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The Online Journal on Electronics and Electrical Engineering (OJEEE) Vol. (1) – No. (2)
On-Line Trained Adaptive Neuro-Fuzzy
Inference System for Distance Relay
of Transmission line Protection
Tamer S. Kamel M. A. Moustafa Hassan
Electrical Power and Machines Department, Faculty of Engineering, Cairo University.
Corresponding E-Mail: mmustafa@eng.cu.edu.eg
Abstract-This paper presents a new distance relay commercial developments. However, both these approaches
technique for transmission line protection by using well are based on deterministic computations on a well defined
known control technique; Adaptive Neuro-Fuzzy model of the system to be protected. This results in difficulty
Inference System (ANFIS). The ANFIS can be viewed in taking system variation into account as the rules are fixed.
either as a fuzzy system, a neural network or fuzzy neural They do not have the ability to adapt dynamically to the
network FNN. The structure is seen as a neural network system operating conditions, and to make correct decisions if
for training and a fuzzy viewpoint is utilized to gain the signals are uncertain. Recently, intelligent soft
insight into the system and to simplify the model. The computational techniques such as Artificial Neural Network
integration with neural network technology enhances (ANN), Fuzzy Inference System (FIS) and (ANFIS) can
fuzzy logic systems on learning capabilities. The model superiority of human knowledge features. They also
integration with neural network technology enhances re-establish the process without plenty of analysis. Thus these
fuzzy logic systems on learning capabilities. It also techniques are attracting great attention in an environment
provides a natural framework for combining both that is obvious with the absence of a simple and well-defined
numerical information in the form of input/output pairs mathematical model. Besides, these models are characterized
and linguistic information in the form of IF–THEN rules by nonrandom uncertainties which associated with
in a uniform fashion. The proposed technique is imprecision and elusiveness in real-time systems [3-4]. Many
accomplished by one ANFIS that achieves accurate and researchers have studied the application of neural networks to
fast estimation of distance to fault from the relay point. overcome most of the problems above outlined. The fuzzy set
The normalized positive sequence impedance of the three theory is also used to solve uncertainty problems [5-11]. The
phases are considered as inputs to the network The input use of neural nets in applications is very sparse due to its
data of the ANFIS were firstly derived from the implicit knowledge representation, the prohibitive
fundamental values of the voltage and current computational effort and so on. The key benefit of fuzzy logic
measurements after making Fourier transform. Computer is that its knowledge representation is explicit, using simple
simulation results are shown in this paper and they IF-THEM relations. However, it is at the same time its major
indicate this approach can be used as an effective tool for limitation. The power system operation in transient period
location of faults for different fault conditions in fault cannot be easily described by artificial explicit knowledge,
inception time, fault impedance, fault distance and fault because it is affected by many unknown parameters. The
types integration of neural network into the fuzzy logic system
makes it possible to learn from the prior obtained data sets.
Keywords: Fuzzy Neural Networks FNN, Adaptive Neuro
This research employs adaptive-network-based fuzzy
Fuzzy Inference System ANFIS, fault location,
inference system for fault location in the transmission lines.
transmission line protection. This novel approach overcomes the difficulties associated
with conventional voltage and current based measurements
I. INRODUCTION for transmission line protection algorithms. These difficulties
are due to effect of factors such as fault inception time, fault
Protection of transmission lines is very important for impedance and fault distance. This research is integrating the
preserving of the power system. With the advent of learning capabilities of neural network to the robustness of
microprocessors and digital electronics, digital-based relaying fuzzy logic systems in the sense that fuzzy logic concepts are
has been developed since the late 1960s. Research activity has embedded in the network structure. It also provides a natural
covered virtually every protection technique. Furthermore, framework for combining both numerical information in the
many novel algorithms and associated hardware form of input/output pairs and linguistic information in the
implementations have emerged. The fundamentals of form of IF–THEN rules in a uniform fashion.
transmission lines protection were developed many years ago
[1-2]. Some of them such as representing transmission lines
by either first- or second order differential equations and
traveling-wave techniques have resulted in several
Reference Number: W09-0013 73
The Online Journal on Electronics and Electrical Engineering (OJEEE) Vol. (1) – No. (2)
II. ADAPTIVE NEURO FUZZY INFERENCE It has no rule sharing. Different rules do not share
SYSTEM (ANFIS) the same output membership function, namely the
number of output membership functions must be
A neural network which can perform pattern matching task
equal to the number of rules.
has a large number of highly interconnected processing
It has unity weight for each rule.
elements (nodes). These elements demonstrate the ability to
learn and generalize from training patterns. Distributed
Figure (1) shows the architecture of the ANFIS, comprising
representation and strong learning capabilities are the major
by input, fuzzification, inference and defuzzification layers.
features of neural network. On the other hand, decisions using
The network can be visualized as consisting of inputs, with N
fuzzy logic systems are based on inputs in the form of
neurons in the input layer and F input membership functions
linguistic variables. These linguistic variables are derived
for each input, with F*N neurons in the fuzzification layer.
from membership functions which are formulas used to
There are F^N rules with F^N neurons in the inference and
determine the fuzzy set to which a value belongs and the
defuzzification layers and one neuron in the output layer.
degree of membership in that set. The variables are then
matched with the specific linguistic IF-THEN rules and the
Input inputmf rules outputmf
response of each rule is obtained through fuzzy implication.
Output
To perform compositional rule of inference, the response of
each rule is weighted according to the values or degree of
membership of its inputs and the centroid of response is
calculated to generate the appropriate output. Neural network
has the shortcoming of implicit knowledge representation.
However, 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.
The ANFIS could be viewed as a fuzzy system, a neural
network or fuzzy neural network. The structure is seen as a
neural network for training and a fuzzy viewpoint is utilized
to gain insight into the system and to simplify the model. The Figure (1): The architecture of the ANFIS
neuro-adaptive learning method works similarly to that of For simplicity, it is assumed that the fuzzy inference system
neural networks. Neuro-adaptive learning techniques provide under consideration has two inputs x and y and one output z
a method for the fuzzy modeling procedure to learn as shown in Figure (1). For a zero-order Sugeno fuzzy model,
information about a data set. It computes the membership a common rule set with two fuzzy if-then rules is the
function parameters that best allow the associated fuzzy following:
inference system to track the given input/output data. A Rule 1: If x is A1 and y is B1, Then f1=r1 (1)
network-type structure similar to that of a neural network can Rule 2: If x is A2 and y is B2, Then f2 = r2 (2)
be used to interpret the input/output map. So it maps inputs Here the output of the ith node in layer n is denoted as On,i:
through input membership functions and associated
parameters. This will be translated through output Layer 1
membership functions and associated parameters to outputs. Every node i in this layer is an adaptive node with a node
The parameters associated with the membership functions function:
changes through the learning process. The computation of O1,i=μAi(x) for i=1,2,3 or (3)
these parameters (or their adjustment) is facilitated by a O1,i =μBi-3(y) for i=4,5,6 (4)
gradient vector. This gradient vector provides a measure of
how well the fuzzy inference system is modeling the Where x (or y) is the input to node i and Ai (or Bi) is a
input/output data for a given set of parameters. When the linguistic label associated with this node. In other words, O1,i
gradient vector is obtained, any of several optimization is the membership grade of a fuzzy set A1, A2 and A3 (or B1,
routines can be applied in order to adjust the parameters to B2 and B3) and it specifies the degree to which the given
reduce some error measure. This error measure (performance input x (or y) satisfies the quantifier A (or B). Here the
index) is usually defined by the sum of the squared difference membership function for A (or B) is triangular membership
between actual and desired outputs. ANFIS uses a function and is given as:
combination of least squares estimation and back propagation
1 if u c L
for membership function parameter estimation.
The suggested ANFIS has several attributes: Left : u \
L 0 ,1 c L u (5)
The output is zero th order Sugeno-type system. Max otherwise
0.5 w L
It has a single output, obtained using weighted
average defuzzification. All output membership
functions are constant.
Reference Number: W09-0013 74
The Online Journal on Electronics and Electrical Engineering (OJEEE) Vol. (1) – No. (2)
0 ,1 c u wi. fi
Max otherwise w1
0 .5 w O4 i i
Centers : u \
f1
wi
C
(6) w1 w2 w3
Max 0 , 1 u c
if u c i
0 .5 w w2 w3
f 2 f3 (11)
w1 w2 w3 w1 w2 w3
1
otherwise
Right : u \ Max 0 , 1 u c
R R
(7) As w1, w2 and w3 are assumed to be constant. Therefore,
if u c R
0 .5 w L equation (2) can be rewritten as follows:
L
Notice that for Equation (5) c specifies the “saturation point” O4,i =c1.r1+c2.r2+c3.r3 (12)
and wL specifies the slope of the nonunity and nonzero part of where
μL as shown in Figure (2) Similarly, for μR. For μC notice that w1
c is the center of the triangle and w is the base-width. cL, cR, c, c1 (13)
w1 w2 w3
wL, wR, and w are the parameters set. As the values of these
parameters change, the triangular function varies accordingly, w2
c2 (14)
thus exhibiting various forms of membership functions for w1 w2 w3
fuzzy set A. Parameters in this layer are referred to as premise w3
parameters. c3 (15)
w1 w2 w3
u
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:
Figure (2) : Input triangular membership
functions Layer 2 O4,i = F(i, S) (16)
Every node in this layer is a fixed node whose output is the Where i is the vector of input variables, F is the overall
product of all the incoming signals: function implemented by the adaptive network, and S is the
set of all parameters which can be divided into two sets:
O2,i= wi = μAi (x) μBi (y) i=1,2,3 (8)
Each node output represents the firing strength of a rule. S = S1 S2 (17)
Where represents direct sum.
Layer 3
Every node i in this layer is an adaptive node with a node Therefore, the hybrid learning algorithm can be applied
function: directly. More specifically, the error signals propagate
backward and the premise parameters are updated by
O3,i = wi fi = wi ri i=1,2,3 (9) Gradient Descent (GD) and node outputs go forward until
Where ri is the parameter set of this node. Parameters in this layer 3 and the consequent parameters are identified by the
layer are referred to as consequent parameters. Least Squares (LS) method. This hybrid learning is organized
as follows:
Layer 4 a) Linear and nonlinear parameters are distinguished
The single node in this layer is a fixed node which computes b) Each iteration (epoch) of GD update the nonlinear
the overall output as the summation of all incoming signals: parameters
c) LS method follows to identify the linear parameters.
wi f i
Overall output = O4i i i=1,2,3 (10) III. SIMULATION ENVIROMENT
wi
i The simulation environment based on MATLAB software
From the ANFIS architecture shown in Figure (1), it is package [12] is selected. It is used as the main engineering
observed that when the values of the premise parameters are tool for performing modeling and simulation of power
fixed, the overall output can be expressed as a linear systems and relays, as well as for interfacing the user and
combination of the consequent parameters. In symbols, the appropriate simulation programs. ATP [13] is used for
final output in Layer 4 can be rewritten as: 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
Reference Number: W09-0013 75
The Online Journal on Electronics and Electrical Engineering (OJEEE) Vol. (1) – No. (2)
implemented in ATP. MATLAB has been chosen due to ii) All type of faults (i.e. single phase to ground, phase to
availability of the powerful set of programming tools, signal phase, double phase to ground or three-phase fault)
processing, numerical functions, and convenient user-friendly iii) Inception fault time (Tf) 2 msec
interface. In this specially developed simulation environment, iv) Fault resistances (Rf) 0, 25, 50 and 100 ohms.
the evaluation procedures can be easily performed.
There are 444 training data. The input data to the ANFIS of
So the power system model was simulated and the different the locating unit are the impedances of the three phases
fault situations were performed by using ATP. Then the (magnitude and phase i.e. 6 inputs) after dividing them by
voltage and current measurements have been sent to their non fault values. They are taken from the fundamental
MATLAB to demonstrate the ANFIS protective relay. values of the voltage and current measurements after
evaluating Fourier transform every 20 msec. The output data
IV. THE PROTECTION SCHEME from the ANFIS are the normalized fault distance value.
A single line diagram for the protected transmission line c) The ANFIS Locator:
(T.L) is illustrated in Figure (3). It consists of two circuits The ANFIS locator consists of six neurons in the input layer
of 80 km length, 66 kV voltage level and 2 GVA short (i.e. N=6), four triangular membership functions for each
circuit level. input (i.e. F=4), and constant membership function for the
output.
d) Testing Data:
The testing data are chosen at different fault conditions which
are carried out at different fault distances, different fault
Figure (3): Single line diagram for the Transmission line resistances, different fault inception times and different fault
types which are not chosen for the training data. Besides that
The overall protection scheme can be demonstrated as in a white noise in introduced in the testing data to model the
Figure (4). Where: errors in the voltage and current measurements. Some of the
simulation results are shown in Table 1.
Vabc (VFabc) and Iabc (IFabc) are the instantaneous
Table 1 can be explained as follows; the first three columns
values of the three phase's voltage and current
are:
respectively (at fault condition).
Fault inception time (Tf);
V*abc (VF*abc) and I*abc (IF*abc) are the
Fault resistance (Rf); and
fundemantal compontents (peak values and the
Fault type respectively.
phases) of the three phases voltage and current
respectively after Fourier transformation (at fault Then the next six columns are impedances (magnitude and
condition). phase) of the three phases and these six values are used as
Z*abc (ZF*abc) are the fundemantal compontents input to the ANFIS detector. Then target fault distance (Df
(magnitudes and the phases) of the three phases p.u), finally the output of the ANFIS locator is shown in the
impedances (at fault condition). next column which is the estimated per unit fault distance and
IoF is the zero sequence current at fault condition. the final column is the percentage error between the accurate
CU is the control unit that receives the outcomes of value and the estimated one where:
the two units and only activates the fault classifier Dactual Destimated
% Error * 100% (18)
block diagram when a fault is detected. Dtotal
The testing data is chosen taking into consideration the
faults on transmission lines are quite random in nature with
respect to the time of occurrence, location, type and fault
resistance. So, the testing data are taken randomly with
random fault distances, fault resistances, fault inception
times and fault types in each training vector.
Figure (4): The proposed protection Layout
V. CONCLUISON
a) Fault Locating Unit: A new digital distance relaying technique based on ANFIS
The fault Location unit is built at different situations of all technique has been developed. ANFIS as control technique
fault types (i.e. single line to ground, double lines, double was used to implement this relay. The relay has been tested
lines to ground and three lines fault). After that, it is tested for different fault resistances, fault locations, fault types and
using different situations of the faulted power system. different system conditions. In all these test cases, the
b) Training data maximum error was found to be less than 8%. The proposed
The training data used to train the ANFIS of the fault location relaying technique has the ability to provide accurate and
unit are taken at: vigorous estimation for the fault distance in transmission
i) Fault distance (Df) 5%, 10%, 15%, 20%, 30%, 40%, lines.
50%, 60%, 70% and 80%
Reference Number: W09-0013 76
The Online Journal on Electronics and Electrical Engineering (OJEEE) Vol. (1) – No. (2)
Table 1: Testing data of the Fault Location Unit and their percentage errors.
fault Za Zb Zc Df
Tf Rf type p.u Za ph p.u Zb ph p.u Zc ph p.u % Error
0.013 91 DL 0.98 142.3 2.59 147.1 1.38 -250 0.76 1.2
0.007 54 TL 0.47 21 0.67 25.3 0.61 21.3 0.56 5.4
0.002 78 DLG 0.09 75.4 1.02 138.7 0.14 5.9 0.79 3.6
0.012 22 TL 0.17 15.4 0.21 -344 0.19 20 0.4 2.5
0.006 86 DL 1 -220 4.95 94.9 1.03 92.8 0.51 0.5
0.014 18 DLG 0.01 -8.7 0.01 128.4 0.8 -141 0.05 2.8
0.003 61 DL 1.03 134.3 1.15 4.2 0.53 69.8 0.18 2.1
0.002 0 DLG 1.06 144.4 0.09 5.3 0.06 56.2 0.56 1.9
0.012 100 DLG 0.58 103 0.03 -1 0.02 -272. 0.15 1.1
0.002 37 TL 0.3 16.5 0.39 18.4 0.36 19.9 0.5 2
0.003 90 DL 0.55 70.4 1 141.5 2.51 -8.7 0.15 3.6
0.016 27 SLG 0.53 37 0.98 143.7 0.98 -209 0.39 3.7
0.009 60 DL 1 -10.4 0.64 75 0.99 -206 0.35 5.4
0.001 66 SLG 1.01 53.1 0.98 145.2 0.97 -209 0.15 0.6
0.006 58 DL 0.59 66.5 1 141.2 2.67 -26.3 0.53 1.1
0.004 66 DLG 0.03 -6.7 0.02 82.9 0.92 -169 0.17 0.9
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