Lithium Battery SOC Estimation
Lithium Battery SOC Estimation
Lithium Battery SOC Estimation
Abstract—A real-time battery model capable of accurately used to obtain their values using the measurable states of the
predicting the battery hysteresis effect is critical for a model- battery cells, such as voltage, current, and surface
based battery conditional monitoring algorithm in advanced temperature. Hence, an accurate battery model is crucial for
battery management systems. Battery condition monitoring the development of a model-based condition monitoring
involves tracking changes in physical parameters and
algorithm. Moreover, a balance between the accuracy and
operational states such as state of charge (SOC) and state of
health (SOH) to ensure the optimal operation and safety of a the complexity of the battery model should be considered
battery system. This paper investigates and models the for real-time condition monitoring of batteries.
hysteresis behavior of lithium-ion battery cells and The model-based methods basically utilize state-space
incorporates the hysteresis model in the real-time battery
model to improve the accuracy of the SOC estimation in both
electrochemical models [3] or electrical circuit models [4] to
charge and discharge modes over the entire operating SOC design an observer for real-time SOC and/or SOH
range and environmental temperature range of the cells. This estimation. Although the electrochemical models are
also leads to accurate maximum capacity estimation to accurate, their implementations are difficult due to the high
determine the SOH of the battery cells. In addition, a method complexity and intensive computation requirement.
for extracting the hysteresis model parameters is proposed. Therefore, electrical circuit models are more suitable for
Experimental results for a cylindrical lithium-ion cell are real-time embedded system applications.
provided to validate the proposed model and method.
The hysteresis effect [5] is a fundamental phenomenon
Keywords—Battery model; condition monitoring; hysteresis of batteries, which shows a difference in the equilibrium
model; lithium-ion battery; parameter estimation; real time open-circuit voltage (OCV) between the charge and
discharge processes of the batteries. The hysteresis effect is
I. INTRODUCTION mainly caused by the mechanical stress, entropic effect, and
Lithium-ion batteries have been widely used in many microscopic distortion in the active materials during the
battery-powered systems owing to the high energy and lithium insertion and extraction process, which lead to a
power densities and long cycle life [1]. While viewed as a phase separation and slow dynamics of the battery cells. The
promising technology, lithium-ion batteries still have difference in the equilibrium OCV depends on the history of
significant limitations in reliability and performance the battery usage, environmental temperature, and properties
degradation due to low thermal stability and aging process. of the active materials in the battery. For some lithium-ion
To overcome these limitations, it is important to include the batteries (e.g., LiFePo4) having a relatively strong
condition monitoring function in a battery management hysteresis effect, the SOC estimation accuracy will
system (BMS). A key function of the condition monitoring deteriorate if the battery model does not incorporate the
is to estimate the states and parameters, such as the state of hysteresis effect. Furthermore, since the battery hysteresis
charge (SOC), state of health (SOH), instantaneous effect depends on the environmental temperature, it is
available power (i.e., state of power (SOP)), internal necessary to include a temperature-dependent hysteresis
impedance, maximum capacity, etc., which reflect the model if the battery system is exposed to a varying
operating and health conditions of the battery cells during temperature environment. Recently, the authors developed a
operation [2]. Since the values of these states and real-time battery model comprising a first-order resistor-
parameters cannot be directly measured by using sensors, capacitor (RC) electrical circuit with a hysteresis model [6],
model-based condition monitoring methods are commonly which, however, did not provide a detailed analysis on the
This work was supported in part by the U.S. National Science
Foundation under grant IIP-1414393.
ª− ηTs / Cmax 0 º 4
VOC
« » ªiB (k ) º
+ « Rc (1 − γ ) 0 » ⋅ «V »
( H − 1) sign(iB )»¼ ¬
h max ¼
«¬0 3.8
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Since the state matrix of the real-time battery model with Estimation Toolbox in MATLAB/Simulink.
the hysteresis effect in (1) is current-dependent, the z
transform cannot be applied to the real-time model directly. IV. VALIDATION
It is not easy to estimate the model parameters using linear A Samsung’s ICR18650-28A cylindrical lithium-ion
regression due to the Vh-dynamics. To facilitate the battery cell is tested to validate the proposed battery model
parameter estimation, the real-time battery model (1) and (2) and parameter estimation method. The nominal current and
is simplified as the following state-space form by assuming voltage of the cell are 2.8 Ah and 3.75 V, respectively. The
that VOC = b1·SOC+b0 = Voc(SOC) + Vh: battery cell is tested in a SUN ELECTRONIC SYSTEMS’
EC12 temperature chamber, as shown in Fig. 4, at three
ª − ηTs º different ambient temperatures: high temperature (35 °C),
ª SOC ( k + 1)º ª1 0 º ª SOC ( k )º « » ⋅ i ( k ) (3)
= ⋅ +
«V ( k + 1) » «0 γ » «V ( k ) » « max C room temperature (21 °C), and low temperature (5 °C). The
» B
¬ d ¼ ¬ ¼ ¬ d ¼ « R (1 − γ )» temperature chamber is connected to a nitrogen tank, which
¬ c ¼
provides the inflow liquid nitrogen for the test at the low
ª SOC (k )º ambient temperature condition. The measured cell voltage
Vcell (k ) = [b1 − 1] « » − Rs ⋅ iB (k ) + b0 (4)
¬Vd (k ) ¼ and current are collected from a CADEX C8000 battery
tester. In the full charge test, the battery cell is charged with
From the simplified model (3) and (4), the electrical
a constant current constant voltage (CCCV) charge method
resistances Rs and Rc and capacitance Cd can be identified
until it is fully charged. The charge cutoff voltage is 4.3 V
using a linear regression method, such as the moving
and the charge cutoff current is 0.01C (i.e., iB = 0.028 A). In
window least square method [4]. In this paper, a general
the full discharge test, the fully charged cell is discharged to
RLS method is applied to estimate the electrical impedance
the discharge cutoff voltage of 3 V.
parameters of the model.
The SOC-Voc look-up table is obtained from offline full
III. HYSTERESIS MODELING AND PARAMETER discharge and charge tests using a very small current (e.g.,
ESTIMATION 0.05C = 0.14 A), which minimally excites the transient
The hysteresis model parameters Vhmax and ȡ are response of the battery cell [10]. The SOC measurement
estimated by using the method shown in Fig. 3. An RLS- during discharge, SOCd, is computed as 1–(present
based online parameter identification algorithm is designed discharged capacity)/(total discharged capacity), and the
to estimate the impedance parameters of the simplified
battery model (3) and (4). The estimated impedances are
then used as the parameters of an ADSMO-based VOC
observer to estimate VOC(k) of a battery cell. The true Vh(k)
can be computed as
Vh (k ) = VOC (k ) − Voc ( SOC (k )) (5)
where SOC(k) is calculated by using the Coulomb counting
method described in (1) with the known initial SOC (i.e.,
SOC(0)) and Cmax of the cell; and Voc(SOC(k)) is obtained
from a SOC-Voc look-up table. Then, the best estimate of the
hysteresis model parameters are obtained by minimizing the
error between the true Vh(k) and the estimated Vˆh (k ) from Fig. 4. The experimental setup.
the hysteresis model described in (1) using a nonlinear least 4
square optimization method provided by the Control and 1.05
x 10
1.04
1.03
iB (k),...,(k-2) Simplified iB(k) Hysteresis
Cmax (As)
Parameter 1.02
Vcell (k),...,(k-2) Model Model
Identification
1.01
Internal Impedance Vh(k)
iB (k),...,(k-2)
VOC VOC(k) Vh(k) 1
Vcell (k),...,(k-2)
Observer 0.99
Fig. 3. Block diagram of the hysteresis model parameter estimation method. Fig. 5. Cmax as a function of ambient temperature.
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3
4.2 3 2
iB (A)
1
2 0
4
-1
0 100 200 300 400 500
1
(V)
T ime (seconds)
3.8
iB (A)
oc
0
V
°
35 C
3.6 21 C
°
°
-1
5C
3.4
-2
0 0.2 0.4 0.6 0.8 1
SOC -3
0 1 2 3 4
(a) 4
T ime (seconds) x 10
(a)
°
0.25 35 C
°
21 C 4.2
0.2 °
5C
(V)
4
hmax
0.15
Vcell (V)
3.8
V
4.3
0.1
3.6 4.2
Vcell (V)
4.1
0.05
3.4 4
3.9
0
0 0.2 0.4 0.6 0.8 1 3.2 3.8
0 100 200 300 400 500
SOC Time (seconds)
(b) 3
0 1 2 3 4
Fig. 6. Voltage versus SOC for the lithium-ion cell at 35 °C, 21 °C, and 5 °C Time (seconds) 4
(ambient temperature): (a) Voc and (b) Vhmax. x 10
(b)
SOC measurement during charge, SOCc, is computed as Fig. 7. Cell current and voltage during the test with an ambient temperature
of 35 °C: (a) iB, and (b) Vcell.
(present charged capacity)/(total charged capacity). The
curves of Vocdischarge versus SOCd and Voccharge versus SOCc
Fig. 8 compares Vocdischarge extracted from the offline
are then plotted, as shown in Fig. 2. The maximum capacity
test in Section III with VOC estimated online by the
Cmax is the same as the total discharged capacity. Fig. 5
ADSMO. The results show that VOC is close to Vocdischarge
shows the temperature dependency of the Cmax. Fig. 6 shows
at a higher temperature of 35 °C. However, the difference
the average OCV (i.e., Voc) and Vhmax versus SOC for the
between Vocdischarge and VOC becomes larger at a lower
lithium-ion cell at the ambient temperatures of 35 °C, 21 °C
temperature, e.g., 5 °C. Therefore, a Vocdischarge-SOC look-
and 5 °C. Two observations are obtained from Fig. 5 and
up table can be used for the SOC estimation only if the cell
Fig. 6. First, the relationship between Voc and SOC depends
is mainly in the discharged mode of operation and the
on temperature in the low operating SOC range (e.g., SOC <
environmental temperature is high. However, the hysteresis
0.2), but the temperature influence is negligible in the main
voltage should be estimated in order to accurately estimate
operating SOC range (e.g., 0.2 SOC 1). Second, a higher
the SOC over the entire charge/discharge operating range
value of Cmax and a lower value of Vhmax are observed at a
and the entire temperature range.
higher temperature since most chemical processes and ion-
conduction speed up at higher temperatures. Fig. 9(a), (c) and (e) compare the estimated hysteresis
The proposed hysteresis model parameter estimation voltage, Vˆh , obtained from the hysteresis model parameter
method shown in Fig. 3 is implemented in estimation and the true hysteresis voltage Vh calculated by
MATLAB/Simulink and validated by experiments. The (5). Table 1 lists the estimated hysteresis model parameters
fully charged battery cell (i.e., SOC(0) = 1) is fully Vhmax and ȡ. It is observed that ȡ and Vhmax decrease when
discharged and then fully charged using a dynamic current the temperature increases. The main SOC estimation error
profile shown in Fig. 7(a). Fig. 7(b) shows the voltage occurs in the low operating SOC range and constant voltage
respond of the battery cell at 35 °C. The parameter (CV) charging region. Fig. 9(b), (d) and (f) compare the
identification algorithm for the internal impedance SOC values estimated using the real-time battery model
estimation is executed by using the data sampled at 1 Hz. with and without the hysteresis model at different
Then, the ADSMO-based VOC observer is executed with a temperatures. Without the hysteresis model, the accuracy of
sampling rate of 100 Hz to estimate the VOC. SOC estimation is unsatisfactory. On the contrary, the SOC
estimation with the hysteresis model is accurate over the
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Table 1: Temperature-dependent optimal hysteresis model parameters and SOC estimation result using the real-time battery model with hysteresis.
Maximum SOC estimation error Maximum SOC estimation error RMS SOC estimation error in the
Ambient temperature Vhmax ȡ
in low operating SOC range in main operating SOC range entire operating SOC range
35° C 0.0489 6.5169e-4 4.31% 3.187% 0.0134
21 °C 0.0649 0.0010 7.25% 3.798% 0.0176
5 °C 0.1174 0.0013 9.62% 4.583% 0.0283
results clearly show that using the hysteresis model with the 0.8 35° C
temperature-dependent parameters significantly improves 0.6
the accuracy of the SOC estimation over the entire
SOC
operating SOC and temperature ranges.
0.4
True
0.2 No Hysteresis
With Hysteresis
V. CONCULUSIONS 0
0 1 2 3 4
SOC
parameters of the hysteresis model. The inclusion of the
0.4
True
No Hysteresis
hysteresis model has improved the accuracy of the SOC 0.2
With Hysteresis
SOC
VOC Estimate
Voltage (V)
4
0.4 True
No Hysteresis
3.9 With Hysteresis
0.2
4.1 ° Vocdischarge
21 C
maximum capacity has been used to determine the SOH of
Voltage (V)
VOC Estimate
4
the cell. Therefore, the proposed real-time battery model
3.9
incorporating the hysteresis effect will improve the
3.8 condition monitoring performance for lithium-ion batteries.
3.7 The proposed model has been implemented in
0 5000 10000
MATLAB/Simulink and validated by experimental results
Time (seconds) for a cylindrical lithium-ion battery cell.
(b)
4.2 APPENDIX
4.1 °
5C
Vocdischarge Samsung ICR18650-28A lithium-ion cell: discharge
VOC Estimate cutoff voltage (Vcutoff): 3 V; charge cutoff voltage (Vover): 4.3
Voltage (V)
4
V; maximum discharge current: 2C (5.6 A).
3.9
3.8
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