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

cs.LGApr 12, 2026

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

Authors: Jaime de Miguel Rodriguez, Artjom Vargunin, Brigitta Robin Raudne, David Solis Martin, Yaroslava Mykhailenko, Kaarel Oja

Organizations: Enefit, Estonia · University of Seville, Spain · University of Tartu, Estonia · Tallinn University of Technology, Estonia

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.

Figures & tables

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 as an interior profit landscape.

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

F_{1}

and

F_{2}

, 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 within the stride interval are retained (highlighted), while the remaining actions are discarded (light gray). The forecast publication interval is denoted by

(t_{F_{2}}-t_{F_{1}})

Figure 3: Illustration of the effective planning horizon under perfect information. The underlying signal (e.g., electricity prices) is shown alongside the profit achieved as a function of optimization window size. Vertical lines mark the myopic horizon (short-sighted planning), the effective planning horizon (window length beyond which additional information does not increase profit), and a redundant horizon (beyond which the window is longer than necessary).

Figure 4: Illustration of the optimal planning horizon in the presence of forecast uncertainty. Ground-truth values ( $GT$ ) and forecast values ( $F$ ) are shown along with the resulting profit as a function of optimization window size. Vertical lines indicate the effective planning horizons under perfect information for the ground truth and the forecast, and the optimal horizon, defined as the window length maximizing profit.

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.

Parameter	DA	mFRR
Non-seasonal order $(p,d,q)$	$(1,0,0)$	$(1,0,0)$
Seasonal order $(P,D,Q,s)$	$(1,0,0,24)$	$(1,0,0,24)$
AR coefficient $ar(L1)$	0.622	0.467
Seasonal AR coefficient $ar(L24)$	0.355	0.146
Innovation variance $\sigma^{2}$	160.55	254.95

Table 1: SARIMA parameters obtained for day-ahead and mFRR price signal generation models.

Dataset	Model	MAE	MSE
Day-ahead	Fourier-only	15.01	374.30
Day-ahead	Fourier + 0.5 SARIMA	15.83	395.30
Day-ahead	Fourier + 1.0 SARIMA	19.31	568.03
mFRR	Fourier-only	13.69	319.22
mFRR	Fourier + 0.5 SARIMA	15.78	410.93
mFRR	Fourier + 1.0 SARIMA	20.70	676.48

Table 2: Accuracy metrics of synthetic series versus real data. Fourier-only series capture the main daily pattern, while the SARIMA component adds variability. MAE: mean absolute error; MSE: mean squared error.

Figure 6: Day-ahead-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.

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.

Panel of 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.

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).

Type	Duration (h)	Power	Efficiency	Technology
1h Lithium-ion	1	10.00	0.95	Li-ion
2h Lithium-ion	2	5.00	0.95	Li-ion
4h Lithium-ion	4	2.50	0.93	Li-ion
6h Flow	6	1.67	0.80	Flow
8h Flow / LDES	8	1.25	0.78	Flow/LDES
24h LDES	24	0.42	0.40	LDES

Table 3: Battery configurations considered in the experiments. All systems have identical energy capacity (10 units), while power and efficiency vary to represent different storage durations and technologies.

Table 4: Optimal horizon (hours) for different battery types and forecast uncertainty factors (u.f.) of the sine wave dataset family.

Table 5: Optimal horizon (hours) for different battery types and forecast uncertainty factors (u.f.) of the day-ahead dataset family.

Table 6: Optimal horizon (hours) for different battery types and forecast uncertainty factors (u.f.) of the mFRR dataset family.

Panel of 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.

Panel of 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.

Panel of 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.

Panel of 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.

Panel of 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.

Panel of 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.

Panel of 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.

Panel of 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.

Panel of 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.

Dataset	Upper bound estimation (EUR/MWh/day)	Obtained revenue (EUR/MWh/day, $u.f.=0.1$ )
Sine wave	40.0	$\sim 6.1$
Day-ahead	37.5	$\sim 7.0$
mFRR	42.5	$\sim 10.1$

Table 7: Comparison between estimated upper-bound revenues and obtained revenues under low uncertainty (

u.f.=0.1

) for different datasets. The upper bound is derived from the total variation of the price signal, while obtained revenues correspond to optimized dispatch results.

Panel of 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 simplicity) would be approximately 9h or 10h instead of 15h. In (b), this plateau is formed after the optimal horizon affecting the effective horizon, which can be visually inferred to be around 8h instead of 34h.

Panel of 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).

Panel of 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 highlight that, under high uncertainty, even fast-response assets may exhibit unexpectedly long effective planning horizons.

Panel of 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.

Panel of 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.

Battery cycle	DA real / synthetic (h)	mFRR real / synthetic (h)
1h	6 / 6	4 / 4
2h	7 / 9	4 / 6* (8)
4h	10 / 14* (19)	5 / 6
6h	18 / 9	5 / 6
* ‘Business’ optimal horizon: denotes a shorter planning horizon that produces revenue very close to the maximum, within a negligible difference.

Table 8: Comparison of optimal planning horizons between real data and synthetic experiments (Fourier + 1.0 SARIMA). Synthetic results correspond to

u.f.=1.0

for DA and

u.f.=10.0

for mFRR.

Battery cycle (h)	DA loss (%) real / synthetic	mFRR loss (%) real / synthetic
1h	0.2 / 0.2	6.4 / 0.1
2h	9.0 / 0.5	78.7 / 0.0
4h	5.4 / 0.2	43.7 / 26.1
6h	1.0 / 13.4	34.6 / 42.3

Table 9: Comparison of revenue losses beyond the optimal planning horizon between real data and synthetic experiments (Fourier + 1.0 SARIMA).

Panel of 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.

Panel of 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.

Panel of 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.

Panel of 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.

Panel of 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.

Panel of 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.

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Decision-focused learning for optimal PV-Battery scheduling

Joris Depoortere, Hussain Kazmi, Johan Driesen

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The use of residential photovoltaics has increased dramatically in recent years. With battery systems becoming more affordable, the optimal operation of a photovoltaic-battery system can bring significant savings to households. Optimal control requires correct forecasts of underlying parameters, such as photovoltaic power generation, to schedule the battery. While forecasting models have become increasingly accurate due to algorithmic advances and data availability, accuracy is typically measured in generic metrics which might not align with the downstream application. This study proposes a decision-focused learning framework that integrates optimization and prediction by training a Long Short-Term Memory photovoltaic energy forecaster on the downstream optimal scheduling of a battery system. The proposed methodology is compared against a standard two-phase approach. Across a 14-month evaluation period, the decision-focused method reduced average electricity costs across twenty buildings by 3.6% when normalized against performance bounds defined by a perfect forecast and a baseline of no optimization. Critically, this financial improvement was achieved despite the model exhibiting a root mean squared error of 19.9%, significantly higher than the decoupled model's 8.2%. Warm-starting the decision-focused model further improves results, lowering average cost by approximately 8%, while also mitigating the negative impact on statistical accuracy (root mean squared error of 13.7%). The findings are statistically significant at the 0.001 level across the twenty households and for each household individually. These results demonstrate that aligning forecast models with optimization goals is key for achieving cost advantages in PV-battery systems. Future research should replicate these findings on other datasets, alternate forecasting models and alternate optimization algorithms.

Abstract

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