A Modified Phenomenological Force Model for Charge Process of Lithium-Ion Battery
Authors: Li Ruihe , Ren Dongsheng , Xu Chengshan , Hou Zhichao , Han Xuebing , Lu Languang , Ouyang Minggao 
Published: February 2020

Lithium-ion batteries have been widely used as an important countermeasure to alleviate the energy crisis and environmental pollution, especially in automobile field. However, batteries still suffer from safety issues which limits wider application and sometimes arises public concern. A robust battery management system (BMS) is critical to detect possible safety problem of the battery pack.
Many researches have been tried different ways to improve the accuracy and robustness of BMS by introducing mechanical signals like force and swelling. Most models reported in articles related SOC or concentration of lithium ions in electrodes with swelling or force through a look-up table. However, it’s not clear what C rate is appropriate for the look up table. Also most of the models are validated only for discharge process. Actually, the charge process is also important since there have been various thermal runaway accidents of automobiles during charging.
In this paper, a modified phenomenological force model is proposed. The deviation of the predicted force and detected ones is shown. Then the effectiveness of utilizing swelling-SOC look-up table at different C-rates is discussed. Finally, it’s pointed out that lithium plating is responsible for the force error at end of charge, which implies that the force signal has the potential to detect lithium plating which is critical for battery aging and safety issues.
The phenomenological force model is built as followed: firstly, swelling at free state and force at constrained state of cells at different C rates (1/6C, 1/3C, 1C, CCCV protocol) of commercial 30.5Ah NCM/C pouch cells is obtained separately. Then force and swelling is plotted together through their relation with SOC, as can be seen is Figure 1 (a) and (b). Finally, cells are regarded as linear springs and a specific experiment is chosen to identify the stiffness as 0.0151kN/µm for force at 1C and 0.0130kN/µm for force at 1/3C. The pure thermal swelling is investigated by 2C pulse test (charge and discharge continuously for 1440s). It’s found that the cell only expands for 1.5µm when temperature rises 8°C and thus thermal swelling for this types of cells will be ignored in further analysis.
For force at 1/3C charging, by substituting swelling at 1/6C with 1/3C, RMSE can be reduced from 0.06713kN to 0.02607kN (accuracy of force sensor is 0.045kN). Similar result can be seen for other situation. Such differences originate from middle SOC which relates to the phase transition of graphite. At high SOC which corresponds to the end of Figure(a), force experiences a downward trend for force at 1C, which can be seen for discharge process or low C rates. This can be explained by the mechanism shown in Figure 1 (c) and (d). For low C rates, graphite particles can absorb all the li-ions in time. Thus, no extra li-ions will accumulate outside those particles. However, for high C rates charging, the number of Li-ions intercalate into a graphite particle per second is much higher. Here we assume that green line in Figure 1(c) indicates the capacity that a graphite particle can absorb per second, which is driven by voltage. Thus for stage ①, Li concentration will increase monotonously and precipitate out at certain point, which occupy larger volume. During constant voltage period (stage ②), as current drops, the precipitated Li will be dissolved and intercalated back to graphite particles which will reduce overall volume of cells. This downward trend can’t be seen for discharge process because during Li-ions will migrate from graphite anode to NCM cathode and won’t accumulated outside graphite particles. Moreover, the volume change of NCM cathode is much smaller.
To conclude, it’s found that by utilizing swelling detected at same C rate as force, the nonlinear effect at middle SOC range arisen from phase transition of graphite can be eliminated. The downward trend of force at high C rates charge process is attributed to Li plating. Further work will focus on further exploiting force signal to identify Li plating and assess safety issue of cells.
Figure 1. A phenomenological force model. (a) Force vs swelling for different C rates during charge, 1/6C-1/3C means swelling is detected at 1/6 and force is detected at 1/3C; (b) Force vs swelling for different C rates during discharge; (c) Force and current during charge; (d) mechanism of Li plating and absorbing for high C rate during charge.

Figure 1