1

Fundamentals of Harmonics

2

Overviews

• Definitions and Nonlinear Loads• Harmonics Power Quantities• Harmonic Sequences• Triplen Harmonics• Harmonics Indices• Harmonic Sources

– Classical Sources and Power Electronics

• Locating Harmonic Sources• Impacts of Harmonics• Interharmonics

3

1.1 Nonlinear Loads• Fundamentals of

Nonlinear Loads• Fourier representation

4

1.2 Harmonic Phenomena

• Harmonics in voltage and current– CAUSE: Current– Effect: Voltage

5

Examples of Harmonics I

6

Examples of Harmonics II

7

Examples of Harmonics III

8

Harmonics versus Transients

9

Power Factor

• Consider first a sinusoidal voltage and current

1rms1rms1

rms1rms1

rms1rms1

T

011

1rms1

coscosIVcosIV

pf

IV

dttcosItcosVT1

SP

pf

2/VV

10

RMS

In case of harmonics,

11

Harmonic Phase Sequences

• In a balanced three-phase circuit:– the fundamental defines the positive phase

sequence (or rotation) such as ABC or xyz or 321, and the 4th, 7th, 10th, …, are also positive sequence

– the 2nd, 5th, 8th, 11th ,…, are negative sequence (eg CBA)

– the 3rd, 6th, 9th, …, are zero seq (all in phase)

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1 +

2 -

3 0

4 +

5 -

6 0

7 +

8 -

9 0

10 +

1 +

3 0

5 -

7 +

9 0

11 -

13 +

15 0

17 -

19 +

13

Triplen harmonics• Harmonic order h values that are multiples

of 3 are called triplen harmonics• If the three phase circuit is balanced, the

triplen harmonics are all in phase (zero sequence)– triplen harmonic line currents will be additive

at the neutral of a wye circuit by KCL (zero triplens if three-wire ungrounded wye or if delta)

– triplen harmonic line-line voltages will be zero by KVL

14

Transformer

15

Harmonic Indices

• Total harmonic distortion = THD

1

h

2h

2h

M

MTHD

max

21

221

21

h

1h

2h

THD1MRMS

THDMMMRMS

:Note

max

16

Harmonic Indices

• Total demand distortion = TDD

L

h

2h

2h

I

MTDD

max

PCC coupling common ofpoint at frequency

lfundamentaat demandcurrent rmsmax I

:Note

L

17

Harmonics Sources• Conventional Sources

– Single-phase power supplies– Fluorescent lighting– ASD for HVAC and elevators

• Industrial Sources– Power converters– DC and AC drives– Saturable devices

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4.1.1 SMPS

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4.1.2 Fluorescent lighting

20

Power Converter