STUDY OF NEURAL NETWORK MODELS FOR SECURITY ASSESSMENT IN POWER SYSTEMS

Transcription

1 STUDY OF NEURAL NETWORK MODELS FOR SECURITY ASSESSMENT IN POWER SYSTEMS S. KALYANI and K. SHANTI SWARUP Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India. ABSTRACT This paper presents the application of different Neural Network (NN) models for classifying the power system states as secure/insecure. Traditional method of security evaluation involves performing load flow and transient stability analysis for each contingency, making it infeasible for real time application. Pattern Recognition (PR) approach is recognized as an alternative tool. The NN models adopted for classification includes Multilayer Perceptron (MLP), Learning Vector Quantization (LVQ), Probabilistic Neural Network (PNN) and Adaptive Resonance Theory Mapping (ARTMAP). The NN models designed are tested on 14 Bus, 30 bus and 57 Bus IEEE standard test systems. The performance of various NN models are studied in training and testing phases and the results are compared. KEYWORDS: Security Assessment, Neural Network, Pattern Recognition, Classification 1. INTRODUCTION wadays, power systems are forced to operate under stressed operating conditions closer to their security limits. Under such fragile conditions, any small disturbance could endanger system security and may lead to system collapse [1]. Fast and accurate security monitoring method has, therefore, become a key issue to ensure secure operation of the system. Power System Security is defined as the system s ability to withstand credible contingencies without violating normal operating limits. Security analysis may be broadly classified as (i) Static Security and (ii) Transient Security [2]. Static security evaluation detects any potential overload of a system branch or an out-of limit voltage following a given list of contingencies [3]. Transient security evaluation pertains to system dynamic behavior in terms of rotor angle stability, when subjected to perturbations. Traditional security assessment involves numerical solution of non-linear load flow equations and transient stability analysis for all credible contingencies [4]. Because of the combinatorial nature of problem, this approach requires a huge amount of computation time and hence found infeasible for real time security analysis of large scale power system networks. Pattern Recognition (PR) techniques have shown great importance as a means of predicting the security of large electric power systems, overcoming the drawbacks of traditional approaches [4-5]. The first step in applying PR technique to the security assessment problem is the creation of an appropriate data set. The required data samples called patterns are generated by off-line simulations or obtained from real time occurrences [5]. The next important aspect in achieving good performance is the selection of input features. Many feature selection algorithms are reported in the literature such as Principal Component Analysis, Entropy Maximization, and Fisher Discrimination [6]. In this paper, a forward sequential method is used for feature selection. Using these input features, a classification function is designed for accessing system security status. The design of a suitable classifier in the pattern recognition system is an important concern for on-line security evaluation. Literatures have reported the use of conventional algorithms like linear programming, least squares [7] for designing the classifier. These existing algorithms seem to work well with linearly separable classes, but not well established on non-linearly separable classes. This led to the idea of applying Artificial Intelligence techniques to handle the problem of non-linear separability. Use of expert systems like neural networks [4], decision trees has been reported in literature. This paper details an exhaustive study of the application of various Neural Network (NN) models in classifier design. The NN models studied include Multilayer Perceptron (MLP), Learning Vector 104

2 Quantization (LVQ), Probabilistic Neural Network (PNN) and Adaptive Resonance Theory Mapping (ARTMAP). The NN models are designed and trained based on the train set and validated using test set samples. The performance of these NN models is evaluated in terms of classification accuracy and misclassification rate. The implementation of NN models is carried out in IEEE 14 bus, 30 bus and 57 bus IEEE standard test systems and the classification results are compared. 2. SECURITY ASSESSMENT (SA) Security Assessment is the process of determining whether and to what extent, a system is `reasonably' safe from serious interference to its operation [4]. It evaluates the robustness of the system (security level) to a set of contingencies in its present state or future state. This section describes in brief the static security assessment and transient security assessment process. 2.1 STATIC SECURITY ASSESSMENT (SSA) Static security of a power system addresses whether, after a disturbance, the system reaches a steady state operating point without violating system operating constraints called Security Constraints [2]. These constraints ensure the power in the network is properly balanced as given by equation (1), bus voltage magnitudes and thermal limit of transmission lines are within the acceptable limits given by equation (2). If any of the constraint violates, the system may experience disruption that could result in a `black-out'. N g min max PGi = PD + PLoss PGi PGi PGi i = 1, 2K Ng (1) i= 1 min max max k = 1, 2... N k k k b km km V V V S S branches k m (2) where P Gi represents real power generation at bus i, P D is the system demand; P Loss is the total real power loss in the transmission network; V k is the voltage magnitude at bus; S km represents complex power flow in branch k-m; N g and N b being the number of generators and buses respectively. In static security assessment process, the status of the power system is evaluated for various probable contingencies by solving non-linear load flow equations. The contingencies may include outage of a transmission line or a transformer or a generating unit. The load flow is solved for various disturbances and the results are compared with system constraints. The system operating state is labeled as Static Secure (SS) (Binary 1) if all the constraints (1)-(4) are satisfied for a specified contingency. If any one constraint violation is identified, the system state is labeled as Static Insecure (SI) (Binary 0). 2.2 TRANSIENT SECURITY ASSESSMENT (TSA) Transient security of a power system addresses whether, after a perturbation, the system proceeds to operate consistently within the limits imposed by system stability phenomena [2]. One of the primary requirements of reliable service in electric power systems is to retain the synchronous machines running in parallel with adequate capacity to meet the load. Transient security assessment consists of determining, whether the system oscillations, following the occurrence of a fault or a large disturbance, will cause loss of synchronism among generators [8]. TSA is a subset of transient stability of the power system. Transient stability pertains to rotor angle stability, wherein the stability phenomena are characterized by rotor dynamics under a severe perturbation. The system state is classified as Transient Secure (TS) (Binary 1) if the relative rotor angle of any generator with respect to slack generator does not exceed after fault clearing, under a specified transient disturbance. On the contrary, if the relative rotor angle exceeds 180 0, the system state is classified as Transient Insecure (TI) (Binary 0). 3. PATTERN RECOGNITION (PR) APPROACH Pattern Recognition (PR) is defined as the act of taking in raw data and taking an action based on the category of data. It deals with the classification of data objects, referred as Patterns, into a number of categories or classes [9]. The basic components of the PR system are preprocessing, feature selection and 105

3 classifier design as shown in Figure 1. The role of preprocessing is to define a compact representation of pattern. The goal of feature selection is to select optimal feature subset by computing numeric information from observations. With the optimal feature vector selected, a classifier is designed that does the job of classifying observations, relying on extracted features. Input Data Pre- Processing Pattern Vector Feature Selection Feature Vector Classifier Design Pattern Space Feature Space Decision Space Figure 1. Block Diagram of Pattern Recognition System 4. APLLICATION OF NEURAL NETWORK BASED PATTERN RECOGNITION (NN-PR) APPROACH TO SECURITY ASSESSMENT The main objective of applying pattern recognition approach to security assessment problem is to reduce the computational requirements in on-line evaluation. This is done at the expense of an extensive off-line computation, generating data points for training set. If the separating surface between the distinguishing classes is evaluated as a security function, the system security can be accessed at any point of time. This is the basic idea of PR approach. The sequence of steps carried out in off-line in applying the PR approach to security assessment is shown in the form of a flowchart in Figure 2. START Stage 1 Off-line Simulation Considering different operating scenarios and contingencies Evaluation of their corresponding Security Status (Static / Transient Security Status) Splitting of Data Set Randomly Training Data Testing Data Stage 2 Stage 3 Stage 4 Feature Selection by Forward Sequential Method Feature Vector Classifier Design by Neural Network Model Decision Function Performance Evaluation of the Neural Network Classifier END Figure 2. Off-Line Stages in the Design of Neural Network Based PR System 106

4 As shown in Figure 2, the design of pattern recognition system using the different Neural Network Models undergoes a series of sequential steps. The main stages are as follows: Stage 1: Data Generation (Pattern Variables) Stage 2: Feature Selection (Feature Variables) Stage 3: Classifier Design (Classification Function) Stage 4: Performance Evaluation of Classifier This section gives a brief outline of each of the above stages and the different Neural Network architectures used in the classifier design phase of the PR system. 4.1 DATA GENERATION The success of pattern recognition relies on a good training set. This set must adequately represent the entire range of system operating states. A large number of characteristic operating points termed patterns are generated through off-line simulation and the security status is evaluated for each contingency under study [10]. Each pattern is characterized by a number of attributes such as load level, voltages, power generation, etc. These attributes form the components of a vector called pattern vector X. Evaluating the security status, each pattern is labeled or classified as belonging to one of the two classes - secure/insecure. The data samples generated in this phase are randomly split into train set and test set samples. It is important to ensure that the train set contains significant number of operating points pertaining to both the classes. 4.2 FEATURE SELECTION Feature selection reduces the dimensionality by selecting only a subset of measured features to create a model. A good set of features needs to be identified to increase the classifier efficiency and accuracy [11]. This phase involves selecting an optimal subset of variables called features from a large set of pattern variables. The selected features must be capable of giving more useful information to build the classification function. The features form the components of a vector called feature vector Z. Features may be selected by engineering judgment. But such selections will be subjective with the possibility of important variables getting rejected. A common method of feature selection is sequential feature selection, consisting of two components - an objective function called criterion and a sequential search algorithm. In this paper, we use a Sequential Forward Selection (SFS) method [9]. The criterion which this method seeks to minimize over all feasible feature subsets is misclassification rate for classification models. The SFS method starts with an empty candidate set and adds feature variables sequentially until addition of further variables does not decrease the criterion (minimization of misclassification rate). 4.3 CLASSIFIER DESIGN Having selected the input feature set, the next step in the PR system is to design a suitable and efficient classifier for the security assessment problem. There are many training algorithms reported in literature for classifier design. Few of them include least squares, linear programming, back propagation, etc. These algorithms, although less time consuming, were found to give poor classification accuracy. The main requirements of a good classifier are high accuracy and less misclassification. This led to the thought of finding a more efficient learning algorithm for classifier design. In this paper, different Neural Network classifier models are designed and trained for static and transient security evaluation. This section gives a brief outline of neural network architecture used for the classification task. The NN models include Multilayer Perceptron (MLP), Learning Vector Quantization (LVQ), Probabilistic Neural Network (PNN) and Adaptive Resonance Theory Mapping (ARTMAP), each of which are discussed in brief herein MULTILAYER PERCEPTRON (MLP) MODEL Perceptron is the simplest single layer network, considered as a linear classifier. The principal weakness of the perceptron model is that it can only solve problems that are linearly separable [12]. However, most of the real world problems are non-linear in nature. A Multilayer Perceptron (MLP) is a feedforward neural network model that maps sets of input data onto a set of appropriate output. It is a 107

5 modification of the standard linear perceptron using three or more layers of neurons (nodes) with nonlinear activation functions. Hence, it is more powerful than the perceptron as it can distinguish data that is nonlinearly separable. The basic structure of a MLP network used for simulation in this work is shown in Figure 3. The network consists of an input and an output layer with one hidden layer of nonlinearly-activating nodes. Each node in one layer connects with a certain weight w ij to every other node in the following layer. The number of neurons in the input layer is same as number of input features and the number of neurons in hidden layer is chosen as 30 with hyperbolic tangent sigmoid activation function. The network is trained with Levenberg-Marquardt back propagation algorithm [13]. Input Weights Z 1 Layer Weights Input Feature Set Z 2 Output Layer Y Z m Input Layer Hidden Layer Figure 3. Structure of Multilayer Perceptron (MLP) Network LEARNING VECTOR QUANTIZATION (LVQ) MODEL Many neural network structures involve a competitive layer to recognize groups of similar input vectors. Learning Vector Quantization (LVQ) is a method of training the competitive layer neurons in a supervised manner [12]. It is a prototype based supervised classification algorithm. The structure of an LVQ network used in this simulation work is shown in Figure 4. It consists of a competitive layer followed by a linear layer. The competitive layer learns to classify the input vectors and the linear layer transforms the competitive layer s classes into user-defined target classifications. The network is given by the prototypes W= {w 1, w 2,.. w n }, which are updated to classify the data samples correctly. Input Feature Vector Z Input Weights Distance C Competitive Transfer Function Linear Weights Linear Transfer Function Y Competitive Layer Linear Layer Figure 4. Structure of Learning Vector Quantization (LVQ) Network 108

6 4.3.3 PROBABILISTIC NEURAL NETWORK (PNN) MODEL Probabilistic Neural Network (PNN) is a kind of multilayer neural network, used in the field of pattern classification. The PNN is a non-linear, nonparametric pattern recognition algorithm that operates by defining a probability density function for each data class based on the train set and optimized kernel width parameter [13]. Figure 5 shows the architecture of probabilistic neural network, consisting of four layers. Radial Basis Function (RBF), an exponential kernel, is used as the activation function in the hidden layer. Weights Input Feature Vector Z Z 1 Z 2 Z m Input Layer CLASS 2 CLASS 1 Summation Layer Decision Layer Y Pattern Layer (RBF) Figure 5. Architecture of Probabilistic Neural Network (PNN) Model The input layer has one neuron for each feature variable. The hidden layer (pattern layer) consists of one neuron for each train data sample. The hidden neurons store the values of feature variables along with target class. The summation layer has one neuron for each category of target variable. The neurons in this layer compute the weighted vote for each class category. The final layer called the decision layer compares the weighted votes in the summation layer and uses the largest vote to predict target category (Y) ADAPTIVE RESONANCE THEORY MAPPING (ARTMAP) Adaptive Resonance Theory (ART) is a neural network model which uses supervised learning method, and addresses problems such as pattern recognition and prediction [14]. ARTMAP is a predictive ART, capable of on-line recognition learning and adaptive naming in response to an arbitrary stream of input patterns. ARTMAP system includes two ART modules, ART a and ART b, linked by an inter-art associative memory as shown in Figure 6. ARTMAP structure combines the two ART-1 units into a supervised learning structure. The ART a unit takes the input data and the ART b takes the correct target data, and then makes the minimum possible adjustment of the vigilance parameter in the first unit in order to make the correct classification. 109

7 Target ART b Map field Gain Control - MAP FIELD - Match Tracking - Map field Orienting Subsystem ART a Train Input Figure 6. Overview of ARTMAP Architecture 4.4 PERFORMANCE EVALUATION OF CLASSIFIER The performance of the various Neural Network based classifiers is gauged by evaluating the following measures during training and testing phases. (a) Mean Squared Error (MSE) n 1 MSE= n N DO k AO k 2 ( Ek ) ; Ek = DOk AOk k= 1. of samples in the data set Desired Output obtained from off-line simulation Actual Output obtained from NN trained classifier (b) Classification Accuracy (CA).of samplesclassifiedcorrectly CA = 100 Total.of samplesin data set (3) (4) (c) Misclassification (MC) Rate (i) Secure Misclassification (SMC) or False Dismissal.of 0 ' classified 1 SMC = s as 100 Total.of Insecure States (5) (ii) Insecure Misclassification (ISMC) or False Alarm.of 1' sclassified as0 ISMC = 100 (6) Total.of Secure states In power system security evaluation, the false alarms do not bring any harm to power system operation. In case of false dismissals, system operation becomes unknown and hence failure of control actions may lead to a severe blackout. It is, therefore, important to ensure that false dismissals are kept at minimal. The classification system must be efficiently designed to meet this requirement. 5. SIMULATION RESULTS AND DISCUSSION The different NN based classifier models for security assessment is implemented in IEEE 14 bus, 30 bus and 57 bus standard test systems [15-16]. The bus voltage magnitude is limited in the range of 0.90pu 110

8 to 1.10pu. The MVA limits of lines and generator data are given in Appendix. The data sets required for training and testing phases are generated by off-line simulation with programs developed in Matlab 7.0. We have considered different operating scenarios by varying generation and load from 50% to 200% of their base case value with generation variation limited to their minimum and maximum limits. 5.1 RESULTS OF STATIC SECURITY ASSESSMENT In Static Security Assessment (SSA), single line outages are simulated for each operating condition. For a given operating condition and specified contingency, load flow solution by Fast Decoupled Load Flow method is obtained. The static security status (secure/insecure) is determined for feasible solutions by evaluating the security constraints given by equations (1)-(2). The steady state variables of the load flow solution are recorded as pattern variables, which includes bus voltage magnitude, bus voltage angle, complex power generation at generator buses, complex power load at load buses and MVA flow in all branches. An optimal subset of pattern vector called feature vector is identified by SFS feature selection method. The results of data generation and feature selection phases for static security assessment are shown in Table 1. Table 1 Data Generation and Features of Static Security Assessment Test Case Studied IEEE 14 Bus IEEE 30 Bus IEEE 57 Bus Operating Scenarios Static Secure (SS) Cases Static Insecure (SI) Cases of Pattern Variables of Features Selected Dimensionality Reduction 6.25 % 5.47 % 9.05 % The data samples of m features are randomly split into train and test set. The classifier is designed based on train set by different NN models as described in Section 4.3. The NN models are designed, trained and tested using the Neural Network toolbox in Matlab 7.0. The classification results of NN classifiers obtained during training and testing phases are shown in Table 2. The MLP classifier is trained with Levenberg Marquardt algorithm (Learning rate=0.05, Goal=0.001, Epochs=600). It was found from repeated experiment trials that a hidden layer of 30 neurons in the MLP network gives promising results. The classification results of different NN classifiers show that the PNN and ARTMAP trained classifiers gives a fairly high classification accuracy and less secure misclassification rate, compared to other NN models. The PNN classifier is capable of classifying unlabeled samples (test set, whose class labels are unknown) with high accuracy. Figures 7(a) and 7(b) shows the comparison of the performance of the NN classifiers for complete data set in terms of Classification Accuracy and False Dismissal rate (SMC) respectively. As seen from Figure 7, the PNN and ARTMAP classifiers give very low false dismissal rate (nearing zero) and hence making it suitable for on-line implementation. 111

9 IEEE 14 Bus IEEE 30 Bus IEEE 57 Bus Table 2 Classification Results of Static Security Assessment on Train Set and Test Set TRAIN SET TEST SET MLP LVQ PNN ARTMAP MLP LVQ PNN ARTMAP Samples CA MSE SMC (153/193 ) (7/193) (0/193) (0/193) (12/24) (1/24) (0/24) (0/24) ISMC (0/168) (1/168) (0/168) (0/168) (0/15) (3/15) (0/15) (5/15) Time (s) Samples CA MSE SMC (43/66) (21/66) (0/66) (0/66) (7/10) (5/10) (0/10) (0/10) ISMC (0/930) (7/930) (0/930) (0/930) (0/40) (1/40) (3/40) (4/40) Time (s) Samples CA MSE SMC (284/581 ) (93/581) (0/581) (0/581) (42/78) (3/78) (14/78) (20/78) ISMC (0/632) (11/632) (0/632) (0/632) (6/87) (1/87) (3/87) (28/87) Time (s) (a) Classification Accuracy (CA) (b) Secure Misclassification (SMC) Figure 7. Performance of Classifiers for Static Security Assessment 112

10 5.2 RESULTS OF TRANSIENT SECURITY ASSESSMENT In transient security assessment process, the static security status of all the operating scenarios is first identified by running load flow program. The operating scenarios which are static insecure (violating constraints) are ignored. Each static secure case is subjected to transient security analysis by simulating transient disturbances (three phase faults) on all lines, one at a time, both near sending and ending buses. The faults are applied at 0 sec and cleared at 0.25 sec (with frequency 60Hz) by tripping the faulted line. The system dynamic equations are solved by numerical integration technique, viz., fourth-order Runge- Kutta method and the transient security status is evaluated for each disturbance. If the relative rotor angle of any generator with respect to reference generator exceeds after fault clearing instant, the corresponding data pattern is labeled as Transiently Insecure(0), else classified as Transiently Secure(1). A simple classical model with each generator represented by a constant voltage behind transient reactance is used in the transient stability simulation program. The steady state variables from static security assessment and the variables pertaining to system dynamic behavior obtained from transient security assessment form the components of pattern vector. The pattern variables are bus voltage magnitude and angle, power generation and load, mechanical input power, electrical output power and relative rotor angle of generators at fault application time and fault clearing time. The size of the pattern vector being large, variables having higher information content are identified by SFS feature selection method, thereby yielding the feature vector for classifier design. The results of data generation and feature selection phases for transient security assessment are shown in Table 3. Table 3 Data Generation and Features of Transient Security Assessment Test Case Studied IEEE 14 Bus IEEE 30 Bus IEEE 57 Bus Operating Scenarios Static Secure (SS) Cases Static Insecure (SI) Cases Operating Scenarios Transient Secure (TS) Cases Transient Insecure (TI) Cases of Pattern Variables of Features Selected Dimensionality Reduction 4.34 % % 3.54 % SSA TSA The classification function is designed based on the train set of the feature vector. The results of classifiers obtained during training and testing phases for transient security assessment are compared in Table 4. Figures 8(a) and 8(b) shows the performance comparison of the classifiers as a bar plot in terms of classification accuracy and secure misclassification rate respectively. It can be seen from Table 4 and Figure 8 that the PNN and ARTMAP based NN classifiers gives a better result, with high classification accuracy and less misclassification rate than other classifiers. Furthermore, the time taken by these classifiers is quite acceptable, making it feasible for on-line security monitoring system. Data robustness, overload detection, voltage monitoring and contingency analysis are widely studied in security assessment. The classifiers designed are useful for all these analysis. TRAIN SET TEST SET 113

11 IEEE 14 Bus IEEE 30 Bus IEEE 57 Bus International Journal of Research and Reviews in Applied Sciences MLP LVQ PNN ARTM AP MLP LVQ PNN ARTMA P Samples CA MSE SMC (120/ ) (22/154) (0/154) (0/154) (2/5) (2/5) (1/5) (0/5) ISMC (0/286) (11/286) (0/286) (0/286) (0/35) (4/35) (0/35) (3/35) Time (s) Samples CA MSE SMC (182/315 ) (220/315 ) (6/315) (0/315) (2/5) (5/5) (5/5) (3/5) ISMC (0/1927) (0/1927) (0/1927 ) (0/1927) (0/47) (0/47) (0/47) (5/47) Time (s) Samples CA MSE SMC (361/676 ) (41/676) (0/676) (0/676) (12/16) (3/16) (1/16) (3/16) ISMC (30/1011 (0/ (0/1011) ) ) (0/1011) (0/61) (4/61) (0/61) (0/61) Time (s) Table 4 Classification Results of Transient Security Assessment on Train Set and Test Set (a) Classification Accuracy (CA) (b) Secure Misclassification (SMC) Figure 8. Performance of Classifiers for Transient Security Assessment 114

12 6. ONLINE IMPLEMENTATION The security system developed based on Neural Network based classifiers is feasible for on-line implementation. In on-line mode, real time system data of the selected feature variables are measured and fed to the trained NN classifier, which evaluates the system security status as shown in Figure 9. Online application allows the system operator to monitor security, providing warning whenever the system goes to alert or emergency state under severe contingency. This can be done by computing the system security status from time to time, the computing time being very short. Power System Real Time Data Measurements NN Classifier Selected Features System Insecure Control Action Figure 9. On-line Implementation of Security Assessment 7. CONCLUSION The application of pattern recognition approach for classifying the input feature vector representing the power system states is presented. The classifier in the PR system is developed by different Neural Network structures, namely, Multilayer Perceptron, Learning Vector Quantization, Probabilistic Neural Network and Adaptive Resonance Theory Mapping. Training set feature vector generated from off-line simulation are presented as inputs to different NN architectures, which uses active supervised learning to adapt its weight vectors. The NN models are tested on IEEE standard test systems for both static and transient security assessment. Simulation results show that high accuracy classifiers with less false dismissal rate are realizable with PNN and ARTMAP classifiers. These classifiers involve less time, making it suitable for real time security monitoring and evaluation. 8. REFERENCES [1] K.R.Niazi, C.M.Arora, S.L.Surana, Power System Security Evaluation using ANN: Feature Selection using Divergence, Electric Power Systems Research, Vol. 69, Issues 2-3, May 2004, pp [2] S.M.Shahidehpour, Communication and Control in Electric Systems, Wiley Interscience, John Wiley & Sons, [3] M.A.Matos, N.D.Hatziargyriou, Pecas Lopes, Multicontingency Steady State Security Evaluation using Fuzzy Clustering Techniques, IEEE Transactions on Power Systems, Vol. 15,.1, February 2000, pp [4] W.P.Luan, K.L.Lo, Y.X.Yu, ANN Based Pattern Recognition Technique for Power System Security Assessment, IEEE Inter. Conference on Electric Utility Deregulation and Restructuring and Power Technologies, 2000, City University, London, 4-7 April 2000, pp [5] Chok K.Pang, Antti J.Kovio, Ahmed H.El.Abiad, Application of Pattern Recognition to Steady State Security Evaluation in a Power System ', IEEE Trans. on Systems, Mans & Cybernetics, Vol.SMC-3,.6, v 1973, pp [6] Craig Jensen, Mohamed A.El.Sharkawi, Robert J.Marks, Power System Security Assessment using Neural Networks: Feature Selection using Fisher Discrimination, IEEE Transactions on Power Systems, Vol. 16,.4, v 2001, pp [7] C.K.Pang, F.S.Prabhakara, A.H.El-Abiad, A.J.Kovio, Security Evaluation in Power Systems using Pattern Recognition, IEEE Transactions on Power Apparatus & Systems, Vol. PAS-93, May/June 1974, pp [8] Hossein Hakim, Application of Pattern Recognition in Transient Security Assessment, Electric Power Components and Systems, Vol. 20, Issue 1, January 1992, pp

13 [9] Sergios Theodoridis, Konstantinos Koutroumbas, Pattern Recognition, John Wiley & Sons, Prentice Hall, 3 rd Edition, [10] Se-Young Oh, Pattern Recognition and Associative Memory Approach to Power System Security Assessment, IEEE Trans. on Systems, Man, Cybernetics, Vol. SMC-16,.1, 1986, pp [11] Siri Weerasooriya, Mohammed A.El. Sharkawi, Feature Selection for Static Security Assessment using Neural Networks, IEEE International Symposium on Circuits & Systems, San Diego, California, May 10-13, 1992, pp [12] Abhisek Ukil, Intelligent Systems and Signal Processing in Power Engineering, Springer-Verlag, [13] Simon Haykin, Neural Networks-A Comprehensive Foundation, Prentice Hall, Second Edition, [14] Carpenter, G.A., Grossberg, S., Reynolds, J.H., ARTMAP : Supervised Real-Time Learning and Classification of n-stationary Data by a Self-Organizing Neural Network, Neural Networks, Vol. 4, 1991, pp [15] M.A.Pai, Computer Techniques in Power System Analysis, Kluwer Academic Publishers, [16] (Power System Test Case Archive) A1. IEEE 14 Bus System Line Limit Line From- To Bus MVA Limit Line From- To Bus APPENDIX MVA Limit Generator Data Gen Bus P min (MW) P max (MW) R a (p.u.) X d (p.u.) H (sec) All Other Remaining Lines (Line 9 - Line 20) All Other Remaining Lines (Line 8 - Line 41) A2. IEEE 30 Bus System Line Limit Generator Data Line From- To Bus MVA Limit Line From- To Bus MVA Limit Gen Bus P min (MW) P max (MW) R a (p.u.) X d (p.u.) H (sec) A3. IEEE 57 Bus System Line Limit Generator Data Line From- To Bus MVA Limit Line From- To Bus MVA Limit Gen Bus P min (MW) P max (MW) R a (p.u.) X d (p.u.) H (sec)

14 All Other Remaining Lines (Line Line 80) ACKNOWLEDGMENT The first author would like to thank the Principal and Management of K.L.N. College of Engineering, Pottapalayam for having given an opportunity to pursue PhD programme in Indian Institute of Technology Madras on study leave with sponsorship under Quality Improvement Programme (QIP) scheme. The authors also like to thank IIT Madras for providing necessary facilities and resources to carry out this research work. BIOGRAPHY: S. Kalyani received her Bachelors Degree in Electrical and Electronics Engineering from Alagappa Chettiar College of Engineering Karaikudi, in the year 2000 and Masters in Power Systems Engineering from Thiagarajar College of Engineering, Madurai in December From 2003 to 2007, she was a faculty member with the Department of Electrical and Electronics Engineering, KLN College of Engineering, Madurai, India. She is currently a Research Scholar in Dept. of Electrical Engineering, Indian Institute of Technology Madras. Her research interests are power system stability, Pattern Recognition, Neural Networks and Fuzzy Logic applications to Power System studies. She is a Member of IEEE since June Dr. K. Shanti Swarup (S 87 M 92 SM 03) is currently a Professor in the Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India. Prior to his current position, he held positions at Mitsubishi Electric Corporation, Osaka, Japan, and Kitami Institute of Technology, Hokkaido, Japan, as a Visiting Research Scientist and a Visiting Professor, respectively, during 1992 to He received his Bachelors Degree in Electrical Engineering from Jawaharlal Nehru Technological University, Kakinada Andhra Pradesh and Masters Degree in Power Systems Engineering from Regional Engineering College, Warangal. His areas of research are artificial intelligence, knowledge-based systems, computational intelligence, soft computing, and object modeling and design of power systems. He is a Senior Member of IEEE since