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Contributors: W. Xu and S. Ranade. Chapter 1: An Overview of Power System Harmonic Analysis. Organized by Task Force on Harmonics Modeling & Simulation Adapted and Presented by Paulo F Ribeiro AMSC May 28-29, 2008. Chapter 1: An Overview of Power System Harmonic Analysis. Outline. - PowerPoint PPT Presentation
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1
Chapter 1: An Overview of Power System Harmonic Analysis
Chapter 1: An Overview of Power System Harmonic Analysis
Organized by
Task Force on Harmonics Modeling & Simulation
Adapted and Presented by Paulo F Ribeiro
AMSC
May 28-29, 2008
Contributors: W. Xu and S. Ranade
2
• Status and methods of harmonic analysis
• New challenges of harmonic analysis
• Summary
Outline
Chapter 1: An Overview of Power System Harmonic Analysis
• Modeling of power system components• Algorithms for harmonic analysis
• Analysis of systems with distributed harmonic sources• Modes of harmonic resonance• Analysis of interharmonics
3
Status and methods of harmonic analysis
Chapter 1: An Overview of Power System Harmonic Analysis
Methods: 1) Frequency scan2) Harmonic power flow
Models: 1) Harmonic source: current source model2) Non H-source: linear impedance model
Variations: 1) Single-phase versus multiphase2) Iterative versus non-iterative H power flow
Applications: Systems with limited number of H-sources andthe sources are typically large in size
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VFD
V I
+
-
V1I1
+
-
P+
jQ
VhIh
+
-
h=2,H
_1
1_
h spch
spc
II I
I _ 1_h h spc spch
VFD load VFD model at60Hz
= +
VFD model atharmonic freq.
spc = given spectrum data
Modeling of harmonic loads as current sources
Chapter 1: An Overview of Power System Harmonic Analysis
5
Example of source modeling
Chapter 1: An Overview of Power System Harmonic Analysis
100 20( )VFDS P jQ j kVA 1 25 / 3 0 14.43 0( )V kV
1 2.355 11.31 ( )3VFDS
I AV
5 1 5_ % 2.355*18.24% 0.4296spcI I I A 5 5_ 1_5 55.68 5 ( 11.31) 112.23spc spc
Typical Spectrum Harmonic CurrentSource
HarmonicOrder
_ (%)h spcI _ ( )h spc ( )hI A ( )h
1 100 0 2.355 -11.315 18.24 -55.68 0.4296 -112.237 11.9 -84.11 0.2802 -163.2811 5.73 -143.56 0.1349 -267.9713 4.01 -175.58 0.0944 -322.6117 1.93 111.39 0.0455 -80.8819 1.39 68.30 0.0327 -146.5923 0.94 -24.61 0.0221 -284.7425 0.86 -67.64 0.0203 -350.39
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Harmonic analysis methods
Chapter 1: An Overview of Power System Harmonic Analysis
Objectives• Check if resonance exists
• Check harmonic distortion levels (safe equipment operation)
• Filter design
• Compliance with standards
Two types of assessments:Frequency response check resonance
(Frequency scan) filter design
Distortion level calculation compliance check
(harmonic power flow) equipment operating conditions
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Network
Frequency Scan:Determine the frequency response of a network at a given bus
Z
f
0
..
..
0
1
..
..
..
......
..
.
.
..
....
..
.
.
..
....
..
.
.
..
..
..
..
1
2
1
1
21
11
2
1
NN
N
N
NN Y
Y
Y
Y
Y
Y
V
V
V
1
Frequency scan analysis
Chapter 1: An Overview of Power System Harmonic Analysis
8
Objective: compute harmonic distortion levels for a given operating condition
• Fundamental frequency power flow results (I1 and q1).• Typical spectrum of harmonic sources (Ih-spc, qh-spc)• System Y(h) matrix, h=harmonic number
What is known for solving the problem
There are many harmonic power flow algorithms proposed. Here we discussthe most useful algorithm.
• Current source model for harmonic sources• Frequency domain• Non-iterative
Harmonic power flow analysis
Chapter 1: An Overview of Power System Harmonic Analysis
• Current source model described earlier
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Solution steps
1) Compute 60Hz power flow
2) Determine drive current (I1 and q1)
3) Determine drive harmonic current I(h) using the formula and typical drive spectrum
4) With known Y(h) matrix and drive current I(h), compute nodal voltage V(h) and branch current IB(h)
5) Compute harmonic indices (THD, IHD) using the V(h), IB(h) results.
Harmonic power flow analysis
Chapter 1: An Overview of Power System Harmonic Analysis
10
• Time domain algorithm (e.g. EMTP simulation) or hybrid algorithm
• Iterative algorithms (frequency domain)
F( [V1], [V2],...,[Vn], [I1], [I2], ..., [In],C) =0
1) Newton method2) Harmonic iteration method (see the diagram below)
Linear network(including powerflow constraints)
Harmonic Source(non-linear)
Bus voltages
Current source
Harmonic power flow analysis - other algorithms
Chapter 1: An Overview of Power System Harmonic Analysis
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New challenges
Chapter 1: An Overview of Power System Harmonic Analysis
Distributed harmonic sources
Fluctuation of harmonic distortions with time
Concerns on interharmonics
Need to identify system deficiency more efficiently
Need to revisit some of the modeling assumptions
New challenges 1 - distributed harmonic sources
Chapter 1: An Overview of Power System Harmonic Analysis
The harmonic-production characteristics of the sources will affect each other. (attenuation and diversity effects)
The harmonic sources may also vary randomly.
0
5
10
15
20
25
30
35
40
45
50
0 20 40 60 80 100 120 140
Bus number
Volt
ag
e T
HD
(%
) Traditional method
Iterative method
Actual results
New harmonic analysis methods need to take into account the characteristics
05
1015
2025
30
1311
97
53
0
20
40
60
80
100Ih
/I1
(%)
VTHD (%)Harmonic Order
New challenges 1 - distributed harmonic sources
Chapter 1: An Overview of Power System Harmonic Analysis
Harmonic attenuation effect
· Which bus can excite a particular resonance more easily?· Where the resonance can be observed more easily?· What are the components involved in the resonance?· How far the resonance can propagate in a system?
0
1
2
3
4
0 5 10 15 20 25 30Frequency (pu)
Impe
danc
e (p
u)
Bus 9
Bus 10
Bus 5
Bus 7
New challenges 2 - analysis of harmonic resonance
Chapter 1: An Overview of Power System Harmonic Analysis
• Some elements of [Y]-1 are large (the extreme case is [Y]-1= )
• Implies that [Y] approaches singularity (something like [Y]=0)
• The singularity of [Y] can only be caused by one or more eigenvalues of the [Y] matrix = 0.
XL XC IVI
jXjXIYV
CL
11 )11
(
If this term = 0 => Resonance
][][][ 1 IYV
New challenges 2 - analysis of harmonic resonance
Chapter 1: An Overview of Power System Harmonic Analysis
]][[][][ 1 TTY Eigen-decomposition of the Y matrix:
Left eigenvectormatrix
Eigenvaluematrix
Right eigenvectormatrix
][][][ 1 JU ][][][ 1 IYV
[U]=[T][V] -- called modal voltage[J] =[T][I] -- called modal current[L] -- can be called modal Y matrix
New challenges 2 - analysis of harmonic resonance
Chapter 1: An Overview of Power System Harmonic Analysis
nnn J
J
J
U
U
U
JU...
000
0...00
000
000
...][][][ 2
1
1
12
11
2
1
1
• Assume l1 is the eigenvalue approaching zero
• modal current J1 will lead to a large modal voltage U1
• Other modal voltages are not affected (since they are
decoupled from l1)
New challenges 2 - analysis of harmonic resonance
Chapter 1: An Overview of Power System Harmonic Analysis
0
1
2
3
4
0 5 10 15 20 25 30Frequency (pu)
Impe
danc
e (p
u)
Bus 9
Bus 10
Bus 5
Bus 7
0
5
10
15
20
0 5 10 15 20 25 30
Frequency (pu)
Mo
da
l im
ped
an
ce (
pu) Resonance mode
Physical domain Modal domain
Summary: In the modal domain, it is much easier to find the ‘locations’ or ‘buses’ (i.e. the modes) that are related to a resonance
Once we know the resonance mode, we can find the buses most affected by thereassurance - based on the eigenvector information
New challenges 2 - analysis of harmonic resonance
Chapter 1: An Overview of Power System Harmonic Analysis
New challenges 2 - analysis of harmonic resonance
Chapter 1: An Overview of Power System Harmonic Analysis
3
G
1
G
2 Converter
SVC C
4 5
6
13
7
8 9
10 11
14
12
Harmonic=5.9
Participation of buses in a resonance
Participation of componentsin a resonance
InverterConverter MotorSource
60Hz 50Hz
DC link reactor
60Hz ripple 50Hz ripple
• Interharmonics produce flicker• Frequency of interharmonic varies with the drive operating condition
New challenges 3 - analysis of interharmonics
Chapter 1: An Overview of Power System Harmonic Analysis
An interharmonic-producing drive cannot be modeled as an interharmonic current source
Inverter MotorSource
60Hz 50Hz
VDC2
IDC2
Converter
IAC2
•VDC2 has ripples associated with the motor frequency•VDC2 produces IDC2 through some impedances (including supply system Z)
•IDC2 is rectified (or penetrate) into the AC side to produce IAC2
•Therefore, interharmonic current of IAC2 is affected by some impedances
New challenges 3 - analysis of interharmonics
Chapter 1: An Overview of Power System Harmonic Analysis
0
100
200
300
400
500
600
700
800
0 10 20 30 40 50 60 70
Drive Output Frequency (Hz)
Inte
rhar
mon
ic F
requ
ency
(H
z)
Positive sequence Negative sequence
A
B
X
Y
Practical operating range
Sequence characteristics of interharmonics
New challenges 3 - analysis of interharmonics
Chapter 1: An Overview of Power System Harmonic Analysis
• Harmonic analysis has become a relatively mature area. This tutorial will focus on the well-established methods
• It is important to note that there are still many subjects remaining to be explored. Three examples have been
used to demonstrate the possible developments in the area
Summary
Chapter 1: An Overview of Power System Harmonic Analysis