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

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.

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

Scaled and Translated Wavelets

The Mother Wavelet

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:

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 published.

-

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:

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)