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This section presents new and advanced methods for characterizing time-varying waveform
distortions. While in the past probabilistic analysis was the most recommended technique, which
was based on the fact that harmonics could be only properly visualized as steady state
components, this section presents a number of techniques which bring greater insight to our
understanding of time-varying harmonic distortions.
Chapter 15 shows how wavelet multi-resolution analysis can be used to help in the visualization
and physical understanding of time-varying waveform distortions. The approach is then applied
to waveforms generated by high fidelity simulation using real time digital simulation on a
shipboard power system.
Chapter 16 utilizes wavelets to characterize several power quality deviation parameters such a as
harmonics, flicker, transients, and voltage sags, while Chapter 17 proposes the utilization of
fuzzy logic to analyze, compare, and diagnose time-varying harmonic distortion indices in a
power system.
Chapter 18 deals with a real time digital simulation as a new tool to model and simulate timevarying phenomena and which can include hardware in the loop for greater accuracy of studies.
In Chapter 19 the use of a statistical signal processing technique, known as Independent
Component Analysis for harmonic source identification and estimation is used. If the harmonic
currents are statistically independent, ICA is able to estimate the currents using a limited number
of harmonic voltage measurements and without any knowledge of the system admittances or
In Chapter 20 enhancements and modifications to the Hilbert-Huang method are presented for
signal processing applications in power systems. The rationale for the modifications is that the
original empirical mode decomposition (EMD) method is unable to separate modes with
instantaneous frequencies lying within one octave. The proposed modifications significantly
improves the resolution capabilities of the EMD method, in terms of detecting weak higher
frequency modes, as well as separating closely spaced modal frequencies.
In Chapter 21 reference is made to ideal supply conditions which allow recognising the
frequencies and the origins of those interharmonics which are generated by the interaction
between the rectifier and the inverter inside the ASD. Formulas to forecast the interharmonic
component frequencies are developed firstly for LCI drives and, then, for synchronous sinusoidal
PWM drives. Afterwards, a proper symbolism is proposed to make it possible to recognize the
interharmonic origins. Finally, numerical analyses, performed for both ASDs considered in a
wide range of output frequencies, give a comprehensive insight in the complex behaviour of
interharmonic component frequencies; also some characteristic aspects, such as the degeneration
in harmonics or the overlapping of an interharmonic couple of different origins, are described.
Although it is well known that Fourier analysis is in reality only accurately applicable to steady
state waveforms, it is a widely used tool to study and monitor time-varying signals, which are
commonplace in electrical power systems. The disadvantages of Fourier analysis, such as
frequency spillover or problems due to sampling (data window) truncation can often be
minimized by various windowing techniques. The last two chapters present two newly developed
methods which allows for overcoming the previous mentioned limitations in a more effective
way and allowing a greater understanding and characterization of time-varying waveforms.
Chapter 22 presents a method to separate the odd and the even harmonic components, until the
15th. It uses selected digital filters and down-sampling to obtain the equivalent band-pass filters
centered at each harmonic. After the signal is decomposed by the analysis bank, each harmonic
is reconstructed using a non-conventional synthesis bank structure. This structure is composed of
filters and up sampling that reconstructs each harmonic to its original sampling rate. This new
tool allows for a clear visualization of time-varying harmonics which can lead to better ways to
track harmonic distortion and understand time-dependent power quality parameters. It also has
the potential to assist with control and protection applications. While estimation technique is
concerned with the process used to extract useful information from the signal, such as amplitude,
phase and frequency; signal decomposition is concerned with the way that the original signal can
be split in other components, such as harmonic, inter-harmonics, sub-harmonics, etc..
Chapter 23 presents a time-varying harmonic decomposition using sliding-window Discrete
Fourier Transform. Despite the fact that the frequency response of the method is similar to the
Short Time Fourier Transform, with the same inherent limitation for asynchronous sampling rate
and interharmonic presence, the proposed implementation is very efficient and helpful to track
time-varying power harmonic. The new tool allows a clear visualization of time-varying
harmonics, which can lead to better ways of tracking harmonic distortion and understand timedependent power quality parameters.
It has also the potential to assist with control and
protection applications.
Chapter 24 describes a PLL (Phase-Locked Loop) based harmonic estimation system which
makes use of an analysis filter bank and multirate processing. The filter bank is composed of
bandpass adaptive filter. The initial center frequency of each filter is purposely chosen equal the
harmonic frequencies. The adaptation makes it possible to track time-varying frequencies as well
as inter-harmonic components. A down-sampler device follows the filtering stage reducing the
computational burden, specially, because an undersampling operation is realized.
Chapter 25 deals with Proni analysis which does not require prior knowledge of existing
It works by detecting frequencies, magnitudes, phases and especially damping
factors of exponential decaying or growing transient harmonics.