1. FUTURE ANALYSIS TOOLS FOR POWER QUALITY P. F. Ribeiro, MBA, PhD, PE Professor of Engineering Calvin College Engineering Department Grand Rapids, Michigan

2. 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.

3. A Complex World: A Philosophical Reflection T hese 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

4. 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 Anonymous

5. Wavelet Theory Expert (Fuzzy) Systems Genetic Algorithms Neural Network

6. - 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

7. -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: I don’t get it... I’ll try later

8. Scaled and Translated Wavelets The Mother Wavelet

9. 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 !

10. Alternatively, expressing the inverse wavelet transform in a discrete form, we have:

11. The Wavelet Transform

12. 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. -

13. Illustration of Flexibility Original Waveform to be analyzed 2 Wavelet Components Reconstruct function

14. Impulsive Transient Commutation Notches

15. 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 Application s -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

16. 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.

17. 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.

18. 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.

19. 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’

21. 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: reproduction mutation crossover. After crossover, using randomly selected mates, and applying the same fitness principle, the desired objective is achieved. GODO x GDOD = GOOD or GODO

22. 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.

23. 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

24. 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.