Boise State University
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5-1-2009
DC-AC Cascaded H-Bridge Multilevel Boost
Inverter with No Inductors for Electric/Hybrid
Electric Vehicle Applications
Zhong Du
Parker Hanni#n Corporation
Burak Ozpineci
Oak Ridge National Laboratory
Leon M. Tolbert
Oak Ridge National Laboratory
John N. Chiasson
Boise State University
(is document was originally published by IEEE in IEEE Transactions on Industry Applications. Copyright restrictions may apply. DOI: 10.1109/
tia.2009.2018978
IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 45, NO. 3, MAY/JUNE 2009 963
DC–AC Cascaded H-Bridge Multilevel Boost
Inverter With No Inductors for Electric/Hybrid
Electric Vehicle Applications
Zhong Du, Member, IEEE, Burak Ozpineci, Senior Member, IEEE,
Leon M. Tolbert, Senior Member, IEEE, and John N. Chiasson, Senior Member, IEEE
Abstract—This paper presents a cascaded H-bridge multilevel
boost inverter for electric vehicle (EV) and hybrid EV (HEV)
applications implemented without the use of inductors. Currently
available power inverter systems for HEVs use a dc–dc boost
converter to boost the battery voltage for a traditional three-phase
inverter. The present HEV traction drive inverters have low power
density, are expensive, and have low efficiency because they need
a bulky inductor. A cascaded H-bridge multilevel boost inverter
design for EV and HEV applications implemented without the
use of inductors is proposed in this paper. Traditionally, each
H-bridge needs a dc power supply. The proposed design uses
a standard three-leg inverter (one leg for each phase) and an
H-bridge in series with each inverter leg which uses a capacitor as
the dc power source. A fundamental switching scheme is used to
do modulation control and to produce a five-level phase voltage.
Experiments show that the proposed dc–ac cascaded H-bridge
multilevel boost inverter can output a boosted ac voltage without
the use of inductors.
Index Terms—Cascaded H-bridge multilevel boost inverter,
electric vehicle (EV)/hybrid electric vehicle (HEV).
I. INTRODUCTION
R
ECENTLY, because of increasing oil prices and envi-
ronmental concerns, hybrid electric vehicles (HEVs) and
electric vehicles (EVs) are gaining increased attention due to
their higher efficiencies and lower emissions associated with the
development of improved power electronics [1]–[3] and motor
technologies [4]–[9]. An HEV typically combines a smaller
Paper IPCSD-08-070, presented at the 2007 Industry Applications Society
Annual Meeting, New Orleans, LA, September 23–27, and approved for
publication in the IEEE T
RANSACTIONS ON INDUSTRY APPLICATIONS by
the Industrial Power Converter Committee of the IEEE Industry Applications
Society. Manuscript submitted for review January 6, 2008 and released for
publication September 30, 2008. Current version published May 20, 2009. This
work was supported by the Oak Ridge National Laboratory, Oak Ridge, TN,
which is managed by UT-Battelle for the U.S. Department of Energy under
Contract DE-AC05-00OR22725.
Z. Du was with Oak Ridge National Laboratory, Knoxville, TN 37932 USA.
He is now with Parker Hannifin Corporation, Olive Branch, MS 38654 USA
(e-mail: zhong.du@parker.com).
B. Ozpineci is with the Power Electronics and Electric Machinery Research
Center, Oak Ridge National Laboratory, Knoxville, TN 37932 USA (e-mail:
ozpinecib@ornl.gov).
L. M. Tolbert is with the Department of Electrical Engineering and Computer
Science, The University of Tennessee, Knoxville, TN 37996 USA, and also
with the Oak Ridge National Laboratory, Knoxville, TN 37932 USA (e-mail:
tolbert@utk.edu).
J. N. Chiasson is with Boise State University, Boise, ID 83725 USA
(e-mail: JohnChiasson@boisestate.edu).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TIA.2009.2018978
internal combustion engine of a conventional vehicle with a
battery pack and an electric motor to drive the vehicle. The
combination offers lower emissions but with the power range
and convenient fueling of conventional (gasoline and diesel)
vehicles. An EV typically uses rechargeable batteries and an
electric motor. The batteries need to be charged regularly.
Both HEVs and EVs need a traction motor and a power
inverter to drive the traction motor. The requirements for the
power inverter include high peak power and low continuous
power rating. Currently available power inverter systems for
HEVs use a dc–dc boost converter to boost the battery voltage
for a traditional three-phase inverter. If the motor is running at
low to medium power, the dc–dc boost converter is not needed,
and the battery voltage will be directly applied to the inverter to
drive the traction motor. If the motor is running in a high power
mode, the dc–dc boost converter will boost the battery voltage
to a higher voltage, so that the inverter can provide higher power
to the motor. Present HEV traction drive inverters have low
power density, are expensive, and have low efficiency because
they need bulky inductors for the dc–dc boost converters.
To achieve a boosted output ac voltage from the traditional
inverters for HEV and EV applications, the Z-source inverter
is proposed, which also requires an inductor [10].
A cascaded H-bridge multilevel boost inverter shown in
Fig. 1 for EV and HEV applications is described in this paper.
Traditionally, each H-bridge of a cascaded multilevel inverter
needs a dc power supply [4]–[6]. The proposed cascaded
H-bridge multilevel boost inverter uses a standard three-leg
inverter (one leg for each phase) and an H-bridge in series
with each inverter leg which uses a capacitor as the dc power
source [11]–[14]. In this topology, the need for large inductors
is eliminated. A fundamental switching scheme is used to do
modulation control and to output five-level phase voltages.
Experiments show that the proposed dc–ac cascaded H-bridge
multilevel boost inverter without inductors can output a boosted
ac voltage.
II. W
ORKING PRINCIPLE OF CASCADED H-BRIDGE
MULTILEVEL BOOST INVERTER WITHOUT INDUCTORS
The topology of the proposed dc–ac cascaded H-bridge
multilevel boost inverter is shown in Fig. 1. The inverter uses
a standard three-leg inverter (one leg for each phase) and an
H-bridge with a capacitor as its dc source in series with each
phase leg.
0093-9994/$25.00 © 2009 IEEE
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964 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 45, NO. 3, MAY/JUNE 2009
Fig. 1. Topology of the proposed dc–ac cascaded H-bridge multilevel boost
inverter.
Fig. 2. Single phase of the proposed dc–ac cascaded H-bridge multilevel
boost inverter.
To see how the system works, a simplified single phase
topology is shown in Fig. 2. The output voltage ν
1
of this
leg of the bottom inverter (with respect to the ground) is
either +V
dc
/2 (S
5
closed) or −V
dc
/2 (S
6
closed). This leg
is connected in series with a full H-bridge, which, in turn, is
supplied by a capacitor voltage. If the capacitor is kept charged
to V
dc
/2, then the output voltage of the H-bridge can take on
the values +V
dc
/2 (S
1
and S
4
closed), 0 (S
1
and S
2
closed or
S
3
and S
4
closed), or −V
dc
/2 (S
2
and S
3
closed). An example
output waveform from this topology is shown in Fig. 3(a).
When the output voltage ν = ν
1
+ ν
2
is required to be zero, one
can either set ν
1
=+V
dc
/2 and ν
2
= −V
dc
/2 or ν
1
= −V
dc
/2
and ν
2
=+V
dc
/2.
Additional capacitor’s voltage regulation control detail is
shown in Fig. 3. To explain how the capacitor is kept charged,
consider the interval θ
1
≤ θ ≤ π, the output voltage in Fig. 3(a)
is zero, and the current i>0.IfS
1
and S
4
are closed (so that
ν
2
=+V
dc
/2) and S
6
is closed (so that ν
1
= −V
dc
/2), then
the capacitor is discharging [i
c
= −i<0; see Fig. 3(b)], and
Fig. 3. Capacitor voltage regulation with capacitor charging and discharg-
ing. (a) Overall output voltage and load current. (b) Capacitor discharging.
(c) Capacitor charging.
ν = ν
1
+ ν
2
=0. On the other hand, if S
2
and S
3
are closed (so
that ν
2
= −V
dc
/2) and S
5
is also closed (so that ν
1
=+V
dc
/2),
then the capacitor is charging [i
c
= i>0; see Fig. 3(c)], and
ν = ν
1
+ ν
2
=0. The case i<0 is accomplished by simply
reversing the switch positions of the i>0 case for charging and
discharging of the capacitor. Consequently, the method consists
of monitoring the output current and the capacitor voltage, so
that during periods of zero voltage output, either the switches
S
1
, S
4
, and S
6
are closed or the switches S
2
, S
3
, and S
5
are closed, depending on whether it is necessary to charge or
discharge the capacitor. It is this flexibility in choosing how to
make that output voltage zero that is exploited to regulate the
capacitor voltage.
The goal of using fundamental frequency switching modula-
tion control is to output a five-level voltage waveform, with a
sinusoidal load current waveform, as shown in Fig. 3(a). If the
capacitor’s voltage is higher than V
dc
/2, switches S
5
and S
6
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DU et al.: H-BRIDGE MULTILEVEL BOOST INVERTER WITH NO INDUCTORS FOR VEHICLE APPLICATIONS 965
are controlled to output voltage waveform ν
1
, and the switches
S
1
, S
2
, S
3
, and S
4
are controlled to output voltage waveform
ν
2
, shown in Fig. 3(b). The highlighted part of the waveform in
Fig. 3(b) is the capacitor discharging period, during which the
inverter’s output voltage is 0 V.
If the capacitor’s voltage is lower than V
dc
/2, the switches
S
5
and S
6
are controlled to output voltage waveform ν
1
, and
switches S
1
, S
2
, S
3
, and S
4
are controlled to output voltage
waveform ν
2
, shown in Fig. 3(c). The highlighted part of the
waveform in Fig. 3(c) is the capacitor charging period, when
the inverter’s output voltage is 0 V. Therefore, the capacitors’
voltage can be regulated by alternating the capacitor’s charging
and discharging control, when the inverter output is 0 V.
This method of regulating the capacitor voltage depends
on the voltage and current not being in phase. That is, one
needs positive (or negative) current when the voltage is passing
through zero in order to charge or discharge the capacitor.
Consequently, the amount of capacitor voltage the scheme can
regulate depends on the phase angle difference of output voltage
and current. In other words, the highest output ac voltage of the
inverter depends on the displacement power factor of the load.
III. S
WITCHING CONTROL OF CASCADED H-BRIDGE
MULTILEVEL BOOST INVERTER WITHOUT INDUCTORS
There are several kinds of modulation control methods
such as traditional sinusoidal pulsewidth modulation (SPWM),
[15]–[19], space vector PWM [20], harmonic optimization or
selective harmonic elimination [21]–[28], and active harmonic
elimination [29], and they all can be used for inverter modu-
lation control. For the proposed dc–ac boost inverter control,
a practical modulation control method is the fundamental fre-
quency switching control for high output voltage and SPWM
control for low output voltage, which only uses the bottom
inverter. In this paper, the fundamental frequency switching
control is used.
The Fourier series expansion of the fundamental frequency
(staircase) output voltage waveform of the multilevel inverter,
as shown in Fig. 3(a), is
V (ωt)=
4
π
V
dc
2
×
∞
n=1,3,5,...
1
n
(cos(nθ
1
)+cos(nθ
2
)) sin(nωt).
(1)
The key issue of fundamental frequency modulation control
is choice of the two switching angles θ
1
and θ
2
. In this paper,
the goal is to output the desired fundamental frequency voltage
and to eliminate the fifth harmonic. Mathematically, this can be
formulated as the solution to the following:
cos(θ
1
)+cos(θ
2
)=m
a
cos(5θ
1
) + cos(5θ
2
)=0. (2)
This is a system of two transcendental equations with two
unknowns θ
1
and θ
2
, and m
a
is the output voltage index.
Traditionally, the modulation index is defined as
m =
V
1
V
dc
/2
. (3)
Fig. 4. Switching angle solutions for proposed dc–ac cascaded H-bridge
multilevel boost inverter control.
Therefore, the relationship between the modulation index m
and the output voltage index m
a
is
m =
4
π
m
a
. (4)
There are many ways one can solve (2) for the angles. Here,
the resultant method is used to find the switching angles. A
practical solution set is shown in Fig. 4, which is continuous
from modulation index 0.75 to 2.42 [26].
Although it can be seen from Fig. 4 that the modulation
index range for the five-level fundamental frequency switching
control method can reach 2.42, which is double that of the
traditional power inverter, it requires the capacitors’ voltage to
be kept constant at V
dc
/2.
Traditionally, the maximum modulation index for the linear
operation of a traditional full-bridge bilevel inverter using
SPWM control method is 1 (without third harmonic compen-
sation) and 1.15 (with third harmonic compensation, and the
inverter output voltage waveform is an SPWM waveform, not
a square waveform). With the cascaded H-bridge multilevel
inverter, the maximum modulation index for linear operation
can be as high as 2.42; however, the maximum modulation
index depends on the displacement power factor, as will be
shown in the next section.
IV. O
UTPUT VOLTAGE BOOST
As previously mentioned, the cascaded H-bridge multilevel
inverter can output a boosted ac voltage to increase the output
power, and the output ac voltage depends on the displacement
power factor of the load. Here, the relationship of the boosted
ac voltage and the displacement power factor is discussed.
It is assumed that the load current displacement angle is ϕ,
as shown in Fig. 5. To balance the capacitor voltage, the net
capacitor charging amount needs to be greater than the pure
discharging amount. That is, to regulate the capacitor’s voltage
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966 IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS, VOL. 45, NO. 3, MAY/JUNE 2009
Fig. 5. Capacitor charging and discharging cases.
with a fundamental frequency switching scheme, the following
must be satisfied:
π
0
i
charging
dθ −
π
0
i
discharging
dθ > 0. (5)
The charging and discharging of the current with an induc-
tance load can be classified into three cases. The fundamental
of the inductive load current is given by
i = I sin(ωt − ϕ) (6)
and the displacement power factor is
pf =cos(ϕ). (7)
The three cases are as follows.
1) 0 ≤ ϕ ≤ θ
1
ϕ
0
|i| dθ +
θ
1
ϕ
idθ+
π
π−θ
1
idθ−
π−θ
2
θ
2
idθ >0. (8)
2) θ
1
<ϕ≤ θ
2
θ
1
0
|i| dθ +
π
π−θ
1
idθ−
π−θ
2
θ
2
idθ >0. (9)
3) θ
2
<ϕ≤ π/2
θ
1
0
|i| dθ +
π
π−θ
1
idθ−
π−θ
2
θ
2
idθ >0. (10)
Combining (6)–(10), it can be concluded that, for 0 ≤
ϕ ≤ θ
1
pf ≤
π
4m
(11)
and, for θ
1
<ϕ≤ π/2.
pf ≤ cos
tan
−1
cos(θ
2
)
sin(θ
1
)
. (12)
Therefore, the conditions for the fundamental frequency
switching scheme to eliminate the fifth harmonic and to regulate
the capacitor’s voltage are (11) and (12).
Fig. 6. Minimum phase displacement angle.
Fig. 7. Displacement power factor and output voltage modulation index.
For practical applications, direct use of (11) and (12) is not
convenient. Using minimum phase displacement angles is a
more convenient way to use (11) and (12). That means that,
if the phase displacement angle is greater than the minimum
angle, the voltage can be regulated anyway.
Fig. 6 shows the minimum phase displacement angle com-
puted by (5)–(12). From the figure, it can be seen that, for mod-
ulation index range m<1.27 (the inverter output is a five-level
waveform, not a bilevel or square waveform), the minimum
phase angle displacement is zero, which means that the capaci-
tor’s voltage can be regulated for all displacement power factors
in this modulation index range. For modulation index range
m>1.27, the required minimum phase displacement angle is
shown in Fig. 6. Fig. 6 also shows the two switching angles.
The phase displacement power factor versus the output volt-
age modulation index is shown in Fig. 7.
It can be derived from Fig. 7 that the highest output voltage
modulation index depends on the displacement power factor.
The inverter can regulate the capacitor’s voltage with a dis-
placement power factor of one if the modulation index is below
1.27; if the modulation index is above 1.27, the displacement
power factor must be less than a specified amount. For practical
applications, the highest output voltage is determined when the
load is determined.
As mentioned previously, there are many methods to do
modulation control for the proposed dc–ac cascaded H-bridge
multilevel boost inverter without inductors. The fundamental
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