2019 6th International Conference on Electric Vehicular Technology (ICEVT)

November 18-21, 2019, Bali, Indonesia

Modeling and Simulation of Lithium-Ion Battery

Pack Using Modified Battery Cell Model
Meilisa Dewi Kharisma Muhammad Ridwan Arinata Fatchun Ilmiawan
Institut Teknologi Bandung Technology Development Technology Development
Engineering Physics PT LEN PT LEN
Bandung, Indonesia Bandung, Indonesia Bandung, Indonesia
meilisadewikharisma@students.itb.ac.id muhammad.ridwan@len.co.id arinata.ilmiawan@len.co.id
Ferdaus Ario Nurman Saiful Rizal
Technology Development Technology Development
PT LEN PT LEN
Bandung, Indonesia Bandung, Indonesia
ferdaus.ario@len.co.id saiful.rizal@len.co.id

Abstract—The equivalent circuit of lithium-ion battery cell specification. For that reasons, simple battery pack model
has been presented in some research to model a state of charge become the main concern.
(SOC) and battery cell electrical behavior. The equivalent
circuit was built from an open circuit voltage, two resistor- Model for a single lithium-battery cell has been proposed
capacitor parallel networks, and a series internal resistance. In in several researches. Tarun [1] stated an equivalent circuit
several application, some battery cells are connected in series- use a first RC block was accurate enough. Chen [2] proposed
parallel configuration to produce a battery pack with specified a battery cell equivalent circuit with accurate and
voltage and capacity. In this paper, a modified battery cell comprehensive model that use second RC block.
model is used to represent the battery pack dynamics. The
battery pack is assumed to be balanced on both series and In this paper, a second RC parallel networks equivalent
parallel side. The model then validated by comparing circuit model is used to developed a single battery cell model
simulation results between battery pack model and battery and a battery pack model, which is shown in Fig. 1. This
cells that connected in series-parallel configuration. Simulation model is combination of runtime-based model and thevenin
results shows small difference between the two models. based model [2]. Runtime-based model is arranged by a
capacitor and control current source that is used for predict
Keywords—lithium-ion battery, battery pack model, battery state of charge (SOC) and run time of the battery. While
cell model, state of charge, parallel-series configuration Thevenin-based model is arranged by open circuit voltage
(OCV), internal resistanse, and RC networks that can
I. INTRODUCTION simulate the transient response.
Electric vehicle (EV) technology has been rapidly Modelling of battery cell and battery pack is developed in
developed in the past decades as it produce zero carbon matlab and simulink platform. Mathematical and physical
emission during operation. The technology itself can be model is combined to calculate state of charge, battery
classified according to its energy storage as: Hybrid EV, voltage, and battery current. Assuming that every cells is
Plug-In Hybrid EV, Fuel Cell EV and Battery EV. Battery balance both in series and parallel conFig.uration.
EV is the most common energy storage used for road Temperature and cycle number of battery can be ignored
vehicle application due to its economic cost and lower with assuming that its not significant affect the parameters of
carbon emission. Among all types batteries that available in battery. Then, the simulation result of parallel-series
the market, Lithium battery lead the market beacuse of its conFig.uration the battery cells will be compared to a battery
higher power density. pack model simulation result. From this comparation result
can be determined the accuration of battery pack model.
One big challenge of battery EV is to expand the lifetime
of its battery pack. Overcharging, hi-temperature, and over
discharging can reduce battery pack lifetime and its usable II. BATTERY CELL MODEL
capacity. Therefore, accurate measurements of battery pack From equivalent circuit in Fig. 1, the simulation model in
State of Charge (SoC) is important to manage battery simulink can be developed which is shown in Fig. 2. This
usage.Commonly, battery pack constructed from some model is constructed by four subsystems in battery cell
battery cells that are connected in parallel-series system. In OCV subsystem there is a SoC subsystem. Thus
configuratoion to achieve particular energy storage OCV subsystems calculate open circuit voltage and SOC. R0

Fig 1. Equivalent Circuit of Battery Model

978-1-7281-2917-4/19/$31.00 ©2019 IEEE 25

Fig.2 Simulation Model of Battery Cell

subsystem is used to calculate voltage drop which is caused B. Open Circuit Voltage(OCV)
by internal resistance. RC1 and RC2 subsystems represent OCV is measured at open circuit terminal voltage of
transient response voltage in large and small time constant. battery at various SOC points in equilibrum state [2].
Every electrical components in the system is using physical Nonlinear relation between SOC and OCV is determined by
signal at simscape. This physical signals are converted to polynomial equation. Subsystem of OCV is shown by Fig. 4.
signal sthat can be calculated with simulink block system. There is SOC calculation subsystem in OCV subsystem
The value of R and C is affected by current and SOC[3][4] because the value of OCV is directly determined by SOC.
thus every element has 2-D lookup table to interpolating and Controlled voltage source is controlled by the value of OCV.
extrapolating its value.
The value of OCV can be identified from the voltage
A. SOC Calculation curve of pulse discharge test (PDT) during relaxation[5].
SOC is the available capacity in battery and expressed by From data experiment can be determined SOC-OCV
percentage of its usable capacity. That’s one of the important polinomial equation using polinomial curve fitting.
parameters of battery that should been estimated in
simulation. In this simulation model, SOC calculation C. Internal resistanse (R0)
subsystem is built in OCV subsystem as shown in Fig. 3. Internal resistanse causes voltage drop in equvalent
From previous research [5], SOC of battery can be accurately circuit. Fig. 5 show subsystem R0 which the value of R0
calculated by (1) using coloumb counting method. In this dependent from the input current and SOC. Variable resistor
equation, the range of SOC battery is from 0% (fully is used to transfer physical signal of resistanse internal value.
discharge) to 100% (fully charge). SOC0 as input in this
subsystem that represents initial SOC. The other input is I The value of internal resistance can be determined from
(Ampere) that represents the current of battery. Cu the immediate voltage after the current pulse was released
(Amperehour) is usable capacity that describing capacitanse [6]. 2-D lookup table is used to determined the most suitable
battery which is affected by current rate and state of charge value of R0 with interpolation-extrapolation lookup method.
battery.
The value of usable capacity is varied by battery current. D. Transient Response
1-D lookup table is used for determining value of usable In this model, transient response is represented by RC
capacity from current input. Continuous discharge test networks, which constructed from RC1 with short time-
(CDT) is method which is used to identify the rate capacity constant response as shown in Fig. 6 and RC2 with long
effect of battery. The usable capacity is usually lower than time-constant response as shown in Fig.7. In previous
theoritical capacity. This results are tabulated in 1-D lookup research [2], it was found that two RC time constant provides
table of SOC calculation subsystem. better tradeoff between accuracy and complexity as it keep
the error within 1mV. There are two subsystem of transient
(1) response in this paper. The first subsystem is RC1 that has
large value of capacitances. The other subsystem is RC2 that
has value of capacitances smallest RC1 subsystem.

Fig 2. Subsystem of SOC Calculation Fig 3. OCV Subsytem

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 battery cell that has been explained in previous section. This
model can simulate the parameter characteristics of battery
pack which include SOC, battery voltage, and battery
current. Fig. 8. shows the proposed battery pack model
simulation in simulink platform. Battery pack model has the
same subsystems as single battery cell model, with
additional input of parallel and series number. This model
Fig 4. R0 subsystem use two RC network, R0 as internal resistance, and voltage
controlled by OCV as function of SOC. In the system of
battery pack there is a section of calculation of parallel and
series input. Voltage of battery pack is multiplication of
battery cell voltage in the series configuration and the
current of battery pack is multiplication of battery cell
current in the parallel configuration. The battery pack model
is expected to make analyze parameters of battery pack
without manually connected battery cell in parallel-series
Fig 6. RC1 subsystem configuration.
In parallel configuration, positive terminal battery is
connected to positive terminal another battery. Battery pack
voltage has the same value with its battery cells as shown in
(2). While the battery pack current is the sum of all its
battery cells current as shown in (3).
Vpack=Vcell1=Vcell2=Vcell3=...=Vcelln (2)
Ipack=Icell1+Icell2+Icell3+...+Icelln (3)
In series configuration, positive terminal battery is
Fig 7. RC2 subsystem
connected to negative terminal another battery. Battery pack
voltage is accumulated of its battery cells voltage that is
The value of R1, R2, C1 and C2 can be determined shown in (4). The current of battery pack same as the
from the voltage transient of CDT. Through the least square current of every battery cells in battery pack that is shown in
algorithm in MATLAB curve fitting tools, the value of each (5).
parameter in RC parallel networks can be identified as Vpack=Vcell1+Vcell2+Vcell3+...+Vcelln (4)
discussed in [6]. Then the results are tabulated in 2-D lookup
table in each subsystem. The subsystem of RC1 there Ipack=Icell1=Icell2=Icell3=...=Icelln (5)
In many application, series and parallel configuration of
III. BATTERY PACK MODEL battery cells is combined to achieve the battery pack
Battery pack is constructed by battery cells in series and spesifications. Parallel configuration will adding the
parallel conFig.uration to achieve required voltage and capacity of battery pack and series configuration will adding
capacity battery pack. Assuming that battery cells in balance the battery voltage.
condition both in parallel and series configuration. The
parameters of battery cells in battery pack are identical [7]. IV. VALIDATION OF BATTERY PACK MODEL
The research to modeling a battery pack still growing
rapidly. Previous research [8] proposed battery pack based LiFePO4 battery that has nominal voltage 3.2 V and 18
on voltage curve transformation of charging cell. Other Ah capacity is used to modeling a battery in this paper. This
research estimate using Kalman filter [9]. There also using paper extract parameters in previous research [5] which the
matrix to modeling battery pack [10] . result experiment has percentage of error from nominal
voltage is less than 2%. Then, the proposed battery pack
In this paper, battery pack model is developed from model will be validated with series-parallel configuration of

Fig 8. Battery pack model simulation

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battery cells. The simulation result of battery pack model
will be compared with the simulation result of battery cells in
parallel-series configuration.
Fig. 9. shows the battery cells model which is
arranged in ten series and ten parallel configuration. This
battery pack simulation is discharge with 180A constant
current. Simulation result of SOC between this battery cells
configuration and battery pack model is shown in Fig. 10(a)
and simulation result of battery voltage is shown in Fig.
10(b). RMS error of SOC and battery voltage in Fig. 10(c)
dan 10(d) show that the RMS error of SOC is 6.1347x10-8 %
and the RMS error voltage of battery pack is 2.1037x10-7 V.
Fig. 11. shows the battery cells model which is arranged
in one hundred series configuration. This battery pack
simulation is charged with 18A constant current. Simulation Fig 2(a) Comparation SOC battery in ten series-parallel battery cells
result of SOC between this battery cells configuration and
battery pack model is shown in Fig. 12(a) and simulation
result of battery voltage is shown in Fig. 12(b). RMS error of
SOC and battery voltage in Fig. 12(c) and 12(d) show that
the RMS error of SOC is 0% and the RMS error of battery
pack is 5.47x10-13 V. In series configuration there is no SOC
difference between battery pack model and series-parallel
configuration of battery cells. Thus the battery pack model
perform accuratly simulation of SOC and battery pack
because the error is not significant.
Fig. 13 shows the battery cells model which is arranged
in ten hundred parallel configuration. Simulation result of
SOC between this battery cells configuration and battery
pack model is shown in Fig. 14(a) and simulation result of
battery voltage is shown in Fig. 14(b). Absolute error of SOC
and battery voltage in Fig. 14(c) dan 14(d) show that the
error of SOC is 3.9043x10-5 and the error of battery pack is
9.59x10-9 V. Thus the battery pack model perform accuratly Fig 10(b) Comparation voltage battery in ten series-parallel battery cells
simulation of SOC and battery pack because the error is not
significant.

Fig 1. Battery cells in ten series-parallel configuration Fig 10(c). Error SOC in ten series-parallel battery cells

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Fig 10(d). Error battery voltage in ten series-parallel battery cells
Fig12(c). Error SOC battery in one hundred series battery cells

Fig 3. Battery cells in one hundred series configuration

Fig 12(d). Error battery voltage in one hundred series battery cells

Fig 4(a). Comparation SOC battery in one hundred series battery cells

Fig. 5. Battery cells in one hundred parallel configuration

Fig 12(b). Comparation voltage battery in one hundred series battery cells Fig 6(a). Comparation SOC battery in one hundred parallel battery cells

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 V. CONCLUSION
Battery pack model can be developed from a single
battery cell model. This simulation model is created in
simulink and simscape with physical and mathematicals
model. The simulation result shows that RMS error in many
various configuration is not significant. Therefore the
proposed battery pack model can be used in many
application.

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Fig 14(d). Error battery voltage in one hundred parallel battery cells

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