C-Vine Copula Mixture Model for Clustering of Residential Electrical Load Pattern Data

Abstract

Abstract-The ongoing deployment of residential smart meters in numerous jurisdictions has led to an influx of electricity consumption data. This information presents a valuable opportunity to suppliers for better understanding their customer base and designing more effective tariff structures. In the past, various clustering methods have been proposed for meaningful customer partitioning. This paper presents a novel finite mixture modeling framework based on C-vine copulas (CVMM) for carrying out consumer categorization. The superiority of the proposed framework lies in the great flexibility of pair copulas towards identifying multi-dimensional dependency structures present in load profiling data. CVMM is compared to other classical methods by using real demand measurements recorded across 2,613 households in a London smart-metering trial. The superior performance of the proposed approach is demonstrated by analyzing four validity indicators. In addition, a decision tree classification module for partitioning new consumers is developed and the improved predictive performance of CVMM compared to existing methods is highlighted. Further case studies are carried out based on different loading conditions and different sets of large numbers of households to demonstrate the advantages and to test the scalability of the proposed method.Index Terms-Clustering, customer classification, C-vine, decision trees, mixture models, pair-copula construction, smart meters. I. INTRODUCTIONlectricity market liberalization has largely unbundled the distribution and supply services in many jurisdictions, providing customers with the freedom to select their electricity supplier. In this competitive environment, retail companies can improve the commercial attractiveness of their product by formulating tariffs aimed at different customer types. An important part of the tariff design process is the identification of meaningful customer classes that exhibit different consumption patterns, enabling the development of diversifiable products. Moreover, electrical customer classification can also play a crucial role in load forecasting [1][2] and modeling [3], electricity market development [4], energy system planning and operation [5] and theft detection [6]. Naturally, information on customer type (e.g. industrial, commercial, residential) provides important information regarding the likely electricity consumption pattern and intensity. However, for further partitioning and exploratory analysis to be carried out effectively, high-frequency demand measurements are necessary [7]. As such, the advent of smart metering has led to large-scale availability of consumption data that render clustering analysis increasingly possible.Load profile clustering aims to allocate consumers into a small number of homogeneous groups, ensuring that elements of the same cluster are similar between them, while being dissimilar to elements of different clusters. A large number of clustering techniques have been proposed in the past and applied to electrical load ...

Review of Smart Meter Data Analytics: Applications, Methodologies, and Challenges

“…The load variation was modeled by a lognormal distribution, and a Gaussian mixture model (GMM)-based load profiling method was proposed in [99] to capture dynamic behavior of consumers. A mixture model was also used in [39] by integrating the C-vine copula method (C-vine copula-based mixture model) for the clustering of residential load profiles. The high-dimensional nonlinear correlations among consumptions of different time periods were modeled using the C-vine copula.…”

A multivariate framework to study spatio‐temporal dependency of electricity load and wind power

“…Based on the bivariate and conditional bivariate distributions, the joint distribution can be constructed. The use of vine copulas to tackle power system uncertainty is reported in the previous studies [33][34][35] and probabilistic forecast for multiple wind farms in Wang et al 36 A regular vine can be decomposed to either i. D (drawable)-vine where each node in T j has a degree of at most 2, and conditioning is done sequentially; or…”

Scalable Clustering of Individual Electrical Curves for Profiling and Bottom-up Forecasting

“…Authors of [17] suggest a k-means clustering to derive daily profiles from 220,000 homes and a total of 66 millions daily curves in California. Other approaches based on mixture models are presented in [18] for customers categorization and load profiling on a data set of 2,613 smart metered household from London.…”