Transcript Fundamentals of Harmonics - University of South Carolina

Fundamentals of Harmonics
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Overviews
•
•
•
•
•
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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
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1.1 Nonlinear Loads
• Fundamentals of
Nonlinear Loads
• Fourier representation
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1.2 Harmonic Phenomena
• Harmonics in voltage and current
– CAUSE: Current
– Effect: Voltage
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Examples of Harmonics I
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Examples of Harmonics II
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Examples of Harmonics III
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Harmonics versus
Transients
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Power Factor
• Consider first a sinusoidal voltage and
current
V1rms  V1 / 2
1T
V1 cost    I1 cost  dt

P T0
pf  
S
V1rms I1rms
V1rms I1rms cos  
pf 
 cos    cos1 
V1rms I1rms
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RMS
In case of harmonics,
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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
4
5
6
+
0
+
0
1
3
5
7
9
11
+
0
+
0
-
7
8
9
10
+
0
+
13
15
17
19
+
0
+
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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
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Transformer
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Harmonic Indices
• Total harmonic distortion = THD
hmax
THD 
Note :
RMS 
hmax
 Mh
2
h 2
M1
2
2
2
2
M

M

M
THD
 h
1
1
h 1
RMS  M1 1  THD 2
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Harmonic Indices
• Total demand distortion = TDD
hmax
TDD 
 Mh
2
h 2
IL
Note :
IL  max rms current demand at fundamental
frequency at point of common coupling PCC
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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
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Power Converter
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