Page 194 - Fluid Power Engineering

166 Chapter Eight

where u i , u j are uncertainty of the components, ρ i, j is the correlation
coefficient between components i and j, and c i , c j are the sensitivity
coefficients of components i and j to AEP.
When components i, jare uncorrelated, that is, ρ i, j = 0 when i =
j, then Eq. 8-21 becomes:

N
2 2
2

U AEP = c u i (8-22)
i
i=1
When i, j are perfectly correlated, that is, ρ i, j = 1, then:
N

U AEP = c i u i (8-23)
i=1
Table 8-8 presents a few sources of uncertainty, sensitivity factors, and
9
net uncertainty. Note the sensitivity of AEP to wind speed is:

∂U AEP
c 1 = / v ref /U AEP (8-24)
∂v
v=v re f
Theoretically, c 1 should be 3; in reality, the power curve determines
the sensitivity, which is in the range of 1.25 and 2. For most of the other
uncertainty factors, the uncertainty is expressed directly in terms of its

Amount of Net Uncertainty
Sensitivity Uncertainty of AEP Because
Component of Uncertainty Factor (%) of Component (%)
Wind speed measurement 1.5 5 7.5
Wind speed spatial 1.5 3 4.5
extrapolation
Wind speed long-term 1.5 3 4.5
correction
Wind shear, height 1.5 2 3
extrapolation
Air density 1 0.3 0.3
Power curve 1 0.6 0.6
Wake losses in wind farm 1 1.7 1.7
Unaccounted for Loss 1 1 1
Total uncertainty of AEP assuming components are 10.5%
uncorrelated is square root of sum of squares

TABLE 8-8 Parameters Used in Uncertainty Computation