Page 230 - Wind Energy Handbook

204 WIND-TURBINE PERFORMANCE

4.11 Errors and Uncertainty

The testing guidelines and subsequent Standards were drawn up with a key
objective of reducing errors and uncertainty. Despite this, inaccuracies will remain.
For some years this has been an area of concern, and the recent IEC standard now
makes clear how these should be assessed.
A comprehensive study funded by the CEC (Christensen and Dragt, 1986)
identified the major sources of inaccuracy. As well as measurement and data
analysis error, uncertainties are also introduced by other factors such as operating
conditions (rain, ice, turbulence etc), blade condition/roughness, generator and
gearbox temperature, yaw error, unmeasured wind velocity components and wind
shear. These cannot be directly assessed, although some will be reflected in an
increase of the scatter in the results which is taken into account in the proposed IEC
analysis.
Work at Riso National Laboratory (Pedersen and Peterson, 1988) used a fre-
quency domain model to quantify the uncertainty associated with factors such as
averaging time, anemometer position and wind turbulence. Accuracy was ex-
pressed in terms of the precision index which is defined by:

ó i
S i ¼ p ffiffiffiffiffiffi (4:14)
N i
where N i is the number of samples and ó i is the standard deviation of power
measurements for the ith bin. The uncertainty in annual energy production S(E)
resulting from a measured power curve was calculated by using the precision index
for each bin:
X
S(E) ¼ 8760 S(P) i f(U i ) (4:15)
i
Where S(P) i is the power error band (computed from S i ) for a given confidence
level and f(U i ) is the annual probability of the wind being in the ith bin. It should
be noted that this treatment only deals with random errors (referred to as category
A uncertainties by the IEC) and that the effect of bias errors associated with the
instruments and other factors (category B uncertainties) should be included sepa-
rately. The RISO work concluded that the testing procedures were not accurate
enough to identify with confidence differences in performance of less than 5
percent.
The current IEC standard presents a detailed methodology for analysing how
errors propagate through the power curve to the energy yield calculations. Because
of its importance, the approach is outlined here.

4.11.1 Evaluation of uncertainty

The measurands are the power curve, or more precisely the individual bin averages
which constitute the curve, and the estimated annual energy production. Uncertain-