Effect of Cell-to-Cell Internal Resistance Variations on the Thermal Performance of Lithium-Ion Batteries for Urban Air Mobility

Abstract

This study examines the thermal behavior of lithium-ion battery modules intended for Urban Air Mobility (UAM), a forthcoming urban transport system designed to facilitate efficient and secure passenger and cargo transport within city centers. UAM applications necessitate batteries with high energy densities capable of sustaining elevated discharge rates during critical phases such as takeoff and landing. The battery module evaluated in this study comprises four cells arranged in series and configured as a submodule for UAM applications. A three-dimensional thermal model was utilized to analyze the impact of external temperature fluctuations and high discharge rates on the performance of the battery module. The numerical findings indicated considerable variations in temperature and internal resistance among the cells, especially under high discharge rates at low temperatures, with a maximum temperature deviation of 32.952 °C observed at an 8 C discharge rate. These thermal non-uniformities were attributed to variations in cell capacity and internal resistance, which were amplified by manufacturing inconsistencies and operational conditions. The study underscores the necessity of robust thermal management strategies to mitigate the risk of thermal runaway and ensure the operational safety and reliability of UAM systems. The results emphasize the critical role of advanced Battery Management Systems (BMS) in monitoring and controlling cell voltage and temperature to achieve consistent performance across the battery module. This research contributes valuable insights into the design of more efficient and reliable battery modules for UAM, highlighting the importance of addressing cell-to-cell performance discrepancies to enhance overall module efficacy and durability.

1. Introduction

Urban air mobility (UAM) is a future air transport system that safely and conveniently transports passengers and cargo in the city center. It is expected to be a new means of transportation as collision avoidance and autonomous flight technologies develop along with the development of batteries with high energy density and high-efficiency motor technology [1,2]. The battery modules for UAM must be developed with careful consideration of power, energy density, safety, durability, and charging time, as these factors significantly impact the direct operating cost (DOC), which is essential for the commercialization of UAMs [3]. The cell-to-pack packaging efficiency of UAM batteries is approximately 60–70%, and based on this efficiency, battery cells with an energy density of over 300 Wh/kg are being developed [3,4]. As high discharge characteristics are required when UAM takes off and lands, a design that considers the heating characteristics due to high discharge along with the packaging design of the battery module is becoming increasingly important [5]. In addition, it is essential to develop a battery management system (BMS) that can effectively monitor and control the voltage and temperature of cells constituting the UAM battery module. When a battery module composed of multiple lithium-ion battery cells is discharged at a high rate, inter-cell performance characteristics caused by the capacity and internal resistance deviations of cells constituting the battery module greatly affect the overall performance of the battery module. The deviation between cell capacity and internal resistance inevitably occurs in the process of manufacturing a battery cell, and the deviation of cells occurring after battery operation affects the battery performance and the deviation of heat generation between cells, resulting in overall performance degradation. Accordingly, there is a need for a technology to predict cell performance, deviations throughout the module, and corresponding responses. A change in the capacity and state of health (SoH) of the cells and a difference in internal resistance, which are inevitably caused in the process of manufacturing lithium-ion battery cells, affect the life of the battery module in which the cells are assembled. In general, a battery module for energy storage systems (ESSs) or electric vehicles (EVs) configures a plurality of lithium-ion batteries in series or in parallel, depending on the target applications. In general, battery cells configured in parallel are more difficult to monitor and manage deviations between cells than battery cells configured in series. When lithium-ion battery cells are connected in parallel, the current of the cell is imbalanced because it is difficult to measure and manage the current deviation. Therefore, when manufacturing a battery module, it is necessary to affect and manage it, and many related studies are being conducted.

Many researchers have studied the differences between battery cells and how they change over time and affect battery life and performance as a result. Paul et al. [6] studied the battery cells connected in series were studied to consider the capacity, initial internal resistance, life rate and heat of the initial battery cells. The analysis showed that the non-uniformity of cell aging was due to the current distribution of the non-uniform cells. Chiu et al. [7] focused on the series of battery cells, and it was confirmed that the decrease in battery capacity increased as temperature changed. Many studies have been conducted on battery cells configured in parallel. Offer et al. [8] reported that the contact resistance of the two internal cells was the cause of the non-uniform current flowing inside the pack. This led to a non-uniform load of each cell. Bruen and Macro [9] experimentally evaluated the imbalance of parallel cells. It was confirmed that a difference of 30% in impedance caused a change of 60% of the peak cell current and 6% during the cycle. Fernandez et al. [10] confirmed that the initial SoH 40% deviation decreased to 10% after 500 cycles because a lithium-ion battery experiment connected in parallel at 25 °C. Shi et al. [11] investigated parallel LIFePO4 current imbalance. Rapid aging could reduce the imbalance by suppressing changes in temperature and current. Gong et al. [12] showed a large deviation between cells when discharging cells with different levels of deterioration composed of parallel, which could accelerate aging and lead to serious problems. Liu et al. [13] applied a thermal single-particle model to a parallel battery and found an irregular overpotential caused by internal connections and temperature gradients that affected the battery pack. Song et al. [14] analyzed the current, degradation rate, state of charge (SoC), and heat dissipation between cells using a thermal, electrical aging model and compared the long-term capacity.

Until now, numerous studies have been carried out on the impact of cell-to-cell variations in lithium-ion batteries connected in parallel on the overall electrical behavior of the module, SoC, degradation due to temperature variations, and SoH. The final structure of the UAM battery module in this research aims to configure 14 lithium-ion battery cells with a capacity of 90 Ah and an energy density of 300 Wh/kg in series. The target battery module will undergo high discharge under external temperature conditions ranging from −20 °C to 43 °C. Notably, the increase in internal resistance variation between cells at low temperatures significantly affects the temperature imbalance among cells, leading to a reduction in overall module performance; therefore, this must be carefully considered during battery module production. In this study, 109 lithium-ion battery prototypes were initially produced for UAM battery module development. Two sample cells from the first prototypes were selected for experiments to measure internal resistance under various temperatures and were modeled for further analysis. Based on this data, a 4S series submodule was modeled. A lithium-ion battery submodule was then assembled, simulations were conducted, and the temperature imbalance during battery module operation was predicted.

2. Methodology

2.1. Lithium-Ion Battery Module

To meet technology requirements of higher energy density and cycle lifetime between 500 and 2000, the UAM needs to employ lithium batteries such as lithium nickel cobalt aluminum oxide (NCA) or different kinds of lithium nickel manganese cobalt oxides (NMC) batteries. Considering an integration factor of 0.75 from cell to module, the energy density of the battery cells must be at least 300 Wh/kg [15]. In addition, a new type of high-performance stretchable lithium-ion battery that can produce constant output power even in continuous dynamic tests is also being developed [16]. The lithium-ion battery manufactured for high discharge, while with the large energy density used in this study, was an NMC series with a maximum capacity of 90 Ah. The maximum voltage of the cell is 4.2 V, and the cut-off voltage is 2.7 V. The lithium-ion battery cell used in this study was developed for UAM with an energy density of 300 Wh/kg and was manufactured to discharge up to a rate of 8 C in consideration of the takeoff and landing conditions of the UAM flight profile. Detailed specifications of the lithium-ion battery cell are summarized in

Table 1. Specifications of the lithium-ion battery cell specially designed for UAM.

Items	Specification
Nominal capacity	90 Ah
Nominal voltage	3.7 V
Energy density	300 Wh/kg
Max. charge voltage	4.25 V
Cut-off voltage	2.75 V
Material system	Cathode: NCM–811 Anode: Graphite Electrolyte: Carbonate-based
Max. continuous discharge current	8 C

.

Figure 1 shows the cell-to-cell variations in internal resistance of 109 prototyped lithium-ion battery cells. The goal of this study is to predict the potential problems that could occur when applying modules to prototypes with significant variations in inter-cell internal resistance. A submodule composed of four serial cells (4S) composed of different internal resistances was constructed, and the thermal behavior performance according to the outside temperature and C-rate changes in the internal resistance deviation of the cell was examined.

Finally, to be applied, the battery module for UAM was composed of 14 serial 1 parallel (14S1P) cells to meet the design requirement of the applied system. Two cells with one thermal insulation pad are connected in series to prevent heat transfer between the cells as submodules, and seven submodules with aluminum covers are connected in series, as shown in Figure 2a. In this study, cells No. 42 and 46 were selected in consideration of the internal resistance deviation out of the 109 prototypes in Figure 1 to analyze the effect of the internal resistance deviation between cells on the module’s thermal behavior performance. Submodules using cells No. 42 and 46 were organized into two groups and connected in series to model the module consisting of the four total serials, as shown in Figure 2b. Cells #1 and #2 belonging to submodule 1 were the cells with high internal resistance; cell No. 42 and cells #3 and #4 of submodule 2 were modeled as cells with relatively low internal resistance, such as cell No. 46. When the cells were connected in series, the tabs were welded using a laser welding machine, and the internal resistance between the tabs was about 0.1 mΩ. A submodule consisting of two cells and one pad was composed of a thin aluminum plate of 0.1 mm for active cooling of the battery cell configured to support two modules so that cooling with external cooling air could be performed more efficiently. The cooling fin has the function of simultaneously serving as a support between the battery submodules along with cooling, as shown in Figure 2.

2.2. Governing Equation and Simulation Setup

In this study, a thermal analysis of the battery module was performed using AVL’s FireM 2020R2, a software widely used for three-dimensional multi-physical analysis of batteries [17]. A hexagonal grid was constructed for the battery module, as shown in Figure 2. The total number of grids used for the analysis was about 840,000. The governing equation for the transient analysis of the battery module used a three-dimensional transient thermal conduction equation, as shown in Equation (1).

$${\displaystyle \frac{\partial ({\rho }_c{C}_{p}T)}{\partial t}}+\nabla (-k\nabla T)={\dot{Q}}^{\prime }$$

(1)

where, ${\rho }_c$ is the density (kg/m³), $C_p$ is the specific heat (J/kg-K), $k$ is the thermal conductivity coefficient (W/m-K), and ${\dot{Q}}^{\prime }$=$\dot{Q}/V_{cell}$ represents the volumetric heating source (W/m³) inside the battery cells respectively.

Heat generation inside a battery cell is known due to the resistance to electrochemical reactions and the movement of species within the cell. The heat generation in a battery cell is usually modeled by two parts: the irreversible heat, including charge and mass transfer over-potentials and ohmic losses and the reversible heat caused by the entropy change [18]. Bernardi et al. [19] developed the following expression to calculate the heat generation inside the battery cell:

$$\dot{Q}=I(Voc-V)-I\left(T{\displaystyle \frac{dVoc}{dT}}\right)=I^2{R}_T-I\left(T{\displaystyle \frac{dVoc}{dT}}\right)$$

(2)

where $I$ denotes cell current, $Voc$ open circuit potential, $V$ cell potential, $R_T$ the total internal resistance, and $T$ absolute temperature of the cell. The current $I$ is positive for discharging and negative for charging. The total internal resistance of the battery $R_T(\mathrm{S}\mathrm{o}\mathrm{C},T)$ depend on the SoC and temperature of the cell. The first term of Equation (2) represents heating due to the Joule effect and irreversible heat generation due to internal resistance to the current flow. The second term is the entropy change (reversible heat generation), attributed to electrochemical reaction [20].

The total internal resistance of lithium-ion batteries is significantly influenced by temperature changes, so the battery heat generation was simplified to the Joule heating value as a function of temperature, as $\dot{Q}\cong I^2{R}_T\left(T\right)$. The overall internal resistance was measured under different temperature conditions through experiments and was then modeled as the heat generation of the battery cells. However, in the case of taps, the change in internal resistance according to temperature was negligibly small, so a constant value was used. The battery cell was cooled to the outside through a thermal insulation pad and a cover, and it is cooled by convective heat transfer from the external cover to the cooling air. The convective heat transfer coefficient on the aluminum cover and tabs was specified as 20 W/m²K. The properties of the cooling air, the aluminum cover, the lithium-ion battery cell, and the thermal insulation pad between the cells used in the battery module thermal analysis are summarized in

Table 2. Material properties of the pouch-typed lithium-ion battery (Reprinted from Ref. [15]).

Material	Air	Cover (Aluminum)	Cell (LIBs)	Thermal Insulation Pad
Density (kg/m3)	1.1841	2702	2100	1060
Specific heat capacity (J/(kg·K))	1003.6	903.0	1100	796
Thermal conductivity (W/(m·K))	0.026	237	1/30/30	0.202

.

Figure 3 shows the capacity and internal resistance of the cell for two samples in Figure 1 through an experiment. As a result of the discharge under the condition of about 0.5 C (40 A), the capacity of cell No. 46 was 87.01 Ah, and the capacity of cell No. 42 was 82.63 Ah, as shown in Figure 3a. Figure 3b shows the result of measuring the internal resistance according to temperature change in the environmental chamber. As shown in the figure, the internal resistance of a lithium-ion battery increased as the temperature decreased and gradually converged as the temperature increased. The experiment is the result of measuring the internal resistance value according to the climatic chamber using Hioki’s BT3562A precision resistance meter after mounting samples in the chamber. The resolution of the equipment is 0.1 μΩ. The internal resistance of cell No. 46 based on 20 °C was 1.1365 mΩ, and the internal resistance of cell No. 42 was 1.3853 mΩ, which was about 21.9% higher than that of cell No. 46. The internal resistance experimental data according to temperature were considered in the modeling of the heating value of the battery cell.

3. Simulation Results

Figure 4 depicts the final heat release in the cell according to the outside temperature change and C-rate change through steady-state analysis of a battery module. As illustrated in the experiment result of Figure 3b, as the internal resistance of a lithium-ion battery increases as the temperature decreases, the heating value also increases. However, when the internal temperature of the cell increased due to heat generation, the internal resistance of the cell also decreased, and the total heat generation also decreased, and the total heat generation had a constant value, as shown in Figure 4a. Based on the outside temperature of 20 °C, the heat generation of cell #1 was 71.4 W, and that of cell #4 was 60.1 W. In the case of 20 °C or higher, the change in the heating value was not large. Figure 4b shows the calorific value according to the outside temperature and C-rate changes, and the heat generation increases significantly as the C-rate increases. In the case of the same cell, the deviation of the internal resistance of the cell and the deviation for the C-rate were larger than the effect of the calorific value for temperature. In this study, the maximum heat generation of cell #1 under the 8 C condition was 4569.3 W, and the maximum heat generation of cell #4 was 3846.7 W. This was a value predicted during continuous discharge at 8 C condition, and the system was stopped before that because a thermal runaway occurred during the actual operation.

Figure 5 shows the change of heating value over time in cells #1 and #4 under the outside temperature and C-rate conditions and shows the results of the transient analysis. The battery submodule generated heat in the cell according to the external air condition, the operating condition, and the C-rate. Therefore, it can be seen commonly that the initial heat generation increased significantly when the temperature of the cells in both cells decreased. The heat generation inside the cell gradually increases the temperature of the cell, thereby reducing the internal resistance of the cell. As a result, the heat generation of the entire cell was also gradually reduced. The figure shows that when the temperature reached 20 °C, there was little change in the internal resistance, and the heating value was maintained constant. As shown in Figure 5b, when the C-rate was increased to 8 C, the heating value or the temperature of the cell was greatly increased, resulting in a significant increase in the temperature of the cell, which resulted in a faster convergence of the heating value change. When high discharge was performed at a low temperature, an electrochemical reaction was slowed inside the cell and heat generation was accompanied by a large internal resistance.

Figure 6 shows the result that the battery module surface temperature distribution after 1 min according to the C-rate change at an external temperature of 20 °C is predicted. As the cell discharged at the initial stage, the temperature rose due to the heat generated inside the cell, and the heat transferred along the thin aluminum plate surrounding the submodule was cooled through heat transfer with external air. The tab had a structure in which the temperature was increased by heat conduction by heat generation inside the cell, and heat transfer with external air was cooled by heat conduction by heat generation inside the tab.

Figure 7 depicts the graph that predicts the average cell temperature and the temperature change in the tab, depending on the C-rate of the battery submodule according to the outside temperature change for 1 min. Since the heat generation was significant at low temperatures, the temperature rose significantly instantaneously, and after that, the temperature gradually rose gradually. Since the internal resistance of the tap was constant according to the temperature change, a gentle temperature increase was shown in the entire operation range. The heat generated by the cell was conducted to the tab, which increased the temperature as heat generated by its own resistance was added. The higher the discharge at low temperatures, the steeper the rise in the temperature curve of the initial cell. These characteristics can be seen because of reflecting the characteristics of internal resistance according to temperature. When the outside temperature reached 40 °C, the effect on the internal resistance was already small, so the temperature increase also had a gentler characteristic.

Table 3. Mean temperature difference between Cells #1 and #4 for various ambient temperatures and C-rates at 60 s.

Ambient Temp.	Mean Temp. Diff. (°C) at 60 s
	1 C	3 C	5 C	8 C
−20	1.473	5.954	13.747	32.952
0	1.073	4.958	13.324	32.545
20	0.747	3.819	12.745	31.994
40	0.498	3.494	12.44	31.712

summarizes the results of the average temperature difference between the cells after 1 min according to the outside temperature and the C-rate change. The average temperature difference between cells increased as C-rate increased at the same ambient temperature and decreased as the temperature increased at the same C-rate. It was predicted that a maximum of 32.952 °C temperature deviation would occur under −20 °C during the 8 C condition.

Based on the study on the temperature deviation of the internal resistance of the cells for manufacturing the UAM battery module, the product deviation between the cells was improved. The results are shown as a box plot in Figure 8.

4. Conclusions

As a study to develop a UAM battery module using pouch-type lithium-ion battery cells, a submodule composed of four cells composed of different internal resistances was constructed, and the thermal behavior performance according to the outside temperature and C-rate changes in the internal resistance deviation of the cell was examined. The initial heat generation of a lithium-ion battery increased as its internal resistance increased at low temperatures. There was little change in the internal resistance of the cell as the temperature increased. Since the heat generation was large at low temperatures, the temperature rose significantly after the temperature increased significantly. At low temperatures, especially as a high discharge was performed, a steeper temperature rise curve of the initial cell could be seen due to the reflection of the characteristics of internal resistance according to the temperature. When the outside temperature reached 40 °C, it had a constant internal resistance, so the rise in temperature also had a gentler characteristic. The average temperature differential between cells increased with higher C-rates and similarly escalated as the ambient temperature decreased under constant C-rate. The maximum temperature deviation of 32.952 °C was predicted at −20 °C during an 8 C-rate discharge. Based on the analysis of temperature deviations and internal resistance among cells in the manufacturing process of the UAM battery module, measures were implemented to reduce product variability between cells.