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Journal of Green Engineering (JGE)

Volume-10, Issue-1, January 2020

Electric Vehicle Battery Modelling Methods Based on State of Charge– Review

1D. Thiruvonasundari and

2K. Deepa

1Research scholar, Department of Electrical and Electronics Engineering, Amrita

School of Engineering, Amrita Vishwa Vidyapeetham University, Bangalore, India.

E-mail: [email protected] 2Assistant professor, Department of Electrical and Electronics Engineering, Amrita

School of Engineering, Amrita Vishwa Vidyapeetham University, Bangalore, India.

E-mail:[email protected]

Abstract

Battery behavior prognostic is an important concern in most of the

applications especially in electric vehicles which are using lithium ion

batteries. Battery performance estimation methods will improve the life span

by preventing over-discharge and overcharge, yielding increased battery life.

It allows the battery user to make out the available energy in the battery

stack. Therefore an accurate, easy to use battery model should be established

to estimate the battery parameters. In this paper five important lithium-ion

battery models such as Empirical, Equivalent circuit, Electro chemical,

Reduced-order and Data driven models are discussed based on the State of

charge estimation and compared along with their advantages and

disadvantages. Battery model parameters are obtained by using Electro-

chemical Impedance Spectroscopy (EIS) test and the implementation details

are presented.

Keywords: Battery model, Electric Vehicle (EV), Battery Management

System (BMS), Lithium-ion (Li-ion) battery, State of Charge (SoC).

Journal of Green Engineering, Vol. 10 1, 24–61. Alpha Publishers

This is an Open Access publication. © 2020 the Author(s). All rights reserved

mailto:[email protected]

25 D. Thiruvonasundari et al

1 Introduction

In the recent years, Li-ion batteries are the most advanced energy

storage device compared to other batteries due to their low self-discharge,

high energy density, compactness, no memory effect and low maintenance.

The cost of the Li-ion batteries are also declining which makes the lithium

based batteries the best choice for electric vehicles application [1]. Due to

these Li-ion batteries have drawn the attention of automobile makers and

researchers to focus on various battery modeling.

For safe and efficient operation of the Li-ion battery stack exact

calculation of battery SoC is important [2]. Battery SoC measurement

during real-time is a challenging task [3] and more research is happening in

this area. Many SoC methods are discussed and classified. Four important

battery SoC estimation methods are classified as [4-7]: Coulomb counting

based, Look-up table based, Data driven and Model based methods. Look

up table method is based on the correlation between SoC and Open Circuit

Voltage (OCV), it takes more time to measure the battery OCV. Since, the

battery needs a lot of rest time to measure accurate OCV, it is only

applicable to the research laboratory. Coulomb counting method measures

SoC by integrating the battery current, its SoC measurement is inaccurate

due to current measurement error. So, it‘s opted to work with other

methods, e.g. model based methods. Data driven methods are based on

battery sample data. It can achieve better results based on their advanced

high fidelity machine learning algorithm. Model based methods uses a set of

non-linear equations and adaptive filters (Kalman filter, sliding mode

observer) to find the battery internal state. Since the lithium ion batteries

exhibit the nonlinear characteristics, choosing the accurate battery model is

a difficult task [8]. The lithium ion model selection is based on the nature of

the application and the system design [9]. This review paper emphasizes the

data driven and model based approaches based on the current SoC

estimation techniques.

This paper is structured as follows: The section 2 describes about the

structure and working principle of lithium ion cell. Section 3, 4 explain

about the detailed modeling methods of lithium ion cell and model based

methods. Section 5 represents data driven models. Comparison of modeling

methods are discussed in section 6. Battery testing methods to find out the

parameters of the battery models are explained in section 7.

Electric Vehicle Battery Modelling Methods Based on State of Charge– Review 26

2 Lithium-ion Cell Structure .

Fig 1. Li- ion Cell Composition [10]

Fig.1 shows the lithium ion cell composition. Each cell has four

important components electrodes (Anode and Cathode), electrolyte and

separator. For charging and discharging, reduction–oxidation process

happens in the positive (cathode) and negative (anode) electrode in which

the electrolyte is typically a lithium salt dissolved in an organic solvent. The

separator is a porous membrane separating the anode and cathode

electrically as well as symmetrically. It allows only Li+ ions to migrate

inside the cell between electrodes [10].

During discharge the cell supplies current to the outside circuit.

Oxidation takes place in the anode

(1)

Reduction takes place in the cathode

(2)

For example, if the anode is made from graphite and cathode is made

from lithium cobalt oxide (LiCoO2) during charging the Li-ion ( ) moves

from the positive electrode and reaches the negative electrode through the

electrolyte. The same way electrons ( ) moves from positive electrode to

the negative electrode through the outer circuit. The Li+ accumulates

between the layers of graphite.

During discharge, the Li+

migrate from the negative electrode and

reaches the positive electrode. When the cell is fully discharged all the Li-

ions are stored in between the layers of Cobalt and Oxide ion. The lithium

ion moves backward and forward between the electrodes as the battery

discharges and charges.


3 Classification of Li-ion Battery Modeling

Fig 2. Battery Modeling Methods

Battery Modeling is to understand the internal cell behavior

mathematically with a simple set of equations. Fig.2 represents the various

battery modeling methods based on the SoC measurement [11]. Data driven

and model based approaches attempt to predict the battery performance and

characteristics accurately with the help of complex algorithms with a set of

battery data and mathematical equations by integrating several factors [12].

4 Model Based Methods

Model based methods are widely used to find out the SoC, terminal

voltage and other battery parameters. It consists of a battery model and a

parameter estimation algorithm. Input to the model is generally temperature,

current and SoC. Based on the input, the model output voltage is measured

and compared with the real battery data. Error in the model output is

corrected by tuning the model parameters to obtain better performance.


4.1 Empirical Model

Empirical model also called as mathematical model or black box model,

is a simplified model which uses the mathematical approach to obtain the

output from the input parameter through transfer functions and not much

concerned about the electrochemical phenomenon happening inside the cell.

Empirical models are easy to configure and provide quick response, but

accuracy is limited. To improve the accuracy it has to be combined with low

level models [4]. The empirical models are classified as classical models,

enhanced self-correcting model and zero-state hysteresis model.

4.1.1 Classical Model

Classical model is a simplified electrochemical model such as Nernst

model, Unnewehr model, Shepherd model and Combination of all. Using

simple set of mathematical and polynomial equations, the empirical model

describes the non-linear response of the battery compared to other higher

order complex battery models. Here, output voltage is expressed as a function of

the battery current and the SoC.

The mathematical representation of the classical empirical models are

listed in Table 1, where E (t) is the battery output voltage, E0 is the OCV of

the battery, Ra is the Ohmic resistance, K1 - K4 are constants used for curve

fitting, i (t) is the battery current. Battery current is considered as positive

for charging & negative for discharging. Q (t) represents battery SoC, time

index is expressed as k and Yk is the terminal voltage.

Table 1 Classical models

S.No Model name Model output Equation Characteristics

1 Shepherd

model ( ) ( )

( )

Continuous

discharging real time

applications

2 Unnewehr

model ( ) ( ) ( )

Simple mathematical

battery model

3 Nernst model ( ) ( ) ( ( )) + ln(1-

Q(t))

Best accurate model

4. Combined

model

( )

( )

It includes all the

above

Characteristics


Based on the performance analysis study Nernst and Unnewehr model

confirms better prediction than the Shepherd model. When the estimated

terminal voltages of the three models are compared with the actual voltage

of the battery Nernst model is reported as the best accurate model since it

involves two more constants K3 and K4 to estimate the dynamically

changing terminal voltage [13] accurately.

Classical battery models represented in Table 1 consists of voltage

sources which is connected with the resistance to model different types of

electrochemical batteries. SoC of the battery is considered as a state variable

to avoid loop issues [14]. Conventional empirical models are not

considering the hysteresis effect of the battery and hence the results are not

accurate during the relaxation period [15]. This type of battery models can

be easily implemented using dynamic simulation tools like

MatLab/Simulink [16].

Combined Model combines Nernst model, Unnewehr model and

Shepherd model. By considering additional parameters and chemical

reaction happening inside the battery, performance of the combined model

can be improved but at the same time implementation complexity is also

increased.

Some alternate methods are implemented to improve the performance

accuracy of the conventional combined empirical models. Modified

empirical model is proposed by considering the discharge and the charge

cycle of the battery separately using shepherd equation [17].

(

( )) (

( )) (3)

(

( )) (

( )) (4)

Where, Q is battery SoC, , are the polarization resistance

coefficient at charge and discharge. , are the polarization over

voltage coefficient at charge and discharge. The E0 term express the

interconnection between the SoC and OCV. The filtered current (i*) of the

battery shows the dynamic behavior of the battery. Exponential term

( ) emulates the hysteresis phenomenon of the battery. Third term ( ) is

added with respect to the polarization voltage. The temperature, batteries

ageing, capacity fading and self-discharge effects are not considered in this

model.

4.1.2 Zero-State Hysteresis Model

When the cell is permitted to take rest then the diffusion voltage Voc

decays to zero and the model voltage (Vt) reaches to zero but this does not


happen in real time. Diffusion voltage change depends on time but the

hysteresis voltage (Vh) depends on the battery SoC.

Fig 3 Zero-state hysteresis model

Fig.3.represents the circuit diagram of zero-state hysteresis model. The

model equation is described as follows

( ) (5)

Where, describes state of charge, M is a constant coefficient

describing the hysteresis level and describes charging or discharging

hysteresis effect. In addition to dynamic hysteresis voltage variation the

instantaneous hysteresis voltage variation should also be considered for

modeling. The model equation combing the dynamic and instantaneous

hysteresis are expressed as follows

( ) (6)

Where, describes the symbol of the current based on charging and

discharging.

4.1.3. Enhanced Self-Correcting Model

It includes OCV, hysteresis, internal resistance and single parallel RC

pair. It can contain more number of RC pairs and all the model parameters

should be positive. It describes all dynamic effects.


Fig.4. ESC model

Fig.4. shows the circuit diagram of Enhanced self-correcting model.

The model equation described as below

( ) ∑ (7)

4.2. Equivalent Circuit Model (ECM)

The next important battery model is an equivalent- circuit model. EC

models are also called as abstract model or grey box model. It‘s a widely

used battery model for electric vehicle battery management system [18-23].

It‘s an alternate way of representing the physical entity. It replaces the

complex electrochemical process happening inside the battery to equivalent

simple electrical circuit, but it needs look up tables to match with the

experimental data. For better accuracy of this model the capacity fading,

temperature and aging factor of the batter y should be considered.

ECMs are the extensively used battery models for the EV BMS to

estimate the dynamic battery characteristics. In order to find out the OCV

which is a function of SoC, a cell is charged and discharged to find the

battery SoC.

∫ ( ) (8)

SoC is calculated from equation (8), SoC0 describes the initial value of

SoC, I (t) represents the battery current in Ampere, C describes the total

capacity at room temperature, η is Coulomb efficiency usually it‘s close to 1

for lithium ion batteries.

EC Model consists of a DC voltage source, resistor-capacitor pair and

an internal resistor, which links the input and the output parameters.

Compared to mathematical models, EC Models are able to give better

insight about the battery and describe the charge and kinetic mass transfer


characteristics. The Partnership for a New Generation of Vehicles (PNGV)

model is now widely used in EV studies.

The choice of the ECM is greatly based on the battery cell chemistry.

So there is no standard method for all the cells and at the same time the

model has to apply appropriate approach for the estimation of the battery

parameter. The Fig.5 represents the individual components of the battery

cell.

Fig.5 Equivalent circuit elements representing cell components [24]

In the ECM, the resistor indicates the internal resistance of the

electrolyte; electrodes, separator and the current collectors etc. The parallel

RC network with different time constants reflects the double layer, charge

transfer effect and as well as diffusion process taking place inside the

electrolyte and electrodes. The Thevenin model, Rint model, PNGV model

is common in the ECMs literature.

4.2.1 Rint Model

It is a basic ECM and it reflects only the steady-state behavior of the

battery as shown in Fig.6. If the requirement is not concerned about

dynamic characterization of the battery then this model is preferred. The

battery OCV is derived from the battery SoC.

Fig 6. Rint Model [25]


The model voltage is expressed as follows

(9)

refers to the output voltage, Voc describes the OCV, Ib represents the

battery discharge current and R0 indicates the battery internal resistance.

4.2.2 Thevenin Model

Thevenin model is also called as resistor-capacitor ECM. The dynamic

behavior of the battery is not taken care by the Rint model. To overcome the

disadvantage of Rint model, this model uses a RC network along with

internal resistance. The RC network is added to characterize the transient

behavior of the battery. The value of the RC pair can be determined from

hybrid pulse power characterization test (HPPC). The number of RC

branches vary based on the type of application.

Fig.7 Thevenin Model [26]

The output voltage equation of the model which is described in Fig.7 is

expressed as follows

- (10)

V1 refers to voltage drop across the parallel RC, C1 indicates the double

layer capacitance and R1 indicates the charge transfer resistance.

Table 2 Different application of ECM [25]

S.No Model name Application

1 Simple model High voltage grid integration

2 1RC,2RC Smart grid integration

3 3RC,4RC,5RC,1RCPE E-mobility

4 2RCPE,3RCPE Diagnosis

Table 2 describes the different application of ECMs. The single R

model is not suitable to describe the transient characteristics of the cell but it


explains the static characteristics. It is applicable for grid integration. One

RC model explains the charge transfer characteristics while the two RC

includes the diffusion process too. Both are suitable for smart grid

integration applications. Three RC and higher order RC models along with

Constant Phase changing Element (CPE) are used in electric mobility for

better accuracy. RC models along with CPE are used in diagnosis tools.

4.2.3 PNGV Model

PNGV model is obtained by adding the additional capacitance in the

Thevenin model. The capacitance describes the changes occurring in the

electromotive force. Fig.8.represents the circuit diagram of PNGV model.

Fig.8 PNGV Model [27]

The PNGV model output voltage is expressed as follows

- - (11)

refers drop across the bulk capacitance. The PNGV model shows

better accuracy compare to other two models. By adding more RC network

in the model the accuracy increases but at the same time it increases the

circuit complexity also. For Li-ion battery SoC measurement, ECMs with

one RC and two RC networks are mostly used.

4.2.4. Improved Models

4.2.4.1 DP model

An improved Thevenin Model [28] is obtained by adding one more RC

network to Thevenin. Rep, Cep indicate the electrochemical polarization

resistance, capacitance and Rcp, Ccp indicate the concentration polarization

resistance and capacitance are used to explain the dynamic behavior during

discharging or charging as shown in Fig.9.


4.2.4.2 Extended Thevenin model

In the extended Thevenin Model as discussed in section 4.2.2.more RC

networks are added to increase the accuracy of the model [27] such as

1RC model

2RC model

3RC model

Fig.9 DP Model

Fig.10 Extended Thevenin Model


Table 3 Model Equations

d

e

s

c

r

i

b

e

s

t

h

e

c

h

a

r

g

e

t

r

a

n

The 1RC model describes the charge transfer characteristics of the

electrolyte, solid electrolyte interface and electrodes. Diffusion process

which takes place in the low frequency area is represented by the 2RC

model. Diffusion as well as charge transfer characteristics are considered in

the 3RC model. Three RC model is accurate compared to other two models.

Fig.10. shows the extended Thevenin model for n number of parallel RC

pairs. Table 3 shows the different equivalent circuit models and their

characteristic equations.

4.2.5 Comprehensive Model (Aging Model)

The Comprehensive model [29] is also called as ―run time‖ based

model. The battery self-discharge and capacity fade is considered in this

model. The circuit consists of two parts. First part captures the battery

degradation over cycling and calendar aging and the second part simulates

the battery dynamic behavior. The capacity and run time of the battery is

S.No Equivalent Circuit Models Equation

1 Rint Model

2

Thevenin Model

( ) (

)

-

3

PNGV Model

( ) (

)

–

4 DP Model

(

) (

)

(

) (

)

5

Extended Thevenin Model

(

) ( )

(

) ( )


modeled as a controlled current source and the voltage controlled source

represents the OCV predicted from the SoC. In the second comprehensive

model [30] a resistance with a capacity fade is added to find out the aging

and remaining useful life of the battery.

Fig.11.Comprehensive-Model 1

Fig.12. Comprehensive-Model 2

Table 3 Models and key influence factor [6]

Model Polarization

Characteristics

Self-discharge Capacity-fade

Rint √ x x

Thevenin √ x x

PNGV √ x x

DP √ x x

Extended Thevenin √ x x

Comprehensive-1 √ √ x

Comprehensive-2 √ √ √


Polarization characteristics are included in all the battery models.

Comprehensive model 2 efficiently covers all the dynamic characteristics of

a battery throughout its entire life. Table 3 explains about the different

equivalent circuit models and their key influence factor.

In this paper [31], more than ten battery models including the

mathematical and Electrical circuit model with multiple RC pairs are

compared based on the modeling accuracy. It highlights that 1RC ECM is

found to be the best applicable battery model for Li-NMC battery and 1RC

model with one state hysteresis is the appropriate model for the LiFePO4

battery.

The battery output error is reduced in the 2RC model compared to the

1RC model under steady state as well as dynamic discharge state, but not

giving significant improvement. Therefore, 1RC model is the preferred

model for portable consumer electronics. However, for precise applications

such as electric vehicles and aerospace, the 2RC model could be the ideal

choice [32]. For sensitive medical diagnostics more RC networks are added

to predict the battery behavior exactly.

4.3 Electrochemical model

Electrochemical modelsalso called as white box models or physical

models, are used to acquire the transient behavior of the cells to achieve

high accuracies and to describe complex electrochemical process happening

inside the cell. Detailed key features of the battery chemical process are

useful for battery designers but, it‘s difficult to use this model for practical

applications. Electrochemical models are based on the following laws

Ohm‘s law; it takes care of the potential distribution in the positive and

negative electrode.

Fick‘s law, it includes the lithium ion material balancing in an active

particle.

Butler–Volmer equation, explains about the flux which exists at the

boundary between the electrolyte and electrodes called as pore-wall flux.

Faraday's law which relates the pore wall flux with the deviation of the

current flow in the electrolyte.

( ) ( )

( )

( )

(12)

The above equation is used to find out the pore wall flux where, i = n

describes the negative electrodes and i = p describes the positive electrode.

No flux in the middle portion of the particle, e.g. flux is zero in the

separator.

Electrochemical models are classified as the Single Particle Model

(SPM), Pseudo-2D model [33], the First principle model and the Quasi three


dimensional full order physical models. The pseudo-2D model is based on

[34-36] porous electrode theory. One of the important aspects of pseudo-2D

model is that it analyses the battery mechanism. It considers the electrode as

a multi particle, but SPM considers it as a single particle. The SPM and P2D

models are very popular compared to other models [37-43]. Fig.13. shows

P2D schematic model with the anode, cathode and separator.

Fig.13 P2D schematic model with the anode, cathode and separator [44]

P2D model includes solid phase diffusion, electrolyte and Butler-

Volmer kinetics. The main drawback of this model is that, it consumes more

time for simulation process as it contains lot of non-linear differential

equations. So computationally this model is not an efficient model for large

battery packs. It is not suitable for BMS applications. To overcome the

drawbacks of this model, researchers prefer the SPM which is represented in

Fig.14.

From the lithium ion concentration profile the SPM model can calculate

the voltage drop in the electrolyte to increase the accuracy and calculates the

battery SoC with minimum calculation error [46-48]. SPM accounts for

solid, electrolyte concentration and thermal constraints. It considers

different particle chemical reaction which is happening inside the positive

and negative electrode as a single spherical particle. It explains the

movement of the lithium ions inside a solid particle in the easiest way while

comparing with the P2D model. Though the model is simplified, the

estimation process is still time consuming and estimation accuracy is not up

to the mark under varying working scenarios.


Fig.14 SPM [45]

The first principle model is used to simulate the capacity fade of the

battery under the constant current constant voltage (CC-CV) charging. The

quasi three dimensional full order physical models represent the various

chemical, physical and electrochemical processes happening inside the cell

during the rest period and operating conditions.

4.4 Reduced Order Model

Simplified reduced order model [49] is a derivative of electrochemical

model by considering with additional assumptions. An average battery

model is made by ignoring the concentration distribution and diffusion

inside the electrode material considered. It is suitable for control system

based applications [50]. By assuming electrolyte material concentration as a

constant, the model can be simplified but due to assumption there is a loss

of information compared to the complete physical model. Nevertheless, it is

the most preferred model for voltage estimation and SoC measurement.

5 Data-Driven Models

The most critical part of electric vehicle BMS is an accurate

measurement of the battery SoC. Especially batteries like Li-ion overcharge

and over discharge will reduce the battery lifespan and induce safety issues;

sometimes it may harm the battery permanently. Thus, a data driven model

is used for improving the accuracy of the SoC estimation. Compare to other

types of battery chemistry the Li-ion battery is a highly complicated

electrochemical structure, its performance vary with battery aging. It is a

challenging task to find out the exact battery SoC using classical battery

models.


Data-driven models are also called as black box models. Data-driven

methods consider the battery current, voltage, temperature and SoC to

develop a controller and based on that it estimates the system behavior

which does not require a precise system model. This control approach can

provide great benefit in the below scenarios [51]:

The mathematical model of the system is not known

The uncertainties happening in the system is high;

The control system which cannot be modeled by using empirical

set of equations

The system which is not suitable for design and analysis

The fuzzy controller [52, 53], the support vector machine [54] and the

neural network [55, 56] algorithms are used by the black box model.

Statistical data is very useful for practical system modeling. Reference [57]

uses the neural logic to build the battery model estimator to calculate SoC,

which considers temperature, current and SoC as input and output is the

battery voltage. Modeling accuracy is very high and can solve non-linear

equations efficiently.

Fig.15 Data-driven model [6]

The data driven model can be combined with the model based method

to achieve a superior data model. The model real time behavior will enhance


the controller performance. The data-driven model in Fig. 15.shows the

relationship between the input and the output voltage.

6 Comparison of the Battery Modeling Methods

Based on the discussion in the previous sections, each method has its

own advantages and the performance of the modeling methods are mainly

based on the environmental condition, operating temperature, battery ageing

and different SoC operating ranges. The accuracy of the same battery model

under various SoC range is analyzed in [58] and the result shows that the

battery models are sensitive for the above operating parameters especially in

the electric vehicle application the pack contains large number of series and

parallel connected cells and this in turn spreads the difference across an

individual cell [59]. The battery stack level current and voltage is used to

measure the SoC of the battery [60] but it cannot ensure in terms of the

safety perspective. Alternate techniques for pack level SoC measurement is

calculating the cell level SoC first then calculating the pack level SoC. It

gives better accuracy but complexity is more and not applicable Electric

vehicle BMS. Comparisons of modeling methods are presented in Table 4.

Table 4 Comparative study on battery modeling

Battery Models Mathematical

Model

ECM Physical

Model

Reduced

order Model

Data-driven

Model

Accuracy Low accuracy Medium

Accuracy

Very High

Accuracy

High

Accuracy

High

Accuracy

Voltage

measurement

Limited

capability

in the terminal

voltage

estimation

Parameter

estimation is

complex for

voltage

measurement

Very complex

and time

consuming

Easy to do

voltage

measurement

Tedious data

collection

process

Physical

interpretability

Low Limited High Medium Medium

Time Simple and low

time consuming

Simple and

Easily

understood so

medium time

consuming

Time

consuming due

to accurate

voltage

calculation

Average time

consumption

Less time

consuming as

prior battery

knowledge is

not required

Computational

Complexity

Low Medium to low High High High

Configuration

Effort

Low Medium High Medium High

Application All energy

storage system

Real-time

monitoring and

BMS

Battery system

design stage &

diagnosis

SoC

estimation,

Control

application

Electric

vehicle,

Hybrid

electric

vehicle


Electrochemical model is the base model for the entire battery model.

By simplifying the electrochemical model the empirical model is obtained.

Chemical process happening inside the battery is replaced by means of

circuit component in the equivalent circuit. Data-driven model expresses the

electrochemical characteristics by high accuracy data analysis.

The model should be as simple as possible for real time applications.

For on line estimation the equivalent circuit model is more reliable and for

high precision SoC measurement artificial neural network and adaptive

filter based models are the perfect one. An electrochemical model explains

the charge transfer between the two electrodes and reveals the

electrochemical phenomenon, but it is not fit for online estimations due to

high complexity.

SoC accuracy is based on how accurate the model is and if the accuracy

is high then the model complexity is also high. So always there is a tradeoff

between model accuracy and simplicity as shown in the table 5.

Performance accuracy is improved by considering the following

Battery system variables are modeled as a function of battery

current, temperature and SoC.

OCV and hysteresis are modeled as a function of temperature

and SOC.

RC network are modeled at different state of charge and

temperatures

Aging effects are included in the model

Table 5 Battery models

Models Merits Demerits Papers

Mathematical Model Simple and less time

consumption

Low accuracy [4,13-17, 26, 61]

Equivalent circuit model Instinctive to be

implemented and

simple

Medium accuracy [18-32, 62-65]

Electrochemical model Very high accuracy Complex and time

consuming

[33-48, 66 ]

Reduced order model Less computational cost Not an accurate model

because of

assumptions

[49,50, 67]

Data driven model Less time consumption

and high accuracy

High complexity [51-57, 68-78]


7 Battery Testing

7.1 Constant – Current Charge or Discharge Test

A simple battery test is done on a cell or a battery which is a constant-

current charge/discharge test, where all cells are charged and discharged to

and from 0% and 100% SoC at a constant current of 0.7A. Then the OCV

(VOC) of the battery is obtained. 18650 Li- ion cells are used for the test.

From this test, it is possible to measure the simple model parameters like

OCV and internal resistance of the battery which is represented in Fig.16

and Fig.17.

Fig.16 SoC Vs OCV

Fig.17 SoC Vs R0


7.2 EIS Test

EIS test is a non-invasive, high efficient technique to analyze the battery

behavior and to find the battery parameters. The impedance studies are used

to analyze the system variables with respect to current, SoC and operating

temperature. Based on this, the State of health (SoH) and aging factor of the

battery can be obtained at various working scenarios [79-84].

The EIS test applies a small sinusoidal signal to measure the system

current, voltage for the given input amplitude and phase by finding out the

impedance of the system while repeating for the range of frequencies which

is continued until the cell is empty.

( ) (13)

( ) (14)

( ) (15)

From the EIS measurement the impedance variation is compared with

the reference cell to untested new cell impedance. The measurement is done

at ambient temperature or calendar cycling temperature for all SoC or

selected SoC range. EIS test was performed mostly under potentio-static

mode and conducted in a periodic manner with a periodicity of 30 minutes

interval to ensure the cell reaches SoC level for each repetition of the test.

EIS test is conducted for 18650, 2200mAh, 4.2 V Li-ion cell by

applying 3mV sinusoidal voltage under potentio-static mode at 20ºC for the

frequency range 1mHz to 100kHz. From the EIS data, the Nyquist plots are

drawn for different SoC ranges.

Nyquist Plot (R, C and L behavior)

Fig.18 100% SoC Fig.19 90% SoC


Fig.20 80% SoC



Fig.23 50% SoC



Fig.26 20% SoC

Fig.27 10% SoC Fig.28. 0% SoC

Fig.18 to Fig.28 shows the Nyquist plot of 100% to 0% SoC curves.

The Nyquist plots show the resistive, inductive and capacitive behaviors of

the battery cell considered at different SoC for the analysis. It shows the real

part of the impedance (resistance on the X-Axis) and the imaginary part of

the impedance (capacitance on the Y-Axis) at different SoC. The negative

value in the impedance curve indicates the battery inductance.


Nyquist Plot (R and C behavior)


Fig.31 80% SoC



Fig.34 50% SoC



Fig.37 20% SoC



The Nyquist plots shown in the Fig.29 to Fig.39 consider only the

resistance and capacitance features of the battery at different SoC. The

inductive part is not considered as it has negligible effect on the battery

modeling.

Fig.40. Equivalent Circuit Models

The semi circles in the plot illustrate the behavior of RC model rather

typical anode-cathode representation, as the cathode and anode impedance

are not differentiated in the commercially available Li-Ion cells. The L

represents the cable inductance; R0 explains the internal resistance of the

battery, R1and R2 describe charge transfer resistance which occurs in both

the electrodes, C1 represents the capacitance of the electrode which is

modeled through constant phase changing element, Zw describes the

Warberg impedance which is related to the diffusion process [85] is

represented in Fig.40. Using Nyquist plot the equivalent circuit parameters

at different SoC and temperature can be measured by using the curve fitting

algorithm.

The impedance variations are observed from 0% to 100% SoC as shown

in the Nyquist plots (figures 18-39). So the impedance of the battery cell


varies based on the SoC. EIS is an accurate analytical technique for

measuring critical battery parameters [57], including: SoC, SoH, Battery

Ageing, temperature and internal faults.

8 Conclusion

Battery modeling is one of the fundamental processes to obtain accurate

battery state analysis. The battery SoC can be influenced by various internal

and external factors, and the battery SoC estimation techniques vary based on

the application (Energy Storage System, EV and Hybrid EV). The modeling

methods discussed in this paper is efficient and reliable for an application

under certain operating conditions. Hence, the selection of the right model is

based on the type of application and the designer choice and this paper helps

in selection of a better model for a particular scenario. The parameters for the

selected battery modeling methods can be obtained from constant discharge

current tests, EIS test as discussed in section 7. This paper also presents the

state of art techniques in battery modeling and testing methods available. The

Li-ion battery ECM feasibility is considered in the analysis, model

parameters are successfully derived from the EIS test.

Acknowledgement This work has been supported by Robert Bosch

Engineering and Business Solution Limited, Bangalore, India

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Biographies

Thiruvonasundari.D is a Ph.D student at Amrita School of Engineering

Bangalore, Amrita Vishwa Vidyapeetham, India since August 2016. She has

completed B.E in Electrical and Electronics Engineering from IRTT,

Bharathiyar University, Tamilnadu, India. She obtained M.Tech in Power

Electronics from TOCE, Viveshvaraiya Technological University,

Bangalore, India. She has worked as an Assistant Professor from 2013. Her

Ph.D work is to improve the operation of Battery Management System used

in the Electric vehicle application.

K. Deepa graduated from Alagappa Chettiar college of engineering and

Technology, T.N, India in 1998. She obtained M.Tech degree from Anna

University, Guindy campus, T.N, India in 2005. She received Doctoral

degree from Jawaharlal Nehru Technological University, Anantapur, A.P,

India in 2017. Currently she is working as Assistant professor in Electrical

and Electronics Engineering Department, Amrita School of Engineering,

Amrita Vishwa Vidyapeetham University, Bangalore, Karnataka, India. She

has 20 years of teaching experience. She is a life Member of IETE and ISTE,

India and a senior member of IEEE. She has authored two textbooks on

―Electrical Machines‖ and ―Control Systems‖. She has published 27

international journal paper, 31 papers in international conference and 6

papers in national conference. 15 M.Tech Degrees were awarded under her

guidance. She is the advisor for the IEEE-PES & IAS student branch joint

chapter and advisor for IEEEWIE in Amrita School of Engineering,


Bangalore from 2015. She is also a joint treasurer for 2018 EXECOM of

IEEE PES Bangalore chapter. Her areas of interests include Power

electronics, Renewable energy technologies and Control Engineering.

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