Simplified Physics-Based Battery Model for Stationary Energy-Storage Applications
Authors: Ohrelius Mathilda , Lindstrom Rakel , Lindbergh Göran 
Published: August 2024

To perform safe battery operation and avoid unnecessary degradation, battery models are needed. How complex, or close to reality the model should be, depends on the purpose of the model and the computational power available. The possibility for accurate parameterization before model implementation is another crucial aspect for the validity. Physics-based models have the advantage to solve for internal battery states, which includes important information to avoid accelerated degradation and to evaluate state of health. But the parameterization effort can be extensive and the computational cost too high to solve for in real time. Identifying the most essential processes and if possible, simplify the model is therefore motivated.
Parameter sensitivity is a powerful tool to investigate how much certain parameters and the related processes effect the output signal, i.e. battery voltage. Under normal operating conditions the cells are rarely completely discharged, and as a result the diffusion processes show low sensitivity during operation [1]. In this work we therefore explore the utilization of a physics-based model solving for the electrolyte dynamics, rather than the solid phase diffusion commonly applied in the so-called single particle model. By neglecting the diffusion processes, the second dimension in the pseudo-two-dimensional (P2D) model can be ignored and the computational complexity simplified. The parameterization strategy and validation of the model is further discussed.
We evaluate our model by comparing simulations with experimental data from batteries subjected to stationary energy storage applications. The cells are commercial 18650-type NMC/Graphite cells with 2.6 Ah capacity. Different service cycles have different needs in terms of current and voltage, see examples in Figure 1. Capturing these behaviours with a physics-based model might pose different challenges and will further affect the degradation of the cells [2]. A wide range of models exist in literature to capture degradation mechanisms during battery operation [3]. To keep the computational and parameterization effort as low as possible, our methodology is not to include more physics, but instead update the parameters to the processes already included in the model [4]. We explore this strategy comparing the behaviour from different types of services, as well as batteries where the application changes, to see the model response and analyse the battery state of health, see Figure 2. Electrochemical techniques such as differential voltage analysis and electrochemical impedance spectroscopy is included to support our conclusions.
Our results highlight the value of application considerations when designing battery models, rather than only focusing on physical extreme points. We present an alternative physics-based model with the ability to capture crucial degradation phenomena and validate it against operational data. We believe our findings can be of value for smarter battery operating strategies and a greater understanding of application dependant lithium-ion battery degradation.
Figure 1. Some of the application duty cycles part of the experimental study. a) Current profile peak shaving b) Current profile frequency regulation c) Voltage response peak shaving d) Voltage response frequency regulation.
Figure 2. Degradation trends from the experimental study. Purple cell initially performing PS following application change to FR_high cycling a) Capacity evolution of the cycled cells b) tortuosity parameter evolution obtained from model parameter fitting c) Measured impedance response during cell reference performance tests d) Calculated charge transfer resistance from measured impedance data.
References
[1] M. Streb, M. Andersson, V. Löfqvist Klass, M. Klett, M. Johansson, G. Lindbergh, Investigating re-parametrization of electrochemical model-based battery management using real-world driving data, eTransportation 16 (2023).
[2] M. Ohrelius, M. Berg, R. Wreland Lindström, G. Lindbergh, Lifetime Limitations in Multi-Service Battery Energy Storage Systems, Energies 16 (2023).
[3] J.M. Reniers, G. Mulder, D.A. Howey, Review and Performance Comparison of Mechanical-Chemical Degradation Models for Lithium-Ion Batteries, Journal of The Electrochemical Society 166 (2019) A3189-A3200.
[4] M. Streb, M. Ohrelius, A. Siddiqui, M. Klett, G. Lindbergh, Diagnosis and prognosis of battery degradation through re-evaluation and Gaussian process regression of electrochemical model parameters, Journal of Power Sources 588 (2023).

Figure 1