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Wind Power Analysis

MIET2032 Renewable Energy Systems

CONTENTS
Given Data
...
3
Question 2
...
5
Question 4
...
7
Question 6
...
13
Question 8
...
18
Question 10
...
20
Question 12
...
22
Question 14
...
23

GIVEN DATA
Three different blade diameter and two hub height of wind turbine data were provided
...
Wind data
set 05 was used as the select wind data
...


Blade Lengths

Tower Height (m)

Installed Cost ($)

G80
G87
G90
G80
G87
G90

78
78
78
100
100
100

5,000,000
5,085,000
5,130,000
5,300,000
5,385,000
5,430,000

Annual Energy Output
(MWh)
10180
...
1
11452
...
3
11418
...
5

QUESTION 2
The annual energy output over per unit costs was measured by dividing the annual energy output
with the installed cost

𝐸𝑛𝑒𝑟𝑔𝑦 𝑂𝑢𝑡𝑝𝑢𝑡 𝑜𝑣𝑒𝑟 𝐶𝑜𝑠𝑡 =

𝐴𝑛𝑛𝑢𝑎𝑙 𝐸𝑛𝑒𝑟𝑔𝑦 𝑂𝑢𝑡𝑝𝑢𝑡
𝐼𝑛𝑠𝑡𝑎𝑙𝑙𝑒𝑑 𝐶𝑜𝑠𝑡

Example:
𝐸𝑛𝑒𝑟𝑔𝑦 𝑂𝑢𝑡𝑝𝑢𝑡 𝑜𝑣𝑒𝑟 𝐶𝑜𝑠𝑡 𝐺80, 𝐻𝑢𝑏 𝐻𝑒𝑖𝑔𝑕𝑡 78 =

10180
...
00203616 𝑀𝑊𝑕/$
5,000,000

Blade Lemgths

Tower Height (m)

Installed Cost ($)

Annual Energy
Output (MWh)

G80
G87
G90
G80
G87
G90

78
78
78
100
100
100

5,000,000
5,085,000
5,130,000
5,300,000
5,385,000
5,430,000

10180
...
1
11452
...
3
11418
...
5

Energy Output
over Cost
(MWh/$)
0
...
00217996066
0
...
00198760377
0
...
00216767955

From the table above, G90 (hub height 78) produces the most amount of Annual Energy per unit
cost each year
...
To obtain useful wind speed data, the log law
was used to convert wind speed from 10m to wind speeds at 78m hub height
...
01)
= 1
...
01)

𝑉 = 0
...
297 = 0
...
5
...


Midpoint(m/s)
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
29

Bin
0
...
5
2
...
5
4
...
5
6
...
5
8
...
5
10
...
5
12
...
5
14
...
5
16
...
5
18
...
5
20
...
5
22
...
5
24
...
5
26
...
5
28
...
5

Frequency(hours)
4
35
101
220
311
441
590
772
878
889
860
823
676
529
443
334
239
167
123
89
78
63
33
19
17
17
2
5
0
2

Relative Frequency
0%
0%
1%
3%
4%
5%
7%
9%
10%
10%
10%
9%
8%
6%
5%
4%
3%
2%
1%
1%
1%
1%
0%
0%
0%
0%
0%
0%
0%
0%

Histogram for Relative Frequency at Hub Height 78m

12
...
00%
6
...
00%
2
...
05%
0
...
15%
2
...
55%
5
...
74%

Relative Frequency

10
...
81%
10
...
15%
9
...
39%
7
...
04%
5
...
81%
2
...
91%
1
...
02%
0
...
72%
0
...
22%
0
...
19%
0
...
06%
0
...
02%

Relative Frequency at Hub Height 78m

0
...
The shape parameter “k” remains constant
...
678 × 1
...
099

Using the new scale parameter the Weibull distribution was found
...
5
1
...
5
3
...
5
5
...
5
7
...
5
9
...
5
11
...
5
13
...
5
15
...
5
17
...
5
19
...
5
21
...
5
23
...
5
25
...
5
27
...
5
29
...
046%
0
...
153%
2
...
550%
5
...
735%
8
...
023%
10
...
817%
9
...
717%
6
...
057%
3
...
728%
1
...
404%
1
...
890%
0
...
377%
0
...
194%
0
...
023%
0
...
000%
0
...
000%
0
...
311%
2
...
032%
5
...
072%
8
...
221%
9
...
573%
9
...
077%
6
...
552%
4
...
094%
2
...
385%
0
...
493%
0
...
138%
0
...
030%
0
...
005%
0
...
001%
0
...
000%
10
...
000%
6
...
000%
2
...
046%
0
...
153%
2
...
550%
5
...
735%
8
...
023%
10
...
817%
9
...
717%
6
...
057%
3
...
728%
1
...
404%
1
...
890%
0
...
377%
0
...
194%
0
...
023%
0
...
000%
0
...
000%
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 29

Wind Speed at 78m (m/s)
Relative Frequency

Weibull Distribution

The Weibull distribution predicted the relative frequency with very marginal errors
...
Wind speeds
from 12m/s until 17m/s was underestimated and from 20m/s to 29m/s the Weibull distribution
underestimated the probability
...


QUESTION 6
Wind power density:
𝑊𝑖𝑛𝑑 𝑃𝑜𝑤𝑒𝑟 𝐷𝑒𝑠𝑛𝑖𝑡𝑦 =
v

:Wind Speed

𝜌

:Air density (1
...
225 × 23 = 49 𝑊 𝑚2 = 0
...
0049 × 101 = 0
...
𝑜𝑓 𝑕𝑜𝑢𝑟𝑠)
(𝑛𝑜 𝑜𝑓 𝑕𝑜𝑢𝑟𝑠)

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑊𝑖𝑛𝑑 𝑃𝑜𝑤𝑒𝑟 𝐷𝑒𝑠𝑛𝑖𝑡𝑦 =
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑊𝑖𝑛𝑑 𝑃𝑜𝑤𝑒𝑟 𝐷𝑒𝑛𝑠𝑖𝑡𝑦 =

8452770
...
9280951 𝑊 2
𝑚
8760

To calculate wind power density at hub height 50
...

𝑉
𝑉 𝑟𝑒𝑓

=

ln 𝑧 − ln⁡ 0 )
(𝑧
ln 𝑧 𝑟𝑒𝑓 − ln⁡ 0 )
(𝑧

Average wind power density at 50m:

=

ln 50 − ln⁡
(0
...
95038
ln 78 − ln⁡
(0
...
9280951 × 0
...
0486446 𝑊 𝑚3

The average wind power density at 50m based on the U
...
𝑜𝑓 𝑕𝑜𝑢𝑟𝑠)
(𝑛𝑜 𝑜𝑓 𝑕𝑜𝑢𝑟𝑠)

𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑊𝑖𝑛𝑑 𝑃𝑜𝑤𝑒𝑟 𝐷𝑒𝑠𝑛𝑖𝑡𝑦 =

87861
= 10
...
5
1
...
5
3
...
5
5
...
5
7
...
5
9
...
5
11
...
5
13
...
5
15
...
5
17
...
5
19
...
5
21
...
5
23
...
5
25
...
5
27
...
5
29
...
046%
0
...
153%
2
...
550%
5
...
735%
8
...
023%
10
...
817%
9
...
717%
6
...
057%
3
...
728%
1
...
404%
1
...
890%
0
...
377%
0
...
194%
0
...
023%
0
...
000%
0
...
m2)

Energy in
wind(kWh/m2)

Cumulative
Energy(kWh/m2)

0
0
...
9
16
...
2
76
...
3
210
...
6
446
...
5
815
...
4
1345
...
7
2067
...
8
3009
...
1
4201
...
3625
6521
...
2875
8467
...
3125
10765
...
837
13445
...
262

0
0
...
4949
3
...
1912
33
...
057
162
...
3408
396
...
75
670
...
4784
711
...
5501
690
...
6032
502
...
3683
373
...
2
357
...
2227
141
...
9424
162
...
5306
60
...
876525

0
0
...
5163375
4
...
3457875
50
...
16685
290
...
6952
962
...
39481
2160
...
81367
3587
...
21923
5022
...
26306
6124
...
16985
6938
...
27108
7677
...
85262
8034
...
38848
8341
...
6144
8422
...
89358
8452
...
The cut-in wind speed is the minimum
amount of wind speed required for the wind turbine to start generating power
...
The wind turbine can
maintain its maximum power output when wind speeds are between 12m/s and 21m/s
...
Increasing wind speeds from 21m/s will not produce
higher power output from the wind turbine
...
The wind turbine blades has to be limited to avoid
damaging the blades and rotor when the wind speeds are over 21m/s
...
The turbine stops producing power after this wind
speed to avoid damages to the rotor
...
5

Power Captured (%)

0
...
3
0
...
1
0
0
-0
...
45% power capture is the highest a modern wind turbine
can capture power from the wind
...
From 10m/s to 25m/s the wind turbine power capture decreases with a gradient
...
Wind speeds from 3m/s to 5m/s
has very little energy and the wind turbine cannot harness much from the power in the wind
...


35

QUESTION 8
Energy Output
𝐸𝑛𝑒𝑟𝑔𝑦 𝑂𝑢𝑡𝑝𝑢𝑡 =

𝑇𝑢𝑟𝑏𝑖𝑛𝑒 𝑂𝑢𝑡𝑝𝑢𝑡 × 𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦
1000

𝑀𝑊𝑕

Example
𝐸𝑛𝑒𝑟𝑔𝑦 𝑂𝑢𝑡𝑝𝑢𝑡 =

21 × 220
= 4
...
95%
8760

Midpoint
(m/s)

Bin

Frequency
(hrs)

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
29

0
...
5
2
...
5
4
...
5
6
...
5
8
...
5
10
...
5
12
...
5
14
...
5
16
...
5
18
...
5
20
...
5
22
...
5
24
...
5
26
...
5
28
...
5

4
35
101
220
311
441
590
772
878
889
860
823
676
529
443
334
239
167
123
89
78
63
33
19
17
17
2
5
0
2

Cumulative
Frequency
(Hours)

Hours as
Percentage

4
39
140
360
671
1112
1702
2474
3352
4241
5101
5924
6600
7129
7572
7906
8145
8312
8435
8524
8602
8665
8698
8717
8734
8751
8753
8758
8758
8760

99
...
55%
98
...
89%
92
...
31%
80
...
76%
61
...
59%
41
...
37%
24
...
62%
13
...
75%
7
...
11%
3
...
69%
1
...
08%
0
...
49%
0
...
10%
0
...
02%
0
...
00%

Turbine
Output
(kW)
0
0
0
21
85
197
364
595
901
1275
1649
1899
1971
1991
1988
2000
2000
2000
2000
2000
2000
2000
1906
1681
1455
1230
0
0
0
0

Energy
output
(MWh)
0
0
0
4
...
435
86
...
76
459
...
078
1133
...
14
1562
...
396
1053
...
684
668
478
334
246
178
156
126
62
...
939
24
...
91
0
0
0
0

Cumulative
Energy
output
(MWh)
0
0
0
4
...
055
117
...
692
792
...
11
2716
...
725
5697
...
998
8083
...
921
9631
...
921
10443
...
921
10867
...
921
11149
...
819
11244
...
493
11290
...
403
11290
...
403
11290
...
00%

10
...
00%

30
...
00%

50
...
00%

70
...
00%

7000

8000

90
...
00%

Hours as Percentage

Duration
2500
2000
1500
1000
500
0
0

1000

2000

3000

4000

5000

6000

9000

10000

-500

The graphs show that the wind turbine produces its rated power (2MW) around 20% of the time in a
year
...
89458125 × 35 = 136
...
97%
105
...
62
26
...
877
214
...
34
791
...
475
1418
...
877
1332
...
239
880
...
898
31
...
735
20
...
403

The total energy output is 11290
...
412541209
19
...
57721484
178
...
6147387
657
...
897014
1393
...
559031
1557
...
636846
1196
...
6430651
745
...
0016299
372
...
6975409
149
...
38763666
44
...
3018
8
...
222274545
0
0
0
0
0

Sum:

12662
...
66174MWh
...
2MWh)
had a 9
...
The wind power calculator produced smaller energy output per year compared to
Weibull distribution
...
403MWh) given from the data files has less energy output than the Weibull
distribution
...
8%

QUESTION 12

4311
...
403MWh = 11
...
290403

= 797
...

Rotor Diameter = 90m
Distance required between wind turbines = 𝑅𝑜𝑡𝑜𝑟 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 × 𝑆𝑎𝑓𝑒 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 90 × 5 = 450𝑚
Square area required for single wind turbine = 4502 = 202500𝑚2
Area required for total amount of wind turbines = 202500 × 798 = 161595000𝑚2 = 161
...
595
8000

× 100 = 2
...
939 MWh
Energy Generated Over a year = 11290
...
403
× 100 = 21
...
939

Average Power Output
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃𝑜𝑤𝑒𝑟 𝑂𝑢𝑡𝑝𝑢𝑡 =
𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑃𝑜𝑤𝑒𝑟 𝑂𝑢𝑡𝑝𝑢𝑡 =

𝐸𝑛𝑒𝑟𝑔𝑦 𝐺𝑒𝑛𝑒𝑟𝑎𝑡𝑒𝑑 𝑂𝑣𝑒𝑟 𝑎 𝑌𝑒𝑎𝑟
8760

11290
...
28885879𝑀𝑤 = 1288
...
85879
× 100 = 64
...
403 × 1000
= 5645
...
403
𝜋

(90)2
4

= 1
...
739207 𝑘𝑊 𝑚2

QUESTION 14
Specific Rated Capacity
𝑆𝑝𝑒𝑐𝑖𝑓𝑖𝑐 𝑅𝑎𝑡𝑒𝑑 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 =

𝑅𝑎𝑡𝑒𝑑 𝑃𝑜𝑤𝑒𝑟
𝑆𝑤𝑒𝑝𝑡 𝐴𝑟𝑒𝑎

Turbine

Rated Power (kW)

Swept Area (m2)

Specific Rated Capacity

G80

2000

5026
...
397887358

G87

2000

5944
...
33643534

G90

2000

6361
...
314380134

QUESTION 15
By using the wind power calculator, the energy output of the G90 wind turbine for the hub height
78m and 100m were obtained
...
2
2
...
5
2
...
5-11452
...
2 MWh
Cost ($)

Percentage in energy between 78m and 100m =

318
...
2

× 100 = 2
...
85%
By upgrading the G90 wind turbine from 78m hub height to 100m hub height we will be getting less
increase in energy output compared to the cost
...
78
whereas the cost percentage increase is 5
...
Moreover, the G90 wind turbine at hub height 78m
produces the most power per unit cost out of all the six turbines availalbe



---

Title: Wind Power Analysis
Description: Three different blade diameter and two hub height of wind turbine data were provided. The table below shows the six different Gamesa 2MW wind turbine that are provided for analysis.Wind data set 05 was used as the select wind data.

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