Multivariate Scenario Generation of Day-Ahead Electricity Prices using Normalizing Flows

TL;DR

This work presents a probabilistic forecasting approach for day-ahead electricity prices using the fully data-driven deep generative model called normalizing flow, and highlights how improvements towards adaptations in changing regimes allow the normalizing flow to adapt to changing market conditions and enable continued sampling of high-quality day-ahead price scenarios.

Abstract

Trading on the day-ahead electricity markets requires accurate information about the realization of electricity prices and the uncertainty attached to the predictions. Deriving accurate forecasting models presents a difficult task due to the day-ahead price's non-stationarity resulting from changing market conditions, e.g., due to changes resulting from the energy crisis in 2021. We present a probabilistic forecasting approach for day-ahead electricity prices using the fully data-driven deep generative model called normalizing flow. Our modeling approach generates full-day scenarios of day-ahead electricity prices based on conditional features such as residual load forecasts. Furthermore, we propose extended feature sets of prior realizations and a periodic retraining scheme that allows the normalizing flow to adapt to the changing conditions of modern electricity markets. Our results highlight that the normalizing flow generates high-quality scenarios that reproduce the true price distribution and yield accurate forecasts. Additionally, our analysis highlights how our improvements towards adaptations in changing regimes allow the normalizing flow to adapt to changing market conditions and enable continued sampling of high-quality day-ahead price scenarios.

Figures (9)

• Figure 1: Time series of day-ahead mean prices of each day from April 20, 2016 to December 31, 2022. We consider October 1, 2021, as the beginning of the 2021/22 energy crisis (shaded period). Data from EPEX Spot, taken from the ENTSO-E transparency platform european_network_of_transmission_system_operators_for_electricity_entso-e_nodate.
• Figure 2: Schematic visualization of the conditional normalizing flow model with presentation of one-dimensional probability density functions. The left side represents the known base distribution $p_Z(z)$. The right side represents the conditional non-Gaussian target distribution $p_{X|Y}(x|y)$. The network in the center shows the diffeomorphism in Equation \ref{['eq:3']} between the two distributions, which depends on a conditional input $y$.
• Figure 3: Example forecasts for May 7, 2017 (top), November 28, 2017 (center) and August 22, 2020 (bottom). The left column shows the solar generation forecast (yellow), wind generation forecast (blue), and load forecast (red) for each day. The right column shows 50 generated scenarios (blue) according to the conditions forecasts and respective price realization (black) for comparison.
• Figure 4: Histogram of prices of all generated scenarios compared to the histogram of the actual day-ahead price time series ("realizations"). Dotted line is a Gaussian fit onto the realizations histogram. The value $D$ gives the Kullback--Leibler divergence between scenario and realization histogram. Time series ranges from April 20, 2016, to December 31, 2022.
• Figure 5: Histograms of prices of generated scenarios compared to histograms of the actual day-ahead price time series ("realizations"). The normalizing flow is trained on all available data at the given time. The left side shows histograms for time series before October 1, 2021. The right side shows histograms for time series after October 1, 2021. Note the different scales on the x-axis. Dotted lines present Gaussian fits onto the realizations histograms. The value $D$ gives the Kullback--Leibler divergences between scenario and realization histograms.