stability monitoring using artificial neural network (ANN) and a systematic way for training the ANN. Separate ANNs are used for different contingencies and for ...
On-line Voltage Stability Monitoring Using Artificial Neural Network Saikat Chakrabarti and B. Jeyasurya Faculty o f Engineering and Applied Science Memorial University o f Newfoundland St. John’s, NL, Canada A IB3X5
Ah.~frucf--This paper proposes a scheme f o r on-line voltage stability monitoring using a r t i f i c i a l neural network (ANN) and a systematic way for training the ANN. Separate ANNs are used for different contingencies and for different load levels under the same contingency. Results o f contingency analysis a r e used along with Principal Component Analysis (PCA) to choose important input features to train the ANN. lmplementation of the feature selection scheme enhances the overall usefulness of the neural network. The proposed scheme i s applied on the New England 39-bus power system model. Index Terms-Feature selection, Networks, Voltage stability.
MW
margin.
Neural
I. INTRODUCTION
p .
RESENT day power systems are being operated closer to
. . . .
their stability limits due to economic and environniental constraints. Voltage stability has become an increasingly important factor in the operation and planning of electric power systems. Due to the ever-changing operating conditions and various unforeseen factors associated with large power systems, off-line stability studies can no longer ensure a secure operation of the power system [I, 21. On-line stability assessment is based on real-time direct measurements and gives better estimates o f power system states and existing topology. A number of tools for voltage stability analysis have been proposed such as P-V curves, V-Q curves, voltage stability indices based on singularity of power flow Jacobian matrix, continuation power flow etc [ 3 ] . Problems associated with online implementation of these tools are that they are computationally demanding and need exact mathematical modeling o f the system. Artificial neural networks have gained widespread attention from researchers in recent years as a toof for on-line voltage stability assessment. Due to the non-linear nature o f the voltage stability assessment problem, neural networks are better used over conventional analytical methods of voltage stability analysis [4]. ANNs have in-built noise rejection capability, which makes them robust in a distributed power network where data collection or transmission error is a possibility. Once trained, execution time of the ANNs subjected to any input is very less, which makes it an attractive alternative compared to conventional voltage stability analysis methods. The most important and useful property o f ANNs is the ability to interpolate unforeseen patterns. 0-7803-8386-9/04/$20.0002004 IEEE
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A scheme for implementation o f ANNs for real-time assessment of voltage stability o f a power system is presented in this paper. Active and reactive line flows are used as input features to the A N N and available active power margin is used as an indicator to the voltage stability o f the system. The systematic way o f selection of highly important features results in a compact and efficient A N N architecture. The online voltage stability monitoring scheme i s applied to the New England 39-bus power system and the simulation results are presented. The paper is organized as follows. The proposed method for on-line voltage stability monitoring i s described in section [I. The new method of selection of features is described in section 111. Case studies and analysis o f results are given in section IV and Section V concludes the paper.
11. ANN-BASEDMETHODFOR ON-LINEVOLTAGE STABILITY MONITORING in this research, loading margin is used as an indicator to the proximity to voltage collapse point. Loading margin is the available active power margin at any operating point and can be directly calculated from the P V curve. Active and reactive line flows are taken as the input data set. Data reduction techniques are applied to reduce dimension o f the input data set. A three layer feed-forward A N N trained with backpropagation algorithm is used to establish mapping between the input data set and the loading margin. The basic scheme of the on-line voltage stability monitoring is shown i n the Fig. 1, followed by detailed description of individual steps. A. identification of Load-area and Generation-areafor online voltage stability monitoring For on-line voltage stability monitoring, it is essential to identify the group o f load buses for which voltage stability i s to be monitored. For a relatively smaller system, all the generators can be included in the generation area that accounts for any change in load in the load area. For a larger system it is more reasonable to include in the generation area only those generators for which generations are highly affected by change in load in the corresponding load area. While generating the data for training the ANN, step increase in load i s distributed equally to all the load buses in the load area, while the generators share the additional generation needed to compensate for the load increase according to some specified generation schedule.
o f training data i s repeated for all feasible generation schedules, including single outage o f the generators. Collection o f all these data points constitutes the training data set.
B. Contingency Analysis Analysis o f ‘N- I’ contingencies, meaning, normal system minus one element, has been the standard procedure for contingency analysis in many utilities [ 5 ] . For the present study, all single line outages are analyzed and are ranked in the decreasing order o f severity in terms o f available M W margin to the point o f voltage instability. A selected number o f worst-case contingencies are considered in this study. Numerous attempts have been made in the literature to train and use a single A N N for all the contingencies, with little success. Separate ANNs are therefore used for different contingencies [6, 7, 81. Even for a specified contingency, a single A N N does not give satisfactory results for all the load levels [9]. Separate ANNs are therefore needed to map the relationship between power system parameters and the voltage stability index for each contingency and different load levels.
D. Selection of Input Variables I t has been observed by many researchers that voltage stability o f a power system i s heavily dependent on the line flows [II].In the research presented here, active and reactive power flows in all the lines are taken as the input variables. Magnitudes of the line flows are noted at each step o f load increase. Available M W margin for each load level i s considered as the desired output of the ANN. Sample values of active and reactive line flows are arranged in two separate matrices, which are further processed with data reduction techniques as described in later sections.
E. Determination of Load Levels to be Consideredfor the ANN Under normal circumstances, protective devices do not allow the load to increase beyond certain limits. Therefore, the load levels for which available M W margin is very less are not considered in the present study. Two different ANNs are used here for two different load ranges termed as light load and medium load. I t is not possible to estimate fixed ranges o f light load and medium load for a power system for different contingencies. A heavy load for one contingency may be termed as light load for other contingency. Light, medium or heavy load levels are therefore defined as an increase in loading by a fixed percentage o f available M W margin. For example, any load level within base case plus 40% of M W margin is taken as the light load, and any load level beyond light load level and within base case plus SO% of M W margin is taken as the medium load. Load levels for other contingencies are also defined in the same manner.
remiti+,tyd MWmqinwithrerped t o h e f l m r I
I
I
111.
Fig. 1. Feature seleclion and saining the Aniticial Neural Nelwork for online voltage stability monitorins
C. Generation of Training Data Training data sets for A N N are generated for the base case and the selected contingencies separately for different load levels. Starting from the initial loading level, load is increased in steps till the point o f voltage instability. In the absence of any specified pattern o f load increase, a step increase in load is equally distributed among all the load buses in the load area. A l l the generators in the generation area share the additional generation needed to meet the increased load demand according to specified generation schedule. Power flow solution at all steps of load is found by VSAT software [ I O ] that uses continuation power flow to find solution near and at the point o f voltage instability. M W margins at each operating point is noted and used as voltage stability indicator as described later. Above-mentioned procedure for generation 72
REDUCTION OF DIMENSION OF INPUT DATA AND TRAINING THE A N N
Objective o f input data reduction is to discard the data that are repetitive in nature and to choose only those data which contain maximum information regarding different patterns or variations o f the whole set o f input data. In this research, feature extraction or reduction of input data dimension is done in two steps. In the first step, input variables are chosen selectively using contingency analysis o f the power system. [n the second step, principal component analysis is used to reduce dimension of selected variables.
A. Selection of lnprrr Variables Using Contingency Analysis Contingency analysis is used to compute sensitivities o f the M W margin at any operating point with respect to line active and reactive power flows. The sensitivities are designated as
S’ and S. , which are linearized sensitivities o f the M W margin with respect to the active and reactive power flows in line .r‘. For different generation schedules, contingency analysis is carried out for all the line outages and corresponding Sy and
load i s distributed equally among the load buses in load area. All the generators in the system equally share this step increase in load. A large number o f sample data patterns are generated by varying generator outputs randomly around their base case generation. Cases involving single generator outages are also considered. Contingency analysis i s carried out for all the single line outages for each generation schedule with the help of VSAT software and the most critical contingencies are identified in terms of available M W margin to the point o f voltage instability.
S: are calculated. Active or reactive power flows in the lines for which S' and Sg are very high, are taken as input features for the ANN.
B. Principal Component Analysis (PC.4) PCA i s applied to each class o f input variables selected by the above-described process, to further reduce the dimension o f the data. Depending on the acceptable level of tolerance, first t projections are chosen, where tcm, the total number o f variables. Remaining (m-t) projections having small variances are discarded since they do not contribute much to the variation of the input vector over the sample space. Dimension of input data is thus reduced without sacrificing much o f the information contained in the data set. For the present study, PCA on the selected input variables are done using M A T L A B Neural Network Toolbox [IZ].
C. Training the ANN An M L P network consisting o f one input layer, one output layer and a hidden layer has been found suitable for the power system voltage stability monitoring problems. Denoting the neurons in input, hidden and output layers for a three-layer M L P network by i,j and k respectively, output of the neuron k in output layer can be written as, rnl
Yi =
M
I,"
I=,,
1-11
'p,~C~~,'pPi~C~,,P,~C~,,Y,~~~ ,=o
Fig. 2. New England 39-bus [est system
where mj is the number o f neurons in hidden layer, m i i s the number o f neurons in input layer and m l i s the dimension o f input to the input layer. 'pi, 'p, and 'p, are the activation functions for input, hidden and output layers respectively. During the learning phase, the A N N is trained with the reduced vector o f line active and reactive flows as input and the corresponding M W margins as target outputs. Error backpropagation algorithm i s used to train the M L P network [ 131.
For any specific contingency, two separate ANNs are used, one for light load and another for medium load. Results for the base case and for outage o f line between buses 29 and 38, i.e., the contingency with smallest M W margin are presented in this paper. Starting from base case, an increase in loading upto 40% o f M W margin i s considered light loading. A n increase o f loading by 40% to 80% o f M W margin in addition to base case loading is considered as medium loading. Active and reactive power flows are used as input parameters. Sensitivities o f the M W margin with respect to line flows are calculated using results o f contingency analysis and the line flows having higher sensitivities are chosen as input features. Those active and reactive power flows are chosen as input
D. Voltage Stabiliw Assessnient Using Ositpur of the ANN Objective of the proposed scheme i s to monitor power system voltage stability in real time. Output o f the A N N i s the available M W margin to the point o f voltage instability. A n operating point, which is having sufficient M W margin, i s taken as voltage stable. Amount o f MW margin for which the power system can be classified as voltage stable is based on past experience and engineering considerations.
features for which Slor Sp values exceed the chosen cut-off values. Table Ishows the reduction ofdata dimension for two different pairs o f cut-off values o f S: andS:.
IV. SIMULATION RESULTS
Subsequent
results given in this section are based on cut-off values o f
The proposed scheme For on-line voltage stability monitoring is applied to New England 39-bus test system [ 141 for which the single line diagram is shown in Fig. 2. The system consists o f 29 load buses, IO generator buses and 46 lines. Being a comparatively small system. load-area i s assumed to be consisting o f all the load buses and generationarea to be consisting of all the generators. Base case load is 5036.9 M W and base case generation is 5620 M W . For generating training data for the ANN, load level i s increased from the base case load by small steps and the step increase in
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S: and S: as I O and 40 respectively. Each class of input data selected in the previous step is assembled in a single matkix and subjected to PCA using M A T L A B Neural Network Toolbox. Table [Ishows the result o f applying PCA on input data for light and medium loading in base case and for most critical contingency, i.e., outage of line L29-38. Tolerance assumed for PCA is I%,which means that, data that contribute less than I % o f total variation, is discarded. The A N N for each case i s trained with the help of reduced data set by error back-propagation algorithm.
Number
Paramelen
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Number of variables
Nurnher of variables
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S . 2 40.0
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methods o f voltage stability monitoring needs exact matheinatical modeling of the power system and they are computationally demanding for a large system. The conventional methods are more suitable for off-line studies since they are helpful in getting a better insight into the system behavior. Under diverse operating conditions o f a distributed power network, i t i s virtually impossible to have exact matheinatical model o f the system for all topologies. Artificial neural network. on the other hand. learns by a set of input'output examples. Once trained with sufficient number o f diverse examples, it can interpolate any unforeseen operating state. Execution time ofthe ANN is also very less and with the possible hardware implementation o f the trained ANNs, i t can relieve much o f the burden o f an Energy Management System. Use o f ANN for on-line voltage stability monitoring i s therefore getting attention as a better alternative to conventional methods.
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TABLE I1 DIMENSION USING PCA FOR DIFFERENTANNS
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1 3000 Base case. medium loadinp Outave of line ~29-38.Iimt
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Fig. 3. Predicted and actual values of M W inilrgins loading Bare case. light loading Base case. medium laading
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Fig. 4. Predicted and aOual values of MW margins For base case with medium loading
Contingency analysis o f a power system is done as a part of the security assessment and the proposed scheme of voltage stability monitoring simplities the taqk o f overall security 74
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analysis by using the results o f the same contingency analysis. MW margins for base case and different selected line outages are available in the power system control center. I t i s not feasible to have MW margins for all possible line outages with all possible load distributions and generation schedules. The ANN can interpolate the unforeseen or unstudied cases by capturing the functional relationships between MW margin and different parameters of the power system. Active and reactive line flows and corresponding topologies in the form o f breaker status are telemetered to the control center as a part o f the state-estimation procedure. The amount o f active and reactive power consumption at the load end i s also available to the control center, which helps in classifying the load into heavy or medium load levels. The set o f ANNs trained for all the possible contingencies and load levels, have the potential to give accurate estimates o f voltage stability margins on a real-time basis. For a large power system having a large number o f interconnecting lines, training ANNs for all credible contingencies and load levels is a demanding task. The proposed method can improve efficiency and speed o f the ANN both during training and execution, by reducing the input data dimension. The sensitivity-based selection o f important line flows provides a systematic way of reducing number o f features. ANN architectures designed by this method have smaller size with sufficient accuracy and high execution speed. The test results indicate the effectiveness o f the proposed method for on-line voltage stability monitoring.
July 2000. 171 D. Popovic. D. Kukolj, F. Kulic. "Monitoring and Assessment of Voltage Stability Marsins Using Anificial Neural Nenvarks with a Reduced Input Set". IEEproc. Val.145. No. 4, July 1998, pp. 355-362. [8] D. Popovic. F. Kulic. -'On Line Monitoring and Preventing o f Vollage Stability Using Reduced systcm Model", Bulk Power System Dynamics and Conirol V- Securrry and Reliabiliry ,n o Changing Environmenr Onomrchi ~ a p o nA U ~ ~ ~ 2nn1, S I . pp. 387-400. [91 A. A. El-Keib. X. M a .'Application o f Artiticial Neiiral Networks in Voltage Stability Assessment". lEEE Tranmcrrons on Power Sysrems. Val. 10, No. 4, Novcmbcr 1995, pp. 1890-1896. [ I O ] Voltage Stability Assessment Tool, version 3.0. Powertech Labs Inc. Surrey, British Columbia. Canada. February 2003. [ I I ] L. Chen. K. Tomsavic. A. Bosc. R. Stuart, "Estimating Reactive Margin for DetermininS Tranrfcr Limils". IEEE Power Engineerrng Sooery Summer M e e l i g , Sratle. USA, July 2000. [I21 M A T L A B versim 6.5.0. Mathworks Inc.. June 18. 2002. [I31 S. Haykin. i\'earal IVenvorks: A Comprehensive Founderron. Pearsan Education. 2002. [I41 M. A. Pai. Energ, Ftmcrion Anoly~isJorPower Sysrern Siabiliry, Kluwcr Academic Publishers. 1989. BIOGRAPHIES
Ssikat Chnkrabarti obtained B. E. in Electrical Enginccring from Regional Engineering College. Durgapur, India and M . E. in Electrical Engineering from Jadavpur University. Kolkata. India in 1997 and 2000 respectively. He worked in Asea Brown Boveri Ltd. India. From 2000 to 2002 he worked in the Electronics Division o f the Bhahha Atomic Research Center, Mumhai. India. Currently he is a PhD candidate i n the Faculty o f Enginrcring and Applied Sciencc. Memorial University o f Newfoundland. St. John's. Newfoundland. Canada H i s research interests are in thc arra ofpuwcr system vollage stability and application of Neural Networks to powcr systems.
REFERENCES [I ]
[2]
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[3] [4]
[SI
B. Jcyarurya. .'Power System Loading Margin Estimalioii Using Artificial Neural Network". IEEE PES Summer Meering. Scatlr. USA.
B. Jeyasurya obtained E. Tech. and M Tech. in Electrical Engiscrrino from IIT Madras and Bombay, India respectively. He received thc Ph.D degrec
PSERC Puhlization 01-05, .' Autoniated Operating Procrdurcs for Transfer limits". Power Systems Engineering Research Center, Cornell Univsrsity. Final report. May 2001. PSERC Publication 03-06. '' Integrated Security Analysis", Pawer System Engineering Research Center, Cornrll Univzrsity, Final report, ay 2003. P. Kundur. P o w r S y ~ r e mSiabiliryond Conrrol. McCraw-Hill. 1993. T. S. Dillon. D. Neibur. rVeurol h'mvorks dpplicoiions in Power Sysfems,CRS Publishing Ltd, 1996. Canada-U.S. Power System Outage Task Forcr. "Interim Rcpon: Cause of the Ausurt 14'h Blackout in the United States and Can;ids". November 2003.
from the University o f New Hmnswi&, Fredericton, Canada. From 1986 10 1991 he was a faculty mcmbcr in the Department o f Electrical Enzinecring, Indian liistitutr of Teehnolugy, Bombay. Currently. hz is a Professor in the Faculty o f Engiiirrring and Applizd Science, Memorial University o f Newfoundland, St. John's. Newfoundland, Canada. He is a registered Professional Engineer i n the province at. Newfoundlmd and Labrador. His research interests includr coinputer relaying, powcr system stability analysir, and intelligent s y s t m applications to power systems.
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