Multivariate Probabilistic Forecasting of Intraday Electricity Prices using Normalizing Flows

Abstract

Electricity is traded on various markets with different time horizons and regulations. Short-term trading becomes increasingly important due to higher penetration of renewables. In Germany, the intraday electricity price typically fluctuates around the day-ahead price of the 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 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. The normalizing flow is compared to a selection of historical data, a Gaussian copula, and a Gaussian regression model. Among the different models, the normalizing flow identifies the trends most accurately and has the narrowest prediction intervals. Notably, the normalizing flow is the only approach that identifies rare price peaks. Finally, this work discusses the influence of different external impact factors and finds that, individually, most of these factors have negligible impact. Only the immediate history of the price difference realization and the combination of all input factors lead to notable improvements in the forecasts.

Sample-based Uncertainty Quantification with a Single Deterministic Neural Network

“…DISCO Net (and DN+) differs from recent approaches based on NF (Sick et al, 2020;Charpentier et al, 2020;Dumas et al, 2021;Sendera et al, 2021;Jamgochian et al, 2022;Rittler et al, 2022;März and Kneib, 2022;Arpogaus et al, 2022;Cramer et al, 2022) in a number of ways. First, NF estimates the joint density p(x, y) to derive the conditional density p(y|x) while DISCO Net directly models the latter with no recourse to the former.…”

“…NF is a generative model that uses a composition of multiple differentiable bijective maps modeled by NN to transform a simple (such as uniform or Gaussian) distribution to a more complex distribution of real data. Examples of probabilistic forecast based on NF can be found in (Sick et al, 2020;Charpentier et al, 2020;Dumas et al, 2021;Sendera et al, 2021;Jamgochian et al, 2022;Rittler et al, 2022;März and Kneib, 2022;Arpogaus et al, 2022;Cramer et al, 2022).…”

Creating Probabilistic Forecasts from Arbitrary Deterministic Forecasts using Conditional Invertible Neural Networks

“…An alternative method, that directly uses normalising flows in the context of probabilistic forecasts, is to learn multi-dimensional distributions of electricity price differences to predict the trajectory of intraday electricity prices (Cramer et al, 2022a). Similarly, normalising flows may be applied multiple times to generate scenario-based probabilistic forecasts (Dumas et al, 2022;Zhang and Zhang, 2019;Ge et al, 2020), or to create a proxy for weather ensemble prediction systems based on numerical weather prediction models (Fanfarillo et al, 2021).…”

Simulation-based Forecasting for Intraday Power Markets: Modelling Fundamental Drivers for Location, Shape and Scale of the Price Distribution

“…The recent and still sparse literature on probabilistic forecasting in intraday markets (Janke and Steinke, 2019;Narajewski and Ziel, 2020a;Uniejewski et al, 2019;Cramer et al, 2022) and the markets' driving fundamentals has, so far, focused on modelling the impact of renewable forecast (Ziel, 2017;Kath, 2019;Pape et al, 2016;Gürtler and Paulsen, 2018;Balardy, 2022) and forecast errors (Ziel, 2017;Kulakov and Ziel, 2020;Kuppelwieser and Wozabal, 2021). A different strand of literature emerged around modelling of the merit-order effect for price changes and price elasticity (Kiesel and Paraschiv, 2017;Kremer et al, 2021Kremer et al, , 2020Kulakov and Ziel, 2019;Balardy, 2022).…”