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the consumptions measured the day before and the week before at the same time
(in Watt, excluding the consumption pro
le of the shiftable loads)
the consumptions measured the hour before (excluding the consumption pro
le
of the shiftable loads). Notice that if the prediction horizon is greater than 2 h,
there are no available measures and this input will be the forecasted
consumption.
the consumption measured the day before one hour before the considered time
(excluding the consumption pro
le of the shiftable loads)
To measure the performance of the proposed algorithm, the normalized Root
Mean Square of the Error e(
) (RMSE), its Standard Deviation (SD) and the per-
centage RMSE have been calculated and summarized in Table
5
. The set of
experimental data is composed of 4,000 pairs of input and output samples. Data
have been also normalized, between 0 and 1, in order to have the same
range. Figures
12
and
13
show a sample of electrical consumptions and PV pro-
duction forecasts respectively, considering different time horizons.
The whiteness test on the prediction errors e(
·
) (residuals) has been also used for
network validation Ljung (
1999
). The whiteness of residuals is usually evaluated by
computing the sample covariances
·
N
X
N
1
R
e
ð
s
Þ
¼
e
ð
n
Þ
e
ð
n
þ
s
Þ
ð
24
Þ
n¼1
with
˄
=1,
…
,P.
If e(
·
) is a white-noise sequence, then the quantity
2
X
P
s¼1
ð
R
e
ð
s
ÞÞ
N
ð
R
e
ð
2
f
N
;
P
¼
ð
25
Þ
0
ÞÞ
2
(P) (Ljung
1999
). The inde-
will have, asymptotically, a chi-square distribution
ˇ
2
(P), the
pendence between residuals can be veri
ed by testing whether
ʶ
N,P
<
ˇ
ʱ
ʱ
2
(P)-distribution, for a signi
level of the
ˇ
cant choice of
ʱ
.
6.3 Load Manager Algorithm
The core of the proposed energy management solution is the load manager that
analyzes the information of the predictor, the decision of the user and monitor
periodically consumption and production to make the intelligent scheduling of the
appliances and to give correct information to the users.
In the scheduling of the loads, two aspects should be considered: the
first is to
reduce the energy payment of the users; the other is to let the user choose the end
time of some critical appliance
'
is cycle. It is clear that these two objectives may be
con
fl
icting in some scenarios. In the proposed approach, we consider both question.
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