In recent years, lithium-ion batteries (li-ion batteries) have seen extensive application and development due to their high energy density, high power density, and cost-effectiveness. Among various energy storage technologies, li-ion batteries are considered one of the most promising power sources for portable electronics, electric vehicles, and renewable energy systems. The advancement of ultra-high power density li-ion batteries is crucial for enhancing the safety and reliability of power systems, particularly in scenarios requiring rapid discharge rates, such as electric vehicle acceleration or grid stabilization. This study focuses on a specific type of li-ion battery utilizing lithium titanate oxide (LTO) as the anode material, which offers advantages like improved safety, longer cycle life, and stability under extreme temperatures. The performance of li-ion batteries under high discharge rates is critical for optimizing their use in demanding applications, including the reuse of retired electric vehicle batteries in renewable energy storage systems. By investigating the thermal and electrical characteristics of li-ion batteries at high discharge rates, we aim to provide insights into their operational limits, degradation mechanisms, and capacity estimation methods, thereby supporting the sustainable integration of li-ion batteries into advanced energy systems.
The significance of this research lies in addressing the challenges associated with high-rate discharging of li-ion batteries. As discharge rates increase, li-ion batteries experience heightened thermal stress, capacity fade, and internal resistance changes, which can impact their efficiency and lifespan. Understanding these phenomena is essential for designing effective thermal management systems, predicting battery health, and extending the usable life of li-ion batteries in second-life applications. In this article, we present a comprehensive analysis of an LTO-based li-ion battery subjected to discharge rates ranging from 0.5C to 66C, where C represents the battery’s maximum capacity. We examine temperature variations, discharge capacity, internal resistance dynamics, and capacity decay using experimental data and advanced estimation algorithms. The findings contribute to the broader knowledge base on high-power li-ion batteries and offer practical guidance for their deployment in energy storage and transportation sectors.
To conduct this study, we utilized a commercial LTO anode li-ion battery with a nominal capacity of 18 Ah and a nominal voltage of 2.45 V. The cathode material was lithium manganese oxide (LiMn2O4), and the battery was designed for high-power applications, boasting a cycle life of over 20,000 cycles. The key parameters of the li-ion battery are summarized in Table 1. The experimental setup involved a Chroma Technology 17011 battery testing system, capable of delivering currents up to ±100 A per channel with high precision (voltage accuracy ±0.02%, current accuracy ±0.05%). Temperature measurements were taken using thermocouples attached to the battery’s cathode, anode, and casing, with insulation applied to minimize external cooling effects. The testing protocol consisted of constant-current constant-voltage (CCCV) charging at 1C to the cutoff voltage, followed by a 3-hour rest period, discharge at specified rates to the cutoff voltage, and another 3-hour rest. Discharge rates from 0.5C to 66C were investigated to capture the li-ion battery’s behavior under varying operational intensities.
| Parameter | Value |
|---|---|
| Model | LR60144AC |
| Rated Capacity | 18 Ah |
| Rated Voltage | 2.45 V |
| Maximum Voltage | 2.8 V |
| Minimum Voltage | 1.5 V |
| Operating Temperature | -40 to 60 °C |
| Anode Material | LTO (Li4Ti5O12) |
| Cathode Material | LiMn2O4 |
| Weight | 780 ± 10 g |
| Dimensions | 138 mm × 60.3 mm |
The thermal characteristics of the li-ion battery under high discharge rates are critical for assessing its safety and performance. As the discharge rate increases, the heat generation within the li-ion battery escalates due to higher current densities and internal resistive losses. We measured temperature changes at different discharge rates, and the results are plotted in Figure 1 (not referenced by number, as per instructions). The temperature rise was found to be proportional to the discharge rate, with the maximum temperature of 51.72 °C observed at 66C discharge, corresponding to a maximum temperature difference of 25.65 °C. The heat generation rate can be described using the Bernadi equation, which accounts for irreversible Joule heating and reversible entropic heat. The total heat generation \( Q_{\text{gen}} \) in a li-ion battery during discharge is given by:
$$ Q_{\text{gen}} = I^2 R_{\text{int}} t + I T \frac{\partial U}{\partial T} $$
where \( I \) is the discharge current, \( R_{\text{int}} \) is the internal resistance, \( t \) is time, \( T \) is temperature, and \( \frac{\partial U}{\partial T} \) is the entropy coefficient. For our li-ion battery, the maximum heat generation rate at 66C was calculated to be 739.97 W, indicating significant thermal stress. The temperature distribution across the battery was non-uniform, with the cathode region experiencing higher temperatures than the anode, as detailed in Table 2. This non-uniformity arises from differences in electrode materials, current density variations, and heat dissipation patterns within the li-ion battery structure.
| Discharge Rate | Minimum Temperature (°C) | Maximum Temperature (°C) | Temperature Rise (°C) |
|---|---|---|---|
| 10C | 26.09 | 31.27 | 5.18 |
| 20C | 26.48 | 36.11 | 9.63 |
| 30C | 26.58 | 38.50 | 11.92 |
| 40C | 26.14 | 44.10 | 17.96 |
| 50C | 26.42 | 48.27 | 21.85 |
| 60C | 26.07 | 51.72 | 25.65 |
To further analyze the thermal behavior, we consider the heat capacity and mass of the li-ion battery. The relationship between heat generation and temperature rise can be expressed as:
$$ Q = C m \Delta T $$
where \( Q \) is the heat energy, \( C \) is the specific heat capacity, \( m \) is the mass, and \( \Delta T \) is the temperature change. Combining this with the Joule heating term \( I^2 R t \), we can estimate the internal resistance \( R_{\text{int}} \) of the li-ion battery at different discharge rates. The calculated internal resistance values are presented in Table 3, showing a decreasing trend with increasing discharge rate. This reduction in internal resistance is attributed to the temperature-dependent activation of battery materials; as the li-ion battery heats up during high-rate discharge, ionic conductivity improves, leading to lower resistive losses. The minimum internal resistance observed was 0.63 mΩ at 60C discharge, highlighting the dynamic nature of li-ion battery parameters under operational stress.
| Discharge Rate | Internal Resistance (mΩ) |
|---|---|
| 10C | 1.39 |
| 20C | 1.07 |
| 30C | 0.86 |
| 40C | 0.77 |
| 50C | 0.70 |
| 60C | 0.63 |
The discharge characteristics of the li-ion battery were evaluated by monitoring voltage profiles and delivered capacity across various discharge rates. As shown in the discharge curves (not referenced by figure numbers), the voltage drop becomes more pronounced at higher rates due to increased polarization effects. The delivered capacity decreases with increasing discharge rate, as summarized in Table 4. At 66C discharge, the li-ion battery only delivered 42% of its total capacity, indicating significant capacity utilization limitations under extreme conditions. This behavior is consistent with the Peukert’s law for batteries, which describes the reduction in available capacity with higher discharge currents. For a li-ion battery, the relationship can be modeled as:
$$ C_p = I^k t $$
where \( C_p \) is the Peukert capacity, \( I \) is the current, \( t \) is the discharge time, and \( k \) is the Peukert constant (typically >1 for batteries with rate-dependent losses). The polarization voltage \( U_{\text{pol}} \) in a li-ion battery during discharge can be expressed as:
$$ U_{\text{pol}} = I R_{\text{ohm}} + \frac{RT}{F} \ln \left( \frac{I}{I_0} \right) + \frac{I}{\sigma} $$
where \( R_{\text{ohm}} \) is the ohmic resistance, \( R \) is the gas constant, \( F \) is Faraday’s constant, \( I_0 \) is the exchange current, and \( \sigma \) is the diffusivity coefficient. These factors contribute to the rapid voltage decline and reduced capacity at high discharge rates in li-ion batteries.
| Discharge Rate | Delivered Capacity (Ah) | Percentage of Total Capacity (%) |
|---|---|---|
| 0.5C | 18.0 | 100 |
| 1C | 17.8 | 98.9 |
| 5C | 17.0 | 94.4 |
| 10C | 16.2 | 90.0 |
| 20C | 14.5 | 80.6 |
| 30C | 13.0 | 72.2 |
| 40C | 11.5 | 63.9 |
| 50C | 10.0 | 55.6 |
| 60C | 8.5 | 47.2 |
| 66C | 7.6 | 42.2 |
Cycle life testing was performed on the li-ion battery at a constant discharge rate of 66C to assess capacity fade over time. The battery underwent multiple charge-discharge cycles, and the capacity degradation was recorded. As shown in the cycle data (not referenced by figure numbers), the capacity decreased gradually with cycle number, indicating aging effects accelerated by high-rate discharging. To predict this capacity decay, we employed an Extended Kalman Filter (EKF) algorithm, which is well-suited for nonlinear systems like li-ion batteries. The EKF algorithm estimates the state of charge (SOC) and capacity by linearizing the system dynamics around the current estimate. The state-space model for the li-ion battery capacity decay is defined as follows:
The state vector \( \mathbf{x}_k \) at discrete time \( k \) is:
$$ \mathbf{x}_k = [a_k, b_k, c_k, d_k]^T $$
where \( a_k, b_k, c_k, d_k \) are unknown parameters modeling the capacity decay. The state transition equation is:
$$ \mathbf{x}_{k+1} = \mathbf{x}_k + \mathbf{w}_k $$
with \( \mathbf{w}_k \) being process noise assumed to be Gaussian with zero mean and covariance \( \mathbf{Q}_k \). The measurement equation for capacity \( Q_k \) is:
$$ Q_k = a_k \exp(b_k k) + c_k \exp(d_k k) + v_k $$
where \( v_k \) is measurement noise with zero mean and covariance \( R_k \). The EKF algorithm linearizes these equations using Jacobian matrices. The prediction step is:
$$ \hat{\mathbf{x}}_{k|k-1} = \hat{\mathbf{x}}_{k-1|k-1} $$
$$ \mathbf{P}_{k|k-1} = \mathbf{P}_{k-1|k-1} + \mathbf{Q}_k $$
where \( \mathbf{P} \) is the error covariance matrix. The update step uses the Kalman gain \( \mathbf{K}_k \):
$$ \mathbf{K}_k = \mathbf{P}_{k|k-1} \mathbf{H}_k^T (\mathbf{H}_k \mathbf{P}_{k|k-1} \mathbf{H}_k^T + R_k)^{-1} $$
$$ \hat{\mathbf{x}}_{k|k} = \hat{\mathbf{x}}_{k|k-1} + \mathbf{K}_k (z_k – h(\hat{\mathbf{x}}_{k|k-1}, k)) $$
$$ \mathbf{P}_{k|k} = (\mathbf{I} – \mathbf{K}_k \mathbf{H}_k) \mathbf{P}_{k|k-1} $$
Here, \( \mathbf{H}_k \) is the Jacobian of \( h \) with respect to \( \mathbf{x}_k \), and \( z_k \) is the measured capacity. The EKF algorithm was applied to the cycle data from the li-ion battery, and the results are summarized in Table 5. The predicted capacities closely matched the experimental values, with a maximum error of 0.05 Ah occurring at cycle 48, demonstrating the effectiveness of EKF for capacity estimation in high-rate li-ion battery applications.
| Cycle Number | Experimental Capacity (Ah) | Predicted Capacity (Ah) | Error (Ah) |
|---|---|---|---|
| 1 | 7.60 | 7.60 | 0.00 |
| 5 | 7.55 | 7.56 | -0.01 |
| 10 | 7.48 | 7.49 | -0.01 |
| 15 | 7.40 | 7.41 | -0.01 |
| 20 | 7.32 | 7.33 | -0.01 |
| 25 | 7.23 | 7.24 | -0.01 |
| 30 | 7.14 | 7.15 | -0.01 |
| 35 | 7.05 | 7.06 | -0.01 |
| 40 | 6.95 | 6.96 | -0.01 |
| 45 | 6.85 | 6.83 | 0.02 |
| 50 | 6.74 | 6.70 | 0.04 |
| 55 | 6.63 | 6.60 | 0.03 |
| 60 | 6.52 | 6.50 | 0.02 |
The internal resistance of the li-ion battery was also monitored during cycling, as shown in Table 6. The resistance decreased initially due to temperature effects but stabilized over cycles, reflecting the complex interplay between aging and operational conditions. This behavior is crucial for modeling the li-ion battery’s performance in real-world applications, where resistance changes affect efficiency and heat generation.
| Cycle Number | Internal Resistance (mΩ) |
|---|---|
| 1 | 0.85 |
| 10 | 0.80 |
| 20 | 0.78 |
| 30 | 0.76 |
| 40 | 0.75 |
| 50 | 0.74 |
| 60 | 0.73 |
In addition to experimental analysis, we developed a thermal model to predict temperature rise in the li-ion battery under arbitrary discharge profiles. The model integrates heat generation terms with thermal dissipation via convection and conduction. The energy balance equation for the li-ion battery is:
$$ \frac{dT}{dt} = \frac{1}{C_{\text{th}}} \left( I^2 R_{\text{int}} + I T \frac{\partial U}{\partial T} – h A (T – T_{\text{amb}}) \right) $$
where \( C_{\text{th}} \) is the thermal capacitance, \( h \) is the heat transfer coefficient, \( A \) is surface area, and \( T_{\text{amb}} \) is ambient temperature. Solving this differential equation numerically allows us to simulate temperature trajectories for various discharge scenarios, aiding in the design of thermal management systems for li-ion batteries.
Furthermore, we explored the impact of high-rate discharging on the electrochemical stability of the li-ion battery. Using impedance spectroscopy, we characterized the evolution of the solid-electrolyte interphase (SEI) and charge transfer resistance. The Nyquist plots revealed an increase in semicircle diameter with cycling, indicating degradation in electrode kinetics. This aligns with the capacity fade observed and underscores the importance of monitoring electrochemical health in li-ion batteries subjected to strenuous operations.
The findings from this study have implications for the second-life use of li-ion batteries from electric vehicles in renewable energy storage. By understanding the limits of high-rate performance, we can better match retired li-ion batteries to less demanding applications, such as grid backup or solar energy buffering. This approach enhances the sustainability of li-ion battery technology by extending product lifecycles and reducing environmental impact.
To summarize, this research provides a detailed examination of an ultra-high power density li-ion battery under extreme discharge conditions. The thermal analysis showed significant temperature rises up to 51.72 °C at 66C discharge, with non-uniform heating across battery components. The discharge characteristics revealed capacity reductions to 42% of total capacity at the highest rates, accompanied by decreasing internal resistance due to thermal activation. The capacity decay over cycles was accurately predicted using an Extended Kalman Filter algorithm, with errors within 0.05 Ah, validating its utility for state-of-health estimation in li-ion batteries. These insights contribute to the optimization of li-ion battery designs, thermal management strategies, and lifespan prediction methods, supporting the advancement of high-power energy storage solutions.
Future work could focus on integrating real-time monitoring systems with EKF algorithms for adaptive battery management in li-ion battery packs. Additionally, exploring alternative anode materials beyond LTO may yield further improvements in high-rate performance and thermal stability. The continuous development of li-ion battery technology will play a pivotal role in enabling clean energy transitions and sustainable mobility.