Finite-time thermodynamic optimal control of energy storage devices : a study of vanadium redox flow batteries

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Paterson, Thomas and Li, Jun and Lue, Leo (2026) Finite-time thermodynamic optimal control of energy storage devices : a study of vanadium redox flow batteries. Journal of Physics: Energy, 8 (2). 025010. ISSN 2515-7655 (https://doi.org/10.1088/2515-7655/ae6e32)

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Abstract

Finite-time thermodynamics (FTT) offers a consistent framework to achieve a desired trade-off between power and efficiency for energy conversion devices operating at steady state. However, energy storage (finite-reservoir) devices operate under transient conditions due to evolving reservoir potentials and kinetic relations throughout charge and discharge. Consequently, dynamic optimisation methods are needed to maintain a desired power-efficiency trade-off for such devices. To address this, FTT optimal control is developed here which can maintain a desired power-efficiency characteristic for transient systems. Optimal operation can be described in terms of any relevant thermodynamic or kinetic control parameter using flux-force relations. FTT path optimisation is applied to the vanadium redox flow battery (VRFB) and operation is optimised in the maximum efficiency, maximum power, ecological,and efficient power regimes. We do so using a new description of electrochemical energy conversion and storage devices in the thermodynamic (De Vos) language of chemical engines and pumps. Application of FTT to real-world devices informs how the adaptability and stability of energy systems may be methodically improved. Crucially, we show that non-thermodynamic physical, practical constraints must be considered to correctly apply FTT beyond theory to practical devices. These constraints prevent devices from operating in particular FTT regimes. The range of accessible regimes is considered a feature of a device which indicates suitability and adaptability. This new form of characterisation is essential for the appropriate selection of energy storage devices for particular roles an energy system (i.e.\ high power, high efficiency, versatility, etc.). For VRFBs, discharging is more versatile than charging. Charging may only occur in the maximum efficiency regime, making it well suited for low power storage. Discharge may occur over a versatile range of higher power regimes, though not maximum power. Discharging in the ecological regime gives improved power with reasonable efficiency, which may be of industrial relevance.

ORCID iDs

Paterson, Thomas, Li, Jun ORCID logoORCID: https://orcid.org/0000-0002-7685-8543 and Lue, Leo ORCID logoORCID: https://orcid.org/0000-0002-4826-5337;
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