APPLICATION OF ARTIFICIAL INTELLIGENCE TECHNIQUES IN POWER SYSTEMS

by

Sukumar Kamalasadan (ETA987083)

Special Study Report

Advisor Dr. D. Thukaram

Electric Power Systems Management, Energy Program, SERD, Asian Institute of Technology, Bangkok, Thailand November 1998

Application of Artificial Intelligence techniques in Power System

ABSTRACT A reliable, continuos supply of electrical energy is essential for the functioning of today's modern complex and advanced society. Electricity is one of the prime factors for the growth and determines the value of the society. Manual calculation, technical analysis and conclusions initially adopted the power system design, operation and control. As the power system grew it became more complex due to the technical advancements, variety and dynamic requirements. Conventional Power System analysis become more difficult due to 1. Complex versatile and large amounts of data that are used in calculation, diagnosis and learning. 2. The increase in the computational time period and the accuracy due to extensive system data handling. The modern power system operates close to their limits due to the increasing energy consumption and impediments of various kinds, and the extension of existing electric transmission networks. This situation requires a significantly less conservative power system operation and control regime which, in turn, is possible only by monitoring the system states in much more detail than was necessary previously. Sophisticated computer tools have become predominant in solving the difficult problems that arise in the areas of Power System planning, operation, diagnosis and design of the systems. Among these computer tools Artificial Intelligence has grown extensively in recent years and has been applied in the areas of the power systems. The most widely used and important ones of Artificial Intelligent tools, applied in the field of Electrical Power Systems are the Artificial Neural networks and the so-called Fuzzy systems. This special study gives a review of the Artificial Intelligence (Both artificial Neural Network and Fuzzy systems) basic principles and the concepts, along with the application of these tools in the power systems areas. A survey of the applications of ANN and Fuzzy systems in the field of power systems is complied and presented and the details of the important application are discussed. Finally the major achievements of this soft computing technique in power system areas are commented and the future scopes of these methods in the modern power system are analyzed.

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Table of Contents

Chapter

Title

Pag e

Title Page Table of Contents Abstract List of Figures 1 Introduction 1.1 Back Ground 1.2 Neural network and its application 1.3 Fuzzy sets/logic and its application 1.4 Structure of the Study 2 Artificial Neural Network 2.1 Definition of the Neural Network 2.2 Fundamentals of artificial Neural Network 2.3 Neural Network Design 2.4 Learning, Recall and Memory in ANN 2.5 When and why using Neural Network 2.6 An Overview of the well known ANN Models Fuzzy Logic and Fuzzy Systems 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 4 Importance of Fuzzy Systems Basic Concepts Fuzzy Sets and Rules Classical Operations of Fuzzy Sets Membership function and membership values Fuzzy Relations Properties of Fuzzy Sets Fuzzy Truth Value Learning in Fuzzy Systems Fuzzy Logic Controllers (FLC) Pattern Recognition in Fuzzy Systems Relational Data Adaptivity features and Adaptive Controllers

i,ii iii iv 1 1 1 2 2 4 4 4 5 6 8 9 17 17 17 18 18 19 19 19 20 20 21 21 22 23 24

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4.1

Introduction on ANN application

24 25 25 26 27 30 31 31 32 32 33 34 34 34 34 38 38 40 40 41 41 42 44 44 44 44 45 45 45 45 46 46 46 48 49

4.2 Major Applications 4.2.1 Power System Stabilizer 4.2.2 Load Forecasting 4.2.3 Fault Diagnosis 4.2.4 Security Assessment 4.2.5 State Estimation 4.2.6 Contingency Screening 4.2.7 Voltage Stability Assessment 4.2.8 Protection 4.2.9 Load Modeling 5 Application of Fuzzy Logic in the Power System 5.1 Introduction onFuzzy logic application 5.2 Major applications 5.2.1 Reactive Power Control 5.2.2 Transient Stability 5.2.3 Generator Operation and Control 5.2.4 State Estimation 5.2.5 Security Assessment 5.2.6 Fault Diagnosis and Restoration 5.2.7 Load Forecasting 5.2.8 Voltage Stability Enhancement 6 Analysis of the Techniques 6.1 Neural Network based Application 6.1.1 Design of Network 6.1.2 Training Set Generation 6.1.3 Hopfield Network 6.1.4 Training the Inputs 6.1.5 Knowledge Consistency and Interaction with the User 6.1.6 Practical Implementation 6.2 Fuzzy Logic based Application 6.2.1 Requirements of Fuzzy based Application 6.2.2 Advantages of Fuzzy Logic Application Conclusion Bibliography

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List of Figures Figure 2.1 Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5 Figure 2.6 Figure 3.1 Figure 3.2 Figure 3.3 Figure 4.1 Figure 4.2 Figure 4.3 Figure 5.1 Schematic Diagram of the Neuron Ways of Implementing a Solution to a Specific Problem Overview of the Main ANN models Three Layer Feedforward Neural Network Back Propagation Algorithm/Network Typical RBF Network Truth Values in Fuzzy Logic The Characterization of Pattern Recognition An Adaptive Fuzzy Controller Modular Neural Network Feedforward Architecture Unsupervised/Supervised forecasting Fault Diagnosis process Procedure Adopted for Load 4 9 10 11 13 14 20 22 23 26 28 29 36

The membership function of controlling ability of controlling devices The membership function of Voltage violation Level Computation Procedure for the solution for Voltage Profile Enhancement

Figure 5.2 Figure 5.3

37 37

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CHAPTER 1 INTRODUCTION 1.1 Back Ground The increasing prominence of the computers has led to a new way of looking at the world. Artificial Neural Networks (referred as ANN here on) and the Fuzzy logic (systems) that are considered as the so called soft computing methods are now a days becoming predominant tools in the area of Artificial Intelligence linked application oriented methods. The Neural network theory was first adopted in 1940 where the starting point was the learning law proposed by ITEBB in 1949, which demonstrated how neurons could exhibit learning behavior. The application further waxed and waned away because of the lack of powerful technological advancement. The resurgence occurred recently due to the new methods that are emerging as well as the computational power suitable for simulation of interconnected neural networks. Further to the technological advancement in the field of ANN, researchers were attracted on their important applications where logical and relational thinking is required. Among the major applications viz., robotics, analysis, optimal control, database, learning, signal processing, semiconductors, Power system related applications became a useful tool for the online researchers in this field. Fuzzy Systems or logic’s as introduced by Zadeh [LAZ 65] in 1965 has basically introduced to solve inexact and vague concepts by relating those using multi-valued ness in a logical way. Earlier research in this field was based on mathematical understanding of set theory and probability. Further as a part of developing it as mathematics the applications of these theories were considered in different areas. The application of fuzzy systems were mainly in the field of modal interface, speech recognition, functional reasoning hybrid application along with Neural nets, information, traction control, business other than in almost all the areas of the power systems. 1.2 Neural Network and its Applications ANN is biologically inspired and represented as a major extension of computation. They embody computational paradigms, based on biological metaphor, to mimic the computations of the brain [VVR 93]. The improved understanding of the functioning of neuron and the pattern of its interconnection has enabled researchers to produce the necessary mathematical modes for testing their theories and developing practical applications. Main applications of the ANN’s can be divided into two principal streams. First stream among this is concerned with modeling the brain and thereby explains its cognitive behavior. The primary aim of researchers in the second stream is to construct useful ‘computers’ for real world problems of classification or Pattern Recognition by drawing on these principles. The application of ANN's in the power systems belongs to this category and is one of the recent interesting topics in the Power System Engineering.

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1.3 Fuzzy sets / logic and its Applications Fuzzy set theory systems provide tools for representing and manipulating inexact concepts and the ambiguity prevalent in the human interpretations and thought process. This theory devices from the fact that almost all natural classes and concepts are fuzzy rather than crisp in nature. They are model free systems, in which all things are matters of degree. Fuzzy logic is a logical system for formalization of approximate reasoning, and is used synonymously with fuzzy set theory. It can be considered as super set of classical (Boolean) logic which users multiple truth-values to handle the concepts of partial truth. They provide an excellent framework to more completely and effectively model uncertainty and the imperious in human reasoning with the use of linguistic variables with membership functions. Fuzzification offers superior expressive power, greater generality and an improved capability to model complex problems at a low solution cost. Due to these reasons, the use of Fuzzy logic / set is increasing in the power systems problems, as it is in all intelligent processing. Many promising applications have been reported in the broad fields of system control, optimization, diagnosis, information processing, decision support, system analysis and planning. 1.4 Structure of the Study This study reviews basics of both ANN and fuzzy logic along with the recent works reported on these tools, in the field of power systems. Since the literatures covering the wide range of topics are extensive, the main consideration is to the important works in the different field of power systems. The purpose of this study is to focus attention on the most significant works as a part of the application of AI in power systems involving typical power systems problems. Subsequently critical evaluations and the potential and scope of further areas of work in the related fields are summarized for the benefit of the researchers interested in these areas. Basic concepts of Neural network including the learning features are explained in the Chapter two. The structure of the Neural network, its design and construction were discussed. The training of ANN, the purpose and use of the ANN were further detailed. Moreover an overview of the well-known ANN models and the comparison between them highlighting the main advantages is reviewed. The concept of Fuzzy Rules and systems, the importance and the technical details are discussed the Chapter three. The basic rules, the properties and definitions of this theory are and the operations are seen. Moreover Pattern Recognition technique, the concept of the socalled Fuzzy Logic Controllers (FLC), and the adaptive features of Fuzzy Sets are analyzed. Chapter four mainly deals with the application of ANN in the field of Power Systems. The various research works on ANN application in the various areas in the Power Systems were reviewed. The basic ANN applications mainly cover the areas like control, forecast, Diagnosis, Assessment, Screening, Modeling.

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Similar in line, Chapter four details the application of Fuzzy Logic’s in Power Systems. Main applications cover Stability Control, Diagnosis, Assessment, Forecasting, Planning and Estimation. Further the analysis of these techniques is done in chapter six with a view to importance of various applications and the further scope of research. Concluding the Strengths of these techniques and the abilities are illustrated.

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CHAPTER 2 ARTIFICIAL NEURAL NETWORK 2.1 Definition of the Neural Network Neural networks are systems that typically consist of a large number of simples processing units, called Neurons. A neuron has generally a high-dimensional Input vector and one single output signal. This output signal is usually a non-linear function of the input vector and a weight vector. The function to be performed on the Input vector is hence defined by the non-linear function and the weight vector of the neuron. The weight vector is adjusted in a training phase by using a large set of examples and the learning rate. The learning rule adapts the weight of all neurons in networks in order to learn an underlying relation in the training example. 2.2 Fundamentals of a Artificial Neural Network Elementary processing unit of ANN’s is neuron. Generally it contains several inputs but has only one output. The main differences between various existing models of ANN are mainly in their architectures or the way their basic processing elements (neurons) are interconnected. As basic element the neurons are not powerful but their interconnections allow encoding relationship between variables of the problems to which it is applied and providing very powerful processing capabilities.

Incoming Weighted Connections

Neuron

Output = F ( Σ Inputs ) Outgoing Weighted Connections

Figure 2.1 Schematic Diagram of the Neuron General model of the processing unit of ANN can be considered to have the following three elements. Weighted Summing Unit The weighted summing unit consists of external or internal inputs (Xi (x1, x2, x3… xn)) times the corresponding weights Wij = (wi1, wi2,……. win). The fixed weighted inputs may be either from the previous layers of ANN or from the output of neurons. If these inputs are derived from neuron outputs, it forms the feedback architecture it has feedforward architecture.

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Linear Dynamical Function It is essentially a single input or single output function block. This block may exist for time varying signals and introduces a function that is an integral, a proportional, a time delay or a combination of these. Example: Following two general functions can be used to relate input Pi with output Qi as (a1,a2)Qi (t) = Pi (t) Qi (t) = Pi (t-T) Non linear function This decides the firing of neuron for a given input values. It is a static nonlinear function which may be pulse type or step type, differentiable (smooth) or non-identification (sharp) and having positive mean or zero mean. Some of the examples of such functions are threshold, sigmoid, Tan hyperbolic or Gaussian functions. Different characteristics of neurons can be evolved using different type and combination of the above three of its basic components. 1. Perception models consist of weighted summing unit having no feedback inputs, no dynamic function and signal as non-linear function. 2. Feedback or dynamic networks utilize the dynamic function block. 2.3 Neural Network Design A neural network element is a smallest processing unit of the whole network essentially forming a weighted sum and transforming it by the activation function to obtain the output. In order to gain sufficient computing power, several neurons are interconnected together. The manner in which actually the neurons are connected together depends on the different classes of the neural networks. Basically neurons are arranged in layers. ANNs have parallel distributed architecture with a large number of nodes and connections. 2.3.1 ANN Architecture Construction of neural Network involves the following tasks. (i) Determination of network topology (ii) Determination of system (activation & synaptic) dynamics Determination of the Network Topology The topology of the neural network refers to its framework as well as its interconnection scheme. The number of layers and the number of nodes per layer often specify the framework. The types of layer include Input Layer where the nodes are called input units, which do not process information but distribute information to other units. Hidden Layer(s) where the nodes are called hidden units, which are not directly observable. They provide into the networks the capability to map or classify nonlinear problems. The Output Layer where the nodes are called output units, which encode possible concepts (or values) to be assigned to the instance under consideration. For example each output unit represents a class of objects. Other main important concept is the weightage for the connected unit. It can be real or integer numbers. They can be confined to a range and are adjustable during network training. When training is completed, all of them attain fixed values.

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Determination of Systems (Activation & Synaptic) Dynamics The dynamics of the network determines its operation. ANN’s can be trainable nonlinear dynamical systems. Neural dynamics consists of two parts one which corresponding to the dynamics of activation states and the other corresponding to the dynamics of synaptic weights. The activation dynamics determines the time evolution of the neural activation’s. Synaptic activation determines the change in the synaptic weights. The synaptic weights form Long Term Memory (LTM) where as the activation's state forms Short Term Memory (STM) of the network. Synaptic weights change gradually, whereas the neuron's activation's fluctuate rapidly. Therefore, while computing the activation dynamics, the system weights are assumed to be constant. The synaptic dynamics dictates the learning process. 2.4 Learning, Recall and Memory in ANN Learning in a neural network essentially consists of modifying in some systematic manner the interconnection strengths between the neural units. This is achieved by observing the system in question to see how the process evolves with time or in response to additional external actions. The development of any ANN involves two phases: Learning or Training phase and Recall or testing phase. ANN uses memory to learn and adapt. Memory, in ANN, is in form of values of weights of the interconnecting links. The memory in ANN can be a Content Addressable Memory (CAM), where it stores the data at stable state in memory (or weight) matrix W or an Associate Memory which provides output response from input stimuli. The mechanism for learning alters the weights associated with the various interconnections and thus leads to a modification in the strength of interconnection. Training patterns with examples carried out training in the network. Once the network has learnt the problem, it may be presented with new unknown patterns and its efficiency can be checked. This is called testing phase. Learning methods can be classified into two categories Supervised learning Unsupervised learning Supervised learning is the process that incorporates an external guidance. In the supervised learning, a training pair consists of an input vector and a desired target vector. The difference constitutes an error that is used to modify network weights in a manner that reduces the error in subsequent training cycles. These techniques include deciding, when to turn off the learning, how long and how often to present each association for training and supplying performance error information. Supervised learning is further classified as Structural learning / Temporal learning. Structural learning encodes the proper auto associate (single pattern vector) or heteroassociate vector of patterns pair mapping into weight matrix W. Temporal learning encodes a sequence of patterns necessary to achieve final outcome.

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In the Unsupervised learning no target vector exists. The input vector is applied to the network and the system “self organizes” so that a consistent output (possibly unpredicted before training) is produced. During the training phase the weights of ANN stabilize and while testing for an unknown pattern gives the output without a time-delay of learning phase. The recall or testing depends on the interconnection of the network. In feedforward network, the network provides output in just one pass and allows flow of signal in only one direction from input to hidden and to output layers. In feedback network, signals can flow amongst neurons in either direction and /or recursively. Some of the most popularly used rules for learning includes Hebb's rule and Delta rule for single layer (perception) ANN, Backpropagation algorithm for multilayer (perception) ANN. Thus its architecture, its processing algorithm and its learning algorithm characterize a neural network. The architecture specifies the way the neurons are connected. The processing algorithm specifies how the neural network with a given set of weights calculates the output vector for any input vector. The learning algorithm specifies how the network adapts its weights for all given vectors. 2.4.1 Learning Tasks The choice of a particular learning procedure is very much influenced by the learning task, which a neural network is required to perform. Some of the learning tasks that benefit the use of neural networks are as follows. a) Approximation Suppose a nonlinear input/output mapping is given described by the functional relationship d = g(x) where x is the input vector and the scalar d is the output. The function g(x ) is assumed to be unknown. The requirement is to design a neural network that approximates the non-linear function g(x), given a set of the input/output pairs (x1,d1),(x2,d2)….(xn ,dn). The approximation problem is the main example for supervised learning. The supervised learning can also be viewed as functional mapping problem. b) Pattern Classification In the pattern classification there are fixed number of categories into which activation's are classified. To resolve this activation classification neural network undergoes training. In the training the network is repeatedly presented a set of patterns along with the categories where the pattern belongs. After that a new pattern is presented to the network, which is new but belongs to the same kind of the patterns used in the network. Further to that the neural network has to classify this new pattern correctly. The advantage of using the neural network to perform pattern classification is that ANN can construct non-linear decision boundaries between the different classes in a nonparametric fashion and thereby offer a practical method of solving otherwise highly complex pattern classification problems. The pattern recognition can be classified as a supervised learning problem. There is also the unsupervised learning in pattern classification, especially

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when there is no prior knowledge of the categories into which the activation patterns are to be classified. Here unsupervised learning is used to perform the role of adaptive feature extraction or clustering prior to Pattern Recognition. c) Prediction Prediction is most basic task. It’s a signal processing problem, where in the set of m past samples that are uniformly spaced in time, are used to predict the present sample x (n). Sample x (n) serves the purpose of the desired response. Based on the previous samples x (n-1), x (n-2), ….. x(n-m) , we may compute the prediction error e(n) = x(n) - x(n | n-1,…. N-m) and thus the error-correction learning is used to modify the weights of the network. Prediction may be viewed as the form of the model building in the sense that smaller the prediction error in a statistical sense the better will the network serve as the physical model of the underlying stochastic process responsible for the generation of the time-series. When the process is of nonlinear in nature then the use of ANN provides a powerful method for solving the prediction problem by virtue of the non-linear processing units built into its construction. d) Association The two types of associations are Auto association and Hetero association. In auto association a neural network is required to store a set of patterns by repeatedly presenting them to the network. Also network is presented a partial and distorted version of an original pattern stored in it. Now the network is asked to recall that particular pattern. Hetero Association differs from Auto association in that an arbitrary set of input patterns are paired with another arbitrary set of output patterns, Auto association involves the use of unsupervised learning whereas the type of learning involved in hetero-association is of a supervised nature. The main difference between different classes of the network can be based on the learning approach. The main type of learning can be supervised and unsupervised learning. Supervised learning is done through a set of examples where each example consists of the input values and target output values. These output values are then used as a basis for the correction of the weights. The single layer feed-forward net and the Backpropagation nets use supervised learning Unsupervised learning has a set of examples where the input conditions are known but the associated target output conditions are not given. The task of the neural net is to group the set of training vectors into clusters based on some kind of similarities. However when simulated with a particular input, it is not known beforehand to which cluster the output obtained from the net belongs. In some of the cases the number of clusters or their diameter is determined before training. In others no assumption is made with respect to the number and the nature of the clusters. Kohonen net uses unsupervised learning. 2.5 When and why using Neural Network Neural set is basically a new way of solving the problems, which way can successfully be followed for a number of problems. For some problem neural network is not however

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useful. Main difference of using the Neural Network and conventional method of solving problems are, Neural Network is trained to perform satisfactory. In a training phase, training examples are presented to the networks and the weights of the neural networks are adapted by a learning rate. Conventional methods typically use an (analytical or empirical) model of the task. The ways of implementing the solution to specific problems can be divided as Problem Problem Level

Solution Level Algorithm Neural Network Implementation Level Software hardware

Figure 2.2 Ways of Implementing a Solution to a Specific Problem Useful Functions of the Neural Network Useful Function to be performed by the Neural network can be subdivided into few categories, which are distinguished by the nature of the problem • Its useful to apply the neural networks on problems for which no direct algorithmic solutions exists but for which problem examples of the desired responses are availed. • It is useful to apply Neural Networks for the problems that change over the time. The adaptability of the neural network will then be used to adapt the implemented solution whenever the problems changes • Its useful to apply Neural Networks to problems for which only too complicated algorithms can be derived. “Too complicated” means that implemented (conventional) algorithms are either too large, or consume too much power. Its not useful to train neural network on problems for which the solution can easily be implemented in an algorithm. Neural Network can also learn these simple algorithms but neural implementation is generally larger and less accurate than the direct algorithmic implementation of the solution. For number of problems the implementation of the solution in Neural Network is useful, while for other problems the solution should not use neural networks. 2.6 Overview of the well known ANN Models In 1943 McCullah and Pitts discussed for the first time the role of mathematical logic in neural activity. It was then the McCulloh_pitts neuron was first described. McCulloh_Pitts

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neuron has fixed threshold, has identical weights of excitatory synapses and the inhibitory synapses are absolute in nature.

ANN MODELS

FEED BACK

FEED FORWARD

CONSTRUCTED

TRAINED

LINEAR

NON LINEAR

UNSUPERVISED

SUPERVISED

HOPFIELD

ADAPTIVE RESONANCE

KOHONON

BACK PROPOGATION

Figure 2.3 Over View of the Main ANN models Hebb in 1949 introduced the fundamental concepts of learning in his classical text Organizational Behavior, and gave the famous learning rule named after him. Neumann, a pioneer in the field of design and development of digital computers made comparisons between the computers and the brain in 1962. An Overview of main types of ANN models are as in figure. The main types of the Neural networks are 2.6.1 Perceptron The perceptron is a single layer adaptive feedforward network of threshold logic Units, which possess some learning capability. Rosenblatt in 1958 invented perceptron, which was proposed as a model for the organization of neural activity in the brain. Single layer perpectron, incidentally, is the most widely studied, but the least applied model of all ANNs. It forms the basis of most of the further advances made in this field. Block in 1964, Minkey and Papert in 1969 studied perceptrons intensively. It was found that the single layer perceptron works well for problems, which are linearly separable, but fails to solve even simple problems, which are non-separable. This is because they lacked an internal representation of stimuli. Rumelharl proposed a multilayer perceptron with an error back propagation learning algorithm using a differential sigmoid activation function to facilitate learning rather than

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using a threshold logic units or linear functions for activation. Therefore a multilayer perceptron possess a better learning capability. Further progress was made with Amari in 1967 propounding the gradient-descent rule and designing of Backpropogation learning algorithm by Werbos in 1974, which was utilized in the multilayer perceptron model. 2.6.2 Multilayer Feedforward Neural Network In the feedforward neural network all the connections are unidirectional in a feedforward way. A multilayer perceptron is the typical example of feedforward neural network. It consists of input layer of input variable, output layer of output variable and at least one hidden layer of hidden neuron. Unidirectional connections exist from the input layer to the hidden layer and from the hidden layer to the output. There is no connection between any neurons in the same layer. The output variables are real-valued functions of input variables and weights. Varying the weights can change the input mapping. It has been proved that they are Universal Approximators. Training in this type of Neural nets are based on a limited number of training samples and it possess good generalization capability. They are used as representational models trained using a learning rule based on set of Input / output data. The main learning rule used is the popular Back propagation algorithm (also known as a generalized Delta Rule). Major application of feedforward neural network is in large-scale systems that contain a large number of variable and complex systems where little analytical knowledge is available.

X1

X2

X3

Input Layer

Hidden Layer

U1

U2

Un Output Layer

Figure 2.4 Three Layer Feedforward Neural Network

2.6.3 Backpropagation Networks It was demonstrated that the ANNs with hidden nodes and nonlinear activation's are able to simulate non-linear and linearly non-separable functions effectively. Backpropagation

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networks are essentially multilayer perceptron networks. Each node of the network is McCulloch- Pits neuron as used in perceptron. The difference is that while perceptron uses hard-limiting threshold functions, Backpropagation network uses sigmoid functions, which are nonlinear, and non-decreasing in nature. Training of the weights is carried out by Generalized delta rule (GDR) also known as Backpropagation algorithm (BPA). In the Back Propagation Algorithms, the network begins with a random set of weights. An input vector is presented and fed forward through the network, and the output is calculated by using this initial weighted matrix. Next, the calculated output is compared to the measured output data, and the squared difference between these two vectors determines the system error. The accumulated error for all the input / output pairs is defined as the Euclidean distance in the weight space, which the network attempts to minimize. Minimization is accomplished via the gradient descent approach, in which the network weights are adjusted in the direction of decreasing error. It has been demonstrated that if a sufficient number of hidden neurons are present, a three-layer Back Propagation network can encode any arbitrary input or output relationship. In the learning phase of Backpropagation network a pattern is presented at the inputs and weights are assigned arbitrary small values. The corresponding actual and target outputs are compared and error is computed. This error is used to readjust weights between the last two layers and feedback to the penultimate layer over the weights connecting it with output layer. The implementation of Backpropagation algorithm, thus involves a forward pass through the layers to estimate the error at the output, and then the error is fed to backward to change the weights in the previous layer and this goes on for all the proceeding layers. Backpropagation algorithm employs gradient descent search in weight space over the error surface to find the point resulting in minimum error. 2.6.4 Hopfield Network Hopfield Network invented by John Hopfield in 1982, has lateral and recurrent connections, that is, the output of a neuron are fed back to itself and intra-layer connections are present. The state of Hopfield network is the set of stable states of all its neurons. It is said to be unstable if it keeps on oscillating from one state to another. Stable configurations achieve a permanent state after a finite number of changes. The learning is unsupervised and takes place offline. Hopfield network is used as associative memories. They can also be used to solve optimization problems. They give better results when the input is perfectly represented as a string of binary bits. A major limitation of Hopfield network is that not more than 0.15 N numbers of patterns can be stored on a network, N being the number of needs in it. Secondly it has got exemplar patterns. Here an exemplar is said to be suitable if it applies at time zero, and the network converges to some of the other exemplars. 2.6.5 Hamming Sets Hamming sets are similar to Hopfield networks. They classify an exemplar by calculating the Hamming distance for each class and selecting that one with the minimum

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Hamming distance. The Hamming distance is the number of bits in the inputs, which do not match the corresponding exemplar bias. Such ANN, implements optimum minimum error classifier when bit errors are random and independent, and therefore their performance is better than or equal to that of Hopfield network. They also require less number of nodes than Hopfield network.

Input Layer Hidden Layer

(K-1) Layer

In ( j,k) Out( I,j)

Kth Layer

Output Layer

Figure 2.5 Back Propagation Algorithm / Network 2.6.6 Adaptive Resonant Theory The binary Adaptive resonance theory (ART-1) introduced by Carpentar and Grossberg in 1968 is a two layer nearest neighbor classifier and trained without supervision which can be used only for binary inputs. It implements a clustering algorithm, which selects the first input as the exemplar for the first cluster. The next input compares to the first cluster exemplar and clustered with it if the distance is less than a threshold. Otherwise the example for a new cluster is performed. This process is iterated for all inputs. The topology of the network is similar to Hopfield Network. Onelayer is the inputlayer, having m nodes, m being the number of classes stored on the network. Input layer revises input from the input layer and has recurrent connection. Thus it has got feedback paradigm. A simple representation of the counterpropagation network consists of three layer. The input layer is a simple fan-out layer. The hidden layer is the Kohonen layer and the output layer is Grossberg outside layer. The counter propagation networks (CPN) have been recently used because of various advantages offered. The advantages of the CPN are that, it is simple,

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easy to train and prevents a good statistical model of its input vector environment. It functions as a look-up table capable of generalization The Time-delay neural network (TDNN) is non-recurrent dynamic neural network which copes with time alignment by explicitly delaying the signal waveform by a fixed time span. The time-delays are introduced into the synaptic structure of the network and their values are adjusted during the training phase. The TDNN can be used for prediction problems. 2.6.7 Radial Basic Function (RBF) Neural networks based on localized basic functions and iterative function approximations are usually referred to as RBF networks. It’s started from Bashkriov and Aizerman at which time the networks are referred to as the method of potential functions. Classification of new patterns is done in much the same way in RBFs as in PNNs. In both the cases the localized basic functions falls of rapidly to the distance between the centers of the basic function as the input gets large. In simplest case the output of the network is a linear combination of all the basic function response. Output Units multiplies pattern activation by a weight, sums them, and adds a bias. Training in RBF consists of iteratively adapting the parameters of the network until the output approach the desired output over the whole range of training patterns. RBF network is generally a regression network and so estimates the value of a customer variable.

Xi

Xj

Xp

Input Units

Pattern Units

Wj Wi Wn +1 W Bias Bias Output Units

Figure 2.6 Typical RBF Network

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2.6.8 Probabilistic Neural Network (PNN) and General Regression Neural Network (GRNN) PNN and GRNN are feedforward neural networks. They respond to the input pattern by processing the input data from one layer to the next with no feedback path. Feedback may or may not be used in the training of networks. These networks learn pattern statistics from a training set. The training may be in terms of global -- or local basis functions. Back propagation error method is training method applied to global basis function which is defined as nonlinear functions of the distance of the pattern vector from a hyperplane. The function that is to be approximated is defined to be a combination of these sigmoidal functions. Since the sigmoidal functions have non-negligible values throughout all measurements space, much iteration are required to find a combination that has acceptable error in all parts of measurement space for which training data are available. Two main types of localized basis function networks are based on 1. Estimation of probability density functions and 2. Iterative functions approximation PNN's and GRNN's used for estimation of values of continuous variables are based on first type i.e. estimation of probability density function. The second types, based on iterative function approximation, are usually referred to as Radial Basis Function (RBF) networks. These networks use functions that have a maximum at some center location and fall off to zero as functions of distance from that center. The function to be approximated is approximated as a linear combination of these basis functions. An obvious advantage of these networks is that training a network to have the proper response in one part of the measurement space does not disturb the trained response in other distant parts of the measurement space.It is possible to train a network of local basis functions in one pass through the data by straightforwardly applying the principles of statistics. PNN's are classifier version obtained when decision making is combined with a nonparametric estimator for probability density functions where as GRNN is a function approximated version, which is useful for estimating the values of continuous variables such as future position, future values, and multivariable interpolation. a) Probabilistic Neural Network There are four variations for implementation of the pattern units in PNN network. In one variation, the topology of PNN is similar in structure to back propagation, differing primarily in that the sigmoidal activation function is replaces by an exponential activation function. Basic forms of PNN and GRNN are characterized by one pass learning and use of same width for the basic function for all dimension of the measurement space. Adaptive PNN and GRNN are characterized by adapting separate widths for the basis function for each dimension. Due to this, PNNs are ideal for exploration of new databases and preprocessing

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techniques, because this use of the neural network typically requires frequent retraining and evaluation, with relatively short test sets. The remaining three implementations of the pattern units are optimized for implementation of the pattern units are optimized for implementation on multiply/accumulate digital signal processors or on special-purpose integer arithmetic processors. b) General Regression Neural Network (GRNN) GRNN provides estimates of continuous variables and converges smoothly to the underlying (linear or nonlinear) regression surface. Like PNN, GRNN features instant learning and a highly parallel structure. Even with sparse data in a multidimensional measurement space, the GRNN provides smooth transitions from one observed value to another. Regression is the least-mean-square estimation of the value of a variables based on examples. The term General Regression implies that being linear does not restrict the regression surface. If the variable to be estimated is future values, the GRNN is a predictor. If they are dependent variables related to input variables in a process, plant or system. Thus GRNN can be used in these applications.

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CHAPTER 3 FUZZY LOGIC AND FUZZY SYSTEMS 3.1 Importance of Fuzzy Systems Fuzzy set theory derives from the fact that almost all-natural classes and concepts are fuzzy rather than crisp in nature. Fuzzy systems are model free systems in which all things are matters of degree. These systems use an inferential approach oriented towards system analysis and decision support. Fuzziness describes event ambiguity. It matters the degree, to which an event occurs, not whether it occurs or occurs in random to what degree it occurs is fuzzy. Whether an ambiguous event occurs - as when we say, "there is 20 percent chance of light rain tomorrow" - involves compound uncertainties, the possibility of fuzzy event emerges. Fuzzy systems store benefits of fuzzy associates or common sense "rules". Fuzzy programming admits degrees. They systems "reason” with parallel associate's interference. When asked a question or given an input, fuzzy systems fire each fuzzy rule in parallel, but to a different degree, to infer a conclusion or output. Thus fuzzy systems reason with sets, “fuzzy" or multivalued sets, instead of bivalent propositions. They estimate sampled functions from input to output. They may use linguistic or numeric samples for example they may use HEAVY, LONGER or number (relative) for the degree of fuzziveness. Fuzzy interpretations of data are a natural and intuitively plausible way to formulate and solve various problems in pattern recognition. Fuzzy logic is a logical system for formalization of approximate reasoning, and in a wider sense, used anonymously with Fuzzy set theory. It is an extension of multi valued logic. Fuzzy logic systems provide an excellent framework to more completely and effectively model uncertainty and imprecision in human reasoning with the use of linguistic variables with membership functions. Fuzzification offers superior expressive power, greater generality, and an improved capability to model complex problems at a low solution cost. Unlike fuzziness the probability dissipates with increasing information. 3.2 Basic Concepts Suppose your are approaching a red light and must advise a driving student when to apply brakes. Would U say " begin braking 14 feet from the cross walk " or shall we say “apply brakes pretty soon. We will say the latter and so the natural language is one example of ways vagueness arises, is used, and is propagated in every day’s life. Imprecision in data and information gathered from and about our environment is either statistical (e.g. a coin toss) the outcome is a matter of chance - or non-statistical - This latter type of uncertainty is called fuzziness.

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3.3 Fuzzy Sets and Rules In fuzzy set theory ' normal 'sets are called crisp sets, in order to distinguish them from fuzzy sets. Let C be a crisp set defined on the universe U, then for any element of u of U, either u (C) or U (C) occurs. In fuzzy set theory this property is generalized, therefore in a fuzzy set F, It is not necessary that either u ∈ F or u (F) exist. In the fuzzy sets theory the generalization of the membership properties are as follows. For any crisp set C it is possible to define a characteristic function µC: U [0,1] instead from the two-element set {0,1}. The set that is defined on the basis of such an extended membership function is called as fuzzy set. Fuzzy rules are elementary or composed proposals. They result from a conjunction between elementary fuzzy proposals. A fuzzy rule is composed of a premise and a conclusion. The classical structure of a rule is “If < premise> then <conclusion>” When the premise is an elementary fuzzy proposal, the rule is described as follows. If <x is A> then < conclusion>. The x is a variable; generally real, defined on a referential called the universe of discourse, given as a capital letter here X. A is a linguistic term, taken in a set of terms noted as TX. Basic concept of fuzzy logic's is fuzzy " If then Rule " or Fuzzy Rule. 3.4 Classical Operations of Fuzzy Sets Zadeh [LAZ 65] defined classical operations for fuzzy sets Let f (X) = all fuzzy subsets of X (that is, m f (X) ïƒŸ The fuzzy sets mA, mB F (x). The fuzzy rules are Definition: Two fuzzy sets are equal (A = B) if and only if ∀X ∈ X: (=) Equality A = B ïƒŸ m A (x) = m B (x) (∀X where x: pointwise, function __ theoretic operations) Definition: A is a subset of B (A ⊆ B) if and only if ∀X ∈ X: (⊂) Containment A ⊂ B ïƒŸ m A (x) ≤ m B (x) The other operations are ∀X ∈ X: (~) Compliment mA (x) = 1-mA (x) ∀X ∈ X: (∩) Intersection m A ∩B (x) = min {mA (x), mB (x)} ∀X ∈ X: (∪) Union mA∪B (x) = min {mA (x), mB(x)} 3.5 Membership Function and Membership Values m: X | (0,1),

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Membership function is the basis idea in fuzzy set theory. Its values measure degrees to which objects satisfy imprecisely defined properties. Fuzziness represents similarities of objects to imprecisely defined properties and probabilities which convey information about value frequencies. The member ship function µF of the fuzzy set F is a function µF: U [0,1]. (u) ∈ {0,1}. F is completely

So, every element u of U has a membership degree µF determined by the set of tuples F = {(u, µF (u)) | u ∈ U} 3.6 Fuzzy Relations

The fuzzy relation can be considered as a fuzzy set of tuples. That means each tuples has membership degree between 0 and 1. Its definition is Let U and V be uncountable (continuous) universe and µR : U X V R= [ 0,1] , then

UxV

∫ µR (u, v) /(u, v)

This is a binary fuzzy relation on U x V. If U and V are controllable (discrete) universes, then R=

UxV

∑ µR (u, v) /(u, v

The integral symbol denoted the set of all tuples on U x V denoted by

µ R ( u , v ) /( u , v )

3.7 Properties of Fuzzy Sets Let A and B be the fuzzy sets, defined respectively on the universes X and Y, and let R be a fuzzy relation defined on XxY. The support of fuzzy set A is the crisp that contains all element of A with non-zero membership degree. This is denoted by S (A), formally defined as S (A) = {u ∈X | µA (u) >0} When one deals with convex fuzzy sets as it is the case in fuzzy control theory the support of a fuzzy set is an interval. Therefore in fuzzy control theory the term width of a fuzzy set is used additionally to the term support. The width of the convex fuzzy set A with support set S (A) is defined by Width (A) which is equal to Sup (S (A)) - Inf (S (A)) where Sup and Inf denote the mathematical

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operations supremum and infimum. If the support set S (A) is bounded as is usual in fuzzy control, Max and Min can replace Sup and Inf. The nucleous of a fuzzy set A is defined by Nucleus ( A) = { µ ∈X |µ A ( u) = 1 } If there is only one point with membership degree equal to 1, then this point is called the peak value of A. 3.8 Fuzzy Truth Value A fuzzy truth-value is defined to be a fuzzy set on the closed interval V = [0,1] as follows. A is a fuzzy truth-value if and only if A is a fuzzy set on [0,1] and L be the set of all fuzzy values, that is L = {a | a is fuzzy set on [0,1]} The same can be graphically written as follows

-1

0

0 1 0 a b 1 0 (a) Numerical Truth Values (b) Interval Truth Values (c) Fuzzy Truth Values Figure 3.1 Truth Values in Fuzzy Logic 3.9 Learning in Fuzzy Systems

1

Generally learning can be well or can be bad. But one cannot learn without changing, and we cannot change without learning. Learning laws describe the synaptic dynamical system, how the system encodes information. They determine how the synaptic web process unfolds in time as the system samples new information. This is one way neural network compute with dynamical systems. Fuzzy systems learn associative rules to estimate functions or control systems through unknown probability (sub set hood) function p (x). The probability density function p (x) describes a distribution of vector patterns or signals X, a few of which the neural or fuzzy systems sample. When a neural or fuzzy system estimates a function f: X Y, it in effect estimates the joint probability density P (x, y). Then solutions points (X, f (x)) should reside in highprobability regions of the input/ output product space X x Y. An unsupervised learning systems process each sample X but does not “know " that X belongs to class Di and not to

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class Dj. Supervised learning use class-membership information and unsupervised learning used unlabelled samples. 3.10 Fuzzy Logic Controllers (FLC) Fuzzy systems, utilizing neuristic knowledge, have been employed very effectively as controllers popularly known as Intelligence Control. Design Problems of FLC are 1) Define Input and Output variables that are determined which status of the process shall be observed and which control actions are to be considered. 2) Define the condition interface, that is, fix the way in which observations of the process are expressed as fuzzy sets. 3) Design the rule base, which is, fixed the way in which observations of the process are expressed as fuzzy sets. 4) Design the computational unit, that is, supply algorithm to perform fuzzy computations those will generally lead to fuzzy outputs. 5) Determine rules according to which fuzzy control statements can be transformed into crisp control actions. (Defuzzification). The difference between expert systems and the fuzzy logic controllers (FLC) are 1) FLC models are rule-based systems. 2) The designer formulates rules of FLC systems. 3) FLC inputs are normally observations of technological systems and their outputs control statements. 3.11 Pattern Recognition in Fuzzy Systems Pattern Recognition is a fixed concerned with machine recognition of meaningful regularities in noisy or complex environments. Pattern Recognition is the search for structure in data. Numerical PR is characterized in four major areas as shown in the figure 3.2. In practice, the successful Pattern recognition is developed by iteratively revisiting each of the four modules until the system satisfies a given set of performance requirements and economic constraints. Main approach to PR is the structural (Synatic) approach. This branch of PR is the less well developed in terms of fuzzy and neural models. Generally two data structures are used in numerical PR systems. Object data vectors (feature vectors, pattern vectors) and relational data (similarities, proximity's). Object data are represented in the sequel as X= {x1,x2, x3,….. xn} a set of n feature vectors in feature space Rp , the jth object observed in the process has vector Xj as its numerical representation: Xjk is the kth characteristic associated with the object j.

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Humans

Process Description Feature Nomination X= Numerical Object Data D : Xx X R R= Pair-Relation Data Design Data Test Data

Sensors

Feature Analysis Preprocessing Extraction 2-D Display Cluster Analysis

Classifier Design Classification Estimation Prediction Control

Exploration Validity

Figure 3.2 Characterization of Pattern Recognition 3.12 Relational Data It may happen that, instead of an object data set X, we have access to a set of n2 numerical relationships say {rjk} between pairs of objects Oj and Ok. That is, rjk represents the extent to which objects j and k are related in the sense of some binary relation ρ. Its is convenient to array the relational values as an n X n matrix R = (rjk) = (ρ (oj, ok)). Many functions convert X x X to relational data. For example every metric d or Rp X Rp produces a dis-similarity relation matrix R (X: d) as in figure. Where we take ρ = d. If every rjk is in {0,1} then it is hard (or clip) binary relation function. If 0<rjk<1 for any j and k we call R as fuzzy relation. Fuzzy models for PR associated with relational data are fairly developed now a day.

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3.13 Adaptivity Features and Adaptive Controllers One of the main topics of high interest to researchers in fuzzy logic (FL) field is the development of automotive-data-driven adaptive controllers. Static Fuzzy logic controllers (FLC) have already been widely used in engineering applications. Adaptive controllers are important for good performance in non-stationary applications.

Process Model

Performance Measure

Identifier

Decision Maker

Process

Model Based Controller Figure 3.3 Adaptive Fuzzy Controllers

Basic Model of Adaptive Fuzzy Controller is as shown. Neural parameter estimators embed directly in an overall fuzzy architecture. Neural networks “blindly " generate and refine fuzzy rules from training data. Adaptive fuzzy systems learn to control complex process very much as we do. It begins with a few crude values of thumb that describes the process. Expert may give them the rules or may extract the rules from the observed expert behavior. Successive experience refined the rules and usually improves performances. Fuzzy Logic (FL) has been used in areas like pattern recognition problems and processing inexact ideas. The emphasis in such problems is to approximate multiple pattern classes in a joint input output space.

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CHAPTER 4 APPLICATION OF ARTIFICIAL NEURAL NETWORKS IN POWER SYSTEMS 4.1 Introduction on ANN Application ANNs can play a richly significant potential role in electric power systems. As a branch of Artificial Intelligence, ANNs take problem-solving one step further. They can match stored examples against a new one, building on experience to provide better answers. On the field of AI, ANN computing shows great potential in solving difficult data-interpreting tasks. Neural networks are based on neurophysical models of human brain cells and their interconnection. Such networks are characterized by exceptional pattern recognition and learning capabilities. The major advantage of the neural networks is its self-learning capability. First, the network is presented with a set of correct input and output values. Then it adjusts the connection strength among the internal network nodes until proper transformation is learned. Second the network is presented with only the input data, and then it produces a set of output values. The development of the input and output data is done several thousand times. After proper number of learning cycles or iterations the network will be able to produce accurate output data from input data similar to those used for learning. ANNs are composed of many simple elements operating in parallel. The network function is determined largely by the connections between elements. They have been trained to perform complex functions in various fields of application including Pattern Recognition, Identification, Classification, Speech, Vision, control systems and EMS. The field of ANNs has a history of nearly five decades but has found solid application only in the past ten years, and the field is still developing rapidly. In recent years, many interesting applications of ANNs have been reported in the power system areas like load forecasting, power system stabilizer design, unit commitment, and security assessment, Economic load Dispatch and fault analysis. ANNs have attracted much attention due to their computational speed and robustness. They have become an alternative to modeling of physical systems such as synchronous machine and transmission line. Absence of full information is not a big as a problem in ANNs as it is in the other methodologies. A major advantage of the ANN approach is that the domain knowledge is distributed in manner. Therefore they reaches the desired solution efficiently. Most of the applications make use of the conventional multilayer Perception (MLP) model based on back propagation algorithm. However, multilayer perception model suffers from slow learning rate and the need to guess the number of hidden layers and neurons in each hidden layer. Many improvements are suggested over the conventional MLP to overcome these advantages.

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4.2 Major Applications 4.2.1 Power System Stabilizer Real time timing of PSS is a complex task. Hsu and Chen [HC 91] proposed a fourlayer perceptron network for this purpose. The network consists of two input nodes, two hidden layer of four nodes each and two output nodes. Input to the ANN was the generator real power output P and the Power Factor. The outputs of ANN were the PSS gain settings. Offline simulations generated the training set for this ANN. To speed up the learning process an adaptation law was used to dynamically update the learning rate of the backpropagation. Another important application is the stable power system stabilizer based on inverse dynamics of the controlled system using an ANN. Y. M. Park, S.H Hyun and J. H. Lee [PHL 96] suggested enhancing the dynamic performance of power system. Here an output feedback control law is driven with some conditions satisfied, which guarantees the internal stability and robustness against the asymptotically stable external disturbances. Then the control law is implemented using the inverse dynamics of the controlled plant. An ANN, inverse dynamics neural network (IDNN), on offline identifies the inverse dynamics of the controlled plant. Backpropagation neural networks have recently been applied to problems in power system stabilizer modeling. When trained to respond differently to different operating conditions, these networks tend to produce interference between conflicting solutions. In recent years, modular neural network architectures have been used for problems in system identification and control. These networks learn different aspects of a problem by partitioning the data space into several different regions and are less susceptible to interference than backpropogations networks. Srinivas Pilutla and Ali keyhani in [SA 97] illustrated the use of the modular neural networks for power system stabilizer modeling. M.K. El-Sherbiny et al [ShSaI 96] introduce a novel Power System Stabilizer (PSS) controller based on a multilayer feedforward artificial neural network (ANN). A feature of the proposed controller is that the ANN parameters can be adapted online in real time according to generator loading conditions. The proposed ANN based PSS consists of three layers, namely, an input layer, a hidden layer and an output layer. The input layer has four nodes. The best number of the nodes for the hidden layer has been found by trial and error to be seven, with a nonlinear transigmoid activation function. The last layer (output layer) has one node whose activation function is transigmoid. Time domain solution with specified state disturbance for a synchronous machine connected to an infinite bus through an external transmission line are employed to prove the effectiveness of the proposed ANN based controller under a wide range of variations of the operating conditions and variety of exciter gains.

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Output Layer

Gatting Layer

Gating Network

Local Expert I

Local Expert L

Fully Connected

Input Layer

* Figure 4.1 Modular Neural Network FeedForward Architecture 4.2.2 Load Forecasting Load forecasting is perhaps the most important SCADA task and also one of the most popular areas for ANN implementation. The availability of historical load data on the utility databases makes this area highly suitable for ANN implementation. ANN schemes using perceptron networks and self-organizing feature maps have been successful in short-term as well as long-term load forecasting with impressive accuracy. Lee et al [LCP 90] used a multi layer perceptron for short-term load forecasting. This ANN was used for a one-day ahead load forecasting, for the winter, spring, summer and fall seasons. An average percent relative error of two % was achieved. Park et al [PEM 91] employed a similar approach to compare the performance of multi layer perceptron with a utility’s numerical forecasting methods. Hsu et al [HY 91] demonstrated the suitability of combining self-organizing feature maps and multilayer perceptron for short-term load forecasting. * Ref [SA 97]

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The self-organizing feature maps were used to identify the day types from historical data. To obtain the hourly load pattern for a day, the hourly load patterns of several days in the past, which are of the same day type, were averaged. To predict the daily load, a multilayer perceptron was used. R.Lamedia A. Prudenzi at el [LPSCO 96] illustrated a new ANN based procedure (SOM + ANNI) in order to enhance the forecasting accuracy in the analysis of the load forecasting. The procedure provides the combined approach (unsupervised + supervised) structured in three subsequent stages. The first stage provides some identification criteria of the characteristics of the days through the classification of historical hourly loads, thus to obtain clusters of the similar load profiles. The classification is performed by means of a Kohenon’s SOM. The second stage consists in an actualization process of the information deduced from the previous day type identification. Human operators perform this activity that gives a meaning of the load classes. The third stage, performing the proper forecasting task, which is realized by means of a multi layer perceptron based on the back propagation learning algorithm already used for the ANN implementation. Success of applying a class of recurrent neural network in short term load forecasting was tested by J. Vermaak, at el [VB98]. Recurrent Neural networks are members of a class of neural network models exhibiting inherent dynamic behavior. The most general of these is the fully connected recurrent neural network. The recurrent network parameters were obtained by training a feedforward network to learn the mapping. Here the feedforward neural networks (including those used for the recurrent network training) employed a single hidden layer, and were trained in batch mode according to the error backpropagation algorithm, using the conjugate gradient descent optimization. The other main works in the area of load forecasting are substation load forecasting C.S. Chen, Y.M.Tzeng [CTH 96] Using SCADA, D. Srinivasan et al [DLC 94] for a short term forecaster using multilayer neural network, three layer feedforward Quasi Optimal neural network for the short term Load forecasting [MCS97] and the window based forecasting procedure using combined Supervised and Unsupervised learning concept [DRSP 95]. 4.2.3 Fault Diagnosis ANN’s has recently invaded fault diagnosis, which has been a traditional area for ES (expert system) implementation. However, at present the ES implementations outnumber the ANN implementations. The explanatory abilities of ESs and their more powerful user interface make them a more attractive alternative. However, still there are certain areas, which require a quick response, and are still open to ANN implementation. Many applications for the various fault diagnosis problems have been reported in the literature. Kanoh et al [HMK 88] proposed a cascade structure of three three-layer perceptron networks for the identification of a faulted transmission section. The ANNs were trained using backpropagation. The first and the second ANN in the cascade structure identify the candidate’s one and two for fault selection, using current amplitude and phase angle distribution patterns.

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The third ANN obtains the final fault location using the above candidates one and two, and a current amplitude distribution pattern. Results of this approach indicates that this method can achieve 98.4 percentage accuracy even when the measured values differed by thirty percentage from the EMTP as mentioned above.

P1 DAY I ……………………….. P24

FORECASTING Supervised Back-propagation Learning

………… P1 DAY(I-2) P24

…………. P1 DAY(I-1)

P24

Cluster Codes Relevent To Days (I-2),(I-1),i

DAY TYPE CLASSIFICATON Kohonen's SOM Learning

EXTRAPOLATION AND REPRODUCTION OF CLASSIFICATION CRITERIA

P1

……….

P24

CALENDER TIME CHARACTERISTICS OF FUTURE DAYS

* Figure 4.2 Unsupervised/Supervised Procedure Adopted for Load Forecasting Ebron et al [EL 90] used a three-layer perceptron network to detect high impedance faults on distribution feeders. Their approach consisted of three parts: collecting sets of sampled, processed feeder line currents, training the ANN with these data and testing the ANN on new patterns. Computer simulations using the EMTP generated the training set. From the results obtained ANN classified ten of these cases correctly. However, the ANN caused a false alarm in seventeen cases as mentioned. * [LPSCO 96]

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ANNs were also successful in incipient fault detection of induction motors [CY90]. Chow and Yee [CY91] used multilayer perceptron networks for incipient fault detection in single- phase squirrel cage induction motors. This approach used two ANNs. 1. A disturbance and noise filter ANN to filter out the transient measurements while retaining the steady-state measurements. 2. An incipient fault detector ANN to detect faults based on data collected from the motor. C.Rodriguez at el [RRMLMP 96] presented a modular and neural network-based solution to power systems alarm handling and fault diagnosis described it overcomes the limitations of ‘toy’ alternatives constrained to small and fixed-topology electrical networks. In contrast with the monolithically diagnosis systems, the neural network-based approach presented here fulfills the scalability and dynamic adaptability requirements of the application. Mapping the power grid onto a set of interconnected modules that model the functional behavior of electrical equipment provides the flexibility and speed demanded by the problem. The way in which the neural system is conceived allows full scalability to realsize power systems.

1 PREPROCESSING

2

DISTURBANCE DETECTION AND CLASSIFICATION

FAULT DIAGNOSIS 3 HYPOTHESIS GENERATION 4 HYPOTHESIS JUSTIFICATION

* Figure 4.3 Fault Diagnosis process * [RMAMP 96]

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4.2.4 Security Assessment Security of a power system is the ability to sustain, without any abnormalities, the worst impending contingency. Security assessment has been at the forefront of ANN applications from the beginning. The goal of security assessment is to supply the operating state so that suitable preventive actions can be undertaken. In one of the early approaches, Sobajic and Pao [PS89] synthesized one of the crucial parameters of the system, the critical clearing time (CCT). A three-layer perceptron network with twelve input nodes, six hidden-layer nodes and one output node was employed for this purpose. The training set was a twelve dimensional pattern set, labeled with the corresponding CCT values. The CCT parameters were obtained by numerical integration of the post-disturbance system equations. The CCT parameters output by the ANN matched closely with the actual values using a three-layer perceptron network to assess the dynamic security of the power systems. The ANN was trained on the results of off-line stability analysis. The transient security assessment analysis is done by M.Djukanovic, D.J Sobajic and Pao et al [DSP 94] by a direct method for the multimachine systems. Here a local approximation of the stability boundary is made by tangent hyper surfaces, which are developed, from Taylor Series Expansion of the transient energy function in the state space near a certain class of unstable equilibrium point. Neural networks are used to determine the unknown coefficients of the hypersurfaces independently of operating conditions. J.N Fidalgo et al [FPV 96] described the ANN based approach for the definition of preventive control strategies of autonomous power systems with a large renewable power penetration. For a given operating point, a fast dynamic security evaluation for a specified wind perturbation is performed using an ANN. If insecurity is detected, new alternative stable operating points are suggested, using a hybrid ANN-optimization approach that checks several feasible possibilities, resulting from changes in power produced by diesel and wind generators and other combinations of diesel units in operation. Security constrained optimal rescheduling of real power using Hopfield network was analyzed by Soumen Ghosh et al [SC 96]. In this paper a new method for security-constrained corrective rescheduling of real power using the Hopfield network is presented. The proposed method is based on solution of a set of differential equations obtained from transformation of an energy function. Results from this work are compared with the results from a method based on dual linear programming formulation of the optimal corrective rescheduling. The minimum deviations in real power generations and loads at buses are combined to form the objective function for optimization. Inclusion of inequality constraints on active flow limits and equality constraint on real power generation and load balance assures a solution representing a secure system. Transmission losses are also considered in the constraint function.

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4.2.5 State Estimation ANNs have been very successful in system identification, parameter estimation and analysis. The power system topological observability is dealt with [TM 89] using a three-layer perceptron network. Bialasiewicz et al [BPW 89] showed that a multilayer perceptron network could be used as a state estimator in a model reference intelligent control system. The ANN was trained using offline simulation data of a test system. The learning rate of the backpropagation was updated dynamically to speed up the learning process. An adaptive linear combiner and a multilayer perceptron network were also used [KF 90] for state estimation. In this implementation, the ANN was trained using several Kalman filter solutions for the power network. The results of the ANN based state estimation compared favorably with that of the Kalman filter. Eryurek et al [EU 90] proposed a three-layer perceptron network for sensor validation in a power plant. An adaptive learning scheme was employed. In this work, the following empirical rule was proposed for calculating the number of hidden nodes in the perceptron network

H = I log 2 N ± I

Where ‘N’ is the number of training patterns, ‘I’ the size of the input vector, and H the number of hidden nodes. The authors claimed that this empirical rule is valid for certain classes of sensor validation problems. A structured ANN was reported in [NA 90], which tackles the power system state estimation problem. This ANN has a generalized structure that is independent of applications. Performance of this network was shown to be superior to that of a back propagation scheme. A P Alvas da Silva and V H Quintana [AQ 95] presented a paper on an ANN topology determination and a supervised learning algorithm for very large training sets using the Optimal Estimate Training 2(OET2). OET2 overcomes the major shortcomings of the backpropagation learning rule and can also be very useful for other problems. Power system network decomposition techniques are used to decrease the computational burden of the topology classifier training session. 4.2.6 Contingency Screening To assess system security, a huge number of possible contingencies are to be evaluated and ranked. Conventional ranking methods suffer from masking and long computing time. Since a systems operational history is available in most utility databases, it should be possible to group contingencies into various subclasses [FKCR 89]. In this paper Fischl et al showed that a two-layer perceptron network could classify power system security status accurately under different loading and contingency conditions. This ANN was trained using simulation results and back-propagation. However it is impossible to generate enough training sets to cover the entire range of power system operation. Hence a Hopfield network was proposed in [FKCRY 90] for contingency screening. This paper used an optimization

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method to find the weights and thresholds of the ANN, in contrast to the learning method of the perceptron networks. The optimization method used linear programming techniques to maximize the probability of correct classification of contingencies. This implementation classifies contingencies according to the number and type of limit violations. The method has interesting applications in combining security monitoring and preventive control. S Gosh and B H Chowdhury [GC 96] modulated a three-layer perceptron artificial neural network with back propagation learning technique that is designed for line flow contingency ranking. Two new indices – severity index and a margin index for line flow – are defined. A regression-based correlation technique is used to select training parameters for the neural network. The technique followed in this paper is the backpropagation method. Training of the neural network continues with the updates in weights in V and W, until the error E reaches a predefined minimum value in a steepest descent manner. In the training process, the network is exposed to a set of patterns, each of which consists of an input vector X, and the corresponding desired vector d. The training process involves the following steps: 1. Selection of input/output parameters for training. 2. Generation of training data. 3. Normalization of training data 4. Testing of the network with unknown set of data 4.2.7 Voltage Stability Assessment ANNs have been recently proposed as an alternative method for solving certain traditional problems in power systems where conventional techniques have not achieved the desired speed, accuracy and efficiency. L index has been popularly used for assessing voltage stability margin. Investigations are carried out on the influence of information encompassed in input vector and target output vector, on the learning time and test performance of Multi Layer Perceptron (MLP) based ANN model. In the ANN model for each loading condition various combination of control variables are generated by running many iterations of LP based reactive power optimization algorithm. Settings of control variable influences the ANN input feature vectors differently. Only active power injection of slack bus and reactive power injection of all generator buses vary in input vectors of ANN2 for a given loading condition while variation in input vectors of ANN-1 is observed in most of the critical line flows.

4.2.8 Protection The application of ANN in this related field too is now days becoming important since the concept of online protection are widely accepted. S.A. Khaparde, N. Warke at el [KWA 96] shows that ANN can be effectively used effectively to achieve adaptive relaying for the above-mentioned problem. Adaptive relaying

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covers a large number of applications and the characteristics of relays vary widely, so the philosophy of adaptive relaying must vary accordingly. A modified multilayered perceptron model employs an additional node in the input layer. These additional input facilities changes in the relay characteristics. The desired change in the quadrilateral relay characteristic is achieved by making appropriate changes in the thresholds and weights of the hidden layer neurons. The other method used by Q. Y. Xuan, Y.H Song [XSJMW 96] illustrated an adaptive protection technique based on neural networks with special emphasis on analysis of the firstzone performance. Here the feedforward multilayer neural network was chosen for the study. However selection of the optimal number of hidden layers and the optimal number of hidden layers, and the optimal number of neurons in each layer, is still an open issue? The guidelines given for the number of the hidden neurons were adopted as a starting point. During further studies and analysis different combinations of the following network training methods were chosen and tested in order to ensure that the model would be continuously refined 4.2.9 Load Modeling The application of the ANN in load modeling is increasing for the past years. Accurate dynamic load models allow more precise calculations of power system controls and stability limits. A. P Alves da Silva and C. Ferreira et al [AFZL 97] detailed the performance of a nonparametric load model based on a new constructive artificial neural network (Functional Polynomial Network) (FPN) and it’s compared with the popular “ZIP” model. The impact of the clustering different load compositions is also investigated. The network architecture proposed here is the Functional Polynomial Network, which is based on the following ANN models: functional link net and polynomial network. The main draw back of the functional link net is that the required non-linear transformation can only be found by trial and error. The polynomial network is a nonparametric ANN model i.e. it does not require the architecture pre-specification.

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CHAPTER 5 APPLICATI0N OF FUZZY LOGIC IN THE POWER SYSTEM 5.1 Introduction on Fuzzy logic applications Fuzzy logic applications are widely used in all parts of the power system planning, design and operations. The main important applications are 1. Stability Assessment / Enhancement 2. Power System Control 3. Fault Diagnosis 4. Security Assessment 5. Load Forecasting 6. Reactive Power Planning and Control 7. State Estimation 5.2 Major Applications 5.2.1 Reactive Power and Voltage Control The rapid growth in the power system coupled with variations in operating conditions leads to better management in voltage profile and reactive power. Reactive sources which are spread throughout the system should be controlled accurately based on the loading conditions (light load or peak load) to optimize and ensure the security of electric power transmission system. These controls are known as voltage/reactive power or voltage/VAR control. The aim of these controls is to reduce voltage deviations or minimum losses or enhancing voltage[ NU 98]. Main types of voltage/ VAR problems are 1. Planning of system reactive demands and control facilities as well as installation of reactive power control resources 2. The operation of existing voltage/VAR resources and control device. The online planning is much more cumbersome and important in the power system operation. This is because in a day to day operation of power system both under/over voltage occurs and VAR sources need to be adjusted to avoid high/low voltage problem. This can be termed as voltage/VAR scheduling and this is very important in the power system security. There are various algorithms employing linear and non-linear optimization technique used for voltage correction. These algorithms involve numerical computations and hence may not be curtailed and also the amount of controller movement needs to be minimized.

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Fuzzy set theory has been applied off late for reactive power control with the purpose of improving the voltage profile of power system. Here the voltage deviation and controlling variables are translated into fuzzy set notations to formulate the relations between voltage deviation and controlling ability of controlling device. Main control variables are VAR compensators, transformer taps and generator excitation. A fuzzy rule system is formed to select these controllers, their movement and step size. The controllers are selected based on 1. Local controllability towards a bus having unacceptable voltage. 2. Overall controllability towards the buses having poor voltage profile. K. H. Abdul_Rehman / S. M. Shahidehpur et al [AS 93] presents a mathematical formulation for the optimal reactive power control problem using the fuzzy set theory. The objectives are to minimize real power losses and improving the voltage profile of the given system. Transmission losses are expressed in terms of voltage increments by relating the control variable, i.e. tap positions of transformers and reactive power injections of VAR sources, to the voltage increments in a modified Jacobian matrix. Main advantage of this method illustrated is that the specific formulation of this problem doesn’t require Jacobian Inversion of matrix and hence it will save computation time and memory space. The objective function and the constraints are modeled by the fuzzy sets. Linear membership functions of the fuzzy sets are defined and the fuzzy linear optimization problem is formulated. The solution space here is defined as the intersection of the fuzzy sets describing the constraints and the objective function. Each solution is characterized by a parameter that determines the degree of satisfaction with the solution. The optimal solution is the one with the maximum value for the satisfaction parameter. Multicase VAR planning problem involves the determination of an installation pattern of location and sizes of new compensators for multiple cases. The problem should basically cover the operating limits, complicated security and economic factors. a) Voltages and VAR controllers must be kept within their operating limits for the entire system under both normal and contingency cases. b) The expansion between cases should be coordinated to avoid excessive investment. c) The amount of compensation (by capacitor and reactors) must be descritized. In the area of the Multicase VAR planning R. A. Fernandus et al [FLBHW 83] proposed augmented Lagrangian type objective function and later augmented Lagrangian and generalized benders decomposition methods were applied [GPM 88] to treat both preventive and corrective controls of VAR planning. The drawbacks of traditional approaches were pin pointed by Hong and Liu et al [HL 92]. An expert system (VPES) (VAR planning Expert System) was introduced. It incorporated constraints resulting from considerations of the voltage collapse and able to handle both fixed and the variable cost and discrete device.

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Fuzzy Set theory has also been applied to solve. Here an extended approach based on VPES is proposed to take fuzzy reasoning rules into account for solving Multicase VAR planning solution. Combination of individual information from each single case is performed by fuzzy relationship the center of gravity algorithm. Thus the coordination of multicase VAR planning is achieved. The other important area is the application of the reactive power compensation in distribution system .The aim is to achieve power and energy loss reduction, voltage regulation, and system capacity release. An approach using fuzzy dynamic programming to decide the optimal capacitor placement and size of compensating shunt capacitor for distribution systems with harmonic distortion is proposed by Hong Chan Chin et al [HC 95]. The problem is formulated as fuzzy dynamic programming of minimization of real power loss and capacitor cost under the constraints of voltage limits and total harmonic distortion. The algorithm proposed greatly reduces the effort of finding optimal location by any exhaustive search. The computational algorithm is narrated in the following steps as given in. 1. Perform the load flow program at the fundamental frequency to calculate the bus voltage. 2. Find the membership functions µP, µV, µH and µD for the fuzzy sets P, V, H and D. 3. Identify the optimal location of shunt capacitor at the bus with the lowest membership Value µp(K) ( bus K ) 4. Try the capacitor placement at bus K with various discrete sizes. Select the optimalsize QC that will result in lowest cost function without violating the constraints. 5. Install the capacitor QC at the bus K and simulate the load flow to calculate the new bus voltage violation. Ching-Tzong Su & Chien_tung Lin [SL 95] illustrated voltage profile enhancement for Power Systems using fuzzy control approach. The voltage violations are transformed to fuzzy set notations to formulate the relation between the voltage violation level and the controlling ability of controlling devices. A feasible solution set is first attained using the min-operation of fuzzy sets, and then the optimal solution is fast determined employing the max- operation. The membership function of the bus voltage violations is represented as in the following figure. Here âˆ†Vi represents the voltage violation level of bus I, and uâˆ†Vi represents the membership function of âˆ†Vi The maximum deviation of the bus voltage is given by

Cij

Cij min 0 Cij max *Figure 5.1 The membership function of controlling ability of controlling devices * [SL 95]

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Uâˆ†Vi

âˆ†V i âˆ†VImin -0.01 0 0.01 âˆ†VImax

âˆ†VImin = Vimin - ViNorm

*Figure 5.2 The membership function of Voltage violation Level The computational procudure of the above algorithm was repersented as

Input data (Including network configuration, line Impedance, bus power, Bus voltage limits, controlling margin)

Perform base Case Load Flow

Find the sensitivity coefficient

Calculate the Controlling Ability

Find the membership value of bus voltage violation level and controlling ability

Evaluate the Optimal control Solution

Modify the value of the Control Variables

Check Voltage level has enhanced to the desired level

YES

Perform the load Flow and output the Results

NO

* Figure 5.3 Computational Procedure for the solution for Voltage Profile Enhancement * [SL 95]

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5.2.2 Transient Stability The most active area of the fuzzy system research in the power systems has been stability assessment and enhancement. The stable performances of the synchronous machines under all anticipated conditions of system transients are essential for ensuring overall system stability. Application of the fuzzy set theory in transient stability evaluation was first reported by Soulfis et al [SMP 89]. The system operating states, classified as belonging to one of the six possible states were represented using the fuzzy membership values in fuzzy Pattern recognition (PR) systems. The developed method is applicable for any power system irrespective of its size, configuration or loading condition [AV 89]. An application of Fuzzy set theory for design of stabilizer to improve the dynamic performance of a multimachine power system was first proposed by Hsu and Cheng [HC 90]. This stabilizer used a fuzzy relation matrix to produce the output based on the fuzzy inputs, speed deviation and acceleration. Only local measurements from each machine were used for this stabilizer, resulting in a simple design. Hassan et al reported another successful application of a fuzzy logic stabilizer for improving the stability of synchronous machines. [MOG 91]. The practical implementation and experimental results of this stabilizer using a digital signal processor were reported in [HM 93]. In another research transient stability limit in power system transmission lines using the fuzzy control of FACTS Devices was studied. S. M. Sadehzadeh and M. Ehsan in et al [SEHFH 98] investigate the application of FACTS devices to increase the maximum loadability of the transmission lines, which may be constrained by a transient stability limit. Hence the on-line fuzzy control of the Super-conducting Magnetic Energy Storage (SMES) and the Static Synchronous Series Compensator (SSSC) are suggested. The fuzzy rule bases are defined and explained. The validity of the suggested control strategies is confirmed by simulation tests. The simulation results show that by the use of the proposed method, the line power transfer can be increased via the improvement of the transient stability limit. Finally the effect of the control loop time delay on the performance of the controller is presented. 5.2.3 Generator Operation and Control The major application lies in the control of excitation system of the Synchronous Generator. Synchronous Generator excitation control is one of the most important measures to enhance power system stability and to guarantee the quality of the electrical power it provides. A number of new control theories have been introduced to design high performance excitation controllers. Among them the linear optimal control theory [JHA 89], the adaptive control theory [CCM 86] the fuzzy logic control theory [HC 90] and the nonlinear control theory [LS 89] are the most commonly used ones.

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Fuzzy logic Controllers are advantageous in many respects. They are simple in structure and relatively easy to realize. Mathematical models of the control systems are not required. Variations of the parameters and operation conditions of the controlled systems do not significantly effect the performance of the controller. All of these advantages have enabled this technique to attract more and more attention in recent years. The main disadvantages of this method are a) Knowledge used to design a fuzzy logical controller mainly comes from the heuristic knowledge or expertise of the human experts. This sort of knowledge is sometimes difficult to acquire and represent in the required form. b) Parameters of the fuzzy logic controller are usually determined by trial and error. This method is time consuming and does not guarantee an optimal controller. Jinyu Wena, O.P. Malik et al [JSM 98] suggested a method to design the FLC based on Genetic Algorithm (G A). In this controller the generator terminal voltage and the rotor speed deviation are used as its inputs. As a result, both the voltage profile and the dynamic stability of the generating unit are enhanced. Also FLC design has been carried out by G.A. Chown, R.C. Hartman et al [CH 98] for Automatic Logic Controller (AGC). The main problem solved by this method is the secondary frequency controller and AGC. The fuzzy controller was implemented in the control ACE calculation, which determines the shortfall or surplus generation unit that has to be corrected. Short term generation scheduling with take-or-pay fuel contract was developed by Kit Po Wong and Suzannah Yin Wa Wong et al [KSY 96] in which a fuzzy set approach is developed to assist the solution process to find schedules which meet as closely as possible the take-or-pay fuel consumption. This formulation is then extended to the entire economic dispatch problem when the fuel consumption is higher than the agreed amount in the take-orpay contract. The extended formulation is combined with the genetic algorithms and simulated- annealing optimization methods for the establishment of new algorithms for the problem. Stabilizer control and the exciter and governor loops using fuzzy set theory and the Neural nets was developed by M.B. Djukanovic and M. S. Calvoic at et al [DCNS 97].Here a design technique for the new hydro power plant controller using fuzzy set theory and ANN was developed. The controller is suitable for real time operation, with the aim of improving the generating unit transients by acting through the exciter input, the guide vane and the runner blade positions. The developed fuzzy logic controller, whose control signals are adjusted using the on-line measurements, can offer better damping effects for generator oscillations over a wider range of operating conditions than conventional regulators. The FLC, based on a set of fuzzy logic operations that are performed on controller inputs, provides a means of converting linguistic control requirements based on expert knowledge into an efficient control strategy. Using unsupervised learning of ANN generates a fuzzy associative matrix.

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5.2.4 State Estimation The power system state estimation is another area were fuzzy logic applications are performed in recent times. State estimation is the task of determining the actual values of the state variables .One of the problems in automating a power system is the construction of reliable models of the system whose state variables can be identified sufficiently accurately using available noisy system data. For the successful operation of large-scale power systems the optimal estimation of the state is required. The weighted Squares (WLS) estimator is widely and extensively used due to their numerical stability and computational stability. The main disadvantage of this method is the presence of the gross errors. An alternative state estimation approach, the weighted least absolute value (WLAV) has been applied to power system problems. This estimator is more robust than the WLS estimator. The notable drawback of this method is the poor computational efficiency for large sized problems. F. Shabani, N. R. Prasad et al [SPS 96] formulated a method which uses the combination of weighted least squares and fuzzy logic based techniques to improve the state estimation of the power systems. In this method variant of the Kalman State Estimation is taken as the basis. The optimal estimator is controlled by the parameter W, which the weight is given to the current state estimate calculated using the WLS method. If W is found to be large, then more weight is placed on the current state estimate in relation to the measured value and vice versa. 5.2.5 Security Assessment On line security assessment of a power system involves monitoring the current operating condition of the system and assessing the effects of probable contingencies (e.g. outages of transmission lines, tripping of generators, etc). The conventional approach based on simulation of probable contingencies is not suitable for on-line security assessment because of the large computation time involved. K. Sinha et al [AKS 95] presented a PR and fuzzy estimation technique. Pattern Recognition is one of the potential methods, which fits the computational requirements of online security assessment. In the past, some pattern recognition methods have been proposed for power system security assessment. These methods security classification schemes are not well suited for large power systems because of convergence problems faced in designing the classifiers in a large dimensional pattern space. Here the knowledge about the system operating conditions is stored in a structured memory by grouping similar patterns into clusters which are arranged into a hierarchical tree structure. This enables a very fast two level search for the near neighbors of the input pattern. The security status of the input pattern is determined using a fuzzy estimation technique. This not only provides a very reliable security classification but the fuzzy grade membership also provides a quantitative ' level of confidence ' for the security classification.

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5.2.6 Fault Diagnosis and Restoration Fault diagnosis and restoration is perhaps the most popular area of the AI implementation where a large number of alarms have to be interpreted in real time to determine possible fault scenarios, based on which suitable restorative actions need to be taken. Expert knowledge is used to model the system behavior and response. Fuzzy expert systems are now being used for these applications to include vague constraints and express uncertainty. Many implementations for various fault diagnosis problems have been reported in the literature. Application of fuzzy set theory in fault diagnosis was first reported by Xu et al [XZL 90]. Fuzzy linguistic variables were used to characterize the load patterns of several types of days. The load of each load points in the distribution system was estimated using a fuzzy expert system. Following a fault an efficient restoration plan was generated using a heuristic search method. A fuzzy method to deal with the uncertainty concerning fault location in distribution networks was also developed. Here some of the advantages and important implementation issues based on practical experience were highlighted. Hyun-Joon Cho and J. K. Park et al [HJ 97] proposes an expert system using fuzzy relations to deal with uncertainties imposed on fault section diagnosis of power systems. The so-called Sagittal diagrams were build which represents the fuzzy relations for power systems and diagnosis were done using these diagrams. The malfunctioning of relays and circuit breakers based on the alarm information and the estimated fault sections were estimated. The system provides the fault section candidates in terms of the degree of membership and the malfunction or wrong alarm. The operator monitors these candidates and is able to diagnose the fault section, coping with uncertainties. 5.2.7 Load Forecasting Load forecasting is an important task for the efficient operation of a power system. Some recent works have reported successful application of fuzzy logic for expressing the vague relationship between forecast load and various parameters in which depends. Hsu and Ho [YK 92] first proposed a fuzzy expert system for short term load forecasting. Considerable improvement in the accuracy of the forecast hourly loads was reported. Torres and Mukhdekar [TM 89] developed a fuzzy knowledge based forecasting tool for distribution feeder load. A fuzzy front-end processor was used in this work to enhance the forecasting accuracy by preprocessing the inputs, both numerical as well as fuzzy. D. K. Ranaweera, N. F. Hubele et al [RHK 96] presented a fuzzy logic based short term load forecasting. The proposed methodology uses fuzzy rules to incorporate historical weather and load data. These fuzzy rules are obtained from the historical data using a learning-type algorithm. One of the major obstacles in implementing and using a SLTF (Short Term Load Forecast) has been the lack of user trust and confidence in the model. The mathematical

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complexity while designed to capture the nonlinear relationships between inputs (past load, past and predicted temperature) and outputs (predicted load) and does not offer the user an intuitive understanding. If these mathematical relationships could be reduced to logical table, such as a set of IF - THEN rule then there is the possibility that the user would gain confidence in the model and therefore use it to generate, or assist in generating the system forecast. The fuzzy logic, which is in essence a set of logical statements, could be well developed solely from expert knowledge. 5.2.8 Voltage Stability Enhancement Fuzzy Control Approach has been effectively presented in the Voltage Stability Enhancement too. The concept is as the same in reactive power planning and control which leads to better voltage profile. G.K.Purushothama, N Udupa and D. Thukaram et al [PuUTPa] presented a new technique using fuzzy set theory for reactive power control with the purpose of improving the voltage stability of the power system. Here the voltage stability index (L index) n and the controlling variables are translated into fuzzy set of notations to formulate the relation between voltage stability level and controlling ability of controlling devices. Then a fuzzy ruled-based system is formed to select the controllers, their movement direction and the step size. The performance obtained from testing the above fuzzy controlled system was found to be encouraging. First the L index is computed for the system. This is found, from the load flow algorithm incorporating the load characteristic and the generator control characteristics. The load flow result is obtained for a given system operating characteristics or from the online state estimator. Then the L index sensitivity is computed. The linguistic variables of the system consists of 1. Voltage stability index, L-index 2. Sensitivity of the voltage stability index to control variables such as OLTC, SVC and generator excitation meetings. The terms of the linguistic variables are used to describe the states of the system. Different states are developed as low (L), medium (M), high (H) and very high (VH) for the L index value. For the controllers three terms are used mainly i.e. small ( S),medium(M) and large(L).For the output of the system the four terms are included as L, M, S, Z. The Fuzzy conditional statements are then prepared Based on the values of the input variables fuzzy sets are formed. Using the terms of the linguistic variables and Rule base, fuzzy computations are performed. Algorithmic steps in the proposed control methodology are 1. Base case load flow is performed ( or from state estimation)

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2. Matrices S l, S' are found. Sensitivity S is computed.

3. Observe the sorted list of nodes according to their L-index. If maximum L- index is acceptable within tolerance go to step 7. 4. Using the available margin of the controller settings are evaluated so as to minimize the Lindex of those nodes where it is more than the acceptable level.

5. Corrections to the controller settings are evaluated so as to minimize the L-index of those nodes where it is more than the acceptable level. 6. Estimate new L- indices with the suggested controller settings. If the maximum L index value is not acceptable within tolerance and margin is available for the controllers to 4.

7. Perform the load flow with the suggested controller settings and output results.

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CHAPTER 6 ANALYSIS OF THE TECHNIQUES 6.1 Neural Network based Applications The most of the applications related to neural network is based on multilayer perceptron. Here the error back scheme is widely used. Fundamental aspects of Multilayer Perceptron networks are random initial start up state and convergence of connection weights to produce minimum error. However there are no set rules for parameter selection associated with these algorithms. So in using ANN models some trial and error is required. 6.1.1 Design of Network As discussed in practical applications Multilayer Perceptron with at least one hidden layer is used. It has been reported that using greater number of hidden layer improve the overall performance. But some experimentation is required to select the number of hidden layers and nodes. Generally at least twice of as many nodes in the hidden layer has been taken as Inputs. Some of the researchers gave an empirical formula as H = ni (ni-1) to calculate hidden layer where 'H' is the number of the hidden layer and 'n i' the input. But still some trial and error is needed to produce quick convergence and acceptable results. The introduction of the concept of structured ANNs (e.g. Perceptrons, Hopfield Network, and SOM) designed for specific tasks simplify the design process. Also research results are available for dynamically designs hidden layers. Cascaded correlation's begins with minimal network, then automatically trains and adds new hidden units one by one. Once the hidden layer is added it becomes a permanent feature detector in ANN. This architecture learns quickly. 6.1.2 Training Set Generation In many applications, there is no efficient way of generating a complete training set to cover all possible operating states. This will be of greater concern in dealing with a problem of large on line data handling. For example, In the cases of power system security problem most of the literatures reports about offline simulation to obtaining the training sets. It is possible to analyze if the samples chosen are small in size. If the sample is large (500 buses, which are the case of the practical system,) the analysis will be extremely difficult. Moreover its not easy to obtain good performance on training data followed by much worse performance on test data. There can be improvement if some knowledge can be incorporated about the domain into the network architecture.

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6.1.3 Hopfield Network Hopfield Networks can be very useful in solving the optimization problems very quickly and efficiently by minimizing energy function, defined in terms of its weights and thresholds. However, this energy function has many local minima. This is not acceptable especially in contingency screening. The reason is that we should get the best rather than the feasible ranking of contingencies. Another drawback is that the weights and thresholds are calculated based on the optimization process, which has to be repeated if any of the input parameters change. The enhancement in the recent development of the architecture reduces these drawbacks. Also a mapping method is formulated from which the weights and thresholds for the particular optimization problem can be easily computed. 6.1.4 Training the Inputs Many of the ANN models (like perceptron, SOM, ART Networks heavily rely on the information retained to the input features. In any power system applications the input patterns space consists of a large number of features. So feature selection is necessary to reduce this pattern space to a reasonable size. These processes make loss of information. 6.1.5 Knowledge Consistency and Interaction with the User Knowledge Consistency is an important concern in the training set of ANN research. The AI implementations are considered complete when they match with human competence and thus further research is needed in this area. In many cases AI technique is required to interact to demonstrate the validity of the decision to the User. For example in the diagnosis of faults in the system, the operator might want to ascertain the validity of the reasoning employed. Similarly in preventive control an explanation might be necessary to validate and verify the control strategy. 6.1.6 Practical Implementation In the hardware part most of the present day ANN schemes are single-processor simulations of the massively parallel ANN models. When using the multilayer perceptron model, most of the implementations use a sequential algorithm on conventional computer to train the ANN, in node by node manner. Ideally ANN schemes should be implemented in parallel processing machines to fully reap the benefits of their massively parallel structure. There is mainly two way of implementation of ANN in the parallel computers. 1. Direct Implementation in which there is a physical-processing element for each neuron in the neural network. This approach can potentially provide a very good performance. However it can support only a specific ANN model since it is fixed in the hardware.

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2. Virtual implementations (with general-purpose neuro computer) in which a processing element takes charge of multiple neurons and simulates them in a time-sharing fashion. 6.2 Fuzzy Logic based Applications 6.2.1Requirements of Fuzzy based Applications The main characteristics and requirement for a problem suitable for fuzzy logic applications are 1. The problem has to be solved by human experts for daily operation and planning. Thus functional knowledge in terms of heuristic rules are available. 2. If the methodology cannot be expressed in terns of mathematical form. 3. If the modeling of mathematical problem requires various many assumptions to be made, leading to an inaccurate models. 4. If the problem involves uncertainty, vague constraints and/or multiple conflicting objectives. 5. The complexity of the problem makes the solution computationally intensive if solved by conventional technique. Fuzzy systems are found to be very effective with problems dealing with most of these issues. 6.2.2 Advantages of Fuzzy Logic Applications The main advantages of the fuzzy systems are 1. Speed 2. Computationally less expensive and simpler tools. 3. Flexibility 4. Ease of computation They are found to be very powerful in applications involving Uncertainties, imprecision and conflicting objectives. It's effective when the problem is non-linear in nature and if there is a convenient way to obtain Input-Output mapping. It cannot be used if Input-Output mapping is difficult. The various issues that needs to be addressed, even though fuzzy logic has found in various applications are Creation of fuzzy logic Creation of fuzzy logic is mostly through experts, which lacks in knowledge engineering. That means it depends on expert opinion and cannot decide the rule networks Genetic Algorithms and fuzzy clusters. Common sense knowledge Representation It’s difficult to represent and manipulate common sense knowledge and there are no effective and sufficient methods to do so.

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Fuzzy Logic Controller Stability Stability of the FLC cannot be assessed and there are no established methods to do that. This needs to be analyzed before they can be considered as alternative for conventional controller. Tools and Practical Consideration The lack of tools for this generic development works handicaps the utilization of these systems. There is a need to support applications that can be provided quality solutions. Moreover very few applications have been Implemented Practically though many applications are reported.

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CHAPTER 7 CONCLUSION The importance of the use of the AI tools has been felt in all the areas of the Power Systems and the need is emphasized. The easiness in evaluating the vague or non-crisp concepts and the ability of these techniques to learn due to the technological improvement elevated the effect of these soft computing techniques. The study presents concepts, survey and the important analysis of typical applications of AI techniques (ANN and FUZZY LOGIC) in the field of Power systems. The fundamentals of the Artificial Neural Network and the Fuzzy Systems are also described. The analysis of these techniques is indicated in a broader sense and the practical difficulties are narrated. Also the future concentration on the modification of the techniques is analyzed to obtain better result and making these techniques competitive to the human brains. The concepts of the AI techniques are reviewed to understand those categories of models, which are used in Power Systems, and the future hybrid models that are useful. It gives the understanding of the strengths of the models. ANNs are mainly used for learning and pattern Recognition for depicting the reference knowledge database. It helps to analyze and gives the result, which can be substituted for any logical analysis. As in the case of Fuzzy Logic applications it can be seen that these techniques can be blended with the conventional systems as well as with the other techniques like Neural Networks and Genetic Algorithms. The hybrid systems thus formed can be the most powerful systems for design, planning and control & Operation of practical problems. Hybrid Systems combining the individual strengths of the ESs and ANNs along with the Fuzzy systems seems to be the most promising area in future and promising for the most of the Power system Applications. Moreover there are sufficient scope in the improvement of the various soft-computing techniques to increase their strengths and capability. The tools for the simulation of these conditions also need to be enhanced for their limitations. The application fields combining the conventional and these techniques can remarkably reduce the difficulties faced in the Power Systems design, operation and control.

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BIBLIOGRAPHY 1965 [LAZ 65] L.A.Zadeh. Fuzzy Sets Information Control, pp 338-353 (1965).

1983 [FLBHW 83] R. A. Fernades, F. Lange, R.C. Burdett, H.H. Happ and K. A. Wirgan. Large Scale Reactive Power Planning, IEEE Trans.Power Apparatus System (PAS), pp 1083-1088 -102 (1983).

1986 [CCM 86] S. J. Cheng, Y.S.Cao ,O.P. Malik and G. S. Hope. An adaptive synchronous Machine Stabilizer, IEEE Trans. Power System , Vol 1, pp 101-109 (1986).

1988 [GPM 88] S. Granville, M.V.F.Pereira and A. Monticelli. An Integrated Methodology for VAR Sources Planning, IEEE Trans. Of Power System , pp 549-557, 3 (1988). H.Kanoh,M. kaneta and K. Kanemaru. Study on fault Location System for Transmission Lines using neural Networks, Doc. System Control Staudy Group, Inst. Electr. Engg. Jpn ; SC 88-22, pp 53 ( 1988).

[HMK 88]

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1994 [DLC 94] Dipti Srinivasan. A.C.Liew and C.S.Cheng. A Neural Network ShortTerm Load Forecaster. EPSR,Vol 28, pp227-234 (1994). M. Djukanovic, D.J.Sobajic and Y. H. Pao. Neural Net Based Tangent Hypersurfaces for Transient Security Assessment of Electric Power Systems. EPSR Vol 16, No.6 ,pp 399-408 (1994). Y.Y.Hsu and H.C. Kuo. Heuristic based fuzzy relationing approach for

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distribution system service restoration. IEEE Trans. On Delivery 9 : 2, (1994).

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1995 [AJA 95] Feed Forward neural Networks Vector Decomposition Analysis, Modelling and Anolog Implementation. Kluwer International Series in Engineering and Computer Science (1995). A.K.Sinha. Power System Security Assessment using pattern Recognition and fuzzy estimation, EPSR, Vol17,No.1, pp11-19( 1995). A.P. Alves DaSilva,V.H. Quintana. Pattern Analysis in Power System State Estimation. EPSR, Vol 17, No.1, pp51-60 (1995). M. Djukanovic, S.Ruzic, B.Babic, D.J. Sobajic, Y.H. Pao. A Neural Net based Short Term Load forecasting using moving Window Procedure. EPSR Vol 17, No 6, pp 391-397 (1995). Hong-Chan Chin.Optimal Shunt Capacitor allocation by Fuzzy Dynamic Programming. EPSR Vol 35, pp 133-139 (1995).

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E.A. Mohammed and N.D.Rao.Artificial Neural Network based Fault Diagnosis System for Electric Power Dustribution Feeders. EPSR 35, pp 1-10 (1995). Witold Pedrycz. Fuzzy Sets Engineering with Foreward by Lotif. A. Zadeh. CRC Press (1995).

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1996 [BIKMM 96] Bann, Irisarri, D. Kirschen, B. Miller, S. Mokkhtari .Integration of Artificial Intelligence Applications in the EMS : Issues and Solution. IEEE Trans. Power System, Vol 11, No1, pp 475-482 (1996). C.S.Chen, Y.M.Tzeng, J.C. Hwang. The Application of Artificial Neural Networks to Substation Load Forecasting. EPSR 38 pp 153-160 (1996). J.J.Fidalgo, J.A. Pecas Lopes and V. Miranda. Neural Networks Applied to Preventive Control Measures for the Dynamic Security of

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Isolated Power Systems with Renewables. IEEE Trans. Power Systems Vol 11 No. 4 pp 1811-1816 (1996). [GC 96] S.Ghosh and B .H. Chowdhury. Design of an ANN for fast line flow contingency ranking. EPSR Vol 18, No. 5 pp 217-277 (1996). Jovitha Jerome .ANN and their Applications in Power Systems-Special Study Report (1996). Kit Po Wong, Suzannah and Yin Wa Wong. Combined Genetic Algorithm/Simulated Annealing/Fuzzy Set Approach to Short- Term Generation Scheduling with Take-Or_pay Fuel Contract. IEEE Trans. Power System, Vol 11, No.1 pp 128-136 (1996). S.A.Khaparde, N. Warke and S.H. Agarwal. An adaptive approach in distance protection using an ANN. EPSR Vol 37 pp 39-44 (1996). R. Lamedica, A. Prudenzi, M. Sforna, M.Caciotta,V.Orsolini Cencellli. A Neural Network Based Technique for short-term Forecasting of Anomolous Load Periods. IEEE Trans. Power Systems, Vol 11, No. 4 , pp 1749-1755 (1996). Y.M.Park, S. H. Hyun and J.H. Lee . Power System Stabilizer based on inverse dynamics using an Artificial Neural Network. EPSR ,Vol 18, No.5 ,pp 297-305 (1996). D.K.Ranaweera, N.F.Hubele and G.G. Karady. Fuzzy logic for short term load forecasting. EPSR ,Vol. 18,No.4, pp 215-222 (1996). C. Rodriguez, S.Rementeria. J.I.Martin, A.Lafuente, J.Muguerza and J.Perez .Fault Analysis with Modular Neural Networks. EPSR, Vol 18, No.2, pp99-110 (1996). S.Ghosh and B .H. Chowdhury. Security-Constrained Optimal Rescheduling of Real Power Using Hopfield Neural Network. IEEE Trans. Power Systems, Vol 11, No.4 pp 1743-1748 (1996). F. Shabani, N.R.Prasad, H.A.Smolleck. A fuzzy logic supported weighted least squares state estimation. EPSR, Vol 39, pp55-60 (1996). M.K.El-Sherbiny, G. El-Saady and E. A. Ibrahim.Speed Deviation Driven Adaptive Neural Network based Power System Stabilizer. EPSR ,Vol 38 ,pp 169-175 (1996).

[JJ 96]

[KSY 96]

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Ching-Tzong Su and Chein-Tung Lin. A new fuzzy Control Approach to Voltage Profile Enhancement for Power Systems.IEEE Trans. Power System, Vol 11, No.3 pp 654-659 (1996). Q.Y.Xuan, Y.H.Song, A.T.Johns, R.Morgan,D.Williams. Performance of an Adaptive Protection Scheme for series compensated EHV transmisssion systems Using Neural Network. EPSR ,Vol 36, pp 57-66 (1996).

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1997 [AFZL 97] A.P.Alves da Silva, C. Ferreira, A.C.Zambroni de Souza and G. lambert-Torres. A new Constructive ANN and its Application to Electric Load Representation. IEEE Trans Power System, Vol 12, No. 4,pp1569-1577 (1997). Bart Kosko. Neural networs and Fuzzy Systems—A dynamical Systems Approach to machine Intelligence. Printed by prentice-Hall of India Pvt. Ltd (1997). M.Bostanci, J.Koplowitz, C. W. Taylor. Identification of Power System Load Dynamics Using ANN. IEEE Trans. Power System,Vol 12, No 4, pp1468-1472 (1997). Ching Tsong Su, Gwo-Jen Chiou .A fast Computation Hopfield Method to Economic Dispatch of Power Systems. IEEE Trans on Power Systems Vol 12, No. 4 , pp 1759-1763 (1997). M.B.Djukanovic,D.M.Dobrijevic,M.S. Calovic,M.Novicevic and D.J.Sobajic.Coordinated strabilising control for the exciter and governor loops using fuzzy set theory and neural nets. EPSR Vol 19, No.8 , pp 489-499 (1997). Hyun-Joon Cho and Jong-Keun Park. An expert System for Fault Diagnosis of Power Systems using Fuzzy Relations. IEEE Trans. Power Systems, Vol.12, No.1, pp 342-348 (1997). M. H.Choueiki, C.A.M.Campbell, S.C.Ahalt. Building A Quasi Optimal Neural Network To Solve The Short-Term Load Forecasting Problem. IEEE Trans. Power Systems, Vol 12, No.4 pp.1432-1439 (1997). Srinivas Pillutla, Ali Keyhani. Power System Stabilization based on Modular Neural Network Architecture. EPSR ,Vol 19,No6, pp 411418 (1997).

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1998 [CH 98] G.A.chown and R.C. Hartman.Design and Experience with a Fuzzy Logic Controller for Automatic generation Control (AGC), IEEE Trans. Power Systems, Vol.13, No.3 pp 965-970 (1998). Jinyu Wen, Shijie Cheng and O. P. Malik. A Synchronous Generator Fuzzy Excitation Controller Optimally Designed with a Genetic Algorithm. IEEE Trans. Power Systems, Vol.13, No.3, pp884-889 (1998). K.G.Nerandra, V. K . Sood, K.Khorasani, R. Patel. Application of a Radial Based Function ( RBF) Neural Network for Fault Diagnosis in a HVDC system. IEEE Trans. Power Systems, Vol 13, No.1, pp 177-183 (1998). Narendra Uduppa. On line development of Intelligent Tools for Applications in Energy Control Center. Phd Thesis (1998). Online Topology Determination and Bad Data Suppression in Power System Operation using ANN. IEEE Trans. Power Systems, Vol 13, No3, pp-796-803 (1998). S.M.Sadeghzadeh, M. Ehsan,N.Hadj Said, R. Feuillet. Improvement of Transient Stability Limit in Power System Transmission Lines Using Fuzzy Control of FACTS Devices. IEEE Trans. Power Systems, Vol.13, No.3, pp917-922 (1998) J. Vermaak, E.C.Botha. Recurrent Neural Networks for Short-Term Load Forecasting. IEEE Trans. Power Systems, Vol 13, No.1, pp 126131 (1996).

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[NSKP 98]

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[SLA 98]

[SEHFH 98]

[VB 98]

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by

Sukumar Kamalasadan (ETA987083)

Special Study Report

Advisor Dr. D. Thukaram

Electric Power Systems Management, Energy Program, SERD, Asian Institute of Technology, Bangkok, Thailand November 1998

Application of Artificial Intelligence techniques in Power System

ABSTRACT A reliable, continuos supply of electrical energy is essential for the functioning of today's modern complex and advanced society. Electricity is one of the prime factors for the growth and determines the value of the society. Manual calculation, technical analysis and conclusions initially adopted the power system design, operation and control. As the power system grew it became more complex due to the technical advancements, variety and dynamic requirements. Conventional Power System analysis become more difficult due to 1. Complex versatile and large amounts of data that are used in calculation, diagnosis and learning. 2. The increase in the computational time period and the accuracy due to extensive system data handling. The modern power system operates close to their limits due to the increasing energy consumption and impediments of various kinds, and the extension of existing electric transmission networks. This situation requires a significantly less conservative power system operation and control regime which, in turn, is possible only by monitoring the system states in much more detail than was necessary previously. Sophisticated computer tools have become predominant in solving the difficult problems that arise in the areas of Power System planning, operation, diagnosis and design of the systems. Among these computer tools Artificial Intelligence has grown extensively in recent years and has been applied in the areas of the power systems. The most widely used and important ones of Artificial Intelligent tools, applied in the field of Electrical Power Systems are the Artificial Neural networks and the so-called Fuzzy systems. This special study gives a review of the Artificial Intelligence (Both artificial Neural Network and Fuzzy systems) basic principles and the concepts, along with the application of these tools in the power systems areas. A survey of the applications of ANN and Fuzzy systems in the field of power systems is complied and presented and the details of the important application are discussed. Finally the major achievements of this soft computing technique in power system areas are commented and the future scopes of these methods in the modern power system are analyzed.

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Table of Contents

Chapter

Title

Pag e

Title Page Table of Contents Abstract List of Figures 1 Introduction 1.1 Back Ground 1.2 Neural network and its application 1.3 Fuzzy sets/logic and its application 1.4 Structure of the Study 2 Artificial Neural Network 2.1 Definition of the Neural Network 2.2 Fundamentals of artificial Neural Network 2.3 Neural Network Design 2.4 Learning, Recall and Memory in ANN 2.5 When and why using Neural Network 2.6 An Overview of the well known ANN Models Fuzzy Logic and Fuzzy Systems 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 4 Importance of Fuzzy Systems Basic Concepts Fuzzy Sets and Rules Classical Operations of Fuzzy Sets Membership function and membership values Fuzzy Relations Properties of Fuzzy Sets Fuzzy Truth Value Learning in Fuzzy Systems Fuzzy Logic Controllers (FLC) Pattern Recognition in Fuzzy Systems Relational Data Adaptivity features and Adaptive Controllers

i,ii iii iv 1 1 1 2 2 4 4 4 5 6 8 9 17 17 17 18 18 19 19 19 20 20 21 21 22 23 24

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4.1

Introduction on ANN application

24 25 25 26 27 30 31 31 32 32 33 34 34 34 34 38 38 40 40 41 41 42 44 44 44 44 45 45 45 45 46 46 46 48 49

4.2 Major Applications 4.2.1 Power System Stabilizer 4.2.2 Load Forecasting 4.2.3 Fault Diagnosis 4.2.4 Security Assessment 4.2.5 State Estimation 4.2.6 Contingency Screening 4.2.7 Voltage Stability Assessment 4.2.8 Protection 4.2.9 Load Modeling 5 Application of Fuzzy Logic in the Power System 5.1 Introduction onFuzzy logic application 5.2 Major applications 5.2.1 Reactive Power Control 5.2.2 Transient Stability 5.2.3 Generator Operation and Control 5.2.4 State Estimation 5.2.5 Security Assessment 5.2.6 Fault Diagnosis and Restoration 5.2.7 Load Forecasting 5.2.8 Voltage Stability Enhancement 6 Analysis of the Techniques 6.1 Neural Network based Application 6.1.1 Design of Network 6.1.2 Training Set Generation 6.1.3 Hopfield Network 6.1.4 Training the Inputs 6.1.5 Knowledge Consistency and Interaction with the User 6.1.6 Practical Implementation 6.2 Fuzzy Logic based Application 6.2.1 Requirements of Fuzzy based Application 6.2.2 Advantages of Fuzzy Logic Application Conclusion Bibliography

7

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List of Figures Figure 2.1 Figure 2.2 Figure 2.3 Figure 2.4 Figure 2.5 Figure 2.6 Figure 3.1 Figure 3.2 Figure 3.3 Figure 4.1 Figure 4.2 Figure 4.3 Figure 5.1 Schematic Diagram of the Neuron Ways of Implementing a Solution to a Specific Problem Overview of the Main ANN models Three Layer Feedforward Neural Network Back Propagation Algorithm/Network Typical RBF Network Truth Values in Fuzzy Logic The Characterization of Pattern Recognition An Adaptive Fuzzy Controller Modular Neural Network Feedforward Architecture Unsupervised/Supervised forecasting Fault Diagnosis process Procedure Adopted for Load 4 9 10 11 13 14 20 22 23 26 28 29 36

The membership function of controlling ability of controlling devices The membership function of Voltage violation Level Computation Procedure for the solution for Voltage Profile Enhancement

Figure 5.2 Figure 5.3

37 37

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CHAPTER 1 INTRODUCTION 1.1 Back Ground The increasing prominence of the computers has led to a new way of looking at the world. Artificial Neural Networks (referred as ANN here on) and the Fuzzy logic (systems) that are considered as the so called soft computing methods are now a days becoming predominant tools in the area of Artificial Intelligence linked application oriented methods. The Neural network theory was first adopted in 1940 where the starting point was the learning law proposed by ITEBB in 1949, which demonstrated how neurons could exhibit learning behavior. The application further waxed and waned away because of the lack of powerful technological advancement. The resurgence occurred recently due to the new methods that are emerging as well as the computational power suitable for simulation of interconnected neural networks. Further to the technological advancement in the field of ANN, researchers were attracted on their important applications where logical and relational thinking is required. Among the major applications viz., robotics, analysis, optimal control, database, learning, signal processing, semiconductors, Power system related applications became a useful tool for the online researchers in this field. Fuzzy Systems or logic’s as introduced by Zadeh [LAZ 65] in 1965 has basically introduced to solve inexact and vague concepts by relating those using multi-valued ness in a logical way. Earlier research in this field was based on mathematical understanding of set theory and probability. Further as a part of developing it as mathematics the applications of these theories were considered in different areas. The application of fuzzy systems were mainly in the field of modal interface, speech recognition, functional reasoning hybrid application along with Neural nets, information, traction control, business other than in almost all the areas of the power systems. 1.2 Neural Network and its Applications ANN is biologically inspired and represented as a major extension of computation. They embody computational paradigms, based on biological metaphor, to mimic the computations of the brain [VVR 93]. The improved understanding of the functioning of neuron and the pattern of its interconnection has enabled researchers to produce the necessary mathematical modes for testing their theories and developing practical applications. Main applications of the ANN’s can be divided into two principal streams. First stream among this is concerned with modeling the brain and thereby explains its cognitive behavior. The primary aim of researchers in the second stream is to construct useful ‘computers’ for real world problems of classification or Pattern Recognition by drawing on these principles. The application of ANN's in the power systems belongs to this category and is one of the recent interesting topics in the Power System Engineering.

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1.3 Fuzzy sets / logic and its Applications Fuzzy set theory systems provide tools for representing and manipulating inexact concepts and the ambiguity prevalent in the human interpretations and thought process. This theory devices from the fact that almost all natural classes and concepts are fuzzy rather than crisp in nature. They are model free systems, in which all things are matters of degree. Fuzzy logic is a logical system for formalization of approximate reasoning, and is used synonymously with fuzzy set theory. It can be considered as super set of classical (Boolean) logic which users multiple truth-values to handle the concepts of partial truth. They provide an excellent framework to more completely and effectively model uncertainty and the imperious in human reasoning with the use of linguistic variables with membership functions. Fuzzification offers superior expressive power, greater generality and an improved capability to model complex problems at a low solution cost. Due to these reasons, the use of Fuzzy logic / set is increasing in the power systems problems, as it is in all intelligent processing. Many promising applications have been reported in the broad fields of system control, optimization, diagnosis, information processing, decision support, system analysis and planning. 1.4 Structure of the Study This study reviews basics of both ANN and fuzzy logic along with the recent works reported on these tools, in the field of power systems. Since the literatures covering the wide range of topics are extensive, the main consideration is to the important works in the different field of power systems. The purpose of this study is to focus attention on the most significant works as a part of the application of AI in power systems involving typical power systems problems. Subsequently critical evaluations and the potential and scope of further areas of work in the related fields are summarized for the benefit of the researchers interested in these areas. Basic concepts of Neural network including the learning features are explained in the Chapter two. The structure of the Neural network, its design and construction were discussed. The training of ANN, the purpose and use of the ANN were further detailed. Moreover an overview of the well-known ANN models and the comparison between them highlighting the main advantages is reviewed. The concept of Fuzzy Rules and systems, the importance and the technical details are discussed the Chapter three. The basic rules, the properties and definitions of this theory are and the operations are seen. Moreover Pattern Recognition technique, the concept of the socalled Fuzzy Logic Controllers (FLC), and the adaptive features of Fuzzy Sets are analyzed. Chapter four mainly deals with the application of ANN in the field of Power Systems. The various research works on ANN application in the various areas in the Power Systems were reviewed. The basic ANN applications mainly cover the areas like control, forecast, Diagnosis, Assessment, Screening, Modeling.

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Similar in line, Chapter four details the application of Fuzzy Logic’s in Power Systems. Main applications cover Stability Control, Diagnosis, Assessment, Forecasting, Planning and Estimation. Further the analysis of these techniques is done in chapter six with a view to importance of various applications and the further scope of research. Concluding the Strengths of these techniques and the abilities are illustrated.

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CHAPTER 2 ARTIFICIAL NEURAL NETWORK 2.1 Definition of the Neural Network Neural networks are systems that typically consist of a large number of simples processing units, called Neurons. A neuron has generally a high-dimensional Input vector and one single output signal. This output signal is usually a non-linear function of the input vector and a weight vector. The function to be performed on the Input vector is hence defined by the non-linear function and the weight vector of the neuron. The weight vector is adjusted in a training phase by using a large set of examples and the learning rate. The learning rule adapts the weight of all neurons in networks in order to learn an underlying relation in the training example. 2.2 Fundamentals of a Artificial Neural Network Elementary processing unit of ANN’s is neuron. Generally it contains several inputs but has only one output. The main differences between various existing models of ANN are mainly in their architectures or the way their basic processing elements (neurons) are interconnected. As basic element the neurons are not powerful but their interconnections allow encoding relationship between variables of the problems to which it is applied and providing very powerful processing capabilities.

Incoming Weighted Connections

Neuron

Output = F ( Σ Inputs ) Outgoing Weighted Connections

Figure 2.1 Schematic Diagram of the Neuron General model of the processing unit of ANN can be considered to have the following three elements. Weighted Summing Unit The weighted summing unit consists of external or internal inputs (Xi (x1, x2, x3… xn)) times the corresponding weights Wij = (wi1, wi2,……. win). The fixed weighted inputs may be either from the previous layers of ANN or from the output of neurons. If these inputs are derived from neuron outputs, it forms the feedback architecture it has feedforward architecture.

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Linear Dynamical Function It is essentially a single input or single output function block. This block may exist for time varying signals and introduces a function that is an integral, a proportional, a time delay or a combination of these. Example: Following two general functions can be used to relate input Pi with output Qi as (a1,a2)Qi (t) = Pi (t) Qi (t) = Pi (t-T) Non linear function This decides the firing of neuron for a given input values. It is a static nonlinear function which may be pulse type or step type, differentiable (smooth) or non-identification (sharp) and having positive mean or zero mean. Some of the examples of such functions are threshold, sigmoid, Tan hyperbolic or Gaussian functions. Different characteristics of neurons can be evolved using different type and combination of the above three of its basic components. 1. Perception models consist of weighted summing unit having no feedback inputs, no dynamic function and signal as non-linear function. 2. Feedback or dynamic networks utilize the dynamic function block. 2.3 Neural Network Design A neural network element is a smallest processing unit of the whole network essentially forming a weighted sum and transforming it by the activation function to obtain the output. In order to gain sufficient computing power, several neurons are interconnected together. The manner in which actually the neurons are connected together depends on the different classes of the neural networks. Basically neurons are arranged in layers. ANNs have parallel distributed architecture with a large number of nodes and connections. 2.3.1 ANN Architecture Construction of neural Network involves the following tasks. (i) Determination of network topology (ii) Determination of system (activation & synaptic) dynamics Determination of the Network Topology The topology of the neural network refers to its framework as well as its interconnection scheme. The number of layers and the number of nodes per layer often specify the framework. The types of layer include Input Layer where the nodes are called input units, which do not process information but distribute information to other units. Hidden Layer(s) where the nodes are called hidden units, which are not directly observable. They provide into the networks the capability to map or classify nonlinear problems. The Output Layer where the nodes are called output units, which encode possible concepts (or values) to be assigned to the instance under consideration. For example each output unit represents a class of objects. Other main important concept is the weightage for the connected unit. It can be real or integer numbers. They can be confined to a range and are adjustable during network training. When training is completed, all of them attain fixed values.

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Determination of Systems (Activation & Synaptic) Dynamics The dynamics of the network determines its operation. ANN’s can be trainable nonlinear dynamical systems. Neural dynamics consists of two parts one which corresponding to the dynamics of activation states and the other corresponding to the dynamics of synaptic weights. The activation dynamics determines the time evolution of the neural activation’s. Synaptic activation determines the change in the synaptic weights. The synaptic weights form Long Term Memory (LTM) where as the activation's state forms Short Term Memory (STM) of the network. Synaptic weights change gradually, whereas the neuron's activation's fluctuate rapidly. Therefore, while computing the activation dynamics, the system weights are assumed to be constant. The synaptic dynamics dictates the learning process. 2.4 Learning, Recall and Memory in ANN Learning in a neural network essentially consists of modifying in some systematic manner the interconnection strengths between the neural units. This is achieved by observing the system in question to see how the process evolves with time or in response to additional external actions. The development of any ANN involves two phases: Learning or Training phase and Recall or testing phase. ANN uses memory to learn and adapt. Memory, in ANN, is in form of values of weights of the interconnecting links. The memory in ANN can be a Content Addressable Memory (CAM), where it stores the data at stable state in memory (or weight) matrix W or an Associate Memory which provides output response from input stimuli. The mechanism for learning alters the weights associated with the various interconnections and thus leads to a modification in the strength of interconnection. Training patterns with examples carried out training in the network. Once the network has learnt the problem, it may be presented with new unknown patterns and its efficiency can be checked. This is called testing phase. Learning methods can be classified into two categories Supervised learning Unsupervised learning Supervised learning is the process that incorporates an external guidance. In the supervised learning, a training pair consists of an input vector and a desired target vector. The difference constitutes an error that is used to modify network weights in a manner that reduces the error in subsequent training cycles. These techniques include deciding, when to turn off the learning, how long and how often to present each association for training and supplying performance error information. Supervised learning is further classified as Structural learning / Temporal learning. Structural learning encodes the proper auto associate (single pattern vector) or heteroassociate vector of patterns pair mapping into weight matrix W. Temporal learning encodes a sequence of patterns necessary to achieve final outcome.

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In the Unsupervised learning no target vector exists. The input vector is applied to the network and the system “self organizes” so that a consistent output (possibly unpredicted before training) is produced. During the training phase the weights of ANN stabilize and while testing for an unknown pattern gives the output without a time-delay of learning phase. The recall or testing depends on the interconnection of the network. In feedforward network, the network provides output in just one pass and allows flow of signal in only one direction from input to hidden and to output layers. In feedback network, signals can flow amongst neurons in either direction and /or recursively. Some of the most popularly used rules for learning includes Hebb's rule and Delta rule for single layer (perception) ANN, Backpropagation algorithm for multilayer (perception) ANN. Thus its architecture, its processing algorithm and its learning algorithm characterize a neural network. The architecture specifies the way the neurons are connected. The processing algorithm specifies how the neural network with a given set of weights calculates the output vector for any input vector. The learning algorithm specifies how the network adapts its weights for all given vectors. 2.4.1 Learning Tasks The choice of a particular learning procedure is very much influenced by the learning task, which a neural network is required to perform. Some of the learning tasks that benefit the use of neural networks are as follows. a) Approximation Suppose a nonlinear input/output mapping is given described by the functional relationship d = g(x) where x is the input vector and the scalar d is the output. The function g(x ) is assumed to be unknown. The requirement is to design a neural network that approximates the non-linear function g(x), given a set of the input/output pairs (x1,d1),(x2,d2)….(xn ,dn). The approximation problem is the main example for supervised learning. The supervised learning can also be viewed as functional mapping problem. b) Pattern Classification In the pattern classification there are fixed number of categories into which activation's are classified. To resolve this activation classification neural network undergoes training. In the training the network is repeatedly presented a set of patterns along with the categories where the pattern belongs. After that a new pattern is presented to the network, which is new but belongs to the same kind of the patterns used in the network. Further to that the neural network has to classify this new pattern correctly. The advantage of using the neural network to perform pattern classification is that ANN can construct non-linear decision boundaries between the different classes in a nonparametric fashion and thereby offer a practical method of solving otherwise highly complex pattern classification problems. The pattern recognition can be classified as a supervised learning problem. There is also the unsupervised learning in pattern classification, especially

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when there is no prior knowledge of the categories into which the activation patterns are to be classified. Here unsupervised learning is used to perform the role of adaptive feature extraction or clustering prior to Pattern Recognition. c) Prediction Prediction is most basic task. It’s a signal processing problem, where in the set of m past samples that are uniformly spaced in time, are used to predict the present sample x (n). Sample x (n) serves the purpose of the desired response. Based on the previous samples x (n-1), x (n-2), ….. x(n-m) , we may compute the prediction error e(n) = x(n) - x(n | n-1,…. N-m) and thus the error-correction learning is used to modify the weights of the network. Prediction may be viewed as the form of the model building in the sense that smaller the prediction error in a statistical sense the better will the network serve as the physical model of the underlying stochastic process responsible for the generation of the time-series. When the process is of nonlinear in nature then the use of ANN provides a powerful method for solving the prediction problem by virtue of the non-linear processing units built into its construction. d) Association The two types of associations are Auto association and Hetero association. In auto association a neural network is required to store a set of patterns by repeatedly presenting them to the network. Also network is presented a partial and distorted version of an original pattern stored in it. Now the network is asked to recall that particular pattern. Hetero Association differs from Auto association in that an arbitrary set of input patterns are paired with another arbitrary set of output patterns, Auto association involves the use of unsupervised learning whereas the type of learning involved in hetero-association is of a supervised nature. The main difference between different classes of the network can be based on the learning approach. The main type of learning can be supervised and unsupervised learning. Supervised learning is done through a set of examples where each example consists of the input values and target output values. These output values are then used as a basis for the correction of the weights. The single layer feed-forward net and the Backpropagation nets use supervised learning Unsupervised learning has a set of examples where the input conditions are known but the associated target output conditions are not given. The task of the neural net is to group the set of training vectors into clusters based on some kind of similarities. However when simulated with a particular input, it is not known beforehand to which cluster the output obtained from the net belongs. In some of the cases the number of clusters or their diameter is determined before training. In others no assumption is made with respect to the number and the nature of the clusters. Kohonen net uses unsupervised learning. 2.5 When and why using Neural Network Neural set is basically a new way of solving the problems, which way can successfully be followed for a number of problems. For some problem neural network is not however

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useful. Main difference of using the Neural Network and conventional method of solving problems are, Neural Network is trained to perform satisfactory. In a training phase, training examples are presented to the networks and the weights of the neural networks are adapted by a learning rate. Conventional methods typically use an (analytical or empirical) model of the task. The ways of implementing the solution to specific problems can be divided as Problem Problem Level

Solution Level Algorithm Neural Network Implementation Level Software hardware

Figure 2.2 Ways of Implementing a Solution to a Specific Problem Useful Functions of the Neural Network Useful Function to be performed by the Neural network can be subdivided into few categories, which are distinguished by the nature of the problem • Its useful to apply the neural networks on problems for which no direct algorithmic solutions exists but for which problem examples of the desired responses are availed. • It is useful to apply Neural Networks for the problems that change over the time. The adaptability of the neural network will then be used to adapt the implemented solution whenever the problems changes • Its useful to apply Neural Networks to problems for which only too complicated algorithms can be derived. “Too complicated” means that implemented (conventional) algorithms are either too large, or consume too much power. Its not useful to train neural network on problems for which the solution can easily be implemented in an algorithm. Neural Network can also learn these simple algorithms but neural implementation is generally larger and less accurate than the direct algorithmic implementation of the solution. For number of problems the implementation of the solution in Neural Network is useful, while for other problems the solution should not use neural networks. 2.6 Overview of the well known ANN Models In 1943 McCullah and Pitts discussed for the first time the role of mathematical logic in neural activity. It was then the McCulloh_pitts neuron was first described. McCulloh_Pitts

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neuron has fixed threshold, has identical weights of excitatory synapses and the inhibitory synapses are absolute in nature.

ANN MODELS

FEED BACK

FEED FORWARD

CONSTRUCTED

TRAINED

LINEAR

NON LINEAR

UNSUPERVISED

SUPERVISED

HOPFIELD

ADAPTIVE RESONANCE

KOHONON

BACK PROPOGATION

Figure 2.3 Over View of the Main ANN models Hebb in 1949 introduced the fundamental concepts of learning in his classical text Organizational Behavior, and gave the famous learning rule named after him. Neumann, a pioneer in the field of design and development of digital computers made comparisons between the computers and the brain in 1962. An Overview of main types of ANN models are as in figure. The main types of the Neural networks are 2.6.1 Perceptron The perceptron is a single layer adaptive feedforward network of threshold logic Units, which possess some learning capability. Rosenblatt in 1958 invented perceptron, which was proposed as a model for the organization of neural activity in the brain. Single layer perpectron, incidentally, is the most widely studied, but the least applied model of all ANNs. It forms the basis of most of the further advances made in this field. Block in 1964, Minkey and Papert in 1969 studied perceptrons intensively. It was found that the single layer perceptron works well for problems, which are linearly separable, but fails to solve even simple problems, which are non-separable. This is because they lacked an internal representation of stimuli. Rumelharl proposed a multilayer perceptron with an error back propagation learning algorithm using a differential sigmoid activation function to facilitate learning rather than

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using a threshold logic units or linear functions for activation. Therefore a multilayer perceptron possess a better learning capability. Further progress was made with Amari in 1967 propounding the gradient-descent rule and designing of Backpropogation learning algorithm by Werbos in 1974, which was utilized in the multilayer perceptron model. 2.6.2 Multilayer Feedforward Neural Network In the feedforward neural network all the connections are unidirectional in a feedforward way. A multilayer perceptron is the typical example of feedforward neural network. It consists of input layer of input variable, output layer of output variable and at least one hidden layer of hidden neuron. Unidirectional connections exist from the input layer to the hidden layer and from the hidden layer to the output. There is no connection between any neurons in the same layer. The output variables are real-valued functions of input variables and weights. Varying the weights can change the input mapping. It has been proved that they are Universal Approximators. Training in this type of Neural nets are based on a limited number of training samples and it possess good generalization capability. They are used as representational models trained using a learning rule based on set of Input / output data. The main learning rule used is the popular Back propagation algorithm (also known as a generalized Delta Rule). Major application of feedforward neural network is in large-scale systems that contain a large number of variable and complex systems where little analytical knowledge is available.

X1

X2

X3

Input Layer

Hidden Layer

U1

U2

Un Output Layer

Figure 2.4 Three Layer Feedforward Neural Network

2.6.3 Backpropagation Networks It was demonstrated that the ANNs with hidden nodes and nonlinear activation's are able to simulate non-linear and linearly non-separable functions effectively. Backpropagation

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networks are essentially multilayer perceptron networks. Each node of the network is McCulloch- Pits neuron as used in perceptron. The difference is that while perceptron uses hard-limiting threshold functions, Backpropagation network uses sigmoid functions, which are nonlinear, and non-decreasing in nature. Training of the weights is carried out by Generalized delta rule (GDR) also known as Backpropagation algorithm (BPA). In the Back Propagation Algorithms, the network begins with a random set of weights. An input vector is presented and fed forward through the network, and the output is calculated by using this initial weighted matrix. Next, the calculated output is compared to the measured output data, and the squared difference between these two vectors determines the system error. The accumulated error for all the input / output pairs is defined as the Euclidean distance in the weight space, which the network attempts to minimize. Minimization is accomplished via the gradient descent approach, in which the network weights are adjusted in the direction of decreasing error. It has been demonstrated that if a sufficient number of hidden neurons are present, a three-layer Back Propagation network can encode any arbitrary input or output relationship. In the learning phase of Backpropagation network a pattern is presented at the inputs and weights are assigned arbitrary small values. The corresponding actual and target outputs are compared and error is computed. This error is used to readjust weights between the last two layers and feedback to the penultimate layer over the weights connecting it with output layer. The implementation of Backpropagation algorithm, thus involves a forward pass through the layers to estimate the error at the output, and then the error is fed to backward to change the weights in the previous layer and this goes on for all the proceeding layers. Backpropagation algorithm employs gradient descent search in weight space over the error surface to find the point resulting in minimum error. 2.6.4 Hopfield Network Hopfield Network invented by John Hopfield in 1982, has lateral and recurrent connections, that is, the output of a neuron are fed back to itself and intra-layer connections are present. The state of Hopfield network is the set of stable states of all its neurons. It is said to be unstable if it keeps on oscillating from one state to another. Stable configurations achieve a permanent state after a finite number of changes. The learning is unsupervised and takes place offline. Hopfield network is used as associative memories. They can also be used to solve optimization problems. They give better results when the input is perfectly represented as a string of binary bits. A major limitation of Hopfield network is that not more than 0.15 N numbers of patterns can be stored on a network, N being the number of needs in it. Secondly it has got exemplar patterns. Here an exemplar is said to be suitable if it applies at time zero, and the network converges to some of the other exemplars. 2.6.5 Hamming Sets Hamming sets are similar to Hopfield networks. They classify an exemplar by calculating the Hamming distance for each class and selecting that one with the minimum

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Hamming distance. The Hamming distance is the number of bits in the inputs, which do not match the corresponding exemplar bias. Such ANN, implements optimum minimum error classifier when bit errors are random and independent, and therefore their performance is better than or equal to that of Hopfield network. They also require less number of nodes than Hopfield network.

Input Layer Hidden Layer

(K-1) Layer

In ( j,k) Out( I,j)

Kth Layer

Output Layer

Figure 2.5 Back Propagation Algorithm / Network 2.6.6 Adaptive Resonant Theory The binary Adaptive resonance theory (ART-1) introduced by Carpentar and Grossberg in 1968 is a two layer nearest neighbor classifier and trained without supervision which can be used only for binary inputs. It implements a clustering algorithm, which selects the first input as the exemplar for the first cluster. The next input compares to the first cluster exemplar and clustered with it if the distance is less than a threshold. Otherwise the example for a new cluster is performed. This process is iterated for all inputs. The topology of the network is similar to Hopfield Network. Onelayer is the inputlayer, having m nodes, m being the number of classes stored on the network. Input layer revises input from the input layer and has recurrent connection. Thus it has got feedback paradigm. A simple representation of the counterpropagation network consists of three layer. The input layer is a simple fan-out layer. The hidden layer is the Kohonen layer and the output layer is Grossberg outside layer. The counter propagation networks (CPN) have been recently used because of various advantages offered. The advantages of the CPN are that, it is simple,

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easy to train and prevents a good statistical model of its input vector environment. It functions as a look-up table capable of generalization The Time-delay neural network (TDNN) is non-recurrent dynamic neural network which copes with time alignment by explicitly delaying the signal waveform by a fixed time span. The time-delays are introduced into the synaptic structure of the network and their values are adjusted during the training phase. The TDNN can be used for prediction problems. 2.6.7 Radial Basic Function (RBF) Neural networks based on localized basic functions and iterative function approximations are usually referred to as RBF networks. It’s started from Bashkriov and Aizerman at which time the networks are referred to as the method of potential functions. Classification of new patterns is done in much the same way in RBFs as in PNNs. In both the cases the localized basic functions falls of rapidly to the distance between the centers of the basic function as the input gets large. In simplest case the output of the network is a linear combination of all the basic function response. Output Units multiplies pattern activation by a weight, sums them, and adds a bias. Training in RBF consists of iteratively adapting the parameters of the network until the output approach the desired output over the whole range of training patterns. RBF network is generally a regression network and so estimates the value of a customer variable.

Xi

Xj

Xp

Input Units

Pattern Units

Wj Wi Wn +1 W Bias Bias Output Units

Figure 2.6 Typical RBF Network

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2.6.8 Probabilistic Neural Network (PNN) and General Regression Neural Network (GRNN) PNN and GRNN are feedforward neural networks. They respond to the input pattern by processing the input data from one layer to the next with no feedback path. Feedback may or may not be used in the training of networks. These networks learn pattern statistics from a training set. The training may be in terms of global -- or local basis functions. Back propagation error method is training method applied to global basis function which is defined as nonlinear functions of the distance of the pattern vector from a hyperplane. The function that is to be approximated is defined to be a combination of these sigmoidal functions. Since the sigmoidal functions have non-negligible values throughout all measurements space, much iteration are required to find a combination that has acceptable error in all parts of measurement space for which training data are available. Two main types of localized basis function networks are based on 1. Estimation of probability density functions and 2. Iterative functions approximation PNN's and GRNN's used for estimation of values of continuous variables are based on first type i.e. estimation of probability density function. The second types, based on iterative function approximation, are usually referred to as Radial Basis Function (RBF) networks. These networks use functions that have a maximum at some center location and fall off to zero as functions of distance from that center. The function to be approximated is approximated as a linear combination of these basis functions. An obvious advantage of these networks is that training a network to have the proper response in one part of the measurement space does not disturb the trained response in other distant parts of the measurement space.It is possible to train a network of local basis functions in one pass through the data by straightforwardly applying the principles of statistics. PNN's are classifier version obtained when decision making is combined with a nonparametric estimator for probability density functions where as GRNN is a function approximated version, which is useful for estimating the values of continuous variables such as future position, future values, and multivariable interpolation. a) Probabilistic Neural Network There are four variations for implementation of the pattern units in PNN network. In one variation, the topology of PNN is similar in structure to back propagation, differing primarily in that the sigmoidal activation function is replaces by an exponential activation function. Basic forms of PNN and GRNN are characterized by one pass learning and use of same width for the basic function for all dimension of the measurement space. Adaptive PNN and GRNN are characterized by adapting separate widths for the basis function for each dimension. Due to this, PNNs are ideal for exploration of new databases and preprocessing

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techniques, because this use of the neural network typically requires frequent retraining and evaluation, with relatively short test sets. The remaining three implementations of the pattern units are optimized for implementation of the pattern units are optimized for implementation on multiply/accumulate digital signal processors or on special-purpose integer arithmetic processors. b) General Regression Neural Network (GRNN) GRNN provides estimates of continuous variables and converges smoothly to the underlying (linear or nonlinear) regression surface. Like PNN, GRNN features instant learning and a highly parallel structure. Even with sparse data in a multidimensional measurement space, the GRNN provides smooth transitions from one observed value to another. Regression is the least-mean-square estimation of the value of a variables based on examples. The term General Regression implies that being linear does not restrict the regression surface. If the variable to be estimated is future values, the GRNN is a predictor. If they are dependent variables related to input variables in a process, plant or system. Thus GRNN can be used in these applications.

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CHAPTER 3 FUZZY LOGIC AND FUZZY SYSTEMS 3.1 Importance of Fuzzy Systems Fuzzy set theory derives from the fact that almost all-natural classes and concepts are fuzzy rather than crisp in nature. Fuzzy systems are model free systems in which all things are matters of degree. These systems use an inferential approach oriented towards system analysis and decision support. Fuzziness describes event ambiguity. It matters the degree, to which an event occurs, not whether it occurs or occurs in random to what degree it occurs is fuzzy. Whether an ambiguous event occurs - as when we say, "there is 20 percent chance of light rain tomorrow" - involves compound uncertainties, the possibility of fuzzy event emerges. Fuzzy systems store benefits of fuzzy associates or common sense "rules". Fuzzy programming admits degrees. They systems "reason” with parallel associate's interference. When asked a question or given an input, fuzzy systems fire each fuzzy rule in parallel, but to a different degree, to infer a conclusion or output. Thus fuzzy systems reason with sets, “fuzzy" or multivalued sets, instead of bivalent propositions. They estimate sampled functions from input to output. They may use linguistic or numeric samples for example they may use HEAVY, LONGER or number (relative) for the degree of fuzziveness. Fuzzy interpretations of data are a natural and intuitively plausible way to formulate and solve various problems in pattern recognition. Fuzzy logic is a logical system for formalization of approximate reasoning, and in a wider sense, used anonymously with Fuzzy set theory. It is an extension of multi valued logic. Fuzzy logic systems provide an excellent framework to more completely and effectively model uncertainty and imprecision in human reasoning with the use of linguistic variables with membership functions. Fuzzification offers superior expressive power, greater generality, and an improved capability to model complex problems at a low solution cost. Unlike fuzziness the probability dissipates with increasing information. 3.2 Basic Concepts Suppose your are approaching a red light and must advise a driving student when to apply brakes. Would U say " begin braking 14 feet from the cross walk " or shall we say “apply brakes pretty soon. We will say the latter and so the natural language is one example of ways vagueness arises, is used, and is propagated in every day’s life. Imprecision in data and information gathered from and about our environment is either statistical (e.g. a coin toss) the outcome is a matter of chance - or non-statistical - This latter type of uncertainty is called fuzziness.

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3.3 Fuzzy Sets and Rules In fuzzy set theory ' normal 'sets are called crisp sets, in order to distinguish them from fuzzy sets. Let C be a crisp set defined on the universe U, then for any element of u of U, either u (C) or U (C) occurs. In fuzzy set theory this property is generalized, therefore in a fuzzy set F, It is not necessary that either u ∈ F or u (F) exist. In the fuzzy sets theory the generalization of the membership properties are as follows. For any crisp set C it is possible to define a characteristic function µC: U [0,1] instead from the two-element set {0,1}. The set that is defined on the basis of such an extended membership function is called as fuzzy set. Fuzzy rules are elementary or composed proposals. They result from a conjunction between elementary fuzzy proposals. A fuzzy rule is composed of a premise and a conclusion. The classical structure of a rule is “If < premise> then <conclusion>” When the premise is an elementary fuzzy proposal, the rule is described as follows. If <x is A> then < conclusion>. The x is a variable; generally real, defined on a referential called the universe of discourse, given as a capital letter here X. A is a linguistic term, taken in a set of terms noted as TX. Basic concept of fuzzy logic's is fuzzy " If then Rule " or Fuzzy Rule. 3.4 Classical Operations of Fuzzy Sets Zadeh [LAZ 65] defined classical operations for fuzzy sets Let f (X) = all fuzzy subsets of X (that is, m f (X) ïƒŸ The fuzzy sets mA, mB F (x). The fuzzy rules are Definition: Two fuzzy sets are equal (A = B) if and only if ∀X ∈ X: (=) Equality A = B ïƒŸ m A (x) = m B (x) (∀X where x: pointwise, function __ theoretic operations) Definition: A is a subset of B (A ⊆ B) if and only if ∀X ∈ X: (⊂) Containment A ⊂ B ïƒŸ m A (x) ≤ m B (x) The other operations are ∀X ∈ X: (~) Compliment mA (x) = 1-mA (x) ∀X ∈ X: (∩) Intersection m A ∩B (x) = min {mA (x), mB (x)} ∀X ∈ X: (∪) Union mA∪B (x) = min {mA (x), mB(x)} 3.5 Membership Function and Membership Values m: X | (0,1),

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Membership function is the basis idea in fuzzy set theory. Its values measure degrees to which objects satisfy imprecisely defined properties. Fuzziness represents similarities of objects to imprecisely defined properties and probabilities which convey information about value frequencies. The member ship function µF of the fuzzy set F is a function µF: U [0,1]. (u) ∈ {0,1}. F is completely

So, every element u of U has a membership degree µF determined by the set of tuples F = {(u, µF (u)) | u ∈ U} 3.6 Fuzzy Relations

The fuzzy relation can be considered as a fuzzy set of tuples. That means each tuples has membership degree between 0 and 1. Its definition is Let U and V be uncountable (continuous) universe and µR : U X V R= [ 0,1] , then

UxV

∫ µR (u, v) /(u, v)

This is a binary fuzzy relation on U x V. If U and V are controllable (discrete) universes, then R=

UxV

∑ µR (u, v) /(u, v

The integral symbol denoted the set of all tuples on U x V denoted by

µ R ( u , v ) /( u , v )

3.7 Properties of Fuzzy Sets Let A and B be the fuzzy sets, defined respectively on the universes X and Y, and let R be a fuzzy relation defined on XxY. The support of fuzzy set A is the crisp that contains all element of A with non-zero membership degree. This is denoted by S (A), formally defined as S (A) = {u ∈X | µA (u) >0} When one deals with convex fuzzy sets as it is the case in fuzzy control theory the support of a fuzzy set is an interval. Therefore in fuzzy control theory the term width of a fuzzy set is used additionally to the term support. The width of the convex fuzzy set A with support set S (A) is defined by Width (A) which is equal to Sup (S (A)) - Inf (S (A)) where Sup and Inf denote the mathematical

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operations supremum and infimum. If the support set S (A) is bounded as is usual in fuzzy control, Max and Min can replace Sup and Inf. The nucleous of a fuzzy set A is defined by Nucleus ( A) = { µ ∈X |µ A ( u) = 1 } If there is only one point with membership degree equal to 1, then this point is called the peak value of A. 3.8 Fuzzy Truth Value A fuzzy truth-value is defined to be a fuzzy set on the closed interval V = [0,1] as follows. A is a fuzzy truth-value if and only if A is a fuzzy set on [0,1] and L be the set of all fuzzy values, that is L = {a | a is fuzzy set on [0,1]} The same can be graphically written as follows

-1

0

0 1 0 a b 1 0 (a) Numerical Truth Values (b) Interval Truth Values (c) Fuzzy Truth Values Figure 3.1 Truth Values in Fuzzy Logic 3.9 Learning in Fuzzy Systems

1

Generally learning can be well or can be bad. But one cannot learn without changing, and we cannot change without learning. Learning laws describe the synaptic dynamical system, how the system encodes information. They determine how the synaptic web process unfolds in time as the system samples new information. This is one way neural network compute with dynamical systems. Fuzzy systems learn associative rules to estimate functions or control systems through unknown probability (sub set hood) function p (x). The probability density function p (x) describes a distribution of vector patterns or signals X, a few of which the neural or fuzzy systems sample. When a neural or fuzzy system estimates a function f: X Y, it in effect estimates the joint probability density P (x, y). Then solutions points (X, f (x)) should reside in highprobability regions of the input/ output product space X x Y. An unsupervised learning systems process each sample X but does not “know " that X belongs to class Di and not to

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class Dj. Supervised learning use class-membership information and unsupervised learning used unlabelled samples. 3.10 Fuzzy Logic Controllers (FLC) Fuzzy systems, utilizing neuristic knowledge, have been employed very effectively as controllers popularly known as Intelligence Control. Design Problems of FLC are 1) Define Input and Output variables that are determined which status of the process shall be observed and which control actions are to be considered. 2) Define the condition interface, that is, fix the way in which observations of the process are expressed as fuzzy sets. 3) Design the rule base, which is, fixed the way in which observations of the process are expressed as fuzzy sets. 4) Design the computational unit, that is, supply algorithm to perform fuzzy computations those will generally lead to fuzzy outputs. 5) Determine rules according to which fuzzy control statements can be transformed into crisp control actions. (Defuzzification). The difference between expert systems and the fuzzy logic controllers (FLC) are 1) FLC models are rule-based systems. 2) The designer formulates rules of FLC systems. 3) FLC inputs are normally observations of technological systems and their outputs control statements. 3.11 Pattern Recognition in Fuzzy Systems Pattern Recognition is a fixed concerned with machine recognition of meaningful regularities in noisy or complex environments. Pattern Recognition is the search for structure in data. Numerical PR is characterized in four major areas as shown in the figure 3.2. In practice, the successful Pattern recognition is developed by iteratively revisiting each of the four modules until the system satisfies a given set of performance requirements and economic constraints. Main approach to PR is the structural (Synatic) approach. This branch of PR is the less well developed in terms of fuzzy and neural models. Generally two data structures are used in numerical PR systems. Object data vectors (feature vectors, pattern vectors) and relational data (similarities, proximity's). Object data are represented in the sequel as X= {x1,x2, x3,….. xn} a set of n feature vectors in feature space Rp , the jth object observed in the process has vector Xj as its numerical representation: Xjk is the kth characteristic associated with the object j.

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Humans

Process Description Feature Nomination X= Numerical Object Data D : Xx X R R= Pair-Relation Data Design Data Test Data

Sensors

Feature Analysis Preprocessing Extraction 2-D Display Cluster Analysis

Classifier Design Classification Estimation Prediction Control

Exploration Validity

Figure 3.2 Characterization of Pattern Recognition 3.12 Relational Data It may happen that, instead of an object data set X, we have access to a set of n2 numerical relationships say {rjk} between pairs of objects Oj and Ok. That is, rjk represents the extent to which objects j and k are related in the sense of some binary relation ρ. Its is convenient to array the relational values as an n X n matrix R = (rjk) = (ρ (oj, ok)). Many functions convert X x X to relational data. For example every metric d or Rp X Rp produces a dis-similarity relation matrix R (X: d) as in figure. Where we take ρ = d. If every rjk is in {0,1} then it is hard (or clip) binary relation function. If 0<rjk<1 for any j and k we call R as fuzzy relation. Fuzzy models for PR associated with relational data are fairly developed now a day.

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3.13 Adaptivity Features and Adaptive Controllers One of the main topics of high interest to researchers in fuzzy logic (FL) field is the development of automotive-data-driven adaptive controllers. Static Fuzzy logic controllers (FLC) have already been widely used in engineering applications. Adaptive controllers are important for good performance in non-stationary applications.

Process Model

Performance Measure

Identifier

Decision Maker

Process

Model Based Controller Figure 3.3 Adaptive Fuzzy Controllers

Basic Model of Adaptive Fuzzy Controller is as shown. Neural parameter estimators embed directly in an overall fuzzy architecture. Neural networks “blindly " generate and refine fuzzy rules from training data. Adaptive fuzzy systems learn to control complex process very much as we do. It begins with a few crude values of thumb that describes the process. Expert may give them the rules or may extract the rules from the observed expert behavior. Successive experience refined the rules and usually improves performances. Fuzzy Logic (FL) has been used in areas like pattern recognition problems and processing inexact ideas. The emphasis in such problems is to approximate multiple pattern classes in a joint input output space.

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CHAPTER 4 APPLICATION OF ARTIFICIAL NEURAL NETWORKS IN POWER SYSTEMS 4.1 Introduction on ANN Application ANNs can play a richly significant potential role in electric power systems. As a branch of Artificial Intelligence, ANNs take problem-solving one step further. They can match stored examples against a new one, building on experience to provide better answers. On the field of AI, ANN computing shows great potential in solving difficult data-interpreting tasks. Neural networks are based on neurophysical models of human brain cells and their interconnection. Such networks are characterized by exceptional pattern recognition and learning capabilities. The major advantage of the neural networks is its self-learning capability. First, the network is presented with a set of correct input and output values. Then it adjusts the connection strength among the internal network nodes until proper transformation is learned. Second the network is presented with only the input data, and then it produces a set of output values. The development of the input and output data is done several thousand times. After proper number of learning cycles or iterations the network will be able to produce accurate output data from input data similar to those used for learning. ANNs are composed of many simple elements operating in parallel. The network function is determined largely by the connections between elements. They have been trained to perform complex functions in various fields of application including Pattern Recognition, Identification, Classification, Speech, Vision, control systems and EMS. The field of ANNs has a history of nearly five decades but has found solid application only in the past ten years, and the field is still developing rapidly. In recent years, many interesting applications of ANNs have been reported in the power system areas like load forecasting, power system stabilizer design, unit commitment, and security assessment, Economic load Dispatch and fault analysis. ANNs have attracted much attention due to their computational speed and robustness. They have become an alternative to modeling of physical systems such as synchronous machine and transmission line. Absence of full information is not a big as a problem in ANNs as it is in the other methodologies. A major advantage of the ANN approach is that the domain knowledge is distributed in manner. Therefore they reaches the desired solution efficiently. Most of the applications make use of the conventional multilayer Perception (MLP) model based on back propagation algorithm. However, multilayer perception model suffers from slow learning rate and the need to guess the number of hidden layers and neurons in each hidden layer. Many improvements are suggested over the conventional MLP to overcome these advantages.

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4.2 Major Applications 4.2.1 Power System Stabilizer Real time timing of PSS is a complex task. Hsu and Chen [HC 91] proposed a fourlayer perceptron network for this purpose. The network consists of two input nodes, two hidden layer of four nodes each and two output nodes. Input to the ANN was the generator real power output P and the Power Factor. The outputs of ANN were the PSS gain settings. Offline simulations generated the training set for this ANN. To speed up the learning process an adaptation law was used to dynamically update the learning rate of the backpropagation. Another important application is the stable power system stabilizer based on inverse dynamics of the controlled system using an ANN. Y. M. Park, S.H Hyun and J. H. Lee [PHL 96] suggested enhancing the dynamic performance of power system. Here an output feedback control law is driven with some conditions satisfied, which guarantees the internal stability and robustness against the asymptotically stable external disturbances. Then the control law is implemented using the inverse dynamics of the controlled plant. An ANN, inverse dynamics neural network (IDNN), on offline identifies the inverse dynamics of the controlled plant. Backpropagation neural networks have recently been applied to problems in power system stabilizer modeling. When trained to respond differently to different operating conditions, these networks tend to produce interference between conflicting solutions. In recent years, modular neural network architectures have been used for problems in system identification and control. These networks learn different aspects of a problem by partitioning the data space into several different regions and are less susceptible to interference than backpropogations networks. Srinivas Pilutla and Ali keyhani in [SA 97] illustrated the use of the modular neural networks for power system stabilizer modeling. M.K. El-Sherbiny et al [ShSaI 96] introduce a novel Power System Stabilizer (PSS) controller based on a multilayer feedforward artificial neural network (ANN). A feature of the proposed controller is that the ANN parameters can be adapted online in real time according to generator loading conditions. The proposed ANN based PSS consists of three layers, namely, an input layer, a hidden layer and an output layer. The input layer has four nodes. The best number of the nodes for the hidden layer has been found by trial and error to be seven, with a nonlinear transigmoid activation function. The last layer (output layer) has one node whose activation function is transigmoid. Time domain solution with specified state disturbance for a synchronous machine connected to an infinite bus through an external transmission line are employed to prove the effectiveness of the proposed ANN based controller under a wide range of variations of the operating conditions and variety of exciter gains.

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Output Layer

Gatting Layer

Gating Network

Local Expert I

Local Expert L

Fully Connected

Input Layer

* Figure 4.1 Modular Neural Network FeedForward Architecture 4.2.2 Load Forecasting Load forecasting is perhaps the most important SCADA task and also one of the most popular areas for ANN implementation. The availability of historical load data on the utility databases makes this area highly suitable for ANN implementation. ANN schemes using perceptron networks and self-organizing feature maps have been successful in short-term as well as long-term load forecasting with impressive accuracy. Lee et al [LCP 90] used a multi layer perceptron for short-term load forecasting. This ANN was used for a one-day ahead load forecasting, for the winter, spring, summer and fall seasons. An average percent relative error of two % was achieved. Park et al [PEM 91] employed a similar approach to compare the performance of multi layer perceptron with a utility’s numerical forecasting methods. Hsu et al [HY 91] demonstrated the suitability of combining self-organizing feature maps and multilayer perceptron for short-term load forecasting. * Ref [SA 97]

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The self-organizing feature maps were used to identify the day types from historical data. To obtain the hourly load pattern for a day, the hourly load patterns of several days in the past, which are of the same day type, were averaged. To predict the daily load, a multilayer perceptron was used. R.Lamedia A. Prudenzi at el [LPSCO 96] illustrated a new ANN based procedure (SOM + ANNI) in order to enhance the forecasting accuracy in the analysis of the load forecasting. The procedure provides the combined approach (unsupervised + supervised) structured in three subsequent stages. The first stage provides some identification criteria of the characteristics of the days through the classification of historical hourly loads, thus to obtain clusters of the similar load profiles. The classification is performed by means of a Kohenon’s SOM. The second stage consists in an actualization process of the information deduced from the previous day type identification. Human operators perform this activity that gives a meaning of the load classes. The third stage, performing the proper forecasting task, which is realized by means of a multi layer perceptron based on the back propagation learning algorithm already used for the ANN implementation. Success of applying a class of recurrent neural network in short term load forecasting was tested by J. Vermaak, at el [VB98]. Recurrent Neural networks are members of a class of neural network models exhibiting inherent dynamic behavior. The most general of these is the fully connected recurrent neural network. The recurrent network parameters were obtained by training a feedforward network to learn the mapping. Here the feedforward neural networks (including those used for the recurrent network training) employed a single hidden layer, and were trained in batch mode according to the error backpropagation algorithm, using the conjugate gradient descent optimization. The other main works in the area of load forecasting are substation load forecasting C.S. Chen, Y.M.Tzeng [CTH 96] Using SCADA, D. Srinivasan et al [DLC 94] for a short term forecaster using multilayer neural network, three layer feedforward Quasi Optimal neural network for the short term Load forecasting [MCS97] and the window based forecasting procedure using combined Supervised and Unsupervised learning concept [DRSP 95]. 4.2.3 Fault Diagnosis ANN’s has recently invaded fault diagnosis, which has been a traditional area for ES (expert system) implementation. However, at present the ES implementations outnumber the ANN implementations. The explanatory abilities of ESs and their more powerful user interface make them a more attractive alternative. However, still there are certain areas, which require a quick response, and are still open to ANN implementation. Many applications for the various fault diagnosis problems have been reported in the literature. Kanoh et al [HMK 88] proposed a cascade structure of three three-layer perceptron networks for the identification of a faulted transmission section. The ANNs were trained using backpropagation. The first and the second ANN in the cascade structure identify the candidate’s one and two for fault selection, using current amplitude and phase angle distribution patterns.

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The third ANN obtains the final fault location using the above candidates one and two, and a current amplitude distribution pattern. Results of this approach indicates that this method can achieve 98.4 percentage accuracy even when the measured values differed by thirty percentage from the EMTP as mentioned above.

P1 DAY I ……………………….. P24

FORECASTING Supervised Back-propagation Learning

………… P1 DAY(I-2) P24

…………. P1 DAY(I-1)

P24

Cluster Codes Relevent To Days (I-2),(I-1),i

DAY TYPE CLASSIFICATON Kohonen's SOM Learning

EXTRAPOLATION AND REPRODUCTION OF CLASSIFICATION CRITERIA

P1

……….

P24

CALENDER TIME CHARACTERISTICS OF FUTURE DAYS

* Figure 4.2 Unsupervised/Supervised Procedure Adopted for Load Forecasting Ebron et al [EL 90] used a three-layer perceptron network to detect high impedance faults on distribution feeders. Their approach consisted of three parts: collecting sets of sampled, processed feeder line currents, training the ANN with these data and testing the ANN on new patterns. Computer simulations using the EMTP generated the training set. From the results obtained ANN classified ten of these cases correctly. However, the ANN caused a false alarm in seventeen cases as mentioned. * [LPSCO 96]

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ANNs were also successful in incipient fault detection of induction motors [CY90]. Chow and Yee [CY91] used multilayer perceptron networks for incipient fault detection in single- phase squirrel cage induction motors. This approach used two ANNs. 1. A disturbance and noise filter ANN to filter out the transient measurements while retaining the steady-state measurements. 2. An incipient fault detector ANN to detect faults based on data collected from the motor. C.Rodriguez at el [RRMLMP 96] presented a modular and neural network-based solution to power systems alarm handling and fault diagnosis described it overcomes the limitations of ‘toy’ alternatives constrained to small and fixed-topology electrical networks. In contrast with the monolithically diagnosis systems, the neural network-based approach presented here fulfills the scalability and dynamic adaptability requirements of the application. Mapping the power grid onto a set of interconnected modules that model the functional behavior of electrical equipment provides the flexibility and speed demanded by the problem. The way in which the neural system is conceived allows full scalability to realsize power systems.

1 PREPROCESSING

2

DISTURBANCE DETECTION AND CLASSIFICATION

FAULT DIAGNOSIS 3 HYPOTHESIS GENERATION 4 HYPOTHESIS JUSTIFICATION

* Figure 4.3 Fault Diagnosis process * [RMAMP 96]

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4.2.4 Security Assessment Security of a power system is the ability to sustain, without any abnormalities, the worst impending contingency. Security assessment has been at the forefront of ANN applications from the beginning. The goal of security assessment is to supply the operating state so that suitable preventive actions can be undertaken. In one of the early approaches, Sobajic and Pao [PS89] synthesized one of the crucial parameters of the system, the critical clearing time (CCT). A three-layer perceptron network with twelve input nodes, six hidden-layer nodes and one output node was employed for this purpose. The training set was a twelve dimensional pattern set, labeled with the corresponding CCT values. The CCT parameters were obtained by numerical integration of the post-disturbance system equations. The CCT parameters output by the ANN matched closely with the actual values using a three-layer perceptron network to assess the dynamic security of the power systems. The ANN was trained on the results of off-line stability analysis. The transient security assessment analysis is done by M.Djukanovic, D.J Sobajic and Pao et al [DSP 94] by a direct method for the multimachine systems. Here a local approximation of the stability boundary is made by tangent hyper surfaces, which are developed, from Taylor Series Expansion of the transient energy function in the state space near a certain class of unstable equilibrium point. Neural networks are used to determine the unknown coefficients of the hypersurfaces independently of operating conditions. J.N Fidalgo et al [FPV 96] described the ANN based approach for the definition of preventive control strategies of autonomous power systems with a large renewable power penetration. For a given operating point, a fast dynamic security evaluation for a specified wind perturbation is performed using an ANN. If insecurity is detected, new alternative stable operating points are suggested, using a hybrid ANN-optimization approach that checks several feasible possibilities, resulting from changes in power produced by diesel and wind generators and other combinations of diesel units in operation. Security constrained optimal rescheduling of real power using Hopfield network was analyzed by Soumen Ghosh et al [SC 96]. In this paper a new method for security-constrained corrective rescheduling of real power using the Hopfield network is presented. The proposed method is based on solution of a set of differential equations obtained from transformation of an energy function. Results from this work are compared with the results from a method based on dual linear programming formulation of the optimal corrective rescheduling. The minimum deviations in real power generations and loads at buses are combined to form the objective function for optimization. Inclusion of inequality constraints on active flow limits and equality constraint on real power generation and load balance assures a solution representing a secure system. Transmission losses are also considered in the constraint function.

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4.2.5 State Estimation ANNs have been very successful in system identification, parameter estimation and analysis. The power system topological observability is dealt with [TM 89] using a three-layer perceptron network. Bialasiewicz et al [BPW 89] showed that a multilayer perceptron network could be used as a state estimator in a model reference intelligent control system. The ANN was trained using offline simulation data of a test system. The learning rate of the backpropagation was updated dynamically to speed up the learning process. An adaptive linear combiner and a multilayer perceptron network were also used [KF 90] for state estimation. In this implementation, the ANN was trained using several Kalman filter solutions for the power network. The results of the ANN based state estimation compared favorably with that of the Kalman filter. Eryurek et al [EU 90] proposed a three-layer perceptron network for sensor validation in a power plant. An adaptive learning scheme was employed. In this work, the following empirical rule was proposed for calculating the number of hidden nodes in the perceptron network

H = I log 2 N ± I

Where ‘N’ is the number of training patterns, ‘I’ the size of the input vector, and H the number of hidden nodes. The authors claimed that this empirical rule is valid for certain classes of sensor validation problems. A structured ANN was reported in [NA 90], which tackles the power system state estimation problem. This ANN has a generalized structure that is independent of applications. Performance of this network was shown to be superior to that of a back propagation scheme. A P Alvas da Silva and V H Quintana [AQ 95] presented a paper on an ANN topology determination and a supervised learning algorithm for very large training sets using the Optimal Estimate Training 2(OET2). OET2 overcomes the major shortcomings of the backpropagation learning rule and can also be very useful for other problems. Power system network decomposition techniques are used to decrease the computational burden of the topology classifier training session. 4.2.6 Contingency Screening To assess system security, a huge number of possible contingencies are to be evaluated and ranked. Conventional ranking methods suffer from masking and long computing time. Since a systems operational history is available in most utility databases, it should be possible to group contingencies into various subclasses [FKCR 89]. In this paper Fischl et al showed that a two-layer perceptron network could classify power system security status accurately under different loading and contingency conditions. This ANN was trained using simulation results and back-propagation. However it is impossible to generate enough training sets to cover the entire range of power system operation. Hence a Hopfield network was proposed in [FKCRY 90] for contingency screening. This paper used an optimization

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method to find the weights and thresholds of the ANN, in contrast to the learning method of the perceptron networks. The optimization method used linear programming techniques to maximize the probability of correct classification of contingencies. This implementation classifies contingencies according to the number and type of limit violations. The method has interesting applications in combining security monitoring and preventive control. S Gosh and B H Chowdhury [GC 96] modulated a three-layer perceptron artificial neural network with back propagation learning technique that is designed for line flow contingency ranking. Two new indices – severity index and a margin index for line flow – are defined. A regression-based correlation technique is used to select training parameters for the neural network. The technique followed in this paper is the backpropagation method. Training of the neural network continues with the updates in weights in V and W, until the error E reaches a predefined minimum value in a steepest descent manner. In the training process, the network is exposed to a set of patterns, each of which consists of an input vector X, and the corresponding desired vector d. The training process involves the following steps: 1. Selection of input/output parameters for training. 2. Generation of training data. 3. Normalization of training data 4. Testing of the network with unknown set of data 4.2.7 Voltage Stability Assessment ANNs have been recently proposed as an alternative method for solving certain traditional problems in power systems where conventional techniques have not achieved the desired speed, accuracy and efficiency. L index has been popularly used for assessing voltage stability margin. Investigations are carried out on the influence of information encompassed in input vector and target output vector, on the learning time and test performance of Multi Layer Perceptron (MLP) based ANN model. In the ANN model for each loading condition various combination of control variables are generated by running many iterations of LP based reactive power optimization algorithm. Settings of control variable influences the ANN input feature vectors differently. Only active power injection of slack bus and reactive power injection of all generator buses vary in input vectors of ANN2 for a given loading condition while variation in input vectors of ANN-1 is observed in most of the critical line flows.

4.2.8 Protection The application of ANN in this related field too is now days becoming important since the concept of online protection are widely accepted. S.A. Khaparde, N. Warke at el [KWA 96] shows that ANN can be effectively used effectively to achieve adaptive relaying for the above-mentioned problem. Adaptive relaying

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covers a large number of applications and the characteristics of relays vary widely, so the philosophy of adaptive relaying must vary accordingly. A modified multilayered perceptron model employs an additional node in the input layer. These additional input facilities changes in the relay characteristics. The desired change in the quadrilateral relay characteristic is achieved by making appropriate changes in the thresholds and weights of the hidden layer neurons. The other method used by Q. Y. Xuan, Y.H Song [XSJMW 96] illustrated an adaptive protection technique based on neural networks with special emphasis on analysis of the firstzone performance. Here the feedforward multilayer neural network was chosen for the study. However selection of the optimal number of hidden layers and the optimal number of hidden layers, and the optimal number of neurons in each layer, is still an open issue? The guidelines given for the number of the hidden neurons were adopted as a starting point. During further studies and analysis different combinations of the following network training methods were chosen and tested in order to ensure that the model would be continuously refined 4.2.9 Load Modeling The application of the ANN in load modeling is increasing for the past years. Accurate dynamic load models allow more precise calculations of power system controls and stability limits. A. P Alves da Silva and C. Ferreira et al [AFZL 97] detailed the performance of a nonparametric load model based on a new constructive artificial neural network (Functional Polynomial Network) (FPN) and it’s compared with the popular “ZIP” model. The impact of the clustering different load compositions is also investigated. The network architecture proposed here is the Functional Polynomial Network, which is based on the following ANN models: functional link net and polynomial network. The main draw back of the functional link net is that the required non-linear transformation can only be found by trial and error. The polynomial network is a nonparametric ANN model i.e. it does not require the architecture pre-specification.

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CHAPTER 5 APPLICATI0N OF FUZZY LOGIC IN THE POWER SYSTEM 5.1 Introduction on Fuzzy logic applications Fuzzy logic applications are widely used in all parts of the power system planning, design and operations. The main important applications are 1. Stability Assessment / Enhancement 2. Power System Control 3. Fault Diagnosis 4. Security Assessment 5. Load Forecasting 6. Reactive Power Planning and Control 7. State Estimation 5.2 Major Applications 5.2.1 Reactive Power and Voltage Control The rapid growth in the power system coupled with variations in operating conditions leads to better management in voltage profile and reactive power. Reactive sources which are spread throughout the system should be controlled accurately based on the loading conditions (light load or peak load) to optimize and ensure the security of electric power transmission system. These controls are known as voltage/reactive power or voltage/VAR control. The aim of these controls is to reduce voltage deviations or minimum losses or enhancing voltage[ NU 98]. Main types of voltage/ VAR problems are 1. Planning of system reactive demands and control facilities as well as installation of reactive power control resources 2. The operation of existing voltage/VAR resources and control device. The online planning is much more cumbersome and important in the power system operation. This is because in a day to day operation of power system both under/over voltage occurs and VAR sources need to be adjusted to avoid high/low voltage problem. This can be termed as voltage/VAR scheduling and this is very important in the power system security. There are various algorithms employing linear and non-linear optimization technique used for voltage correction. These algorithms involve numerical computations and hence may not be curtailed and also the amount of controller movement needs to be minimized.

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Fuzzy set theory has been applied off late for reactive power control with the purpose of improving the voltage profile of power system. Here the voltage deviation and controlling variables are translated into fuzzy set notations to formulate the relations between voltage deviation and controlling ability of controlling device. Main control variables are VAR compensators, transformer taps and generator excitation. A fuzzy rule system is formed to select these controllers, their movement and step size. The controllers are selected based on 1. Local controllability towards a bus having unacceptable voltage. 2. Overall controllability towards the buses having poor voltage profile. K. H. Abdul_Rehman / S. M. Shahidehpur et al [AS 93] presents a mathematical formulation for the optimal reactive power control problem using the fuzzy set theory. The objectives are to minimize real power losses and improving the voltage profile of the given system. Transmission losses are expressed in terms of voltage increments by relating the control variable, i.e. tap positions of transformers and reactive power injections of VAR sources, to the voltage increments in a modified Jacobian matrix. Main advantage of this method illustrated is that the specific formulation of this problem doesn’t require Jacobian Inversion of matrix and hence it will save computation time and memory space. The objective function and the constraints are modeled by the fuzzy sets. Linear membership functions of the fuzzy sets are defined and the fuzzy linear optimization problem is formulated. The solution space here is defined as the intersection of the fuzzy sets describing the constraints and the objective function. Each solution is characterized by a parameter that determines the degree of satisfaction with the solution. The optimal solution is the one with the maximum value for the satisfaction parameter. Multicase VAR planning problem involves the determination of an installation pattern of location and sizes of new compensators for multiple cases. The problem should basically cover the operating limits, complicated security and economic factors. a) Voltages and VAR controllers must be kept within their operating limits for the entire system under both normal and contingency cases. b) The expansion between cases should be coordinated to avoid excessive investment. c) The amount of compensation (by capacitor and reactors) must be descritized. In the area of the Multicase VAR planning R. A. Fernandus et al [FLBHW 83] proposed augmented Lagrangian type objective function and later augmented Lagrangian and generalized benders decomposition methods were applied [GPM 88] to treat both preventive and corrective controls of VAR planning. The drawbacks of traditional approaches were pin pointed by Hong and Liu et al [HL 92]. An expert system (VPES) (VAR planning Expert System) was introduced. It incorporated constraints resulting from considerations of the voltage collapse and able to handle both fixed and the variable cost and discrete device.

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Fuzzy Set theory has also been applied to solve. Here an extended approach based on VPES is proposed to take fuzzy reasoning rules into account for solving Multicase VAR planning solution. Combination of individual information from each single case is performed by fuzzy relationship the center of gravity algorithm. Thus the coordination of multicase VAR planning is achieved. The other important area is the application of the reactive power compensation in distribution system .The aim is to achieve power and energy loss reduction, voltage regulation, and system capacity release. An approach using fuzzy dynamic programming to decide the optimal capacitor placement and size of compensating shunt capacitor for distribution systems with harmonic distortion is proposed by Hong Chan Chin et al [HC 95]. The problem is formulated as fuzzy dynamic programming of minimization of real power loss and capacitor cost under the constraints of voltage limits and total harmonic distortion. The algorithm proposed greatly reduces the effort of finding optimal location by any exhaustive search. The computational algorithm is narrated in the following steps as given in. 1. Perform the load flow program at the fundamental frequency to calculate the bus voltage. 2. Find the membership functions µP, µV, µH and µD for the fuzzy sets P, V, H and D. 3. Identify the optimal location of shunt capacitor at the bus with the lowest membership Value µp(K) ( bus K ) 4. Try the capacitor placement at bus K with various discrete sizes. Select the optimalsize QC that will result in lowest cost function without violating the constraints. 5. Install the capacitor QC at the bus K and simulate the load flow to calculate the new bus voltage violation. Ching-Tzong Su & Chien_tung Lin [SL 95] illustrated voltage profile enhancement for Power Systems using fuzzy control approach. The voltage violations are transformed to fuzzy set notations to formulate the relation between the voltage violation level and the controlling ability of controlling devices. A feasible solution set is first attained using the min-operation of fuzzy sets, and then the optimal solution is fast determined employing the max- operation. The membership function of the bus voltage violations is represented as in the following figure. Here âˆ†Vi represents the voltage violation level of bus I, and uâˆ†Vi represents the membership function of âˆ†Vi The maximum deviation of the bus voltage is given by

Cij

Cij min 0 Cij max *Figure 5.1 The membership function of controlling ability of controlling devices * [SL 95]

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Uâˆ†Vi

âˆ†V i âˆ†VImin -0.01 0 0.01 âˆ†VImax

âˆ†VImin = Vimin - ViNorm

*Figure 5.2 The membership function of Voltage violation Level The computational procudure of the above algorithm was repersented as

Input data (Including network configuration, line Impedance, bus power, Bus voltage limits, controlling margin)

Perform base Case Load Flow

Find the sensitivity coefficient

Calculate the Controlling Ability

Find the membership value of bus voltage violation level and controlling ability

Evaluate the Optimal control Solution

Modify the value of the Control Variables

Check Voltage level has enhanced to the desired level

YES

Perform the load Flow and output the Results

NO

* Figure 5.3 Computational Procedure for the solution for Voltage Profile Enhancement * [SL 95]

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5.2.2 Transient Stability The most active area of the fuzzy system research in the power systems has been stability assessment and enhancement. The stable performances of the synchronous machines under all anticipated conditions of system transients are essential for ensuring overall system stability. Application of the fuzzy set theory in transient stability evaluation was first reported by Soulfis et al [SMP 89]. The system operating states, classified as belonging to one of the six possible states were represented using the fuzzy membership values in fuzzy Pattern recognition (PR) systems. The developed method is applicable for any power system irrespective of its size, configuration or loading condition [AV 89]. An application of Fuzzy set theory for design of stabilizer to improve the dynamic performance of a multimachine power system was first proposed by Hsu and Cheng [HC 90]. This stabilizer used a fuzzy relation matrix to produce the output based on the fuzzy inputs, speed deviation and acceleration. Only local measurements from each machine were used for this stabilizer, resulting in a simple design. Hassan et al reported another successful application of a fuzzy logic stabilizer for improving the stability of synchronous machines. [MOG 91]. The practical implementation and experimental results of this stabilizer using a digital signal processor were reported in [HM 93]. In another research transient stability limit in power system transmission lines using the fuzzy control of FACTS Devices was studied. S. M. Sadehzadeh and M. Ehsan in et al [SEHFH 98] investigate the application of FACTS devices to increase the maximum loadability of the transmission lines, which may be constrained by a transient stability limit. Hence the on-line fuzzy control of the Super-conducting Magnetic Energy Storage (SMES) and the Static Synchronous Series Compensator (SSSC) are suggested. The fuzzy rule bases are defined and explained. The validity of the suggested control strategies is confirmed by simulation tests. The simulation results show that by the use of the proposed method, the line power transfer can be increased via the improvement of the transient stability limit. Finally the effect of the control loop time delay on the performance of the controller is presented. 5.2.3 Generator Operation and Control The major application lies in the control of excitation system of the Synchronous Generator. Synchronous Generator excitation control is one of the most important measures to enhance power system stability and to guarantee the quality of the electrical power it provides. A number of new control theories have been introduced to design high performance excitation controllers. Among them the linear optimal control theory [JHA 89], the adaptive control theory [CCM 86] the fuzzy logic control theory [HC 90] and the nonlinear control theory [LS 89] are the most commonly used ones.

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Fuzzy logic Controllers are advantageous in many respects. They are simple in structure and relatively easy to realize. Mathematical models of the control systems are not required. Variations of the parameters and operation conditions of the controlled systems do not significantly effect the performance of the controller. All of these advantages have enabled this technique to attract more and more attention in recent years. The main disadvantages of this method are a) Knowledge used to design a fuzzy logical controller mainly comes from the heuristic knowledge or expertise of the human experts. This sort of knowledge is sometimes difficult to acquire and represent in the required form. b) Parameters of the fuzzy logic controller are usually determined by trial and error. This method is time consuming and does not guarantee an optimal controller. Jinyu Wena, O.P. Malik et al [JSM 98] suggested a method to design the FLC based on Genetic Algorithm (G A). In this controller the generator terminal voltage and the rotor speed deviation are used as its inputs. As a result, both the voltage profile and the dynamic stability of the generating unit are enhanced. Also FLC design has been carried out by G.A. Chown, R.C. Hartman et al [CH 98] for Automatic Logic Controller (AGC). The main problem solved by this method is the secondary frequency controller and AGC. The fuzzy controller was implemented in the control ACE calculation, which determines the shortfall or surplus generation unit that has to be corrected. Short term generation scheduling with take-or-pay fuel contract was developed by Kit Po Wong and Suzannah Yin Wa Wong et al [KSY 96] in which a fuzzy set approach is developed to assist the solution process to find schedules which meet as closely as possible the take-or-pay fuel consumption. This formulation is then extended to the entire economic dispatch problem when the fuel consumption is higher than the agreed amount in the take-orpay contract. The extended formulation is combined with the genetic algorithms and simulated- annealing optimization methods for the establishment of new algorithms for the problem. Stabilizer control and the exciter and governor loops using fuzzy set theory and the Neural nets was developed by M.B. Djukanovic and M. S. Calvoic at et al [DCNS 97].Here a design technique for the new hydro power plant controller using fuzzy set theory and ANN was developed. The controller is suitable for real time operation, with the aim of improving the generating unit transients by acting through the exciter input, the guide vane and the runner blade positions. The developed fuzzy logic controller, whose control signals are adjusted using the on-line measurements, can offer better damping effects for generator oscillations over a wider range of operating conditions than conventional regulators. The FLC, based on a set of fuzzy logic operations that are performed on controller inputs, provides a means of converting linguistic control requirements based on expert knowledge into an efficient control strategy. Using unsupervised learning of ANN generates a fuzzy associative matrix.

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5.2.4 State Estimation The power system state estimation is another area were fuzzy logic applications are performed in recent times. State estimation is the task of determining the actual values of the state variables .One of the problems in automating a power system is the construction of reliable models of the system whose state variables can be identified sufficiently accurately using available noisy system data. For the successful operation of large-scale power systems the optimal estimation of the state is required. The weighted Squares (WLS) estimator is widely and extensively used due to their numerical stability and computational stability. The main disadvantage of this method is the presence of the gross errors. An alternative state estimation approach, the weighted least absolute value (WLAV) has been applied to power system problems. This estimator is more robust than the WLS estimator. The notable drawback of this method is the poor computational efficiency for large sized problems. F. Shabani, N. R. Prasad et al [SPS 96] formulated a method which uses the combination of weighted least squares and fuzzy logic based techniques to improve the state estimation of the power systems. In this method variant of the Kalman State Estimation is taken as the basis. The optimal estimator is controlled by the parameter W, which the weight is given to the current state estimate calculated using the WLS method. If W is found to be large, then more weight is placed on the current state estimate in relation to the measured value and vice versa. 5.2.5 Security Assessment On line security assessment of a power system involves monitoring the current operating condition of the system and assessing the effects of probable contingencies (e.g. outages of transmission lines, tripping of generators, etc). The conventional approach based on simulation of probable contingencies is not suitable for on-line security assessment because of the large computation time involved. K. Sinha et al [AKS 95] presented a PR and fuzzy estimation technique. Pattern Recognition is one of the potential methods, which fits the computational requirements of online security assessment. In the past, some pattern recognition methods have been proposed for power system security assessment. These methods security classification schemes are not well suited for large power systems because of convergence problems faced in designing the classifiers in a large dimensional pattern space. Here the knowledge about the system operating conditions is stored in a structured memory by grouping similar patterns into clusters which are arranged into a hierarchical tree structure. This enables a very fast two level search for the near neighbors of the input pattern. The security status of the input pattern is determined using a fuzzy estimation technique. This not only provides a very reliable security classification but the fuzzy grade membership also provides a quantitative ' level of confidence ' for the security classification.

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5.2.6 Fault Diagnosis and Restoration Fault diagnosis and restoration is perhaps the most popular area of the AI implementation where a large number of alarms have to be interpreted in real time to determine possible fault scenarios, based on which suitable restorative actions need to be taken. Expert knowledge is used to model the system behavior and response. Fuzzy expert systems are now being used for these applications to include vague constraints and express uncertainty. Many implementations for various fault diagnosis problems have been reported in the literature. Application of fuzzy set theory in fault diagnosis was first reported by Xu et al [XZL 90]. Fuzzy linguistic variables were used to characterize the load patterns of several types of days. The load of each load points in the distribution system was estimated using a fuzzy expert system. Following a fault an efficient restoration plan was generated using a heuristic search method. A fuzzy method to deal with the uncertainty concerning fault location in distribution networks was also developed. Here some of the advantages and important implementation issues based on practical experience were highlighted. Hyun-Joon Cho and J. K. Park et al [HJ 97] proposes an expert system using fuzzy relations to deal with uncertainties imposed on fault section diagnosis of power systems. The so-called Sagittal diagrams were build which represents the fuzzy relations for power systems and diagnosis were done using these diagrams. The malfunctioning of relays and circuit breakers based on the alarm information and the estimated fault sections were estimated. The system provides the fault section candidates in terms of the degree of membership and the malfunction or wrong alarm. The operator monitors these candidates and is able to diagnose the fault section, coping with uncertainties. 5.2.7 Load Forecasting Load forecasting is an important task for the efficient operation of a power system. Some recent works have reported successful application of fuzzy logic for expressing the vague relationship between forecast load and various parameters in which depends. Hsu and Ho [YK 92] first proposed a fuzzy expert system for short term load forecasting. Considerable improvement in the accuracy of the forecast hourly loads was reported. Torres and Mukhdekar [TM 89] developed a fuzzy knowledge based forecasting tool for distribution feeder load. A fuzzy front-end processor was used in this work to enhance the forecasting accuracy by preprocessing the inputs, both numerical as well as fuzzy. D. K. Ranaweera, N. F. Hubele et al [RHK 96] presented a fuzzy logic based short term load forecasting. The proposed methodology uses fuzzy rules to incorporate historical weather and load data. These fuzzy rules are obtained from the historical data using a learning-type algorithm. One of the major obstacles in implementing and using a SLTF (Short Term Load Forecast) has been the lack of user trust and confidence in the model. The mathematical

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complexity while designed to capture the nonlinear relationships between inputs (past load, past and predicted temperature) and outputs (predicted load) and does not offer the user an intuitive understanding. If these mathematical relationships could be reduced to logical table, such as a set of IF - THEN rule then there is the possibility that the user would gain confidence in the model and therefore use it to generate, or assist in generating the system forecast. The fuzzy logic, which is in essence a set of logical statements, could be well developed solely from expert knowledge. 5.2.8 Voltage Stability Enhancement Fuzzy Control Approach has been effectively presented in the Voltage Stability Enhancement too. The concept is as the same in reactive power planning and control which leads to better voltage profile. G.K.Purushothama, N Udupa and D. Thukaram et al [PuUTPa] presented a new technique using fuzzy set theory for reactive power control with the purpose of improving the voltage stability of the power system. Here the voltage stability index (L index) n and the controlling variables are translated into fuzzy set of notations to formulate the relation between voltage stability level and controlling ability of controlling devices. Then a fuzzy ruled-based system is formed to select the controllers, their movement direction and the step size. The performance obtained from testing the above fuzzy controlled system was found to be encouraging. First the L index is computed for the system. This is found, from the load flow algorithm incorporating the load characteristic and the generator control characteristics. The load flow result is obtained for a given system operating characteristics or from the online state estimator. Then the L index sensitivity is computed. The linguistic variables of the system consists of 1. Voltage stability index, L-index 2. Sensitivity of the voltage stability index to control variables such as OLTC, SVC and generator excitation meetings. The terms of the linguistic variables are used to describe the states of the system. Different states are developed as low (L), medium (M), high (H) and very high (VH) for the L index value. For the controllers three terms are used mainly i.e. small ( S),medium(M) and large(L).For the output of the system the four terms are included as L, M, S, Z. The Fuzzy conditional statements are then prepared Based on the values of the input variables fuzzy sets are formed. Using the terms of the linguistic variables and Rule base, fuzzy computations are performed. Algorithmic steps in the proposed control methodology are 1. Base case load flow is performed ( or from state estimation)

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2. Matrices S l, S' are found. Sensitivity S is computed.

3. Observe the sorted list of nodes according to their L-index. If maximum L- index is acceptable within tolerance go to step 7. 4. Using the available margin of the controller settings are evaluated so as to minimize the Lindex of those nodes where it is more than the acceptable level.

5. Corrections to the controller settings are evaluated so as to minimize the L-index of those nodes where it is more than the acceptable level. 6. Estimate new L- indices with the suggested controller settings. If the maximum L index value is not acceptable within tolerance and margin is available for the controllers to 4.

7. Perform the load flow with the suggested controller settings and output results.

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CHAPTER 6 ANALYSIS OF THE TECHNIQUES 6.1 Neural Network based Applications The most of the applications related to neural network is based on multilayer perceptron. Here the error back scheme is widely used. Fundamental aspects of Multilayer Perceptron networks are random initial start up state and convergence of connection weights to produce minimum error. However there are no set rules for parameter selection associated with these algorithms. So in using ANN models some trial and error is required. 6.1.1 Design of Network As discussed in practical applications Multilayer Perceptron with at least one hidden layer is used. It has been reported that using greater number of hidden layer improve the overall performance. But some experimentation is required to select the number of hidden layers and nodes. Generally at least twice of as many nodes in the hidden layer has been taken as Inputs. Some of the researchers gave an empirical formula as H = ni (ni-1) to calculate hidden layer where 'H' is the number of the hidden layer and 'n i' the input. But still some trial and error is needed to produce quick convergence and acceptable results. The introduction of the concept of structured ANNs (e.g. Perceptrons, Hopfield Network, and SOM) designed for specific tasks simplify the design process. Also research results are available for dynamically designs hidden layers. Cascaded correlation's begins with minimal network, then automatically trains and adds new hidden units one by one. Once the hidden layer is added it becomes a permanent feature detector in ANN. This architecture learns quickly. 6.1.2 Training Set Generation In many applications, there is no efficient way of generating a complete training set to cover all possible operating states. This will be of greater concern in dealing with a problem of large on line data handling. For example, In the cases of power system security problem most of the literatures reports about offline simulation to obtaining the training sets. It is possible to analyze if the samples chosen are small in size. If the sample is large (500 buses, which are the case of the practical system,) the analysis will be extremely difficult. Moreover its not easy to obtain good performance on training data followed by much worse performance on test data. There can be improvement if some knowledge can be incorporated about the domain into the network architecture.

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6.1.3 Hopfield Network Hopfield Networks can be very useful in solving the optimization problems very quickly and efficiently by minimizing energy function, defined in terms of its weights and thresholds. However, this energy function has many local minima. This is not acceptable especially in contingency screening. The reason is that we should get the best rather than the feasible ranking of contingencies. Another drawback is that the weights and thresholds are calculated based on the optimization process, which has to be repeated if any of the input parameters change. The enhancement in the recent development of the architecture reduces these drawbacks. Also a mapping method is formulated from which the weights and thresholds for the particular optimization problem can be easily computed. 6.1.4 Training the Inputs Many of the ANN models (like perceptron, SOM, ART Networks heavily rely on the information retained to the input features. In any power system applications the input patterns space consists of a large number of features. So feature selection is necessary to reduce this pattern space to a reasonable size. These processes make loss of information. 6.1.5 Knowledge Consistency and Interaction with the User Knowledge Consistency is an important concern in the training set of ANN research. The AI implementations are considered complete when they match with human competence and thus further research is needed in this area. In many cases AI technique is required to interact to demonstrate the validity of the decision to the User. For example in the diagnosis of faults in the system, the operator might want to ascertain the validity of the reasoning employed. Similarly in preventive control an explanation might be necessary to validate and verify the control strategy. 6.1.6 Practical Implementation In the hardware part most of the present day ANN schemes are single-processor simulations of the massively parallel ANN models. When using the multilayer perceptron model, most of the implementations use a sequential algorithm on conventional computer to train the ANN, in node by node manner. Ideally ANN schemes should be implemented in parallel processing machines to fully reap the benefits of their massively parallel structure. There is mainly two way of implementation of ANN in the parallel computers. 1. Direct Implementation in which there is a physical-processing element for each neuron in the neural network. This approach can potentially provide a very good performance. However it can support only a specific ANN model since it is fixed in the hardware.

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2. Virtual implementations (with general-purpose neuro computer) in which a processing element takes charge of multiple neurons and simulates them in a time-sharing fashion. 6.2 Fuzzy Logic based Applications 6.2.1Requirements of Fuzzy based Applications The main characteristics and requirement for a problem suitable for fuzzy logic applications are 1. The problem has to be solved by human experts for daily operation and planning. Thus functional knowledge in terms of heuristic rules are available. 2. If the methodology cannot be expressed in terns of mathematical form. 3. If the modeling of mathematical problem requires various many assumptions to be made, leading to an inaccurate models. 4. If the problem involves uncertainty, vague constraints and/or multiple conflicting objectives. 5. The complexity of the problem makes the solution computationally intensive if solved by conventional technique. Fuzzy systems are found to be very effective with problems dealing with most of these issues. 6.2.2 Advantages of Fuzzy Logic Applications The main advantages of the fuzzy systems are 1. Speed 2. Computationally less expensive and simpler tools. 3. Flexibility 4. Ease of computation They are found to be very powerful in applications involving Uncertainties, imprecision and conflicting objectives. It's effective when the problem is non-linear in nature and if there is a convenient way to obtain Input-Output mapping. It cannot be used if Input-Output mapping is difficult. The various issues that needs to be addressed, even though fuzzy logic has found in various applications are Creation of fuzzy logic Creation of fuzzy logic is mostly through experts, which lacks in knowledge engineering. That means it depends on expert opinion and cannot decide the rule networks Genetic Algorithms and fuzzy clusters. Common sense knowledge Representation It’s difficult to represent and manipulate common sense knowledge and there are no effective and sufficient methods to do so.

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Fuzzy Logic Controller Stability Stability of the FLC cannot be assessed and there are no established methods to do that. This needs to be analyzed before they can be considered as alternative for conventional controller. Tools and Practical Consideration The lack of tools for this generic development works handicaps the utilization of these systems. There is a need to support applications that can be provided quality solutions. Moreover very few applications have been Implemented Practically though many applications are reported.

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CHAPTER 7 CONCLUSION The importance of the use of the AI tools has been felt in all the areas of the Power Systems and the need is emphasized. The easiness in evaluating the vague or non-crisp concepts and the ability of these techniques to learn due to the technological improvement elevated the effect of these soft computing techniques. The study presents concepts, survey and the important analysis of typical applications of AI techniques (ANN and FUZZY LOGIC) in the field of Power systems. The fundamentals of the Artificial Neural Network and the Fuzzy Systems are also described. The analysis of these techniques is indicated in a broader sense and the practical difficulties are narrated. Also the future concentration on the modification of the techniques is analyzed to obtain better result and making these techniques competitive to the human brains. The concepts of the AI techniques are reviewed to understand those categories of models, which are used in Power Systems, and the future hybrid models that are useful. It gives the understanding of the strengths of the models. ANNs are mainly used for learning and pattern Recognition for depicting the reference knowledge database. It helps to analyze and gives the result, which can be substituted for any logical analysis. As in the case of Fuzzy Logic applications it can be seen that these techniques can be blended with the conventional systems as well as with the other techniques like Neural Networks and Genetic Algorithms. The hybrid systems thus formed can be the most powerful systems for design, planning and control & Operation of practical problems. Hybrid Systems combining the individual strengths of the ESs and ANNs along with the Fuzzy systems seems to be the most promising area in future and promising for the most of the Power system Applications. Moreover there are sufficient scope in the improvement of the various soft-computing techniques to increase their strengths and capability. The tools for the simulation of these conditions also need to be enhanced for their limitations. The application fields combining the conventional and these techniques can remarkably reduce the difficulties faced in the Power Systems design, operation and control.

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1998 [CH 98] G.A.chown and R.C. Hartman.Design and Experience with a Fuzzy Logic Controller for Automatic generation Control (AGC), IEEE Trans. Power Systems, Vol.13, No.3 pp 965-970 (1998). Jinyu Wen, Shijie Cheng and O. P. Malik. A Synchronous Generator Fuzzy Excitation Controller Optimally Designed with a Genetic Algorithm. IEEE Trans. Power Systems, Vol.13, No.3, pp884-889 (1998). K.G.Nerandra, V. K . Sood, K.Khorasani, R. Patel. Application of a Radial Based Function ( RBF) Neural Network for Fault Diagnosis in a HVDC system. IEEE Trans. Power Systems, Vol 13, No.1, pp 177-183 (1998). Narendra Uduppa. On line development of Intelligent Tools for Applications in Energy Control Center. Phd Thesis (1998). Online Topology Determination and Bad Data Suppression in Power System Operation using ANN. IEEE Trans. Power Systems, Vol 13, No3, pp-796-803 (1998). S.M.Sadeghzadeh, M. Ehsan,N.Hadj Said, R. Feuillet. Improvement of Transient Stability Limit in Power System Transmission Lines Using Fuzzy Control of FACTS Devices. IEEE Trans. Power Systems, Vol.13, No.3, pp917-922 (1998) J. Vermaak, E.C.Botha. Recurrent Neural Networks for Short-Term Load Forecasting. IEEE Trans. Power Systems, Vol 13, No.1, pp 126131 (1996).

[JSM 98]

[NSKP 98]

[NU 98]

[SLA 98]

[SEHFH 98]

[VB 98]

Special Study Report

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