Optimal Battery Bidding under Decision-Dependent State-of-Charge Uncertainties

The gist: The uncertainty-aware formulation outperforms other constraint-tightening approaches in maximizing revenue while ensuring reliable frequency reserve provision by treating SOC uncertainty as an endogenous process within the operational strategy.

Introduction and Problem Statement

Lithium Iron Phosphate (LFP) Battery Energy Storage Systems (BESSs) are key enablers for the energy transition, but they exhibit significant inaccuracies in State of Charge (SOC) estimation which directly impact market participation. For LFP systems, SOC estimation is challenging due to the characteristic voltage plateau and significant hysteresis of their Open-Circuit Voltage (OCV) curves <ref:2604.12594#pg2>. Continued participation in ancillary services can aggravate SOC estimation errors because BESSs maintain a mid-range SOC rarely leaving the 20% to 80% SOC range <ref:2604.12594#pg2>. These inaccuracies can reach or even exceed 20% of the battery capacity, leading to suboptimal dispatch decisions and financial penalties <ref:2604.12594#pg2>. The paper investigates bidding strategies that account for SOC uncertainty by treating it as a decision-dependent process <ref:2604.12594#pg2>.

Methodology of SOC Error Modeling

The relationship between the true physical SOC, s true, and the reported value from the Battery Management System (BMS), s rep, is given by s true t = s rep t + w t <ref:2604.12594#pg3>. The estimation error w t can be modeled as wt+1 = a(s true t) · wt + p true t · η, where η ∼ N (β, σ2) is a stochastic term representing measurement bias and variability <ref:2604.12594#pg3>. The function a(s) is piecewise linear in the true SOC and reflects the characteristic of LFP batteries where estimation certainty is regained near the SOC boundaries <ref:2604.12594#pg4>. A battery model simulates the true SOC trajectory using s true t+1 = s true t + ∆t C ηch p true ch,t − η − 1dis p true dis,t <ref:2604.12594#pg4>.

Constraint-Tightening Optimization Approaches

The paper proposes three constraint-tightening optimization approaches to account for SOC uncertainty <ref:2604.12594#pg4>. These approaches are:

1. Naive, fixed-margin optimization: This approach chooses a constant constraint tightening mt = m, where choosing m ≥ wmax guarantees robust constraint satisfaction but introduces excessive conservatism <ref:2604.12594#pg5>.

2. Adaptive-margin optimization: This uses a time-dependent tightening defined by m(t) = (m(t − 1) + ¯w, if b < s(t − 1) < c, γm(t − 1) otherwise), which accounts for the fact that estimation certainty is regained near the SOC boundaries <ref:2604.12594#pg5>.

3. Uncertainty-aware optimization: This approach treats the tightening margin as dependent on dispatch decisions by introducing an uncertainty set [−δt, δt], where predicted scaling δt is a decision variable, allowing the optimizer to actively reduce constraint tightening <ref:2604.12594#pg5>.

Performance Analysis and Conclusion

The uncertainty-aware formulation performs best in terms of the trade-off between total revenue and FCR compliance. While the fixed-margin approach robustly reduces shortfall hours to zero, its conservativeness directly translates into reduced total revenue. The adaptive-margin approach is less conservative but performs worse than the uncertainty-aware optimizer over the whole region of high FCR compliance. Table II shows that the uncertainty-aware approach yields higher Total Net Revenue and FCR Revenue compared to the other two approaches. The paper concludes that treating SOC uncertainty as an endogenous process within the operational strategy allows for a more robust and revenue-maximizing bidding strategy.

Case Study Results

In the case study on the German Day-Ahead Market (DAM) and FCR market, the uncertainty-aware approach achieves compliance in more than 98% of hours with a total revenue of 786.0k€. The adaptive-margin approach maintains compliance at almost all times but results in a lower mean margin and less revenue. The uncertainty-aware approach leverages the decision-dependent nature of SOC uncertainty to accept suboptimal DAM dispatch and reduced FCR participation in certain intervals to reduce the margin in favor of future profits. This demonstrates that it is essential to introduce margins to account for SOC uncertainty in battery bidding. The underlying methodology of treating uncertainty as decision-dependent remains generalizable across different market settings and battery applications.

Conclusion

The paper demonstrates that ignoring SOC uncertainty in the bidding strategy leads to increased non-compliance with submitted bids and an increased risk of failing to sustain a worst-case activation of FCR. The uncertainty-aware constraint tightening on the SOC allows for strategic leverage of decision-dependent SOC uncertainty and planning actions to reduce it. Although all three approaches can be used effectively to robustify the bidding against SOC errors, the uncertainty-aware formulation yields higher revenues at the same compliance level than the constant or adaptive approaches. This clearly showcases the significance of incorporating decision-dependent SOC uncertainty into the operational strategy. The underlying methodology of treating uncertainty as decision-dependent remains generalizable across different market settings and battery applications.

Acknowledgments and References

This work was supported by the NCCR Automation, a National Centre of Competence in Research, funded by the Swiss National Science Foundation (grant number 51NF40 225155). The authors also wish to thank Dr. Georgios Darivianakis for his valuable support and insights throughout this project. The references listed are [1] D Koolen, M De Felice, and S Busch, “Flexibility requirements and the role of storage in future European power systems,” Publications Office of the European Union, 2023 [1], [2] M I Gonzalez Cuenca, “Overview of the energy storage deployment in Europe: an analysis of current status and policy framework on energy storage,” Publications Office of the European Union, 2025 [3] IEA, “Batteries and Secure Energy Transitions,” International Energy Agency, 2024 [4] A Oudalov, D Chartouni, and C Ohler, “Optimizing a battery energy storage system for primary frequency control,” IEEE Transactions on Power Systems, vol. 22, Aug. 2007 [5] J Figgener et al., “The development of stationary battery storage systems in Germany – A market review,” Journal of Energy Storage, vol. 29, Jun. 2020 [6] IRENA, “Innovation landscape brief: Utility-scale batteries,” International Renewable Energy Agency, 2019 [7] S Englberger, A Jossen, and H Hesse, “Unlocking the potential of battery storage with the dynamic stacking of multiple applications,” Cell Reports Physical Science, vol. 1, Nov. 2020 [8] D Jost et al., “Towards robust state estimation for LFP batteries: Model-in-the-loop analysis with hysteresis modelling and perspectives for other chemistries,” Journal of Energy Storage, vol. 92, Jul. 2024 [9] Powin and Tierra Climate, “The economic value of SOC accuracy: Quantifying revenue impacts of state-of-charge estimation in LFP battery systems,” Whitepaper, Mar. 2025 [10] K Jacque et al., “The influence of frequency containment reserve on the operational data and the state of health of the hybrid stationary large-scale storage system,” Energies, Feb. 2022 [11] T Thien et al.

1. textbfAdaptive Uncertainty Reduction Strategy for Bidding Decisions: The uncertainty-aware optimization allows the optimizer to take decisions to actively reduce the constraint tightening μt. This enables AI systems managing BESS operations to proactively steer SOC trajectories toward high or low regions, as this reduces uncertainty and narrows the margin.

2. textbfRevenue-Optimized Robustness Trade-off: The uncertainty-aware formulation performs best in terms of the trade-off between total revenue and FCR compliance. This allows AI systems to achieve a balance where they accept suboptimal DAM dispatch and reduced FCR participation in certain intervals in order to reduce the margin in favor of future profits.

3. textbf Real-time Uncertainty Quantification: By treating SOC error as decision-dependent, the system can use realized trajectories to update margins, specifically using the adaptive approach where the margin m(t) is recalibrated based on the realized trajectories before each optimization step. This allows for dynamic risk management rather than relying on a fixed or purely reactive margin.

4. textbf High-Fidelity Operational Planning: The framework enables AI systems to solve complex, time-dependent problems by integrating market constraints with SOC error dynamics within the Model Predictive Control (MPC) optimization framework. This allows the BESS controller to make hourly dispatch decisions while simultaneously managing the risk of delivery failures, including the inability to meet promised frequency reserves.

5. textbf Quantifiable Risk Assessment: The methodology provides metrics like Cumulated FCR Shortfall Energy [MWh] and Shortfall Hours (%) for different strategies. This allows AI systems to quantify operational risk precisely, enabling operators to select a strategy based on the desired level of compliance versus revenue maximization.