Ieee power quality distribution systems

Fundamentals of PowerFundamentals of Power
Quality
IEEE CEU Oct. 26, 2010
Presented by: Vincent W. Wedelich PE MBA
Reference Material
Fundamentals of Electric Power Quality by: Surya Santoso
Power Quality Course by Paul Ortmann PE University of Idaho
Govind Gopakumar,p
Huihua Yan, Dr. Bruce A. Mork Michigan Technological University
Power Quality Course by Electotek/Drantez
1Presented by Vincent W. Wedelich PE MBA Burns & McDonnell IEEE PES 2010 Presentation: reference data IEEE, University of Idaho, Electrotek,/Dranetz

What you will learnWhat you will learn.
• Power Quality issues are only issues if someone
complainscomplains.
• Any sudden load increase can cause a voltage
sagsag.
• Sudden changes in the electric power system
will result in transientswill result in transients.
• Transient analysis requires waveform analysis
and capturing.and capturing.
• When mitigating power quality issues use the
simplest method.
p

Topics we will coverTopics we will cover
• Part 1
Power Quality Fundamentals– Power Quality Fundamentals
• Part 2
– Voltage Sags and Short Interruptions
• Part 3
– Transients
• Part 4
– Harmonics
• Conclusion
• Conclusion

• Part 1
• Part 2
• Part 3
– Transients
• Part 4
– Harmonics
• Conclusion
• Conclusion

The growth of power reliability and power quality-related spending has now
reached more than $1 billion per year, according to one EPRI study (when
equipment such as uninterruptible power systems are included)
equipment such as uninterruptible power systems are included).

The deleterious factors affecting
electric power quality show nop q y
signs of improving in the near
future.

Earlier this year the DOE said,
"In the 1980s electrical load from sensitive electronic"In the 1980s, electrical load from sensitive electronic
equipment, such as chips (computerized systems,
appliances and equipment) and automated
manufacturing was limited.
In the 1990s, chip share grew to roughly 10%.In the 1990s, chip share grew to roughly 10%.
Today, load from chip technologies and automated
manufacturing has risen to 40% and the load ismanufacturing has risen to 40% and the load is
expected to increase to more than 60% by 2015."

Power Quality FundamentalsPower Quality Fundamentals
• Power Quality = Voltage QualityPower Quality = Voltage Quality
• FrequencyFrequency
• Amplitude
• Distortion

• Power quality can be defined from two differentq y
perspectives, depending on whether you supply or
consume electricity.
• Power quality at the generator usually refers to the
generator’s ability to generate power at 60 Hz with littlegenerator s ability to generate power at 60 Hz with little
variation,
• while power quality at the transmission and distribution
level refers to the voltage staying within plus or minus 5
percent.
percent.

• Temporary voltage quality issuesTemporary voltage quality issues
(transients)
• Faults
• Switching
• Lightning• Lightning

• Continuous voltage quality issuesContinuous voltage quality issues
(harmonics)
• Non-linear loads
• Use of power conductors for data

• TransmissionTransmission
• System design problemsSystem design problems

• More appropriate to define a “PQMore appropriate to define a PQ
problem”.
“Any power problem manifested in
lt t fvoltage, current, or frequency
deviations that results in failure or mis-
ti f t i t ”operation of customer equipment.”

Power Quality Fundamentals
• Do these voltage waveforms represent PQ
problems?
• Only if they cause equipment to
misoperate or fail
misoperate or fail.

A PQ problem?A PQ problem?
• A network server reboots randomly.
• Certain power factor correction capacitors on a utility• Certain power factor correction capacitors on a utility
distribution feeder repeatedly have blown fuses.
• Variable speed drives at a sewage treatment plant tripp g p p
off occasionally while the rest of the plant keeps running.
• A retail store reports that individual cash registers
sometimes stop working properlysometimes stop working properly.
• Various parts of a large industrial plant trip off.
• The DVD call recorder at a 911 dispatch center stopsThe DVD call recorder at a 911 dispatch center stops
working and must be manually reset occasionally.
• A radio station transmitter trips periodically, usually
restarting by itself.

Why is power quality important?Why is power quality important?
• Power quality problems impact us more often:q y p p
– New equipment:
• more efficient, more features, but also more sensitive
and probably “always on”.
– Emphasis on efficiency:
increased use of power electronics• increased use of power electronics
• 24/7 production streams operating at 100% capacity.
• Increased use of automationIncreased use of automation.
• Use of capacitors on distribution lines to reduce losses.

Why is power quality important?Why is power quality important?
• Increased customer awareness
• Clocks as PQ monitors
• “Always on” equipment
– Interconnected/interdependent systems
• We are increasingly dependent on power systems and
computers that may be far away.
– Business networksBusiness networks
– Building Automation

What is Power Quality
Engineering?
• PQ Engineers investigate equipmentPQ Engineers investigate equipment
malfunctions and failures to determine:
– Is the malfunction or failure a “PQ problem”,Q p ,
i.e., was it caused by a deviation in the
voltage waveform?
– Can the cause be eliminated?
– What mitigation is appropriate? (disturbance,
path, vulnerability, some combination?)
• We may find that the problem isn’t strictly a
“Power Quality problem” after all!

Why are power electronics
i PQ?important to PQ?
Top Four Reasons:Top Four Reasons:
1 Th h i di t ti1. They cause harmonic distortion.
2. The presence of harmonic distortion from
power electronics can affect the powerp p
system and other loads.

Why are power electronics
i PQ?important to PQ?
3. Power electronic devices have particular
vulnerabilities when it comes to PQvulnerabilities when it comes to PQ.
4. The use of power electronic devices is
increasing.

Where are power electronics?Where are power electronics?
• Almost everywhere…Almost everywhere…
– Industrial systems
• Motors
• Control systems
• Lighting

Where are power electronics?Where are power electronics?
• Electronic ballasts in fluorescent lightsElectronic ballasts in fluorescent lights
Di i t• Dimming systems
• Convert DC from solar, or AC from Wind
to 60Hz AC

How power electronics create harmonics
• Generally, a power electronic device
draws current in “pulses” from the powerdraws current in pulses from the power
system. (continuously)
Non-linear current – harmonics
As we learned with the Fourier
Series (FFT), the non-linear
current can be “assembled”
from sinusoids.

Some PQ issues with power
l ielectronics
• Impact on line voltageImpact on line voltage
– “flat-topping” reduces
ride through time ofride through time of
electronic loads during
voltage sagsg g
– Distorted voltage resultsg
in distorted current,
even in linear loads.

Power electronics vulnerabilitiesPower electronics vulnerabilities
• Flat-topped voltageFlat topped voltage
– reduces dc bus voltage,
reducing stored energy for
voltage sag ride-through.
• Capacitor switching.
Wh t ill h h– What will happen when
this voltage waveform
passes through thep g
rectifier and into the dc
bus capacitor?

• Part 1
• Part 2
• Part 3
– Transients
• Part 4
– Harmonics
• Conclusion
• Conclusion

Voltage Sags and InterruptionsVoltage Sags and Interruptions
• Definitions:Definitions:
• Magnitude (of nominal voltage)
Sag: 0 1 pu 0 9 pu– Sag: 0.1 pu - 0.9 pu
– Interruption: less than 0.1 pu
D ti• Duration
– Instantaneous: 0.5 cycles - 30 cycles
– Momentary: 30 cycles - 3 seconds
– Temporary: 3 seconds - 1 minutes

Sources of Voltage Sags and or
i iinterruptions
Any sudden increase in load, if large
enough will cause a voltage sagenough, will cause a voltage sag
Motors– Motors
Faults– Faults
– Switching
– Switching

Sources - MotorsSources Motors
• Motors may start and stop frequently.Motors may start and stop frequently.
• “Across the line” or full voltage starting• Across the line or full voltage starting
– 6 to 8 times normal running current
– Inexpensive– Inexpensive
– Fast acceleration
• Results in largest voltage sag or flicker
compared to using a “soft starting” system
compared to using a soft starting system.

Sources – Motors – starting 500HpSources Motors starting 500Hp
80% voltage sag A good argument could be made here not to put a 500HP
80% voltage sag. A good argument could be made here not to put a 500HP
motor on a 480V system.

Sources - FaultsSources Faults
• Faults cause both voltage sags andFaults cause both voltage sags and
interruptions.

Distribution voltage sag and
i iinterruption
• Fault occursFault occurs
– Voltage sags.
• Fuses, circuit breakers, and reclosers, start to heat
up or time-out.
• Fault is cleared
– Fuse, circuit breaker, or recloser opens.
– Voltage returns to normal for upstream loads.
V l d f d l d– Voltage drops to zero for downstream loads.
• Possible reclosing

Recloser operationRecloser operation
• A recloser is an automatic circuit breaker.A recloser is an automatic circuit breaker.
It can “test” for the continued presence of
a fault. Since most faults on overhead
systems are temporary, it reduces outages
to interruptions.
Log of recloser
operations during aoperations during a
temporary fault.

System protection overviewSystem protection overview
• Typical Objectives:yp j
– Distinguish fault current from load current
– Minimize number of customers off
– Minimize interruption duration– Minimize interruption duration
• Issues:
– Fault current varies system impedance, fault
i dimpedance
– Coordinating multiple devices can be difficult

Clearing faultsClearing faults
• FusesFuses
– Inexpensive
Require manual replacement– Require manual replacement
– Help locate faults
In general fuses are used to disconnect or– In general, fuses are used to disconnect, or
“sectionalize” portions of the system with
permanent faults from the rest of the systempermanent faults from the rest of the system.
– “Current Limiting” fuses can have a PQ
benefit.
benefit.

Clearing faultsClearing faults
• Reclosers and fuses work togetherReclosers and fuses work together
– Fuse saving
• Recloser trips very quickly to clear a temporary
fault before a fuse can operate.p
• If the fault is still present when the recloser closes,
the recloser trips more slowly to allow a
downstream fuse to operate.

How a voltage sag turns into an
outage
Because the relays used in “EMO” circuits
may be particularly vulnerable to voltage
sags, the process equipment will trip offsags, the process equipment will trip off
as if someone pressed the emergency stop
button.
• Emergency shutdowns are typically not
orderly or controlled.

Typical voltage sag tolerance – IEEE 1346Typical voltage sag tolerance IEEE 1346

Motor starting voltage sag estimateg g g
– Motor draws 5MVA starting.
System can deliver 30 MVA to a 3 phase– System can deliver 30 MVA to a 3-phase
fault at the motor location.
What if this voltage sag is too large?
g g g

Motor StartingMotor Starting
• Autotransformer startersAutotransformer starters
R d lt li d d di– Reduce voltage applied and corresponding
current and starting torque
– Starting current and torque are reduced to
25% 42 25% or 64% of full voltage values25%, 42.25%, or 64% of full voltage values.

• Resistance or Reactance startersResistance or Reactance starters
I t i i d hi h d th– Insert a series impedance which reduces the
voltage applied to the motor.
• Starting current and torque reduction varies.

• Part-winding startersPart winding starters
L lt l l i li d t f t– Lower voltage level is applied to one of two
parallel windings during starting.
• Starting current and torque are reduced to 50% of
full voltage values.full voltage values.

• Delta-wye startersDelta wye starters
St t t d i f t ti th– Stator connected in wye for starting, then
changed to delta.
• Starting current and torque reduced to 33% of full-
voltage values.g

Motor Starting
• All of these methods reduce the startingAll of these methods reduce the starting
current drawn by the motor and result in
reduced starting torquereduced starting torque.
Wh t if l d lt t t i• What if we apply a delta-wye starter in our
example?

Impact of “soft starting” the motorImpact of soft starting the motor
• In our example a voltage sag to 85 7% ofIn our example, a voltage sag to 85.7% of
nominal voltage is reduced to a “voltage
fluctuation” or flicker of about 5 2%fluctuation or flicker of about 5.2%.

How much flicker is acceptable?How much flicker is acceptable?
– Energy providers usually limit the maximumEnergy providers usually limit the maximum
system fluctuation, or how much one can
flicker the neighbor’s voltage.
– Providers usually also include flicker
considerations in sizing service transformers
and conductors.

Allowable flicker

Tests indicate that some individuals are irritated by a ficker that is barely
noticeable to others.

Evaluating voltage sag performanceg g g p
• Voltage sag performance
R f t th lt f ilit– Refers to the voltage sags a facility
experiences and the impact of those voltage
sags on the facilitysags on the facility.
IEEE standard 1346 “Recommended– IEEE standard 1346 – Recommended
Practice for Evaluating Electric Power System
Compatibility with Electronic ProcessCompatibility with Electronic Process
Equipment”

Evaluating voltage sag performanceg g g
Objectives of the evaluation
• Determine the expected number depth and• Determine the expected number, depth, and
duration of voltage sags
• Determine equipment vulnerability to voltage sags
• Identify and address incompatibilities
• Build the compatibility template

Voltage Sag Mitigation principlesg g g
• Mitigation is any equipment or modification
that sufficiently resolves a voltage sagthat sufficiently resolves a voltage sag
incompatibility issue.
• Mitigation should be “the simplest thing
that could possibly work.”

Voltage Sag Mitigation principles
• “Perfect Power” is not necessary.
• Possible Solutions
D i S C t (D SC) (A ti i– Dynamic Sag Corrector (DySC) (Active series
compensator)
– Ferroresonant Transformer– Ferroresonant Transformer
– UPS
– Voltage Dip Compensator; A multi-tapVoltage Dip Compensator; A multi tap
transformer with solid-state switching between
taps

SEMI F47 is an industry standard for voltage sag immunity.

More and more wafer fabs are insisting that front-end
wafer processing equipment comply with SEMI F47.
Many of the contactors and pilot relays used on
equipment, particularly in the EMO circuit, are not
able to meet the standard.
As a result, equipment can drop out during a voltage
sag of 50% in magnitude and 200ms in duration,
causing equipment shutdown.

• Part 1
• Part 2
• Part 3
– Transients
• Part 4
– Harmonics
• Conclusion
• Conclusion

Power System TransientsPower System Transients
• Sudden changes in the electric power systemSudden changes in the electric power system
are called transients. All transients are caused
by one of two actions:
1. Connection or disconnection of elements within the
electric circuit
2 Injection of energy due to a direct or indirect2. Injection of energy due to a direct or indirect
lightning stroke or static discharge.

Power System TransientsPower System Transients
• Transient overvoltages and overcurrentsTransient overvoltages and overcurrents
are classified by:
– Peak magnitude
– Frequency
– Duration

Characterizing Transient
Di bDisturbances
• Transient Oscillations:Transient Oscillations:
O ill ti– Oscillations
• Low Frequency – less than 330 Hz
• Medium Frequency – 300 Hz to 2 kHz
• High Frequency – 2kHz to 5 kHz

Characterizing Transient
Di bDisturbances
• Transient Impulses:Transient Impulses:
U idi ti l– Unidirectional
L th 200 i d ti• Less than 200usec in duration
• Frequency components greater than 5kHz• Frequency components greater than 5kHz
• Characterized by magnitude and duration.
y g

How do Transients Propagate?How do Transients Propagate?
• High frequency transients do notHigh frequency transients do not
propagate over long distances:
– This is a good reason for separating sensitive
loads and disturbing loadsloads and disturbing loads.

• Local resonances can cause oscillationLocal resonances can cause oscillation
remote from the transient source:
– This can be particularly important for
transients caused by utility capacitortransients caused by utility capacitor
switching..

• Lower frequency transients will appearLower frequency transients will appear
throughout the system facility:
– Capacitor switching transients are usually less
than 1kHzthan 1kHz.

TransientTransient
• Sudden change in the power systemSudden change in the power system
• Classified by peak magnitude, frequency,
and durationand duration.

We have both a transient and a
d b h iresonance caused by the capacitor.

Sources of Transient Disturbances
• Power Quality – Related sources of transient
Voltages and Currents:Voltages and Currents:
• Lightning
• Load SwitchingLoad Switching
• Transformer Switching
• Ferroresonance
• Capacitor Switching
• Voltage notching (rectifier switching)g g ( g)
• ASD Motor transients (inverter switching)
• And many more.

LightningLightning
• Lightning transients are caused by theLightning transients are caused by the
injection of current impulses into the
systemsystem.
Hi h f hi h it d t i t• High frequency, high magnitude transients
can propagate on the system and into
t f iliticustomers facilities.

LightningLightning
• A direct stoke to a distribution line willA direct stoke to a distribution line will
cause the voltage to rise rapidly, resulting
in an arrester operation or line flashover.p
• Fast wavefront’s can couple throughFast wavefront s can couple through
transformers by capacitor ratio, rather than
turns ratio
– High rate of rise can cause failures in power
electronic equipment (e.g. SCRs, etc..)

Simulating Lightning Current
Waveforms
8 x 20usec8 x 20usec
1.2 x 50usec

Load SwitchingLoad Switching
• High frequency transients are oftenHigh frequency transients are often
initiated by some type of switching event.
• Circuit switching (de-energizing) and
i d ti l d li d ffinductive loads cycling on and off
(contactors) can produce a burst of high
f i lfrequency impulses

Load SwitchingLoad Switching
• Most high frequency transients occurringMost high frequency transients occurring
within customers facilities do not have
significant energy associated with themsignificant energy associated with them
(less than 1 joule).
• This means that equipment can often be
t t d ith i l t tiprotected with simple surge protection
devices.

Load Switching WaveformsLoad Switching Waveforms.

Transformer Switching
• When a transformer (device with magnetic core)
is energized, a transient inrush current flows:g
– Current interacts with the system impedance to create
a voltage waveform that can have significant
harmonic components (full load current by a factor ofharmonic components (full load current by a factor of
8 to 10)
– May excite local resonances (cables, capacitors),y ( p )
causing dynamic overvoltages
– Current typically decays in several seconds
C f– Characteristic of the current is determined by:
• Magnitude of input voltage at the instant of energization
• Residual flux in the core
• Impedance of the supply current

Measured Transformer
E i iEnergization

FerroresonanceFerroresonance
• Ferroresonance is a term generallyFerroresonance is a term generally
applied to a wide variety of interactions
between capacitors and iron corebetween capacitors and iron core
inductors that results in unusual voltage
and or currentsand or currents

Ferroresonance Basics
• A “Resonance” involving a capacitance in series
with a saturable inductance LM.
• Unpredictable due to nonlinearities.
• More likely when little load or damping, and for
unbalanced 3-phase excitation
• Examples of capacitances:
– Series Compensated Lines.Series Compensated Lines.
– Shunt Capacitor Banks.
– Underground Cable.
– Systems grounded only via stray capacitance.
Systems grounded only via stray capacitance.
– Grading capacitors on Circuit Breakers.
– Generator Surge Capacitors.

What’s special about FerroresonanceWhat s special about Ferroresonance
• Ferromagnetic materials (likeg (
steel transformer cores)
exhibit hysteresis, and can
saturate.
• The inductance is non-linear
XL is no longer just a function
of frequency it is also aof frequency, it is also a
function of the applied
voltage
• Circuit will have multiple• Circuit will have multiple
stable and unstable operating
points and may jump
between points
between points.

Necessary conditions for
fferroresonance
• Capacitance with non-linear inductance
• At least one point where the voltage is not
fixed by the external system
• Light loading – minimal damping

Preventing ferroresonancePreventing ferroresonance
• Use grounded-wye/grounded-wye systems
• Keep primary cable runs short
• Use three-phase switching and protectionp g p
• Place switch/protection directly upstream
of the transformerof the transformer
• Have some load on the transformer when
switchingswitching
• Surge arrestors may be used to help
lt
suppress overvoltages

Capacitor SwitchingCapacitor Switching
• Capacitor Bank Energizing TransientCapacitor Bank Energizing Transient
The voltage across a capacitor cannot change– The voltage across a capacitor cannot change
instantaneously
– The step change in voltage when a capacitor bank
is energize results in an oscillation between theis energize results in an oscillation between the
capacitance and the system inductance.

• Typical MagnitudesTypical Magnitudes
– 1.2 to 1.7 p.u. (x normal)
• Typical Frequencies
– 250 to 1000 Hz

To illustrate, we begin with CB1 and CB4 closed, energizing C1 by closing S1.

Energizing the second bank C2 when the first bank C1 is already energized is called
back-to-back switching [5], and is simulated by closing switch S2 when C1 is already
back to back switching [5], and is simulated by closing switch S2 when C1 is already
operating in steady state.

Energizing the second bank C2 when the first bank C1 is already energized is called
b k t b k it hi [5] d i i l t d b l i it h S2 h C1 i l d
back-to-back switching [5], and is simulated by closing switch S2 when C1 is already
operating in steady state.

Voltage Notching (Rectifier Switching)Voltage Notching (Rectifier Switching)
• Voltage notches are a special case that falls inVoltage notches are a special case that falls in
between transients and harmonic distortion.
• Natural result of commutation in powerp
electronic devices:
– Notching of the input voltage waveform is a normal
characteristic of the switching that occurs in the
power electronics of a rectifier during continuous
current operations.current operations.
• High Frequency components.
• Additional zero crossing timing problems
Additional zero crossing timing problems.

Motor Transients (Inverter Switching)Motor Transients (Inverter Switching)
• Voltage reflections (up to 2 per unit) at the motor
t i l i l ti f ilterminals can cause insulation failure.
• Quantities that impact the voltage include:p g
– PWM switching frequency
– Cable length
– Damping
• Possible solution to ASD motor transients:
– Change cable lengthg g
– Change PWM frequency
– Surge capacitors across motor terminals
– Line reactors (chokes) at the drive terminal

Output of a PWM VFDOutput of a PWM VFD

Motor Terminal VoltageMotor Terminal Voltage

Analysis of transient overvoltages
• Transient analysis typically requires waveform data
• Collecting waveforms requires instruments with faster
sampling and more data storage
• Typical high-end power quality recorder will detect
transients and briefly record at a higher sampling ratetransients and briefly record at a higher sampling rate
• Oscilloscopes may also be useful for capturing transientsOscilloscopes may also be useful for capturing transients

Three ways waveforms help identify
sources of transient overvoltages
• Waveform characteristicsWaveform characteristics
– Impulsive or oscillatory
Frequency of oscillation– Frequency of oscillation
– Rise time, decay time, etc.
Ti t• Time-stamp
– Correlation with known events
• Time-of-arrival
– Used to determine transient direction

Characterizing transient overvoltages
• Impulsive
Nanosecond– Nanosecond
• 5ns rise, lasts <50ns
Mi d– Microsecond
• 1μs rise, lasts 50ns – 1ms
Milli d– Millisecond
• 0.1ms rise, lasts >1ms
• Caused by lightning, removal of an inductive
load, loose wiring, and other arcing events

• Oscillatory
• Low frequency: <5kHz, 0.3 – 50ms, 0 – 4 puLow frequency: 5kHz, 0.3 50ms, 0 4 pu
– Capacitor switching, ferroresonance, transformer
energization
• Medium frequency: 5–500 kHz, 20μs, 0 – 8 pu
– Back-to-back capacitor switching, cable switching,
impulse response
• High frequency: 0.5 – 5 MHz, 5 μs, 0 – 4 pu
– Response of system to an impulsive transient
Response of system to an impulsive transient

• Common Mode (N-G)
caused by lightning utility switching ground– caused by lightning, utility switching, ground
potential differences in a network, and radio
and T.V. transmittersand T.V. transmitters
• Normal Mode
caused by power electronics switching power– caused by power electronics, switching power
supplies, and arcing loads

Some real transient waveformsSome real transient waveforms

• Impact on loads
– A few “symptoms”
– Hard disk crash
– Power supply failure
– Component failureComponent failure
– SCR failure
– Circuit board failuresCircuit board failures
– Process interruptions
“letting the smoke out”– letting the smoke out

• Part 1
• Part 2
• Part 3
– Transients
• Part 4
– Harmonics
• Conclusion
• Conclusion

HarmonicHarmonic
• Steady state distortion of the waveformSteady state distortion of the waveform
• Periodic and continuous in nature.

Harmonic Sources（nonlinear loads）Harmonic Sources（nonlinear loads）
– Single-phase loads: fluorescent lights,
personal computerspersonal computers
– Three-phase loads: arc furnaces, ac/dc
converters

Basic Harmonic PrinciplesBasic Harmonic Principles
• Harmonics are persistent distortions in aHarmonics are persistent distortions in a
wave shape.
• They represent integers multiples of the• They represent integers multiples of the
fundamental frequencies.

Harmonic Spectrum AnalysisHarmonic Spectrum Analysis

All periodic signals of frequency “f" can be represented in the
f f itform of a composite sum:
1. of a sinusoidal term at frequency “f": the FUNDAMENTAL
(H1).( 1)
2. of sinusoidal terms of which frequencies are integer multiples
of fundamental H1: the HARMONICS (Hn).
3 of a possible continuous component (DC component)3. of a possible continuous component (DC component)
y(t) = h1(t) + h3(t)

Harmonics :Order and Spectrum
Order:Order:
The order of the harmonic is the
value of the integer which
determines its frequency.
Example: harmonic of order 5,
frequency = 250 Hzfrequency 250 Hz
(when fundamental f is 50 Hz)
Spectrum:
The spectrum of a signal is the
h i li dgraph representing amplitudes
of the harmonics as a function
of their frequency.
q y

To summarize: the harmonics are nothing less than the
t f di t t d f d th i ll tcomponents of a distorted waveform and their use allows us to
analyze any periodic non-sinusoidal waveform through different
sinusoidal waveform components.
Figure below shows a graphical representation of this concept.
Non sinusoidal waveform Third harmonic
Non-sinusoidal waveform
First harmonic (fundamental)
Third harmonic
Fifth harmonic

Two sinusoidal sources connected in series
U1max = 60 V @ 50 Hz
U2max = 20 V @ 150 Hz
U1 U2
U3
fundamental and third harmonic
U3
60
80
20
0
20
40
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37
fundamental
third harmonic
total
-80
-60
-40
-20 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 total
80

EXAMPLE OF HARMONICS
harmonics analyzis
25
10
15
20
0
5
10
mpers
Basic harmonic
3th harmonic
5th harmonic
7th harmonic
15
-10
-5
Am
9th harmonic
11th harmonic
total curent
-25
-20
-15

HARMONICS IN POWER SYSTEM
A harmonic is any voltage or current whose frequencies are
integral multiples of f. For example a set of sine waves whose
f i 50 150 250 450 H i id t thfrequencies are 50, 150, 250, 450 Hz is said to possess the
following components:
Fundamental frequency 50 Hz (the lowest frequency)
Third harmonic: 150 Hz (3 x 50 Hz)
Fifth harmonic: 250 Hz (5 x 50 Hz)Fifth harmonic: 250 Hz (5 x 50 Hz)
Ninth harmonic: 450 Hz (9 x 50 Hz)
The distortion of a voltage or current can be traced to theThe distortion of a voltage or current can be traced to the
harmonics it contains. This distortion can be produced by
magnetic saturation in the core of transformers or by the
i hi f h i IGBT i l i d i
switching of thyristors or IGBTs in electronics drive.

fundamental + harmonics
25
10
15
20
25
-5
0
5
10
1 22 43 64 85 106 127 148 169 190 211 232 253 274 295 316 337 358
-20
-15
-10
5 1 22 43 64 85 106 127 148 169 190 211 232 253 274 295 316 337 358
-25
fundamental all harmonics total current

How harmonics are generated?
Harmonics are generated by nonlinear loads. When we apply
a sinusoidal voltage to a load of this type, we shall obtain a
current with non-sinusoidal waveformcurrent with non-sinusoidal waveform.
i i
u ut t
Nonlinear loadLinear load
t

Linear and non-linear loads
A load is said to be linear when there is a linearA load is said to be linear when there is a linear
relationship between current and voltage.
In simpler terms, a linear load absorbs a
sinusoidal current when it is supplied by a
sinusoidal voltage: this current may be displaced
by an angle ϕ compared with voltage.
When this linear relationship is not verified,
the load is termed non-linear.
It absorbs a nonsinusoidal current and thus
harmonic currents, even when it is supplied
by a purely sinusoidal voltage
t b b d b
current absorbed by
a non-linear load.

GENERATING HARMONICS IN TRANSFORMER
MAGNETIZING CURRENTMAGNETIZING CURRENT
The excitation current Ie is split into two components: the
magnetizing current I and I proportional to the coremagnetizing current I µ and IFe, proportional to the core
power losses. These currents are displaced from each other
by an angle Π/2. This displacement can be explained by
means of excitation current waveform. If the coil is supplied
with sinusoidal voltage the flux Φ must be sinusoidal too.
Since the magnetizing characteristic B-H is nonlinear, andg g ,
has a hysteresis loop, the current waveform obtained from
magnetizing curve is far from sinusoidal.

Definition and characteristic quantities related to harmonics
Joseph FOURIER proved that all non-sinusoidal periodic
functions can be represented by a sum of sinusoidal terms, the
fi t f hi h t th f f th f tifirst one of which, at the recurrence frequency of the function,
is said to be fundamental, and the others, at multiple
frequencies of the fundamental, are said to be harmonic. A DCq
component may complete these purely sinusoidal terms.
F i ' f l y (t) = Y + Σ Y √2 sin (n t )
n =
Fourier's formula: y (t) = Yo + Σ Yn √2 sin (nωt – ϕn)
n = 1
where:
- Y : DC component value generally nil and would not be- Yo: DC component value, generally nil and would not be
considered
- Yn: rms value of the n
th
harmonic component,
l f f th f d t l
- ω: angular frequency of the fundamental,
- ϕn: displacement of the n
th
harmonic component.

Harmonics: Effective (RMS - Root Mean Square) Value
The effective value of a non-sinusoidal periodic value is equal to:
1 T
2 n =
Yrms =
1
T 0
y
2
(t)dt = Σ Y
2
nn=1
n
Effective value = Y
2
1 + Y
2
2 + Y
2
3 + Y
2
4 +…..+Y
2
n
Calculation of effective current absorbed by single-phase load:
Y1 = fundamental component; Y2,..,Yn = harmonic components.
Calculation of effective current absorbed by single-phase load:
I fund. = 56.2A ; Ih3 = 27.2A ; Ih5 = 2.7A ; Ih7 = 9.2A ; Ih9 = 7.8A
Irms = 56.2
2
+ 27.2
2
+ 2.7
2
+ 9.2
2
+ 7.8
2
= 63.6 A

Total harmonic distortion
Total harmonic distortion is a parameter globally defining
distortion of the alternating quantity.
This is the ratio of the RMS
value of the harmonics over
the RMS value of thethe RMS value of the
fundamental:
2 2 2 2 2
Y
2
2 + Y
2
3 + Y
2
4 + Y
2
5 +…..+Y
2
n
Y
THD = 100
Y1

There is another definition which replaces the fundamentalThere is another definition which replaces the fundamental
Y1 with the total rms value Yrms. This definition is used by
some measuring instruments.
(distortion factor) =
1
1 + (THD)
2
Distortion factor vs. THD
1 + (THD)
2

Individual harmonic ratio
This quantity represents the ratio of the value of an harmonic
over the value of the fundamental (Y1), according to the
standard definition or over the value of the alternating quantitystandard definition or over the value of the alternating quantity
(Yrms).
R t ti f h i lit d f ti f th i
(Frequency) spectrum
Representation of harmonic amplitude as a function of their
order: harmonics value is normally expressed as a
percentage of the fundamental.
g

Power factor (PF) and Displacement Power Factor (DPF)
It is important not to confuse these two terms when harmonics
are present, as they are equivalent only when currents and
voltages are completely sinusoidalvoltages are completely sinusoidal.
The power factor (λ) is the
ratio between active power P
The displacement power
factor (cos ϕ1) relates toratio between active power P
and apparent power S:
λ = P / S
factor (cos ϕ1) relates to
fundamental quantities, thus:
cos ϕ 1 = P1 / S1ϕ 1 1 1
In pure sinusoidal waveform: cos ϕ1 = cos ϕ = λ
Distortion factor
The IEC 146-1-1 defines this factor as the ratio between the
f t d th di l t f t
power factor and the displacement power factor cos ϕ1 :
ν = λ / cos ϕ1

Peak factor
The ratio of peak value over rms value of a periodic quantity.
Fc = Ypeak / Yrms
Some peak factor examples:
• Linear load Fc = 1.41
• IT load Fc = 2 to 2.5
• Micro computing load Fc = 2.2 to 3p g c

The current drawn by non-linear loads passes through all of the impedance between
the system source and load.the system source and load.
This current produces harmonic voltages for each harmonic as it flows through the
system impedance.
These harmonic voltages sum and produce a distorted voltage when combined with
the fundamental.
The voltage distortion magnitude is dependent on the source impedance and the
harmonic voltages produced.

A non linear load is effectively drawing current from the power source at the
fundamental frequency, and generating current back at higher frequencies.fundamental frequency, and generating current back at higher frequencies.
This results in a distorted current waveform as shown previously.
Current harmonics disturb the supply voltage and this also results in a distorted
lt t th i t f livoltage at the point of common coupling.
Example: Consumer A and B are fed from the same line. The non linear loads of
consumer A will distort the voltage of consumer B even if the latter has only linear
loadsloads.
Point of common couplingPoint of common coupling
A
system
impedance

Voltage and current total harmonic distortion
A non-linear load generates harmonic voltage drops in the
circuits supplying it. In fact all upstream impedances need to
be taken into consideration right through to the sinusoidalbe taken into consideration right through to the sinusoidal
voltage source.
Consequently a load absorbing harmonic currents always hasq y g y
a non-sinusoidal voltage at its terminals. This is characterized
by the voltage total harmonic distortion:
where Zn is the total source impedance at the frequency of
harmonic n, and In the rms value of harmonic n.

Output impedance of the various sources as a function of
ffrequency.

Sources of Harmonics
There are many sources of power system harmonics Some examples of harmonicThere are many sources of power system harmonics. Some examples of harmonic
producing devices are:
Transformers:
Third harmonic currents are present in the magnetizing current (a small portion of
the transformer full load current). If the transformer saturates (due to over-voltage),
the harmonic distortion level of the current increases substantially.
Fluorescent Lamps:
These devices produce a predominantly third order harmonic current on the order of
20% to 30% of the fundamental current. Electronic ballasts have slightly different
h t i ti b t hibit i il l l f h icharacteristics but exhibit similar levels of harmonics.
Pulse-Width Modulated Converters:
These devices use an external controller for switching the input transistors allowingg p g
the current waveform to be shaped more desirably. However, these converters are
limited in power and typically used in applications less than a few hundred kilowatts.

S it h d M d P S liSwitched Mode Power Supplies:
Typically found in single-phase electronic devices such as computers and other
business and consumer electronics, these devices use a switching regulator to, g g
precisely control the DC voltage.
The input of these power supplies normally consists of a full-wave bridge rectifier
and a DC filter capacitor which produces an alternating pulse current waveformand a DC filter capacitor which produces an alternating pulse current waveform
rich in third harmonic.
Though they are not used in large power applications, the cumulative effects of
many devices may create concerns, particularly for 400/230 Volt Y systems.

Wave shape of current absorbed by some non-linear loads.
Light dimmer or heating regulator
H3 H5 H7 H9 H11 H13 H15 H17 H19
54 18 18 11 11 8 8 6 654 18 18 11 11 8 8 6 6
Switch mode power supply rectifier
H3 H5 H7 H9 H11 H13 H15 H17 H19
75 45 15 7 6 3 3 3 2

Three-phase rectifier with front end capacitor
H3 H5 H7 H9 H11 H13 H15 H17 H19
0 80 75 0 40 35 0 10 5
Three-phase rectifier with DC filtering reactor
H3 H5 H7 H9 H11 H13 H15 H17 H19
0 25 7 0 9 4 0 5 3

Harmonic currents in three phase systems
Neutral conductor
Harmonics get more complicated in three phase applications.
Here not only do we have to deal with phase conductors, but also the neutral
conductor triplen (odd multiples of 3 i e 3rd 9th 15th etc ) harmonics andconductor, triplen (odd multiples of 3 i.e. 3 , 9 , 15 etc,) harmonics, and
sequence harmonics.
The triplen harmonics are the major cause of heat because they add together in
th t l d tthe neutral conductor.
The magnitude of the harmonic current produced by the triplens can approach
twice the phase current.p
This causes the neutral conductor to overheat because neutral conductors were
historically designed with the same ampacity as the phase conductors.

For example, a 3rd harmonic of 75%, the current flowing in the
neutral is 2.25 times the fundamental. The current in each phase
is only SQR (1+ 0.752 ) = 1.25 times the fundamental.
neutral current
150
100
150
0
50
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37
-100
-50
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37
-150
Ia Ib Ic Ia 3rd Ib 3rd Ic 3rd neutral current

Induction motor
A situation that produces abnormal amounts of heat in motors is the combination
of positive and negative sequenced harmonics.of positive and negative sequenced harmonics.
The positive sequenced harmonics are the fundamental, 7th, 13th, 19th, etc.
They tend to apply an additional forward force in the direction of the motor
t tirotation.
The negative sequenced harmonics are the 5th, 11th, 17th, etc. They present a
force that opposes the motor rotation and tries to make the motor rotate in thepp
opposite direction.
The force of these harmonics acting upon each other creates heat which leads to
premature failurepremature failure.
Harmonic voltage distortion causes increased eddy current losses in the motors,
in the same way as seen for transformers.

Transformers
The effects of harmonics inside the transformers involve
mainly three aspects:
a) increase of iron losses (or no-load losses)
b) increase of copper losses
c) presence of harmonics circulating in the windings
a) The iron losses are due to the hysteresis phenomenon and) y p
to the losses caused by eddy currents; the losses due to
hysteresis are proportional to the frequency, whereas the
losses due to eddy currents depend on the squarelosses due to eddy currents depend on the square
of the frequency.

b) Th l d t th di i t d b J l ff t i thb) The copper losses correspond to the power dissipated by Joule effect in the
transformer windings.
As the frequency rises (starting from 350 Hz) the current tends to thicken on theq y ( g )
surface of the conductors (skin effect); under these circumstances, the
conductors offer a smaller cross section to the current flow, since the losses by
Joule effect increase.
These two first aspects affect the overheating which sometimes causes a de-
rating of the transformer

c) The third aspect is relevant to the effects of the triple-N harmonics (homopolar
harmonics) on the transformer windingsharmonics) on the transformer windings.
In case of delta windings, the harmonics flow through the windings and do not
propagate upstream towards the network since they are all in phase; the delta
windings therefore represent a barrier for triple-N harmonics, but it is necessary
to pay particular attention to this type of harmonic components for a correct
dimensioning of the transformer.
The triplen harmonics are trapped and circulate in the delta primary of the
transformer. Since most loads produce high levels of the 3rd harmonic (one of the
triplens), the harmonic content reflected back to the source is reduced.
The circulating harmonics in the primary of the transformer creates heat because
of their higher frequencies.
For this reason, a transformer that can handle the excess heat is needed. This
transformer is called a K-rated transformer

Skin effect losses
The transmission distribution grid was designed to carry the fundamental 50/60
Hertz frequency.
A problem exists with higher frequencies (harmonics), that is, they do not fully
penetrate the conductor.
They travel on the outer edge of the conductor This is called skin effect When skinThey travel on the outer edge of the conductor. This is called skin effect. When skin
effect occurs, the effective cross sectional area of the conductor decreases;
increasing the resistance and the I2R losses, which in turn heats up the conductors
and anything connected to them.
This heating effect can cause circuit breakers to trip, neutral and phase conductors
to heat up to critical flash over temperatures, and premature failure of motors and
transformerstransformers.
This is costly in terms of downtime, loss of production, repair, and possible
reconstruction.

In the presence of high-order harmonics, it is necessary to take
skin effect into account, because it affects the life of cables.
In order to overcome this problem, it is possible to use multiple
conductor cables or busbar systems formed by more
elementary isolated conductors.

Harmonic currents in three-phase four-wire networks
ia(t) = Σ Ian cos (nωt – ϕan)
n=1
n =
uan(t) = Um cos ωt
ib(t) = Σ Ibn cos [n(ωt – 120) - ϕbn]
n=1
n =
n =
ubn(t) = Um cos (ωt-120)
ic(t) = Σ Icn cos [n(ωt + 120) - ϕcn]
n=1
n
ucn(t) = Um cos (ωt-120)

Neutral current
If the load is unbalanced, then the neutral connection may
contain currents having spectrum similar to the line currents.
iN(t) = Σ { Ian cos (nωt – ϕan) + Ibn cos [n(ωt – 120) – ϕbn] + Icn
n=1
n =
cos [n(ωt + 120) – ϕcn] }
n 1
In the balanced case, Ian = Ibn = Icn = In and ϕan = ϕbn = ϕcn =
ϕn , for all n; i.e., the harmonics of the three phases all have
equal amplitudes and phase shifts. The neutral current isq p p
then
iN(t) = Σ 3 In cos (nωt – ϕn)
n =
iN(t) Σ 3 In cos (nωt ϕn)
n=3.6.9..

3 6 9
n =
n=3.6.9..
Fundamental and most harmonics cancel out
Triplen (triple-n, or 3, 6, 9, ...) harmonics do not cancel out,
but add.
rms neutral current is INrms = 3 Σ
n=3,6,9..
n =
I
2
n
2n 3,6,9.. 2

Example
A balanced nonlinear load produces line currents containing
fundamental and 20% third harmonic: ian(t) = I1 cos(ωt – ϕ1) +
0.2 I1 cos(3ωt – ϕ3). Find the rms neutral current, and compare
its amplitude to the rms line current amplitude.
= 3
( 0.2 I1 )2
2
= 0.6
I1
2
INrms = 3 Σ
n=3 6 9
n =
I
2
n
2
INrms = 60% of I1rms
2 2n=3,6,9.. 2
The triplen harmonics in the three phases add, such that 20%
third harmonic leads to 60% third harmonic neutral current.
Si ifi t t d t l t fl
Significant unexpected neutral current flows.

G ll h Σ
n =
I
2
n
Generally the rms current = Σ
n=1
n
2
=
( I1 )2
2
I1rms = Σ
n=1
n =
I
2
n
2
( I3 )2
2
+
n 1 2
( I1 )2
I
(0.2 I1 )2
+
I1
1 + 0 04
I1
=
2
I1rms =
2
+
2
1 + 0.04
2
Yet the presence of the third harmonic has very little effect on
the rms value of the line current.

Y-connected nonlinear load, no neutral connection:
If the load is balanced, then it is still true that
n =
iN(t) Σ 3 In cos (nωt ϕn)
n=3.6.9..

But iN (t) = 0, since there is no neutral connection and the ac
line currents cannot contain triplen harmonicsline currents cannot contain triplen harmonics.
What happens?
A voltage is induced at the load neutral point, that causes the
line current triplen harmonics to become zero.
The load neutral point voltage contains triplen harmonics.
With an unbalanced load, the line currents can still contain,
triplen harmonics

Harmonic Currents add in the Neutral
The 120°
phase shiftphase shift
between linear
load currents
ill l iwill result in
their balanced
portionsp
instantaneously
canceling in the
neutral
With linear loads, the neutral can be the same size as the
phase conductors because the neutral current cannot be
neutral.
larger than the largest phase current, even when the load
is completely unbalanced.

When the load is non-
li h thlinear however, the
current pulse on one
phase will not have a
pulse on either of thepulse on either of the
other phases for which
to cancel. The pulses
are additive which oftenare additive which often
leads to heavier current
on the neutral
conductor than on anyy
phase conductor. The
frequency of this
neutral current is
With non-linear loads, the neutral
current generally exceeds the largest
phase current, even when the loads
primarily 150 Hz (3rd
harmonic).
p ase cu e t, e e e t e oads
are in perfect RMS current balance.

Delta-connected load
There is no neutral connection, so the ac line currents contain
no triplen harmonicsno triplen harmonics.
The load (phase) currents may contain triplen harmonics: with
a balanced nonlinear load, these circulate around the delta.

Harmonic currents in power factor correction capacitors
PFC capacitors are usually not intended to conduct significant
harmonic currents.
Heating in capacitors is a function of capacitor equivalent
series resistance (esr) and rms current. The maximum( )
allowable rms current then leads to the capacitor rating:
t d lt U
Irms
rated rms voltage Urms =
2 π f C
2
rated reactive power QC =
I
2
rms
2 π f C

Average power
Voltage and current as
Fourier series:
Power per cycle
T
u (t) = Σ Un cos (nωt – ϕn)
n=1
Pcycle = v(t) i(t) dt
0
i (t) = Σ In cos (nωt – θn)
n=1 This is related to average
power as follows:p
Pav =
Pcycle
T
=
1
T
v(t) i(t) dt
T
influence of harmonics on
average power:
av
T T
0
1
T
Σ U ( t )] [[ Σ I ( t )] dt
Pav =
1
T
0
Σ Un cos (nωt – ϕn)] [
n=1
[ Σ In cos (nωt – θn)] dt
n=1

Integrals of cross-product terms are zero
T
0
Un cos (nωt – ϕn)] [[ In cos (mωt – θm)] dt
{
0 if n = m So net energy is
{
0 if n = m
Un In
cos (ϕn – θm) if n = m
=
So net energy is
transmitted to the load
only when the Fourier
i f (t) d i(t)
{ cos (ϕn θm) if n m
2
Expression for average power
series of u(t) and i(t)
contain terms at the
same frequency. For
becomes
P = Σ
Un In
cos (ϕ – θ )
q y
example, if the voltage
and current both
contain third harmonicPav = Σ
n=1
cos (ϕn – θn)
2
contain third harmonic,
then they lead to the
average power:
U I
U3 I3
cos (ϕ3 – θ3)
2

Example 1
u (t) i (t)
Voltage: fundamental only
Current: third harmonic only
i (t)
Current: third harmonic only
Power: zero averagePower: zero average

Example 2
u (t), i (t)
Voltage: third harmonic only
Current: third harmonic only,
i h ith ltin phase with voltage
Power: nonzero average

Example 3
Fourier series:
u(t) = 1.2 cos (ωt) + 0.33 cos (3ωt) + 0.2 cos (5ωt)
i(t) = 0.6 cos (ωt + 30°) + 0.1 cos (5ωt + 45°) + 0.1 cos (7ωt + 60°)
Average power calculation:
(1 2)(0 6) (0 2)(0 1)
Pav =
(1.2)(0.6)
2
cos (30°) +
(0.2)(0.1)
2
cos (45°) = 0.32 W

Voltage: 1st, 3rd, 5th
Current: 1st 5th 7thCurrent: 1st, 5th, 7th
Power: net energy is
transmitted at
fundamental and fifthfundamental and fifth
harmonic frequencies

In AC circuits the fundamental current and fundamental voltage together
produce fundamental power.p p
This fundamental power is the useful power that cause motor to rotate and
deliver work on the rotor’s shaft or to make electrical heater to deliver heat.
The product of a harmonic voltage times the corresponding harmonic current
also produces a harmonic power.
That one is usually dissipated as a heat and does not do useful work.
Harmonic currents and voltages should be kept as small as possibleHarmonic currents and voltages should be kept as small as possible.
The product of a fundamental voltage and a harmonic current yields zero net
power.
power.

GENERATING HARMONICS WITH SWITCH
I 70 7 A
Synchronous I = 1000/10 = 100 A
Closed switch
Irms = 70.7 A
1000 V
60 Hz
Synchronous
switch R
10Ω P = I
2
R = 100
2
x10
= 100 kW
Operational switch
(half time opened)
1410 V
141 A
(half time opened)
Dissipated power = 50 kW
I
2
P/R 50000/10 5000I
2
= P/R = 50000/10 = 5000
I = 70.7 A
2
P = I
2
x R = 70.7
2
x 10
P = 50 kW

1410 V
Chopped current
The chopped current can be
decomposed to fundamentalFundamental
141 A
decomposed to fundamental
and harmonics component.
84 A
Fundamental
component
The 10Ω resistor absorbs a fundamental
32.5
0
A t f d t l li d
The 10Ω resistor absorbs a fundamental
active power
P = I
2
x R = 59.3
2
x 10 = 35.2 kW
Apparent fundamental power supplied
by source
S = U x I = 1000 x 84/1.414 = 59.3 kVA
The difference of 50 – 35.2 = 14.8 kW
goes to the harmonic power absorbed
by resistor
Active fundamental power supplied by
source
P = S x cosϕ = 59.3 x cos 32.5 = 50 kW
by resistor
IF = 59.3 A-32.5
14.8kW
Reactive fundamental power supplied
by source
1 kV
31.9kVAr
14.8kW
Q = V S2
- P2
= V 59.32
– 502
= 31.9
kVAr 10Ω50kW 35.2kW

The switch carries a fundamental current of 59.3 A and it
absorbs 14.8 kW and 31.9 kVAr, it can be represented byabsorbs 14.8 kW and 31.9 kVAr, it can be represented by
resistance and inductive reactance connected in series.
R = P / I2
= 14800 / 59.3
2
= 4.21 Ω 4.21Ω j9.07Ω
X = Q / I
2
= 31900 / 59.3
2
= 9.07 Ω
Effective value of the
10Ω1kV
IF = 59.3AEffective value of the
harmonic current is
I V I
2
I
2
V 70 7
2
59 3
2
F
Equivalent circuit for the
IH = V I
2
- IF
2
= V 70.7
2
– 59.3
2
= 38.5 A
fundamental component
Consequently the voltage
across the 10Ω resistor is
U = I x R = 38 5 x 10 =
10Ω
385 V
U = I x R = 38.5 x 10 =
385 V. Equivalent circuit for all
harmonic components

Low-power harmonic limits
In a city environment such as a large building, a large fraction
of the total power system load can be nonlinear
• Example: a major portion of the electrical load in a building
is comprised of fluorescent lights, which present a veryp g , p y
nonlinear characteristic to the utility system.
• A modern office may also contain a large number of• A modern office may also contain a large number of
personal computers, printers, copiers, etc., each of which
may employ peak detection rectifiers.
• Although each individual load is a negligible fraction of the
total local load, these loads can collectively become
y
significant.

Short Term Effects
Over consumption of RMS current
Unwanted tripping of protections
Malfunction of sensitive applications
Interference of remote control and telecommunication systems
Abnormal vibration and noise (LV panels, motors, transformers)Abnormal vibration and noise (LV panels, motors, transformers)
Long Term Effects-Overheating
Overheating of capacitor banks
Overheating of transformers, alternatorsOverheating of transformers, alternators
Overheating of phases, particularly neutral

Harmful Effects on Receivers
Cables:
Overheating of cables
Additional losses due to skin effectAdditional losses due to skin effect
Increase in dielectric losses of insulation
Induction motors:
Increase in core (stator) and Joule losses
P l ti t i ffi i d tiPulsating torques causing efficiency reduction,
abnormal vibration, rotor overheating

General Solutions
Limit injected harmonic currents:
Install limitation induction coils for speed drivesp
Install specific rectifiers called active front end
Install anti-harmonics induction coilsInstall anti harmonics induction coils
Install filters to trap harmonics:
Passive filters
Active filters
Hybrid filtersHybrid filters
Oversize equipment

The presence of harmonic currents can also lead to some
special problems in three-phase systems:
In a four-wire three-phase system, harmonic currents can
lead to large currents in the neutral conductors, which mayg , y
easily exceed the conductor rms current rating
Power factor correction capacitors may experiencePower factor correction capacitors may experience
significantly increased rms currents, causing them to fail

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