24-01-2010, 09:43 PM

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ARTIFICIAL INTELLIGENCE tECHNIQUES In POWERSYSTEMS

ABSTRACT

This paper reviews five artificial intelligence tools that are most applicable to engineering problems fuzzy logic, neural networks and genetic algorithms. Each of these tools will be outlined in the paper together with examples of their use in different branches of engineering.

INTRODUCTION

Artificial intelligence emerged as a computer science discipline in the mid 1950s. Since then, it has produced a number of powerful tools, many of which are of practical use in engineering to solve difficult problems normally requiring human intelligence. Three of these tools will be reviewed in this paper. They are: fuzzy logic, neural networks and genetic algorithms. All of these tools have been in existence for more than 30 years and have found applications in engineering. Recent examples of these applications will be given in the paper, which also presents some of the work at the Cardiff Knowledge-based Manufacturing center, a multi-million pound research and technology transfer center created to assist industry in the adoption of artificial intelligence in manufacturing.

A.I METHODS USED IN POWER SYSTEMS

1.FUZZY LOGIC,

2.NUERAL NETWORKS

3.GENETIC ALGORITHM

First our discussion starts with fuzzy logic.

FUZZY LOGIC

INTRODUCTION

Fuzzy logic has rapidly become one of the most successful of today's technologies for developing sophisticated control systems. The reason for which is very simple. Fuzzy logic addresses such applications perfectly as it resembles human decision making with an ability to generate precise solutions from certain or approximate information. It fills an important gap in engineering design methods left vacant by purely mathematical approaches (e.g. linear control design), and purely logic-based approaches (e.g. expert systems) in system design.

While other approaches require accurate equations to model real-world behaviors, fuzzy design can accommodate the ambiguities of real-world human language and logic. It provides both an intuitive method for describing systems in human terms and automates the conversion of those system specifications into effective models.

As the complexity of a system increases, it becomes more difficult and eventually impossible to make a precise statement about its behavior, eventually arriving at a point of complexity where the fuzzy logic method born in humans is the only way to get at the problem.

(Originally identified and set forth by Lotfi A. Zadeh, Ph.D., University of California, Berkeley)

Fuzzy logic is used in system control and analysis design, because it shortens the time for engineering development and sometimes, in the case of highly complex systems, is the only way to solve the problem.

The first applications of fuzzy theory were primarily industrial, such as process control for cement kilns. However, as the technology was further embraced, fuzzy logic was used in more useful applications. In 1987, the first fuzzy logic-controlled subway was opened in Sendai in northern Japan. Here, fuzzy-logic controllers make subway journeys more comfortable with smooth braking and acceleration. Best of all, all the driver has to do is push the start button! Fuzzy logic was also put to work in elevators to reduce waiting time. Since then the applications of Fuzzy Logic technology have virtually exploded, affecting things we use everyday.

HISTORY

The term "fuzzy" was first used by Dr. Lotfi Zadeh in the engineering journal, "Proceedings of the IRE," a leading engineering journal, in 1962. Dr. Zadeh became, in 1963, the Chairman of the Electrical Engineering department of the University of California at Berkeley.

The theory of fuzzy logic was discovered. Lotfi A. Zadeh, a professor of UC Berkeley in California, soon to be known as the founder of fuzzy logic observed that conventional computer logic was incapable of manipulating data representing subjective or vague human ideas such as "an attractive person" or "pretty hot". Fuzzy logic hence was designed to allow computers to determine the distinctions among data with shades of gray, similar to the process of human reasoning. In 1965, Zadeh published his seminal work "Fuzzy Sets" which described the mathematics of fuzzy set theory, and by extension fuzzy logic. This theory proposed making the membership function (or the values False and True) operate over the range of real numbers [0.0, 1.0]. Fuzzy logic was now introduced to the world.

Although, the technology was introduced in the United States, the scientist and researchers there ignored it mainly because of its unconventional name. They refused to take something, which sounded so child-like seriously. Some mathematicians argued that fuzzy logic was merely probability in disguise. Only stubborn scientists or ones who worked in discrete continued researching it.

While the US and certain parts of Europe ignored it, fuzzy logic was accepted with open arms in Japan, China and most Oriental countries. It may be surprising to some that the world's largest number of fuzzy researchers is in China with over 10,000 scientists. Japan, though currently positioned at the leading edge of fuzzy studies falls second in manpower, followed by Europe and the USA. Hence, it can be said that the popularity of fuzzy logic in the Orient reflects the fact that Oriental thinking more easily accepts the concept of "fuzziness". And because of this, the US, by some estimates, trail Japan by at least ten years in this forefront of modern technology.

UNDERSTANDING FUZZY LOGIC

Fuzzy logic is the way the human brain works, and we can mimic this in machines so they will perform somewhat like humans (not to be confused with Artificial Intelligence, where the goal is for machines to perform EXACTLY like humans). Fuzzy logic control and analysis systems may be electro-mechanical in nature, or concerned only with data, for example economic data, in all cases guided by "If-Then rules" stated in human language.

The Fuzzy Logic Method

The fuzzy logic analysis and control method is, therefore:

1. Receiving of one, or a large number, of measurement or other assessment of conditions existing in some system we wish to analyze or control.

2. Processing all these inputs according to human based, fuzzy "If-Then" rules, which can be expressed in plain language words, in combination with traditional non-fuzzy processing.

3. Averaging and weighting the resulting outputs from all the individual rules into one single output decision or signal which decides what to do or tells a controlled system what to do. The output signal eventually arrived at is a precise appearing, defuzzified, "crisp" value.

Fuzzy logic is a superset of conventional (Boolean) logic that has been extended to handle the concept of partial truth- truth-values between "completely true" and "completely false". As its name suggests, it is the logic underlying modes of reasoning which are approximate rather than exact. The importance of fuzzy logic derives from the fact that most modes of human reasoning and especially common sense reasoning are approximate in nature.

The essential characteristics of fuzzy logic as founded by Zadeh Lotfi are as follows.

Â¢ In fuzzy logic, exact reasoning is viewed as a limiting case of approximate reasoning.

Â¢ In fuzzy logic everything is a matter of degree.

Â¢ Any logical system can be fuzzified.

Â¢ In fuzzy logic, knowledge is interpreted as a collection of elastic or, equivalently, fuzzy constraint on a collection of variables

Â¢ Inference is viewed as a process of propagation of elastic constraints.

The third statement hence, defines Boolean logic as a subset of Fuzzy logic.

Professor Lofti Zadeh at the University of California formalized fuzzy Set Theory in 1965. What Zadeh proposed is very much a paradigm shift that first gained acceptance in the Far East and its successful application has ensured its adoption around the world.

A paradigm is a set of rules and regulations, which defines boundaries and tells us what to do to be successful in solving problems within these boundaries. For example the use of transistors instead of vacuum tubes is a paradigm shift - likewise the development of Fuzzy Set Theory from conventional bivalent set theory is a paradigm shift.

Bivalent Set Theory can be somewhat limiting if we wish to describe a 'humanistic' problem mathematically.

The whole concept can be illustrated with this example. Let's talk about people and "youthness". In this case the set S (the universe of discourse) is the set of people. A fuzzy subset YOUNG is also defined, which answers the question "to what degree is person x young?" To each person in the universe of discourse, we have to assign a degree of membership in the fuzzy subset YOUNG. The easiest way to do this is with a membership function based on the person's age.

Young (x) = {1, if age (x) <= 20,

(30-age (x))/10, if 20 < age (x) <= 30,

0, if age (x) > 30}

a graph of this looks like:

Given this definition, here are some example values:

Person Age degree of youth

--------------------------------------

Johan 10 1.00

Edwin 21 0.90

Parthiban 25 0.50

Arosha 26 0.40

Chin Wei 28 0.20

Rajkumar 83 0.00

So given this definition, we'd say that the degree of truth of the statement "Parthiban is YOUNG" is 0.50.

Fuzzy Rules

Human beings make decisions based on rules. Although, we may not be aware of it, all the decisions we make are all based on computer like if-then statements. If the weather is fine, then we may decide to go out. If the forecast says the weather will be bad today, but fine tomorrow, then we make a decision not to go today, and postpone it till tomorrow. Rules associate ideas and relate one event to another.

Fuzzy machines, which always tend to mimic the behavior of man, work the same way. However, the decision and the means of choosing that decision are replaced by fuzzy sets and the rules are replaced by fuzzy rules. Fuzzy rules also operate using a series of if-then statements. For instance, if X then A, if y then b, where A and B are all sets of X and Y. Fuzzy rules define fuzzy patches, which is the key idea in fuzzy logic.

A machine is made smarter using a concept designed by Bart Kosko called the Fuzzy Approximation Theorem (FAT). The FAT theorem generally states a finite number of patches can cover a curve as seen in the figure below. If the patches are large, then the rules are sloppy. If the patches are small then the rules are fine.

Fuzzy Patches

In a fuzzy system this simply means that all our rules can be seen as patches and the input and output of the machine can be associated together using these patches. Graphically, if the rule patches shrink, our fuzzy subset triangles get narrower. Simple enough? Yes, because even novices can build control systems that beat the best math models of control theory. Naturally, it is math-free system.

Fuzzy Control

Fuzzy control, which directly uses fuzzy rules, is the most important application in fuzzy theory. Using a procedure originated by Ebrahim Mamdani in the late 70s, three steps are taken to create a fuzzy controlled machine:

1) Fuzzification (Using membership functions to graphically describe a situation)

2) Rule evaluation (Application of fuzzy rules)

3) Defuzzification (Obtaining the crisp or actual results)

Block diagram of Fuzzy controller.

TERMS USED IN FUZZY LOGIC

Degree of Membership - The degree of membership is the placement in the transition from 0 to 1 of conditions within a fuzzy set. If a particular building's placement on the scale is a rating of .7 in its position in newness among new buildings, then we say its degree of membership in new buildings is .7.

Fuzzy Variable - Words like red, blue, etc., are fuzzy and can have many shades and tints. They are just human opinions, not based on precise measurement in angstroms. These words are fuzzy variables.

Linguistic Variable - Linguistic means relating to language, in our case plain language words.

Fuzzy Algorithm - An algorithm is a procedure, such as the steps in a computer program. A fuzzy algorithm, then, is a procedure, usually a computer program, made up of statements relating linguistic variables.

An example for a fuzzy logic system is provided at the end of the paper.

A Fuzzy Proportional controller

A Fuzzy PD controller

A Fuzzy PID controller

Time response of FPID controller.

These are some of the controllers used in engineering.

CONCLUSION

Fuzzy logic potentially has many applications in engineering where the domain knowledge is usually imprecise. Notable successes have been achieved in the area of process and machine control although other sectors have also benefited from this tool. Recent examples of engineering applications include:

1.controlling the height of the arc in a welding process

2. Controlling the rolling motion of an aircraft

3. Controlling a multi-fingered robot hand

4. Analyzing the chemical composition of minerals

5. Determining the optimal formation of manufacturing cells

6. Classifying discharge pulses in electrical discharge machining.

Fuzzy logic is not the wave of the future. It is now! There are already hundreds of millions of dollars of successful, fuzzy logic based commercial products, everything from self-focusing cameras to washing machines that adjust themselves according to how dirty the clothes are, automobile engine controls, anti-lock braking systems, color film developing systems, subway control systems and computer programs trading successfully in the financial markets.

NUERAL NETWORKS

INTRODUCTION

Like inductive learning programs, neural networks can capture domain knowledge from examples. However, they do not archive the acquired knowledge in an explicit form such as rules or decision trees and they can readily handle both continuous and discrete data. They also have a good generalization capability as with fuzzy expert systems.

UNDERSTANDING NUERAL NETWORKS

A neural network is a computational model of the brain. Neural network models usually assume that computation is distributed over several simple units called neurons, which are interconnected and operate in parallel (hence, neural networks are also called parallel-distributed-processing systems or connectionist systems).

The most popular neural network is the multi-layer perceptron, which is a feed forward network:

All signals flow in a single direction from the input to the output of the network. Feed forward networks can perform static mapping between an input space and an output space: the output at a given instant is a function only of the input at that instant.

Recurrent networks, where the outputs of some neurons are fed back to the same neurons or to neurons in layers before them, are said to have a dynamic memory: the output of such networks at a given instant reflects the current input as well as previous inputs and outputs.

Implicit Ëœknowledgeâ„¢ is built into a neural network by training it. Some neural networks can be trained by being presented with typical input patterns and the corresponding expected output patterns. The error between the actual and expected outputs is used to modify the strengths, or weights, of the connections between the neurons. This method of training is known as supervised training. In a multi-layer perceptron, the back-propagation algorithm for supervised training is often adopted to propagate the error from the output neurons and compute the weight modifications for the neurons in the hidden layers.

Some neural networks are trained in an unsupervised mode, where only the input patterns are provided during training and the networks learn automatically to cluster them in groups with similar features.

A neuro-fuzzy can be used to study both neural as well as fuzzy logic systems. A neural network can approximate a function, but it is impossible to interpret the result in terms of natural language. The fusion of neural networks and fuzzy logic in neuro fuzzy models provide learning as well as readability. Control engineers find this useful, because the models can be interpreted and supplemented by process operators.

Figure 1: Indirect adaptive control: The controller parameters are updated indirectly via a process model.

A neural network can model a dynamic plant by means of a nonlinear regression in the discrete time domain. The result is a network, with adjusted weights, which approximates the plant. It is a problem, though, that the knowledge is stored in an opaque fashion; the learning results in a (large) set of parameter values, almost impossible to interpret in words.

Conversely, a fuzzy rule base consists of readable if-then statements that are almost natural language, but it cannot learn the rules itself. The two are combined in neuro fuzzy in order to achieve readability and learning ability at the same time. The obtained rules may reveal insight into the data that generated the model, and for control purposes, they can be integrated with rules formulated by control experts (operators).

Assume the problem is to model a process such as in the indirect adaptive controller in Fig. 1. A mechanism is supposed to extract a model of the nonlinear process, depending on the current operating region. Given a model, a controller for that operating region is to be designed using, say, a pole placement design method. One approach is to build a two-layer perceptron network that models the plant, linearise it around the operating points, and adjust the model depending on the current state (NÃƒÂ¸rgaard, 1996). The problem seems well suited for the so-called Takagi-Sugeno type of neuro fuzzy model, because it is based on piecewise linearisation.

Extracting rules from data is a form of modeling activity within pattern recognition, data analysis or data mining also referred to as the search for structure in data.

TRIAL AND ERROR

The input space, that is, the coordinate system formed by the input variables (position, velocity, error, change in error) are partitioned into a number of regions. Each input variable is associated with a family of fuzzy term sets, say, â„¢negativeâ„¢, â„¢zeroâ„¢, and â„¢positiveâ„¢. The expert must then define the membership functions. For each valid combination of inputs, the expert is supposed to give typical values for the outputs.

The task for the expert is then to estimate the outputs. The design procedure would be

1. Select relevant input and output variables,

2. Determine the number of membership functions associated with each input and output, and

3. Design a collection of fuzzy rules.

Considering data given,

Figure 2: A fuzzy model approximation (solid line, top) of a data set (dashed line, top). The input space is divided into three fuzzy regions (bottom).

CLUSTERING

A better approach is to approximate the target function with a piece-wise linear function and interpolate, in some way, between the linear regions.

In the Takagi-Sugeno model (Takagi & Sugeno, 1985) the idea is that each rule in a rule base defines a region for a model, which can be linear. The left hand side of each rule defines a fuzzy validity region for the linear model on the right hand side. The inference mechanism interpolates smoothly between each local model to provide a global model. The general Takagi-Sugeno rule structure is

If f (e1is A1, e2 is A2, Â¦ Â¦,ek is Ak), then y=g(e1,e2,Â¦..)

Here f is a logical function that connects the sentences forming the condition, y is the output, and g is a function of the inputs e1. An example is

If error is positive and change in error is positive then

U=Kp (error + Td*change in error)

Where x is a controllerâ„¢s output, and the constants Kp and Td are the familiar tuning constants for a proportional-derivative (PD) controller. Another rule could specify a PD controller with different tuning settings, for another operating region. The inference mechanism is then able to interpolate between the two controllers in regions of overlap.

Figure 3: Interpolation between two lines (top) in the overlap of input sets (bottom).

FEATURE DETERMINATION

In general, data analysis (Zimmermann, 1993) concerns objects, which are described by features. A feature can be regarded as a pool of values from which the actual values appearing in a given column are drawn.

E.g.,

Some other techniques are HARD CLUSTERS ALGORITHM, FUZZY CLUSTERS ALGORITHM, SUBTRACTIVE ALGORITHM, and NEURO FUZZY APPROXIMATION, ADAPTIVE NEURO FUZZY INFERENCE SYSTEM.

Above is an example of clusters.

CONCLUSION

Thus, better system modeling can be obtained by using neuro fuzzy modeling as seen above, as resultant system occupies a vantage point above both neural and fuzzy logic systems.

GENETIC ALGORITHM

A problem with back propagation and least squares optimization is that they can be trapped in a local minimum of a nonlinear objective function, because they are derivative based. Genetic algorithm-survival of the fittest! -Are derivative-free, stochastic optimization methods, and therefore less likely to get trapped. They can be used to optimize both structure and parameters in neural networks. A special application for them is to determine fuzzy membership functions. A genetic algorithm mimics the evolution of populations. First, different possible solutions to a problem are generated. They are tested for their performance, that is, how good a solution they provide. A fraction of the good solutions is selected, and the others are eliminated (survival of the fittest). Then the selected solutions undergo the processes of reproduction, crossover, and mutation to create a new generation of possible solutions, which is expected to perform better than the previous generation. Finally, production and evaluation of new generations is repeated until convergence. Such an algorithm searches for a solution from a broad spectrum of possible solutions, rather than where the results would normally be expected. The penalty is computational intensity. The elements of a genetic algorithm are explained next (Jang et al., 1997).

1.Encoding. The parameter set of the problem is encoded into a bit string representation.

For instance, a point (x, y)=(11,6) can be represented as a chromosome which is a concatenated bit string

1 0 1 1 0 1 1 0

Each coordinate value is a gene of four bits. Other encoding schemes can be used, and arrangements can be made for encoding negative and floating-point numbers.

2.Fitness evaluation. After creating a population the fitness value of each member is calculated.

3.Selection. The algorithm selects which parents should participate in producing off springs for the next generation. Usually the probability of selection for a member is proportional to its fitness value.

4.Crossover. Crossover operators generate new chromosomes that hopefully retain good features from the previous generation. Crossover is usually applied to selected pairs of parents with a probability equal to a given crossover rate. In one-point crossover a crossover point on the genetic code is selected at random and two parent chromosomes interchange their bit strings to the right of this point.

5.Mutation. A mutation operator can spontaneously create new chromosomes. The most common way is to flip a bit with a probability equal to a very low, given mutation rate.

The mutation prevents the population from converging towards a local minimum. The mutation rate is low in order to preserve good chromosomes.

ALGORITHM

An example of a simple genetic algorithm for a maximization problem is the following.

1. Initialize the population with randomly generated individuals and evaluate the fitness of each individual.

(a) Select two members from the population with probabilities proportional to their fitness values.

(b) Apply crossover with a probability equal to the crossover rate.

© Apply mutation with a probability equal to the mutation rate.

(d) Repeat (a) to (d) until enough members are generated to form the next generation.

3. Repeat steps 2 and 3 until a stopping criterion is met.

If the mutation rate is high (above 0.1), the performance of the algorithm will be as bad as a primitive random search.

CONCLUSION

This is how genetic algorithm method of analysis is used in power systems.

These are the various Artificial Intelligence techniques used in power systems.

CONCLUSION

Over the past 40 years, artificial intelligence has produced a number of powerful tools. This paper has reviewed five of those tools, namely fuzzy logic, neural networks and genetic algorithms. Applications of the tools in engineering have become more widespread due to the power and affordability of present-day computers. It is anticipated that many new engineering applications will emerge and that, for demanding tasks, greater use will be made of hybrid tools combining the strengths of two or more of the tools reviewed. Other technological developments in artificial intelligence that will have an impact in engineering include data mining, or the extraction of information and knowledge from large databases and multi-agent systems, or distributed self-organizing systems employing entities that function autonomously in an unpredictable environment concurrently with other entities and processes. This paper is an effort to give an insight into the ocean that is the field of Artificial Intelligence.

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thesis.lib/cycu

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