Change Detection in Smart Grids Using Dynamic Mixtures of t-Distributions

The analysis of massive amounts of data collected via smart grids can contribute to manage more efficiently energy production and water resources. Within this framework, a method is proposed in this article to detect changes in panel data from smart electricity and water networks. The adopted approach is based on a representation of the data by clusters whose occurrence probability varies in the course of time. Because of the cyclical nature of the studied data, these probabilities are designed to be piecewise periodic functions whose break points reflect the intended changes. A mixture of t-distributions with a hierarchical structure forms the basis of our proposal. This model was also chosen for its robustness properties. The weights of the mixture, at the top of the hierarchy, constitute the change detectors. At the lowest hierarchy level, the mixture weights are designed to model the periodic dynamics of the data. The incremental strategy adopted for parameter estimation makes it possible to process large amounts of data. The practical relevance of the proposed method is illustrated through realistic urban data.