Interharmonics Pq

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


Sources of Interharmonics

Includes at least:

PWM power electronic systems (Asynchronous Switching)

Arc Furnaces (Rapid Current Changes)

Cycloconverters (Asynchronous Switching)

29


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.


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


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


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 : 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


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 .


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


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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Interharmonics Pq