Electrical Vehicle Design and Modeling 19
3.2 Battery charging control
During the charging of the battery, i.e., both due to the regenerative braking and the grid, it is
very important that the maximum battery charging current and voltage not are exceeded. The
maximum allowed cell charging current can be calculated from the inner and outer voltage of
the battery cell, i.e.,
i
Bat,cell,cha,max
=
⎧
⎨
⎩
V
Bat,max,cell
−v
Bat,int,cell
R
Bat,cell,cha
,
V
Bat,max,cell
−v
Bat,int,cell
R
Bat,cell,cha
≤ I
Bat,1,cell
I
Bat,1,cell
,
V

i
Bat,cha,max
= N
Bat,p
i
Bat,cell,cha,max
. (76)
During the charging of the battery the battery cell voltage v
Bat,cell
should not exceed
V
Bat,max,cell
= 4.2 V and the maximum cell charging current should not be higher than
I
Bat,1,cell
= 7 A (Saft, 2010). In order to charge the battery as fast as possible either the
maximum voltage or maximum current should be applied to the battery. The requested
battery charging current, i.e., the output current of the boost converter i
BC
, is therefore
i
∗
BC
= i
Bat,cha,max
, (77)
which means that the requested output power of the boost converter is
p
∗
BC

RF

2
−4R
BC
p
∗
BC
2R
BC
. (79)
The grid RMS-current can therefore from Equation 34 be calculated as
I
Grid
=
⎧
⎪
⎨
⎪
⎩

2
3
i
∗
RF
,

2
3

2
Aerodynamic drag coefficient C
drag
0.3
Table 4. Parameters of the vehicle used for the case study.
Thereby it is ensured that the maximum RMS grid current is not exceeded. The actual values
can therefore be obtained by calculating backwards, i.e.,
i
RF
=

3
2
I
Grid
(81)
p
RF
= v
RF
i
RF
(82)
p
BC
= p
RF
−R
BC
i

4.3 Results
In Fig. 13 the battery state-of-charge, current, voltage, and the power of the grid and battery
can be seen. It is understood from Fig. 13(a) that the battery is designed due to its energy
requirement rather than the power requirement as the state-of-charge reaches the minimum
allowed value of SoC
Bat,min
= 0.2. In Fig. 13(b) and (c) the battery current and voltage are
shown, respectively. It is seen that when the current becomes higher the voltage becomes
lower as the power should be the same. In Fig. 13(d) the battery and grid power are shown.
It is seen that the charging of the battery is limited by the maximum allowed grid power
P
Grid,max
. After approximately two hours the battery reaches the maximum voltage, and it is
therefore seen that the battery then is charged under constant-voltage approach, which means
that the battery current and power and grid power slowly are decreased until the battery
reaches its initial state-of-charge value.
20
Electric Vehicles – Modelling and Simulations
Electrical Vehicle Design and Modeling 21
0 200 400 600 800 1000
0
20
40
60
80
100
120
Time [s]
Speed [km/h]
Fig. 12. New European Driving Cycle (NEDC). This driving cycle will be repeated 14 times

148.3 Wh/km. The rest of the energy is lost in the path between the wheels and the grid. The
auxiliary loads are responsible for the biggest energy loss at 17 %. However, it is believed that
this can be reduced significant by using diodes for the light instead of bulbs, and to use heat
pumps for the heating instead of pure resistive heating.
The battery is responsible for the second largest energy waist as 14 % of the grid energy is
lost in the battery. The battery was only designed to be able to handle the energy and power
requirements. However, in order to reduce the loss of the battery it might be beneficial to
oversize the battery as the battery peak currents then will become closer to its nominal current
21
Electrical Vehicle Design and Modeling
22 Will-be-set-by-IN-TECH
0 1 2 3 4 5 6 7
0.2
0.4
0.6
0.8
0 1 2 3 4 5 6 7
0
20
40
0 1 2 3 4 5 6 7
700
800
900
0 1 2 3 4 5 6 7
−10
0
10
20
30

Bat,max
Time
[
h
]
Fig. 13. Simulation results of the vehicle with 14 repeated NEDC cycles as input. (a) Battery
state-of-charge. (b) Battery current. (c) Battery voltage. (d) Power of the battery and grid.
22
Electric Vehicles – Modelling and Simulations
Electrical Vehicle Design and Modeling 23
which will reduce the negative influence of the peukert phenomena. However, a heavier
battery will also increase the traction power, so the gained reduction in battery loss should be
higher than the increased traction power. A bigger battery will of course also make the vehicle
more expensive, but these issues are left for future work.
E
t
:49%
E
Loss,TS
:4%
E
Loss,EM
:10%
E
Loss,Inv
:2%
E
Loss,BC
:2%
E

Applications 141(5): 235 – 239.
Chan, C. C., Bouscayrol, A. & Chen, K. (2010). Electric, hybrid, and fuel-cell vehicles:
Architectures and modeling, IEEE Transactions on Vehicular Technology 59(2): 589 –
598.
Ehsani, M., Gao, Y., Gay, S. E. & Emadi, A. (2005). Modern Electric, Hybrid Electric, and Fuel Cell
Vehicles - Fundamentals, Theory, and Design, first edn, CRC Press LLC.
Emadi, A. (2005). Handbook of Automotive Power Electronics and Motor Drives,firstedn,Taylor
&Francis.
Gao, D. W., Mi, C. & Emadi, A. (2007). Modeling and simulation of electric and hybrid
vehicles, Proceedings of the IEEE 95(4): 729 – 745.
Jensen, K. K., Mortensen, K. A., Jessen, K., Frandsen, T., Runólfsson, G. & Thorsdóttir, T.
(2009). Design of spmsm drive system for renault kangoo, Aalborg University .
Lukic, S. & Emadi, A. (2002). Performance analysis of automotive power systems: effects of
power electronic intensive loads and electrically-assisted propulsion systems, Proc.
of IEEE Vehicular Technology Conference (VTC) 3: 1835 – 1839.
Mapelli, F. L., Tarsitano, D. & Mauri, M. (2010). Plug-in hybrid electric vehicle: Modeling,
prototype realization, and inverter losses reduction analysis, IEEE Transactions on
Industrial Electronics 57(2): 598 – 607.
Mohan, N., Underland, T. M. & Robbins, W. P. (2003). Power electronics, third edn, John Wiley.
Saft (2010). Saftbatteries. URL:
Schaltz, E. (2010). Design of a Fuel Cell Hybrid Electric Vehicle Drive System, Department of
Energy Technology, Aalborg University.
UQM (2010). Uqm technologies. URL:
24
Electric Vehicles – Modelling and Simulations
2
Modeling and Simulation of High Performance
Electrical Vehicle Powertrains in VHDL-AMS
K. Jaber, A. Fakhfakh and R. Neji
National School of Engineers, Sfax

VHDL (Very High Speed Integrated Circuit Hardware Description Language) is a
commonly used modelling language for specifying digital designs and event-driven
systems. The popularity of VHDL prompted the development of Analog and Mixed-Signal

Electric Vehicles – Modelling and Simulations

26
(AMS) extensions to the language and these extensions were standardized as IEEE VHDL-
AMS in 1999. Some of the main features of this ASCII-based language include Model
Portability, Analog and Mixed-Signal modeling, Conserved System and Signal Flow
Modeling, Multi-domain modeling, Modeling at different levels of abstraction, and Analysis
in time, frequency and quiescent domains. Since VHDL-AMS is an open IEEE standard,
VHDL-AMS descriptions are simulator-independent and models are freely portable across
tools. This not only prevents model designers from being locked in to a single tool or tool
vendor but also allows a design to be verified on multiple platforms to ensure model
fidelity. Fig. 1. Model of traction chain
VHDL-AMS is a strict superset of VHDL and inherently includes language support for
describing event-driven systems such as finite state machines. The standard not only
provides language constructs for digital and analog designs but also specifies the
interactions between the analogue and digital solvers for mixed-signal designs. The
analog (continuous time) extensions allow the description of conserved energy systems
(based on laws of conservation) as well as signal-flow models (based on block diagram
modeling).
VHDL-AMS distinguishes between the interface (ENTITY) of a model and its behavior
(ARCHITECTURE). VHDL-AMS allows the association of multiple architectures with the
same entity and this feature is typically used to describe a model at different levels of
abstraction.

be written as (Jalalifar et al., 2007):

RR
V
fg
M
F
=´ ´
(1)
The aerodynamic drag is due to the friction of the body of vehicle moving through the air.
The formula for this component is as in the following:

2
1
.
2
DA
x
S
CV
F
= 
(2)
An other resistance force is applied when the vehicle is climbing of a grade. As a force in the
opposite direction of the vehicle movement is applied:

.
g
.sin
Lv

v
g
-
=
(6)

( )
.
em m wheels RR DA L
vwheels
Tr R F F F
MR



(7)

.( )
lwheelsRRDAL
TR F F F
(8)

.
m
m
wheels
r
d
W
Rdt

Usage of permanent magnet synchronous motors (PMSMs) as traction motors is common in
electric or hybrid road vehicles (Dolecek
et al., 2008). The dynamic model of the PMSM can
be described in the d-q rotor frame as follows
:

di
d
VRiL Li
ddd e
qq
dt
w=+ -
(10)

di
d
VRiL LiK
qqq
edd m
dt
ww=+ + +
(11)
Where
KP
m
f=
is the electric constant of back-electromotive-force (EMF), it is calculated
according to the geometrical magnitudes of the motor so that it can function with a high
speed. The equations giving the stator current can be written in the following form:

() 
em
TKIpLLII
qdqdq
(14)
The equation giving the angle by the motor can be written in the following form:

.
m
d
p
W
dt
q
=
(15)
Figure 3 shows the description of the model of the PMSM in Simplorer 7.0 software. Fig. 3. SIMPLORER model of the PMSM in the d-q rotor frame

Electric Vehicles
– Modelling and Simulations

30
4. Control strategy
In recent years, vector-controlled ac motors, such as induction motor, permanent-magnet
synchronous motor (PMSM), and synchronous reluctance motor, have become standard in
industrial drives and their performance improvement is an important issue. Particularly,
improvement of control performance and drive efficiency is essentially required for drives


d
q
rotor ma
g
netic axis
p

s

2
s
p




a

s
I
EMF

Fig. 4. Stator current and EMF in the d-q rotor frame
The first part (A) in figure 1 illustrates the control strategy. It presents a first
PI speed control
used for speed regulation. The output of the speed control is I
qref
; its application to a second PI
current regulator makes the adjustment of phase and squaring currents. The outputs of current

=
(20)

44
.cos( ) .sin( )
33
cdref qref
VV V
pp
qq=
(21)

Modeling and Simulation of High Performance Electrical Vehicle Powertrains in VHDL-AMS

31
The generation of the control signals of the inverter is made by comparison of the simple
tensions obtained following the regulation with a triangular signal. Its period is known as
switching period.
The different blocks constituting the traction chain were described in a VHDL-AMS
structural model by including all expressions detailed above.
5. Inverter model
The structure of a typical three-phase VSI is shown in figure 6. As shown below, Va, Vb and
Vc are the output voltages of the inverter. S1 through S6 are the six power transistors IGBT
that shape the output, which are controlled by a, a’, b, b’, c and c’. When an upper transistor
is switched on (i.e., when a, b or c are 1), the corresponding lower transistor is switched off
(i.e., the corresponding a’, b’ or c’ is 0). The on and off states of the upper transistors, S
1
, S
3


c
V
V
V
é
ù
é
ùéù
-
êú
ê
úêú
êú
ê
úêú
=-
êú
ê
úêú
êú
ê
úêú
-
ê
ú
ë
ûëû
ë
û


úêú

êú
ë
ûëû
ëû

The different blocks constituting the traction chain were introduced both in MATLAB and
SIMPLORER 7.0 softwares. They were described in structural models by including all
expressions detailed above. The different simulation parameters are summarized in table 1:

Electric Vehicles
– Modelling and Simulations

32
Parameters Designation Values
Vmax Max Speed 80 km/h
Cx Drag coefficient of the vehicle 0.55
S Frontal surface of the vehicle 1.8 m2
f Coefficient of rolling friction 0.025
Mv Total mass of the vehicle 800 kg
p Pair of pole number 4
Table 1. Simulation parameters
6. Simulation results
6.1 MATLAB environment
Figure 6 details the vector control (Id=0 strategy) of the vehicle, implemented under
Matlab/simulink software. Fig. 6. SIMULINK models for a vector control and his interaction in a chain of traction for


34

Fig. 9. Dynamic response of the vehicle speed in Simplorer and Matlab

Software Simulation runtime Time response of max speed
Matlab
24s 8.5 s
Simplorer
66s 6.5 s
Table 2. Simulation runtime simulation
To conclude, Matlab executes simulations more rapidly (24s); we obtained a dynamic response
equal to 8.5s. Simplorer simulation runtime is three times longer due to the fact that the
modelling abstraction level is lower compared to the functional description with Matlab; the
dynamic response is about 6.5s. The power of the Electric Vehicule is about 42 kW.
To resume, we can clearly conclude that simulating a mathematical model with MATLAB
software is useful to verify the ideal response of our EV. But with Simplorer environment
we can attend the lower abstraction models. In this case, it is possible to simulate the effect
of physical parameters such as temperature, battery voltage, etc.
7. Optimization with experimental designs
To optimize our control strategy, we have adopted an experimental design approach by
applying the Doehlert design. Six factors have been considered as shown on table 3: Ke, Ld,
Ts, E, R and rm. According to the number of factors, in order to limit the number of runs
and to take into account the major effects, a screening study is necessary. Consequently, a
first step of screening was conducted using a fractional factorial design. The last with six
factors is a design involving a minimum of 45 experiments (see appendix).
For each factor, we define three levels: low, center and high levels as detailed on table 3.

Naturel
Variable

Modeling and Simulation of High Performance Electrical Vehicle Powertrains in VHDL-AMS

35
Our goal is to optimize both the response time and the power of the studied system. The
analysis of results and the building of experimental designs were carried out with the
NEMRODW mathematical statistical software (El Ati-Hellal et al., 2009).
Because of the none-linearity of the studied system, the experimental response Y
i
can be
represented by a quadratic equation of the response surface (Elek et al., 2004):

66
1,2 0
1
1
2
ii i
j
i
j
i
i
j
ij
Yb bx bxx
=
=
=
¹
=+ +

We found R² = 0.976; it is well within acceptable limits of R
2
>= 0.8 which revealed that the
experimental data well fitted the second-order polynomial equation as detailed on table 4.

Y
Standard error of response 8.4837
R
2
0.976
R
2
A 0.939
R
2
pred 0.777
PRESS 11512.167
Degrees of freedom 17
Table 4. Statiscal data and coefficients of y response model: y= f(x1, x2, x3, x4, x5, x6)
To estimate the quality of the model and validate it, analysis of the variance and the residual
values (difference between the calculated and the experimental result) were examined.
According to the residual (Figure 10), the choice of the model was appropriate: a systematic
behavior was not observed in the plot, for example, an increase in residual suggesting the
necessity to transform the response.
After the validation of the proposed second-order polynomial model, we can draw 2D and 3D
plots representing the evolution of Y versus 2 factors.
Using contour plot graphs makes the evaluation of the influences of the selected factors easier.
Figure 11 illustrates the experimental response obtained by the simultaneous variation of X2
(Ld&Lq) and X6 (rm). We concluded that in order to increase the response Y, an increase of
X6 and decrease of X2 is necessary (Danion et al., 2004) & (El Hajjaji et al., 2005).

X1 K 1.0094 0.1 0.2
X2 Ld=Lq 0.3976 0.416 mH 0.216 mH
X3 Ts 1.0086
300
s 500 s
X4 E 1.0052 300 V 400 V
X5 R 1.0061 0.05 Ω 0.08 Ω
X6 rm 0.9934 3 5
Table 6. Optimal values of variables
The speed response shows the good dynamic suggested of our vehicle. The reference speed
is attained in 4.65 second. The direct current is equal to zero in the permanent mode, the
quadratic current present the image of the electromagnetic torque. The power is increased to
reach 58 kW.

0
100.00
50.00
0 18.001.00 3.00 5.00 7.00 9.00 11.00 13.00 15.00
Speed
SUM1.VAL
dynamic_model

Fig. 10. Dynamic response of the vehicle speed after optimization
10. Conclusion
In this paper, we developed a VHDL-AMS description of a vehicle traction chain and we
adopt the vector control Id=0 strategy to drive the designed PMSM. The simulation of the
dynamic response of the vehicle shows the effectiveness of this mode of control and the
PMSM in the field of the electric traction. The obtained result with Simplorer differs from
that obtained with Matlab because we used more accurate models. We think that VHDL-
AMS is more suitable to predict the electric vehicle behavior since it is a multidisciplinary

Ø
m
Flux created by rotor magnets (Wb).
w
m
Angular speed of the motor (rad/s).
f
Coefficient of rolling friction.
M
v
Total mass of the vehicle (kg).
g
Acceleration of terrestrial gravity (m/s
2
).
l
Density of the air (kg/m
3
).
S
Frontal surface of the vehicle (m
2
).
C
x
Drag coefficient of the vehicle.
V
Speed of vehicle (m/s).
α
Angle that make the road with the horizontal (in °).


Ke
Ld=Lq
[mH]
Ts
[µs]
E [V]
R
[ohm]

rm
Y1(Tr)
[s]
Y2(P)
[Kw]
Response
(Y)
1 -1 -1 -1 -1 -1 -1 12.62 13.08 35.582
2 1 -1 -1 -1 -1 1 12.10 52.80 60.600
3 -1 1 -1 -1 -1 1 12.08 20.00 40.973
4 1 1 -1 -1 -1 -1 12.64 12.78 35.358
5 -1 -1 1 -1 -1 1 4.80 58.00 107.710
6 1 -1 1 -1 -1 -1 12.67 12.72 35.256
7 -1 1 1 -1 -1 -1 12.63 12.85 35.422
8 1 1 1 -1. -1 1 12.09 24.70 43.770
9 -1 -1 -1 1 -1 1 3.89
100.00
149.974
10 1 -1 -1 1 -1 -1 12.63 12.50 35.212
11 -1 1 -1 1 -1 -1 12.64 13.00 35.490

35 0 -1 0 0 0 0 6.71 60.40 88.401
36 0 1 0 0 0 0 9.12 31.00 57.000
37 0 0 -1 0 0 0 7.24 45.15 75.432
38 0 0 1 0 0 0 7.18 45.30 76.000
39 0 0 0 -1 0 0 9.14 30.55 56.623
40 0 0 0 1 0 0 6.72 58.37 87.105
41 0 0 0 0 -1 0 7.24 45.50 75.642
42 0 0 0 0 1 0 7.13 46.39 77.000
43 0 0 0 0 0 -1 12.65 12.55 35.198
44 0 0 0 0 0 1 5.73 46.70 89.102
45 0 0 0 0 0 0 7.16 46.00 76.480
13. References
Jalalifar, M.; Payam, A. F.; Nezhad, S. & Moghbeli, H. (2007). Dynamic Modeling and
Simulation of an Induction Motor with Adaptive Backstepping Design of an Input-
Output Feedback Linearization Controller in Series Hybrid Electric Vehicle, Serbian
Journal of Electrical Engineering, Vol.4, No.2, (November 2007), pp. 119-132.
Feller, A. & Stephan, M. (2009). Modeling Germany
＇s Transition to the EV until 2040 in
System Dynamics, Thesis, Vallendar, July 27, 2009.
Jaber, K.; Fakhfakh , A. & Neji, R. (2010). High Level Optimization of Electric Vehicle Power-
Train with Doehlert Experimental Design, 11 th International Workshop on Symbolic
and Numerical Methods, Modeling and Apllications to Circuit Design, Sm2ACD 2010,
pp. 908-911, ISBN 978-1-4244-5090-9, Tunis-Gammarth, Tunisia, 2010.

Electric Vehicles
– Modelling and Simulations

40
Jaber, K.; Ben Saleh, B.; Fakhfakh , A. & Neji, R. (2009). Modeling and Simulation of electrical
vehicle in VHDL-AMS, 16 th IEEE International Conference on, Electonics, Circuits, and

Maurette, M T. & Aries, L. (2005). Preparation and characterization of electrolytic
alumina deposit on austenitic stainless steel. Science and Technology of Advanced
Materials, Vol.6, No.5, (2005), pp. 519-524, ISSN 1468-6996.
3
Control of Hybrid Electrical Vehicles
Gheorghe Livinţ, Vasile Horga, Marcel Răţoi and Mihai Albu
Gheorghe Asachi Technical University of Iaşi
Romania
1. Introduction
Developing cars is a major factor that has determined the increasing of the civilization
degree and the continuous stimulation of the society progress. Currently, in Europe, one in
five active people and in the US, one in four, directly work in the automotive industry
(research, design, manufacture, maintenance) or in related domains (fuel, trade, traffic
safety, roads, environmental protection). On our planet the number of the cars increases
continuously and he nearly doubled in the last 10 years. With increasing number of cars
entered in circulation every year, is held and increasing fuel consumption, increased
environmental pollution due to emissions from internal combustion engines (ICE), used to
their propulsion. Reducing oil consumption takes into account the limited availability of
petroleum reserves and reducing emissions that affect the health of population in large
urban agglomerations. The car needs a propulsion source to develop a maximum torque at
zero speed. This can not be achieved with the classic ICE. For ICE power conversion
efficiency is weak at low speeds and it has the highest values close to the rated speed.
Pollution reduction can be achieved by using electric vehicles (EV), whose number is still
significant. The idea of an electrical powered vehicle (EV) has been around for almost 200
years. The first electric vehicle was built by Thomas Davenport in 1834 [Westbrook, 2005]]
But over time, the batteries used for energy storage could provide the amount of electricity
needed to fully electric propulsion vehicles. Electric vehicles are powered by electric
batteries which are charged at stations from sources supplied by electrical network with
electricity produced in power plants. Currently, a lot of researches are focused on the
possibility of using fuel cells for producing energy from hydrogen. EV with fuel cell can be a

disadvantages of the pure electric vehicles, whose engines are powered by electric batteries:
the limited duration of use (low autonomy) and time recharging for batteries.
2. Hybrid electric vehicles
A hybrid electric vehicle is distinguee from a standard ICE driven by four different parts: a)
a device to store a large amount of electrical energy, b) an electrical machine to convert
electrical power into mechanical torque on the wheels, c) a modified ICE adapted to hybrid
electric use, d) a transmission system between the two different propulsion techniques.
Figure 1 shows the possible subsystems of a hybrid vehicle configuration [Chan, 2002],
[Ehsani, 2005] Fig. 1. Main components of a hybrid electric vehicle

Transmission
ICE

Control
Hardware
MPU/MCU
DSP/DSC
FPGA

Energy storage
- battery
- ultracapacitor
- fuel cell
Software
VVVF
FOC
DTC

vehicles, in addition to the main battery, special batteries or capacitors, as a secondary energy
source are used. These secondary energy sources are designed to provide power for short
periods of peak operating conditions - for example, during the ascent of a slope or during
acceleration. This is necessary because some batteries with the highest energy density have
low power density. Since power density is required at least 150 [W/kg] for a good acceleration
and slope climbing performance, a secondary source with high power density is essential. This
power density is easily obtained from a lead-based battery and this is an auxiliary battery that
is suitable for use with an aluminum-air battery in a hybrid-electric vehicle.
A combination of hybrid electric vehicle that is under development and of great interest,
thanks to improvements in fuel cell, is the electric vehicle powered with fuel cell and an
auxiliary battery. This battery can provide a high current necessary to start and can also
serve as a load limiting device which allows the fuel cell to operate at low power first and
then warm for a high power operation. This arrangement enhances the efficiency of the
entire system and also allows the vehicle to use the recuperative braking.
Another class of hybrid electric vehicles, called hybrid electromechanical vehicles, use in
addition to the main electric drive powered by batteries and a mechanical energy storage
device such as a flywheel, or a hydraulic accumulator [Westbrook, 2005]. Hybrid electric
vehicles represents a bridge between the present vehicle powered by ICEs and vehicles of
the future characterized by a near-zero emissions , ULEV (Ultra-Low-Emission-Vehicle) or,
in some cases even without pollution (ZEV-Zero-Emission Vehicle), as it is expected to be
electrically propelled vehicles powered by fuel cells supplied with hydrogen.
It is very important to be reminded that without taking the technology steps and to improve
the hybrid propulsion systems it is not possible to achieve higher level of the propulsion
technology which uses fuel cells.
Currently a number of construction companies sell hybrid electric vehicles in series
production: Toyota, Honda, Ford, General Motors. Many other companies have made
prototypes of hybrid electric vehicles, the shift in mass production is only a matter of time
that depends on the improvement of operating parameters and manufacturing cost
reductions. Regarding the line of a hybrid electric vehicle powertrain, it is complex in terms
of construction, operation and electronic control system than the most evolved similar