CALIFORNIA STATE UNIVERSITY, NORTHRIDGE POWER SYSTEM VOLTAGE STABILITY ANALYSIS AND ASSESSMENT USING ARTIFICIAL NEURAL NETWORK A graduate project submitted in partial fulfillment of the requirements For the degree of Master of Science in Electrical Engineering By Rohan Shetty December 2014
The graduate project of Rohan Shetty is approved: Dr. Ali Amini Date Prof. Benjamin Mallard Date Prof. Bruno Osorno, Chair Date California State University, Northridge ii
ACKNOWLEDGEMENT I express my deepest gratitude and special thanks to Prof. Bruno Osorno for being extremely patient and supportive all the while I was working on such a complex and interesting topic like Neural Networks. I am very glad to present Power System Voltage Stability Analysis and Assessment using Artificial Neural Networks towards the partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering. Also, I would like to thank Dr. Ali Amini and Prof. Benjamin Mallard for supporting me in completing this project and acknowledging my efforts. Lastly, I am extremely happy and fortunate to find constant support and motivation from my family and friends during the entire course of my Master s degree. iii
TABLE OF CONTENTS Signature Page Acknowledgement List of Figures List of Tables Abstract ii iii v vi vii 1. INTRODUCTION 1 1.1 Introduction to Voltage Instability 1 1.2 Introduction to Artificial Neural Network 2 1.3 ANN Design and Architecture 4 1.4 Neural Network Algorithm 4 2. ANALYTICAL METHODOLOGY 6 2.1 Modal Analysis Method 6 2.2 Derivation of Voltage Stability Index 6 3. ANN BASED APPROACH 8 3.1 ANN Architecture 8 3.2 Learning Algorithm 8 3.3 Training and Testing 9 4. APPLICATION AND TEST PARAMETERS 10 4.1 IEEE 14-Bus System 10 5. CONCLUSION 14 BIBLIOGRAPHY 15 APPENDIX A 16 iv
LIST OF FIGURES Figure 1.1 A Biological Neuron 2 Figure 1.2 Basic layers of ANN 3 Figure 1.3 Basic three-layer architecture of feed forward ANN 4 Figure 3.1 Neural Network Architecture 8 Figure 3.2 IEEE 14-Bus System 9 Figure 4.1 Simulink Model 10 Figure 4.2 Neural Network Sub-system 11 Figure 4.3 Neural Network Transfer Function 11 Figure 4.4 L-Index Plots 12 Figure 4.5 Performance Comparison 12 Figure 4.6 Three-phase MVA at Bus 1 13 Figure 4.7 Three-phase MVA at Bus 14 14 Figure A.1 Neural Network Training Toolbox 17 Figure A.2 Regression plot 18 Figure A.3 Performance plot 18 v
LIST OF TABLES Table 1.1 List of ANN algorithms 5 vi
ABSTRACT POWER SYSTEM VOLTAGE STABILITY ANALYSIS AND ASSESSMENT USING ARTIFICIAL NEURAL NETWORK By Rohan Shetty Master of Science in Electrical Engineering Electrical power systems in any part of the world are expected to deliver continuous, uninterrupted and reliable power to the consumers irrespective of the geographical and weather conditions throughout the year. But they are affected by various factors causing problems such as power loss, voltage fluctuation, blackouts, etc. Many modern power systems are regularly facing problems due to voltage instability which is a threat for a reliable and secure operation. The protection of power systems is hugely dependent on the use of the wide range of distance relays based on electromechanical, solid-state and digital electronics technologies. In my study, an Artificial Neural Network (ANN) model is used along with Continuation Power Flow methods to assess the voltage stability of a power system. The Modal Analysis Method is first implemented to identify the most vulnerable load buses of the power system. Hundreds of loading patterns are generated by varying the real and reactive power. With the help of the input patterns and the target outputs, an appropriate ANN is trained and thereafter it is tested with a new set of loading patterns. The proposed method is applied to the IEEE 14 bus test system and the trained ANN provides results for all the vulnerable load buses of the power system. vii
1.1 Introduction to Voltage Instability 1. INTRODUCTION The phenomenon of voltage instability has been a persistent problem for the past few decades in modern power systems all over the world. It is considered as one of the major concern in the planning, reliable operation and security of electrical power systems. The ability of a power system to maintain operational voltages at all the buses under nominal operating conditions even when subjected to disturbances is termed as Voltage Stability. A system exhibits voltage instability and results in voltage collapse when there is a change in system operating condition, abrupt fluctuation in load demand and external disturbances. Voltage instability is widely seen in heavily loaded power systems that are invariably required to operate at the optimum reactive power limits of the transmission network. A good power system needs to provide adequate reactive support in case of system instability due to heavy reactive power flowing through the transmission lines. The current scenario of the restructured power systems requires the use of FACT devices and compensators to extract the maximum capacity of the network. This hampers the anticipation of voltage instability by observing the system voltage profile. The system operator fails to receive well-timed indications from the SCADA systems and the automatic protective systems trips the network before any action is taken. Therefore, it is necessary to have a fast method to evaluate static voltage stability comprehensively by examining and quantifying the production, transmission and consumption of the reactive power on a system wide basis and relate this to the voltage stability margins at the vulnerable load buses [3]. The voltage stability analysis and assessment is performed by various techniques but the most widely used method is the Modal Analysis Method. The key advantage of using this method is that we can identify the most vulnerable load buses of a given power system. But the drawback of this method is that the computation required is very expensive and it fails to account the effects of high reactive power sources in the system. As mentioned above, the problem of voltage instability occurs when the reactive power sources of the system fails to meet the reactive power demands. Thus, the QV and PV curves of a system are used for the voltage stability analysis. Using suitable parameters like the reactive power loading margins, nose point from the QV curves and the operating points for selected load buses of the system, the Voltage Collapse Proximity Indicator (VCPI) is obtained [6]. Since an extensive amount of computation is required for the above analytical methods, they are used in conjunction with Artificial Neural Network (ANN). Using ANN helps to overcome the computational difficulties and also gives extremely close matching results compared to the analytical methods. An ANN can be designed and trained with the input and output loading patterns of the selected system so as to obtain reactive power margins at the output for all the identified vulnerable load buses before the voltage collapses [2]. 1
1.2 Introduction to Artificial Neural Network The phenomenon of Artificial Neural Networks (ANN) is associated with various fields of science like mathematics, neurosciences, statistics, physics, computer science and engineering. Neural networks find applications in such diverse fields as modeling, time series analysis, pattern recognition, signal processing and control by virtue of an important property: the ability to learn from input data with or without a teacher [8]. The human brain is a good example of an intelligent and complex system with a dense network of neurons that work in tandem making decisions in nanoseconds. The biological structure of the brain, left-hand side and right-hand side, are capable of performing deductive reasoning of if-then rules and inductive reasoning of intuitions or pattern recognition respectively. Today s intelligent systems are modeled on this capability of the human brain to solve nonlinear complex problems in various engineering fields. ANN is one such intelligent system. Figure 1.1: A Biological Neuron [10] The development of ANN was motivated by looking at the functioning of the human brain. The human brain works as a complex system which learns every minute with electrochemical processes occurring continuously due to external stimuli. So, in a way, our brain gets trained by absorbing the various and recurrent experiences and reacts to a testing condition. The methodology of using ANN in power systems is developed in reference to the extensive and dense network of neurons present in the human brain. There are millions of neurons and trillion connections in the human brain. Due to the presence of neurons, the human brain performs functions at a very high speed and processes information and decision making effectively [8]. It is a set of elementary neurons that are usually connected in biologically inspired architectures and organized in several layers [7]. An ANN consists of a collection of arithmetic computing units connected together in a network of interconnected layers. The most basic model of ANN is shown in the Figure 1.2 below. 2
Figure 1.2: Basic layers of ANN [11] There are a number of connections at the input side each having a specific weight that specifies the influence between two neurons. The weights determine the behavior of the network similar to a computer program. In the hidden layer, all the inputs are first summed up and then passed through different types of logic functions to produce the output of the neuron. The multilayer perceptron (MLP) model is extensively used out of the wide range of ANN architectures available. The input layer, hidden layer and the output layer are stacked in a feed-forward pattern. The input layer acquires the input through its nodes and feeds into the hidden layer which has the non-linear transfer functions. The nature of the problem that is to be processed defines the number of neurons or nodes in the output and hidden layer. Usually the MLP network requires one output and hidden layer. As seen in figure 1.3 for the feed-forward ANN, the neurons in each of the input layer are interconnected and they are subjected with the excitation signals. Multiple weights and biases are attached to each neuron and the ANN is trained by adjusting these weights according to the specific training set. The learning curve of the ANN depends on the repetitive adjustments in the node weights for an input and hence we require training data set for its training. 3
Figure 1.3: Basic three-layer architecture of feed forward ANN [9] The input set to the ANN is x 1, x 2, x 3... x j and the transfer functions in the hidden layer computes the data and provides result to the output layer. The different types of ANN used are: 1. Supervised artificial neural networks, e.g.; the multilayer perceptron (MLP) and the finite impulse response artificial neural network (FIRANN) 2. Massively parallel interconnected artificial neural networks, e.g.; the Hopfield net (HN) 3. Unsupervised artificial neural networks, e.g.; the Kohonen net (KN) 1.3 ANN Design and Architecture The basic segments of the ANN architecture are the input layer, hidden layer and the output layer. The dotprod function available in the ANN toolbox is used to tune the weights and biases of the neurons, whereas, the adaptation which changes both the weights and biases is implemented using the adaptwb function. The toolbox functions required are: Neural network architecture and types Training functions Activation functions Learning functions Initialization functions Performance functions 1.4 Neural Network Algorithm In order to utilize neural networks, it is critical to train them for the specific application. The weights and biases can be finely tuned by using the training and learning functions 4
which are nothing but basic mathematical algorithms. These algorithms are not problem specific and they vary depending on various factors like the complexity of the problem, accuracy required, strength of the training data set and the number of weights and biases. Different algorithms are used for pattern recognition and function approximation. The following table lists the algorithms that are tested and the acronyms used to identify them: [16] Acronym Algorithm Description LM trainlm Levenberg-Marquardt BFG trainbfg BFGS Quasi-Newton RP trainrp Resilient Backpropagation SCG trainscg Scaled Conjugate Gradient CGB traincgb Conjugate Gradient with Powell/Beale Restarts CGF traincgf Fletcher-Powell Conjugate Gradient CGP traincgp Polak-Ribiére Conjugate Gradient OSS trainoss One Step Secant GDX traingdx Variable Learning Rate Backpropagation Table 1.1: List of ANN algorithms 5
2.1 Modal Analysis Method 2. ANALYTICAL METHODOLOGY The foremost step in voltage stability assessment is to identify the most vulnerable bus in the power system and this can be done by implementing the Modal Analysis method. A large number of loading patterns are generated by varying the real and reactive power loadings of the system and the program is run to identify all the vulnerable load buses. The bus with the recurring high value is termed as the most vulnerable load bus. The modal analysis method also provides the target input and output patterns which are required to train the neural network. 2.2 Derivation of Voltage Stability Index By using the improved distribution load flow technique [15], the voltage stability index can be mathematically formulated from the voltage equation. Consider a line connecting the bus i to i+1, P Li, Q Li P Li+1, Q Li+1 The voltage equation is given as:- V i+1 4 + V i+1 2 [2(P i+1 r i + Q i+1 x i ) V i 2 ]+P i+1 2 + Q i+1 2 r i 2 + x i 2 = 0 (1) Where, P i,q i = Real and reactive power injection at bus i V i = Voltage at bus i r i, x i = resistance and reactance of line connecting bus i and i+1 By simplifying the above quadratic equation we get, 8P i+1 Q i+1 r i x i 4V i 2 (P i+1 r i + Q i+1 x i ) + V i 4 4(P i+1 2 x i 2 + Q i+1 2 x i 2 ) 0 (2) Equation (2) is further simplified to, 4[V i 2 (P i+1 r i +Q i+1 x i )+(P i+1 x i Q i+1 r i ) 2 ] V i 4 1 (3) 6
Thus, the voltage stability index can be given as, From the power flow equations, L = 4[V i 2 (P i+1 r i +Q i+1 x i )+(P i+1 x i Q i+1 r i ) 2 ] V i 4 (4) V i V i+1 cos(θ i θ i+1 ) V i+1 2 = (P i+1 r i + Q i+1 x i ) (5) V i V i+1 sin(θ i θ i+1 ) = (P i+1 x i Q i+1 r i ) (6) By substituting equations (5) and (6) in equation (4) we get, L = 4[V iv i+1 cos(θ i θ i+1 ) V i+1 2 cos(θ i θ i+1 ) 2 ] V i 2 (7) Further, we make use of the Thevenin s equivalent circuit at the load bus to derive the voltage stability index. The Thevenin s equivalent circuit comprises of the open circuit voltage at the bus called as the Thevenin voltage, the equivalent impedance of the connected load and the Thevenin impedance across the load bus [15]. Now by applying equation (7) to the Thevenin s equivalent circuit we get, L = 4[V ov L cos(θ o θ L ) V L 2 cos(θ o θ L ) 2 ] V o 2 (8) The voltage stability index needs to be less than unity so as to maintain voltage stability. If this value goes above 1.0, then the bus voltage becomes imaginary as per equation (3) indicating a voltage collapse in the power system. The simplified voltage stability index is thus given as, Where, L = Voltage Stability Index, V o = No load voltage, V L = Load voltage. L = 4(V ov L V L 2 ) V o 2 (9) For any power system network to remain sustained in a stable voltage condition, the index value L should always be less than 1.0 for any load bus. If this value reaches 1.0 for any load bus, then the network approaches a state of voltage collapse. [15] 7
3. ANN BASED APPROACH The next step for the voltage stability assessment is implementing the Artificial Neural Network (ANN). A suitable type of network along with multiple learning and training algorithm is used for the application. The ANN is developed according to the following three vital steps:- 1. ANN Architecture 2. Learning Algorithm 3. Training and testing 3.1 ANN Architecture The selection of the ANN architecture depends on the type of neural network that is to be used. We use a multilayer feed-forward type of neural network which consists of one input layer, one hidden layer and one output layer. Each layer requires the sigmoid activation function. Within each layer, there are multiple training functions for each of the neuron which process as per the set biases and weights. For a specific system, a suitable ANN architecture can be obtained by trying various combinations of training functions in the three layers and the number of neurons in each of the layers. The architecture of the developed ANN is shown below in figure 3.1. 3.2 Learning Algorithm Figure 3.1: Neural Network Architecture [15] The ANN is developed using the MATLAB Neural Network toolbox. This toolbox has a wide range of training and learning algorithms that can be used according to the required application. For the multilayer feed-forward network, we use the error back propagation algorithm to train and process the network with a set of input and target outputs. In this algorithm, if the weights in each neuron is adjusted (increased or decreased), then the 8
error between the target output and the actual output is reduced effectively. The neural network computes the error derivative and calculates the error changes as and when the weights are adjusted. 3.3 Training and Testing The neural network is successfully trained by subjecting it with a problem or a process repetitively resulting in very low errors after each iteration. Selecting crucial training parameters affects the learning ability and the accuracy of the network. A total of 300 input and output patterns are generated wherein, 250 patterns are used for training the network and the rest are used for the testing. The network is repeatedly subjected with these patterns until a very small Mean Squared Error (MSE) is achieved. The transfer functions that are used for the neurons in the network are TANSIG and PURELIN, the training function is TRAINLM and the error function is MSE. The test system uses an IEEE 14 bus system which comprises of 2 generators, 3 synchronous compensators and 20 lines. The single-line diagram for the modified 14-bus system is shown below in figure 3.2. Figure 3.2: IEEE 14-Bus System [15] 9
4.1 IEEE 14-Bus System 4. APPLICATION AND TEST PARAMETERS The IEEE 14 bus system was implemented using the MATLAB Simulink tool. Two swing type generators are connected to bus 1 and bus 2 through three-phase transformers. Three synchronous compensators are connected to bus 3, bus 6 and bus 8. They help in regulating the voltage and improving the power factor. Three-phase RLC load is connected to all the buses except the buses 1 and 8. Figure 4.1: Simulink Model As seen from the Simulink model, two Power System Stabilizers are connected at bus 6 and 14. The neural networks are embedded in the stabilizers as a sub-system. Each neural 10
network consists of three nodes in the hidden layer. The transfer functions TANSIG and PURELIN are applied in these nodes. Figure 4.2: Neural Network Subsystem Figure 4.3: Neural Network Transfer Function Two different neural network architectures were trained to determine the most closest to the actual voltage stability index. Back-propagation Neural Network (BPNN) and Genetic Algorithm Neural Network (GANN) were trained and plotted along with the actual values of voltage stability index for all the 14 buses as shown below in figure 4.4 and 4.5. 11
Figure 4.4: L-Index plots Figure 4.5: Performance Comparison 12
Figure 4.6: Three-phase MVA at Bus 1 Figure 4.7: Three-phase MVA at Bus 14 13
5. CONCLUSION The voltage stability analysis and assessment using ANN was documented. The neural network with the back propagation error architecture was developed using the MATLAB neural network toolbox and it was applied to the IEEE 14-bus test system. It was observed that the selected neural network was efficient enough in calculating the voltage stability L-index for the vulnerable load buses. Additionally, the L-index value from the ANN was very close to the actual L-index from the analytical method, thus giving low error values. The use of neural networks proves to be very beneficial in computing complex power system processes in comparison to the expensive and extensive analytical methods. The ANN can also be applied to real-time voltage monitoring and voltage stability margin prediction and also in various other aspects of power system protection. 14
BIBLIOGRAPHY 1. V. R. Dinavahi, S. C. Srivastava, ANN based voltage stability margin prediction, Power Engineering Society Summer Meeting, 2001, Vol. 2, pages 1275-1280, July 2001. 2. R. Balasubramanium, Rhythm Singh, Power system voltage stability analysis using ANN and continuation power flow methods, Intelligent System Application to Power system, 2011, pages 1-7, September 2011. 3. R. Balasubramanium, BhavikSuthar, Application of an ANN based voltage stability assessment tool to restructured power systems, Bulk power systems dynamics and control, 2007, pages 1-8, August 2007. 4. R. Balasubramanium, BhavikSuthar, A novel ANN based method for online voltage stability assessment, Intelligent System Application to Power system, 2011, pages 1-6, November 2007. 5. R. A. Schlueter, A voltage stability security assessment method, IEEE Trans. Power System, Vol. 13, pages 1423-1438, Nov 1998. 6. C. W. Taylor, Power system voltage stability, New York, Mc-Graw-Hill, 1994 7. Cichoki A, Unbehauen R., Neural networks for Optimizing and signal processing, John Wiley & sons, Inc., New York, 1993. 8. Haykin S. Neural networks: A comprehensive foundation, Macmillan Collage Publishing Company, Inc., New York, 1994. 9. Rajveer Singh, Fault detection of electric power transmission line by using neural network, IJETAE, Vol 2, Issue 12, Dec 2012. 10. Retrieved on April 11, 2014www.neuralpower.com/technology 11. Retrieved on April 11, 2014http://en.wikipedia.org/wiki/User:Mariam_Hovhannisyan 12. Hiroyuki Mori, Fuzzy Neural Network Application for Power Systems, Power engineering society winter meeting, 2000, IEEE, Vol 2, pages 1284-1288. 13. Jen Hao-Teng, Power Flow and Loss Allocation for deregulated transmission systems, Electrical Power and Energy Systems, vol 27, no.4, pages 327-333, Jan. 2005. 14. Hadi Saadat, Power System Analysis, McGraw Hill, 1996. 15. O.P.Rahi, Amit Yadav, Hasmat Malik, Abdul Azeem, Bhupesh K, Power System Voltage Stability Assessment through Artificial Neural Network, International Conference on Communication Technology and System Design, 2011. 16. MATLAB Neural Network toolbox, User s guide, Math Work, Inc. 17. Retrieved on November 12,2014 www.neuralnetworksanddeeplearning.com 15
APPENDIX A The Neural Network Toolbox that is present in all versions of MATLAB has an extensive collection of functions, systems, functional blocks and applications that can be used to train, assess, model and evaluate complex nonlinear systems in areas of power systems, control systems, computer science, mathematics and statistics and physics. This tool works in conjunction with the analytical approach and provides very fast and accurate results. Using this tool we can develop, train, process and simulate a neural network for any given system. The toolbox consists of various networks that can be selected according to the system under execution. These networks are part of the Neural Network Architecture and form the basis of the simulation. The different networks are: feed-forward, radial basis, dynamic and learning vector quantization. There are multiple algorithms within these networks that comprises of training and learning functions which can be used to adjust the weights and biases of the network. The network can be trained with the input values and getting the desired output closest to the target values. A sample MATLAB code is implemented to illustrate the working of the Neural Network Toolbox. MATLAB Code:- a = rand(1,1000); b = rand(1,1000); c = rand(1,1000); n = rand(1,1000); y = a*5+b.*c+7*c+n; I = [a;b;c]; T = y; R = [0 1;0 1;0 1]; S = [5 1]; net = newff([0 1;0 1;0 1],[4 1],{'tansig','purelin'}); nte = train(net,i,t); T1 = sim(net,i); plot(1:1000,t,1:1000,t1); scatter(t,t1); 16
The training function in the algorithm is TRAINLM and the transfer functions are TANSIG and PURELIN. When the nte = train(net,i,t) function is run, the Neural Network Training (nntraintool) dialog box appears which shows the algorithm that is used and also the training parameters. Figure A.1: Neural Network Training Toolbox As seen from the above figure, we can make changes in the weights and biases in the hidden layers of the network, control the training and get different plots regarding the performance, training state and regression of the network. The code is executed as soon as the function is called and the network starts getting trained until it is stopped by the user. Here, the network training was stopped after it reached 166 iterations and the plots for performance and regression were plotted as shown below. 17
Figure A.2: Regression plot Figure A.3: Performance plot 18