Modeling a Wind Turbine Model

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SimulationBased Design
Study Modeling
a Wind Turbine
Chris Gloss, Andrew Lincoln, Matthew Mustard, John Semmens, & Shereef Shehab
Introduction
2
Scope
To develop a model of a wind turbine that will provide its
expected utility using the Dymola and Model Center software.
• Goals
o Develop a fully functional model of
a 1.5 MW wind turbine based on
industry standards
o Utilize available wind data for
Atlanta’s Airport
o Determine the feasibility of installing
a wind turbine in Atlanta
• Design Variables
o Rotor Radius
o Tower Height
Wind Turbine Modeling
3
Influence Diagram
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4
Blades
• NACA 4412 Airfoil
• Triangular planform.
• Assumed to be made of
fiberglass and hollow.
• Moment of inertia of the
blade about the base
was calculated.
Wind Turbine Modeling
5
Dymola Model: Overview
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Implementation of a PID
Controller
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7
Role of Uncertainty
• The central composite experiment showed which
uncertain variables have the greatest effect.
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8
Wind Turbine Modeling
Cost of Electricity ($/kWh)
>1.36
1.28-1.36
1.20-1.28
1.12-1.20
1.04-1.12
0.96-1.04
0.88-0.96
0.80-0.88
0.72-0.80
0.64-0.72
0.56-0.64
0.48-0.56
0.40-0.48
0.32-0.40
0.24-0.32
0.16-0.24
0.08-0.16
0-0.08
Frequency
Monte Carlo Analysis
Monte Carlo Results Histogram
3000
2500
2000
1500
Frequency
1000
500
0
9
Dymola Model: Cost
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10
Total Turbine System Cost*
AEP (kW-h)
Year Rand#
Years of Operation
Cost of Capital Rand#
Cost of Capital
Year
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
Wind Turbine Modeling 29
30
$1,770,000.00
3,950,000
1.00
24
0.55
0.13
Triangular Distributions
Minimum
Most Likely
Maximum
Years of Operation
10
20
Utility Rate
$0.01
$0.07
Cost of Capital
0.01
0.15
Demand (kW-h)
1,316,667
2,633,333
Utility Rand# Utility Rate
0.55
0.66
0.99
0.29
0.33
0.64
0.55
0.98
0.85
0.40
0.05
0.52
0.10
0.55
0.93
0.95
0.55
0.68
0.08
0.34
0.18
0.07
0.12
0.21
$0.09
$0.10
$0.16
$0.07
$0.07
$0.10
$0.09
$0.16
$0.13
$0.07
$0.03
$0.09
$0.05
$0.09
$0.14
$0.15
$0.09
$0.10
$0.05
$0.07
$0.06
$0.04
$0.05
$0.06
Demand Rand#
0.87
0.39
0.70
0.78
0.51
0.34
0.99
0.52
0.92
0.18
0.37
0.79
0.84
0.32
0.61
0.28
0.91
0.09
0.61
0.45
0.66
0.66
0.87
0.04
Demand
3,058,387
2,481,096
2,869,197
2,963,799
2,640,777
2,403,537
3,171,980
2,654,834
3,104,736
2,111,968
2,453,465
2,973,503
3,027,528
2,368,422
2,773,283
2,295,123
3,091,594
1,888,677
2,774,641
2,566,567
2,829,171
2,830,131
3,056,485
1,678,043
Revenue
$269,164.88
$246,009.48
$473,286.18
$194,610.79
$182,951.26
$234,506.45
$279,190.64
$422,195.86
$390,259.24
$157,331.60
$80,821.08
$255,100.96
$159,312.26
$208,321.29
$391,709.26
$334,891.83
$272,301.31
$193,291.30
$140,909.47
$178,922.10
$163,737.63
$106,234.38
$163,450.74
$101,118.69
NPV Model
30
$0.17
0.2
3,950,000
Discounted Cash Flow
($1,770,000.00)
$237,293.33
$191,199.22
$324,283.78
$117,553.47
$97,425.15
$110,092.47
$115,550.23
$154,046.22
$125,532.86
$44,615.66
$20,205.20
$56,223.48
$30,954.37
$35,684.00
$59,152.20
$44,583.97
$31,958.84
$19,999.57
$12,853.33
$14,388.21
$11,608.02
$6,639.60
$9,005.98
$4,911.82
11
@Risk – Monte Carlo within Excel
AEP = 3,950,000 kW-hr
Left: Cost = $1,880,000
Right: Cost = $1,770,000
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Determination of r
• NPV Maximum = $3,856,616.88
• NPV Minimum = ($1,173,934.14)
At what dollar amount are we indifferent
between the NPV maximum and minimum?
• Chosen value = $200,000
• Using a Matlab script the risk aversion
coefficient is 4.2438x10-7

1
( 4.243810 7 ) NPV
u
1 e
7
4.24 10
Wind Turbine Modeling

13
Full Factorial Exploration
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Deterministic
Optimization
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Optimization with
Uncertainty
Results
Optimum Rotor
Radius
43.65 m
Optimum Hub Height
Maximum Expected
Utility
Wind Turbine Modeling
85 m
-$14,205.40
Statistic
Expected Utility ($)
Minimum
-1,917,290
Maximum
950,206
Mean
-14,205.40
Median
53,432.20
Lower 25%
-134,740
Upper 25%
265,559
Standard
Deviation
521,651
16
Thank You
Does any one have any questions?
Wind Turbine Modeling
17
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