Page 232 - Wind Energy Handbook

206 WIND-TURBINE PERFORMANCE

The same sensitivity factor applies to all other influences on wind-speed measure-
ment such as flow distortion and anemometer mounting effects.
Measurement uncertainties directly affecting power such as those associated with
current transformers, power traducers etc, all take a sensitivity factor of unity.
Annex D (ISO, 1995) gives a comprehensive specification of all the sensitivity factors
to be used.

4.11.3 Estimating uncertainties

Category A uncertainties are based on the standard deviation of the scatter in each
bin, calculated in the conventional way. The main uncertainties in this category are
for power variation and the relevant standard deviation is ó P,i . Statistical theory
(the central limit theorem) requires that the standard uncertainty also reflects the
number of points in the bin. The appropriate expression is:

ó P,i
S i ¼ S P,i ¼ p ffiffiffiffiffiffi (4:17)
N i
This is the same as the sensitivity factor defined in Equation (4.14). Other statistical
uncertainties such as climatic variation could in theory be calculated by experi-
ments designed to isolate these effects. In practice such an approach is unlikely.
Category B uncertainties must be estimated from knowledge of the instrument. If
for example a sensor has an accuracy of U, it is reasonable to assume that the real
value is equally likely to take any value within this interval. Such a rectangular
p
probability distribution implies that the standard uncertainty ó ¼ U= 3. If the
probability distribution is better represented by a triangular distribution, then
p
ó ¼ U= 6.

4.11.4 Combining uncertainties

Uncertainty components are the individual contributions to the overall uncertainty
associated with particular measurements. The general expression for the combined
uncertainty in the ith bin, u c,i , is given by:

X X
M
M
u 2 c,i ¼ c k,i u k,i c i,j u l,j r k,l,i, j (4:18)
k¼1 l¼1
where: c k,i is the sensitivity factor of component k in bin i, u k,i is the standard
uncertainty of component k in bin i, M is the number of uncertainty components in
each bin, and r k,l,i, j is the correlation between uncertainty component k in bin i and
uncertainty component l in bin j.
Note that in Equation (4.17), components k and l both are both in bin i. The
correlation coefficients are in practice almost impossible to estimate and assump-
tions are usually made. For example, that different components are independent