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In the following section a description of the energy management problem and a
set of solution will be presented.
6 Energy Management Techniques
The installation of a PV plant can have a great impact on the energy behavior of
users. They can use an energy manager, forecasting tools or simply plan to start
appliances according to weather forecast. The energy management problem can be
expressed as the minimization of a cost function X, given a certain number of
electrical tasks N
TASKS
(e.g. the appliance starts) to arrange in N
TIME
time samples:
X
X
N
TASKS
N
TIME
i¼0
x
k
ð
min x
¼
i
Þ
L
k
ð
i
Þ
C
k
ð
i
Þ
ð
3
Þ
k
¼
1
where
ω
k
(i) express if wether or not a task is running at time i, C
k
(i) is the energy
cost at time i, as computed in 6, L
k
(i) is the energy consumed by the task in the time
interval i. In particular this minimization problem is subject to the following con-
strains considering the total power absorbed at each time and the absence of
interruptions for each task:
X
k
x
k
ð
8
i
!
i
Þ
L
k
ð
i
Þ
P
max
ð
4
Þ
T
start
T
end
8
k
!
x
k
ð
i
Þ
¼
1
;
8
i
:
i
ð
5
Þ
\
\
if
P
k
6
¼k
x
k
ð
i
ð
i
L
k
ð
i
R
Þ
Þ
Þ
[
P
PV
C
k
ð
i
if
P
k
6
¼k
x
k
ð
i
Þ
¼
ð
6
Þ
L
k
ð
i
0
Þ
Þ
P
PV
In the energy management problem considered in this work we use only two
shiftable tasks: the dishwasher and the washing machine. For these tasks
ω
k
(i) can
be set to 1 according to a forecasting policy.
In particular since in this model we represent the typical user behavior, for what
regards the starting of one of these two tasks we need to consider the best time to
start the appliance according to user needs (the maximum end cycle time of the
appliance has to be
fixed by the user) and the optimization of the cost function.
To model the user behavior a new input DX(t) is added in the model, repre-
senting the time distance from the best time to start an appliance.
According to this new input, the same rule discussed above will change:
if h(t) is afternoon and DT/T(t) is late and DX(t) is very low, then the proba-
bility to start the appliance is very high.
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