Preface
The well-known and ever-present time-varying nature of waveform distortions in power
systems requires a comprehensive and precise analytical basis that needs to be incorporated in
the system studies and analyses. This time-varying behavior is due to continuous changes in
system configurations, linear load levels and operating modes of nonlinear load / equipment
present conceptual and practical challenges.
Figure 1 illustrates the nature of the problem by
indicating the possible methods to analyze waveform distortions, that is, connecting the time
domain to the frequency domain as a function of its time-varying condition. For example, for
steady-state waveforms Fourier analysis is sufficient, whereas the time-varying conditions
prevail spectral, probabilistic, evolutionary spectrum and time-frequency techniques are
required.
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Figure 1 – Time-Varying Distortions – Connecting Time and Frequency Domains
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This publication has been on the making for over three years and many people have
contributed to it. In the process the understanding we have evolved and agreed on a more
encompassing perspective of the subject. First we moved away from the strict “harmonic
distortion” definition to a “waveform distortion” deviation where the time varying nature (the
main challenge of the problem) can be dealt with frequency/spectral, time-frequency,
probabilistic, artificial/computational intelligence methods. Second, several new techniques
became available or were applied for the first time to power systems problems and this
prompted the contributors to seek better understanding and additional contributions.
What seemed a settled issue, that is, that harmonics are steady-state components and
the time-varying nature of waveforms could only analyzed by probabilistic methods applied to
short intervals rms averages of individual harmonic components, has now being revised. The
new signal processing methods based on time-frequency decomposition such as wavelet
transform and multi-rate filter methods presented here have allowed us much more precise
analyses of the behavior of time-varying waveform distortions and opened up new
opportunities for monitoring and investigating power systems phenomena.
The publication reviews the nature, analytical concepts, special situations and problems
associated with the time-varying nature of waveform distortions (harmonics), suggests
solutions and ways to more effectively deal with the problem.
The text covers time-varying varying harmonics produced by different sources from
single-phase appliances to Multi-Mega Watt power electronics converters. Also analytical
aspects related to background distortion, harmonic summation and harmonic impedance are
discussed. The time-varying and time-frequency aspects are considered in the establishment of
an integrated approach to deal with waveform distortions.
Figure 2 below illustrates the big-picture of how stationary, non-stationary and specialnon-stationary signals can be analyzed.
Propagating
Evolutionary Spectrum
Evolutionary Spectrum
Spectrogram
Multi-Resolution
Space-Time
Methods
Fourier Analysis
Fourier Transform
Hartley
Short-Term Fourier
Windowed Fourier
Music
Esprit
Kalman
Picture
Graph
PDF
Spectrum
Principal Component D.
Independent
Component
Blind Separation
High Order Statistics
Kalman
Garbor
Wavelet
S-Transform
Hilbert
Prony
Neural Nets
Fuzzy Logic
Fractals
Space-Time
Processing
Spectral
Time-Frequency
Statistical
Stationary Signals
Intelligent
Graphical
Non-Stationary Signals
Spatial
Non-Stationary Signals
I would like to acknowledge the invaluable contribution of all authors and in particular
to Yahia Bagzouz, Alfrdo Testa, Roberto Langella, and Tom Ortimyer, for helping with making
this publication more readable and useful to the power sector and in particular to those who
deal with harmonics and want to understand more clearly the mechanisms of generation and
ways analyze them and design systems more cost/performance effective systems. I also would
like to make a special mention to Dr. Robert Morrison who in the early eighties became one of
the foremost influential researchers in this subject and the use of probabilistic methods.
I would like to thank the Center for Advanced Power Systems at Florida State University, and
New Mexico State University for funding some of my time for preparing and editing the
chapters of this text.
Finally, I would like to thank my wife for her encouragement, support and resignation for
canceling some of our kayak trips to work on the demanding but enjoyable effort.