Parameter Identiﬁcation of an Electrical Battery Model

using DC-IR Data

Ayse Cisel Aras and Emre Yonel

AVL Research and Engineering, Istanbul, Turkey

Keywords:

Electrical Battery Model, Parameter Identiﬁcation, DC-IR Data, Curve Fitting, Genetic Algorithm.

Abstract:

Parameter identiﬁcation of an electrical battery model is signiﬁcant for the analysis of the performance of a

battery. In order to obtain an accurate electrical battery model, a series of cell characterization tests should be

conducted which will take a considerable amount of time. In this study, in order to identify the parameters of

the electrical battery model in a short amount of time with an acceptable accuracy, DC-IR data is used. DC-IR

test will take less time compared to the cell characterization tests. For the parameter identiﬁcation, one of

the most commonly used evolutionary algorithm (EA), Genetic Algorithm (GA) is used for the curve ﬁtting

problem and its performance is compared with the Levenberg-Marquardt algorithm.

1 INTRODUCTION

The battery systems are having a bigger role in au-

tomotive industry since the emergence and develop-

ment of Electrical Vehicles (EVs) and Hybrid Elec-

trical Vehicles (HEVs). The performance metrics for

batteries become more important, as the demand for

electrical vehicles continues and sustains a competi-

tion on higher efﬁciencies, lower consumptions in an

environment of stricter emission standards.

In automotive applications it is a necessity to es-

timate and control State of Charge (SOC), capacity,

State of Health (SOH), remaining useful life, remain-

ing available power of a battery since the performance

of the vehicle is highly dependent on those battery

states. Modern Battery Management Systems (BMS)

use various methods to estimate these battery states in

order to make sure that battery is working in a safe op-

erating region. One of the methods that helps estimat-

ing the states of the battery and analyzing the battery

performance is to obtain an accurate battery model.

In this study, battery model for lithium-ion batteries

are considered.

In literature, there are methods based on equiva-

lent circuit model for the battery modeling, such as;

electrochemical and electrical models (Waag et al.,

2014). Electrochemical models deﬁne the chemi-

cal processes in a battery and are highly accurate

models. However, they possess a high computa-

tional burden (Seaman et al., 2014). One of the most

widely used methods among the electrical models is

the Electrochemical Impedance Spectroscopy (EIS),

but its complexity of the equipment and process are

preventing the applications of EIS on to vehicles.

EIS can estimate many properties of a battery; Re-

sistance (ohmic, polarization), Capacitance (double-

layer, coating), Constant-Phase Elements and Induc-

tance, with an equivalent circuit approximation. But

this method requires relevantly high precision equip-

ment and AC-stimulation of the battery (Khan et al.,

2016).

In this study, in order to beneﬁt the advantage

of using electrical equations, an electric equivalent

circuit model is used. In literature, there are vari-

ous studies that estimates the parameters of electri-

cal equivalent circuit models (Sepasi et al., 2014),

(Nejad et al., 2016), and (Mesbahi et al., 2016). In

(Sepasi et al., 2014), a novel approach, model adap-

tive extended Kalman ﬁlter (MAEKF), is proposed

in order to estimate the SOC of a lithium-ion bat-

tery. The SOC is not a measurable value, so it has

to be estimated. An electrical battery model is used

for this estimation and the parameters of the electri-

cal model are identiﬁed by using an optimization al-

gorithm in the proposed MAEKF method. The per-

formance of the proposed approach is compared with

the extended Kalman ﬁlter (EKF). The drawback of

the EKF method is that it relies on the electric model

parameters and may not handle the aging of the cell,

accurately. The obtained results show that the pro-

posed approach is able to handle this drawback of

the EKF method. In (Nejad et al., 2016), the most

Aras, A. and Yonel, E.

Parameter Identiﬁcation of an Electrical Battery Model using DC-IR Data.

DOI: 10.5220/0006422705750581

In Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2017) - Volume 1, pages 575-581

ISBN: 978-989-758-263-9

575

commonly used lumped-parameter equivalent circuit

models used in literature for modeling lithium-ion

batteries are examined. The model parameters and

states of the battery model are estimated by using

dual Extended Kalman Filter (dual-EKF) and its per-

formance is veriﬁed through pulsed current test re-

sults and the New European Drive Cycle (NEDC)

driving cycle proﬁle over a temperature range be-

tween 5∼45

◦

C. Two cell chemistries are tested,

lithium iron phosphate (LiFePO

) and lithium nickel-

manganese-cobalt oxide (LiNMC). The simulation

studies indicate that two RC model structure is the

optimum lumped-parameter equivalent circuit model

for the battery energy and management applications.

In (Mesbahi et al., 2016), a 40Ah lithium-ion battery

cell is modeled by a dynamic equivalent circuit model

to be used in Electric Vehicle (EV) applications. A

hybrid Particle Swarm-Nelder-Mead (PSO-NM) opti-

mization algorithm is used in the identiﬁcation of the

model parameters of the battery model. The perfor-

mance of the battery model is tested with a dynamic

driving cycle and a constant current/constant voltage

(CC/CV) charge proﬁle. The obtained results show

that the modeling error is below 0.5% within a differ-

ent operating conditions.

This paper proposes a simpliﬁcation on equivalent

circuit approximation by the usage of DC-IR data val-

ues. DC-IR values are internal resistance values of the

battery, which are dependent both on SOC and tem-

perature. For the calculation of the internal resistance,

two measured voltage and current values are needed.

These tests can be conducted in a short amount of

time. In this work, the aim is to obtain an acceptable

battery model in a reasonable amount of time.

In this study, two methods are used for the esti-

mation of the electrical battery model, Genetic Algo-

rithm(GA) and Nonlinear Least Squares (Levenberg-

Marquardt Algorithm) and their performances are

compared.

Genetic Algorithm is one of the most commonly

used Evolutionary Algorithms (EAs) that can be ap-

plied to both constrained and unconstrained optimiza-

tion problems. It can be used in a wide variety of

engineering problems, such as; image analysis, opti-

mization, classiﬁcation, and etc. (Sopov and Ivanov,

2014), (Kaabi and Jabeur, 2015), and (Gasanovaet al.,

2014). In (Sopov and Ivanov, 2014), an image anal-

ysis problem, age recognition, is investigated. In this

work, genetic algorithm is used with a novelty search.

The obtained results indicate that the computational

cost of the proposed approach is high compared to

traditional approaches. However, it can be imple-

mented to the problems that do not have a prior in-

formation about the problem. In (Kaabi and Jabeur,

2015), a Multi-Compartment Vehicle Routing Prob-

lem with Time Windows (MCVRPTW) with proﬁt is

considered. This problem is handled via a hybrid ap-

proach, genetic algorithm with Iterated Local Search

(ILS). The novelty of this work is that the problem

is formulated considering the time windows and col-

lected proﬁt. The genetic algorithm is used to obtain

a minimum traveling cost and this solution is solved

via Iterated Local Search considering temporal, ca-

pacity, and proﬁt constraints. In (Gasanova et al.,

2014), text classiﬁcation problem is handled. The size

of the text classiﬁcation is reduced based on hierar-

chical agglomerative clustering algorithm. Then, the

weights of the clusters are optimized with cooperative

coevolutionary genetic algorithm.

The performance of the genetic algorithm

is compared with one of the most commonly

used parameter identiﬁcation method, Levenberg-

Marquardt. There are several applications that uses

Levenberg-Marquardt method for parameter identiﬁ-

cation (Talebitooti and Torabi, 2016), (Dkhichi et al.,

2014), and (Khan et al., 2014). In (Talebitooti and

Torabi, 2016), a semi-epirical tire is modeled with a

hybrid identiﬁcation method, genetic algorithm and

Levenberg-Marquardt method. The advantage of the

hybrid method is indicated with a comparison of ex-

isting methods in literature, Starting Values Opti-

mization technique (SVO), IMMa Optimization Al-

gorithm (IOA) in terms of accuracy and convergence

rate. In (Dkhichi et al., 2014), a highly non-linear

solar cell is modeled based on Levenberg-Marquardt

(LM) method with simulated annealing (SA). The ob-

tained results of the proposed approach (LMSA) are

compared to the methods in literature and it is ob-

served that the proposed approach has a higher ac-

curacy as compared to the other methods in literature.

In (Khan et al., 2014), the State of Charge (SOC) es-

timation of the battery is estimated online based on

parameter identiﬁcation methods of the battery model

and a linear recursive Kalman ﬁlter. The parame-

ters of the battery model is identiﬁed through a com-

bination of modiﬁed genetic algorithm and modiﬁed

Levenberg-Marquardt algorithm. The proposed esti-

mation framework is online and the SOC is estimated

with an acceptable accuracy.

This study is organized as follows; In section 2,

the electrical battery model is presented. In section

3, the parameter identiﬁcation methods that are used

in this study are given. In section 4, the simulation

studies and results are presented. In section 5, the

obtained results are analyzed and the future work in

this area is discussed.

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

576

2 MODEL BASED APPROACH

A commonly used approach for battery modeling is

the model-based approach. In literature, there are ba-

sically two methods for the model-based approach;

electrical and electrochemical models.

Electrochemical models are highly non-linear and

it is hard to implement them in a real time application

(Waag et al., 2014). In this study, due to the highly

complex structure of the electrochemical models, an

electrical model is used for the battery model.

2.1 Electrical Battery Model

Electrical model of the battery has the advantage of

using the electrical equations (Waag et al., 2014). In

Fig. 1, a general representation of an n

order elec-

trical model is given. Depending on the degree of

the electrical model, the accuracy is improving; how-

ever, the implementation in real-time systems will be

harder due to the increased number of parameters.

In this work, for simplicity and computational ef-

ﬁciency, a second-order RC electrical model is used

as seen in Fig. 2. In this model, the fast and slow

dynamics of the battery are given by R

fast

, τ

fast

and

slow

, τ

slow

, respectively.

The output of the electrical model is given as in

the following:

cell

= u

OCV

+ u

Ohmic

+ u

fast

+ u

slow

(1)

where u

OCV

is the open circuit voltage (OCV), u

Ohmic

presents the ohmic losses from the R

Ohmic

resistance.

It indicates the pure resistive effect at high frequen-

cies. u

fast

indicates the losses due to the double-

layer effects (Butler-Volmer) between the electrode

and electrolyte of the battery. u

slow

represents the

mass transport (Warburg) effect in the battery cell due

to diffusion (Jossen, 2006).

cell

= u

OCV

+ I

pack

∗

Ohmic

+ R

fast

∗



1− e

(−t/τ

fast

)



+ R

slow

∗



1− e

(−t/τ

slow

)



(2)

Figure 1: n

order electrical equivalence circuit of a battery

model.

Figure 2: Second order electrical equivalence circuit of the

battery model.

3 PARAMETER

IDENTIFICATION OF AN

ELECTRICAL BATTERY

MODEL

In this work, the aim is to ﬁnd the parameters of the

electrical battery model based on DC-IR data. In or-

der to obtain an accurate electrical battery model, cell

characterization tests should be realized. However,

these tests can be time consuming and they can last

for weeks. In this time frame, the battery cannot be

modeled and simulation studies, for instance, devel-

opment of Battery Management System (BMS), esti-

mation of the states of the battery, eg. State of Charge

(SOC), remaining available power, etc., cannot be re-

alized. In order to alleviate this problem, DC-IR test

results can be used for the estimation of the parame-

ters of the electrical battery model with an acceptable

accuracy.

In literature, there are various methods for the in-

ternal resistance determination, (Ratnakumar et al.,

2006) and (Ansen et al., 2013). In this study, a 42Ah

lithium iron phosphate (LiFePO

) type battery cell is

studied. The DC-IR values are obtained by using the

result of a pulse test. In this pulse test, the following

C-rate charge and discharge pulses are applied: C/5,

C/ 3, 1C, and 2C for 10 seconds at 25

◦

C. In order to

stabilize the chemical reactions in the battery, the rest

between two consecutive pulse is 10 minutes. The

pulses are applied from 90% SOC until 10% SOC and

SOC decreases 10%, incrementally. For each SOC

decrement, the mentioned C-rate pulses are applied.

From the last pulse until the pulse for SOC decrement,

the rest is for 20 minutes. From the SOC decrement

until the ﬁrst pulse, the rest is for 10 minutes. The

DC-IR values are obtained by measuring the charge

and discharge voltage and current values by using the

highest C-rate, 2C, at 0.1, 1, 3, 6, and 10 time sec-

onds. In Fig. 3, the voltage response of a 10 sec-

ond 2C charge and discharge current pulse for 70%

Parameter Identiﬁcation of an Electrical Battery Model using DC-IR Data

577

Figure 3: Voltage response of a 10 second 2C charge and

discharge current pulse (at 70%SOC for 25

◦

C).

Table 1: R

internal,Ch

(Ω) values at 25

◦

C and 70% SOC.

Pulse(sec) R

internal,Ch

(Ω)

0.1 0.0002

1 0.0012

3 0.0021

6 0.0023

10 0.0025

SOC at 25

◦

C is given as an example. The charge and

discharge internal resistance values for 0.1 second is

driven as follows:

Internal,Ch,0.1s

−V

Ref,Ch

(3)

Internal,DCh,0.1s



Ref,DCh

−V

Ref,DCh



(4)

An example of the derived internal resistance values

for charge current at 0.1, 1, 3, 6, and 10 seconds for

70% SOC at 25

◦

C are given in Table 1.

Initially, it is considered that 1 Ampere is given to

the electrical battery model described by Eq. 2. Thus,

the output of the electrical battery model is the resis-

tance values derived from the pulse test. In Fig. 4,

the voltage response of the model is shown. As it is

seen, the result at 0.1 second can be considered as the

ohmic resistance, R

Ohmic

of the electrical model. The

unknown parameters of the electrical model are the

time constants τ

fast

, τ

slow

and the gain values, R

fast

and R

slow

, of the fast and the slow dynamics of the

electrical battery model, respectively. By applying a

curve ﬁtting approach, these unknown parameters of

the electrical battery model can be estimated. The de-

rived DC-IR values are used as the desired voltage

values, which are used in the parameter identiﬁcation

methods described in the subsequent subsections.

0 2 4 6 8 10

0.5

1.5

2.5

x 10

−3

Time (Sec)

internal

Figure 4: An example of the DC-IR data and curve ﬁtting

(For 2C charge current, for 70%SOC at 25

◦

C).

3.1 Parameter Identiﬁcation of

Electrical Battery Model based on

Genetic Algorithm

Genetic Algorithm (GA) is one of the Evolutionary

Algorithms (EAs) that can be applied to a wide range

of optimization problems. The fundamental ideas

of Genetic Algorithm have been developed by John

Holand in late 1960s and early 1970s. Genetic Algo-

rithm is not a traditional optimization algorithm that

uses gradient or Hessians. It uses probabilistic search

method (Chong and Zak, 2001).

Genetic Algorithm is based on a biological pro-

cess that uses natural selection. Every iteration, the

parents are selected randomly from the current pop-

ulation and the offsprings of these parents are pro-

duced. This evolving procedure continues until the

algorithm reaches the optimal solution.

In this work, genetic algorithm is used to ﬁnd the

parameters of the electrical battery model by using

DC-IR data. DC-IR data set is composed of DC inter-

nal resistance valuesat different time seconds depend-

ing on the temperature and SOC values. The ﬁrst it-

eration starts with an initial population which is com-

posed of randomly generated individuals. Then, in

the next iteration, the result of the current population

is used. This iteration continues until the stopping

criteria (ε), the change in the ﬁtness function is below

1e-6 (ε <1e-6), is reached. The ﬁtness function is the

absolute value of the difference between the desired

voltage value (DC-IR values) and the voltage value

of the electrical battery model. It is given as in the

following:

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

578

fitnessfunction



desired,R

1sec

− u

fitted,R

1sec



desired,R

3sec

− u

fitted,R

3sec



desired,R

6sec

− u

fitted,R

6sec



desired,R

10sec

− u

fitted,R

10sec



(5)

The pseudo code of a general genetic algorithm is

given in the following (Man et al., 1996):

function A general genetic algorithm()

{

% Start with counter

k = 0;

% Randomly initialize the population

Initialize Population: P(t)

% Evaluate the ﬁtness of the all

initial individuals inside the population

Evaluate: f(P(t))

Get the best solution

while (not terminate) (stopping criteria)

% Increase the counter

k = k + 1;

% Select parents from

the population for the offsprings

Selection Parents: P

′

(t)

% Create a combination of selected parents

Combination: P

′

new

(t)

% Mutate the offspring

Mutate: P

′

new

(t)

% Evaluate the offspring

Evaluate: f(P

′

new

(t))

% Select the best ﬁts

Population: BestFit(P(t), P

′

new

(t))

}

3.2 Parameter Identiﬁcation of

Electrical Battery Model based on

Nonlinear Least Squares Algorithm

In literature, Levenberg-Marquardt algorithm has

been used for decades for non-linear ﬁtting problems.

It has been ﬁrst introduced by Levenberg (Leven-

berg, 1944) and improved by Marquardt (Marquardt,

1963). Levenberg-Marquardt algorithm is one of the

non-linear least squares algorithms and it is obtained

by applying Levenberg-Marquardtmodiﬁcation to the

Gauss-Newton method (Chong and Zak, 2001). In

this study, the aim is to minimize the following error:

e = (u

desired,R

1sec

− u

fitted,R

1sec

)

+ (u

desired,R

3sec

− u

fitted,R

3sec

)

+ (u

desired,R

6sec

− u

fitted,R

6sec

)

+ (u

desired,R

10sec

− u

fitted,R

10sec

)

(6)

The objective function is given as follows:

objective

∑

k=1

(x))

(7)

where

(k+1)

= x

(k)

−



J(x)

J(x) + µ



−1

J(x)

r(x) (8)

where x = [τ

fast

,τ

slow

fast

slow

]

, J(x) is the Jaco-

bian matrix of e, I is the unity matrix, µ is the adjust-

ment factor (µ > 0), and k = 1,..., N.

In this study, the performance of the genetic algo-

rithm is compared with Levenberg-Marquardt algo-

rithm.

4 THE SIMULATION STUDIES

Battery modeling is critical in order to analyze the

performance and to estimate the states of a battery.

In this study, DC-IR data is used to obtain the param-

eters of a second order electrical model of a LFP type

battery.

The DC-IR data set is composed of DC internal

resistance values at different time seconds depending

on the temperature and SOC values. The data is ob-

tained at 25

◦

C considering different SOC values (be-

tween 10% and 90% with 10% increment). In DC-IR

data, the pulse that corresponds to the smallest pulse

time can be selected as the R

Ohmic

, ohmic resistance

of the battery model. Thus, the number of the esti-

mated parameters are reduced to four instead of ﬁve.

These parameters are the time constants and the re-

sistance values of the fast and slow dynamics of the

electrical battery model, τ

fast

, τ

slow

, R

fast

, and R

slow

respectively. In addition, charge and discharge state

of the battery is also taken into account for these pa-

rameters. These parameters are estimated by using

0 200 400 600 800 1000 1200

3.05

3.1

3.15

3.2

3.25

3.3

3.35

3.4

3.45

3.5

Time(sec)

Cell Voltage (V)

Cell Simulated

Cell Measured

Figure 5: The comparison of the measured cell voltage with

the simulation result via Genetic Algorithm.

Parameter Identiﬁcation of an Electrical Battery Model using DC-IR Data

579

0 200 400 600 800 1000 1200

3.05

3.1

3.15

3.2

3.25

3.3

3.35

3.4

3.45

3.5

Time(sec)

Cell Voltage (V)

Cell Simulated

Cell Measured

Figure 6: The comparison of the measured cell voltage with

the simulation result via Levenberg Marquardt Algorithm.

two curve ﬁtting methods, namely, Genetic Algorithm

and Levenberg-Marquardt algorithm.

The obtained battery model is validated through

a driving cycle at 25

◦

C with an initial SOC value of

∼76%. The obtained results based on Genetic Algo-

rithm and Levenberg-Marquardt algorithm are given

in Figures 5 and 6, respectively. The obtained mean

absolute error (MAE) values are given in Table 2. As

it is observed, genetic algorithm has a less mean ab-

solute error value and has a better convergence com-

pared to the Levenberg-Marquardt algorithm.

Table 2: Comparison of Mean Absolute Error (MAE) val-

ues of the parameter identiﬁcation methods.

MAE (V) (Genetic

Algorithm (GA)) 0.0081

MAE (V) (Levenberg

Marquardt Algorithm) 0.0198

5 CONCLUSION

In this study, DC-IR data is obtained from a pulse test

and it is used to obtain the parameters of an equiva-

lent electric circuit of a LFP type lithium-ion battery.

For this aim, two parameter identiﬁcation algorithms

are used, namely; genetic algorithm and Levenberg-

Marquardt algorithm. The obtained results are ver-

iﬁed through a driving cycle and the performances

of the these two algorithms are compared in terms of

mean absolute error (MAE) value.

The simulation studies indicate the utility of the

genetic algorithm. The future work in this area will

be to increase the order of the electrical battery model,

eg., a third order battery model and to obtain a more

accurate battery model.

ACKNOWLEDGEMENTS

The authors would like to acknowledge the support of

Ihsan Caner Boz, who worked as an intern for AVL

Research and Engineering, Istanbul, Turkey.

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