# Data Analytics for Profiling Low-Voltage Customers with Smart Meter Readings
## 4 Results and Discussion
### LP Attribution  
Once LPs representative of a given group of customers are identified, the analysis of the characteristics of the customers belonging to each cluster allows for the identification of a set of features that justify the existence of the clusters. These features are used to find a proper LP for customers not in the DSO customers' database due to the absence of smart meters or their novelty. LPs' attribution to existing but unmonitored customers can be used to assess the operating conditions of the network components (i.e., lines and transformers), calculate the power losses, and determine the expected voltage profile. The association starts with the analysis of the customers in each cluster to find common features such as  
* geographical (e.g., municipality, region, or altitude, etc. );
* electrical, related to the contract or the consumption (e.g., rated power, or annual energy, etc. );
* inherent to the shape of the profiles (e.g., monthly or season peaks, the hour of the day of the peak or the valley). Many tests were performed, and as a result, only a few features were proven to be effective for some customer categories for the databases studied in this paper. The chosen few features were the annual energy (subdivided in quarterly energy, for considering each season separately) and the monthly or seasonal peak values, easily known by the DSO for each customer. These features were modeled as normally distributed random variables in the cluster. Thus median, mean, and standard deviation were calculated for each feature. Cluster features are the input of the scoring method used for choosing the suitable LPs for a new single customer, according to the procedure described in Section 3.4 The accuracy of the proposed method was evaluated with a simple process. Each customer was associated with the cluster with the maximum score. The percentages of the right customer/cluster associations for the 2017 database are reported in Table 4. In the table the color scale emphasizes the results: i.e., in each row the worst value is in dark blue and the best is in bright red. \begin{table}
\begin{tabular}{l|c c c c c c c c c c c} \hline \hline
**Type of Contract** & **T1-td1** & **T1-td2** & **T1-td3** & **T2-td1** & **T2-td2** & **T2-td3** & **T3-td1** & **T3-td2** & **T3-td3** & **T4-td1** & **T4-td2** & **T4-td3** \\ \hline
**Main residence** & **31.0\%** & **30.1\%** & **26.8\%** & 51.5\% & 60.9\% & 48.3\% & 71.8\% & 71.0\% & 62.9\% & 51.0\% & 36.0\% & 33.4\% \\
**Secondary** & 39.7\% & 35.1\% & **31.0\%** & 37.6\% & 25.4\% & 28.1\% & 44.4\% & 44.5\% & 40.6\% & 38.2\% & 25.0\% & 18.6\% \\
**COM** & 43.8\% & 50.0\% & 59.1\% & 52.5\% & 57.6\% & 66.4\% & 50.7\% & 50.1\% & **66.0\%** & 47.3\% & 48.3\% & 63.1\% \\
**IND** & 36.2\% & **31.1\%** & **76.0\%** & 41.7\% & 47.0\% & 72.5\% & 37.3\% & 28.6\% & 67.6\% & 43.2\% & 39.3\% & 64.1\% \\
**AGR** & 71.1\% & 63.6\% & 55.3\% & **72.9\%** & 73.3\% & 75.0\% & **86.2\%** & 83.7\% & **92.5\%** & 84.8\% & 85.7\% & 86.7\% \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Number of the right customer/cluster associations for the customer included in the DB2017. The association to the right group succeeded in the range 26.8% \(\div\) 71.8% of the main residence customers depending on the typical day considered. For the other customer categories, the rate of success was similar. Although most of these results are encouraging, in some cases, the success rate was minimal (e.g., the minimum percentage of success was 18.6% for the autumn holiday, T4-td3). There are several reasons for this low success rate. The most significant reason is that the clusters' features are not normally distributed for all the clusters, and their probability density function is far from a normal distribution. It is worth noticing that Gaussian approximation's accuracy increases with the number of customers in the cluster and the feature's correlation with the centroid shape.