# A Probabilistic Forecast-Driven Strategy for a Risk-Aware Participation in the Capacity Firming Market: extended version

arXiv: https://arxiv.org/abs/2105.13801 · HTML: https://mlsanity.com/paper/2105.13801/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 48 references that are in the map.
- First posted on arXiv 28 May 2021.

## Builds on (most cited first, 8 of 8)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Masked Autoregressive Flow for Density Estimation](https://mlsanity.com/paper/1705.07057/) (2017)
- [Parallel WaveNet: Fast High-Fidelity Speech Synthesis](https://mlsanity.com/paper/1711.10433/) (2017)
- [Unconstrained Monotonic Neural Networks](https://mlsanity.com/paper/1908.05164/) (2019)
- [Introduction to Normalizing Flows for Lattice Field Theory](https://mlsanity.com/paper/2101.08176/) (2021)
- [A Scalable Algorithm for Two-Stage Adaptive Linear Optimization](https://mlsanity.com/paper/1807.02812/) (2018)
- [A New Approach to Electricity Market Clearing With Uniform Purchase Price and Curtailable Block Orders](https://mlsanity.com/paper/1711.07731/) (2017)

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

- [A deep generative model for probabilistic energy forecasting in power systems: normalizing flows](https://mlsanity.com/paper/2106.09370/) (2021)
- [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)

## Abstract (arXiv)

This paper addresses the energy management of a grid-connected renewable generation plant coupled with a battery energy storage device in the capacity firming market, designed to promote renewable power generation facilities in small non-interconnected grids. The core contribution is to propose a probabilistic forecast-driven strategy, modeled as a min-max-min robust optimization problem with recourse. It is solved using a Benders-dual cutting plane algorithm and a column and constraints generation algorithm in a tractable manner. A dynamic risk-averse parameters selection strategy based on the quantile forecasts distribution is proposed to improve the results. A secondary contribution is to use a recently developed deep learning model known as normalizing flows to generate quantile forecasts of renewable generation for the robust optimization problem. This technique provides a general mechanism for defining expressive probability distributions, only requiring the specification of a base distribution and a series of bijective transformations. Overall, the robust approach improves the results over a deterministic approach with nominal point forecasts by finding a trade-off between conservative and risk-seeking policies. The case study uses the photovoltaic generation monitored on-site at the University of Li`ege (ULi`ege), Belgium.