Open Circuit Voltage (OCV) models play a crucial role in estimating the State of Charge (SoC) of Lithium-ion batteries (LIBs). This comparative study analyzes various OCV models, evaluating their performance and suitability for different battery chemistries, specifically Nickel Manganese Cobalt (NMC) and Lithium Iron Phosphate (LFP) batteries. The analysis focuses on sensitivity to SoC regions, number of data points, ambient temperatures, and aging stages, ultimately aiming to identify the most robust and accurate model for SoC estimation.
Sensitivity Analysis of OCV Models
Impact of SoC Regions on Model Accuracy
Most OCV models prioritize fitting data from the middle SoC regions (10% – 90%). However, accurate SoC initialization often requires reliable OCV data across the entire SoC range (0% – 100%). This study investigates the performance of various models in both middle and entire SoC regions. Results indicate that some models exhibit significant inaccuracies in the low (0% – 10%) and high (90% – 100%) SoC regions when trained solely on middle SoC data. This discrepancy highlights the importance of utilizing data from the entire SoC spectrum for model development. Figure 3 illustrates the fitted OCV-SoC curves for different models at 25°C for both NMC and LFP cells. The RMSEs for different SoC regions, shown in Figure 4, confirm that certain models struggle to accurately represent the OCV behavior in the extreme SoC ranges.
Figure 3: OCV-SoC curves of various models at 25°C for fresh NMC and LFP cells.
Figure 4: RMSE comparison for different SoC regions at 25°C for fresh NMC and LFP cells.
Polynomial models of varying orders were evaluated. While higher-order polynomials theoretically offer greater flexibility, results indicate that models 16, 17, and 18 (higher-order polynomials) demonstrate superior performance for NMC cells across the entire SoC range. For LFP cells, models 7, 17, and 18 exhibit similar robustness.
Influence of Data Point Quantity on Model Performance
The number of experimental data points used for model fitting significantly impacts accuracy. This study compares models trained with 11, 21, and 51 data points. Figure 5 shows that LFP cell models are more sensitive to data point quantity than NMC cell models. Increasing data points generally improves accuracy, particularly for LFP cells. However, the marginal gain diminishes beyond 21 data points for most models. Considering the trade-off between accuracy and experimental time, using 21 data points offers a reasonable balance. Models 4, 16, and 17 demonstrate robustness against data point variations for NMC cells, while models 4, 7, and 17 exhibit similar stability for LFP cells.
Figure 5: RMSE comparison for different numbers of data points at 25°C for fresh NMC and LFP cells.
Effect of Temperature and Aging on Model Accuracy
Temperature and aging significantly influence battery OCV. Figure 6 presents the performance of OCV models at different temperatures. Most models exhibit sensitivity to temperature, especially at low temperatures. Models 16, 17, and 18 demonstrate superior robustness against temperature variations for NMC cells. For LFP cells, models 4, 17, and 18 perform consistently well across different temperatures.
Figure 6: Performance comparison of OCV models at different temperatures.
Figure 7 illustrates the impact of aging on model accuracy. Models 3, 17, and 18 exhibit the least sensitivity to aging effects for NMC cells, while models 4, 17, and 18 maintain good performance for aged LFP cells.
Figure 7: Performance comparison of OCV models at different aging stages.
OCV Model Impact on SoC Estimation
The chosen OCV model directly affects SoC estimation accuracy. Figure 8 presents the SoC estimation performance using different OCV models within an Unscented Kalman Filter (UKF) framework. Models 16, 17, and 18 consistently deliver accurate SoC estimations for both NMC and LFP cells.
Figure 8: Impacts of different OCV models on SoC estimation.
Conclusion
This comparative study highlights the importance of selecting an appropriate OCV model for accurate LIB SoC estimation. Considering the comprehensive analysis across different influencing factors, the 9th order polynomial (Model 17) emerges as the most robust and accurate choice for both NMC and LFP chemistries. Its ability to handle variations in SoC regions, data point quantities, temperatures, and aging stages makes it a suitable candidate for real-world applications. While the 10th order polynomial (Model 18) shows marginally better performance in some cases, the 9th order offers a good balance between accuracy and complexity, particularly when considering practical constraints on data acquisition and computational resources.
