C-Vine copula mixture model for clustering of residential electrical load pattern data

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

Copulas as High Dimensional Generative Models: Vine Copula Autoencoders

We introduce the vine copula autoencoder (VCAE), a flexible generative model for high-dimensional distributions built in a straightforward three-step procedure. First, an autoencoder (AE) compresses the data into a lower dimensional representation. Second, the multivariate distribution of the encoded data is estimated with vine copulas. Third, a generative model is obtained by combining the estimated distribution with the decoder part of the AE. As such, the proposed approach can transform any already trained AE into a flexible generative model at a low computational cost. This is an advantage over existing generative models such as adversarial networks and variational AEs which can be difficult to train and can impose strong assumptions on the latent space. Experiments on MNIST, Street View House Numbers and Large-Scale CelebFaces Attributes datasets show that VCAEs can achieve competitive results to standard baselines