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Learning for Interval Prediction of Electricity Demand: A Cluster-based Bootstrapping Approach

Rohit Dube, Natarajan Gautam, Amarnath Banerjee, Harsha Nagarajan

TL;DR

This work tackles day-ahead interval forecasting for low-aggregation electricity demand in microgrids by introducing a Cluster-based Block Bootstrap (CBB) method. It combines NN-based spectral clustering to group days with similar demand patterns and a block residual bootstrapping scheme to preserve temporal dependence, selecting the closest cluster to generate residual blocks for each test day. Compared against Prophet and quantile-regression benchmarks, CBB achieves comparable coverage with notably narrower intervals, while reducing computation time relative to ensemble methods. The approach hinges on robust point forecasts, cluster-informed residual memory, and adaptive updates to residuals, offering practical, scalable uncertainty quantification for microgrid operation. The results suggest substantial benefits for risk-aware decision-making in energy markets and distributed generation contexts, where reliable prediction intervals are essential.

Abstract

Accurate predictions of electricity demands are necessary for managing operations in a small aggregation load setting like a Microgrid. Due to low aggregation, the electricity demands can be highly stochastic and point estimates would lead to inflated errors. Interval estimation in this scenario, would provide a range of values within which the future values might lie and helps quantify the errors around the point estimates. This paper introduces a residual bootstrap algorithm to generate interval estimates of day-ahead electricity demand. A machine learning algorithm is used to obtain the point estimates of electricity demand and respective residuals on the training set. The obtained residuals are stored in memory and the memory is further partitioned. Days with similar demand patterns are grouped in clusters using an unsupervised learning algorithm and these clusters are used to partition the memory. The point estimates for test day are used to find the closest cluster of similar days and the residuals are bootstrapped from the chosen cluster. This algorithm is evaluated on the real electricity demand data from EULR(End Use Load Research) and is compared to other bootstrapping methods for varying confidence intervals.

Learning for Interval Prediction of Electricity Demand: A Cluster-based Bootstrapping Approach

TL;DR

This work tackles day-ahead interval forecasting for low-aggregation electricity demand in microgrids by introducing a Cluster-based Block Bootstrap (CBB) method. It combines NN-based spectral clustering to group days with similar demand patterns and a block residual bootstrapping scheme to preserve temporal dependence, selecting the closest cluster to generate residual blocks for each test day. Compared against Prophet and quantile-regression benchmarks, CBB achieves comparable coverage with notably narrower intervals, while reducing computation time relative to ensemble methods. The approach hinges on robust point forecasts, cluster-informed residual memory, and adaptive updates to residuals, offering practical, scalable uncertainty quantification for microgrid operation. The results suggest substantial benefits for risk-aware decision-making in energy markets and distributed generation contexts, where reliable prediction intervals are essential.

Abstract

Accurate predictions of electricity demands are necessary for managing operations in a small aggregation load setting like a Microgrid. Due to low aggregation, the electricity demands can be highly stochastic and point estimates would lead to inflated errors. Interval estimation in this scenario, would provide a range of values within which the future values might lie and helps quantify the errors around the point estimates. This paper introduces a residual bootstrap algorithm to generate interval estimates of day-ahead electricity demand. A machine learning algorithm is used to obtain the point estimates of electricity demand and respective residuals on the training set. The obtained residuals are stored in memory and the memory is further partitioned. Days with similar demand patterns are grouped in clusters using an unsupervised learning algorithm and these clusters are used to partition the memory. The point estimates for test day are used to find the closest cluster of similar days and the residuals are bootstrapped from the chosen cluster. This algorithm is evaluated on the real electricity demand data from EULR(End Use Load Research) and is compared to other bootstrapping methods for varying confidence intervals.
Paper Structure (20 sections, 17 equations, 10 figures, 5 tables, 2 algorithms)

This paper contains 20 sections, 17 equations, 10 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Data Collection
  3. Problem Definition
  4. Input Variable Selection
  5. Point Estimate Metrics
  6. Interval Estimation
  7. Residual Block
  8. Clustering Approach
  9. Performance Metrics
  10. Cluster-based Block Bootstrap Algorithm
  11. Results
  12. Prophet
  13. Quantile-Regression Benchmarks
  14. Loss function.
  15. Prediction.
  16. ...and 5 more sections

Figures (10)

  • Figure 1: Plot of average demand aggregated over $25$ houses (a) and $150$ houses (b) over period of $1$ day of $15$-minute intervals showing higher stochasticity in lower house aggregation.
  • Figure 2: One-day moving average of aggregate electricity demand for $50$ sites in Washington
  • Figure 3: ACF plot (left) and PACF plot (right) of electricity demand
  • Figure 4: Temperature vs. Electricity Demand
  • Figure 5: Residual errors of GBR on the training set with moving average of observed demand
  • ...and 5 more figures