# Data Analytics for Profiling Low-Voltage Customers with Smart Meter Readings
## 2 Load Profiling  
In the literature, several techniques have been proposed for obtaining LPs. Each method is specialized for the specific study's goal or on the group of customers represented [3; 6; 7]. Models for network planning generally use a probabilistic approach by exploiting probabilistic load flow (PLF) calculation algorithms, Monte Carlo methods, or analytical methods [4; 8]. The PLF input variables (load and generation) are commonly represented by suitable probability density functions (PDFs). However, it is not straightforward to represent each load and generator with a PDF. The dynamic nature of consumer behavior is heavily time-dependent. Correlations and time dependencies should be considered simultaneously to ensure a good characterization of load and generation [8]. For instance, other studies, with the aim of elaborating market balancing mechanisms in competitive frameworks or for devising marketing strategies, exploit predictive analyses, such as the multi-linear regression analysis. With such analysis, they avoid the considerable investment of putting half-hourly metering into every market customer and calculate the profile coefficients of several customer classes [9]. In this case, customer behavior profiling can be used as a useful tool for tariff rate formulation. Bottom-up methods can be performed for (smart) home energy systems design. They aim to build load profiles or PDFs of specific electrical devices by using detailed information on devices' usage and elaborate and combine them to make profiles that aspire to represent other households and areas [1; 3; 8]. Any probabilistic or predictive method produces results affected by a certain, sometimes measurable, uncertainty level by seeking a compromise between computational burden and accuracy. On the other hand, the data gathered from smart meters may help and reduce such uncertainty. Among all the techniques and regardless of the database origin (any meters, new or old), clustering techniques have been extensively applied to measured consumption patterns of end-users to categorize customers and define typical LPs for each category. Clustering allows grouping similar load patterns in classes. Then, once the profiles are grouped, each class's centroid can be chosen as the LP of the cluster whose it belongs. Moreover, a neighborhood of the centroid identifies the subspace where similar load profiles can be found. Various clustering algorithms have been proposed in the literature, i.e., deterministic, statistical, and artificial intelligence methods. Clustering methods can be split into hierarchical and partitional methods [10]. The hierarchical methods provide a dendrogram of nested clusters that allows for an overview of all possible clustering outcomes. Suchtechniques can be based on agglomerative or divisive approaches. In the agglomerative approach, the clustering process starts by defining a cluster for each individual, and these clusters are then iteratively merged according to the respective similarity. Conversely, in the divisive approach, a unique cluster formed by all the dataset individuals is iteratively split. The conditional clustering methods do not provide clusters as an outcome but a unique partition of the dataset. The key idea of these methods is based on optimizing a criterion function by alternating the initial partitioning of individuals. \(k\)-means is the simplest and most popular partitional clustering algorithm [10; 11; 12; 13]. Past and recent literature show a great diversity in terms of approaches, used databases, clustering algorithms (e.g., partitional, hierarchical, fuzzy, neural networks), and similarity/dissimilarity criteria (e.g., Euclidean distance, mean of the inner distance, mean square error, mean index adequacy, clustering dispersion indicator, the within-cluster sum of squares to between-cluster variation) [14]. The most appropriate clustering technique should be chosen according to the analysis's goal and the dataset's characteristics [10].