A Critical Review of Modulation Techniques

A. Aktaibi, graduate student member, IEEE, M. A. Rahman, life fellow, IEEE, A. Razali, graduate student member, IEEE

Faculty of Engineering and Applied Science

Memorial University of Newfoundland

St. Johns, NL, Canada, A1B 3X5 aama38@.mun.ca; mrahman@mun.ca; azziddin.razali@mun.ca

Abstract A review of the state-of-art of Modulation Techniques, used for switching the Power electronics inverters and converters, is presented in this paper. It presents a comparison

among various modulation strategies and reviewing their advantages and disadvantages. Also it gives a short explanation about the principle of operation of the classic and the advanced

modulation techniques starting with the standard PWM and finishing with the invention of the wavelet modulation technique (WM). The output of the wavelet modulated power inverter is found to be the best approximation of the continuous-time sinusoidal reference signal over all other modulation techniques.

Index terms critical review, Carrier based modulation, Carrier less based modulation, PWM, wavelet modulation.

I. INTRODUCTION

he DC-AC inverters are electronic devices used to

produce AC power from DC source. This makes them

very suitable for whenever you need AC power as AC mains

power is not always available in remote areas.

Most inverters do their job by performing two main

functions: first they convert the incoming DC into AC, and

then they step up the resulting AC to the needed voltage level

using a transformer. There are many ways to control the

output of the inverters; one of the efficient conventional

methods is the pulse-width modulation (PWM). PWM is a

very efficient way of providing intermediate amounts of

electrical power. A simple power switch with a typical power

source provides full power only when switched on. It is a

comparatively recent technique, made practical by modern

electronic power semiconductor switches.

Modulation techniques are used for switching and operating

inverters and controlled converters in order to produce output

voltages and currents with higher qualities for different types

of loads. By using these modulation techniques we can control

the switching electronic device to get the desired amplitude

and frequency with the desired quality.

Several switching techniques have been so far proposed to

meet the aforementioned objectives by achieving wide linear

modulation range, minimum switching losses and improved

overall inverter efficiency and finally simple implementation

for practical applications [15]. There are many types of

modulation and some of them are:

Carrier based modulation, such as;

1- Sinusoidal pulse width modulation (SPWM)

2- Modified pulse width modulation (MPWM)

3- Random pulse width modulation (RPWM)

4- 3rd harmonic injection PWM

5- Space vector modulation (SVM)

Carrier less modulation, such as;

1- Delta modulation (DM)

2- Specific harmonic elimination (SHE)

3- Wavelet modulation (WM).

The main aim of all of these techniques is to enhance the

output of the inverters in terms of the following reasons. In

other words, these various techniques are designed to control

the inverter switches in order to shape the output ac voltage

and currents to be as close to sine wave as possible. Pulse

width modulation (PWM) is the first approach of modulation

techniques which was developed in the mid of 60s by

Kirnnich, Heinrick and Bowes. The quality of these

techniques can be measured by six factors:

1- The amplitude of the fundamental component,

2- The harmonic content in the inverter output,

3- The effect of harmonics on the source,

4- The switching losses,

5- Controllability,

6- Implementation.

II. THE MODULATION TECHNIQUES

1-Conventional Pulse Width Modulation (SPWM):

The conventional pulse-width modulation is the most

widely used technique all over the world because of its

advantages or because of that its disadvantages do not have

that big concern in most of the applications compared with its

advantages. Some of the advantages of PWM based switching

power converter over the other techniques can be in its easy to

implement and control and in its compatibility with almost all

the modern digital applications. However it has also some

disadvantages that might reduce its volubility in some

applications, such as its attenuation of the fundamental

frequency amplitude, its THD is reduced by increasing the

switching frequency but that will lead to the increase of

switching losses; which means greater stresses on the

associated switching devices and creation of high-frequency

components with high amplitudes.

2-Modified Pulse Width Modulation (MPWM):

The main principle of the MPWM is based on the

comparisons between two low-frequency modulating signals

with a triangular high frequency carrier. The first modulating

signal is similar to the fundamental signal of the desired

output voltage. The other modulating signal is also similar to

the first signal but with a phase shift of 180 electrical degrees.

The advantage of the MPWM over the conventional SPWM is

T

in the location of the first harmonic. Where the SPWM is

pushing back the harmonics towards the high frequencies by

which the first significant sideband of the output voltage

spectrum is located in the switching frequency sideband,

However the MPWM is able to shift back the first significant

harmonic to a frequency equal to twice of the switching

frequency. This means that the THD of the MPWM is less

than that of the SPWM with the same switching frequency, but

the fundamental component is not too high. This method is

easy to implement and control, but it has some disadvantages

in high switching stresses on the semiconductor devices and

also its effect of the harmonic content on the input side is high

as well.

3- Random pulse width modulation (RPWM):

Random pulse width modulation technique is basically

based on randomizing the frequency of the carrier signal in

order to distribute the concentrated energy of the harmonic

frequency of the inverter output voltage in a narrow high

frequency band. The main purpose and advantage of this

technique is to reduce the energy of the harmonics, which in

turn will reduce the THD of the inverter output voltage.

However, this action will also affect the energy of the

fundamental frequency component, i.e. the amplitude of the

fundamental frequency component will be reduced as well,

which is the main disadvantage of this technique. Also it has a

significant drawback, which is the rapid deterioration of

quality of operation at low values of modulation index.

Moreover, randomizing the carrier frequency adds an extra

switching losses and extra stresses to the semiconductor devices

which in turn lead to add more harmonics to the current signal in

the input side.

This technique can be summarized in three different

strategies as follows [8]:

A) Randomized Switching Frequency, which is also, can be

divided into two ways: the regular and the natural sampling

mode. In which the regular sampling mode is characterized

by randomly changing of the switching intervals from cycle

to cycle by an integer number N in the output frequency.

Whereas the natural sampling method is obtained using

either the classic triangular carrier method or space vector

method. The triangular carrier signal, with which the

reference voltage signal is compared, can be generated with

a randomly varying slope In the case of space vector

RPWM; these are the consecutive increments of the angular

position of the reference voltage vector that are randomized.

B) Randomized Pulse Position; in which the pulses of

switching signals are randomly placed in individual

switching intervals.

C) Random Switching; in this method, randomly fractional

numbers, having uniform probability distribution, are

compared with the desired duty cycle of the switching

signals for individual phases of the inverter.

4- 3rd Harmonic injection PWM (3HPWM):

By injecting the 3rd

harmonic to the three-phase sinusoidal

modulating signals, the inverter fundamental frequency

voltage can also be increased without causing over

modulation. In which, the modulating signal is composed of

the fundamental component and the third harmonic

component, making the signal somewhat flattened on the top.

As a result, the peak fundamental component can be higher

than the peak triangular carrier wave which boosts the

fundamental voltage.

The injected third harmonic component will not increase the

harmonic distortion in the output voltage. Although it appears

in each of the inverter terminal voltages, the third-order

harmonic voltage does not exist in the line to line voltage.

This is because the line to line voltage is given by the relation

Vab=Van - Vbn, where the third-order harmonics in Van and Vbn

are of zero sequence with the same magnitude and phase

displacement and thus cancel each other. The main

disadvantage of this technique is that there is no defined

procedure for determining the proper amount of the added

third harmonic component [15].

5- Space vector modulation (SVM)

Space vector modulation for three-leg VSI is based on the

representation of the three phase quantities as vectors in a two-

dimensional (, ) plane. To make the output current must

always be continuous, and also the input lines must never be

shorted, the voltage source inverter can assume only eight

distinct switching topologies. The desired three phase voltages

at the output of the inverter could be represented by an

equivalent vector U rotating in the counter clock wise

direction. There are four types of SVM [29, 30, 31];

1) The right aligned sequence,

2) The symmetric sequence which has the lowest THD

because of the symmetry and the switching losses are almost

similar to the first one,

3) The alternating zero vector sequence, where the switching

losses for this scheme are to be ideally low as compared to

those of the previous two schemes and the THD is

significantly higher due to the existence of the harmonics at

half of the sampling frequency,

4) The highest current not switched sequence in which the

switching losses are the lowest compared with the others

because it avoids switching the phase carrying the highest

current. However, the sampling period Ts is the same in all

of them.

The converter input voltage can be represented by the space

vector U. The space vector U once can take one of the eight

different positions resulting from the permissible

combinations of the conduction states. Vectors U1 to U6 have

fixed modulus of Udc and are phase-shifted by /3. They

are called active vectors and refer to the conduction states of

the power semiconductor switches during which the respective

phases are supplying the DC-link load. While the three upper

or three lower power semiconductor switches are conducting

simultaneously, the supply line is short-circuited. These states

are described by two zero vectors U0 and U7. The zero vectors

are located in the origin of coordinates and they are

represented by the two concentric points. The converter input

PWM voltage space vector would change its position every

/3inside the hexagon if the six active conduction states were

successively forced in the rectifier. The optional position of

the reference vector U* inside the sector can be reached by

providing the symmetrical control pulses represented by the

following switching sequence: U0-U1-U2-U7-U2-U1-U0. In

case when the reference vector U* is moving throughout the

first sector. In the other sectors two next adjacent vectors

should be considered [31].

The Total Harmonic Distortion ratio of the line current and

voltage are equal THDI = 1.6% and THDV = 26.7%

respectively [15]. For the linear modulation the maximal

length of the reference vector U* is equal to U*max = Udc/ 3 .

The space vector modulation corresponds to the sinusoidal

modulation with the additional zero sequence signals.

6- Delta modulation (DM):

Delta modulation technique has the advantage of easy

implementation, continuous converter voltage control, and a

direct control of the line harmonics. However, the DM control

has the drawback of low fundamental output value and

asymmetrical operation. This technique is similar to other

modulation technique, but the inherent self-carrier generating

feature of the DM technique allows simple control process for

varying the output voltage. With the normal delta modulation

technique, in which the carrier signal has equal rising and

falling edges, the output voltage is maximally have the

available voltage. This limitation can be mitigated by

asymmetrical control of the modulator. In this way, the rising

slope is not equal to the falling slope of the estimated wave

and the quantizer threshold levels p and n control the

output voltage. When p > n, the output increases with the

increase of p; and n > p, the output decreases with the

increase of n [10].

The delta modulation technique has recently drawn great

attention as a promising control scheme for static power

converters to achieve fast response [11, 12]. However, the DM

control has the drawback of low fundamental output value and

asymmetrical operation [10, 14] which was overcame by

proposing the rectangular wave DM, which can control the

output harmonics by adjusting its modulator parameters.

Because of its inherent V/f feature and the attenuation of low

order harmonics, the rectangular wave DM is suitable for AC

motor control. However, the inverter output waveform is not

synchronized with the control signal because the duty ratio

modulation depends on the slope of the control signal.

This asynchronous operation introduces a periodic

asymmetry resulting in the generation of sub-harmonics which

will cause unwanted torque pulsations. There are many

approached of DM are proposed so far, such as; conventional

delta modulator, delta modulator with PI control, carrier

synchronized DM, tuned delta modulator and feed forward

delta modulation.

7- Specific harmonic elimination (SHE):

Specific harmonic elimination is based on predefining sets

of switching angles in order to determine locations and widths

of the switching pulses. This type of inverter has shown the

possibility of eliminating certain harmonics in the inverter

output [2, 12, 15].

Essentially, to eliminate the same number of low order

harmonics, PWM-SHE requires the use of 50% less switching

pulse over the conventional carrier modulated SPWM method

[27]. This automatically implies less stress on the switching

device and hence less switching loss. Higher quality inverter

output voltage and current waveform and a smaller filter size

is attainable without the expense of high switching loss.

This technique is a non-carrier based PWM scheme, and it

is based on the fact that conditions of quarter and half wave

symmetry are capable of eliminating even indexed harmonics.

Another key advantage of PWM-SHE switching pattern is the

inverters higher fundamental output voltage component [27].

By extending this concept it has led to consider angles of

switching pulses in the first quarter cycle as variables for

optimization in order to eliminate more harmonics from the

inverter output. The main disadvantage of this method is its

complicated implantation especially in finding the switching

angles [15].

8- Hysteresis-Band Current Control (HBCC)

It is based on calculating the error between the reference

output and the measured output signals. The switching

elements states are changed when the instantaneous calculated

error falls outside a pre-defined hysteresis band in order to

drive the error back within that hysteresis band. Where the

targeted output was the inverter output current, and the early

implementations of hysteresis-band current control switching

scheme were based on a fixed hysteresis band. An adaptive

current controller was developed which uses a variable

hysteresis band. This controller suffered from the stability

problems as the load changes [15].

The sinusoidal hysteresis band was able to limit the

maximum switching frequency and improved both output

current and voltage of the operated inverter. However, this

method requires that the controlled output quantity of the

inverter be integrated either by the load or as a part of the

controller. Thus, sub-harmonics may be present in inverter

outputs. These reasons made the hysteresis band current

control switching scheme not very useful for industrial

applications with low switching frequencies.

The conventional fixed hysteresis-band current control

generates excessive current ripple because modulation

frequency varies within a band. In an adaptive hysteresis-band

method, the band is modulated as a function of system

parameters to maintain the modulation frequency to be nearly

constant. Systematic mathematical analysis has been

presented, and band expressions have been derived as a

function of the load machine and supply parameters for

connected and isolated neutral cases [25].

9- Wavelet modulation (WM):

The seeds of the wavelet theory were planted in the

beginning of 20th century by Alfred Haar. In 1909, he found

an orthogonal system of functions defined on (0, 1), that form

a series converging uniformly to a continuous function f. What

Haar found was the simplest basis of the family of wavelet

bases. Then the rapid progress in the field was made in the

beginning of the 1980s. In the early 1980s, the wavelet

transform was studied theoretically in geophysics and

mathematics by Morlet, Grossman and Meyer [28].

In the late 1980s, links with digital signal processing were

pursued by Daubechies and Mallat, thereby putting wavelets

firmly into the applications domain. From 1990s many

applications are developed by utilizing wavelet transform in

all fields of research. In 2007, Saleh and Rahman developed

the wavelet modulation techniques for AC-DC converters,

which gave a new application for the wavelets. They have

successfully developed and experimentally tested a new type

of inverters that is capable of producing outputs with

significantly improved quality. This new type of inverters is

called the wavelet modulated (WM) inverter [15, 18].

Any continuous time signal can be expanded using sets of

wavelet basis functions. These sets can be generated for every

scaling function at each scale by integer translations. Also a

dual scaling function will exists for the same scaling function,

when these dual functions generate other sets of basis

functions which are required to complete the expansion of any

CT signal. Both of these sets of basis functions are capable of

constructing a multiresolution analysis (MRA) which called

dyadic-type MRA. However all known scaling functions have

basis functions that can only support uniform sampling. In the

case of inverters switching, the uniform sampling is not useful

for switching these inverters. [1, 15, 18, 26]

Alternatively, a non-uniform sampling can be used for

switching the inverters, which require designing a special class

of scaling and dual scaling functions that can construct a MRA

of a non-dyadic type. The inverter function with a non-

uniform recurrent sampling reconstruction case means that the

output pulses have a quarter cycle symmetry. This non-

uniform recurrent sampling requires designing a unique non-

dyadic type MRA by using a special unique form of Haar

wavelet function. This function generates a train of non-

uniform recurrent pulses used to pulsate the inverter

semiconductor switches matrix. Generating switching pulses

are dilated and shifted versions of the synthesis scaling

function.

Saleh and Rahman has experimentally developed and tested

this new type of inverters that is capable of producing an

inverter output voltage with significantly higher fundamental

frequency component voltage and lower higher harmonic

component. This new type of inverters is called the wavelet

modulated WM inverter. The advantages of this approach are

it is able to produce output voltages and currents with higher

magnitudes of the fundamental component and lower

harmonic contents better than the other types of modulation

techniques. The basis of the wavelet modulation technique lies

in the definition of the scale-based linearly combined scaling

function, which is used to sample the reference-modulating

signal in a non-uniform recurrent manner [15, 26].

In a three phase six-pulse inverter, three reference-

modulating signals are used to generate the required switching

pulses. As a consequence, three scaling functions are needed

to sample these three signals. It is to be noted that these three

reference-modulating signals have the same frequency and

magnitude with a phase shift of 2/3 from each other. Finally, the new WM modulated inverter is mainly based on

constructing three shifted non-dyadic type MRAs to sample

and reconstruct three sinusoidal reference-modulating signals.

[1, 26]

III. CONCLUSION

This paper has presented an analysis of the various state of

art of modulation techniques. An investigation is carried out

on the most important modulation techniques. All of the

investigated techniques have advantages and disadvantages

except the wavelet modulation which have been recently

invented. It has been found that this technique is met with all

measuring factors that are used to calibrate the performance of

any other modulation techniques:

1- The amplitude of the fundamental component is high,

2- The harmonic content in the inverter output is low,

3- The effect of harmonics on the source is low,

4- The switching losses are low,

5- Controllability is easy,

6- Implantation is simple.

On the other hand, all other techniques have shortcoming in

at least one of the aforementioned factors. That is in turn will

reduce the efficiency of that technique.

The three phase wavelet modulated WM inverter has shown

significant capabilities in terms of the quality of the output

voltages and currents. It provided output voltages and currents

with low harmonic content along with high magnitudes of the

fundamental frequency component of the output voltage. In

addition, the performance comparison of the WM and all the

other modulation techniques revealed that the new WM

inverter can out-perform all of them under same operating

conditions.

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