1. Chapter 1: An Overview of Power System Harmonic Analysis
Contributors: W. Xu and S. Ranade
Organized by
Task Force on Harmonics Modeling & Simulation
Adapted and Presented by Paulo F Ribeiro
AMSC
May 28-29, 2008
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2. Outline Status and methods of harmonic analysis
Chapter 1: An Overview of Power System Harmonic Analysis
Outline
Status and methods of harmonic analysis
New challenges of harmonic analysis
Summary
Modeling of power system components
Algorithms for harmonic analysis
Analysis of systems with distributed harmonic sources
Modes of harmonic resonance
Analysis of interharmonics
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3. Status and methods of harmonic analysis
Chapter 1: An Overview of Power System Harmonic Analysis
Status and methods of 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
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4. Modeling of harmonic loads as current sources
Chapter 1: An Overview of Power System Harmonic Analysis
Modeling of harmonic loads as current sources
VFD V I + - V1 I1 + -
P+jQ Vh Ih + -
h=2,H = +
VFD model at
60Hz
VFD model at
harmonic freq.
VFD load
spc = given spectrum data

5. Example of source modeling
Chapter 1: An Overview of Power System Harmonic Analysis
Example of source modeling
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6. Harmonic analysis methods
Chapter 1: An Overview of Power System Harmonic Analysis
Harmonic analysis methods
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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7. Frequency scan analysis
Chapter 1: An Overview of Power System Harmonic Analysis
Frequency scan analysis 1
Frequency Scan:
Determine the frequency response of a network at a given bus
Network Z f
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8. Harmonic power flow analysis
Chapter 1: An Overview of Power System Harmonic Analysis
Harmonic power flow analysis
Objective: compute harmonic distortion levels for a given operating
condition
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
What is known for solving the problem
Fundamental frequency power flow results (I1 and q1).
Typical spectrum of harmonic sources (Ih-spc, qh-spc)
System Y(h) matrix, h=harmonic number
Current source model described earlier
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9. Harmonic power flow analysis
Chapter 1: An Overview of Power System Harmonic Analysis
Harmonic power flow analysis
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.
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10. Harmonic power flow analysis - other algorithms
Chapter 1: An Overview of Power System Harmonic Analysis
Harmonic power flow analysis - other algorithms
Time domain algorithm (e.g. EMTP simulation) or hybrid algorithm
Iterative algorithms (frequency domain)
F( [V1], [V2],...,[Vn], [I1], [I2], ..., [In],C) =0
Newton method
Harmonic iteration method (see the diagram below)
Bus voltages
Linear network
(including power
flow constraints)
Harmonic Source
(non-linear)
Current source
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11. New challenges Distributed harmonic sources
Chapter 1: An Overview of Power System Harmonic Analysis
New challenges
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
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12. New challenges 1 - distributed harmonic sources
Chapter 1: An Overview of Power System Harmonic Analysis
New challenges 1 - distributed harmonic sources
The harmonic-production characteristics of the sources will affect each other.
(attenuation and diversity effects)
Actual results
The harmonic sources may also vary randomly.
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13. Harmonic attenuation effect
Chapter 1: An Overview of Power System Harmonic Analysis
New challenges 1 - distributed harmonic sources
Harmonic attenuation effect
New harmonic analysis methods need to take into account the characteristics
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14. New challenges 2 - analysis of harmonic resonance
Chapter 1: An Overview of Power System Harmonic Analysis
New challenges 2 - analysis of harmonic resonance
· 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?
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15. New challenges 2 - analysis of harmonic resonance
Chapter 1: An Overview of Power System Harmonic Analysis
New challenges 2 - analysis of harmonic resonance XL XC V I
If this term = 0 => Resonance
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.
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16. New challenges 2 - analysis of harmonic resonance
Chapter 1: An Overview of Power System Harmonic Analysis
New challenges 2 - analysis of harmonic resonance
Eigen-decomposition
of the Y matrix:
Right
eigenvector
matrix
Left
eigenvector
matrix
Eigenvalue
matrix
[U]=[T][V] -- called modal voltage
[J] =[T][I] -- called modal current
[L] -- can be called modal Y matrix
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17. New challenges 2 - analysis of harmonic resonance
Chapter 1: An Overview of Power System Harmonic Analysis
New challenges 2 - analysis of harmonic resonance
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)
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18. New challenges 2 - analysis of harmonic resonance
Chapter 1: An Overview of Power System Harmonic Analysis
New challenges 2 - analysis of harmonic resonance
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
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19. New challenges 2 - analysis of harmonic resonance
Chapter 1: An Overview of Power System Harmonic Analysis
New challenges 2 - analysis of harmonic resonance
Participation of components
in a resonance
Participation of buses
in a resonance
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20. New challenges 3 - analysis of interharmonics
Chapter 1: An Overview of Power System Harmonic Analysis
New challenges 3 - analysis of interharmonics
Interharmonics produce flicker
Frequency of interharmonic varies with the drive operating condition
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21. New challenges 3 - analysis of interharmonics
Chapter 1: An Overview of Power System Harmonic Analysis
New challenges 3 - analysis of interharmonics
An interharmonic-producing drive cannot be modeled as an interharmonic current source
IDC2
Source
Motor
VDC2
Converter
Inverter
IAC2
60Hz
50Hz
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

22. New challenges 3 - analysis of interharmonics
Chapter 1: An Overview of Power System Harmonic Analysis
New challenges 3 - analysis of interharmonics
Sequence characteristics of interharmonics
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23. Chapter 1: An Overview of Power System Harmonic Analysis
Summary
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
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