Environmental Engineering Reference
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which gives the number of hours per year that the wind speed is within each given range or
bin
. Bin width is usually 0.5 to 1.0 m/s. System output power as a function of wind speed is
also needed, calculated using the
mean air density
at the selected site. The general equation
for calculating
gross annual energy output
(
i.e.
output exclusive of energy consumed for sta-
tion-keeping, down-time losses, array effects, etc.) is
K
k
=1
K
k
=1
P
k
D
t
k
AEO
g
=
D
E
a
,
k
=
(5-8)
where
AEO
g
= gross annual energy output (kWh/y)
k
= index of wind speed bin, from 1 to K
D
E
a
,
k
= gross annual energy output in the
k
th wind speed bin (kWh/y)
P
k
= average power output over the wind speed range D
U
k
(kW)
D
t
k
= cumulative time the wind speed at the elevation of the center of the swept
area is in the range D
U
k
(h/y)
Table 5-1 illustrates the application of Equation (5-8) using design performance data for
the Boeing Mod-2 2.5-MW HAWT [ASME 1988]. Analytical expressions for the system
power and for the wind frequency distribution (
e.g.
the single-parameter
Rayleigh distribu-
tion
and the two-parameter
Weibull distribution
) can sometimes produce closed-form esti-
mates for annual energy production, but the tabular approach shown in Table 5-1 recom-
mended because of its clarity and flexibility. The accuracy obtained in representing actual
power curves and wind distributions by analytical expressions is often poor.
Table 5-1. Typical Calculation of Gross Annual Energy Output
[ASME 1988]
Bin
Wind speed range
Duration
Power output
1
Energy output
k
P
k
(kW)
D
U
k
(m/s)
D
t
k
(h/y)
D
E
a, k
(MWh/y)
1
0.0 - 6.25
2,147
0
0
2
6.25 - 6.75
416
175
73
3
6.75 - 7.25
440
318
140
4
7.25 - 7.75
458
460
211
5
7.75 - 8.25
468
603
282
6
8.25 - 8.75
470
745
350
7
8.75 - 9.25
466
949
442
8
9.25 - 9.75
453
1,153
522
9
9.75 - 10.25
435
1,316
572
10
10.25 - 10.75
410
1,479
606
11
10.75 - 11.25
381
1,642
626
12
11.25 - 11.75
349
1,805
630
13
11.75 - 12.25
314
1,968
618
14
12.25 - 12.75
278
2,120
589
15
12.75 - 13.25
242
2,263
548
16
13.25 - 13.75
208
2,385
496
17
13.75 - 14.25
175
2,500
438
18
14.25 - 22.40
648
2,500
1,620
19
>22.40
2
0
0
Totals:
8,760
8,763
AEO
g
= 8,763 MWh/y
1
at an air density of 1.15 kg/m
3
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