A336 Journal of The Electrochemical Society,161 (3) A336-A341 (2014)
0013-4651/2014/161(3)/A336/6/$31.00 ©The Electrochemical Society
Optimized Operating Range for Large-Format LiFePO4/Graphite
Jiuchun Jiang,a,zWei Shi,a,b Jianming Zheng,bPengjian Zuo,bJie Xiao,b,∗Xilin Chen,b,∗∗
Wu Xu,b,∗and Ji-Guang Zhangb,z
aSchool of Electrical Engineering, Beijing Jiaotong University, Beijing 100044, China
bEnergy & Environment Directorate, Paciﬁc Northwest National Laboratory, Richland, Washington 99352, USA
Long-term cycling performances of LiFePO4/graphite batteries have been investigated in different state-of-charge (SOC) ranges.
It is found that batteries cycled in the medium SOC range exhibit superior cycling stability over those cycled at both ends of
the SOC ranges. A variety of characterization techniques, including galvanostatic intermittent titration technique (GITT) analysis,
model-based parameter identiﬁcation, electrochemical impedance spectroscopy analysis, and entropy change test, were used to
investigate the performance difference of the batteries cycled in different SOC ranges. The results reveal that batteries at the end
of SOC exhibit much higher polarization impedance than those within the medium-SOC range. This result can be attributed to the
signiﬁcant structural change of the cathode and anode materials as revealed by the large entropy change within these SOC regions.
Identiﬁcation of the best operating conditions for LiFePO4/graphite batteries will signiﬁcantly extend their cycle life. The general
control principle obtained in this work, such as modulating the charge/discharge current to minimize the impedance extremes can
also be used in the operation control of other battery systems.
© 2013 The Electrochemical Society. [DOI: 10.1149/2.052403jes] All rights reserved.
Manuscript submitted September 20, 2013; revised manuscript received December 16, 2013. Published December 31, 2013.
The increasing concern over global warming and energy security
has stimulated great interest in developing electric vehicles (EV), in-
cluding pure EVs, plug-in hybrid vehicles, and hybrid EVs powered
by high-energy density rechargeable lithium-ion batteries (LIBs).1–4
Although various types of EVs using lithium ion batteries have been
marketed in the United States, Europe, Asia, and elsewhere in recent
years, mass market penetration of EVs still requires signiﬁcant im-
provement in the energy density, reduction of cost, and enhancement
of cycle life of Li-ion batteries. Among the various Li-ion batter-
ies used in EVs, the battery based on LiFePO4/graphite chemistry
is very attractive because of its good safety characteristics and ex-
cellent cycle life. The long-term charge/discharge characteristics of
commercial LiFePO4/graphite batteries have been studied along with
applications of a battery management system in pure electric buses
during the Beijing Olympic Games and the Shanghai World Expo,
as well as in electric sanitation trucks in Beijing. To maximize the
charge/discharge performance and cycle life of batteries, it is criti-
cally important to develop a comprehensive method for understanding
the impact of actual operating conditions on battery cycle life. The
performance of LiFePO4-based batteries with olivine structures has
been studied extensively via approaches ranging from material studies
to modeling.5–9Correlations between capacity fading or power decay
and cell internal resistance as well as polarization impedance have
been investigated in many laboratories.10–13
To maintain safe operation and long cycle life of batteries,
battery management systems play an important role. Temperature,
charge/discharge rate, and the state-of-charge (SOC) operating ranges
usually are considered to be the main factors that affect battery ag-
ing and degradation.14 Experience gained from EV use suggests that
different SOC ranges impact the battery cycle life to varying degrees,
and it is suspected that operating over a wide SOC range results in in-
creased capacity fade. Various equivalent circuit models (ECM) have
been used to simulate dynamic voltage and current, and to identify
the resistance and impedance of a battery system.15–17 More precise
electrochemical models typically employ partial differential equations
with a number of unknown parameters, such as Li-ion concentration,
potential gradient in the electrolyte and the solid electrode material,
and other dynamic variables during battery operation.9,18 These pa-
rameters are useful for understanding the electrochemical reactions
between electrodes and the electrolyte, but are not desirable for use in
actual battery management systems. Moreover, the accuracy of these
models is still questionable. One source of error is that the ECM
∗Electrochemical Society Active Member.
∗∗Electrochemical Society Student Member.
parameters used in numerical ﬁtting may vary with the SOC, temper-
ature, and state of health (SOH) of a battery, so the simulation results
are insufﬁcient to reﬂect the practical operating conditions, especially
for a LiFePO4battery that exhibits a very ﬂat voltage plateau.
Electrochemical impedance spectroscopy (EIS) analysis is an ef-
fective and non-destructive technique that can be used to obtain in-
formation about ion-transfer kinetics in an electrode and at the elec-
trode/electrolyte interface within different SOC ranges.19–23 Perfor-
mance differences in different SOC ranges can be interpreted by com-
bining the universal parameters from the ECM and detailed parameters
from the EIS technique. In this work, a ﬁrst-order ECM was used to
simulate the polarization voltage of the full cell, and then a second-
order ECM in combination with EIS parameters was used to deter-
mine the alternating current impedance of the battery under different
SOC regions. Various parameters such as ohmic resistance, polariza-
tion impedance, and electrode/electrolyte interface impedance were
identiﬁed and used to explain the battery degradation results when
cycled in different SOC ranges. The fundamental mechanisms respon-
sible for the different performances at different SOC ranges are also
Two types of LiFePO4/graphite batteries were investigated in this
work. Large format 20 Ah energy-type batteries supplied by ATL
(Amperex Technology Limited, China) were used for long-term cy-
cling and electrochemical impedance analysis. For entropy change
analysis, small coin cells consisting of LiFePO4cathode electrodes
and/or graphite anode electrodes disassembled from a 2 Ah cell man-
ufactured by A123 Systems were used. Electrochemical properties
of the batteries were measured galvanostatically in a voltage range
between 2.5 and 3.65 V on an Arbin-BTS2000 battery tester. The
batteries were tested in a thermostat chamber controlled at 25◦Cwith
a temperature ﬂuctuation of ±0.1◦C. In the long-term cycle-life tests,
the batteries were cycled in four different SOC ranges, which are
0 to 25%, 25 to 50%, 50 to 75%, and 75 to 100%. The batteries
were charged/discharged for two hundred cycles at a C/2 charge rate
(1 C =20 A) and a 1 C discharge rate with a ﬁxed capacity of 5 Ah,
followed by three full cycles. Then, the ﬁxed capacity was readjusted
with the obtained full discharge capacity.
The galvanostatic intermittent titration technique (GITT) analysis
was conducted on the Arbin-BTS2000 battery tester at C/3 rate.24 The
cell was charged or discharged to a capacity corresponding to 5%
SOC (9 min) followed by a rest time interval of 30 min and the data-
logging interval was 1 s. This procedure was repeated in the voltage
Journal of The Electrochemical Society,161 (3) A336-A341 (2014) A337
window of 2.5 ∼3.65 V with varying state of charge (SOC). The cell
resistance induced voltage drop or IR drop (U) was measured 1 s after
a current pulse was applied; the polarization voltage drop (Up)was
measured after 30 min of relaxation. EIS tests were carried out using an
electrochemical workstation (Zahner-Zennium) in a frequency range
from 1 kHz to 100 mHz with a perturbation current of 2 A. In the EIS
tests, rest time means the duration after charging or discharging to
the next 5% higher or lower SOC value. EIS spectra were tested with
different rest times to study the impact of rest time after the current
Entropy change, S, data were tested as a function of temperature
using an electrochemical thermodynamic measurement system (Vi-
aspace, ETMS-1000). To investigate the origin of the battery degra-
dation, the entropy changes of cathode, anode, and full cells were
measured and compared separately. Because the ETMS system can
only hold small cells, coin type cells consisting of a LiFePO4/Li half-
cell, a graphite/Li half-cell, and a LiFePO4/graphite full cell were pre-
pared. Ideally, the same electrode as those used in above-mentioned
electrochemical tests should be used for the entropy study. However,
it is very difﬁcult to disassemble a 20 Ah cell due to safety con-
cern. As an alternative, LiFePO4cathode and graphite anode were
obtained from a disassembled 2 Ah cells manufactured by A123 Sys-
tems. The obtained electrodes were washed with dimethyl carbonate
(DMC) several times, punched into disks (ø =1.60 cm) and dried
completely under vacuum. CR2032 coin-type cells were assembled
with the electrodes as-prepared. Metallic lithium foil was used as the
counter electrode in the case of half-cells. Celgard K2045 polyethy-
lene (PE) membrane was used as the separator, and 1 M LiPF6dis-
solved in ethyl carbonate (EC) and dimethyl carbonate (DMC) (1:2
in volume) was used as the electrolyte. Samples were prepared in an
argon-ﬁlled glove box (MBraun Inc.). The temperature range used
during entropy measurements was 15 to 35◦C. Five continuous tem-
peratures with a temperature interval of 5◦C and a sustained time of
15 min were used to calculate the value of S. The voltage detection
resolution is 1 μV for entropy evaluation.
Results and Discussion
Cycling performance of high capacity cells at different SOC
ranges.— To identify the effects of operating SOC range on the long-
term cycling performance of LiFePO4/graphite batteries, cycle-life
tests were conducted with 20 Ah batteries at four different SOC ranges:
0 to 25%, 25 to 50%, 50 to 75%, and 75 to 100%. Two duplicate bat-
teries were tested in each SOC range for repeatability. To minimize
possible over-charge and decrease side reactions between the elec-
trodes and electrolyte, no constant voltage charge step was applied
during cycling. After every 200 cycles, three full charge/discharge
cycles were performed to obtain a retained reversible capacity and
thus readjust the capacity at each SOC range to be used in subsequent
cycles. The initial voltage proﬁles and the capacity retentions for bat-
teries cycled at the four SOC ranges are compared in Figure 1a and
1b, respectively. The results shown in Figure 1clearly indicate that
the battery cycled in SOC range of 75 to 100% exhibits the fastest
capacity degradation, followed by the battery cycled in the SOC range
of 0 to 25%. In comparison, batteries cycled in the mid-SOC ranges,
such as 25 to 50% and 50 to 75% SOC ranges, show superior cycling
performance with signiﬁcantly reduced capacity fade, revealing that
the medium SOC range (25 to 75%) could be the preferred operating
range for the LiFePO4/graphite batteries.
To further verify the above results, cycling performance of
LiFePO4/graphite batteries (20 Ah cells from ATL) also were eval-
uated in other SOC ranges, including the mid-SOC range of 20 to
80%, both ends of SOC (0 to 20%, 80 to 100%), and full SOC range
(0 to 100%) at a charge/discharge rate of 1 C as shown in Figure 2.
The results clearly demonstrate that the battery cycled within the full
SOC range (0 to 100%) triggers an early termination at 80% of rated
capacity, followed by those cycled at two ends of SOC ranges (0 to
20% SOC or 80 to 100%). In contrast, the battery cycled in the mid-
SOC range of 20 to 80% (which used 60% of the rated capacity in
Figure 1. Performance of LiFePO4/graphite batteries cycled in various SOC
ranges: (a) voltage proﬁles (charged at C/2, discharged at 1 C rate); (b) capacity
retention as a function of cycle number.
each cycle) demonstrates signiﬁcantly improved capacity retention,
as compared to those cycled in other SOC ranges. This result further
reveals the inﬂuence of the SOC range on the cycle life of the batteries
and conﬁrms that cycle life of the batteries could be largely prolonged
if cycled within the medium SOC ranges.
Impedance of high capacity cells at different SOC ranges.— To
gain insight into the origin for the different cycling performance in
different SOC ranges, the evolution of battery resistance as a function
of SOC has been carefully investigated. GITT analysis was performed
to obtain the battery polarization during charge/discharge processes.
Figure 3a shows the open circuit voltage (OCV) of the battery as a
function of time or SOC (every current pulse represents a charge or
discharge capacity corresponding to 5% SOC). The cell resistance
induced voltage drop or IR drop (U) and the polarization voltage
drop (Up) are indicated in the inset of Figure 3a.
Figure 2. Effect of other SOC ranges (0 to 20%, 80 to 100%, and 0 to 100%)
on the cycling life of a 20 Ah LiFePO4/Graphite battery (charge/discharge at
1 C rate).
A338 Journal of The Electrochemical Society,161 (3) A336-A341 (2014)
Figure 3. (a) GITT curve as a function of time for LiFePO4/graphite cell. The current density and the amount of charge passed in a current pulse correspond to a
C/3 Rate and 5% SOC for the battery, respectively. (b) First-order RC equivalent circuit model. (c) Corresponding resistance Rand polarization impedance Rp
during charge/discharge processes.
The whole cell polarization (i.e., R, cell resistance; Rp, polariza-
tion impedance of whole cell, containing charge-transfer impedance
(Rp1) and diffusion impedance (Rp2); Cp, capacitance of interface)
in different SOC ranges was simulated with the ﬁrst-order resis-
tance/capacitance (RC) model as shown in Figure 3b, which used a
RC circuit network to describe battery polarization and relaxation.12,25
The whole polarization voltage, Uo–Uocv, can be obtained from the
equivalent circuit impedance Z, which is calculated using the follow-
When the circuit has a current input, I,Uo–Uocv can be expressed
by the inverse Laplace transformation as follows:
The internal resistances, R, and polarization impedances, Rp,at
different SOCs are calculated from the measured Uand Upvalues
shown in the inset of Figure 3a. The ﬁtted results of Rand Rpare
plotted as a function of SOC in Figure 3c. The ﬁgure shows that the
cell resistance R, including contributions from the current collector,
electrolyte, and other cell parts, is very stable throughout the entire
SOC range. However, polarization impedances, Rp(=(Uo–Uocv
–U)/I), exhibits a bowl shape as shown in Figure 3c;thatis,Rp
becomes much higher at both the end of charge (EOC) or the end
of discharge (EOD) states than in the middle range of SOC (which
corresponds to the voltage plateau region of LiFePO4).
EIS analysis is another effective and non-destructive technique
that can be used to gain insight into the charge transfer kinetics in
the electrode and at the electrode/electrolyte interface at different
SOC ranges.19–21 EIS spectra in the whole SOC ranges (5% SOC
interval) were recorded with different rest times and ﬁtted with the
second-order RC/LRC model (Figure 4a)(L, wiring between elec-
trode paste and current collector;16 R, cell resistance; Rp1,charge-
transfer impedance; Cp1, capacitance of electrode surface layer; Rp2,
diffusion impedance; Cp2, capacitance of concentration polarization,
which occurs at certain SOCs and lower frequency ranges).17,26 Rp1
Figure 4. (a) Second-order RC/LRC Model, (b) curve ﬁtting of the second-
order RC or LRC model via EIS test data measured at 50% SOC.
Journal of The Electrochemical Society,161 (3) A336-A341 (2014) A339
Figure 5. Impedance spectra at different SOC values: (a) EIS test at different rest times with various polarization states, (b) Rp1curve with 0 min, 10 min, and
60 min rest when charging, (c) Rp1curve with 0 min, 10 min, and 60 min rest when discharging, (d) EIS tests when charge with 10 min rest time /25◦C; (e) EIS
tests when discharge with 10 min rest time /25◦C, (f) Rp1curve with 10 min rest time.
is the impedance caused by electrode potential and surface electrode
processes, while Rp2 is the diffusion impedance mainly affected by
ionic concentrations. The second RC element is usually considered
as a Warburg impedance if the value of Rp2increases sharply at low
frequency,27–29 although Rp1and Rp2are sometimes considered as a
united Rpduring EIS ﬁtting process.15 Obviously, the second-order
ECM model, which includes information obtained from EIS mea-
surements, is more accurate than the ﬁrst-order model (Figure 3b)in
estimating the battery internal resistance and polarization.
Because more precise charge-transfer impedance, Rp1, could be
identiﬁed from the second-order RC or LRC model, one can obtain
the diffusion impedance or Warburg impedance, Rp2, by subtracting
Rp1from the total Rpin the ﬁrst-order RC model. By taking into
account the difference of the frequency response characteristics of an
actual battery and a “pure capacitor,” Cpis replaced by a constant
phase element, Q, which represents a certain degree of deviation
from capacitive characteristics. Impedance, ZQ, is represented by the
where Yis a physical quantity used to describe the electric double-layer
and nis the strength of deviation. The closer the value of napproaches
1, the closer its characteristics approach those of an ideal capacitor.
Figure 4b shows ﬁtting results of two kinds of second-order models
with and without inductance L, which shows that the second-order
model with Lprovides more accurate parameter analysis.30
Figure 5a compares EIS spectra collected with different rest times
for a fully charged battery.The ﬁgure shows that the battery impedance
increases with the increase of rest time. If the EIS spectra were not
tested in a full equilibrium state, a large hysteresis effect was ob-
served between charge and discharge at the same SOC. However, the
hysteresis effect varies with SOC, reﬂecting the ability of the Li-ion
transport rate and electronic conductivity at different SOCs. There-
fore, the model-based parameters also are affected by the polarization
state according to actual charge-discharge proﬁles, and different hys-
teresis characteristics with or without sufﬁcient rest time could be
EIS spectra evolutions also were recorded with different rest times
to examine the effect of cell relaxation on the EIS spectra. The ﬁtted
results of the charge-transfer impedance (Rp1) during charge/discharge
processes are summarized in Figure 5b–5c, respectively. Obvious dif-
ferences of Rp1with different rest times can be clearly observed.
Although the Rp1increases with the increase of rest time (more
A340 Journal of The Electrochemical Society,161 (3) A336-A341 (2014)
equilibrated state), the evolution of charge-discharge polarization
impedance follows the same trend. Therefore, ﬁtted results from EIS
spectra obtained with a 10-min rest time (Figure 5d,5e)isusedfor
further comparison, as shown in Figure 5f. At a low-SOC region, the
Rp1obtained during the charge process is higher than those obtained
during the discharge process, which becomes reverse at high SOC
region. Moreover, the differences between the values of Rp1curves
during the charge and discharge processes are broader near EOD and
EOC than in the mid-ranges of SOC as shown in Figure 2c,which
shows a signiﬁcant polarization Rp. In this regard, the EIS technique
provides more accurate prediction of the favorable SOC range for
sustaining battery operation. A decreased power (i.e., current density
for charge or discharge) near the two ends of the SOC range will
signiﬁcantly reduce possible structural deterioration, micro-cracking,
graphite exfoliation, lithium plating, and electrolyte decomposition in
It is worth to note that the large polarization at the EOC (SOC
=100%) could result in poor rate performance of the LiFePO4/
graphite battery and increased capacity fading at lower SOC regions.
At the fully charged state, the electrochemical potential of the car-
bon anode may fall below the ELUMO of the carbonate electrolyte,
and the electrochemical potential of LiFePO4cathode approaches the
EHOMO of the carbonate electrolyte.31 This ﬁnding suggests that the
battery is not stable at the fully charged state (SOC =100%) when
side reactions between the electrolyte and the electrodes occur easily.
Evolution of the EIS spectra may indicate irreversible side reactions
at the EOC state, which is responsible for the fast capacity decay
of a battery cycled at higher SOC regions (75 to 100% SOC, see
Curve ﬁtting with both the ﬁrst-order RC model and the EIS test
with the second-order LRC model signiﬁcantly contributes to the
description of battery kinetic responses studied at various SOC ranges.
We made estimates of the ECM parameters to analyze the electrode
kinetic processes containing charge-transfer impedance and diffusion
impedance at each SOC point. The results discussed above illustrate
that drastic cell polarization and hysteresis occur at both ends of the
SOC range. This ﬁnding is well correlated with faster capacity fading
for batteries cycled at both ends of the SOC range. The principles
discussed above reveal the correlation between a deep polarization
state and poor cycling behavior, so a rational operating range should
be identiﬁed to expand the lifetime of the batteries.
Entropy changes and effect of SOC on the performance of small
LiFePO4/graphite cells.— Recently, entropy change has been used to
study the reversible heat generated by battery electrode material dur-
ing charge/discharge processes as well as the structural evolution of
electrode materials.32,33 Entropy changes will be signiﬁcantly different
when positive and negative electrode materials with different crystal
structures are used in the battery. A large entropy change in some SOC
ranges is directly related to a large structural change/rearrangement.
Batteries cycled within these ranges may show faster capacity fade
than in other ranges during lithium ion insertion/de-insertion pro-
cesses. To compare the performance of the full battery and the entropy
changes of its components, coin type cells consisting of a LiFePO4/Li
half-cell, a graphite/Li half-cell, and a LiFePO4/graphite full cell were
prepared. The LiFePO4cathode and graphite anode were recovered
from a 2-Ah fresh commercial cell manufactured by A123 as described
in the experimental section. By comparing the half-cell and full-cell
capacities, the loading ratio of battery and Li-ion insertion/extraction
regions in both electrodes can be determined. As shown in Figure 6a,
the LPF cathode shows slightly higher capacity than that of graphite
anode (which may due to its speciﬁc design for high power oper-
ation). However, in the reassembled coin cell, the capacity of full
cell is lower than those of LFP cathode and graphite anode, indi-
cating that some graphite is still not fully charged during lithium
insertion process. Figure 6b shows the corresponding entropy change
curves for the Li/graphite half-cell, the Li/LiFePO4half-cell, and the
LiFePO4/graphite full cell. The LiFePO4cathode shows more en-
tropy change in the initial 10% and last 10% SOC regions than in
0 0.4 0.8 1.2 1.6 2 2.4 2.8
0 0.4 0.8 1.2 1.6 2 2.4 2.8
0 20 40 60 80 100 120 140 160 180 200
Figure 6. (a) Voltages proﬁles, (b) Scurves, (c) effect of SOC ranges on
the cycling performance of reassembled coin cells using electrodes (positive
electrode (LiFePO4), the negative electrode (graphite)) from A123 cells.
the mid-SOC ranges. Considering the fact that both the LiFePO4and
FePO4phases are very stable during charge/discharge processes, the
large entropy change in both ends of SOC regions can be ascribed
to the structural change or rearrangement during lithium insertion/de-
insertion process. On the other hand, the negative electrode exhibits
much more irregular entropy changes, which are attributed to the
multiple-phase changes of graphite at different Li+ion intercalation
stages, especially the phase transformation from Li0.5C6to LiC6.28,34
We need to notice that the contribution of the entropy change to
the cell operation depends on several other factors, especially on the
charge/discharge rate.33 In the high rate condition, the contribution of
the entropy change to the cell operation is relatively small. However,
in the low rate condition, the entropy change may make a signiﬁcant
contribution to the battery operation.35
Cycling performance of LiFePO4/graphite coin cells (using re-
assembled electrodes taken from 2 Ah A123 cells) were evaluated
in SOC ranges of 0 to 30%, 35 to 65%, and 70 to 100% at a
charge/discharge rate of 1 C as shown in Figure 6c. During the for-
mation cycles, about 5% capacity loss is observed. The best capac-
ity retention appears with a battery cycled within the 35% to 65%
SOC range, which reveals that the method of dividing SOC range
by combining parameters from ECM and ﬁtting parameters from EIS
technique is desirable and demonstrates the importance of the cycling
Journal of The Electrochemical Society,161 (3) A336-A341 (2014) A341
SOC range on the cycle life of the batteries. It is believed that this
methodology could also be widely applicable to predict the perfor-
mance of the batteries with different cell chemistries.
Long-term cycling performances of LiFePO4/graphite batteries
were investigated within different SOC ranges. The results show that
batteries cycled in the medium SOC range exhibit superior cycling
stability than those cycled at the two opposite ends of the SOC. A
variety of techniques, including GITT analysis, model-based param-
eter identiﬁcation, and EIS spectra, reveal that batteries at both ends
of the SOC range exhibit much higher polarization impedance than
batteries cycled at the middle of the SOC range. These results can
be attributed to the signiﬁcant side reactions that occur between elec-
trodes and electrolytes and the signiﬁcant structural change of cathode
and anode materials at the ends of the SOC range. The general control
principle found in this work, such as modulating the charge/discharge
current to minimize the impedance extremes not only can improve
cycling performance of LiFePO4/graphite lithium ion batteries, but
also can be used in the operation control of other battery systems.
This work was supported by the National High Technology
Research and Development Program of China (Grant Numbers
2011AA05A108 and 2011AA11A246), the National Natural Science
Foundation of China (Grant Number 51277010), and by the Ofﬁce
of Vehicle Technology of the U.S. Department of Energy through the
Batteries for Advanced Transportation Technologies Program.
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