Lijo Jacob et al., International Journal of Advanced Engineering Technology
E-ISSN 0976-3945
Research Paper
A SURVEY OF MODULATION TECHNIQUES FOR A SERIES
CONNECTED VOLTAGE SOURCE INVERTERS
Lijo Jacob Varghese1*, Dr. C. KeziSelvaVijila2, Dr. I. Jacob Raglend3
Address for Correspondence
*1 Department of Electrical and Electronics Engineering, Christian College of Engineering and Technology, Oddanchatram624619, Tamil Nadu
2
Department of Electronics and Communication Engineering, Christian College of Engineering and Technology,
Oddanchatram-624619 Tamil Nadu
3
Department of Electrical and Electronics Engineering, Noorul Islam University, Thuckalay-629 180, Tamil Nadu
ABSTRACT
The concept to achieve higher power using a series of power semiconductor switches with several lower voltage dc sources
produces a staircase voltage waveform called a multilevel inverter has brought about a revolution in catering the demands of
medium and high power industrial applications. The Multi-Level Inverter extends its application to industrial motor drives,
interfacing with renewable energy sources, Flexible AC transmission Systems and also to applications like traction drives. A
numerous modulation techniques and control schemes have been developed like the Sinusoidal Pulse Width Modulation
(SPWM), Selective Harmonic Elimination Pulse Width Modulation (SHE-PWM), Space Vector Modulation (SVM), etc.
This paper brings about a survey of various configurations of modulating techniques for a Multilevel Inverter.
KEYWORDS- Inverter, Multilevel Inverter, Modulation, Pulse Width Modulation, Total Harmonic Distortion.
I.
INTRODUCTION
A Multilevel inverter is power electronic systems that
synthesize a desired voltage from several levels of
direct current voltage as inputs. It is impossible to
connect only one power semiconductor switch
directly to a medium voltage grid which can be
effectively done by a multilevel inverter which
achieves high power ratings. The Multilevel inverter
also enables the use of renewable energy sources like
such as photovoltaic, wind, and fuel for a high power
application .The concept of multilevel converters has
been introduced since 1975[1] to begin with the
three-level converter. The term multilevel was started
with the three-level inverter introduced by Nabae et
al. [2]. By increasing the number of levels in the
inverter, the output voltages waveform has more
steps generating a staircase waveform, with a reduced
harmonic distortion. The Higher number of levels
increases the control complexity and introduces
voltage imbalance problems. The concept of a
multilevel inverter to achieve higher power is to use a
series of power semiconductor switches with several
lower voltage dc sources to perform the power
conversion by producing a staircase voltage
waveform. The rated voltage of the power
semiconductor switches depends on the rating of the
DC voltage sources to which they are connected.
A multilevel converter has several advantages over a
conventional two-level converter as a Multilevel
converters not only can generate the output voltages
with very low distortion, but also can reduce the
dv/dt stresses which reduces electromagnetic
compatibility (EMC) problems, lesser Commonmode (CM) voltage can be reduced draws input
current with low distortion and can be operated at
both fundamental switching frequency and high
switching frequency PWM. The advantages of using
multilevel topology also include reduction of power
ratings of power devices and lower cost. Today,
multilevel inverters find its application in high-power
applications with medium voltage levels which
include laminators, mills, conveyors, pumps, fans,
blowers, compressors, etc. This paper focuses on
analyzing and bringing about the different
modulation techniques of the multilevel inverter.
II. MULTILEVELINVERTER CONFIGURATION
The output waveform obtained by the series
connection of several dc sources for achieving a
Int J Adv Engg Tech/Vol. VII/Issue II/April-June,2016/571-581
multilevel output can be realized by several
combinational structures which are being proposed
for their unique advantages. Even though there are
many configurations of Multilevel Inverter, the three
common topologies that are prevalent includes diode
clamped [2], flying capacitor [3] and cascaded [4]
Multilevel Inverter.
2.1. Diode-Clamped Inverter
The diode clamped multilevel proposed by Nabae,
Takashi, and Akagi [2] was named as neutral point
converter and was essentially a five-level diode
clamped inverter as shown in Figure 1(a). In this
circuit, the dc-bus voltage by using two seriesconnected capacitors can split the supply voltage into
three voltage levels and the midpoint of the
capacitors is called the neutral point. The diodes are
being utilized for clamping the switch voltage to half
the dc-bus voltage magnitude.
If the output is drawn out, then the circuit has five
output voltage levels: 2Vdc, Vdc, 0, -Vdc and -2Vdc.
For a ‘m’ level output, assuming the same voltage of
the blocking diode to that of the active device voltage
rating, the requirement for the number of diodes for
each phase can be given by (m-1)(m-2). This number
represents a quadratic increase in ‘m’. When the
number of levels in the output become very high, the
requirement for the number of diodes in the circuitry
becomes impractical to implement.
(a)
(b)
(c)
Fig.1.Multilevel inverter topologies: five-level (a) DCMLI, (b) FC-MLI, (c) CHB-MLI
2.2. Flying Capacitor Inverter
The fundamental building block of a five level flying
capacitor inverter is shown in Fig. 1(b). Independent
capacitors are used to clamp the device voltage for
different voltage levels. The topology provides a five
levels across the output: 2Vdc, Vdc, 0, -Vdc and 2Vdc. By having a proper selection of switch
combination for different output levels, the charge of
C1can be balanced. Even for this topology, the
capacitor clamping, a large number of bulky
capacitors are required to clamp the voltage as in the
case of diode clamping. If the voltage rating of each
Lijo Jacob et al., International Journal of Advanced Engineering Technology
capacitor used is assumed to have the same voltage
rating as that of the main power switch, an ‘m’ level
converter requires about (m-1)(m-2)/2 numbers of
per phase clamping capacitors and in addition to that
the topology requires (m-1) numbers of main DC-bus
capacitors.
2.3. Cascaded Multilevel Inverters
Similar to a two level single-phase inverter, a series
connection of the same brings about a new converter
topology with independent dc sources, which is
shown in Fig. 1(c). Fig. 1(c) shows the power circuit
for a single phase leg of a five-level inverter with two
H-bridges of four cells in each bridge. The resultant
output voltage is synthesized by adding the voltages
generated by the various
cells. The circuitry
generates five levels of voltages at the output: 2Vdc,
Vdc, 0, -Vdc and -2Vdc. With different possible
combinations of these switches(S1-S4), in the two Hbridges, the converter can generate five different
voltage outputs in combination with the individual dc
sources. The AC outputs of different full bridge
converters in the same phase are connected
accordingly so that the resultant output voltage
waveform is the sum of all individual inverter
outputs. Even though various multilevel inverter
structures are used, the Cascaded Multi-Level
Inverter (CMLI) appears to be superior to other
inverter topologies in the application at high power
rating due to its modular nature of modulation,
control and protection requirements of each full
bridge inverter [5]. A cascaded multilevel inverter
eliminates the large number of large transformers
requirements, clamping diodes requirements, as in a
diode-clamped multilevel inverter and the flying
capacitors
III. MODULATION TECHNIQUES
Mainly power electronic converters are operated in
the “switched mode” which means the switches
within the converter are always in either one of the
two states - turned off (no current flows), or turned
on (saturated with only a small voltage drop across
the switch). Any operation in the linear region, other
than for the unavoidable transition from conducting
to non-conducting, leads to high switching power
losses resulting in the reduction of efficiency. As a
measure to control this power flow, the switches are
made to alternate between these two states (i.e. on
and off). The switched component is eliminated and
retention of the desired components of DC or lowfrequency AC is done which is called Pulse Width
Modulation (PWM), as the pulse width is modulated
to control the desired average output value. Several
modulation and control strategies have been
developed or adapted for multilevel inverters
including the following: Sinusoidal pulse width
modulation
(SPWM),
selective
harmonic
elimination(SHE), space-vector modulation(SVM),
etc. In a conventional two-level inverter
configuration, the harmonic reduction of an inverter
output current is achieved mainly by raising the
switching frequency. But in high power applications,
the switching frequency of the power device has to be
restricted below 1 KHz due to the increased
switching losses and also the level of dc- bus voltage.
Figure.2. shown the different classification of
modulation techniques for multilevel inverter
topologies. The main classification of these
techniques is done by whether the technique is a
Int J Adv Engg Tech/Vol. VII/Issue II/April-June,2016/571-581
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single technique or implemented by incorporating
one or more such techniques. Based on these
criterions, if a single independent technique is
adopted, it is classified as Standalone Modulation
Techniques and a combinational technique is termed
as the Hybrid Modulation Techniques. The
standalone modulation techniques are techniques that
are being implemented without any combinational
techniques which can be classified based on the
method it is being implemented as analog modulation
techniques and digital modulation techniques.
Analog modulation techniques can further be
classified based on the electrical parameters such as
voltage, current, and frequency whichever is used as
a reference in the adopted modulation technique.
Likewise, they are classified as Voltage reference
Modulation
Techniques,
Current
reference
Modulation Techniques and Frequency based
Modulation Techniques.
3.1. Voltage reference Modulation Techniques
When a voltage signal is used as a reference for
adopting the modulation technique, such a technique
falls under voltage reference modulation technique.
The basic principle of pulse width modulation is
meant to modulate the pulse by the comparing two
signals, one, the carrier and two, the reference
signals. The resultant of this comparative state
provides a pulse output that is used to trigger the
power electronic controllable switches. The primary
function of pulse width modulation is to make the
power electronic switches to operate alternate
between these two states and as a result, the pulse
width is modulated to control the desired average
output. The PWM control is a better way of
controlling the switches with minimum harmonics in
the output and losses.
Such modulation technique can be further classified
based on the whether the voltage signal is used as a
reference signal or a carrier signal for the particular
Pulse Width Modulation technique. Based on the
above, voltage reference modulation techniques are
classified as reference modulated Pulse Width
Modulation and carrier modulated Pulse Width
Modulation.
3.1.1.
Reference
modulated
Pulse
Width
Modulation
The PWM can be realized with any one of the
following reference waveforms such as Sinusoidal,
Trapezoidal, Stepped, Staircase waveform, etc. Based
on the type of the reference waveform used, these
techniques can further be classified as follows:
Multiple pulse width modulation
The multiple pulse width modulation is used in order
to reduce the harmonic content. The reduction in
harmonic content is achieved by generating a number
of pulses in each half cycle. Here gate signal is
generated by comparing the triangular wave with the
dc reference signal. The width of the pulse is
maintained uniformly in a sequence. The lower order
harmonics is reduced compared to the ordinary single
pulse width modulation. Frequency modulation index
of this PWM is Mf = fc/fo and the number of pulses
per half cycle is P=fc/2fo the no of pulses generated
in the positive have cycle increases this leads to
increase turn-on time of the switch so switching
losses will increase and this leads a disadvantage in
this PWM technology.
Lijo Jacob et al., International Journal of Advanced Engineering Technology
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PWM Modulation Techniques
Hybrid
Modulation
Techniques
Stand alone
Modulation
Techniques
Digital
Modulation
Techniques
Analog
Modulation
Techniques
Selective
Harmonic
Elimination
Space Vector
Modulation
Techniques
Combinational
Modulation
Techniques
Voltage reference
Modulation
Techniques
Artificial
Neural
Networks
Genetic
Algorithm
Current reference
Modulation
Techniques
Linear current control
Multi-band Hysteresis
current control
Multi-offset-band Hysteresis
current control
Particle
Swarm
Optimisation
Frequency based
Modulation
Techniques
Hysteresis current
control
Optimised current
control
Reference modulated
Modulation Techniques
Multiple
PWM
Fuzzy
Logic
Control
Sigma-Delta
Modulation
Techniques
Soft Computing aided
Modulation
Techniques
High
Switching
frequency PWM
Fundamental
Switching
Frequency
Time based Hysteresis
current control
Carrier modulated
Modulation Techniques
Sinusoidal
PWM
Modified
Sinusoidal PWM
Trapezoidal
PWM
Single carrier based
PMW
Staircase
PWM
Multi carrier based
PMW
Sub Harmonic
PWM
Level shifted Modulation
Techniques
In-phase
Disposition
Stepped
PWM
Phase
Opposition
Disposition
Switching Frequency
Optimal PWM
Phase shifted Modulation
Techniques
Alternate
Phase Opposition
Disposition
Fig 2.Classification of Modulation Techniques for Multilevel inverter topologies
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Harmonic Injected
PWM
Lijo Jacob et al., International Journal of Advanced Engineering Technology
E-ISSN 0976-3945
Fig 3.Multiple Pulse Width Modulation
Sinusoidal PWM
The sinusoidal pulse width modulation is used to
vary the width of the pulse by comparing the sine
wave with the triangular carrier wave. The lower
order harmonics is reduced here. The bidirectional
triangular carrier wave is compared with sine wave
here width of the pulse can be easily varied by
varying the frequency of the carrier wave. The
positive start sine wave is for one switch and the
negative start sine wave is for the other switch of the
same leg which means two switches of the same leg
have different excitation; g1 and g4 represent the gate
signals of the two switches.
reduces the switching losses by minimizing the
switching action.
Fig 5. Modified Sinusoidal Pulse Width Modulation
Fig 4.Sinusoidal Pulse Width Modulation
The modulation index M= Ar/Ac
By this if the modulation index is less than
one higher order harmonics appears and if
modulation index is greater than one lower order
harmonics appears. This type of PWM is normally
used in industry because it reduces the complexity,
heat generated by the processor is less and the
algorithm for generating the signals is easy.
Modified Sinusoidal PWM
Modified sinusoidal PWM do not change the pulse
widths with respect to the modulation index. The
carrier wave is operated for the first and last half 60
degree (0 - 60 degrees and 120 -180 degrees) of the
sine wave similarly to the negative half cycle. A
positive half cycle of sine wave starts from 0 to 180
degrees and the negative half cycle starts at 180
degrees and ends at 360 degrees. Due to the
separation of carrier wave includes number of pulses
in the positive half cycle and improved harmonic
character is present than the sinusoidal PWM. It
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Trapezoidal PWM
Here the high-frequency carrier wave is compared
with a trapezoidal wave. This can be done by
removing the respective amplitude by means of the
proper algorithm. The amplitude of the carrier wave
is Ac which is of higher frequency and greater
magnitude is compared with the generated
trapezoidal wave Amplitude reference signal Ar. The
output of the compared signals results in the PWM
pulse that is used to trigger the gate of power
electronic switches. Here Ar=σAr (max) where σ is
the triangular factor that decides the amplitude of the
reference signal. The modulation index M=Ar/Ac
this can be varied from zero to one. The output
voltage can be varied by changing the triangular
factor.
Fig 6. Trapezoidal Pulse Width Modulation
Lijo Jacob et al., International Journal of Advanced Engineering Technology
Stepped Modulation
The stepped modulation as in Figure 6. shows the
gate signal generation where the high-frequency
carrier wave is compared with the stepped wave these
results in pulse for switches.
The reference
waveforms were separated by 20 degrees of interval
and the individual control the reference wave
magnitude leads to control in fundamental harmonic.
If the carrier frequency and the fundamental
magnitude is high then it leads to the reduction in the
current distortion.
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heating of the switching devices due to the
conduction of the switches.
Fig 9. Harmonic Injected Pulse Width Modulation
Fig 7. Stepped Modulation
Staircase PWM
The staircase wave is specially used to selective
harmonic elimination. The number of steps
determines the quality of output. This type of PWM
is mainly used for higher output voltage where the
minimum number of pulses to be generated in a half
cycle is 15.In the staircase modulation, the switching
angles can be calculated.
Input current harmonics in the power distribution line
can be minimized by this PWM technique. Here by
comparing the staircase wave reference wave and the
carrier wave, the number of pulses can be easily
generated.
Fig 8. Staircase Pulse Width Modulation
Harmonic Injected PWM
The harmonic injected modulation is formulated by
using a harmonic injected signal as the reference
wave. The reference wave is formed by clamping the
common mode signal with the sine wave while it
does not affect the output voltage waveform. The
type of harmonic added may be of order 2, 3 or lower
order harmonics. The 3rd order harmonic reference
signal can be used for the three-phase inverter alone.
By adding this, harmonic injected PWM we can
easily achieve 15% more amplitude of the
fundamental wave than the normal sinusoidal PWM.
This type of PWM is mainly used to reduce the
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3.1.2. Carrier modulated Pulse Width Modulation
The Pulse Width Modulation techniques can be
divided based upon the number of carrier signals
utilized for the technique that feeds for the power
electronic switches of the Inverter.
Single carrier based Pulse Width Modulation:
For a two level conventional inverter, a single carrier
waveform is sufficient enough to provide the required
pulse modulated output, which can be classified
under Single carrier based Pulse Width Modulation.
Any PWM that utilizes only a single carrier signal
falls under this category.
Multiple carrier based Pulse Width Modulation:
The number of carriers that are utilized for a multilevel inverter depends on the number of the output
levels of the inverter. Any pulse width modulation
technique that engages more than one carrier
waveforms can be classified under multiple carrier
based pulse width modulation. This can be classified
into two: Sub Harmonic PWM and Switching
Frequency Optimal PWM.
Sub-Harmonic PWM:
Carrara[6],.[7]adopted a multilevel sub-harmonic
PWM which consists of (m-1) number of carrier for
a ‘m’ level multilevel inverter .The carrier signal with
frequency FC and amplitude AC are distributed as
bands in their adjacent neighborhood. It consists of a
reference waveform of frequency FM and amplitude
AM is being centered at the middle of these carrier
bands.
When the carrier and the reference
waveforms are continuously compared, the power
semiconductor switch turns ON if the reference wave
exceeds the carrier signal and the device turns OFF if
otherwise.
The amplitude modulation is given by
ma=Am/(m-1).Ac
(1)
mf=fc/fm
(2)
Carrara also classified the carrier bands based on the
disposition of the carrier waveform with respect to its
contiguous carrier. They can be broadly classified as
level shifted PWM and phase shifted PWM.
Level Shifted PWM:
There are three PWM strategies classified based upon
the phase relationships between the adjacent levels of
the carrier bands namely, In-phase disposition, Phase
opposition disposition, and Alternative phase
opposition disposition.
Lijo Jacob et al., International Journal of Advanced Engineering Technology
In-phase disposition PWM:
In the In-phase disposition (IPD) technique, all the
different carriers employed are arranged in such a
way that all the carrier waves are in phase with each
other. For an ‘m’ level multi-level inverter, (m-1)
numbers of carrier waveforms are arranged in phase
with the adjacent carrier waveform.
For a 3 level inverter, having two carrier waveforms,
the converter is turned ON in the positive cycle when
the reference is greater than both these carrier
waveforms, OFF when the reference waveform is
greater than the lower carrier waveform and turned
ON in the negative cycle when the reference is lesser
than both these carrier waveforms.
Fig 10. Carrier-based PWM scheme using the inphase disposition (IPD).
Phase Opposition Disposition PWM
In a phase opposition disposition (POD) PWM
technique, the carrier waveforms are in phase above
the zero reference and out of phase by 180ᵒ below the
zero reference.
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Considering an ‘m’ level inverter with m=5, having
(m-1) =4, with 4 carrier waveforms arranged with
each other by a phase shift of180ᵒ.
When the reference is greater than all the four carrier
waveforms, the converter hasVdc/2 voltage across
the switches, which becomes Vdc/4, when the
reference is lesser than the uppermost carrier, zero
voltage, when the reference is lesser than the two
uppermost carriers and greater than the two lower
carriers. The output voltage becomes -Vdc/2 when
the reference is lesser than all the four carrier
waveforms and becomes -Vdc/4, when the reference
is greater than the two lowermost carriers and lower
than the other two carriers.
Phase Shifted PWM:
This type of PWM is generally utilized in the
cascaded multi-level inverter as, it can be easily
implemented independently for any number of
inverters.[ 8] and also can provide even power
distribution among the switches.
Fig 12.Carrier-based PWM scheme using the Phase
Shifted PWM
In this modulation technique, the phase of each
carrier is shifted by a phase to each other as it
effectively imposes a harmonic reduction of the
output voltage. Moreover, this modulation technique
can be worked in the over modulated region, when a
common mode is added to the reference.
Switching Frequency Optimal PWM Method
Steinke [9] suggested a carrier-based modulation
technique switching frequency optimal PWM (SFOPWM) which was identical to Carrara’s proposal
except that a zero sequence voltage is added to each
of the carrier waveforms. Here it takes the
instantaneous average of the maximum and minimum
of the three reference voltages and subtracts this
value from each of the individual reference voltages
to obtain the modulation waveforms.
Fig 11. Carrier-based PWM scheme using the
Phase Opposition disposition (POD).
For a three-level inverter, with two carrier
waveforms, the switches taking the positive currents
are ON, when the reference is greater than both
these carrier waveforms, the switches taking are in
the OFF state when the reference waveform is
greater than the lower carrier waveform and the
switches taking the negative currents are ON when
the reference is lesser than both these carrier
waveforms.
Alternative Phase Opposition Disposition PWM:
In this method, every carrier waveforms are out of
phase with each of its neighboring carrier by 180ᵒ.
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Fig 13.Multilevel carrier-based SFO-PWM showing
carrier bands
The addition of this triplen-offset voltage
continuously centers all of the three reference
waveforms in the carrier band, which Holmes [10]
showed for carrier-based two-level PWM is similar to
using space vector PWM with the zero voltage state
divided evenly at the beginning and end of each half
carrier interval.
Lijo Jacob et al., International Journal of Advanced Engineering Technology
3.2. Current reference Modulation Techniques
3.2.1 Linear Current Controller
Linear current controllers are classified into three
types. Namely, ramp comparison controller,
stationary vector controller, and synchronous vector
controller. The output current ripple and feedback is
used to control the switching instances in ramp
comparison current controller. Two linear
compensators are used because the sum of threephase currents in a three phase isolated neutral load
to topology is zero. The basic linear current controller
consists of a tracking regulator with a proportional
integrator compensator for PV inverters.
3.2.2 Optimized Current Controller
PWM controllers based on a real-time optimization
algorithm
Very high power applications require low switching
frequencies. This is implemented by using a
rectangular current error boundary which is aligned
to the rotor flux vector of the machine. Switching
states are selected based on a prediction, provided
switching is minimized.
Trajectory tracking control
Convertor currents which have dynamic tracking
error are compensated for using optimization. Steadystate is controlled using off-line optimization. A
transient operation is controlled using on-line
optimization. Therefore, the advantages of both the
method are exploited. The fundamental current and
the actual phase angle of the voltage reference vector
determine the location of a moving target which
represents the current space vector on the template
trajectory.
Minimum switching frequency predictive current
control
Minimum switching frequency predictive current
control is based on the space-vector analysis. The
current command vector determines the location of
the error curve if one hysteresis controller is used.
Different trajectories of the current are depicted for
each possible inverter output voltage vectors when
the current vector reaches a point on the error curve.
The voltage vector which minimizes the mean
inverter switching frequency is selected.
Delta Modulation
In delta modulation method, encoded pulses are
locally decoded into analog signals. An integrator is
used in the feedback loop for this purpose. This
signal is subtracted from the input signal to calculate
the error signal. The polarity of pulses is modified by
the sign of the error signal because it uses closed loop
arrangement.
3.2.3 Hysteresis Current Controller
The hysteresis current control for n-level inverter can
be implemented by defining n-1 evenly spaced
hysteresis bands on either side of the commanded
current. Whenever the current crosses a hysteresis
band, the voltage level is increased by one. When the
measured current crosses the lowermost hysteresis
band, it implies that voltage level is at its highest
value and when it crosses the uppermost band, it
implies that it is at its lowest, thus making sure that
the current regulates about the commanded value.
Current controllers are used to control the load
currents to follow the reference currents. The
maximum current deviation is specified by the
Hysteresis Band (HB). The inverter switching
frequency will vary over fundamental inverter period.
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The switching command for the converter is created
by comparing the controlled system variable against
the hysteresis bands.
Hysteresis current control can be classified into the
following three types: multiband hysteresis current
control, multi-offset band hysteresis current control
and time-based hysteresis current control.
Multi- Band Hysteresis
Multiband hysteresis current control makes use of
symmetrical hysteresis bands to control the
switching. There are two hysteresis bands - the inner
band and the outer band. The inner band is
responsible for switching between adjacent states.
The outer band is used when additional switching is
necessary.
Multi-Offset Band Hysteresis Modulation
Multi-offset band modulation can be done in two
ways. One is what is called the conventional Multioffset band hysteresis modulation and the other is the
modified Multi-offset band hysteresis modulation. As
the name implies, the multi-offset band uses bands
placed with an offset around the zero current error
line. Implementation of different bands becomes easy
while using offset bands. Another advantage is,
during implementation, voltages appearing at the
boundary of a band are allowed to flow to the other
band if it is insufficient to force the error back. In the
conventional hysteresis current control scheme, we
use (n-1) offset bands for the n-level inverter. The
maximum allowable excursion of the actual current
from desired current. This introduces a steady-state
tracking error. Complexity in implementation is
another drawback.
A more effective way is to use modified MOB
hysteresis control. In this scheme for an n-level
inverter, we need to use (n-2) offsets in both positive
and negative current error regions. Each band
represents switching between two adjacent voltage
levels. Another feature of this scheme is that the
output voltage at the band crossing points depends on
the previous voltage levels i.e. just before the
crossing point. This value is not fixed. The advantage
of modified scheme is that the current exactly follows
the reference with a minimum change in voltage.
Time-Based Modulation
In Time Based hysteresis modulation the system
variable within a single band is controlled so that
current offset can be avoided. This overcomes the
issue of error of the MB scheme. Selection of output
voltage levels one by one allow the current error to
be controlled. An optional outer band was added to
provide switching for to extreme levels of voltage for
detecting sudden changes in current error. This
technique however only works for three level
inverter. As the number of levels increases beyond
three, more bands are needed.
The size of the band is determined by many factors,
which include the permitted level of current
distortion, load values, input voltage and the desired
switching frequency. Though this technique does not
have any steady state error and the implementation is
also very simple it can still be improved for narrow
bands and for all loading conditions.
The modified Time Based Multiband Hysteresis
current control requires (n-2) outer bands at the offset
for an n-level inverter. In this scheme only if the error
touches the outer band at the offset from the main
band the voltage level will be switched. Instead of
Lijo Jacob et al., International Journal of Advanced Engineering Technology
checking both horizontal and vertical movement of
current error and time, the modified Time Based
Multiband Hysteresis current control only checks the
vertical movement and decides when to switch to the
next voltage level.
Digital Modulation Techniques
Selective Harmonic Elimination
Patel [11[12]. Formulated the concept of selective
harmonic elimination method also called fundamental
switching frequency method which is based on the
harmonic elimination theory. The Fourier series
expansion of the output voltage waveform as follows
f(x)=(4dc)/π+∑_(n=1)([cos(nθ1)+cos(nθ2)+⋯cos(
nθs)] sin(nwt)/n )
(3)
The conducting angles θ1,θ2,…θs, can be chosen
such that the voltage total harmonic distortion is a
minimum. To minimize harmonic distortion and to
achieve adjustable amplitude of the fundamental
component, up to (m-1), harmonic contents can be
removed from the voltage waveform. In general, the
most significant low-frequency harmonics are chosen
for elimination by properly selecting angles among
different level inverters, and high-frequency
harmonic components can be readily removed by
using additional filter circuits.
Normally, these angles are chosen so as to cancel the
predominant lower frequency harmonics [13].
For the 11-level case in Figure 31.2, the 5th, 7th,
11th, and 13th harmonics can be eliminated with the
appropriate choice of the conducting angles.
cos(5θ1)+cos(5θ2)+⋯cos(nθ5)]=0
cos(7θ1)+cos(7θ2)+⋯cos(7θ5)]=0
cos(11θ1)+cos(11θ2)+⋯cos(11θ5)]=0
cos(13θ1)+cos(13θ2)+⋯cos(13θ5)]=0
cos(θ1)+cos(θ2)+⋯cos(θ5)]=5Ma(4)
All these nonlinear equations are solved by the
iterative method like Newton-Raphson method.
Generally, these pre-calculated switching angles are
stored as a look-up table. Therefore, any digital
methodology has to be adapted to generate the PWM
gate drive signals. A wide range of modulation
indexes can be achieved with minimal harmonic
distortion for the synthesized waveforms, a selective
harmonic modulation method was proposed, which is
called virtual stage PWM [14] which combines
Bipolar Programmed PWM or Unipolar Programmed
PWM along with the fundamental frequency
switching scheme which could be used for low
modulation indices for the applicability of the
multilevel fundamental frequency.
Space Vector Modulation Techniques
SVPWM is a digital modulating technique where the
objective is to generate; PWM load line voltages that
are in average equal to a given reference load line
voltages. With PWMs, the inverter can be thought of
as three separate push-pull driver stages, which create
each phase waveform independently. When the
number of the output levels increases, multilevel
inverters have a large number of vector states which
are utilized to modulate the reference. Moreover,
each state vector has a number of redundancies.
Redundant switching states are those states for which
a particular output voltage can be generated by more
than one switch combination.
Multilevel SVM must take care of this redundant
behaviour to optimize the search of the modulating
vectors and to apply an appropriate switching
sequence. However, the same properties of state and
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E-ISSN 0976-3945
switching redundancy allow the improvement of the
modulation technique to fulfill additional objectives
like reducing the common-mode output voltage
reducing the effect of over modulation on the output
currents improving the voltage spectrum and
minimizing the switching frequency and controlling
the dc-link voltage when floating cells are used.
Sector identification and look-up table requirement to
determine the switching intervals for all vectors make
SVM method quite complicated. Although the
difficulty of determining sectors and switching
sequences according to increased n-level inverter,
digital techniques adopted through DSP and
microprocessor to give the optimal solution.
Sigma-Delta Modulation Techniques
The delta modulation (DM) technique was firstly
introduced as a 1-bit coding method of pulse code
modulation (PCM) by Jager in1952. Originally the
DM was proposed as a 1-bit audio and video signal
encoding method in digital modulating and control
techniques issues. A SDM system was obtained [15]
adding a sample and hold block to a basic DM
modulator. A multilevel SDM generates multi-bit
data sequence and decoding the output yields several
output states which can be used to control on/off
states of the switches of the multilevel inverter. The
interaction of SDM modulator and inverter is
managed using a multilevel decode logic block that
adopts the quantized SDM signals and decodes to
switching signals for the inverter. It was found that
the sigma–delta modulators can be developed to
control multilevel inverters using logic interfaces,
reducing irregular voltage distribution and system
nonlinearity.
Combinational Modulation Techniques:
Any Hybrid Modulation Technique adopted by the
combination of any two of the Modulation
Techniques, needless of any type of category it
comes under can be termed under Combinational
Modulation Techniques.
Soft Computing Aided Modulation Techniques:
Fuzzy Logic Control
The basic idea behind FLC is to incorporate the
expert experience of a human operator in the design
of the controller in controlling a process whose input
– output relationship is described by the collection of
fuzzy control rules involving linguistic variables
rather than a complicated dynamic model. The
utilization of linguistic variables, fuzzy control rules,
and approximate reasoning provides a means to
incorporate human expert experience in designing the
controller.
The fuzzy logic approach has been objected of an
increasing interest and has found application in many
domains of control problem. The main advantage of
fuzzy logic control method as compared to
conventional control techniques is that no
mathematical model is required for controller design.
Fuzzy logic can be considered as an alternative
approach to conventional feedback control. In a
closed-loop operation, the system remains stable even
when external disturbances occur.
A firing circuit can be designed which comprises of a
PID-like fuzzy- I controller [16] used to provide to
generate the switching pulses for the inverter
switches to operate at required frequency and output
voltage magnitude.
Lijo Jacob et al., International Journal of Advanced Engineering Technology
E-ISSN 0976-3945
approach the optimal point through iteration of the
algorithm. The optimum result is the end product
containing the best elements of previous generations
where the attributes of a stronger individual tend to
be carried forward into the following generation [23].
The GA iteration algorithm explores the search space
using information from the points it has to bias the
search towards the optimal point.
Fig 15. ANN for 11-level cascaded inverter for switching
Figure 14.Staircase voltage of the proposed cascade
multilevel inverter
PID-like fuzzy controllers which can work at multioperating points with no much effort in calculating
the PID gain factors is designed in is paper. The
design of this controller based on the combination of
fuzzy logic and conventional PID control techniques.
This controller has to deal with three signals, the
error signal (e),the change of the error signal (Δe) are
the input signals, and the integral of the error signal
(∫e) is the output signal. Triangular membership
functions are used to represent the input and output of
the fuzzy block. Both the error and change of error
are represented by 3 membership functions and the
output is represented by 5 membership functions. In
the defuzzification stage of the fuzzy logic controller,
a crisp value of the output variable (V) is obtained by
using the center of area method. The idea of this
controller based on the combination of fuzzy logic
and conventional PID control techniques [17].
Artificial Neural Networks:
The Artificial Neural Networks (ANN) have found a
number of applications in engineering such as pattern
recognition, control, and classification, among others
[18][19].[20] One of the main factors for choosing
this technique is its generalization ability in nonlinear
problems that are complex in nature and/or
calculation intensive [21].
The ANN is trained such a way that switching angles
are produced by it helps in selective harmonic
elimination approximates the selective harmonic
elimination for an 11 level cascaded inverter [22].
The trained ANN is suitable for generalization of the
angles’ precision for a supply frequency of 50/60 Hz.
For a generation of the switching pulses in multilevel
inverters, a truth table is formed using the switching
angle and switching time manually using
calculations. This lookup table can be replaced by an
artificial neural network (ANN), which can be trained
and has an inherent capability of generating
switching time if the switching angle is provided.
Since ANN can determine the switching time from
the given input angle quickly it is more efficient than
the real time control real-time control which is a time
consuming one. The ANN is a feed-forward
multilayer perceptron with one hidden layer of 20
neurons and a second hidden layer of 10 neurons that
are interconnected through weighting functions.
When ANN was trained with a mixed data set it has
the ability for eliminating harmonics.
Genetic Algorithms:
Genetic Algorithms is a soft computing technique
based on the evolutionary process. It resembles the
behaviour of populations during generations based on
the idea that, through subsequent generations, the
best individuals have more probability to survive to
pass its genetic information, by the action of the
biological operators to its future generations. That
means that a set of possible solutions tends to
Int J Adv Engg Tech/Vol. VII/Issue II/April-June,2016/571-581
angle generation
Genetic Algorithms is a stochastic search method that
has been shown to be well suited for problems where
there are many global minimum and/or highly
dimensional search spaces. Each individual of a set
has an associated cost value, called fitness function
that is a measure of how good this individual is in the
population. Genetic Algorithms first because this
range is used to calibrate it to perform in the range
where there is no analytical solution. Therefore, the
correct GA parameters are found to bias the
algorithm through the desired solution. Second, it is
possible to adjust the algorithm to perform its
solutions looking at the previous results giving a
future solution, or angles in this case, which are
smooth so that the ANN training can be easier.
In a practical situation in a multilevel converter, all
the dc sources vary to some degree. This variation
can be proportional to the state of charge as it is in a
battery or fuel cell system, or it can be a function of
solar irradiation as in a solar panel. In this way, it is
necessary to control the switching angles to keep the
desired output voltage characteristics.
A new approach for modulation using selective
harmonic elimination using GA-based ANN is
utilized for an 11-level cascade multilevel inverter
[24]. Genetic algorithms are used to obtain switching
angles offline for different DC source values. Then,
artificial neural networks are used to determine the
switching angles that correspond to the real-time
values of the dc sources for each phase. The
modulating switching angles are updated at each
cycle of the output fundamental voltage thereby the
harmonics
can
be
eliminated
selectively.
Conventionally for accurate representation of every
solution for every different DC source case, large
lookup table would be required for some situations,
the solutions might be missing and some kind of
interpolation would be required hence the lookup
table is replaced by an ANN, which, if well trained,
Lijo Jacob et al., International Journal of Advanced Engineering Technology
has the inherent capability of generalizing solutions.
ANNs are computational models that were inspired
by the biological neurons. It has a series of nodes
with interconnections where mathematical functions
are applied to do an input/output (I/O) mapping. An
important feature of an ANN that made it suitable for
this problem is its flexibility to lead in its domain and
outside it, as well as work with the nonlinear nature
of the problem. The ANN used is feed forward ANN
with a tangent sigmoid function activation hidden
layer and a linear activation function output layer.
Different feed forward topologies were taken under
different training methods to investigate which one
fits for this application. When multiple solutions
occur, those that provide a smoother angle transition
are chosen since this data set will be more easily
learned by the ANN. A more challenging situation
may occur and happens when no solution exists,
which means that, at some input voltages, there are
no solutions to satisfy to completely cancel the loworder harmonics. Here GA can be used for an
approximate solution that is near to the requirement.
A set of solutions that partially satisfies the set of
output values are introduced. This procedure will
allow the harmonics to be below its nominal value.
Particle Swarm Optimization (PSO):
This technique may be utilized in conjunction with
any of the PWM technique to optimize various
parameters for an effective Pulse Width Modulation.
Kennedy and Eberhart first introduced PSO in 1995
as a new heuristic method [25]. Basically, the PSO
was inspired by the sociological behavior associated
with swarms such as a flock of birds and fish
schooling. The individuals in the population are
called a particle. Each particle is a potential solution
for the optimization problem and tries to search the
best position through flying in a multidimensional
space. The sociological behavior which is modeled in
the PSO system is used to guide the swarm so that
probing the most promising areas of search space.
Each particle is determined by two vectors in Ddimensional search space; the position vector Xi=[xi1,xi2,xi3,…….xiD]; and the velocity vector
Vi=[vi1,vi2,vi3,…….viD]
Each particle in the swarm refine sits search through
its present velocity, previous experience and the
experience of the neighboring particles. The best
position of particle i, has found so far is called
personal
best
and
is
denoted
by
Pi=[pi1,pi2,pi3,…….piD], and the best position in
entire swarm is called global best and is denoted by
Pg=[pg1,pg2,pg3,…….PgD] At first, the velocity of
the ith particle on the dth dimension is updated and
then modify the position of that particle.
In a cascade multilevel inverter, particle swarm
optimization is used for the harmonic elimination by
considering non-equality of separated DC sources
[26]. The proposed approach can be applied to solve
the problem in a simpler manner, even when the
number of switching angles is increased and
determination of them using resultant theory
approach is not possible. Particle swarm optimization
approach is developed to deal with the SHE problem
with unequal DC sources while the number of
switching angles is increased and determination of
them using conventional iterative methods as well as
resultant theory is not possible. Also, for a low
number of switching angles, the proposed PSO
Int J Adv Engg Tech/Vol. VII/Issue II/April-June,2016/571-581
E-ISSN 0976-3945
approach reduces the computational burden to find
the optimal solution compared with iterative methods
and resultant theory approach. The proposed method
solves the asymmetry transcendental equations set,
which has to be solved in cascade multilevel
inverters. Here the switching angles are created for
various switching angles and a swarm is created from
the PSO algorithm to operate. The swarm is created
in such a way that the DC sources values are changed
and corresponding harmonic values are noted. A
fitness function is prescribed for getting the switching
angles and the dc source values with reduced
harmonics. Then this fitness function is inserted in
the PSO code for getting the best values such a way
that that the fundamental harmonics are below 5%
and lower harmonic orders are reduced.
IV. CONCLUSION
This paper brings about an elaborate survey of the
different modulation techniques used in multi-level
inverters
highlighting
its
advantages
and
disadvantages. The same can be extended for
research and classification can be updated with
progressive researches under either of the categories
of techniques or under a new classification
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