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CHAPTER 2
LITERATURE REVIEW
In 1973, Hasmukh S Patel & Richard G Hoft (1973) introduced the
theoretical problem of eliminating harmonics in the inverter-output voltage
waveforms. Generalized methods were developed for eliminating a fixed
number of harmonics in the half bridge and full bridge inverter-output voltage
waveforms, which required the solution of a set of nonlinear algebraic
transcendental equations. Numerical techniques were applied to solve the non
linear algebraic transcendental equations of the problem on the computer.
They presented solutions for eliminating up to five harmonics. Again
Hasmukh S Patel & Richard G Hoft (1974) introduced theoretical techniques
of voltage control for the half bridge and full bridge inverters in 1974.
Detailed analytical results for the symmetrical pulse width modulation
method of voltage control were also presented. So voltage control techniques
are derived whereby harmonic elimination is possible in variable frequency
and variable voltage three phase inverter circuits also.
Two popular but totally different approaches have been attempted
to solve the set of related non linear algebraic transcendental equations of
Selective Harmonic Elimination Pulse Width Modulation (SHEPWM) in
general. In 1987 Enjeti & Lindsay (1987) solved the equations by numerical
iterative techniques such as the Newton-Raphson method. These iterative
methods require an initial guess; such methods also do not guarantee the
alleviation of possible divergence. Some of the examples of these methods are
listed as follows. In 1990, Enjeti et al (1990) proposed Programmed Pulse
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Width Modulation for eliminating several lower-order harmonics and solved
the SHEPWM equations by Newton -Raphson method. Those solutions gave
high quality output spectra, which in turn resulted in minimum current ripple,
reduced torque pulsations, thereby satisfying several performance criteria and
contributing to the overall improved performance.
In 1992, Holtz (1992) evaluated the state of the art in pulse
width modulation for AC drives fed from three-phase voltage source
inverters. Feed forward and feedback pulse width modulation schemes with
relevance for industrial application are described and their respective merits
and shortcomings are explained. Secondary effects such as the influence of
load-current dependent switching time delay and transients in synchronized
pulse width modulation schemes were discussed, and adequate compensation
methods were presented. In the same year, Jang et al (1992) provided a
guideline and quick reference for the practicing engineer to decide which
methods should be considered for an application of a given power level,
switching frequency, and dynamic response.
In 1994, Holtz (1994) proposed efficient and fast control of
electric power that forms part of the key technologies of modern automated
production. It is performed using electronic power converters. The converters
transfer energy from a source to a controlled process in a quantized fashion,
using semiconductor switches which are turned on and off at fast repetition
rates. The algorithms which generate the switching functions-pulsewidthmodulation techniques-are manifold. They range from simple averaging
schemes to involved methods of real-time optimization.
In 1995, Do-Hyun Jang et al (1995) described the asymmetrical
pulse width modulated (APWM) control technique for single phase AC
choppers, which improves the input power factor and eliminates
the harmonics of
the
output
voltage
up
to
a
specified
order.
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This technique also enables linear control of the fundamental component of
the output voltage. The APWM switching patterns at the specified phase
angle are obtained by the Newton-Raphson method and can be implemented
by a one-chip microprocessor.
The selected harmonic-elimination (HE) method, which is widely
used for efficient inverter control, forms the basis of off-line digital PWM
modulation techniques in the power electronics field. The method is based on
numerical solutions of a set of selected HE equations which are often
considered to be impractical to solve. Up to the previous year, any effective
method for this subject has not been reported. In 1999, Kato (1999), proposed
a systematic method which makes it possible to solve and analyze the
equations sequentially by applying a homotopy method and a mathematical
induction algorithm even if there are multiple solutions. According to the
proposed method, unique HE solutions for single-phase cases and multiple
solutions for three-phase cases are computed and reported.
In the year 2004, the SHEPWM and control has been a widely
researched alternative to traditional PWM techniques. Moreover it is
identified that the equations that governs the SHEPWM technique have
multiple solutions too. Each solution has a unique distribution of energy in the
uncontrolled harmonic content. Ultimately, it is shown that there exists an
optimal harmonic control solution for a given application which minimizes
power loss. In 2004 Wells et al (2004), by using modern control theory, had
optimized the half bridge inverter subject to the constraint of switching
eliminate harmonics in the output spectra of single phase and three phase
inverters were possible. In the same year, Chaiasson et al (2004) converted
the non linear algebraic transcendental equations that specify the harmonic
elimination problem into an equivalent set of polynomial equations. They
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used the mathematical theory of resultants, then presented the all solutions for
the elimination of 5th, 7th, 11th and 13th harmonics. But the above procedure
is more complicated and time consuming. In the year 2006, Tianhao Tang
et al (2006)
roots of the non linear algebraic transcendental equations that specify the
harmonic elimination problem. Though the solutions are handy with
MATLAB they have their limitations, when a dedicated isolated electrical
application is the requirement.
Finding a set of solution has also been carried out using the
Homotopy algorithm in the year 2007 by Hosseini Aghdam et al (2007).
The second approach that views the situation as an optimization
problem and various optimization techniques have been adopted for solving
the SHEPWM equations. Evolutionary search algorithms find place in this
approach.
Some examples are as follows. In the year 2004, the above
mentioned SHEPWM technique has been applied to AC/AC chopper by
Sundareswaran & Kumar (2004) for the elimination of harmonics in the
output voltage waveform by using GA technique. In the year 2004 Agelidis
et al (2004) showed that a minimization technique in combination with a
random search resulted in a relatively simple approach that found all possible
sets of solutions. In the year 2006 Agelidis et al (2006) found the Multiple
Sets of Solutions for Harmonic Elimination PWM Bipolar Waveforms using
Nelder-Mead simplex algorithm.
Kashefi Kaviniani et al (2007) proposed Harmonic optimization of
Multilevel Inverters using Particle Swarm Optimization in the year 2007
where they have showed that
compared to the binary GA technique,
improvement in precision and rate of convergence have been achieved in the
Particle Swarm Optimization (PSO)
algorithm. Agelidis et al (2008)
extended the function minimization technique in Selective Harmonic
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Elimination PWM to three-level waveforms to attain a multiple sets of
solution in the year 2008. Barkati et al (2008) setting the initial guess for the
NR method proposed in the year 2008 using the GA, PSO methodology, thus
using NR to enhance the precision of GA and PSO. Wang shi et al (2008)
introduced an online optimization approach to the SHEPWM technology
based on genetic algorithm and BP neural network. The method needed to
preset the initial values and to predict the trend of these values over whole
range of modulation index when solving the SHE nonlinear and
transcendental equations. Hence, easy convergence and less computing-time
are achieved. Simulation and experimental results demonstrate the validity of
the proposed method. The method can achieve online SHEPWM control of
the NPC inverter. In 2012, Sadr et al (2012) used the particle swarm
optimization to find an optimal solution for the SHE problem in PWM
AC/AC voltage regulators.
So the aim of this method is to eliminate the lower order harmonics
or at least to minimize them. This optimization approach renders solution for
cases where it is possible to eliminate the low order harmonics and supplies
optimum switching angles where there is no feasible solution that can be
found otherwise without much computational overhead and analytical
expressions. Despite the versatility of the evolutionary algorithms, they suffer
from the drawback of slow speed of operation, also invariably requiring a
computer, suggest their lack of suitability for direct real time applications.
Since the solutions that suit a continuously variable modulation
index has been the continuing pursuit of the industry, none of the above
methods comes out with a generalized optimized solution applicable for all
possible modulation indices. Also none of the algorithms mentioned above
are suitable for real time implementation due their sluggishness in providing
results.
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Since SHEPWM technique has become a significant PWM method
for low switching loss for voltage source inverter, real time implementation is
necessary. There are two approaches in the real time implementation- one is
on line approach and the other is off-line approach. For off-line approach, the
various sets of commutation angles in relation to modulation index are
determined in advance and look-up tables are required. Therefore, huge
number of tables of data of switching instants pertaining to different
Modulation indices is needed to be stored. This trouble can be avoided in online approach. On-line solution of switching angles of Selective Harmonic
Elimination (SHE) PWM inverter has been a subject of research since the
1970s. As per the reference (2012) recent research has suggested new on- line
control
techniques
based
on
microprocessor, microcontroller DSP and
FPGA as key elements of implementation
of
SHEPWM
for
modern
power converters.
In 2003, Salim & Azli (2003) implemented the HEPWM technique
on a multilevel inverter using FPGA. In the year 2006, Arvindan et al (2006)
presented a single-phase bi-directional A.C. power control circuit using
power MOSFET embedded discrete component four quadrant switch (4QSW)
realizations that operate in a high-frequency chopping mode presented.
Microprocessor based gate drive circuits are used for triggering the 4QSWs at
the appropriate instants.
In the year 2007, Ali Eltamaly (2007) implemented a digital speed
control strategy for three-phase induction motor. This strategy depends on
varying the stator voltage to control the speed of induction motor. The digital
control strategy uses saw-tooth waveform with twice the supply frequency as
a control signal to be compared with triangular waveform as a carrier signal.
The voltage output from ac voltage in regulator can be controlled by varying
the voltage level of saw-tooth waveform. The control strategy is implemented
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by using FPGA. A detailed digital design of control system has been
introduced in details.
In the year 2008, Mohamed et al (2008) extended SHE-PWM
Technique for Single-Phase AC-AC Matrix Converters using FPGA. In the
same year, Woei-Luen Chen, Yung-Ping Feng and Chun-Hao Pien (2008)
presented a low-cost and effective approach to generate harmonic elimination
PWM (HEPWM) waveforms for three-phase voltage-sourced inverters
(VSIs). In the developed approach, the off-line computations of switching
patterns based on harmonic elimination strategy
are
stored
in
EPROM,
thereby allowing a microprocessor-free design. With the proposed
configurration, the circuits for the adjustments of modulation index and phase
angle are synthesized onto a field-programmable gate array (FPGA) by means
of hardware description language (VHDL).
Salim & Azli (2008) presented an FPGA-based gate signal
generator for a multilevel inverter employing an online optimal PVVM
switching strategy to control its output voltage. FPGA is chosen for the
hardware implementation of the switching strategy mainly due to its high
computation speed that can ensure the accuracy of the instants
that gating signals are generated. The gate signal generator has been realized
by an FPGA (FLEX10K20) from Altera. Jinping Chen et al (2008) proposed a
new power balance control strategy to solve the problem that the output
power and switch burden of each DC-DC converter cell in the multilevel DClink (MLDCL) inverter imbalance. By adjusting the control angles of
selective harmonic elimination PWM (SHEPWM) in each cell during quarter
output cycle of phase voltage to overcome the adverse effects of the control
angles in conventional SHEPWM, it can balance the output power of each
cell with a wide range of modulation indexes using FPGA based design.
Manyuan
Ye
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et al (2008) introduced an multi-level inverter SHEPWM technique based on
Walsh transform, and analyzes the models of multi-level inverter PWM
output waveforms. Using the Walsh function waveform analytic technique,
the multi-level inverter's switching angles are optimized by solving linear
algebraic equations instead of solving nonlinear transcendental equations. By
searching all feasible initial conditions, the solutions are the piecewise linear
equations with the fundamental amplitude. The problem of on-line solving
the multi-level inverter's switching angles is resolved by the piecewise linear
equations. In the same year, Wang Tiejun et al (2008) presented a scheme of
special harmonics elimination to solve the problem of torque pulsation. The
proposed PWM, which is derived by comparing the difference between
a dual three-phase system and a fourfold three-phase system, has the same
function as traditional SHEPWM. ZhongYu-lin & ZhaoZheng-ming (2008)
and et al (2008) presented a practical implementation of SHEPWM
technique in a closed loop scheme.
Yanlei Zhao (2008), presented a new method to solve SHE
equation in Walsh domain. Based on the feature of harmonic distribution of
the SHEPWM pulses, he presented the design principle of inverter filter.
Wang Liqiao & Wang Yong (2008) presented the selected harmonic
elimination
pulse
width
modulation
(SHEPWM)
technique
for
multilevel CSC. SHEPWM is a very effective control strategy applicable
to multilevel CSC. Bierk et al
(2008)
presented a new technique that
employs one inverter (the reference inverter) using a conventional SHEPWM scheme to eliminate a number of specific low order harmonics, while
a second inverter is phase shifted with a pre-calculated angle to eliminate the
first significant surplus harmonic. This set of two inverters is to be connected
to a second similar set of two inverters, with a second pre-calculated phase
shift, to eliminate the second significant surplus harmonic and so on.
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In the years 2009 and 2011, neural network based approach is used
to solve the real time implementation SHEPWM problem. One such approach
of the real time implementation of SHEPWM was done by using feed forward
artificial neural network. By selecting suitable switching instants, the
fundamental was kept at the desired level and the low-order harmonics are
either minimized or eliminated. A nondeterministic method was used to solve
the system of nonlinear algebraic transcendental equations to obtain the data
set for the ANN training. The method also provides a set of acceptable
solutions in the space where solutions are not obtained by analytical methods.
The trained ANN is a suitable tool that brings a small generalization effect on
the angles' precision and is able to perform in real time. The ANN was
implemented in hardware by using an FPGA by Saied Basil (2009). Haoran
Bai et al (2009) introduced the structure and control strategy of a combined
PWM inverter in their paper. The simulation and experimental results show
the feasibility of the proposed design and control strategy. Xiao Fu et al
(2009) proposed a digital implement method of selective harmonic
elimination pulse width modulation (SHEPWM) based on digital signal
processor (DSP). First, the switching angles for eliminating selective
harmonics are calculated with computer-aided software, and functional
relationships between modulation indexes and switching angles are obtained.
The curve fitting technique is then used to fit the switching angle-modulation
index curves, and fitting coefficients are stored in the memory of DSP. In
vector control, the reference voltage is generated by the control loop. The
modulation index is defined by its amplitude and switching angles are then
calculated with the modulation index and fitting coefficients. By comparing
the switching angles and the reference voltage phase angle, the PWM
switching states are determined. Finally, experimental results are provided to
verify the proposed method. Bierk et al (2009) presented a novel technique
that uses one inverter (the reference inverter) utilizing a conventional SHEPWM scheme to eliminate a number of specific low order harmonics in the
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induction motor load. The first inverter directly feeds the induction motor
load. The second inverter is phase shifted with a pre-calculated angle to
eliminate the first significant surplus harmonic. This set of two inverters is
connected to a second similar set of two inverters, with a second precalculated phase shift, to eliminate the second significant surplus harmonic
and so on. Harmonic currents profiles using MATLAB and PSpice simulation
are compared for a three-phase high-power medium voltage induction motor
load, with and without a phase-shifting transformer. Kehu Yang et al (2009)
studied the real solution number of the switch angles for the inverters which
are based on the Selective Harmonic Eliminated PWM (SHEPWM)
technology.
By the
method
of
variable
substitution,
the nonlinear
transcendental equations can be transformed to a Semi-Algebraic system.
Then, with the help of the latest progress in the mechanical proving software
for the Semi-Algebraic systems, an analytical method to classify
the real solution number of the switching angles is proposed. In order to
verify the effectiveness of this method, the real solution classifications for the
three phase bipolar and unipolar inverters with N = 3 are given. Compared
with the exiting numerical results, this method can find out the exact
boundary points and the final results are analytical. Salam & Bahari (2010)
proposed the application of Differential Evolution(DE) algorithm to the
selective harmonics
elimination pulse- width modulation
(SHE-PWM)
scheme. The aim is to solve the set of transcendental equations that determine
the switching angles of the SHE-PWM waveform. The objective function of
DE is designed to minimize the selected harmonics to near zero. Furthermore
the fundamental component of the output voltage can be controlled
independently. To verify the viability of the method, simulation is carried out
using MATLAB-simulink. The computed switching angles are applied to a
three phase voltage source inverter. Typical results are shown and discussed
in relation to the known concepts of SHEPWM. Bingjie Zhao et al (2010)
proposed a novel multi-level structure topology with zigzag transformer for
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three- level inverter used in STATCOM.Moreover, Selective Harmonic
Elimination Pulse Width Modulation (SHEPWM) is applied in the topology
to reduce switching frequency while restraining harmonics at the same time.
Simulation models are set up with Matlab. Finally, SHEPWM method for the
proposed topology is realized with digital signal processor (DSP) and
experiments are given for verification. Jiajia Ren et al (2010) proposed a
novel multi-level structure topology with zigzag transformer for three level
inverter used in STATCOM. Moreover, Selective Harmonic Elimination
Pulse Width Modulation (SHEPWM) is applied in the topology to reduce
switching frequency while restraining harmonics at the same time. Simulation
models are set up with MATLAB. Finally, SHEPWM method for the
proposed topology is realized with digital signal processor (DSP) and
experiments are given for verification. In the year 2010, Zhenggang Yin et al
have used Specific Harmonic Elimination Pulse Width Modulation
(SHEPWM) in a neutral-point-clamped converter and implemented
SHEPWM in a DSP chip by software. In addition, they have showed transient
current between different PWM in open loop operation is small. Moreover,
the work of SHEPWM in dynamic process requires the voltage vector rotate
steadily while the requirement on its length change is not so strict (2010).
Imarazene et al (2010) proposed solution is based on the redundant
switching vectors using the selective harmonics elimination SHEPWM
instead of space vector modulation. The inverter supplies a high power
induction motor of 20MW. The obtained results prove that the balancing of
the dc capacitor is kept with cancelling the most undesirable harmonics row
5th, 7th and 11th.
In the year 2010, Kouzou et al (2010) presented the problem of the
SHEPWM by a constrained nonlinear objective function which has to be
minimized. The main aim is the calculation of the switching angles vector
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solution presenting the best minimal value for the objective function. The
results obtained with the present application show the effectiveness of the use
of the Particle Swarm Optimization. On the other side, the application of the
PSO with SHE-PWM is a promising solution, which can make a great
improvement with different power electronics converters. Filho et al (2011) in
the years 2009 and 2011 approximated the selective harmonic elimination
problem using Artificial Neural Networks (ANN) to generate the switching
angles. A non-deterministic method is used to solve the system for the angles
and to obtain the data set for the ANN training. The method also provides a
set of acceptable solutions in the space where solutions do not exist by
analytical methods. The trained ANN shows to be a suitable tool that brings a
small generalization effect on the angles' precision. Banaei & Kazemi (2011)
Selective Harmonic Elimination Pulse Width Modulation (SHEPWM)
switching strategy is commonly applied for the elimination of low order
harmonics in the multilevel converter with stepped waveform. In this paper,
this switching algorithm is utilized to a Hybrid Flying Capacitor Multicell
converter to produce the required fundamental voltage and in the same time
cancel out specified higher order harmonics in this converter. Hybrid
Flying Capacitor Multicell is a new multilevel converter that reduces elements
for same level of output voltage compared with the classic multilevel
converters. For a range of the modulation index (M), angles obtained from
resultant theory are trained to neural network. Since the neural network is
trained, it gives the best angles for the entire modulation index. In the
resultant theory for a range of the modulation index (M> 1.15) in the sevenlevel converter, the switching angles can be chosen to produce the desired
fundamental output while making the fifth and seventh harmonics identically
zero. But the main drawback is that for a range of the modulation index
(M<1.15) there are not any solutions in the resultant theory, to overcome this
problem a DC-DC buck converter has been used to have adjustable dc source
in input of converter to coordination between modulation index and output
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voltage. The simulation results have been carried out using SIMULINK/
MATLAB to present the effectiveness of the SHEPWM strategy for the
proposed converter. Yongchang Zhang et al (2011) proposed the threelevel neutral-point-clamped (NPC) inverter-fed high-power adjustable-speed
drives, which uses asynchronous SVPWM at low frequency and SHEPWM
at high frequency. For SHEPWM, a novel formula is proposed to obtain the
initial values of switching angles, leading to another valid solution that is
different from the known ones in the literature. Furthermore, it is shown that,
by
eliminating
the
quarter-wave
symmetry,
unlimited
groups
of
solutions to three-level SHEPWM can be obtained. The characteristics of the
multiple solutions in terms of harmonic distribution, pulse width, and total
harmonic distortion are investigated for the application of SHEPWM in
practical drives. Switching between SVPWM and SHEPWM is problematic if
no appropriate measure is taken, particularly when the influence of the
minimum pulse width (MPW) is considerable. A simple but effective method,
taking into account the MPW, is proposed in this paper to address this
problem. The multiple groups of solutions to SHEPWM are simulated and
experimentally verified on a low-voltage three-level NPC inverter prototype.
Experimental results obtained from a low-voltage prototype and an industrial
6-kV/1250-kW three-level drive is presented to validate the smooth switching
between SVPWM and SHEPWM.
Wei Cong et al (2011) presented a combinational approach based
on mathematical software toolboxes, which is fast and convenient for
engineering applications. Detailed explanation of calculating switching-angle
curves is listed. Another undocumented set of switching-angle curves for N=4
is shown to confirm the proposed approach's effectiveness. Finally, certain
switching-angle curves below 60 are picked for simulation and experiments,
which are both based on closed-loop vector control system of induction
machines. Results prove that harmonics selected are eliminated effectively.
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Etesami et al (2011) compared the results between these methods
to show an appropriate privilege of ICA over other methods. The comparisons
are based on probability of converging to global minimum. Effect of number
of runs is investigated. The comparisons are done for 13 and 17
level inverters as case studies. Wei Cong et al (2011) aimed to analyze
harmonic characteristics of multiple solutions and showed experimental
results to verify their difference. Song Li & Manyuan Ye (2011) described
multi-level inverter SHEPWM technology based on the Walsh function
model, The Walsh function is constructed using the linear algebraic equations
to replace the traditional nonlinear SHEPWM equations. This method can
solve the difficulties in solving nonlinear equations, and the online multilevel switching angles calculation become possible. Finally, simulation and
experiment verify the feasibility and correctness. Yongxing Wang et al (2011)
proposed drive control system with selective harmonic elimination PWM
(SHEPWM) for induction motor presented. Designed control is based on
rotor-field oriented vector control of Induction motor with employed PWM
strategy, which holds four different modulations. SHEPWM principle is
introduced. The results of simulations are presented to verify the feasibility
of control method in medium voltage high power system (1.6 MW). And the
correctness of this proposed control system is verified by experimental results
in a small-scale laboratory prototype.
Veeranna et al (2011) presented the performance analysis and
comparison of different PWM
strategies
for
cascaded H-bridge three-
level inverter in terms of line voltage and motor current THD with their
fundamental components. It is shown that harmonic loss minimized optimalSHEPWM strategy gives better results in terms of voltage THD were
compared with SPWM, SVPWM and SHEPWM strategies. Kavousi et al
(2011) designed a controller based on PI controller to overcome such
problems. Thus, Modulation Index and phase angle of inverter are used as
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input control variables to regulate DC capacitor voltage and track reference
reactive power. Simulations are worked out in MATLAB/Simulink
environment.
Bierk (2011) employed a novel SHEPWM technique to run single,
two parallel, and four parallel current source inverters with different values of
modulation index (MI). This technique is straightforward to implement, is
cost effective and efficient in terms of the reduction of total harmonic
distortion (THD) of the load output currents. The calculation of the low order
harmonics amplitude and the THD of all these schemes is simulated with
MATLAB and verified with PSpice. Wei Kekang et al (2011) presented
a hybrid PWM method under a low switching frequency based on SVPWM
and SHEPWM, which use asynchronous carrier modulation SVPWM at low
frequency, and SHEPWM at high frequency, a square wave after rated
conditions. The transitive strategy is proposed to realize smooth transition of
individual modes including SVPWM, SHEPWM and square wave.
Simulation and experimental results confirm this hybrid modulation method
and their transition is reasonable and correct.
Zhang Wenyi (2011) involved the solutions of nonlinear,
transcendental equations set representing the relation between the amplitude
of fundamental wave and each order harmonic and the switching angles.
Newton iteration method is usually applied to solve the equations set, but the
convergence depends on the selection of initial value. By using a trial method,
the rule is found for many initial values of voltage-source SHE inverter, thus
many solutions of switching angles can be obtained. Numerical simulation is
conducted to obtain the value of the switching angles in the specified
amplitude of fundamental wave and tracks of switching angles changing with
the amplitude of fundamental wave. According to the switching angles
obtained, the value of each order harmonic and total harmonic distortion for i
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(THDi) in the specified amplitude of fundamental wave and their tracks
changing with the amplitude of fundamental wave are obtained. The variable
voltage variable frequency (VVVF) of a voltage-source SHE inverter is also
studied to lay a foundation for the design of the voltage-source SHE inverter.
Experiment of the output waveforms of the voltage-source SHE inverter has
been conducted to validate the correctness of the theory analysis.
Ahmadi (2011) developed harmonics injection and equal area
criteria-based
four-equation method to
realize
OPWM
for
two-level
inverters and multilevel inverters with unbalanced dc sources. For the cases,
where only small number of voltage levels are available, weight oriented
junction point distribution is utilized to enhance the performance of the fourequation method. A case study of multilevel inverter at low-modulation index
is used as an example. Compared with existing methods, the proposed
method does not involve complex equation groups and is much easier to be
utilized in the case of large number of switching angles, or multiple switching
angles per voltage level in multilevel inverters.
Da Silva et al (2011) reviewed the nonsinusoidal CPWM and
SVPWM techniques and deal with the three possibilities of calculation of
pulse widths after the addition of a zero-sequence signal. A general algorithm
is proposed and adapted for dealing with the control of the three-level NPC
inverter and also the Z-source converter. Experimental results corroborate the
proposed technique. Hassan Feshki Farahani & Somayeh Salehi Feshki
(2011) and Filho Faete et al (2012) demonstrated SHEM has been applied for
a several levels inverter as well and its harmonic condition has been studied.
Roberge & Tarbouchi (2012) presented a parallel implementation of the
Particle Swarm Optimization (PSO) on graphical processing units (GPU)
using CUDA. By fully utilizing the processing power of graphic processors,
we show how our parallel CUDA-PSO can be used to minimize harmonics in
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multi-level inverters. Nisha et al (2012) proposed an effective online method
to arrive optimal PWM switching angles based on Curve Fitting Technique
(CFT) for three phase inverters. Polynomial functions for optimal switching
angles are generated using CFT in MATLAB. The correctness and harmonic
performance of the proposed method is verified by comparing the results with
the Newton-Raphson (N-R) iterative method.
Mohan et al (2012) presented an adaptive filtering algorithm for
the selective current harmonic elimination in voltage source inverter (VSI) fed
drive system. The algorithm used for the proposed adaptive selective
harmonic elimination (ASHE) is based on Recursive Least Squares (RLS).
This method eliminates the dominant harmonics in line current and it requires
only the knowledge of the frequency of the particular harmonic to be
eliminated. The algorithm is simulated using MATLAB/SIMULINK tool and
its performance is analyzed based on total harmonic distortion (THD),
magnitude of eliminated harmonics, output voltage and current waveform.
Zhengming Zhao et al Ting Lu (2012) proposed a hybrid selective
harmonic elimination pulse width modulation (SHEPWM) scheme for
common-mode voltage reduction in three-level neutral-point-clamped
inverter-based induction motor drives. The scheme uses the conventional
SHEPWM (C-SHEPWM) to control the inverter
motor rated frequency) and uses the modified SHEPWM (M-SHEPWM) to
control the inverter at low frequency. It also uses a scheme to ensure the
smooth transition between the two SHEPWM schemes. As a result, at high
frequency, the C-SHEPWM provides the required high modulation index for
the motor, while at low frequency, when a passive filter is less effective
for common-mode voltage reduction; the M-SHEPWM is used to suppress the
common-mode voltage. Marzoughi & Imaneini (2012) implemented a special
selective harmonic mitigation pulse width modulation (SHMPWM) method
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where
a
very
low
switching
frequency
is
introduced
for
multilevel cascaded H-bridge converters to mitigate selected harmonics below
the standard levels and to satisfy the grid codes from the THD point of view.
In the proposed method, using a 150Hz switching frequency for power
switches, the harmonic components are mitigated up to the 41st harmonic.
Ebrahimi et al (2012) proposed a hybrid approach to surmount all
disadvantages of mentioned approaches. Simulation results, as well as
experimental results are presented to verify the theoretical results. Imarazene
et al (2012) dealt with the DC-link voltage balancing problem in 3-level
rectifier-3-level inverter-Induction Motor (IM) cascade In order to improve
the performance cascade, we have proposed the use of the redundant states
with the selective harmonics elimination PWM instead of space vector PWM
to control the DC-link voltages and the inverter switches in the same time.
Yongxing Wang et al (2012) introduced selective harmonic
elimination PWM (SHEPWM) technology applied in PMSMs. According to
the model of PMSMs, the relation between harmonic currents and voltages is
derived. From this relation, selection principle of SHEPWM is different for
salient pole PMSMs and non-salient pole PMSMs. Besides, the method of
smooth transition between different SHEPWMs is introduced.
In the year 2012, Shubhangi et al (2012) used Hopfield neural
network, which is a single layer feedback neural network to solve the
SHEPWM problem. Gourisetti et al (2013) introduced a novel method where
selective harmonic elimination is achieved by comparing a modified
reference signal against a high frequency carrier. A triangular or sinusoidal
carrier can be used in its implementation. Unlike other selective harmonic
elimination techniques, no on-the-fly signal processing is necessary.
Imarazene et al (2013) described two different PWM methods to improve
the quality of the output voltage waveform provided from five level inverter.
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The first one is the selective harmonics elimination (SHEPWM). The purpose
is to cancel the 5 th, 7thand 11th harmonic row. The second technique is
proposed
to
optimize the total harmonic distortion (OTHD)
using
the
differential evolution method.
Ghoreishy et al
(2013) proposed a new SHE-PWAM control
strategy and its realization in a drive application. Analysis and simulations are
carried out on a five-level CHB inverter. The results demonstrate that the new
SHE-PWAM technique improves the performance of the drive compared
where with the conventional SHE-PWM.
Prashanth L Gopal & Josh (2013) presented the Genetic
optimization method for harmonic elimination in a cascaded multilevel
inverter and an optimal solution for eliminating pre specified order of
harmonics from a stepped waveform of a multilevel inverter topology with
equal dc sources. The main challenge of solving the associated non linear
equation which are transcendental in nature and therefore have multiple
solutions is the convergence of the relevant algorithm. The main objective of
selective harmonic elimination pulse width modulation strategy is eliminating
low-order harmonics by solving nonlinear equations. The performance of
cascaded multilevel inverter is compared based on the computation of
switching angle using Genetic Algorithm as well as conventional Newton
Raphson approach. A significant improvement in harmonic profile is achieved
in the GA based approach. A nine level cascaded multi level inverter is
simulated in MATLAB/Simulink and a hardware model has been fabricated
to validate the simulation results.
George & Benny (2013) and Filho (2013) proposed a novel
methodology for calculating switching angles for a multilevel-cascaded Hbridge converter connected to the solar panels. Here the desired voltage is
synthesized from separate solar panels connected to each series-connected
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bridges of the cascaded multilevel inverter. This is obtained by generating the
suitable switching angles there by achieving the required fundamental
frequency and the lower order harmonics minimizing. Particle Swarm
Optimization (PSO) algorithm is used to find the solution for the set of
equations where the input voltages are the known variables and the switching
angles are the unknown variables and the Artificial Neural Networks (ANN)
are to determine the switching angles that correspond to the real-time values
of the solar panel voltages.