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Electricity Price Forecasting: Bridging Linear Models, Neural Networks and Online Learning

Btissame El Mahtout, Florian Ziel

TL;DR

The paper tackles day-ahead electricity price forecasting in volatile European markets by introducing a linear–nonlinear hybrid neural network that combines a skip-connected linear predictor with a nonlinear NN component, trained via partial online learning and aggregated with fully adaptive Bernstein Online Aggregation (BOA). The approach explicitly models fundamental drivers (renewables, demand, fuel, and carbon markets) as well as autoregressive and calendar effects, and is evaluated across the German–Luxembourg and Spanish markets over six years. Key contributions include the first implementation of this hybrid architecture, the application of a fully adaptive BOA ensemble, and a novel non-parametric online-learning scheme that reduces computational cost while maintaining accuracy. Results show substantial improvements over LEAR and DNN baselines, with RMSE and MAE reductions of roughly 12–13% and 15–18% respectively, and runtimes reduced from hours to minutes, highlighting practical viability for fast electricity market forecasting.

Abstract

Precise day-ahead forecasts for electricity prices are crucial to ensure efficient portfolio management, support strategic decision-making for power plant operations, enable efficient battery storage optimization, and facilitate demand response planning. However, developing an accurate prediction model is highly challenging in an uncertain and volatile market environment. For instance, although linear models generally exhibit competitive performance in predicting electricity prices with minimal computational requirements, they fail to capture relevant nonlinear relationships. Nonlinear models, on the other hand, can improve forecasting accuracy with a surge in computational costs. We propose a novel multivariate neural network approach that combines linear and nonlinear feed-forward neural structures. Unlike previous hybrid models, our approach integrates online learning and forecast combination for efficient training and accuracy improvement. It also incorporates all relevant characteristics, particularly the fundamental relationships arising from wind and solar generation, electricity demand patterns, related energy fuel and carbon markets, in addition to autoregressive dynamics and calendar effects. Compared to the current state-of-the-art benchmark models, the proposed forecasting method significantly reduces computational cost while delivering superior forecasting accuracy (12-13% RMSE and 15-18% MAE reductions). Our results are derived from a six-year forecasting study conducted on major European electricity markets.

Electricity Price Forecasting: Bridging Linear Models, Neural Networks and Online Learning

TL;DR

The paper tackles day-ahead electricity price forecasting in volatile European markets by introducing a linear–nonlinear hybrid neural network that combines a skip-connected linear predictor with a nonlinear NN component, trained via partial online learning and aggregated with fully adaptive Bernstein Online Aggregation (BOA). The approach explicitly models fundamental drivers (renewables, demand, fuel, and carbon markets) as well as autoregressive and calendar effects, and is evaluated across the German–Luxembourg and Spanish markets over six years. Key contributions include the first implementation of this hybrid architecture, the application of a fully adaptive BOA ensemble, and a novel non-parametric online-learning scheme that reduces computational cost while maintaining accuracy. Results show substantial improvements over LEAR and DNN baselines, with RMSE and MAE reductions of roughly 12–13% and 15–18% respectively, and runtimes reduced from hours to minutes, highlighting practical viability for fast electricity market forecasting.

Abstract

Precise day-ahead forecasts for electricity prices are crucial to ensure efficient portfolio management, support strategic decision-making for power plant operations, enable efficient battery storage optimization, and facilitate demand response planning. However, developing an accurate prediction model is highly challenging in an uncertain and volatile market environment. For instance, although linear models generally exhibit competitive performance in predicting electricity prices with minimal computational requirements, they fail to capture relevant nonlinear relationships. Nonlinear models, on the other hand, can improve forecasting accuracy with a surge in computational costs. We propose a novel multivariate neural network approach that combines linear and nonlinear feed-forward neural structures. Unlike previous hybrid models, our approach integrates online learning and forecast combination for efficient training and accuracy improvement. It also incorporates all relevant characteristics, particularly the fundamental relationships arising from wind and solar generation, electricity demand patterns, related energy fuel and carbon markets, in addition to autoregressive dynamics and calendar effects. Compared to the current state-of-the-art benchmark models, the proposed forecasting method significantly reduces computational cost while delivering superior forecasting accuracy (12-13% RMSE and 15-18% MAE reductions). Our results are derived from a six-year forecasting study conducted on major European electricity markets.
Paper Structure (12 sections, 10 equations, 11 figures, 1 table)

This paper contains 12 sections, 10 equations, 11 figures, 1 table.

Table of Contents

  1. Introduction
  2. Data
  3. Model Design
  4. Linear Networks
  5. Non-Linear Networks and Combined structures
  6. Ensembling
  7. Training and Evaluation Setup
  8. Learning Algorithm
  9. Study Design
  10. Benchmarks and Evaluation
  11. Results and Discussion
  12. Conclusion

Figures (11)

  • Figure 1: Time Series of Day-Ahead Electricity Prices in German-Luxembourg
  • Figure 2: Day-Ahead Forecasts of Load and Renewable Generation, and Commodity Prices in the German-Luxembourg Electricity Market
  • Figure 3: MLP with Reduced Linear Model architecture to forecast the hourly electricity price
  • Figure 4: Visualisation of the online learning algorithm
  • Figure 5: Hourly RMSE of selected models for German-Luxembourg bidding zone
  • ...and 6 more figures