Building a P2D Model for the NiMH Battery
Authors: Börjesson Axén Jenny , Ekström Henrik , Widenkvist Zetterström Erika , Lindbergh Göran 
Published: February 2024

For understanding a battery when working under realistic conditions, a dynamic battery model is a useful tool. One of the most known electrochemical model types for batteries is the Newman P2D model.[1] This model has a good balance between complexity and computational efficiency. Due to the level of complexity, using a P2D model allows us to make simulations to optimize battery design by adjusting parameters such as electrode porosity and tortuosity, electrode thickness, and overall cell thickness. But it can also be used to optimize battery management system (BMS) functionality. There are many studies made on different Li-ion type batteries when it comes to P2D modelling, but to our knowledge there is no dynamic NiMH P2D model reported in literature. In this study we have created a dynamic P2D model through combining it with two previously developed models focused on the specific difficulties on NiMH modelling: Hysteresis estimation and gas behavior. [2,3]
Two phenomena are paramount to include in dynamic NiMH battery models: the open circuit voltage (OCV) hysteresis; and the oxygen evolution/recombination reactions in the cell. The OCV hysteresis manifests as an OCV dependence on battery charge/discharge history. In the NiMH battery, the OCV hysteresis is of such a magnitude that one OCV value can be indicative of an SOC ranging between 20% and 90%, making any type of SOC determination algorithm unusable without taking the hysteresis behavior into account.[2] The hysteresis can predominantly be traced to the phase changes that takes place in the positive electrode as it is charged and discharged. This suggests that models of other battery electrodes with significant phase changes, such as LiS and Si, will have to take this behavior into account as well. While the hysteresis effect affects the energy efficiency of the battery, the gas reactions affect the coulombic efficiency of the battery. Since the NiMH battery has a water-based electrolyte, once the positive electrode voltage reaches above the oxygen evolution potential oxygen is produced.[3] This parasitic reaction diverts current from charging the battery, decreasing the coulombic efficiency. Once the oxygen reaches the negative electrode it is recombined and releasing the lost energy as heat. A model that fails to take the gas behavior into account will have difficulties to properly simulate the temperature behavior in the cell. In addition, the decreased coulombic efficiency affects any coulomb counting done as a part of SOC tracking in the cell.
A dynamic model that takes both these behaviors into account can be used for many different purposes. Algorithms for use in battery management systems (BMS), for example end of charge criteria and state of charge estimation, will have higher accuracy when optimized using the model. A digital twin based on such a model can be used to monitor battery performance and deviations. System dimensioning can be optimized to achieve the best cost-to-life ratio. It can also be used to develop better usage patterns to get the most out of the battery. Through using the model to develop more efficient usage patterns, the influence of hysteresis and the gas evolution can be minimized, thereby increasing the efficiency of the system.
[1] K.E. Thomas, J. Newman, R.M. Darling, Mathematical Modeling of Lithium Batteries, in: Adv. Lithium-Ion Batter., Springer US, Boston, MA, 2002: pp. 345–392. https://doi.org/10.1007/0-306-47508-1_13.
[2] J.B. Axén, H. Ekström, E.W. Zetterström, G. Lindbergh, Evaluation of hysteresis expressions in a lumped voltage prediction model of a NiMH battery system in stationary storage applications, J. Energy Storage. 48 (2022). https://doi.org/10.1016/j.est.2022.103985.
[3] J. Börjesson Axén, H. Ekström, E. Widenkvist Zetterström, G. Lindbergh, A NiMH dynamic pressure composition model for on-line applications, Manuscript