In battery management systems for electric vehicles, the state of charge (SOC) is a crucial parameter. Accurate and timely estimation of SOC helps in limiting the maximum discharge and alerting drivers to recharge, thereby enhancing vehicle safety and driving experience. Among various SOC estimation methods, the open-circuit voltage (OCV) method is one of the simplest. However, its accuracy heavily depends on the resting time required for the battery to stabilize after discharge. In this study, I focus on investigating the factors affecting the resting time and OCV values for LiFePO4 batteries, specifically examining the influences of discharge rates and aging levels (cycle counts). The findings aim to provide insights for methods like the ampere-hour integration that require precise initial SOC values.
My experiments involve using single-cell LiFePO4 batteries with a nominal voltage of 3.7V and capacity of 2800mAh. The test setup includes an electronic load instrument for discharge cycles, and software for real-time monitoring of current, voltage, and discharged capacity. All tests are conducted at room temperature to minimize external influences. To begin, I validate the feasibility of the simplified OCV method by charging and discharging a LiFePO4 battery at a constant rate, recording OCV values after different resting periods. The results indicate that resting time significantly affects OCV readings, with longer resting leading to more stable values. This underscores the importance of determining optimal resting times for accurate SOC estimation.
The SOC of a LiFePO4 battery can be defined as the ratio of remaining capacity to nominal capacity, often expressed as: $$SOC(t) = SOC(0) – \frac{1}{C_n} \int_0^t \eta I(\tau) d\tau$$ where $C_n$ is the nominal capacity, $\eta$ is the coulombic efficiency, and $I$ is the current. The OCV method relies on the relationship between SOC and OCV, typically represented as $OCV = g(SOC)$, where $g$ is a function determined experimentally. For LiFePO4 batteries, this relationship is relatively stable, but factors like discharge rates and aging can introduce variations. In my analysis, I explore these aspects through systematic experiments.
First, I examine the effect of different discharge rates on OCV values after varying resting times. Discharge rates are defined relative to the battery’s capacity; for instance, 0.5C means discharging at a current that would deplete the battery in 2 hours. I test rates of 0.5C, 1.0C, 1.5C, and 2.0C, discharging the LiFePO4 battery in increments corresponding to 10% SOC changes (280mAh each). After each discharge step, I rest the battery for 2, 4, and 8 hours, recording the OCV values. The data are summarized in the table below.
| SOC (%) | 0.5C OCV (V) at Resting Time | 1.0C OCV (V) at Resting Time | 1.5C OCV (V) at Resting Time | 2.0C OCV (V) at Resting Time | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2h | 4h | 8h | 2h | 4h | 8h | 2h | 4h | 8h | 2h | 4h | 8h | |
| 90 | 3.993 | 4.049 | 4.039 | 4.045 | 4.078 | 4.054 | 4.076 | 4.088 | 4.069 | 4.092 | 4.105 | 4.086 |
| 80 | 3.928 | 3.980 | 3.984 | 3.987 | 4.014 | 4.001 | 4.027 | 4.068 | 4.027 | 4.066 | 4.069 | 4.034 |
| 70 | 3.853 | 3.907 | 3.910 | 3.922 | 3.944 | 3.929 | 3.965 | 3.983 | 3.944 | 4.023 | 3.998 | 3.877 |
| 60 | 3.783 | 3.821 | 3.825 | 3.845 | 3.858 | 3.843 | 3.901 | 3.899 | 3.859 | 3.958 | 3.926 | 3.877 |
| 50 | 3.707 | 3.752 | 3.751 | 3.771 | 3.792 | 3.788 | 3.826 | 3.833 | 3.809 | 3.892 | 3.859 | 3.832 |
| 40 | 3.653 | 3.705 | 3.706 | 3.695 | 3.746 | 3.722 | 3.752 | 3.789 | 3.740 | 3.819 | 3.817 | 3.756 |
| 30 | 3.598 | 3.644 | 3.645 | 3.643 | 3.687 | 3.662 | 3.682 | 3.729 | 3.681 | 3.743 | 3.758 | 3.696 |
| 20 | 3.543 | 3.585 | 3.594 | 3.588 | 3.628 | 3.600 | 3.636 | 3.667 | 3.617 | 3.676 | 3.693 | 3.634 |
| 10 | 3.484 | 3.523 | 3.521 | 3.529 | 3.567 | 3.529 | 3.582 | 3.609 | 3.534 | 3.631 | 3.637 | 3.563 |
From the table, I observe that for a LiFePO4 battery, the OCV values after 2 hours of resting show minimal differences across discharge rates. As resting time increases to 4 and 8 hours, the discrepancies further diminish. This suggests that discharge rate is not a dominant factor affecting OCV, and its impact reduces with longer resting periods. To quantify this, I derive a relationship: let $\Delta OCV_{rate}$ be the OCV difference due to discharge rate, then $\Delta OCV_{rate} \propto e^{-kt}$, where $k$ is a constant and $t$ is resting time. For practical purposes, after 8 hours, the OCV values converge, indicating that for accurate SOC estimation using the OCV method, resting times beyond 8 hours can mitigate rate-induced variations.
Next, I investigate the influence of aging, measured by cycle counts, on resting time and OCV values. A cycle refers to a full charge-discharge process from 100% SOC to 0% SOC. As a LiFePO4 battery ages, its internal resistance increases and active material activity decreases, potentially altering the required resting time. I conduct experiments by cycling a LiFePO4 battery up to 500 times, recording the actual capacity after every 100 cycles and the resting time needed for voltage stabilization (defined as voltage rise rate less than 1mV/min). The results are tabulated below.
| Cycle Count | Actual Capacity (mAh) | Resting Time (hours) at SOC 10% | Resting Time (hours) at SOC 50% | Resting Time (hours) at SOC 90% |
|---|---|---|---|---|
| 0 | 2800 | 2.5 | 2.0 | 1.5 |
| 100 | 2576 | 3.0 | 2.5 | 2.0 |
| 200 | 2470 | 3.5 | 3.0 | 2.5 |
| 300 | 2410 | 4.0 | 3.5 | 3.0 |
| 400 | 2330 | 4.5 | 4.0 | 3.5 |
| 500 | 2256 | 5.0 | 4.5 | 4.0 |
The data show that resting time increases with cycle count, particularly at lower SOC levels. For instance, at 10% SOC, resting time rises from 2.5 hours for a new LiFePO4 battery to 5.0 hours after 500 cycles. This can be modeled as: $$t_{rest}(SOC, N) = t_0(SOC) + \alpha(SOC) \cdot N$$ where $t_{rest}$ is the required resting time, $t_0$ is the initial resting time at a given SOC, $\alpha$ is a growth coefficient dependent on SOC, and $N$ is the cycle count. For LiFePO4 batteries, $\alpha$ tends to be higher at lower SOC, indicating that aging exacerbates the relaxation process in depleted states.
Furthermore, I measure OCV values at different cycle counts for various SOC points. The LiFePO4 battery is cycled in increments of 100 cycles, and after each set, it is discharged to specific SOC levels, rested until stable, and OCV recorded. The findings are summarized in the following table.
| SOC (%) | OCV (V) at 100 Cycles | OCV (V) at 200 Cycles | OCV (V) at 300 Cycles | OCV (V) at 400 Cycles | OCV (V) at 500 Cycles |
|---|---|---|---|---|---|
| 90 | 3.233 | 3.208 | 3.255 | 3.301 | 3.348 |
| 80 | 3.506 | 3.551 | 3.597 | 3.643 | 3.691 |
| 70 | 3.567 | 3.612 | 3.659 | 3.706 | 3.753 |
| 60 | 3.647 | 3.694 | 3.741 | 3.788 | 3.835 |
| 50 | 3.692 | 3.739 | 3.786 | 3.833 | 3.881 |
| 40 | 3.800 | 3.846 | 3.893 | 3.940 | 3.987 |
| 30 | 3.933 | 3.979 | 4.026 | 4.073 | 4.119 |
| 20 | 4.063 | 4.109 | 4.156 | 4.203 | 4.249 |
| 10 | 4.161 | 4.208 | 4.255 | 4.302 | 4.348 |
Analyzing this data, I note that the SOC-OCV curve for the LiFePO4 battery maintains its characteristic shape across cycle counts: a steep rise at low SOC (10-30%), a plateau in mid-SOC (30-70%), and another rise at high SOC (70-90%). However, the entire curve shifts upward with aging. Quantitatively, for every 100 cycles, the OCV increases by approximately $\Delta V = 0.047$ V across all SOC points. This can be expressed as: $$OCV(SOC, N) = OCV_0(SOC) + \beta \cdot N$$ where $OCV_0$ is the initial OCV at a given SOC, $\beta = 0.047$ V per 100 cycles, and $N$ is the cycle count in hundreds. This linear shift indicates that aging does not alter the fundamental SOC-OCV relationship but adds a voltage offset, likely due to increased internal resistance and changes in electrode kinetics.
To incorporate these findings into SOC estimation models, I propose a corrected OCV function for LiFePO4 batteries: $$OCV_{corr}(SOC, t, N) = OCV_{base}(SOC) + f(t) + g(N)$$ where $OCV_{base}(SOC)$ is the standard SOC-OCV curve, $f(t)$ accounts for resting time effects (decaying with $t$), and $g(N)$ represents the aging offset (linear in $N$). For instance, using exponential decay for discharge rate effects: $$f(t) = \sum_{i} a_i e^{-b_i t}$$ where $a_i$ and $b_i$ are coefficients fit from experimental data. Similarly, $g(N) = \beta N$ with $\beta = 0.047$ V per 100 cycles.
In practice, for ampere-hour integration methods that require an accurate initial SOC, these corrections can improve precision. For example, the initial SOC can be derived from OCV using: $$SOC_0 = h(OCV_{corr})$$ where $h$ is the inverse function of the SOC-OCV relationship. By accounting for resting time and aging, errors from assuming a fixed OCV-SOC curve can be reduced.
My experiments also highlight the importance of considering battery history in BMS algorithms. For a LiFePO4 battery, frequent high-rate discharges may necessitate longer resting for reliable OCV readings, but this effect diminishes over time. Conversely, aging steadily increases both resting time and OCV values, mandating periodic calibration in real-world applications. I recommend that for electric vehicles using LiFePO4 batteries, BMS software should include adaptive resting time algorithms based on cycle count and discharge patterns.
In conclusion, through detailed experimentation on LiFePO4 batteries, I demonstrate that discharge rate has a diminishing impact on OCV as resting time increases, while aging significantly affects both resting time and OCV values. Specifically, resting time extends with cycle count, especially at low SOC, and OCV rises by about 0.047 V per 100 cycles. These insights aid in refining SOC estimation techniques, particularly for methods reliant on OCV initialization. Future work could explore temperature effects and integrate these findings into machine learning models for adaptive BMS.
The robustness of LiFePO4 batteries makes them suitable for such studies, but continuous monitoring is essential for maintaining accuracy over the battery’s lifespan. By leveraging these results, developers can enhance the reliability of electric vehicle power systems, ensuring safer and more efficient energy management.