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arxiv: 2507.04813 · v2 · submitted 2025-07-07 · 📡 eess.SY · cs.SY

Accounting for Subsystem Aging Variability in Battery Energy Storage System Optimization

Melina Graner , Martin Cornejo , Holger Hesse , Andreas Jossen This is my paper

Pith reviewed 2026-05-19 06:46 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords battery energy storageaging variabilityoptimization frameworkenergy arbitragedegradation costmulti-string systemsSOH losssubsystem modeling
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The pith

Accounting for varying aging in battery strings improves revenue per capacity loss by 21% in energy arbitrage.

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

This paper shows that optimization for battery energy storage systems performs better when it accounts for different aging rates among individual strings and includes the cost of aging in the decisions. A reader would care because real systems have unevenly aged parts, and ignoring that can create schedules that cannot be followed and lower overall earnings. The work compares four different ways of modeling this and finds that the most detailed approach, using exact string models and aging costs, gets 21% more money for each unit of state-of-health lost than the simple baseline. This matters especially for systems that will run for many years.

Core claim

The fully informed scenario, which combines aging-cost-aware optimization with precise string-level modeling, achieves 21% higher revenue per unit of SOH loss compared to the baseline scenario. Ignoring heterogeneity of subunits may lead to infeasible dispatch plans and reduced revenues, while accurate representation of degraded subsystems and consideration of aging costs improves operational accuracy and economic efficiency.

What carries the argument

The degradation-cost-aware optimization framework that evaluates four scenarios varying in model precision and aging cost treatment for multi-string battery systems.

If this is right

  • Ignoring subunit aging heterogeneity leads to infeasible dispatch plans and reduced revenues.
  • Combining precise string-level modeling with aging costs in the objective function improves both accuracy and efficiency.
  • The fully informed approach yields 21% higher revenue per unit of SOH loss.
  • Modeling aging heterogeneity supports better long-term asset value in extended BESS operations.

Where Pith is reading between the lines

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

  • Similar modeling of component variability could improve optimization in other distributed energy resources.
  • Real deployments may benefit from sensors that track individual string aging to enable these gains.
  • Market designs that reward longevity might encourage adoption of such detailed models.

Load-bearing premise

The four scenarios represent the typical range of modeling choices used in actual operations and that the simulated market and degradation behave like real battery systems.

What would settle it

Comparing the revenue per SOH loss from a real multi-string BESS running the fully informed optimization versus a baseline on the same hardware and market data.

Figures

Figures reproduced from arXiv: 2507.04813 by Andreas Jossen, Holger Hesse, Martin Cornejo, Melina Graner.

Figure 1
Figure 1. Figure 1: The proposed simulation framework for evaluating the influence of [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Depiction of the different model accuracies in the scenarios. String [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Exemplary day of operation: SOC trajectories for strings A and B [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Cumulative revenues and SOH degradation of strings A and B [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Cumulative revenues and SOH degradation of strings A and B in [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
read the original abstract

This paper presents a degradation-cost-aware optimization framework for multi-string battery energy storage systems, emphasizing the impact of inhomogeneous subsystem-level aging in operational decision-making. We evaluate four scenarios for an energy arbitrage scenario, that vary in model precision and treatment of aging costs. Key performance metrics include operational revenue, power schedule mismatch, missed revenues, capacity losses, and revenue generated per unit of capacity loss. Our analysis reveals that ignoring heterogeneity of subunits may lead to infeasible dispatch plans and reduced revenues. In contrast, combining accurate representation of degraded subsystems and the consideration of aging costs in the objective function improves operational accuracy and economic efficiency of BESS with heterogeneous aged subunits. The fully informed scenario, which combines aging-cost-aware optimization with precise string-level modeling, achieves 21% higher revenue per unit of SOH loss compared to the baseline scenario. These findings highlight that modeling aging heterogeneity is not just a technical refinement but may become a crucial enabler for maximizing both short-term profitability and long-term asset value in particular for long BESS usage scenarios.

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

3 major / 2 minor

Summary. The manuscript presents a degradation-cost-aware optimization framework for multi-string battery energy storage systems (BESS) that accounts for inhomogeneous subsystem aging. It evaluates four scenarios in an energy arbitrage setting that differ in model precision and treatment of aging costs. Key metrics include operational revenue, power schedule mismatch, and revenue per unit of SOH loss. The central claim is that the fully informed scenario (aging-cost-aware optimization combined with string-level modeling) achieves 21% higher revenue per unit of SOH loss compared to the baseline, and that ignoring heterogeneity can lead to infeasible dispatch plans.

Significance. If the simulation results prove robust, the work is significant for BESS operations because it isolates the economic impact of modeling aging variability at the string level. The scenario-based comparison provides a clear way to quantify trade-offs between modeling fidelity and performance, which could guide operators managing long-duration assets where capacity fade directly affects value.

major comments (3)
  1. [Abstract and Results] Abstract and Results section: The 21% revenue-per-SOH-loss improvement is reported as the key quantitative outcome, yet no sensitivity analysis is shown with respect to the market price series, the parameters of the inhomogeneous aging model, or the string-to-string variability distribution. Because the central claim that heterogeneity modeling is a 'crucial enabler' rests on this single simulated arbitrage market, the absence of such sweeps is load-bearing for the broader conclusion.
  2. [Methods] Methods section: The performance metric 'revenue per unit of SOH loss' is constructed from the same degradation model that is embedded in the optimization objective for the aging-cost-aware scenarios. This creates a circularity risk; the reported gain may partly reflect the chosen functional form of capacity fade rather than an independent validation of the modeling approach.
  3. [Results] Results section: The four scenarios are presented as representative of real BESS operations, but the manuscript provides no evidence that the simulated energy-arbitrage price data or the degradation parameters were fitted to field measurements or cross-validated on other markets. This assumption is load-bearing for translating the 21% figure into operational recommendations.
minor comments (2)
  1. [Abstract] Notation for SOH and capacity loss should be introduced with explicit units and definitions in the first use to avoid ambiguity for readers unfamiliar with battery terminology.
  2. [Results] Figure captions for the scenario comparison plots would benefit from explicit labels indicating which curves correspond to each of the four scenarios.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their thoughtful comments on our manuscript. We address each of the major comments below, providing clarifications and proposing revisions to strengthen the paper where appropriate.

read point-by-point responses

  1. Referee: [Abstract and Results] Abstract and Results section: The 21% revenue-per-SOH-loss improvement is reported as the key quantitative outcome, yet no sensitivity analysis is shown with respect to the market price series, the parameters of the inhomogeneous aging model, or the string-to-string variability distribution. Because the central claim that heterogeneity modeling is a 'crucial enabler' rests on this single simulated arbitrage market, the absence of such sweeps is load-bearing for the broader conclusion.

    Authors: We agree that sensitivity analysis would enhance the robustness of our findings. The presented results use representative parameters drawn from literature on battery degradation and typical energy market price profiles. To address this, we will perform additional simulations in the revised manuscript, varying key parameters such as price volatility, aging model coefficients, and the degree of string-to-string variability. This will demonstrate that the reported improvement is not specific to the chosen instance. revision: yes

  2. Referee: [Methods] Methods section: The performance metric 'revenue per unit of SOH loss' is constructed from the same degradation model that is embedded in the optimization objective for the aging-cost-aware scenarios. This creates a circularity risk; the reported gain may partly reflect the chosen functional form of capacity fade rather than an independent validation of the modeling approach.

    Authors: We appreciate the referee highlighting this potential issue. The metric is indeed based on the degradation model, but it is used consistently to evaluate all scenarios, including those that do not optimize for aging costs. The improvement in the fully informed scenario stems from the optimization avoiding degradation through better-informed decisions, rather than from the metric construction. We will revise the Methods section to explicitly discuss the metric's role in cross-scenario comparison and clarify that it serves as a normalized efficiency measure independent of the optimization objective. revision: partial

  3. Referee: [Results] Results section: The four scenarios are presented as representative of real BESS operations, but the manuscript provides no evidence that the simulated energy-arbitrage price data or the degradation parameters were fitted to field measurements or cross-validated on other markets. This assumption is load-bearing for translating the 21% figure into operational recommendations.

    Authors: The work is a simulation study intended to isolate the impact of modeling fidelity and aging cost awareness. The price series are derived from real historical market data, and degradation parameters are based on established models from the battery literature. We do not present it as a direct empirical study with field validation. In the revision, we will add a limitations subsection discussing the assumptions and how the framework can be calibrated with operational data for specific deployments. revision: partial

Circularity Check

0 steps flagged

No circularity: simulation results are independent of input definitions

full rationale

The paper defines four explicit scenarios that differ in modeling precision and whether aging costs enter the objective function. It then runs an energy-arbitrage simulation and reports the resulting revenue-per-SOH-loss values as outputs. The 21 % figure is the numerical difference between two of those scenario outputs; it is not obtained by re-using a fitted parameter, by renaming an input, or by invoking a self-citation that itself assumes the target result. No equation or claim reduces to its own inputs by construction, and the study contains no load-bearing uniqueness theorem or ansatz smuggled via prior work. The derivation is therefore self-contained as a controlled modeling comparison.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract does not enumerate free parameters or axioms; the framework implicitly relies on standard battery degradation models and electricity price time series whose details are not provided.

pith-pipeline@v0.9.0 · 5715 in / 1184 out tokens · 34866 ms · 2026-05-19T06:46:18.890078+00:00 · methodology

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Reference graph

Works this paper leans on

14 extracted references · 14 canonical work pages

  1. [1]

    Battery energy-storage system: A review of technologies, optimization objectives, constraints, approaches, and outstanding issues,

    M. A. Hannan, S. B. Wali, P. J. Ker, M. A. Rahman, M. Mansor, V . K. Ramachandaramurthy, K. M. Muttaqi, T. Mahlia, and Z. Y . Dong, “Battery energy-storage system: A review of technologies, optimization objectives, constraints, approaches, and outstanding issues,” Journal of Energy Storage, vol. 42, 2021

    work page 2021

  2. [2]

    Energy management for stationary elec- tric energy storage systems: A systematic literature review,

    T. Weitzel and C. H. Glock, “Energy management for stationary elec- tric energy storage systems: A systematic literature review,” European Journal of Operational Research , vol. 264, no. 2, 2018

    work page 2018

  3. [3]

    Unlocking extra value from grid batteries using advanced models,

    J. M. Reniers, G. Mulder, and D. A. Howey, “Unlocking extra value from grid batteries using advanced models,” Journal of Power Sources , vol. 487, 2021

    work page 2021

  4. [4]

    Battery energy storage models for optimal control,

    D. M. Rosewater, D. A. Copp, T. A. Nguyen, R. H. Byrne, and S. Santoso, “Battery energy storage models for optimal control,” IEEE Access, vol. 7, 2019

    work page 2019

  5. [5]

    Exploring the effects of cell-to-cell variability on battery aging through stochastic simulation techniques,

    E. Barbers, F. E. Hust, F. E. A. Hildenbrand, F. Frie, K. L. Quade, S. Bihn, D. U. Sauer, and P. Dechent, “Exploring the effects of cell-to-cell variability on battery aging through stochastic simulation techniques,” Journal of Energy Storage , vol. 84, 2024

    work page 2024

  6. [6]

    Analysis of ageing inhomogeneities in lithium-ion battery systems,

    S. Paul, C. Diegelmann, H. Kabza, and W. Tillmetz, “Analysis of ageing inhomogeneities in lithium-ion battery systems,” Journal of Power Sources, vol. 239, 2013

    work page 2013

  7. [7]

    Inhomogeneous temperature distribution affecting the cyclic aging of li-ion cells. part ii: Analysis and correlation,

    D. Werner, S. Paarmann, A. Wiebelt, and T. Wetzel, “Inhomogeneous temperature distribution affecting the cyclic aging of li-ion cells. part ii: Analysis and correlation,” Batteries, vol. 6, no. 1, 2020

    work page 2020

  8. [8]

    Lithium-ion battery second life: pathways, challenges and outlook,

    A. N. Patel, L. Lander, J. Ahuja, J. Bulman, J. K. H. Lum, J. O. D. Pople, A. Hales, Y . Patel, and J. S. Edge, “Lithium-ion battery second life: pathways, challenges and outlook,” Frontiers in chemistry, vol. 12, 2024

    work page 2024

  9. [9]

    Increas- ing the lifetime profitability of battery energy storage systems through aging aware operation,

    N. Collath, M. Cornejo, V . Engwerth, H. Hesse, and A. Jossen, “Increas- ing the lifetime profitability of battery energy storage systems through aging aware operation,” Applied Energy, vol. 348, 2023

    work page 2023

  10. [10]

    Depreciation cost is a poor proxy for revenue lost to aging in grid storage optimization,

    V . Kumtepeli, H. Hesse, T. Morstyn, S. M. Nosratabadi, M. Aunedi, and D. A. Howey, “Depreciation cost is a poor proxy for revenue lost to aging in grid storage optimization,” in 2024 American Control Conference (ACC), IEEE, 2024

    work page 2024

  11. [11]

    Simses: A holistic simula- tion framework for modeling and analyzing stationary energy storage systems,

    M. M ¨oller, D. Kucevic, N. Collath, A. Parlikar, P. Dotzauer, B. Tepe, S. Englberger, A. Jossen, and H. Hesse, “Simses: A holistic simula- tion framework for modeling and analyzing stationary energy storage systems,” Journal of Energy Storage , vol. 49, 2022

    work page 2022

  12. [12]

    Anal- ysis and modeling of calendar aging of a commercial lifepo4/graphite cell,

    M. Naumann, M. Schimpe, P. Keil, H. C. Hesse, and A. Jossen, “Anal- ysis and modeling of calendar aging of a commercial lifepo4/graphite cell,” Journal of Energy Storage , vol. 17, 2018

    work page 2018

  13. [13]

    Analysis and modeling of cycle aging of a commercial lifepo4/graphite cell,

    M. Naumann, F. B. Spingler, and A. Jossen, “Analysis and modeling of cycle aging of a commercial lifepo4/graphite cell,” Journal of Power Sources, vol. 451, 2020

    work page 2020

  14. [14]

    Optimal sizing of a grid- connected pv system for various pv module technologies and incli- nations, inverter efficiency characteristics and locations,

    G. Notton, V . Lazarov, and L. Stoyanov, “Optimal sizing of a grid- connected pv system for various pv module technologies and incli- nations, inverter efficiency characteristics and locations,” Renewable Energy, vol. 35, no. 2, 2010

    work page 2010