TESCO Tuesday: Harmonics

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10/02/2012 Slide 2
HARMONICS
Prepared by William H. (Bill) Hardy, PhD
CTO TESCO
For TESCO Tuesday
Tuesday November 17, 2020

Harmonics
What? Where? Why? How?
 Today we will try to answer the following:
• What are harmonics?
• Where do they come from?
• Why are they important?
♦ Power Quality
♦ Distribution System Effects
♦ Billing Issues
• How do we measure them?

• The presence of harmonics in power systems
means that current and voltage waveforms are
distorted and deviate from sinusoidal
waveforms.
4
What are Harmonics?

What are Harmonics?
 Any content of a repetitive waveform other
than the FUNDAMENTAL (dominant
frequency).
• For the US, the fundamental frequency is 60
Hz.
• Under perfect conditions the waveform is a
perfect sine wave.
What are Harmonics?

• Harmonics are one of the most important issues effecting power
quality. Even though the issue of harmonics seems relatively new,
the issue has been around for a long time.
• In 1893, only eight years after first AC power plant was built,
engineers conducted a harmonic analysis to identify and solve a
motor heating problem.
• A paper written by E.J. Houston and A.E. Kennely in 1894, was one
of the first documents in which the word harmonic was used.
6
Background

A Perfect Sinewave
V(t)=Vrms●cos(ω0t+θ)

Harmonic Voltage Waveform
𝑉𝑉 𝑡𝑡 = 𝑎𝑎0 + � 𝑎𝑎𝑛𝑛 cos(𝑛𝑛ω0t+θn) = 𝑎𝑎0 + � 𝑎𝑎𝑛𝑛 cos(𝑛𝑛ω0t) + 𝑏𝑏𝑛𝑛 sin(𝑛𝑛ω0t
∞
𝑛𝑛=1
∞
𝑛𝑛=1

Harmonic Current Waveform
𝑉𝑉 𝑡𝑡 = 𝑎𝑎0 + � 𝑎𝑎𝑛𝑛 sin(𝑛𝑛ω0t+θn) = 𝑎𝑎0 + � 𝑎𝑎𝑛𝑛 cos(𝑛𝑛ω0t) + 𝑏𝑏𝑛𝑛 sin(𝑛𝑛ω0t
∞
𝑛𝑛=1
∞
𝑛𝑛=1

Background
𝑉𝑉 𝑡𝑡 = 𝑎𝑎0 + � 𝑎𝑎𝑛𝑛 sin(𝑛𝑛ω0t+θn) = 𝑎𝑎0 + � 𝑎𝑎𝑛𝑛 cos(𝑛𝑛ω0t) + 𝑏𝑏𝑛𝑛 sin(𝑛𝑛ω0t
∞
𝑛𝑛=1
∞
𝑛𝑛=1
Fourier’s Theorem
A mathematical theorem stating that a
PERIODIC function f(x) which is
reasonably continuous may be expressed
as the sum of a series of sine or cosine
terms (called the Fourier series), each of
which has specific AMPLITUDE and
PHASE coefficients known
as Fourier coefficients.
Joseph Fourier 1827

Harmonic Sources
 Changes to our loads have changed our
world.
 When loads were linear the power triangle
was all we needed to know
George Westinghouse
Tesla

• Up to the 1960’s, most of the electric loads were linear
loads - in other words, the current flowing through the
appliances had a sinusoidal sine wave.
• These electric loads included induction motors, domestic
lighting, stoves and other household appliances.
13
Harmonic Sources

 Resistors, Inductors and Capacitors are LINEAR
devices
 Any load that is a combination of these is a
LINEAR load.
 When a sinusoidal voltage is applied to a linear
load, the current drawn by the load is
proportional to the voltage
 Examples of linear loads are resistive heaters,
incandescent lamps, and constant speed
induction and synchronous motors.
Basic Concept

Background
 Then John Bardeen, Walter Brattain and William
Shockley invented the transistor.
 With the transistor and what came after the world of non-
linear loads was born.

• UPS (uninterruptible power supply) systems convert the
incoming AC supply to DC in order to charge batteries in
the event of a power outage.
• The DC component has a very high frequency signal and
interferes with the AC power supplies.
• Most of the distortion in the modern distribution system is
customer generated.
16
Harmonic Sources

Harmonic Sources
YESTERDAY
TODAY

Harmonic Sources
TODAY

Harmonic Sources
-150
-100
-50
0
50
100
150
0.00 60.00 120.00 180.00 240.00 300.00 360.00
Voltage/Current
Current for CCFL Light Bulb
Voltage
Current
• Today’s loads look more like these

Harmonic Sources
100-HP
VFD
with
series
reactor,
operatin
g at
40Hz
output

Harmonic Sources
-150
-100
-50
0
50
100
150
0 60 120 180 240 300 360
Voltage/Current
Variable Speed Motor
Voltage
Current

Harmonic Sources
UPS POWER SUPPLY

Harmonic Sources
-150
-100
-50
0
50
100
150
0.00 60.00 120.00 180.00 240.00 300.00 360.00
Voltage
Current for Switching Power Supply
Voltage
Current

 Devices such as SCRs, TRIACs, FETs,
transistors and many more semiconductor
devices who can generate loads that are not
proportional to the applied voltage. These are
termed are NON-LINEAR loads
 Most modern loads: electronics, dc motors,
variable speed AC motors, light dimmers, LED
lights, CCFL lights are NON-LINEAR loads
Basic Concept

Why Are Harmonics Important?
Motors
 Reduced efficiency
• Harmonic content makes it harder to magnetize the copper and iron in
the motor’s stator and rotor, causing higher eddy current and hysteresis
losses.
• If harmonic frequencies exceed 300 Hertz, the skin effect compounds
these losses.
 Losses equal heat
• Heat is perhaps the most damaging stress the motor experiences.
• It degrades winding insulation
• It causes bearing grease to lose lubricity and reduces the motor’s life.
• Depending on the level of harmonic content,
the heat generated may cause nuisance
tripping of thermal protection systems in the
motor.

 Trigger bearing currents
• Bearing currents cause arcing between the
bearing raceway and journal or balls, creating
a much rougher surface, increasing friction
losses and potentially causing the bearing to
seize. The arcing also accelerates breakdown
of the lubricant. All in all, bearing currents
cause the bearings to fail sooner.
 Partial discharge arcing
• Harmonics with high rates of change in
voltage (high dV/dt), such as notching and
ringing, may cause partial-discharge arcing in
windings, accelerating degradation in the
winding insulation.
Motors

 Over heating caused by:
• Eddy current losses
• Hysteresis losses
• Core saturation
• Increase in copper losses due to skin effect
 Causes these issues
• Need to overate transformer
• Reduced life expectancy
• Higher insulation stresses on many components
Transformers

 Most of the same issues that occur
transformers can happen in capacitors.
Capacitor Banks

Capacitor Banks
 Unique to systems with capacitor banks is the
issue of resonance.
• Resonant conditions are created when the inductive and
capacitive reactance become equal in an electrical system.
• Resonance in a power system may be classified as series or
parallel resonance, depending on the configuration of the
resonance circuit.
♦ Series resonance produces voltage amplification
♦ Parallel resonance causes current
• During resonant conditions, if the amplitude of the offending
frequency is large, considerable damage to capacitor banks
would result.
• There is a high probability that other electrical equipment on the
system would also be damaged.

Background
 Fourier came up with the math in 1827
 1930s selenium power diodes became
practical
 Bardeen et al created the transistor in
1947
 1960s silicon diodes become available
 Cooley and Tukey develop modern FFT

Sidebar
 John Tukey invented the modern FFT in
1964 while at Princeton working on a
problem related to the space program.
 He enlisted James Cooley at IBM to
implement and test the algorithm.
 Their paper on the FFT published in 1965
is considered one of the most important
developments in practical mathematics
ever.
 All modern instruments and electric meters use some
variant of the FFT to analyze the harmonic content of
signals.

How Do We Measure Harmonics?
 Modern systems digitize waveforms converting the analog waveform
to a series of evenly spaced in time values
 Depending on the target accuracy, systems may sample up to 1024
points per cycle. 128 and 256 are common sampling rates.

Measurement Standards
 ANSI C12.20-2015 added six tests for harmonic
performance of meters
-400
-200
0
200
400
-150
-100
-50
0
50
100
150
0 90 180 270 360
-200
-100
0
100
200
-150
-100
-50
0
50
100
150
0 90 180 270 360
-10
-5
0
5
10
-200
-100
0
100
200
0 90 180 270 360
-150
-100
-50
0
50
100
150
0 60 120 180 240 300 360
-250
-200
-150
-100
-50
0
50
100
150
200
250
-150
-100
-50
0
50
100
150
0.00 100.00 200.00 300.00
-150
-100
-50
0
50
100
150
-150
-100
-50
0
50
100
150
0.00 100.00 200.00 300.00
Current
Voltage

Measurement Standards
 ANSI C12.20 and C12.1 are being combined into a new
C12.1-2021 which includes these same tests
 ANSI C12.46, the next generation replacement for C12.1
contains the same tests and extends them to provide
accuracy requirements for both watts and VA
 ANSI C12.35 provides a complete set of definitions for
watts and VA fully including harmonics. These
definitions are used in C12.46

C12.31
RMS Voltage
Basic Definition
Time Domain
Frequency Domain
Waveform

C12.31
RMS Current
Basic Definition
Time Domain
Frequency Domain
Waveform

C12.31
Active Power
Basic Definition
Time Domain
Frequency Domain

C12.31
Apparent Power
Basic Definition
Time Domain
Frequency Domain

Real measurements?
 Modern test equipment
like the TESCO
CAT6330 provides
extensive harmonic
analysis capabilities.

Real measurements!
 Modern test equipment
like the TESCO
CAT6330 provides
extensive harmonic
analysis capabilities.

Real measurements!
 When there are no harmonics waveforms are nice, clean
sinewaves

Real measurements!
 Waveforms with harmonics are a whole different story.

Real measurements!
 ANSI C12.20 Phase fired waveform

Real measurements!
 ANSI C12.20 Pulse waveform

• Created by NON-LINEAR loads
• Cause losses in the distribution system
• Cause problems and failures in utility equipment:
transformers, capacitor banks
• Cause problems and failures in customer
equipment: motors, electronics, control systems
• Create Metering problems and challenges
• Solution: Eliminate them if at all possible.
50
Summary

• Harmonics can damage customer equipment
and parts of the distribution system.
• Harmonics can cause premature aging of
equipment – more frequent replacement costs.
• Overload on the distribution network means
higher equipment rating, increased subscribed
power level for the industrial customer, and
increased power losses.
• Unexpected current distortion can lead to
nuisance tripping and production interruptions
for the customer.
51
Economic Impacts of Harmonics

 One of the best complete discussions of
Power Systems Harmonics is:
Reference Resource
https://web.ecs.baylor.edu/faculty/grady/Understanding_Power_Syst
em_Harmonics_Grady_April_2012.pdf
Don’t let all of the math discourage you

Bill Hardy
TESCO – The Eastern Specialty Company
Bristol, PA
1-215-228-0500
Questions and Discussion

Q&A and Upcoming
TESCO Tuesday Presentations
Presentation Date
Complete Site Testing 12/1
Electric Vehicle Trends & Calibration of Commercial Chargers 12/8
Streetlights & 5G Metering and Testing 12/15
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session.
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December 1, 2020 | 11:00 AM Eastern
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TESCO Tuesday: Harmonics

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