Optimal Intraday Power Trading for Single-Price Balancing Markets: An Adaptive Risk-Averse Strategy using Mixture Models

TL;DR

This work tackles profitable intraday trading in single-price imbalance markets by forecasting the future system imbalance price with a two-component mixture model that separates down- and up-regulation prices and modulates their probabilities with a logistic mixture weight. It then converts these probabilistic forecasts into intraday trading decisions through a risk-averse stochastic optimization that accounts for the price impact of trades via a market-reactivity parameter and price sensitivities, using coherent risk measures with online adaptive tuning of the risk level $\alpha$. The approach is validated on Belgian market data, showing that the mixture model outperforms implicit and explicit benchmarks across probabilistic metrics and that the adaptive risk-parameter strategy yields higher absolute profits with fewer trades, even under misestimated market impact. The results highlight the practical importance of incorporating both price impact and prediction uncertainty in intraday trading, and the analysis discusses real-world extensions (deadbands, shared reserves) and potential extensions to dual-price or ex-post markets.

Abstract

Efficient markets are characterised by profit-driven participants continuously refining their positions towards the latest insights. Margins for profit generation are generally small, shaping a difficult landscape for automated trading strategies. This paper introduces a novel intraday power trading strategy tailored for single-price balancing markets. The strategy relies on a strategically devised mixture model to forecast future system imbalance prices and is formulated as a stochastic optimization problem with decision-dependent distributions to address two primary challenges: (i) the impact of trading positions on the system imbalance price and (ii) the uncertainty inherent in the model. The first challenge is tackled by adjusting the model to account for price changes after taking a position. For the second challenge, a coherent risk measure is added to the cost function to take additional uncertainties into account. This paper introduces a methodology to select the tuning parameter of this risk measure adaptively by continuously quantifying the performance of the strategy on a window of recently observed data. The strategy is validated with a simulation on the Belgian electricity market using real-time market data. The adaptive tuning approach leads to higher absolute profits, while also reducing the number of trades.

Figures (10)

• Figure 1: System imbalance price and volume in Belgium on May 26 2023. Depending on the sign of the system imbalance volume $s_t$, the system imbalance price $p^{\mathrm{SI}}_t$ continuously alternates between the upregulation and downregulation price. This data has been obtained from the Belgian TSO Elia.
• Figure 2: A sketch of the pdf of the future system imbalance prices $f^{\mathrm{SI}}_t$. Using a mixture model, we relieve the model from having to predict this bimodal distribution directly. Instead, we predict the regulation price distributions $f^{\mathrm{MDP}}_t$ and $f^{\mathrm{MIP}}_t$ separately, and combine these together with the mixture weight $\pi_t$.
• Figure 3: A visual representation of the price model. The softmax operation ensures that $\boldsymbol{w}(\boldsymbol{z}_t)$ represents a valid probability distribution, with nonnegative elements that sum to one. This probability vector is then multiplied with the order book prices $\boldsymbol{o}_t$ to obtain a prediction of the regulation price $g(\boldsymbol{z}_t, \boldsymbol{o}_t)$.
• Figure 4: The average regulation price for different system imbalance volumes on the Belgian balancing market between May 2021 and May 2023. The sensitivity of the regulation prices to the system imbalance volume is approximated by fitting two linear slopes. This seems like a reasonable approximation.
• Figure 5: The average historical absolute loss of the strategy over the past $N=500$ trading periods for different values of $\alpha$ (cost function of Eq. \ref{['eq:opt-alpha']}) on the test set of the case study on 2023-06-26 18:30. Negative values indicate profits. For both strategies, the naive approach ($\alpha=1$) results in suboptimal returns. The adaptive trading strategy chooses $\alpha_{t+1}$ as the minimizer of this function.

Theorems & Definitions (2)

• Proposition
• proof