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arxiv: 2604.15360 · v2 · submitted 2026-04-12 · 💻 cs.LG · cs.SY· eess.SY

Mapping High-Performance Regions in Battery Scheduling across Data Uncertainty, Battery Design, and Planning Horizons

Jaime de Miguel Rodriguez , Artjom Vargunin , Brigitta Robin Raudne , David Solis Martin , Yaroslava Mykhailenko , Kaarel Oja This is my paper

Pith reviewed 2026-05-10 15:06 UTC · model grok-4.3

classification 💻 cs.LG cs.SYeess.SY
keywords battery schedulingforecast uncertaintyplanning horizonenergy arbitragemodel predictive controlsynthetic datarevenue optimizationparametric analysis
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The pith

Greater forecast uncertainty systematically shortens the optimal planning horizon for battery scheduling in energy arbitrage across different designs.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper builds a parametric method to create synthetic energy price signals and run multi-stage predictive control simulations for battery arbitrage. It explores how battery specifications, price signal patterns, levels of forecast error, and the length of the planning window interact to determine revenue. If the patterns hold, it would let operators pick planning lengths that avoid unnecessary computation while limiting revenue loss from bad forecasts. The analysis reveals that as forecast reliability drops, the best horizon length decreases consistently for all tested battery types. Comparisons to actual market data confirm that the main trends appear in real settings as well.

Core claim

The study presents a controlled parametric framework for analyzing energy storage planning under uncertainty in a multi-stage model predictive control setting. Through parametrized generation of synthetic datasets in energy price arbitrage, it characterizes the joint effects of battery characteristics, signal structure, forecast uncertainty, and planning horizon on operational revenue. The central discovery is that increasing forecast uncertainty systematically reduces the optimal planning horizon across battery types, reflecting the diminishing value of long-term information under unreliable forecasts. The framework provides meaningful guidance for horizon selection and a compact parametriz

What carries the argument

Parametrized synthetic dataset generation within a multi-stage model predictive control model for energy price arbitrage, which maps the dependencies between battery properties, data features, uncertainty levels, and horizon performance.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Such mappings could support the development of adaptive algorithms that select planning horizons dynamically based on observed forecast quality.
  • Battery designers might use these insights to prioritize characteristics that perform well under short-horizon constraints.
  • The method offers a way to test planning strategies for new energy markets without access to proprietary data.

Load-bearing premise

The synthetic dataset generation and multi-stage model accurately reflect the real combined effects of battery characteristics, price signal structure, and forecast uncertainty.

What would settle it

Collecting data from actual battery operations in energy markets and verifying whether optimal planning horizons decrease as forecast uncertainty increases in a similar systematic manner.

Figures

Figures reproduced from arXiv: 2604.15360 by Artjom Vargunin, Brigitta Robin Raudne, David Solis Martin, Jaime de Miguel Rodriguez, Kaarel Oja, Yaroslava Mykhailenko.

Figure 1
Figure 1. Figure 1: Diagram illustrating the interplay between battery design parameters (e.g., C-rate and charge efficiency), data and uncertainty characteristics (underlying signal amplitude, frequency and phase, combined with stochastic forecast errors), and the planning horizon length used in the MPC optimization. Different combinations within this triangular space give rise to different profit levels, conceptualized here… view at source ↗
Figure 2
Figure 2. Figure 2: Rolling-horizon Model Predictive Control (MPC) scheme with overlapping optimization windows. Two consecutive optimization runs (optimization window 1 and 2) are shown, using forecast inputs F1 and F2, respectively, and ground-truth values GT. The windows are shifted forward by a stride shorter than the optimization horizon, resulting in overlapping action sequences {x 1 n} and {x 2 n}. Only the actions wit… view at source ↗
Figure 3
Figure 3. Figure 3: considers an idealized setting in which the optimization algorithm has access to agnostic (i.e., perfect or uncertainty-free) future values of the underlying signal, such as electricity prices or net demand. On the same timeline, we report the total profit obtained by solving the rolling-horizon optimization problem for increasing sizes of the optimization window. effective horizon (t) Profit GT myopic hor… view at source ↗
Figure 4
Figure 4. Figure 4: extends this reasoning to the realistic case in which future values are not known perfectly but are instead provided through forecasts. The figure shows the same underlying ground-truth signal (GT), a corresponding forecast (F), and the resulting profit as a function of the optimization window size. optimal horizon (t) F GT Profit effective horizon (GT) effective horizon (F) horizon uncertainty gap [PITH_… view at source ↗
Figure 5
Figure 5. Figure 5: Synthetic sine-wave dataset illustrating the three ground truth signal variants used in the experiments: the undistorted base sine-wave signal, a day-ahead distorted version, and an mFRR distorted version. constructed from both sub-markets: mFRR-up and mFRR-down, by combining the two signals according to their activation volumes. Each family includes three instances formulated as signal = F ourier + α · SA… view at source ↗
Figure 6
Figure 6. Figure 6: Day-ahead-inspired series illustrating the three reconstruction approaches: the Fourier-only series (cap￾turing daily phase harmonics), the hybrid series with Fourier + 0.5 SARIMA, and the hybrid series with Fourier + 1.0 SARIMA [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: mFRR-inspired series illustrating the three reconstruction approaches: the Fourier-only series (capturing daily phase harmonics), the hybrid series with Fourier + 0.5 SARIMA, and the hybrid series with Fourier + 1.0 SARIMA. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Mean Absolute Error (MAE) between ground truth and forecast curves for both synthetic and real datasets over a 24h span. Left: day-ahead (DA) series with an uncertainty factor of 1.0; right: mFRR series with an uncertainty factor of 10.0. values are chosen such that u.f. = 1.0 approximately matches the uncertainty level observed in real day-ahead forecasts over a 24-hour time span, while u.f. = 10.0 corres… view at source ↗
Figure 9
Figure 9. Figure 9: Example of forecast curve for uncertainty factor (u.f.) = 1.0. The image shows one forecast of the day-ahead series (Fourier + 1.0 SARIMA) [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Optimal planning horizon and revenue results by battery c-rate and forecast variance factor (uncertainty level) of the sine wave dataset family. (a) DA, Fourier-only. (b) DA, Fourier + 0.5 SARIMA. (c) DA, Fourier + 1.0 SARIMA [PITH_FULL_IMAGE:figures/full_fig_p021_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Optimal planning horizon and revenue results by battery c-rate and forecast variance factor (uncertainty level) of the day-ahead dataset family. (a) mFRR, Fourier-only. (b) mFRR, Fourier + 0.5 SARIMA. (c) mFRR, Fourier + 1.0 SARIMA [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Optimal planning horizon and revenue results by battery c-rate and forecast variance factor (uncertainty level) of the mFRR dataset family. 21 [PITH_FULL_IMAGE:figures/full_fig_p021_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Sine wave with day-ahead SARIMA distortion dataset: revenue as a function of planning horizon length for four battery configurations with cycle times of 1h, 2h, 4h, and 6h (as indicated in the plots). Each curve corresponds to a different forecast uncertainty factor. All results are based on rolling forecasts with a 3-hour publishing interval [PITH_FULL_IMAGE:figures/full_fig_p022_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Sine wave with mFRR SARIMA distortion dataset: revenue as a function of planning horizon length for four battery configurations with cycle times of 1h, 2h, 4h, and 6h (as indicated in the plots). Each curve corresponds to a different forecast uncertainty factor. All results are based on rolling forecasts with a 3-hour publishing interval. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Day-ahead + 1.0 SARIMA dataset: revenue as a function of planning horizon length for four battery configurations with cycle times of 1h, 2h, 4h, and 6h (as indicated in the plots). Each curve corresponds to a different forecast uncertainty factor. All results are based on rolling forecasts with a 3-hour publishing interval [PITH_FULL_IMAGE:figures/full_fig_p023_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: mFRR + 1.0 SARIMA dataset: revenue as a function of planning horizon length for four battery configurations with cycle times of 1h, 2h, 4h, and 6h (as indicated in the plots). Each curve corresponds to a different forecast uncertainty factor. All results are based on rolling forecasts with a 3-hour publishing interval. 23 [PITH_FULL_IMAGE:figures/full_fig_p023_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Day-ahead (left) and mFRR (right) Fourier + 0.5 SARIMA datasets: revenue as a function of planning horizon length for a battery configuration with cycle time of 1h. Each curve corresponds to a different forecast uncertainty factor. All results are based on rolling forecasts with a 3-hour publishing interval. When these same values are compared for larger uncertainty factors, the ratios decrease even furth… view at source ↗
Figure 18
Figure 18. Figure 18: Day-ahead (left) and mFRR (right) Fourier + 0.5 SARIMA datasets: revenue as a function of planning horizon length for a battery configuration with a cycle time of 1h and an uncertainty factor of 3.0. The revenue drop due to uncertainty is defined as the relative decrease from the maximum revenue. As expected, when running the optimizations using Fourier-only ground truth signals (i.e., without SARIMA comp… view at source ↗
Figure 19
Figure 19. Figure 19: Illustration of plateau effects in revenue as a function of planning horizon: (a) mFRR market, and (b) Day-ahead market, both under Fourier + 1 SARIMA models. In (a), the revenue curve exhibits a broad plateau around the maximum, indicating that shorter horizons can achieve near-optimal performance. This suggests that a ‘business’ optimal horizon (trading off marginal revenue gains against operational sim… view at source ↗
Figure 20
Figure 20. Figure 20: Two examples of effective horizons in 4h batteries, (a) Sine wave with mFRR distortion and u.f. = 3.0, and (b) mFRR with Fourier + 1.0 SARIMA and u.f. = 0.1. In both cases, despite the wide difference in uncertainty factors (3.0 vs. 0.1), quite long effective planning horizons are observed in 4h batteries, reaching 26h in (a) and 29h in (b). (a) Sine wave + day-ahead SARIMA distortion. (b) Day-ahead, Four… view at source ↗
Figure 21
Figure 21. Figure 21: Two examples of unusually long effective planning horizons for fast batteries under high uncertainty conditions (u.f. = 10): (a) 1h battery and (b) 2h battery. In (a), the effective horizon exceeds the study bound (36 h), while in (b) it remains within but still significantly extended. These effects appear as isolated irregularities in the revenue curves and are not representative in frequency, yet they h… view at source ↗
Figure 22
Figure 22. Figure 22: Revenue as a function of planning horizon under low uncertainty (u.f. = 1.0): (a) mFRR dataset for a 2h battery, and (b) day-ahead dataset for a 4h battery, both using Fourier + 0.5 SARIMA. In both cases, noticeable declines in revenue are observed beyond the optimal horizon, leading to moderate losses for the 2h battery and more sizeable losses for the 4h battery. However, for u.f. ≥ 3.0, revenue degrada… view at source ↗
Figure 23
Figure 23. Figure 23: Revenue as a function of planning horizon under moderate uncertainty (u.f. = 3.0): (a) sine wave with mFRR distortion dataset for a 2h battery, and (b) the same dataset for a 4h battery. In both cases, noticeable declines in revenue are observed beyond the optimal horizon, leading to moderate losses for both batteries. In practice, the performance of very fast batteries may also be constrained by operatio… view at source ↗
Figure 24
Figure 24. Figure 24: Day-ahead dataset with real ground truth and forecasts: revenue as a function of planning horizon length for four battery configurations with cycle times of 1h, 2h, 4h, and 6h (as indicated in the plots). All results are based on rolling forecasts with a 3-hour publishing interval [PITH_FULL_IMAGE:figures/full_fig_p033_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: mFRR dataset with real ground truth and forecasts: revenue as a function of planning horizon length for four battery configurations with cycle times of 1h, 2h, 4h, and 6h (as indicated in the plots). All results are based on rolling forecasts with a 3-hour publishing interval. 7 Conclusions and future work This work has introduced a methodological framework for analysing planning horizon selection in roll… view at source ↗
Figure 26
Figure 26. Figure 26: Sine wave + day-ahead SARIMA distortion dataset: revenue as a function of planning horizon length for four battery configurations with cycle times of 1h, 2h, 4h, and 6h (as indicated in the plots). Each curve corresponds to a different forecast uncertainty factor. All results are based on rolling forecasts with a 6-hour publishing interval [PITH_FULL_IMAGE:figures/full_fig_p041_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Sine wave + mFRR SARIMA distortion dataset: revenue as a function of planning horizon length for four battery configurations with cycle times of 1h, 2h, 4h, and 6h (as indicated in the plots). Each curve corresponds to a different forecast uncertainty factor. All results are based on rolling forecasts with a 6-hour publishing interval. 41 [PITH_FULL_IMAGE:figures/full_fig_p041_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: Day-ahead + 1.0 SARIMA dataset: revenue as a function of planning horizon length for four battery configurations with cycle times of 1h, 2h, 4h, and 6h (as indicated in the plots). Each curve corresponds to a different forecast uncertainty factor. All results are based on rolling forecasts with a 6-hour publishing interval [PITH_FULL_IMAGE:figures/full_fig_p042_28.png] view at source ↗
Figure 29
Figure 29. Figure 29: mFRR + 1.0 SARIMA dataset: revenue as a function of planning horizon length for four battery configurations with cycle times of 1h, 2h, 4h, and 6h (as indicated in the plots). Each curve corresponds to a different forecast uncertainty factor. All results are based on rolling forecasts with a 6-hour publishing interval. 42 [PITH_FULL_IMAGE:figures/full_fig_p042_29.png] view at source ↗
read the original abstract

This study presents a controlled parametric framework for analyzing energy storage planning under uncertainty in a multi-stage model predictive control setting. The framework enables a broad and systematic exploration through parametrized generation of synthetic datasets in the context of energy price arbitrage. It facilitates the study of the joint effects of battery characteristics, signal structure, forecast uncertainty, and planning horizon on revenue performance in energy storage optimization, which are rarely considered together. The analysis is driven by two objectives. First, it characterizes how these interacting factors influence operational revenue and its sensitivity to planning horizon selection, including economic losses caused by deviations from optimal horizons. This provides guidance on expected horizon ranges and their impact on revenue and computational cost. Second, it enables a compact parametrization of the relationships between battery properties, data characteristics, forecast uncertainty, and horizon-dependent performance, providing a basis for future modelling of optimal planning horizon length. Results show that the framework captures consistent structural dependencies across configurations and provides meaningful guidance for horizon selection under uncertainty. In particular, increasing forecast uncertainty systematically reduces the optimal planning horizon across battery types, reflecting the diminishing value of long-term information under increasingly unreliable forecasts. Comparison with real market data shows that the parametrization reproduces the main qualitative trends of optimal horizon behavior, suggesting its potential as a lightweight surrogate for more complex simulation-based analysis.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces a parametric framework that uses synthetic dataset generation to systematically explore the joint effects of battery characteristics, price signal structure, forecast uncertainty, and planning horizon length on revenue in multi-stage MPC for energy price arbitrage. It reports that increasing forecast uncertainty consistently shortens the optimal planning horizon across battery types, provides guidance on horizon selection and associated revenue/computational trade-offs, and shows qualitative agreement with trends in real market data, positioning the approach as a lightweight surrogate for more complex analyses.

Significance. If the synthetic generation process accurately reflects real joint distributions, the work offers practical value for selecting planning horizons under uncertainty in battery scheduling and a compact parametrization that could support future surrogate modeling. The systematic coverage of interacting factors (rarely studied together) is a positive contribution to the energy storage optimization literature.

major comments (2)
  1. [Methods (synthetic data generation)] Methods section on synthetic dataset generation: the process for generating price signals, injecting forecast uncertainty, and coupling these with battery parameters is not shown to be free of confounding structure (e.g., implicit coupling of uncertainty magnitude to autocorrelation or variance). This is load-bearing for the central claim that uncertainty systematically reduces optimal horizon, because an artifact in the generation procedure could produce the reported monotonic relationship rather than reflecting real market dynamics.
  2. [Results and validation] Results and validation sections: the headline result and guidance for horizon selection rest on qualitative trend matching to real market data only, with no quantitative metrics (error bars, R² values, sensitivity sweeps over generation hyperparameters, or out-of-sample real-data horizon computations) reported. This weakens the claim that the framework 'reproduces the main qualitative trends' sufficiently to generalize beyond the tested configurations.
minor comments (2)
  1. [Methods] Notation for the multi-stage MPC formulation and uncertainty parametrization could be clarified with an explicit equation or table summarizing all free parameters and their ranges.
  2. [Abstract and Conclusions] The abstract states that the framework 'enables a compact parametrization' of relationships, but the main text does not detail the functional form or fitting procedure used to obtain it.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed comments, which help clarify the robustness of our framework. We respond to each major comment below, indicating planned revisions.

read point-by-point responses

  1. Referee: [Methods (synthetic data generation)] Methods section on synthetic dataset generation: the process for generating price signals, injecting forecast uncertainty, and coupling these with battery parameters is not shown to be free of confounding structure (e.g., implicit coupling of uncertainty magnitude to autocorrelation or variance). This is load-bearing for the central claim that uncertainty systematically reduces optimal horizon, because an artifact in the generation procedure could produce the reported monotonic relationship rather than reflecting real market dynamics.

    Authors: We acknowledge the referee's concern regarding potential confounding in the synthetic generation process. The framework parametrizes price signal generation independently via controllable parameters for mean, variance, and autocorrelation structure, with forecast uncertainty introduced as additive scaled noise that does not modify the base signal statistics. To address this explicitly, we will revise the Methods section to provide the full algorithmic description of the generation procedure and include empirical verification (such as pairwise correlation analyses across uncertainty levels and signal properties) confirming independence. This addition will directly support that the observed reduction in optimal horizon with increasing uncertainty arises from the modeled dynamics rather than generation artifacts. revision: yes

  2. Referee: [Results and validation] Results and validation sections: the headline result and guidance for horizon selection rest on qualitative trend matching to real market data only, with no quantitative metrics (error bars, R² values, sensitivity sweeps over generation hyperparameters, or out-of-sample real-data horizon computations) reported. This weakens the claim that the framework 'reproduces the main qualitative trends' sufficiently to generalize beyond the tested configurations.

    Authors: We agree that incorporating quantitative metrics would provide stronger validation for the generalization claims. The manuscript prioritizes qualitative trend matching to illustrate the framework's utility in capturing directional behaviors across configurations. In the revision, we will augment the Results and validation sections with error bars on key plots, R² values quantifying the uncertainty-horizon relationship, sensitivity sweeps over generation hyperparameters to demonstrate robustness, and additional out-of-sample horizon computations on real market data. These changes will offer a more rigorous quantitative foundation while preserving the focus on practical guidance. revision: yes

Circularity Check

0 steps flagged

No significant circularity; simulation results are independent of inputs

full rationale

The paper conducts a forward simulation study using parametrized synthetic price signals, injected forecast uncertainty, and multi-stage MPC optimization to map performance across battery designs, uncertainty levels, and horizons. Key observations (e.g., uncertainty shortening optimal horizons) are outputs of these numerical experiments rather than algebraic identities or parameters fitted to the target quantities and then relabeled as predictions. No equations reduce to their own inputs by construction, no load-bearing self-citations close the argument, and the qualitative match to real market data is presented as external corroboration rather than internal validation. The framework therefore remains self-contained against its own generation process.

Axiom & Free-Parameter Ledger

3 free parameters · 1 axioms · 0 invented entities

Based on abstract only; the framework relies on standard MPC assumptions and tunable parameters for synthetic data and battery specs, but exact free parameters and their selection process are not detailed.

free parameters (3)
  • synthetic dataset generation parameters
    Control variations in price signal structure and forecast uncertainty levels
  • battery design parameters
    Varied to map effects on revenue across different characteristics
  • planning horizon values
    Swept to study sensitivity and identify high-performance regions
axioms (1)
  • domain assumption Standard assumptions of multi-stage model predictive control for energy arbitrage
    The framework operates within an MPC setting without stating deviations from common formulations

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