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Harmonic Source ModelingHarmonic Source Modeling
Zs ZLVs Ih
Vh
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Harmonic Source Modeling
1
Traditionally, harmonic sources were represented by current
injection source.
Values of injected current should be determined by
measurement.
In the absence of measurements it is common to assume that
the
harmonic content is inversely proportional to the harmonic
number.
hIIh 1
Representing a nonlinear load with a harmonic current source
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Harmonic Source Modeling
2
Typical values for analysis of several types of devices.
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Computer Tools for Harmonics Analysis
3
An estimate of the voltage distortion due to the current Ih .
The voltages Vh are given by
where =2
(hf1 )h =2, 3, 4,
f1 =fundamental frequency of power system
hh IRCjLCLjRV
21
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Example Tutorial 3
4
A Diode rectifier drives a quasi-square current of 10 A (peak
value) from a three-phase 11 kV, 50 Hz busbar feeder to a factory.
The load is a star-connected inductive load with RL= 180 Ohm, LL=
0.3 H. A star-connected capacitance of 1.75 F is used for power
factor correction at the same bus. The 11 kV busbars are fed from
an 132 kV/11 kV, 800 kVA transformer having an equivalent impedance
of ZT =0.01 + j 0.06 pu. The short circuit impedance of 132 kV
system ZS = 0.005 + j 0.02 pu.
Sketch the diagram of the system and determine the harmonic
current and voltage levels up to 23rd order harmonic.
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Example
5
11 kV
0.8 MVA ZT=0.01+ j0.06 pu
GID
RL=180
LL=0.3 HC=1.75 F
Zs=0.005+ j0.02 pu
132 kV
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Example
6
Inspection of the waveform shows that there are no cosine terms,
no even harmonics, and that there is quarter-wave symmetry
6
cos4)sin(42
6
nn
ItnIbn
The series is
19)19sin(
17)17sin(
13)13sin(
11)11sin(
7)7sin(
5)5sin()sin(
6cos4)(
tt
tttttIti
The value for each harmonic is: Ann
I n8.710
234
I1 =7.8 A, I5 =1.56 A, I7 =1.11 A, I11 =0.709 A, I13 =0.600 A,
I17 =0.459 A, I19 =0.410 A.
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Example
7
Harmonic Source Representation
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Example
9
Base of 800 kVA, relating the per unit values to 11 kV The Base
Impedance
Transformer Impedance @ 50Hz
Capacitive Reactance @ 50Hz
25.1518.0
112211
base
LLbasekVbase MVA
VZ
Load Reactance @ 50Hz
System Impedance @ 50Hz
075.9and5125.1
075.95125.125.151)06.001.0(
TT
baseTpuTTT
XRjpujZZjXRZ
025.3and75625.0
025.375625.025.151)02.0005.0(
SS
baseSpuSSS
XRjpujZZjXRZ
25.943.05022 fLLX L 1819101.75502
12
116- jfCC
X C
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Example
9
AZZZZZZ
ZZIZZZZZZ
ZZI RC 2.1752735.056.121313232
213132
32
AI L 1.161973.0
AI S 7.26443.1V
XIV cCB 5.995.3632735.05
VVS 8.29811/132)5025.3()75625.0(6443.122
For 5th harmonic values, frequency=250Hz, n=5, IR =1.56 A.
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Example
10
Magnitudes of Harmonic Currents and Voltages Up to the 23rd
Harmonic
n 1 5 7 11 13 17 19 23f (Hz) 50 250 350 550 650 850 950 1150IR
(A) 7.80 1.56 1.11 0.71 0.6 0.46 0.41 0.34
IC (A) 3.49 0.27 0.46 1.77 22.3 1.11 0.77 0.50
IL (A) 31.26 0.20 0.17 0.28 2.52 0.07 0.04 0.02
IS (A) 37.16 1.64 1.40 2.20 19.83 0.58 0.32 0.14
VB (V) 6351 99 119 293 3120 118 74 39
VS (V) 78189 299 356 880 9360 355 222 118
Topic4 Harmonic Source ModelingSlide Number 2Slide Number 3Slide
Number 4Slide Number 5Slide Number 6Slide Number 7Slide Number
8Slide Number 9Slide Number 10Slide Number 11
