Modeling of Lithium-Ion Battery for Energy Storage System Simulation

Modeling of Lithium-Ion Battery for Energy Storage
System Simulation
S.X. Chen, SMIEEE , K.J. Tseng, SrMIEEE and S.S. Choi, MIEEE
Division of Power Engineering
School of Electrical and Electronic Engineering
Nanyang Technological University, Singapore
nosper@pmail.ntu.edu.sg, K.J.Tseng@pmail.ntu.edu.sg, esschoi@ntu.edu.sg
Abstract—Batteries are the power providers for almost all
portable computing devices. They can also be used to build
energy storage systems for large-scale power applications. In
order to design battery systems for energy-optimal architectures
and applications with maximized battery lifetime, system
designers require computer aided design tools that can
implement mathematical battery models, predict the battery
behavior and thus help the designers search for the optimal
schemes. This paper presentss a lithium-ion battery model which
can be used on SIMPLORER software to simulate the behavior
of the battery under dynamic conditions. Based on measured
battery data, a mathematical model of the battery is developed
which takes into account battery operating temperature and the
rates of the battery charge/discharge currents. In addition,
thermal characteristics of the battery are also studied.
Keywords- Lithium-ion battery; dynamic model; energy storage
system; SIMPLORER
I. INTRODUCTION
In recent years, several approaches on energy storage for
power systems have been studied intensely. For example,
reference [1] describes the use of battery and hydrogen energy
storage systems (ESS) in wind generation schemes. The
storage systems are intended to achieve energy/power
management of the renewable energy system. There are other
forms of ESS, such as fuel cells, super-capacitors, compressed
air energy storage, pumped storage and superconducting
magnetic energy storage systems. Selection of suitable ESS is
governed by several factors, including consideration on
capacity, relative maturity of technology, cost, safety,
environmental concern and performance.
For some applications, lithium-ion (abbreviated Li-ion)
batteries are suitable as ESS because of their high energy
densities and long lifetimes. Moreover, lithium-ion is a low
maintenance battery, an advantage that most other chemistries
cannot claim. There is no memory effect, and no scheduled
cycling is required to prolong the battery's life. In addition, the
self-discharge is less than half compared to nickel-cadmium,
making lithium-ion well suited for energy storage systems [2].
While detailed physics-based models have been built to study
the internal dynamics of lithium-ion batteries [3]-[4], these
models are not quite suitable for system-level design exercise.
In this paper, a novel battery model suitable for system-level
simulation is presented. The proposed model in terms of circuit
representation is described first. Its mathematical equations are
then presented and the model implementation in SIMPLORER
is then described. Simulation results obtained from the model
IEEE Power & Energy Society (PES) and Wuhan University
978-1-4244-2487-0/09/$25.00 ©2009 IEEE
are then compared with test results under various operating
temperature, charge/discharge current rates conditions.
II. MODEL FORMULATION
The approach used here begins with the experimental data
obtained from a ULTRALIFE UBBL10 lithium-ion battery.
The data are expressed in terms of curves of battery terminal
voltage during various constant-current discharge levels at
different constant operating temperatures. A second set of data
are the battery voltages following a step change of its current.
V (t)
i(t)
Fig. 1. Equivalent circuit representation of lithium-ion battery
To describe adequately the behavior of the battery under
these operating conditions, the battery model should have two
components:
1) An equilibrium potential E;
2) An internal resistance R having two components int
1 R and 2 R
The electrical schematic of these components is shown in
Fig. 1. This proposed model extend that described in [5], in
the terms of the new components included in Fig. 1. The roles
of these components and the mathematical relations that
describe each will be explained, as follows.
A. Description of the Equilibrium Potential
The equilibrium potential of the battery depends on the
temperature and the amount of active material available in the
electrodes. This can be specified in terms of the state of
discharge (SOD) of the battery. In fact, in general the
discharge capacity of the battery also depends on the discharge
current, temperature and lifecycle. Thus it is necessary to seek
a general expression for the potential E(t,T(t),i(t),l), where T(t)
is battery temperature, i(t) is the discharge current and l is the
lifecycle of the lithium-ion battery [5].
In view of the above, one can model the equilibrium
potential E(t,T,i,l) based on experimental data, by
1) Firstly, arbitrarily chose a typical battery voltage vs SOD
curve as a reference curve. The terminal voltage V(i,T,t,l) is
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E
R2
R1

then explained in terms of the battery SOD in a n th order
polynomial. Also, from Fig. 1, the equilibrium potential
E(t,T,i,l) is also seen as a function of V(i,T,t,l) and current i(t).
These relationships are expressed as (1) and (2).
2) Secondly, the discharge rate and temperature corresponding
to the reference curve are treated as the reference discharge
rate and temperature.
Therefore in view of the above, expressions for E, V(i,T,t,l),
SOD and Rint are
Eit [ ( ), T( t), tl , ] = vit [ ( ), T( t), tl , ] + R i( t)
(1)
n
�
int r
v[ i( t), T( t), t, l] = c SOD [ i( t), T( t), t, l]
(2)
k
k = 0
k
t
1
SOD[(), i t T (), t t, l] = � i() t dt
(3)
Q 0
R = R + R
(4)
int 1 2
Where ck is the coefficient of the k th -order term in the
polynomial representation of the reference curve and Qr is the
battery capacity referred to the cutoff voltage for the reference
curve. For k = 0, E = c0 is the open-circuit voltage at the
beginning of discharge at the reference temperature of the
reference curve.
B. Description of the Internal Resistance
Normally, the internal resistance Rint will increase with the
state of discharge. In this model, Rint has two components R1
and R2. R1 is defined as the internal resistance of the lithiumion
battery at SOD=0. It depends on the discharge condition,
i.e. temperature, current level and lifecycle. R2 is the increase
in Rint as SOD increases. R2 can also be affected by the
temperature. However, it is proposed that an n th -order
polynomial is used instead to describe the relationship
between R2 and SOD. A correction factor �(T) will then be
used later to compensate for variation of R2 with T.
Based on the above, R can be defined as a function of
1
discharge current, temperature and lifecycle, as follows,
R = f( i( t), T( t), l)
(5)
1
Take derivative on both sides of (5),
δ f δ f δ f
∂ R = ∂ i+ ∂ T + ∂l
(6)
1
δi δT δl
R1 can be calculated by dividing the initial voltage drop
(shown in Fig. 2) by the discharge current i(t) at SOD=0. From
T
1 n
the experimental data, [ ∂R ∂R
]
1 1
1 1 1
�∂i ∂T ∂l
�
�
�
�
� n
�∂i �
n
∂T �
� can be easily calculated.
�
n
∂l
�
�
Expressed in matrix form,
1 1
�∂R � �∂i � � �
� = �
� � �
n
n
�∂R �
� � i 1 � �∂ 1
∂T �
n
∂T 1
∂l
�
��δ
f
�
���
δi n
∂l
�
�
δ f
δT δ f �
δl
��
1 T
� and
(7)
17
V
16.5
16
15.5
15
0 0.1 0.2
SOD
T=25� I=2 A
Fig. 2 Determination of the voltage drop at SOD=0 for
different discharge condition
Then using least-square method to obtain the values
δ f δ f δ f
of , ,
δiδT δ l
. Then R1 can be obtained as
δ f δ f δ f
R = ( i− i ) + ( T − T ) + ( l − l ) + R (8)
1 ref ref ref 1_ref
δi δT δl
where, iref, Tref, lref are the discharge rate, temperature and
lifecycle of the reference curve. R1_ref is the internal resistance
of the reference curve at SOD=0.
Returning to R2, in general, R2 can be defined as a function
of SOD and temperature, as follows:
R = g( T( t), SOD)
(9)
2
Firstly choose another temperature discharge curve which
is of the same discharge rate (the reference discharge rate).
Then define i*R2_ref as the voltage drop (the difference between
this curve and reference curve) at the same SOD, as for
example shown in Fig. 3. The selection of the SOD point can
be arbitrarily because as shown subsequently, it does not cause
significant difference to the final simulation result. Normally,
selection of the SOD point at the middle of these curves yields
higher overall accuracy. An n th -order polynomial can be used
to fit to that relationship between R2_ref and SOD. The same
order polynomial as that with the potential E is recommended,
again to yield higher accuracy. A correction term �(T) is used
to compensate for the variation of R2 at different discharge
condition. This is illustrated as follows.
The method to determine R2 is illustrated in Fig. 3, where
experimental data from the ULTRALIFE UBBL10 lithium-ion
battery is used. The reference curve and another curve at -20�
are chosen to calculate R2_ref, which is shown in Fig. 4. Then,
n
k
R = � r * SOD [ i( t), t]
(10)
2_ref
k
k = 0
Fig. 3. Determination of the R2 for discharge condition at
different temperatures.
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In (10), rk is the coefficient of the kth order term in the
polynomial representation of R2_ref. SOD selected is less than
the SOD level at the termination of discharge. The terminal
SOD chosen in this paper is 0.7. Then the correction term is
i* R ( T)
2
α ( T ) =
(11)
i* R2_ref
From (9)-(11), R2 of the internal resistance can be expressed as
n
k
R = α ( T) * r * SOD [ i( t), t]
(12)
2 � k
k = 0
Fig. 4. R2_ref for the lithium-ion battery based on the 25�and -
20� curves.
C. Description of the Thermal Characteristics
Since E is temperature dependent, temperature must be
calculated dynamically so that it is available for computation of
E during each time step [6]. The temperature change of the
battery is governed by the thermal energy balance [7] described
by�
dT () t
2
m* c * = i() t *( R + R ) −h A[ T() t −T
] (13)
p 1 2 c a
dt
In (13), m is the battery mass (in kg), cp is the specific heat
(J/kg/K), hc is the heat transfer coefficient (W/m 2 ), A is the
battery external surface area (m 2 ), Tc is the ambient
temperature.
The heat power terms include resistive heating and heat
exchange to the surroundings. Heat generation due to entropy
change or phase change, changes in the heat capacity and
mixing have all been ignored here because from [5], it has been
concluded that such omission will not cause significant loss of
model accuracy.
D. Implementation based on the VHDL model in
SIMPLORER
Equations (1)-(4), (8), (12) and (13) provide complete
description of the battery. From the derived mathematical
model, the model can be simulated using VHDL-AMS method
in SIMPLORER [8]. Unfortunately, lifecycle has not been
considered in the battery model implementation since there is
insufficient experimental data at the time of the writing of this
paper.
III. COMPARISON OF SIMULATION AND TEST RESULTS
A. Discharge Characteristics
A dynamic model of the ULTRALIFE UBBL10 lithiumion
battery on the methodology given above was constructed
for use in the SIMPLORER software. The parameters are
given in TABLE 1.
The rate dependence of potential was validated by testing
the Ultralife UBBL10 lithium-ion VHDL model. The initial
SOD is set to 0. The battery is maintained at room temperature
(25° C) by setting a large cooling coefficient (hc = 100 W/m 2
K). This simulates the idealized constant-temperature case.
Comparison of the simulation and test results of discharge
currents at 1 A and 4 A are shown in Fig. 5. As can be seen
from the figure, a most satisfactory match between the model
and test data has been obtained for the reference curve (2A)
and while good agreement has also been obtained for all other
discharge rates.
TABLE I. SPECIFICATIONS OF LITHIUM BATTERY TESTED IN THIS PAPER
Model Tested UltraLife UBBL10
Type of Battery
Cylindrical 18650 Li-ion cells
assembly
Operating Temperature -32°C to 60°C
Storage Temperature
Range
-32°C to 60°C
Voltage 16.33 V
Capacity 6.2 Ah
Heat capacity 925(J/kg/K)
Fig. 5. Simulation and test data at different current levels for
the Ultralife UBBL10 lithium-ion batter
The simulation data were processed to obtain the relation
between the voltage and the SOD. The results are compared
with the test data, as shown in Fig. 6. Again excellent match
was achieved for the operating temperatures of -30� and 60
�.
������� Simulation and test data at different temperature levels
for the Ultralife UBBL10 lithium-ion battery
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B. Charge Characteristics
In this part of the study, the Ultralife UBBL10 lithium-ion
battery was charged by a constant current 0.8A until the
battery voltage reached 16.33V. Then the charging mode
changed to constant voltage and the charge current eventually
decayed to zero. This charging procedure is common, as can
be seen in [9].
Fig. 7 shows the voltage increases during the charging
operation. When the voltage reaches the maximum value of
16.34 V, it remains at this value. That is reasonable for the
lithium-ion battery studied.
Fig. 7. Charging of the Ultralife UBBL10 lithium-ion battery:
comparison between simulation and test results
C. Thermal Characteristics
In this part, the model is used to study how heat sink can
affect battery operation. Using the same lithium-ion battery
model written in VHDL-AMS with the initial SOD of the
battery set to 0 and the load set to draw a constant current of 2
A, the heat transfer coefficient was varied.
Fig. 8 shows the simulation results of the battery
temperature during discharge under different cooling
conditions. Notice that the final temperatures are 28.2°C
(301.2°K) and 33.5°C (306.5°K) respectively for the constant
cooling coefficients of 5 W/m 2 K and 1 W/m 2 K. The battery
temperature is nearly equaled to the ambient (25°C) for very
large cooling coefficients (hc = 100 W/m 2 K). From the
simulation results, it can be concluded that the battery
temperature increases faster when the constant cooling
coefficient is lower.
Fig. 8. Simulation results of battery temperature during
discharge (2A, 25� ambient) for different cooling conditions
IV. CONCLUSIONS
A model of a lithium-ion battery suitable for energy storage
application has been shown. The model was formulated in a
general sense, but specifically for use in the SIMPLORER
software. The method accounts for current rate- and
temperature- dependence of the capacity and thermal
dependence of the equilibrium potential. The modeling
procedure, based on the experimental data, allows the model
to have both good accuracy and the flexibility to represent
other types of batteries. The mathematical description of the
battery has been coded to a VHDL-AMS model in the
SIMPLORER software.
The battery model is shown to perform satisfactorily, up to
the cutoff voltage. It is governed by the k th order term in the
polynomial representation of the reference curve. Simulation
results of the battery model agree well with the experimental
data of an Ultralife UBBL10 lithium-ion battery in all static
characteristics. This is because the internal resistance was
defined based on the experimental data. It has two components
R1 and R2. R1 is the initial resistance of the lithium-ion battery.
It depends on the different discharge condition of
temperatures, current levels and lifecycle. R2 is the increased
resistance with the SOD.
ACKNOWLEDGMENTS
The authors would like to thank the technical staff of the Power
Electronics and Drives Laboratory for the support given.
Special thanks to Mdm Lee-Loh for her technical support in the
equipment usage and software installation. Special thanks also
go to D.L.Yao and T.D. Nguyen.
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