Power System Dynamic Security Classification Using ...

Power System Dynamic Security Classification Using Kohenen Neural Networks M. R. Aghamohammadi , F. Mahdavizadeh , R. Bagheri

Abstract: In this paper a novel approach for transient stability based dynamic security classification and screening of power systems is presented. A Kohenen neural network is implemented as neural network security classifier. The precontingency steady state operating condition of power system is used as the input pattern of the neural network classifier for proper classification of dynamic characteristic. Transient stability is the dynamic behavior by which system security is assessed and classified. Critical clearing time (CCT) is used as security index for both feature extraction and classification of system dynamic security states. For the purpose of feature extraction, correlation between pre contingency operating condition and system dynamic characteristic is used. The proposed approach has been demonstrated on the IEEE-39 bus system with promising results for relatively accurate classification and screening of power system dynamic security. Keywords: dynamic security, power system transient stability, classification, screening, neural networks, feature extraction

S

I. INTRODUCTION

ecurity is a vital requirements for power system operation. An inherent characteristic for electric power systems is its operation under the presence of disturbances. The stability of power systems deals with the character of the electro-mechanical oscillations of synchronous generators created by a disturbance. Whether or not the post-disturbance behavior leads to loss of synchronous operation is the subject of primary concern. Power system security assessment can be classified into three main aspects namely, steady sate, dynamic and transient security assessment respectively. Steady state security assessment involves primarily the checking of operating limit violations of various components of power system [1]. Transient security analysis entails evaluation of power system's ability to withstand a set of severe but credible contingencies and to survive transition to an acceptable steady-state condition [1]. The purpose of dynamic security assessment (DSA) is to determine which contingencies may cause power system instability. In this process, the objective is to derive operating

M. R. Aghamohammadi is with Electrical Department, Iran Dynamic Research Center, Power & Water University of Technology, Tehran, Iran, (phone: 982177312176; fax: 982173932591; e-mail: [email protected] , r_aghamohammadi@ yahoo.com). F. Mahdavizadeh is with Electrical Department of Power & Water University of Technology, Tehran, Iran R. Bagheri is with Electrical Department of Tehran Azad University, Tehran, Iran,

guidelines for defining secure operating areas. A DSA process mainly consists of two steps, 1) selection of critical contingencies and 2) performing a detailed stability analysis for each critical contingency. Historically, the dynamic security contingency screening methods unlike their static security counter parts have not received a great deal of attention. With the recent progress in analytical techniques [2] and major advancements in computer hardware, contingency screening for DSA seems to be more feasible and justified. So far, the most common used methods suggested for dynamic security screening are the analytical methods using the transient energy function (TEF) [2] and the use of artificial intelligence including expert systems and neural networks [3]. For large complex power systems, it is impractical and unnecessary to perform full detail dynamic analysis on the impact of every conceivable contingency. Instead, accurate but fast contingency screening indices can be used to reduce the computation to a manageable level. For successful screening, the indices should be a good measure of system severity in the transient condition [4]. In [8], B.C. Hydro conducted a project about application of neural network to online dynamic security assessment and various areas of dynamic security assessment were analyzed and potential areas for neural-network application were identified and ranked. A power system is transiently stable if the clearing time of the fault is less than the critical clearing time (CCT). CCT is a complex and fully non linear function of pre-fault operating condition of power system, location and type of the fault and protective relaying strategy. In a stability-limited power system, security determination requires analysis of the dynamic behavior of the system under prescribed sequence of events, known as contingencies. The stability of the system depends on many factors and its analysis involves analysis of complex patterns of system behavior. Artificial neural networks based classification could provide fast assessment of dynamic security of power systems. This is the main motivation for applying the artificial neural network technique for dynamic security assessment of a stability-limited system. In recent years artificial neural networks have been proposed as an alternative method for solving certain difficult power system problems where the conventional techniques have not achieved the desired speed and efficiency [5]. In [6], the artificial neural networks technique is applied to the concept of system vulnerability within the recently developed framework for fast pattern recognition and classification of system dynamic security status. In [7], a neural network is successfully used to provide a fast transient stability screening

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within a dynamic security assessment. Recently Belhomme [8] proposed a pragmatic pattern recognition technique for synthesizing CCT based on the use of two features derived from the Lyapunov energy function. It was found that the accuracy of results is sensitive to changes in the system topology and in the search strategy employed in feature space. In this paper, by using Kohenen neural network, a novel approach for transient stability based dynamic security assessment and classification is proposed. The idea is based on the use of information on the prevailing operating condition and directly provides contingency screening using neural network. In this work, the preference was only to use operating features that can be easily measured or calculated from measurements such as steady state pre-contingency operating variables and avoid dynamic ones which could require time consuming simulations or complex measurements. The idea behind the proposed approach is similar to that of EPRI project [3] except that the implementation including the neural-network design, the choice of features and outputs are considerably different. II. TRANSIENT STABILITY BASED SECURITY CLASSIFICATION For transient stability based dynamic security assessment, four broad approaches could be used [7]. 1) Numerical integration methods in which by using a step by step numerical integration method, the network and machine equations could be solved. Considerable progress has been made in speeding up these methods [9]-[10]. However, these methods currently remain too slow to be used for contingency screening in an online DSA environment, if a large number of contingencies is to be evaluated. However, this is the most accurate method for stability assessment, and establishes the benchmark against which the other stability assessment methods are judged. 2) Energy function methods use a stability criterion based on the construction of a Lyapunov function [11] to determine the stability of the postcontingency operating point of the system. These methods are less computationally demanding compared to the numerical integration approach, but do not achieve the same level of accuracy due to the use of reduced order modeling. 3) Expert system methods rely on decision trees to assess the system stability in terms of selected precontingency parameters [12]-[13]. These approaches tend to be less robust to changes in the power system state and can result in misclassification of unstable contingencies as stable. 4) Pattern recognition methods rely on reducing the online computational overhead to a minimum at the expense of intensive offline studies. By performing offline training of a pattern classifier using results obtained from time domain simulation, accuracy close to that of a numerical integration method may

be achieved. The task of pattern recognition consists of defining a pattern vector V, whose components contain sufficient information about the stability of the power system so that a classifier can decide purely on the basis of V what the system stability will be. This vector is then evaluated at many different representative operating points of the power system to generate a training data set. In order to provide a proper classification, a classifier index is needed to be defined. Numerous feature extraction methods have been developed [14]-[17] but few of these methods are easily scaled to large power system models. In this paper, a novel approach is presented for classification of system pre contingency operating conditions with respect to its potential for being transiently unstable in the case of line fault and outage. For this purpose, an unsupervised Kohenen Neural Network is trained to be a dynamic security classifier (ANNSC). By presenting any given pre-contingency operating condition to the proposed ANNSC, it can classify system dynamic state into secure or insecure classes. A secure class represents a pre contingency operating state of power system in which no critical line fault with the potential for causing instability exists. An insecure class represents a pre contingency operating state of power system in which at least one line fault or more are critical with the potential for causing instability. A line is critical if its fault and outage can cause at least one generator transiently unstable. In this paper, the critical clearing time (CCT) associated with each line fault is adopted as criterion for criticality of the line. Therefore, if CCT associated with a line is less than fault clearing time (here adopted as 100 msec.), then that line will be recognized as critical. The degree of criticality of an operating condition is determined by the number of critical lines existing for that condition. The proposed ANNSC can be used for classification and screening power system dynamic security in an on-line environment in which for any given operating condition of power system, the most critical lines could be recognized and screened for detail stability analysis. III. NEURAL NETWORK SECURITY CLASSIFIER In this paper, the main objective is classification and ranking system pre contingency operating conditions with respect to their potential for causing dynamic instability in the case of line fault and outage. The input pattern vector for ANNSC consists of pre-contingency system operating variables such as line power flows, load/generation powers and bus voltages. The number of input neurons is equal to the number of operating variables selected as feature of the input pattern vector. Each output neuron of ANNSC represents a security class with a certain degree of criticality. The size of output neurons is determined by the number of neurons required for a proper and discriminative security classification. Each group of output neurons are assigned to one security class. The proper number of output neurons is determined based on the try and error using a classification index.

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A. FEATURE SELECTION Features are system attributes with necessary and sufficient information to construct input pattern and internal structure of the neural network. Selection of proper system operating variables as representative for featuring system dynamic characteristic is an elaborating task. In dynamic security assessment, it was shown [17] that for proper reconstruction of system model, three types of information are required: 1) initial conditions; 2) network connectivity at pre contingency; and 3) contingency. This information includes two types of features, namely static and dynamic features. Static features are those attributes representing steady state pre and post contingency conditions. Dynamic features are those which reflect dynamic system conditions following the contingency. However, in this paper, for the seek of simplicity and availability of the required information for security classification, only steady state pre contingency operating features are adopted for feature selection. Table I shows those features for IEEE 39-bus test system. The input pattern vector for ANNSC can be constructed by a proper combination of the features shown in Table I. TABLE I PRE CONTINGENCY STATIC FEATURES

N o. 1 2 3 4 5 6 7

Parameters Line Active power Flow Line Reactive Power Flow Active Generation Reactive Generation Active Load power Reactive Load power Bus voltage Magnitude Total

Variable Pline Qline PG QG Pload Qload V

No. of Variable 34 34 10 10 19 19 39 165

A feature selection algorithm based on the correlation between the pre contingency operating variables and system dynamic behavior has been used. Since the final goal of classification is screening and ranking operating conditions with respect to their potential for causing transient instability, so critical clearing time (CCT) associated with the lines of an operating condition is selected as a criterion for both feature extraction and classification. The objective is to select features which provide accurate security classification. For this purpose, those operating features which could effectively represent system dynamic characteristic are selected to construct input pattern vector. In order to find the most representative variables for the input pattern, correlation factor between pre contingency operating variables and CCT associated with each specific line fault is adopted as a criterion. As a result, those features with the highest correlation are selected for the input pattern. To implement this application, detailed transient stability studies is carried out for different operating cases. For each case, by applying single contingency (3 phase fault) on system lines, the CCT associated with each line is calculated. The

pre contingency steady state operating condition associated with each case is used for constructing input pattern for training and testing ANNSC. By presenting input patterns to ANNSC, it classifies system dynamic security through actuating different neurons at its output. Proper categorizing actuated output neurons into security classes with similar security attributes is the most important task for proper and meaningful classification. For this purpose, CCT of lines is used as a criterion and guideline for checking and interpretation of security classes such that all those operating patterns categorized in a specific class have similar critical lines. IV. SIMULATION STUDIES In order to demonstrate the effectiveness of the proposed approach for classification and screening system security, the proposed neural network security classifier ANNSC is applied for IEEE 39-bus system consisting of 39 buses, 34 lines, 10 generators and 19 load buses [19].

A. Training Data To implement this application, proper training data should be prepared by detailed load flow and transient stability studies for different operating cases. For each case, steady state pre contingency operating condition and CCTs associated with all lines are calculated. These values are then used for training and testing ANNSC. Training data should be able to represent whole operating space of power system. For this purpose, 1800 operating cases are produced as follows. For each load bus a corresponding max

upper and lower limit ( PL

, PLmin ) is defined which

represent boundary of daily load variation. Then, load variation of all load buses within their upper and lower limits are divided equally into 10 levels. At each load level, by adding all load buses a corresponding load level for the system will be obtained. By this way, 10 load levels ranging from 5000 MW to 9000 MW (%60 to %140 of base load) are defined for the system. In the same way, by taking upper and max

lower limits of generators ( PG

, PGmin ) and similarly

dividing generator outputs into 10 equal levels, corresponding to each load level one generation level will be obtained. By combining each load level with corresponding generation level, 10 basic load-generation patterns are produced. In order to produce more load-generation patterns in the operating space, around each specific basic load-generation pattern by randomly perturbing load and generation of buses, 200 patterns are created. For this purpose, for each basic loadgeneration level, in 10 times and each time 10 load buses are randomly selected and their loads are randomly increased or decreased from %5 to %15 with respect to its basic value. Similarly, in 20 times and each time 10 generators are randomly selected and their generation is randomly changed from -%40 to +%40 of their generations. For each basic load level, by cross combination of 10 randomly loads and 20

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randomly generations, 200 new load-generation patterns are created. Finally, for 10 basic load levels 2000 load-generation patterns are produced. By applying each load-generation pattern to the test system and performing load flow calculation using DigSilent software, corresponding initial steady state operating condition of the system is obtained. Those load-generation patterns with the potential for causing violation in the steady state operating condition are removed which resulted in 1800 remaining acceptable patterns. The steady state pre-contingency operating variables shown in Table I corresponding to each operating pattern are selected for feature extraction ad elaborating input pattern. B. Structure of Input Pattern Input pattern vector could be elaborated by proper combination of the most effective operating variables shown in Table I. Table II shows possible combinations of operating variables suggested for feature extraction and input pattern construction. TABLE II POSSIBLE COMBINATION OF OPERATING VARIABLES FOR INPUT PATTERN

No.

Combinatorial Pattern

1 2 3 4 5 6 7 8

PLine PLine & PG PLine & PG & V PLine & QLine & PG PLine & QLine & PG & V PLine & V PLine & QLine & V PLine & QLine & PG & PLoad & QG PLoad & PG PLoad & QLoad

9 10

V &

No. of Variables 34 44 83 78 117 73 107 146 29 38

In order to extract the most representative operating variables for input pattern, correlation factor is used. For each operating case, CCT associated with each line fault is a function of system pre contingency operating variables. Operating variables with significant effect on line CCT are recognized as dominant representative of system condition for security classification. Within 1800 operating cases, for each operating variable (X) with respect to CCT of a specific line (Y) a correlation factor r is evaluated using equation (1).

∑ n

r=

i =1

∑

⎡n ⎢ X ⎢ ⎣ i =1

2

−(

1 n

X iY i − ( n1 )

∑ ∑Y n

i =1

Xi

2 ⎛ n ⎞ ⎤⎡ n )⎜ X ⎟ ⎥ ⎢ Y ⎝ i =1 ⎠ ⎥⎦ ⎢⎣ i =1

∑

∑

n

i =1

2

−(

i

1 n

2 ⎛ n ⎞ ⎤ )⎜ Y ⎟ ⎥ ⎝ i =1 ⎠ ⎥⎦

∑

(1)

factor r represents correlation between MVar flow of line 8-5 with CCT of line 9-8 and its magnitude shows the effectiveness of this line flow on the CCT and criticalness of line 9-8. The operating variables with the highest correlation factor with respect to CCT of all lines are selected as the most dominant feature for elaborating input pattern. There are 1800 operating cases and for each case, 165 operating variables as shown in Table I and there exists 34 CCT associated with 34 lines. Using 1800 operating patterns, the correlation of 165 operating variables with 34 line CCT are evaluated using Eq. (1). With respect to the CCT of each line, 10 operating variables with the highest correlation are selected as 10 top priority variables with dominant effect on the criticality of that line. Table III shows 10 top variables among 165 operating variables of Table I which have highest correlation with CCT of lines 9-8, 10-13, 2-1, 39-9, 3-2 and 25-2. As it can be seen, the priority of operating variables with the highest correlation differs from line to line. For example, the most correlated variable with CCT of line 9-8 is reactive power flow of line 8-5 while for CCT of line 13-10 is reactive power flow of line 32-1. TABLE III EXAMPLE OF DOMINANT VARIABLES FOR SOME LINE CCT CCT Lin_25_2

Lin_3_2

Lin_2_1

Lin_13_10 Lin_9_8

Pirority QG_30_1

QLine_8_5

VB_4

QLine_39_9

VB_39

VB_14

PG_37_1

QLine_2_1

VB_5

VB_35

VB_9

VB_9

QLine_6_5

VB_1

VB_6

PLine_38_1

PLine_7_6

VB_13

VB_30

PLine_14_4

VB7

VB_31

QLine_9_8

VB_8

VB_37

QLine_8_7

VB_12

VB_38

QG_30_1

PLine_9_8

QLine_8_ QLine_8_5 QG_32_1 5 VB_28 PLine_6_5 VB_30 PLine_13_1 VB_29 VB_1 0 PLine_14_1 PLine_8_ VB_30 3 7 VB_26 QG_32_1 VB_28 QLine_15_1 VB_37 VB_29 4 PLine_15_1 VB_25 VB_26 4 VB_38 QLine_4_3 VB_2 QLine_2_ VB_1 PG_31_1 1 PLine_2_1 PLine_5_4 VB_25

1 2 3 4 5 6 7 8 9 10

Therefore, with respect to CCT of each line, 10 top priority operating variables with the highest correlation are found for all 34 lines. Considering 10 top variables of all 34 lines, the frequency of falling each operating variables into 10 top priority variables is adopted as a criterion for selecting most effective features. Table V shows the number and percentage of falling each dominating variable into 10 top priorities with highest correlation. TABLE IV DOMINATING VARIABLES WITH HIGHEST CORRELATION

Variable

PLine 147 %correlation 43.4

No. of Falling

Where X represents a specific operating variable (e.g. MVar flow of line 8-5) and Y represents CCT of a line (e.g. line 9-8) respectively within 1800 operating cases. Then the correlation

Lin_39_9

QLine V 85 53 25.2 15.7

QG 24 7.21

PG 21 6.18

According to the results obtained from correlation analysis,

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operating variables PLine, QLine and V are selected as most dominant features for constructing input pattern. C. Structure of Neural Network The structure of Kohene neural network is determined by the number of input/output neurons. The number of input neurons is as the size of input pattern vector. The number of output neurons which is very crucial for proper classification could be determined based on classification performance of ANNSC. For this purpose, two types of Kohenen neural network named operating state classifier (OSANN) and CCT classifier (CCTANN) are proposed. OSANN classifies system security based on the steady state pre contingency operating condition with input pattern consisting of PLine, QLine and V. CCTANN classifies system security based on the stability performance of power system with input pattern consisting of CCT of 34 lines. It should be noted that CCT classifier neural network (CCTANN) is only defined for checking performance of OSANN and decide the number of its output neurons, while operating state classifier OSANN is the main neural network to be trained and work as security classifier. In order to decide proper number of output neurons, first, both OSANN and CCTANN are trained for 1800 operating cases with corresponding input patterns for different number of output neurons as 16, 25, 100, 196, 225, 256 and 400. By presenting corresponding input patterns of 1800 operating cases to both neural networks, they classify all operating cases by actuating output neurons. In both neural networks, each output neuron will be actuated by a group of operating cases which constitute an associated class of security. Each output neuron of OSANN should be corresponding to one output neuron of CCTANN. Two output neurons of OSANN and CCTANN are corresponding and representing one security class if their associated security classes have maximum common operating cases. If output neurons I and k belonging to OSANN and CCTANN are corresponding neurons, then a corresponding factor (CF) could be defined as equation (2).

CFik = 12 (

NM

ik + i

ik ) ×100 k

NM

M

N

(2)

Where Mi and Nk are the number of operating cases represented by the corresponding output neurons I and k respectively, NMik is the number of common operating cases with similar security attributes represented by neurons I and k. For each structure of neural network with a specific number of output neurons a total weighted corresponding factor is defined by applying equation (2) for all actuated neurons. NC

WCFT =

∑ CF j × N j j =1

NC

∑Nj

(3)

j =1

Where CFj is corresponding factor of class j evaluated by (2),

Nj is number of common operating cases belonging to class j and NC is the number of classes introduced by the neural networks. With respect to the number of output neurons, table V shows total weighted corresponding factor for different structure of neural networks. In order to have an acceptable classification performance and less number of output neurons, 196 output neurons is selected for structure of OSANN. D. Training Classifier After deciding input pattern and number of output neurons, in order to train OSANN, from 1800 operating cases, 300 cases with different security level as shown in Table VI are selected as training patterns and the remaining 1500 operating cases are considered for testing it. By 5000 iterations training, all training patterns are well categorized in 74 actuated output neurons while 116 output neurons remained inactivated as dead neurons. Every neuron represents one security class in which all operating cases have similar critical lines. First, it is assumed that each output neuron is representative for an individual security class, but at the end of training it is found that some of the neurons have similar security attributes which can be categorized in the same class. Finally all 74 neurons are categorized in 20 classes. Table VII shows the final 20 classes with associated output neurons and their severe and critical lines. In a class, critical lines are those lines whose CCT are less than 100 milliseconds and severe lines are whose CCT are greater than 100 msec. but smallest with respect to other uncritical lines. The numbers shown in the parenthesis refer to lines which may sometimes become critical instead of the last one. For example, for class 20, line 12 may sometimes become critical instead of line 18 TABLE V WEIGHTED CORRESPONDING FACTOR FOR DIFFERENT NUMBER OF OUTPUT NEURONS

No. of output neurons

16 25 100 196 225 256 400

Max. CF In all classes

Min. CF In all classes

37 40 37 41 40 41 41

Total weighted CF for all classes

100 100 100 100 100 100 100

66.5 66.75 84.5 86.5 87.5 89 90

TABLE VI SECURITY LEVEL OF TRAINING PATTERN

Security Level Secure Pattern with no critical line Pattern with 1 critical line Pattern with 2 critical line Pattern with 3 critical line Pattern with 4 critical line Pattern with 5 critical line

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No. of Pattern 30 76 117 44 30 3

E. Testing Classifier After training OSANN, its classification performance was examined by applying 1500 unseen testing operating cases to OSANN. Table VIII shows the classification result for 80 unseen operating cases. The result shows that it correctly classified all cases with only 8 misclassifications. For example, 8 operating cases recognized as class 14 and only in one case line 12 was misrecognized as sever line. Using equation (3), total corresponding factor for 1500 test patterns was calculated as 0.91.

Class No.

V. CONCLUSIONS In this paper, by using an unsupervised Kohenen neural network a novel approach is presented for classification of system pre contingency operating conditions with respect to its potential for being transiently unstable in the case of line fault and outage. The proposed neural network classifies system operating condition with respect to dynamic security based on the information extracted from steady state pre contingency operating condition. Using correlation factor between steady state pre contingency operating variables and CCT associated with system lines, the most dominant operating features with high correlation factor are selected for training neural network ANNSC. The proposed security classification approach is applied on IEEE 39-bus system with promising result. After training OSANN, the testing performance shows that it was able to recognize and classify %90 of cases correctly. Most of misclassification cases were due to recognizing a non critical line as critical. The proposed neural network is also able to be used as dynamic security contingency screening in which the critical lines and most sever lines could be recognized. TABLE VII CLASSIFICATION OBTAINED BY OSANN

Class No.

Output neurons belonging to class

Sever Lines

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

141, 142, 143, 127, 128 182, 168 183, 184, 169 187, 188, 189, 174 191, 192, 193, 194, 195, 180 176 178, 163, 164 158, 159, 145 149, 134, 136, 137 140, 126, 111, 112, 98 121, 105, 106, 108, 91, 92, 79 85, 71 96, 81, 82, 68 72, 58, 30 74, 75, 61, 47, 48, 34, 21, 6, 7 77

14, 11, 8 1, 3, 30 13, 14, 8 15, 26, 12 14, 24, 23 (13) 1, 2, 3 8, 13, 14 1, 7, 8 14, 24, 23 (13) 22, 23, 24 22, 23, 24 18, 12, 26 23, 14, 24 18, 24, 23 (11) 14, 15, 24 (13) 12, 24, 26

17 18 19 20

65, 66, 52 58, 42, 28 1, 2, 3, 15 1, 12

14, 24, 23 12, 24, 26 14, 24, 23 12, 14, 18

Critical Lines

12

14 (24) 24 24 (12) 12, 26 14, 24 14 (15) 12, 24, 14 (26) 24 (14) 12 (26) 14, 18, (12)

TABLE VIII TEST RESULTS (IN THE BEST SITUATION) No. of Sever Lines Critical Operating Lines Cases

1 2 6 7 8 10 11 12 14 15

11 12 5 2 6 11 1 3 8 11

11, 14, 8 1, 2, 30 1, 2, 3 8, 13, 14 1, 7, 8 22, 23, 24 12, 22, 23, 24 12, 26, 18 18, 24, 23 (11) 14, 15, 24 (13)

16

4

12, 24, 26

17

6

14, 23, 24

Misclassification

24 24 (12) 12, 26

1 case (14)

14 (15)

1 case (12) 5 cases (12, 14)

12, 24, 14 (26) 24 (14)

1 case (22)

VI. REFERENCES [1] [2] [3] [4]

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Ranking and Generation Reallocation Using Time Domain Simulation based severity indices", Power System Technology, 2000. Proceedings. PowerCon 2000. International Conference on Volume 3, Issue , 2000 Page(s):1275 - 1280 vol.3 [5] El-Sharkawi, M. A. "Neural Networks and Their Application to Power Engineering," Control and Dynamic Systems 41, Academic Press, 1991. [6] Q. Zhou, J. Davidson, A. A. Fouad , "Application of Artificial Neural Networks in Power System Security and Vulnerability Assessment", IEEE Transactions on Power Systems, Vol. 9, No. 1, February 1994

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[9] Berry, T., Daniels, A.R., and Dunn, R.W.: ‘Parallel processing of sparse power system equations’, IEE Proc., Gener., Transm. Distrib., 1994, 141, (l), pp. 68-74 [10] Berry, T., Chan, K.W., Daniels, A.R., and Dunn, R.W.: Interactive real time simulation of the dynamic behaviour of Vge

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power systems’. Proceedings of IEE Japan Power & Energy 93, 1993, pp. 5-10

[11] Kakimoto,

N., Ohnogi,.Y., Matsuda, H., and Shibwa, H.: ‘Transient stability analysis of large-scale power system by lypanov’s direct method’, IEEE Trans., 1984, PAS-103, [12] Akimoto, Y., Tanaka, H., Yoshizawa, J., Klap Per, D., and Price, K.A.W.: ‘Transient stability expert system’, case study’, IEEE Trans. Power Syst., 1989, 4, (l), pp. 312-320 [13] Wehenkel, L., Pavella, M., Euxibie, E., and Heilbronn. B.: ‘Decision tree based transient stabilitv method – a case study", IEEE Trans. Power Syst., 1994, 8, pp. 459-469 [14] EPRI: ‘On-line transient stability assessment’. EPRI seminar and demonstration, Toronto, Ontario, Canada, EPRI, 6-7 December 1993 [15] Pang, C.K., Prabhakara, F.S., El-Abiad, A.H., and Kovio, A.J.: ‘Security evaluation in power systems using pattern recognition’, IEEE Trans., 1974, PAS-93, pp. 969-976 [16] H., Hakimmashhadi, and Heydt, T.G.: ‘Fast transient security assessment’, IEEE Trans., 1983, PAS-102, (12), pp. 3816-3824 [17] Yakout Mansour, Ebrahim Vaahedi, Mohammed A. El-Sharkawi, , " Dynamic Security Contingency Screening and Ranking Using Neural Networks" , IEEE Transaction Neural Networks, VOL. 8, No. 4, July 1997 [18] Y. Mansour, E. Vaahedi, A. Chang, M. A. El-Sharkawi, and S. Weerasooriya, “Potential use of neural-network techniques for on-line dynamic security assessment of power systems,” CEA Rep. ST-347C-P, Sept.1994 [19] M.R. Aghamohammadi, A. Maghami, "On-Line Dynamic Security Assessment Using Sensitivity Analysis of Artificial Neural Network ", 20th PSC2005, Nov. 20, 2005, Tehran, Iran

Mohammad Reza Aghamohammadi was born in Iran on August 5, 1955. He received his BSC degree from sharif University of Technology 1989, MSc degree from Manchester University (UMIST) in 1985 and his PhD from.Tohoku University, Japan in 1994. He is head of Iran Dynamic Research Center and his research interest includes application of Neural Network for power system security assessment and operation

Fazel Mahdavizadeh was born in Iran on 1984. He received his B.Sc. degree in Electrical Power engineering from Power & Water University of Technology (PWUT) in 2007. He is currently MSc student of electrical railway engineering in Iran University of Science and Technology (IUST). His research interest is power system security assessment with neural network and Electric Railway Traction Power Supply. Reza Bagheri Ghahvachi was born in Iran on 1974. He received his B.Sc. degree in Electrical Power engineering in 1999, his MSc degree in Electrical Power engineering from Tehran Azad university in 2007. His research interest is power system security assessment and Electric machines.

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