Wind power forecasting - Wind Power Integration: Connection and System Operational Aspects - page 223

have been summarised in Madsen et al. (2004) and the notation used there has been
adopted below.
The forecast error at a particular look-ahead time k is defined as the difference
between the measured value and the forecast value at that time:

e ð t þ k j t Þ¼ P ð t þ k Þ P P ð t þ k j t Þ

where P P ð t þ k j t Þ is the forecast for time t þ k made at time t and P ( t þ k )isthe
measured value at time t þ k . Note that this definition produces the counter-intuitive
result that, if wind power is over-predicted, then the error is negative, whereas an
under-prediction results in a positive error. In order to produce results which are
independent of the wind farm size, the power specified is usually the normalised
power, that is, the actual power (MW) divided by the installed capacity of the wind
farm (MW).
Forecast errors can be resolved into systematic and random components:

e ¼ m e þ n e
The systematic component m e is a constant and the random component n e has a zero
mean value. The model bias or systematic error is the average error over all of the
test period and is calculated for each look-ahead time.

N X

N

1

BIAS ð k Þ¼m e ð k Þ¼ e ð k Þ¼ e ð t þ k j t Þ

t ¼ 1

Two of the measures most widely used for forecast performance are the mean
absolute error (MAE) and the root mean square error (RMSE). The MAE is given by

N X

N
t ¼ 1 j e ð t þ k j t Þj
The mean square error (MSE) is given by

1

MAE ð k Þ¼

X N
t ¼ 1 ð e ð t þ k j t ÞÞ

2

MSE ð k Þ¼

N
The RMSE is given by

s

X N
t ¼ 1 ð e ð t þ k j t ÞÞ

2

RMSE ð k Þ¼

p

MSE ð k Þ ¼

N

It should be noted that both systematic and random errors contribute to both
the MAE and the RMSE.
An alternative to the RMSE which is also widely used is an estimate of the
standard deviation of the error distribution, that is, the standard deviation of errors
(SDE) given by

s

X N
t ¼ 1 ð e ð t þ k j t Þ e ð k ÞÞ

2

SDE ð k Þ¼

N