DC/DC Converters for Electric Vehicles

319
Where:
 V
out
: the output voltage,
 ∆IL
max
: the inductor current ripple,
 F : the switching frequency.
 IL
max
: the maximum input current,
 ∆V
out_max
: the maximum output voltage ripple.
Table 1 shows the specifications of the converter. The inductor current ripple value is
desired to be less than 5% of the maximum input current in the case of interfacing a Fuel
Cell. A ripple factor less than 4% for the Fuel Cell’s output current will have negligible
impact on the conditions within the Fuel Cell diffusion layer and thus will not severely
impact the Fuel Cell lifetime (Yu et al., 2007).

∆V
out_max
Output voltage ripple (1% of V
out
= 4 V)
V
out

out
Lout
di
vL uv
dt
dv
iuC i
dt
ì
ï
ï
=+-
ï
ï
ï
í
ï
ï
-= +
ï
ï
ï
î
(30)
This model can be used directly to simulate the converter. By replacing the variable u by its
average value which is the duty cycle during a sampling period makes it possible to obtain
the average model of the converter as illustrated in the following system of differential
equations:

()

(31)

Electric Vehicles – Modelling and Simulations

320
Current control loop
The current control loop guarantees limited variations of the current trough the inductor
during important load variations. The inductor current and voltage models are given by
Equation 32 and Equation 33, respectively.

() () ()
()
()
(
)
1
1
in out
IL s V s s V s
Ls
a= ⋅
(32)

(
)
(
)
(
)
(

Thus, a linear transfer between VL’(s) and IL(s) is obtained by:

()
(
)
(
)
1
1
IL s
Ts
VL s Ls
==
¢
(35)
The structure of the regulator is a RST form. The polynomials R, S and T are calculated
using the methodology explained above. The bandwidth of the current loop ω
i
should be ten
times lower than the switching frequency.

2
,
10 10
ii
ff
f
p
w££
(36)

zS

Fig. 6. Boost converter inductor current loop
From the reference value of the current and its measured value, The RST current controller
block will calculate the duty cycle as explained above.
Voltage control loop
The output voltage loop was designed following a similar strategy to the current loop. To
define the voltage controller, it is assumed that the current control loop is perfect. The
capacitor current and voltage models are given by Equation 37 and Equation 38, respectively.

DC/DC Converters for Electric Vehicles

321

(
)
(
)
(
)
(
)
(
)
1
out
IC s s IL s I sa=- ⋅ - (37)

() ()
()

Lref out
in
IC s I s
IL s
s
Vs
Is ICsIs
Vs
a
¢
+
=
-
¢
= +
(39)

Where IC’ is a new control variable represents the current reference of the capacitor.
Thus, a linear transfer between Vout(s) and IC’(s) is obtained by:

()
(
)
()
2
1
out
Vs
Ts
IC s Cs

C
I
Boost
Converter
PWM
generator
Lref
I
RST Current
Loop

out
V
L
I
RST
voltage
controller


1
zR


1
zT


11 
zS

Efficiency Standard BOOST 30KW
Efficiency

Fig. 8. Boost converter efficiency versus current load

0 150 KHz500 KHz 5 MHZ 10 MHz 15 MHz 20 M Hz 25 MHz 30 MHz
0
40
50
60
70
80
10 0
15 0
Frequency [Hz]
Spectrum [dBuV]
EMI BOOST 30KW without EMI filter
VDEClassA
VDEClassB
IECClassA
IECClassB
Fig. 9. EMI simulation results of boost DC/DC converter.

DC/DC Converters for Electric Vehicles

323
6.3 Interleaved 4-channel DC/DC converter
Fig. 10 shows a basic interleaved step-up converter of 4 identical levels where the
inductances L1 to L4 are built by a separate magnetic core. The gate signals to the power
switching devices are successively phase shifted by T/N where T is the switching period

100
4
out
k
In
V
LH
FN I
m==
´´ ´D
(43)
Where:
 N

: the number of channels,
 ∆I
In_max
: the input current ripple,
 F : the switching frequency.
 I
In_max
: the maximum input current,
 ∆V
out_max
: the maximum output voltage ripple.

Electric Vehicles – Modelling and Simulations

324
As control signals are interleaved and the phase angle is 360°/N, the frequency of the total

Inductor current (250 A)
∆I
In_max
Input current ripple (5% of I
In_max
= 12.5 A)
Table 2. Interleaved 4-channels DC-DC converter parameters
6.3.1 Modeling and control
The 4-channel converter is modeled in the same way of the boost converter. The current and
voltage loop are designed also using the same methodology used for boost converter. The
calculated current reference is divided by 4 (number of channels). The output voltage
control loop is shown is Fig. 11.

Vref
+
-
Linearization
'
C
I
4-channel
Boost
Converter
4 PWM
generator
shift (T/4)
Lref
I
RST Current
Loop

Thanks to the interleaving technique, the total current ripples are reduced and can be
neglected; the voltage ripples are about 0.5V. The results show that the converter follows the
demand on power.
The efficiency of the 4-channels dc/dc converter is about 92% at full load as shown in Fig.
12. The drop in efficiency is due to the changing from discontinuous mode (DCM) to
continuous mode (CM). In DCM, the technique of zero voltage switching (ZVS) is operating
which permits to reduce the switching losses in the switch, thus the efficiency is increased.
Fig. 13 shows the EMI of the interleaved 4-channels DC/DC converter. It is seen that the
level of conducted interference due to converter is not tolerable by the regulations. As a
consequence this converter without EMI filter suppression does not meet the terms of the
regulations. Thus, EMI filter suppression is required.

DC/DC Converters for Electric Vehicles

325
25 30 35 40 45 50 55 60 65 70 75 80
80
82
84
86
88
90
92
94
96
98
100
Current [A]
Efficiency [%]
Efficiency 4-channels 30KW


_min
1
2
sout
pin
NV
n
NVa
==´
(45) Fig. 14. Full-bridge step-up DC-DC converter
The output filter inductor and capacitor values could be calculated based on maximum
ripple current and ripple voltage magnitudes. The calculations are done considering the
converter is working in CCM. max
1.2mH
2
in
nV
L
IL F
a´´
==
´D ´
(46)

: the inductor current ripple,
 F : the switching frequency,
 ∆V
out_max
is the maximum output voltage ripple.
Table 3 shows the simulations parameters of the converter.

DC/DC Converters for Electric Vehicles

327
∆V
out_max
Output voltage ripple (1% of V
out
= 4 V)
V
out
Output voltage (400 V)
F Switching frequency (40 KHz)
∆IL
max
Inductor current ripple (5% of ILmax = 3.75 A)
n Transformer turns ratio (= 4)
Table 3. Full-Bridge DC-DC converter parameters.
6.4.1 Modeling and control
The Full-Bridge DC/DC converter will have to maintain a constant 400V DC output. By
increasing and decreasing the duty cycle α=t/T of the PWM signals, the output voltage can
be held constant with a varying input voltage. The output voltage can be calculated as
follows:


=´-
÷
ç
÷
÷
ç
èø
(49)

() () () ()
42
Linout
n
Vs s V s V sa
p
=´- (50)
The linearization of the system is done by using an inverse model. Thus an expression
between the output of corrector and the voltage of the inductor should be found. Thus, the
following expression is proposed:

()
(
)
(
)
() ()
'
42
Lout
in

Is
Ts
Ls
Vs
== (52)
The bandwidth of the current loop ω
i
should be ten times lower than the switching
frequency.

2
,
10 10
ii
f
f
f
p
w££
(53)

Electric Vehicles – Modelling and Simulations

328
The inductor current loop is shown in Fig. 15.

ILref
+
-
Linearization

define the voltage controller, it is assumed that the current control loop is perfect. The
capacitor current and voltage models are obtained by expressions 54 and 55:

(
)
(
)
(
)
CLout
Is Is I s=- (54)

() () ()
()
1
CLout
Vs Is I s
Cs
=-
(55)

The linearization of the system is done by the following expression:

(
)
(
)
(
)
(

Ts
Cs
Is
==
(57)

The bandwidth of the voltage loop ω
v
should be ten times lower than the current loop
bandwidth ω
i
which means hundred times lower than the switching frequency.

2
,
100 100
vv
f
f
f
p
w££
(58)

The output voltage control loop is shown in Fig. 16.

Vref
+
-
Linearization


11 
zS

Fig. 16. Full-bridge converter output voltage control loop.

DC/DC Converters for Electric Vehicles

329
Simulation results
The efficiency of the Full-bridge dc/dc converter is about 91.5% at full load as shown in Fig.
17. The efficiency of this converter can be increased by using phase shifted PWM control
and zero voltage switching ZVS technique.

10 20 30 40 50 60 70 80
80
82
84
86
88
90
92
94
96
98
100
Current [A]
Efficiency [%]
Efficiency Full-Bridge 30KW
Efficiency

inductor volume and weight were approximated. It can be noticed that the full-bridge
converter has the biggest volume and weight due to the output inductance. This inductance
value can be reduced by increasing the switching frequency of the converter. We can notice
that the best candidate for the application is the Interleaving multi-channel topology which
has the higher efficiency and lower weight and volume. Weight and volume estimation
takes into account only the IGBT, DIODE, Inductor and capacitor (transformer for full
bridge) and it doesn’t take into account the cooling system and the arrangement of
components in the casing of the converter.

DC/DC converter EMI Volume(cm3) Weight(g) Efficiency at full load
Boost -+ 2167 6325 83%
Interleaved 4-channels + 1380 3900 92%
Full-Bridge 3033 9268 91.5%
Table 4. Recapitulative table.
Fig. 19 gives an idea about the difference in the weight, volume and efficiency of each
converter.

2167
1380
3033
Volume(cm3)
6325
3900
9268
Weight(g)
83
92
91,5
Efficiency(%)


the «HY-LIGHT» - vehicle,
VDI Tagung Innovative Fahrzeugantriebe 2006, pp. 415-
429, Dresden, Germany, 2006
Cacciato, M., Caricchi, F., Giuhlii, F. & Santini, E. (2004). A Critical Evaluation and Design of
Bi-directional DC/DC Converters for Super-Capacitors Interfacing in Fuel Cell
Applications,
Proceedings of IAS 39
th
IEEE Industry Applications Conference Annual
Meeting
, pp. 1127–1133, ISBN 0-7803-8486-5, Rome, Italy, October 3-7, 2004
Chiu, H.J., & Lin, L.W. (2006). A Bidirectional DC–DC Converter for Fuel Cell Electric
Vehicle Driving System,
in Power Electronics IEEE Transactions, Vol.21 Issue 4,
(2006), pp. 950–958, ISSN 0885-8993
Destraz, B., Louvrier, Y., & Rufer, A. (2006). High Efficient Interleaved Multi-channel dc/dc
Converter Dedicated to Mobile Applications,
Proceedings of IAS 41st IEEE Industry
Applications Conference Annual Meeting
, pp. 2518–2523, ISBN 1-4244-0364-2, Tampa,
Florida, USA, October 8-12, 2006
Farhadi A., Jalilian A. (2006). Modeling and Simulation of Electromagnetic Conducted
Emission Due to Power Electronics Converters,
Proceedings of PEDES'06
International Conference on Power Electronics, Drives & Energy Systems
, pp. 1-6, ISBN
0-7803-9772-X, New Delhi, India, December 12-15, 2006
Fengyan, W., Jianping, X., & Bin, W. (2006). Comparison Study of Switching DC-DC
Converter Control Techniques,
Proceedings of International Conference on

Engineering Practice
, Vol.6, Issue 2, (February 1998), pp. 155-165
Pepa, E. (2004). Adaptive Control of a Step-Up Full-Bridge DC-DC Converter for Variable
Low Input Voltage Applications,
Faculty of the Virginia Polytechnic Institute and State
University
, Blacksburg, Virginia, 2004
Schaltz, E., & Rasmussen, P.O. (2008). Design and Comparison of Power Systems for a Fuel
Cell Hybrid Electric Vehicle,
Proceedings of IAS'08 IEEE Industry Applications Society
Annual Meeting
, pp. 1-8, ISBN 978-1-4244-2278-4, Edmonton, Alberta, Canada,
October 5-9, 2008
Yu, W., & Lai, J.S. (2008). Ultra High Efficiency Bidirectional DC-DC Converter With Multi-
Frequency Pulse Width Modulation,
Proceedings of APEC 2008 23
rd
Annual IEEE
Conference and Exposition on Applied Power Electronics
, pp. 1079-1084, ISBN 978-1-
4244-1873-2 Austin, Texas, USA, February 24-28, 2008
Yu, X., Starke, M.R., Tolbert, L.M, & Ozpineci, B. (2007). Fuel cell power conditioning for
electric power applications: a summary,
Journal of IET electric power
applications
, Vol.1, No.5, (2007), pp. 643-656, ISSN 1751-8660
14
A Comparative Thermal Study of Two
Permanent Magnets Motors Structures with
Interior and Exterior Rotor

L and the pole-pitch
p
L .
This relationship is used to adjust the magnet angular width according to the motor pole-
pitch.

Electric Vehicles – Modelling and Simulations

334

m
p
L
L



(1)

p
L
p



(2)
The ratio
ldla
R is the relationship between the angular width of a principal tooth and the
magnet angular width. This ratio is responsible for the regulation of the principal tooth size

two SMPMM configurations which are the PMSMER and the PMSMIR.
Figure 1 represents the PMSMER and the PMSMIR with the number of pole pairs is p=4 and
a number of principal teeth is 6, between two principal teeth, an inserted tooth is added to
improve the wave form and to reduce the leakage flux (Ben Hadj, N. et al., 2007). The slots
are right and open in order to facilitate the insertion of coils and to reduce the production
cost (Magnussen, F. et al., 2005; Bianchi, N. .et al., 2003; Libert , F. et al., 2004).
Fig. 1. Permanent magnets motors with exterior rotor and interior rotor
A Comparative Thermal Study of Two
Permanent Magnets Motors Structures with Interior and Exterior Rotor

335
2.3 Analytical sizing of the two SMPMM structures
The analytical study of motor sizing is based on the schedules data conditions parameters
(Table 1), the constant characterizing materials (Table 2), the expert data and configurations
of the two motors.

Definition Symbol Value
Electric vehicle mass M 1000 kg
Angle of starting a
d
3°
Time of starting t
d
4 s

Magnetic induction in teeth B
tooth
0,9 T
Magnets permeability μ
a
1,05
Mechanical losses coefficient k
m
1%
Copper resistivity at 95°C R
cu
17,2 10
-9
Ωm
The copper resistivity variation coefficient α 0,004
Density of the electrical sheets M
vt
7850 kg
Density of magnets M
va
7400 kg
Density of copper M
vc
8950 kg
Sheets quality coefficient Q 1,1
Table 2. Specific constants of materials
Expert data
The expert data are practically represented by three sizes which are, the magnetic induction
in the air gap B
e

2. The slots height h
s
and the tooth height h
tooth

3. The rotor yoke height, h
ry

4. The stator yoke height, h
sy

5. The air gap thickness, e Fig. 2. PMSMER and PMSMIR parameters
In the stator of the PMSMIR, geometrical sizes are defined by:
The slot average width:
s
W

2
mtooth
ss
Deh
WA


(5)
The principal tooth section:
tooth
12
22
m
s tooth toothi m
tooth
De
SAAl
N






(8)
In the stator of the PMSMER, geometrical sizes are defined by:
The slot average width:
s
W

2
m tooth
ss
Deh
WA




s
S

12
22
m
s tooth toothi m
tooth
De
SAAl
N






(12)
The teeth height
tooth
h of the PMSMIR and the PMSMER are expressed by equation 13 and 14
where
s
p
h
N is the number of turns per phase,
n
I is the rated current and
teeth
N in the number

De De
h
NKA







(14)
The stator yoke thickness
s
y
h is obtained by the application of the flux conservation theorem,
where
tooth
B
is the magnetic induction in the tooth.

2
tooth tooth
sy
msy
BS
h
lB

(15)
In the rotor of the two structures, geometrical sizes are defined by:

M
Ta at Ta°C is defined by:



() 1 ( 20)maMTa M T

 
(17)
The rotor yoke thickness
r
y
h is defined:

Electric Vehicles – Modelling and Simulations

338

2
e tooth
ry
f
um r
y
BS
h
klB

(18)
2.5 Electrical sizing



 

 
 
(20)
The electromagnetic torque :
em
T


3
1
1
() ()
em i i
i
Tt EMFtit




(21)
where
i
EMF ,
i
i and
m

RRT
I


(23)
where
()
co w
RT is the copper receptivity at the temperature of winding
w
T and
s
p
L is the spire
average length (Ben Hadj et al., 2007).
3. Comparative thermal study between the two SMPMM
In this study, the comparison between the two SMPMM structures consists on the thermal
analysis which is based upon lumped-circuit analysis. It represents the thermal problems by
using the thermal networks, analogous to electrical circuits. The thermal circuit in the steady
state consists of thermal resistances and heat sources connected between motor component
nodes. For transient analysis, the heat/thermal capacitances are used additionally to take
into account the change in internal energy of the body with time. The thermal resistances for
conduction and convection can be obtained by:


/
convection
l
RKW
A

(26)
Where V is the volume,

is the density and c is the heat capacity of the material. The
simplified stator for the thermal study of the two SMPMM structure are given by
figures 3 and 4, also the thermal model for the two structures are implemented in
MATLAB simulater where the different radius for the PMSMER dimensions are defined
as follow:

1
2
carter
f
mr
y
carter
e
RRR hhe


(27)

2
2
rotor
y
oke
f
mr
y

e
RRR

(31)

65insolator s
RRRh
(32)

75s insolator
RRht
(33)

87s
y
RRh
(34)
The thermal resistances are calculated along the radial direction. The
i
R
radius are
calculated from dimensions of motor, where
f
R is the Bore raduis and
insolator
t
is the
thickness insulator.
The different radius for the PMSMIR dimensions are defined as follow:


(37)

4
2
f
tooth isnolator s
y
e
RR h t h
  
(38)

5
2
f
tooth insolator s
y
carter
e
RR h t h t
  
(39) Fig. 3. Simplified stator for the thermal study in the PMSMER Fig. 4. Simplified stator for the thermal study in the PMSMIR
A Comparative Thermal Study of Two
Permanent Magnets Motors Structures with Interior and Exterior Rotor

coil
mcoil
RR
R
lR
RR



(40)
inso
R represents the isolator thermal resistance (
1
.KW ).

3
2
ln
2
inso
inso m
R
R
R
l



(41)
R

jco
iron m
R
R
R
l



(43)

Electric Vehicles – Modelling and Simulations

342
f
co
R represents the thermal resistance of conduction in the stator yoke (
1
.KW ).

-
-
2
3
4
22
3
43
1
[1 2 ln ]

Rl



(45)
ca
R represent the thermal resistance of carter (
1
.KW ).

5
4
ln
2
ca
ca m
R
R
R
l



(46)
ext
R represents the convection thermal resistance between the carter and ambient air
(
1
.KW ).





(48)
The expressions of heat capacities of the PMSMIR are given by the following equations:
coil
C represents the heat capacity of coil (
1
JK ).

coil co co th co
CVC




(49)
inso
C represents the heat capacity of insolator (
1
JK ).

inso inso inso th inso
CVC




(50)
s


343
Figure 6 shows the thermal model in transient behaviour of the PMSMER. Fig. 6. Thermal model of the PMSMER in transient behaviour
The expressions of the PMSMER thermal resistances obtained from the resolution of the heat
equation at the fields borders.
s
y
R represents the stator yoke thermal resistance (
1
.KW ).

2
8
7
22
8
78
1
12 ln
4
sy
miron
R
R
R
lR
RR

R
R
R
lR
RR












(54)
coil
R
represents the coil thermal resistance (
1
.KW ).2
65
22
6
56

2
2
mag
ma
g
m
R
R
R
l



(56)
r
y
R represents the rotor yoke thermal resistance (
1
.KW ).

2
3
ln
2
ry
iron m
R
R
R
l