Topological Observability: Artificial Neural Network Application Based Solution for a Practical Power System

Transcription

1 Topological Observability: Artificial Neural Network Application Based Solution for a Practical Power System Amit Jain, Member, IEEE, R. Balasubramanian, Senior Member, IEEE, and S. C. Tripathy, Abstract An artificial neural network application based method for solving the topological observability problem of power systems is presented in this paper. Back-propagation and quickprop algorithms have been used for training the artificial neural networks used for present solution technique and the method has been successfully implemented on the standard 5-bus power system and on a practical 87 bus power system and the results are presented. Index Terms Artificial neural network, power systems, state estimation, topological observability. O I. INTRODUCTION NE of the most important functions for real time monitoring and control of power systems is state estimation. It is a process for determining the node voltage magnitudes and angles from a set of measurements, which consists of real and reactive line flow powers, real and reactive node injection powers and node voltage magnitudes. Depending on the number and distribution of the available measurements, state estimation may or may not be able to provide the reliable estimates. In the positive case the network is said to be observable. An observability test should be executed prior to performing the state estimation. The initial works on the network observability problem were published in mid-seventies where this problem was dealt using either linear system theory or logical procedures. In early eighties, Krumpholz, Clements and Davis, presented one of the most important work for network observability analysis in a series of research papers, which is based on network topology [1]-[4]. In this a characterization of observable networks is given in terms of spanning tree of full rank. Another important contribution presenting an alternative graph theoretic method for the analysis of topological observability problem came from Quintana, Simoes-Costa and Mandel [5]. Their method directly searches for an observable spanning tree in the measurement graph to solve the network Amit Jain is with the International Institute of Information Technology, Hyderabad, 532 India ( amit@iiit.ac.in). R. Balasubramanian is with the Centre for Energy Studies, Indian Institute of Technology, New Delhi 1116 India ( rbmanian@ces.iitd.ernet.in). S. C. Tripathy is with the Institute of Technology and Management Gurgaon, Haryana India. observability problem, which is called topological observability in this case. For power network observability problem, the topological observability is mostly used in utilities now days. Therefore, it is crucial to have an efficient topological observability test to achieve a satisfactory performance of the state estimation and whole real time monitoring and control process of power systems. The artificial neural networks (ANN) have been studied in the last few decades to apply the neural concepts for innovative technical problem solving. One of the most important characteristics of ANN is the ability to utilize examples taken from data and to organize the information into a form that is useful. This form typically constitutes a model that represents the relationship between the input and output variables. The model usually adjusts the arc weights of a set of connections, which interconnects the layers of neurons, according to a specific learning rule. The ANN act on data instantly in a massive parallel manner and when implemented in hardware, there computational outputs occur virtually instantaneously. ANN are fault tolerant and also capable of pattern recognition and show a capacity to generalize. For a complex system with many sensors and possible fault types, real time response is a difficult challenge to both human operators and expert systems where as trained neural networks, being good pattern recognizers, can produce reasonable results even when the information comprising the patterns is noisy, sparse, or incomplete. In last few years, the ANN have found many applications in the power system like load flow studies, load forecasting (short term and long term), security assessment, alarm processing and diagnosis, control, state estimation and many others [6]-[8]. The multi-layered perceptron model in the ANN is receiving the most attention as a good candidate for application to the power systems. The layered perceptron is taught by example. The abundance of data typically available from the power industry, coupled with the ability of the multi layered perceptron to learn significantly nonlinear relationships, make it a good candidate in using ANN for solving the power systems engineering problems. An ANN based method for solving the topological observability problem of power systems is presented in this

2 paper. An ANN model, based on the multilayer perceptrons is trained using two different training algorithms separately, for finding the topological observability of the power systems. In the first case, the ANN model has been trained using the back-propagation algorithm for finding the topological observability of the power network [9]. In the second case, the same ANN model is also trained using the quickprop algorithm that uses the computation of the second order derivatives of the error function and helps in speeding up the learning [1]. These models have been applied on standard 5 bus power system and on a practical 87 bus power system, which is a part of Northern region power grid of India, and the results are presented and discussed. II. TOPOLOGICAL OBSERVABILITY The network observability problem in the power systems determines whether the currently available set of measurements for the state estimation provides sufficient information to allow the computation of the state estimation. A power network is said to be observable, in the static state estimation sense with respect to a given measurement set M, if the node voltage magnitude and angle throughout the power network can be determined by processing the measurements in M by a static state estimator. Otherwise, the power network is said to be unobservable with respect to M. The measurement model for state estimator is z = h(x) + n (1) where z: Measurement vector h(x): Non-linear vector function relating the measurement vector to the state vector n: Vector of measurement error The above measurement model is approximated by a linear plus constant term model z = [ Η] x + n (2) where HPθ H = H QV From the above approximate model: "An N-node power system is observable with respect to a given measurement set M if and only if the rank of the matrix H is equal to 2N-1". By applying the MW-θ / MVAR-V decoupling principal to the above equation, the observability problem is decoupled. A network is said to be P-θ observable if the rank of matrix H Pθ is equal to N-1. Also, network is said to be Q-V observable if the rank of the H QV matrix is equal to N. In the particular case when the voltage magnitude is measured only at the reference bus and the real and reactive measurements are taken in pairs, the two observability problems (P-θ and Q-V) are in fact equivalent. Then the (3) condition of topological observability is defined with a spanning tree where a spanning tree in a connected graph is a tree connecting all the vertices of graph [11]. The condition is that a power network with respect to a measurement set M is topologically observable if there exists a spanning tree of its graph, representing the network topology and the measurements in the P-θ network, which is an observable spanning tree and whose branches are associated with measurements of M [5]. A spanning tree of the network graph is an observable spanning tree if and only if it is possible to assign a measurement Z ε M, where M is set of measurements taken in a power system, to each one of the tree branches such that no two branches are associated with the same measurement. A network graph is defined as a graph whose vertices correspond to the power system buses and whose links correspond to the transmission lines, as represented in the single-line diagram of the power system. In the present study, topological observability problem is split in P-δ observability and Q-V observability by P-δ/Q-V decouple characteristic of power systems and the P-θ topological observability problem is considered. A similar approach can be used for the Q-V topological observability problem. III. ARTIFICIAL NEURAL NETWORK APPLICATION FOR TOPOLOGICAL OBSERVABILITY ANALYSIS In the present study for the topological observability problem, an ANN with three basic layers was selected which had input layer, output layer and hidden layer where hidden layer may has one or more layers of neurons itself. The ANN topology is depicted in the Fig. 1. Inputs Input layer Weights Hidden layer Fig. 1. Three layer artificial neural network. Output layer Output For determining the topological observability, inputs for the current problem are the measurements on the buses and lines and output is the observability or unobservability result. Each neuron in the input layer of the ANN is given a certain input quantity. An exhaustive measurement set for the system will comprise of an injection measurement at each bus and a flow measurement on the each line. A network corresponding to this measurement set will have as many neurons as the total number of buses and lines in the system. For selecting a

3 particular input pattern, 1's or 's are given as the inputs representing the availability or unavailability of the corresponding injection or flow measurement. The output of the ANN model is observable or unobservable status. Hence, there is only one neuron in the output layer of the ANN for the present problem. If the system is observable then the value of the output should be 1 otherwise. Each neuron is associated with an activation function. Sigmoid activation function has been used in current implementation. For the current problem the input and output values are either or 1, therefore, scaling is not required. In first case, back-propagation technique is used for ANN training [9]. For final training of the ANN, sum of square error (SSE) is minimized. Training patterns were developed by the method described in [5]. In the second case of the present study, the quickprop algorithm is used for training the ANN. This is an algorithm to speed up the learning and it uses the information about the curvature of the error surface. This requires the computation of the second order derivatives of the error function. Quickprop assumes the error surface to be locally quadratic and computes the derivatives in the direction of each weight. After computing the first gradient with regular backpropagation, it evaluates another function that uses the partial derivatives of the error function and tries to take a direct step from the current position to the error minimum [1]. For the final training of the ANN, the SSE is minimized. The same training patterns as used when training with back propagation are also used for training the ANN in this case. IV. SYSTEM STUDIES AND RESULTS The ANN have been successfully trained for the standard 5 bus power system and for a practical 87 bus power system, which is a part of Northern region power grid of India, for topological observability analysis. ANN with the input, hidden and the output layers are used for training and these are implemented using Stuttgart Neural Network Simulator (SNNS) [1]. In case of 5 bus system hidden layer has one layer where as for practical 87 bus system hidden layer has two layers. A. 5 Bus System For the 5-bus system, there are 12 inputs representing 5 bus injection measurements and 7 line measurements and one output representing the observability or unobservability status. The single line diagram of 5-bus power system is shown in Fig. 2. The ANN with three layers, one input layer with 12 neurons, one hidden layer with 24 neurons and one output layer with 1 neuron, has been used for training of the 5 bus power system. Training patterns were developed by a method based on the graph theory and the matroid theory that is used for determining the topological observability [5]. For the final training of the network, the SSE is minimized. In case of training with the back-propagation algorithm, the initial training characteristic of the SSE is shown in Fig. 3. SSE reduced to about.1 in the initial 5 iterations and in 5 2 Fig bus power system. 2 iterations its value reduced to.2. After this, the convergence of training was very slow and the value of SSE reduced to.1 in 246 iterations where network was found to be giving quite accurate results when tested with the Sum of square error novel patterns not included in the training set. For training with the quickprop, the training characteristic of the SSE is shown in Figure 4. Convergence was extremely fast and the SSE reduced to less than.1 in 1 iterations where the network was found to be giving quite accurate results. After the training, the trained ANN were tested on the novel patterns corresponding to different measurement sets. These test patterns were not included in the training set. The typical results of the 5 novel patterns for the ANN trained with the back-propagation (BP) algorithm and the quickprop (QP) algorithm are presented as follows: (1) Injections: 1, 2, 3, 4, 5 Flows: 2-4, 3-4 Result with BP: 1 Result with QP: No. of iterations Fig. 3. Training of artificial neural network using back propagation algorithm for topological observability analysis of 5 bus power system. 4 1

4 (2) Injections: 1, 3, 4, 5 Flows: 3-4 Result with BP: 1 Result with QP: 1 representing the observability or unobservability status, for the practical 87 bus power system when we consider it for the ANN modeling. The single line diagram of the practical 87- bus power system, which is a part of Northern region power grid of India, is shown in Fig. 5 (3) Injections: 3, 5 Flows: 2-3, 2-4, 2-5, 3-4 Actual output: Result with BP:.19 Result with QP:.7 (4) Injections: 1, 2 Flows: 1-2, 2-3 Result with BP: Result with QP: 1 Sum of square error No. of iterations (5) Injections: 1, 4 Flows: 1-2, 2-4, 3-4 Actual output: Result with BP:.16 Result with QP:.1 B. Practical 87 Bus System There are 26 inputs, representing 87 bus injection measurements and 119 line measurements, and one output, Fig. 4. Training of artificial neural network using quickprop algorithm for topological observability analysis of 5 bus power system. The ANN with basic layers, one input layer with 26 neurons, hidden layer made of two layers with 26 neurons each and one output layer with 1 neuron, has been used for training separately by using back-propagation algorithm and quickprop algorithm for the 87 bus system for the topological observability problem. The training patterns were developed in a similar way as have been developed for the 5 bus system. Fig bus power system. While training the ANN by the back-propagation algorithm, an initial training characteristic of the SSE for practical 87 bus system is shown in Fig. 6. The SSE reduced to about in the initial 99 iterations and in 56 iterations its value reduced to Further convergence of the training was somewhat slow and the value of SSE reduced to.46 in 2427 iterations. After this, the convergence of the training was more slow and the value of the SSE reduced to.3 in 4326 iterations where network was found to be giving quite accurate results when tested with the novel patterns not included in the training set. In training of ANN with quickprop algorithm, network was

5 Sum of square error No. of iterations Fig. 6. Training of artificial neural network using back propagation algorithm for topological observability analysis of practical 87 bus power system. unable to train. SSE was moving in very large and medium range and it seems the network was always getting trapped to local minima. So the present ANN model for practical size power system was not so successful for the ANN training trough the quickprop algorithm. The trained ANN through back propagation algorithm was tested on the novel patterns corresponding to different measurement sets, which were not included in the training set. The results for the ANN trained with back-propagation algorithm (BP) for the practical 87 bus power system for 3 novel patterns are presented as follows (1) Injections: 3, 6, 7, 15, 16, 18, 26, 3, 32, 33, 34, 35, 36, 37, 45, 47, 48, 53, 54, 57, 58, 59, 6, 61, 62, 63, 66, 67, 68, 7, 71, 72, 73, 75, 76, 77, 78, 79, 8, 81, 82, 83, 84, 85, 86, 87 Flows: 1-11, 1-77, 3-74, 4-11, 4-15, 4-43, 4-46, 5-45, 5-47, 7-8, 8-9, 9-1, 1-11, 1-69, 11-12, 11-7, 12-13, 12-43, 13-45, 14-15, 14-48, 15-44, 17-58, 19-63, 2-21, 2-24, 21-23, 21-24, 21-5, 22-5, 22-52, 23-24, 24-25, 25-26, 27-28, 27-29, 28-42, 29-39, 29-41, 32-68, 36-67, 37-42, 39-4, 4-41, 41-42, 42-65, 42-66, 43-44, 43-62, 44-45, 46-61, 49-51, 49-64, 49-65, 5-65, 5-66, 51-52, 52-53, 52-57, 58-59, 64-66, 64-67, 65-66, 69-7 Result with BP: (2) Injections: 3, 6, 7, 15, 16, 18, 26, 3, 32, 33, 34, 35, 36, 37, 45, 47, 48, 53, 57, 58, 59, 6, 61, 62, 63, 66, 67, 68, 7, 71, 72, 73, 75, 76, 78, 79, 8, 81, 82, 83, 84, 85, 86 Flows: 1-11, 2-3, 3-56, 3-74, 4-11, 4-15, 4-43, 4-46, 5-45, 5-47, 7-8, 8-9, 9-1, 1-11, 1-69, 11-12, 11-7, 12-13, 12-43, 13-45, 14-15, 14-48, 15-44, 17-58, 19-63, 2-21, 2-24, 21-23, 21-24, 21-5, 22-5, 22-52, 23-24, 24-25, 25-26, 27-28, 27-29, 28-42, 29-39, 29-41, 32-68, 36-67, 37-42, 39-4, 4-41, 41-42, 42-65, 42-66, 43-44, 43-62, 44-45, 46-61, 49-51, 49-64, 49-65, 5-65, 5-66, 51-52, 52-53, 52-57, 58-59, 64-66, 64-67, 65-66, 69-7 Actual output: Result with BP:.575 (3) Injections: 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 12, 13, 14, 15, 16, 17, 18, 19, 2, 21, 22, 23, 24, 25, 26, 27, 28, 29, 3, 31, 32, 33, 34, 35, 36, 37, 38, 39, 4, 41, 42, 43, 44, 45, 46, 47, 48, 5, 53, 54, 55, 56, 57, 58, 59, 6, 61, 62, 63, 64, 65, 66, 67, 68, 69, 7, 71, 72, 73, 74, 75, 76, 77, 78, 79, 8, 81, 82, 83, 84, 85, 86, 87 Flows: 1-11, 1-6, 2-3, 2-73, 3-11, 3-56, 3-74, 4-46, 4-78, 5-45, 5-79, 6-15, 6-87, 7-11, 9-1, 1-11, 14-15, 14-48, 15-44, 17-58, 19-2, 2-21, 2-24, 21-23, 21-24, 21-5, 21-63, 22-5, 22-52, 23-24, 24-47, 25-26, 26-86, 27-28, 27-29, 27-69, 28-42, 29-39, 3-85, 31-4, 32-33, 32-81, 34-35, 34-82, 35-54, 35-75, 36-67, 37-38, 38-83, 39-4, 4-41, 42-65, 42-66, 43-44, 43-62, 44-45, 46-61, 46-71, 49-51, 49-64, 49-65, 51-52, 51-84, 52-53, 53-8, 57-58, 58-59, 6-67, 64-66, 64-67, Result with BP: The results from these trained ANN when used with novel patterns, also given above for some novel patterns, are in very good agreement with the actual results of the system, which we found using other prevalent methods for finding the topological observability. Both the back propagation and the quickprop trained artificial neural networks give correct results for 5 bus system and are very near in their result values though back propagation is quite slower than quickprop in this case. But for large size practical 87 bus system quickprop is not able to train the ANN where back propagation is successful in training the ANN and results with novel patterns are in good agreement with the actual results of the system. This clearly validates the success of the ANN application based solution for the power system topological observability analysis.

6 V. CONCLUSION This paper has presented an ANN application based solution technique for determining the topological observability of the practical power systems. The standard back-propagation algorithm and the quickprop algorithm have been applied for the training. It was observed that quickprop is very fast in successful network training for small systems but for large systems it may not be suitable. Back-propagation algorithm is slow in the training phase but gives good convergence for small size sample power systems as well as for larger practical power systems and reaches a very low value of SSE. The adequacy of training of the ANN are tested by feeding some novel input patterns not included in the training set and the output results obtained were validated by comparing the results from the other method. Therefore, it can be concluded from these findings that the ANN application based technique is a quite suitable methodology for determining the topological observability of the power system. ANN are inherently extremely fast and present study provides an extremely fast technique for topological observability analysis for practical size power system, very much suitable for Energy Management System (EMS) applications used in control centers. REFERENCES [1] G. R. Krumpholz, K. A. Clements and P. W. Davis, "Power system observability: a practical algorithm using network topology," IEEE Trans. on Power Apparatus and Systems, vol. PAS-99, pp , July/Aug [2] K. A. Clements, G. R. Krumpholz and P. W. Davis, "Power system state estimation with measurement deficiency: an algorithm using network topology," IEEE Trans. on Power Apparatus and Systems, vol. PAS-1, pp , April [3] K. A. Clements, G. R. Krumpholz and P. W. Davis, "Power system state estimation with measurement deficiency: an algorithm that determines the maximal observable subnetwork," IEEE Trans. on Power Apparatus and Systems, vol. PAS-11, pp , September [4] K. A. Clements, G. R. Krumpholz and P. W. Davis, "Power system state estimation with measurement deficiency: an observability/measurement placement algorithm," IEEE Transactions on Power Apparatus and Systems, vol. PAS-12, pp , July [5] V. H. Quintana, A. Simoes-Costa and A. Mandel, "Power system topological observability using a direct graph-theoretic approach", IEEE Trans Power Apparatus and Systems, Vol. PAS-11, pp , April [6] T. S. Dillon, "Artificial neural network applications to power systems and their relationship to symbolic methods", International Journal of Electrical Power and Energy System, Vol. 13, pp [7] H. Mori, "Artificial neural net based method for power system state estimation", in Proceedings of International Joint Conference on Neural Networks, Part 2 (of 3), Vol. 2, 1993, pp [8] D. Kukoji, F. Kulic, D. Popovic and Z. Gorecan, "Determining topological changes and critical load levels of a power system by means of artificial neural network", Electric Machines and Power systems, Vol. 25, pp , Oct [9] P. D. Wasserman, Neural computing theory and practice, New York, Van Nostrand Reinhold, [1] SNNS (Stuttgart Neural Network Simulator) Version 4.1, developed at Institute for Parallel and Distributed High Performance System (IPVR), University of Stuttgart, Postfach, Germany, [11] N. Deo, Graph theory with applications to engineering and computer science, Englewood Cliffs, N.J., U.S.A., Prentice-Hall, Inc., VI. BIOGRAPHIES Amit Jain (M, 25) graduated from KNIT, India in Electrical Engineering. He completed his masters and Ph.D. from Indian Institute of Technology, New Delhi, India. He was working in Alstom on the power SCADA systems. He was working in Korea in 22 as a Postdoctoral researcher in the Brain Korea 21 project team of Chungbuk National University. He was Post Doctoral Fellow of the Japan Society for the Promotion of Science (JSPS) at Tohoku University, Sendai, Japan. He also worked as a Post Doctoral Research Associate at Tohoku University, Sendai, Japan. Currently he is an Assistant Professor in IIIT, Hyderabad, India. His fields of research interest are power system real time monitoring and control, artificial intelligence applications, power system economics and electricity markets, renewable energy, reliability analysis, GIS applications, parallel processing and nanotechnology. R. Balasubramanian obtained his Ph.D. degree from IIT Kanpur. He is a professor at Indian Institute of Technology, New Delhi, India. He is a senior member of IEEE. He was chairman of IEEE Delhi section for year 21 and 22. His areas of research include Power System Planning, Operation & Control, Energy System Modeling & Management, and Power from Nonconventional Energy Sources including Energy Storage Devices. He has guided 1 doctoral scholars and published about 8 research papers in the national and international journals of repute. S. C. Tripathy obtained his Ph.D. degree in Electrical Engineering from University of Minnesota, Minneapolis, USA in 197. Then he joined the faculty of the Indian Institute of Technology, New Delhi, India. He was professor there till he retired in He is currently a professor at the Institute of Technology and Management Gurgaon, India. He had also been Head of the Center for Energy Studies at Indian Institute of Technology, New Delhi. He is Fellow of IEE (London) and IE (India). He has been visiting professor to many reputed universities in Europe and Canada. His fields of interest are Electric Power System Analysis and Control.