Journal of Scientific & Industrial Research
Vol. 73, March 2014, pp. 168-172
Low Order Harmonic Reduction of Three Phase Multilevel Inverter
A. Maheswari1 and I. Gnanambal2
1
Department of EEE, K.S.R College of Engineering, Tiruchengode, Tamilnadu
Department of EEE, Government College of Engineering, Salem, Tamilnadu
2
Received 11 August 2012; revised 09 September 2013; accepted 02 January 2014
In this paper, a cascaded H-Bridge multilevel inverter has been proposed using unequal dc power sources and less
number of switches. A standard cascaded multilevel inverter requires h number of dc sources for (2h + 1) levels. This
proposed scheme allows less number of unequal DC power sources without the requirement of transformers. Cascaded HBridge multilevel inverter fed induction motor shows the better performance due to fundamental frequency switching
scheme. High quality output is derived due to the absence of lower order harmonics. High conversion efficiency is also
achieved for induction motor drive when it is operated with the proposed inverter. The performance of three phase cascaded
H-Bridge multilevel inverter with unequal dc sources is simulated by using MATLAB platform. Harmonic analysis is done
on cascaded H-Bridge seven level inverter and experimental results are presented to demonstrate the superiority of the
proposed system.
Keywords: Fundamental frequency switching scheme, multilevel inverter, Total Harmonic Distortion (THD),
Unequal dc sources.
Introduction
The recent development in solid-state electronics
are widely used in industries to control motor drives,
power systems, switched mode power supplies
(SMPS),auto motives, etc. The inverter is one of the
most extensive assemblies in power electronics. The
main aspects for the development of multilevel
inverters are multilevel voltage waveform; low total
harmonic distortion (THD) and division of voltage to
the switching devices1. Multilevel inverters have
received high attention because of their reliable
operation, high efficiency and low electromagnetic
interference (EMI). The desired output of a multilevel
converter is synthesized by several sources of dc
voltages. With an increasing number of dc voltage
sources, the inverter output voltage approaches nearly
sinusoidal waveform while adopting a fundamental
frequency switching scheme. Transformers less
multilevel inverters are uniquely suited for this
application because of the high VA ratings is possible
with this inverters2-4. Structure of the multilevel
voltage source inverters allows them to reach high
voltages with low harmonics without the use of
transformers or series-connected synchronized
switching devices. Multilevel inverters also have
——————
*
Author for correspondence
Email: dramaheswari@gmail.com
several advantages with respect to hard switched two
level pulse width-modulation (PWM) based inverter
fed variable-speed drives. Motor damage and failure
have been reported by industry as a result of some
variable-speed drives operated by the inverters which
has high voltage change rates (dv/dt), which produced
a common-mode voltage across the motor windings.
High frequency switching creates many problems
because of common-mode voltage is impressed
numerous times upon the motor at each cycle. The
main problems of high frequency switching are
“failure of motor bearing” and “insulation breakdown
in motor winding” because of dielectric stresses,
circulating currents, voltage surge and corona
discharge5, 6. Multilevel inverters can be able to
overcome these problems because their individual
devices have a much lower stress per switching
action. They can also operate at high efficiencies,
because they can switch at a much lower frequency
than traditional PWM based inverters.
There are variety of topologies are available in
multilevel inverters. They are diode-clamped, flying
capacitor and H-bridge cascaded multilevel inverters.
Compared with diode-clamped multilevel inverter and
flying capacitor multilevel inverter, the cascaded
inverter needs less number of components and simple
control methods. In the high voltage fields, the
cascaded multilevel inverters are widely used. The
MAHESHWARI & GNANAMBAL: LOW ORDER HARMONIC REDN OF INVERTER
advantages of cascaded multilevel inverters are good
output waveform and low switching stress. Its
structure is suitable for modularization. Now a day,
the existing PWM inverters are replaced by cascaded
multilevel inverters. In the multilevel inverters,
cascaded H-bridge multilevel inverter with unequal dc
voltage sources is preferred, because it does not get
affected from capacitor voltage balancing problems7-9.
This paper presents a new topology of seven level
inverter which uses less number of unequal
dc sources, switching devices and eliminates the need
of capacitors. In this proposed work, a novel method
is given to compute the switching angles for a
multilevel inverter so as to produce the required
output voltage while at the same time cancel
out specified higher order harmonics. Particularly,
a complete analysis is given for a seven level
inverter and validated the performance with the
hardware results.
Cascaded H- Bridge Multilevel Inverter Topology
A cascaded multilevel inverter consists of a series
of H-bridge (single-phase full-bridge) inverter cells.
The general function of a multilevel inverter is to
synthesize a desired voltage from the separate dc
sources. A single phase structure of cascaded
asymmetric multilevel inverter is constructed with
two H-bridges. The ac output of each level is
connected in series such a way that the synthesized
voltage waveform is the sum of the H- bridge
outputs10.For the asymmetric multilevel inverter, the
value of the each dc source and voltage level is
obtained as follows:
Vk =2(k-1) Vdc k=1,2,…h
… (1)
NL=2(h+1) 1
… (2)
Where, Vk and NL denote the value of each dc
source and number of output voltage levels. By
having different values of dc sources, any number of
voltage levels can be obtained at the output.The
general function of a multilevel inverter is to
synthesize a desired voltage from the separate dc
sources, which may be obtained from fuel cells,
batteries or ultra capacitors11, 12. Symmetric multilevel
inverter requires 12 switching devices to produce
seven level output voltage whereas asymmetric
multilevel inverter uses only 8switching devices for
the same output voltage levels. This is the advantage
of the asymmetric topology over the symmetric
topology. However, this kind of multilevel inverter
169
requires dc voltage sources with different values,
providing of the dc voltage sources with different
values which is a challenging issue.
By opening and closing the switches of bridge-1
properly, the output voltage of bridge-1 can be made
equal to −Vdc, 0, or Vdc, while the output voltage of
bridge-2 can be made equal to – (Vdc/2), 0 or (Vdc/2).
Therefore, the output voltage of the inverter can have
the following values –(1.5Vdc,)–(Vdc,)–(0.5Vdc), 0,
0.5Vdc,Vdc, 1.5Vdc, which forms seven levels at the
output voltage.With enough levels, the proposed
fundamental frequency switching technique results in
an output voltage of the inverter is almost sinusoidal.
Quasi-square waveform is generated by phase shifting
its positive and negative phase leg switching timings.
By using this switching method, current stress of the
active devices is made equal.
Switching Angles
Pulse width modulation control or space vector
PWM methods are widely used techniques in the
inverter control. These conventional methods will
cause extra losses due to high frequency switching.
To overcome this problem, low switching control
methods is used. In this proposed method,
fundamental frequency switching is used. Output
voltage of the waveform can be evaluated by Fourier
series expansion. It is clear that 5th and 7th
order harmonic can be eliminated by solving the
equations (3) to (5). The triplen harmonics will be
cancelled automatically in the three phase system. In
this case, the desire is to cancel the 5th and 7th order
harmonics as they tend to dominate the total harmonic
distortion. Mathematically, the statement of these
conditions is then
Cos (θ1) + Cos (θ2) + Cos (θ3) =V1
… (3)
Cos (5θ1) + Cos (5θ2) + Cos (5θ3) =0
… (4)
Cos (7θ1) + Cos (7θ2) + Cos (7θ3) =0
… (5)
Three transcendental equation set can be solved to
get the three unknowns θ1, θ2 and θ3. V1 is the desired
fundamental voltage. The widely used methods are
resultant theory, iterative method such as the NewtonRaphson method. MATLAB nonlinear solver can also
be used to solve the above set of equations. Among all
the methods, resultant theory which produces possible
solutions is selected to find the solutions of the above
set of equations13-15. The transcendental equations
characterizing the harmonic content can be converted
170
J SCI IND RES VOL 73 MARCH 2014
into polynomial equations. The resultant method is
used to find the solutions when they exist. Total
harmonic distortion (THD) is calculated for the
arrived set of solutions to select the set which
generate the lowest harmonic distortion (mostly due
to the 5th and 7th harmonics). The quality of the
multilevel waveform depends on the selection of
switching angles. Varying the switching angle also
controls the magnitude of RMS value of output
waveform and affects the total harmonic distortion.
Simulation Study
The simulation of three phase seven level cascaded
H-Bridge multilevel inverter fed three phase induction
motor was done using MATLAB/Simulink. In the
simulation study all the switches are considered to be
ideal. The frequency of the output voltage is 50 Hz.
In this proposed multilevel inverter, only eight power
switches with two dc sources are required to obtain
the required output voltage for each phase. In the
symmetrical type inverter, twelve power switches
with three dc sources are required to achieve the same
output voltage for each phase.The dc voltage sources
used in the simulation studies are separate dc sources.
In practice, these dc voltage sources are available
via distributed energy resources like photovoltaic
panels, fuel cells etc. If the available source is an ac
source, then the required dc voltage sources can be
obtained by a transformer with multiple secondary
windings and rectifiers. There are different
modulation strategies that can be applied for
multilevel inverters. In this paper the fundamental
frequency switching scheme is used. In this method,
the switching angles are selected such that to
eliminate lower order harmonics or minimization of
total harmonics distortion. Since the proposed
multilevel inverter uses unequal dc sources, the
voltage stress among the switches will be
asymmetrically distributed. Hence care should be
taken while selecting power switches for this type of
configuration. The simulation diagram of three phase
seven level cascaded H-Bridge multilevel inverter is
shown in Fig. 1. Simulation is carried out using the
switching table shown in the Table 1.
The spectrum of the output voltage and current is
taken to determine the Total Harmonic Distortion
(THD) of three phase induction motor drive. The
simulation results of three phase voltage and current
is presented in the Fig. 2 (a) and Fig. 2 (b). It clearly
shows that the desired voltage levels are generated.
From the figures, it is clear that the output current
waveform is smoother than the output voltage. FFT
spectrum for stator voltage and current were presented
in the consecutive Fig. 3(a) and Fig. 3(b).From the
normalized FFT analysis, it can be derived that the
magnitude of lower order harmonics are very low and
the magnitude of higher order harmonics are nearly
equal to zero.
Symmetric and asymmetric cascaded seven level
inverter comparisons are given in Table 2. The
proposed asymmetric cascaded H- Bridge Multilevel
inverter topology has the advantage of its reduced
number of switches and dc sources compared to
conventional cascaded H-bridge multilevel inverter.
Cost and weight is also reduced. Switching losses are
considerably reduced intern heat produced in the
converter is also reduces. It can be extended to any
number of levels. The above features give the keen
interest to use the proposed cascaded seven level
inverter in the industry where the conventional
inverters are used.
Experimental Results and Discussion
To experimentally validate the proposed topology,
hardware of the three phase cascaded H bridge
Fig.1—Simulation diagram of three phase cascaded H-bridge seven
level Inverter
Table 1—Switching table for cascaded H-bridge seven level
inverter
Voltage
levels
switches
S1
S2
S3
S4
S5
S6
S7
S8
3Vdc
Vdc
Vdc
2
2
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0 
Vdc
2
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
Vdc 
1
1
0
0
0
1
1
0
3Vdc
2
0
1
1
0
0
1
1
0
171
MAHESHWARI & GNANAMBAL: LOW ORDER HARMONIC REDN OF INVERTER
Fig. 2—(a) Three phase stator voltage waveforms (b) Three phase stator current waveforms
Fig. 3—(a) FFT spectrum of stator voltage (b) FFT spectrum of stator current
Table 2—Comparison between conventional cascaded H-bridge seven level inverter and proposed cascaded H- bridge
seven level inverter
Topology
Conventional cascaded H- Bridge
Proposed cascaded H- Bridge
Percentage Reduction
seven
level
inverter
Seven level inverter
Parameters
Number of switches per phase
12
8
33.33%
Number of DC sources per phase
3
2
33.33%
8.67%
6.73%
1.94%
THD%
multilevel inverter has been built. Eight IGBT with
freewheeling diodes are used as the switching device.
Diode bridge rectifier is used to get the dc voltage. In
this hardware, two diode bridges are used to produce
133V and 266V.ATmega16 Microcontroller is used to
generate eight different gate pulses for IGBT power
switch. Control algorithm for the switching is written
in the high level language and then it is embedded in
the ATmega16 microcontroller. Output of the inverter
terminal is connected to the three phase squirrel cage
induction motor. Fluke 435 Power Quality Analyzeris
used to analyse the output voltage of the inverter.
Output voltage and its FFT spectrum is exposed in
Fig. 4 (a) and Fig. 4 (b).The result of the analyser
shows a good accordance between the simulation and
experimental results.
172
J SCI IND RES VOL 73 MARCH 2014
variable speed ac drives (conveyors, rolling mills,
printing machines, etc.,) are required and considerable
amount of energy can be saved as the proposed
system has lower harmonics.
References
1
2
3
4
5
6
7
8
9
Fig. 4—(a) Phase voltage waveform (b) FFT spectrum of phase
voltage
Conclusion
The proposed cascaded H-Bridge multilevel
inverter fed three phase induction motor uses unequal
dc sources is simulated and validated by hardware. A
fundamental frequency switching control algorithm
was developed and implemented. The total harmonic
distortion is reduced considerably. The simulation
result of stator current waveforms shows that the
lower order harmonics have been reduced and also
higher order harmonics are eliminated. Harmonic
elimination reduces the heat generated in the stator
winding of the induction motor. The torque of the
induction motor is improved with the significant level
due to the elimination of lower order harmonics
which is the main cause for the production of negative
torque.The proposed seven level cascaded H-bridge
inverter can be used for the industries where the
10
11
12
13
14
15
Malinowski M, Gopakumar K, Jose Rodriguez & Marcelo A
Perez, A survey on Cascaded Multilevel inverters,
IEEE Trans Ind Elect, 57 (2010) 2197 – 2206.
Lai J S & Peng F Z, Multilevel converters-A new breed of
power converters, IEEE Trans Ind Appl, 32 (1996) 509–517.
Tolbert L M, Peng F Z & Habetler T G, Multilevel
converters for large electric drives, IEEE Trans Ind Appl,
35 (1999) 36–44.
Menzies W, Steimer P & Steinke J K, Five-level GTO
inverters for large induction motor drives, IEEE Trans
Ind Appl, 30 (1994) 938–944.
Bell S & Sung J, Will your motor insulation survive a new
adjustable frequency drive? IEEE Trans Ind Appl, 33 (1997)
1307–1311.
Erdman J, Kerkman R, Schlegel D, & Skibinski G, Effect of
PWM inverters on AC motor bearing currents and shaft
voltages, IEEE Trans Ind Appl 3 (1996) 250–259.
Manjrekar M D, Steimer P K & Lipo T A, Hybrid multilevel
power conversion system: a competitive solution for highpower applications, IEEE Trans IndAppl, 36 (2000)
834–841.
Marchesoni M & Tenca P, Diode-clamped multilevel
converters: a practicable way to balance DC-link voltages,
IEEE Trans Ind Elect, 49 (2002) 752–65.
Peng F Z, Lai J S, McKeever J W, & Van Covering J,
A multilevel voltage-source inverter with separate dc sources
for static var generation,IEEE Trans Ind Appl, 32 (1996)
1130–1138.
Ebrahimi J, Babaei E & Gharehpetian G B, A new multilevel
converter topology with reduced number of power electronic
components, IEEE Trans Ind Elect, 59 (2010) 655–667.
Dixon J, Pereda J, Castillo C & Bosch S, Asymmetrical
multilevel inverter for traction drives using only one
dc supply, IEEE Trans Vehicular Tech, 59 (2010)
3736–3743.
Pereda J & Dixon J, High-frequency link: a solution for
using only one dc source in asymmetric cascaded multilevel
inverters, IEEE Trans Ind Elect 58 (2011) 3884–3892.
Chiasson J N, Tolbert L M, Mckenzie K J & Du Z, Control
of a Multilevel Converter Using Resultant Theory, IEEE
Trans Control Sys Theory, 11 (1998) 345-354.
Chiasson J N, Tolbert L M, McKenzie K J & Du Z,
Elimination of harmonics in a multilevel converter using the
theory of symmetric polynomials, IEEE Trans on Control
Sys Theory, 13 (2005) 216–223.
Patel H S & Hoft R G, Generalized Techniques of Harmonic
Elimination and Voltage Control in Thyristor Inverters: Part I
– Harmonic Elimination, IEEE Trans Ind Appl, 3 (1973)
310-317.