Explainable representative-days clustering on low-voltage grid meters and feeders, with noise-aware multi-objective Bayesian optimization, applied to grid-congestion events

Abstract

Low-voltage grid (LVG) state estimations help in expansion planning and preventing congestion events. However, country-scale simulations pose high computational burdens. A solution that reduces calculation time is to cluster similar days, and only simulate the most representative day of each cluster. Using real-world, quarter-hour residential consumption time series from 925 meters, congestion event probabilities from 146 real feeders, 51 daily meteorological and 12 calendar features, we propose a novel end-to-end representative-days clustering framework. Along with $k$-medoids clustering, we use dimensionality reduction (kernel principal component analysis, factor analysis, …) and pre/post-processing. To emphasize quarter-hour extremes, we apply dynamic data squeezing/expansion, based on the LVG consumption median. Our approach is scalable because dimensionality reduction compresses thousands of daily variables into up to 300 components, regardless of the amount of meters and exogenous features (weather, calendar, …). Multi-objective Bayesian optimization for noisy functions, along with Sobol sampling, finds the hyperparameters that minimize the $k$ representative-day reconstruction error compared to the full-year simulation. Explainability is achieved via tree ensemble classification on the decided clusters: ranking of the most important meteorological and calendar features, along with rule induction for future clustering decisions. We applied these techniques to successfully cluster all days of 2016 of the Flemish LVG (in Belgium). Our approach works well on both meter consumptions and feeder congestion event approximations. Photosynthetic radiation (visible spectrum and solar panel absorption wavelengths), water temperature, soil water volume/temperature (variables with a recent weather memory effect) and albedo were the most important meteorological factors, along with calendar features.