Multivariate Probabilistic Forecasting of Intraday Electricity Prices using Normalizing Flows

TL;DR

This paper introduces a normalizing flow-based probabilistic model for intraday electricity price differences in Germany, capturing hourly patterns and external factors, outperforming traditional models in accuracy and interval narrowness.

Contribution

The work presents a novel multivariate normalizing flow approach for modeling intraday price differences, incorporating external impacts and outperforming existing probabilistic models.

Findings

Normalizing flow achieves higher trend accuracy.

Prediction intervals are narrower with the flow model.

External factors like recent price history significantly influence predictions.

Abstract

Electricity is traded on various markets with different time horizons and regulations. Short-term intraday trading becomes increasingly important due to the higher penetration of renewables. In Germany, the intraday electricity price typically fluctuates around the day-ahead price of the European Power EXchange (EPEX) spot markets in a distinct hourly pattern. This work proposes a probabilistic modeling approach that models the intraday price difference to the day-ahead contracts. The model captures the emerging hourly pattern by considering the four 15 min intervals in each day-ahead price interval as a four-dimensional joint probability distribution. The resulting nontrivial, multivariate price difference distribution is learned using a normalizing flow, i.e., a deep generative model that combines conditional multivariate density estimation and probabilistic regression. Furthermore, this work discusses the influence of different external impact factors based on literature insights and impact analysis using explainable artificial intelligence (XAI). The normalizing flow is compared to an informed selection of historical data and probabilistic forecasts using a Gaussian copula and a Gaussian regression model. Among the different models, the normalizing flow identifies the trends with the highest accuracy and has the narrowest prediction intervals. Both the XAI analysis and the empirical experiments highlight that the immediate history of the price difference realization and the increments of the day-ahead price have the most substantial impact on the price difference.