Hybrid Cascade Multilevel Inverter Using a
Single DC Source for Energy Quality
V. Fernão Pires * д, J. Fernando Silva д and P. Rodrigues,

Instituto Superior Técnico / Univ. Técnica de Lisboa, Lisboa, Portugal
Sup. Tecnologia Setúbal / Inst. Politécnico Setúbal, Setúbal , Portugal
д
CIEEE, Lisboa, Portugal
* Escola
Abstract— In this document a new hybrid multilevel
inverter using a single DC source for Energy Quality is
proposed. This power converter uses one three phase bridge
inverter and three single-phase inverters. However, this
topology uses only one DC source and three capacitors. Due
to the type of the topology, this power converter works as
three single-phase inverters. In order to maximize the
inverter output voltage levels there is an asymmetry
between the amplitude of the three phase bridge inverter
DC source and the single-phase inverters’ capacitors’
voltages. To control the three-phase inverter a SPWM
modulator is used. Since the three single-phase inverters do
not have DC sources an algorithm is required to maintain
the capacitor voltage balanced. In this work a sliding mode
control based approach is used to control the capacitor
voltage of the single-phase inverters. In order to verify the
proposed topology and proposed system converter, several
simulation results are presented.
Index Terms— Hybrid multilevel inverter, single DC
source, sliding mode controller, power converter.
I. INTRODUCTION
In recent years multilevel inverters have become a very
interesting field of study in what regards their industrial
application. This converter type allows for synthesizing of
a sinusoidal voltage waveform starting from several levels
of dc voltages. However, besides that advantage there are
other important advantages such as reduced switching
losses, low dv/dt’s and reduced common mode voltages.
Due to these characteristics several multilevel inverter
topologies have been developed and studied [1-2]. The
majority of applications for these multilevel inverters can
be found in electric vehicles, interfaces for renewable
energies, manufacturing plants and energy conversion.
The diode-clamped multilevel converter is one of the
most used multilevel topologies. This power converter
consists of two capacitor voltages in series and uses the
central tap as the neutral [3-5]. However, this power
converter needs a complex control system in order to
balance the capacitor voltages. The flying capacitor
converter is another of the important multilevel topologies
[6-9]. This multilevel structure does not need clamping
diodes, but still has dc-link voltage unbalancing problems.
The third important multilevel topology is the cascade Hbridge inverter [10-13]. This last multilevel inverter has
become very important due to its modular structure and
easiness of operation. Another advantage is that does not
have the voltage balancing problems common to dc
capacitors of diode-clamped or flying multilevel inverter.
However, this topology has an important disadvantage
related with the required number of isolated dc sources. In
order to maximize the number of the inverter output
voltage levels, the amplitude of all DC sources devoted to
supply the H-bridge cells must obey a certain relation
[14].
A multilevel power converter with the structure of the
cascade H-bridge inverter, but using only one DC source,
was also proposed [15-18]. This topology uses an Hbridge with a dc source and another H-bridge where the dc
voltage source is only a capacitor.
In this paper, instead of a classical multilevel inverter, a
hybrid multilevel inverter with a single DC source is
proposed. The proposed topology includes a three-phase
H-bridge inverter supplied by a dc voltage and three
single-phase H-bridge inverters with a capacitor as DC
voltage supply. To maximize the output voltage levels of
the hybrid multilevel inverter, the single-phase inverters’
voltage is half the value of the three-phase bridge inverter
DC source. To control this multilevel structure two control
loops are used. For the three-phase H-bridge inverter a
SPWM modulator, controlled by a proportional-integral
(PI) controller, is used to control the d component of the
three-phase currents. For the single-phase H-bridge
inverters a sliding mode controller (to maintain the
capacitor voltage near the required value), and a simple
integral controller for the q component of the three-phase
currents are used.
This paper is organized in five sections. Besides this
introduction, the proposed topology of the hybrid
multilevel inverter using a single DC source is presented
in section II. The control system for the proposed
multilevel inverter is described in section III. Several
simulation results of the power converter (with the
correspondent control system) are presented in section IV.
In section V the conclusions of this work are presented.
II. HYBRID MULTILEVEL TOPOLOGY USING A SINGLE DC
SOURCE
The classical multilevel inverter consists of one threephase H-bridge inverter supplied by a DC voltage source
and three single-phase H-bridge inverters, also supplied
by a DC voltage source.
The new topology proposed, uses only one dc source
and three capacitors for the single phase H-bridge
inverters (Fig. 1). For each arm of hybrid multilevel
inverter the voltage output is the sum of two output
voltages from both inverters: the three-phase inverter
voltage and the correspondent single-phase voltage in that
arm. In this way, it is possible to use a hybrid multilevel
inverter without using more bridge inverters, more power
switches or more power sources. This topology can also
work as three single-phase multilevel inverters.
T
T
1
1
vPWM dt   v1 dt

T 0
T 0
(2)
Using equation (1) in (2), the control relation is
obtained (3).



T

1
  vPWM  K vC ref  vC iL dt  L iL t   0 (3)
T 0

In order to implement this controller, equation (3) can
be considered the sliding surface of a sliding mode
controller, where the switching law can be implemented
using two hysteretic comparators. The difference between
the capacitors voltages output and its reference will have
an error, eV, and will serve as a control variable for the
switches from the single-phase inverters in order to
reduce/eliminate this error. Equation 5 shows this error
relation. In order to have stability in the system, the error
needs to fulfill the condition:
Fig. 1.Proposed hybrid multilevel inverter with a single DC source.
The single-phase H-bridge inverter capacitor voltages
are maintained close to VDC/2, which optimizes the
number of different levels generated by the inverter. In
this way, the inverter generates seven different voltage
levels.
III.
CONTROL STRATEGY
ev
deV
0
dt
(4)
The error condition will follow the hysteretic
comparators limits to switch on or off the semiconductors
from the single-phase inverter. Two limits were chosen,
where ε1 is bigger than ε2. This procedure will be able to
charge and discharge the capacitors according to
difference between capacitor voltage and reference.



The proposed multilevel inverter will be controlled by
suitable controllers (for the single-phase and the threephase inverters) to ensure tracking of the d. q components
of the three-phase current references (idref, iqref).
T

1
  vPWM  K vCref  vC iL dt  L iL t   eV
T 0

A. Single-phase bridge inverters
The single-phase bridge inverters can not supply active
power, only reactive power, since their dc supply
capacitor voltages must be almost constant. Since only
reactive power can be supplied, the single-phase inverter
will be considered to be behaving as a negative (or
positive) inductor L. In order to ensure that the capacitor
voltage is constant, a virtual resistor rL (representing the
losses of the inverter) should be considered. This resistor
value must be proportional to the difference between the
capacitor voltage reference vCref and the capacitor voltage
vC. The virtual resistor is given by rL=K(vCref - vC), where
K is a chosen constant, inversely proportional to the
inverter current iL maximum magnitude. According to this
consideration, the AC output voltage v1 fundamental
component of the single-phase inverter is expressed as:
Since the single-phase inverter will be controlled to
behave as an inductor L, the needed iqref error must define
the L value present in (3). To obtain a suitable L value
controller, it is considered that AC currents must be
sinusoidal (with magnitude slowly varying in time,
regarding the period T) with iq= LG(s), where G(s) is the
converter transfer function. Therefore, a relatively slow
first order system (with time constant tp) is needed:
v1  L


diL
di
 rL iL  L L  K vCref  vC iL
dt
dt
(1)
iq
iqref

i i
1
G 1 ( s)
iqref  iq 
 iq  qref q  L 
1  st p
st p
st p
(5)
(6)
Considering, for simplicity, that G(s)=10-3, the previous
equation results in an integral controller (Fig. 2). This
simplification is considered, since the variable L must
change slowly, and feedback ensures some gain
insensitivity. In this way, the time constant tp must be
bigger than 20 ms.
Considering vPWM the three-level PWM inverter
voltage, in order to achieve the desired converter voltage
the following relation must be achieved:
Fig. 2. Block diagram of the iq current loop.
B. Three-phase bridge inverter
The id component error will control the modulation
index m of the SPWM used in the three-phase inverter,
through the use of a PI compensator [21-22].
The block diagram of the system controller (related
with the id component) is presented in Fig. 3. The first
block represents the PI controller, the second one the
power converter (and correspondent modulator) and the
third one is the load, assumed inductive for simplification
purposes.
Fig. 3. Block diagram of the id current loop.
Fig. 4. Result of the output voltage waveform.
From the closed loop transfer function (Fig. 3), the
parameters of the PI controller can be obtained. Equations
(7) and (8) provide these parameters, which allow for
cancelling of the load pole with the PI’s zero. 2 /2 is
used as the required damping factor of the resulting
second order system.
KP 
Lo
2 K td
(7)
KI 
Ro
2 K td
(8)
IV.
R ESULTS
To evaluate the dynamic performances of the proposed
hybrid cascaded multilevel inverter and the control
system, numerical simulations have been carried-out. The
parameters of the simulated system are presented in
table I.
Fig. 5. Result of the output currents waveforms.
The output voltage of the proposed multilevel inverter
is presented in Fig. 4. As can be seen in this figure, the
output voltage has seven levels. This is achieved due to
the relation between the amplitude of the DC voltage
source and the capacitors’ voltage. The DC voltage of the
capacitors is regulated to half the value of the DC source
voltage. Fig. 5 shows the three-phase output currents
waveforms. From this result it is possible to verify that the
multilevel inverter provides near-sinusoidal currents. The
capacitor voltage as a function of time is plotted in Fig. 6.
This result shows that the capacitor voltage is balanced.
TABLE I
PARAMETERS OF THE SYSTEM
Description
DC Source voltage
Capacitor voltage reference
Frequency
Capacitor
Load inductor
Load resistor
Value
400 V
200 V
50 Hz
10 mF
5 m
10 Ω
Fig.6. Result of the capacitor voltage waveforms.
In order to verify the transient response of the
system, simulations for a sudden change on the output
currents have been made. Figs. 7-9 show the obtained
results for a current decrease of 30% in 0.1 s. Fig. 7 shows
the obtained output voltage waveform. The output
currents waveforms are presented in Fig. 8. From this
result it is possible to verify that the currents’ amplitude
change for the desired value. This result also shows that
the current distortion is almost the same. The capacitor
voltage waveform is presented in Fig. 9. This result shows
that the capacitor voltage is always regulated even for
transient responses. The ripple of the capacitor voltage is
reduced, which also happens to the amplitude of the
output currents. As can be seen by these results, the
proposed control system is stable for different conditions.
The proposed control system also allows for the
obtainment of fast regulation with capacitor voltage
balancing.
Fig.9. Result of the capacitor voltage waveforms for a change in the
current reference.
V. CONCLUSIONS
Fig.7. Result of the output voltage waveform for a change in the current
reference. (reduz a corrente em 30%)
A hybrid cascade multilevel inverter using a single DC
source has been proposed in this paper. In the proposed
scheme a three phase bridge inverter (supplied by a DC
source and three single phase bridge inverters) is used.
Due to the design of this topology, this multilevel inverter
can work as three single phase power converters. The
voltage amplitude of the DC source doubles the singlephase inverter capacitor voltages. This allows for
maximizing of the inverter output voltage levels. To
control the multilevel inverter, suitable controllers for the
three inverter and single phase inverters were used. For
the three-phase inverter, the classical SPWM was used. A
sliding mode approach was used to regulate the singlephase inverters’ capacitor voltage. From the obtained
results it was possible to verify the effectiveness of the
proposed topology and system controller.
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