Fast-Charging Model of Lithium Polymer Cells

Abstract

Lithium-polymer (LiPo) batteries are valued for their high energy density, stable voltage output, low self-discharge, and strong reliability, making them a popular choice for high-performance and portable applications. Despite these advantages, the charging behavior of LiPo batteries—especially during rapid charging—remains an area with limited understanding. This research examines the electro-thermal characteristics of VARTA LiPo batteries when subjected to high charging currents (2C, 3C, and 4C rates). A temperature-sensitive charging model is developed to address safety and efficiency concerns during fast charging. Experimental data indicate that charging at 45 °C yields the best performance, achieving 80% state of charge (SoC) within 25 min. However, charging at temperatures above or below this level (such as 25 °C) reduces efficiency due to increased internal resistance and accelerated battery aging. The model, validated across a range of temperatures (25 °C, 35 °C, 45 °C, and 60 °C), shows that longer constant-current (CC) charging phases at higher temperatures are associated with lower internal resistance. These results highlight the importance of effective thermal management for optimizing both safety and performance in LiPo battery applications.

1. Introduction

The increasing demand for small, lightweight, and highly functional portable electronic devices has underscored the need for advanced battery technologies capable of supporting power-hungry and energy-demanding applications, particularly under challenging operating conditions [1,2,3]. Lithium-polymer batteries (LiPo) have garnered significant attention in various applications due to their favorable characteristics, including moderate energy density (typically 150–200 Wh/kg [4]), elevated voltage levels, minimal self-discharge rates, and robust stability [5,6,7]. However, it is important to recognize that LiPo batteries use a gel-like polymer electrolyte [6], which, while providing flexibility in shape and improved safety [4], generally results in lower electrolyte conductivity compared to the liquid electrolytes found in standard lithium-ion batteries [8,9]. This lower conductivity can limit the power capability of LiPo cells, especially at high discharge rates, making them less suitable for applications where sustained high power output is required [10].

Despite these limitations, LiPo batteries continue to expand their presence in consumer electronics, drones, and other specialized markets. Their performance and safety, however, are critically influenced by factors such as thermal stability, cell design, assembly quality, and operational conditions—including temperature [11], charge–discharge currents, and voltage [5,12]. High charging C-rates, for instance, can reduce battery lifespan and cause irreversible damage [13,14]. These considerations are important for accurately positioning LiPo technology within the broader landscape of advanced battery chemistries.

Nonetheless, the charging capability of LiPo batteries, especially under fast-charging profiles with high current rates, remains insufficiently studied, raising concerns about durability and thermal management [15,16]. Under such conditions, LiPo cells are susceptible to adverse effects such as rupturing, ignition, or even explosion, particularly when exposed to inadequate ventilation, overcharging, or overheating [17,18]. If heat dissipation fails to match internal heat generation, thermal runaway risks are exacerbated. To address these challenges, it is essential to develop robust battery models.

Recent advances in LiPo battery modeling have produced a variety of electrothermal and electrochemical frameworks that are essential for understanding and predicting battery behavior under diverse operating conditions. Electrothermal models, including both lumped-parameter and multi-dimensional approaches, have been widely adopted to capture the interplay between electrical performance and heat generation, providing insights into temperature rise, heat dissipation, and the effects of thermal gradients within cells and packs. Electrochemical models, grounded in porous electrode theory and detailed reaction kinetics, offer a physics-based perspective on charge transfer, diffusion, and degradation processes, though they are often computationally intensive. To bridge the gap between accuracy and practical application, many studies employ reduced-order or equivalent circuit models with temperature-dependent parameters, enabling real-time prediction and control in battery management systems.

In this context, the present study not only analyzes the electro-thermal characteristics of VARTA LiPO batteries under high-charging currents (2C, 3C, and 4C), but also develops and validates a comprehensive charging model across a range of temperatures (25 °C, 35 °C, 45 °C, and 60 °C). The model based on reduced-order methodology accurately predicts battery temperature and state of charge during charging, providing critical insights into safe and efficient fast-charging protocols. By integrating experimental validation at different temperatures, the research offers practical solutions for optimizing LiPO charging strategies and mitigating safety risks, thereby supporting the broader adoption of LiPO batteries in modern electronics and electric vehicle platforms.

2. Fast-Charging Testing Matrix

2.1. Battery Feature

The batteries evaluated in this study were pouch-type VARTA LPP 1.16 Ah cells (VARTA, Stockholm, Sweden), each weighing approximately 26 g and constructed with a Li(NiMnCo)1/31/3O22 cathode and a graphite anode (Figure 1). Key specifications include a nominal capacity of 1.16 Ah, internal resistance of 0.2 mΩ, and a nominal voltage of 3.7 V [19]. Battery testing was conducted using the computer-controlled Neware CT-4008 system (Neware, Shenzhen, China), which supports a voltage range from 25 mV to 5 V and currents from 0.5 mA to 6 A, allowing for precise control of charging and discharging protocols in accordance with the manufacturer’s guidelines [19]. Throughout the experiments, a type-K thermocouple was attached to each cell to continuously monitor temperature.

2.2. Charging Test Matrix

The charging test follows a standardized mission profile for battery charging [20,21], incorporating multiple phases to thoroughly evaluate battery performance. The procedure begins with high charging currents of 2C (2.32 A), 3C (3.48 A), and 4C (4.64 A) applied during the constant current (CC) phase, continuing until the battery voltage reaches 4.2 V. This is followed by a constant voltage (CV) phase, where charging is maintained at 4.2 V until the current drops to C/20 (0.15 A), with ‘C’ representing the cell’s nominal capacity [22].

The specific stages of the charging protocol are depicted in Figure 2 and described as follows:

• Charging at C/3 from 0% to 10% State of Charge (SoC) to avoid rapid aging under 10% SoC.
• Charging at 4C from 10% SoC up to the upper cut-off voltage of 4.2 V.
• Maintaining a CV phase until the charge rate reaches C/20.

To assess thermal effects under fast charging, tests are conducted at different ambient temperatures: 25 °C, 35 °C, 45 °C, and 60 °C. This approach enables a comprehensive analysis of both electrical and thermal battery behavior across a range of operating conditions.

2.3. Fast-Charging Results

Figure 3 illustrates the charging profile of the LiPo battery at 25 °C under three different charge rates: 2C, 3C, and 4C. The data, presented as current, state of charge (SoC), and temperature over time, highlight several key behaviors. Initially, charging begins at a lower current rate (C/3 or 0.386 A), gradually increasing SoC to 10% over 20 min. Once the high current phase starts, the constant current (CC) phase transitions rapidly to the constant voltage (CV) phase. This swift transition is due to the battery’s high internal resistance (0.2 Ω at 25 °C), which causes the cell voltage to quickly reach the upper limit of 4.2 V when subjected to high current, thereby shortening the CC phase significantly. As a result, only a modest temperature rise is observed, but the overall charging time to reach 80% SoC is prolonged to over 55 min, reflecting the lesser performance of these cells at room temperature.

Further tests at elevated temperatures (35 °C, 45 °C, and 60 °C) were conducted using only the 2C charge rate for safety and to minimize degradation. The results, shown in Figure 4, compare voltage, current, SoC, and temperature curves across these conditions. At higher temperatures, the CC phase is notably extended, primarily because internal resistance decreases as temperature rises. Notably, at 45 °C, the battery achieved 80% SoC in just 23 min (compared to 36 min at 25 °C), indicating that raising the cell temperature to this level can significantly enhance fast-charging performance. This suggests that effective thermal management, maintaining the battery around 45 °C during charging, may be crucial for optimizing LiPo applications.

3. Fast-Charging Model

To accurately develop an optimal thermal management strategy, it is essential to construct an electro-thermal model. In this section, the one-dimensional (1D) electro-thermal model of the LiPO battery is introduced and validated.

3.1. Model Methodology

The methodology outlined in this paper describes the development of a comprehensive battery model by integrating and validating specialized sub-models within a unified modeling framework. This framework incorporates both electrical and thermal models, as illustrated in Figure 5. The entire model was developed using MATLAB/Simulink^® 2024. The electro-thermal component simulates the electrical and thermal behaviors of the battery cell, capturing key parameters, such as voltage, state of charge (SoC), and temperature. The following subsections provide detailed descriptions of each part of the model.

3.2. LiPo 2nd Order Model

For model development, a one-dimensional electro-thermal model is employed, utilizing a semi-empirical approach within the MATLAB/Simulink^® 2024 environment. The model is designed to simulate the electrical and thermal behavior of the battery cell through two main modules: the electrical and thermal components. The electrical module determines the SoC by analyzing electrical parameters, while the thermal module estimates the cell’s temperature using heat generation equations.

The electrical model, depicted in Figure 6, is based on the second-order Thevenin model [23,24], consisting of a voltage source in series with two parallel RC networks and an ohmic resistor. According to the equivalent circuit model, the output voltage of the Li-ion battery cell is calculated as the voltage drop across the open-circuit voltage (OCV), the ohmic resistance (R₀), the concentration polarization resistance (R₁C₁ circuit), and the activation polarization resistance (R₂C₂ circuit). The resulting output voltage is computed using the following equation [25,26]:

$$V_{cell}=OCV-R_1{I}_1-R_2{I}_2-R_0{I}_{batt}$$

(1)

where I_batt is the flowing current in the battery (A). The SoC is subsequently determined using the Coulomb-counting method, defined as follows [27,28]:

$$SoC={SoC}_0-{\displaystyle \frac{1}{C_{init}}}\int I_{batt}dt$$

(2)

where SoC₀ represents the initial state of charge of the cell, and C_init is the initial capacity (Ah), which is assumed to depend on temperature and to be influenced by both the applied current and cell degradation. In Equation (1), the OCV values were directly obtained from OCV tests. The resistances, which vary with temperature, SoC, and aging, were determined using a parameter extraction algorithm. Based on Hybrid Pulse Power Characterization (HPPC) test results, a fitting algorithm was used to match simulation data with experimental results, enabling the extraction of individual parameters. These extracted parameters were then mapped into lookup tables within MATLAB/Simulink^®. To enable a CC-CV profile, the model uses a Simulink block called Battery CC-CV, which is specifically designed to implement the constant-current, constant-voltage charging algorithm. During charging, the block first applies a constant current until the cell voltage reaches the specified threshold (in this case, 4.2 V). Once this voltage is reached, the block transitions to the CV phase, where it maintains the cell voltage at 4.2 V by automatically reducing the charging current as needed. This is achieved through an internal control logic—typically a proportional-integral (PI) controller—that continuously monitors the cell voltage and adjusts the charging current to ensure the voltage does not exceed the set value. The charging process in the CV phase continues until the current drops to a predefined cutoff, at which point charging is terminated. This approach accurately replicates the standard CC-CV charging protocol used in battery management systems.

The thermal aspect of the model incorporates thermodynamic equations specific to cylindrical cells. It assumes a single temperature point, where heat is generated at a specific location on the cell’s surface, defined by its specific heat capacity and mass. Heat dissipation from the cell’s surface to the surrounding environment is modeled using a heat balance equation, which describes the thermal exchange between the cell and the ambient environment as follows [29]:

$$\left\{\begin{array}{c}{\displaystyle \frac{{dU}_{cell}}{dt}}=Q_{gen} (t)-Q_{loss }(t)=m.Cp.{\displaystyle \frac{dT}{dt}}\\ Q_{gen}=R_{int}.{\left(I_{batt}\right)}^2\\ {Q_{loss}=Q}_{conv}=h_{conv}{.S}_{area}.(T_{cell}-T_{amb})\end{array}\right\}$$

(3)

In these equations, U_cell is the internal energy of the cell (J), Q_gen is the rate of heat generation (W), and Q_loss is the heat loss (W). C_p is the specific heat of the cell (kJ/kg·K), and m is the cell mass (kg). The model operates under the following assumptions:

• The cell’s surface temperature (T_cell) is uniformly distributed, representing the overall battery temperature;
• Joule heating is used to estimate heat generation, and natural convective heat transfer is considered, with parameters such as ambient temperature (T_amb, °C), surface area for heat exchange (S_area, m²), and the convective heat transfer coefficient (h_conv, W/m²·K).
• The specific heat capacity was obtained from thermal pulse tests, and the surface area was calculated directly from cell dimensions (S_area = 0.0024 m²). A natural convection coefficient of h_conv = 15 W/m²·K was applied [30].
• Significant temperature gradients can develop between the surface and the interior of lithium-ion cells, particularly at high current rates such as 3C and 4C [31,32]; however, LiPo 1.16 Ah are exceptionally thin (4 mm) and made of conductive casing material, resulting in minimal thermal resistance across the cell thickness. Thus, the temperature gradient between the surface and the interior remains negligible in this study.

Figure 6. The schematic of the second-order Thévenin model [33].

Figure 6. The schematic of the second-order Thévenin model [33].

4. LiPo Model Results

This section presents the validation results for the developed LiPo battery model. The model’s performance was rigorously validated through a series of experiments designed to evaluate both electrical and thermal behaviors. These validation tests, detailed in the following subsections, consist of a 2C charging current performed at different temperatures: 25 °C, 35 °C, 45 °C, and 60 °C. The next subsections compare simulation results with experimental data to confirm the model’s accuracy for the electrical and thermal aspects of the model.

4.1. Electrical Model Validation

The accuracy of the developed electrical model was assessed by comparing simulated and experimental voltage profiles under various temperature conditions, as illustrated in Figure 7. The results show that the simulated voltage curves (red lines) closely follow the measured data (black lines) across all tested temperatures—25 °C, 35 °C, 45 °C, and 60 °C. This strong agreement demonstrates the model’s ability to capture the essential dynamic behaviors of the LiPo cell, including the initial voltage rise, plateau regions, and sharp transitions during charging. The model effectively reflects the influence of temperature on cell voltage, with only minor deviations observed during rapid voltage changes, which may be attributed to measurement noise or unmodeled transient phenomena. Quantitatively, the root mean square error (RMSE) values for all temperatures are listed in

Table 1. RMSE values for the LiPo electro-thermal model.

Temperature (°C)	25 °C	35 °C	45 °C	60 °C
RMSE electrical (%)	1.10	1.12	1.87	1.59
RMSE thermal (%)	1.54	1.2	1.34	1.73

, and all values are below 2%, indicating a high degree of accuracy in the voltage prediction. Overall, these results confirm that the electrical model reliably predicts the voltage response of the battery under different thermal conditions, validating its suitability for further system-level simulations and control applications.

4.2. Thermal Model Validation

Thermal model validation was performed by comparing the simulated temperature evolution of the battery cell with experimental measurements at the same set of ambient temperatures, as shown in Figure 8. The model successfully captures the overall thermal response of the cell, including the initial temperature stabilization, the subsequent rise during charging, and the cooling phase after current interruption. The simulated temperature curves (red lines) closely match the experimental data (black lines), particularly in capturing the peak temperatures and the general shape of the temperature profile at each condition. Some discrepancies are observed during the transient heating and cooling phases, which may be due to simplifications in the lumped thermal model or uncertainties in the heat transfer coefficients (e.g., natural convection coefficient). Nevertheless, the RMSE values for all cases are below 2%, as listed in Table 1.

Despite these minor differences, the model demonstrates a robust ability to estimate the cell’s thermal behavior across a range of operating temperatures, providing a reliable basis for thermal management and safety analysis in practical applications.

5. Conclusions

This study comprehensively investigated the electro-thermal behavior of VARTA LiPo batteries under fast-charging conditions and developed a robust, temperature-dependent electro-thermal model validated through extensive experimentation. The findings demonstrate that charging performance and safety are highly sensitive to temperature, with optimal results achieved at 45 °C, where the battery reached 80% state of charge in just 23 min. Charging at temperatures below and above this threshold led to diminished efficiency due to increased internal resistance and accelerated cell degradation, underscoring the importance of precise thermal management.

The one-dimensional second-order electro-thermal model, implemented in MATLAB/Simulink^®, accurately captured both the electrical and thermal dynamics of the battery. Model validation against experimental data at multiple temperatures (25 °C, 35 °C, 45 °C, and 60 °C) showed excellent agreement, with RMSE values consistently below 2% for both voltage and temperature predictions. This high level of accuracy confirms the model’s suitability for use in battery management systems and for optimizing fast-charging protocols.

However, several limitations should be acknowledged. The current validation approach is based solely on thermal and voltage data and does not directly assess degradation mechanisms such as lithium plating, which is a key safety and performance risk during fast charging. Comprehensive validation of the proposed fast-charging protocol will require future studies incorporating differential voltage analysis and post-mortem characterization to evaluate degradation and lithium plating risks. Additionally, the model assumes a single lumped temperature node, a constant convective heat transfer coefficient, and neglects spatial temperature gradients within the cell. While these simplifications are justified for the thin pouch cells and moderate conditions studied here, they may not fully capture the thermal behavior of large-format or high-power cells or cell-to-cell interactions in battery packs.

Future research should address these limitations by extending the modeling framework to include aging effects (such as capacity fade and impedance growth), spatial temperature gradients, and multi-cell configurations to better reflect real-world operating conditions. Incorporating established aging models would improve the realism and long-term applicability of the approach. Moreover, validation against additional charging protocols (e.g., multi-stage constant current) and the development of real-time battery thermal management algorithms are promising directions. In this context, model predictive control (MPC) is especially promising, as it enables dynamic optimization of charging currents while considering both battery state and thermal constraints, leading to safer and more efficient charging processes.

Overall, this work highlights the critical role of integrated electro-thermal modeling in advancing the safety, efficiency, and longevity of LiPo batteries under fast-charging scenarios. The validated model provides a powerful tool for the design of advanced thermal management strategies, paving the way for safer and more efficient deployment of LiPo batteries in high-performance applications.