[Paper Review] Online Hierarchical Forecasting for Power Consumption Data

Margaux Brégère, Malo Huard|arXiv (Cornell University)|Mar 1, 2020

Energy Load and Power Forecasting34 references20 citations

TL;DR

This paper proposes a novel online hierarchical forecasting framework for power consumption data, integrating feature generation via generalized additive models or random forests, ensemble aggregation using ML-Pol, and projection onto a constrained subspace to enforce summation consistency across hierarchical levels. The method achieves state-of-the-art performance, with the 'aggregated and projected' strategy reducing global consumption forecast error by up to 17.5% compared to benchmarks on UK smart meter data.

ABSTRACT

We study the forecasting of the power consumptions of a population of households and of subpopulations thereof. These subpopulations are built according to location, to exogenous information and/or to profiles we determined from historical households consumption time series. Thus, we aim to forecast the electricity consumption time series at several levels of households aggregation. These time series are linked through some summation constraints which induce a hierarchy. Our approach consists in three steps: feature generation, aggregation and projection. Firstly (feature generation step), we build, for each considering group for households, a benchmark forecast (called features), using random forests or generalized additive models. Secondly (aggregation step), aggregation algorithms, run in parallel, aggregate these forecasts and provide new predictions. Finally (projection step), we use the summation constraints induced by the time series underlying hierarchy to re-conciliate the forecasts by projecting them in a well-chosen linear subspace. We provide some theoretical guaranties on the average prediction error of this methodology, through the minimization of a quantity called regret. We also test our approach on households power consumption data collected in Great Britain by multiple energy providers in the Energy Demand Research Project context. We build and compare various population segmentations for the evaluation of our approach performance.

Motivation & Objective

• To improve electricity demand forecasting accuracy across multiple aggregation levels (e.g., national, regional, consumer profiles) using hierarchical time series constraints.
• To address the challenge of inconsistent forecasts across hierarchical levels due to independent modeling at each level.
• To develop a robust, online forecasting framework that leverages both hierarchical structure and ensemble learning for improved prediction.
• To evaluate the impact of different household segmentation strategies (geographic, profile-based, random) on forecasting performance.

Proposed method

• Feature generation: produce benchmark forecasts for each group (e.g., region, profile) using generalized additive models or random forests.
• Aggregation: apply online ensemble methods (e.g., ML-Pol algorithm) to combine forecasts across groups, minimizing regret via weighted combination.
• Projection: enforce hierarchical consistency by projecting aggregated forecasts into the subspace defined by summation constraints using orthogonal projection.
• The framework operates in three sequential steps: (1) feature generation, (2) aggregation, (3) projection, with theoretical guarantees on regret minimization.
• The method is designed for online learning, allowing incremental updates as new data arrives.
• The hierarchical structure is encoded via a matrix K such that K·yt = 0, ensuring that higher-level forecasts are consistent with lower-level sums.

Experimental results

Research questions

• RQ1 How does combining ensemble aggregation with projection-based reconciliation improve forecasting accuracy in hierarchical power consumption data?
• RQ2 What is the impact of different household segmentation strategies (e.g., region, Acorn, NMF, random clustering) on forecast performance?
• RQ3 Does the proposed method outperform baseline strategies such as bottom-up, top-down, or standalone benchmark forecasts?
• RQ4 How robust is the method to increasing numbers of clusters in the segmentation?
• RQ5 Can theoretical regret bounds be established for the proposed online hierarchical forecasting framework?

Key findings

• The 'aggregated and projected' strategy consistently outperforms all other methods, achieving the lowest global consumption forecast error across all segmentations.
• The 'Region + NMF(16)' segmentation configuration achieved the best performance, reducing the mean squared error for global consumption to 170.3 ± 8.5 kWh², a 17.5% improvement over the benchmark.
• Bottom-up forecasting based on regional clusters significantly outperformed the benchmark, reducing error from 205.8 ± 9.3 to 189.9 ± 8.3 kWh².
• Aggregation and projection are robust to high cluster counts: performance remains stable or improves slightly up to 64 clusters, with no significant degradation.
• Segmentations based on household profiles (e.g., Acorn, Fuel+Tariff) performed similarly to random clustering, indicating limited predictive value for these features in this context.
• The projection step alone improved forecasts when regions were included, but the full 'aggregation + projection' strategy delivered the most substantial gains, especially in complex hierarchies.