A Phenomenological Open Circuit Voltage Model for Lithium-Ion Cells
Authors: Birkl Christoph Robert , McTurk Euan , Roberts Matthew , Bruce Peter G , Howey David Alastair 
Published: February 2020

We propose a generic parametric open circuit voltage (OCV) model to simulate electrode and cell voltages of commercial secondary lithium-ion (li-ion) cells. The model accounts for the phase transitions occurring during the intercalation and de-intercalation processes in both positive and negative electrodes by calculating the redox potential of each phase of the two electrode materials using Fermi-Dirac statistics [1].
Models for OCV are important in both electrochemical and empirical dynamic battery models, which are used for design studies and also to construct estimators for internal battery states, such as the state of charge (SOC) and the state of health (SOH). Most OCV functions used in dynamic battery models are purely empirical and parameterised by fitting the measured cell voltage at a single operating point [2-4]. This approach does not generally allow for variable operating temperatures or the estimation of the SOH of the electrodes. However, physically motivated OCV models may be complex [5, 6], or may lack capability to model the subtle impact of the phase transitions within the electrode materials on the OCV [7].
The proposed phenomenological model consists of two electrode sub-models and a unifying cell model. The electrode sub-models are comprised of a flexible number of additive terms to calculate the redox potential of each phase transition in the positive electrode (PE) and each graphite stage in the negative electrode (NE). This approach facilitates adaptation to different cell chemistries. The parameters of the electrode sub-models are estimated by fitting the models to half-cell measurements using a constrained minimisation algorithm. The electrode sub-models are combined into the full cell model by fitting the loading ratio (the capacity ratio between NE and PE) and the offset of the electrodes (unutilized portion of the PE capacity).
To validate the model using electrode and cell voltage measurements, PE and NE half-cells were constructed from a commercial 740 mAh LiNiMnCoO2 pouch cell, in a coin cell format. Disks of PE and NE material were cut out from the commercial electrodes and used as working electrodes against lithium counter electrodes in the coin cells. The half-cells and the commercial cell were cycled at C/30 to obtain voltage profiles close to OCV. We demonstrate minimal errors of less than 2 mV RMS between the C/30 discharge measurement and the simulated cell voltage (see Figure 1).

Acknowledgements

We would like to thank Jaguar Land Rover Limited and the UK Engineering and Physical Sciences Research Council for their kind support.

References

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[7] V. Pop et al, J. Electrochem. Soc., 153 (11), pp. A2013-A2022, (2006).

Figure 1