes up, look for an error.
LRC The Levelized Replacement cost is simple. Use:
LRC = Cost of turbine / Expected life
LRC = $1.3 million / 20 years
LRC = $65,000/yr
O&M Operations and Maintenance cost simply runs about 8% of annual gross revenue. Hence:
O&M = AEP x average revenue/kWh x 0.08
O&M = 3,416,400 kWh x $0.072/kWh x 0.08
O&M = $19,678
LLC The Land Lease Cost is a variable as well but according to AWEA statistics its runs 5% of annual revenue
With these few figures, we can calculate a value for Equation 1.
Pcost to gen = [(0.07 x $1,300,000) / 3,416,400] + [($65,000 + $19,678 + $12,220) / 3,394,400
Pcost to gen = 0.0266 + 0.0284
Pcost to gen = 0.055
Pcost to gen = 5.50 ¢/kwh
Next, find a total annual expense (Tae) using
Tae = Pcost to gen x AEP
Tae = $0.055 /kwh x 3,416,400 kwh
Tae = $187,902
This is the total annual expense.
From here, find annual Gross Income (Ig) using:
Ig = $0.072 x 3,416,400
Ig = $245,980
Find annual profit (Pa) from the turbine using:
Pa = (Pselling price – Pcost to gen ) x AEP
Pa = ($0.072 − $0.055) x 3,416,400 kWh
Pa =$0.017 x 3,416,400
Pa = $58,079
Now that we know how much the wind farm (of one turbine) makes each year, we can calculate a return on investment or ROI using:
ROI = Pa / Total investment
ROI = $58,079 / $1.3 million
ROI = 0.0447 or 4.47%.
This seems a fairly low number for an ROI. Generally, companies require an ROI of 8% or higher if they are to invest in an idea or product.
Another important figure, the Break Even Point, tells how long until your investment is paid for. To find a BEP, use:
BEP = Cturbine / Pa
BEP = $1,300,000 / $58,079/yr
BEP = 22.38 years
Hence, with a product life of 20 years, the product will have to work for more than 22 years before it is paid for. The reader-accountant might apply these figures to a spreadsheet to make playing with the variables more interesting.
What do we learn from this? At this time in 2009 and considering the current costs of turbines, turbine installation, and maintenance, along with the current price of 7.2 ¢/kWh, wind-generated power seems not the best financial decision a power company could make. This explains the necessity of federal grants and stimulus available to the renewables market.
However, I still believe that wind-generated power is the future of energy production around the world. It takes time to integrate new ideas into the marketplace and for prices to become competitive. It is rare to find a new product or technology that competes economically with an established base or technology. If we do not start building and expanding now, when it becomes necessary to do so, we may not have the resources or infrastructure or both to make the necessary changes.
− Taylor Johnson
2018 Editor’s note: There are other financial mechanisms, such as depreciation and Renewable Energy Credits, that brings down the cost of ownership. While the figures provide some insight to wind-farm costs, readers are welcome to comment on the methods and values used in the calculations. We don’t pretend to be adept on things financial.
− Paul Dvorak