IEEE Power & Energy Magazine - May/June 2022 - 56

client in our sample. The mean consumption throughout the
year in the household sample is around 330 Wh, while the
corresponding standard deviation is around 400 Wh, and
these are roughly the same numbers for the first selected client.
In some periods [Figure 1(a)], the consumption drops
while in others the consumption is clearly above the mean.
On the other hand, the second client has a mean consumption
of around 1,000 Wh and a standard deviation of around
1,000 Wh [Figure 1(b)]. This client has a consumption pattern
more volatile than that of the first one. Finally, the third
client [Figure 1(c)] has the highest consumption in our sample.
This client has a different consumption trend (more in
the summer and less during the winter). For these reasons,
an appropriate clustering tool should be able to classify these
customers into different groups.
To illustrate the behavior pattern for all of the household
consumptions in the sample, there are several visualization
alternatives. Figure 1(d) summarizes each time series by a
point representing the hourly average consumption (in Wh)
Consumption, Customer Number: 1,768
4,000
3,000
2,000
1,000
Apr. 2018
July 2018 Oct. 2018 Jan. 2019 Apr. 2019
(a)
Consumption, Customer Number: 2,738
Customer 2,738
15,000
10,000
5,000
Apr. 2018
July 2018 Oct. 2018 Jan. 2019 Apr. 2019
(c)
4,000
3,000
2,000
1,000
6,000
4,000
2,000
Apr. 2018
July 2018 Oct. 2018 Jan. 2019 Apr. 2019
(b)
in a year for a household (x-axis) and its corresponding standard
deviation (y-axis). We have highlighted in red the three
customers selected for illustrative purposes.
There is a clear relation between the hourly average consumptions
and their corresponding dispersion. On average,
the household consumptions are around 300 Wh with a standard
deviation of around 400 Wh. That means the dispersion
is higher than the mean consumption level. Note also that
the distribution of the hourly average consumption and the
standard deviation is highly asymmetric. For instance, 75%
of the clients have an hourly average consumption of less
than 440 Wh and a standard deviation of less than 525 Wh.
Finally, there are several households with an almost-constant
and close-to-zero consumption along the year (standard deviation
smaller than 1 Wh).
The individual time series contains the consumption
behavior of the clients across time, so we can infer many
interesting aspects, such as static quantile hourly profiles
(i.e., how consumption is statistically distributed within the
Consumption, Customer Number: 3,143
Customer 3,143
Customer 1,768
2,000
Average (Wh)
(d)
figure 1. (a)-(c) Hourly consumption throughout a year for three clients selected for illustrative purposes. (d) Scatterplot
of the average consumption for each household versus the standard deviation for 10,000 households.
56
ieee power & energy magazine
may/june 2022
4,000
Electricity Consumption (Wh)
Electricity Consumption (Wh)
Standard Deviation (Wh)
Electricity Consumption (Wh)
IEEE Power & Energy Magazine - May/June 2022

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