Chapter 1 An Overview of Power System Harmonic Analysis .ppt

An Overview of Power System Harmonic Analysis

1. 1
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. 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. 3
Status and methods of harmonic analysis
Chapter 1: An Overview of Power System Harmonic Analysis
Methods: 1) Frequency scan
2) Harmonic power flow
Models: 1) Harmonic source: current source model
2) Non H-source: linear impedance model
Variations:1) Single-phase versus multiphase
2) Iterative versus non-iterative H power flow
Applications:Systems with limited number of H-sources and
the sources are typically large in size

4. 4
VFD
VI
+
-
V
1
I
1
+
-
P
+
j
Q
V
h
I
h
+
-
h=2,H
_
1
1_
h spc
h
spc
I
I I
I
 _ 1_h h spc spc
h   
VFD load VFD model at
60Hz
= +
VFD model at
harmonic freq.
spc = given spectrum data
Modeling of harmonic loads as current sources
Chapter 1: An Overview of Power System Harmonic Analysis

5. 5
Example of source modeling
Chapter 1: An Overview of Power System Harmonic Analysis
100 20( )
VFD
S P jQ j kVA   
1
25/ 3 0 14.43 0( )V kV

   

1
2.355 11.31 ( )
3
VFD
S
I A
V

   


5 1 5_
% 2.355*18.24% 0.4296
spc
I I I A   
5 5_ 1_
5 55.68 5 ( 11.31) 112.23
spc spc
         
Typical Spectrum Harmonic Current
Source
Harmonic
Order
_
(%)
h spc
I
_
( )
h spc
 ( )
h
I A ( )
h

1 100 0 2.355 -11.31
5 18.24 -55.68 0.4296 -112.23
7 11.9 -84.11 0.2802 -163.28
11 5.73 -143.560.1349 -267.97
13 4.01 -175.580.0944 -322.61
17 1.93 111.39 0.0455 -80.88
19 1.39 68.30 0.0327 -146.59
23 0.94 -24.61 0.0221 -284.74
25 0.86 -67.64 0.0203 -350.39

6. 6
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

7. 7
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. 8
Objective: compute harmonic distortion levels for a given operating
condition
• Fundamental frequency power flow results (I
1 and q
1).
• Typical spectrum of harmonic sources (I
h-spc, q
h-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 discuss
the 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

9. 9
Solution steps
1) Compute 60Hz power flow
2) Determine drive current (I
1
and q
1
)
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 I
B
(h)
5) Compute harmonic indices (THD, IHD) using the V(h), I
B
(h)
results.
Harmonic power flow analysis
Chapter 1: An Overview of Power System Harmonic Analysis

10. 10
• Time domain algorithm (e.g. EMTP simulation) or hybrid algorithm
• Iterative algorithms (frequency domain)
F( [V
1], [V
2],...,[V
n], [I
1], [I
2], ..., [I
n],C) =0
1)Newton method
2)Harmonic iteration method (see the diagram below)
Linear network
(including power
flow constraints)
Harmonic Source
(non-linear)
Bus voltages
Current source
Harmonic power flow analysis - other algorithms
Chapter 1: An Overview of Power System Harmonic Analysis

11. 11
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

12. 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
V
o
l
t
a
g
e

T
H
D

(
%
)
Traditional method
Iterative method
Actual results

13. New harmonic analysis methods need to take into account the characteristics
0
5
10
15
20
25
30
13
11
9
7
5
3
0
20
40
60
80
100
I
h
/
I
1
(
%
)
VTHD (%)Harmonic Order
New challenges 1 - distributed harmonic sources
Chapter 1: An Overview of Power System Harmonic Analysis
Harmonic attenuation effect

14. · 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 30
Frequency (pu)
I
m
p
e
d
a
n
c
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

15. • 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.
X
L X
C IV
I
jXjX
IYV
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

16. ]][[][][
1
TTY 

Eigen-decomposition
of the Y matrix:
Left
eigenvector
matrix
Eigenvalue
matrix
Right
eigenvector
matrix
][][][
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

17. 











































nnn
J
J
J
U
U
U
JU
...
000
0...00
000
000
...
][][][
2
1
1
1
2
1
1
2
1
1



• Assume l
1
is the eigenvalue approaching zero
• modal current J
1
will lead to a large modal voltage U
1
• Other modal voltages are not affected (since they are
decoupled from l
1
)
New challenges 2 - analysis of harmonic resonance
Chapter 1: An Overview of Power System Harmonic Analysis

18. 0
1
2
3
4
0 5 10 15 20 25 30
Frequency (pu)
I
m
p
e
d
a
n
c
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)
M
o
d
a
l
im
p
e
d
a
n
c
e

(
p
u
)
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 the
reassurance - based on the eigenvector information
New challenges 2 - analysis of harmonic resonance
Chapter 1: An Overview of Power System Harmonic Analysis

19. 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 components
in a resonance

20. InverterConverter MotorSource
60Hz 50Hz
DC link reactor
60Hz ripple50Hz 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

21. An interharmonic-producing drive cannot be modeled as an interharmonic
current source
Inverter MotorSource
60Hz 50Hz
V
DC2
I
DC2
Converter
I
AC2
•V
DC2 has ripples associated with the motor frequency
•V
DC2 produces I
DC2 through some impedances (including supply system Z)
•I
DC2
is rectified (or penetrate) into the AC side to produce I
AC2
•Therefore, interharmonic current of I
AC2 is affected by some impedances
New challenges 3 - analysis of interharmonics
Chapter 1: An Overview of Power System Harmonic Analysis

22. 0
100
200
300
400
500
600
700
800
0 10 20 30 40 50 60 70
Drive Output Frequency (Hz)
I
n
t
e
r
h
a
r
m
o
n
ic

F
r
e
q
u
e
n
c
y

(
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

23. • 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