*(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 (*P _{cost to gen}* ) with a wind turbine or farm is:

* **P _{cost to gen}* = [(

*FCR*x

*IC*) /

*AEP*] + [(

*LRC*+

*O&M*+

*LLC*) /

*AEP*]

**(1)**

where:

*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:

*1,000 kW x 24 hr/day x 365 day/yr x 0.39,*

AEP =

AEP =

*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

about $

**12,220**

**Results**

With these few figures, we can calculate a value for Equation 1.

*P _{cost to gen }* = [(0.07 x $1,300,000) / 3,416,400] + [($65,000 + $19,678 + $12,220) / 3,394,400

*P*= 0.0266 + 0.0284

_{cost to gen}*P*= 0.055

_{cost to gen}*P*= 5.50 ¢/kwh

_{cost to gen}Next, find a total annual expense (*T _{ae}*) using

*T _{ae} = P_{cost to gen } x AEP_{
}T_{ae} *= $0.055 /kwh x 3,416,400 kwh

*T*=

_{ae}**$187,902**

This is the total annual expense.

From here, find annual Gross Income (*I _{g}*) using:

*I*= $0.072 x 3,416,400

_{g}*I*245,980

_{g }= $Find annual profit (*P _{a}*) from the turbine using:

*P*= (

_{a}*P*–

_{selling price}*P*) x

_{cost to gen }*AEP*

*P*= ($0.072 − $0.055) x 3,416,400 kWh

_{a}*P*=$0.017 x 3,416,400

_{a}*P*= $58,079

_{a }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* =

*P*/

_{a}*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* = *C _{turbine}* /

*P*

_{a}*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.

**Summary**

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 *

Tade says

If the exact quantity (q) produce follow a uniformly distributed between 5 and 20 and in the market each unit can be sold at price p$ per unit and unit sold represent a contract deliver. the next day additional unit was sold for s$ per unit during the market balancing phase. If the company has sold more than it produce in terms of unit during the market balancing phase, it buys extra unit at v$ per unit.. if the company policy is selling 15 unit per day (q=15). How can we use Monte Carlo simulation by hand calculation to generate 3 random number and calculate expected profit.

Jessica bixler says

How does this compare to coal or gas

I know you said the common is 8% roi but is that what they make? My Dad worked in some of the first retrofitting for coal filtration during the Obama era. He said it was so expensive do do it asnt worth it and many just swittched to natural gas

Vasishta bhargava says

Hi,

Firstly, the profitability of wind farm/project is expressed as the quadratic equation of time (yr), if you look at the units of each term in the equation,

(FCR*ICC)/AEP – ((USD/kWh/yr )*(USD))/kWh —> ((USD/kWh)^2)*(yr)

(LRC+O&M +LLC)/AEP (USD/yr)/kWh after rearranging —-> ( USD/kWh)/yr

LRC, O&M, LLC each have unit (USD)/yr and AEP – kWh

So, the equation is right, and please refer to the publication from NREL for further reference. Further, the unit for LCOE is expressed in terms of per unit rate for the Capital Cost element, while for other cost elements it is not.

I hope it clears the doubt now.

Vasishta bhargava

Daryl says

Your link for power produced per day is down so I can’t verify your assumption of 9.3 hr. of energy produced per day. This number is highly suspect since you are assuming that the wind blows at the optimum speed for 9.3 hr/day. The power generation curve is dependent on the cube of the wind speed. Most 1-3 MW wind generators have peak efficiency at about 30 mph. But the wind generators installed east of me (Idaho Falls, Idaho) are idle several days per week and only a mild breeze blows the rest of the time. Sometimes there will be strong winds for 8-12 hr/day but it doesn’t average out to 30+ mph for 9.3 hrs/day. I’ll bet the average over the wind farm is no more than 15 mph for about 12 hrs/day, and that would be a good week for them. Since 15 mph only produces 1/8 (0.5^3) of the energy as 30 mph, even at 12 hrs/day, the energy produced is equivalent to 1.5 hrs at full rated power. Even on a good week, plug in 3 hrs instead of 9.3 and you will see that these wind generators are not money-makers.

Daryl

afatladysings says

One of the major expences that are left out saleries, benifits and pensions. $54000 would not cover the cost of one utility employee. What about cost envolved to support the employees to do there job office space, office equipment, office supplies, tools, test equipment vehicals (cars, trucks)vehical parking, vehical maintance, record maintance, evil fuel for vehicals, evil fossil fuel generated electricty to prevent blackouts and brownouts for those low wind and down for maintance periods . Note if a system requires a backup system some of that cost needs to be included. End result raise rates and or taxes.

Shehan says

This is a wrong caluclation after all.

1. What do you expect by FCR*ICR? Units are not consistent

2. The break even point of this machine is 20 years itself. Remeber when you calculate the cost of enrgy unit additional 65000 USD was included. (1300000USD/20 year)So this capital cost was included in the cost of energy unit. You dont have to consider it again.

These calculaions contain many errors..

(Someone may comment on this and clarify whether I am wrong)

Mt says

Hi,

Why are FCR multiplIed with ICC in the cost of energy equation? The units does not match with the rest of the equation parameters or am I mistaken?

Paul Dvorak says

Thanks for your comment, Mark, and too for the cost figures.

I’m not sure what type of power generation can improve on $0.05/kWh.

— Paul Dvorak

Paul Dvorak says

Thanks for your comment, Mark, and thanks too for the cost figures.

I’m not sure what type of power generation could improve on $0.05/kWh.

–Paul dvorak

Mark says

Unfortunately, this post greatly generalizes a few things, the most important of which is the average selling price of electricity. In some markets, electricity is considerably more expensive to consumers and businesses than other markets.

In Québec for example, electricity costs the average consumer (residential use) about $0.05/kwh. In islands throughout the Caribbean, the cost is as high as $0.40/kwh. Wind farms are not perfect for EVERY market, they’re perfect for specific markets.

One way or another, the price of energy derived from non-renewable sources (oil, coal, nuclear, gas) is going to go up very soon. Renewables such as hydro, wind, and solar are much more constant and costs can be kept down in the long term. But it’s important that governments not give grants blindly to companies building wind farms in areas that don’t need them.

Dr R.E.Shore says

woops. expense, that is cost, is not the same as profit.

one step is missing in the calculation. Profit = Revenue – cost.

the total cost for the year is not the total revenue nor the total profit.

if the cost is 5.6 cents per KWH and the price you can sell if for is 8.6

then the profit is 3 cents per KWH.

If the price were 25.6 cents/KWH then the profit would be 20 cents per KWH.

here is a quote rom wikepedia

http://en.wikipedia.org/wiki/Cost-Volume-Profit_Analysis

TC = TFC + X

TR = P x X

where

TC = Total Costs

TFC = Total Fixed Costs

V = Unit Variable Cost (Variable Cost per Unit)

X = Number of Units

TR = S = Total Revenue = Sales

P = (Unit) Sales Price

Profit is computed as TR-TC; it is a profit if positive, a loss if negative.