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Modeling and Control of a Cascaded Boost
Converter for a Battery Electric Vehicle
A. Ndtoungou, Ab. Hamadi, A. Missanda and K. Al-Haddad, Fellow member,
IEEE
EPEC 2012 OCTOBER 10-12

Introduction
contents
Comparison between boost and cascade boost
Modeling and control of cascade boost converter
Space average model of the system
Control law for output voltage control
Design of the Proportional Integral (PI) controller
Control Scheme of cascade boost for voltage control
Simulation results
Control of Battery current
Simulation results
Cascade boost converter used as non polluting converter
Control scheme
Simulation results
Conclusion
EPEC 2012 OCTOBER 10-12

INTRODUCTION
I’s a new modeling technique of a cascade Boost converter;
The nonlinear control is applied and gives good performances in grid side
and in dc side.
PI controller eliminates efficacy the steady state error of the dc bus voltages;
The configuration proposed may be used to fast charging electrical vehicle
battery by controlling the time charging;
The configuration connected to the grid compensates current harmonics,
reactive power, the THD of the grid current is less than 5%.
EPEC 2012 OCTOBER 10-12

Comparison between Boost and cascade Boost
Characteristics of boost converter and cascade boost converter
The boost converter provides high currents, while the cascade boost converter
achieves high voltage.
The advantage of the high voltage of the cascade boost converter make it very
suitable for high battery voltage charging current.
EPEC 2012 OCTOBER 10-12

Modeling and control of cascade
boost converter
D 2
iL 1
L 1
D 1
i L 2
v 1
L 2
D 3
i o
V C 1
Q C2
R vo
in
ON
OFF
i
L1
i
L2
i o
i v
L 1
1
L
v 1
i
L2
v
L2
i o
V in
L 1
i
C1
v
L1
v
C1
i
C2
C
v 1 L 2
v
L2
v
1
C2
C2
R
vo
Vin
L 1
i
C1
v
C1
i
C2
L 2
C v
1 C2
C2
R
vo
EPEC 2012 OCTOBER 10-12

Space average model of the system
( − )
⎧ diL
1 d
1
1
⎪ = − vC
+ V
1
⎪ dt L1 L1
⎪ diL
( − )
2
1 1 d
⎪ = v C −
1
v 0
⎪ dt L2 L2
⎨
⎪ dvC
( 1 − d )
1
1
⎪
= iL
− i
1 L2
dt C1 C1
⎪
⎪ dv 1
⎪
⎩
o
( 1 − d )
= iL
−
2
dt C RC
2 2
v
o
in
EPEC 2012 OCTOBER 10-12

Control law for output voltage control :
The dynamics of the output voltage is given by
dv0
1
C + v = ( 1 − d ) i = u
2 o L
dt R
2
The control law is
u u
d = 1−
i
L 2
The right term of this equation which is linear uses PI
controller to regulate the voltage v0 and we extract the
control law from this equation
Where :
i L2
is the output of the controller PI
is the current in inductance
L 2
EPEC 2012 OCTOBER 10-12

Design of the Proportional Integral
(PI) controller
k k +
i
= + = p s k
G(s) k
i
p
s s
v0ref
k s + k v
p i u R 0
s
RC s + 1
Closed loop output voltage regulation
2
G
F
⎧1 + Rk
⎪ RC2
⎨
k
( k p s + k i )
1
G 0 C 2
= =
1 + G ⎛ 1 + R k ⎞ k
s + ⎜ ⎟ s +
⎝ R C ⎠ C
p
0 2 p
i
⎪ i 2
2
= ω
⎪
0
ki = ω0 C
⎪
⎩
2
C2
⎩
2 2
= 2ξω0
⎧
1
⎪k p = 2ξω0C2
−
⇔ ⎨
R
G
1
C
( k p s + k i )
2
F =
2 2
s + 2 ξ ω 0 s + ω 0
The choice of the PI controller is based
on the desired performance of The
damping factor ζ and pulsation ω 0 to
give best response.
EPEC 2012 OCTOBER 10-12

Control scheme of cascade boost for voltage
control
Output voltage
d
1
u
v 0
i L2
v 0 ref
Output reference
voltage is chosen
by user
EPEC 2012 OCTOBER 10-12

Cascade boost converter is able to
regulate the output voltage
The best choice of inductance L2 can
give iL2 positive
Simulation results
For the high voltage, the boost
converter is not able to regulate the
output voltage
Simulation results with cascade boost
converter
Simulation results with boost converter
EPEC 2012 OCTOBER 10-12

CONTROL OF BATTERY CURRENT
i L1
D 2
D 1
i L2
We test the cascade boost converter
to charge the battery and to compare
it with the boost converter
L 1
v 1
L 2
D 3
i 0
V in
C 1
Q
C 2
v 0
Control law :
1
d = + u − V
1
( )
1 1 in
vC
Control scheme of cascade boost for current control
EPEC 2012 OCTOBER 10-12

Simulation results
The both system gives the same performance to charge the battery
The slight difference is observed in the boost converter that the current flowing in the
inductance presents the high ripple current compared of the cascade boost converter
Simulation results of cascade boost
with battery current control
Simulation results of boost with
battery current control
EPEC 2012 OCTOBER 10-12

CASCADE BOOST CONVERTER USED AS NON POLLUTING
CONVERTER
D 2
iL 1
D 1
i L 2
L 1
v 1
L 2
D 3
i o
L f
D a
D c
Vin
C 1
Q
C2
R vo
D b
D d
Cascade boost
Spectrum of the grid current
EPEC 2012 OCTOBER 10-12

Control law
Control Scheme
Reference current : i L1ref
1
eq. 31 d = 1+ ( ui −Vin
)
v
eq. 29
C
1
i
v ⎛
u
V
i
⎝
0
in
L1ref = v + C
V ⎜
in v0
1
⎞
⎟
⎠
EPEC 2012 OCTOBER 10-12

Grid current and grid voltage are in phase
The THD of the grid current is less than 5%
Simulation results
During the output reference voltage variation we see that
the output voltage well regulated , that the grid voltage
and the grid current are in phase and sinusoidal
Steady state response of a non polluting
converter: upper - voltage and current
source, lower - output voltage
Dynamic response of a non polluting
converter: upper- voltage and current
source, lower- output voltage and its
reference
EPEC 2012 OCTOBER 10-12

CONCLUSION
• The modeling of the cascade boost converter and the nonlinear
control technique are presented.
• The simulations results have shown good performances of the
cascade Boost compared to the classical Boost converter.
• The cascade Boost converter is suitable for high voltage battery.
•The cascade Boost converter used as non polluting converter
gives a THD less than 5% in the grid side.
•The control of the battery current will help to control the
charging time which may be used to fast charging electrical
vehicle battery.
EPEC 2012 OCTOBER 10-12

THANK YOU
?
EPEC 2012 OCTOBER 10-12