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Power Quality Seminar Report ‘03
1. INTRODUCTION
Since last 25 years there has been an increase in the use of solid state electronic
technology. This new, highly efficient, electronic technology provides product quality
with increased productivity. Today, we are able to produce products at costs less than in
the years passed, with the introduction of automation by using the solid state electronic
technology .This new technology requires clear electric power.
The conventional speed control systems are being replaced by modern power
electronic systems, bringing a verity of advantages to the users. Classic examples are
DC $ AC drives, UPS, soft stators, etc. Since the thrusters converter technology is
rapidly gaining in the modern industrial plants, the power supply systems are
contaminated as the ideal sinusoidal current and voltage waveforms are getting
distorted. This is in turn is affecting the performance of the equipment in the electrical
network.
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Power Quality Seminar Report ‘03
2. WHAT IS POWER QUALITY?
Adequate to superior power quality is essential for the smooth functioning of
critical industrial processes. As industries expand, utilities become more interconnected
and usage of electronically controlled equipment increases, power quality is
jeopardized. Most large industrial and commercial sites are served by overhead lines
with feeders that are subject to unpredictable and sporadic events, e.g. lightning and
contact with tree limbs. Most distribution circuits have resoling devices that clear
temporary faults through a timed series of trip and close operations.
This minimizes the possibility of long-term outages but leads to a number of
minor power disturbances. These typically occur several times a month. Many electric
utilities have increased the voltage at which they distribute power. This allows a single
circuit to serve more customers or deliver higher loads, and reduces energy losses in the
system. But it often means the overhead distribution circuit is longer, with more
exposure to disturbances. And disturbances travel farther because of lower system
impedances associated with higher voltage circuits. Sophisticated new systems are
providing vastly increased efficiency and control in critical processes. But with their
high sensitivity even to brief variations in electric power quality, today's computer-
driven devices fail when power is disturbed for even a few milliseconds.
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Power Quality Seminar Report ‘03
3. HARMONICS-BASIC CONCEPTS
A pure sinusoidal voltage is conceptual quantity produced by an ideal AC
generator build with finely distributed stator and field windings that operate in a
uniform magnetic field. Since neither the winding distribution nor the magnetic field is
uniform in a working AC machine, voltage waveform distortion is created, and the
voltage time relation-ship deviates from the pure sine function. The distortion at the
point of generation is very small (about 1%to 2%), but nonetheless it exists.
Because this is a deviation from a pure sine wave, the deviation is in the form of
a periodic function and by definition, the voltage distortion contains harmonics. When a
sinusoidal voltage is applied to a certain type of load, the current drawn by the load is
proportional to the voltage and impedance and follows the envelope of the voltage wave
form .These loads are referred to as linear loads (loads where the voltage and current
follow one another without any distortion to their pure sine waves).examples of
nonlinear loads are resistive heaters, incandescent lamps and constant speed induction
and synchronous motors.
In contrast some loads cause the current to vary disproportionately with the
voltage during each half cycle. These loads are classified as nonlinear loads and the
current and voltage have waveforms that are non sinusoidal containing distortions
where by 50 Hz waveform has numerous additional waveforms superimposed upon it
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Power Quality Seminar Report ‘03
creating multiple frequencies within the normal 50 Hz sine wave .The multiple
frequencies are harmonics of the fundamental frequency.
Normally current distortion produce voltage distortions .However when there is
a stiff sinusoidal voltage source there is a low impedance path from the power source
which has sufficient capacity so that loads placed upon it will not affect the voltage one
need not be concerned about current distortions producing voltage distortions Examples
of non linear loads are battery chargers, electronic ballasts; variable frequency drives,
and switched mode power supplies.
As nonlinear currents flows through a facility's electrical system and the
distribution - transmission lines, additional voltage distortions are produced due to the
impedance associated with the electrical network. Thus as electrical power is generated,
distributed and utilized, voltage and current waveforms distortions are produced.
Power systems designed to function at the fundamental frequency which is 50
Hz in India are prone to unsatisfactory operation and at times failure when subjected to
voltages and currents that contains substantial harmonic frequency elements. Very often
the operation of electrical equipment may seem normal but under a certain combination
of conditions the impact of harmonics is enhanced with damaging results.
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Power Quality Seminar Report ‘03
4. THE AFFECTS
The actual problems of any building/industry will vary depending on the type
and number of installed harmonics producing loads. Most electrical network can
withstand nonlinear loads of up to 15% of the total electrical system capacity without
concern but when the nonlinear loads exceed 15% some non expected negative
consequences can be expected. .for electrical networks , they have on linear loading of
more than 25% particular problems can be apparent.
The following is a short summery of most problems caused by harmonics:
Blinking of incandescent lights-transformer saturation
Capacitor failure-harmonics resonance
Circuit breaker tripping-inductive heating and over loading
Computer malfunctioning-voltage distortion
Transformer failure-inducting
Motor failure-inductive heating
Fuses blowing for no apparent reason-inductive heating & over load
Electronic component shut down- voltage distortion
Flickering of florescent lights-transformer saturation
The heating effects of harmonic currents can cause destruction of equipment,
conductors, and fires. The results can be unpredictable legal and financial ramifications
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Power Quality Seminar Report ‘03
apart from safety risks. Voltage distortions can lead to over heating of equipment
failure, expensive down time and maintenance difficulties. Harmonic currents and
voltage distortions are becoming the most severe and complex electrical challenge for
the electrical industry .The problems associated with nonlinear loads were once limited
to isolated devices and computer rooms, but now the problem can appear through the
entire network and utility system
The point at which the harmonic limits are applied is called the point of
common coupling (PCC). When the input transformer is the point of measurement then
the PCC refers to this point where the facility electrical system is common to the
facility of additional consumers. If there is a distortion present on the electrical power
system at this point it may be experienced by the neigh boring facilities as well. So we
need to avoid this situation
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Power Quality Seminar Report ‘03
5. SOLUTION
Users of variable frequency drives often have strict demands placed on them to
mitigate harmonic distortion caused by the nonlinear loads. Many choices are available
to them including line reactors, harmonic traps, 12 pulse rectifier, 18 pulse rectifiers,
and low pass filters.
5.1 LINE REACTORS
The input harmonic current distortion can be reduced by simple addition of
input line reactance. The inductive reactance of an input line reactor allows 50 Hz or 60
Hz currents to pass easily but presents considerably higher impedance to all other
harmonic frequencies. Harmonic currents are thus attenuated by the reactance offered
by the line reactor.
These reactors are also used to solve the problems in variable frequency drive
installations.Eg: harmonic attenuation , drive tripping .The line reactors are always used
in the line side or input of the variable frequency drives. Thus they are called the line
reactors. The line reactors cannot be used at the output of the variable frequency drives
Because the reactors are over heated due to the harmonic content of the output
waveform of the VFD Harmonic compensated reactors can be used on the either side of
the variable frequency drives .Due to the introduction of the Harmonic compensated
reactors the following problems are eliminated: motor noise, low efficiency of the
motors, temperature rise in motors and variable frequency drives short circuit problem.
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Power Quality Seminar Report ‘03
5.2 HARMONIC FILTERS
In some cases, reactors alone will not be capable of reducing the harmonic
current distortion to the desired levels. In these cases, a more sophisticated filter will be
required. The common choices include shunt connected, tuned harmonic filters
(harmonic traps) and series connected low pass filters (broad band suppressors). They
consist of a capacitor and an inductor which are tuned to a single harmonic frequency.
Since they offer very low impedance to that frequency, the specific (tuned) harmonic
current is supplied to the drive by the filter rather than from the power source. If tuned
harmonic filters (traps) are selected as the mitigation technique, then multiple tuned
filters are needed to meet the distortion limits which are imposed.
When employing tuned harmonic filters, we need to take special precautions to
prevent interference between the filter and the power system. A harmonic trap presents
a low impedance path to a specific harmonic frequency regardless of its source. The
trap cannot discern harmonics from one load versus another. Therefore, the trap tries to
absorb that entire harmonic which may be present from all combined sources (non-
linear loads) on the system. This can lead to premature filter failure.
Since harmonic trap type filters are connected in shunt with the power system,
they cause a shift in the power system natural resonant frequency. If the new frequency
is near any harmonic frequencies, then it is possible to experience an adverse resonant
condition which can result in amplification of harmonics and capacitor or inductor
failures. Whenever using harmonic trap type filters, one must always perform a
complete system analysis. You must determine the total harmonics which will be
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Power Quality Seminar Report ‘03
absorbed by the filter, the present power system resonant frequency, and the expected
system resonant frequency after the filter (trap) is installed. Field tuning of this filter
may be required if adverse conditions are experienced.
5.3 12 PULSE RECTIFIERS
12 Pulse drives are frequently specified by the engineers for heating, ventilating
and air conditioning applications because their ability to reduce harmonic current
distortion. In the mid 1960s when power semiconductors were only available in limited
ratings, twelve-pulse drives provided a simpler and more cost effective approach to
achieving higher current ratings than direct paralleling of power semiconductors.
A typical diagram of a large twelve-pulse drive appears in figure the drive's
input circuit consists of two six-pulse rectifiers, displaced by 30 electrical degrees,
operating in parallel. The 30-degree phase shift is obtained by using a phase shifting
transformer. The circuit in figure simply uses an isolation transformer with a delta
primary, a delta connected secondary, and a second wye connected secondary to obtain
the necessary phase shift. Because the instantaneous outputs of each rectifier are not
equal, an inter phase reactor is used to support the difference in instantaneous rectifier
output voltages and permit each rectifier to operate independently. The primary current
in the transformer is the sum of each six-pulse rectifier or a twelve-pulse wave form.
Theoretical input current harmonics for rectifier circuits are a function of pulse
number and can be expressed as:
h = (np + 1) where n= 1, 2, 3, and p = pulse number
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Power Quality Seminar Report ‘03
For a six-pulse rectifier, the input current will have harmonic components at the
following multiples of the fundamental frequency.
5, 7, 11, 13, 17, 19, 23, 25, 29, 31, etc.
For the twelve-pulse system shown in figure 1, the input current will have
theoretical harmonic components at the following multiples of the fundamental
frequency:
11, 13, 23, 25, 35, 37, etc.
Note that the 5th and 7th harmonics are absent in the twelve-pulse system. Since
the magnitude of each harmonic is proportional to the reciprocal of the harmonic
number, the twelve-pulse system has a lower theoretical harmonic current distortion.
12 PULSE RECTIFIERS
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Power Quality Seminar Report ‘03
Figure shows the actual measurement of input current harmonic distortion for 12
pulse rectifier supplied from a balanced 3 phase voltage source while operating at full
load conditions. For test purpose transformer has delta primary and delta,wye secondary
windings. To obtain the best results, the bridge rectifier is connected in series so equal
dc windings. To obtain the best results, the bridge rectifier is connected in series so
equal dc
The data shows when the current through both sets of the rectifiers is equal,
harmonics can be as low as 10% to 12% total harmonic current distortion, at full load.
Current sharing reactors will help parallel connected bridge rectifiers to share current
equally. Even with balanced current harmonic current distortion can increase
appreciably at light loaded conditions. Even with perfectly balanced line voltages, the
resultant % total harmonic current distortion increases as the load increases. As the load
reduced, that is 23% total harmonic current distortion at 20% load.
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Power Quality Seminar Report ‘03
5.4 18 PULSE RECTIFIER
A typical diagram of a series connected eighteen pulse drive constructed from a
standard six-pulse drive, two external rectifiers and a conventional 18 pulse isolation
transformer appears in figure 1. The drive has terminals available to connect a DC link
choke. These terminals are used to connect the two external rectifiers in series with the
drives internal rectifier. The eighteen pulse transformer is designed to provide one third
the normal input voltage to each of the three rectifiers at a 20 degree phase
displacement from each other. The 20-degree phase shift is obtained by phase shifting
the transformers secondary windings. The circuit in figure 1 simply uses an isolation
transformer with a delta primary, and three delta connected secondary windings, one
shifted + 20 degrees, one shifted -20 degrees and one in phase with the primary.
The primary current in the transformer is the sum of each six-pulse rectifier or
an eighteen-pulse wave form.
Theoretical input current harmonics for rectifier circuits are a function of pulse
number and can be expressed as:
h = (np ± 1) where n= 1, 2, 3,... and p = pulse number
For a six-pulse rectifier, the input current will have harmonic components at the
following multiples of the fundamental frequency.
5, 7, 11, 13, 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, 53, 55, etc.
For the eighteen-pulse system shown in figure 1, the input current will have
theoretical harmonic components at the following multiples of the fundamental
frequency:
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Power Quality Seminar Report ‘03
17, 19, 35, 37, 53, 55, etc.
Note that the 5th and 7th, 11th and 13th harmonics are absent in the theoretical
eighteen-pulse system. Since the magnitude of each harmonic is proportional to the
reciprocal of the harmonic number, the eighteen-pulse system has a lower theoretical
harmonic current distortion.
To determine how an eighteen-pulse drive system operates under unbalanced
line voltage conditions, we constructed a 30 HP eighteen-pulse drive from a
conventional isolation transformer and standard six-pulse drive using the series bridge
connection shown in figure 1. An auto transformer could have been used in place of the
isolation transformer. The auto transformer costs less and requires less mounting space,
but the isolation transformer was selected because it provides better performance and is
readily available as a modified standard transformer.
Care was taken in the physical construction of the transformer to balance the
leakage reactance and output voltage of the three secondary windings. The system was
tested with line voltage unbalance ranging from 0% to 3% and with loads ranging from
5% to 100%. The input total harmonic current distortion, THID, is shown in figure 3.
THID varied from 7.4% at full load with balanced line voltages to 59% at 30% load
with a 3% unbalance. The data show that the harmonic performance of eighteen-pulse
drives degrades rapidly with increasing line voltage unbalance and decreasing load.
Simply focusing on harmonic performance under the best operating conditions,
perfectly balanced line voltages and full load, is not a useful indicator of performance
under practical operating conditions. In heating, ventilating and air conditioning
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Power Quality Seminar Report ‘03
applications where drives will operate for long periods of time at 30% to 60% load
eighteen pulse drives to not meet expectations.
18 PULSE RECTIFIER
To determine how an eighteen-pulse drive system operates under unbalanced line
voltage conditions, we constructed a 30 HP eighteen-pulse drive from a conventional
isolation transformer and standard six-pulse drive using the series bridge connection
shown in figure 1. An auto transformer could have been used in place of the isolation
transformer. The auto transformer costs less and requires less mounting space, but the
isolation transformer was selected because it provides better performance and is readily
available as a modified standard transformer. Care was taken in the physical
construction of the transformer to balance the leakage reactance and output voltage of
the three secondary windings. The system was tested with line voltage unbalance
ranging from 0% to 3% and with loads ranging from 5% to 100%. The input total
harmonic current distortion, THID, is shown in figure 3. THID varied from 7.4% at full
load with balanced line voltages to 59% at 30% load with a 3% unbalance. The data
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Power Quality Seminar Report ‘03
show that the harmonic performance of eighteen-pulse drives degrades rapidly with
increasing line voltage unbalance and decreasing load. Simply focusing on harmonic
performance under the best operating conditions, perfectly balanced line voltages and
full load, is not a useful indicator of performance under practical operating conditions.
In heating, ventilating and air conditioning applications where drives will operate for
long periods of time at 30% to 60% load eighteen pulse drives to not meet expectations.
Figure 3
Obviously, any unbalance in the eighteen-pulse transformer's leakage reactance
and output voltage will degrade performance. Unfortunately perfect transformers can
not be built. Output voltage depends on turns ratios which are limited to plus or minus
one turn. As a result the output voltage of the three secondary windings cannot be
perfectly balanced. Leakage reactance is a function of coil position and volume. Clever
Mechanical design of the transformer windings will help to minimize the differences in
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Power Quality Seminar Report ‘03
leakage reactance between the three groups of secondary windings but perfect balance
can not be achieved. Data for the transformer used in this test appears in Tables 1 and 2.
Transformer Design
Secondary
Winding Phase Shift
Degrees
Leakage
Reactance
%
Nominal Output Voltage
Based on Turns Ratios
Volts
0 3.67 160.00
-20 4.73 160.50
+20 5.33 160.50
Table 1
Transformer Full Load Data
Secondary
Winding
Phase Shift
Degrees
Secondary Phase Voltage
At Full Load
Unbalance
Per
Secondary
Group
%
Unbalance
Across
Secondary
Groups
%
Volts
A B C Average
0 154.3 154.4 154.1 154.26 0.10
-20 157.9 157.0 157.6 157.50 0.32
+20 156.6 155.4 156.9 156.30 0.57
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Power Quality Seminar Report ‘03
Average 156.02 1.12
Table 2
The addition of 5% line reactors at the input to each of the three rectifiers results
in a significant improvement in the operation Drives are applied in heating, ventilating,
and air conditioning applications because loads are variable and users demand energy
efficiency and comfort. Varying loads result in load unbalances within building power
distribution systems which add to the utility line voltage unbalance at the point of
common coupling. Harmonic mitigation techniques which are not effective with line
voltage unbalances of 1% to 3% at the point of utilization will not as a practical matter
achieve useful results. The data in this report show that a standard six-pulse drive fed
from a low pass Matrix Filter provides superior harmonic performance to an eighteen-
pulse drive in applications with variable loads and line voltage unbalances ranging from
0% to 3%.
5.5 LOW PASS HARMONIC SUPPRESSORS
Low pass harmonic filters, also referred to as broad band harmonic suppressors,
offer a non-invasive approach to harmonic mitigation. Rather than being tuned for a
specific harmonic, they filter all harmonic frequencies, including the third harmonic.
They are connected in series with the non-linear load with a large series connected
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Power Quality Seminar Report ‘03
impedance, therefore they don’t create system resonance problems. No field tuning is
required with the low pass filter.
Due to the presence of the large series impedance, it is extremely difficult for
harmonics to enter the filter / drive from the power source. Rather they are supplied to
the drive via the filter capacitor. For this reason, it is very easy to predict the distortion
levels which will be achieved and to guarantee the results.
A low pass (broad band) harmonic filter can easily offer guaranteed harmonic
current levels, right at the drive / filter input, as low as 8% to 12% THID. (To achieve
8% maximum current distortion one can typically select the broad band harmonic
suppressor based on a HP / KW rating which is 25-30% larger than the total drive load
to be supplied). In most cases, this results in less than 5% THID at the facility input
transformer and meets most international standards.
Fig. 6 Actual input current waveform for VFD fitted with Broad Band
Harmonic Suppressor.
The low pass filter not only offers guaranteed results, it is also more economical
than 12 or 18 pulse rectifier systems, active filters or in many cases even harmonic
traps. They are intended for use with 6-pulse drives having a six diode input rectifier in
variable torque applications. This typically means fan and pump applications. For the
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Power Quality Seminar Report ‘03
sake of economy, a single Broad Band Harmonic Suppressor may be used to supply
several drives (VFDs). When operating at reduced load, the THID at the filter input will
be even lower than the guaranteed full load values.
6. BENEFITS
MOTOR TEMPERATURE REDUCTION
Motors operated on a VFD tend to run warmer than when they are operated on
pure 60hz, such as in an across-the-line stator application. The reason is that the output
waveform of the VFD is not pure 60hz,, but rather it contains harmonics which are
currents flowing at higher frequencies. The higher frequencies cause additional watts
loss and heat to be dissipated by the iron of the motor, while the higher currents cause
additional watts loss and heat to be dissipated by the copper windings of the motor.
Typically the larger horsepower motors (lower inductance motors) will experience the
greatest heating when operated on a VFD.
Reactors installed on the output of a VFD will reduce the motor operating
temperature by actually reducing the harmonic content in the output waveform. A five
percent impedance, harmonic compensated reactor will typically reduce the motor
temperature by 20 degrees Celsius or more. If we consider that the typical motor
insulation system has a "Ten Degree C Half Life" (Continual operation at 10 degrees C
above rated temperature results in one half expected motor life), then we can see that
motor life in VFD applications can easily be doubled. Harmonic compensated reactors
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Power Quality Seminar Report ‘03
are actually designed for the harmonic currents and frequencies whereas the motor is
not.
MOTOR NOISE
Because the carrier frequency and harmonic spectrum of many Pulse Width
Modulated (PWM) drives is in the human audible range, we can actually hear the
higher frequencies in motors which are being operated by these drives. A five percent
impedance harmonic compensated reactor will virtually eliminate the higher order
harmonics (11th & up) and will substantially reduce the lower order harmonics (5th &
7th). By reducing these harmonics, the presence of higher frequencies is diminished and
thus the audible noise is reduced. Depending on motor size, load, speed, and
construction the audible noise can typically be reduced from 3 - 6 dB when a five
percent impedance harmonic compensated reactor is installed on the output of a PWM
drive. Because we humans hear logarithmically, every 3dB cuts the noise in half to our
ears. This means the motor is quieter and the remaining noise will not travel as far.
MOTOR EFFICIENCY
Because harmonic currents and frequencies cause additional watts loss in both
the copper windings and the iron of a motor, the actual mechanical ability of the motor
is reduced. These watts are expended as heat instead of as mechanical power. When a
harmonic compensated reactor is added to the VFD output, harmonics are reduced,
causing motor watts loss to be reduced. The motor is able to deliver more power to the
load at greater efficiency. Utility tests conducted on VFD's with and without output
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Power Quality Seminar Report ‘03
reactors have documented efficiency increases of as much as eight percent (at 75%
load) when the harmonic compensated reactors were used. Even greater efficiency
improvements are realized as the load is increased.
SHORT CIRCUIT PROTECTION
When a short circuit is experienced at the motor, very often VFD transistors are
damaged. Although VFD's typically have over correct protection built-in, the short
circuit current can be very severe and its rise time can be so rapid that damage can
occur before the drive circuitry can properly react. A harmonic compensated reactor
(3% impedance is typically sufficient) will provide current limiting to safer values, and
will also slow down the short circuit current rise time. The drive is allowed more time
to react and to safely shut the system down. You still have to repair the motor but you
save the drive transistors.
The above methods solve other problems on the load side of VFD's in
specialized applications also. Some of these include: Motor protection in IGBT drive
installations with long lead lengths between the drive and motor, Drive tripping when a
second motor is switched onto the drive output while another motor is already running,
and Drive tripping due to current surges from either a rapid increase or decrease in the
load.
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Power Quality Seminar Report ‘03
7. CONCLUSION
VFD users have many choices when it comes to harmonic filtering. Of course
they may do nothing, or they may choose to employ one of the many techniques of
filtering available. Each filtering technique offers specific benefits and has a different
cost associated with it. Some may have the potential to interfere with the power system
while others will not.
For best overall results when using reactors or harmonic filters, be sure to install
them as close as possible to the non-linear loads which they are filtering. When you
minimize harmonics directly at their source you will be cleaning up the internal facility
mains wiring. This will also reduce the burden on upstream electrical equipment such as
circuit breakers, fuses, disconnect switches, conductors and transformers. The proper
application of harmonic filtering techniques can extend equipment life and will often
improve equipment reliability and facility productivity.
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Power Quality Seminar Report ‘03
8. REFERENCES
INDUSTRIAL REFERENCE MAY 2003 PAGE 178
WWW.POWERQUALITY.COM
WWW.ECONOMICSOULTIONSTOMEETHARMONICDISTORTION.COM
WWW.POWERQUALITYUSINGREACTORS.COM
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Power Quality Seminar Report ‘03
ABSTRACT
Power quality is essential for smooth functioning of industrial process. As
industries expand, utilities become more interconnected and usage of electrically
equipment increases, power quality is jeopardized. The quality of power in the power
system is severely affected by the presence of harmonics. This harmonics adversely
effects the power system performance. Some of the effects are over heating of metal
parts, noise in motors, low efficiency in motors etc. The effects produced by the
harmonics are reduced by adopting some corrective measures.
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Power Quality Seminar Report ‘03
CONTENTS
1. INTRODUCTION 1
2. WHAT IS POWER QUALITY? 2
3. HARMONICS BASIC CONCEPT 3
4. THE AFFECTS 5
5. SOLUTION 7
5.1. LINE REACTORS 7
5.2. HARMONIC TRAPS 8
5.3. 12 PULSE RECTIFIER 9
5.4.18 PULSE RECTIFIER 12
5.5. LOW PASS SUPPRESSORS 17
6. BENEFITS 19
7. CONCLUSION 22
8. REFERENCES 23
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Power Quality Seminar Report ‘03
ACKNOWLEDGEMENT
I express my sincere gratitude to Dr.Nambissan, Prof. & Head,
Department of Electrical and Electronics Engineering, MES College of
Engineering, Kuttippuram, for his cooperation and encouragement.
I would also like to thank my seminar guide Mrs. Nafeesa K.
(Lecturer, Department of EEE), Asst. Prof. Gylson Thomas. (Staff in-charge,
Department of EEE) for their invaluable advice and wholehearted cooperation
without which this seminar would not have seen the light of day.
Gracious gratitude to all the faculty of the department of EEE &
friends for their valuable advice and encouragement.
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