Fast voltage contingency selection using fuzzy parallel ... - IEEE Xplore

IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 18, NO. 2, MAY 2003

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Fast Voltage Contingency Selection Using Fuzzy Parallel Self-Organizing Hierarchical Neural Network Manjaree Pandit, Laxmi Srivastava, and Jaydev Sharma

Abstract—A fuzzy neural network comprising of a screening module and ranking module is proposed for online voltage contingency screening and ranking. A four-stage multioutput parallel self-organizing hierarchical neural network (PSHNN) has been presented in this paper to serve as the ranking module to rank the screened critical contingencies online based on a static fuzzy performance index formulated by combining voltage violations and voltage stability margin. Compared to the deterministic crisp ranking, the proposed approach provides a more informative and flexible ranking and is very effective in handling contingencies lying on the boundary between two severity classes. Angular distance-based clustering has been employed to reduce the dimension of the fuzzy PSHNN. The potential of the fuzzy PSHNN to provide insight into the ranking process, without having to go through the complicated task of rule framing is demonstrated on IEEE 30-bus system and a practical 75-bus Indian system. Index Terms—Angular distance-based clustering, contingency ranking, fuzzy neural network, fuzzy overall performance index, linguistic categories, membership values, parallel self-organizing hierarchical neural network, ranking module, screening module.

I. INTRODUCTION

D

UE to the ever-increasing economical and environmental pressures power systems are increasingly being operated near their limits of operation. Fast and accurate security assessment, therefore, has become a key issue to ensure secure operation of power system. Steady-state security assessment enables the operating personnel to know which system disturbances or contingencies may cause limit violations and force the system to enter into the emergency state. Due to time limitation in real-time situations, it is not feasible to carry out detailed analysis of all the possible contingencies. Hence, contingency selection is performed to pick out those contingencies, which are potentially harmful to the system, so as to reduce the number of contingencies that need detailed analysis. Fuzzy-set theory has been proposed for voltage contingency ranking [1]–[3] as it offers an efficient framework to model uncertainties existing in power system. Artificial neural networks (ANNs) have also been applied for online static [4]–[7] and dynamic [8], [9] voltage contingency ranking and for contin-

Manuscript received September 19, 2002. This work was supported in part by the All India Council of Technical Education (AICTE), India, under R&D Project 8017/RDII/R&D/DEG (657)/98-99 and in part by the Director M.I.T.S., Gwalior. M. Pandit and L. Srivastava are with the Department of Electrical Engineering, MITS, Gwalior, India (e-mail: [email protected]; [email protected]). J. Sharma is with the Department of Electrical Engineering, Indian Institute of Technology, Roorkee, India (e-mail: [email protected]). Digital Object Identifier 10.1109/TPWRS.2003.810993

gency ranking in planning studies [10] due to their ability to provide accurate results instantaneously. Presently, integration of fuzzy logic with artificial neural network (ANN) is a major area of research as it combines the advantages of both these fields [11]–[16]. Rule based, single output, hybrid fuzzy-neural networks (FNN) have become fairly common for handling a variety of power system problems, but providing a flexible and informative ranking through a multioutput FNN without forming complicated fuzzy rules has not received enough attention. A simple multioutput two-stage approach is presented in this paper for voltage contingency ranking, in which heuristics and past experience can be incorporated in the modeling process, both at the input as well as at the output stage. The input vector consists of the membership values of loads to the overlapping linguistic classes such as low, medium, high, etc. while the output vector presents the operator with the probability of a contingency belonging to different severity classes. Therefore, the proposed method can accept and analyze data in linguistic as well as quantitative form. The fuzzy load modeling enables the handling of the stochastic nature of power system loads and a whole set of scenarios is analyzed at one time. The fuzzy PSHNN produces a flexible, realistic, and more informative ranking compared to conventional neural network approaches [4]–[9], which follow a binary logic and assign a pattern to the class producing highest activation. Hence, they often misclassify the boundary cases. As demonstrated in the result section of the paper, the motivation behind the proposed method is that it eliminates the possibility of misranking, particularly for cases where a contingency may belong to more than one class with a finite degree of membership. It also provides ranking within a severity class. In modern power systems, voltage alone cannot be used for assessing voltage security. Due to the increased use of compensating devices, which raise voltages to normal levels even when adequate reactive support is lacking, voltage becomes a poor indicator of security. Thus voltage stability has become an important limit in practical systems for ensuring system security and its enhancement. A new fuzzy overall performance index, formulated from voltage deviations and stability margin both, is proposed in this paper which is observed to be very effective in screening and ranking of voltage contingencies. It was observed that a contingency might be critical for a loading condition but noncritical for another loading condition. Therefore, the fuzzy neural network is designed for two-stage (screening module and ranking module) operation. The screening module [5], [17] classifies the selected contingencies as critical or noncritical for every loading condition using a modified BP algorithm producing faster learning and efficient classification. For

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collapse. The magnitude of the performance index should reflect the severity of a contingency. Hence, the margin based performance index for a contingency may be defined as (2) where is the normalized value of post contingent loadability margin for each load pattern. To estimate the proposed fuzzy , the normalized values of overall performance index and are modeled as fuzzy quantities having memberships in different severity classes. Then, the proposed index is comand puted based on the membership values of both and can be expressed as

Fig. 1. Contingency analysis by fuzzy PSHNN.

online ranking, the critical contingencies are fed to the ranking module. II. PROBLEM FORMULATION A fuzzy neural scheme consisting of a screening module and ranking module is employed for voltage contingency selection and ranking. Load uncertainty is dealt with by representing loads as fuzzy variables in different linguistic categories. A is proposed fuzzy overall voltage performance index to screen and rank critical contingencies online. This index is fuzzified in different severity classes to get a more informative ranking compared to conventional crisp approaches. The excellent nonlinear mapping characteristics of PSHNN [18] are utilized to map inputs (fuzzy memberships of loads representing an operating state) with the expected outputs which give the severity order). Fuzziness (memberships of incorporated at the input as well as at the output level provides flexibility and insight into the ranking process and a whole set of load scenarios are analyzed at one time. Fuzzy if-then rule extraction becomes redundant due to the application of an efficient PSHNN as a fuzzy inference engine. To reduce the burden on the ranking PSHNN, a screening module is installed to screen out the noncritical contingencies, online. Once the fuzzy PSHNN is properly trained, contingencies are ranked on . It is assumed the basis of the class membership values of that the contingency belongs to the severity class having highest value of membership but its probability of belonging to other severity classes is also available. The block diagram of the proposed contingency screening and ranking approach is given in Fig. 1. A. Overall Performance Index For voltage contingency, selection the severity of a contingency can be evaluated using the voltage performance index [5], [19] given by (1) where is the post contingent voltage Function is the upper/lower voltage limit at the bus, is the and is the order of the exponent. Masking weighing factor, and and . Post-contineffect is minimized by using gent maximum loadability margin has also been effectively used to assess the severity of a contingency [6], [20], [21] for voltage

(3) and are the memberships (highest value) of the where severity class to which the contingency belongs according to and , respectively, and and are the memberships (next highest value) of the adjoining severity class toward which the contingency is inclined. Membership values to other classes are found to be insignificant in ranking and are the weighing factors of respective severity classes for voltage and margin based indices, respectively. Critical contingencies and values calculated from are selected based on their full ac load flow and continuation power flow [22], [23], respectively, for a large number of operating conditions, to include the complete operating range of the power system. For selected conis computed, normalized and fuzzified into five tingencies severity classes. B. Angular Distance Based Feature Selection For voltage contingency screening and ranking, it is proposed to use reactive loads as inputs to the neural network. A feature selection technique is essential to reduce the number of inputs to the fuzzy PSHNN so that its dimension and training time is reduced. A number of load scenarios are generated using which the reactive loads are clustered on the basis of angular distance between between them [24]. The cosine value of the angle and is defined as two vectors (4) and are rewhere load patterns. If active loads at th bus corresponding to is greater than a specified threshold, the two vectors and are grouped into the same cluster; otherwise, a new cluster is formed. The process is repeated at all the load buses of the system until stable clusters of load buses are formed. Then, one reactive load from each cluster is selected as an attribute for training the fuzzy PSHNN. C. Fuzzy Modeling of Reactive Loads and Membership values in the range 0 to 1 are assigned to the in five severity classes. Load crisp normalized values of uncertainty is modeled by representing it as a fuzzy variable with memberships in different linguistic categories, such as,

PANDIT et al.: FAST VOLTAGE CONTINGENCY SELECTION USING FUZZY PARALLEL NEURAL NETWORK

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very very small (VVS), very small (VS), small (S), medium (M), large (L), and very large (VL). Nonlinear membership functions are found to be most suitable to fuzzify power system variables ) as they represent a more practical transition of (loads and loads from one category to the other compared to the common triangular or trapezoidal functions. The membership value is calculated as [14] (5)

where is the membership value in th linguistic category, is the crisp value to be fuzified, and are parameters cordetermines the responding to linguistic category such as center value of the corresponding category, where the membership value is equal to 1.0 and controls the width of the corresponding category [14]. These values can be determined by carrying out simulations offline under various operating conditions and topologies for the expected range of load variation. D. Screening Module The screening module is a three-layered feed-forward artificial neural network with a single output, trained by modified BP algorithm [5], [17] such that its target output is high (0.9) when (noncritical class, that is, class presented with a sample from (critV) and low (0.1) when presented with a sample from ical class, that is, class I to class IV). The outputs greater than 0.9 are clamped to 0.9 and similarly, outputs smaller than 0.1 are clamped to 0.1 to reduce the likelihood of the network getting stuck at local minima [5]. The training set for the screening than for class module contains larger number of samples for . Standard back-propagation gives very poor convergence for such a two-class problem, because the negative gradient vector computed by back-propagation is dominated by the class having larger samples, and hence, does not initially decrease the error for the other class having lesser samples. To solve this problem, a modified algorithm is used, which calculates a direction in weight-space such that descent vector must point in downhill directions for both the classes, that is satisfies and where

refers to the error due to class

Fig. 2. Block diagram of a four-stage ranking PSHNN.

III. MULTIOUTPUT PSHNN FOR CONTINGENCY RANKING The superiority of PSHNN [6], [18] has been exploited in this paper by developing a multioutput PSHNN and employing it as a fuzzy inference engine. The PSHNN designed is shown in Fig. 2. It has four stage neural networks (SNN) possessing is linear input and output units and nonlinear hidden units. , , , and are obtained the input vector and by applying different nonlinear transformations NLT1, NLT2, NLT3, and NLT4 on the input vector, respectively. These nonlinearities are employed in each SNN using the revised back propagation algorithm (RBP). Each stage of the PSHNN consists of a RBP network, except the first stage. The hidden layer of the SNN represents the nonlinear transformation of the input vector. The RBP algorithm is used to train each SNN in two steps. During step I, it is the same as the usual back propagation algorithm. In step II, the weights between the input layer and the hidden layer are fixed, only the weights between the hidden and output layers are retrained. After SNN1 has been trained, the error signal is considered as the desired output of the next stage neural network (SNN2) and the weights are updated accordingly. The training is continued for all four SNNs till convergence is obtained. The output of the th node of the th layer for th pattern may be written as

(8)

(6) number of input nodes of the th layer, output vector of the th node of the th Weights connecting the th layer and th layer, a differentiable nonlinear activation function. layer, and After first stage neural network (SNN1) is trained using RBP algorithm, the vector of error signal of SNN1 for the th pattern and th node is

where

and

refers to the error due to . Direction of is set so that it bisects the angle between and (7)

(9) In this way, the rate of learning is accelerated for a two-class problem [17]. The learning rate can be further improved by using adaptive learning rate with this approach [25]. Once the screening module is trained offline it is found to screen the critical contingencies online for any loading condition almost instantaneously.

(membership values of ) is the desired/target where is the actual output of value of the th output node and the th node of SNN1. To train the next stage neural network (SNN2), the error is taken as the desired output of the th node signal

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of SNN2 and is its input vector. The error signal for the second stage is given by (10) The same procedure is adopted to train SNN3 and SNN4. The final output of the pth node of PSHNN is (11) The RBP is applied identically to all the four stages. In the first step of RBP algorithm, the sum of squared errors is minimized and the connection weights are updated using equations (12) where for th node of the output layer Fig. 3.

Representation of reactive load in fuzzy categories.

(13) and for the th node of the hidden layer

TABLE I FUZZY MODELING OF REACTIVE LOADS

is found by (14)

In the second step, the weights between the output and hidden ) are retrained using (11)–(13). The procedure layer (i.e., is continued till the error becomes negligible. The same procedure is adopted for the succeeding stages. The final error signal for the th output is given by

TABLE II FUZZY REPRESENTATION OF VOLTAGE INDEX PI

(15) After all the four SNNs are trained, the retraining of SNN3 and SNN2 is performed, which constitutes one sweep and is referred to as forward-backward training [18]. IV. TEST RESULTS The fuzzy PSHNN was tested for voltage contingency screening and ranking of IEEE 30-bus system [26] and a 75-bus Indian system [27]. In the proposed fuzzy PSHNN NLT1 is equal to the identity operator. The nonlinearity NLT2 is chosen a sigmoidal function, NLT3 is hyperbolic tangent function and NLT4 is SIG II function. The combination of nonlinearities used has a direct influence in minimizing the output error [18] and may change from problem to problem. The nonlinearities were selected here after conducting a number of trials and were found to produce optimum performance in terms of accuracy and training speed. For both the test systems, the weighing factors were taken equal to 5, 4, 3, 2, and 1 for severity classes I, II, III, IV, and V, as well as . A 50 random variarespectively, for tion of load around the base values was found to cover almost the complete operating range for online application. The fuzzy PSHNN was found to screen and rank voltage contingencies quite accurately for both the test systems. Ranking results of fuzzy PSHNN for the two systems for single line outages, which are normally the most frequent, are presented here. A. Feature Selection To reduce the dimension and training time of the Fuzzy PSHNN available, inputs were reduced to an optimum value by

TABLE III FUZZY REPRESENTATION OF MARGIN-BASED INDEX PI

TABLE IV FUZZY REPRESENTATION OF PI

using angular distance based clustering. A vigilance parameter equal to 0.998 was found suitable for clustering reactive loads at the 60 load buses of 75-bus Indian system to get six stable clusters. Representative reactive loads at bus numbers 16, 34, 46, 49, 52, 58, were selected as inputs. The values of parameters and for fuzzifying theses loads in six linguistic categories were selected by observing the range of the generated reactive loads. Extensive studies based on the generated load data resulted in the membership functions shown in Fig. 3. The modeling parameters are listed in Table I.


TABLE V COMPARISON OF PI , PI AND PI

B. Training and Testing Set Generation For creating training and test patterns, 100 load scenarios were generated by varying the load randomly at all the buses in the range of 50–150% of their base values. Full ac load flow and continuation power flow [22] were run for all the load scenarios and for 69 single line outages of 75-bus to obtain system. Out of the 69 cases, contingencies resulting in zero or negliand were not selected in the contingible values of gency list for online analysis. In this way, 18 contingencies were was computed selected for online screening and ranking. for the selected 1800 patterns, using fuzzy modeling data listed was normalized and fuzzified in Tables II and III. Then, into five fuzzy categories using parameters from Table IV. Patensures accurate ranking under tern wise normalization of peak as well as off-peak times of the day, because the selected contingencies are ranked for the current load based on their relative severity. Out of the 1800 patterns generated, 1440 were used for training the screening module while remaining 360 unseen patterns were used to test its performance. Utility derived load compositions may be employed to train the fuzzy PSHNN instead of theoretically generated data. is normalized for each pattern using the relation

where , values of . of

and are the actual, maximum and minimum for a load pattern, and is the normalized value

C. Effectiveness of The ranking of contingencies on the basis of , and is compared in Table V for one load scenario. It was ob-

FOR

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75-BUS SYSTEM

TABLE VI RESULTS OF THE SCREENING MODULE

served that for most of the contingency patterns the ranking and is approximately the same but for some based on contingencies the effectiveness of the overall performance index can be clearly seen. Line outages between bus no. 40–48, 48–49, and 49–50 were in class V when ranked according to and, as a result, would be considered nonsevere from loadability margin point of view [16], whereas these were most se. Similarly, line outages 17–19 and 19–26 vere (class I) for was used for ranking [15] as would be filtered out if only

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TABLE VII RANKING OF CRITICAL CONTINGENCIES FOR 75-BUS INDIAN SYSTEM

Fig. 4.

Contingencies belonging to class I. Fig. 5. Contingencies belonging to class II.

these contingencies were in class V, but from margin point of view these belonged to class II, and therefore, were quite severe. and are far apart because their For these cases, severity level judged from margin point of view is different from voltage limit violation viewpoint. By using an overall index , the effect of both indices was included for voltage security assessment so that no critical contingency goes undetected. and, may be adWeighing factors associated with justed based on past experience and system behavior to give reliable assessment for a given system. D. Training and Testing Details The membership values of reactive loads at 6 selected buses along with a five digit topology number representing 18 selected contingencies were used as inputs to the fuzzy PSHNN making the number of neurons in the input layer equal to 41 for the 75-bus system. The three-layer screening having 20 neurons in the hidden layer, module classified 730 as critical and 710 patterns as noncritical. The trained screening module was tested for the remaining 360 patterns (20 load scenarios) and was found to screen all the 180 critical cases correctly. The result for one load scenario is given in Table VI. The 730 critical cases (80 load scenarios) passed on by screening module were used to train the four-layer fuzzy . The performance of the trained PSHNN PSHNN was tested on 180 unseen critical patterns. Test results of one load scenario are presented in Table VII. Test results for all the 180 patterns are presented in Figs. 4–7 and it can be seen that Fuzzy PSHNN is capable of producing membership values

Fig. 6. Contingencies belonging to class III.

Fig. 7. Contingencies belonging to class IV.

of the class to which a contingency belongs as well as membership to its neighboring class for the test patterns within tolerable error.


TABLE VIII EFFECT OF OPERATING LIMITS ON PI

E. Ranking Performance Standard BP neural network misranks patterns due to the error in estimation of membership values. The existing FNNbased methods for voltage contingency ranking [12] assign a contingency to any one of five severity classes based on the input vector. Boundary cases cannot be identified by this approach. On the other hand, the proposed method eliminates any possibility of misranking by giving increased information in the form of membership values to neighboring classes also, which are found to be very useful for contingencies lying on the class boundaries. When a contingency strongly belongs to a particular class, it shows almost negligible values to adjoining classes. It can also distinguish between contingencies belonging to the same class. For example, the last three line outages in Table VII belong to class II but their inclinations toward class I can be clearly seen and based on their memberships to class I they can be further ranked. A conventional crisp approach [4]–[9] or rule-based FNN approach [12] would assign equal severity level to all these three contingencies by ranking them in class II whereas the present approach also distinguishes between contingencies belonging to the same class. The Fuzzy PSHNN approach incorporates flexibility in ranking and eliminates the possibility of misranking. As the system size increases, the dimension of fuzzy PSHNN also increases and accurate mapping of output may not be guaranteed by a single fuzzy PSHNN for a very large system. To overcome this difficulty, the power system may be divided into smaller subsystems and a separate fuzzy PSHNN may be designed for each subsystem on the same lines as demonstrated in the paper. These fuzzy PSHNNs may be connected at the output [28]. It was observed that the training time of fuzzy PSHNN was very small compared to conventional neural networks of similar dimensions using deterministic inputs and outputs. F. Effect of Operating Limits For effective implementation of the proposed method to actual power systems, it is necessary to include the effect of generator Q-limits, tap changer limits etc. for calculating these indices. When all ac operating limits were imposed, it was observed that the value of overall performance index increased significantly compared to the unlimited condition. This is because when limits were imposed, loadability margin decreased and voltage violations increased resulting in increase and . The values of normalized on the same of scale, for six critical contingencies of IEEE 30-bus system [26] are presented in Table VIII for cases with and without limit, for one pattern.

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TABLE IX RANKING RESULTS WITH AC LIMITS IMPOSED

Ranking results of fuzzy PSHNN with ac limits imposed are given in Table IX for one testing sample, for the class to which in the form of fuzzy memberships of a contingency belongs and its neighboring class. The same fuzzy PSHNN was trained for cases when ac limits were off. In both the cases all critical contingencies were correctly ranked and the training performance was comparable for the samples tested. V. CONCLUSION A fuzzy PSHNN is developed for online voltage contingency screening and ranking. The proposed overall performance index developed using the combined effect of stability margin and bus voltage limit violation is found to be very efficient for ranking voltage contingencies compared to methods, which use conventional PIs. It has been demonstrated that fuzzy environment increases the amount of information available from the PSHNN output and also provides ranking within a severity class, making the approach very effective even for contingencies that are on class boundaries. The screening module screens the critical contingencies under changing loading conditions so that only severe contingencies are subjected to further analysis and ranking and thus the burden on the ranking module is reduced. Loads are modeled as fuzzy variables in contrast to the conventional deterministic approaches. By using a trained PSHNN as an inference engine the complicated task of fuzzy rule framing is made redundant. The computational time and complexity of conventional approaches increases when all ac limits are incorporated in the model, but in case of Fuzzy PSHNN there will be no such effect as once it is trained offline using data obtained from conventional methods, the results will be produced instantaneously, during the online application. REFERENCES [1] Y. Y. Hsu and H. C. Kuo, “Fuzzy-set based contingency ranking,” IEEE Trans. Power Syst., vol. 7, pp. 1189–1195, May 1992. [2] S. K. Tso, T. X. Zhu, and K. L. Lo, “Fuzzy-set approach to dynamic voltage security assessment,” Proc. Inst. Elect. Eng.—Gener. Transm. Distrb, vol. 142, pp. 190–194, Mar. 1995. [3] J. Nahman and I. Okljev, “Fuzzy logic and probability based real-time contingency ranking,” Electrical Power & Energy Systems, vol. 22, pp. 223–229, 2000. [4] S. Weerasooria, M. A. El-Sharkawi, M. Damborg, and R. J. Marks, “Toward static-security assessment of a large scale power system using neural networks,” Proc. Inst. Elect. Eng.—Gen., Transm. Dist., vol. 139, pp. 64–70, Jan. 1992. [5] L. Srivastava, S. N. Singh, and J. Sharma, “A hybrid neural network model for fast voltage contingency screening and ranking’,” Electrical Power & Energy Systems, vol. 22, pp. 35–42, Jan. 2000.

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Manjaree Pandit received the M.Tech. degree in electrical engineering from Maulana Azad College of Technology, Bhopal, India, in 1989, and the Ph.D. degree from Jiwaji University Gwalior, India, in 2001. Currently, she is a Reader with the Department of Electrical Engineering, Madhav Institute of Technology and Science (M.I.T.S.), Gwalior, India. Her areas of interest are power system security analysis, optimization, and ANN and Fuzzy neural applications to power system.

Laxmi Srivastava received the M.Tech., degree in electrical engineering from Indian Institute of Technology, Kanpur, India, in 1990, and the Ph.D. degree from the University of Roorkee, India, in 1998. Currently, she is Professor and Head of the Department of Electrical Engineering, Madhav Institute of Technology And Science (M.I.T.S.), Gwalior, India. She is currently involved in research in the areas of power system optimization and control, security analysis, and ANN and fuzzy neural applications to power system. She has published many research papers in national and international journals/conferences.

Jaydev Sharma received the M.E. and Ph.D. degrees in electrical engineering from University of Roorkee, India, in 1971 and 1974, respectively. Currently, he is Professor in the Department of Electrical Engineering at the Indian Institute of Technology, Roorkee, India. He is actively involved in research in the areas of power system planning and operation, security analysis and optimization, small hydroplant design and simulation, and ANN and fuzzy neural applications to power system. He has published many technical papers in journals/conferences.