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by

Sukumar Kamalasadan (ETA987083)

Special Study Report

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Electric Power Systems Management,

Energy Program, SERD,

Asian Institute of Technology,

Bangkok, Thailand

November 1998

Application of Artificial Intelligence techniques in Power System

Special Study Report Page i

AABBSSTTRRAACCTT

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.


Special Study Report Page ii

Table of Contents

Chapter Title

Pag

e

Title Page

Table of Contents i,ii

Abstract iii

List of Figures

iv

1 Introduction

1

1.1 Back Ground 1

1.2 Neural network and its application 1

1.3 Fuzzy sets/logic and its application 2

1.4 Structure of the Study 2

2 Artificial Neural Network

4

2.1 Definition of the Neural Network 4

2.2 Fundamentals of artificial Neural Network 4

2.3 Neural Network Design 5

2.4 Learning, Recall and Memory in ANN 6

2.5 When and why using Neural Network 8

2.6 An Overview of the well known ANN Models 9

3 Fuzzy Logic and Fuzzy Systems

17

3.1 Importance of Fuzzy Systems 17

3.2 Basic Concepts 17

3.3 Fuzzy Sets and Rules 18

3.4 Classical Operations of Fuzzy Sets 18

3.5 Membership function and membership values 19

3.6 Fuzzy Relations 19

3.7 Properties of Fuzzy Sets 19

3.8 Fuzzy Truth Value 20

3.9 Learning in Fuzzy Systems 20

3.10 Fuzzy Logic Controllers (FLC) 21

3.11 Pattern Recognition in Fuzzy Systems 21

3.12 Relational Data 22

3.13 Adaptivity features and Adaptive Controllers 23

4

Application of Artificial Neural Networks in Power Systems

24


Special Study Report Page iii

4.1 Introduction on ANN application

24

4.2 Major Applications 25

4.2.1 Power System Stabilizer 25

4.2.2 Load Forecasting 26

4.2.3 Fault Diagnosis 27

4.2.4 Security Assessment 30

4.2.5 State Estimation 31

4.2.6 Contingency Screening 31

4.2.7 Voltage Stability Assessment 32

4.2.8 Protection 32

4.2.9 Load Modeling 33

5 Application of Fuzzy Logic in the Power System

34

5.1 Introduction onFuzzy logic application 34

5.2 Major applications 34

5.2.1 Reactive Power Control 34

5.2.2 Transient Stability 38

5.2.3 Generator Operation and Control 38

5.2.4 State Estimation 40

5.2.5 Security Assessment 40

5.2.6 Fault Diagnosis and Restoration 41

5.2.7 Load Forecasting 41

5.2.8 Voltage Stability Enhancement 42

6 Analysis of the Techniques

44

6.1 Neural Network based Application 44

6.1.1 Design of Network 44

6.1.2 Training Set Generation 44

6.1.3 Hopfield Network 45

6.1.4 Training the Inputs 45

6.1.5 Knowledge Consistency and Interaction with the User 45

6.1.6 Practical Implementation 45

6.2 Fuzzy Logic based Application 46

6.2.1 Requirements of Fuzzy based Application 46

6.2.2 Advantages of Fuzzy Logic Application 46

7 Conclusion 48

Bibliography 49


Special Study Report Page iv

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Figure 2.1 Schematic Diagram of the Neuron

4

Figure 2.2 Ways of Implementing a Solution to a Specific Problem

9

Figure 2.3 Overview of the Main ANN models

10

Figure 2.4 Three Layer Feedforward Neural Network

11

Figure 2.5 Back Propagation Algorithm/Network

13

Figure 2.6 Typical RBF Network

14

Figure 3.1 Truth Values in Fuzzy Logic

20

Figure 3.2

The Characterization of Pattern Recognition 22

Figure 3.3 An Adaptive Fuzzy Controller

23

Figure 4.1

Modular Neural Network Feedforward Architecture 26

Figure 4.2

Unsupervised/Supervised Procedure Adopted for Load

forecasting

28

Figure 4.3 Fault Diagnosis process

29

Figure 5.1 The membership function of controlling ability of controlling

devices

36

Figure 5.2 The membership function of Voltage violation Level

37

Figure 5.3 Computation Procedure for the solution for Voltage Profile

Enhancement

37

Application of Artificial Intelligence techniques in Power Systems

Special Study Report Page 1 of 56

CHAPTER 1

IINNTTRROODDUUCCTTIIOONN

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.



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 so-

called 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.



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.



CHAPTER 2

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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

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.

Neuron



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.



Determination of Systems (Activation & Synaptic) Dynamics

The dynamics of the network determines its operation. ANN’s can be trainable non-

linear 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 hetero-

associate vector of patterns pair mapping into weight matrix W. Temporal learning encodes a

sequence of patterns necessary to achieve final outcome.



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 non-

parametric 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



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



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



neuron has fixed threshold, has identical weights of excitatory synapses and the inhibitory

synapses are absolute in nature.

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

ANN MODELS

UNSUPERVISED

NON

LINEAR

LINEAR

FEED FORWARD

ADAPTIVE

RESONANCE

TRAINED CONSTRUCTED

HOPFIELD

FEED BACK

SUPERVISED

KOHONON BACK

PROPOGATION



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



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



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.

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,

Kth Layer

Output

Layer

(K-1) Layer

Input

Layer

Hidden

Layer

In ( j,k)

Out( I,j)



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.

Figure 2.6 Typical RBF Network

+1

Input

Units

Pattern

Units

Output

Units

Bias

Xi Xj

Xp

W Bias

Wj Wn

Wi



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 non-

parametric 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



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.



CHAPTER 3

FFUUZZZZYY LLOOGGIICC AANNDD FFUUZZZZYY SSYYSSTTEEMMSS

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.



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) � m: X |� (0,1),

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 � 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 � 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



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

µµµµF: U �� [0,1].

So, every element u of U has a membership degree µF (u) ∈ {0,1}. F is completely

determined by the set of tuples

F = {(u, µµµµF (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 � [ 0,1] , then

R = ∫UxV

)v,u/()v,u(Rµµµµ

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

R = ∑UxV

v,u/()v,u(Rµµµµ

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

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

),/(),( vuvuRµ



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

0 1 0 a b 1 0 1

(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

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 high-

probability 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

-1

0



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 j

th object

observed in the process has vector Xj as its numerical representation: Xjk is the kth characteristic associated with the object j.



Humans Sensors

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 R

p 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.

Process Description

Feature Nomination

X= Numerical Object Data

D : Xx X � R

R= Pair-Relation Data

Design Data Test Data

Classifier Design

Classification

Estimation

Prediction

Control

Feature Analysis

Preprocessing Extraction

2-D Display

Cluster Analysis

Exploration

Validity



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.

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.

Process

Model

Process

Identifier Performance

Measure

Decision

Maker



CHAPTER 4

AAPPPPLLIICCAATTIIOONN OOFF AARRTTIIFFIICCIIAALL NNEEUURRAALL NNEETTWWOORRKKSS IINN PPOOWWEERR SSYYSSTTEEMMSS

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.



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 four-

layer 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.



* 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]

Gatting Layer

Gating Network

Fully Connected

Local Expert I Local Expert L

Output Layer

Input Layer



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 back-

propagation. 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.



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.

* 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]

………… ………….

P1 DAY(I-2) P24 P1 DAY(I-1) P24 Cluster Codes

Relevent To

Days (I-2),(I-1),i

P1 DAY I P24

………………………..

FORECASTING

Supervised Back-propagation Learning

EXTRAPOLATION AND

REPRODUCTION OF

CLASSIFICATION

CRITERIA

DAY TYPE CLASSIFICATON

Kohonen's SOM Learning

P1 ………. P24 CALENDER TIME

CHARACTERISTICS

OF FUTURE DAYS



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 real-

size power systems.

* Figure 4.3 Fault Diagnosis process

* [RMAMP 96]

FAULT DIAGNOSIS

1

PREPROCESSING

2 DISTURBANCE

DETECTION AND

CLASSIFICATION

3

HYPOTHESIS

GENERATION

4

HYPOTHESIS

JUSTIFICATION



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.



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 back-

propagation 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

logIH = 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



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



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 first-

zone 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 non-

parametric 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.



CHAPTER 5

AAPPPPLLIICCAATTII00NN OOFF FFUUZZZZYY LLOOGGIICC IINN TTHHEE PPOOWWEERR SSYYSSTTEEMM

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.



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.



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 ΔVi represents the voltage violation level of bus I, and uΔVi represents

the membership function of ΔVi The maximum deviation of the bus voltage is given by

Cij min

0 Cij max

*Figure 5.1 The membership function of controlling ability of controlling devices

* [SL 95]

Cij



ΔVImin

= Vimin

- ViNorm

*Figure 5.2 The membership function of Voltage violation Level

The computational procudure of the above algorithm was repersented as

* Figure 5.3 Computational Procedure for the solution for Voltage Profile Enhancement

* [SL 95]

NO

YES

ΔV i

UΔVi

ΔVImin -0.01 0 0.01 ΔVI

max

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

Evaluate the

Optimal control

Solution

Find the membership

value of bus voltage

violation level and

controlling ability

Modify the value of the

Control Variables

Check Voltage

level has enhanced

to the desired level

Perform the load

Flow and output

the Results



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.



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-or-

pay 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.



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 on-

line 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.



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



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 on-

line 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)



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 L-

index 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.



CHAPTER 6

AANNAALLYYSSIISS OOFF TTHHEE TTEECCHHNNIIQQUUEESS

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.



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.



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.



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.



CHAPTER 7

CCOONNCCLLUUSSIIOONN

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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