The propulsion system of a battery electric car is fundamentally dependent on the performance and reliability of its high-voltage battery pack. Among various electrical stresses encountered during operation, ripple current and voltage constitute a significant yet often underestimated factor. This alternating component superimposed on the DC bus can originate from power electronic converters, such as the motor inverter and the onboard charger. Prolonged exposure to ripple can induce additional heating, accelerate electrochemical degradation, interfere with battery management system (BMS) measurements, and ultimately compromise the safety and longevity of the battery electric car. Therefore, a systematic investigation into the effects of injected ripple under varied environmental and electrical conditions is crucial for robust design and validation.
This work presents an experimental study conducted on a commercial lithium-ion battery pack rated at 60 Ah. The primary objective was to characterize its behavioral response to controlled ripple injection across a wide frequency and amplitude spectrum, while the main contactors were closed, simulating a key-ready or driving state of the battery electric car.
1. Experimental Methodology
The test campaign was designed to evaluate ripple susceptibility under controlled yet demanding conditions, reflecting real-world scenarios for a battery electric car.
1.1 Test Setup and Equipment
A dedicated ripple test bench was constructed. The core system integrated a precision battery cycler, a programmable ripple generator, a thermal chamber, and a high-speed data acquisition unit. The battery pack under test was a Nickel Manganese Cobalt (NMC) ternary lithium-ion pack, representing a common chemistry in modern battery electric cars.
| Item | Specification / Model | Purpose |
|---|---|---|
| Battery Pack | NMC, 60 Ah Nominal Capacity | Device Under Test (DUT) |
| Thermal Chamber | Temperature range: -40°C to +100°C | Environmental conditioning |
| Battery Test System | High-precision, multi-channel | Applying DC bias, measuring voltage/current |
| Ripple Generator | Programmable frequency (80 Hz – 150 kHz), adjustable VPP | Injecting AC ripple signal |
| Data Acquisition Unit | ≥1 kHz sampling rate, isolated channels | Recording voltage, current, temperature, BMS data |
1.2 Ripple Injection Protocol and Test Matrix
The test protocol was structured according to international standards and automotive OEM requirements. Ripple was injected onto the DC bus of the energized pack. Five distinct test profiles (P1-P5) were executed, varying temperature, State of Charge (SOC), and ripple parameters as detailed below. Each frequency step was held for more than 2 seconds, and Diagnostic Trouble Codes (DTCs) were monitored.
| Profile | Temperature | Initial SOC | Ripple Voltage (UVPP) vs. Frequency (f) |
|---|---|---|---|
| P1 | (23 ± 2) °C | 50% ± 1% | f: 80 Hz – <1 kHz (step 10 Hz), UVPP: 12 V. f: 1 – <5 kHz (step 100 Hz), UVPP: 12V→24V. f: 5 – <10 kHz, UVPP: 24 V. f: 10 – <40 kHz (step 1 kHz), UVPP: 24 V. f: 40 – <50 kHz, UVPP: 24V→8V. f: 50 – <150 kHz, UVPP: 8 V. |
| P2 | (23 ± 2) °C | 95% ± 1% | Identical to P1. |
| P3 | (-25 ± 2) °C | 50% ± 1% | Identical to P1. |
| P4 | (-25 ± 2) °C | 95% ± 1% | Identical to P1. |
| P5 | (23 ± 2) °C | 50% ± 1% | f: 80 Hz – <1 kHz (step 10 Hz), UVPP: 4 V. f: 1 – <10 kHz (step 100 Hz), UVPP: 4 V. f: 10 – <150 kHz (step 1 kHz), UVPP: 4 V. |
2. Data Acquisition and Analytical Framework
Time-synchronized data for over 20 parameters, including bus voltage, current, power, cell voltages, pack temperature, and BMS status were recorded at a millisecond resolution. Analysis involved statistical evaluation, time-series visualization, and frequency-domain examination. Crucially, to quantify the primary effect, we focused on modeling the ripple-induced current fluctuation amplitude ($I_{\text{fluct}}$) as a function of ripple frequency ($f$). The fluctuation amplitude was calculated as the standard deviation of the current signal over a stable window at each frequency step.
Preliminary analysis revealed a non-linear relationship between $f$ and $I_{\text{fluct}}$. A single linear regression model was insufficient. The data suggested a clear change in behavior around the 1 kHz boundary. Therefore, a piecewise linear regression approach was adopted, segmenting the frequency domain into a low-frequency ($f_1$) and a high-frequency ($f_2$) regime, defined as:
$$
f_1 = \begin{cases} f & \text{if } f \leq 1000 \text{ Hz} \\ 1000 & \text{if } f > 1000 \text{ Hz} \end{cases}, \quad
f_2 = \begin{cases} 0 & \text{if } f \leq 1000 \text{ Hz} \\ f – 1000 & \text{if } f > 1000 \text{ Hz} \end{cases}
$$
The proposed model structure is:
$$
I_{\text{fluct}} = \beta_0 + \beta_1 f_1 + \beta_2 f_2 + \epsilon
$$
where $\beta_0$ is the intercept, $\beta_1$ and $\beta_2$ are the regression coefficients for the low and high-frequency segments, respectively, and $\epsilon$ is the error term. This model was fitted using data from profiles P1-P4 (high amplitude profiles).
3. Results and Discussion
3.1 Observed Effects of Ripple Injection
The injection of ripple had immediate and measurable impacts on the operational parameters of the battery pack for a battery electric car.
Electrical and Thermal Response: Under high-amplitude ripple (Profiles P1-P4), the battery current and power exhibited significant alternating components. The magnitude of this fluctuation was frequency-dependent. This AC current leads to additional Joule heating ($P_{\text{loss}} = I_{\text{rms}}^2 R_{\text{internal}}$), causing a measurable temperature rise in the pack. For instance, at room temperature and high SOC (P2), the pack temperature increased by approximately 2.5°C more than the baseline at the end of the high-frequency sweep, compared to a 1.8°C rise in the low SOC case (P1). In the low-temperature profiles (P3, P4), the absolute temperature rise was smaller (~1.5°C) due to the initially higher internal resistance and suppressed chemical activity, but the relative impact on performance was more severe.
Impedance Characteristics: The effective AC impedance of the pack, derived from the ratio of ripple voltage to ripple current, showed a complex profile. A notable increase was observed at higher frequencies (e.g., above 70 kHz in P1), as shown in the representative data snippet below. This increased impedance reduces the efficiency of energy transfer and can lead to higher voltage stresses on components within the battery electric car’s powertrain.
BMS Interference: While no critical DTCs were logged in room-temperature tests, the low-temperature, high-SOC profile (P4) triggered several warnings related to voltage consistency and cell balancing. This indicates that ripple can push already sensitive BMS algorithms (e.g., for state estimation at low temperature) closer to their fault detection thresholds, posing a risk of unnecessary derating or shutdown in a battery electric car.
| Ripple Frequency (Hz) | Ripple Voltage UVPP (V) | Battery Current Fluctuation $I_{\text{fluct}}$ (A) | Power Fluctuation (W) | Notes |
|---|---|---|---|---|
| 80 | 12.0 | 0.55 | ~220 | Low frequency, high fluctuation. |
| 1000 | 12.0 | 1.82 | ~700 | Peak fluctuation near segment boundary. |
| 10000 | 24.0 | 0.95 | ~900 | High frequency, lower current fluctuation. |
| 70000 | 8.0 | 0.31 | ~80 | Very high frequency, low current, impedance rise. |
3.2 Piecewise Linear Regression Model
The piecewise linear model provided an excellent fit to the experimental data from the high-amplitude tests. The fitted parameters were:
$$
\beta_0 = 0.30,\quad \beta_1 = 0.0015,\quad \beta_2 = -0.0005
$$
Thus, the final predictive model for current fluctuation is:
$$
I_{\text{fluct}} = 0.30 + 0.0015 \cdot f_1 – 0.0005 \cdot f_2
$$
In practical terms:
For the low-frequency regime ($f \leq 1$ kHz): Every 10 Hz increase in frequency increases the current fluctuation amplitude by approximately 0.015 A. This positive correlation likely reflects the increasing influence of inductive effects in the pack and test loop as frequency rises.
For the high-frequency regime ($f > 1$ kHz): Every 1 kHz increase in frequency decreases the current fluctuation amplitude by approximately 0.0005 A. This negative correlation is attributed to the capacitive filtering effect of the battery pack’s intrinsic capacitance and any parallel filtering components, which shunt high-frequency currents.
The model’s goodness-of-fit was evaluated. The coefficient of determination ($R^2$) was calculated as:
$$
R^2 = 1 – \frac{SSE}{SST} = 1 – \frac{\sum_{i=1}^{n} (I_{\text{fluct},i} – \hat{I}_{\text{fluct},i})^2}{\sum_{i=1}^{n} (I_{\text{fluct},i} – \bar{I}_{\text{fluct}})^2}
$$
where $SSE$ is the sum of squared errors, $SST$ is the total sum of squares, $I_{\text{fluct},i}$ is the observed value, $\hat{I}_{\text{fluct},i}$ is the model prediction, and $\bar{I}_{\text{fluct}}$ is the mean of observed values. The model achieved an $R^2$ value of 0.88, explaining 88% of the variance in the observed current fluctuations. The Root Mean Square Error (RMSE) was approximately 0.27 A, which is acceptable given the fluctuation range of 0.5-3.0 A. Residual analysis confirmed homoscedasticity and approximate normality.
3.3 Impact of Reduced Ripple Amplitude
Profile P5, with a constant low ripple amplitude of 4 V, provided a critical contrast. In this scenario, all electrical parameter fluctuations were markedly subdued. No DTCs were registered, and the temperature rise was negligible. This underscores a key finding: the severity of ripple impact on a battery electric car’s pack is highly amplitude-dependent. While high-amplitude ripple presents clear risks, ensuring that powertrain design limits ripple amplitude on the DC bus can effectively mitigate these adverse effects.
4. Implications for Battery Electric Car Design
The findings of this study have direct consequences for the development of robust battery systems for battery electric cars.
1. BMS Algorithm Robustness: BMS software must account for the presence of ripple, particularly when performing sensitive measurements for State of Charge (SOC) and State of Health (SOH) estimation. Advanced filtering techniques or synchronous sampling strategies may be required to obtain accurate DC values.
2. Pack and Module Design: The frequency-dependent impedance behavior should be considered during the electrical design of the pack. Strategic placement of busbar capacitors or the integration of dedicated filters might be warranted to attenuate high-frequency ripple, especially above 10 kHz where impedance can spike.
3. Powertrain Component Co-Design: Inverter and converter designs for battery electric cars should prioritize minimizing the ripple current injected back into the DC bus. Specifications for maximum allowable ripple amplitude (e.g., as tested in P5) should be part of the interface requirements between the battery pack and the electric drive unit.
4. Low-Temperature Performance: The exacerbated effects (more DTCs, higher impedance) at low temperatures, especially at high SOC, highlight a critical stress case. Battery electric car conditioning strategies should aim to warm the battery not only for discharge power but also to improve its immunity to electrical noise from other subsystems.
5. Conclusion
This comprehensive ripple injection study on a 60 Ah NMC battery pack quantifies the significant influence of AC ripple on the operational parameters critical to a battery electric car. The key conclusions are:
- Ripple current induces measurable fluctuations in pack current and power, leading to additional Joule heating and accelerated thermal stress, which can degrade the long-term health of the battery in a battery electric car.
- The pack’s AC impedance exhibits a non-linear frequency response, with potential sharp increases at very high frequencies, affecting system efficiency.
- The impact is strongly modulated by environmental temperature and SOC. The most challenging condition is low temperature combined with high SOC, where BMS interference is most likely.
- The relationship between ripple frequency and induced current fluctuation amplitude is effectively modeled by a piecewise linear function, characterized by a positive slope (0.0015 A/Hz) below 1 kHz and a negative slope (-0.0005 A/kHz) above 1 kHz. This model provides a valuable tool for predicting electrical stress.
- Limiting the injected ripple voltage amplitude (e.g., to 4 VPP as in P5) effectively mitigates all adverse effects, underscoring the importance of strict ripple control in the powertrain design of a battery electric car.
This work provides a foundational dataset and an analytical model that can inform the design of more resilient battery systems, robust BMS algorithms, and clearer component interface specifications, ultimately contributing to the enhanced safety, reliability, and longevity of battery electric cars.