IEEE Power & Energy Magazine - May/June 2022 - 60

Subgroups With 1,613, 1,066, and 846 Households, Respectively
40
30
20
10
hour
(a)
Subgroups With 1,938, 1,891, and 583 Households, Respectively
40
30
20
10
hour
(b)
Subgroups With 998, 354, and 244 Households, Respectively
40
30
20
10
hour
(c)
figure 4. Subgroups in metagroups 1, 2, and 3 clustered by median (50th
percentile). (a) Cluster centers for each division of metagroup 1. (b) Cluster
centers for each division of metagroup 2. (c) Cluster centers for each division
of metagroup 3.
60
ieee power & energy magazine
Subgroup
1
2
3
Subgroup
1
2
3
For the other two macrogroups,
the clustering identifies two consumption
peaks and two valleys,
but at different times and with different
sizes.
Finally, Figure 6 shows the
cluster centers for the three finer
divisions of each metagroup based
on the third approach: autocorrelations.
In particular, for a given
h-lagged hour, each vertical line
represents the hth autocorrelation
for the hourly consumption in
each group, that is, the correlation
between the consumption at hour t
in a group and the same consumption
but at hour t - h.
The sizes for each minor division
of the first macrogroup are
1,373, 732, and 1,420 households.
For the second macrogroup, the
sizes are 2,749, 1,145, and 518. The
third macrogroup's sizes are 992,
451, and 153.
The autocorrelation clustering
Subgroup
1
2
3
provides information about the different
dynamics of the time series,
not only in the short term (lags
1-13), but also on a daily (lags 24,
25, 48, 49, 72, and 73) and weekly
basis (lag 168). Although the median
and the 95th-percentile hourly
profiles take into account the dynamics,
these profiles do not measure
the strength of the relationship
between the consumption of contiguous
hours, which is something
that we can measure using
autocorrelation functions. In this
framework, autocorrelations allows
us to separate clients with highly
persistent dependence in the short
term from those with smaller dependencies.
The second group can
be divided further into two groups:
those with small but positive correlations
and those with small and
negative values at lags 8-13. This
reveals a clear difference in consumption
behavior.
In Figure 6 (macrogroup 1),
the first and second minor groups
in the clustering identify those
consumers with a steep consumption
peak in the morning (10 a.m.)
may/june 2022
Percentage of Normalized
Percentage of Normalized
Consumption (Respect to the Maximum)
-1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Consumption (Respect to the Maximum)
-1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
-1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Percentage of Normalized
Consumption (Respect to the Maximum)

IEEE Power & Energy Magazine - May/June 2022

Table of Contents for the Digital Edition of IEEE Power & Energy Magazine - May/June 2022

Contents
IEEE Power & Energy Magazine - May/June 2022 - Cover1
IEEE Power & Energy Magazine - May/June 2022 - Cover2
IEEE Power & Energy Magazine - May/June 2022 - Contents
IEEE Power & Energy Magazine - May/June 2022 - 2
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IEEE Power & Energy Magazine - May/June 2022 - Cover3
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