The Harmonic
Spectra of Interharmonics
Gary MalhoitSRP
August 26, 2010
Overview Brief overview on harmonics and
periodicity Fourier’s Method and the DFT Interharmonic Defined Picket-Fence Effect & Spectral Leakage Genuine & Non-Genuine Interharmonics Interharmonic standards and allowed
limits Sources of Interharmonics Interharmonic Problems Measuring Interharmonics IEC Grouping Standard and
Understanding Spectra Measurements
2
Sinusoids
Sinusoids are the basic building block of all periodic signals.
Periodic waveforms are comprised of component sinusoids having distinct frequencies. This includes distorted periodic waveforms.
3
Fourier
1822, a French mathematician named Joseph Fourier, claimed that continuous periodic signals can be represented by the sum of properly chosen sinusoids.
4
Limitations to Fourier Methods
55Source: Wikipedia
Fourier Tool Kit
6The Scientist and Engineer's Guide to Digital Signal ProcessingBy Steven W. Smith, Ph.D.
Assumptions in Applying DFT
for PQ Measurements The signal is strictly periodic and
stationary. The sampling frequency is an
integer multiple of the fundamental. The sample frequency is at least
twice the highest frequency being measured.
7
Non-Stationary Signal
82Pi
DFT Window
Source: A Notebook Compiled While Reading Understanding Digital Signal Processing by Lyons
Non-periodic Signal
9
DFT Window
Half a sinusoidIn time domain
Spectral Leakagein the frequencydomain
Source: A Notebook Compiled While Reading Understanding Digital Signal Processing by Lyons
What is Harmonic Spectra?
Harmonic spectra includes sub-harmonics, harmonics and interharmonics.
10
Harmonic
Interharmonic
Subharmonic
f = n f1 where n is an integer > 0.f = nf1 where n is an integer > 0.
0 < f < f1
f1= fundamental frequency
Source: Power Quality Application Guide: European Copper Institute, AGH University of Science and Technology and Copper Development Association.
Harmonic Spectra
Characteristic Harmonics“Those harmonics produced by semiconductor converter equipment in the course of normal operation. In a six-pulse converter, the characteristic harmonics are the non-triple odd harmonics, for example, the 5th, 7th, llth, 13th, etc.”
11
Source: IEEE 519
Harmonic Spectra (cont.)
Non-Characteristic Harmonics“Harmonics that are not produced by semiconductor converter equipment in the course of normal operation. These may be a result of beat frequencies; a demodulation of characteristic harmonics and the fundamental; or an imbalance in the ac power system, asymmetrical delay angle, or cycloconverter operation.”
12Source: IEEE 519
Interharmonics
Interharmonics- “Between the harmonics of the power frequency voltage and current, further frequencies can be observed which are not an integer of the fundamental. They can appear as discrete frequencies or as a wide-band spectrum.”
Source: IEC 61000-2-1
13
Interharmonics Redefined
Interharmonics- “Any frequency which is not an integer multiple of the fundamental frequency”
Source: IEC-61000-2-2
14
One-Cycle Window
1515
60 Hz
The 60 Hz component competes 1 cycle within the DFT window.
-1.5
-1
-0.5
0
0.5
1
1.5
DFT Window
16.67 ms
Frequency Resolution
16
DFTtheofcyclesofnumberp
frequency
_____
60
psolutionFrequencyAngular
Re__
...)60,48,36,24,12__(_125
60_.__
...)150,120,90,60,30__(_302
60_.__
...)300,240,180,120,60__(_601
60_.__
HzCWindowDFT
HzBWindowDFT
HzAWindowDFT
-1.5
-1
-0.5
0
0.5
1
1.5
CBA
Time
Picket Fence Effect
17
Source: Azima DLI
Expanded DFT Window
In order to see interharmonics the DFT window
must be larger than one cycle of the fundamental
frequency.
18
Source: Interharmonics: basic concepts & techniques for their detection & measurement, Chun Li, et al.
The Fundamental with Harmonics
1919
-1.5
-1
-0.5
0
0.5
1
1.5 60 Hz-Fundamental180 Hz-Third Harmonic300 Hz-Fifth Harmonic
60 180 300
FrequencyTime
16.67 ms
DFT Window
A Genuine Interharmonic
20
DFT Window
33.34 ms-1.5
-1
-0.5
0
0.5
1
1.5
Frequency (Hz)Mag
nit
ud
e
60 90
Genuine Interharmonic
Source: Interharmonics: Theory and Modeling, IEEE Task Force on Harmonics Modeling and Simulation
The 90 Hz component completes 3 cycles within the DFT window.
The 60 Hz component competes 2 cycles within the DFT window.60 Hz
90Hz
Non-Genuine Interharmonics
21
DFT Window
33.34 ms
100 HzThe 100 Hz component completes 3.33 cycles within DFT window.
60 HzThe 60 Hz component completes two cycles within the DFT window.
-1.5
-1
-0.5
0
0.5
1
1.5
Frequency (Hz)
Mag
nit
ud
e
60 90 120 150 180
Non-Genuine Interharmonics (Black)
Source: Interharmonics: Theory and Modeling, IEEE Task Force on Harmonics Modeling and Simulation
DFT Assumes Signal Repetitive
22
DFT Window
Discontinuities
Time
Magnitude
Time DomainSource: Oppenheim, et al. “Discrete-Time Signal Processing” Frequency Domain
Determining if Interharmonics Are Real The voltage and current spectral
components should show correlation.
If the magnitude of the signal appears modulated, it is highly likely that the signal contains interharmonics.
Interharmonics usually coexist with harmonics.
If the signal is substantially non-varying or stationary, a longer DFT window can improve the frequency resolution.
23Source: Interharmonics: basic concepts & techniques for their detection & measurement, Chun Li, et al.
Interharmonics
The main reason for lack of interharmonic concerns is that interharmonics are produced by relatively few types of loads, unlike harmonics.
24
Survey of Interharmonics in Indian Power System Network, B.E. Kushare, et al.
Spectra & Noise Magnitudes
25
% o
f N
om
inal
Volt
ag
e o
f Fu
nd
am
en
tal
.01
.1
1.0
10.0 Harmonics
Interharmonics
White Noise
5%
.2%
.02%
Sources: IEEE 519 & IEC 61000-2-2 & IEC 1000-2-1
Interharmonic Limits
26
Standard
IEEE 519-1992
IEC 1000-2-2
Limits
IEC 1000-2-4
EN 50160
Not covered
0.2% at ripple control frequencies
0.2% for classes 1 & 2, up to 2.5% for class 3
Under consideration
Survey of Interharmonics in Indian Power System Network, B.E. Kushare, et al.
All %’s are of nominal fundamental frequency
Proposed Interharmonic Limits
Current Standards* use 0.2% Other Proposed Limits
Less than 1%, 3% or 5% depending on the voltage level.
Adopt limits correlated with Pst
Develop appropriate limits for particular equipment and systems.
27
All %’s are of nominal fundamental frequency*IEC 61000-2-2
Source: Survey of Interharmonics in Indian Power System. Network, B.E. Kushare, et al.
Causes of Interharmonics
Asynchronous switching (i.e., not synchronized with the power system frequency); and
Rapid changes of the load current causing the generation of sideband components adjacent to the fundamental supply frequency and its harmonics; and
A combination of the above can occur at the same time in many kinds of equipment.
28
Source: Power Quality Application Guide: European Copper Institute, AGH University of Science and Technology and Copper Development Association.
Sources of Interharmonics
Includes at least:
PWM power electronic systems (Asynchronous Switching)
Arc Furnaces (Rapid Current Changes)
Cycloconverters (Asynchronous Switching)
29
Source: Power Quality Application Guide: European Copper Institute, AGH University of Science and Technology and Copper Development Association.
Cycloconverter
30
021 )1( nfpfmpf I FrequencyPowerf
FrequencyOutputf
nicsInterHarmoCurrentf I
_
_
_
0
Variable Speed Drives
31
Ld
Converter 2Converter 1
Id
f1 f2AC/DC DC/AC
DC-Link
Variable Speed Drives (cont.)
32
HzHzHzHzHzHzf
f
ff
FrequencyOutputfwherefnpfHzf
HzHzHzf
pulsep
fpnf
I
I
rI
rr
h
h
597,477,243,237,123,117
177420,177300,17760
)___(__177
............420,300,60
_6
)1(
002
If the reactor and/or capacitor at the DC Link is infinite there will not be any DC ripple at the DC Link.
Source: Interharmonics: basic concepts & techniques for their detection & measurement, Chun Li, et al.
An Arc Furnace is a Varying Load
33
Varying Loads
34
)sin(1
)sin(
)(
)()(
tr
t
tR
tVtI
m
,......3,2,)( mmmtI
Hz
rHzm
60
5.0,8
HzHzHzHzHzHzHz 84&76,68,60,52,44,36
2460,1660,860
Source: Interharmonics: basic concepts & techniques for their detection & measurement, Chun Li, et al.
Modulated Power
35Source: Interharmonics: basic concepts & techniques for their detection & measurement, Chun Li, et al.
RMS Deviation from Interharmonics
36
36
0.05
0.1
0.15
0.2
0.00 50 100 150 200 Interharmonic Frequency
% R
MS
Devi
ati
on
Du
e t
o I
nte
rharm
on
ics
Source: Power Quality Application Guide: European Copper Institute, AGH University of Science and Technology and Copper Development Association.
Problems Caused by Interharmonics
Lamp Flicker; Heating; and Interharmonics vary with the
operating conditions of the interharmonic producing load. This makes interharmonics more difficult to mitigate than harmonics.
37
Lamp Flicker
38
erharmonicoffrequency
harmonicorlfundamentafrequency
i
hf
ihf
int__
___/
/nfluctuatio
Human eye is sensitive to frequencies between about8 Hz and 12 Hz
Source: Interharmonics: basic concepts & techniques for their detection & measurement, Chun Li, et al.
Source : EPRI
42 Hz 58 Hz
Minimum Interharmonic Amplitude Causing Perceptible Flicker
39
Source: Detection of Flicker Caused by InterharmonicsTaekhyun Kim, Student Member, IEEE, Edward J. Powers, Fellow, IEEE, W. Mack Grady, Fellow, IEEE, andAri Arapostathis, Fellow, IEEE
Flickermeter
Rolling Mill Case
4040
Bus
Source: Leonardo Energy by Michele De Witte
Harmonic Impedance at Resonance
41
Source: Harmonic Impedance Study for SouthwestConnecticut Phase II Alternatives by KEMA, Inc.
Rolling Mill Case (cont.)
42
180
330
485
Source: Leonardo Energy by Michele De Witte
notchnotch
notch
Interharmonic Conclusions
Interharmonics have always been around, they are just becoming more important and visible.
Power electronic advances are resulting in increasing levels of interharmonic distortion.
Traditional filter designs can result in resonances that make interharmonic problems worse.
Light flicker is the most common impact.
Measurement is difficult, but standards make them possible and the results comparable.
43
IEC Groupings Number of cycles to sample chosen to provide 5
Hz frequency bins 10 Cycles for 50 Hz Systems 12 Cycles for 60 Hz Systems
Grouping concept Harmonic factors calculated as the square
root of the sum of the squares of the harmonic bin and two adjacent bins.
Interharmonic factors calculated as the square root of the sum of the squares of the bins in between the harmonic bins (not including the bins directly adjacent to the harmonic bin).
44
Source: Power Quality Application Guide: European Copper Institute, AGH University of Science and Technology and Copper Development Association.
IEC 61000-4-7 (Groupings)
45
n n+1 n+2
Harmonic subgroupHarmonic groupHarmonic subgroup
The time-window is 12 cycles at 60 Hzand has 5 Hz resolution.
The RMS value of the fundamental and adjacent Harmonic components
The RMS value of the two harmonic components immediately adjacent tothe fundamental .
Source: Power Quality Application Guide: European Copper Institute, AGH University of Science and Technology and Copper Development Association.
IEC 61000-4-7 (Groupings)
46
n n+1 n+2
Interharmonic subgroup
Interharmonic group
The RMS value of all interharmonics components in the interval between two consecutive harmonics.
The RMS value of all interharmoniccomponents in the intervalbetween two consecutive harmonic frequencies, excluding components adjacent to the harmonicfrequencies
Source: Power Quality Application Guide: European Copper Institute, AGH University of Science and Technology and Copper Development Association.
Options Using PX-5
47
Show Harmonics Only (PX-5)
48
0 60 120 180 240 300 360Frequency (Hz)
Mag
nit
ud
e
1 3 5
Harmonic Sub-Groups
Show Harmonics & Interharmonics (PX-5)
49
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125Frequency (Hz)
Mag
nit
ud
e
1 2
Harmonics Calculated Including
Interharmonics (PX-5)
50
0 5-55 55-65 70-110 115-125 130-170 175-185
Mag
nit
ud
e
1 2 3
HarmonicSub-Groups
InterharmonicSub-Groups
Questions & Comments
51
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