Adaptive Neuro Fuzzy Inference System (ANFIS) For Fault Classification in the Transmission Lines

Transcription

1 Adaptive Neuro Fuzzy Inference System (ANFIS) For Fault Classification in the Transmission Lines Tamer S. Kamel M. A. Moustafa Hassan Electrical Power and Machines Department, Faculty of Engineering, Cairo University. Corresponding Abstract- This paper introduces the application of Adaptive Neuro-Fuzzy Inference System (ANFIS) for fault classification in transmission lines. It will be addressed clearly in this paper. The ANFIS can be viewed either as a fuzzy system, a neural network or fuzzy neural network ( FNN). This paper is integrating the learning capabilities of neural network to the robustness of fuzzy logic systems in the sense that fuzzy logic concepts are embedded in the network structure. It also provides a natural framework for combining both numerical information in the form of input/output pairs and linguistic information in the form of IF THEN rules in a uniform fashion. The proposed algorithm is achieved by the intelligent scheme ANFIS. This intelligent scheme is used to classify the fault type and deduce if it is single phase to ground, phase to phase, double phase to ground, or three phases. The input data of the ANFIS are firstly derived from the fundamental values of the voltage and current measurements after making Fourier transform. Computer simulation results are shown in this paper and they indicate this approach can be used as an effective tool for classification of faults for different fault conditions in fault inception time, fault impedance, fault distance and fault type. Keywords - Fuzzy Neural Networks FNN, Adaptive Neuro Fuzzy Inference System ANFIS, fault detection, fault classification, Transmission line protection. I. INTRODUCTION The protection of transmission lines is very significant because large amounts of power are commonly shipped across a transmission system. Although the fundamentals of transmission lines protection were considered many years ago [1-2], theoretical principles as well as practical applications are still common topics of investigation. With digital technology and advanced control strategies being ever increasingly adopted in power substations, more particularly in the protection field, protective relays have experienced some improvements, mainly related to efficient filtering methods (such as Fourier, Kalman, etc.). As a consequence, shorter decision time has been the main objective, and was achieved in many researches. The trip and no trip decision will be improved, compared to electromechanical/solid state relays. Furthermore, the conventional protection is usually designed on the basis of fixed relay settings. The reach accuracy of a protective relay can therefore be affected by the different fault conditions as well as network configuration changes. In order to face such a problem in conventional settings, a safety margin is necessary so as to avoid overreaching. However, the safety margin will not be adequate solution for this problem. Besides that these schemes are deterministic computations assuming system modeling based on conventional mathematical tools (such as differential equations). Such system representation is not well suited for dealing with ill-defined and uncertain systems. On the other hand, intelligent computational techniques such as Fuzzy Inference System (FIS), ANFIS and Artificial Neural Network (ANN) can model qualitative aspects of human knowledge. Besides they restore the processes without employing quantitative analysis. Thus these techniques are fetching great attention in the research environment with the absence of a simple and well-defined mathematical model. These models are characterized by nonrandom uncertainties associated with vagueness and imprecision in real-time systems [3-4]. Recently some advanced works using neural network and fuzzy-logic based techniques for transmission line fault classification and location have been reported. Such techniques involve removal of DC offset and non-harmonic components as well as determination of sequence components of line currents [5-11]. This research work employs Adaptive Neuro Fuzzy Inference System (ANFIS). This adaptive-network-based fuzzy inference system is used mainly here for fault classification in the transmission lines. This technique overcomes the difficulties associated with conventional voltage and current based measurements for transmission line protection algorithms. These difficulties are due to effect of factors such as fault inception time, fault impedance and fault distance. This research work is integrating the learning capabilities of neural network to the robustness of fuzzy logic systems. Neural network has the shortcoming of implicit knowledge representation, whereas, fuzzy logic systems are subjective and heuristic. The determination of fuzzy rules, input and output scaling factors and choice of membership functions depend on trial and error that makes the design of fuzzy logic system a time consuming task. These drawbacks of neural network and fuzzy logic systems are overcome by the integration between the neural network technology and the fuzzy logic systems. It also provides a natural framework for combining both numerical information in the form of Reference Number: W

2 input/output pairs and linguistic information in the form of IF THEN rules in a uniform fashion. II. BACKGROUND OF ANFIS The basic structure of the type of fuzzy inference system could be seen as a model that maps input characteristics to input membership functions. Then it maps input membership function to rules and rules to a set of output characteristics. Finally it maps output characteristics to output membership functions, and the output membership function to a singlevalued output or a decision associated with the output. It has been considered only fixed membership functions that were chosen arbitrarily. Fuzzy inference is only applied to only modeling systems whose rule structure is essentially predetermined by the user's interpretation of the characteristics of the variables in the model. However, in some modeling situations, it cannot be distinguish what the membership functions should look like simply from looking at data. Rather than choosing the parameters associated with a given membership function arbitrarily, these parameters could be chosen so as to tailor the membership functions to the input/output data in order to account for these types of variations in the data values. In such case the necessity of the adaptive Neuro fuzzy inference system becomes obvious. The Neuro-adaptive learning method works similarly to that of neural networks. Neuro-adaptive learning techniques provide a method for the fuzzy modeling procedure to learn information about a data set. It computes the membership function parameters that best allow the associated fuzzy inference system to track the given input/output data. A network-type structure similar to that of a neural network can be used to interpret the input/output map so it maps inputs through input membership functions and associated parameters, and then through output membership functions and associated parameters to outputs,. The parameters associated with the membership functions changes through the learning process. The computation of these parameters (or their adjustment) is facilitated by a gradient vector. This gradient vector provides a measure of how well the fuzzy inference system is modeling the input/output data for a given set of parameters. When the gradient vector is obtained, any of several optimization routines can be applied in order to adjust the parameters to reduce some error measure (performance index). This error measure is usually defined by the sum of the squared difference between actual and desired outputs. ANFIS uses a combination of least squares estimation and back propagation for membership function parameter estimation. The suggested ANFIS has several properties: The output is zero th order Sugeno-type system. It has a single output, obtained using weighted average defuzzification. All output membership functions are constant. It has no rule sharing. Different rules do not share the same output membership function, namely the number of output membership functions must be equal to the number of rules. It has unity weight for each rule. Figure (1) shows the architecture of the ANFIS, comprising by input, fuzzification, inference and defuzzification layers. The network can be visualized as consisting of inputs, with N neurons in the input layer and F input membership functions for each input, with F*N neurons in the fuzzification layer. There are F^N rules with F^N neurons in the inference and defuzzification layers and one neuron in the output layer. For simplicity, it is assumed that the fuzzy inference system under consideration has two inputs x and y and one output z as shown in Figure (1). For a zero-order Sugeno fuzzy model, a common rule set with two fuzzy if-then rules is the following: Rule 1: If x is A1 and y is B1, Then f1 = r 1 (1) Rule 2: If x is A2 and y is B2, Then f2 = r 2 (2) Here the output of the i th node in layer n is denoted as O n,i : Layer 1 Every node i in this layer is an adaptive node with a node function: O 1,i =μa i (x) for i=1,2,3 or (3) O 1,i =μb i-3 (y) for i=4,5,6 (4) Where x (or y) is the input to node i and A i (or B i ) is a linguistic label associated with this node. In other words, O 1,i is the membership grade of a fuzzy set A 1, A 2 and A 3 (or B 1, B 2 and B 3 ) and it specifies the degree to which the given input x (or y) satisfies the quantifier A (or B). Here the membership function for A (or B) is triangular membership function and is given as: Left : L u C Centers : 1 L c u Max 0,1 L 0.5 w u c u Max 0,1 0.5 w u c Max 0,1 0.5 w L if u c otherwise otherwise if u c Notice that for Equation (5) c L specifies the saturation point and w L specifies the slope of the nonunity and nonzero part of μ L as shown in Figure (2) Similarly, for μ R. For μ C notice that c is the center of the triangle and w is the base-width. c L, c R, c, w L, w R, and w are the parameters set. As the values of these parameters change, the triangular function varies accordingly, thus exhibiting various forms of membership functions for fuzzy set A. Parameters in this layer are referred to as premise parameters. (5) (6) Reference Number: W

3 Input inputmf rules outputmf Output Figure (1) : The architecture of the ANFIS 1 otherwise R Right : u (7) R u c R Max 0,1 if u c L 0.5 w μ(u) Figure (2) : Input triangular membership functions Layer 2 Every node in this layer is a fixed node whose output is the product of all the incoming signals: O 2,i = w i = μa i (x) μb i (y) i=1,2,3 (8) Each node output represents the firing strength of a rule. Layer 3 Every node i in this layer is an adaptive node with a node function: O 3,i = w i f i = w i r i i=1,2,3 (9) Where r i is the parameter set of this node. Parameters in this layer are referred to as consequent parameters. Layer 4 The single node in this layer is a fixed node which computes the overall output as the summation of all incoming signals: wi.fi i Overall output = O 4i i=1, 2, 3 (10) wi i From the ANFIS architecture shown in Figure ( 1), it is observed that when the values of the premise parameters are fixed, the overall output can be expressed as a linear combination of the consequent parameters. In symbols, the final output in Layer 4 can be rewritten as: wi. fi O i 4i wi (11) i w1 w2 w3 f1 f2 f3 w1 w2 w3 w1 w2 w3 w1 w2 w3 As w1, w2 and w3 are assumed to be constant. Therefore, equation (2) can be rewritten as follows: O 4,i =c 1.r 1 +c 2.r 2 +c 3.r 3 (12) Where w1 c 1 w1 w2 w3 (13) w2 c 2 w1 w2 w3 (14) w3 c 3 w1 w2 w3 (15) This is linear in the consequent parameters r1, r2, and r3. From this observation, It can be concluded that: S = set of total parameters, S1 = set of premise (nonlinear) parameters, S2 = set of consequent (linear) parameters Therefore the overall output will be: O 4,i = F(i, S) (16) Where i is the vector of input variables, F is the overall function implemented by the adaptive network, and S is the set of all parameters which can be divided into two sets S = S1 S2 (17) Where represents direct sum. Therefore, the hybrid learning algorithm can be applied directly. More specifically, the error signals propagate backward and the premise parameters are updated by Gradient Descent (GD) and node outputs go forward until layer 3 and the consequent parameters are identified by the Least Squares (LS) method. This hybrid learning is organized as follows: a) Linear and nonlinear parameters are distinguished b) Each iteration (epoch) of GD update the nonlinear parameters c) LS follows to identify the linear parameters. III. SIMULATION ENVIROMENT The simulation environment based on MATLAB software package [12] is selected. It is used as the main engineering tool for performing modeling and simulation of power systems and relays, as well as for interfacing the user and appropriate simulation programs. ATP [13] is used for Reference Number: W

4 detailed modeling of power network and simulation of interesting events. It possesses excellent power networks modeling capabilities, exceptional libraries of elements and provides fast and accurate simulation results. Scenario setting and neural network relaying algorithm will be implemented in MATLAB and interfaced with the power network model implemented in ATP. MATLAB has been chosen due to availability of the powerful set of programming tools, signal processing, numerical functions, and convenient user-friendly interface. In this specially developed simulation environment, the evaluation procedures can be easily performed. So the power system model was simulated and the different fault situations were performed by using ATP. Then the voltage and current measurements have been sent to MATLAB to demonstrate the ANFIS protective relay. IV. THE PROTECTION SCHEME A single line diagram for the protected transmission line (T.L) is illustrated in Figure (3). It consists of two circuits of 80 km length, 66 kv voltage level and 2 GVA short circuit level. Figure (3): Single line diagram for the Transmission line The overall protection scheme can be demonstrated as in Figure (4). Where: Vabc (V F abc) and Iabc (I F abc) are the instantaneous values of the three phase's voltage and current respectively (at fault condition). V * abc (V F* abc) and I * abc (I F* abc) are the fundemantal compontents (peak values and the phases) of the three phases voltage and current respectively after Fourier transformation (at fault condition). Z * abc (Z F* abc) are the fundemantal compontents (magnetuides and the phases) of the three phases impedances (at fault condition). Io F is the zero sequence current at fault condition. CU is the control unit that receives the outcomes of the two units and only activates the fault classifier block diagram when a fault is detected. Figure (4): The proposed protection scheme a) Fault Detection Unit: The fault detection unit is built by using various training data at fault and no fault conditions. After that, it is tested using different situations of the simulated power system. b) Training Data for Fault Detection Unit: The training data used to train the ANFIS of the fault detection unit are taken at the no fault conditions and fault conditions. The fault conditions are carried out as follows: i) All different fault types (i.e. single line to ground, double lines, double lines to ground and three lines fault ) ii) Fault distance (Df) 5%, 40% and 80% of the line iii) Inception fault time (Tf) 5 msec iv) Fault resistances (Rf) 0 and 100 ohms. There are 69 training data. The input data to the FNN detection unit are the impedances of the three phases (magnitude and phase i.e. 6 input) after dividing them by their non fault values. They are taken from the fundamental values of the voltage and current measurements after making Fourier transform every 10 msec. While the output data from FNN are: -1 output <0.5 for no fault conditions 0.5 output < 3 for fault conditions c) The ANFIS detector: The ANFIS detector consists of six neurons in the input layer i.e. N=6, three triangular membership functions for each input i.e. F=3 and constant membership function for the output. d) Testing Data for Fault Detection Unit: The testing data are chosen at different fault and no fault conditions. The fault conditions are done at different fault distances, different fault resistances, different fault inception times and different fault types which are not chosen for the training data. Some of these testing data are shown in Table 1. Table 1 can be explained as follows; the first four columns are: Fault inception time (Tf); Fault resistance (Rf); Fault distance (Df p.u); and Fault type respectively. Then the next six columns are impedances (magnitude and phase) of the three phases and these six values are used as input to the ANFIS detector. Finally the output of the ANFIS detector is shown in the last column to determine the situation if it is fault or not. The no fault conditions are performed at different states of variations in the voltage and the frequency of the two generators within the allowable limits to emulate the deviations in the feeding and the loading conditions in the power systems. Some of these fault conditions (different states of variations) are presented in Table 2. The variations in the voltage and the frequency of the two generators are introduced in Table 2. Reference Number: W

5 e) Fault Classification Unit: The fault classification unit is built at different situations of all fault types (i.e. single line to ground, double lines, double lines to ground and three lines fault). Then the unit is tested using testing data different from those of the training stage. f) Training data for Fault Classification Unit: The training data used to train the FNN of the fault classification unit are taken at: a) Fault distance (Df) 5%, 10%, 20%, 30%, 40%, 50%, 60%, 70% and 80% of the line b) All type of faults (i.e. single phase to ground, phase to phase, double phase to ground or three-phase fault) c) Inception fault time (Tf) 2 msec d) Fault resistances (Rf) 0, 25, 50 and 100 ohms. There are 396 training data.the input data to the ANFIS Classification are the impedances of the three phases (magnitude and phase) and the zero sequence component of the currents (i.e. 7 input s) after dividing them by their non fault values. They are taken from the fundamental values of the voltage and current measurements after making Fourier transform every 20 msec. While the output data from FNN are: 0.5 output <1.5 for single phase to ground fault 1.5 output < 2.5 for phase to phase fault 2.5 output <3.5 for double phase to ground fault 3.5 output < 4.5 for three-phase fault g) The ANFIS Classifier: The ANFIS classifier consists of seven neurons in the input layer i.e. N=7, three triangular membership functions for each input i.e. F=3 and constant membership function for the output. h) Testing data for Fault Classification Unit: The testing data are chosen at different fault conditions which are carried out at different fault conditions. These different fault conditions are: Different fault distances, Different fault resistances, Different fault inception times and Different fault types which are not chosen for the training data. Some of these testing data are shown in Table 3. Table 3 can be explained as follows; the first four columns are fault inception time, fault resistance, fault distance and fault type respectively. Then the next seven columns are zero sequence current in per unit and impedances (magnitude and phase) of the three phases and these seven values are used as input to the ANFIS classifier. Finally the output of the ANFIS classifier is shown in the last column to determine the fault type as described previously. Table 1 Testing data of the Fault Detection Unit and their Outputs for the fault conditions Tf Rf Df p.u Fault type Za p.u Za ph Zb p.u Zb ph Zc p.u Zc ph Output B-G B-C B-C-G A-B-C A-B-C-G A-G A-B A-B-G A-B-C A-B-C-G C-G C-A C-A-G A-B-C A-B-C-G Table 2: Testing data of the Fault Detection Unit and their Outputs for the no fault conditions % V1 % V2 f1 Hz f2 Hz Za p.u Za ph Zb p.u Zb ph Zc p.u Zc ph Output Reference Number: W

6 V. CONCLUISON An efficient protective relaying scheme based on ANFIS is proposed in this paper. Besides that a white noise is introduced in the testing data to model the errors in the voltage and current measurements. The trained networks are capable of providing robust and precise detection and classification of fault for a variety of system conditions, different inception time, fault locations, fault types and fault resistances. VI. REFERENCE [1] Sunil S. Rao, "Switchgear and Protection", 10 th Edition, KHANNA Publishers, Delhi, [2] W. Mark Carpenter "IEEE Guide for Protective Relay Applications to Transmission Lines", IEEE Std C37.113, [3] Jacek M. Zurada, "Introduction to Artificial Neural Systems", 1 st Edition, PWS Publishing Company, Boston, [4] Kevin M. Passino and Stephen Yurkovich, "Fuzzy Control", 1 st Edition, Addison Wesley Longman, Inc., California, [5] Dalia Farouk Mohamed," A New Design of an Intelligent Digital Distance Protective Relay" PhD Dissertation Submitted to the Office of Graduate Studies of Cairo University, [6] SlavkoVasilic," Fuzzy Neural Network Pattern Recognition Algorithms For Classification Of The events In Power System Network", PhD Dissertation Submitted to the Office of Graduate Studies of Texas A&M University [7] Abeer Galal Saad,"Digital Relaying of High Voltage Transmission Lines by Artificial Neural Networks", Master Dissertation Submitted to the Office of Graduate Studies of Cairo University [8] P. K. Dash, A. K. Pradhan, and G. Panda: "A Novel Fuzzy Neural Network Based Distance Relaying Scheme", IEEE Transactions on Power Delivery, Vol. 15, No. 3, pp , 2000 [9] D. V. Coury and D. C. Jorge, "Artificial Neural Network Approach to Distance Protection" IEEE Transactions on Power Delivery, Vol. 13, No. 1, pp , [10] Huisheng Wang and W. W. Keerthipala, "Fuzzy-Neuro Approach to Fault Classification for Transmission Line Protection" IEEE Transactions on Power Delivery, Vol. 13, No. 4, pp , [11] M. Jayabharata Reddy and D.K. Mohanata, "Performance Evaluation of Adaptive Network Based Fuzzy Inference System Approach for Location of Faults on Transmission Lines Using Monte Carlo Simulation" This paper has been accepted for publication in a future issue of IEEE journal, but has not been fully edited, [12] MATLAB R2008a. [13] ATP Draw version 3.5 Table 3 Testing data of the Fault Classification Unit and their Outputs Tf Rf Df p.u Fault type Io p.u Za p.u Za ph Zb p.u Zb ph Zc p.u Zc ph Output A-G A-B A-B-G A-B-C A-B-C-G B-G B-C B-C-G A-B-C A-B-C-G C-G C-A C-A-G A-B-C A-B-C-G A-G B-C C-A-G A-B-C A-B-C-G Reference Number: W