UNIT 2

HARMONIC CONTROL AND POWER FACTOR IMPROVEMENT

PART B
1. Write short notes about the control techniques and switching waveforms, output
voltage equations of the following.
a. Pulse width modulation (PWM) control
b. Sinusoidal Pulse width modulation (PWM) control
Pulse width modulation (PWM) control
Pulse Width Modulation technique used in wide variety of applications: power
electronics, sound production, telecommunication, lighting systems, etc. In electronics and
telecommunications, modulation is the process of varying one or more properties of a
periodic waveform, called carrier signal (high frequency signal), with a modulating signal
that typically contains information to be transmitted. Modulator in power control systems (in
which PWM was used): It’s a device that breaks up a DC voltage into pulses which can be
changed to our needs. When we change the width of the pulses, we are modulating them.
Pulse Width Modulation (PWM) is a powerful method for generating an analog signal using
a digital source. A PWM signal consists of two main components that define its behavior: a
duty cycle and a frequency. The duty cycle describes the amount of time the signal is in a
high (on) state as a percentage of the total time of it takes to complete one cycle. The
frequency determines how fast the PWM completes a cycle (i.e. 1000 Hz would be 1000
cycles per second), and therefore how fast it switches between high and low states. By
cycling a digital signal off and on at a fast enough rate, and with a certain duty cycle, the
output will appear to behave like a constant voltage analog signal when providing power to
devices. Output signal alternates between on and off within specified period, yields Controls
power received by a device. The voltage seen by the load is directly proportional to the
source voltage. The on-off behavior changes the average power of signal .A PWM signal is
not constant, the main parameter is a duty cycle D that is a part of PWM period and describes
the proportion of on time to regular interval. Equation (1), Figure (1) describes the duty cycle
as the following:

PWM GENERATION
Several methods were used to Generate PWM signals. One of them is Analogue method.
Analogue PWM signals (comparator output) can be made by combining a saw- tooth
waveform and a sinusoid, the higher the DC level is, the wider the PWM pulses are. The DC
level is the demand signal .as shown in figure

Control of inverter output voltage: -PWM frequency is the same as the frequency of Vtri -
Amplitude is controlled by the peak value of Vcontrol -Fundamental frequency is controlled
by the frequency of Vcontrol
Modulation Index (m)

Sinusoidal Pulse width modulation (PWM) control

For PWM control, two inputs are required: a sinusoidal reference signal, also called a control
signal or a modulating signal, and a carrier signal. The triangle wave controls the switching
frequency of the inverter. Bipolar and unipolar switching are the two available methods of
switching. Both methods compare the reference signal and the carrier signal and cause
switching conditions that correspond to the two signals.
2. Explain in details the following classes of forced commutation methods
a) Class A (Self commutated by resonating the load)
b) Class B (Self commutated by an L-C circuit)
c) Class C ( C or L-C switched by another load–carrying SCR )
d) Class D ( L-C or C switched by an auxiliary SCR )
e) Class E ( External pulse source for commutation )
f) Class F ( AC line commutated )

Class A (Self commutated by resonating the load)

When the SCR is triggered, anode current flows and charges up C with the dot as
positive. The L-C-R form a second order under-damped circuit. The current through the SCR
builds up and completes a half cycle. The inductor current will then attempt to flow through
the SCR in the reverse direction and the SCR will be turned off.
The current may be expressed as

The solution of the above equation is of the form

The capacitor voltage is at its peak when the SCR turns off and the capacitor
discharges into the resistance in an exponential manner. The SCR is reverse-biased till the
capacitor voltages returns to the level of the supply voltage V.

Class B (Self commutated by an L-C circuit)

The Capacitor C charges up in the dot as positive before a gate pulse is applied to the
SCR. When SCR is triggered, the resulting current has two components. The constant load
current Iload flows through R - L load. This is ensured by the large reactance in series with the
load and the freewheeling diode clamping it. A sinusoidal current flows through the resonant
L-C circuit to charge-up C with the dot as negative at the end of the half cycle. This current
will then reverse and flow through the SCR in opposition to the load current for a small
fraction of the negative swing till the total current through the SCR becomes zero. The SCR
will turn off when the resonant–circuit (reverse) current is just greater than the load current.
The SCR is turned off if the SCR remains reversed biased for tq > toff, and the rate of rise of
the reapplied voltage < the rated value.
Class C (C or L-C switched by another load–carrying SCR)
This configuration has two SCRs. One of them may be the main SCR and the other
auxiliary. Both may be load current carrying main SCRs. The configuration may have four
SCRs with the load across the capacitor, with the integral converter supplied from a current
source. Assume SCR2 is conducting. C then charges up in the polarity shown. When SCR1 is
triggered, C is switched across SCR2 via SCR1 and the discharge current of C opposes the
flow of load current in SCR2

Class D (L-C or C switched by an auxiliary SCR)

The circuit shown in Figure 3 (Class C) can be converted to Class D if the load
current is carried by only one of the SCR’s, the other acting as an auxiliary turn-off SCR.
The auxiliary SCR would have a resistor in its anode lead of say ten times the load resistance.
 SCRA must be triggered first in order to charge the upper terminal of the capacitor as
positive. As soon as C is charged to the supply voltage, SCR A will turn off. If there is
substantial inductance in the input lines, the capacitor may charge to voltages in excess of the
supply voltage. This extra voltage would discharge through the diode-inductor-load circuit.
When SCRM is triggered the current flows in two paths: Load current flows through the load
and the commutating current flows through C- SCR M -L-D network. The charge on C is
reversed and held at that level by the diode D. When SCR A is re-triggered, the voltage across
C appears across SCRM via SCRA and SCRM is turned off. If the load carries a constant
current as in Figure the capacitor again charges linearly to the dot as positive.
Class E (External pulse source for commutation)
The transformer is designed with sufficient iron and air gap so as not to saturate. It is
capable of carrying the load current with a small voltage drop compared with the supply
voltage. When SCR1 is triggered, current flows through the load and pulse transformer. To
turn SCR1 off a positive pulse is applied to the cathode of the SCR from an external pulse
generator via the pulse transformer. The capacitor C is only charged to about 1 volt and for
the duration of the turn-off pulse it can be considered to have zero impedance. Thus the pulse
from the transformer reverses the voltage across the SCR, and it supplies the reverse
recovery current and holds the voltage negative for the required turn-off time.
Class F (AC line commutated)
If the supply is an alternating voltage, load current will flow during the positive half
cycle. With a highly inductive load, the current may remain continuous for some time till the
energy trapped in the load inductance is dissipated. During the negative half cycle, therefore,
the SCR will turn off when the load current becomes zero 'naturally'. The negative polarity of
the voltage appearing across the outgoing SCR turns it off if the voltage persists for the rated
turnoff period of the device. The duration of the half cycle must be definitely longer than the
turnoff time of the SCR. The rectifier in Fig.3.6 is supplied from an single phase AC supply.
The commutation process involved here is representative of that in a three phase converter.
The converter has an input inductance Ls arising manly out of the leakage reactance of the
supply transformer. Initially, SCRs Th1 and Th1' are considered to be conducting. The
triggering angle for the converter is around 600. The converter is operating in the continuous
conduction mode aided by the highly-inductive load. When the incoming SCRs, Th2 and
Th2' are triggered, the current through the incoming devices cannot rise instantaneously to
the load current level. A circulating current Isc builds up in the short-circuited path including
the supply voltage, Vs-Ls-Th1'- Th2 and Vs- Ls-Th2'-Th1 paths. This current can be
described by:
This expression is obtained with the simplifying assumption that the input inductance
contains no resistances. When the current rises in the incoming SCRs, which in the outgoing
ones fall such that the total current remains constant at the load current level. When the
current in the incoming ones reach load current level, the turn-off process of the outgoing
ones is initiated. The reverse biasing voltage of these SCRs must continue till they reach their
forward blocking state. As is evident from the above expression, the overlap period is a
function of the triggering angle. It is lowest when α ~ 900. These SCRs being 'Converter
grade', they have a larger turn-off time requirement of about 30-50 μsecs. The period when
both the devices conduct is known as the 'overlap period'. Since all SCRs are in conduction,
the output voltage for this period is zero. If the 'fully-controlled' converter in is used as an
inverter with triggering angles > 900 , the converter triggering can be delayed till the 'margin
angle' which includes the overlap angle and the turn-off time of the SCR - both dependent on
the supply voltages.

3. Briefly explain about square wave voltage harmonics for a single phase bridge.
Voltage source inverters (VSI) have been introduced in Lesson-33. A single-phase
square wave type voltage source inverter produces square shaped output voltage for a single-
phase load. Such inverters have very simple control logic and the power switches need to
operate at much lower frequencies compared to switches in some other types of inverters,
discussed in later lessons. The first generation inverters, using thyristor switches, were
almost invariably square wave inverters because thyristor switches could be switched on and
off only a few hundred times in a second. In contrast, the present day switches like IGBTs
are much faster and used at switching frequencies of several kilohertz. Single-phase inverters
mostly use half bridge or full bridge topologies. Power circuits of these topologies are
redrawn in Figures.

In this lesson, both the above topologies are analyzed under the assumption of ideal
circuit conditions. Accordingly, it is assumed that the input dc voltage (Edc) is constant and
the switches are lossless. In half bridge topology the input dc voltage is split in two equal
parts through an ideal and loss-less capacitive potential divider. The half bridge topology
consists of one leg (one pole) of switches whereas the full bridge topology has two such legs.
Each leg of the inverter consists of two series connected electronic switches shown within
dotted lines in the figures. Each of these switches consists of an IGBT type controlled switch
across which an uncontrolled diode is put in anti-parallel manner. These switches are capable
of conducting bi-directional current but they need to block only one polarity of voltage. The
junction point of the switches in each leg of the inverter serves as one output point for the
load. In half bridge topology the single-phase load is connected between the mid-point of the
input dc supply and the junction point of the two switches (these points are marked as ‘O’
and ‘A’ respectively). For ease of understanding, the switches Sw1 and Sw2 may be assumed
to be controlled mechanical switches that open and close in response to the switch control
signal. In fact it has been shown that the actual electronic switches mimic the function of the
mechanical switches. Now, if the switches Sw1 and Sw2 are turned on alternately with duty
ratio of each switch kept equal to 0.5, the load voltage (VAO) will be square wave with a
peak-to-peak magnitude equal to input dc voltage shows a typical load voltage waveform
output by the half bridge inverter. VAO acquires a magnitude of +0.5 Edc when Sw1 is on
and the magnitude reverses to -0.5 Edc when Sw2 is turned on. The fundamental frequency
component of the square wave voltage, its peak-to-peak magnitude being equal to 4 π Edc .
The two switches of the inverter leg are turned on in a complementary manner. For a general
load, the switches should neither be simultaneously on nor be simultaneously off.
Simultaneous turn-on of both the switches will amount to short circuit across the dc bus and
will cause the switch currents to rise rapidly. For an inductive load, containing an inductance
in series, one of the switches must always conduct to maintain continuity of load current. In a
case of inductive load has been considered and it has been shown that the load current may
not change abruptly even though the switching frequency is very high. Such a situation,
demands that the switches must have bidirectional current carrying capability.

4. Derive the value of the fundamental and the harmonic voltage for the three
phase bridge convertor.
A 3-phase bridge type VSI with square wave pole voltages has been considered. The
output from this inverter is to be fed to a 3-phase balanced load. Fig. shows the power circuit
of the three-phase inverter. This circuit may be identified as three single-phase half-bridge
inverter circuits put across the same dc bus. The individual pole voltages of the 3-phase
bridge circuit are identical to the square pole voltages output by single phase half bridge or
full bridge circuits. The three pole voltages of the 3-phase square wave inverter are shifted in
time by one third of the output time period. These pole voltages along with some other
relevant waveforms have been plotted in Fig The horizontal axis of the waveforms in has
been represented in terms of ‘ωt’, where ‘ω’ is the angular frequency (in radians per second)
of the fundamental component of square pole voltage and ‘t’ stands for time in second. the
phase sequence of the pole voltages is taken as VAO, VBO and VCO. The numbering of the
switches in has some special significance vis-à-vis the output phase sequence.
 To appreciate the particular manner in which the switches have been numbered, the
conduction pattern of the switches marked in Fig. 35.2 may be noted. It may be seen that
with the chosen numbering the switches turn on in the sequence:- Sw1, Sw2, Sw3, Sw4,
Sw5, Sw6, Sw1, Sw2, ….and so on. Identifying the switching cycle time as 360 degrees (2π
radians), it can be seen that each switch conducts for 1800 and the turning on of the adjacent
switch is staggered by 60 degrees. The upper and lower switches of each pole (leg) of the
inverter conduct in a complementary manner. To reverse the output phase sequence, the
switching sequence may simply be reversed. Considering the symmetry in the switch
conduction pattern, it may be found that at any time three switches conduct. It could be two
from the upper group of switches, which are connected to positive dc bus, and one from
lower group or vice-versa (i.e., one from upper group and two from lower group). According
to the conduction pattern indicated in Fig. 35.2 there are six combinations of conducting
switches during an output cycle:- (Sw5, Sw6, Sw1), (Sw6, Sw1, Sw2), (Sw1, Sw2, Sw3),
(Sw2, Sw3, Sw4), (Sw3, Sw4, Sw5), (Sw4, Sw5, Sw6). Each of these combinations of
switches conducts for 600 in the sequence mentioned above to produce output phase
sequence of A, B, C. As will be shown later the fundamental component of the three output
line-voltages will be balanced.
5. Explain about generalized technique of harmonic elimination and voltage
control.
Description of Some Popular PWM Techniques
The logic described to select notch angles is also specific to one particular PWM
technique that is known as selective harmonic elimination technique. There are several other
PWM techniques, the important ones are:- SINE-PWM technique, Space Vector based PWM
technique, Hysteresis current controller based PWM technique etc. Some of the PWM
techniques can be realized using analog circuits alone; some others are more easily realized
with the help of digital processors like microprocessor, Digital signal processor (DSP) or
Personal Computer (PC), whereas some other PWM controllers could be a hybrid between
analog and digital circuits. For example, the selective harmonic elimination technique
described above requires numerical solutions of the transcendental equations for arriving at
the required notch angles. These transcendental equations are solved off-line and the
information regarding notch angles (switching instances) is stored in digital memory, like
EPROM. It may be realized that the notch instances may not occur at regular time intervals.
Similarly fundamental output voltage requirement may not remain fixed for all output
frequencies and hence the transcendental equations (similar to Eqns. 36.3 to 36.6) will be
different for different output frequencies. Also, as per Eqn. 36.7, if the switching frequency is
kept constant, there will be more notch angles (per quarter cycle) at low output frequencies
and less number of notches at higher frequencies. Thus the set of notch angles for one
frequency may be different from the notch angles at some other frequency.
For satisfactory implementation of this technique, generally the desired output frequency
range is divided in few discrete frequencies. For example, it may be desired to output a 3-
phase balanced voltage in the frequency range of 5 Hz to 50 Hz with the constraint that the
ratio between output voltage magnitude and output frequency should remain fixed to some
predetermined value. Under this situation the output voltage range may be discretized in
steps of, say, 1Hz. Thus the available output may vary from 5 Hz to 50 Hz through the
following discrete values of intermediate frequencies: 6 Hz, 7 Hz, 8 Hz, …, 49 Hz. The
desired magnitudes of output voltage for all these discrete frequencies is found out and
accordingly the notch angles are calculated to eliminate as many unwanted harmonics as
possible (keeping in mind the constraint on switching frequency). Now switching
information for successive output frequencies may be stored in successive memory blocks.
For each of these output frequencies, it may be convenient to discretize one complete output
cycle time interval in small steps (say, in steps of 10 microseconds) and the inverter
switching word (as described below) at these successive time intervals are then stored in the
successive memory locations. The switching word combines the switching information for all
three legs (all six switches) of the inverter and may be obtained in the form of a six bit binary
word, each bit corresponding to one particular switch. When a particular bit value is ‘1’ that
particular switch may require being turned-on. Similarly ‘0’ bit value may correspond to
turn-off command of the switch. Now if the memory block, containing switching information
is addressed sequentially after every 10 microsecond (this being the time step, chosen above,
to discretize the output cycle time period) the desired switching pattern for the inverter
switches may be obtained.
 The notch angles can thus be realized with a maximum time error of 10 microseconds
(which for 50 Hz output corresponds to an error of 0.180 only). After completion of one
output cycle the next cycle is simply repeated like the previous one. One may move from one
memory block to another memory block (by suitably multiplexing the memory address-
word) to obtain the inverter switching pattern for some other output frequency. The selective
harmonic elimination technique described above is also known as stored-PWM technique.
The overall memory requirement may be large but since the memory cost has been reducing
over the years the stored-PWM technique remains one of the most attractive techniques. In
contrast to the selective harmonic elimination technique discussed above, some other PWM
techniques, notably SINE-PWM and Space Vector-PWM techniques, try to match the mean
value of load voltage under the rectangular PWM waveform with the mean voltage of the
desired output waveform over every small time interval of the output cycle. If, for example,
the desired output voltage is a sinusoidal waveform of a given magnitude and of frequency
‘f1’, then for every small time interval ‘Δt’ of the output cycle period (such that Δt << 1/ f1)
the mean (dc) magnitude under desired sine wave and the mean dc voltage under the PWM
pulses are made equal.
Now barring the mismatch in the instantaneous magnitudes of the sine wave and the
PWM wave within the small time period ‘Δt’, the two waveforms are matching. Thus the
PWM waveform may be considered to be the superposition of the desired output waveform
and ripple voltages of time period Δt. The ripple voltage waveform in each ‘Δt’ time interval
may not be identical and hence ripple voltage may consist of a band of harmonics of high
frequency. In the frequency axis the high frequency harmonic voltages are far away from the
desired voltage of fundamental frequency ‘f1’ and hence suitable low pass filter circuits may
be used to block the unwanted harmonic currents without affecting the magnitude of the
fundamental frequency current.

Another popular PWM technique is current controlled PWM (CCPWM) technique.

Here the instantaneous magnitude of load current is directly controlled, within some tolerable
error band, to match the desired current shape. This technique is described below for a
single-phase half bridge inverter shown in Fig.36.2. The positive sense for the load current
(IL) is taken along the direction of arrow in Fig. 36.2. The actual load current is sensed with
the help of a current sensor and compared with its reference magnitude. The error in load
current can be controlled, as described below, by proper switching of the inverter switches.
The load could be a R-L load or a R-L-E load. In case of R-L-E load, it is assumed that the
back emf (E) of the load has a peak magnitude lower than the magnitude of instantaneous
pole voltage (0.5Edc). To increase the actual current along the direction of arrow (or to
reduce the current flowing in a direction opposite to the arrow) upper switch ‘SU’ needs to be
turned on, whereas turning on of lower switch ‘SL’ will produce the reverse effect. This can
be verified simply by writing and analyzing the loop voltage equation.

6. Explain with proper curves for the harmonic variations about the
a) AC voltage Harmonics for a thyristor based converter.
b) DC voltage Harmonics for a thyristor based converter.
AC voltage Harmonics for a thyristor based converter
With three phase conversion equipment, such as drives, the current demand on the
distribution system will depend on three things. They are the characteristics of the input three
phase voltage, the operating speed of the drive, and the drive output load demand. Evaluating
a single operating point of a drive will permit determining the input current demand and the
cause of the harmonic content of that input current.
Input voltage-line = 480 VAC, Full load amps = 100, Output Frequency 60 Hz These
value will be used in the following text as the example system. The drawing shown indicates
how current follows the frequency when the load is linear only a phase angle change is
shown.
 When the load become non-linear, the current is not continuous and will contain
many Frequencies. Figure 2 shows what the current might look like in a non-linear circuit.

Each current pulse will contain many frequencies. The frequencies will be made up of
the fundamental, 60 Hz, and frequencies which are a multiple or sub-multiple of the
fundamental. The description can be mathematically defined by a Fourier series. Since the
pulses are of both polarities, the even order harmonics will be canceled. In a three phase
circuit, any harmonic divisible by 3 will be canceled in each phase. However, the sum of
those harmonics divisible by 3 will be found in the neutral of the distribution system. It is for
that reason the neutral wire in a distribution system is often sized to carry up to three times
the value of the phase currents.
For distribution systems which must handle a large percentage of non-linear loads,
the percentage of harmonic currents can be very high. It is important to remember that the
greatest contributor to harmonic currents is single phase lighting circuits which used
magnetic or electronic lighting controls. The next largest contributor is computers. In fact,
any single phase device which contains a switching mode power supply, a SMPS, will cause
high percentages of the third harmonic. The third harmonic causes the greatest amount of
current distortion on the ac line. In factories and office buildings where the load type is
lighting and computers, that type of load is often as much as 50% of the total power used.
The addition Of non-linear, 3 phase drive products, whether ac or dc, is usually less than
20% of the total load. Since the most significant harmonic in a three phase load is the fifth
harmonic, the current distortion caused by drives is much less than caused by lighting and
computer loads.
The main reason for the concern is that drives must be considered since they can add
to the harmonic currents already present. It the harmonic currents are not considered, it
would be like ignoring some of the loading when picking a transformer or the wire size in a
distribution system. If the transformer is sized too small, it could cause a fire. Using a
standard transformer, with exactly the listed KVA load for each drive or non-linear load is
like using too small a transformer. A 50 KVA SMPS lighting load would require 65 KVA
due to the 33% additional 3rd harmonic current load. The higher frequency harmonic current
will cause more transformer heating because of eddy current losses in the core and higher
wire resistance caused by skin effect.
There are two main affects of harmonic currents on a distribution system. The first is
that harmonic currents add to the RMS value of the fundamental. This additional current will
increase losses in wire, bus bars, transformers and power factor correction capacitors used in
the distribution system. A typical value for the additional RMS loss would be 3% if skin
effect and core losses could be ignored. Unfortunately, they cannot be ignored. The second
affect is the additional heating caused by each of the harmonic currents. Transformers,
capacitors, circuit breakers, wires and bus bars must be designed to handle the higher
frequency currents. If these components are not correctly sized for the harmonic currents, the
harmonic currents can cause additional heating in those components. This heating can result
in premature component failure and the possibility of fire. New transformer ratings will soon
be on the market. These ratings will cover transformers for non-linear loads. Underwriters
Laboratory, UL will begin to rate transformer based on the percentage of non-linear loads,
whether single phase or three phase.
In a six pulse converter or 3 phase full-wave bridge, the most significant harmonics
are the number of pulses ±1. That means a six pulse converter will create harmonic currents
with a frequency 5 times 60 Hz and 7 times 60 Hz. The amplitude of those harmonics will be
approximately 1/5 and 1/7 of the amplitude of the fundamental current. In the example, a
fundamental or 60 Hz current of 100 amps would contain a 300 Hz current with an amplitude
of 1/5 times 100 or 20 amps and a 420 Hz current with an amplitude of If 7 times 100 or 14.3
amps. In RMS terms, the harmonic current distortion value will only amount to
approximately:

This additional 3% RMS current would not significantly overheat the components in
a distribution system that is not overloaded and used components rated for non-linear loads.
1t linear load rated transformers and capacitors are used, the heating caused by 20% of the
5th harmonic and 14.3% of the 7th harmonic could cause destructive heating if the
components are not derated. The chief concern with harmonic currents is that their
characteristics are known so that correct sizing can take place.