To manage and operate batteries effectively and efficiently, precise simulation models are of paramount importance. They are primarily used for the diagnosis and prognosis of the internal state of the cell to ensure the battery’s performance, and safe operation [1]. The presentation focuses on electrical modelling and introduces an improved pulse-fitting method for the parameterization of equivalent circuit models based on pulse tests using an evolutionary algorithm.
The high frequency model relies on n-RC elements, with the inductive behaviour being described via a series-connection of m-RL elements. In contrast to the conventional approach that uses electrochemical impedance spectroscopy for high-frequency behaviour and pulse tests for long-term behaviour [2], this work utilizes pulse tests with sampling rates of up to 100 kHz to capture the complete behaviour of the cell. To the best of our knowledge, pulse tests with sampling rates of up to 100 kHz have not been performed yet. The results conclude that precise modelling requires the identification of fast to considerably slow processes. To capture especially fast processes, a sampling rate of at least 10 kHz is necessary to describe the complete high frequency capacitive behaviour and at least 100 kHz for the inductive behaviour.
The introduced high-order model showcases the importance of determining the optimal model order to prevent over- and underfitting as results show that low-order models such as the widely adopted 2RC-model [3, 4] fail to yield stable parameter extraction due to the phenomenological model being heavily underfitted. This relationship between model order and sampling rate has not been studied yet and is therefore further addressed in this study.
As is well known, the resistance and aging processes are a function of the temperature, the degree of cycling, as well as the state of charge (SoC) and state of health (SoH) [5]. Consequently, it seems intuitive that the same dependencies apply to the extracted parameters. Therefore, this study aims to help developing a more rigorous understanding on the factors that influence the parameter extraction by performing pulse-fitting with changing hybrid pulse power characterization parameters (HPPC) such as current rate and direction, length of relaxation, and sampling rate at different SoCs and temperatures.
The performance of the model is validated by its ability to simulate the charge and discharge behaviour of the cell and its ability to derive the impedance spectrum based on the estimated parameters. The latter is verified by its comparison to an electrochemical impedance spectroscopy. The introduced model can precisely simulate the battery cell’s electric behaviour with high fidelity and the voltage error being predominantly within the range of the noise (0.6 mV). In addition, the estimated parameters have been implemented in COMSOL to build a model capable of simulating the electrical and thermal behaviour of the cell with high fidelity, as validated by experimental data. The proposed approach has been verified for three battery types: one cylindrical and one pouch-cell with NMC/graphite chemistry, as well as one cylindrical-cell with NMC/graphite silicon doped chemistry.
[1] M. Böttiger, M. Paulitschke, T. Bocklisch, Systematic experimental pulse test investigation for parameter identification of an equivalent based lithium-ion battery model, Energy Procedia 135 (2017) 337–346.
[2] J. P. Schmidt, E. Ivers-Tiffée, Pulse-fitting–a novel method for the evaluation of pulse measurements, demonstrated for the low frequency behavior of lithium-ion cells, Journal of Power Sources 315 (2016) 316–323
[3] J. Sun, J. Kainz, Optimization of hybrid pulse power characterization profile for equivalent circuit model parameter identification of li-ion battery based on taguchi method, Journal of Energy Storage 70 (2023) 108034.
[4] S. J. Navas, G. C. González, F. Pino, J. Guerra, Modelling li-ion batteries using equivalent circuits for renewable energy applications, Energy Reports 9 (2023) 4456–4465.
[5] S. Barcellona, S. Colnago, G. Dotelli, S. Latorrata, L. Piegari, Aging effect on the variation of li-ion battery resistance as function of temperature and state of charge, Journal of Energy Storage 50 (2022) 104658.