Price Information Is Not Enough: Ordering and Decision Rules in Storage Bidding

Technical Summary: Price Information Is Not Enough: Ordering and Decision Rules in Storage Bidding

Problem Statement
The literature on electricity price forecasting is extensive but evaluates forecasts almost exclusively in price units (e.g., Mean Absolute Error, Root Mean Squared Error). However, energy storage operators do not consume forecasts; they consume schedules and are paid in revenue (euros). The link between forecast accuracy (price units) and realized value (revenue) is mediated by the decision rule. This paper investigates the connection between the information content of a price signal (measured in nats) and the revenue it can generate for a price-taking storage asset. It challenges the assumption that higher information content or lower prediction error necessarily translates to higher revenue, arguing that the ordering of price intervals is the critical, often overlooked, determinant of value.

Methodology
The study employs a combination of theoretical bounds, pre-registered numerical experiments, and ordinal analysis on French day-ahead electricity prices (939 days from January 2024 to July 2026).

1. Theoretical Framework:

   • Decision Problem: A storage asset with a fixed feasible set of schedules $X$ (defined by power limits, energy capacity, and round-trip efficiency) seeks to maximize revenue $\langle x, \Pi \rangle$.
   • Information Bound: The author derives an upper bound on the revenue gain of any signal $S$ over a climatological baseline (knowing only average prices by month and hour). Using the sub-Gaussian property of prices and transport-entropy inequalities, they prove that the optimal gain is bounded by $Ls\sqrt{2I(S; \Pi | C)}$, where $L$ is daily throughput, $s$ is the sub-Gaussian scale, and $I$ is conditional mutual information.
   • Ordinal Sufficiency: On a relaxed version of the storage problem (dropping intra-day state-of-charge path constraints), the author proves that an optimal schedule depends solely on the ordering of intervals (pairing the cheapest charging intervals with the most expensive discharging intervals) and a profitability threshold, rather than the absolute magnitude of prices.

2. Experimental Design:

   • Signals: A "Gaussian garbling" family was constructed where the signal is the true price plus independent Gaussian noise ($S = \Pi + \epsilon$). The noise level ($\sigma$) was swept from 1 to 1280 EUR/MWh. This design allows for the closed-form calculation of mutual information.
   • Decision Rules: Three plug-in policies were tested:
     • Direct: Bidding the raw signal.
     • Bayes (Pooled): Linear shrinkage of the signal toward the climatological mean using a single pooled variance.
     • Bayes (Heteroscedastic): Shrinkage using variance specific to month and hour.
   • Metrics: Revenue was measured as a share of the "uplift" (the difference between perfect foresight revenue and climatological revenue).

Key Contributions

1. A Square-Root Information Bound: The paper establishes a theoretical ceiling for the value of information: $V(S|C) - V_0 \leq Ls\sqrt{2I}$. Crucially, this is an upper envelope, not a prediction of revenue for a specific policy.
2. Non-Monotonicity of Revenue: The study demonstrates that realized revenue is not monotone with respect to information content. In the tested Gaussian family, policies can destroy revenue (performing worse than ignoring the signal entirely) even when the signal contains significant information.
3. Ordinal Dominance: The paper identifies that the decision rule relies on the ordering of price intervals, not their magnitudes. Mutual information aggregates all dependence but fails to distinguish between signals that preserve the correct ordering and those that do not.
4. A New Diagnostic Metric: The author proposes a "spread-weighted rank score" ($S_R$) that weights rank agreement by the financial spread between intervals, arguing this is a more relevant metric for storage valuation than standard prediction scores.

Results

• Climatology is Powerful: A bidder knowing only the average price for a specific month and hour captures 78% of the perfect-foresight revenue (47.5 kEUR/MW-year vs. 61.1 kEUR/MW-year). The entire value of forecasting is confined to the remaining 22%.
• The Bound is Loose: The theoretical information bound is orders of magnitude higher than the actual revenue uplift achieved by any policy. It fails to discriminate between policies.
• Revenue Destruction: At residual noise levels (where the signal is still "informative" in a statistical sense), the best Gaussian-shrinkage rule achieved -46% of the uplift (i.e., it lost money compared to the climatological baseline). The direct rule performed even worse (-121%).
• Rank Agreement Explains Variance: While the logarithm of the information upper bound explains only 0.34 of the revenue variance, the mean daily rank agreement between the bid vector and the settlement price explains 0.99 of the variance.
• Sensitivity to Ordering:
  • A signal containing only the correct ranking (no cardinal price information) captured 90% of the uplift.
  • A signal with exact prices (to the cent) but with the cheapest and dearest intervals swapped lost 53% of total revenue, performing significantly worse than the climatological baseline.

Significance and Claims
The paper claims that the quantity of information (mutual information) or the magnitude of prediction error (MSE) is insufficient to value a forecast-driven storage policy. The "currency" of value for storage is ordering.

• Evaluation: Forecasts for storage should be evaluated based on the realized revenue of the induced schedule and the ordering it produces, not just price error metrics.
• Deployment Threshold: A forecast must not only beat the climatological error but must do so by a significant margin (factor of 2–4 in the tested Gaussian case) to avoid destroying revenue. A forecast that improves on climatology by only 20% in MSE may still be detrimental if it corrupts the ordering.
• Limitations: The author acknowledges that the Gaussian garbling is a designed experiment, not a model of real-world forecast errors (which are biased and heteroscedastic). However, a sensitivity test with serially correlated, heteroscedastic noise confirmed that the ordinal mechanism remains the dominant factor, even if the magnitude of revenue destruction is slightly reduced.

In conclusion, the paper argues that for storage assets, "information quantity alone does not value a forecast-driven policy; realised schedules and ordering must be evaluated explicitly." The primary constraint on value is not the amount of information, but the preservation of the correct ordinal structure of prices.