Battery power system
Ambient (or operating) temperature and cell (surface) temperature affects the state-of-charge (SOC) estimation of battery in electric vehicles and smart grid systems. A unified battery cell model that considered both the ambient and cell temperature, hysteresis voltage dynamics and thermal aging on cell’s capacity is required in battery management system (BMS) design.
An ambient and cell temperature-dependent equivalent circuit model (ECM) in Figure 1 is used. The ambient temperature refers to the operating temperature where the battery cell operates while the cell temperature is the surface temperature of the battery cell. The battery cell used was obtained from cylindrical lithium iron phosphate battery cells (ANR26650M1-B) and the cell simulation model can be obtained from the website .
Figure 1. Circuit model of temperature-dependent ECM of a battery cell
The terms are incorporated into to represent the temperature dependency in obtaining the terminal voltage as shown in Figure 2. The plot was taken at ambient temperature of 25oC.
Figure 2. as a function of ambient and cell temperature
Figure 3. values as a function of SOC and ambient temperature
Figure 4. values as a function of SOC and ambient temperature
Figure 5. values as a function of SOC and ambient temperature
In addition, the open-circuit voltage (OCV) is a function of SOC and ambient temperature as observed in Figure 6.
Figure 6. OCV values as a function of SOC and ambient temperature
The proposed battery cell model also provides the current-voltage behavior compensated by the hysteresis effect, for the battery cell model. The curve for can be seen in Figure 7 where the load current and SOC profile are plotted below it.
Figure 7. as a function of SOC and load current
The time response of is modeled using the model proposed by Bernardi et al. . The plot can be seen in Figure 8 where the ambient temperature of the cell was set at 25oC.
Figure 8. Cell temperature at ambient temperature of 25oC
The terminal voltage at ambient temperatures such as 25oC can be seen in Figure 9. It can be observed that the simulated terminal voltage matches experimental data near to the end of discharging cycle or at a low SOC value.
Figure 9. Terminal voltage at ambient temperature of 25oC
As seen in Figure 11, with the extended Kalman filter (EKF) on the proposed cell model in (1) to (5), the SOC values converge to the experimental data obtained by Ah counting method. The maximum root mean square error (RMSE) of the resulting SOC estimate is around 0.09.
Figure 10. SOC estimate as compared to experimental result (by Ah counting method) obtained at ambient temperature of 25oC
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