Depth-based Outlier Detection for Grouped Smart Meters: a Functional Data Analysis Toolbox

Abstract

Smart metering infrastructures collect data almost continuously in the form of fine-grained long time series. These massive time series often have common daily patterns that are repeated between similar days or seasons and shared between grouped meters. Within this context, we propose a method to highlight individuals with abnormal daily dependency patterns, which we term evolution outliers. To this end, we approach the problem from the standpoint of Functional Data Analysis (FDA), by treating each daily record as a function or curve. We then focus on the morphological aspects of the observed curves, such as daily magnitude, daily shape, derivatives, and inter-day evolution. The proposed method for evolution outliers relies on the concept of functional depth, which has been a cornerstone in the literature of FDA to build shape and magnitude outlier detection methods. In conjunction with our evolution outlier proposal, these methods provide an outlier detection toolbox for smart meter data that covers a wide palette of functional outliers classes. We illustrate the outlier identification ability of this toolbox using actual smart metering data corresponding to photovoltaic energy generation and circuit voltage records