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     P. F. Ribeiro, MBA, PhD, PE
        Professor of Engineering
             Calvin College
        Engineering Department
        Grand Rapids, Michigan
-growing utilization of SVCs, ASDs, FACTS devices, etc.
-dynamics of distortion generation, propagation and interaction
 with the system

-more powerful techniques to analyze non-stationary distortions.

Analytical Advances:
-several techniques have been unfolded recently

-to present the basic concepts for some of these new tools
-to investigate the potential for its application in power system
 distortion analysis.
A Complex World:
A Philosophical Reflection

These things are so delicate and numerous that it takes a
sense of great delicacy and precision to perceive them and
judge them correctly and accurately: Most often it is not
possible to set it out logically as in mathematics, because
the necessary principles are not ready to hand, and it
would be an endless task to undertake. The thing must be
seen all at once, at a glance, and not as a result of
progressive reasoning, at least up to a point.

Blaise Pascal, 1650
A Complex World:
A Philosophical Reflection

Because we have to use numbers so much we tend to
think of every process as if it must be like the numeral
series, where every step, to all eternity, is the same kind
of step as the one before. There are progressions in
which the last step is 'sui generis' - incommensurable
with the others - and in which to go the whole way is to
undo all the labor of your previous journey.
C.S. Lewis, 1955

Everything is a matter of degree
Wavelet Theory

Expert (Fuzzy) Systems

Genetic Algorithms

Neural Network
-Limitations of The Classical Spectral Analysis

-Fourier Analysis inadequate for dealing with transient distortions
-works for periodic function
-difficulties dealing with non-stationary distortions.
-works around the first problem by windowing the input signal so that
 sampled values converge to zero at the endpoints.

-Window Functions

-disadvantage: window is fixed
-it does not treat all frequency components in the same way

-need for a flexible time-frequency window that would adjust
 automatically for low or high frequencies
-The Wavelet Theory

Wavelet theory is the mathematics associated with building a
model for a signal with a set of special signals, or small waves,
called wavelets. They must be oscillatory and have
amplitudes which quickly decay to zero.
                                                                    I don’t
The required oscillatory condition leads to sinusoids as the        get it...
building blocks (particularly for electrical power systems).        I’ll try
However wavelets do not need to be damped sinusoids.                later

Mathematically speaking, the wavelet transform or
decomposition of a function, f(t), with respect to a mother
wavelet, h(t), is:

                       1                  t b
 Wf (a, b)                      f (t )h     dt

                                           a 
                      a   2
  The Mother Wavelet

Scaled and Translated Wavelets
The inverse transform creates the original function by summing
appropriately weighted, scaled and translated versions of the
mother wavelet, as indicated by the following equation .
The weights are the wavelet coefficients, Wf(a,b).

                                                         Yes !
         1                 1        t  b  dadb
f (t ) 
         Ch    Wf (a, b) a      h
                                    a  a
                                            2

Ch  
           h( w) dw
   Alternatively, expressing the inverse wavelet
   transform in a discrete form, we have:

                                     m
f (t )  k     Wf
             m 0 n  0
                          ( m, n )   a  2 0 g ( a m 0    nb0 )
The Wavelet Transform
Wavelets were originally derived to
analyze seismic signals in petroleum
research. At present they are used in
image processing and analysis, and in
sound (speech or music) analysis.

Although the idea of utilizing wavelets for
power systems applications has been
proposed, no results have yet been
                                   Illustration of Flexibility

Original Waveform to be analyzed

          2 Wavelet Components

          Reconstruct function
Impulsive Transient

Commutation Notches
Wavelets in Power Systems?
Same principle:
establishing libraries of waveforms which would fit a certain type of
disturbance or transient. These libraries equipped with fast
numerical algorithms can enable real-time implementation of a variety
of signal processing tasks.

This characterization of the signal provides efficient superposition in
terms of oscillatory modes on different time scales .

Power Systems Applications
-Transient Analysis
-Non-stationary Voltage Distortions
-Power Signature Recognition
-Signal/System Identification
-Non-Invasive Testing/Measurements
-Power System Analysis in General
-Integrated characterization of voltage
 disturbances, e.g. transients and harmonic distortions
Expert Systems

Expert systems are computer systems implemented by methods
and techniques for constructing human-machine systems with
specialized problem-solving expertise.

The rules usually take the form of "IF .... THEN ..." statements
which can be chained together to form a conclusion from the
data. The main drawback with expert systems is that the rules
of inference must be collected from a human expert and
converted to an acceptable form.

Fuzzy Systems
Fuzzy systems are a type of expert system but with fuzzy rules.
Neural Networks

Neural networks consist of a number of very simple and highly
interconnected processors called neurodes, which are the
analogs of the biological neural cells, or neurons, in the brain.
The neurodes are connected by a large number of weighted
links, over which signals can pass.

As a pattern classifier neural networks can be used for a
number of PQ applications, such as waveform classification,
system identification, etc. Recently neural nets have been
used for waveform classification, and identification of
harmonic sources where sufficient direct measurement data

are not available.
Expert Systems Plus Neural Networks

The combination of expert systems and
neural networks for power quality analysis
capitalizes on the strengths of both
methods and minimize the drawbacks.
Disturbance 1:


Disturbance 2:


x2                                                                                                                     y1

x3                                                                                                                     y2

      Input                                                                                   Output
      layer                                                                                   layer
                              Hidden                      Hidden
                              Layer                       Layer

                   in p u t 1                                 O u tp u t

                                      Sum             In t.

                      n                 th re sh o ld

                              D e sire d a n sw e r                   A g g rg a te E rro r
 x1                x2

                                Co mp a re r

              W e ig h t U p d a te In fo                                                                           W e ig h t y

                                                                    W e ig h t x              Id e a l W e ig h t
Evolutionary Systems - Genetic Algorithms

A GA (genetic algorithm) provides an efficient method of
searching through a wide range of possibilities. Simple GAs
use three key operators to explore their search space:


After crossover, using randomly selected mates, and applying the
same fitness principle, the desired objective is achieved.

 GODO x            GDOD = GOOD or              GODO
Neural Networks plus Genetic Algorithms

It may not be obvious how genetic algorithms
can be combined with neural networks to make
evolutionary networks. In fact, however, the
process is simple. The genetic code of a
network is specified by weights between layers.
These weights can be stored in an ordered
array that acts just like the genetic codes.

In complex power quality situations / problems
that are difficult for a neural network to learn,
there may be a real potential for evolutionary
systems to improve the speed of training.
Developing a Comprehensive PQ
Waveform Identification System

An integrated way to develop a comprehensive
PQ identification waveform identification
system would utilize a combination of:

expert (fuzzy) systems
wavelet theory / advanced Signal Processing
neural networks
genetic algorithms, etc
The acceptance of the new tools
 will take time, due to the computational
requirements and educational barriers.

The flexibility and adaptability of these new
techniques indicate that they will become
part of the tools for solving power quality
problems in this increasingly complex
electrical environment.
                                    Input Wavef orms

       (periodic distortions)                           (non stationary distortions)

                Spectral Analysis                         Wavelet Analysis

(non stationary)                                                             (periodic)

                         Basic Classif ication of Disturbances
                                   by E  xpert System

                         Advanced Classif ication of Disturbances
                                  B y F u zzy S ys te m
                                (T ra in e d b y N e u ro N e t)

                       Neural Netw ork Trained to Identif y
                            Periodic and Non-Periodic
                                      Wavef orms

                                   Genetic Algorithms

                           Fuzzy Logic                   Neuro Net

 Load type 1             Load type 2                  Cap. Sw itching        .............