With the increasing global focus on environmental protection and sustainable development, battery electric cars have gained widespread adoption as clean and efficient transportation solutions. The battery system, serving as the core component of a battery electric car, directly impacts the operational safety and performance of the vehicle. During the operation of a battery electric car, the battery pack is subjected to various electrical disturbances, among which ripple is a common and significant interference factor. The presence of ripple can adversely affect battery lifespan, performance, and the normal operation of the battery management system (BMS), potentially compromising overall vehicle safety in severe cases. Therefore, investigating the performance changes of battery packs under ripple influence holds substantial practical significance. This study aims to provide theoretical foundations and data support for the anti-ripple design and optimization of battery systems in battery electric cars, thereby enhancing BMS reliability and battery pack service life.
Existing research on ripple effects in battery packs has primarily focused on single operating conditions or limited parameter variations, lacking systematic investigations across diverse temperatures, state-of-charge (SOC) levels, and wide ranges of ripple frequencies and amplitudes. In this study, we conduct comprehensive ripple injection tests on a ternary lithium battery pack with a rated capacity of 60 A·h under closed main positive and negative relay conditions. The tests are performed at two temperatures, (23±2)°C and (-25±2)°C, and two SOC levels, 50%±1% and 95%±1%, with various ripple frequency and amplitude settings. Data on time, voltage, current, power, and other parameters are collected. Our analysis reveals significant differences in ripple effects on current and power fluctuations, as well as AC impedance, across different conditions. Based on these findings, we establish a piecewise linear regression model between current fluctuation amplitude and ripple frequency. The results indicate that in the low-frequency range (f ≤ 1 kHz), current fluctuation amplitude increases by 0.0015 A for every 10 Hz increase in frequency, while in the high-frequency range (f > 1 kHz), it decreases by 0.0005 A for every 1 kHz increase. This study offers insights for improving the reliability of battery electric cars under electrical disturbances.
Experimental Method
We established a specialized test bench for battery pack ripple evaluation, incorporating high-precision equipment to ensure accurate and repeatable measurements. The core components include a battery testing system, ripple simulation device, environmental chamber, and data acquisition system. The battery testing system enables precise measurement of battery pack parameters such as voltage, current, and power. The ripple simulation device generates ripple signals with specific frequencies and amplitudes, injecting them steadily into the battery pack circuit. The environmental chamber controls temperature precisely to simulate different operating conditions. The data acquisition system records all parameters in real-time with millisecond-level sampling frequency, guaranteeing data accuracy and completeness.
The test sample is a ternary lithium battery pack with a rated capacity of 60 A·h, representing typical characteristics of battery packs commonly used in modern battery electric cars. High-precision temperature sensors are employed to monitor ambient and battery pack temperatures throughout the tests, ensuring consistency in experimental conditions.
In accordance with ISO 21498-2:2021, “Electrically propelled road vehicles — Electrical specifications and tests for voltage class B systems and components — Part 2: Electrical tests for components,” and relevant standards from major automotive enterprises, we designed five distinct test conditions. Each condition integrates variations in temperature, SOC, and ripple parameters. The detailed conditions are summarized in Table 1.
| Condition | Temperature | SOC | Ripple Frequency Range | Ripple Voltage Peak-to-Peak (UVPP) | Steps and Duration |
|---|---|---|---|---|---|
| Condition 1 | (23±2)°C | 50%±1% | 80 Hz to <1 kHz | Battery voltage + 12 V | 10 Hz steps, >2 s per point, repeated twice |
| 1 kHz to <5 kHz | 12 V to 24 V (increasing) | 100 Hz steps, >2 s per point | |||
| 5 kHz to <10 kHz | 24 V | 100 Hz steps, >2 s per point | |||
| 10 kHz to <40 kHz | 24 V | 1 kHz steps, >2 s per point | |||
| 40 kHz to <50 kHz | 24 V to 8 V (decreasing) | 1 kHz steps, >2 s per point | |||
| 50 kHz to <150 kHz | 8 V | 1 kHz steps, >2 s per point | |||
| Condition 2 | (23±2)°C | 95%±1% | Same as Condition 1 | Same as Condition 1 | Same as Condition 1 |
| Condition 3 | (-25±2)°C | 50%±1% | Same as Condition 1 | Same as Condition 1 | Same as Condition 1 |
| Condition 4 | (-25±2)°C | 95%±1% | Same as Condition 1 | Same as Condition 1 | Same as Condition 1 |
| Condition 5 | (23±2)°C | 50%±1% | 80 Hz to <1 kHz | 4 V | 10 Hz steps, >2 s per point, repeated twice |
| 1 kHz to <10 kHz | 4 V | 100 Hz steps, >2 s per point, repeated twice | |||
| 10 kHz to <150 kHz | 4 V | 1 kHz steps, >2 s per point |
The test procedure began by placing the battery pack in the environmental chamber, adjusting it to the target temperature, and stabilizing it for 2 hours. The SOC was then adjusted to the target value using charge-discharge equipment. During testing, ripple parameters were set strictly according to the conditions, and over 20 parameters, including time, local voltage, bus voltage, current, power, and SOC, were collected in real-time. This meticulous approach ensures the reliability of data for subsequent analysis in the context of battery electric car applications.
Data Acquisition and Analysis
We collected extensive data covering electrical performance, thermal behavior, and BMS-related parameters of the battery pack. The data acquisition system operated with millisecond-level time resolution, capturing rapid changes during ripple injection. Measurement accuracy for key parameters like voltage and current was within ±0.1% of full scale (FS), ensuring precision. Data were stored and backed up in real-time for detailed analysis.
Multiple analytical methods were employed to process and interpret the data. First, statistical analysis provided overall descriptions, calculating averages, maximums, minimums, and standard deviations for each parameter. Time-series plots were generated to visualize trends, particularly dynamic responses during ripple injection. Spectral analysis methods were used to investigate frequency characteristics and energy distribution of ripple voltage amplitudes and frequencies. Correlation analysis explored relationships between different parameters, such as battery voltage versus current, power, and ripple parameters versus battery performance metrics. Finally, regression modeling based on the least squares method quantified the influence of ripple frequency on key parameters, which is crucial for optimizing battery electric car systems.
Results and Discussion
Under Condition 1, battery pack parameters exhibited clear trends with varying ripple frequencies. In the low-frequency range (80 Hz to <1 kHz) with UVPP at 12 V, battery current and power fluctuations were relatively large and gradually increased with frequency. As frequency entered the 1 kHz to <5 kHz range, with UVPP rising from 12 V to 24 V, current and power fluctuations diminished significantly. Battery temperature began to rise moderately in the 80 Hz to 5 kHz range. During the 40 kHz to <50 kHz range, as UVPP decreased, parameters stabilized with minor fluctuations. In the 50 kHz to <150 kHz range with UVPP at 8 V, AC impedance showed notable changes, increasing from around 70 kHz, which could affect charge-discharge efficiency. No diagnostic trouble codes (DTCs) were detected, indicating that the battery pack and BMS functioned normally under this condition, though ripple effects on performance remained evident for battery electric car applications.
Condition 2 results were similar to Condition 1 but with some differences. In the low-frequency segment, current fluctuations were pronounced. As ripple frequency and amplitude increased, power fluctuations gradually stabilized. In the high-frequency range (10 kHz to <150 kHz), battery temperature rise was more significant (up to 2.5°C) compared to Condition 1, attributed to higher chemical activity at elevated SOC levels. No DTCs were detected, but the battery pack’s tolerance to ripple appeared weaker at high SOC, necessitating attention in practical battery electric car scenarios.
Under Condition 3, battery performance was significantly impacted by low temperature, which substantially increased internal resistance. During ripple injection, current and power variation amplitudes were slightly smaller than in room temperature conditions. In low frequencies, battery response was sluggish; with increasing frequency, parameter changes were relatively mild. Battery temperature rose slowly, with a maximum increase of only 1.5°C, due to suppressed ripple response in cold environments. DTC checks revealed warnings related to low-temperature battery performance but no critical faults, suggesting that the battery pack and BMS maintained basic operation under low-temperature ripple conditions, though performance was limited, a key consideration for battery electric cars in cold climates.
Condition 4 combined low temperature and high SOC, presenting adverse conditions. High SOC implies higher chemical activity, but low temperature inhibits performance. AC impedance remained elevated in mid-to-high frequency ranges, and temperature rise was consistent with Condition 3. More DTCs related to battery performance and safety were detected, indicating reduced ripple tolerance and heightened safety risks under these conditions, which is critical for the reliability of battery electric cars.
Under Condition 5, with lower ripple voltage amplitude (UVPP = 4 V), battery pack parameters changed more steadily. No DTCs were found, suggesting stable operation of the battery pack and BMS with minimal ripple impact at lower amplitudes, which could inform design thresholds for battery electric car systems.
To summarize the effects, ripple influences battery performance in several ways. In terms of electrothermal characteristics, ripple causes current and power fluctuations, increasing Joule heating losses and elevating battery temperature; prolonged exposure accelerates aging and shortens lifespan. Regarding impedance characteristics, ripple affects AC impedance, with increases at certain frequencies reducing charge-discharge efficiency, impacting the range and power performance of battery electric cars. Ripple also potentially interferes with BMS operation by distorting sensor signals, leading to measurement errors that affect SOC and state-of-health (SOH) estimation. In severe cases, ripple-induced parameter excursions may trigger false protection mechanisms, disrupting vehicle operation.
Differences in ripple effects across temperature and SOC conditions are evident. At room temperature (23±2)°C, high SOC renders batteries more sensitive to ripple, with greater current and power fluctuations and more pronounced temperature rise, due to enhanced chemical activity. In low temperature (-25±2)°C, increased internal resistance leads to sluggish responses, but even small ripples can significantly affect performance, especially when combined with high SOC, posing safety hazards. These insights are vital for designing robust battery systems for battery electric cars.
Model Establishment
Based on the observed characteristics, we developed a regression model relating current fluctuation amplitude ($I_{ ext{fluct}}$) to ripple frequency ($f$). Given the nonlinear relationship, we segmented frequency into different bands for analysis. Initially, a linear regression model was attempted:
$$ I_{ ext{fluct}} = \beta_0 + \beta f + \epsilon $$
where $\beta_0$ is the intercept, $\beta$ is the frequency coefficient, and $\epsilon$ is the error term. Using Python’s statsmodels library on data from Conditions 1 to 4 (covering 80 Hz to <150 kHz, with approximately 25 frequency points per condition repeated twice, totaling 200 samples), we found that the frequency coefficient $\beta$ was not statistically significant, and the model systematically underestimated current fluctuation attenuation at high frequencies, with large residuals.
To improve the model, we divided frequency into low-frequency band $f_1$ ($f \leq 1 ext{ kHz}$) and high-frequency band $f_2$ ($f > 1 ext{ kHz}$), defined as:
$$ f_1 = \min(f, 1000) $$
$$ f_2 = \max(f – 1000, 0) $$
A piecewise linear model was constructed:
$$ I_{ ext{fluct}} = \beta_0 + \beta_1 f_1 + \beta_2 f_2 + \epsilon $$
where $\beta_1$ and $\beta_2$ are coefficients for the low- and high-frequency bands, respectively. After parameter estimation, we obtained $\beta_1 = 0.0015$ and $\beta_2 = -0.0005$. The coefficient of determination $R^2$ was calculated to assess goodness-of-fit:
$$ R^2 = 1 – \frac{\sum_{i=1}^n (I_{ ext{fluct}_i} – \hat{I}_{ ext{fluct}_i})^2}{\sum_{i=1}^n (I_{ ext{fluct}_i} – \bar{I}_{ ext{fluct}})^2} $$
where $I_{ ext{fluct}_i}$ is the $i$-th observed value, $\hat{I}_{ ext{fluct}_i}$ is the predicted value, $\bar{I}_{ ext{fluct}}$ is the sample mean, and $n$ is the sample size. The computed $R^2 = 0.88$, indicating that the model explains 88% of the variance in current fluctuation amplitude, demonstrating good fit.
The root mean square error (RMSE) was calculated as:
$$ ext{RMSE} = \sqrt{\frac{\sum_{i=1}^n (I_{ ext{fluct}_i} – \hat{I}_{ ext{fluct}_i})^2}{n – k – 1}} $$
where $k$ is the number of predictors. We found $ ext{RMSE} \approx 0.27 ext{ A}$, which is acceptable given the current fluctuation range of 0.5 A to 3.0 A. Residual analysis, including quantile-quantile plots, showed approximate normal distribution without evident heteroscedasticity, confirming model validity.
The final regression model is:
$$ I_{ ext{fluct}} = 0.3 + 0.0015 \min(f, 1000) – 0.0005 \max(f – 1000, 0) $$
This model implies that in the low-frequency band ($f \leq 1 ext{ kHz}$), current fluctuation amplitude increases by 0.0015 A for every 10 Hz increase in frequency, reflecting enhanced inductive effects with frequency. In the high-frequency band ($f > 1 ext{ kHz}$), it decreases by 0.0005 A for every 1 kHz increase, indicating capacitive effect suppression of high-frequency fluctuations. Cross-validation with an 80-20 train-test split yielded $R^2 = 0.86$ on the test set, confirming generalization capability. Prediction on Condition 5 data (UVPP = 4 V) showed errors below 5%, validating model applicability to low-amplitude conditions relevant to battery electric cars.
The model’s utility lies in enabling real-time prediction of ripple effects for BMS in battery electric cars, allowing dynamic adjustment of filtering parameters and charge-discharge strategies to mitigate performance degradation and safety risks. This contributes to the advancement of battery electric car technology by enhancing system resilience against electrical disturbances.
Conclusion
This study conducted multi-condition ripple tests on a ternary lithium battery pack with a rated capacity of 60 A·h, yielding several key conclusions. First, ripple significantly affects battery pack performance, causing current and power fluctuations, temperature rise, AC impedance variations, and abnormal chemical reactions, which accelerate aging and pose safety threats. Ripple also interferes with BMS operation, leading to signal measurement errors and potential false protection triggers, compromising the reliability of battery electric cars.
Second, ripple effects vary with temperature and SOC conditions. At room temperature and high SOC, batteries are more sensitive to ripple; at low temperature, performance is inhibited with reduced tolerance; and at low temperature combined with high SOC, safety hazards increase. However, at lower ripple voltage amplitudes (e.g., UVPP ≤ 4 V), system operation remains relatively stable, offering design guidelines for battery electric car systems.
Third, the established piecewise linear regression model between current fluctuation amplitude and ripple frequency reveals a dual-segment characteristic: “low-frequency enhancement and high-frequency suppression.” This model provides a theoretical basis for BMS to predict ripple effects in real-time, dynamically adjust filtering parameters and charge-discharge strategies, thereby reducing battery pack performance loss and safety risks in battery electric cars.
These findings underscore the importance of considering ripple in the design and optimization of battery systems for battery electric cars. Future work could expand to other battery chemistries, larger packs, and integrated vehicle testing to further enhance the robustness and longevity of battery electric car technologies.