Betting vs. Trading: Learning a Linear Decision Policy for Selling Wind Power and Hydrogen

TL;DR

This paper tackles risk management in day-ahead bidding for a hybrid wind-electrolyzer power plant under single imbalance pricing, where conventional strategies yield all-or-nothing betting. It introduces data-driven linear decision policies that map contextual features to both power bids and hydrogen production, supplemented by explicit risk constraints to transform betting into diversified trading. The framework trains policies from historical data, constructs bidding curves for testing, and includes a feasibility restoration step to ensure actionable decisions. Empirical results show that risk-constrained trading achieves robust, diversified trading decisions and approaches the performance of an oracle with perfect foresight, with only minor differences across different risk constraints and grid-buying conditions, indicating practical applicability.

Abstract

We develop a bidding strategy for a hybrid power plant combining co-located wind turbines and an electrolyzer, constructing a price-quantity bidding curve for the day-ahead electricity market while optimally scheduling hydrogen production. Without risk management, single imbalance pricing leads to an all-or-nothing trading strategy, which we term 'betting'. To address this, we propose a data-driven, pragmatic approach that leverages contextual information to train linear decision policies for both power bidding and hydrogen scheduling. By introducing explicit risk constraints to limit imbalances, we move from the all-or-nothing approach to a 'trading" strategy', where the plant diversifies its power trading decisions. We evaluate the model under three scenarios: when the plant is either conditionally allowed, always allowed, or not allowed to buy power from the grid, which impacts the green certification of the hydrogen produced. Comparing our data-driven strategy with an oracle model that has perfect foresight, we show that the risk-constrained, data-driven approach delivers satisfactory performance.

Figures (5)

• Figure 1: The overall framework of the proposed model: The feature vector $\mathbf{x}_t$ and the uncertainty realization vector $\mathbf{y}_t$ during the training period $t \in \mathcal{H}^{\rm{train}}$ are used to determine the optimal linear policies for power trading ($\mathbf{q}^{\rm{DA}}$) and hydrogen scheduling ($\mathbf{q}^{\rm{H}}$). In the testing period $\tau \in \mathcal{H}^{\rm{test}}$, a subset of the feature vector, $\Breve{\mathbf{x}}_\tau$, is used to construct a bidding curve (power trade as a function of day-ahead electricity price) to be submitted to the day-ahead market, as well as to determine the hydrogen production schedule. If these outcomes are infeasible during testing, a feasible solution is restored. Once the realizations $\mathbf{y}_\tau$ of wind power production, day-ahead prices, and imbalance prices are available during the testing phase, the accepted power bid $\hat{p}_\tau^{\rm{DA}}$, the hydrogen schedule $\hat{p}_\tau^{\rm{H}}$ and the final profit are calculated.
• Figure 2: Bidding curve examples: Plot (a) illustrates the transition from one price domain $k$ to the next price domain $k+1$. Plot (b) shows the discretization (gray triangles) of the bidding function (\ref{['eq:12']}) and the resulting bidding curve (orange). Plot (c) visualizes the feasibility restoration of the resulting bidding curves. The original curve (black) is modified to stay within the feasible space for the different models $\mathcal{T}$, $\mathcal{T}^{\rm{res}}$, and $\mathcal{T}^{\rm{cond}}$.
• Figure 3: The distribution of realized hourly trades $\hat{p}_\tau^{\rm{DA}}$ made by the HPP operator under models $\mathcal{B}$ (plot a) and $\mathcal{T}_{\rm{CVaR}}$ (plot b) is shown for three hydrogen prices: €2/kg, €4/kg, and €6/kg. Plots (a) and (b) display the results obtained from the proposed learning method, while plots (c) and (d) show the results in hindsight, assuming perfect foresight into future realizations.
• Figure 4: Impact of hydrogen price on the profit obtained in both the training and testing phases, as a percentage of the profit in hindsight, for the trading model $\mathcal{T}_{\rm{CVaR}}$.
• Figure 5: Comparison of all nine trading models in terms of their profit during the testing period divided by their profit in hindsight.