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sampling of voltage noise, which provides an additional feature vector that can be
used to distinguish more accurately between energy usage signatures. Appliances
conduct a variety of noise voltage back onto the home's power wiring, yielding
measurable noise signatures that are easily detectable using appropriate hardware.
An important advantage of voltage noise signatures is that any electrical outlet inside
the home can be used as a single installation point.
10.3 Notation
Since different devices tend to draw different amounts of power, which are consistent
over time, total power is a reasonable feature to use for classification [
4
]. Most
devices have predictable current consumption and can be categorized according to
the magnitude of real/reactive power. Given a household with
N
devices, the power
consumption of an individual appliance
i
∈{
1
,...,
N
}
over a period of
T
time
y
(
i
)
1
y
(
i
)
2
y
(
i
)
T
points can be expressed as:
y
(
i
)
={
,
,...,
}
. Usually, we only observe
y
t
=
i
=
1
y
(
i
)
the sum of all power outputs at each time:
T
.
Given the aggregated power signal, most research on energy disaggregation
[
1
,
22
,
23
] aims at inferring the individual device consumption. Since we aim to
infer the context or rather occupancy states in residential environments in order to
optimize heating control, we are mainly interested in the
¯
, with
t
=
1
,...,
t
on
/
off
states of individ-
ual appliances
s
(
i
)
, where
s
(
i
)
=
1ifdevice
i
is turned “on” at time point
t
, and
t
t
s
(
i
)
t
0 otherwise. The appliance state identification task can be framed as an infer-
ence problem. Given an aggregated power signal
=
y
1
,...,
¯
¯
y
T
, we intend to compute
s
(
i
)
of individual appliance states
s
(
i
)
the posterior probability
p
(
|¯
y
t
)
for each device
t
t
i
T
.
Due to the fact that the aggregated power signal is super-imposed and unnormal-
ized, and, therefore, unsuitable for the appliance state identification, we consider the
changes in power consumption as features, which can be derived by the first-order
difference of the power signal
=
1
,...,
N
and each time point
t
=
1
,...,
y
(
i
)
y
(
i
)
y
(
i
)
t
T
. Thus the appli-
ance state identification task could also be formulated as a classification problem,
where a certain change in power consumption categorizes a device into either “
Δ
=
−
1
for
t
=
2
,...,
t
t
−
on
”
or “
off
” state.
10.4 Framework and Algorithms
Figure
10.1
shows a flowchart of our proposed framework for heating control and
scheduling by means of energy disaggregation. The input for our heating control
framework is an aggregated energy signal, such as that coming from a smart meter in
a residential home. In the first step (i) we extract features from the energy signal, i.e.
changes in consumption, which can be used to categorize the individual electrical
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