Colloidal tectonics for tandem synergistic Pickering interfacial catalysis: Oxidative cleavage of cyclohexene oxide into adipic acid

Article abstract of DOI:10.1039/c8sc03345e

Supramolecular preorganization and interfacial recognition can provide useful architectures for colloidal building. To this aim, a novel approach, based on colloidal tectonics involving two surface-active particles containing both recognition and catalytic sites, has been developed for controlling the formation and the properties of Pickering emulsions. This was illustrated by the combination of dodecyltrimethylammonium phosphotungstate nanoparticles, [C₁₂]₃[PW₁₂O₄₀], and silica particles functionalized with alkyl and sulfonic acid groups, [C_n/SO₃H]@SiO₂. The interfacial self-assembly occurs by the penetration of the alkyl chains of [C_n/SO₃H]@SiO₂ into the [C₁₂]₃[PW₁₂O₄₀] supramolecular porous structure constituted of polar and apolar regions. The emulsions were used as a non-nitric acid route for adipic acid synthesis from the one-pot oxidative cleavage of cyclohexene oxide with aqueous H₂O₂. The catalytic performance was significantly boosted due to the synergistic interactions between the particles.

Full text of DOI:10.1039/c8sc03345e

AppliedEnergy237(2019)682–694
Contents lists available at ScienceDirect
Applied Energy
journal homepage: www.elsevier.com/locate/apenergy
The improved open-circuit voltage characterization test using active
polarization voltage reduction method
⁎
Jufeng Yanga,b, Wenxin Huanga, Bing Xiab,c, Chris Mib,
a Department of Electrical Engineering, Nanjing University of Aeronautics and Astronautics, 29 Jiangjun Street, Nanjing, Jiangsu 211106, China
b Department of Electrical and Computer Engineering, San Diego State University, 5500 Campanile Drive, San Diego, CA 92182, USA
c Department of Electrical and Computer Engineering, University of California San Diego, 9500 Gilman Dr., La Jolla, CA 92093, USA
H I G H L I G H T S
Applied an extra current excitation to reduce polarization voltage.
•
Analyzed parametric sensitivity of current excitation to model parameters.
•
Developed a method to determine the parameters for the current excitation.
•
Shortened the test time due to the active polarization voltage reduction.
•
Validated the feasibility and superiority with experiments.
•
A R T I C L E I N F O
A B S T R A C T
Keywords:
The correlation between state of charge (SoC) and open-circuit voltage (OCV) is a crucial characteristic para-
meter in many aspects of the battery management system (BMS). However, it is a challenging task to obtain the
accurate SoC-OCV correlation with a high test efficiency. In this paper, an improved OCV characterization test is
proposed to actively reduce the polarization voltage. Based on the third-order equivalent circuit model (ECM),
two sets of current pulses are applied to accelerate the convergence of the battery terminal voltage, thus the test
time is effectively shortened compared to the conventional incremental OCV characterization test. Furthermore,
the parametric sensitivity of the imposed current excitation to battery model parameters is analyzed.
Subsequently, the parametric determination method for the imposed current excitation is provided. Experiments
are conducted on a lithium-ion polymer battery to prove the feasibility of the proposed test procedure.
Comparison with the conventional OCV characterization test further demonstrated the superiority of the pro-
posed test procedure.
Lithium-ion battery
Open-circuit voltage (OCV)
OCV characterization test
Equivalent circuit model (ECM)
Polarization effect
Relaxation behavior
1. Introduction
coulomb counting-based estimation method is often combined with the
OCV-based estimation method to determine the initial SoC and recali-
In recent years, lithium-ion batteries have become the favorable
choice for electric vehicles (EVs) due to their low self-discharge rate,
long cycle life, high energy and power capabilities [1,2]. Nevertheless,
despite the above advantages, a well-designed battery management
system (BMS) is still crucial to ensure the safe and reliable operation of
the battery system. Several essential states of batteries, including the
state of charge (SoC) [3], state of power (SoP) [4], and state of health
(SoH) [5,6] should be monitored accurately by the BMS. In advanced
monitoring algorithms, the accurate estimation of battery states is
generally associated with the correlation between SoC and open-circuit
voltage (OCV). In the SoC estimation technique, the commonly used
brate the estimation result [7,8]. For the SoP estimation, the SoC-OCV
correlation is also an important characteristic parameter to calculate
the peak current [9]. In addition, the SoC-OCV curve can be employed
to identify the battery aging level through differential voltage analysis
or incremental capacity analysis techniques [10,11]. Hence, the OCV as
a function of SoC is a critical characteristic parameter in many aspects
of the battery technology.
1.1. Review of the literature
When the battery is under the current excitation, the measured
⁎ Corresponding author.
E-mail addresses: nuaayjf@163.com (J. Yang), huangwx@nuaa.edu.cn (W. Huang), bixia@eng.ucsd.edu (B. Xia), cmi@sdsu.edu (C. Mi).
https://doi.org/10.1016/j.apenergy.2019.01.060
Received 13 May 2018; Received in revised form 1 January 2019; Accepted 7 January 2019
0306-2619/©2019ElsevierLtd.Allrightsreserved.

J. Yang et al.
AppliedEnergy237(2019)682–694
terminal voltage involves not only the OCV but also the overvoltage
representing a series of polarization effects. Since these effects cannot
be measured directly by physical sensors and can exist up to several
hours after the current interruption, the battery terminal voltage only
approximates the OCV after the long-time relaxation process, until all
polarization effects nearly vanish [12]. Hence, it is a challenging task to
obtain OCV values over a wide SoC range with high accuracy and ef-
ficiency. Generally, there are two typical kinds of methods to determine
the SoC-OCV correlation: model-based and test-based methods.
battery is discharged/charged incrementally (e.g. 10% SoC interval),
and followed by
a long-time relaxation process [26–30]. Refs.
[14,17,24] have concluded that the SoC-OCV correlation obtained from
the incremental OCV characterization test is more reliable than from
the low-current OCV characterization test. It is mainly because in the
incremental OCV characterization test, polarization effects are nearly
eliminated after the long-time relaxation process. Thus, the directly
measured terminal voltage can be considered as the battery OCV.
However, due to the long-time relaxation process, an extensive test time
is required to obtain the complete SoC-OCV correlation for the incre-
mental OCV characterization test.
The model-based methods generally estimate the polarization vol-
tage Vp based on the equivalent circuit model (ECM), then the battery
OCV can be calculated by subtracting Vp from the measured terminal
voltage. This type of methods can be further classified into two groups,
namely, the OCV prediction methods in the idle condition and the OCV
estimation methods in the operation condition. The former group of
methods generally utilize the voltage relaxation model to asymptoti-
cally fit the measured battery terminal voltage after the current inter-
ruption, then the OCV can be predicted by extrapolating the employed
voltage relaxation model. In [13] the battery OCV is predicted by an
adaptive approach, and the employed model consists of a ZARC-ele-
ment and a voltage source in series. Ref. [14] establishes an asymptotic
function to approximate the battery relaxation behavior, and the ex-
trapolation of the voltage relaxation allows a fast prediction of the
battery OCV. From the perspective of the OCV estimation methods in
the operation condition, the battery OCV along with other battery
parameters (e.g., SoC, impedance parameters, and capacity) are usually
identified based on the estimation difference between the model output
voltage and the measured terminal voltage. A variety of filters or ob-
servers, such as recursive least squares [15], extended Kalman filter
[16], H-infinity filter [17], adaptive observer [18], etc., are employed
to recursively minimize the estimation difference. One common ad-
vantage of the model-based methods is that the long-time relaxation
process is not needed to eliminate the influence of the polarization
voltage, as the battery OCV can be obtained online. However, it has to
be noted that three disadvantages exist concerning this type of tech-
nique. Firstly, the accuracy of the obtained OCV is closely related to the
fidelity of the employed model. However, because of the limited com-
putational capability of the onboard microcontroller, the employed
model is not guaranteed to characterize the polarization effects as
precisely as possible [19]. As a result, the estimated OCV generally
deviates from the actual value as it consists of the overvoltages re-
presenting slow-dynamics polarization effects (e.g., the effect of diffu-
sion processes etc.). Secondly, the complete SoC-OCV correlation is only
available when the battery experiences the full discharge/charge pro-
cess. In fact, only pieces of the SoC-OCV correlation can be obtained
due to the incomplete real conditions (especially driving cycles in EVs).
In order to obtain a complete SoC-OCV correlation, Ref. [20] proposes a
data pieces-based parameter identification method to connect multiple
SoC-OCV pieces. However, it requires a large amount of test data pieces
to cover a wide SoC range. Thirdly, the OCV and other model para-
meters are integrated together in the estimation process, thus the cross
interference caused by the integration can lead to an inaccurate OCV
estimation, which is especially pronounced for the OCV estimation
methods in the operation condition [15,21].
1.2. Contributions of the paper
Based on the aforementioned analysis, the test-based methods,
especially the incremental OCV characterization test, can obtain the
SoC-OCV correlation with a higher accuracy, in comparison to model-
based methods. However, the long relaxation time makes the whole test
too time-consuming. As the long-time relaxation process is used to
eliminate the influence of the polarization voltage, we had a question,
why not we actively minimize the polarization voltage to accelerate the
convergence speed of the battery terminal voltage? Hence, an improved
OCV characterization test using active polarization voltage reduction
method is proposed in this paper. The main contributions of this paper
are:
(1) A certain form of the current excitation is first introduced to ac-
celerate the voltage convergence of the RC network. By analyzing
the overvoltage across the first-order RC network, it is proved that
the voltage response under the specific current excitation shows a
faster convergence performance, in comparison to that under the
self-rest condition.
(2) Two sets of current pulses are applied to ensure a fast convergence
of the battery terminal voltage. According to the frequency range of
physical processes occurring under the open-circuit condition, a
third-order ECM is adopted to describe the relaxation behavior.
Based on the employed ECM, two sets of current pulses are utilized
to actively minimize the overvoltages across the middle- and long-
term RC networks, which correspond to the effects of middle- and
low-frequency polarizations, respectively.
(3) The parameter calculation method is provided to predetermine the
imposed current excitation. The impact of the model parameter
variation on the imposed current parameters is investigated. Based
on this, the parameter calculation method considering the influence
of the SoC is provided. The experiment results demonstrate the
superiority of the proposed test method in terms of the convergence
speed.
2. Battery relaxation model
The ECM is widely employed to characterize the physical processes
occurring in the battery [31–33]. The common structure of an ECM is
shown in Fig. 1, where the ideal voltage source VOC stands for the OCV,
the Ohmic resistance Ro is related to the electrolyte and connection
For the test-based methods, the polarization voltage is generally
reduced or even eliminated during the test procedure, thus the OCV can
be obtained directly from the battery terminal voltage. One of the
commonly used test-based methods is the low-current OCV character-
ization test, which employs the low C-rate (e.g. C/20) constant-current
(CC) to discharge/charge the battery [8,22–24]. The advantage of this
method is that the resolution of the SoC-OCV correlation is high, be-
cause of the continuous SoC variation during the test. However, even
with the low C-rate, the polarization effects still exist because of the
continuous current excitation, especially at extreme SoC ranges, which
affects the accuracy of the obtained OCV [25]. An alternative test-based
method is the incremental OCV characterization test. In which the
Rct
Ro
Zw
Cdl
VOC
Fig. 1. The general equivalent circuit model.
683

J. Yang et al.
AppliedEnergy237(2019)682–694
Rw
Rp,3
Rp,1
Cp,1
Rp,2
Cp,2
Zw
Ro
I
Cp,3
CPE
Vp,1
Vp,2
Vp,3
VOC
Vt
Rp,n
Cp,n
Rp,1
Cp,1
Rp,2
Cp,2
V/I
voltage
current
Fig. 2. The equivalent circuit models to represent the concentration polariza-
tion processes.
time
resistance, the RC network (Rp,ct//Cp,dl) represents the effect of the
activation polarization (charge-transfer and double-layer), and the
Warburg impedance Zw is correlated with the effect of the concentra-
tion polarization (mass transport), which is mainly due to the diffusion
processes.
Fig. 3. The third-order equivalent circuit model.
dVp,i
dt
Vp,i
Rp,i
Cp,i
+
= I
(2)
(3)
In general, the majority of the concentration polarization processes
have larger time constants compared to the Ohmic resistance and ac-
tivation polarization processes [34]. Hence, the concentration polar-
ization is largely responsible for the overvoltage variation during the
long-term relaxation process. Typically, considering a limited-length
diffusion condition and neglecting the high-frequency dynamics, the
Warburg impedance Zw can be represented by a parallel resistance Rw
and constant phase element (CPE) circuit as illustrated in Fig. 2, and the
corresponding impedance is expressed as [13,35]
3
V = VOC + IRo
+
Vp,i
t
i=1
where Rp,i and Cp,i represent the polarization resistance and the polar-
ization capacitance, respectively, Vt represents the battery terminal
voltage, and I is the load current (the positive value denotes charging
and the negative value denotes discharging).
Specifically, the detailed expression of Vp,i can be derived by solving
(2),
Rw
ZR
=
//Z
CPE
w
1 + Rw·A0 ·(j· )
(1)
Vp,i (t) = Vp,i (0) exp( t/ p,i) + IRp,i [1 exp( t/ p,i)]
(4)
where Vp,i(0) represents the initial overvoltage across the corresponding
RC network, which is caused by the preceding charge or discharge
period, τp,i (i = 1, 2, 3) is the time constant of the corresponding RC
where A0 is a parameter of CPE, α is the depression parameter. By
applying an inverse transformation on (1) to the time domain, it can be
found that the Rw//ZCPE circuit can be completely modeled by an in-
finite number of RC networks with slightly different time constants, as
shown in Fig. 2 [36].
network and τp,i = Rp,i·Cp,i
.
It should be noted that the load current I equals zero under the
open-circuit condition, thus the overvoltage across Ro can be omitted.
Hence, the overvoltage caused by the polarization effects during the
relaxation period can be expressed as
The ECM shown in Fig. 2 consists of a large number of circuit
parameters, which would result in the massive parameterization effort
and the convergence problem [4,37]. Generally, the frequency domain
of the concentration polarization covers a wide range of frequency,
from 10-5 Hz up to 100 Hz [38]. It is a good compromise to abandon the
extremely low-frequency component because the corresponding over-
voltage built up during the incremental charge/discharge period is
negligible. Besides, compared to completely modeling of polarization
effects, the RC networks which represent typical dynamic character-
istics of polarization effects would be needed for the proposed method
as will be discussed in Section 3. Hence, considering the tradeoff among
the parameterization effort, the convergence performance and the
model fidelity, a third-order RC network with different orders of time
constants is employed to characterize the effect of the concentration
polarization in this study. Specifically, effects of activation and high-
frequency concentration polarizations are modeled as one RC network
(Rp,1//Cp,1) due to similar frequency characteristics.
3
Vp,i (t) = V (t) VOC (t) =
Vp,i (0) exp( t/
)
p,i
t
(5)
i=1
3. Proposed active polarization voltage reduction method
As mentioned above, the overvoltages caused by the middle- and
low-frequency polarization effects can be modeled as Vp,2 and Vp,3 in
the third-order ECM, and a long period of relaxation time is generally
required for them to reach the steady state. However, based on the
characteristic of the RC network, a certain form of the current excita-
tion can be applied to accelerate the voltage convergence, which will be
illustrated in detail as follows.
The detailed architecture of the ECM with the third-order RC net-
work is shown in Fig. 3 [39,40], where Vp,i (i = 1, 2, 3) denotes the
overvoltage across the corresponding RC network (Rp,i//Cp,i). Specifi-
cally, the time constant of Rp,i//Cp,i increases with the increasing index,
i.e., Vp,1, Vp,2 and Vp,3 model the overvoltages caused by the high-,
middle- and low- frequency polarization effects, respectively, as illu-
strated in Fig. 3.
3.1. Analysis of the RC network voltage response
3.1.1. The first-order RC network
Considering a scenario that the RC network is firstly discharged by a
current pulse with amplitude |Ip| and time duration Tp, the corre-
sponding voltage response at time Tp (point B in Fig. 4(a)) can be de-
rived based on (4),
The electrical behavior of the third-order ECM can be expressed as
Vp,curr (Tp) = Vp (0) exp( Tp/
)
|Ip| Rp [1 exp( Tp/ p)]
p
(6)
684

J. Yang et al.
AppliedEnergy237(2019)682–694
Vp
Ip
D
A
C
|Ip|
Ip
Vp
B
Tp
(a) Scenario 1.
(b) Scenario 2.
Fig. 4. Schematic of current excitations (solid line) and corresponding voltage responses (dashed line).
3.1.2. The second-order RC network
H
Based on the aforementioned analysis, the RC network voltage
shows a faster convergence speed under the specific set of current
pulses. In addition, since the charge and discharge pulses possess the
same current amplitude and duration, the values of SoC before and after
the current excitation are identical. Hence, in the incremental OCV
characterization test, the predesigned current excitation can be em-
ployed to actively reduce the polarization voltage, and thus the test
time is shortened. For the fast-dynamics polarization effects, a short
period of relaxation time is required for the corresponding overvoltage
Vp,1 to reach the steady state. Hence, in this study, only the polarization
voltages represented by Vp,2 and Vp,3 are actively reduced due to the
slow dynamic characteristics. To simplify the discussion, only the in-
cremental discharge test is considered in this study. The derivation for
the charge case can be conducted in a similar way.
Vp,2
Ip
J
G
E
F
Vp,3
|Ip,2
|
|Ip,3
|
2Tp,3
2Tp,2
Fig. 5. Schematic of the proposed current excitation (solid line) and corre-
sponding voltage responses (dashed lines).
Since Vp,3 caused by the low-frequency polarization effects is the
main factor to the long relaxation time, a set of current pulses (the
waveform is similar to that in Fig. 4(a)) are first imposed on the battery
to accelerate the convergence of Vp,3. Assuming Vp,3 equals zero at the
end of the current excitation (point G in Fig. 5), the relevant current
amplitude |Ip,3| and the time duration Tp,3 should be constrained by the
following equation
where Ip represents the imposed current, a positive value represents the
charging case and a negative value represents the discharging case,
Vp(0) is the overvoltage across the RC network at the beginning of the
current pulse (point A in Fig. 4(a)), which can be expressed as
Vp (0) = IdRp [1 exp( T / p)]
d
(7)
V
p,3 (2Tp,3) = Vp,3 (0) exp( 2Tp,3
/
p,3) + |Ip,3| Rp,3 [1 exp( Tp,3
/
p,3)]2
where Id and Td are the current and the time duration of the preceding
charge/discharge period, respectively.
(12)
= 0
Afterwards, the RC network is immediately charged by a current
pulse with the same amplitude and time duration, as shown in Fig. 4(a).
The corresponding voltage response at the end of the second current
pulse (point C in Fig. 4(a)) can be expressed as
where Vp,3(0) is negative after the preceding discharge period (point
E in Fig. 5).
For the middle-term RC network (Rp,2//Cp,2), the corresponding
overvoltage at time 2Tp,3 can be expressed as
Vp,curr (2Tp) = Vp,curr (Tp) exp( Tp/ p) + |Ip| Rp [1 exp( Tp/ p)]
(8)
V
p,2 (2Tp,3) = Vp,2 (0) exp( 2Tp,3
/
p,2) + |Ip,3| Rp,2 [1 exp( Tp,3
/
p,2)]2
(13)
Substituting (6) into (8), Vp,curr(2Tp) can be further expressed as
Considering the values of Td and Tp,3, (referring to Section 4), and
the change rate of the exponential function (referring to Appendix A), it
can be obtained that
Vp,curr (2Tp) = Vp (0) exp( 2Tp/ p) + |Ip| Rp [1 exp( Tp/ p)]2
(9)
For the self-rest scenario, the RC network voltage at time 2Tp is
expressed as
exp( T /
)
exp( Tp,3
/
)
p,i
d
p,i
(14)
Vp,rest (2Tp) = Vp (0) exp( 2Tp/
)
p
(10)
Hence, (12) can be further rewritten as follows on the basis of (7)
and (14).
It can be concluded from (9) and (10) that Vp,curr(2Tp) is larger than
p,rest(2Tp) because of the second term in (9). In other words, if Vp(0) is
V
V
p,3 (0) exp( 2Tp,3
/
)
Id exp( 2Tp,3
|Ip,3|[1 exp( Tp,3/ p,3)]
/
)
p,3
p,3
1 =
=
negative, Vp,curr will converge toward zero first in comparison to Vp,rest
.
|Ip,3| Rp,3 [1 exp( Tp,3
/
p,3)]2
Similarly, if the RC network is imposed by the current excitation as
shown in Fig. 4(b) (scenario 2), the corresponding voltage response at
point D is expressed as
(15)
Since τp,2 and τp,3 are well-separated (time constants can be con-
sidered as well-separated if τp,3 ≥ 5τp,2 [41]), it can be derived that
exp( 2Tp,3
Vp,curr (2Tp) = Vp (0) exp( 2Tp/
)
|Ip| Rp [1 exp( Tp/ p)]2
p
(11)
/
p,2) < exp( 2Tp,3
/
)
p,3
(16)
(17)
It can be concluded from (10) and (11) that Vp,curr after this kind of
current excitation is lower than Vp,rest after the relaxation time of 2Tp,
which means that Vp,curr also shows a faster convergence speed with the
1
exp( Tp,3
/
p,2) > 1 exp( Tp,3
/
)
p,3
positive initial value compared to Vp,rest
.
Based on (15), (16) and (17), the following relationship can be
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J. Yang et al.
AppliedEnergy237(2019)682–694
8
6
4
2
0
80
obtained.
|Ip,3
|
V
p,3 (0) exp( 2Tp,3
/
)
V
p,2 (0) exp( 2Tp,3
/
)
p,3
p,2
1 =
<
|Ip,3| Rp,3 [1 exp( Tp,3
/
p,3)]2
|Ip,3| Rp,2 [1 exp( Tp,3
/
p,2)]2
SoC3
60
40
20
0
(18)
K
< 0
Considering (13) and (18), it can be further obtained that
V
p,2 (2Tp,3) = Vp,2 (0) exp( 2Tp,3
/
p,2) + |Ip,3| Rp,2 [1 exp( Tp,3
/
p,2)]2
(19)
> 0
It concludes that Vp,2(2Tp,3) can be qualitatively determined as the
positive value, as shown in Fig. 5 (point H). Hence, the polarization
voltage represented by Vp,2 cannot be eliminated or effectively reduced
by the above current excitation, and another set of current pulses, with
the waveform similar to that in Fig. 4(b), are applied immediately after
the first current excitation to overcome the above problem, as shown in
Fig. 5. Assuming Vp,2 equals zero at the end of the current pulses, the
following relationship can be derived on the basis of (11).
5
8
11
14
17
20
Time (min)
Fig. 6. Evolution of |Ip,3| and ΔSoC3 with respect to Tp,3
.
seen from the figure that both |Ip,3| and ΔSoC3 achieve high values with
the low Tp,3. For example, when Tp,3 is selected as 6 min, the corre-
sponding |Ip,3| and ΔSoC3 are 4.614C and 46.14%, respectively (i.e.,
point K in Fig. 6). For most of the lithium-ion batteries, such a long
duration and high C-rate load current are harmful. Moreover, the bat-
tery terminal voltage will reach the cutoff value easily because of the
large values of |Ip,3| and ΔSoC3 [42]. Besides, due to the variation of
battery model parameters, |Ip,3| and Tp,3 with respect to the large ΔSoC3
will differ greatly from the value shown in Fig. 6, which will be further
discussed in Sections 3.2.2 and 5.1. For this reason, Vp,3 may not be
effectively reduced under the current excitation with respect to the
large ΔSoC3. On the other hand, it can be observed from Fig. 6 that both
|Ip,3| and ΔSoC3 decrease exponentially with the increase of Tp,3, which
means that a larger Tp,3 can overcome above problems. However, a
larger Tp,3 results in a longer test time. Hence, a compromise between
the test time and |Ip,3| (or ΔSoC3) must be considered when determining
the appropriate parameters of the current excitation.
V
p,2 (2Tp,2 + 2Tp,3) = Vp,2 (2Tp,3) exp( 2Tp,2
/
)
p,2
|Ip,2| Rp,2 [1 exp( Tp,2
/
p,2)]2 = 0
(20)
Theoretically, Vp,2 can be eliminated after the second set of current
pulses. On the other hand, since
V
p,3(2Tp,3) = 0, Vp,3 at time
2Tp,3 + 2Tp,2 (point J in Fig. 5) can be expressed as
V
p,3 (2Tp,3 + 2Tp,2) = |Ip,2| Rp,3 [1 exp( Tp,2
/
p,3)]2
(21)
Generally, Tp,2 is far less than τp,3, which can be verified from the
designed parameters in Section 4. Hence, the term [1 − exp(−Tp,2
/
τp,3)]2 in (21) is close to zero and Vp,3 maintains a low value after the
second set of current pulses.
3.2. Parameter determination of the imposed current excitation
3.2.1. Relationship between |Ip,i| and Tp,i
Based on (12) and (20), |Ip,i| can be obtained with the pre-
determined Tp,i
.
3.2.2. Sensitivity of |Ip,3| to battery model parameters
It can be concluded from (22) that besides Tp,3 and Vp,3,init, battery
model parameters, i.e., Rp,3 and τp,3, also have a great influence on the
determination of |Ip,3|. Hence, the sensitivity of |Ip,3| to battery model
parameters is worth investigating.
|Vp,i,init| exp( 2Tp,i
/
)
p,i
|Ip,i| =
,
i = 2,
3
Rp,i [1 exp( Tp,i/
p,i)]2
(22)
where |Vp,i,init| is the amplitude of the initial RC network voltage at the
beginning of relevant current pulses, such as point E (i = 3) and point H
(i = 2) in Fig. 5. For the long-term RC network (i = 3), |Vp,3,init| is de-
fined as
Considering the variations of battery model parameters, Eq. (22)
can be rewritten as
|Vp,3,init| exp( 2Tp,3
R
/
)
p,3
|Ip,3| =
|Vp,3,init |=|Id| Rp,3,d [1 exp( T / p,3)]
p,3 [1 exp( Tp,3/
p,3)]2
d
(23)
(25)
where Rp,3,d is the average long-term resistance covering the incre-
where |Ip,3| is the amplitude of the current pulse when parameter var-
iations exist, Rp,3and p,3are battery model parameters considering var-
iation values, which can be expressed as
mental discharge period.
For the middle-term RC network (i = 2), |Vp,2,init| is defined as
|Vp,2,init | = |Vp,2 (T )|exp( 2Tp,3
/
p,2) + |Ip,3| Rp,2 [1 exp( Tp,3
/
p,2)]2
d
Rp,3 = Rp,3
+
Rp,3
|Vp,2 (T )|=|Id| Rp,2,d [1 exp( T / p,2)]
d
d
=
+
p,3
p,3
p,3
(26)
(24)
where Rp,2,d is the average middle-term resistance covering the incre-
mental discharge period, Vp,2(Td) is the overvoltage caused by the in-
cremental discharge period (point F in Fig. 5).
where ΔRp,3 and Δτp,3 are variation values on model parameters.
By subtracting (22) and (25), |Ip,3| = |Ip,3
|
|Ip,3| is obtained to
quantitatively evaluate the variation of |Ip,3| caused by the model
parameter variation. Similar to the previous analysis, the assumed
model parameters are extracted from the impedance characterization
test data at 30% SoC, and Tp,3 is predetermined as 10 min. Simulation
results are shown in Fig. 7. It can be summarized that: (1) |Ip,3| is more
sensitive to the parameter variation on τp,3 when the corresponding
variation rate is above −40%. (2) The impact of the model parameter
variation is not negligible. The |Ip,3| change can reach up to 1.49C and
2.181C with −50% variation rate on Rp,3 and 50% variation rate on
τp,3, respectively. Hence, the sensitivity study gives us an important
guide for the parametric determination of the imposed current pulses.
It can be concluded from (22)–(24) that except the definition of the
initial voltage, the expressions of |Ip,i| for two sets of current pulses
have the identical form. In order to simplify the analysis, only the re-
lationship between |Ip,3| and Tp,3 is discussed in this section.
Based on (22) and (23), the evolution of |Ip,3| (in the form of C-rate)
with respect to Tp,3 is plotted as a solid curve in Fig. 6. In addition, the
dashed curve in Fig. 6 illustrates the SoC variation during one charge/
discharge pulse (ΔSoC3) with respect to the different Tp,3. The para-
meters in (22) and (23), i.e., |Id|, Td, Rp,3,d, Rp,3 and τp,3, are obtained
from the impedance characterization test at around 30% SoC. It can be
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J. Yang et al.
AppliedEnergy237(2019)682–694
3
Table 1
Specifications of the tested battery.
Rp,3
τp,3
2.5
Type
Li[NiCoMn]O2
2
Nominal capacity
20 Ah
Nominal voltage
3.65 V
1.5
Maximum charge voltage
4.15 V
Recommended voltage limit for discharge
Maximum discharge current (continuous)
Maximum discharge current (peak < 10 s)
3.0 V
Up to 5 C current
10 C current
1
0.5
procedure and record the test data. Voltage and current measurement
ranges of the battery cycler are 0–5 V and 100 A, respectively. All of
0
-50 -40 -30 -20 -10
0
10 20 30 40 50
Parameter variation rate (%)
the tests are conducted at room temperature (25
2 °C), and the
measured data sets, including current, voltage and accumulative ca-
pacity, are collected with the sampling rate of 1 Hz.
Fig. 7. Sensitivity of |Ip,3| to the variation of battery model parameters.
3.2.3. Determination of |Ip,i| and Tp,i
4.2. Impedance characterization test
As indicated in the sensitivity analysis, the stability of battery model
parameters, especially τp,i, during the imposed current pulse is vital to
determine current excitation parameters. Since battery model para-
meters can be considered as functions of SoC, ΔSoCi should be con-
strained to a certain range to reduce the model parameter variation.
Hence, |Ip,i| and Tp,i can be determined by the following two con-
strained equations
It can be inferred from the aforementioned analysis that battery
model parameters, especially the RC network parameters (i.e., Rp,2,
Rp,3, τp,2 and τp,3), are needed in advance to determine |Ip,i| and Tp,i
(i = 2, 3). In this paper, the battery impedance parameters are identi-
fied through the hybrid pulse power characterization (HPPC) test.
4.2.1. Test procedure
|Ip,i | Rp,i [1 exp( Tp,i/¯p,i)]2 = 0
¯
|Vp,i,init| exp( 2Tp,i/¯p,i
)
i
In the HPPC test, the battery is first completely charged/discharged
at 0.5C rate with the constant-current constant-voltage (CCCV) charge/
CC discharge procedure, followed by a 2 h rest. After that, the battery is
incrementally discharged/charged in 10% of the nominal capacity with
0.5C rate to the next SoC level, and followed by a certain length of the
relaxation period. To stimulate the battery dynamically, one pair of
discharge and charge current pulses, each lasting for 10 s and with the
amplitude of 2C, is imposed before each incremental discharge/charge
period. The above test cycle is repeated until the discharge/charge
cutoff voltage is reached.
|Ip,i | Tp,i/(3600Ccap) = SoCi
= 2,
3
(27)
¯
where Ccap is the capacity of the battery in Ah, Rp,i and ¯p,i are average
values of relevant battery model parameters covering the SoC variation
period (ΔSoCi). Besides, ΔSoCi should be determined based on the
battery impedance identification results. The above equations can be
solved by the MATLAB fsolve function.
Generally, the RC network parameters can be identified through the
battery terminal voltage measured from the relaxation period. Based on
the previous research work, the identified parameters, especially the
time constants, are closely related to the length of the relaxation period
[34,43]. Besides, the relaxation behaviors at extreme SoC ranges, i.e.,
the low SoC range for the discharge scenario and the high SoC range for
the charge scenario, show a slower dynamic characteristic, compared to
those in the middle SoC range [12,27]. Hence, the relaxation time at
extreme SoC ranges is selected as 120 min and others are selected as
90 min, as a trade-off between the testing effort and the accuracy of
model parameters.
4. Experimental validation
4.1. Experimental setup
A test platform as shown in Fig. 8 is established to validate the
proposed OCV characterization test. A lithium-ion polymer pouch-type
battery with 20 A h nominal capacity (model C020 manufactured by
EIG) is adopted in this study. The cathode material is Li[NiCoMn]
O2–based and the anode material is graphite-based. Detailed specifi-
cations of the tested battery are listed in Table 1. An Arbin BT2000
cycle-based tester and a host computer are used to conduct the test
4.2.2. Analysis of test results
Current
Voltage
The evolution of the relaxation process and the energy efficiency at
different SoCs are plotted in Fig. 9.
Fig. 9(a) shows the polarization voltage curves over the relaxation
period (Vp,I=0) at different SoCs, where the solid and dashed lines re-
present the experimental results from charge and discharge tests, re-
spectively. The polarization voltage is obtained by subtracting the
battery terminal voltage at the end of the relaxation period (Vt,end) from
the battery terminal voltage during the relaxation period (Vt,I=0), i.e.,
Accumulative
capacity
Tested battery
Vp,I=0 = Vt,I=0 − Vt,end. It can be observed from Fig. 9(a) that the bat-
tery’s polarization voltage does not reach the steady state immediately,
and the slow-dynamics part dominates the majority of the relaxation
period. Moreover, the SoC affects the relaxation behavior of the battery
in terms of the shape and convergence performance. This phenomenon
is more obvious at 60% and 70% SoCs for the charge test.
Furthermore, the energy efficiency ƞe, which is defined as (28), is
adopted to quantitatively relate the measured data with the polariza-
tion effects [44,45].
TCP/IP
Host computer
Arbin BT2000
Fig. 8. Configuration of the experimental setup.
687

J. Yang et al.
AppliedEnergy237(2019)682–694
60
40
20
0
which is in agreement with the test results shown in Fig. 9. This
confirms the necessity of considering the model parameter variation
when determining |Ip,i| and Tp,i (i = 2, 3).
50%
60%
30%
40%
(3) Parameters of the long-term RC network show larger values at ex-
treme SoC ranges, i.e., below 30% SoC for the discharge scenario
and above 80% SoC for the charge scenario, compared to values in
the other SoC range.
70%
4.3. Comparison of OCV characterization tests
-20
-40
It can be inferred from (27) that besides the RC network parameters,
ΔSoCi should also be determined in advance. Based on the analysis in
Section 3.2, the value of ΔSoC3 is selected around 10% at extreme SoC
ranges, and selected around 20% for the other SoC range. For the
second set of current pulses, the value of ΔSoC2 is selected no more than
5%. Hence, the parameters of the imposed current excitation are ob-
tained as illustrated in Fig. 11.
0
720
1440
2160
2880
3600
Time (s)
(a) Polarization voltages after charging and discharging
at different SoCs under open-circuit condition.
To verify the advantages of the proposed OCV characterization test
method, the conventional one is also performed for the purpose of
comparison. The current profiles of the conventional and the proposed
OCV characterization tests during each SoC interval are schematically
shown in Fig. 12. In this paper, the conventional incremental OCV
characterization test is conducted with a 4 h relaxation period to allow
the battery to approximate the equilibrium. For ease of comparison, a
relaxation period of 3.5 h is also employed after the current excitation
in the proposed method.
97
96.5
96
95.5
95
The comparison results between the conventional and the proposed
OCV characterization tests at different SoCs are demonstrated in
Fig. 13. Specifically, Fig. 13(a)–(c) and (d)–(f) shows the battery’s po-
larization voltage curves over the relaxation period from discharge and
charge OCV characterization tests, respectively. It can be observed from
Fig. 13 that by the conventional method, the polarization voltage shows
the slow convergence performance, and the gradient of the polarization
voltage over time is relatively low during the majority of the relaxation
period (approximate 2 mV over the last 2.5 h). Moreover, even after the
long period of relaxation time, i.e., 4 h in this paper, the polarization
voltage still cannot reach the equilibrium state totally. This phenom-
enon is specifically obvious at 20% SoC of the discharge scenario and
80% SoC of the charge scenario, which is in agreement with the iden-
tified time constants demonstrated in Section 4.2. Therefore, it can be
concluded that the battery terminal voltage at the end of the relaxation
period is still an approximation of the OCV.
40~50 50~60 60~70 70~80 80~90
SoC interval (%)
10~20
20~30 30~40
(b) Energy efficiencies during charging
and discharging at different SoC intervals.
Fig. 9. Impact of SoC on polarization effects of the battery.
= Edis/Echa
(28)
e
where Edis and Echa represent the discharged energy and the charged
energy, respectively. The definitions of Edis and Echa are expressed as
Edis
=
=
V (t)·I (t)dt = I < 0 [VOC (t) + Zim·I (t)]·I (t)dt
t
I < 0
I > 0
Echa
V (t)·I (t)dt = I > 0 [VOC (t) + Zim·I (t)]·I (t)dt
t
(29)
By comparison, the polarization voltage obtained from the proposed
method converges to the steady state rapidly after the imposed current
excitation. Some transient overshoots occur when the current excitation
is finished, such as black circle regions in Fig. 13(a), (c) and (d).
However, the overshoot dies out shortly and the polarization voltage
converges to the steady state as time evolves. The overshoot phenom-
enon is mostly due to the imposed current excitation. As analyzed be-
forehand in Section 3.1.2, the imposed current excitation can only
eliminate or reduce overvoltages across the middle- and long-term RC
networks, which characterize the diffusion processes occurring in
middle- and low-frequency regions. For the short-term RC network re-
presenting the fast-dynamics polarization effects, the corresponding
overvoltage would be discharged/charged away from the steady state
under the current excitation. Thus, an extra short-term relaxation
period (e.g., 10 min) is required to allow the fast-dynamics polarization
effects to finish.
where Zim is the impedance representing the Ohmic resistance and the
polarization effects, ∫ I < 0 and ∫ I > 0 are the time integrals over the
incremental discharge and charge periods in the impedance char-
acterization test. It can be inferred from (28) and (29) that Zim is mainly
responsible for ƞe when I(t) is kept constant during the time integral.
The evolution of the energy efficiency is shown in Fig. 9(b). It can be
observed that the efficiency generally reduces with decreasing SoC.
This variation is mainly contributed to the change in the polarization
loss, which is closely related to the battery impedance including Ohmic
resistances and polarization effects [45–47]. Hence, it can be pre-
liminarily concluded that the battery impedance is significantly influ-
enced by the SoC.
Based on the curve fitting method presented in Ref. [43], the
identified impedance parameters are plotted in Fig. 10. It can be con-
cluded that
Additionally, it has to be noted that at 20% SoC of the discharge
scenario, the polarization voltage still shows a slightly increasing ten-
dency after the current excitation, as shown in Fig. 13(c). It is because
the relaxation behavior in the low SoC range shows the slow-dynamics
(1) Three time constants are well-separated. Specifically, values of the
short-, middle- and long-term are in the order of 10 s, 102 s and
103 s, respectively. Hence, polarization effects occurring in the vi-
cinity of the relevant time constant can be eliminated or reduced by
current pulses separately.
characteristic [12], while RC networks (i.e., Rp,2//Cp,2 and Rp,3//Cp,3
)
identified from the HPPC test cannot accurately describe relevant
electrochemical reactions due to the limited data points, and only the
polarization voltage around specific frequency ranges (correspond to
(2) The identified impedance parameters vary over a wide SoC range,
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J. Yang et al.
AppliedEnergy237(2019)682–694
5
charge
discharge
4.5
4
3.5
3
2.5
0
10 20 30 40 50 60 70 80 90 100
SoC (%)
(a) Ohmic resistances.
55
4
3.5
3
charge
discharge
charge
50
discharge
45
40
35
30
25
2.5
2
1.5
1
0
10 20 30 40 50 60 70 80 90 100
0
10 20 30 40 50 60 70 80 90 100
SoC (%)
SoC (%)
(b) Short-term resistances.
(c) Short-term time constants.
400
350
300
250
200
150
3
2.5
2
charge
charge
discharge
discharge
1.5
1
0.5
0
10 20 30 40 50 60 70 80 90 100
SoC (%)
0
10 20 30 40 50 60 70 80 90 100
SoC (%)
(e) Middle-term time constants.
(d) Middle-term resistances.
3500
3000
2500
2000
1500
1000
4
3.5
3
charge
charge
discharge
discharge
2.5
2
1.5
1
0
10 20 30 40 50 60 70 80 90 100
SoC (%)
0
10 20 30 40 50 60 70 80 90 100
SoC (%)
(f) Long-term resistances.
(g) Long-term time constants.
Fig. 10. Identification results of RC network parameters.
identified time constants) can be reduced by the imposed current ex-
citation. However, it can be observed from Fig. 13(c) that the gradient
of the polarization voltage over time is considerably small (i.e., 1 mV
over 2.5 h), and thus the remaining polarization effect is negligible.
In summary, the proposed method can ensure a fast convergence of
the polarization voltage caused by the incremental discharge/charge
period, especially with middle- and low-frequency dynamics. In addi-
tion, since the long-time relaxation process is unnecessary, the
proposed method proves to be more time-saving in comparison to the
conventional one.
5. Discussion
5.1. Benefit of considering the model parameter variation
It can be learnt from the HPPC test results that the identified model
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2
1.75
1.5
1.25
1
25
22.5
20
charge
charge
discharge
discharge
17.5
15
12.5
10
0.75
0.5
0.25
0
7.5
5
0
10 20 30 40 50 60 70 80 90 100
SoC (%)
0
10 20 30 40 50 60 70 80 90 100
SoC (%)
(a) Evolution of |Ip,3| with respect to SoC.
(b) Evolution of Tp,3 with respect to SoC.
3.75
2
1.75
1.5
1.25
1
charge
3.5
3.25
3
charge
discharge
discharge
2.75
2.5
2.25
2
0.75
0.5
0.25
0
1.75
0
10 20 30 40 50 60 70 80 90 100
SoC (%)
0
10 20 30 40 50 60 70 80 90 100
SoC (%)
(c) Evolution of |Ip,2| with respect to SoC.
(d) Evolution of Tp,2 with respect to SoC.
Fig. 11. Calculated parameters of the imposed current excitation.
higher than the value obtained from the conventional method, there
still exists the pronounced increasing tendency during the relaxation
period. By contrast, the polarization voltage obtained from the pro-
posed method #1 is closer to the steady state. Moreover, the gradient of
the polarization voltage over time also decreases to low enough (i.e.,
1 mV over 2.5 h) to be neglected.
Relaxation period (4 h)
Incremental
discharge period
(a) In the conventional method.
5.2. OCV measurements at extreme SoC ranges
Taking the discharge OCV characterization test as an example, due
to the slow-dynamics relaxation behavior in the low SoC range, large
values of |Ip,3| or Tp,3 are generally required to ensure a fast con-
vergence of the polarization voltage. On the one hand, the large Tp,3
will result in the long test time and reduce the advantage of the pro-
posed method. On the other hand, the large |Ip,3| can make the battery
terminal voltage reach the cutoff value easily, which in turn leads to the
incomplete SoC-OCV correlation [42]. Similarly, for the charge OCV
characterization test in the high SoC range, the battery will be charged
in the CV mode by the imposed charge current pulse. This will cause the
SoC variation at the end of the current excitation to be nonzero, and the
shifted SoC-OCV correlation will be obtained eventually. Hence, the
conventional long-time relaxation process is employed to measure the
OCV at extreme SoC ranges, i.e., below 20% SoC for the discharge
scenario and above 80% SoC for the charge scenario in this paper.
Relaxation period (3.5 h)
Active polarization voltage
reduction period
Incremental
discharge period
(b) In the proposed method.
Fig. 12. Schematic representation of the current profiles of OCV characteriza-
tion tests during each SoC interval.
parameters change over a wide SoC range, such as the time constant in
a SoC range below 30% for the discharge scenario, as demonstrated in
Fig. 10. Based on the analysis beforehand in Section 3.2.2, the impact of
the model parameter variation on the parametric determination of the
current excitation is not negligible. Fig. 14 shows the comparison result
of the polarization voltage curves obtained from the conventional and
proposed methods, where proposed method #1 and #2 represent the
method with and without considering the model parameter variation,
respectively. It can be observed from Fig. 14 that for the proposed
method #2, although the obtained polarization voltage is generally
5.3. Future work
Generally, the battery aging state and the temperature significantly
affect the battery relaxation behavior. In this paper, the tested battery is
in a new state and all of the characterization tests are conducted at
room temperature (25
2 °C). In order to further verify the feasibility
of the proposed method, the performance of the proposed OCV char-
acterization method at different battery aging states and temperatures
will be investigated comprehensively in our future work.
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AppliedEnergy237(2019)682–694
2
0
2
0
-2
-4
-6
-8
-2
-4
-6
-8
steady state
proposed method
conventional method
steady state
proposed method
conventional method
0
3600
7200
10800
14400
0
3600
7200
Time (s)
10800
14400
Time (s)
(a) Discharge test at 80% SoC.
(b) Discharge test at 50% SoC.
2
0
-2
-4
-6
-8
steady state
proposed method
conventional method
0
3600
7200
Time (s)
10800
14400
(c) Discharge test at 20% SoC.
8
6
6
5
steady state
steady state
proposed method
conventional method
4
3
proposed method
conventional method
4
2
2
1
0
0
-1
-2
-2
0
3600
7200
Time (s)
10800
14400
0
3600
7200
Time (s)
10800
14400
(d) Charge test at 80% SoC.
(e) Charge test at 50% SoC.
6
5
steady state
proposed method
4
conventional method
3
2
1
0
-1
-2
0
3600
7200
Time (s)
(f) Charge test at 20% SoC.
10800
14400
Fig. 13. Evolution of polarization voltage curves after discharge/charge at different SoCs during relaxation period.
6. Conclusion
magnitude of relevant time constants, and the third-order ECM is em-
ployed to describe this behavior. Secondly, based on the characteristic
of the RC network, two sets of current pulses are proposed to actively
minimize overvoltages across the long- and middle-term RC networks,
which correspond to the polarization effects dominating the majority of
the relaxation period. Furthermore, the parametric sensitivity of the
imposed current excitation to battery model parameters is analyzed,
and the parametric determination method for the imposed current ex-
citation is provided subsequently. A lithium-ion polymer battery is
An improved incremental OCV characterization test is proposed in
this paper. Compared with the conventional incremental OCV char-
acterization test, the extra current excitation is imposed immediately
after the incremental discharge/charge period, and thus the fast con-
vergence of the battery terminal voltage is achieved. Firstly, the bat-
tery’s relaxation behavior is broadly divided into three regions (i.e.,
fast-, middle- and long-frequency regions) according to the order of the
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J. Yang et al.
AppliedEnergy237(2019)682–694
Experimental results proved the feasibility of the proposed test proce-
dure, and demonstrated advantages over the conventional one. At last,
the benefit of considering the battery model parameter variation and
the OCV measurements at extreme SoC ranges are further illustrated in
the later discussion.
1
0
-1
-2
-3
-4
-5
-6
steady state
proposed method #1
proposed method #2
conventional method
Acknowledgments
The authors would like to acknowledge the funding support from
the China Scholarship Council (CSC); the US DOE Graduate Automotive
Technology Education (GATE) Center of Excellence; the National
Science Foundation (1507198); and Nanjing Golden Dragon Bus Co.,
Ltd.
0
3600
7200
10800
14400
Time (s)
Fig. 14. Comparison of polarization voltage curves obtained after discharge at
20% SoC during relaxation period.
adopted under test to validate the proposed test procedure.
Appendix A
For the exponential function expressed as
y = exp( x/a)
(A.1)
where a is a constant, x is the input variable, and y is the output variable. The differentiation of (A.1) in respect to x is expressed as.
dy/dx = exp( x/a)/a
(A.2)
Based on (A.2), Fig. A1 is plotted to illustrate the relationship between x and dy/dx.
It can be concluded from (A.2) and Fig. A1 that the value of dy/dx increases with the increasing x , and the change rate of y approaches zero when
x is greater than zero.
dy/dx
0.01
0
-0.01
-0.02
-0.03
-0.04
-0.05
x>0
-500 -250
0
250
500 750 1000
x
Fig. A1. Relationship between x and dy/dx (exemplarily with a = 230.7, which equals τp,2 at around 30% SoC).
Appendix B
BMS
CC
battery management system
constant-current
CCCV
CPE
ECM
EV
constant-current constant-voltage
constant phase element
equivalent circuit model
electric vehicle
HPPC
OCV
SoC
SoH
SoP
A0
hybrid pulse power characterization
open-circuit voltage
state of charge
state of health
state of power
parameter of CPE
Ccap
Echa
Edis
capacity of the battery in Ah
charged energy
discharged energy
I
load current
|Id|
amplitude of the current during the incremental discharge period
amplitude of the imposed current pulse
|Ip|
|Ip,3|, |Ip,2
|
amplitude of the first and the second set of current pulses
amplitude of the imposed current pulse considering battery model parameter variations
|Ip,3
|
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J. Yang et al.
AppliedEnergy237(2019)682–694
Cp,1, Cp,2, Cp,3
capacitances of three RC networks that model the polarization effects
resistance of the circuit that represents the Warburg impedance
Rw
R
p,2,d, Rp,3,d
average middle- and long-term resistance covering the incremental discharge period
resistances of three RC networks that model the polarization effects
average value of Rp,i covering the SoC variation period
Rp,1, Rp,2, Rp,3
¯
Rp,i
resistance of Rp,3//Cp,3 considering the variation value
Rp,3
Rp,ct//Cp,dl
RC network represents the effect of the activation polarization
Ro
Ohmic resistance
Td
time duration of the incremental discharge period
time duration of one current pulse
Tp
2Tp,3, 2Tp,2
VOC
time duration of the first and the second set of current pulses
ideal voltage source stands for the OCV
Vp(0)
overvoltage across the RC network at the beginning of the first current pulse
overvoltages of three RC networks that model the polarization effects
initial overvoltages of three RC networks that model the polarization effects
voltage response of the RC network under the current excitation
polarization voltage during the relaxation period
RC network voltage at the beginning of relevant current pulses
voltage response of the RC network under the self-rest condition
battery terminal voltage
V
p,1, Vp,2, Vp,3
Vp,1(0), Vp,2(0), Vp,3(0)
Vp,curr
Vp,I=0
Vp,i,init
Vp,rest
Vt
Vt,end
Vt,I=0
Zim
battery terminal voltage at the end of the relaxation period
battery terminal voltage during the relaxation period
impedance representing the Ohmic resistance and polarization effects
Warburg impedance
Zw
α
depression parameter of CPE
τp,1, τp,2, τp,3
time constants of three RC networks that model the polarization effects
average value of τp,i covering the SoC variation period
¯
p,i
time constant of Rp,3//Cp,3 considering the variation value
p,3
ƞe
energy efficiency
Δ|Ip,3
|
variation of |Ip,3| caused by the battery model parameter variation
SoC variation during one charge/discharge pulse
variation values of τp,3 and Rp,3
ΔSoC2, ΔSoC3
Δτp,3, ΔRp,3
[16] He H, Xiong R, Guo H. Online estimation of model parameters and state-of-charge
References
of LiFePO4 batteries in electric vehicles. Appl Energy 2012;89:413–20. 2012/01/
01/.
[1] Mi C, Masrur MA, Gao DW. Hybrid electric vehicles: principles and applications
with practical perspectives; 2011.
[17] Lin C, Yu Q, Xiong R, Wang LY. A study on the impact of open circuit voltage tests
on state of charge estimation for lithium-ion batteries. Appl Energy
2017;205:892–902. 2017/11/01/.
[2] Lu L, Han X, Li J, Hua J, Ouyang M. A review on the key issues for lithium-ion
battery management in electric vehicles pp. 272–288, 2013/03/15 J Power Sources
2013;226:/.
[18] Chiang Y-H, Sean W-Y, Ke J-C. Online estimation of internal resistance and open-
circuit voltage of lithium-ion batteries in electric vehicles. J Power Sources
2011;196:3921–32. 2011/04/15/.
[3] Yang J, Xia B, Shang Y, Huang W, Mi CC. Adaptive state-of-charge estimation based
on a split battery model for electric vehicle applications. IEEE Trans Veh Technol
2017;66:10889–98.
[19] Hu X, Li S, Peng H. A comparative study of equivalent circuit models for Li-ion
batteries. J Power Sources 2012;198:359–67. 2012/01/15/.
[4] Farmann A, Sauer DU. Comparative study of reduced order equivalent circuit
models for on-board state-of-available-power prediction of lithium-ion batteries in
electric vehicles 2018/09/01/ Appl Energy 2018;225:1102–22.
[5] Li S, Pischinger S, He C, Liang L, Stapelbroek M. A comparative study of model-
based capacity estimation algorithms in dual estimation frameworks for lithium-ion
batteries under an accelerated aging test. Appl Energy 2018/02/15/
2018.;212:1522–36.
[20] Gao W, Zou Y, Sun F, Hu X, Yu Y, Feng S. Data pieces-based parameter identifi-
cation for lithium-ion battery. J Power Sources 2016;328:174–84. 2016/10/01/.
[21] Yang J, Xia B, Shang Y, Huang W, Mi CC. Adaptive state-of-charge estimation based
on a split battery model for electric vehicle applications. In: IEEE Transactions on
Vehicular Technology, vol. PP; 2017. p. 1–1.
[22] Plett GL. Extended Kalman filtering for battery management systems of LiPB-based
HEV battery packs: Part 2. Modeling and identification. J Power Sources
2004;134:262–76. 2004/08/12/.
[6] Yang J, Xia B, Huang W, Fu Y, Mi C. Online state-of-health estimation for lithium-
ion batteries using constant-voltage charging current analysis. Appl Energy 2018/
02/15/ 2018.;212:1589–600.
[23] Dai H, Wei X, Sun Z, Wang J, Gu W. Online cell SOC estimation of Li-ion battery
packs using a dual time-scale Kalman filtering for EV applications. Appl Energy
2012;95:227–37. 2012/07/01/.
[7] Ng KS, Moo C-S, Chen Y-P, Hsieh Y-C. Enhanced coulomb counting method for
estimating state-of-charge and state-of-health of lithium-ion batteries. Appl Energy
2009/09/01/ 2009.;86:1506–11.
[24] Zheng F, Xing Y, Jiang J, Sun B, Kim J, Pecht M. Influence of different open circuit
voltage tests on state of charge online estimation for lithium-ion batteries. Appl
Energy 2016;183:513–25. 2016/12/01/.
[8] Xing Y, He W, Pecht M, Tsui KL. State of charge estimation of lithium-ion batteries
using the open-circuit voltage at various ambient temperatures. Appl Energy 2014/
01/01/ 2014.;113:106–15.
[25] Newman and Srinivasan. Existence of path-dependence in the LiFePO4 electrode.
Electrochem Solid-State Lett 2006;9:A110–4.
[9] Sun F, Xiong R, He H, Li W, Aussems JEE. Model-based dynamic multi-parameter
method for peak power estimation of lithium–ion batteries. Appl Energy
2012;96:378–86. 2012/08/01/.
[26] Antaloae C, Marco J, Assadian F. A novel method for the parameterization of a li-
ion cell model for EV/HEV control applications. IEEE Trans Veh Technol
2012;61:3881–92.
[10] Liu G, Ouyang M, Lu L, Li J, Han X. Online estimation of lithium-ion battery re-
maining discharge capacity through differential voltage analysis. J Power Sources
2015;274:971–89. 2015/01/15/.
[27] Huria T, Ludovici G, Lutzemberger G. State of charge estimation of high power
lithium iron phosphate cells. J Power Sources 2014;249:92–102. 2014/03/01/.
[28] Zhu L, Sun Z, Dai H, Wei X. A novel modeling methodology of open circuit voltage
hysteresis for LiFePO4 batteries based on an adaptive discrete Preisach model. Appl
Energy 2015;155:91–109. 2015/10/01/.
[11] Gong X, Xiong R, Mi CC. A data-driven bias-correction-method-based lithium-ion
battery modeling approach for electric vehicle applications. IEEE Trans Ind Appl
2016;52:1759–65.
[29] Barai A, Widanage WD, Marco J, McGordon A, Jennings P. A study of the open
circuit voltage characterization technique and hysteresis assessment of lithium-ion
cells. J Power Sources 2015;295:99–107. 2015/11/01/.
[12] Farmann A, Sauer DU. A study on the dependency of the open-circuit voltage on
temperature and actual aging state of lithium-ion batteries. J Power Sources
2017;347:1–13. 2017/04/15/.
[30] Arora S, Shen W, Kapoor A. Critical analysis of open circuit voltage and its effect on
estimation of irreversible heat for Li-ion pouch cells. J Power Sources
2017;350:117–26. 2017/05/15/.
[13] Waag W, Sauer DU. Adaptive estimation of the electromotive force of the lithium-
ion battery after current interruption for an accurate state-of-charge and capacity
determination. Appl Energy 2013;111:416–27. 2013/11/01/.
[14] Petzl M, Danzer MA. Advancements in OCV measurement and analysis for lithium-
ion batteries. IEEE Trans Energy Convers 2013;28:675–81.
[31] Do DV, Forgez C, Benkara KEK, Friedrich G. Impedance observer for a li-ion battery
using Kalman filter. IEEE Trans Veh Technol 2009;58:3930–7.
[32] Schweighofer B, Wegleiter H, Recheis M, Fulmek P. Fast and accurate battery model
applicable for EV and HEV simulation. In: 2012 IEEE International Instrumentation
and Measurement Technology Conference Proceedings; 2012. p. 565–70.
[33] Vyroubal P, Kazda T. Equivalent circuit model parameters extraction for lithium ion
[15] Wei Z, Tseng KJ, Wai N, Lim TM, Skyllas-Kazacos M. Adaptive estimation of state of
charge and capacity with online identified battery model for vanadium redox flow
battery. J Power Sources 2016;332:389–98. 2016/11/15/.
693

J. Yang et al.
AppliedEnergy237(2019)682–694
batteries using electrochemical impedance spectroscopy. J Storage Mater
high-power lithium-ion batteries by electrochemical impedance spectroscopy. II:
Modelling. J Power Sources 2011;196:5349–56. 2011/06/15/.
[41] Hentunen A. Electrical and thermal characterization of large lithium-ion batteries
for non-road mobile machinery applications; 2016.
2018;15:23–31. 2018/02/01/.
[34] Pei L, Wang T, Lu R, Zhu C. Development of a voltage relaxation model for rapid
open-circuit voltage prediction in lithium-ion batteries. J Power Sources
2014;253:412–8. 2014/05/01/.
[42] Diao W, Xue N, Bhattacharjee V, Jiang J, Karabasoglu O, Pecht M. Active battery
cell equalization based on residual available energy maximization. Appl Energy
2018;210:690–8. 2018/01/15/.
[35] Mu H, Xiong R, Zheng H, Chang Y, Chen Z. A novel fractional order model based
state-of-charge estimation method for lithium-ion battery. Appl Energy
2017;207:384–93. 2017/12/01/.
[43] Yang J, Xia B, Shang Y, Huang W, Mi C. Improved battery parameter estimation
method considering operating scenarios for HEV/EV applications. Energies
2016;10:5.
[36] Fleischer C, Waag W, Heyn H-M, Sauer DU. On-line adaptive battery impedance
parameter and state estimation considering physical principles in reduced order
equivalent circuit battery models: Part 1. Requirements, critical review of methods
and modeling. J Power Sources 2014;260:276–91. 2014/08/15/.
[37] Hentunen A, Lehmuspelto T, Suomela J. Time-domain parameter extraction method
for thévenin-equivalent circuit battery models. IEEE Trans Energy Convers
2014;29:558–66.
[44] Kang J, Yan F, Zhang P, Du C. Comparison of comprehensive properties of Ni-MH
(nickel-metal hydride) and Li-ion (lithium-ion) batteries in terms of energy effi-
ciency. Energy 2014;70:618–25. 2014/06/01/.
[45] Büngeler J, Cattaneo E, Riegel B, Sauer DU. Advantages in energy efficiency of
flooded lead-acid batteries when using partial state of charge operation. J Power
Sources 2018;375:53–8. 2018/01/31/.
[38] Jossen A. Fundamentals of battery dynamics. J Power Sources 2006;154:530–8.
2006/03/21/.
[46] Zhang Y, Song W, Feng Z. An energy efficiency evaluation research based on heat
generation behavior of lithium-ion battery. J Electrochem Soc 2013;160:A1927–30.
[47] Zhu WH, Zhu Y, Davis Z, Tatarchuk BJ. Energy efficiency and capacity retention of
Ni–MH batteries for storage applications. Appl Energy 2013;106:307–13. 2013/06/
01/.
[39] Kroeze RC, Krein PT. Electrical battery model for use in dynamic electric vehicle
simulations. In: 2008 IEEE Power Electronics Specialists Conference; 2008. p.
1336–42.
[40] Andre D, Meiler M, Steiner K, Walz H, Soczka-Guth T, Sauer DU. Characterization of
694