Power System Harmonics

1. Chapter 1
Introduction
1.1 Motivation:
The primary motivation behind the study of Power System Harmonics is
the power quality in a power system has become an important issue nowadays
with significant development of power electronics technology application of
power electronic equipments and nonlinear loads in recent years lead to harmonic
interference problems in a power system. The loads are nonlinear and harmonic
currents generated by the loads will cause a voltage drop across source impedance
which causes decrease in power quality.
Power System may also contain sensitive loads such as computers or
electronic controllers which consume less power are connected in parallel with
nonlinear loads. The harmonics generated by these nonlinear loads may be
harmful to sensitive loads and could even damage the sensitive loads.
1.2 Background:
A good assumption for most utilities in the United States is that sine-wave
voltage generated in central power stations is very good. In most areas, the
voltage found on distortion system typically has much less than 1.0 percent
distortion. However, the distortion increases closer to the load. At some loads, the
current waveform barely resembles a sine wave. Electronics power converters can
chop the current into seemingly arbitrary waveforms.
While there are a few cases where the distortion is random, most distortion
is periodic, or an integer multiple of the power system fundamental frequency.
When electronics power converters first became commonplace in the late
1970s, many utility engineers became quite concerned about the ability of the
power system to accommodate the harmonic distortion. Many dire predictions
were made about the fate of power system if these devices were permitted to

2. exist. While some of these concerns were probably overstate, the field of power
quality analysis owes a great debt of gratitude to these people because their
concern over “new” problem of harmonics sparked the research that has
eventually led too much of the knowledge about all aspect of power quality.
Presence of harmonics has been a lot since the 1990’s and has led to
deterioration in the quality of power. Moreover, there has also been an increase in
use of devices and equipments in power system also including the nonlinear loads
and electronic loads used in residential areas there by loading the transmission
and the distribution systems. This is because they operate at very low power
factors which increases the losses in line and also causes poor regulation in
voltage further leading the power plants to supply more power. Also, some
nonlinear loads and electronics equipment are such that instead of drawing current
sinusoidally they tend to draw current in short pulses thus creating harmonics.
Some of the examples of nonlinear loads would be rectifiers, inverters, etc. Some
of the examples of electronics equipments would be computers, scanners, printers,
etc.

3. Chapter 2
Cause of Power Quality Deterioration
2.1 Introduction:
As always, the main objective of the power system would be generation of
electrical energy to the end user. Also, associated with power system generation
is the term power quality. So much emphasis has been given to power quality that
it is considered as a separate area of power engineering. There are many reasons
for the importance given to the power quality. One of the main reasons is, the
consumers are well informed about the power quality issues like interruptions,
sagging and switching transients. Also, many power systems are internally
connected into a network. Due to this integration if a failure exists in any one of
the internal network it would result into unfavorable consequences to the whole
power system. In addition to all this, with the microprocessor based controls,
protective devices become more sensitive towards power quality variation than
were the past generation protective devices.
Following are some of the disturbances which are common in affecting the
power system.
1.) Transients
2.) Sagging
3.) Variations in voltage
4.) Harmonics
2.2 Transients:
In terms of power system, the transients can be defined as an action or a
situation in power system with variations in power system and which is not
desirable in nature. A general understanding of transient is considered to be an
oscillatory transient who is damped due to the RLC network. A person who is
new to the power system also uses the term “surge” to define transient. A surge

4. may be analyzed as a transient who is resulting from the stroke of lightening
where protection is done by using a surge arrester. A person who is more
groomed in the field of power engineering would avoid using the term “surge”
unless it is specified as to what exactly
2.3 Variations in Voltage:
There are two types of variations in the voltages.
 Short duration voltage variations
 Long duration voltage variations.
2.3.1 Short Duration Voltage Variations:
Short duration voltage variations are usually caused by faults in the power
system. Short duration voltage variations consist of sags which are caused
depending on the system conditions and faults that are caused in the power
system. It really depends on what kind of fault is caused in the power system
under what condition which may lead to voltage drops, voltage rise and even
interruptions in certain conditions. When such faults take place, protective
devices are used in order to clear the fault. But, the impact of voltage during such
faulty conditions is of short-duration variation.
 Interruptions:
When there are reductions in the voltage or current supply interruptions
take place. Interruptions may occur due to various reasons, some of them being
faults in the power system, failures in the equipment, etc.
 Sagging:
A short duration voltage variation is often referred to as sagging. When
there is a decrease between 0.1 to 0.9pu in rms voltage sagging takes place. There
are many ways to obtain the magnitude of sagging from the rms voltages. Most
of the times lowest value obtained during the event are considered. Sagging
normally has constant rms value during the deep part of the sag. Thus, lowest
value is an acceptable approximate value

5. 2.3.2 Long Duration Voltage Variations:
Long duration voltage variations are comprised of over voltages as well as
under voltages conditions. These under voltage and over voltage conditions are
caused by variations in the power system and not necessarily due to the faults in
the system. The long duration voltage variations refer to the steady state
condition of the rms voltage of the power system. The long duration voltage
variations are further divided into three different categories i.e. interruptions, over
voltage and under voltage.
 Under Voltage :
There are many reasons for the under voltage conditions in the power
system. When there is a decrease in the rms ac voltage to less than 90% of a
power system for some amount of time then under voltage condition exists. Load
switching on or switching off of a capacitor bank can also cause under voltage
condition. Also, when a power system is overloaded it may result into under
voltage condition.
 Over Voltage:
Compared to the under voltage condition, over voltage is an increase in
the rms ac voltage to greater than 110% of the power system for some amount of
time. Unlike under voltage condition, load switching off or capacitor bank getting
energized are main reasons for the over voltage conditions.
2.4 Harmonics:
Harmonics are one of the major concerns in a power system. Harmonics
cause distortion in current and voltage waveforms resulting into deterioration of
the power system. The first step for harmonic analysis is the harmonics from
non-linear loads. The results of such analysis are complex. Over many years,
much importance is given to the methods of analysis and control of harmonics.
Harmonics present in power system also has non-integer multiples of the
fundamental frequency and have periodic waveform. The harmonics are
generated in a power system from two distinct types of loads.

6. First category of loads is described as linear loads. The linear time-invariant
loads are characterized such that application of sinusoidal voltage results
in sinusoidal flow of current. A constant steady-impedance is displayed from
these loads during the applied sinusoidal voltage. As the voltage and current are
directly proportional to each other, if voltage is increased it will also result into
increase in the current. An example of such a load is incandescent lighting. Even
if the flux wave in air gap of rotating machine is not sinusoidal, under normal
loading conditions transformers and rotation machines pretty much meet this
definition. Also, in a transformer the current contains odd and even harmonics
including a dc component. More and more use of magnetic circuits over a period
of time may get saturated and result into generation of harmonics. In power
systems, synchronous generators produce sinusoidal voltages and the loads draw
sinusoidal currents. In this case, the harmonic distortion is produced because of
the linear load types for sinusoidal voltage is small.
Non-linear loads are considered as the second category of loads. The
application of sinusoidal voltage does not result in a sinusoidal flow applied
sinusoidal voltage for non-linear devices. The non-linear loads draw a current
that may be discontinuous. Harmonic current is isolated by using harmonic filters
in order to protect the electrical equipment from getting damaged due to harmonic
voltage distortion. They can also be used to improve the power factor. The
harmful and damaging effects of harmonic distortion can be evident in many
different ways such as electronics miss-timings, increased heating effect in
electrical equipments, capacitor overloads, etc. There can be two types of filters
that are used in order to reduce the harmonic distortion i.e. the active filters and
the passive filters. Active harmonic filters are electronic devices that eliminate
the undesirable harmonics on the network by inserting negative harmonics into
the network. The active filters are normally available for low voltage networks.
The active filters consist of active components such as IGBT-transistors and
eliminate many different harmonic frequencies. The signal types can be single
phase AC, three phases AC. On the other hand, passive harmonic filters consist

7. of passive components such as resistors, inductors and capacitors. Unlike the
active filters which are used only for low voltages, the passive filters are
commonly used and are available for different voltage levels

8. Chapter 3
Fundamentals Of Harmonics
3.1 General:
When we talk about ac we are talking about alternating current. The
voltage pushing that current through the load circuit is described in terms of
frequency and amplitude. The frequency of the current will be identical to the
frequency of the voltage as long as the load resistance/impedance does not
change. In a linear load, like a resistor, capacitor or inductor, current and voltage
will have the same frequency. As long as the characteristics of the load
components do not change, the frequency component of the current will not
change. When we deal with non-linear loads such as switching power supplies,
transformers which saturate, capacitors which charge to the peak of the supply
voltage, and converters used in drives, the characteristics of the load are dynamic.
As the amplitude of the voltage changes and the load impedance changes, the
frequency of the current will change. That changing current and resulting complex
waveform is a result of: these load changes. The complex current waveform can
be described by defining each component of the waveform. The component of
any waveform can be defined in terms of dc, and all frequencies from 0 to
infinity. The frequencies that are normally dealt with using drives are 50 and 60
Hertz. By definition, these frequencies are termed fundamental in their respective
distribution systems.
3.2 Definition:
The Fourier theorem states that all non-sinusoidal periodic functions can
be represented as the sum of terms (i.e. a series) made up of:
1. Sinusoidal term at the fundamental frequency
2. Sinusoidal terms (harmonics) whose frequencies are whole multiples of the
fundamental frequency
3. DC component, where applicable

9. The nth order harmonic (commonly referred to as simply the nth
harmonic) in a signal is the sinusoidal component with a frequency that is n times
the fundamental frequency.
The equation for the harmonic expansion of a periodic function is presented
below:
∞
y(t)=Y0+ΣYn√2 sin (nωt-φn)
n=1
Where:
Yo: value of the DC component, generally zero and considered as such here in
after
Yn: rms value of the nth harmonic
ω: angular frequency of the fundamental frequency
ϕn: displacement of the harmonic component at t = 0.
 Example of signals (current and voltage waves) on the French electrical
distribution System:
The value of the fundamental frequency (or first order harmonic) is 60 hertz (Hz)
The third harmonic has a frequency of 180 Hz
The fifth harmonic has a frequency of 300 Hz
The seventh harmonic has a frequency of 420 Hz
etc.
A distorted signal is the sum of a number of superimposed harmonics

10. Fig 3.2 Voltage waveform showing the effect of harmonics
3.3 Representation of harmonics: the frequency spectrum
The frequency spectrum is a practical graphical means of representing the
harmonics contained in a periodic signal.
 The graph indicates the amplitude of each harmonic order.
 This type of representation is also referred to as spectral analysis.
 The frequency spectrum indicates which harmonics are present and their relative
importance.
Fig 3.3 Graph of Harmonics Spectrum

11. 3.4 Triplen Harmonics:
The triplen harmonics are defined as the odd multiples of the 3rd
harmonic (ex. 3rd, 9th, 15th, 21st etc.).They deserve special consideration
because the system response is often considerarably different for triplens than
for rest of harmonics.The normal mode for tripplen harmonics is to be zero
sequence. During imbalances, triplen harmonics may have positive or negative
sequence components.

12. Chapter 4
Harmonic indices
The two most commonly used indices for measuring the harmonic content
ofa waveform are the total harmonics distortion(THD) and the total demand
distortion. Both are measures of the effective value of waveform and may be
applied to eitger voltage or current.
4.1 Total Harmonic Distortion
Total harmonics distortion is the ratio between the RMS value of sum of
harmonics to the RMS value of the fundamental.
THD can be used to describe voltage or current distortion and is calculated as
follows:
푆푢푚 표푓 푠푞푢푎푟푒푠 표푓 푎푚푝푙푖푡푢푑푒푠 표푓 푎푙푙 ℎ푎푟푚표푛푖푐푠
푇퐻퐷 = √
푠푞푢푎푟푒 표푓 푎푚푝푙푖푡푢푑푒 표푓 푓푢푛푑푎푚푒푛푡푎푙
× 100
The THD is very useful quantity for many applications, but its limitation
must be realized. It can provide a good idea of how much extra heat will be
realized when distorted voltage is applies across a resistive load. It can give an
idea about the additional losses caused by the current flowing through a
conductor.
4.2 Total Demand Distortion
Current distortion levels can be characterized by a THD value, as has been
described, but this can often be misleading. A small current have a high THD but
not be a significant threat to the system.
Some analysts have attempted to avoid this difficulty by referring THD to
the fundamental of peak demand load current rather than to the fundamental of
the peak demand load current rather than the fundamental of present sample. This
is called total demand distortion and serves as the basis for the guidelines in IEEE
standard 519-1192

13. 푇퐷퐷 =
ℎ푚푎푥 2
ℎ=2
IL
Σ 퐼ℎ
IL is the peak, or maximum, demand load current at the funamental
frequency component measured at the point of common coupliing

14. Chapter 5
Sourecs of Harmonics
Devices causing harmonics are present in all industrial, commercial and
residential installations. Non-linear equipment or components in the power system
cause distortion of the current and to a lesser extent of the voltage.
5.1 Non-linear loads
5.1.1 Definition:
A load is said to be non-linear when the current it draws does not have the same
wave form as the supply voltage.
Fig 5.1.1 Current waveform in non-linear load
5.1.2 Harmonics in non-linear load:
DC Bus will only charge when the AC sine wave voltage is greater than
the DC capacitor voltage, this results current draw only at the peaks of the sine

15. waves instead of the whole sine wave
Fig 5.1.2 Common Single Phase Bridge Rectifier Circuit and waveform
5.2 Types of equipment that generate harmonics
Harmonic load currents are generated by all non-linear loads. These include:
Single phase loads, e.g.
 Switched mode power supplies (SMPS)
 Electronic fluorescent lighting ballasts
 Small uninterruptible power supplies (UPS) units
Three phase loads, e.g.
 Variable speed drives
 Large UPS units
5.2.1 Single phase loads
 Switched mode power supplies (SMPS):
The majority of modern electronic units use switched mode power
supplies (SMPS). These differ from older units in that the traditional step-down
transformer and rectifier is replaced by direct controlled rectification of the supply
to charge a reservoir capacitor from which the direct current for the load is
derived by a method appropriate to the output voltage and current required. The
advantage to the equipment manufacturer is that the size, cost and weight is
significantly reduced and the power unit can be made in almost any required form
factor. The disadvantage to everyone else is that, rather than drawing continuous
current from the supply, the power supply unit draws pulses of current which
contain large amounts of third and higher harmonics and significant high

16. frequency components. A simple filter is fitted at the supply input to bypass the
high frequency components from line and neutral to ground but it has no effect on
the harmonic currents that flow back to the supply. Single phase UPS units exhibit
very similar characteristics to SMPS.For high power units there has been a recent
trend towards so-called power factor corrected inputs. The aim is to make the
power supply load look like a resistive load so that the input current appears
sinusoidal and in phase with the applied voltage. It is achieved by drawing input
current as a high frequency triangular waveform that is averaged by the input
filter to a sinusoid.
Fig 5.2.1 a. Harmonic spectrum of a typical PC
 Fluorescent lighting ballasts
Electronic lighting ballasts have become popular in recent years following
claims for improved efficiency. Overall they are only a little more efficient
than the best magnetic ballasts and in fact, most of the gain is attributable to
the lamp being more efficient when driven at high frequency rather than to
the electronic ballast itself. Their chief advantage is that the light level can be
maintained over an extended lifetime by feedback control of the running
current a practice that reduces the overall lifetime efficiency. Their great

17. disadvantage is that they generate harmonics in the supply current. So called
power-factor corrected types are available at higher ratings that reduce the
harmonic problems, but at a cost penalty. Smaller units are usually
uncorrected. Compact fluorescent lamps (CFL) are now being sold as
replacements for tungsten filament bulbs. Miniature electronic ballast, housed
in the connector casing, controls a folded 8mm diameter fluorescent tube.
CFLs rated at 11 watt are sold as replacements for a 60 watt filament lamp
and have a life expectancy of 8000 hours. The harmonic current spectrum is
shown in Figure. These lamps are being widely used to replace filament bulbs
in domestic properties and especially in hotels where serious harmonic
problems are suddenly becoming common.
Fig 5.2.1 a. Harmonic spectrum of a typical CFL
5.2.2 Three Phase load
Variable speed controllers, UPS units and DC converters in general are
usually based on the three-phase bridge, also known as the six-pulse bridge
because there are six pulses per cycle (one per half cycle per phase) on the DC
output. The six pulse bridge produces harmonics at 6n +/- 1, i.e. at one more and
one less than each multiple of six. In theory, the magnitude of each harmonic is

18. the reciprocal of the harmonic number, so there would be 20 % fifth harmonic and
9 % eleventh harmonic, etc.
Fig 5.2.2 Harmonic spectrum of a typical 6-pulse bridge

19. Chapter 6
Effect of Harmonics
The effects of three-phase harmonics on circuits are similar to the effects
of stress and high blood pressure on the human body. High levels of stress or
harmonic distortion can lead to problems for the utility's distribution system, plant
distribution system and any other equipment serviced by that distribution system.
Effects can range from spurious operation of equipment to a shutdown of
important plant equipment, such as machines or assembly lines. Harmonics can
lead to power system inefficiency. Some of the negative ways that harmonics may
affect plant equipment are listed below:
6.1 Current Harmonics
These important non-linear circuits produce current harmonics. Current
Harmonics do have an effect on the electrical equipment supplying harmonic
current to the device (transformers, conductors). Current Harmonics can cause
issues with distribution equipment with has to handle the current from the utility
transformer all the way down to the device, but generally don’t affect other
equipment connected to the electrical system. Harmonic currents can cause
excessive heating to transformers. For electrical systems feeding single phase
loads the third harmonic has gained attention in design consideration and
transformer selection for causing the neutral conductor to draw excessive current.
6.2 Voltage Harmonics
Voltage Harmonics can affects sensitive equipment throughout your
facility. Voltage Harmonics arise when Current Harmonics are able to create sags
in the voltage supply. When any device draws current it creates a voltage dip
which is required for current to flow. This voltage dip is visible with larger loads
when turning on a hair dryer or a table saw and seeing the lights dim down. The
amount of sag depends on many factors like transformer impedance wire size.
Current Harmonics create Voltage Harmonics, but the magnitude of the Voltage

20. Harmonics depends on the “Stiffness” of your electrical distribution’s “System
Impedance”.
6.3 Effect of Harmonics
 Conductor overheating: a function of the square rms current per unit volume of
the conductor. Harmonic currents on undersized conductors or cables can cause a
“skin effect”, which increases with frequency and is similar to a centrifugal force.
 Capacitors: can be affected by heat rise increases due to power loss and reduced
life on the capacitors. If a capacitor is tuned to one of the characteristic harmonics
such as the 5th or 7th, overvoltage and resonance can cause dielectric failure or
rupture the capacitor.
 Fuses and Circuit Breakers: harmonics can cause false or spurious operations
and trips, damaging or blowing components for no apparent reason.
 Transformers: have increased iron and copper losses or eddy currents due to
stray flux losses. This causes excessive overheating in the transformer windings.
Typically, the use of appropriate “K factor” rated units is recommended for non-linear
loads.
 Generators: have similar problems to transformers. Sizing and coordination is
critical to the operation of the voltage regulator and controls. Excessive harmonic
voltage distortion will cause multiple zero crossings of the current waveform.
Multiple zero crossings affect the timing of the voltage regulator, causing
interference and operation instability.
 Utility Meters: may record measurements incorrectly, result in higher billings
to consumers.
 Drives/Power Supplies: can be affected by misoperation due to multiple zero
crossings. Harmonics can cause failure of the commutation circuits, found in DC
drives and AC drives with silicon controlled rectifiers (SCRs).

21. Chapter 7
Power and Harmonics
7.1 Active Power
The active power P of a signal distorted by harmonics is the sum of the
active powers corresponding to the voltages and currents in the same frequency
order. The expansion of the voltage and current into their harmonic components
may be written as:
∞
P = Σ VhIh cos φh
h=1
Where ϕ h is the displacement between voltage and current of harmonic order h.
Note:
 it is assumed that the signal does not contain a DC component, i.e. V0= I0 = 0
 When the signal is not distorted by harmonics, the equation P = V1 I1 cos ϕ1
again applies, indicating the power of a sinusoidal signal, where cos ϕ1 is equal
to "cos ϕ").
7.2 Reactive Power
Reactive power applies exclusively to the fundamental and is defined by
the equation:
Q = V1I1 sin φ1
7.3 Distortion Power
Consider the apparent power S:
S=VrmsIrms

22. In the presence of harmonics, the equation becomes:
∞
S2 = (Σ Vh
h=1
∞
) (Σ Ih
h=1
)
Consequently, in the presence of harmonics, the equation S2=P2+Q2 is no longer
valid. The distortion power D is defined as S2=P2+Q2+D2, i.e.:
퐷 = √푆2 − 푃2 − 푄2
7.4 Power factor in presence of harmonics
There are two different types of power factor that must be considered
when voltage and current waveforms are not perfectly sinusoidal.
 Input Displacement Factor (IDF) =which refers to the cosine of the angle
between the 50/60 Hz voltage and current waveforms.
 Distortion Factor (DF) is defined as follows:
DF =
1
√1 + THD2
Total Power Factor (PF) = Product of the Input Displacement Factor and the
Distortion Factor as follows:
PF = IDF × DF

23. Chapter 8
Harmonics Reduction Techniques
8.1 Genral Tecniques
Following techiques are use to reduce the effect of harmonics
 Grouping the disturbing loads
 Separating the sources
 Using transformers with special connections
 Installing inductors
8.1.1 Grouping the disturbing loads:
When preparing the single-line diagram, separate where possible the
disturbing equipment from the other loads. Practically speaking, the different
types of loads should be supplied by different bus bars.
By grouping the disturbing loads, the possibilities of angular
recomposition are increased. The reason is that the vector sum of the harmonic
currents is lower than their algebraic sum.
An effort should also be made to avoid the flow of harmonic currents in
the cables, thus limiting voltage drops and temperature rise in the cables.
Fig 8.1.1 Grouping of non-linear loads and supply as far upstream as possible

24. 8.1.2 Separating the sources
In efforts to attenuate harmonics, an additional improvement may be
obtained by supplying the different loads via different transformers, as indicated
in the simplified diagram below
Fig 8.1.2 Supply of the disturbing loads via a separate transformer
This disadvantage of this solution is the increase in the cost of the installation.
8.1.3 Using transformers with special connections
Special types of connection may be used in transformers to eliminate
certain harmonic orders.
The harmonic orders eliminated depend on the type of connection implemented:
 A delta-star-delta connection eliminates harmonic orders 5 and 7
 A delta-star connection eliminates harmonic order 3 (the harmonics flow
in each of the phases and loop back via the transformer neutral)
 A delta-zigzag connection eliminates harmonic order 5 (loop back via the
magnetic circuit).
Fig 8.1.3 A delta-star-delta transformer prevents propagation of harmonic orders 5 and 7
upstream in the distribution system.

25. 8.1.4 Installing inductors
In installations comprising variable-speed drives, the current can be
smoothed by installing line inductors. By increasing the impedance of the supply
circuit, the harmonic current is limited.
Use of harmonic inductors on capacitor banks is a means of increasing the
impedance of the inductor and capacitor assembly, for harmonics with high
frequencies.
8.2 Solutions when limit values are exceeded
8.2.1 Passive Filter
Operating principle: an LC circuit, tuned to each of the harmonic
frequencies requiring filtering, is installed in parallel with the device causing the
harmonic distortion this bypass circuit draws the harmonics, thus avoiding the
flow of harmonics to the power source.
Fig 8.2.1 Operating principle of a passive filter.
Generally speaking, the passive filter is tuned to a harmonic order near the
one to be eliminated. A number of parallel-connected filters may be used when a
significant reduction in distortion over a range of orders is required.

26. Typical applications:
 Industrial installations comprising a set of devices causing harmonics with
a total power rating greater than approximately 200 kVA (variable-speed
drives UPSs, rectifiers, etc.)
 installations where power factor correction is required
 situations where voltage distortion must be reduced to avoid disturbing
sensitive loads
 situations where current distortion must be reduced to avoid overloads
8.2.2 Active filters (active harmonic conditioners)
Operating principle: active filters are systems employing power
electronics, installed in series or in parallel with the non-linear load, to provide
the harmonic currents required by non-linear loads and thereby avoid distortion
on the power system
.
Fig 8.2.2 Operating principle of an active filter.
The active filter injects, in opposite phase, the harmonics drawn by the
load, such that the line current is remains sinusoidal.

27. Typical applications:
 Commercial installations comprising a set of devices causing harmonics with a
total power rating less than 200 kVA (variable-speed drives, UPSs, office
equipment, etc.)
 situations where current distortion must be reduced to avoid overloads
8.2.3 Hybrid filters
Operating principle: The two types of filters presented above can be combined in
a single device, thus constituting a hybrid filter. This new filtering solution
combines the advantages of the existing systems and provides a high-performance
solution covering a wide power range.
Fig 8.2.3 Operating principle of a hybrid filter.
Typical applications:
 Industrial installations comprising a set of devices causing harmonics with a total
power rating greater than 200 kVA approximately (variable-speed drives, UPSs,
rectifiers, etc.)
 installations where power factor correction is required.
 situations where voltage distortion must be reduced to avoid disturbing sensitive
loads.
 situations where current distortion must be reduced to avoid overloads.
 situations where conformity with strict harmonic-emission limits is required.

28. 8.2.4 12-pulse Rectifiers
This is effectively two six-pulse bridges, fed from a star and a delta
transformer winding, providing a 30 degrees phase shift between them.
Fig 8.2.4 12-Pulse Rectifier
Very effective in the elimination of 5th and 7th harmonics. Stops
harmonics at the source. Insensitive to future system changes.

29. Chapter 9
Conclusion
9.1 Conclusion
Virtually all modern electrical and electronic equipment contains a SMPS or
involves some form of power control and so is a non-linear load. Linear loads are
comparatively rare, the fundamental voltage, applied on a non-linear load, cause
harmonic currents (called characteristic harmonics). The main distortion consists of odd
multiples of the fundamental component (50 or 60 Hz). Single phase non-linear loads
have a current distortion, THD, around 120 %. All odd harmonics exist in the current
spectrum. Three phase non-linear loads have a current distortion, THD, up to 200 %. All
odd harmonics exist in the spectrum, except triplen harmonics. As the quantity of
installed equipment rises, and without very strong standards backed up by rigid
enforcement measures, it is likely that harmonic pollution will continue to increase

30. References
1. IEEE Std 519-1992, “IEEE Recommended Practices and Requirements for Harmonic
Control in Electric Power Systems,” © Institute of Electrical and Electronics Engineers,
Inc. 1993.
2. Boger C.Dugan, Mark F.McGRANAGHN, Electrical Power System Quality, Tata
McGRAW-Hill
3. en.wikipedia.org/wiki/Harmonics_(electrical power)
4. literature.rockwellautomation.com/idc/groups/.../mvb-wp011_-en-p.pdf