Estimation of SOC and SOH of Li-Ion Batteries

International Journal of Computer Applications (0975 – 8887)
Volume 104 – No.4, October 2014
Estimation of SOC and SOH of Li-Ion Batteries
Prashanth K I
Dinesh Rao B
Aravind Sharma
Masters in Embedded Systems
Manipal University, Manipal
Manipal University, Manipal
Serge Technologies, Bangalore
Battery is the most widely used energy storage device. Since
its invention, it has become a common power source for
various household, commercial and industrial applications.
Despite its ever increasing importance, many challenges
remain unsolved to characterize and manage the battery.
Among them, one fundamental issue is the estimation of state
of charge (SoC), and Sate of health (SOH) of battery. SoC
expressed in percentage, refers to the amount of capacity
available in a battery. SoC is critical for modelling and
managing batteries. If SoC is 100%, reflects a full battery and
if SoC is 0%, reflects an empty battery. This project aims at
developing an estimate the SoC and remaining runtime of a
rechargeable battery. The combined estimation of SOC
method is based on Coulomb Counting technique.
General Terms
Battery level Indicator, State of Charge (SOC), State of
Health (SOH) Li-ion Battery.
SOC of Li-Ion Battery, SOH of Li-ion Battery.
State of Charge (SoC) of a battery indicates the capacity
remaining inside the battery. SoC is usually expressed in
percentage. If SOC is 100%, it indicates that the battery is
fully charged. If SoC is 0%, it indicates that the battery is
empty [1]-[12]. The SoC of a battery is simply calculated as,
I dt
SoC  SoCi  
SoCi  InitialSoC
Qnom  NominalCapacityof Battery
I  Currentflowingthroughthebattery
The magnitude of current is taken as positive for discharging
process and negative for charging process.
SoC determination is an increasingly important issue in
battery technology. A precise knowledge of SoC provides
additional control over charging and discharging process,
which can be employed for better utilization of stored energy.
Accurate SoC determination for battery powered applications
is also important for user convenience. A good SoC
estimation leads to longer battery life, better utilization of
stored energy and increased reliability of the battery pack.
SoC has strong dependency on temperature and age of the
battery. The terminal voltages, operating currents and surface
temperatures are the direct measurable parameters of a
battery. But, the complex inter-relationship between these
parameters makes SoC estimation an intricate task. Many
attempts have been made in literature to estimate SoC
accurately. Developing efficient yet accurate SoC estimation
algorithms remains a challenging task.
1.1 SoC Estimation Methods
There are two methods existing in literature for SoC
estimation of a battery [5].
Direct Measurements
Book-Keeping Systems
1.1.1 Direct Measurements
The direct measurement method is based on a reproducible
and pronounced relation between a measured battery variable
and the SoC [4]-[6]-[10]. This battery variable should be
electrically measurable in the practical set-up. Examples of
such battery variables are battery terminal voltage “V” and
battery impedance “Z”. Most relations between battery
variables depend on the temperature “T”. Therefore, besides
the voltage (or) the impedance, the battery temperature should
also be measured. The relation “fTd” is between the measured
battery variable and the SoC, can be stored in the system. The
basic principle for SoC estimation based on direct
measurement is shown in figure 1.
Fig 1: SoC estimation based on direct measurement.
1.1.2 Book-Keeping Systems
Book-Keeping systems are based on current measurement and
integration [6]-[10]. This method is also known as “Coulomb
Counting” method, which literally means “counting the
charge flowing into (or) out of the battery. This yields an
accurate SoC estimation when all the charge applied to the
battery can be retrieved under any condition and at any time.
The basic principle for SoC estimation based on book-keeping
system is shown in the Figure 2.
Fig 2: SoC estimation based on book-keeping system.
International Journal of Computer Applications (0975 – 8887)
Volume 104 – No.4, October 2014
approach is combined estimation of SOC. The block diagram
of the combined estimation of SOC is shown in figure 4.
2.1. Equivalent Circuit Model
Fig. 3 A Two-RC-Pair Equivalent Circuit Model of a
Various equivalent circuit models have been combined
estimation of SOC to evaluate the state of charge of LithiumIon batteries [8]-[9]. The RC model was designed by the
famous SAFT Battery Company, and has achieved good
application via the Advisor software [12]. As shown in Figure
1, it consists of two capacitors (Cdl, Cdf) and three resistors
(Rohm, Rct, Rdf). Resistors Rohm, Rdf, Rct are named ohmic
resistance, charge transfer resistor and diffusion resistance,
respectively. The capacitor Cdl, is named double layer
capacitor and capacitor Cdf is named diffusion capacitance.
SOC can be determined by the voltage across the two RC
pairs each of which accounts for the dynamic of double layer
and diffusion respectively. Voc, Vo and Vh are open circuit
voltage, thermodynamic voltage and hysteresis voltage,
respectively. Voltage equation of two-RC-pair equivalent
circuit model is described by
V( ) =
+ ( ) ohm +
( )+
( ) (1)
Thus the dynamic behaviour of a Li-ion battery can be
characterized as a second-order system approximately and to
characterize a second-order system, a two-RC-pair equivalent
circuit shown in Fig. 1 is widely used.
For some batteries, the relationship between OCV and SOC is
history and path dependent. This phenomenon is known as
battery hysteresis, resulting in a nonlinear many-to-many
mapping between OCV and SOC. It should be noted that
battery hysteresis is a static phenomenon which distorts the
one-to-one OCV-to-SOC static mapping. To compensate for
the battery hysteresis, the OCV is further divided into two
and h, where
is the thermodynamic voltage
which has a one-to-one relationship to SOC, and h
represents the battery hysteresis voltage. The sum of
h gives
Fig 4: Combined estimation of SOC.
The measured current and voltage at the battery terminals are
summed with an offset to obtain accurate measurement
values. The measured current “I” is integrated with time. The
procedure for obtaining “SoCi” is explained in the next
section. Then the SoC is estimated using Coulomb Counting
method as explained by equation 2.1. The corresponding
Open-Circuit Voltage (OCV) for the SoC estimated by
Coulomb counting method is obtained from an OCV-SoC
relationship. The procedure for obtaining OCV-SoC
relationship is explained in the next section.
The voltage “OCV (SoC)” and battery current “I” are applied
to the battery model and terminal voltage “Vbat, model” is
obtained. The combined estimation battery model is explained
in the next section. The parameters of the battery model such
resistances and capacitances change with age and temperature.
The procedure for capturing parameters of the battery model
is also explained in the next section.
The terminal voltage obtained from the battery model (i.e.)
“Vbat, model” is compared with the measured terminal voltage
“Vbat”. The error “ε” in the terminal voltage is processed by a
controller producing a correction factor “SoCcf”. This
correction factor is summed with the SoC determined from
Coulomb counting method to estimate the accurate state-ofcharge “SoCe”. The method for designing and tuning a
controller is presented in the next section.
The MATLAB/Simulink model of the \coulomb Counting
technique is shown in Figure. The capacity of the battery is
considered to 1000mAh. The initial SOC is assumed to be
100%. The model is simulated for 20000 seconds and the
SOC is shown in figure 5.
SoC estimation is an increasingly important issue in battery
technology [7]-[11]. This paper presents a new algorithm for
SoC estimation of a rechargeable battery. The combined
estimation of SOC method estimates the SoC of a battery
based on book-keeping, direct measurement and model-based
The SoC estimated from Coulomb counting can include a
large error due to flaws in terminal current measurement
and/or initial SoC estimation. To recalibrate the SoC
estimated by Coulomb counting method, a method combining
Coulomb counting, direct measurement and model-based
International Journal of Computer Applications (0975 – 8887)
Volume 104 – No.4, October 2014
Fig 5: MATLAB/Simulink Model of Coulomb Counting
Method& Simulation Result for SoC Estimation by
Coulomb Counting Method.
3.3 MATLAB/Simulink Model of
combined estimation of SOC Method
Fig 7: Hardware test set up.
The MATLAB/SIMULINK model of Coulomb Counting
technique is shown in Bellow. The controller employed is a PI
controller. The correction factor obtained from the controller
is summed up with the SoC obtained from Coulomb Counting
4.1 Battery
The battery used for validating the combined estimation of
SOC algorithm is a Lithium-Ion battery. Li-Ion battery
chemistry has many advantages. The major advantage of LiIon battery is its negligible self-discharge. Since, the
combined estimation of SOC algorithm doesn’t account for
self-discharge; it would be advantageous for estimating the
SoC accurately [2]-[3]. The battery is enclosed in a separate
chamber which is provided with cooling facilities. This is to
ensure that the operating temperature of the battery remains
almost constant.
4.2 Programmable DC Supply
The test setup shown in figure 5.1 can be used to estimate
SoC for any battery chemistry. Since, different battery
chemistry demands for a different charging regime, a
programmable DC supply is used. For instance, Li-Ion battery
should be charged using Constant Current Constant Voltage
(CCCV) principle. So, this DC supply can be programmed for
different voltages and currents as required for battery
Fig 6: MATLAB/Simulink Model of the combined
estimation of SOC Method.
The proportional and integral constants of the PI controller are
obtained by tuning. The tuning of these parameters is done
using the Simulink Response Optimization toolbox. The
above model is run in real-time where the battery current and
voltage are acquired from the hardware test bench.
The combined estimation of SOC algorithm is validated on a
sophisticated hardware test bench. This part of the paper will
explain the hardware test set up used for validating the
combined estimation of SOC algorithm.
Block Diagram
The block diagram of the hardware test set up is shown in
figure 7.
The programmable DC supply can be programmed using
SCPI commands. This DC supply is controlled from the hyper
terminal of the host PC. Using SCPI commands it is possible
to set the output voltage and currents of the DC supply. This
DC supply can be operated in Constant Current (CC) mode
and Constant Voltage (CV) mode as required. The DC supply
employed in this test bench is a 60V, 250A load.
4.3 Programmable Electronic Load
The battery has to be tested with various discharge current
profiles. So, a programmable load is used for this purpose.
This load can be controlled from the hyper terminal of the
host PC. Using SCPI commands it is possible to configure the
load for sinking required currents with required voltage.
4.4 Contactor Panel
The contactor panel consists of three contactors K1, K2 and K3
used to connect the battery, DC supply and load to a common
bus bar. These contactors can be driven from the host PC
using Opto 22 modules and relays. The drive signals for these
contactors are obtained from signal conditioning box which in
turn receives the command signals from the target PC. The
contactor panel also consists of current transducers for sensing
various currents flowing in the circuit. The currents flowing in
the circuit are sensed by using current transducer. The current
transducer gives a voltage output proportional to current
International Journal of Computer Applications (0975 – 8887)
Volume 104 – No.4, October 2014
flowing. This voltage is routed to target PC by using Signal
Conditioning Box (SCB) and DAQ devices. The voltages at
various points in the circuit are routed directly to the SCB and
are acquired by target PC using DAQ device.
4.5 Signal Conditioning
The currents flowing through various components are sensed
by using current transducer and the voltages across various
components are measured. Many sensors and transducers
require signal conditioning before a computer-based
measurement system can effectively and accurately acquire
the signal. The sensed current signals and the measured
voltage signals are conditioned by using SCB. Then, these
signals are acknowledged by data acquisition (DAQ) devices.
The voltages measured at various points are sensed using a
voltage divider networks consisting of resistors in series. The
SCB acquires digital signals from target PC through DAQ
devices and provides drive signals for the contactors. The
analog and digital signal conditioning are shown in the figure
7 and 8.
Industrial PC - This computer is booted from a
special target boot disk, or with the xPC Target
Embedded Option, booted from a hard disk or a
flash memory.
4.7 Host PC
The host PC is the machine on which programs are written
compiled. The host PC can be a desktop PC (or) notebook PC.
All of the development tools are installed on this machine.
The compiler is built to run on this machine. The executables
are built on host PC and are transferred to target PC. The
debugger, which is running on the host machine, has to talk to
the program running on the target machine.
The battery is tested with a discharge current of pulse profile
as shown in figure 10. The amplitude of pulse current is
chosen to be 10A. Various voltages and currents acquired by
target PC are displayed in the target PC and also in the GUI of
host PC developed for the hardware test bench. When SoC
button is enabled, the estimated SoC is displayed in the target
PC as well as the GUI of host PC. The SoC estimated by
Coulomb counting method and proposed method are shown in
figure 11.
Fig 8: Analog Signal Conditioning
Fig 10: SoC Estimated by Coulomb Counting Technique
Fig 9: Digital Signal Conditioning
4.6 Target PC
A target PC may be a general-purpose computer, a specialpurpose device employing a single-board computer or any
other intelligent device. Usually the target machine is not able
to host all the development tools. The target PC acquires
required voltage and current signals for SoC estimation. The
target PC can be one of the following:
Desktop PC - This computer is booted from a
special target boot disk created by xPC Target.
When you boot the target PC from the target boot
disk, xPC Target uses the resources on the target PC
(CPU, RAM, and serial port or network adapter)
without changing the files already stored on the hard
drive. After you are done using your desktop
computer as a target PC, you can easily reboot your
computer without the target boot disk. You can then
resume normal use of your desktop computer using
the pre-existing operating system and applications.
Fig 11: SoC Estimated by Combined estimation of SOC
Comparison of Test Results
The figure 12 shows comparison between measured and
estimated battery terminal voltage wave form. Here voltage
discharge with respect to time is shown. The battery last up to
20000 sec.
International Journal of Computer Applications (0975 – 8887)
Volume 104 – No.4, October 2014
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Fig 12: Comparison of Measured and Estimated Battery
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Figure 13 shows the comparison of estimated SOC which is
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Fig 13: Comparison of Estimated SoC
With the rising importance for battery, both in the automotive
industry and the energy sector, it is of critical importance to
develop more accurate algorithms for SOC estimation of the
battery. This paper presents a novel technique for SoC
estimation of the battery where the SoC estimated by
Coulomb Counting method is corrected using the battery
model and a PI controller. The combined estimation of SOC
method has an advantage of estimating SoC accurately even if
there is an error in determining initial SoC and flaws in
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