A Seven-Level Converter Using a Combination of
Staircase and PWM Switching Methods
Hossein Sepahvand, Mehdi Ferdowsi, and Keith A. Corzine
Missouri University of Science and Technology
Rolla, MO 65409 USA
Abstract- In this paper, a new method is proposed for
switching a multilevel converter. In this converter two HBridge cells are connected in series with each phase of a
three-phase diode-clamped converter. Operation of main
converter and one of H-Bridge cells is based on the
staircase switching method. Switching angles of the three
phase converter and one of the H-Bridges are selected in a
way to generate the fundamental harmonic of the phase
and eliminate the fifth and seventh harmonics. However,
the switching pattern of the second H-Bridge cell is based
on PWM method. This cell generates the remaining parts
of the desired sinusoidal waveform. Combination of these
converters and their switching methods results in an
output waveform with low harmonics. Simulation and
experimental results agree with each other and show the
proper operation of the proposed method.
I INTRODUCTION
Multilevel converters are formed by combining two or
more separate voltage sources to synthesize single or threephase (commonly sinusoidal) voltage waveforms [1]. In
general, by increasing the number of levels, the synthesized
voltage waveform becomes closer to its sinusoidal reference.
This leads to reduced harmonic distortions when compared
with conventional converters. In addition, multilevel
converters benefit from other advantage such as low
electromagnetic emissions, high efficiency, lower voltage
stress on switches, and modularity [1-6]. Furthermore, due to
high VA (volt-amp) ratings of multilevel converters, they are
one of the best choices for electric motor drives in hybrid
power-trains [2, 3, 7, 8]. The cascaded H-Bridge multilevel
converter consists of two or more H-Bridge cells connected in
series. This type of converter has been applied to high-power
and high-quality applications including static VAR generation
(SVG) [9, 10], active filters, reactive power compensators
[11], photovoltaic power conversion [10, 12], and
uninterruptable power supplies (UPS).
In this paper, a seven-level converter is investigated. First,
a three-phase diode-clamped converter is used as main
converter. Then, each phase of the main converter is cascaded
with two H-Bridge cells. The main converter and the first HBridge generate a staircase waveform. Their switching angles
are selected in a way to eliminate the fifth and seventh
harmonics of the output voltage. In addition these two
converters generate the fundamental harmonic of each phase.
The second H-Bridge which operates based on a PWM
978-1-4244-5226-2/10/$26.00 ©2010 IEEE
method generates the subtraction of the reference signal
(sinusoidal waveform) and the waveform that the main and
first H-Bridge converters generate. The task of this converter
is to eliminate the remaining low frequency harmonics
generated in the first two converters and it does not contribute
in generating the fundamental harmonic of the output.
Therefore the voltage source of this converter can be replaced
with a capacitor voltage source.
Furthermore, in this topology if the second H-bridge cell of
a phase is out of the circuit there will not be any change in the
fundamental harmonic of that phase. Therefore if any fault
happens in the second H-bridge cell it can be removed from
the active circuit with the bypass circuit.
In this paper the proposed method is described and
switching angles are chosen in a way to eliminate the fifth
and seventh harmonics of the output voltage waveform. Then
simulation results using MATLAB/Simulink are provided.
Finally, the experimental results of the proposed method are
presented.
II TOPOLOGY AND SIMULATION OF THE SEVEN LEVEL
CONVERTER
Inverter topology which is used in this paper consists of
two cascaded H-bridge cells per phase and one three-phase
staircase inverter. The topology of the seven-level inverter is
shown in Fig. 1. In this topology, the main converter is a
three phase inverter fed with a dc voltage of 4 . Each phase
2301

V


V3a
Vdc


V2a
Vdc

4Vdc

a
Vb

V

c

Vdc
V3b V
dc
V3c

Vdc
V2b

V2c

 Vdc
V1a
Fig. 1. Topology of the converter


90
80

3
70
 1, 2, and  3
60
50

2
40

30
1
20
10
1.147
0
1
1.852
1.488
1.2
1.4
1.6
2.523
1.8
2
2.2
2.4
2.6
Modulation Index (m)
Fig. 3. Solutions for the switching angles when the elimination of the fifth
and seventh harmonics is intended
Fig. 2. Staircase output voltage waveform made by combination of
main converter and H-bridge1
of the main converter is connected in series with two Hbridges to form the final voltage of each phase of the multilevel converter. The voltage sources feeding the two Hwhich is one fourth of the
bridges are chosen to be
voltage source of the main converter. The output of the
second H-bridge cell in each phase is connected in parallel
with a bypass circuit. This bypass circuit removes the second
H-bridge cell when any fault happens on this H-bridge cell.
The main converter and the first H-bridge (H-bridge1) in
each phase operate in the staircase waveform generation
mode. However the second H-bridge (H-bridge2) of each
phase operates in PWM. Switching angles of the main and the
first H-bridge are selected in a way to eliminate the fifth and
seventh harmonics of the synthesized voltage. The sum of the
output waveforms of the main inverter and H-bridge1
) for phase a is shown in Fig. 2.
(
Since in a three-phase system, the third harmonics is
naturally canceled; therefore, switching angles can be chosen
to eliminate the fifth and seventh harmonics. In the other
words, the solution of the following system of equations
yields the desired modulation index and eliminates the fifth
and seventh harmonics in the output voltage waveform of the
first two converters (i.e. main and H-bridge cells). Nonlinear
system of equations for elimination of the fifth and seventh
harmonics is as follow:
5
7
5
7
5
7
,
,
4
∞ 1
cos
, , ,..
sin nωt
cos
(1)
where , , and
are switching angles of the output
voltage waveform. Equation (1) consists of three variables
, and
) which can be chosen to satisfy three
( ,
conditions. Since it is required to generate an output voltage
waveform which has variable amplitude in its fundamental
harmonic, one of the variables is already committed.
Therefore, it is possible to satisfy two other conditions with
the remaining variables.
(2)
here m denotes the modulation index and is defined as
4
A. Elimination of the Fifth and Seventh Harmonics
The Fourier series expansion of the staircase output voltage
waveform which is shown in Fig. 2 is [6, 13, 14]:
0
0
(3)
where
is the peak voltage of the desired fundamental
frequency of the converter.
In order to solve the system of equations in (2), several
approaches, including resultant theory, have been proposed
[13, 15, 16]. In addition to the discussed methods, one can
use MATLAB nonlinear solvers to solve these nonlinear
systems of equations. This method can be used without
dealing with the complexity of the previously proposed
methods [13, 15, 16]. The results are depicted in Fig. 3 [6].
As it is shown, when m is between 1.488 and 1.852, two sets
of solutions exist.
B. Switching Fundamentals of H-bridge2
The reference for PWM switching of H-Bridge2 is
generated by subtracting the sum of output waveforms of the
main inverter and H-Bridge1 from the desired sinusoidal
waveform (reference). The amplitude of sinusoidal waveform
2302
(a)
V 1 a (V)
100
0
-100
0.01
V 2 a (V)
V 1 a +V 2 a (V)
0.01
0.02
0.03
0.02
0.03
0.02
0.03
0.02
0.03
0.02
0.03
(c)
100
0
-100
PWM Ref (V)
V 3 a (V)
0.03
0
-40
0.01
(d)
40
0
-40
0.01
(e)
40
0
-40
0.01
(f)
100
V a (V)
0.02
(b)
40
0
-100
0.01
time (s)
Fig. 4. Simulation results (a) Main converter output, (b) H-bridge1 output, (c) desired sinusoidal waveform and sum of the main and H-bridge1
converters, (d) PWM reference waveform of H-bridge2, (e) H-bridge3 output, (f) total converter output waveform
( ) is equal to the amplitude of the fundamental harmonic of
the sum of the voltages generated by the main inverter and H). In the other word, the main and the first
bridge1 (
H-Bridge make a staircase waveform and the second HBridge makes the rest of a sinusoidal waveform. By choosing
this reference for H-Bridge2, this H-bridge will have no
contribution in generation of the fundamental harmonic of the
output of the corresponding phase. Note that if the H-bridge2
is bypassed at least 5th and 7th harmonics are still eliminated
in the output of the corresponding phase.
The converter is simulated in MATLAB/Simulink to verify
the operation of the proposed method. Fig. 4 shows the output
waveforms of all inverters. In Fig. 4(a) and (b) the output
waveform of the main and H-bridge1 converters are shown,
respectively. The desired sinusoidal waveform and sum of the
voltages generated by the main and H-bridge1 converters
) are shown in Fig. 4(c). Note that based on the
(
desired amplitude of the output waveform, modulation index
can be found and by using (2) and Fig. 3 the switching angles
for the main and H-bridge1 converters can be obtained. The
difference between the desired output waveform and (
) is shown in Fig. 4(d). In Fig. 4(e) and (f), the output of
H-Bridge2 and the total output of the converter are shown,
respectively.
III EXPERIMENTAL RESULTS
In order to verify the simulation results, a hardware
prototype of the system is developed. The voltage source of
the main converter is 120 V and 30 V voltage sources are
used for H-bridge1 and H-bridge2 cells. The control scheme
is implemented in a TMS320F2812 digital signal processor
(DSP) which is connected to the IGBTs using fiber optic
cables. The switching frequency for H-bridge2 is 6 kHz.
Experimental result for the converter when m is equal to
2.137 is shown in Fig. 5. In this figure, the top waveform is
the output of phase a of the converter ( ). The middle
waveform is the summation of the voltage generated by the
). The waveform in
main and H-bridge2 converters (
the bottom of the Fig. shows the output waveform of Hbridge2 ( ).
IV CONCLUSION
In this paper, a new method to implement and control a
multilevel converter is proposed. In the proposed topology,
two H-Bridge cells are connected in series with each phase of
a three-phase conventional converter. Operation of main
converter and one of H-Bridges is based on the staircase
switching method and the three switching angles are chosen
in a way to eliminate the fifth and seventh harmonics. The
second H-Bridge cell generates the remaining parts of the
desired sinusoidal waveform. Combination of these
2303
(a )
0
1a
V +V
2a
(V)
100
-100
0. 01
0. 02
(V)
40
0. 04
0. 03
0. 04
0. 03
0. 04
0
V
3a
0. 03
(b)
-40
0. 01
0. 02
(c )
0
a
V (V)
100
-100
0. 01
Fig. 5. Experimental results (a)
0. 02
time (s )
, (b) H-bridge2 output waveform, and (c) output waveform of phase a of the converter
converters and their switching methods results in an output
voltage waveform with low harmonics. Simulation and lab
result show the proper operation of proposed method.
REFERENCES
[1]
J.-S. Lai and F. Z. Peng, “Multilevel converters-a new breed of power
converters,” Industry Applications, IEEE Transactions on, vol. 32, no.
3, pp. 509 –517, may/jun 1996.
[2]
C. Cecati, A. Dell’Aquila, M. Liserre, and V. Monopoli, “Design of hbridge multilevel active rectifier for traction systems,” Industry
Applications, IEEE Transactions on, vol. 39, no. 5, pp. 1541 – 1550,
sept.-oct. 2003.
[3]
L. Tolbert, F. Z. Peng, and T. Habetler, “Multilevel converters for large
electric drives,” Industry Applications, IEEE Transactions on, vol. 35,
no. 1, pp. 36 –44, jan/feb 1999.
[4]
J. Chiasson, L. Tolbert, K. McKenzie, and Z. Du, “A new approach to
solving the harmonic elimination equations for a multilevel converter,”
in Industry Applications Conference, 2003. 38th IAS Annual Meeting.
Conference Record of the, vol. 1, oct. 2003, pp. 640 – 647 vol.1.
[5]
[6]
L. Franquelo, J. Rodriguez, J. Leon, S. Kouro, R. Portillo, and M. Prats,
“The age of multilevel converters arrives,” Industrial Electronics
Magazine, IEEE, vol. 2, no. 2, pp. 28 –39, june 2008.
H. Sepahvand, M. Khazraei, M. Ferdowsi, and K. Corzine, “Feasibility
of capacitor voltage regulation and output voltage harmonic
minimization in cascaded h-bridge converters,” in Applied Power
Electronics Conference and Exposition (APEC), 2010 Twenty-Fifth
Annual IEEE, feb. 2010, pp. 452 –457.
[7]
M. Carpita, M. Marchesoni, M. Pellerin, and D. Moser, “Multilevel
converter for traction applications: Small-scale prototype tests results,”
Industrial Electronics, IEEE Transactions on, vol. 55, no. 5, pp. 2203–
2212, may 2008.
[8]
F. Khoucha, S. Lagoun, K. Marouani, A. Kheloui, and M. El Hachemi
Benbouzid, “Hybrid cascaded h-bridge multilevel-inverter inductionmotor-drive direct torque control for automotive applications,”
Industrial Electronics, IEEE Transactions on, vol. 57, no. 3, pp. 892 –
899, march 2010.
[9]
G. Joos, X. Huang, and B.-T. Ooi, “Direct-coupled multilevel cascaded
series var compensators,” Industry Applications, IEEE Transactions
on,vol. 34, no. 5, pp. 1156 –1163, sep/oct 1998.
[10] P. Flores, J. Dixon, M. Ortuzar, R. Carmi, P. Barriuso, and L. Moran,
“Static var compensator and active power filter with power injection
capability, using 27-level inverters and photovoltaic cells,” Industrial
Electronics, IEEE Transactions on, vol. 56, no. 1, pp. 130 –138, jan.
2009.
[11] J. Dixon, L. Moran, J. Rodriguez, and R. Domke, “Reactive power
compensation technologies: State-of-the-art review,” Proceedings of the
IEEE, vol. 93, no. 12, pp. 2144 –2164, dec. 2005.
[12] A. Beig, U. Kumar, and V. Ranganathan, “A novel fifteen level inverter
for photovoltaic power supply system,” in Industry Applications
Conference, 2004. 39th IAS Annual Meeting. Conference Record of the
2004 IEEE, vol. 2, oct. 2004, pp. 1165 – 1171 vol.2.
[13] Z. Du, L. Tolbert, J. Chiasson, and B. Ozpineci, “A cascade multilevel
inverter using a single dc source,” in Applied Power Electronics
Conference and Exposition, 2006. APEC ’06. Twenty-First Annual
IEEE, March 2006, p. 5 pp.
[14] J. Liao, K. Wan, and M. Ferdowsi, “Cascaded h-bridge multilevel
inverters -a reexamination,” in Vehicle Power and Propulsion
Conference, 2007. VPPC 2007. IEEE, Sept. 2007, pp. 203 –207.
[15] J. Chiason, L. Tolbert, K. McKenzie, and Z. Du, “Elimination of
harmonics in a multilevel converter using the theory of symmetric
polynomials and resultants,” Control Systems Technology, IEEE
Transactions on, vol. 13, no. 2, pp. 216 – 223, march 2005.
[16] L. Tolbert, J. Chiasson, Z. Du, and K. McKenzie, “Elimination of
harmonics in a multilevel converter with nonequal dc sources,”
Industry Applications,, IEEE Transactions on, vol. 41, no. 1, pp. 75 –
82, Jan.-Feb. 2005.
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