15th International Power Electronics and Motion Control Conference, EPE-PEMC 2012 ECCE Europe, Novi Sad, Serbia
Design and Control of a Bidirectional DC/DC
Converter for an Electric Vehicle
L. Albiol-Tendillo, E. Vidal-Idiarte, J. Maixé-Altés, J.M. Bosque-Moncusí, H. Valderrama-Blaví;
University Rovira i Virgili, Tarragona, Spain
laura.albiol@urv.cat, enric.vidal@urv.cat, xavier.maixe@urv.cat, josepm.bosque@urv.cat, hugo.valderrama@urv.cat
Abstract — The recent emergence of plug-in electric
vehicles in a global market can offer big challenges and
opportunities for both basic and applied research. Although
the electrical architecture of a Electric Vehicle (EV) or an
Hybrid Electric Vehicle (HEV) can be considered
standardized, the development of its different building
blocks is an open problem whose solution could contribute
to improve significantly the global performance of the
vehicle. This paper details the design and control of a
bidirectional DC/DC converter for an electric vehicle. The
particularity of the chosen topology is the DC/DC converter
control by means of a sliding mode control, using only one
surface. The designed converter has been modelled and
simulated together with an inverter, a motor and a load,
which form the electric vehicle traction system.
Keywords — Electric vehicles, power electronics, electric
drives
I. INTRODUCTION
The growing concern on a post-petrol scenario,
environment protection, energy conservation and global
warming has prompted governments, companies and
individuals to bet for an emerging market in which
renewable energies appear in the horizon as one of its
more solid foundations. A paradigmatic example is the
electric vehicle (EV), becoming a subject of social
interest and a coveted topic for researchers [1].
However, electric vehicles do not constitute a mature
technology and important contributions can be expected,
among others, in control of the electrical architecture.
Fig. 1. Parts of an electric vehicle modeled in this article.
Fig. 2. Topology of the bidirectional boost converter.
978-1-4673-1972-0/12/$31.00 ©2012 IEEE
This paper details the design and control of an electric
vehicle traction system.
The traction system of a plug-in electric vehicle
consists of an energy storage system –a battery, in this
case–, a DC/DC bidirectional converter –because DC bus
voltage is higher than battery voltage–, an inverter and a
motor [2]. In this paper, the traction system is designed,
modelled and simulated with the aforementioned parts,
plus a mechanical load, as depicted in Fig. 1. The load
forces the motor to operate the machine either as a motor
or as a generator.
The described topology has been chosen considering
that the power of the drive for an EV would be comprised
between 60 and 100 kW. We have simulated a 2.2 kW
plant, because it will be power level of our test bed.
In section II, the bidirectional DC/DC converter is
analysed. Section III is devoted to the design of a traction
system test bed. In III.A the value of its passive
components is determined. Section III.B details the
choice of the inverter topology and its control. In III.C,
the motivation for using a Permanent Magnet
Synchronous Machine (PMSM) is explained, and the
modelled motor characteristics are detailed, for
simulation reproducibility. The results and conclusion are
presented in sections IV and V, respectively.
II. BIDIRECTIONAL DC/DC CONVERTER
The bidirectional operation of the DC/DC converter
(alongside a bidirectional inverter) allows the PMSM to
work either as a motor or as a generator. During
motoring, the current will flow from the battery to the
PMSM, and so the converter will act as a boost converter.
During regenerative braking, the current will flow from
the PMSM to the battery, and then the converter will act
as a buck converter.
A. Boost Converter Analysis
The proposed converter is a bidirectional boost
converter with output filter [3], since the output filter
reduces the size of the bulky capacitors of both the
inverter and the converter itself. The schematic is shown
in Fig. 2. Considering continuous conduction mode, the
converter is represented in the state-space during Ton by
X ( t ) = A X ( t ) + B
(1)
ON
ON
where
⎡ iL1 ⎤
⎢ ⎥
X ( t ) = ⎢ iL 2 ⎥ ;
v
⎢ vC1 ⎥
⎣ C0 ⎦
LS4d.2-1
⎡ iL1 ⎤
⎢i ⎥
X (t ) = ⎢ L2 ⎥
vC1
⎢⎣ vC 0 ⎥⎦
(2)
AON
⎡0 0 0
1
⎢
⎢0 0 L
2
⎢
= ⎢0 −1 0
⎢ C1
⎢
1
0
⎢0
⎣ C0
0 ⎤
−1 ⎥
⎡ vg ⎤
⎢ ⎥
L2 ⎥
⎥
⎢ L1 ⎥
0 ⎥ ; BON = ⎢ 0 ⎥
⎥
⎢0⎥
−1 ⎥
⎣0⎦
⎥
R0C0 ⎦
matrix obtained is the jacobian matrix (J) of the system.
⎡
1
⎢0
L2
⎡ eiLo 2 ⎤ ⎢
⎢
−1
⎢ o ⎥
⎢ evC1 ⎥ = ⎢ C 0
o ⎥
⎢ 1
⎢evC
⎣ 0⎦ ⎢ 1
0
⎢
⎣⎢ C0
(3)
During Toff, the converter is represented by
X ( t ) = AOFF X ( t ) + BOFF
(4)
where
AOFF
−1
⎡
⎤
0 ⎥
⎢0 0 L
1
⎢
⎡ vg ⎤
1
−1 ⎥
⎢0 0
⎥
⎢L ⎥
L2
L2 ⎥
⎢
⎢ 1⎥
;
B
=
=
OFF
⎢ 1 −1
⎥
⎢0⎥
0
0 ⎥
⎢
⎢0⎥
⎢ C1 C1
⎥
⎣0⎦
−1 ⎥
⎢0 1 0
⎢⎣
C0
R0C0 ⎥⎦
s3
s2
s
and the matrices values are the following
A = AOFF ; B = AON − AOFF
δ = BOFF ; γ = BON − BOFF
(7)
Sliding mode control has been used for its robustness
and fast response [4]. Besides, it enables the use of one
control law for both the motoring and the regenerative
braking of the drive. The chosen sliding surface is
S ( X ) = iL1 − k
(8)
where k is a constant. We can verify that the
transversality condition is accomplished, since
∇S , BX + γ =
1
vC1 ≠ 0
L1
(9)
The equivalent control can be calculated as
ueq =
∇S , AX + δ
∇S , BX + γ
=
vC1 − vg
vC1
(10)
1
s0
1
R0C0
1
L2C0
1
C1 L2 R0C0
(13)
0
1
0
C1 L2 R0 C0
Note that L2, C1 y C0 are positive, so the first column
terms are positive whenever R0 is positive. It means that
the system under the sliding model control law defined in
(8) will be stable when the machine operates as a motor
(R0 negative values would mean that the machine is
operating as a generator). The stability of the converter
operating in buck mode is evaluated in the next section.
B. Buck Converter Analysis
After proving that the DC/DC converter operation in
boost mode is stable with the sliding surface (8), it is
necessary to perform the same analysis for the converter
operating in buck mode. The inverter has been modelled
as a voltage source and a series resistance, vi and Ri,
respectively. The topology is represented in Fig. 3.
The buck converter can be represented during TON by (1),
and during TOFF by (4), where
AON
1
⎡
⎤
0 ⎥
⎢0 0 L
⎡ − vg ⎤
1
⎢
−1 1 ⎥
⎢ L ⎥
⎢0 0
⎥
⎢ 1 ⎥
L2
L2 ⎥
⎢
=
; BON = ⎢ 0 ⎥
⎢ −1 1
⎥
⎢ 0 ⎥
0
0 ⎥
⎢C C
⎢ vi ⎥
1
⎢ 1
⎥
⎢⎣ Ri C0 ⎥⎦
−1 ⎥
⎢ 0 −1 0
C0
Ri C0 ⎦⎥
⎣⎢
(14)
AOFF
0 ⎤
⎡0 0 0
⎡ −vg ⎤
−1 1 ⎥
⎢
0
0
⎢ L ⎥
⎢
L2
L2 ⎥
⎢ 1 ⎥
⎢
⎥
⎢ 0 ⎥
B
;
= ⎢0 1 0
=
OFF
0 ⎥
⎢ 0 ⎥
⎢ C1
⎥
⎢ vi ⎥
⎢ −1
−1 ⎥
⎢⎣ Ri C0 ⎥⎦
0
⎢0
⎥
Ri C0 ⎦
⎣ C0
(15)
The expression of the equivalent control leads us to the
following steady-state values of the state-space variables,
represented as a transposed vector
⎛
⎞
v k
T
⎡⎣ X * ( t ) ⎤⎦ = ⎜ k , g , R0 vg k , R0 vg k ⎟
⎜
⎟
R0
⎝
⎠
C1 + C0
C1 L2C0
1
(5)
(6)
(12)
From the jacobian, we obtain the characteristic
polynomial of the system. In order to determine the
stability of the system, we have applied the RouthHurwitz criterion to the characteristic polynomial,
obtaining
The bilineal state-space equation is:
X ( t ) = [ AX + δ] + [ BX + γ ]U
−1 ⎤
⎥
L2 ⎥
⎡e ⎤
⎥ ⎢ iL 2 ⎥
0 ⎥ ⎢ evC1 ⎥
⎥ ⎢e ⎥
⎣ vC 0 ⎦
−1 ⎥
⎥
R0C0 ⎦⎥
(11)
In sliding regime, the order of the system ideal
dynamics is reduced. Then, we can represent the system
dynamics with the error between the steady state value
and the real value of the state-space variables. The 3 × 3
Fig. 3. Topology of the bidirectional buck converter.
LS4d.2-2
The state-space variables of the converter during buck
operation can be expressed by the bilinear equation in (6).
The matrices A, B, δ and γ have to be recalculated
according to (7). The sliding surface is (8), the same that
during the boost operation. As we can see, in buck mode
the transversality condition is also accomplished.
∇S , BX + γ =
1
vC1 ≠ 0
L1
(16)
In this case, the equivalent control is
ueq =
∇S , AX + δ
∇S , BX + γ
=
vg
(17)
vC1
and the value of the state-space variables at steady state is
⎛
⎜
⎜
⎜ vi +
*
⎡⎣ X ( t ) ⎤⎦ = ⎜ 1
⎜ vi +
⎜ 12
⎜ vi +
⎝2
(
(
⎞
⎟
⎟
vi 2 − 4 Ri vg k ⎟
⎟
vi 2 − 4 Ri vg k ⎟
⎟
vi 2 − 4 Ri vg k ⎟
⎠
k
2v g k
)
)
(18)
A. Converter Parameters
The converter inductors L1 and L2, and capacitors C1
and C0 have to be sized according to the desired output
voltage and ripple of the waveforms. Both the current in
inductor L1 and voltage in capacitor C1 have triangular
waveforms. In this case, we can use the small-ripple
approximation to express the component value as a
function of its state variable ripple [6]. So the value of the
inductor L1 is
L1 =
1 vg
TON
2 ΔiL1
(22)
and the value of the capacitor C1 is
In sliding regime, the dynamics of the error around the
equilibrium point is represented by
⎡
−1 1 ⎤
⎢0
⎥
L2
L2 ⎥
o
⎢
⎡ eiL 2 ⎤
⎡e ⎤
⎥ ⎢ iL 2 ⎥
⎢ o ⎥ ⎢1
0 ⎥ ⎢ evC1 ⎥
⎢ evC1 ⎥ = ⎢ C 0
o ⎥
⎢ 1
⎥ ⎢e ⎥
⎢evC
⎣ vC 0 ⎦
⎣ 0 ⎦ ⎢ −1
−1 ⎥
0
⎢
⎥
Ri C0 ⎥⎦
⎢⎣ C0
III. DESIGN OF AN EV TRACTION TEST BED
In order to test the DC/DC converter and its control,
we have designed a test bed of an EV traction system.
The voltage specifications will be the same that in an EV.
However, since the final objective of the test bed is a
physical implementation, the power rating has been
reduced. The test bed has to meet the characteristics
specified in Table I.
(19)
Calculating the characteristic polynomial and applying
the Routh-Hurwitz criterion, we obtain
C1 =
1 iL 2
TON
2 ΔvC1
(23)
To design C0 the current iL2 is taken into account. Its
DC component flows only through the output resistance
R0, while the AC flows through C0 and R0. It is desirable
that most of the AC component flows through C0 instead
of R0. Considering this, the current and voltage
waveforms in the output capacitor are represented in Fig.
4.(a). The shadowed area is the charge of C0. It can be
calculated as the integral of iL2 during the interval in
which it is positive
1
( d +1)Ts
2
1
C0
dTs
2
qC 0 = ∫
i
( t ) dt =
1
ΔiL 2Ts
4
(24)
C1 + C0
C1 L2 C0
but it can be also calculated as
1
Ri C0
1
C1 L2 Ri C0
Matching (24) and (25), the value of C0 is expressed
depending on the ripple of iL2 and vC0.
s
1
L2 C0
0
s0
1
C1 Ri C0 L2
0
s3 1
s
2
1
qC 0 = 2ΔVC 0C0
(20)
C0 =
Dual to boost stability analysis, the converter operation
in buck mode is stable as long as Ri is positive. That is,
the DC/DC converter operation will be stable whenever
the machine acts as a generator. This means that the
sliding surface (8) can be used regardless of the direction
of the power flow.
C. Voltage Control Loop
We have added a second control loop, slower than the
current loop. Its aim is to regulate the converter output
voltage[5]. The sliding surface after including the voltage
loop is
S ( X ) = iL1 − k1 ( vref − vC 0 ) − k2 ∫ ( vref − vC 0 )
(25)
1 Ts ΔiL 2
8 ΔvC 0
(26)
In a similar manner, L2 value is selected to ensure that
most of the AC component of vC1 falls across its
terminals. This means that the output voltage vC0 is nearly
the DC component of vC1. The current and voltage
waveforms in the inductor L2 are represented in Fig.
4.(b). The flux linkage of L2 can be calculated with two
different expressions
λL 2 = 2ΔiL 2 L2
1
λL 2 = ∫12
2
( d +1)Ts
dTs
(27)
vL 2 ( t ) dt =
1
ΔvC1Ts
4
(28)
Matching (27) and (28), the value of L2 is obtained in
function of vC1 and iL2 ripples
(21)
LS4d.2-3
electric vehicles, due to its suitability for regenerative
operation and its smaller footprint [7]. Choosing a threelevel topology is a trade-off between achieving higher
DC link voltages and less stress in devices, and keeping
losses and cost of the circuit reasonably low.
We use vector control because it enables the use of
synchronous motor drives for high-performance
applications [8, 9], like traction in the electric vehicle. In
particular, the speed is controlled by a PI controller, and
has an inner current loop. This current is decomposed
into a magnetic field-generating part and a torquegenerating part, in the same way that in [10].
TABLE I
DESIGN CRITERIA FOR DC/DC CONVERTER
battery voltage
300 V
DC bus voltage
550 V
iL1 ripple
10 %
iL2 ripple
10 %
vC1 ripple
2.5 %
vC0 ripple
0,5 %
switching period (Ts)
50 μs
TABLE II
VALUE OF COMPONENTS
L1
2.045 mH
L2
94.53 μH
C1
7.5 μF
C0
2.1 μF
C.
(a)
(b)
Fig. 4. Current and voltage waveforms of (a) the output capacitor C0,
and (b) the filter inductor L2.
L2 =
1 Ts ΔvC1
8 ΔiL 2
(29)
To calculate the values of the passive components, the
relative ripple is set according to Table I. From (22), (23)
(26), (29) and the ripple criteria, the values of the
designed components are calculated, and annotated in
Table II.
B.
Three-Level Inverter
The aim of the demonstrative platform for electric
vehicle’s traction study is to offer a hardware basis on
which test and develop new control strategies, and also to
allow topology modifications. Considering that this
topology has been chosen for a 60-100 kW EV, it is
convenient to use a multilevel inverter. The advantages of
using a multilevel inverter at this power are reducing the
stress of the components (compared with the H-bridge),
improving the system efficiency and achieving higher
voltages, extending the constant power region of the
motor. Among the large list of topologies, we have
chosen the voltage source inverter NPC (Neutral Point
Clamped). It is an adequate starting point for traction
Motor
For vehicle traction, the most important parameter to
select the electric motor is torque density, and permanentmagnet synchronous machines (PMSM) have the best
torque density, apart from a good efficiency. The higher
the torque density, the lower the weight and volume of
the motor [11]. The main drawback of PMSM is their
short constant power range. However, it can be extended
by an adequate control.
After considering the PMSM advantages and
inconveniences, we have chosen this machine as our
traction motor for the electric vehicle. In order to test the
complete traction system as depicted in Fig. 1, a scale
platform instead of the full-power system will be used for
feasibility. The characteristics of the motor chosen for the
scale platform are summarized in Table III.
IV. SIMULATION RESULTS
The objective of the simulations is to validate the
chosen model with the low-power test bed. The
simulation of the inverter control is performed with
Simulink. The battery, the DC/DC converter, the sliding
mode control, the inverter and the motor are modelled in
PSIM, and included in the Simulink model. The values of
the constants from the sliding surface have been adjusted
experimentally.
TABLE III
PMSM CHARACTERISTICS
voltage rating (Vrms)
380 V
current rating (Irms)
4.1 A
power rating (Pr)
2.2 kW
speed rating (nr)
1750 rpm
stator resistance (Rs)
3.3 Ω
d-axis inductance (Ld)
0.04159 H
q-axis inductance (Lq)
.04159 H
voltage constant (Ke)
261 V/krpm
number of poles (p)
6
moment of inertia (J)
0.01007 kg·m2
mechanical time constant (tm)
4.9266 s
Fig. 5. Motor starting at nominal load.
LS4d.2-4
Fig. 7. Load torque transition.
Fig. 6. Regenerative braking.
The result of starting the motor at nominal load is
shown in Fig. 5. The DC bus voltage is 550 V, but the
voltage ripple depends on the current consumption. More
current consumption causes more ripple. The sliding
motion can be appreciated in the battery current
waveform. Fig. 6 shows the performance of the motor
decelerating from the nominal speed, at 50% of the
nominal voltage. The DC bus voltage remains stable at
550 V. It is clearly shown that when reference speed is
reduced, there is regenerative braking, and current flows
from the motor to the battery (current reaches negative
values). In the third test, the motor is started at nominal
load, and after 0.8 s the load is reduced a 70%. The
results of this torque transition are reproduced in Fig. 7.
The current consumption drops when the load torque is
reduced. The DC bus voltage regulation is performed
despite the load perturbation.
V. CONCLUSION
This paper has presented the design and control of a
bidirectional DC/DC converter for an electric vehicle.
The particularity is the use of only one sliding mode
control law to control the bidirectional DC/DC converter.
Once designed and controlled, the converter has been
modelled and simulated along with the rest of the traction
system for an electric vehicle –inverter, motor and load.
Results summarized in the previous section validate
the operation of the bidirectional DC/DC converter and
the inverter. Moreover, sliding mode control is verified.
The studied sliding surface is successfully used to control
the DC/DC converter operation, both during the motoring
and the regenerative braking of the machine.
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LS4d.2-5
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