Online Energy Storage Arbitrage under Imperfect Predictions: A Conformal Risk-Aware Approach

TL;DR

The paper tackles the challenge of downside risk in online energy storage arbitrage arising from imperfect price forecasts. It develops a conformal risk-aware controller that online-calibrates decision conservativeness using prediction sets, with the temporal-difference error serving as a practical proxy for unobservable value error. Two online calibration strategies—prediction-error-based and value-error-based—are proposed, each with convergence guarantees and an eventual safety property, allowing risk control without distributional assumptions. Case studies with real NYISO data show that the conformal approaches balance risk and opportunity, recovering substantial profits under poor forecasts while remaining competitive when forecasts are accurate. The framework offers a scalable, online, distribution-free approach that can extend to broader sequential decision problems under uncertainty in energy systems and beyond.

Abstract

This work proposes a conformal approach for energy storage arbitrage to control the downside risk arising from imperfect price forecasts. Energy storage arbitrage relies solely on predictions of future market prices, while inaccurate price predictions may lead to significant profit losses. Based on conformal decision theory, we describe a controller that dynamically adjusts decision conservativeness through prediction sets without distributional assumptions. To enable online calibration when online profit loss feedback is unobservable, we establish that a temporal difference error serves as a measurable proxy. Building on this insight, we develop two online calibration strategies: prediction error-based adaptation targeting forecast accuracy, and value error-based calibration focusing on decision quality. Analysis of the conformal controller proves bounded long-term risk with convergence guarantees in temporal difference error, which further effectively manages risk exposure in potential profit losses. Case studies demonstrate superior performance in balancing risk and opportunity compared to benchmarks under varying forecast conditions.

Figures (8)

• Figure 1: A flowchart of the proposed conformal risk-aware energy storage arbitrage strategy.
• Figure 2: Marginal opportunity valuation and energy storage arbitrage decision-making using conformal prediction set $P = 0.5 MW$, $E = 1.0 MWh$
• Figure 3: Single time step decision-making and value analysis given various marginal opportunity value function forecast accuracy ($P = 0.5 MW$, $E = 1.0 MWh$).
• Figure 4: Arbitrage performance comparison across different algorithms under varying opportunity value function forecast accuracy (measured by $R^2$): Offline Optimal represents the optimum assuming perfect knowledge; Risk Neutral deploys \ref{['eq:arbitrage']}; CVaR sets risk scaling factor $\mu=1$; Chance Constrained assumes $\lambda_t$ following normal distribution and sets threshold $\Gamma=0.6$; Robust Optimization estimates an ellipsoid uncertainty set and sets threshold $\Gamma=1.0$; Switching Cost sets the penalty factor $\zeta=400$; CC--prediction err sets the mapping function with $\hat{\gamma} = 3.0$ and $k=0.1$; both CC--prediction err and CC--value err set $\rho = 0.001$ and $\sigma = 10$.
• Figure 5: Daily dispatch decisions comparing risk-neutral baseline and proposed conformal risk-aware strategies for good-accuracy ($R^2 = 0.4$) and poor-accuracy ($R^2 = -0.4$) forecasters.

Theorems & Definitions (15)

• Remark 1
• Remark 2
• Definition 1: Eventually Safe Dispatch
• Theorem 1: Conformal Controller for Storage Arbitrage
• Proposition 1
• Remark 3
• Proposition 2
• Definition 2: Temporal Prediction Error
• Proposition 3
• Definition 3: Temporal Value Error