of 24
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density cal output our output difference new reg regression reg. Diff. compare lin reg
1.095 87 97 10 10 87 0.2 87
1.1 87 97 10 10 87 -0.2 87
1.15 91 97 6 6 91 -0.1 1 91
1.2 95 97 2 2 95 0.0 2 951.25 99 97 -2 -2 99 0.0 2 99
1.3 103 97 -6 -6 103 0.1 1 103
1.221 97 97 0 0 97 0.3 97
1.23 98 97 -1 -1 97 0.6 98
1.24 98 97 -1 -1 98 -0.2 1 98
1.25 99 97 -2 -2 99 0.0 2 99
1.26 100 97 -3 -3 100 0.2 100
1.27 101 97 -4 -4 101 0.4 101
1.28 102 97 -5 -5 101 0.6 102
1.29 102 97 -5 -5 102 -0.2 1 102
1.3 103 97 -6 -6 103 0.1 1 103
1.4 111 97 -14 -14 111 0.2 1111.19 94 97 3 3 94 -0.3 1 94
1.18 94 97 3 3 93 0.5 94
1.17 93 97 4 4 93 0.3 93
1.16 92 97 5 5 92 0.1 92
1.15 91 97 6 6 91 -0.1 1 91
1.14 90 97 7 7 90 -0.3 1 90
1.13 90 97 7 7 90 0.5 90
1.12 89 97 8 8 89 0.3 89
1.11 88 97 9 9 88 0.1 88
1.1 87 97 10 10 87 -0.2 87
1.35 107 97 -10 -10 107 0.1 1 107
1.32 105 97 -8 -8 105 0.5 105
1.38 110 97 -13 -13 109 0.7 110
1.225 97 97 0 0 97 0.0 15 97
95
100
105
110
115
original
100
105
110
115
regression
-20
-15-10
-5
0
5
10
15
1.09 1.19 1.29
original density Vs diff to
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85
90
1.05 1.15 1.25 1.35 1.45
85
90
1.05 1.15 1.25
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diff compare simple reg diff
0.201 87 0.200
-0.199 87 -0.200
-0.199 91 -0.200
-0.199 95 -0.200-0.199 99 -0.200
-0.199 103 -0.200
0.121 1 97 0.120
0.401 1 98 0.400
-0.399 98 -0.400
-0.199 99 -0.200
0.001 2 100 0.000
0.201 1 101 0.200
0.401 1 102 0.400
-0.399 102 -0.400
-0.199 103 -0.200
-0.199 111 -0.200-0.399 94 -0.400
0.401 1 94 0.400
0.201 1 93 0.200
0.001 2 92 0.000
-0.199 91 -0.200
-0.399 90 -0.400
0.401 1 90 0.400
0.201 1 89 0.200
0.001 2 88 0.000
-0.199 87 -0.200
-0.199 107 -0.200
0.201 1 105 0.200
0.401 1 110 0.400
-0.199 16 97 -0.200
1.39
ours
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1.35 1.45
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K C Vi P(Vi)
1 3.376 0 #NUM!
1 0.22
2 0.16
MODE 3 0.120.00 4 0.09
5 0.07
Avg (1.13) 6 0.05
2.99 7 0.04
8 0.03
Avg (Gamma) 9 0.02
3.376 10 0.02
11 0.01
12 0.01
13 0.01
14 0.00
15 0.0016 0.00
17 0.00
18 0.00
19 0.00
20 0.00 85.68992
21 0.00
22 0.00 c k 1/k
23 0.00 5 2 0.5
24 0.00
25 0.00 85.86742
26 0.00 k 1+1/k
27 0.00 0.1 11.000028 0.00 0.2 6.0000
29 0.00 0.3 4.3333
30 0.00 85.90779 0.4 3.5000
31 0.00 0.5 3.0000
32 0.00 0.6 2.6667
33 0.00 0.7 2.4286
34 0.00 0.8 2.2500
35 0.00 0.9 2.1111
36 0.00 1 1 2.0000
37 0.00 2 1.1 1.9091
38 0.00 3 1.2 1.8333
39 0.00 4 1.3 1.7692
40 0.00 85.91905458 5 1.4 1.7143
41 0.00 6 1.5 1.6667
42 0.00 7 1.6 1.6250
43 0.00 8 1.7 1.5882
44 0.00 9 1.8 1.5556
45 0.00 10 1.9 1.5263
46 0.00 11 2 1.5000
47 0.00 12 2.1 1.4762
weibull distribution using shape K and scale C parameters
0.00
0.05
0.10
0.15
0.20
0.25
1 3 5 7 9 11 13 15 1
K=4.5 & C=7
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48 0.00 13 2.2 1.4545
49 0.00 14 2.3 1.4348
50 0.00 85.91963717 15 2.4 1.4167
51 0.00 16 2.5 1.4000
52 0.00 17 2.6 1.3846
53 0.00 18 2.7 1.3704
54 0.00 19 2.8 1.357155 0.00 20 2.9 1.3448
56 0.00 21 3 1.3333
57 0.00 22 3.1 1.3226
58 0.00 23 3.2 1.3125
59 0.00 24 3.3 1.3030
60 0.00 25 3.4 1.2941
61 0.00 26 3.5 1.2857
62 0.00 27 3.6 1.2778
63 0.00 28 3.7 1.2703
64 0.00 29 3.8 1.2632
65 0.00 30 3.9 1.2564
66 0.00 31 4 1.250067 0.00 32 4.1 1.2439
68 0.00 33 4.2 1.2381
69 0.00 34 4.3 1.2326
70 0.00 35 4.4 1.2273
71 0.00 36 4.5 1.2222
72 0.00 37 4.6 1.2174
73 0.00 38 4.7 1.2128
74 0.00 39 4.8 1.2083
75 0.00 40 4.9 1.2041
76 0.00 41 5 1.2000
77 0.00
78 0.00
79 0.00
80 0.00
81 0.00
82 0.00
83 0.00
84 0.00
85 0.00
86 0.00
87 0.00
88 0.00
89 0.00
90 0.00
91 0.0092 0.00
93 0.00
94 0.00
95 0.00
96 0.00
97 0.00
98 0.00
99 0.00
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 2.1
Average Wind 5.0 4.8 4.7 4.6 4.6 4.5 4.5 4.5 4.4 4.4 4.4 4.4
Mode 0.0 0.6 1.1 1.6 2.0 2.4 2.7 3.0 3.2 3.4 3.5 3.7
0.0
1.0
2.0
3.0
4.0
5.0
6.0
m/s
Relation b
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100 0.00 85.91966894
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1-1/k (1-1/k)^1/k mode avg
0.5 0.707 3.536 4.431
mean mode
G(1+1/k) (1-1/k) (1/k) #VALUE! 5
3628800 3.487E+09 18144000.000 17433922005.000120 -1024 600.000 -5120.000
9.26 #NUM! 46.303 #NUM!
3.32 #NUM! 16.617 #NUM!
2.00 1 10.000 5.000
1.50 #NUM! 7.523 #NUM!
1.27 #NUM! 6.329 #NUM!
1.13 #NUM! 5.665 #NUM!
1.05 #NUM! Average Wind Mode
1.00 0.00 5.0 0.0
0.96 0.11 4.8 0.6
0.94 0.22 4.7 1.1
0.92 0.32 4.6 1.6
0.91 0.41 4.6 2.0
0.90 0.48 4.5 2.4
0.90 0.54 4.5 2.7
0.89 0.59 4.5 3.0
0.89 0.64 4.4 3.2
0.89 0.67 4.4 3.4
0.89 0.71 4.4 3.5
0.89 0.73 4.4 3.7
7 19 21 23 25
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0.89 0.76 4.4 3.8
0.89 0.78 4.4 3.9
0.89 0.80 4.4 4.0
0.89 0.82 4.4 4.1
0.89 0.83 4.4 4.1
0.89 0.84 4.4 4.2
0.89 0.85 4.5 4.30.89 0.86 4.5 4.3
0.89 0.87 4.5 4.4
0.89 0.88 4.5 4.4
0.90 0.89 4.5 4.4
0.90 0.90 4.5 4.5
0.90 0.90 4.5 4.5
0.90 0.91 4.5 4.5
0.90 0.91 4.5 4.6
0.90 0.92 4.5 4.6
0.90 0.92 4.5 4.6
0.91 0.93 4.5 4.6
0.91 0.93 4.5 4.70.91 0.93 4.5 4.7
0.91 0.94 4.5 4.7
0.91 0.94 4.6 4.7
0.91 0.94 4.6 4.7
0.91 0.95 4.6 4.7
0.91 0.95 4.6 4.7
0.91 0.95 4.6 4.8
0.92 0.95 4.6 4.8
0.92 0.95 4.6 4.8
0.92 0.96 4.6 4.8
2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 5
4.4 4.4 4.4 4.4 4.4 4.4 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.5 4.6 4.6 4.6 4.6 4.6 4.6 4.6 4.6
3.8 3.9 4.0 4.1 4.1 4.2 4.3 4.3 4.4 4.4 4.4 4.5 4.5 4.5 4.6 4.6 4.6 4.6 4.7 4.7 4.7 4.7 4.7 4.7 4.7 4.8 4.8 4.8 4.8
K
tween Wind Speed and mode with k
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Avg V st. dev K C Vi P(Vi)
3 1.72 1.829657 3.376017 0 0
1 0.177293
2 0.239159
3 0.2195384 0.159502
5 0.096496
C (1.13) 6 0.049821
3.39 7 0.022269
8 0.008699
9 0.002989
rho 10 0.000908
1.225 11 0.000245
12 5.89E-05
power density C1 13 1.26E-05
21 14 2.43E-06
15 4.18E-07power density C2 16 6.47E-08
21 17 9.01E-09
18 1.13E-09
19 1.28E-10
20 1.31E-11 97.69935
21 1.21E-12
22 1.02E-13
23 7.73E-15
24 5.32E-16
25 3.33E-17 97.69935
26 1.89E-18
27 9.76E-2028 4.59E-21
29 1.96E-22
30 7.64E-24 97.69935
31 2.71E-25
32 8.78E-27
33 2.59E-28
34 7E-30
35 1.72E-31
36 3.88E-33
37 7.99E-35
38 1.5E-36
39 2.59E-38
40 4.09E-40 97.69935
41 5.9E-42
42 7.81E-44
43 9.47E-46
44 1.05E-47
45 1.07E-49
46 1.01E-51
47 8.63E-54
weibull distribution using Average wind speed & st. dev.
0
0.05
0.1
0.15
0.2
0.25
0.3
1 3 5
using Ave
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48 6.81E-56
49 4.93E-58
50 3.28E-60 97.69935
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Bonus 600/44 Nordex 43/600
Vi power curve power curve difference
0 0 0 0
1 0 0 0
2 0 0 0
3 3.9 2 -1.94 21.2 17 -4.2
5 49.3 45 -4.3
6 83.2 72 -11.2
7 130.7 124 -6.7
8 202 196 -6
9 280.8 277 -3.8
10 361.3 364 2.7
11 433.7 444 10.3
12 498.6 533 34.4
13 548.1 584 35.9
14 577.3 618 40.7
15 596 619 2316 610 618 8
17 606.9 619 12.1
18 593.4 620 26.6
19 571.3 610 38.7
20 545.6 594 48.4
21 524.7 592 67.3
22 510 590 80
23 500.7 580 79.3
24 478.7 575 96.3
25 457.7 570 112.3
0
100
200
300
400
500
600
700
1 3 5 7 9 11 13 15 17 19 21 23 25
Nordex 43/600
0
100
200
300
400
500600
700
1 3 5 7 9 11 13 15 17 19 21 23 25
Bonus 600/44
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bonus 600/44
k=2
avg V input=X output=Y X^2 X^3 X^4 X*Y X^2*Y
3 32 11 1024 32768 1048576 352 11264
3.5 50 19 2500 125000 6250000 950 47500
4 75 29 5625 421875 31640625 2175 163125
4.5 107 42 11449 1225043 131079601 4494 4808585 146 56 21316 3112136 454371856 8176 1193696
5.5 195 71 38025 7414875 1445900625 13845 2699775
6 253 87 64009 16194277 4097152081 22011 5568783
6.5 321 103 103041 33076161 10617447681 33063 10613223
7 401 120 160801 64481201 25856961601 48120 19296120
7.5 494 136 244036 120553784 59553569296 67184 33188896
8 599 151 358801 214921799 1.28738E+11 90449 54178951
8.5 718 165 515524 370146232 2.65765E+11 118470 85061460
9 853 178 727609 620650477 5.29415E+11 151834 129514402
9.5 1003 190 1006009 1009027027 1.01205E+12 190570 191141710
10 1170 201 1368900 1601613000 1.87389E+12 235170 275148900
10.5 1353 210 1830609 2476813977 3.35113E+12 284130 38442789011 1556 218 2421136 3767287616 5.8619E+12 339208 527807648
expirement 238 56644 13481272 3208542736
N summ Xi summ Yi summ X^2 summ X^3 summ X^4 summ X*Y summ X^2*Y
17 9326 1987 8880414 10307097248 1.31251E+13 1610201 1720544201
0
50
100
150
200
250
0 500 1000 1500 2000
scatter gram b/w input & output
0
50
100
150
200
250
0 500
cubic
100
150
200
250
quadra
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0
50
0 500
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cubic reg diff quadratic diff
14.00693 3.006926 21.37978 10.37978
20.72931 1.72931 26.50065 7.50065
29.77073 0.770729 33.49795 4.49795
40.8536 -1.1464 42.25933 0.25932653.63772 -2.36228 52.64097 -3.35903
68.6145 -2.3855 65.22319 -5.77681
84.85147 -2.14853 79.45239 -7.54761
101.9481 -1.05189 95.21812 -7.78188
119.5734 -0.42661 112.4992 -7.50084
136.9869 0.98689 130.8668 -5.13315
153.1281 2.128115 149.38 -1.61997
167.5752 2.575223 167.5094 2.509438
179.987 1.987023 184.4074 6.407388
190.1797 0.179695 198.6086 8.608638
198.9573 -2.04272 208.7549 7.75489
207.9897 -2.01029 213.0199 3.019888220.7068 2.706768 209.3667 -8.6333
80.8025 75.84144
1000 1500 2000
regression
ic regression
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1000 1500 2000
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rho
Nordex
43/600
K C Vi
excel
weibull P(Vi)
power of
each
power
density
power
curve
output
Nordex
0 0.0000 #NUM! 0.0 #NUM! 0 #NUM!
1 0.1238 0.1238 0.6 0.07 0 0.00
2 0.1074 0.1074 4.4 0.47 0 0.00
3 0.0931 0.0931 14.9 1.38 2 0.19
4 0.0807 0.0807 35.2 2.84 17 1.37
5 0.0699 0.0699 68.8 4.81 45 3.15
6 0.0606 0.0606 118.8 7.20 72 4.36
7 0.0526 0.0526 188.7 9.91 124 6.52
8 0.0456 0.0456 281.6 12.83 196 8.93
9 0.0395 0.0395 401.0 15.83 277 10.94
10 0.0342 0.0342 550.0 18.83 364 12.46
11 0.0297 0.0297 732.1 21.73 444 13.18
12 0.0257 0.0257 950.4 24.45 533 13.71
13 0.0223 0.0223 1208.4 26.95 584 13.0214 0.0193 0.0193 1509.2 29.18 618 11.95
15 0.0168 0.0168 1856.3 31.11 619 10.37
16 0.0145 0.0145 2252.8 32.73 618 8.98
17 0.0126 0.0126 2702.2 34.03 619 7.80
18 0.0109 0.0109 3207.6 35.02 620 6.77
19 0.0095 0.0095 3772.5 35.70 610 5.77
20 0.0082 0.0082 4400.0 36.10 594 4.87
21 0.0071 0.0071 5093.6 36.23 592 4.21
22 0.0062 0.0062 5856.4 36.11 590 3.64
23 0.0053 0.0053 6691.9 35.77 580 3.10
24 0.0046 0.0046 7603.2 35.23 575 2.66
25 0.0040 0.0040 8593.8 34.52 570 2.2926 0.0035 0.0035 9666.8 33.66
27 0.0030 0.0030 10825.7 32.68
28 0.0026 0.0026 12073.6 31.59
29 0.0023 0.0023 13414.0 30.43
30 0.0020 0.0020 14850.0 29.20
31 0.0017 0.0017 16385.1 27.93
32 0.0015 0.0015 18022.4 26.63
33 0.0013 0.0013 19765.4 25.32
34 0.0011 0.0011 21617.2 24.00
35 0.0010 0.0010 23581.3 22.70
36 0.0008 0.0008 25660.8 21.41
37 0.0007 0.0007 27859.2 20.15 rotor Dia 43
38 0.0006 0.0006 30179.6 18.92 rotor Area 1451.47
39 0.0005 0.0005 32625.5 17.73
40 0.0005 0.0005 35200.0 16.59
shape K scale C 921 Nordex
1 7 area % 93 93 938 95
input output
rho 930 111
1.1 969
power output W/m^2
KWh/m^2/year
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1406850
27
a)
b)
If we multiply the power of each wind speed with the probability of each wind speed from the W
The area under the curve (all the way to the axis at the bottom) gives us the amount of wind po
KWh/year
Capacity Factor
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rotor dia rotor area
Bonus
600/44 44 1520.53
power
curve
output
Bonus output 2 per unit power coeff.
0 #NUM! #NUM! 0.00 #DIV/0!
0 0.00 0.00 0.00 0.0000
0 0.00 0.00 0.00 0.0000
3.9 0.36 0.22 0.00 0.0002
21.2 1.71 1.01 0.01 0.0004
49.3 3.45 2.04 0.03 0.0005
83.2 5.04 2.99 0.05 0.0005
130.7 6.87 4.07 0.09 0.0005
202 9.20 5.45 0.13 0.0005
280.8 11.09 6.57 0.18 0.0005
361.3 12.37 7.33 0.24 0.0004
433.7 12.87 7.63 0.29 0.0004
498.6 12.83 7.60 0.33 0.0003
548.1 12.22 7.24 0.36 0.0003577.3 11.16 6.61 0.38 0.0003
596 9.99 5.92 0.39 0.0002
610 8.86 5.25 0.40 0.0002
606.9 7.64 4.53 0.40 0.0001
593.4 6.48 3.84 0.39 0.0001
571.3 5.41 3.20 0.38 0.0001
545.6 4.48 2.65 0.36 0.0001
524.7 3.73 2.21 0.35 0.0001
510 3.14 1.86 0.34 0.0001
500.7 2.68 1.59 0.33 0.0000
478.7 2.22 1.31 0.31 0.0000
457.7 1.84 1.09 0.30 0.0000
44
1519.76
Bonus
92 #NUM! 0.01
output
101 103 92 0.57
901
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1368548
26
ibull graph, we have calculated the distribution of wind energy at different wind speeds = the power densi
er per square metre wind flow we may expect at this particular site
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y
