Wind Energy - Research Papers

8/2/2019 Wind Energy - Research Papers

1/22

Wind Energy Production Efficiency:

An Empirical Research Paper

Jeff Spencer

May 2005


2/22

Section 1: Statement of the Problem

Rising concerns on the way the planet is treated has brought popularity to new

sources of energy in recent years. According to Brian Walting of Scotian Windfields,

wind energy production is a very new concept in Canada; companies like NS power,

Scotian Windfields, and North Cape Wind farm in Prince Edward Island are leading the

way in Atlantic wind development. This paper is directed toward the production of wind

energy and the inputs that are associated with it. This paper also seeks the optimal wind

speed for energy production, whether or not a constant wind is important and explores

how different mixes of technology mix with the rest of the inputs.

It is the preferences of Canadians, that determine the goods that they will be able

to consume in Canada. Whether it be the food that they eat, the amount that theyre

taxed, the quality of their education, or the way they produce their power, it is the

majority of preferences that will decide on the final goods.

In the last 20 years there has been rising concern with the way the planet is

treated. It started off with scientists informing the citizens of the world about different

crises that are going to be present in the upcoming years. Destruction of rainforests,

rising of planet temperatures, melting glaciers, and extinction or degeneration of animal

species were just some to note. Consumers groups began to respond. Groups such WWF,Sierra Club, The Green Party, Friends of The Earth and alike began to organize.

Pressures from these types of groups helped give birth to The Kyoto Accord. The Kyoto

accord is an agreement among countries involved to reduce the amount of green housing

gases that we produce and release into the air.1 The Canadian government signed this

agreement.

In 2001 the Canadian government announced a plan to start to eliminate green

house gases (GHG). Wind energy is a clean and renewable source of electricity. In a 5

year time period the government wanted to have 1000 MW of renewable wind energy

production in Canada along with a 3 million ton decrease in green house gas emissions.

To ensure that firms would be enticed to go along with this idea a $260 million incentive

1 Canada. Natural Resources Canada. WPPI Production Inventive. Ottawa: Wind PowerProduction Inventive Program, 1999 p. 7


3/22

program was developed to be paid out to firms who were producing electricity by means

of wind. This started the Wind Power Production Incentive (WPPI) program. For the

first 10 years of the program the Canadian government offered 1 per Kw/h in addition to

market price of power. The ongoing plan is that the financial incentive will bring enough

firms into the market to make wind energy a sustainable market. Also over the programs

lifetime the expansion is to develop into productivity and technology gains that will

decrease the cost of producing and the selling price of electricity. By the time the WPPI

program has come to an end, the goal of the government is that the wind energy sector

will be able to compete with all the leading suppliers of power. 2

At present, wind energy is a very profitable sector for those who have committed

to the set up and. There are large amounts of profit to be made if the company has done

their research correctly.3 As an economist it is a very exciting time to be looking at this

market because it is so new and many concepts are being put to the test. This is a perfect

example of a microeconomic situation. With all these firms and investors flocking to this

market it would be interesting to see what the production function of wind energy would

look like. With a production function it can be determined what the most important

factors are in combination to produce large amounts of energy. With this function it can

also be determined which inputs do not seem to be as important to output. The results of

this project will be important to the manufacturers of the wind turbines, the wind power

production incentive program, and economists.

The manufacturers test all of their different models of wind turbines before they

release them for commercial use. Each of the production tests are run under perfect

conditions. The result is the optimized output, which in commercial use is a lot harder to

come by.4 The manufacturers would be interested to see how their turbines are

performing in sites across the Atlantic Provinces.

The wind power production incentive program is trying to assure that this industry

can look after itself and compete with the leading power suppliers. The WPPI will be

2WPPI Production Inventive p. 1-9

3 Walting, Brian. Scotian WindFields 29th Nov. 2004www.scotianwindfields.org

4 Vestas Homepage welcome 29th Nov. 2004


4/22

interested in this because they hope to see the industry grow over time. They can observe

the industry. Their hopes are that the industry will improve their outputs by investing in

more efficient equipment, thus demonstrating a viable energy sector worthy of

investment.5

As an economist, it would be of interest to know how efficiently this market is

running. It may turn out that this production function determines wind energy to be a

waste of resources, and there could be a cheaper way to make renewable energy. It will

also be interesting to know what inputs seem to be the most important to output, and what

kind of relationship they have.

There are eight different parts of this essay to follow this one. I will give brief

descriptions of what you can expect to see in the upcoming sections.

Section 2 holds the reviewing literature that has been discussed in order

competently comment and analysis results of the regressions and predict future action in

the wind energy sector. Section 3 is the whereabouts of the economic model. In this part

the economic model will be set up and also the paper will reveal the economic variables.

Section 4 will cover the econometric model that has been designed for this project. The

reader will see the model set up for the first time with all the variables in place. Section 5

is based on the data that will be used to put legs on this whole project. The entire data set

will be explained in great detail. The origin of the data and who supplied the data will

also be noted in this section. Section 7 will be the climax of the paper. This sections

focus is the report parameter estimates and their interpretation. Once the value of each

variable and their effect on output has been explored the paper will highlight the

economic importance of these results and the implications that the results might have.

Section 8 covers what the model has left out and the limitations that it holds. Section 9

will give credit to those who helped make this paper gain substance and body.

Section 2: Review of the literature

In order to comment accurately on wind energy production it was first necessary

to understand how wind energy works. An article by MAH was a good starting point to

5 WPPI Production Inventive p. 6


5/22

get familiar with the important factors that are used in wind energy.6

The greatest source

of knowledge was people in the wind energy field. Scotian Windfields and North Cape

Wind Farms helped tie together all the loose ends. The firms put into perspective the

rush to get into this market before the economic profit is taken up. They also stressed the

importance of not jumping into land investment. Testing the site for the right conditions

is one of the most important choices to be made. These firms expressed interest in

knowing that a production function was being created for their industry.

The WPPI paper by the government of Canada highlighted the fact that this is a

new industry and economic profits are being offered to anyone willing to put in the time

and money to seize them.7

This paper confirmed the reports that the firms were claiming;

there is great money to be made in the wind energy sector.

Section 3: The Economic Model

The model used has one dependant variable and 4 independent variables.

Kilowatt produced each hour (Kw/h) is the dependant variable in use. Wind,

temperature, barometric pressure, and direction of wind are the inputs that are going to

predict the output.

The dependant variable being used in this model is output. The output is the

amount of energy that is produced which is a result from the combination of inputs

included in the model. The output is electricity generated by each wind turbine. The

electricity is measured in Kw/h. The output in this model is retrieved from 2 different

locations. The first location is in Grand Etang which is a site located in Nova Scotia.

The other 3 sets of output come from North Cape Wind Farms on PEI. The PEI turbines

are all on the same site; however their outputs are not the same. The ideal scenario with

output was to get results from as many sites as possible so that there would be a broad

range of different types of outputs given the inputs they were exposed to. The mean and

standard deviation was found for each turbine. The mean was taken from the monthly

6 MAH Wind Energy Nov. 30th 2004

7 WPPI Production Inventive p. 6


6/22

averages of each turbine. The mean of the outputs for the Grand Etang site was 126368

Kw/h and it had a standard deviation of 57499.67. The first turbine on the PEI site had a

mean output of 187113.64 Kw/h and a standard deviation of 59809.93. The second

turbine on the PEI site had a mean of 214399.3 and a standard deviation of 57919.75.

The 3rd turbine on the PEI site had a mean of 177095.8 Kw/h and a standard deviation of

66068.28. As you can see from the means it would seem that the PEI site is the overall

better site at making output. The Nova Scotia site seems to be less productive than each

of the 3 turbines on PEI. However the variance is just about the same across the board.

It would seem that they are deviating to the same degree. The inputs might be less

effective on the Grand Etang site however they do seem to be proportional to the inputs

on PEI. The second turbine on the PEI site also seems to have higher output than the

other two turbines on the PEI wind farm. It is important to remember that a site that

produces all the right input variables must also be near a power grid system. If the site

can not produce electricity that can be consumed then there is no point in making the

wind field in the first place. This could be a factor in the Grand Etang site. They might

be too far away from a power grid to recover significant energy gains.

The first and possibly the most important input in the data set is the variable wind.

The wind speed was measured by an anemometer on each site. The propellers on the

turbines are of massive length, larger than any aircrafts wing span.8 When choosing a

site to build a wind farm on the firm must look at when the wind is blowing the hardest

and consider this along with economic implications. For instance suppose the wind with

the most speed blows during the summer and it seems to lull during the winter months.

Canadians consume the peak amount of power in the winter months.9 This is so that they

can heat their homes. If there is a wind site that produces most of the output during the

summer and the majority of electricity is used during the winter then selling the power

might be difficult. The same goes for a southern site. Places that use air conditioners too

keep their houses cool in the summer might not be willing to buy wind power if the

strong winds are in the winter months. Wind on a specific site will determine many of

the choices that have to be made when building on and buying supplies for a site. The

8www.scotianwindfields.org 9 Canadian Electricity Industry News and Information Oct 9 th 2004

< http://www.canelect.ca/english/electricity_in_canada.html l>


7/22

consistency of the speed that wind blows is a very important factor when choosing a site.

Turbines come in different sizes that all operate best at a certain wind speed. You dont

want to have a lot of variance in the wind at your site, otherwise, the machine will have

too little wind to operate or too much wind to operate. For this reason I also will used the

variable wind squared. This variable will allow us to see if there is a wind speed that

optimizes the amount of output. The mean wind speed on the PEI site is 8.2437 m/s with

a standard deviation of 1.784227 m/s. The mean wind speed on the Grand Etang site is

7.33 m/s with a standard deviation of 1.2578 m/s. The PEI site is averaging higher winds

which could be a reason why the PEI sites are experiencing higher outputs. There is

something to be said about the lower standard deviation of the Grand Etang site however.

The wind might be blowing less however it is more consistent than the PEI site.

Temperature is the next variable to be examined. Temperature data was collected

on each site. Each wind turbine is equipped with an anemometer which sits on the back

of the gear box. This means that all wind data is collected at 50 meters. The mean

temperature of air at 50 meters is much colder than the mean temperature on ground

level. Canadians will want to have the majority of their energy produced in the winter

time when the most of their electricity is consumed.10

This will be confirmed by looking

at the colder months to see if the wind blows the strongest when the temperature is low.

Temperature is one of 3 variables that determine the mass of air. Density of air is going

to affect the output of each of our turbines. Imagine a scenario in which a person had to

choose to be tackled by a member of the girl scouts or a Black Rhino that you

inadvertently offended. Of course the person would choose the Girl Scout. This is

because the Girl Scout doesnt have as much mass as the rhino so when she collides with

the person the impact will be significantly less. The same case works for wind energy.

The wind collides into the massive blades on the turbine and the force of the wind on the

sail shaped blades makes the turbine spin. As air temperature warms up the mass of the

air decreases which means the density decreases. On the other hand as air temperature

drops and becomes cold its density increases along with its mass. A less dense air will

have less impact on the propellers of the turbine when compared against a very dense

10 CANSIM II data Feb 10th 2005< http://dc2.chass.utoronto.ca/cgi-b in/cansim2/getSeriesData.pl?s=V340861&f=plot&style=lines&b=&e=>


8/22

air.11

Canada has the benefit of needing the majority of its energy during the winter

months. It appears the cold does have some economic benefits. The mean temperature

of North Cape Wind Farms is 4.76155364C and it has a standard deviation of 9.2935C.

The Grand Etang site has a mean temperature of 1.91C and a standard deviation of

9.1293C. The 2 sites are quite close in average temperature with the Grand Etang site

showing slightly colder conditions.

Barometric pressure is the second variable considered when determining the

density of the air. Barometric pressure is measured in pounds per square inch (PSI). A

barometer collected the air pressure on each site. Barometric pressure is the force that the

air exerts on a surface. Deep underwater there is high pressure which will crush a human.

The air exerts this same kind of pressure but to a lesser degree. The higher the air

pressure is the greater the density of the air will be.12 The mean barometric pressure of

the PEI site is 940.67psi with a standard deviation of 224.22psi. The mean barometric

pressure of the Grand Etang site is 1004.86psi and a standard deviation of 12.30psi. The

low PEI pressure discussed further in section 5 where irregularities in the data are

discussed.

Direction of the wind is the 4th

input. This variable was chosen because it can

help determine where the wind is originating from. The wind data was collected by an

anemometer on each site. The wind direction was measured in degrees. Wind direction

could be important because these sites might be inflicted by the strongest winds from a

certain direction. For example the Grand Etang site is right on the water. They would

expect their highest winds to come right off of the ocean. This could be useful for future

site decisions. The mean direction in terms of degrees for the Grand Etang site is 203.70

which is a SSW wind and the standard deviation is 14.04. The PEI site had a mean of

199.71 which is also a SSW with a standard deviation of 9.60. There doesnt seem to be

any difference in the direction of wind that blows onto each site. At each site a SSW

wind comes off of the water.

Section 4: The Econometric model

11

12


9/22

The model set up for this paper will include all of the inputs from above and they

will describe the Kw/h. There are 3 main models used in this project. There are two

different sites where data has been collected from.

The first site is the North Cape Wind Farms site in PEI. This model only includes

data that was retrieved from this site. It looks like this:

Yt = 0 + 1Wind + 2Wind2 + 3Temp + 4Bpressure + 5Turbine2 + 6Turbine3 +

7Year + 8Wsw + 9Sw + 10Ssw

The econometric model for Grand Etang has its own econometric model as well.

It looks like this:

Yt = 0 + 1Wind + 2Wind2 + 3Temp + 4Bpressure + 5Year + 8Sw + 9Ssw

The last of the 3 main models used was composed from a combination of the

Grand Etang and PEI data. It looks like this:

Yt = 0 + 1Wind + 2Wind2 + 3Temp + 4Bpressure + 5Turbine2 + 6Turbine3 +

7Turbine4 + 8Year + 9Wsw + 10Sw + 11Ssw

The first thing to be noticed about the econometric models is that there are a lot

more independent variables in it than there were announced in Section 3. The new

variables all spawn from the independent variables from section 3. Yt is the variable that

represents the output from the 3 different turbines. Output is in monthly intervals starting

in November 2003 and goes to December 2004 for the PEI site. Output for the Grand

Etang site is also monthly and ranges from January 2003 to August 2004. Each month is

a monthly average of the output produced by the Kw/h.

The wind variable represents the monthly averages of wind speed on the site. If

the coefficient to wind is positive then as wind speed increases then output will increase


10/22

as well. It can be expected that wind will have a positive coefficient and that the

coefficient will be quite large. There are only going to be 2 different sets of this data,

monthly averages on PEI and monthly averages on Grand Etang. Each turbine was built

for a range of wind that will maximize its output; a constant wind speed is good because

the turbine will have to make fewer adjustments for change in wind speed. For this

reason the variance of the wind was added. Unfortunately wind data for the Grand Etang

site was retrieved as monthly wind speed averages. Therefore only the PEI model will

have wind variance included in it. This variable will be able to explain whether or not

large fluctuations in wind speed are detrimental to output production.

This is where the variable Wind2 comes from. This variable is the square of all

the wind data entries. If you took the derivative of the econometric model in respects to

wind2 and plotted each point on a graph you would be given a curve. The curve would

increase to a maximum point and then it would decrease. This maximum point represents

the wind speed that the turbine produces the most output at. We can test the statistical

significance of this variable to see if there is in fact a wind speed that makes the most

output and we can check this against what the manufacturer suggests the best wind

speeds are for the same turbine.

The variable temp is representative of temperature. One would expect

temperature to have a negative coefficient with output. As temperature increases by one

degree the output should decrease. This is due to the air becoming less dense. The

temperature data is over a monthly period as well. There are two sets of temperature data,

one for PEI and one for Grand Etang.

Barometric pressure is represented by Bpressure. 4 will determine how much this

variable will affect output. If4 is negative then as the Barometric pressure increases by

one then output will go down by the value of the coefficient 4. It is expected Barometric

pressure to have a positive coefficient. Since the density of the air increases with a rise in

barometric pressure it would make sense for this variable to affect output in a positive

way.

The PEI and the combined econometric models have variables called turbine. PEI

has output for three different turbines and Grand Etang has output for one turbine. The

turbine variables are going to measure to see if there is statistical significance in being


11/22

Turbine 1, 2, 3, or 4. The turbine variables are set up as dummy variables. If output from

turbine 1 is being used in the regression then the turbine 1 variable will be a 1 and all the

other turbine variables will be 0. This means that none of the other turbine variables are

being used because the data was produced from the first turbine. In the combination

model it has been set up so if Turbines 2, 3, and 4 all equal zero then it means the data is

for the turbine in Grand Etang. This turbine is the base turbine. Since the mean of the

Grand Etang turbine is the lowest it is expected that all the coefficients on turbines 1, 2,

and 3 would be positive. This suggests that if the turbine is from PEI it will be producing

more electricity per Kw/h than the Grand Etang turbine.

Another variable that was introduced into the econometric model was the variable

year. This variable is also set up as a dummy variable, similar to turbine variables. The

variable year can either be 2003 or 2004. Those are the only 2 years that the data came

from. If the data comes from 2003 then the variable year will be turned off. If the data is

from 2004 then the variable year will be turned on. This variable will report if it makes a

difference what year the output was recorded in. If the coefficient is positive then it

means that being in 2004 will produce more output then what was produced in 2003.

The last 3 variables in the econometric model are reserved for the direction

variable. Direction was measured in 360, but for the project they were converted into 4

different compass directions, WSW, SW, SSW, and S. With degrees there is never an

end point, so the direction was converted into compass direction so that there would be a

minimum point. It turned out that the monthly wind averages only blew in 4 different

directions as shown above. These directions are all set up as dummy variables as well

with S being the base direction. The coefficients will reveal which wind directions

produces higher output levels. This could be from a wind that is denser, or it could also

suggest that winds come at higher speeds from other directions.

Section 5: The Data

All of this data is from microeconomic sources. The data comes from three

different firms. Before a firm even buys capital for each wind site they must invest at

least 8 months of data collection. Firms must be sure that the wind speeds are constant


12/22

and that the wind speeds are properly matched with the turbines that are to be installed on

them. Scotian Windfields is one of the newest firms in operation in the Atlantic

Provinces. They do not have any sites that are producing output to date, but they have 7

different potential sites across Nova Scotia from which data is being collected. Scotian

Windfields supplied me with the wind speed, direction, temperature, and barometric

pressure for the Grand Etang site. Nova Scotia Power has a site in operation in Grand

Etang however they no longer have easy access to the inputs for years that they have

outputs. Since Scotian Windfields is putting a site up a few hundred yards next to the

Nova Scotia Power site the Scotian Windfields inputs were paired with the Nova Scotia

Power outputs.13

North Cape Wind in PEI is the hub of all wind research for Canada.

They were able to supply data for 3 different turbines and inputs to match.

The Grand Etang site uses a Turbowinds T600 turbine. The rotor diameter is

46m. North Cape Wind Farms uses 3 Vestas V47 turbines. The rotor diameter is 47m.

The extra meter on the Vestas means it has a little more resistance against the wind so it

will be able to catch more of the available wind.14

All of the input data is collected electronically by an anemometer. The

anemometer will record data each day on every ten minute interval. It takes the ten

minute average of the wind speed, direction, temperature, and barometric pressure. In

this project 10 minute intervals would not prove very useful since all the output was

recorded on a monthly basis. All of the inputs had to be averaged by month so they could

correspond to the output data points. The data collecting equipment requires electricity to

operate. If there is a power failure some of the data can be corrupted. If there is a power

outage engineers will quickly comb through the data eliminating pieces that do not

belong. They will then take a second look through and find individual data points that

may have been recorded in error. The data recorded by the anemometer on PEI had been

combed through once by their lead engineer. However the data was not checked a second

time but was assured to be 98% error free.

There was only one monthly average that seemed to be out of place with the rest

of the data. The 2004 April barometric average was calculated to be 169.67psi. The

13www.scotianwindfields.org 14 Vestas Homepage


13/22

mean of the barometric pressure with this value is 940.67psi with a standard deviation of

224.22psi., compared to the Grand Etang site with a standard deviation of 12.30psi.

When this variable is excluded from the monthly averages the mean becomes 999.98psi

and the standard deviation is 33.44psi. This seems to be the more likely case than leaving

the April average of 169.67psi in the data set.

The Grand Etang site had no evident errors in it.

Section 6: The estimation and inference procedures

Similar tests were conducted on all three econometric models. Each model will

have OLS run on it to determine the coefficients and the statistical significance of each

input.

Each model will be tested for heteroskedasticity using the Breusch and Pagan test.

This data would not be expected to have heteroskedasticity within any of the models.

The 3 PEI turbines have a very large mean of output compared to the Grand Etang

site. It is very likely that PEI is the better wind site to produce output. A joint

significance test will be run to see if it is significantly different to be one of the PEI

turbines or the Grand Etang turbine. This test should find that it is significantly different

to be a PEI turbine.

The 3 different wind directions seem to have little importance since the turbines

can rotate with the wind. A joint significance test will be run to see if it is significantly

different to be one wind direction over another. The test should say that it makes no

difference what wind direction is present.

A test will have to be run to see if wind is linear or non-linear in respect to output.

If wind is non-linear then it means that there will be a point at which if the wind blows

harder and softer then output will decrease. If the wind is linear then it means that as the

wind increases so does the amount of output. To find the maximum point, the derivative

of output will be taken in respect to wind squared. Solving for X will give you the point

where wind optimizes output.


14/22

The last test to be run will determine if there is autocorrelation present in the

model. Using the Durbin-Watson test it can be determined whether or not there is

autocorrelation in the error term.

Section 7: The empirical results and conclusions

PEI without wind2. Grand Etang without wind2.

Number of obs = 39 Number of obs = 20

F( 9, 29) = 22.46 F( 6, 13) = 5.65

Prob > F = 0.0000 Prob > F = 0.0044

R-squared = 0.8745 R-squared = 0.7230

Output Coef. Std.Err. P>| t | Output Coef. Std.Err. P>| t |

wind 29849.3 7085.798 0.000 wind 33735.96 13693.46 0.028

temp -1086.925 708.6313 0.136 temp -442.7121 2101.481 0.836

bp -1.397659 145.3976 0.992 bp 919.2555 904.9181 0.328

Turbine 2 29049.08 9928.803 0.007 sw 428.9799 32320.81 0.990Turbine 3 -9068.308 9928.803 0.369 ssw -14896.89 24065.02 0.547

wsw 7973.907 27869.02 0.777 year 03 32994.48 18703.53 0.101

sw -5726.19 22193.36 0.798 cons -1055517 865119.9 0.244

ssw -7525.116 17389.37 0.668 R-squared = 0.7361

year 03 15001.14 29211.51 0.611 wind -21428.63 72669.45 0.773

cons -63527.83 182040.8 0.730 wind2 3537.337 4573.642 0.454

R-squared = 0.8997 When wind2 is introduced wind

wind2 -5273.617 1987.93 0.013 becomes insignificant

variance -19094.41 17049.08 0.272

test turbine2 turbine3 turbine4

Combined data without wind2

Number of obs = 59 ( 1) turbine2 = 0F( 9, 29) = 27.78 ( 2) turbine3 = 0

Prob > F = 0.0000 ( 3) turbine4 = 0

R-squared = 0.8526

Output Coef. Std.Err. P>| t | F( 3, 47) = 7.66

wind 29312.1 4861.785 0.000 Prob > F = 0.0003

temp -593.4733 675.1386 0.384

bp 78.61253 149.5244 0.601 . test wsw sw ssw

Turbine 2 33111.98 14394.04 0.026

Turbine 3 62161.06 14394.04 0.000 ( 1) wsw = 0

Turbine 4 24043.67 14394.04 0.101 ( 2) sw = 0

wsw 19183.2 23074 0.410 ( 3) ssw = 0

sw -4007.86 15031.63 0.791ssw -23071.19 11905.58 0.059 F( 3, 47) = 2.22

year 03 -15759.84 10610.24 0.144 Prob > F = 0.0981

cons -146369.7 156521.9 0.354

R-squared = 0.8581

wind2 -2552.304 1905.473 0.187


15/22


16/22

significant. Turbine 3 had a slightly lower mean than turbine one and the coefficient

reports this. Turbine 3 had a coefficient of -9068. Turbine 2 had a p-value of 0.007

which suggests that it matter is you are turbine 1 or turbine 2. Turbine 3 however had a

p-value of 0.369 which doesnt make it a significant variable.

The variable year had a coefficient of 15001. This suggests that producing output

in 2004 will yield a higher Kw/h. This is going to be based on the inputs from year to

year. Since the data set only runs 2 years worth of data this variable really doesnt

suggest much implication at all. With a p-value of 0.611 it is not statistically significant.

The direction of the wind turned out to be an interesting result. The base direction

of wind was south. SSW had a coefficient of -7525, SW had a coefficient of -5726 and

WSW had a coefficient of 7973. As wind went from SSW, to SW, to WSW the

coefficients grew. This suggests that the best direction for optimal output is WSW,

followed by S and then SW and lastly SSW. The wind variable suggests there is The p-

values all range in between 0.668 and 0.798, which makes all of these dummy values

insignificant.

After adding the variable wind squared OLS is rerun. All of the results are

essentially the same. Wind squared has a coefficient of -5273.61 which is to be expected

since we are looking for a maximum point. With a p-value of 0.04 this is significant at

the 5% significance level. If we take the derivative of the PEI econometric model in

respects to wind2 we can solve for X to see what the maximum value of wind is until we

see decreasing returns to scale. When you take the second derivative and solve X=

11.18m/s or 21.73 knots. Under the best case scenario the firm would hope that the wind

would always blow at this speed to ensure the maximum amount of output was being

produced. It is interesting to note that Vestas has a different number than 11.18m/s.

They claim that the optimum wind speed is between 15m/s and 16m/s.15

When Vestas

tests their machines it is likely that they test the turbines under perfect conditions. It

would be very unlikely for PEI to get these perfect conditions; that is why the optimum

wind speed is 11.18m/s on PEI.

15The Good Geeks (2004) Hull Wind.org C.A.R.E, www.hullwind.orgURL: < http://www.hullwind.org/School%20Kit/Wind%20Turbines/V-4 7%20Brochure.pdf>


17/22

First, the model excluding wind squared was tested for heteroskedasticity. Using

the Breusch and Pagan test to detect heteroskedasticity we find that there is none present

and homoskedasticity. Next, we test the model with wind squared to see if it is

heteroskedastic. With a p-value of 0.0216 it is less than 5% so the model has

heteroskedasticity present. To correct for this the robust regression is run and the model

is re-estimated. None of the significance changes with the robust test.

Next OLS was run on the Grand Etang site. This model was also run with and

without the wind squared variable. There are a total of 20 observations in this data set.

Again wind had a very high and positive coefficient of 33735. As wind increases

by 1m/s output is going to increase by 33735 Kw/h. Also with a p-value of 0.028 this is

significant to the 5% significance level.

Temperature again had an expected coefficient which was negative at -442. As

temperature rises by 1C the output will decrease by 442 Kw/h. The p-value for

temperature is 0.8336 which says that temperature wasnt a significant input at the Grand

Etang site.

Barometric pressure had a coefficient of 919psi which is positive as the density

theory would have predicted to be. As the barometric pressure increases by 1 output also

increases by 919 Kw/h. However with a p-value of 0.328 this is not a significant input.

The dummy value year had surprising results for the Grand Etang site. With a

large coefficient of 32994 it would seem that the 2004 year had much better production

than the 2003 year. This would suggest that something in the un-measured inputs has

changed from one year to another. Perhaps since the 2004 year isnt a complete year it

wouldnt be a safe assumption to make that 2004 was the better year for output. With a

p-value of .101 this is significant at the 10% significance level. Again since this is only 2

years of data the year variable really doesnt hold much economic implications.

There is one less wind variable in the Grand Etang site. S is still the base

direction and SSW and SW are the two dummy variables. SSW has a coefficient of

-14896.9 and SW has a coefficient of 429. SSW has the same results that the PEI site

saw, a very large negative coefficient. SW was about at par with S on the Grand Etang


18/22

site, which was different what we saw on the PEI site. With p-values of 0.547 for SSW

and 0.990 for SW neither of these inputs is significant.

When wind squared is put into this regression and OLS is run the results are

surprising. The one variable which was significant, wind, becomes insignificant with a p-

value of 0.773. Wind squared is not significant as well.

After checking for heteroskedasticity using the Breusch and Pagan test on both

models the results suggest that heteroskedasticity isnt present in either of these models.

Therefore there is no need to run the robust estimation.

In the last econometric model both data sets were combined. There are a total of

62 observations in the data set. This model will be run with OLS both with and without

the wind squared variable.

Wind, again, had a positive coefficient of 29312. The model also had a p-value of

0.000. This shows that wind is significant. After looking at the three different models

we can begin to learn why one year worth of data must be collected to determine if a site

is able to support turbines or not. It is such an important input in determining what your

output is going to be.

Temperature had very similar results as before. The coefficient had a negative

value of -593. Again it had an insignificant p-value of 0.384. The coefficients of

temperature have all been predicted correctly however it doesnt seem to be an important

determinant of output.

The barometric pressure was again positive with a coefficient of 78.61. Again it

was not significant with a p-value of 0.601. Like temperature, barometric pressure is

necessary to determine the density of the air, however in the case of output at each site it

doesnt seem to be important to output levels. Also the only time that barometric

pressure had a negative coefficient was in the PEI model, the same model where the

suspected faulty entry was found. It could be possible that more of those entries are

faulty and could be the reason for the unexpected negative coefficient.

When setting up the turbine dummy variables the Grand Etang site was set as the

base. This was done so it could be shown if the PEI turbines had the expected positive

coefficients. The prediction was correct. Turbine 2, the original base in the PEI model,


19/22

had a coefficient of 34971. Turbine 3, the 2nd

turbine in the PEI model, had a very large

coefficient of 64020. The last Turbine on the PEI site had a coefficient of 25903.

Turbine 2 had a p-value of 0.019 and turbine 3 had a p-value of 0.000 which both prove

to be significant. Turbine 4 however, had a p-value of 0.101, which is only almost

significant at the 10% significance level. These results show that is makes a difference

which site your turbines are on. The PEI turbines seem to have quite a bit better output

returns, especially turbine 3 which exhibits output that is 64020 Kw/h higher than the

turbine on Grand Etang.

The year variable has a coefficient of -17059 which says that being in 2003 will

produce higher levels of output. Again this should only be taken lightly since the data

only covers 2 years of data. It is also not significant with a p-value of 0.113.

South was again the base direction for the direction dummy variables. SSW had a

coefficient of -22519. SW had a coefficient of -4433 and WSW still had a positive

coefficient of 23754. The only direction which held significance was the SSW variable

at the 10% significance level with a p-value of 0.069. A joint significance test was run

on WSW, SW, and SSW. With a p-value of 0.0981 we see that the directions are jointly

significant. This means that regardless of the direction of the wind, it will cause no

difference in output produced.

Adding wind squared to the model does not affect any of the other variables to

any great degree. Wind squared has the expected negative coefficient, which would

suggest that there is a maximum point that wind can reach which will optimize output.

With a p-value of 0.187 which doesnt warrant this variable to be significant. The

derivative of output was still taken in respect to wind and it was found that the optimum

wind speed was 13.94m/s. Wind squared might not be of importance in this model is

because there are simply not enough data points. With more data points it is likely to be

some outliers in wind speeds, and then the optimum wind speed would be revealed.

Using the joint significance test we test the 3 PEI turbines against the Grand

Etang turbine. The p-value was 0.0003. This means that regardless of the PEI turbine

you choose it will be more productive on the PEI site than the turbine on the Grand Etang

site.


20/22

Both of the combined models were tested for heteroskedasticity using the Breusch

and Pagan test. The p-values were very high which exhibits no heteroskedasticity. Both

of these models are homoskedastic so there is no need to correct for heteroskedasticity.

This data has been treated as cross sectional data despite there being 2 years of

data. It would seem unlikely that there would be autocorrelation in the error term. With

the chosen inputs and data points there offers little reason for autocorrelation. Using the

Durbin Watson test a p-value of 2.143331 was retrieved. If the test result was close to 4

there would be negative autocorrelation. A test result close to 0 would suggest positive

autocorrelation. With the test result of 2.143331 it is determined that there is no

autocorrelation in the model.

Section 8: Possible extension and imitations of the study

The largest problem with this research project was the amount of data that was

collected. The largest amount of observations in a model was 62. With that amount of

data it is difficult to determine if variables like temperature and barometric pressure are

really insignificant. Originally wind data was collected as far back as 1994 from the PEI

site however there was no output to be matched up with it. This would have provided 11

years of output, and would have shown some very interesting results.

Actual labor times would also be a welcome extension to this project. Although

they may be small and miniscule each turbine does have to have a certain amount of

yearly maintenance and repairs.

Section 9: Acknowledgements

Scotian Windfields, Nova Scotia Power and North Cape Wind Farms have all

been very understanding and have generously supplied this paper with data and

knowledge. Despite having their own busy schedules and deadlines to meet they found it

in their time to make this project take shape.


21/22

Nelson Patterson was also a vital aid in shaving off precious hours on this project.

With his strong understanding of data manipulation the large wind data bases were

quickly turned into monthly means.


22/22

Section 10: Bibliography

Canadian Electricity Association Canadian Electricity Industry News and InformationCanadian Electricity Association Oct 9

th 2004URL: < http://www.canelect.ca/english/electricity_in_canada.html>

Hines, Joe (2005) MAH Wind Energy (unpublished) November 30th 2004URL:

Natural Resources Canada. WPPI Production Inventive. Ottawa: Wind PowerProduction Inventive Program, 1999

Scotian WindFields (2004) Scotian WindFields (unpublished) November 29th

2004URL:

The Good Geeks (2004) Hull Wind.org C.A.R.E, www.hullwind.orgURL: < http://www.hullwind.org/School%20Kit/Wind%20Turbines/V-47%20Brochure.pdf>

University of Toronto CANSIM II data February 10th 2005URL:< http://dc2.chass.utoronto.ca/cgi-bin/cansim2/getSeriesData.pl?s=V340861&f=plot&style=lines&b=&e=>

Vestas (2005) Vestas Homepage welcome (unpublished) November 29th 2004< http://www.vestas.com >

Documents

Wind Energy - Research Papers