FUTURE ANALYSIS TOOLS FOR POWER QUALITY
P. F. Ribeiro, MBA, PhD, PE
Professor of EngineeringCalvin College
Engineering DepartmentGrand Rapids, Michigan
Motivation:
-growing utilization of SVCs, ASDs, FACTS devices, etc.-dynamics of distortion generation, propagation and interaction with the system
Requirements:
-more powerful techniques to analyze non-stationary distortions.
Analytical Advances:
-several techniques have been unfolded recently
Objectives:
-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 degreeAnonymous
-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.
The required oscillatory condition leads to sinusoids as the
building blocks (particularly for electrical power systems).
However wavelets do not need to be damped sinusoids.
Mathematically speaking, the wavelet transform or
decomposition of a function, f(t), with respect to a mother
wavelet, h(t), is:
dta
bthtf
abaWf
*
2
1 )(1
),(
I don’tget it...I’ll try later
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).
dwwhw
C
a
dadb
a
bth
abaWf
Ctf
h
h
2
2
)(1
1),(
1)(
Yes !
f t k Wf m n a g a nbnm
mm( ) ( , ) ( )
00
2 0 0 0
Alternatively, expressing the inverse wavelet transform in a discrete form, we have:
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 published.
-
Illustration of Flexibility
Original Waveform to be analyzed
2 Wavelet Components
Reconstruct function
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:
RULE 1: IF 'THD_VOLTAGE'<5%AND
RULE 2: IF 'THD_CURRENT'<5%AND
RULE 3: 'FUNDAMENTAL_VOLTAGE'<80%THEN
DISTURBANCE='VOLTAGE SAG'
Disturbance 2:
RULE 1: IF 'THD_VOLTAGE'<5%AND
RULE 2: IF 'THD_CURRENT'<5%AND
RULE 3: 'FUNDAMENTAL_VOLTAGE'<85%AND
RULE 4"FUNDAMENTAL _CURRENT>500%THEN
DISTURBANCE='MOTOR STARTING’
x1
x2
x3
y1
y2
Inputlayer
HiddenLayer
HiddenLayer
Outputlayer
Sum Int.
input 1
2
n
Output
threshold
Comparer
Desired answerx1 x2
y
w1w2
Weight Update Info
Weight x
Weight y
Aggrgate Error
Ideal Weight
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:
reproductionmutationcrossover.
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) systemswavelet theory / advanced Signal Processing neural networks genetic algorithms, etc
Conclusions
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 Waveforms
Spectral Analysis
Basic Classification of Disturbancesby Expert System
Load type 1 Load type 2 Cap. Switching
Wavelet Analysis
(non stationary distortions)(periodic distortions)
(periodic)(non stationary)
Genetic Algorithms
.............
Neural Network Trained to Identify
Periodic and Non-Periodic
Waveforms
Advanced Classification of Disturbances By Fuzzy System
Fuzzy Logic Neuro Net
(Trained by Neuro Net)