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2.1 Introduction

Pulse width modulated (PWM) inverters are mostly used power electronic circuits in

practical applications. These inverters are able to produce ac voltages of variable magnitude

and frequency. The quality of the output voltage of PWM inverter is better as compared to

square wave inverters. The PWM inverters are commonly used in variable speed ac drives.

Wide speed variation of drive can be obtained by varying the frequency of the applied ac

voltage. There should be linear relationship between applied voltage and frequency. The

PWM inverters could be implemented for use in single phase and three phase types. There

are different kind of PWM techniques, depending on the methods of implementation.

However, in all these techniques, the generated output voltage after filtering, obtain a good

quality sinusoidal voltage waveform having desired fundamental frequency and magnitude

respectively.

PWM inverters are used to control the voltage and to reduce the harmonic contents in the

output voltage. In case of PWM inverters, the width of the output pulses are modulated to

achieve the desired voltage control (Lavanya et. Al., 2012). Among the large number of

modulation techniques, some modulation techniques are discussed in the coming section.

• Single Pulse-Width Modulation (SPWM)

• Multiple or Uniform Pulse-Width Modulation (UPWM)

• Sinusoidal Pulse-Width Modulation (sin-PWM)

• Modified Sinusoidal Pulse Width Modulation.

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2.2 Single pulse width modulation

In single pulse width modulation control technique only one pulse is present

in every half cycle. By adjusting the width of the single pulse we can control the

output voltage of the inverter. The gating signals are generated by comparing

rectangular reference signal of amplitude (Ar) and a triangular carrier wave (Ac),

which has been shown in Figure 2.1. This generated gating signal can be used to

control the output of single phase full bridge inverter. The fundamental

frequency of the output voltage can be obtained by the frequency of the

reference signal.

For this technique the amplitude modulation index (M) can be defined as

𝑀 =𝐴𝑐

𝐴𝑟

,

whereas the instantaneous output voltage of the inverter can be given as

V0 = V1(S1 – S4)

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Ac

Ar

Ac

wt

wt

wt

wt2π

2π

2π

π

π

π

π/2

π/2

π/2 – δ/2 π/2 + δ/2

δ

α1 α20

S1

0

S4

0

V0

Vs

-Vs

0

Carrier Signal

Reference Signal

Figure 2.1 Generation of Single pulse width modulation

2.3 Multiple Pulse Width Modulation (MPWM)

The main drawback of single PWM technique is high harmonic content. The

multiple PWM technique is used in order to reduce the harmonic content. In this

technique, a number of pulses are given in each half cycle of output voltage. The

gating signal are generated by comparing the reference signal of the amplitude (Ar)

with a triangular carrier wave (Ac) as shown Figure 2.2.

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Ac

Ar

0

0

wt

wt

wt2π

2π

π/2

α1

α2

ππ/2

π

δ

Carrier Signal

Reference Signal

S4

S1

Figure 2.2 Generation of Multiple pulse width modulation

The frequency (fo) of the output can be determined by the frequency of the

reference signal. By varying the modulation index the output voltage can be controlled.

The number of pulses ‘P’ per half cycle is calculated by the carrier frequency (fc). Number

of pulses per half cycle is found by

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𝑃 =𝑓𝑐

2𝑓𝑜

= 𝑀𝑓

2

Where

𝑀𝑓 =

𝑓𝑐

𝑓𝑜

, called as frequency modulation ratio.

The instantaneous output voltage of the inverter can be given as

V0 = V1(S1 – S4).

2.4 Sinusoidal Pulse Width Modulation (SPWM)

The generation of a sinusoidal Pulse Width Modulation signal has been shown in

Figure 2.3. This technique has been used in industries. The gating signal can be

generated by comparing a sinusoidal reference signal with a triangular carrier wave.

The width of each pulse is changed proportionally to the amplitude of a sine wave

evaluated at the center of the same pulse.

The output frequency ‘fo’ of the inverter can be determined by using the frequency of

the reference signal ‘fr’. The output voltage (Vo) can be controlled by modulation index

‘M’ and in turn peak amplitude ‘Ar’ controlled the modulation index. The output voltage

can be determined by Vo = Vs(S1 – S4). The number of pulses per half cycle depends on the

carrier frequency. The gating signal can be generated by using an unidirectional triangular

carrier wave.

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Figure 2.3 Generation of Sinusoidal pulse width modulation

2.5 Modified Sinusoidal Pulse Width Modulation

In a sinusoidal PWM waveform, the pulse width is not changed considerably by the

variation of modulation index due to the characteristics of the sine wave. Hence, this

technique can be modified in a manner that the carrier signal is applied during the first

and last 60º intervals per half cycle (Panahi, 1997) as shown in Figure 2.4. So in this

way the fundamental component is increased and its harmonic characteristics are

improved. The main advantages of this technique are increased fundamental

component, better harmonic characteristics, reduced number of switching power

devices and low switching losses.

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Ar

Ac

0

S1

0

0

S4

Carrier Signal

Reference Signal

π/2 π 2π

2ππ

wt

wt

wt

Figure 2.4 Generation of Modified sinusoidal pulse width

modulation

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2.6 Need of grid-tie Inverter in Renewable Energy System

A grid-tied inverter is a power inverter that converts direct

current (DC) into alternating current (AC) and it has an ability to synchronize and could be

interfaced with the utility grid. They found applications in converting direct current obtained

from solar panels into AC before being tied to the utility grid. The residential and

commercial loads are grid-tied in many countries which sell their surplus energy to the utility

grid. There are several ways of taking compensation of the electricity which is delivered to

the grid. By net metering, the consumer that has the renewable energy power source receives

compensation from the utility for its net outflow of power. For example, if during a given

month a power system feeds 500 kilowatt-hours of electricity into the grid and uses only 100

kilowatt-hours from the grid, it would get a compensation for 400 kilowatt-hours of

electricity. Feed-in tariff is another policy, by which the person is paid for delivering

electricity to the grid for every kilowatt hour by a special tariff which is based on a contract

with distribution company.

Inverters changes DC power into AC power so it can be fed to the utility grid. But

before feeding it to the grid the frequency of the grid tie inverter (GTI) must synchronize

with that of the grid (e.g. 50 or 60 Hz) using a local oscillator and also its voltage is limited

from having magnitude higher than that of grid voltage. A high-quality modern GTI having

fixed power factor of unity, which means its output voltage and current are entirely lined up,

and its phase angle is within one degree of the AC power grid. The inverter has an on-board

computer for sensing the current AC grid waveform and the output voltage should

correspond to that of the grid voltage. However, to keep the voltage within its allowed limit

in the local grid supplying reactive power to the grid might be necessary. Otherwise, the grid

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segment with significant power from renewable sources, voltage levels may rise in excess at

times of high production, i.e. at noon.

Grid-tie inverters are designed in a manner that it could be disconnected quickly from

the grid if the utility grid fails. An NEC requirement ensures that in the event of a blackout,

the GTI shall be shut down to prevent the energy transfers and harming any line man or

worker responsible for maintenance work.

Grid tie inverter enables a person to use an alternative power generation sources at

home like solar or wind power without extensive rewiring and without batteries. If the non

conventional source generate power which is insufficient, then this deficit would be taken

from the utility grid.

2.7 Needs & problems of synchronisation with PWM inverters

It is very essential that the PWM inverters should be synchronized before tied to the

utility grid. Phase, frequency, and phase voltages amplitude are the most important and basic

parameters which are needed to be controlled for grid-connected applications (Rajan, 2015).

The synchronization is generally carried out with respect to the voltage, phase angle of

voltage (or current) signal and frequency of the utility system. In order to provide the

required load voltage, inverter system works in standalone or grid connected mode. In load

scheduling condition or grid off condition, the inverters works in standalone mode and

provide the required power to the load. The power available via renewable systems is of DC

form so inverters are preferred to alternators. The Parameters of the inverter such as voltage,

frequency and phase could be controlled for the purpose of synchronization with the

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respectives parameters of the grid system. Synchronization of inverter parameters like

voltage, frequency and phase with grid systems shall be possible using specific control

system with embedded controller. To meet the load sharing requirement, the output from the

inverter system could be varied in synchronism with the grid system (Yeng and Sng, 2006;

Wu et. Al., 2007; Hua et. Al., 2012) .

Sinusoidal pulse width modulation technique have several pulses per half-cycle and

the width of each pulse is changed with respect to the magnitude of sine wave (Rajan,

2015). Pure sine wave dc-to-ac conversion will introduce smallest amount of harmonics into

an electrical system, but these methods are also expensive. Since the AC sine wave is to be

originated from a DC source, the static devices shall be switched in a logical way such that

the energy which is delivered to a load approaches to that of a pure sine wave. This means

that an extra components and design considerations are involved in its control circuitry in

case of a pure sine wave inverter thereby driving up its cost. A modified sine wave method of

dc-to-ac conversion is more precise method, which introduces a dead time in a normal square

wave output so that higher peak voltages can be used to produce the same average voltage as

a sinusoidal output. This method generates lesser harmonics than square wave generation, but

it is also not as the AC power that we get from an AC supply. The harmonics are still present

in a modified sine wave, so the modified sine wave inverters are unsuitable for use and

moreover an electrical noise is of concern. Synchronization and symmetry can be obtained by

using the space vector pulse width modulation (SVPWM) algorithm, with proper selection of

switching states. This is standard approach without any additional computational

requirements or feedback signals. This synchronization algorithm can be used for open-loop

constant v/f ac drives (Beig, 2012). Further implementation of modified synchronized space

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vector pulse width modulation (SVPWM) algorithm for three level voltage source inverter

(VSI) with Synchronized and Symmetrical Waveforms can be obtained by maintaining the

synchronization, half-wave symmetry, quarter-wave symmetry, and three-phase symmetry in

the pulse width modulation (PWM) waveforms. Another approach is shifted synchronized

space vector pulse width modulation (SVPWM). This method is used to Control DC Link

Resonant Inverters. Its FPGA realization increase the switching frequency of the inverter,

also it reduces the switching frequency of the dc-link resonant circuit (Chung et. Al., 2010,

Serban and Serban 2010, Beig 2012, Beig et. Al., 2007, Pan et. Al., 2012)

2.8 AC to DC Converter as Inverter

A converter circuit with RLE load can be operated in two modes i.e. rectification

mode and inverter mode. It works in inversion mode when the switching angle of the

converter is greater than 90º. If the polarity of the battery of single phase full converter is

reversed and switching angle becomes greater than 90º then the converter can act as a line-

commutated inverter. A line commutated inverter is basically a phase controlled converter

with an RLE load. The power flow is from ac source to the dc source in some part of voltage

cycle whereas it is from the dc source to the ac source in some other part of the cycle.

However, the average value of the power flow is negative (Tariq et. Al.,2011). Normally

switching angle is varied upto 1650 in inversion mode of operation to facilitate the line

commutation voltage for SCR. As the converter can acts as a line-commutated inverter so

there is no need of synchronization. The line current is of square type in shape so the total

harmonic distortion (THD) is very high. Thus, we go for 3-phase, 6-pulse ac-to-dc converter

with RLE load which can act as a line commutated inverter for switching angle greater than

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90º. The wave shape of the line current is somewhat improved but the T.H.D is still high.

Thus for high power demand and to improve the wave shape of the line current thereby

reducing T.H.D, the better option is to use a multilevel Inverter. In the next chapter, basics of

multilevel inverter and its topologies have been discussed.