2017 Harmonic Analysis

Bill Gatheridge
Consultant
Yokogawa Meters & Instruments Corporation
Power Measurement
and
Harmonic Analysis
on
Distorted Waveforms

2 Copyright © Yokogawa Meters & Instruments Corporation
Host
Harmonic Analysis
Kristin Porche
Marketing Specialist
Yokogawa Corporation of America
Newnan, GA
webinars@us.yokogawa.com
1-800-888-6400 ext. 5656
tmi.yokogawa.com

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Harmonic Analysis
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Presenter
Harmonic Analysis
Bill Gatheridge
Consultant
Newnan, GA

Harmonic Analysis

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Harmonic Analysis
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Yokogawa Corporate History
Fundamentals of Power Measurement
1930 Vintage
Standard AC Voltmeter
0.2% Accuracy Class
• Founded in 1915.
• First to produce and sell electric
meters in Japan.
• North American operation established
in 1957
• World wide sales in excess of $3.78B
• 84 companies world wide
• Over 18,000 employees worldwide
• Operations in 59 Countries
WT3000E
Precision Power Analyzer

Harmonic Analysis
Newnan, GA

Harmonic Analysis

Today’s Topic
Harmonic Analysis
Power Measurement
and
Harmonic Analysis
on Distorted Waveforms

Objective
Harmonic Analysis
 Provide tips and techniques for making
accurate power measurements on
distorted waveforms and methods for
making and analyzing harmonic content of
various power waveforms.

Harmonic Analysis
Harmonic Analysis
Why are we concerned
with
Harmonics
on the
Power System?

Harmonic Analysis
Harmonic Analysis
Harmonics can –
•Cause excess heat in electrical equipment
•Cause inefficient operation – wasted power, higher
electric operating costs
•Damage electrical equipment
Some examples:
•Less efficient Transformers
•Circuit Breakers & GFI’s trip
•Less efficient Electric Motors because of reverse
power in some of the harmonics.
•Overheating in Neutral Conductors

Overview – What We Plan to Do
Harmonic Analysis
 Basic Power Measurements -
Review of Basic Power Measurements
Power Measurements on Distorted Waveforms
 Harmonic Analysis
Fundamentals of Harmonics
Measurements on Distorted Waveforms
Instrument Considerations and Current Sensors
Power Factor of Distorted Waveforms

Overview – What We Plan to Do
Harmonic Analysis
 Harmonic Analysis Applications
Practical Power & Harmonic Analysis of:
Power Supplies
Electronic Lighting Loads
Variable Speed PWM Motor Drives
Power Quality Standards, IEC Introduction
 Answer YOUR Power Measurement and Harmonic
Analysis Questions

Part 1
Harmonic Analysis
ELECTRICAL POWER
MEASUREMENTS
on
DISTORTED WAVEFORMS

Review OHM’S LAW
Harmonic Analysis

Average and RMS Values
Harmonic Analysis
Average, RMS, Peak-to-Peak Value
Conversion for Sinusoidal Wave
(multiplication factor to find)
Known Value Average RMS Peak Peak-to-Peak
Average 1.0 1.11 1.57 3.14
RMS 0.9 1.0 1.414 2.828
Peak 0.637 0.707 1.0 2.0
Peak-to-Peak 0.32 0.3535 0.5 1.0

Average and RMS Values
Harmonic Analysis

Measurement of Power
Harmonic Analysis
DC Source:
AC Source:
W = V x A
W = V x A x PF
A unit of Power equal to one
Joule of Energy per Second
What’s A Watt ?

Harmonic Analysis
Active Power:
Also referred to as True Power or Real Power
Apparent Power:
AC Power Measurement
𝑃 = 𝑉𝑟𝑚𝑠 × 𝐴 𝑟𝑚𝑠 × 𝑃𝐹 [𝑊]
𝑆 = 𝑉𝑟𝑚𝑠 × 𝐴 𝑟𝑚𝑠 [𝑉𝐴]

Harmonic Analysis
■Digital Power Analyzers are entirely electronic and
use some form of DIGITIZING TECHNIQUE to convert
analog signals to digital form.
•higher end analyzers use DIGITAL SIGNAL
PROCESSING techniques to determine values
■Digital Power Oscilloscopes use SPECIAL
FIRMWARE to make true power measurements.
■Digitizing instruments are somewhat RESTRICTED
because it is a sampled data technique.
■Many Power Analyzers and Power Scopes apply FFT
algorithms for additional power and harmonic
analysis.

Harmonic Analysis
■Yokogawa Digital Power Analyzers and Digital
Power Scopes use the following method to
calculate power:
■Using digitizing techniques, the
INSTANTANEOUS VOLTAGE is multiplied by
the INSTANTANEOUS CURRENT and then
INTEGRATED over some time period.
𝑷 𝒂𝒗𝒈 =
𝟎
𝑻
𝒗 𝒕 ∗ 𝑰 𝒕 𝒅𝒕

Measurement of AC Power
Harmonic Analysis
Watts P = Vrms x Arms x PF = Urms1 x Irms1 x λ1
Volt-Amps S = Vrms x Arms = Urms1 x Irms1

True RMS Measurements
Harmonic Analysis
These calculation methods provide a True Power
Measurement and True RMS Measurement on any
type of waveform, including all the harmonic
content, up to the bandwidth of the instrument.
𝑷 𝒕𝒐𝒕𝒂𝒍 =
𝟏
𝑻 𝟎
𝑻
𝑼 𝑹𝑴𝑺 =
𝟏
𝑻 𝟎
𝑻
𝒗(𝒕) 𝟐 𝒅𝒕
𝑰 𝑹𝑴𝑺 =
𝟏
𝑻 𝟎
𝑻
𝒊(𝒕) 𝟐 𝒅𝒕

Single Phase Power Measurement
Harmonic Analysis
Wattmeter
Single - phase
two - wire
Load
V(t)
I(t)
.
AC
Source
A +
V
+
W
Single Wattmeter
Method

Single-Phase Two-Wire System
Harmonic Analysis
■The voltage and current detected by the
Watt Meter are the voltage and current applied
directly to the Load.
■The indication on the Watt Meter is the POWER
being dissipated by the load.

Power Factor Measurement on Distorted Waveforms
Harmonic Analysis
If Power
Factor =
Cosine Ø
• Where is the
Zero
Crossing for
the Current
Waveform?
• How do we
accurately
measure Ø
between
these two
waveforms?

Phasor Diagram of Power for R - L Circuit
Harmonic Analysis
P
QS
0
WATTS
TRUE POWER FACTOR
PF = W / VA
VARVOLT-AMPS
“POWER TRIANGLE”

Power Factor Measurement
Harmonic Analysis
For SINE WAVES ONLY
PF = Cos Ø
This is defined as the DISPLACEMENT
Power Factor
---------------------------------------------------------
For All Waveforms
PF = W/VA
This is defined as TRUE Power Factor

Instrument Bandwidth Considerations
Harmonic Analysis
RMS Current
Measurement
Channel 1
2 MHz B/W
Channel 2
500 kHz B/W

Current Sensors
Harmonic Analysis
Ram Meter
DC Shunts
Yokogawa
CT’s
AEMC
0.3% - 0.5% AC
1.5% - 3%
AC/DC
Yokogawa/LEM
CT System 0.05%
Yokogawa
Scope
Probes
Pearson
Electronics
0.1%
0.33%
0.2%
1%
1% - 2%

Current Sensors
Harmonic Analysis
SELECTION CONSIDERATIONS
• Accuracy, CT Turns Ratio Accuracy
• Phase Shift
• 1 or 2 Degrees Maximum: Cosine 2 Deg = 0.9994
• Frequency Range
• DC to line frequency, sine waves: DC Shunts
• DC & AC: Hall Effect or Active type CT
• AC Approximately 30 Hz and higher: Various types
of Instrument CT’s

Current Sensors
Harmonic Analysis
SELECTION CONSIDERATIONS
• Instrument Compatibility
• Output: Millivolts/Amp, Milliamps/Amp; or Amps
• Impedance and Load, Burden
• Scope Probes - - CAUTION! Use on Scopes, NOT
Power Analyzers. Check the Specs!
• Physical Requirements
• Size
• Connections: Clamp-On or Donut type
• Distance from Load to Instrument

Current Sensors
Harmonic Analysis
A WORD OF CAUTION
 NEVER Open Circuit the Secondary side of a Current
Transformer while it is energized!
• This could cause serious damage to the CT and could
possibly be harmful to equipment operators.
• A CT is a Current Source.
• By Ohm’s Law E = I x R
• When R is very large, E becomes very high
• The High Voltage generated inside the CT will cause a
magnetic saturation of the core, winding damage, or other
damage which could destroy the CT.

Part 2
Harmonic Analysis
Harmonic Analysis

Distorted AC Waveforms
Harmonic Analysis
■Distortion of AC wave shapes can take various
forms:
unbalanced polyphase wave shapes in which the
phases do not have the same magnitudes and/or
the phases are not 120 degrees apart
wave shapes that are not ideal sinusoids
■We are concerned with the latter for the remainder
of this seminar.

Harmonic Analysis
There are many causes of distortion on AC systems:
 non-linear magnetic circuits
 rectifiers
 capacitors interacting with inductances
 switching power electronic loads
phase-controlled rectifiers
ac voltage controllers
inverters
electronic ballasts

Harmonic Analysis
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
10
5
0
5
10
.
current
reference
Distorted Current Wave vs. Time
Time, seconds
Current,amperes

Harmonic Analysis
Elements of a distorted
or non-sinusoidal
waveform consist of
Sine Waves of various:
• Amplitudes
• Frequencies
• Phase
Because of the Phase
differences in some of
the harmonics, negative,
or reverse power can
actually be produced.

Harmonic Analysis
• Harmonics are defined as Voltages, Currents or
Power at frequencies that are a multiple of the
fundamental frequency.
• For a 60 Hz fundamental, harmonic frequencies
could be 120 Hz, 180 Hz, 240 Hz, ……….

Harmonic Analysis
• Harmonics are usually specified as Orders
For a 60 Hz Fundamental:
180 Hz = 3rd Order
(60 Hz x 3 = 180 Hz )
• Harmonics are also referred to as Even-order
and Odd-order.
• In some complex waveforms, there can be Inter-
Harmonics, or non-integer orders.

Harmonic Analysis
■Yokogawa Digital Power Analyzers and Digital
Power Scopes use the following method to
calculate power:
■Using digitizing techniques the
INSTANTANEOUS VOLTAGE is multiplied by the
INSTANTANEOUS CURRENT and then
INTEGRATED over some time period.
𝑷 𝒂𝒗𝒈 =
𝟎
𝑻

Harmonic Analysis
Total RMS Value of the Distorted
Waveform is Calculated as:
Vrms = V0 + V1 + V2 + V3 + . . . + Vn
* OR More Precisely *
Vrms = V0 +  Vn

Harmonic Analysis
Total Power of the Distorted
Waveform is Calculated as:
Ptotal = V0 x I0 + V1 x I1 x Cos 1 + V2 x I2 x Cos 2 +
V3 x I3 x Cos 3 + . . . + Vn x In x Cos n
* OR More Precisely *
Ptotal = V0 x I0 + min Vn x In x Cos n
max

True RMS Measurements
Harmonic Analysis
These calculation methods provide a True Power and
True RMS Measurement on any type of waveform,
including all the harmonic content, up to the bandwidth of
the instrument.
𝑷 𝒕𝒐𝒕𝒂𝒍 =
𝟏
𝑻 𝟎
𝑻
𝑼 𝑹𝑴𝑺 =
𝟏
𝑻 𝟎
𝑻
𝒗(𝒕) 𝟐 𝒅𝒕
𝑰 𝑹𝑴𝑺 =
𝟏
𝑻 𝟎
𝑻
𝒊(𝒕) 𝟐 𝒅𝒕

Harmonic Analysis
Harmonic Analysis
• The approach used to get the Frequency-Domain
information for Harmonic Analysis, is to apply a
Mathematical technique known as the
Fourier Analysis.
• When the waveform is digitized, the Discrete
Fourier Transform (DFT) can be used to obtain
the frequency- domain information.
• The Fast Fourier Transform (FFT) is the
commonly used algorithm for evaluating the
Discrete Fourier Transform (DFT).

Harmonic Analysis
Harmonic Analysis
• The Yokogawa Digital Power Analyzers and
Power Scopes use the FFT algorithm.
• FFT Analysis must be performed on a periodic
waveform with a true integer number of cycles.
• Yokogawa Power Analyzers use a Phase Lock
Loop (PLL) circuit to sync on the fundamental
frequency and adjust the sample rate to obtain a
true integer number of cycles.

Harmonic Analysis – FFT Function
Harmonic Analysis
• Window Function: Rectangular
• Word Length: 32 Bit Processing
• FFT Data Length: From 1024 on the
WT310E/WT330E to 9000 points on the WT3000E.
• Sample Rate: Function of the Fundamental
Frequency; set automatically by the PLL Circuit.
• Frequency Resolution =
Sample Rate S/Sec
Points in FFT

Simple Math FFT Analysis Function
Harmonic Analysis

Harmonic Analysis Function with Power Analyzer
Harmonic Analysis

Part 3
Harmonic Analysis
Harmonic Measurement
Applications

Power Supply Input Waveforms
Harmonic Analysis

Power Supply Input Measurement Data
Harmonic Analysis
Typical
Data
Display

Power Supply Input Harmonic Display
Harmonic Analysis
Typical FFT
Display
Voltage
Current
Power

Power Supply Input with Harmonic Data
Harmonic Analysis
DC and AC
Components

Power Supply Input with Harmonic Order Data
Harmonic Analysis
Dual Data
Display
Voltage
Current
&
Harmonic
Distortion
Factor
% Total

Harmonic Analysis
Dual Data
Display
Power
Current
&
Harmonic
Distortion
Factor
% Total

Harmonic Analysis
Dual Data
Display
Voltage
Phase
&
Current
Phase

Power Factor Measurement
Harmonic Analysis
True
Power Factor
PF = W / VA
PF = 72.03/99.78
PF = 0.7219

Power Factor of a Sinewave
Harmonic Analysis
True
Power Factor
PF = W / VA
PF = 70.24/75.06
PF = 0.9358
Displacement
Power Factor
PF = Cos Ø
Cos 20.64 =
0.9358

Compact Florescent Lamp Waveforms
Harmonic Analysis

Compact Florescent Lamp Measurements
Harmonic Analysis

Compact Florescent Lamp Harmonic Analysis
Harmonic Analysis
Typical
FFT
Display
Voltage
&
Current

Harmonic Analysis
Typical
FFT
Display
Current
&
Power

Harmonic Analysis
Total Harmonic Distortion (Example 1)

Harmonic Analysis
Total Harmonic Distortion (Example 2)

THD Calculations
Harmonic Analysis
ITHD =
K = min
K =
  I (k)2
* 100
ITHD =
max
k = 2
I (k=1)
* 100
  I (k)2
k = 2
max
I (Total)
Typical UL and CSA
Method
k = Harmonic Order; 1, 2, 3, . . .etc
Typical IEC Method

PWM Motor Drive Power Measurement
Harmonic Analysis

Harmonic Analysis Measurements
Harmonic Analysis
NORMAL MODE
2 MHz
BANDWIDTH
HARMONICS MODE
30 kHz BANDWIDTH
Measured over 500
Orders

Harmonic Analysis
• Measurements made in the Harmonics Mode of the
Power Analyzer can be Bandwidth Limited .
• Some measurements of RMS Voltage or Current may
be different in the Harmonic Mode as compared to
the Normal Power Measurement Mode.
• Normal Mode: RMS Measurements are made to the
Bandwidth of the instrument.
• Harmonics Mode: RMS Measurements are made
ONLY to the Maximum Harmonic Order of the
instrument.

Harmonic Calculations
Harmonic Analysis
Normal Mode Harmonics Mode
P = 1/T 0 v(t) * i (t) dt P =  P (k)
URMS = 1/T 0 v(t)2 dt U =   U (k)2
IRMS = 1/T 0 i(t)2 dt I =   I (k)2
True RMS Measurement NOT True RMS Measurement
T
T
T
K = min
k = min
max
k = min
max
max
k = min
k = Harmonic Order; 1, 2, 3, . . .etc

Instrument Considerations
Harmonic Analysis
Model Instrument Harmonic Harmonic
Bandwidth Orders Bandwidth
(At 60Hz Fundamental)
WT310E 100 KHz 50 3000 Hz
WT330E 100 KHz 50 3000 Hz
WT500 100 KHz 50 3000 Hz
WT1800E 1 MHz 500 30,000 Hz
WT3000E 1 MHz 100 6000 Hz
PX8000 20 MHz 500 30,000 Hz
DLM4000 500 MHz 40 2400 Hz
(IEC 61000-3-2)

Harmonic Analysis
Some Applications require doing Harmonic
Analysis on two different frequency sources. The
Input and Output of an Inverter is an example.
In addition this Harmonic Analysis might need to be
performed Simultaneously in order to verify the
product design and Power Quality compliance.

Dual Harmonic Analysis Measurements
Harmonic Analysis
Input and Output of a Variable Frequency Motor Drive
OUTPUT
PWM Variable
Frequency
Drive
INPUT
Inverter Drive
Power Supply

Harmonic Analysis
Harmonic Spectrum
of
Power Supply Input
Harmonic Spectrum
of
Drive Output
Voltage
Voltage
Current
Current

Harmonic Analysis
INPUT OUTPUT
Frequency
THD

Power Quality Standards
Harmonic Analysis
• IEEE Standard 519: www.ieee.org
IEEE Recommended Practices and Requirements
for Harmonic Control in Electrical Power Systems.
• General Harmonic Evaluation Procedures for
Industrial, Commercial & Residential
applications
• Methods for evaluating Harmonic levels
• Provides examples of measurement
procedures

Harmonic Analysis
IEC Electromagnetic Compatibility
• IEC61000-3-2 Rev 2.2
• IEC61000-4-7 Ed 2 Requirements.
Includes 10/12 cycles at 50/60 Hz, Inter-Harmonic
Measurements, and Grouping.
• Deals with and specifies the limits of Harmonic
Currents injected into the public 220 Volt supply
system. Limited to 16 Amps per phase.

Harmonic Analysis
IEC Testing
• Full Compliant Test
• Must use latest test equipment meeting the
IEC measurement and analysis requirements
• Pre Compliant Test
• Could use a basic instrument for harmonic
analysis to test basic product performance
before sending to a Compliant Test Lab.

Introduction to IEC61000-3-2
Harmonic Analysis
Measurement of Harmonic Currents
• For electrical and electronic equipment having
input currents up to and including 16 A per phase
and to be connected to low voltage distribution
systems.
Equipment Classifications
• Class A: All motor driven equipment, household appliances, and
three-phase equipment less than 16 Amps per phase
• Class B: Portable electric tools
• Class C: All Lighting equipment & dimmers greater than 25 W
• Class D: PC’s, monitors and television receivers from 75 to 600W
Each class of equipment has a set of harmonic limits

Harmonic Analysis
Inter-Harmonic Measurements

Harmonic Analysis
IEC Harmonic Groups
• There are three types of Harmonic Grouping
methods in the IEC Harmonic Measurement
specifications.
• The method to calculate the amplitude of the RMS
value of the harmonic varies depending on the
grouping method.

Harmonic Analysis
IEC Harmonic Groups
• No Grouping (OFF)
Only the components of the Integer Multiples of the
Fundamental Frequency are considered Harmonics.
Inter-Harmonic components are not considered.

Harmonic Analysis
IEC Harmonic Groups
• Type 1 Grouping
The Harmonic Subgroup is considered a component
of the corresponding order. Therefore, Harmonics
could have a larger value when Subgroups are
included in the calculation as compared to when
Grouping is OFF.

Harmonic Analysis
IEC Harmonic Subgroup
IEC Harmonic Group Type 1

Harmonic Analysis
IEC Harmonic Groups
• Type 2 Grouping
The Harmonic Group is considered a component of
the adjacent inter-harmonics. Therefore, Harmonics
could have a larger value when Harmonic Groups
are included in the calculation as compared to when
Grouping is OFF.

Harmonic Analysis
IEC Harmonic Group Type 2

Harmonic Analysis

Introduction to IEC62301
Harmonic Analysis
 International Standard IEC62301
 Household Electrical Appliances –
Measurement of Standby Power
 Hardware and Software Measurement
Solution

Harmonic Analysis
This International Standard specifies methods of
measurement of electrical power consumption in
Standby Mode. It is applicable to mains powered
electrical household appliances.
The objective of this standard is to provide a
method of test to determine the power
consumption of a range of appliances and
equipment in standby mode.

Harmonic Analysis
The Standard references Twenty Five (25) IEC
Standards for various Household electrical
appliances.
These standards define the various test
parameters with the limits for items such as THD,
Power and other items for the appropriate product.
In the US and North America, the Energy Star®
standard is typically used for the testing limits.

Harmonic Analysis
The Test Report
identifies the
following:
• The Appliance
• Test Equipment
• Test Limits
• Measured Data

Other Harmonic Standards
Harmonic Analysis
• MIL-STD-1399 (Navy Shipboard Systems)
• MIL-STD-704 (Air Force Aircraft Systems)
• DO160 Commercial Aircraft
• Others: Industry or Product Specific

Conclusion
Harmonic Analysis

Harmonic Analysis
Harmonic Analysis
 Basic Power Measurements -
Review of Basic Power Measurements
 Harmonic Analysis
Fundamentals of Harmonics
Measurements on Distorted Waveforms
Instrument Considerations and Current Sensors
Power Factor of Distorted Waveforms

Harmonic Analysis
Harmonic Analysis
 Harmonic Analysis Applications
Practical Power & Harmonic Analysis of:
Power Supply
Electronic Lighting Load
Variable Speed PWM Motor Drive
Power Quality Standards, IEC Introduction
 Answered YOUR Power Measurement
and Harmonic Analysis Questions

Conclusion
Harmonic Analysis
 Yokogawa offers the Most Complete Line of Power
Analyzers to meet your Application and Budget.
 Product, Application and Software support provided
from a network of Field Sales Reps, Factory Regional
Sales Managers and Factory Support Application
Engineers in Newnan, GA
 Guaranteed Measurement Accuracy over the Bandwidth
of the Instrument. Available NIST Traceable and ISO17025
Calibration provided by Factory Trained technicians in
Newnan, GA.
 All Yokogawa Power Analyzers are covered by a 3-Year
Warranty.

Harmonic Analysis
Join Us for Future Web Seminars
Visit our Web Site
tmi.yokogawa.com
Go to > Technical Library
> Webinars On-Demand
Future Webinars

Harmonic Analysis
Educational Webinars
• Basic Power Measurements
• Harmonic Analysis
• Motor Analysis
• Watch for Digital Oscilloscope Webinars
• Register at tmi.yokogawa.com > Technical
Library

Harmonic Analysis
Harmonic Analysis Webinar
Thank You
For
Attending

Harmonic Analysis
Yokogawa’s Power Measuring Solutions
Precision Power
Analyzers

Harmonic Analysis
Yokogawa’s Power Measuring Solutions
Digital Oscilloscopes
with Power Analysis

Contact Us
Harmonic Analysis
Yokogawa Corp of America
Test & Measurement Div.
2 Dart Rd.
Newnan, GA 30265
tmi.yokogawa.com
Tel: 1-800-888-6400
Sam Shearman
Product Manager
sam.shearman@us.yokogawa.com

2017 Harmonic Analysis

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