# Data Analytics for Profiling Low-Voltage Customers with Smart Meter Readings
## 4 Results and Discussion
### Resulting in Typical Load Profiles  
The result of the single customer's characterization process is graphically shown in Figure 6 wherein the real consumption profiles of a given customer on winter workdays are drawn. The variability of consumption in winter weekdays causes the aggregation into three clusters represented by their relevant centroids. In Figure 7 the most crowded cluster in Figure 6 is zoomed in for showing the difference between the centroid (blue line), which can be used to represent that customer in that quarter of the year, and the average profile (red line), obtained by averaging all the real profiles of Figure 6. The average profile tends to flat the valleys in the early hours of the day and reduce morning and evening peaks. Figure 6: Resulting clusters of a given residential customer (first quarter weekday); the most crowded cluster is the first one. Figure 7: Comparison between the centroid of the most crowded cluster (blue line) and the average profile of all the first quarter weekday profiles of Figure 6 (red line). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Database** & **Main** & **Secondary** & **Agricultural** & **Commercial** & **Industrial** \\
**(Year)** & **Residence** & **Residence** & **Agricultural** & **Commercial** & **Industrial** \\ \hline
2013 & 41,289/38,928 & 4577/4577 & 182/180 & 8963/8937 & 1023/1023 \\
2017 & 24,453/22,838 & 2532/2527 & 112/112 & 3537/3533 & 1156/1145 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Share of valid customers/final number of customers clustered (outliers excluded) in the two considered databases. In the following section, for the sake of brevity, the description and discussion of the results focus on three categories of customers (i.e., commercial, industrial, and main residence contract) and two typical days, one in winter and one in summer (i.e., the working days of the first and third quarter. Figures 8-16 show the two databases' resulting centroids, DB2013, and DB2017. The resulting clusters are in descending order, from the largest to the smallest. Furthermore, the comparison between seasons within the same year, and, finally, the comparison between years, for the three categories of customers, are reported. The comparison considers the most similar normalized profiles besides the crowdedness of each cluster with a calculation of the minimum root sum square error:  
* The number of resulting clusters may vary from season to season both in DB2013 (i.e., Figures 8a,b and 14a,b) and in DB2017 (i.e., Figures 9a,b and 15a,b) for commercial customers and residential ones; this did not happen for the industrial customers (Figures 11a,b and 12a,b). * The profiles of the two typical days during the two seasons can be similar, as shown in Figures 8c, 9c, 11c, 12c, 14c and 15c, even if in some cases the peaks can be slightly moved or reduced. * Profiles of different years can be almost overlapped (i.e., Figures 10a, 13 and 16). * In some cases, the two-year comparison makes very similar shapes but higher/lower peak values in the two DBs (i.e., Figure 10b). Figure 10: Commercial (COM) end-users, comparison between normalized centroids of the two databases (DB2013 vs. DB2017): **(a)** winter workdays, **(b)** summer workdays. Figure 9: Database 2017, commercial (COM) end-users, normalized centroids: **(a)** winter workdays (four clusters), **(b)** summer workdays (three clusters), **(c)** comparison between the two typical days. Figure 11: Database 2013, industrial (IND) end-users, normalized centroids: (**a**) winter workdays (three clusters), (**b**) summer workdays (three clusters), (**c**) comparison between the two typical days. Figure 12: Database 2017, industrial (IND) end-users, normalized centroids: (**a**) winter workdays (five clusters), (**b**) summer workdays (five clusters), (**c**) comparison between the two typical days. Figure 13: Industrial (IND) end-users, comparison between normalized centroids of the two databases (DB2013 vs. DB2017): (**a**) winter workdays, (**b**) summer workdays.