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

arXiv: https://arxiv.org/abs/2311.14033 · HTML: https://mlsanity.com/paper/2311.14033/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 61 references that are in the map.
- First posted on arXiv 23 Nov 2023.

## Builds on (most cited first, 21 of 21)

- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Learning Likelihoods with Conditional Normalizing Flows](https://mlsanity.com/paper/1912.00042/) (2019)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [Forecasting day-ahead electricity prices: A review of state-of-the-art algorithms, best practices and an open-access benchmark](https://mlsanity.com/paper/2008.08004/) (2020)
- [Model-Free Renewable Scenario Generation Using Generative Adversarial Networks](https://mlsanity.com/paper/1707.09676/) (2017)
- [Distributional neural networks for electricity price forecasting](https://mlsanity.com/paper/2207.02832/) (2022)
- [Day-ahead electricity price forecasting with high-dimensional structures: Univariate vs. multivariate modeling frameworks](https://mlsanity.com/paper/1805.06649/) (2018)
- [Ensemble Forecasting for Intraday Electricity Prices: Simulating Trajectories](https://mlsanity.com/paper/2005.01365/) (2020)
- [Multivariate Probabilistic Forecasting of Intraday Electricity Prices using Normalizing Flows](https://mlsanity.com/paper/2205.13826/) (2022)
- [Electricity Price Forecasting: The Dawn of Machine Learning](https://mlsanity.com/paper/2204.00883/) (2022)
- [Deep Distributional Time Series Models and the Probabilistic Forecasting of Intraday Electricity Prices](https://mlsanity.com/paper/2010.01844/) (2020)
- [Principal Component Density Estimation for Scenario Generation Using Normalizing Flows](https://mlsanity.com/paper/2104.10410/) (2021)
- [Understanding electricity prices beyond the merit order principle using explainable AI](https://mlsanity.com/paper/2212.04805/) (2022)
- [Validation Methods for Energy Time Series Scenarios from Deep Generative Models](https://mlsanity.com/paper/2110.14451/) (2021)
- [Bidding and Scheduling in Energy Markets: Which Probabilistic Forecast Do We Need?](https://mlsanity.com/paper/2203.13159/) (2022)
- [Probabilistic Forecasting of Day-Ahead Electricity Prices and their Volatility with LSTMs](https://mlsanity.com/paper/2310.03339/) (2023)
- [Normalizing Flow-based Day-Ahead Wind Power Scenario Generation for Profitable and Reliable Delivery Commitments by Wind Farm Operators](https://mlsanity.com/paper/2204.02242/) (2022)
- [Initial analysis of the impact of the Ukrainian power grid synchronization with Continental Europe](https://mlsanity.com/paper/2204.07508/) (2022)

## Built on by (most cited first, 2 of 2)

- [Least Squares and Marginal Log-Likelihood Model Predictive Control using Normalizing Flows](https://mlsanity.com/paper/2409.17632/) (2024)
- [Energy-Arena: A Dynamic Benchmark for Operational Energy Forecasting](https://mlsanity.com/paper/2604.24705/) (2026)

## Abstract (arXiv)

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.