Electrical and thermal modeling of battery cell grouping for analyzing battery pack efficiency and temperature

Nomenclature

A

surface area [m²]

C

capacitance [F]

C _c

the heat capacity of the core [J K⁻¹]

C _p

specific heat [J/kg K]

C _s

the heat capacity at the surface [J K⁻¹]

F

faraday constant [Coulombs/mole]

H

heat generation [J]

h

heat transfer coefficient [W/m² K]

I _bat

battery current [A]

I _t

total current [A]

m

mass of the cell [kg]

n

the number of the transferred electrons in the electrochemical reaction

P _b

power of the battery pack [W]

Q

heat generation [W]

R _c

heat conduction resistance [Ω]

R _eq

equivalent resistance [Ω]

R _i

resistance of ith cell [Ω]

R _p

resistance of parallel strings [Ω]

R _s

series resistance [Ω]

R _se

resistance of series strings [Ω]

R _u

convection resistance between T _s and T _f [Ω]

SoC

state of charge [%]

T

temperature [^°C or K]

t

time [s]

T _a

ambient temperature [^°C or K]

T _c

temperature at the center of the cell [^°C or K]

T _f

temperature at coolant convection point [K]

T _s

temperature at the surface of the cell [^°C or K]

V _bat

battery actual voltage [V]

V _oc

Open circuit voltage [V]

V _soc

battery state of charge voltage [V]

V _t

terminal voltage of battery pack [V]

ΔS

change in entropy [J/mol K]

ε

emissivity coefficient

η

efficiency [%]

σ

the Boltzmann constant [J K⁻¹]

Abbreviation

AC

alternating current

BMS

battery management system

BTMS

battery thermal management system

C-rate

charge/discharge current divided by the rated battery capacity

DC

direct current

ECM

equivalent circuit model

EV

electric vehicle

GHG

green house gas

HEV

hybrid electric vehicle

Li NMC

lithium nickel manganese cobalt oxides

LiFeYPO₄

lithium iron phosphate

Li-Ion

lithium ion

mA

mili ampere

OCV

open circuit voltage

PCM

phase change material

PEV

plug in electric vehicle

SoC

state of charge

TCO

total cost of ownership

TS

temperature sensor

1 Introduction

Currently, the world is facing challenges of adverse environmental effects caused by fossil fuel (such as coal, oil, gas etc.) based economy in power system and in transportation sector. The major effects are greenhouse gas (GHG) emission and environmental pollution. In order to minimize greenhouse gas emission, researchers and environmentalists have suggested to shift towards renewable energy based sources (such as solar, wind etc.) in power sector. In transportation, traditional vehicles produce a large amount of GHGs which are harmful for the environment. Moreover, the fuels used in vehicles such as oil and gas are depleting and the cost is rapidly increasing. As an alternative, for a better sustainable environment, fuel economy and energy savings, EVs have obtained increasing attention in recent years. EV, plug in electric vehicles (PEV), hybrid electric vehicles (HEV), fuel cells based vehicles have gained popularity in transportation sector to mitigate the negative impacts of gasoline and diesel oil based engines (Young et al. 2013). Globally electric vehicle market was more than USD 425 billion in 2022, which increased about 50 % compared to the market of 2021 (Alsauskas et al. 2023).

Battery packs are used in EV as the source of energy. Battery packs are connected with power electronic converters and electric motors to drive the electric vehicles as shown in Figure 1. Battery packs of EV consist of multiple cells. EV battery charger includes an AC input filter and an AC/DC converter. The charging power flows from the grid through the charger and bidirectional DC/DC converter to the battery pack. The bidirectional DC/DC converter is used during discharge condition also. Discharging occurs through this converter and a DC/AC converter to the motor. The DC loads are also powered by the battery pack.

Figure 1:

Block diagram of an electric car drive train.

Battery cells in EV are designed mainly in three ways such as pouch cells, cylindrical cells, and prismatic cells (Budde-Meiwes et al. 2013). Single cell is not able to drive the load. Several cells in series connection make series strings which enable to achieve the voltage required to run the motor. Series strings are then paralleled for high current requirements. For example, Nissan leaf battery, (96 cells in series, 2 strings in parallel, 96s2p) are made from pouch cells and Tesla uses cylindrical cells (96 cells in series, 74 strings in parallel, 96s74p) for their battery pack (Rothgang et al. 2015). When a large number of cells are used in the battery pack, it becomes difficult to equalize the voltage. This problem is acute, firstly, when hybrid battery super-capacitors with different voltage levels are used (Wang et al. 2018). Secondly, some cells charge/discharge faster than other cells due to slight difference in internal resistance. Innovative methods such as cell balancing strategies have been proposed (Hemavathi 2021; Omariba et al. 2019). However, balancing strategies are helpful to balance the cells during first few cycles and with time when the unbalance is high, balancing becomes inefficient. Usage of large number of cells raises the question and necessity to determine the battery pack efficiency and temperature. These two parameters are of utmost importance to improve the economy of the electric vehicle.

In previous research, necessity to improve battery pack design has been discussed (Rothgang et al. 2015). In that paper, topologies of battery packs have been discussed, and reliability/lifetime of battery packs have been improved considering different part of the battery pack. A mathematical model has been proposed to simulate battery packs and an experimental platform has been built for validation (Chang et al. 2018). The number of paralleled cell has been evaluated in Monte–Carlo experiments in that research work. However, due to the assumption of high quality and homogenous battery cells, the effect of cell unbalance has not been considered. The effect of different paralleled cells on efficiency has not been achieved. A genetic algorithm is applied to optimize the battery pack grouping topology with the view to minimizing the total cost of ownership (TCO) (Chen et al. 2017). In that paper, it has been demonstrated that optimized grouping of number of series parallel configuration can improve electric vehicle economy and performance. A techno-economic analysis of Li NMC prismatic pouch battery and pack design have been conducted for electric vehicle applications (Sakti et al. 2015). Power capability and manufacturing operations have been modeled with the view to finding minimum cost for various PHEVs in that paper. Process based cost breakdown of lithium-ion battery has been projected for future electric vehicles (Berckmans et al. 2017). That paper has compared the present and future sale price of Lithium Ion batteries for electric automotive industries. It has also been recommended to improve energy density and safety of battery packs to be able to drive the force for mass production. Unbalance in parallel connected Lithium Ion cells has been modeled and experimentally evaluated in (Bruen and Marco 2016). Equivalent circuit model (ECM) for the cells has been developed and experiments have been done to explore the effect of parallel connection of four battery cells, instead of series connection among them. A number of system topologies for hybrid electrical energy storage systems were reviewed in (Zimmermann et al. 2016). Cell level and module level reconfiguration were presented for different grouping of series parallel cells. Degradation modeling at various conditions for battery pack asymmetry analysis has been done (Ganesan et al. 2016). The paper has included case studies of physical parameters contributing to asymmetry and control of individual cell has been analyzed with regards to battery pack life extension.

To balance temperature in different parts of the battery pack and to absorb the heat generated from the battery pack advanced battery thermal management system (BTMS) are being developed recently (Thakur et al. 2023). Numerical analysis 18,650 Li-Ion battery (BTMS) has been performed using ANSYS FLUENT software. The impact of phase change material (PCM) on heat transfer has been investigated (Joshi et al. 2023). To improve thermal design and PCM further, novel metallic separator has been coupled which allows to increase temperature delay efficiency (Talele et al. 2023). Combination of PCM, metal foam, and fins of different shapes has been used to investigate the performance of BTMS (Khaboshan et al. 2023).

However, to this date, a few research papers have been found that describe both the electrical and thermal model of a battery pack and determination of the electrical and thermal model parameters. This paper focuses on examination of the thermal behavior and efficiency of EV battery pack. The heat generation is investigated based on the temperature rise for two different battery cells in a simulation model. And the electrical efficiency is examined based on the electrical model and experimental setup of the battery pack.

Rest of the paper is organized as follows, problems in traditional EV battery pack are discussed in Section 2, and battery pack modeling is discussed in terms of electrical and thermal model in Section 3. In Section 4, methodology of the research is presented. Sections 5 and 6 include results obtained and Section 7 includes the discussions, analysis of the results and some recommendations.

2 Problems in traditional EV battery pack

The problems with current battery packs can be described as unbalance and degradation of cells that reduce battery pack performance. The solution to this problem is that the cells should be matched and combined in groups which is known as balancing strategy (Ci et al. 2016; Dubarry et al. 2016; Song et al. 2021).

The problems, that limit the performance of battery packs, can be divided into following categories (Rahman et al. 2022):

3 Battery pack modeling

Battery pack model is realized from electrical equivalent circuit model (ECM) of a battery cell and thermal modeling point of view. Battery packs are formed by a limited number of battery modules. A battery module is made through series, parallel, or series-parallel connection of cells. Electrical equivalent resistance, R _eq and heat generation, H are assumed as two parameters which are involved in the loss mechanism within the battery pack. Hence, minimization of these two parameters can maximize the battery efficiency.

3.1 Electrical model

There are several types of equivalent circuit models of battery available (Zhang et al. 2016). The simplest battery model should consist of a voltage source which depends on the state of the charge (SoC) of the battery, and a series resistance. A battery model, shown in Figure 2, consists of a voltage source which depends on the SoC of the battery, and a series resistance. The battery actual voltage, V _bat is modeled by three blocks. First block is the open circuit voltage, V _oc. SoC is calculated and open circuit voltage, OCV is computed using a look up table. Second block is the series resistance, R _s . This resistance is approximated by another look up table based on the current, i _bat, temperature, T and SoC. Finally, the over voltage is represented in the model using RC networks (Andre et al. 2011). However, in Figure 2 the RC networks are not shown for simplicity.

Figure 2:

Equivalent circuit model of a battery.

According to the discussions above, following equation of battery voltage with respect to time can be written.

(1) V b a t ( t ) = V o c ( V S o C ( t ) ) − i b a t ( t ) × R s

3.1.1 Equivalent resistance

In an EV battery, battery modules are formed by a number of paralleled cells connected in series. Then one or more modules are connected in series to form the battery pack. For the cells connected in parallel, following equation can be written, where R _i is the resistance of ith cell of the paralleled string.

(2) R p = 1 ∑ i = 1 n 1 R i

And for the paralleled cells, which are connected in series, following equation can be written as the resistance of the module,

(3) R s e = ∑ i = 1 n R p i

The equivalent resistance can be written as the function of R _p and R _se, as shown in the following equation.

(4) R e q = f ( R p , R s e )

3.1.2 Total discharge current

With series and parallel connected strings the battery pack is formed. Now, the total power of the battery pack, P _b can be written in terms of total battery voltage, V _t and total current I _t and equivalent resistance R _eq as following equation.

(5) P b = V t × I t + I t 2 × R e q

Due to the loss in the resistances, following equation can be derived for determining the total discharge current from the battery pack to the load.

(6) I t = − V t ± V t 2 + 4 × R e q × P b 2 × R e q

3.1.3 Efficiency of the battery pack

Efficiency of the battery pack can be written as following equation which is expressed as the ratio of the output power to the input power.

(7) η = V t − I t × R e q V t

4 Methodology

To measure the electrical and thermal parameters both simulation and experimental setup are implemented. A 4S4P battery pack with 3.7 V, Li-Ion 18,650 cylindrical battery cells is constructed, where one module is kept as reserve. Firstly, voltage, current and temperature of each cell are measured through voltage, current and temperature sensors (Ex:TS1-TS16). Then the data are sent to a microcontroller. The microcontroller has the ability to connect or disconnect a battery module as well as the battery pack from the load through switches. The voltage, current and temperature data can also be monitored through a display. The battery pack is discharged to an e-bike DC motor of 12 V, 120 W as shown in Figure 3.

5 Results of the electrical model

Firstly, a single cell is discharged across a 100 Ω resistive load to obtain the discharge characteristics. Figure 4 represents the voltage versus capacity curve of the battery cell.

Figure 3:

Experimental setup for measuring voltage, temperature and current of the 4S4P battery pack.

Figure 4:

Voltage versus capacity curve of Li-Ion 18,650 cylindrical battery cell.

Secondly, 4 cells are connected in parallel to form a module 3 of these modules are connected in series through switches to deliver to the 12 V motor with no load. Module 4 is kept as reserve. Table 1 represents the voltage of cell groups measured by the voltage sensors for a no load current of 0.23 A.

Finally, efficiency of the battery pack can be shown as Figure 5. It can be seen that efficiency drops slightly with respect to time. However, at 110 min efficiency curve increases steeply. This is because of the switching of module 3 to module 4.

Figure 5:

Electrical efficiency of the battery pack.

6 Simulation results of the thermal model

The main properties of the battery cells which are used in the thermal model can be found in Table 2. Two types of battery cell are used for simulating the thermal models.

Following Figures 6 and 7 have been plotted to show the temperature rise of the battery (LiFeYPO₄ and Li-Ion 18,650) by implementing the governing equation under different C-rates simulated in MATLAB. Ambient temperature is 25 °C. It can be noticed from Figure 6 that temperature rises significantly with a higher C-rate. This is because of the heat loss in the resistive components which increases as the C-rate increases. If the battery cells are discharged at a lower C-rate such as 0.5 C, then the corresponding temperature curve remains flat almost.

Figure 6:

LiFeYPO₄ cell temperature for C-rate.

Figure 7:

Li-Ion 18,650 cylindrical battery cell temperature for C-rate.

In Figure 7 it can be seen that temperature rise is not much increased with respect to time. Temperature varies from 26 to 27.5 °C in a Li-Ion 18,650 cell. When C-rate is increased temperature also increases, however, at a lower rate than LiFeYPO₄ battery cell. This is also compared with the actual temperature sensor data in the experimental setup. Temperature of Li-Ion 18,650 cell does not vary much and remains constant at room temperature.

7 Discussion

From the results, it is evident that the battery pack voltage depends on the series connected cells and the capacity of the battery pack depends on the parallel connected cells. Efficiency is slightly decreased with respect to time. This is why, the efficiency is reduced for the series cells. Also in reality, series connected cells add more internal resistances and switch resistances. As a result, equivalent resistance is increased and efficiency should be decreased. The discharge current from the battery pack depends on the type of load. Higher motor current is required from the battery during acceleration in an electric vehicle. Electric car battery also has to provide this current to the load very quickly. It is recommended that a parallel connected ultra-capacitor or super capacitor branch can be used to deliver this current during high current requirement (Ju et al. 2014). Otherwise, battery cells can be discharged at an abnormal rate and exhibit faulty operation.

The resistance varies with regards to the cell connection, hence, an economic path search algorithm should be employed if battery cells need to change their connection in real time (Hahnsang and Kang 2009). However, changing the connection frequently increases the resistive losses and heat generation. It is suggested that during a 24 h duration of operation time the configuration is changed not more than 2 to 3 times.

Due to the switches the volume and space of the battery pack are increased. In battery packs the electronic components applied are large in number. Addition of the switching is another electronic component which increase placement, component and cost complexities. Moreover, heat production is increased and for safety, expensive and big coolers may need to be employed. However, efficiency is expected to be improved, even at the cost of resistive drop in the switches. During charging the battery, individual cells can be charged if the battery cells contain the switching circuit. Modern safe and reliable semiconductor switches used in EVs such as MOSFETS and solid state relays are used in the circuit design. This enhances the safety and performance of the battery pack. Another important aspect related to the challenge in switching circuit design is the ON and OFF time during switching. It has been analyzed that the efficiency drops when soft switching is employed. On the other hand, hard switching increases the burden and decreases the lifetime of the switches. The major disadvantage of the switching circuit is increased cost and complexity. In this paper, the consideration of switching circuit evaluated is only during the discharging cycle.

8 Conclusions

Battery systems placed in electric vehicles are heavily dependent on the performance of individual battery cells. Real time measurement and control of the battery parameters enable better performance in terms of lifetime, safety and reliability. This paper provides an idea how efficiency and heat may vary if switches are employed in a battery pack in real scenario. For this reason actual data are used for electrical and thermal modeling. Some parameters such as cost and computational complexity rise, while efficiency and heat are optimized in this method. Future work will be focused on the implementation of BTMS and measurement of cell temperature at different parts of the battery pack. In addition, improvement in thermal management by different PCM methods will be investigated.