energies
Article
New Electro-Thermal Battery Pack Model of
an Electric Vehicle
Muhammed Alhanouti 1, *, Martin Gießler 1 , Thomas Blank 2 and Frank Gauterin 1
1
2
*
Institute of Vehicle System Technology, Karlsruhe Institute of Technology, Karlsruhe 76131, Germany;
martin.giessler@kit.edu (M.G.); frank.gauterin@kit.edu (F.G.)
Institute of Data Processing and Electronics, Eggenstein-Leopoldshafen 76344, Germany;
thomas.blank@kit.edu
Correspondence: muhammed.alhanouti@partner.kit.edu; Tel.: +49-721-608-45328
Academic Editor: Michael Gerard Pecht
Received: 30 May 2016; Accepted: 12 July 2016; Published: 20 July 2016
Abstract: Since the evolution of the electric and hybrid vehicle, the analysis of batteries’ characteristics
and influence on driving range has become essential. This fact advocates the necessity of accurate
simulation modeling for batteries. Different models for the Li-ion battery cell are reviewed in this
paper and a group of the highly dynamic models is selected for comparison. A new open circuit
voltage (OCV) model is proposed. The new model can simulate the OCV curves of lithium iron
magnesium phosphate (LiFeMgPO4 ) battery type at different temperatures. It also considers both
charging and discharging cases. The most remarkable features from different models, in addition
to the proposed OCV model, are integrated in a single hybrid electrical model. A lumped thermal
model is implemented to simulate the temperature development in the battery cell. The synthesized
electro-thermal battery cell model is extended to model a battery pack of an actual electric vehicle.
Experimental tests on the battery, as well as drive tests on the vehicle are performed. The proposed
model demonstrates a higher modeling accuracy, for the battery pack voltage, than the constituent
models under extreme maneuver drive tests.
Keywords: temperature influence; new OCV model; battery circuit model; synthesized battery model;
thermal model; electric vehicle
1. Introduction
The global climate change, escalation in fuel cost, and the energy consumption, urged the necessity
to replace the fossil fuel with renewable and environment friendly energy sources. Battery electric
vehicles (BEV) are one major application, demonstrating the replacement of fossil fuel by renewable
energy. Li-ion batteries have become the preferable energy storage for the future electric vehicles [1].
They receive greater attention than other battery types, such as lead-acid and nickel-cadmium batteries,
due to their practical physical characteristics. They have a high specific energy, specific power, power
density and a long life cycle. Moreover, their self-discharge rate is lower compared to other types of
batteries [1–3].
Figure 1 demonstrates a typical discharge characteristic curve of a lithium-ion battery. The battery
voltage extends between an upper and lower voltage limits V full and V cut-off , respectively. V cut-off
represents the empty state of the battery where the minimum allowable voltage is reached.
This restriction is meant to protect the battery from deep depletion. The section formed between V full ,
V exp and the correspondences capacity rates (C-rate) 0 and Qexp is identified as the exponential region
of the discharge characteristic curve, at which the discharged voltage changes exponentially regarding
to the battery capacity. The voltage holds an approximately steady value for C-rates beyond Qexp up to
the nominal C-rate Qnom , where the nominal V nom voltage is reached. Not only is the battery voltage
Energies 2016, 9, 563; doi:10.3390/en9070563
www.mdpi.com/journal/energies
Energies 2016, 9, 563
2 of 17
Energies 2016, 9, 563 2 of 18 influenced
by the discharge rate, but the battery capacity is also diminished at high discharge rates.
influenced by the discharge rate, but the battery capacity is also diminished at high discharge rates. This occurs
as a sharp voltage drop at the end of the discharge process, as indicated in Figure 1. At that
This occurs as a sharp voltage drop at the end of the discharge process, as indicated in Figure 1. At rate the
discharge terminates at V cut-off [4].
that rate the discharge terminates at V
cut‐off [4]. Figure 1. Typical discharge characteristic curve of Li‐ion battery [4,5]. Figure 1. Typical discharge characteristic curve of Li-ion battery [4,5].
The vehicle under test (VUT) is equipped with battery cells of a cathode type LiFeMgPO4. Lithium iron phosphate cells are characterized by their flat open circuit voltage curve (OCV). Hence, The
vehicle under test (VUT) is equipped with battery cells of a cathode type LiFeMgPO4 .
the cell stays almost constant over the complete charge (SOC) voltage
range [2,3,6]. Lithium
ironvoltage phosphate
cells are
characterized
by theirstate flat of open
circuit
curveThe (OCV).
battery pack of the VUT consists of 19 modules. Each module comprises six cell blocks connected in Hence, the cell voltage stays almost constant over the complete state of charge (SOC) range [2,3,6].
series; a single cell block is constructed out of 50 LiFeMgPO4–graphite cells, connected in parallel. In The battery pack of the VUT consists of 19 modules. Each module comprises six cell blocks connected
total, there are 300 cells within the single battery module. Each cell block has a nominal voltage of 3.2 in series; a single cell block is constructed out of 50 LiFeMgPO4 –graphite cells, connected in parallel.
V, amounting to a total voltage of 19.2 V. The battery specifications are given in Table 1. A Controller In total,
there are 300 cells within the single battery module. Each cell block has a nominal voltage of
Area Network (CAN) communication environment is used for the control and management of the 3.2 V, battery modules. More technical information about the VUT is available in the Appendix. amounting to a total voltage of 19.2 V. The battery specifications are given in Table 1. A Controller
Area Network (CAN) communication environment is used for the control and management of the
Table 1. Technical data of LiFeMgPO
Battery [7]. battery modules. More technical
information about the VUT 4is
available in the Appendix.
Parameter (Unit)
Value
Table 1. Technical data of LiFeMgPO4 Battery [7].
Nominal Module Voltage (V) 19.2 Nominal Module Capacity (Ah) 69 Parameter (Unit)
Value
Max Continuous Load Current (A) 120 Nominal
Module Voltage (V)
19.2
Peak Current for 30 s (A) 200 Nominal Module Capacity (Ah)
69
Continuous
Current
(A) modeling 120 methods to decide which In this paper, we will Max
investigate the Load
different battery Peak Current for 30 s (A)
200
approach will be the most appropriate for modeling the battery pack of VUT. Then, we will select a group of the most thorough models for Li‐ion batteries. These models will contribute to the development of the proposed battery model, which will be considered for modeling actual battery In this paper, we will investigate the different battery modeling methods to decide which approach
pack voltage response when the VUT undergoes severe driving maneuvers. will be the most appropriate for modeling the battery pack of VUT. Then, we will select a group of the
The paper is organized as follows. Section 2 presents the different modeling techniques of Li‐ion most thorough models for Li-ion batteries. These models will contribute to the development of the
batteries. Three models are elected from the reviewed models and are discussed in more details in proposed
battery model, which will be considered for modeling actual battery pack voltage response
Section 3. In Section 4 the thermal behavior of the battery is elaborated. The experimental tests are whendescribed the VUT in undergoes
driving
Section 5. severe
The models are maneuvers.
evaluated and a new, improved model is developed and The
paper
is
organized
as
follows.
Section 2 presents the different modeling techniques of Li-ion
proposed in Section 6. Finally, the conclusions are stated at the end of the paper. batteries. Three models are elected from the reviewed models and are discussed in more details in
Section 3. In Section 4 the thermal behavior of the battery is elaborated. The experimental tests are
described in Section 5. The models are evaluated and a new, improved model is developed and
proposed in Section 6. Finally, the conclusions are stated at the end of the paper.
Energies 2016, 9, 563
3 of 17
2. Existing Battery Models
Different modeling approaches are found in the literature. The most prominent battery modeling
techniques are: Electrochemical, analytical, and circuit-based models [8]. Electrochemical models
employ non-linear differential equations to model the chemical and electrical behavior of the cell [4,9].
Detailed knowledge of the battery chemistry, material structure and other physical characteristics
are essential to achieve high accuracy and cover a large number of different operating points.
However, the producers of batteries will rarely reveal the full parameters set of their products.
Another shortcoming of electrochemical models is the high computational effort required to solve the
non-linear partial differential equations [8]. Electrochemical models are better suited for research in
battery’s components fabrication, like electrodes and electrolyte [4,10]. The analytical modeling, on the
other hand, reduces the computational complexity for the battery. However, that would be on the
expense of capturing the circuit physical features of the battery, such as open circuit voltage, output
voltage, internal resistance, and transient response [8].
Lumped electrical circuit models offer low complexity combined with high accuracy and
robustness in simulating batteries dynamics [11–13]. Models with single or double resistor-capacitor
(RC) networks are the best candidates for simulating the battery module [12–14]. RC parameters
employed to model the battery characteristic show a dependency on temperature, charge/discharge
rates and the SOC. Several techniques had been discussed in literature [1,15–19] for SOC estimation.
Lam and Bauer [20] proposed a circuit model for the Li-ion battery with variable open circuit
voltages, resistances and capacitances. The equivalent circuit components were represented as
empirical functions of the current direction, the SOC, the battery temperature and the C-rate.
Tremblay et al. [5,21] proposed an improved version Shepherd’s model [22]. This model considers the
influence of SOC on the OCV by considering the polarization voltage in the discharge-charge model.
Different dynamic models for Li-ion, lead-acid, NiMH and NiCd battery typed were presented in
Reference [5]. However, neither the temperature effect nor the variation of the internal resistance
were considered. Saw et al. [23] investigated the thermal behavior for a LiFePO4 –graphite battery
by coupling the empirical equations of the modified Shephard’s battery model with a lumped
thermal model for the battery cell. The temperature development of a complete vehicle battery
pack under different driving cycles was simulated in [23]. Tan et al. [24] have incorporated the thermal
losses to Shephard’s model for Li-ion battery cells by adding temperature dependent correction
terms to the model. Wijewardana et al. [1] proposed a generic electro-thermal model for Li-ion
batteries. The model considers potential correction terms accounting for electrode film formation and
electrolyte electron transfer chemistry. In addition, the constant values in the empirical equations
that represent the equivalent circuit components of the battery were adjusted. These equations were
employed to model the electrical components in dependence of SOC and temperature. Wijewardana
et al. consider the C-rate effect in the estimation of SOC by employing an extended Kalman filter
technique. Computational thermal models and temperature distribution estimations were proposed
in References [25–28]. Additionally, finite element analysis models to estimate the temperature
distribution in the battery were presented in References [25,27–29]. This kind of simulation requires
knowledge of thermal properties of the battery cell materials, such as thermal capacity, density,
mechanical construction and cooling of the battery. For an accurate parameterization intensive and
precise measurements are necessary.
3. Overview of Selected Dynamic Battery Models
The equivalent circuit battery model provides a generic, dynamic way of modeling Li-ion batteries
with moderate complexity. The moderate model complexity supports the integration of the model in
a multiphysical simulation, allowing to analyze dynamic effects of the electric drive train. Three models
are selected from the literature as the best candidates for Li-ion battery modeling, since they are the
most thorough among the reviewed models. These models are:
Energies 2016, 9, 563
4 of 17
Energies 2016, 9, 563 ‚
‚
‚
4 of 18 Tremblay et al. [5] (battery model 1)

Tremblay et al. [5] (battery model 1) Lam and Bauer [20] (battery model 2)

Lam and Bauer [20] (battery model 2) et al. [1] (battery model 3)
Wijewardana
Wijewardana et al. [1] (battery model 3) 3.1. Tremblay
Battery Model (Battery Model 1)
3.1. Tremblay Battery Model (Battery Model 1) Tremblay
andand Dessaint
[5] improved
their
own
model
in Reference
[21].
The
new
model
is is shown
Tremblay Dessaint [5] improved their own model in Reference [21]. The new model shown in Figure 2. Only three points on the steady state manufacturer’s discharge curve are required in Figure
2. Only three points on the steady state manufacturer’s discharge curve are required to
to parametrize the model, which are the full voltage, the end point of exponential voltage region, and parametrize
the model, which are the full voltage, the end point of exponential voltage region, and the
the nominal voltage. The variation of the OCV from a reference constant voltage (E
) is related to SOC nominal
voltage. The variation of the OCV from a reference constant voltage0(E
0 ) is related to SOC
changes by incorporating a polarization constant (K). changes by incorporating a polarization constant (K).
Figure 2. Tremblay and Dessaint battery discharge model. Figure
2. Tremblay and Dessaint battery discharge model.
In case of discharging the output voltage reads: In case of discharging the output voltage reads:
∙
∙
∗
∙
(1) Q
Vbatt “ E0 ´ R ¨ i ´ K
¨ pit ` i˚ q ` Ae´B ¨ it
and for charging, the equation becomes: Q ´ it
and for charging, the equation becomes:
∙
0.1
∙
∗
∙
∙
(1)
(2) Q
Q
the variables and constants in Equations (1) and (2) are defined in Table A1 in the Appendix A. Vbatt “ E0 ´ R ¨ i ´ K
¨ i˚ ´ K
¨ it ` Ae´B ¨ it
(2)
Although, the charging and discharging characteristics Qare extensively modeled, some other it ´ 0.1Q
´ it
influential factors like the variations in internal resistance (R) and temperature influence are not the variables
and constants in Equations (1) and (2) are defined in Table A1 in the Appendix A.1.
considered. The capacity fading effect is not taken into account in this model as well. Although, the charging and discharging characteristics are extensively modeled, some other
3.2. Lam and Bauer Battery Model (Battery Model 2) influential
factors like the variations in internal resistance (R) and temperature influence are not
considered.
capacity
fading
effectequivalent is not taken
into model accountis inshown this model
as well.
The The
Lam and Bauer battery circuit in Figure 3. The model demonstrates the VOC as a function of SOC, a variable ohmic resistance Ro, and two variable 3.2. Lam
and Bauer Battery
Model (Battery Model 2)
RC‐networks: R
SCS and RlCl for the short and the long time transient responses, respectively. Lam and also showed the relation between to aging and model
different stress The Bauer Lam and
Bauer
battery
equivalent
circuitcapacity model isfading showndue in Figure
3. The
demonstrates
influences, which are the cell’s temperature, C‐rate, SOC and intensity of discharge. Lam and Bauer the V OC as a function of SOC, a variable ohmic resistance Ro , and two variable RC-networks: RS CS
parametrized their equations through curve fitting of experimental measurements. They employed and Rl Cl for the short and the long time transient responses, respectively. Lam and Bauer also showed
in their tests the LiFePO4 battery cell. The equivalent circuit resistors and capacitors equations for the relation
between capacity fading due to aging and different stress influences, which are the cell’s
temperatures from 20 °C and above are detailed in Equations (7)–(28) in Reference [20]. We refer also temperature,
C-rate, SOC and intensity of discharge. Lam and Bauer parametrized their equations
to the VOC equation with the corrected constants as proposed in Reference [20]: through curve fitting of experimental measurements. They employed in their tests the LiFePO4 battery
.
(3) SOC resistors
0.5863
3.414
0.1102 for
SOCtemperatures
0.1718
20 ˝ C and
cell. The equivalent circuit
and capacitors
equations
from
above
are detailed in Equations (7)–(28) in Reference [20]. We refer also to the V OC equation with the corrected
constants as proposed in Reference [20]:
8ˆ10´3
VOC pSOCq “ ´0.5863 e´21.9 SOC ` 3.414 ` 0.1102 SOC ´ 0.1718 e´ 1´SOC
(3)
Energies 2016, 9, 563
5 of 17
Energies 2016, 9, 563 5 of 18 Energies 2016, 9, 563 5 of 18 Figure 3. Lam and Bauer battery circuit model. Figure 3. Lam and Bauer battery circuit model.
3.3. Wijewardana Battery Model 3.3. Wijewardana Battery Model
Figure 3. Lam and Bauer battery circuit model. A different perception, than the two previous models, is adopted in this model. The electrical components, R
S, CS, RL, Cthan
L are functions of SOC and independent of the temperature. Only the series A3.3. Wijewardana Battery Model different perception,
the two previous models, is adopted in this model. The electrical
internal is a function of SOC temperature of(Rthe
intS(SOC,T)). The temperature components,
RSresistance , CS , RL , resistor CL are functions
of SOC
andand independent
temperature. Only the series
A different perception, than the two previous models, is adopted in this model. The electrical influence is considered by adding potential correction terms, which are voltage due to electrode film components, R
S
, C
S
, R
L
, C
L
are functions of SOC and independent of the temperature. Only the series internal resistance resistor is a function of SOC and temperature (RintS (SOC,T)). The temperature
formation (ΔE) and voltage due to electrolyte transfer (R
formation (ΔVChe). The capacity internal resistance resistor is a function of SOC electrons and temperature intS(SOC,T)). The temperature influence
is considered
by adding
potential
correction
terms,
which are
voltage due to electrode film
fading effect is modeled as an additional series resistance R
cyc. The battery output voltage is computed influence is considered by adding potential correction terms, which are voltage due to electrode film formation
(∆E) and voltage due to electrolyte electrons transfer formation
(∆V Che ). The capacity
by subtracting the voltage drop of each circuit element from the V
OC value. Figure 4 demonstrates formation (ΔE) and voltage due to electrolyte electrons transfer formation (ΔVChe). The capacity fading effect
is modeled as an additional series resistance Rcyc . The battery output voltage is computed
Wijewardana battery model. fading effect is modeled as an additional series resistance Rcyc. The battery output voltage is computed by subtracting
the voltage drop of each circuit element from the V
value. Figure 4 demonstrates
by subtracting the voltage drop of each circuit element from the V
OCOC
value. Figure 4 demonstrates Wijewardana
battery model.
Wijewardana battery model. Figure 4. Wijewardana battery circuit model. The battery output voltage of this model reads [1]: Figure 4. Wijewardana battery circuit model. Figure
4. Wijewardana battery circuit model.
∆
∆
The battery output voltage of this model reads [1]: The battery output voltage of this
∆ model1reads ∆[1]:
∆ ∆
∆
(4) (5) (4) Vbatt “ VOC ´ i RintS⁄` Rcyc ´ V1 ´ V2 ´ ∆E pTq ´ ∆VChe pTq
`
∆
β ∆
˘
∆1
∆
∆ ∆
1
β ∆ (5) (6) (4)
ˇ
dVr ˇˇ
∆E pTq “
∆T ∆ 1 β ∆ (5)
The values of the model parameters are listed in the Appendix A. ⁄ p1 ` CE1 ∆Tq
∆
β ∆
(6) dT ˇT“Tcell
ˇ
3.4. Assessment of Battery Models Qualities dV
The values of the model parameters are listed in the Appendix A. Che ˇˇ
pC
∆VChe pTq “ βw expp´1{tq ∆T `
` CChe1 ∆Tq p1 ` βq ∆T
(6)
Three different highly dynamic to model Li‐ion batteries have been proposed. Each model has dT ˇT“Tcell Che
3.4. Assessment of Battery Models Qualities its dominant features. Table 2 summaries the qualities of each model. The (+) sign implies that the The values
of the model
parameters
are listed
inmodel. the Appendix.
corresponded feature is considered in the Whereas, a (++) sign denotes an extensive Three different highly dynamic to model Li‐ion batteries have been proposed. Each model has consideration to the related feature. In contrast, the (‐) sign means that the related feature was its dominant features. Table 2 summaries the qualities of each model. The (+) sign implies that the 3.4. Assessment
Models
assigned of
as Battery
a feature constant it Qualities
is not considered at all in the model. Battery 2 considers more corresponded is or considered in the model. Whereas, a (++) sign model denotes an extensive factors than the other models. However, each model must be evaluated with experimental data to Three
differentto highly
dynamic
to model
Li-ion
have been
proposed.
Each model
consideration the related feature. In contrast, the batteries
(‐) sign means that the related feature was has
investigate its accuracy. assigned as a constant or it 2is not considered in the of
model. Battery considers more its dominant
features.
Table
summaries
theat all qualities
each model.model The 2 (+)
sign implies that
factors than the other models. However, each model must be evaluated with experimental data to the corresponded
feature is considered in the model. Whereas, a (++) sign denotes an extensive
investigate its accuracy. consideration to the related feature. In contrast, the (-) sign means that the related feature was assigned
as a constant or it is not considered at all in the model. Battery model 2 considers more factors than
the other models. However, each model must be evaluated with experimental data to investigate
its accuracy.
Energies 2016, 9, 563
6 of 17
Table 2. Comparison between the battery models.
Feature
Charge-Discharge
hysteresis
Open circuit voltage
Internal resistance (R)
Temperature
influence
Capacity fading
Battery Model 1
Battery Model 2
-
Considered in the
output voltage
Constant value for E0
Constant value
+
++
-
Not considered
+
-
Not considered
+
++
Total Assessment
2
+
Battery Model 3
Considered in the internal
resistance (R) equations
V OC (SOC)
R(SOC,T,C-rate)
Considered in the internal
resistance model
-
Charge-discharge
+
+
Considered in the battery’s
used capacity estimation
+
V OC (SOC)
R(SOC,T)
Considered as potential
correction terms
Considered in the
battery’s internal
resistance (R) estimation
4
+
6
4. Battery Thermal Model
A general energy balance is applied to estimate the battery cell temperature. It is assumed that
the thermal distribution inside the cell is uniform and that the conduction resistance inside the battery
cell is negligible compared with the convection and radiation heat transfer [1,23,27,28]. The change in
temperature depends significantly on the battery thermal capacity (Cp ) and the difference between
the generated heat and the dissipated heat. The dissipation of the heat to the battery surrounding
is performed by convection and radiation. Generated heat comprises two sources, irreversible heat
generation by means of the effective ohmic resistance of the cell’s material, and reversible generated
heat due to the entropy change in both cathode and anode. The total entropy changes in the battery
cell can be considered as zero according to References [1,29,30]. The temperature development inside
the battery cell is described as:
mC p
´
¯
dTcell
4
4
“ i pVOC ´ Vbatt q ´ hAcell ∆T ´ σAcell Tcell
´ Tamp
dt
(7a)
where ∆T is the difference between the battery cell and the ambient temperatures (Tcell ´ Tamp ), h is the
natural convection coefficient, m is the cell mass, i is the cell current, Acell is the surface area of the
single battery cell, σ is Stefan-Boltzmann constant, and ε is the emissivity of heat. Assuming that the
temperature differences between the cells in the single battery module are small, Equation (7a) can be
generalized for the whole battery module as:
MC p
´
¯
dTcell
4
4
“ I pVOC ´ Vbatt q ´ hA∆T ´ σA Tcell
´ Tamp
dt
(7b)
where M is the total cells mass, I is the battery current, A is the surface area of the cells blocks in the
single battery module.
Saw et al. [23] has pointed out to the contribution of the contact resistance in heat generation.
The contact resistance can be neglected in the investigated batteries, since the cells are realizing low
ohmic over wide cell connectors by means of welded connections. Fifty individual cells are connected
in parallel and we have a nominal current about 1.4 A per cell. The resistance of the single contact
is 0.2 mΩ. With four welding points per cell connectors, the contact resistance for the single battery
cell became 50 µΩ. The power loss in the single cell due to contact resistance is determined as:
Ploss = Icell 2 Rcontact = 0.098 mW/cell, which is a negligible amount, thermally, as well as electrically.
5. Experimental Characterization of the Battery and the Vehicle under the Test
5.1. Battery Measurements
In order to characterize the LiFeMgPO4 -battery, several experimental tests were implemented on
the battery at different conditions. OCV vs. SOC measurements were performed at 10, 20 and 40 ˝ C.
The battery was discharged until the cut-off voltage of 2 V was reached and then recharged up to the
nominal capacity. A Low C-rate of C/10 was used to minimize the dynamic effects and to achieve
a good approximation to an open circuit. Figure 5 demonstrates the charge and discharge OCV curves
Energies 2016, 9, 563
7 of 17
over the SOC for various temperatures. It is noticeable that the lower the operating temperatures,
the higher
the difference between charging and discharging.
Energies 2016, 9, 563 7 of 18 7 of 18 OCV[V]
OCV[V]
Energies 2016, 9, 563 Figure 5. Charge and discharge OCV curves over SOC. Figure 5. Charge and discharge OCV curves over SOC.
5.2. Driving Tests on the Real Vehicle 5.2. DrivingThe Testsobjective on the Real
Vehicle
of a real test is to find a real driving maneuver reference signal to validate the Battery pack voltage
[V] pack voltage [V]
Battery
100
50
250
200
0
150
-50
100
-100
0
50
50
100
150
200
Time[s]
250
300
350
(a) 0
-50
250
Battery current [A]
Battery current [A]
-100
0
200
50
100
150
150
200
Time[s]
250
300
(a) 100
150
200
Time[s]
250
300
350
(b)
330
380
50
100
150
200
Time[s]
250
300
350
(b)
360
380
350
370
340
360
50
200
150
0
0
50
340
320
0
370
350
100
250
100
-50
0
50
350
380
340
370
330
360
320
350 0
Battery voltage Battery
[V]
voltage [V]
Battery pack current [A]
Battery pack current [A]
battery model performance. Nevertheless, the battery model should be able to simulate the actual Figure 5.
The
objective of a real test
is to Charge and discharge OCV curves over SOC.
find a real driving maneuver reference
signal to validate the
system in real operating conditions, not merely charging‐discharging cycles. Two driving tests were battery performed model
performance.
Nevertheless,
the
battery
model
should
be
able
to
simulate the actual
5.2. Driving Tests on the Real Vehicle with the test vehicle for the purpose of investigation the system and collecting the system experimental data. The tests were executed on the testing ground at Karlsruhe Institute of Technology in real operating conditions, not merely charging-discharging cycles. Two driving tests
The objective of a real test is to find a real driving maneuver reference signal to validate the were performed
with the test vehicle for the purpose of investigation the system and collecting the
(KIT). The experimental data attained from the CAN bus are displayed in Figures B1 and B2 in the battery model performance. Nevertheless, the battery model should be able to simulate the actual Appendix B. Then, the data were processed in MATLAB. In the first test, the vehicle was driven in a experimental
data.
The tests were executed on the testing ground at Karlsruhe Institute of Technology
system in real operating conditions, not merely charging‐discharging cycles. Two driving tests were counterclockwise circular direction for about 230 s. Then the direction for driving was reversed and performed with test attained
vehicle for the purpose of bus
investigation the system and collecting the A2 in the
(KIT). The experimentalthe data
from
the CAN
are displayed
in Figures
A1 and
the test was resumed. A variable pedal input was implemented in order to cover a broader range of experimental data. The tests were executed on the testing ground at Karlsruhe Institute of Technology Appendix A.2. Then, the data were processed in MATLAB. In the first test, the vehicle was driven
data. This test represents an aggressive driving scenario, leading to discharge rate of up to 3.4 C. The (KIT). The experimental data attained from the CAN bus are displayed in Figures B1 and B2 in the in a counterclockwise
circular direction for about 230 s. Then the direction for driving was reversed
second test was implemented by subjecting the vehicle to a sequence of sudden accelerations and Appendix B. Then, the data were processed in MATLAB. In the first test, the vehicle was driven in a and thedecelerations. These tests were performed this way to create highly fluctuating signals in the battery test
was resumed. A variable pedal input was implemented in order to cover a broader range
counterclockwise circular direction for about 230 s. Then the direction for driving was reversed and the test was resumed. A variable pedal input was implemented in order to cover a broader range of which are shown Figure 6. The dynamic responses of battery voltage can be used of data.system, This
test
represents
anin aggressive
driving
scenario,
leading
to discharge
rate
of upto to 3.4 C.
data. This test represents an aggressive driving scenario, leading to discharge rate of up to 3.4 C. The evaluate the battery models, discussed above. The second test was implemented by subjecting the vehicle to a sequence of sudden accelerations
second test was implemented by subjecting the vehicle to a sequence of sudden accelerations and and decelerations. These tests were performed this way to create highly fluctuating signals in the
decelerations. These tests were performed this way to create highly fluctuating signals in the battery 250
380
battery system,
which
areshown shownin in
Figure
6. The
dynamic
responses
of battery
canto be used to
200
system, which are Figure 6. The dynamic responses of battery voltage voltage
can be used 370
evaluate evaluate the battery models, discussed above. the150battery models, discussed above.
360
50
100
Time[s]
(c) 150
200
330
0
350
340
50
100
Time[s]
150
200
(d)
Figure 6.
CAN bus measurements: (a) Battery pack current for the circular driving test; (b) Battery -50
330
0
50
100
150
200
0
50
100
150
200
Time[s]
pack voltage for the circular driving test; (c) Battery pack current for the Time[s]
rapid acceleration and (d)
deceleration driving (c) test; (d) Battery pack voltage for the rapid acceleration and deceleration driving test. Figure 6. CAN bus measurements: (a) Battery pack current for the circular driving test; (b) Battery Figure 6.pack CANvoltage bus measurements:
(a) Battery
pack
current
the circular
driving
test; (b) and Battery pack
for the circular driving test; (c) Battery pack for
current for the rapid acceleration voltage for
the circular
driving
(c) Battery
current
forrapid the rapid
acceleration
and deceleration
deceleration driving test; test;
(d) Battery pack pack
voltage for the acceleration and deceleration driving test. driving test;
(d) Battery pack voltage for the rapid acceleration and deceleration driving test.
Energies 2016, 9, 563
8 of 17
6. Battery Models Validation
6.1. Evaluating the Open Circuit Voltage Models (VOC )
Wijewardana et al. [1] have employed a common model for VOC that is widely used and found in
literature. Lam and Bauer [20] have redefined the model equation to suit the LiFeMgPO4 cathode type
batteries. They concluded that the OCV is temperature independent. They justified this conclusion
based on small changes of the OCV measurements due to temperature variations, which were in the
range 2–8 mV [20]. An absolute error of 30 mV for LiFeMgPO4 battery cell will lead to an uncertainty of
13% in the SOC estimation at 1 C discharge and 25 ˝ C, according to Blank et al. [31]. The battery of our
vehicle is LiFeMgPO4 -cathode type. Its OCV curves are presented earlier in Figure 6. According to our
measurements, the OCV temperature alteration is from 15 to 90 mV, which is about 10 times higher than
the result presented in Reference [20]. In our study, we use a battery module that contains 6 cellblocks
in series, with 50 cells in parallel for each. Moreover, the vehicle’s battery pack has 19 modules.
With this combination of battery cells, the range of voltage alteration becomes 1.71–10.26 V, which is
a considerable change in the battery pack output voltage.
We validated both V OC models in References [1,20] by comparing the simulation results with our
own measurements, as shown in Figure 7. We selected the charge-discharge curves at T = 20 ˝ C to be
the references for validation. The V OC model utilized in battery model 3 does not fit our measurements.
The V OC of battery model 2 better fits the experimental data. The deviation in an SOC range spanning
from 10% to 90% is about 0.03 V. This deviation increases at low temperature.
The influence of the temperature variation on the OCV curves is defined as dVOC {dT. From the
measurements shown in Figure 6, the value of this term was found to be 1.25 mV in case of discharge
and 0.69 mV for charging. The V OC model 2 model is modified for better fitting of the OCV curve along
the SOC range and the temperature influence is considered. The new V OC is modeled by Equations (8)
and (9) and the constants values of the new V OC are presented in Table 3. The validation results are
shown in Figure 8 and in Table 4.
a6
VOC,discharge pSOC, Tq “ a1 e´a2 SOC ` a3 ` a4 SOC ` a5 e´ 1´SOC ` T dVOC,d {dT
(8)
b6
VOC,charge pSOC, Tq “ b1 e´b2 SOC ` b3 ` b4 SOC ` b5 e´ 1´SOC ` T dVOC,c {dT
(9)
Table 3. V OC parameter values.
Constant
Value
Constant
Value
a1
a2
a3
a4
a5
a6
´1.166
´35
3.344
0.1102
´0.1718
´2 ˆ 10´3
0.00125
b1
b2
b3
b4
b5
b6
´0.9135
´35
3.484
0.1102
´0.1718
´8 ˆ 10´3
0.00069
dV OC,d /dT
dV OC,c /dT
6.2. Evaluating the Battery Models Output Voltage
The accuracy of each model is yet to be proved. For objective comparison, the thermal model
elaborated in Section 4 is employed for all models. The battery currents in Figure 6a,c are designated
as the inputs for all models and the output voltage of each model is investigated against the voltage
response signal, shown in Figure 6b,d. The V OC of model 3 [1] showed a large deviation from the
actual curve, as shown in Figure 7. Therefore, the V OC derived from model 2 [20] will be also utilized
in model 3. Figures 9 and 10 demonstrate the responses of the three models for both driving test.
The simulation results gained from model 1 reveal the highest accuracy for the first test. The mean
Energies 2016, 9, 563
9 of 17
squared error between the measured voltage and the simulated voltage by model 1 is less than 1%.
However, it performed the worst in the second test. The good performance of model 1 in the first test
Energies 2016, 9, 563 9 of 18 ascribed
to the fact that the test conditions were nearly matching the standard condition for
defining
Energies 2016, 9, 563 9 of 18 ˝
the constant voltage (E0 ). E0 is equal to the nominal voltage at 20 C, which is equal to 3.21 V and the
ascribed to the fact that the test conditions were nearly matching the standard condition for defining ascribed to the fact that the test conditions were nearly matching the standard condition for defining initial
voltage of the single0). E
battery
cell is estimated as 3.25 V. When the test second driving test was
the constant voltage (E
0 is equal to the nominal voltage at 20 °C, which is equal to 3.21 V and the the constant voltage (E
0). E0 is equal to the nominal voltage at 20 °C, which is equal to 3.21 V and the performed
at different circumstances, the outcome was not as good as it in the first case. Figure 10a
initial voltage of the single battery cell is estimated as 3.25 V. When the test second driving test was initial voltage of the single battery cell is estimated as 3.25 V. When the test second driving test was reveals
a relatively large offset error in the response of battery model 1 with a mean square error (MSE)
performed at different circumstances, the outcome was not as good as it in the first case. Figure 10a performed at different circumstances, the outcome was not as good as it in the first case. Figure 10a reveals a relatively large offset error in the response of battery model 1 with a mean square error of about
2.24%. Model 2 performed moderately with percentage errors between 1% and 2%. The offset
reveals a relatively large offset error in the response of battery model 1 with a mean square error errors(MSE) of about 2.24%. Model 2 performed moderately with percentage errors between 1% and 2%. between the reference signal and initial voltage value of both battery models 2 and 3 were minor,
(MSE) of about 2.24%. Model 2 performed moderately with percentage errors between 1% and 2%. The Equation
offset errors between the reference signal and voltage value models 2 of
whereas
(3) is
employed
in both models
for initial the estimation
of Vof of both . both Thebattery simulation
results
The offset errors between the reference signal and initial voltage value OC
battery models 2 and 3 were minor, whereas Equation (3) is employed in both models for the estimation of V
OC. The model
3 indicate less dynamic response than the other two models. It could not conduct the
drastic
and 3 were minor, whereas Equation (3) is employed in both models for the estimation of V
OC. The simulation results of model 3 indicate less dynamic response than the other two models. It could not changes
in the battery current input signal.
simulation results of model 3 indicate less dynamic response than the other two models. It could not conduct the drastic changes in the battery current input signal. conduct the drastic changes in the battery current input signal. 4.5
4.5
4
OCV[V]
OCV[V]
4
3.5
3.5
3
3
2.5
2.5
2
0
20
2
0
20
Discharge measured at T=20°C
Charge measured at T=20°C
Voc
of battery
model 2 at T=20°C
Discharge
measured
Voc
of battery
modelat3T=20°C
Charge
measured
Voc
2
40
60 of battery model
80
100
SOC[%] Voc of battery model 3
40
60
80
100
SOC[%]
Figure 7. Comparing the Voc model with measured experimental results. Figure 7. Comparing the Voc model with measured experimental results.
Figure 7. Comparing the Voc model with measured experimental results. Table 4. Accuracy of the proposed VOC model. Table 4. Accuracy of the proposed V OC model.
Temperature °C Table 4. Accuracy of the proposed V
MSE in Discharge Model %
MSE in Charge Model % OC model. 10 0.5232 0.8914 ˝
Temperature C
MSE
in Discharge Model %
MSE
in Charge Model %
Temperature °C MSE in Discharge Model %
MSE in Charge Model % 20 0.5320 0.5719 10 0.5232 0.8914 10
0.5232
0.8914
40 0.5751 0.4522 20 0.5320 0.5719 20
0.5320
0.5719
40 0.5751 0.4522 40
0.5751
0.4522
(a) (b)
(a) (b)
(c) Figure 8. The new Voc model and measured experimental data: (a) T = 10 °C; (b) T = 20 °C; (c) T = 40 °C. (c) Figure 8. The new Voc model and measured experimental data: (a) T = 10 °C; (b) T = 20 °C; (c) T = 40 °C. Figure 8. The new Voc model and measured experimental data: (a) T = 10 ˝ C; (b) T = 20 ˝ C; (c) T = 40 ˝ C.
Energies 2016, 9, 563 10 of 18 Energies 2016, 9, 563
10 of 17
10 of 18 10
MSE = 0.9453%
105
Error [%]
Error [%]
Battery pack voltage [V]
Battery pack voltage [V]
Energies 2016, 9, 563 MSE = 0.9453%
50
0
-5
-5
-10
0
50
-10
0
(a) (a) 50
100
100
150
150
200
Time[s]
200
Time[s]
250
250
(b) (b) 10
350
350
MSE = 1.75%
10
MSE = 1.75%
5
Error
[%][%]
Error
300
300
5
0
0
-5
-5
-10
-10 0
0
50
50
100
100
150
150
250
300
300
350
350
(d) (d) 10
10
Battery pack voltage [V]
= 1.7841%
MSEMSE
= 1.7841%
55
Error [%]
Error
[%]
Battery pack voltage [V]
(c)(c)
200
200
Time[s]250
Time[s]
00
-5-5
-10
-10
0
50
0
50
100
100
150
200
250
150
Time[s]200
Time[s]
300
250
350
300
350
(f) (e) (f) (e) Figure 9. Battery simulation models and reference voltage signal for circular driving test: (a) Battery Figure
9. Battery simulation models and reference voltage signal for circular driving test: (a) Battery
Figure 9. Battery simulation models and reference voltage signal for circular driving test: (a) Battery model 1 response; (b) Mean square error of battery model 1; (c) Battery model 2 response; (d) Mean model
1 response; (b) Mean square error of battery model 1; (c) Battery model 2 response; (d) Mean
model 1 response; (b) Mean square error of battery model 1; (c) Battery model 2 response; (d) Mean square error of battery model 2; (e) Battery model 3 response (f) Mean square error in battery model 3. square
error of battery model 2; (e) Battery model 3 response (f) Mean square error in battery model 3.
square error of battery model 2; (e) Battery model 3 response (f) Mean square error in battery model 3. 10
MSE = 2.2373%
Error [%]
Error [%]
5
0
0
-5
-5
-10
0
-10
0
(a) 50
100
Time[s]
50
10
(a) Error [%]
200
150
Time[s]
(b) 200
MSE = 1.0347%
MSE = 1.0347%
Error [%]
05
-5 0
-10
-5
0
(c) 150
(b) 100
10
5
Battery voltage [V]
Battery voltage [V]
MSE = 2.2373%
5
Battery voltage [V]
Battery voltage [V]
10
-10
0
(c) 50
100
Time[s]
200
(d) 50
100
Time[s]
(d) Figure 10. Cont.
150
150
200
Energies 2016, 9, 563
Energies 2016, 9, 563 11 of 17
11 of 18 10
MSE = 1.5176%
Energies 2016, 9, 563 11 of 18 5
Error [%]
10
5
Error [%]
(e) MSE = 1.5176%
0
-5
0
-10
0
-5
-10
0
50
100
Time[s]
150
200
(f) 50
100
150
200
Time[s]
Figure 10. Battery simulation models and reference voltage signal for rapid acceleration and Figure 10. Battery simulation
models and reference voltage signal for(f) rapid acceleration and
(e) deceleration driving test: (a) Battery model 1 response; (b) Mean square error of battery model 1; deceleration driving test: (a) Battery model 1 response; (b) Mean square error of battery model 1;
Figure 10. Battery simulation models and reference voltage signal for rapid acceleration and (c) Battery model 2 response; (d) Mean square error of battery model 2; (e) Battery model 3 response (c) Battery model 2 response; (d) Mean square error of battery model 2; (e) Battery model 3 response
deceleration driving test: (a) Battery model 1 response; (b) Mean square error of battery model 1; (f) Mean square error in battery model 3.
(f) Mean square error in battery model 3.
(c) Battery model 2 response; (d) Mean square error of battery model 2; (e) Battery model 3 response (f) Mean square error in battery model 3. 6.3. The Proposed Synthesized Battery Model 6.3. The Proposed Synthesized Battery Model
It is explicable that each model has some flaws, as determined in Table 2. The simulation results 6.3. The Proposed Synthesized Battery Model It is explicable that each model has some flaws, as determined in Table 2. The simulation
in Figures 9 and 10 prove that even the best performing models need to be further improved. It is explicable that each model has some flaws, as determined in Table 2. The simulation results results
in Figures
9 and 10 prove that even the best performing models need to be further improved.
Accordingly, a synthesized model that holds the best qualities of each model has been developed. in Figures 9 and 10 prove that that
even holds
the best models need model
to be further improved. Accordingly,
a synthesized
model
theperforming best qualities
of each
has been
developed.
First, the charge‐discharge characteristics of model 1 are considered. Additionally, the discharging Accordingly, a synthesized model that holds the best qualities of each model has been developed. First,
the
charge-discharge
characteristics
of
model
1
are
considered.
Additionally,
the
discharging
part
part our proposed V
OC(SOC,T) is employed instead of constant (E0) value. Then, the highly detailed First, the charge‐discharge characteristics of model 1 are considered. Additionally, the discharging our
proposed
V
(SOC,T)
is
employed
instead
of
constant
(E
)
value.
Then,
the
highly
detailed
internal
OC
internal resistance model of battery model 2 in case of 0discharging, which is represented by part our proposed V
OC(SOC,T) is employed instead of constant (E
0) value. Then, the highly detailed resistance
model
of
battery
model
2
in
case
of
discharging,
which
is
represented
by Equations (7)–(11),
Equations (7)–(11), (17)–(19), (21), (27) in Referance [20], is taking the place of the constant internal internal resistance model of battery model 2 in case of discharging, which is represented by (17)–(19),
(21),
(27)
in
Referance
[20],
is
taking
the
place
of
the
constant
internal
resistance (R).
resistance (R). The capacity fading effect is considered by adding R
cyc from battery model 3 to the internal Equations (7)–(11), (17)–(19), (21), (27) in Referance [20], is taking the place of the constant internal The
capacity
fading
effect
is
considered
by
adding
R
from
battery
model
3
to
the
internal
resistance.
cyc
resistance (R). The capacity fading effect is considered by adding R
cyc from battery model 3 to the internal resistance. The empirical equations in case of discharging are implemented because the charging‐
The
empirical
in case of discharging
implemented
because the
charging-discharging
resistance. equations
The empirical equations in case of are
discharging are implemented because the charging‐
discharging hysteresis is properly modeled by model 1. The synthesized model is shown in Figure 11. discharging hysteresis is properly modeled by model 1. The synthesized model is shown in Figure 11. hysteresis
is properly modeled by model 1. The synthesized model is shown in Figure 11.
Figure 11. The proposed synthesized battery model. Figure 11. The proposed synthesized battery model. Figure
11. The proposed synthesized battery model.
In case of discharging, the output voltage reads: In case of discharging, the output voltage reads: In case of discharging, the output voltage reads:
∗
∙
∙
∙
∗
∙ (10) (10) ˘∙
Q ∙
˚
´ B ¨ it
Vbatt “ VOC,discharge pSOC, Tq ´ RO ` Rcyc ` VS ` VL ¨ i ´ K
¨ pit ` i q ` Ae
(10)
Q ´ it
and for charging, the equation expressed as: and for charging, the equation expressed as: ∙
and for charging,
the equation expressed as:
∙
∙ ∗
∙
(11) OC,discharge SOC,
∙
0.1 ∙ ∗
∙
∙
(11) OC,discharge SOC,
0.1Q
`
˘
Q
˚
´
B
¨
it
Vwhere (11)
batt “ VOC,discharge pSOC, Tq ´ RO ` Rcyc ` VS ` VL ¨ i ´ K it´0.1Q ¨ i ´ K Q´it ¨ it ` Ae
where where
(12) dVS
i
VS (12) “
´
(12)
dt
CS RS CS
SOC,
OC,discharge
SOC,
OC,discharge
`
dVL
i
VL “
´
dt
CL R L CL
(13) (13) (13)
Energies 2016, 9, 563
12 of 17
The resistances and capacitors values are determined through Equations (14)–(18):
´
¯
Rs pSOC, ϑq “ c1 epc2 SOCq ` c3 ` c4 SOC ` c5 ∆ϑ ` c6 SOC∆ϑ
(14)
´
¯
Cs pSOC, ϑq “ c7 SOC3 ` c8 SOC2 ` c9 SOC ` c10 ` c11 SOC∆ϑ ` c12 ∆ϑ
(15)
´
¯ `
˘
12 of 18 IC´rate q “ pc13 epc14 SOCq ` c15 ` c16 SOCq ` c17 ∆ϑepc18 SOCq ` c19 ∆ϑ ˆ c20 pIC´rate
qc21 ` c22
Rl pSOC, ϑ,Energies 2016, 9, 563 (16)
´
¯
The resistances and capacitors values are determined through Equations (14)–(18): Cl pSOC, ϑq “ c23 SOC6 ` c24 SOC5 ` c25 SOC4 ` c26 SOC3 ` c27 SOC2 ` c28 SOC ` c29 ` c30 ec31 {ϑ
(17)
SOC,
SOC
∆
SOC ∆ (14) ´
¯
3
c38 {pϑ´c39 q (15) SOC
SOC`
∆ c36 c∆
Ro pSOC, ϑq “SOC,c32 SOC4SOC
` c33 SOC
` c34SOC
SOC2 ` c35 SOC
37 e SOC, ,
SOC
∆
∆
(18)
where ϑ is the battery cell temperature in Kelvin (˝ K) and c1 –c39 are constants, which (16) their values are
listed in Table 5.
SOC,
SOC
SOC
SOC
SOC
SOC
SOC
(17) /
Table 5. Constants
values of Equations (14)–(18).
/
(18) SOC,
SOC
SOC
SOC
SOC
Constant
Value
Constant
Value
Constant
Value
Constant
Value
where ϑ is the battery cell temperature in Kelvin (°K) and c1–c39 are constants, which their values are c31
c1
c11
´6.580
c21
1.080 ˆ 10´2
´6.919 ˆ 10´1
´2.398 ˆ 103
listed in Table 5. c2
´11.03
c12
12.11
c22
c32
2.902 ˆ 10´1
1.298 ˆ 10´1
c3
c13
c23
c33
1.827 ˆ 10´2
2.950 ˆ 10´1
2.130 ˆ 106
´2.892 ˆ 10´1
Table 5. Constants values of Equations (14)–(18). c14
´20.00
c24
c34
c4
´6.462 ˆ 10´3
´6.007 ˆ 106
2.273 ˆ 10´1
´4
Constant Constant Value Value c5
c15Constant 4.722 ˆValue c25
c35
´3.697 ˆ 10Value 10´2
6.271
ˆ 106 Constant ´7.216 ˆ 10´2
−2
´4
c2.225
1 1.080 × 10
c16 c11 ´2.420 ˆ
−6.580 c21 −6.919 × 10
6
c31 c36 −2.398 × 10
c6
c26
ˆ 10
10´2
´2.958 ˆ−110
8.9803 ˆ 10´2
−1
−1
2
´3
5
c
2 −11.03 c
12 12.11 c
22 2.902 × 10
c
32 1.298 × 10
c7
c17
c27
c37
1.697 ˆ 10
6.718 ˆ 10
5.998 ˆ 10
7.613 ˆ 10´1
−2
c13 2.950 × 10−1 c23 2.130 × 106 4
c33 −2.892 × 10−1 c3 c8
c
´20.00
c
c
10.14
´1.007 ˆ1.827 × 10
103
´3.102
ˆ
10
18
28
38
−6.462 × 10−3 c14 −20.00 c24 −6.007 × 106 3
c34 2.273 × 10−1 c4 c9
c19
c29
c39
1.408 ˆ 103
´5.967 ˆ 10´4−2
2.232 ˆ 610
2.608
ˆ 102
−4
−2
c5 −3.697 × 10
c15 4.722 × 10
c25 6.271 × 10 3
c35 −7.216 × 10 2
´1
c10
c
c
3.897
ˆ
10
6.993
ˆ
10
3.128
ˆ
10
−4
−2
6
−2
20
30
2.225 × 10 c16 −2.420 × 10 c26 −2.958 × 10 c36 8.980 × 10 c6 1.697 × 102 c17 6.718 × 10−3 c27 5.998 × 105 c37 c7 −1.007 × 103 c18 −20.00 c28 −3.102 × 104 c38 c8 The new model
shows
a 3significant
improvement
inc29the
simulation
1.408 × 10
c19 −5.967 × 10−4 2.232 × 103 response,
c39 c9 3.897 × 102 c20 6.993 × 10−1 c30 3.128 × 103 c10 7.613 × 10−1 10.14 2 in Figure 12.
as2.608 × 10
shown
The mean square error was reduced to only 0.256%. The new model shows also the best result when it
The new model significant improvement in the simulation response, shown it
in had
employed for simulating
theshows rapida acceleration
and deceleration
driving
test, as though
a small
Figure 12. The mean square error was reduced to only 0.256%. The new model shows also the best offset error at
the
beginning
of
3.2
V.
This
error
yielded
from
an
absolute
voltage
error
of
0.028
V in
result when it employed for simulating the rapid acceleration and deceleration driving test, though proposed VOC
model, represented by Equation (8), at the specified SOC and temperature values.
it had a small offset error at the beginning of 3.2 V. This error yielded from an absolute voltage error of 0.028 V in simulated
proposed VOC model, represented by Equation (8), at the specified SOC and The battery models
are
in MATLAB/Simulink
environment.
Figure
13 shows
the Simulink
temperature values. The battery models are simulated in MATLAB/Simulink environment. Figure 13 model for the
proposed battery model.
shows the Simulink model for the proposed battery model. 10
MSE = 0.2559%
Error [%]
5
0
-5
-10
0
50
100
150
200
Time[s]
250
300
350
(b)
(a) 10
MSE = 0.7862%
Error [%]
5
0
-5
(c) -10
0
50
100
Time[s]
150
200
(d) Figure 12. The proposed synthesized battery model and reference voltage signal: (a) Proposed model
response for the circular driving test; (b) Error of proposed model voltage for the circular driving
test; (c) Proposed model response for the rapid acceleration and deceleration driving test; (d) Error of
proposed model voltage for the rapid acceleration and deceleration driving test.
Energies 2016, 9, 563 13 of 18 Figure 12. The proposed synthesized battery model and reference voltage signal: (a) Proposed model response for the circular driving test; (b) Error of proposed model voltage for the circular driving test; Energies(c) 2016,
9, 563 model response for the rapid acceleration and deceleration driving test; (d) Error of 13 of 17
Proposed proposed model voltage for the rapid acceleration and deceleration driving test. SOC0
3
-KGain4
K Ts z
f(u)
z-1
Discrete-Time
Integrator2
OCV(SOC,T)_dis2
SOC
T[°C]
|u|
Abs
E0-R*i
U_R
-K-
I_cell
C-Rate
Calculation
R
1/s
Lam, Bauer
RC Model
Saturation
exp
e%
Sim
Subsystem
PE
Integrator
it
6
E_batt
Cell Blocks
Lowpass
1
Measured battery
pack current
2
Actual battery
pack voltage
Q(Capacitance)
I_Crate
Cells current
i*
19
i
number of
Modules
Lowpass Filter
1/50
U
Discharge-Charge
dynamics
V_cell
VOC
|u|
4
T_ambient
5
T_Cell
i_cell
Battery Temperature
Ambient Temp
Tbatt0
Battery Temperature Model
Figure
13. The proposed synthesized battery simulation model.
Figure 13. The proposed synthesized battery simulation model. 7.7. Conclusions Conclusions AA battery is a sophisticated system, which necessitates a detailed model for accurate simulation. battery is a sophisticated system, which necessitates a detailed model for accurate
Many factors must be considered in the battery model for accurate simulation Charging‐
simulation.
Many
factors
must be considered
in the
battery
model for
accurate results. simulation
results.
discharging dynamics, battery internal resistance, and open circuit voltage are the most significant Charging-discharging dynamics, battery internal resistance, and open circuit voltage are the most
aspects for battery Temperature is an influential factor for all of The significant
aspects
formodeling. battery modeling.
Temperature
is an influential
factor
forthese all of aspects. these aspects.
difference between the charging and discharging in the OCV curves increases at low temperatures. The
difference between the charging and discharging in the OCV curves increases at low temperatures.
This phenomenon occurs due to the decrement in battery capacity, which in turn appears as a result This
phenomenon occurs due to the decrement in battery capacity, which in turn appears as a result
rise ofof the
the internal
internal resistance.
resistance. Neglecting
Neglecting the ofof aa rise
the effect effect of of temperature temperature will will lead leadto toinaccuracy inaccuracyin in
simulation. Even the slightest errors in the simulation results of the battery cell model, would grow simulation. Even the slightest errors in the simulation results of the battery cell model, would grow
significantly when the model is extended to the complete battery pack. Battery model 1 has two flaws. significantly
when the model is extended to the complete battery pack. Battery model 1 has two flaws.
Firstly, it assumes the initial voltage value to be the nominal battery cell voltage. This assumption led Firstly,
it assumes the initial voltage value to be the nominal battery cell voltage. This assumption led
toto large offset from the actual value, when the vehicle was tested at about 30 °C. Secondly, it considers large offset from the actual value, when the vehicle was tested at about 30 ˝ C. Secondly, it considers
a constant internal resistance of the battery, which is in fact a very fluctuating quantity that affects a constant internal resistance of the battery, which is in fact a very fluctuating quantity that affects the
the battery cell current the response
voltage asresponse well. The proposed model has battery
cell current
and the and voltage
well. Theas proposed
battery
model battery has compensated
for
compensated for these shortages and it has accurately simulated the battery pack voltage response these shortages and it has accurately simulated the battery pack voltage response on the real vehicle.
on the real vehicle. Author
Contributions:
Muhammed
Alhanouti
made
the literature
review
on theon current
battery models,
Author Contributions: Muhammed Alhanouti made the literature review the current battery proposed
models, the synthesized battery model, developing the simulation models, and wrote the paper. Martin Gießler and
proposed the synthesized battery model, developing the simulation models, and wrote the paper. Martin Gießler Thomas Blank designed and performed the battery measurements, and they helped in editing the paper content.
and Thomas Blank designed and performed the battery measurements, and they helped in editing the paper Frank
Gauterin supervised the work of this paper and approved the results
content. Frank Gauterin supervised the work of this paper and approved the results Conflicts of Interest: The authors declare no conflict of interest.
Conflicts of Interest: The authors declare no conflict of interest. Appendix
Appendix A.1. Nomenclature
Table A1. Battery models parameters.
Parameter (Unit)
Symbol
Value
Constant voltage (V)
Constant internal resistance (Ω)
Polarization constant (V/(Ah)) or polarization resistance (Ω)
Battery capacity (Ah)
E0
R
K
Q
3.21 [23]
0.0833
0.0119 [23]
Variable
Energies 2016, 9, 563
14 of 17
Table A1. Cont.
Parameter (Unit)
Symbol
Value
Actual battery charge (Ah)
Exponential zone amplitude (V)
Exponential zone time constant inverse (Ah)´1
Battery current (A)
Filtered current (A)
Voltage change due to electrolyte electrons transfer
formation
the effective voltage gradient
Constant property of electrolyte
Constant property of electrolyte
Constant property of electrolyte
Constant property of electrolyte
Voltage change due to electrode film formation
voltage gradient
Constant property
Battery module surface area (m2 )
Battery cell mass (kg)
Battery module mass (kg)
Specific heat capacity (J¨ kg´1 ¨ K´1 )
Stefane-Boltzmann constant (W¨ m´2 ¨ K4 )
Emissivity of heat
Natural heat convection constant (W¨ m´2 ¨ K´1 )
it
A
B
i
i*
Variable
0.2711 [23]
152.130 [23]
Variable
Variable
∆V Che
Variable
dV Che /dT
CChe
CChe1
b
w
∆E
dVr /dT
CE1
A
m
M
Cp
σ
ε
h
0.0016 [1]
0.07 [1]
0.001 [1]
0.0012 [1]
0.012 [1]
Variable
0.00003 [1]
0.00011 [1]
0.283954
0.04 [23]
12
1360 [27]
5.67 ˆ 10´8
0.95
4
Energies 2016, 9, 563 Appendix A.2. Driving
Tests
15 of 18 Battery
temperature [°C]
SOC [%]
Battery
voltage [V]
Battery
current [A]
Car
Speed [km/h]
Appendix B. Driving Tests Figure B1. The measured data of the circular drive test. Figure A1. The measured data of the circular drive test.
Car
Speed [k
Battery
current [A]
Energies 2016, 9, 563
15 of 17
16 of 18 Battery
current [A]
SOC [%]
Battery
voltage [V]
Battery
temperature [°C]
Battery
temperature [°C]
SOC [%]
Battery
voltage [V]
Car
Speed [km/h]
Energies 2016, 9, 563 Figure B2. The measured data of the rapid acceleration and deceleration drive test. Figure
A2. The measured data of the rapid acceleration and deceleration drive test.
Figure B2. The measured data of the rapid acceleration and deceleration drive test. Appendix C. The Vehicle under the Test An electric hydrogen front wheel passenger car (Figure C1) was modified by the institute for Appendix
A.3. The
Vehicle under the Test
Appendix C. The Vehicle under the Test “FAhrzeug‐SystemTechnik” (FAST) of the Karlsruhe Institute of Technology to a battery electric vehicle (BEV), [30]. A battery pack was installed in the vehicle. This vehicle is used for research in An
electricdifferent automotive engineering and e‐mobility related projects. The propulsion systems comprises hydrogen front wheel passenger car (Figure A3) was modified by the institute for
An electric hydrogen front wheel passenger car (Figure C1) was modified by the institute for an induction motor with a single gear transmission. The motor specifications are listed in Table C1. “FAhrzeug-SystemTechnik”
“FAhrzeug‐SystemTechnik” (FAST)
(FAST) of
of the
the Karlsruhe
Karlsruhe Institute
Institute of
of Technology
Technology to
to aa battery
battery electric
electric vehicle
(BEV), [30]. A battery pack was installed in the vehicle. This vehicle is used for research in
vehicle (BEV), [30]. A battery pack was installed in the vehicle. This vehicle is used for research in different
automotive engineering and e-mobility related projects. The propulsion systems comprises
different automotive engineering and e‐mobility related projects. The propulsion systems comprises an
induction motor with a single gear transmission. The motor specifications are listed in Table A2.
an induction motor with a single gear transmission. The motor specifications are listed in Table C1. Figure C1. Vehicle under test. Figure C1. Vehicle under test. Figure A3. Vehicle under test.
Table A2. Technical data of electric motor.
Parameter
Value
Rated Power, PN
Peak Power, Pmax
Peak Torque, Tmax
Rated Speed, nN
45 kW
68 kW
210 N¨ m
3000 rpm
Energies 2016, 9, 563
Parameter
Rated Power, PN Peak Power, Pmax Peak Torque, Tmax Rated Speed, nN Value
45 kW 68 kW 210 N∙m 3000 rpm 16 of 17
The The motor motor shown shown in in Figure Figure C2 A4 is is powered powered by by the the AC AC current, current, delivered delivered from from the the power power
electronics that converts the DC current supplied by the battery. As the driver presses the accelerator electronics that converts the DC current supplied by the battery. As the driver presses the accelerator
pedal, a corresponding “torque demand” signal is converted by the vehicle control unit (VCU) to an pedal, a corresponding “torque demand” signal is converted by the vehicle control unit (VCU) to
appropriate signal for the motor control unit (power electronics), which in turn transforms it into a an appropriate signal for the motor control unit (power electronics), which in turn transforms it into
current frequency signal. a current
frequency
signal.The Themotor motorcontrol controlunit unit(MCU) (MCU)is isincorporated incorporatedwith with a a thermal thermal derating derating
system in order to limit the torque demand received by the power electronics and to prevent any system in order to limit the torque demand received by the power electronics and to prevent any
critical operating conditions for the motor. The assigned powertrain can accelerate the vehicle to a critical operating conditions for the motor. The assigned powertrain can accelerate the vehicle to
maximum speed of 120 km/h. a maximum speed of 120 km/h.
Figure C2. The basic drive train topology of the Mercedes A‐Class research vehicle [30]. Figure A4. The basic drive train topology of the Mercedes A-Class research vehicle [30].
References References
1.
1.
Wijewardana, S.; Vepa, R.; Shaheed, M.H. Dynamic battery cell model and state of charge estimation. J. Wijewardana, S.; Vepa, R.; Shaheed, M.H. Dynamic battery cell model and state of charge estimation.
Power Sources 2016, 308, 109–120. J. Power Sources 2016, 308, 109–120. [CrossRef]
2.
Doppebattery Model 2auer, M. Hybrid and Electric Vehicles—Lecture Notes; ETI‐HEV, Karlsruhe Institute of 2.
Doppebattery Model 2auer, M. Hybrid and Electric Vehicles—Lecture Notes; ETI-HEV, Karlsruhe Institute of
Technology: Karlsruhe, Germany, 2014. Technology: Karlsruhe, Germany, 2014.
3.
Ivers‐Tiffee, E. Batteries and Fuel Cells—Lecture Notes; IWE, Karlsruhe Institute of Technology: Karlsruhe, 3.
Ivers-Tiffee, E. Batteries and Fuel Cells—Lecture Notes; IWE, Karlsruhe Institute of Technology: Karlsruhe,
Germany, 2012. Germany, 2012.
4.
Illig, J. Physically Based Impedance Modelling of Lithium‐Ion Cells. Ph.D Thesis, Karlsruhe Institute of 4.
Illig, J. Physically Based Impedance Modelling of Lithium-Ion Cells. Ph.D. Thesis, Karlsruhe Institute of
Technology, Karlsruhe, Germany, 2014. Technology, Karlsruhe, Germany, 2014.
5.
Tremblay, O.; Dessaint, L.‐A. Experimental validation of a battery dynamic model for EV applications. Tremblay, O.; Dessaint, L.-A. Experimental validation of a battery dynamic model for EV applications.
5.
World Electr. Veh. J. 2009, 3, 1–10. World Electr. Veh. J. 2009, 3, 1–10.
6.
Padhi, A.K.; Nanjundaswamy, K.S.; Goodenough, J.B.D. Phospho‐olivines as positive‐electrode materials 6.
Padhi, A.K.; Nanjundaswamy, K.S.; Goodenough, J.B.D. Phospho-olivines as positive-electrode materials for
for rechargeable lithium batteries. J. Electrochem. Soc. 1997, 144, 1188–1194. rechargeable lithium batteries. J. Electrochem. Soc. 1997, 144, 1188–1194. [CrossRef]
7.
Valence Technology. U‐Charge® XP Rev 2 User Manual; Valence Technology, Inc.: Austin, TX, USA, 2011. 7.
Valence Technology. U-Charge®XP Rev 2 User Manual; Valence Technology, Inc.: Austin, TX, USA, 2011.
8.
Lin, N.; Ci, S.; Li, H. An enhanced circuit‐based battery model with considerations of temperature effect. 8.
Lin, N.; Ci, S.; Li, H. An enhanced circuit-based battery model with considerations of temperature effect.
In Proceedings of the 2014 IEEE Energy Conversion Congress and Exposition (ECCE), Pittsburgh, PA, USA, In Proceedings of the 2014 IEEE Energy Conversion Congress and Exposition (ECCE), Pittsburgh, PA, USA,
14–18 September 2014; pp. 3985–3989. 14–18 September 2014; pp. 3985–3989.
9.
Doyle, M., Fuller, T.F.; Newman, J. Modeling of galvanostatic charge and discharge of the 9.
Doyle, M.; Fuller, T.F.; Newman, J. Modeling of galvanostatic charge and discharge of the lithium/polymer/
lithium/polymer/insertion cell. J. Electrochem. Soc. 1993, 140, 1526–1533. insertion cell. J. Electrochem. Soc. 1993, 140, 1526–1533. [CrossRef]
10. Dees, D.W.; Battaglia, V.S.; Bélanger, A. Electrochemical modeling of lithium polymer batteries.
J. Power Sources 2002, 110, 310–320. [CrossRef]
11. He, H.; Xiong, R.; Guo, H.; Li, S. Comparison study on the battery models used for the energy management
of batteries in electric vehicles. Energy Convers. Manag. 2012, 64, 113–121. [CrossRef]
Energies 2016, 9, 563
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
31.
17 of 17
Hu, X.; Li, S.; Peng, H. A comparative study of equivalent circuit models for Li-ion batteries. J. Power Sources
2012, 198, 359–367. [CrossRef]
He, H.; Xiong, R.; Fan, J. Evaluation of lithium-ion battery equivalent circuit models for state of charge
estimation by an experimental approach. Energies 2011, 4, 582–598. [CrossRef]
Hussein, A.A.; Batarseh, I. An overview of generic battery models. In Proceedings of the 2011 IEEE Power
and Energy Society General Meeting, San Diego, CA, USA, 24–29 July 2011; pp. 1–6.
Kroeze, R.C.; Krein, P.T. Electrical battery model for use in dynamic electric vehicle simulations.
In Proceedings of the 2008 IEEE Power Electronics Specialists Conference, Rhodes, Greece, 15–19 June
2008; pp. 1336–1342.
Liu, X.; Ma, Y.; Ying, Z. Research of SOC estimation for lithium-ion battery of electric vehicle based on
AMEsim-simulink co-simulation. In Proceedings of the 32nd Chinese Control Conference (CCC), Xi’an,
China, 26–28 July 2013; pp. 7680–7685.
Szumanowski, A.; Chang, Y. Battery management system based on battery nonlinear dynamics modeling.
IEEE Trans. Veh. Technol. 2008, 57, 1425–1432. [CrossRef]
Zhang, C.; Jiang, J.; Zhang, W.; Sharkh, S.M. Estimation of state of charge of lithium-ion batteries used in
HEV using robust extended Kalman filtering. Energies 2012, 5, 1098–1115. [CrossRef]
Watrin, N.; Roche, R.; Ostermann, H.; Blunier, B.; Miraoui, A. Multiphysical lithium-based battery model for
use in state-of-charge determination. IEEE Trans. Veh. Technol. 2012, 61, 3420–3429. [CrossRef]
Lam, L.; Bauer, P.; Kelder, E. A practical circuit-based model for Li-ion battery cells in electric vehicle
applications. In Proceedings of the 2011 IEEE 33rd International Telecommunications Energy Conference
(INTELEC), Amsterdam, The Netherlands, 9–13 October 2011; pp. 1–9.
Tremblay, O.; Dessaint, L.A.; Dekkiche, A.I. A generic battery model for the dynamic simulation of hybrid
electric vehicles. In Proceedings of the 2007 IEEE Vehicle Power and Propulsion Conference, Arlington, TX,
USA, 9–12 September 2007; pp. 284–289.
Shepherd, C.M. Design of primary and secondary cells II. An equation describing battery discharge.
J. Electrochem. Soc. 1965, 112, 657–664. [CrossRef]
Saw, L.H.; Somasundaram, K.; Ye, Y.; Tay, A.A.O. Electro-thermal analysis of Lithium Iron Phosphate battery
for electric vehicles. J. Power Sources 2014, 249, 231–238. [CrossRef]
Tan, Y.K.; Mao, J.C.; Tseng, K.G. Modelling of battery temperature effect on electrical characteristics of Li-ion
battery in hybrid electric vehicle. In Proceedings of the 2011 IEEE Ninth International Conference on Power
Electronics and Drive Systems (PEDS), Singapore, Singapore, 5–8 December 2011.
Pesaran, A.A. Battery thermal models for hybrid vehicle simulations. J. Power Sources 2002, 110, 377–382.
[CrossRef]
Kim, Y.; Siegel, J.B.; Stefanopoulou, A.G. A computationally efficient thermal model of cylindrical battery
cells for the estimation of radially distributed temperatures. In Proceedings of the 2013 American Control
Conference (ACC), Washington, DC, USA, 17–19 June 2013; pp. 698–703.
Rad, M.S.; Danilov, D.L.; Baghalha, M.; Kazemeini, M.; Notten, P.H. Thermal modeling of cylindrical
LiFeMgPO4 Batteries. J. Mod. Phys. 2013, 4, 1–7. [CrossRef]
Fan, L.; Khodadadi, J.M.; Pesaran, A.A. A parametric study on thermal management of an air-cooled
lithium-ion battery module for plug-in hybrid electric vehicles. J. Power Sources 2013, 238, 301–312. [CrossRef]
Sun, Y. Construction and Validation of a Thermal FEM-Model of an Automobile Battery. Master’s Thesis,
Karlsruhe Institute of Technology, Karlsruhe, Germany, 2011.
Gießler, M.; Fritz, A.; Paul, J.; Sander, O.; Gauterin, F.; Müller-Glaser, K.D. Converted vehicle for battery
electric drive: Aspects on the design of the software-driven vehicle control unit. In Proceedings of the 2nd
International Energy Efficient Vehicle Conference (EEVC), Dresden, Germany, 18–19 June 2012.
Blank, T.; Lipps, C.; Ott, W.; Hoffmann, P.; Weber, M. Influence of environmental conditions on the sensing
accuracy of Li-Ion battery management systems with passive charge balancing. In Proceedings of the 17th
European Conference on Power Electronics and Applications, Geneva, Switzerland, 8–10 September 2015;
pp. 1–9.
© 2016 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access
article distributed under the terms and conditions of the Creative Commons Attribution
(CC-BY) license (http://creativecommons.org/licenses/by/4.0/).