IEEE Power & Energy Magazine - May/June 2022 - 59

given season (instead of a complete year). In our case,
we have selected the spring season with 2,184 hours.
✔ Scalability: An efficient algorithm should scale well
for large data sets. Partitioning methods and, in particular,
k-means clustering are usually good choices in
terms of computational time.
✔ Number of clusters: In partitioning methods, a critical decision
is the number of groups. This number should be determined
by combining 1) knowledge from domain experts:
a number large enough to properly separate consumer behaviors,
but small enough to include it in possible actions as
an additional feature (e.g., marketing or tariff campaigns);
and 2) technical criteria: based on a specialized statistical
analysis. To illustrate our case study, we have considered
k 10= groups to segment 10,000 households.
✔ Outliers: Note that there may be several consumers with
no (or very low) consumption. These consumers should
not be considered by a clustering tool but, instead, be
included in a particular and extra group. In our case,
there are 244 households with no consumption; they are
assigned to group 0.
Clustering for Major Divisions
The clustering for major divisions is based on the static behavior
of the households to capture global properties given by the
nine consumption deciles in a season (spring in our case). Hence,
the input for the k-means tool is a matrix containing 9,756 households
(10,000 minus 244 with no consumption) and nine deciles.
Figure 3(a) shows the cluster centers for each group. In
particular, the y-axis contains, for each of the four groups,
the normalized consumption for all hourly consumptions
in the corresponding group and a given decile probability
(x-axis). The clustering divides the clients into groups based
on total seasonal electricity consumption computed by the
nine deciles. There is a large group (group 1) with small and
occasionally moderate consumption. Another small group
(group 4) has high consumption and is occasionally close to
the maximum. The sizes for macrogroups 1, 2, 3, and 4 are
3,525, 4,412, 1,596, and 223 households, respectively.
Figure 3(b) shows the hourly consumption profile for
households in each group for 24 h. The black line represents
the average consumption for all households in a given
group for each hour. The corresponding 80% confidence
intervals are shown in shaded colors. Note that the higher
the consumption, the higher the volatility. Moreover, group 4
has a high peak demand for all hours in a day. For the other
groups, peak demand is concentrated on the usual peak
hours but with different magnitudes.
In particular, groups 1, 2, and 3 capture those consumers
with two daily consumption peaks: morning and evening.
Group 2 presents an afternoon peak at around 2 p.m., while
group 3's is around 11 a.m. The consumption pattern is more
stable for group 4. In summary, previous groups characterize
customers based on their total amount of electricity consumed
given by their percentiles. Next, each of the three groups will be
may/june 2022
divided again based on their dynamic behavior. Group 4 will be
excluded from the analysis as it contains only 233 households.
Clustering for Finer Divisions
To capture the dynamic behavior of electricity consumers,
we can consider the following three approaches:
✔ An approach based on median hourly profiles for
each consumer: For each household, the 24-h medians
(features) are computed, and a k-means algorithm
is applied to each macrogroup using these 24 features.
In this case, the number of subgroups is three.
✔ An approach based on the 95th-percentile hourly profiles
for each consumer: This method is like the preceding
approach, but it uses 95th percentiles instead of medians.
This approach may be useful when the focus is
on the peak demand.
✔ An approach based on autoconsumption: For each household,
the autocorrelation function of the corresponding
time series is computed to capture individual dynamic
behavior. In this case, we have considered the first 168
autocorrelations, but to reduce the dimensionality, we
have selected the 19 most relevant ones: 1, 2, 3, 4, 5, 6, 8,
9, 10, 11, 12, 13, 24, 25, 48, 49, 72, 73, and 168. Note that
they capture dynamics in the very short term but also in
the first, second, third, and seventh previous days.
Figure 4 shows the cluster centers for three finer divisions
of each macrogroup computed in the previous subsection. The
finer division is based on the first approach (median hourly
profiles). The sizes for each minor division of the first macrogroup
are 1,613; 1,066; and 846 households. For the second
macrogroup, the sizes are 1,938; 1,891; and 583. For the third
macrogroup, the sizes are 998, 354, and 244.
In Figure 4 (macrogroup 1), note that the division of the
first macrogroup can isolate the third minor group: consumers
who increase their loads during the evening. For macrogroup
2, the clustering can identify in the third minor group
those consumers with a higher consumption during mornings,
while the other two minor groups consume more in the
evenings. Finally, for macrogroup 3, the clustering can identify
in the third minor group those consumers with a higher
consumption load in the morning. Those in the first and second
minor groups prefer to consume during evenings.
On the other hand, Figure 5 shows the cluster centers for
the three finer divisions of each of the macrogroups computed
in the previous section. The finer division is based on the
second approach: 95th-percentile hourly profiles. The sizes
for each minor division of the first macrogroup are 946,
1,525, and 1,054 households. For the second macrogroup,
the sizes are 1,699, 1,267, and 1,446. Finally, for the third
macrogroup, the sizes are 691, 612, and 293.
In Figure 5 (macrogroup 1), note that, for the first macrogroup,
the clustering can identify in the second and third
minor groups consumers with two daily consumption peaks:
morning and evening. In the first minor group, the consumption
is more constant with a small peak in the mornings.
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IEEE Power & Energy Magazine - May/June 2022

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