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KALU OBINNA OBUMA
PG/M.ENG/14/68136
APPLICATION OF ARTIFICAIL NEURAL NETWORK FOR ENHANCED
POWER SYSTEMS PROTECTION ON THE NIGERIAN 330kV NETWORK
DEPARTMENT OF ELECTRICAL ENGINEERING
FACULTY OF ENGINEERING
Godwin Valentine
Digitally Signed by: Content manager’s Name
DN : CN = Webmaster’s name
O= University of Nigeria, Nsukka
OU = Innovation Centre
2
UNIVERSITY OF NIGERIA, NSUKKA
FACULTY OF ENGINEERING
DEPARTMENT OF ELECTRICAL ENGINEERING
APPLICATION OF ARTIFICIAL NEURAL NETWORK FOR
ENHANCED POWER SYSTEM PROTECTION IN THE NIGERIAN
330kV NETWORK
A THESIS SUBMITTED IN PARTIAL FULFILMENT FOR THE
REQUIREMENT OF THE AWARD OF M.ENG
(POWER SYSTEMS ENGINEERING)
BY
KALU OBINNA OBUMA
PG/M.ENG/14/68136
DECEMBER, 2015
3
Title Page
APPLICATION OF ARTIFICAIL NEURAL NETWORK FOR
ENHANCED POWER SYSTEMS PROTECTION ON THE NIGERIAN
330kV NETWORK
A THESIS SUBMITTED IN PARTIAL FULFILMENT FOR THE
REQUIREMENT OF THE AWARD OF M.ENG
(POWER SYSTEMS ENGINEERING)
BY
KALU OBINNA OBUMA
PG/M.ENG/14/68136
SUPERVISOR: PROF. T.C. MADUEME
DECEMBER 2015
4
APPROVAL PAGE
APPLICATION OF ARTIFICIAL NEURAL NETWORK FOR ENHANCED POWER
SYSTEM PROTECTION IN THE NIGERIAN 330kV NETWORK
BY
KALU OBINNA OBUMA
(PG/M.EMG/14/68136)
A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS
FOR THE AWARD OF MASTER OF ENGINEERING DEGREE (M.ENG) IN
ELECTRICAL ENGINEERING
DECEMBER, 2015
Kalu Obinna Obuma Signature: Date:
(Student)
Engr. Prof. T.C. Madueme Signature: Date:
Engr. Prof. A.O. Ibe Signature: Date:
(External Supervisor)
Engr. Prof. E.C Ejiogu Signature: Date:
(Head of Department)
Engr. Prof. E.S. Obe Signature: Date:
(Fac. Of Engineering Rep. SPGS)
(Supervisor)
5
Certification
Kalu Obinna Obuma, a master’s degree student in the department of electrical engineering
with registration number, PG/M.ENG/14/68136 has satisfactorily completed the requirements
for the award of the degree of Masters of Engineering (M.Eng) in Electrical Engineering.
The work embodied in this project is original and has not been submitted in part or full for
any other diploma or degree of this or any other university to the best of my knowledge.
Engr. Prof. T.C. Madueme
(Supervisor)
Engr.Prof. E.C Ejiogu
(Head of Department)
Engr. Prof. E.S Obe
(Fac. of Engineering Rep. SPGS)
6
Dedication
I dedicate this work to all students of 2014 post graduate set of the department of Electrical
Engineering Department.
7
Acknowledgement
This work would not have been possible without the contribution of others, truly the saying
‘no man is an island’ adequately applies.
Many thanks to my supervisor, Prof T.C Madueme, whose consistency in lending assistance,
being there when you need him and giving needed assistance where necessary, truly a father.
Prof. Obe, your assistance with procuring much needed research materials is greatly
appreciated. Truly this thesis would not have taken much longer if not for your assistance in
procuring needed materials.
Prof A.U.Ekwue, many thanks to you as well, even from a distance your assistance be it
electronically, your tutelage as my lecturer made understanding this thesis easy. I will not fail
to mention Prof. Anih who answered important questions relating to my work. Dr Ogbuka,
your input with my Matlab Simulation saved me a lot of blunders, many thanks.
To the staff of the Protection, Control and Metering department of the New Haven & Onistha
Transmission Station, I can’t thank you enough for obliging me with needed data to make my
simulation more realistic, the head of department of both Departments for answering my
questions and granting me supervised access to the control room.
To my friends who supported me during my project work I will never forget; Onwaokangba
Anthony, Odoh Benjamin, Uzoeto Ifeanyi, Nwaogu Chijioke; am really grateful. To my
family, always a constant in my life, your prayers and support really kept me going. To my
siblings, thanks for looking up to me, truly responsibility, duty, and discipline. All these traits
I’ve developed thanks to you guys.
I thank almighty God, during the stressful moments trying to figure out my project, my
travels to transmission companies up to the moment it finally made sense. To you I give all
the glory.
8
Contents
Approval Page I
Certification II
Dedication III
Acknowledgement IV
Abstract V
List of Figures VIII
List of Tables X1
Chapter 1: INTRODUCTION
1.1 Introduction 1
1.2 Statement of problem 1
1.3 Aim/objective of the study
1.4 Significance of the study 3
1.5 Scope of the work 3
Chapter 2: LITERATURE REVIEW
2.1 State of the art power system protection 4
2.2 Faults in Power System 4
2.3 Symmetrical Faults 4
2.3.1 Transient on a Transmission Line 4
2.3.2 Symmetrical Components 6
2.3.3. Symmetrical Component Transformation 6
2.4. Unsymmetrical Fault Analysis 8
2.4.1 Single Line to Ground Fault 8
2.4.2 Line to Line Fault 10
2.4.3 Double Line to Ground Fault 12
2.5. Types of Protection 14
2.5.1 Distance Relays 14
2.5.2 Pilot protection 16
9
2.6. Single Auto Reclosure Technique 17
2.7. System Configuration 17
2.8 Transmission Line Protection 17
2.8.1 Fault Detection & Location 18
2.8.2 Fault Classification 19
2.8.3 Enhanced Power System Protection 19
2.9 Artificial Neural Network 20
2.9.1 Multi-Layer Perceptron 21
2.9.2 Feed Forward Artificial Neural Network & Back Propagation Algorithm 21
2.9.3 Unsupervised Learning Algorithm 22
2.9.3.1 Self Organized Map Function 24
2.9.4. Clustering 26
Chapter 3: METHODOLOGY 27
3.1 Power System under Consideration 27
3.2 Data Pre-processing using fast Fourier transform 28
3.3 Overview of the Training Process 29
3.4 Overview of the Testing Process 31
3.5 Performance Evaluation 33
3.6 Clustering with Self-Organized Neural Network Algorithm 34
3.7 Neural Network Methodology for Adaptive Reclosure 35
3.8 Arc Modelling in Adaptive Reclosure Scheme 37
Chapter 4: SIMULATION RESULTS
4.1 Structure & training of neural fault detector 38
4.2 Discussion of Figures for A.N.N. Fault Detector 42
4.3 Structure & Training of A.N.N. fault location Algorithm 42
4.3.1 Discussion of plots from A.N.N. Fault Location Algorithm 48
4.4 Simulation Results for Fault Classification via Self Organising Map Function 49
10
4.4.1 Discussion of Results of Fault Classification via Self Organising Map Function 50
4.5 Simulation Results for Adaptive Auto Reclosure Scheme 50
4.5.1 Discussion of Results for Adaptive Fault Classifier Plots 54
4.6 Testing the Neural Network Fault Detection Algorithm 54
4.6.1 Discussion of Test Results of A.N.N. Fault Detector Algorithm 59
4.7 Test Results for Neural Network Fault Location Algorithm 59
4.7.1 Discussion of Simulation Results from Testing Fault Location Algorithm 62
4.8 Test Results for Neural Network Fault Classification Algorithm 62
Chapter 5: CONCLUSION
5.1 Conclusion 79
5.2 Recommendations 79
11
List of Abbreviations
O.H.L Overhead Line
A.A Adaptive Autoreclosure
C.B Circuit Breaker
A.N.N Artificial Neural Network
F.F.N.N Feed Forward Neural Network
S.O.M Self Organized Map
R.O.C Receiver Operating Characteristics
C.V.T Current VoltageTransformer
E.H.V Extra High Voltage
S.P.A.R Single Pole Auto Reclosure
A.D.S.P.A.R Adaptive Single Pole Auto Reclosure
C.E Cross Entropy
%E Percentage Entropy
M.S.E Mean Square Error
R Regression
12
List of Figures
Fig 2.1 RL model circuit 5
Fig 2.2 Single line to ground fault 8
Fig 2.3 Connection of sequence network for a single line to ground fault 9
Fig 2.4 Line to line fault 10
Fig 2.5 Sequence network for L-L fault 11
Fig 2.6 Double line to ground fault
Fig 2.7 Connection of Sequence Networks for LLG Fault 13
Fig 2.8 Three zone step distance relaying to protect 100% of a line and back up neighbouring line 16
Fig 2.9 Three layer network 22
Fig 2.10 Self organising map neighbourhoods 25
Fig 3.1 Fault current graph of A-G fault 27
Fig 3.2 Voltage signal of A-G fault 28
Fig 3.3 F.F.T. analysis of voltage waveform 28
Fig 3.4 F.F.T analysis of current waveform 29
Fig 3.5 Flow Chart of ANN Fault Diagnostic Algorithm 32
Fig 3.6 Block diagram of neural network training algorithm 34
Fig 3.7 Flow Chart of Adaptive Auto Reclosure Scheme 36
Fig 4.1 Current signal of B-C fault 38
Fig 4.2 Voltage signal of A-B-C fault 38
Fig 4.3 Current signal of A-B-C fault 39
Fig 4.4 Receiver Operating characteristics of fault detector using current values 40
Fig 4.4b Confusion matrix of fault detector 40
Fig 4.5a Receiver operating characteristics of fault detector using voltage & current values 41
Fig 4.5b Confusion Matrix for Fault detector using voltage & current values 41
Fig 4.6 Plot of regression fit for fault location on zone 1 42
Fig 4.7 Error histogram of fault locator using current values 43
13
Fig 4.8 Regression plot for fault using current values on zone 2 43
Fig 4.9 Error histogram for fault locator using current values on zone 2 44
Fig 4.10 Regression fit for fault locator using current values on zone 3 44
Fig 4.11 Regression fit for fault locator using voltage & current values on zone 1 45
Fig 4.12 Error histogram for fault locator using voltage & current values on zone 1 45
Fig 4.12b Output Plot for Fault Locator using voltage & current values in zone 1 46
Fig 4.13 Regression fit for fault locator using voltage & current values on zone 2 46
Fig 4.14 Error histogram for fault locator using voltage & current values on zone 2 47
Fig 4.15 Regression fit for fault locator using voltage & current values on zone 3 47
Fig 4.16 Error histogram for fault locator using voltage and current values on zone 3 48
Fig 4.17 Plot of S.O.M sample hits 49
Fig 4.18 Plot of S.O.M neighbour weight distances 49
Fig 4.19 Plot of S.O.M input planes 50
Fig 4.20 Transient Fault waveform for A-G fault 51
Fig 4.21 Permanent fault waveform of A-G fault 52
Fig 4.22 Confusion matrix for fault classifier using voltage and current values 52
Fig 4.23 Receiver operating characteristics for fault classifier using voltage & current values 53
Fig 4.24 Regression plot of adaptive reclosure scheme using voltage & current values 53
Fig 4.25 Receiver operating characteristics plot for adaptive reclosure scheme using voltages &
current values 54
Fig 4.26 Confusion matrix plot for testing fault detector using current values 55
Fig 4.27 Plot of training state for testing fault detector using current values 55
Fig 4.28 Error histogram for testing fault detector using current values 56
Fig 4.29 Receiver operating characteristics for testing fault detector using current values 56
Fig 4.30 Plot of training state for testing fault detector using voltage & current values 57
Fig 4.31 Error histogram for testing fault detector using voltage & current values 57
Fig 4.32 Confusion matrix for testing fault detector using voltage and current values 58
14
Fig 4.33 Confusion matrix for testing fault detector using voltage & current values 58
Fig 4.34 Training state results for testing fault locator using current & voltage values 59
Fig 4.35 Error histogram for testing fault detector using current values 59
Fig 4.36 Regression plot for testing for testing fault locator using current values 60
Fig 4.37 Training state plot for testing fault locator using voltage & current values 60
Fig 4.38 Error histogram for testing fault locator using voltage & current values 61
Fig 4.39 Regression plot after testing fault locator using voltage & current values 61
Fig 4.40 S.O.M neighbour weight distances for testing fault locator 62
Fig 4.41 S.O.M input planes for fault classifier 63
Fig 4.42 Sample hits plots for testing fault classifier 63
Fig 4.43 Confusion matrix for test on adaptive reclosure 64
Fig 4.44 Receiver operating characteristics for test results on adaptive reclosure scheme. 65
15
List of Tables
Table 4.1 Performance table for fault detector network 65
Table 4.2 Performance table for adaptive fault classifier neural network 66
Table 4.3 Performance table for adaptive reclosure scheme network 66
Table 4.4 Performance table for fault locator using neural network 67
Table 4.5 Output of trained faulted phase detector network using current values only for zone 1 68
Table 4.6 Output of trained faulted phase detector network using current & voltage values 69
Table 4.7 Output of trained faulted phase detector network using current values for zone 2 70
Table 4.8 Output of trained faulted phase detector using voltage & current values for zone 2 71
Table 4.9 output of trained fault phase detector using current values for all zones 72
Table 4.10 output of trained faulted phase detector using voltage and current values for all zones 73
Table 4.11 Comparison of estimated and target output for fault locator zone 2 74
Table 4.12 Comparison of estimated and target output of fault locator zone 1 75
Table 4.13 Comparison of estimated and target output for fault locator zone 3 76
Table 4.14 Adaptive fault classifier for transient or permanent fault 78
16
Abstract
This work investigates an improved protection solution based on the use of artificial neural
network on the 330kV Nigerian Network modelled using Matlab R2014a. Measured fault
voltages and currents signals decomposed using the discrete Fourier transform implemented
via fast Fourier transform are fed as inputs to the neural network. The output plots of the
neural network shows its successful application to fault diagnosis (fault detection, fault
classification and fault location). The neural networks application to fault location shows a
mean square error of 3.5331 and regression value of 0.99976 which shows a very close
relationship between the output and target values fed to the neural network. Unlike
conventional protection schemes, the neural network can be adapted to distances which can
cover the entire length of the protected line. Numerical assessment carried out on the neural
network fault locator shows a reduced time of operation of 5.15miliseconds as compared to
the 0.350seconds with the use of ordinary numerical relays. This work also investigates the
adaptive auto reclosure scheme implemented using artificial neural network. The adaptive
reclosure scheme has been adapted for use in the Nigerian Network successfully to
distinguish transient and permanent faults. Simulation results prove that the adaptive
reclosure scheme was able to detect a line-to-ground transient fault and clear this fault in 0.1s
while the line-to-ground permanent fault is cleared after 0.14s. The auto reclosure scheme is
designed using two separate neural networks, one nework to distinguish the faults either as
transient or permanent fault, and using this fault distinguishing network as input to the second
network to classify decision, either as ‘safe to reclose’ represented by logic ‘1’ or ‘do not
reclose’ represented as logic ‘0’. The Fault diagnostic algorithm designed using artificial
neural network (A.N.N.) for the 330kV network was tested on a 132kV network. Results
show and prove that the algorithm is flexible and can be adopted to other networks.
17
CHAPTER ONE
INTRODUCTION
1.1 Background of the study
The demand for constant power supply in Nigeria is ever increasing; however the demand is
met with lots of constraint. One of them being system faults. Faults on transmission line in
particular is of great interest to the power holding company of Nigeria as more investment is
put into restructuring the current infrastructure and also expanding existing ones.
The power sector of Nigeria is subdivided into policy, regulations, customers, operations. The
operations division brings to light the activities of the transmission company of Nigeria that
controls the high voltage delivery of power from generating plants to the substations for
transmission to distribution stations. T.C.N handles a 330kv system capacity of 6870MW
over a total distance of 5650Km[1], their focus is to maintain power system stability,
reliability and sustainability.
The major protection schemes currently employed are distance protection, over current
protection, differential protection e.t.c. distance protection being the predominant suffers
from inaccuracy due to restraints of relays on protection schemes i.e. reach settings. The relay
cannot fully adapt to fluctuations in power system conditions especially in parallel lines as
well as distinguish between transient and permanent fault following a short circuit.
This work brings to view the application of artificial neural network for enhanced power
system protection in regards to fault detection, fault location, and application of the adaptive
auto reclosure schemes as opposed to conventional approach; travelling wave approach[2][3],
synchronous compensators[4] to name a few.
1.2 Statement of the Problem
Among several power system components, transmission line is one of the most important
components of the power system network and is mostly affected by several types of faults.
Generally, 80%-90% of the fault occurs on the transmission line and the rest of substation
equipment and bus bar combined[5]. The necessary requirement of all the power system is to
maintain reliability of operation which may be done by detecting, classifying and isolating
various faults occurring in the system. It is required that a corrective decision should be made
by the protective device to minimize the period of trouble and limit outage time, damage and
related problems. If any fault or disturbances occurred in the transmission is not detected,
located, and eliminated quickly, it may cause instability in the power system and causes
significant changes in system quantities like over-current, under or over voltage, power
factor, impedance, frequency and power. The appropriate percentage of occurrence of single
line to ground fault is about 70-80%, line to line to ground faults is 10-17%, line to line fault
is 8-10% and three phase is 3%[6]. The three faults occur rarely but if it exists in a system it
is quite expensive.
18
1.3 Significance of the Study
Distance protection is considered covering various effects like high fault impedance, non-
linear arc resistance and variable source impedance. Distance relaying principle, due to their
high speed fault clearance compared with over current relays is widely used protective
scheme for high voltage transmission lines in Nigeria. A distance relay estimates the
electrical distance to the fault and compares the result with a given threshold, which
determines the protection zone. There is need for measuring algorithms that have the ability
to adapt dynamically to the system operating conditions such as changes in the configuration.
Numerical relays acquire sequential samples of A.C. quantities in numeric (digital) data form
through the data acquisition system, process the data using the algorithm to calculate fault
discriminate and make trip decision. The reach accurateness of an electromechanical, static or
a microprocessor based distance relay is affected by different fault conditions and network
configuration settings. Artificial neural network makes use of samples of currents and
voltages directly as inputs without calculation of phasor and related symmetrical components.
The algorithm makes available automatic determination of fault direction and fault location
after one cycle from the initiation of fault. For protection of transmission line using artificial
neural network, it doesn’t necessitate any communication link to recover remote end data
from local end only i.e. voltages and currents are captured from the bus bar. Then, pre
processing of obtained signal can be done to pass it into A.N.N level making it the best tool
to solve under reach and overstretch problems which are very regular with conventional
distance relay design.
1.4 Aim/Objective of the study
The aim of this project is to demonstrate the application of artificial neural network to fault
diagnostic as well as implementation of adaptive single pole auto reclosure scheme in power
system protection. This work presents the outcomes of both the feed forward A.N.N and self-
organized neural network application to;
Fault detection of all types of faults
Fault classification (line to ground, line to line, line to line to ground, three phase
faults, three phase to ground faults)
Fault location on three zones presented in this work
Application to adaptive single pole auto-reclosure scheme
The objectives of the study are;
Fault pattern generation from transmission network modelled on Matlab Simulink
Environment.
Pre-processing of voltage and current signals using Fast Fourier transform.
Normalization of the extracted features in order to match A.N.N input level of ± 1.
19
Selection of appropriate neural network architecture for various protection problems;
fault detection, location e.t.c.
Training of appropriate neural network.
1.5 Scope of the Work
This work centres on the application of artificial neural networks on the Nigerian 330kv
network. For the purpose of this project, three transmission networks are considered; Onistha,
Benin and new-haven. Needed data’s like single line diagram of each network as well as line
and bus data of this networks are collated for the purpose of this work. The author did his
best to create a Simulink model of these networks taking Onistha network as the reference to
other networks represented as one entity. The fault breaker block is placed on each line
representing the three different protection zones to induce different fault types on each line.
Certain assumptions were made in the modelling of these networks; the generator as well as
step-up transformer data of a different generating plant but giving the same output voltage as
desired for this work, fault data also retrieved from Onistha T/S was used to compare
simulated to real time data
20
CHAPTER TWO
LITERATURE REVIEW
2.1 State of the Art Power System Protection
Power system protection is a branch of electrical power engineering that deals with the
protection of power systems from faults through the isolation of faulted parts from the rest of
the network. Protection systems in electricity delivery networks have a major role to play in
increasing of systems, and a broad understanding of their current and future application can
aid in better taking them into account for achieving future energy networks that adapt for the
incorporation of renewable energy generation sources. This chapter provides a survey of
faults generally, state of art of some protection techniques as well as protection schemes. The
unifying theme of this work is to highlight the potentials of artificial intelligence namely
artificial neural networks in overcoming the restraints of traditional protection techniques[7]
thus the enhanced protection scheme is introduced .
2.2 Faults in Power System
Fault is an unwanted short circuit condition that occurs either between two phases of wires or
between a phase of wire and ground. Short circuit is the most risky type of fault as flow of
heavy currents can cause overheating or create mechanical forces which may damage
equipment and other elements of power system. Faults can be classified into three types,
which are symmetrical faults, unsymmetrical faults, and open faults.
2.3 Symmetrical Faults
The fault that results in symmetrical fault current (equal currents with 120 displacement) is
known as symmetrical fault. Three phase faults is an example of symmetrical fault where all
three phases are short circuited with or without involving the ground.
2.3.1 Transient on a Transmission Line
To consider the short circuit transient on a transmission line, certain simplifying assumptions
made at this stage
The line is fed from a constant voltage source
Short circuit takes place when the line is unloaded
Line capacitance is negligible and the line is represented by a lumped RL series
circuit
With the above assumptions the line can be represented by the circuit model of fig 1 below.
The short circuit is assumed to take place at t=0. The parameter α controls the instant on the
voltage wave when the short circuit occurs. It is known from the circuit theory that the
current after short circuit is comprised of two parts i.e.
21
i = i + i (2.1)
where i = steady state current = √( )|| sin(ωt + α − ɵ)
Z = (R + ωL) < ɵ = tan! ω"# $ (2.2)
Where i = transient current'it is such that i(0) = i(0) + i (0) = 0) Being an inductive circuit, it decays correspondingly to the time constant L R . i = −i(0)e!*+$ = √|| sin(θ − α) e,*+$- (2.3)
This short circuit is given by
i = √ || sin(ωt + α − θ) + √ || sin(θ − α) e!.# " / (2.4)
In power system terminology, the sinusoidal steady state current is called the symmetrical
short circuit current and the unidirectional transient component is called the DC offset
current, which causes the total circuit current to be unsymmetrical till the transient
decays[17]. The maximum momentary short circuit current i012 corresponds to the first peak.
If the decay of transient current in this short time is neglected,
i012 = √|| sin(θ − α) + √|| (2.5)
Since transmission line reactance is small, θ≅90
Symmetrical short circuit
current
DC offset
R
L
Fig 2.1 RL model circuit
22
i012 = √|| cosα + √|| (2.6)
This has the maximum possible value for α=0, that is short circuit occurring when the
voltage wave is going through zero. Thus i012 = √|| is twice the maximum symmetrical
short circuit current (doubling effect).
2.3.2 Symmetrical Components
Under such operations the system impedances in each phase are identical and the three phase
voltages and currents throughout the system are completely balanced that is they have equal
magnitudes in each phase and are progressively displaced in time phase by 120 (phase ‘a’
leads/lags phase ‘b’ by 120 and phase ‘b’ leads/lags phase ‘c’ by 120 ). In a balanced system,
analysis can proceed on a single-phase basis. The knowledge of voltage and current in one
phase is sufficient to completely determine voltages and currents in other two phases. Real
and reactive powers are simply three times the corresponding per phase values. A method of
analyzing unbalanced operation is through symmetrical components where the three phase
voltages (and currents) which may be unbalanced are transformed into three sets of balanced
voltages and currents called symmetrical components.
2.3.3 Symmetrical Component Transformation
A set of three balanced voltages (phasors) 67, 69, 6: is characterized by equal magnitudes and
interphase difference of 120 . The three phasors can be expressed in terms of the reference
phasor 67 as
V1 = V1, V< =∝ V1,V> = αV1 (2.7)
Where the complex number operator α is defined as α=e@A, it has the following parameters
α = e@BA° = e!@A° =∝∗
(∝)∗ =∝
∝E= 1
1+ ∝ + ∝= 0
If the phase sequence is acb (negative sequence), then
V1 = V1,V< =∝ V1,V> =∝ V1 (2.8)
Thus a set of balanced phasors i is fully characterized by its reference phasor (sayV1 ) and its
phase sequence (positive or negative).
Suffix 1 is normally used to indicate positive sequence. A set of balanced negative sequence
phasors is written as
23
Va,Vb =∝ Va,Vc =∝ Va (2.9)
Similarly, suffix 2 is used to indicate negative sequence, a set of balance negative sequence
phasors is written as
Va,Vb =∝ Va,Vc =∝ Va (2.10)
A set of three voltages (phasors) equal in magnitude and having the same phase is said to
have zero sequence. Thus a set of zero phase sequence phasors is written as
VaA = Vb = VcA = 0 (2.11)
Consider now a set of three voltages (phasors) 67, 69, 6: which in general may be unbalanced.
According to fortesque’s theorem the three phasors can be expressed as the sum of positive,
negative, and zero phasors defined. Thus
V1 = Va + Va + VaA (2.12)
V< = Vb + Vb + VbA (2.13)
V> = Vc + Vc + VcA (2.14)
The three phase sequences (positive, negative and zero) are called the symmetrical
components of the original phasor Va, Vb, Vc.
Equations (12),(13),(14) can be expressed in terms of reference phasors Va,Va and VaA. thus
V1 = Va + Va + VaA (2.15)
V< =∝ Va +∝ VaA + VaA (2.16)
V> =∝ Va +∝ Va + VaA (2.17)
Construction of current phasors from their symmetrical components:
Ia = E (I1 +∝ I< +∝ I>) (2.18)
Ia = E (I1 +∝ I< +∝ I>) (2.19)
IaA = E (I1 + I< + I>) (2.20)
24
2.4 Unsymmetrical Fault Analysis
Various types of unsymmetrical faults that occur in power systems are:
Single line-to-ground (LG) fault
Line-to-line (LL) fault
Double line-to-ground (LLG) fault
2.4.1 Single line-to-ground (LG) fault
Figure 2.2 shows a line-to-ground fault at F in a power system through a fault impedance Zf.
The phases are so labelled that the fault occurs on phase a.
At the fault point F, the current out of the power system and the line to ground voltage are
constrained as follows:
I< = 0 (2.21)
I> = 0 (2.22)
V1 = ZJI1 (2.23)
The symmetrical components of the fault currents are
KIaIaIaEL = 13 K1 ∝ ∝1 ∝ ∝1 1 1 L KI100L
Zf
Ib=0
Ic=0
Fig 2.2 Single Line to Ground fault at F
a
b
c
25
For which it is easy to see that
Ia = Ia = IaA = E I1 (2.24)
Expressing (23) in terms of symmetrical components, we have
Va + Va + VaA = ZJI1 = 3ZJI1 (2.25)
As per (3.24) and (3.25) all sequence currents are equal and the sum of sequence
voltages3ZJIa.. Therefore, these equations suggests a series connection of sequence
networks through an impedance 3ZJ as shown in figs.3
NO = PQ(RSTRUTRV)TERW (2.26)
Fault current N7 is given by
N7 = 3NO = EPQ(RSTRUTRV)TERW (2.27)
F
F
6O
6O
6OA
NOA = NO
NO
NO = NO
3XY N7XY
NO = NO = NOA = 13 N7
Fig 2.3: connection of sequence network for a single line to ground fault (LG) fault
F
26
The above results can also be obtained directly from (24) to (25) by using 6O, 6O OZ[ 6OA
and from the equation below
K6O6O6OAL = K\700 L − KX 0 00 X 00 0 XA
L KNONONOAL (2.28)
Thus,
(\7 − NOX) + (−NOX) + (−NOXA) = 3XYN7
Or
NO = \7(X + X + XA) + 3XY
The voltage of line b to ground under fault condition is
69 =∝ 6O+∝ 6O + 6OA
=∝ ]\7 − X N73 ^ +∝ ]−X N73 ^ + ]−XA N73 ^
Substituting for N7 from (27) and reorganizing we get,
69 = \7 E∝URWTRU.∝U!∝/TRV(∝U!)(RSTRUTRV)TERW (2.29)
2.4.2 Line to Line Fault
Fig 4 shows a line to line fault at F in a power system on phases ‘b’ and ‘c’ through fault
impedance XY .
The currents and voltages at the fault can be expressed as
N7
a
b
c
F
XY N9 N:
Fig 2.4: Line to Line (L-L) fault through impedance XY
27
N_ = K N7 = 0N9N: = −N9L ; 69 − 6: = N9XY (2.30)
The symmetric components of the faults currents are
KNONONOAL = 13 K1 ∝ ∝1 ∝ ∝1 1 1 L K 0N9−N9
L
From which we get
NO = −NO (2.31)
NOA = 0 (2.32)
The symmetrical components of voltage at F under fault are
K6O6O6OAL = E K1 ∝ ∝1 ∝ ∝1 1 1 L a 676969 − XYN9
b (2.33)
The first two equations
36O = 67 + (∝ +∝)69 −∝ XYN9
36O = 67 + (∝ +∝)69 −∝ XYN9
From which we get
3(6O − 6O) = (∝ −∝)XYN9 = c√3 XYN9 (2.34)
Now,
N9 = (∝ ∝)NO (NO = NO; NOA = 0)
= d√3NO (2.35)
Substitute N9 from (3.31) and (3.35) parallel connection of positive and negative sequence
networks through a series impedance XY as shown in fig 5 since NOA = 0, the zero sequence
network is unconnected
28
In terms of the thevenin equivalents, we get
NO = \7X + X + XY
From (2.35) we get
N9 = N: = c√3 \7X + X + XY
2.4.3 DOUBLE LINE TO GROUND (LLG) FAULT
Fig 6 shows a double line to ground fault at F in a power system. The fault may be in general
having impedance XY as shown.
XY
NO NO
6O 6O
Fig 2. 5 sequence network for L-L fault
a
b
c
F
XY N9 N: 3NOA
NOA = 0
Fig 2.6: double line to ground (LLG) fault through impedance XY
29
The current and voltage (to ground) conditions at the fault are expressed as
N7 = 0
NO + NO + NOA = 0 (2.36)
69 = 6: = XY(N9 + N:) = 3XYNOA (2.37)
The symmetrical components of voltages are given by
K6O6O6OAL =
E K1 ∝ ∝1 ∝ ∝1 1 1 L K67696:
L (2.38)
From which it follows that
6O = 6O = E '67 + (∝ +∝)69) (2.39a)
6OA = E (67 + 269) (2.39b)
From (2.39a) and (2.39b)
6OA 6O = 13 (2∝ ∝)69 = 69 = 3XYNOA
Or
6OA = 6O + 3XYNOA
The sequence connections is shown in fig 2.7
3XY
F F F 6O 6O
6OA
Fig2. 7 Connection of sequence networks for a double line to ground (LLG) fault
30
In terms of the thevenin equivalents, the new equation translates from
NO = \7X + X (XA + 3XY)
= PQRSTRU.RVTERW/.RUTRVTERW/ (2.40)
2.5 Types of Protection
Protection of transmission or distribution network serves to protect the plant as well as the
personnel by disconnecting equipment which experiences an overload or a short to the earth.
Some forms of protection are;
Overload and backup for distance (over-current): overload protection requires a
current transformer which simply measures the current in a circuit. There are two
types of overload protection; instantaneous over current and time over current
(T.O.C). Instantaneous over current requires that the current exceeds a pre-determined
level for the circuit breakers to operate.
Earth-fault: earth fault protection again requires current transformers and series an
imbalance in a three-phase circuit. Normally the three phase currents are in balance,
which is roughly in magnitude. If one or two phases become connected to earth via
long impedance fault, their magnitudes will increase dramatically and cause
imbalance. If this imbalance exceeds a pre-determined value, a circuit breaker should
operate.
Distance (impedance relay): distance protection detects both the voltage and current.
A fault on a circuit will generally create a sag in the voltage level. If the ratio of
voltage to current measured at the relay terminals, which equates to impedance, leads
within a pre-determined level the circuit breaker will operate. This is useful for
reasonable length lines, lines longer than 10 miles because its operating characteristics
are based on the line characteristics. This means that when a fault appears on the line
the impedance setting relay is compared to the apparent impedance of the line from
the relay terminals to the fault. If the relay setting is determined to be below the
apparent impedance it is determined that the fault is within the zone of protection[8].
Back up: the objective of protection is to remove only the affected position of a plant
and nothing else. A circuit breaker or protection relay may fail to operate. In
important systems, a failure of primary protection will usually result in the operation
of back-up protection[9]. Remote back up protection will generally remove the
affected and unaffected items of plant to clear the fault. Local back-up protection will
remove the affected items of plant to clear the fault. Local back-up protection will
remove the affected items of the plant to clear the fault.
31
2.5.1 Distance Relays
The distance protection scheme is the dominant scheme used in the Nigerian 330Kv networks
thus a further review of this scheme and its implication as regards this work is paramount.
The distance protection is implemented in a transmission network by the protection
equipment known as distance relays. Distance relays respond to the voltage and current i.e.
impedance at the relay location. The impedance per mile is fairly constant so these relays
respond to the distance between the relay location and a fault location. As the power systems
becomes more complex and the fault current varies with changes in generation and system
configuration, directional over current relays are more difficult to apply and to set for all
contingencies, whereas the distance relay setting is constant for a wide variety of changes
external to the protection line. There are three general types; impedance relay, admittance
relay, reactance relay each is distinguished by its application and its operating characteristics.
In a three phase power system, 11 types of fault are possible; three single phase to ground,
three phase –phase to ground, three double phase to ground, and two three phase faults. It is
essential that the relays provided have the same setting regardless of the type of fault. This is
possible if the relays are connected to respond to delta voltages and currents. The delta
quantities are defined as the difference between any two phase currents, for example, \7 \9 is the delta quantity between phases ‘a & b’. In general, for multiphase-fault between
phases x and y,
PQ!PefQ!fe = X (2.41)
Where X is the positive sequence impedance between the relay location and the fault. For
ground distance relays, the faulted phase voltage, and a compensated faulted phase must be
used.
PQfQTgfV = X (2.42)
Where m is a constant depending on the line impedance, and NA is zero sequence current in
the transmission line. A full complement of relays consisting of three phase distance relays
and three ground relays. This is the preferred protective scheme for high and extra high
voltage systems[6].
32
2.5.2 Pilot Protection
Step distance protection does not offer instantaneous clearing of faults over 100% of line
segment. To cover the 10-20% of the line not covered by zone 1, the information regarding
the location of the fault is transmitted from each terminal to the other terminals. A
communication channel is used for this transmission. Pilot channels can be over power line
carrier, microwave, fibre optic, or wire pilot. Power line carrier uses the protected line itself
as a channel, superimposing a high frequency signal on-top of the 50Hz power frequency.
Since the line being protected is also the medium used to actuate the protective devices, a
blocking signal is used. This means a trip will occur at both ends of the line unless a signal is
received from the remote end. Pilot protection is not in use in the south-eastern Nigerian
transmission network due to some stations yet to be connected to the grid.The issues
associated with the distance relay, problems of under reach and over reach introduce a high
error in distance relaying. In the case of pilot protection, cost of implementing
communication channel presents a setback to its use regardless of its efficiency. The
constraints presented, informs the decision to research on a cost effective and robust
protection scheme; many research on improved protection, enhanced protection can be
characterized as ADAPTIVE PROTECTION; Adaptive protection is a protection philosophy
Fig 2.8 Three zone step distance relaying to protect 100% of a line and backup neighbouring line. (From
S.Horowitz,Transmission Line Protection, 2nd ed..,2007.CRC Press, Taylor % Francis Group)
33
which permits and seeks to make adjustments to various protection functions automatically in
order to make them more attuned to prevailing power system conditions. The ADAPTIVE
DISTANCE PROTECTION[10] is one of such research areas in power system protection;
this scheme seeks to keep the protected zone constant at a predetermined boundary by
adapting the tripping impedance under varying power system conditions. Another research
area is BOUNDARY PROTECTION[11][12], which happens to be a step beyond the
adaptive distance protection. A fast growing research interest is the single pole auto reclosure
technique further developed to the ADAPTIVE SINGLE POLE AUTO RECLOSURE
SCHEME[13][14][15].
2.6 Single Pole Auto Reclosure Technique
The most common faults on EHV transmission lines are single phase to ground types and for
such faults SPAR provides an improvement in the overall protection of transmission
system[13]. S.P.A.R is imperative in applications construction of additional circuits may not
be possible due to environmental pressure/costs, a practical example is the Nigerian
Transmission Network which does not utilize the scheme in the protection of its transmission
lines. The conventional S.P.A.R has cases of unsuccessful reclosures due to a fixed dead time
in the case of transient fault, or reclosure onto a permanent fault may aggravate the potential
damage to the system and equipment. Notwithstanding, the method of auto reclosure is
economical and effective technique for high capacity electric power systems to improve
reliability and stability if auto reclosure is successfully executed, it usually restores the
stability of the system and maintains the continuity of electric power transmission. In auto
reclosure techniques, it is very important to distinguish permanent fault from temporary faults
and to apply an adaptive algorithm in each case. In this respect, adaptive S.P.A.R offers many
advantages such as increased rate of successful reclosure, improved system stability and
reduction in system and equipment shock under a permanent fault.
2.6.1 Auto Reclosure Relaying System
A research work on auto reclosure scheme[16] proposes the utilization of adjustable dead
times by accurately identifying arc extinction times. It is inferred that if the dead time is too
short, is possible to reignite the arc, which leads to re-striking arc faults, so we must ensure a
long enough dead time to ensure improvement in power system stability and reduction in
system shock can be achieved easily by applying adaptive reclosing. In this study, the
adaptive S.PA.R is implemented using artificial neural network.
2.7 System Configuration
Although the fundamentals of transmission line protection apply in almost all system
configurations, there are different applications that are more or less dependent upon specific
situations.
Operational Voltages- transmission lines will be those lines operating at 138kV and
above, sub transmission lines are 34.5kV to 138kV, and distribution lines are below
34
34.5kV. These are not rigid definitions are only used to generically identify a
transmission system and connote the type of protection usually provided. The higher
voltage systems would normally be expected to have more complex, hence more
expensive, relay systems. This is so because higher voltages have more expensive
equipment associated with them and one would expect that this voltage class is more
important to the security of the power system. The higher relay costs, therefore, are
more easily justified.
Multi-Terminal Lines - occasionally, transmission lines may be tapped to provide
intermediate connections to additional sources without the expense of a circuit
breaker or other switching device. Such a configuration is known as a multi-terminal
line and, although it is an inexpensive, measure for strengthening the power system, it
presents special problems for the protection engineer. The difficulty arises from the
fact that a relay receives its input from the local transducers, i.e., the current and
voltage at the relay location. The total fault current is the sum of the local current plus
the contribution from the intermediate source, and voltage at the relay location is the
sum of the two voltage drops, one of which is the product of the unmonitored current
and the associated line impedance.
Line Length- the length of a line has a direct effect on the type of protection, the
relays applied, and the settings. It is helpful to categorize the line length as “short,”
“medium,” or “long” as this helps establish the general relaying applications although
the definition of “short,” “medium,” and “long” is not precise. A short line is one in
which the ratio of the source to the line impedance of a line varies more with the
nominal voltage of the line than with its physical length or impedance. So a “short”
line at one voltage level may be a “medium” or “long” line at another.
2.8 Transmission line protection
The study of transmission line protection presents many fundamental relaying considerations
that apply, in one degree or another, to the protection of other types of power system
protection. Each electrical element of course will have problems unique to itself, but the
concepts of reliability, selectivity, local and remote backup, zones of protection, coordination
and speed which may be present in the protection of one or more other electrical apparatus
are all present in the considerations surrounding transmission line protection.
Since transmission lines are also the links to adjacent lines or connected equipment,
transmission line protection must be compatible with the protection of all of these other
elements. This requires coordination of settings, operating times and characteristics[17]. The
purpose of power system protection is to detect faults or abnormal operating conditions and
to initiate corrective action. Relays must be able to evaluate a wide variety of parameters to
establish that corrective action is required. Obviously, a relay cannot prevent the fault. Its
primary purpose is to detect the fault and take the necessary action to minimize the damage to
the equipment or to the system. The most common parameters which reflect the presence of a
35
fault are the voltages and currents at the terminals of the protected apparatus or at the
appropriate zone boundaries. The fundamental problem in power system protection is to
define the quantities that can differentiate between normal and abnormal conditions. In this
study, Transmission line protection is carried out in the following categories; fault detection,
fault classification, fault location and adaptive auto reclosure technique
2.8.1 Fault Detection & Location
When a fault occurs on a transmission line, it is very important to quickly detect and locate it
in order to make necessary repairs and to restore power as soon as possible, the time needed
to determine the fault point along the line will affect the quality of power delivery. Fault
location has been a subject of interest for many years. Many fault locating algorithms have
been developed; the power frequency based approach[18], transient signals based
approach[19] and super imposed component based approach[20]. Currently the most widely
used method of overhead line fault location is to determine apparent reactance of the line
during the time the fault is flowing and to convert the Ohmic result into distance based on the
parameter of the line, however this method is subject to errors when the fault resistance is
varied and the line is fed from both ends.
Many successful applications of artificial neural networks to power systems have
demonstrated the use of artificial neural networks for direction estimation[21], faulted phase
selection[8], fault location under CT saturation. However these applications merely use the
A.N.N ability of classification i.e. the ANNs output of 1 or 0 and mainly work on singly fed
source without consideration to different zones of protection. In this study, three fault
detectors carried out on all zones of protection as well as fault locators are implemented using
A.N.N.
2.8.2 Fault Classification
Overhead transmission lines are vulnerable to faults since they extend over long distances
and are often exposed to severe climate conditions. Symmetrical faults and unsymmetrical
faults can easily be classified into transient and permanent faults. The fault classification
problem is mostly treated as a pattern recognition problem[22][23] which is implemented
using the back propagation learning algorithm, the usual case in many research works,
however this algorithm has generalization and convergence problems associated with it, an
algorithm with convergence issues has a high percentage error thus low effectiveness[24].
The paper[3] also utilizes feed forward ANN to fault classification current signals only as
input signals due to high economical cost of such devices. The use of only current signals
gives room for errors in fault detection and location for faulted phases to ground takes into
account zero sequence and voltage of faulted phases thus in this study, a different approach
that employs both voltage and current signals as well as zero sequence of both quantities is
used as input to the neural network designed. The approach implemented in most research
work treats fault classification as a pattern recognition problem carried out using the feed
forward back propagation algorithm[3][25]; however this algorithm is beset with
36
generalization problems if the input data set is not large enough which cause intolerable
percentage error. A different approach is treated in this work, the use of unsupervised
competitive layer self-organised map algorithm implemented as a clustering problem. Results
shown in chapter four proves the problems inherent in the previous algorithm are taken care
of with this approach.
2.8.3 Enhanced Power System Protection
The traditional line protection scheme based on fundamental frequency components of the
fault generated transient voltage and current signals can be classified into two categories;
non-unit protection and unit protection. The non-unit protection schemes use one end
transmission line data whilst the unit protection schemes use data from the two ends. The
non-unit protection such as distance relay cannot protect the entire length of the primary line
because it cannot differentiate the internal faults from external occurring around multi zone
boundaries. Back up protection may be introduced as a trade-off for protecting the entire
length of the transmission line. For unit protection such as pilot protection, it usually requires
a communication link to transmit the blocking or transfer tripping signals therefore the
reliability of the protection scheme highly relies on the reliability of the communication
link[5][6][11]. The cost of communication link also needs to be taken into account. Recently,
new techniques using high frequency components of the faulted generated signals were
studied and some useful solutions were obtained[11][12][15]. An approach known as
“adaptive single pole auto reclosure scheme” for solving the disadvantages of conventional
non-unit protection scheme was proposed. This approach introduces the possibility of
differentiating the permanent and transient fault using data from one end only; other proposed
solutions are boundary protection and adaptive distance protection[10].
Regarding the fault selection or classification, the traditional method is based on the
fundamental frequency phasors. The feature formed by a non-linear ratio between voltage
and current phasors is compared to the threshold to find out the faulted phase. This kind of
method is affected by different conditions such as fault resistance, mutual coupling of parallel
lines e.t.c. This study proves an alternative solution in the use of neural network based
algorithm based on fast Fourier transform and self-organized neural network and back
propagation neural network to realise fault classification as well as adaptive reclosure
scheme. A similar research[12][26] work utilized same self-organized neural network for
fault classification as well as adaptive reclosure for fault classification and boundary
protection. Although different, this study proves that both algorithms can be combined to
solve the generalization problems associated with fault classification problems associated
with only back propagation algorithm. To further illustrate the functionality of neural
network and its various algorithms, a summary of neural network description, back
propagation algorithm and self-organised neural network is presented in the next section.
37
2.9 Artificial Neural Network
A neural network is a massively parallel distributed processor made up of simple processing
unit that has a natural propensity for storing experimental knowledge and making it available
for use. Artificial neural network is inspired by biological neural network and is composed of
a number of interconnected units known as artificial neurons. Artificial neurons are used to
transmit signal from one layer to the other, its complex network of interconnected neurons is
analogous to firing of electrical pulses via its connections that leads to information
propagation. A.N.N. consists of three layers i.e. input layer, hidden layer and output layer
having number of neurons present in it[8].
Neural networks are primarily of three basic learning algorithms such as supervised learning,
unsupervised and reinforced learning. For the sake of this work only supervised and
unsupervised training algorithm is utilized. The supervised learning algorithm is the popular
error back propagation for diagnosis of faults in power systems. However due to slow
training speeds and generalization issues, the unsupervised was also adapted in this work. A
review of the multilayer perceptron, error back propagation as well as unsupervised training
algorithm is carried out for the purpose of better understanding of its functionality as applied
to this research.
2.9.1 Multilayer Perceptron
The cascaded layer perceptron is an example notation of the multilayer perceptron as
illustrated in fig 9 below. The output of the first network is the input to the second network,
and the output of the second network is the input to the third network. Each layer may have a
different number of neurons, and even a different transfer function. The weight matrix for
the first layer is written as h and the weight matrix for the second layer is h. to identify
the structure of a multilayer network, the following shorthand notations, where the number of
inputs is followed by the number of neurons in each layer[27].
i j j jE (2.43)
38
2.9.2 Feed forward Artificial Neural Network & Back Propagation Learning Algorithm
The feed forward multilayer network was utilized and training done using the back
propagation algorithm. The F.F.N.N consists of an input layer, hidden layer and output layer
representing the response of the network after training[3]. The log sigmoid transfer function
is the transfer function implemented with this algorithm[27]; this transfer function takes in
the input and squashes it into this expression
O = Tk,l (2.44)
Back propagation is an approximate steepest descent algorithm, in which the performance
index is the mean square error.
OgT = mgT(ngTOg + ogT)mpq r = 0,1, … r 1 (2.45)
M is the number of layers in the network. The neurons in the first layer receive external
inputs OA = t which provides the starting point for (1). The output of the neurons in the last
layer are considered the network outputs
O = Og (2.46)
The steepest descent algorithm for approximate mean square error is
ngu,v(w + 1) = ngc(w)∝ xYxyz,| (2.48)
Fig 2.9: three layer network (from M. T. Hagan and M. H. Beale, “Neural Network Design.”,2nd
edition,ebook
39
Where α is the learning rate
oug(w + 1) = og(w) ~Y~9z (2.49)
xYxy,|z = xY
xz ∗ xzxyz,| (2.50)
xYx9z = xY
xz ∗ xzx9z (2.51)
jg = xYxz (2.52)
Zug = ∑ hu,vgOvg! + ougz,Sv (2.53)
xzxy,|z = Ovg!, xz
x9z = 1 (2.54)
Approximate steepest algorithm is
hu,vg(w + 1) = hu,vg(w)∝ jugOv g! (2.56)
oug(w + 1) = oug(w) jug (2.57)
In matrix form, this becomes
og(T) = og()∝ jg (2.58)
Afterwards comes computing the sensitivities Sm , which requires application of chain rule
and gives us the term back propagation, because it describes a recurrence relationship in
which the selectivity at layer m is computed from the sensitivity at layer m+1
ZgTZvg =
ZgTZg ZgT
Zg ZgTZgjg
ZgTZg ZgT
Zg ZgTZgjrZzSgT
Zg ZzS gTZg ZzS gT
Zz g
2.9.3 Unsupervised Learning Algorithm
In unsupervised learning, the weights and biases are modified in response to network inputs
only. There are no target outputs available. At first glance this might seem to be impractical.
How can you train a network if you don’t know what it is supposed to do? Most of these
algorithms perform some kind of clustering operation. They learn to categorize the input
patterns into a finite number of classes. This is especially useful in such applications as vector
40
quantization. A good example of unsupervised learning algorithm is the self-organized map
function[27].
2.9.3.1 Self Organized Map Function
In order to emulate the activity bubbles of biological systems, without having to implement
the nonlinear on-centre/off-surround feedback connections, Kohonen designed the following
simplification. His self-organizing feature map (SOFM) network first determines the winning
neuron using the same procedure as the competitive layer. Next, the weight vectors for all
neurons within a certain neighbourhood of the winning neuron are updated using the
Kohonen rule,
h() = h( 1)+∝ .() h( 1)/
= (1∝)uh( 1)+∝ () ∈ u∗([), (2.59)
Where the neighbourhood contains the indices for all of the neurons that lie within a radius of
the winning neuron ∗: ([) = .c, [uv [/.
When a vector is presented, the weights of the winning neuron and its neighbours will move
towards. The result is that, after many presentations, neighbouring neurons will have learned
vectors similar to each other. To demonstrate the concept of a neighbourhood, consider the
two diagrams shown in Figure 10. The left diagram illustrates a two-dimensional
neighbourhood of radius around neuron. The right diagram shows a neighbourhood of radius
.The definition of these neighbourhoods would be
Fig 2.10: Self Organising Map Neighbourhoods
41
We should mention that the neurons in an SOFM do not have to be arranged in a two-
dimensional pattern. It is possible to use a one-dimensional arrangement, or even three or
more dimensions. For a one-dimensional SOFM, a neuron will only have two neighbours
within a radius of 1 (or a single neighbour if the neuron is at the end of the line). It is also
possible to define distance in different ways. For instance, Kohonen has suggested
rectangular and hexagonal neighbourhoods for efficient implementation. The performance of
the network is not sensitive to the exact shape of the neighbourhoods.
The diagram in the left margin shows the initial weight vectors for the feature map. Each
three-element weight vector is represented by a dot on the sphere. (The weights are
normalized therefore they will fall on the surface of a sphere.) Dots of neighbouring neurons
are connected by lines so you can see how the physical topology of the network is arranged in
the input space. The diagram to the left shows a square region on the surface of the sphere.
We will randomly pick vectors in this region and present them to the feature map. Each time
a vector is presented, the neuron with the closest weight vector will win the competition. The
winning neuron and its neighbours move their weight vectors closer to the input vector (and
therefore to each other). For this example we are using a neighbourhood with a radius of
1.The weight vectors have two tendencies: first, they spread out over the input space as more
vectors are presented; second, they move toward the weight vectors of neighbouring neurons.
These two tendencies work together to rearrange the neurons in the layer so that they evenly
classify the input space.
Fig 2.11: Self-Organizing Feature Map (M. T. Hagan and M. H. Beale, “Neural Network Design.”,2nd
edition,ebook
42
2.9.4 Clustering
In clustering problems, you want a neural network to group data by similarity. For example,
market segmentation can be done by grouping people according to their buying patterns, data
mining can be done by partitioning data into related subsets, and bioinformatics analysis can
be done by grouping genes with related expression patterns. In clustering problems, we
generally don’t have a set of network targets available, so clustering networks are trained by
unsupervised training algorithms. Instead of training a network to produce a desired response,
we want to analyze a data set to look for hidden patterns. There are many application areas
for clustering. It is widely used in data mining, in which we analyze large data sets to identify
similarities within subsets of the data. It is used in city planning, when town councils
apportion regions of the city into areas of similar home type and land usage. It is used in
image compression, in which a small set of prototype sub-images are identified and combined
to represent a large collection of images[27]. It is used in speech recognition systems, in
which speakers are clustered into categories in order to simplify the problem of speaker-
independent recognition. Clustering is used by marketers to identify distinct groups in their
customer bases. It has also been used to organize large bibliographic data bases so that related
material can be quickly accessed. The neural network that we will use in this application is
the self-organizing feature map (SOFM). This clustering network has a unique attribute that
enables us to visualize large data sets in many dimensions.
43
CHAPTER THREE
METHODOLOGY FOR RESEARCH
The supervised and unsupervised learning algorithm of neural networks discussed in previous
chapter is used in the implementation of the fault detection and fault location as well as
adaptive auto reclosure scheme. The methodology of this research describes in details the
neural network based approach for fault detection, fault location, fault classification and
adaptive auto reclosure.
3.1 Power System under Consideration
The transmission line network considered in this research is the Onistha, Benin, and New
Haven 330kV transmission network. A model of this work is simulated using Matlab
Simulink R2014a. The transmission lines are represented by four distributed parameters, two
sources, one at the sending end and another at the receiving end. The sending end source
consists of a synchronous generator and a three phase step-up transformer. The synchronous
generator gives an output of 13.8kV, the step up transformer steps it up to a peak value of
346kV for transmission to Onistha transmission station, which is used as the reference station
for this model supplying Benin T/S and New Haven T/S respectively. Each T/S is assigned a
particular load according to protocols by the electricity regulatory body of Nigeria. This load
parameter used in the simulation is ascertained by calculating the average MW hourly
reading taken from the bus data log book at the Onistha T/S. A 3-ϕ VI measurement block
from the Simulink power library is used to represent the several buses used in the simulated
network. A 3-ϕ circuit breaker block also used but modelled with parameters gotten from the
New Haven T/S. A Fault block is used to induce different faults at varied fault resistance
however the same fault inception time was used for the entire simulation. The summary of
collated data used in the simulation are listed below, with figures represented as appendix A,
B, C, D;
Line data
Bus data
Generator data
Single line diagram of each network considered
Transformer data
Fault data
3.2 Data Pre-processing using Fast Fourier Transform
The Discrete Fourier transform of a sequence or it’s inverse. Fourier analysis converts a
signal from its original domain (often time or space) to a representation in the frequency
domain and vice versa. An F.F.T rapidly computes such transformations by factorizing the
D.F.T matrix into a product of sparse (mostly zero) factors. As a result, it manages to reduce
its complexity of computing the D.F.T from Ѻ (n2) which arises if one simply applies the
44
definition of D.F.T, to Ѻ (ZpZ), where n is the data size. Many F.F.T algorithms are also
much more accurate than evaluating the D.F.T definition directly as discussed below.
Let A, … . . , ! be the complex numbers. The D.F.T formula is given by
!l
!
A
By far the most commonly used F.F.T is the Cooley-Turkey algorithm[28]. This is a divide
and conquer algorithm that recursively breaks down a D.F.T of any composite size N=N1N2
into many smaller D.F.T of sizes N1 and N2 along with Ѻ (N) multiplications by complex
roots of unity. The known use of Cooley-Turkey algorithm is to divide the transform into two
pieces of size N/2 at each step, and is therefore limited to power of two sizes, but any
factorization can also be used in general. The F.F T algorithm is used to obtain the voltage
and current magnitudes of each phase; the output of the F.F.T is scaled accordingly and used
as input to the neural network. Fig 12 shows the waveform obtained for voltage and current
when a line to ground fault is introduced on the line. Fig 13 shows the F.F.T window
displaying the magnitudes with respect to fundamental and harmonic frequencies.
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (seconds)
da
ta
Time Series Plot:
Fig 3.1 Fault Current Graph of A-G fault at 50Km, Fault Resistance 30ohm Zone 1
45
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
Time (seconds)
da
ta
Time Series Plot:
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-0.2
0
0.2
Selected signal: 10 cycles. FFT window (in red): 3 cycles
Time (s)
Fig 3.2 voltage signal of A-G fault at 50Km, fault resistance 30ohm zone 1
Fig 3.3 F.F.T analysis for voltage waveform after A-G fault
46
3.3 Overview of the Training Process
Two important steps in the application of neural networks for any purpose are training and
testing. Training is the process by which the neural network learns from the inputs and
updates its weight accordingly. In order to train the neural network, we need a set of data
called training data which is a set of input output pairs fed into the network. Thereby, we
teach the neural network what the output should be, when that particular input is fed into it.
The ANN slowly learns the training set and slowly develops an ability to generalize upon this
data and will eventually be able to produce an output when a new data is fed into it. During
the training process, the neural network’s weights are updated with the prime goal of
minimizing the performance function. This performance function can be user defined, but
usually feed-forward neural networks employ Mean Square Error as the performance
function and the same is adopted throughout this work. The outputs, depending upon the
purpose of the neural network might be fault detection, the type of fault or the location of the
fault on the transmission line.
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
0
0.2
0.4
0.6
0.8
Selected signal: 10 cycles. FFT window (in red): 3 cycles
Time (s)
Fig 3.4 F.F.T analysis of current waveform after fault
47
For the task of training the neural networks for different stages, sequential feeding of input
and output pair has been adopted. In order to obtain the training set, the fault distance and
fault resistance are varied simultaneously for each type of fault. A total of 426 fault samples
are used in this implementation throughout this work.
3.4 Overview of Testing Process
The next important step to be performed before the application of artificial neural networks is
to test the trained network. Testing the neural network is very important in order to make sure
the trained network can generalize well and produce desired outputs when new data is
presented to it.
There are several techniques used to test the performance of a trained network, one of such
technique is to plot the best linear regression fit between the actual neural networks and
desired targets. Analysing the slope of this line gives us an idea on the training process.
Ideally the slope should be 1. Also, the correlation coefficient(r), of the outputs and the
targets measures how well the ANN’s outputs track the desired targets. The closer the value
of ‘r’ is, to 1, the better the performance of the neural network. Another technique employed
to test the neural network is to plot the confusion matrix and look at the actual number of
cases that have been classified positively by the neural network. Ideally this percentage is 100
which means there has been no confusion in the classification process hence if the confusion
matrix indicates very low positive classification rates, it indicates that the neural network
might not perform well. The last and very obvious means of testing the neural network is to
present new data different from the dataset used for the training process. If the average
percentage error in the A.N.N’s output is acceptable, the neural network has passed the test
and can be readily used for future use. The flow chart in fig 3.5 below illustrates the
algorithm adopted for fault diagnostic using neural network for this work.
48
Receive Voltage &
current Values
Data pre-processing using FFT
Fault on Phase C Fault on Phase B Fault on Phase C
ANN Fault Classifier
Single Phase Fault
Phase-Phase Fault
Line-Line
Ground Fault
Three Phase Fault
No Fault
Three Phase
Fault Location
Line-Line-
Ground ANN
Fault Location
Phase-Phase ANN Fault
Location
Single Phase ANN Fault
Location
Fault Location
Fig 3.5 flowchart of ANN Fault Diagnostic Algorithm
49
3.5 Performance Evaluation
Neural networks represent a technology that is at the mercy of the data. The training data
must span the full range of the input space for which the network will be used. The amount of
data required depends on the complexity of the underlying problem case we are trying to
implement. For the model in this research, the fault cases has many inflexion points thus the
need for large amount of data. The performance function for pattern recognition is cross
entropy given by the expression
() = − ∑ ∑ u,Z 7,, f¡ (3.1)
Fig 5-6 represents the confusion matrix and receiver operating characteristics plot realised
after the training of the network Minimizing cross entropy error results in good classification,
lower values are better zero means no error. Confusion matrix is a table whose columns
represent the target class and whose rows represent the output class. The diagonal columns
represent good classification as shown in fig 7. The values for C.E show the neural network
for the fault detector (pattern recognition) is adequate.
In the case of the fault locator, a useful tool used to analyse the neural network is a regression
between the trained network outputs and the corresponding targets, this is expressed as
O = r + ¢ + £ (3.2)
M=slope, C=offset, is the target value, O is a trained network output, £ is the residual
error of the regression. In addition to computing the regression coefficients, the correlation
coefficient between the and O which is known as R value.
i = ∑ . − /(O −¡ O¥) (3.3)
Where j = ¦ ¡! ∑ ( − ) §¡! (3.4)
and j7 = ¦ ¡! ∑ (O − O¥¡ ) (3.5)
The square of the correlation can also be used.
50
3.6 Clustering with Self Organized Neural Network Algorithm
The major advantage of neural network is that it can take into account several features of the
input signals simultaneously and compare the patterns according to their mutual similarity
instead of the ‘hard’ thresholds.
There are several types of neural networks used for power system protection the (M.L.P)
neural network with back propagation algorithm is one that was dominantly used in the
power system studies since it can be easily realized. Dealing with large input set, selecting
the number of hidden neurons, and facing convergence problems are inherent issues when
applying M.L.P neural networks.
Clustering is the process of training a neural network on patterns so that the network comes
up with its own classifications according to pattern similarity and relative topology. The
Collect/Pre Process
Data
Select Network
Type/Architecture
Select Training
Algorithm
Initialize Weights &
Train Network Analyze Network
Performance
Analyze Network
Performance
Fig 3.6 Block Diagram of Neural Network Training Procedure
51
scaled fault data used for the fault detector and fault locator is used as input to the network.
The self-organised learning algorithm is utilized; no target is used for this algorithm. Several
plots are used to test the generalization properties of the trained network such as S.O.M
topology, S.O.M neighbour distances, S.O.M input planes, S.O.M sample hits, S.O.M weight
positions.
3.7 Neural Network Methodology for Adaptive Reclosure Scheme
Adaptive auto reclosing on overhead lines is the ability to distinguish between a transient or
permanent fault following a short circuit and then issue a reclose signal if and only if the
transient fault no longer exists. Permanent fault has a constant resistance since it usually
involve a physical short circuit due to vegetarian, downed line, or broken conductor. In
contrast, a transient fault involves arcing across the arcing horns and is usually caused by
lightning or adverse weather conditions.
The behaviour of the arc occurs in two stages, before and after the circuit breaker opens, the
primary arc is a heavy current, high energy arc, fed by the short circuit on the associated
phase conductor. The secondary arc initiates after the CB opens, following the single phase
breaking opening, the healthy phases( those that remain energized) mutually couple and drive
a highly non-linear lower current secondary arc on the faulted phase. When this arc finally
extinguishes, it is safe to reclose the CB and brings the line back into normal service.
The notable difference between second arcing and a permanent fault gives rise to the
possibility of robust diagnosis between the two cases. However, there is a complex interplay
of parameters that determine voltage signatures some of which cannot be known pre-fault.
Researchers have addressed this problem a number of ways, including signal processing and
neural networks[15], fuzzy logic[29] and wavelet transforms[12]and straightforward
numerical techniques[15][30]. However only the A.N.N have been deployed on a real system
and documented in the literature. The flow chart displayed in fig 3.7 shows the algorithm
carried out to achieve the neural network adaptive auto reclosure.
52
Voltage & Current Input
Pre-Process Input Samples
Using FFT
Single Phase
Fault
Phase to phase
Fault
Line-Line Ground
Fault
Three Phase
Fault
No Fault
Adaptive Fault Classifier
If Fault
Time >0.14s Do Not Reclose Reclose Yes No
Yes
Yes
Yes
Yes
No
No
No
No
Figure 3.7 Flow Chart of Adaptive Auto Reclosure Scheme
53
3.8 Arc Modelling in Adaptive Auto Reclosing Schemes
In AA schemes, it is necessary to determine whether a fault is transient or permanent.
Transient faults exhibit arcing behaviour with high frequency signatures due to dynamic
resistance.
Arcing behaviour can be described by the primary and secondary stages. The primary arc is
in the period before CB opens and is due to fault current flowing from energised phase to
ground. The lower current secondary is saturated by the mutual coupling between the faulted
and healthy phases and only present when one or more of the phases remain energised.
The behaviour of both arcs are governed by time varying conductance, and can be described
by the dynamic equation for unconstrained arcs in the air.
¨©¨ = ª (« − ) (3.6)
G is stationary arc conductance; g is the time dependent arc conductance and ¬ is the time
constant. During a single phase to ground, the current and voltage waveforms were measured
at the O.H.L terminating bus bars in front of the breakers. Reduced current is due to much
less real power transfer on both circuits.
54
CHAPTER FOUR
EXPERIMENTAL RESULTS AND DISCUSSION
4.1 Structure and Training of Neural Fault Detector
The fault detection task can be formulated as a pattern classification problem. The feed
forward multilayer network used to classify the input dataset into fault/no-fault response
using the back propagation algorithm. The datasets for the input are six consecutive samples
sampled at 2KHz corresponding to different types of faults (a-g ,b-g, c-g, a-b-g, a-c-g, b-c-g,
a-b-c, a-b-c-g) where a, b, c are related to the different phases and g corresponds to ground at
various locations and fault resistance on the three zones .the distance of the lines on the three
zones are; line 1 spans a length of 95km,line2 137km,and line 3 95km. For this simulation,
the reach settings of the relays at the different zones are; zone 1(91% of line 1), zone 2(99.5%
of line2), zone 3(100% of line 3). Fault resistance (3Ω-62Ω).
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-3
-2
-1
0
1
2
3
Time (seconds)
Cu
rre
nt
Time Series Plot:
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-0.2
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
Time (seconds)
Vo
lta
ge
Time Series Plot:
Fig 4.1 current signal of B-C fault, 30Km, fault resistance 48ohms zone 2
Fig 4.2 Voltage signal A-B-C Fault at 88Km, fault resistance 60 ohms zone 3
55
Figs 4.1-4.3 shows the time plot waveform of the voltage and current post fault condition for
varied fault types at different protection zones in the transmission network modelled in the
Matlab Simulink Environment. It is easily observed, the sag and spikes of faulted phase in
relation to other phases. The effect of the faulted phase on other phases is as a result of
mutual coupling between healthy and faulted phase. This signal is imported to the Matlab
workspace for use in the F.F.T window to get the magnitudes of individual phases for current
and voltage signals at fundamental frequency as well as other harmonic frequencies. The
maximum frequency set for total harmonic distortion calculations is set at Nyquist frequency.
The Nyquist theorem states that the frequency for T.H.D calculations should be at least twice
the maximum frequency of the signal in question.
The next step is to divide the total dataset to be used for the training process as well as
testing data. The data samples were divided as such; 70% of the input dataset to be used for
training, 15% to be used for validation and 15% to be used for testing. The output of the
neural network is just a yes or a no (1 or 0) depending on whether or not a fault has been
detected[31].
The Levenberg-Marquardt optimization technique was employed for this classification
problem[3]. Three fault detectors are designed using current values alone, voltage values
alone and voltage and current values combination. The figures 4.4-4.5b show the
performance plots for the fault detector neural network.
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Time (seconds)
Cu
rre
nt
Time Series Plot:
Fig 4.3 Current Signal A-B-C fault at 88Km, fault resistance 60ohms zone 3
56
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
True P
ositive R
ate
Training ROC
Class 1
Class 2
Class 3
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
True P
ositive R
ate
Validation ROC
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
True P
ositive R
ate
Test ROC
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
True P
ositive R
ate
All ROC
1 2 3
1
2
3
14
34.1%
0
0.0%
0
0.0%
100%
0.0%
0
0.0%
12
29.3%
0
0.0%
100%
0.0%
0
0.0%
0
0.0%
15
36.6%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut C
lass
Training Confusion Matrix
1 2 3
1
2
3
3
33.3%
0
0.0%
0
0.0%
100%
0.0%
0
0.0%
3
33.3%
0
0.0%
100%
0.0%
0
0.0%
0
0.0%
3
33.3%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut C
lass
Validation Confusion Matrix
1 2 3
1
2
3
3
33.3%
0
0.0%
0
0.0%
100%
0.0%
0
0.0%
5
55.6%
0
0.0%
100%
0.0%
0
0.0%
0
0.0%
1
11.1%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut C
lass
Test Confusion Matrix
1 2 3
1
2
3
20
33.9%
0
0.0%
0
0.0%
100%
0.0%
0
0.0%
20
33.9%
0
0.0%
100%
0.0%
0
0.0%
0
0.0%
19
32.2%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut C
lass
All Confusion Matrix
Fig 4.4 Receiver Operating Characteristics of fault detector network using current values
Fig 4.4b Confusion Matrix of Fault Detector Network zone 1 current values
57
4.2 Discussion of Figures for A.N.N. Fault Detector
The figures 4.4-4.5b show receiver operating characteristics and confusion matrix for A.N.N.
fault detector using pre-processed current values alone as well as combining current and
voltage values as input data. Confusion matrix is a table whose columns represent the target
class and whose rows represent the output class. The green squares show the level of accurate
responses and red squares show the level of incorrect responses. A high number in green
squares shows a high accuracy of classification and the zero value signifies no
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
True Positive Rate
Training ROC
Class 1
Class 2
Class 3
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
True Positive Rate
Validation ROC
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
True Positive Rate
Test ROC
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
True Positive Rate
All ROC
1 2 3
1
2
3
11
26.8%
0
0.0%
0
0.0%
100%
0.0%
0
0.0%
16
39.0%
0
0.0%
100%
0.0%
0
0.0%
0
0.0%
14
34.1%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut Class
Training Confusion Matrix
1 2 3
1
2
3
6
66.7%
0
0.0%
0
0.0%
100%
0.0%
0
0.0%
2
22.2%
0
0.0%
100%
0.0%
0
0.0%
0
0.0%
1
11.1%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut Class
Validation Confusion Matrix
1 2 3
1
2
3
3
33.3%
0
0.0%
0
0.0%
100%
0.0%
0
0.0%
2
22.2%
0
0.0%
100%
0.0%
0
0.0%
0
0.0%
4
44.4%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut Class
Test Confusion Matrix
1 2 3
1
2
3
20
33.9%
0
0.0%
0
0.0%
100%
0.0%
0
0.0%
20
33.9%
0
0.0%
100%
0.0%
0
0.0%
0
0.0%
19
32.2%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut Class
All Confusion Matrix
Fig 4.5b: Confusion Matrix for fault detector using voltage and current values
Fig 4.5 Receiver Operating Characteristics of Fault Detector using Current and Voltage values
58
misclassification occur. Figure 4.4.b and 4.5b shows 100% in the green squares showing
maximum classification and zero value in the red squares showing no misclassification of the
A.N.N. fault detector on each phase. The R.O.C. factor is a plot of receiver operating
characteristics. The coloured line in each axis is a deviation between the output and target
class. The figure 4.4a and 4.5a shows no deviation thus the output corresponds perfectly to
the target output fed to it.
4.3 Structure and Training of Fault Locator
The fault location task can be formulated as an approximation function problem[31][32]. The
back propagation algorithm was utilized in training the network; the inputs are the
magnitudes of voltage and current phasors corresponding to fundamental frequency of 50Hz.
The number of inputs to the network as well as neurons in the input and hidden layers are
selected empirically through trial and error procedure on various network configurations in
order to obtain appropriate network with satisfactory performance. The network for fault
location was trained using Levenberg-Marquardt and Scaled Conjugate Gradient algorithm as
optimization techniques. Three fault locators7, 9, : were designed by using scaled
current values, voltage values, and voltage and current combination. The output consists of
one neuron to estimate fault location. The simulated fault samples used for fault detector
forms the input data sets for fault locator network. The performance graph of the trained
network are shown in figures 4.6-4.16.
0.2 0.4 0.6 0.8
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Target
Output ~= 1*Target + -0.0057
Training: R=0.9998
Data
Fit
Y = T
0.4 0.5 0.6 0.7
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
Target
Output ~= 1.1*Target + -0.028
Validation: R=1
Data
Fit
Y = T
0.2 0.4 0.6
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Target
Output ~= 1*Target + -0.033
Test: R=0.99999
Data
Fit
Y = T
0.2 0.4 0.6 0.8
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Target
Output ~= 1*Target + -0.013
All: R=0.99879
Data
Fit
Y = T
Fig 4.6 Plot of regression fit for fault location on zone 1
59
0
0.5
1
1.5
2
2.5
3
3.5
4
Error Histogram with 20 Bins
Insta
nces
Errors = Targets - Outputs
-0.0
1449
-0.0
12
-0.0
095
-0.0
0701
-0.0
0452
-0.0
0202
0.0
00472
0.0
02966
0.0
05461
0.0
07955
0.0
1045
0.0
1294
0.0
1544
0.0
1793
0.0
2043
0.0
2292
0.0
2541
0.0
2791
0.0
304
0.0
329
Training
Validation
Test
Zero Error
0.1 0.2 0.3 0.4 0.5 0.6
0.1
0.2
0.3
0.4
0.5
0.6
Target
Outp
ut ~= 1
*Targ
et + -6.2
e-0
5
Training: R=1
Data
Fit
Y = T
0.44 0.46 0.48 0.5 0.52 0.54
0.44
0.46
0.48
0.5
0.52
0.54
Target
Outp
ut ~= 1
.2*T
arg
et + -0.1
2
Validation: R=0.99811
Data
Fit
Y = T
0.3 0.4 0.5 0.6
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
Target
Outp
ut ~= 1
*Targ
et + 0
.0095
Test: R=0.99985
Data
Fit
Y = T
0.1 0.2 0.3 0.4 0.5 0.6
0.1
0.2
0.3
0.4
0.5
0.6
Target
Outp
ut ~= 1
*Targ
et + -0.0
0053
All: R=0.99952
Data
Fit
Y = T
Fig 4.7 Error Histogram of fault locator using current values on zone 1
Fig 4.8 Regression plot for fault locator using current values on zone 2
60
0
1
2
3
4
5
6
7
8
9
10
11Error Histogram with 20 Bins
Insta
nces
Errors = Targets - Outputs
-0.0
1467
-0.0
1305
-0.0
1143
-0.0
0982
-0.0
082
-0.0
0658
-0.0
0497
-0.0
0335
-0.0
0173
-0.0
0011
0.0
01502
0.0
03119
0.0
04736
0.0
06353
0.0
07969
0.0
09586
0.0
112
0.0
1282
0.0
1444
0.0
1605
Training
Validation
Test
Zero Error
0.2 0.4 0.6 0.8
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Target
Outp
ut ~= 1
*Targ
et + -4.1
e-0
5
Training: R=1
Data
Fit
Y = T
0.2 0.25 0.3 0.35 0.4 0.450.2
0.25
0.3
0.35
0.4
0.45
Target
Outp
ut ~= 1
*Targ
et + 0
.012
Validation: R=0.99946
Data
Fit
Y = T
0.2 0.3 0.4 0.5
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Target
Outp
ut ~= 1
.1*T
arg
et + -0.0
25
Test: R=0.9996
Data
Fit
Y = T
0.2 0.4 0.6 0.8
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Target
Outp
ut ~= 1
*Targ
et + 0
.0018
All: R=0.99949
Data
Fit
Y = T
Fig 4.9 Error Histogram for fault location using current values on zone 2
Fig 4.10 Regression fit for fault locator using current values on zone 3
61
0.2 0.4 0.6 0.8
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Target
Outp
ut ~= 1
*Targ
et + -0.0
0062
Training: R=0.99998
Data
Fit
Y = T
0.05 0.1 0.15 0.20.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
Target
Outp
ut ~= 0
.78*T
arg
et + 0
.047
Validation: R=0.99815
Data
Fit
Y = T
0.25 0.3 0.35 0.4
0.24
0.26
0.28
0.3
0.32
0.34
0.36
0.38
0.4
Target
Outp
ut ~= 1
.1*T
arg
et + -0.0
35
Test: R=0.99928
Data
Fit
Y = T
0.2 0.4 0.6 0.8
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Target
Outp
ut ~= 0
.99*T
arg
et + 0
.0096
All: R=0.99916
Data
Fit
Y = T
0
1
2
3
4
5
6
7
8
9
Error Histogram with 20 Bins
Insta
nces
Errors = Targets - Outputs
-0.0
3457
-0.0
3207
-0.0
2958
-0.0
2709
-0.0
2459
-0.0
221
-0.0
196
-0.0
1711
-0.0
1462
-0.0
1212
-0.0
0963
-0.0
0713
-0.0
0464
-0.0
0215
0.0
00347
0.0
02841
0.0
05335
0.0
07829
0.0
1032
0.0
1282
Training
Validation
Test
Zero Error
Fig 4.11 Regressions fit for fault locator using voltage and current values on zone 1
Fig 4.12: Error histogram for fault locator using voltage and current values on zone 1
62
0
2
4
6
8
10
12
14
16
18
20
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
FAULT LOCATOR PLOT
INPUT VALUES DISTANCE
0.1 0.2 0.3 0.4 0.5 0.6
0.1
0.2
0.3
0.4
0.5
0.6
Target
Outp
ut ~= 0.97*T
arg
et + 0.0047
Training: R=0.99976
Data
Fit
Y = T
0.1 0.2 0.3 0.4 0.5
0.1
0.2
0.3
0.4
0.5
Target
Outp
ut ~= 0.93*T
arg
et + 0.019
Validation: R=0.99992
Data
Fit
Y = T
0.2 0.3 0.4 0.5
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Target
Outp
ut ~= 0.73*T
arg
et + 0.12
Test: R=0.99707
Data
Fit
Y = T
0.1 0.2 0.3 0.4 0.5 0.6
0.1
0.2
0.3
0.4
0.5
0.6
Target
Outp
ut ~= 0.93*T
arg
et + 0.027
All: R=0.99529
Data
Fit
Y = T
Fig 4.13 Regression fit for fault locator using voltage and current values in zone 2
Fig 4.12b Output Plot for Fault Locator using current and voltage values Zone 1
63
0
1
2
3
4
5
6
Error Histogram with 20 Bins
Insta
nces
Errors = Targets - Outputs
-0.08336
-0.07815
-0.07294
-0.06773
-0.06252
-0.05732
-0.05211
-0.0469
-0.04169
-0.03648
-0.03127
-0.02607
-0.02086
-0.01565
-0.01044
-0.00523
-2.4e-05
0.005184
0.01039
0.0156
Training
Validation
Test
Zero Error
0.2 0.4 0.6 0.8
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Target
Outp
ut ~= 1
*Targ
et + -0.0
0065
Training: R=1
Data
Fit
Y = T
0.45 0.5 0.55 0.6 0.65 0.70.45
0.5
0.55
0.6
0.65
0.7
Target
Outp
ut ~= 0
.93*T
arg
et + 0
.054
Validation: R=0.99906
Data
Fit
Y = T
0.1 0.2 0.3 0.4 0.5 0.6
0.1
0.2
0.3
0.4
0.5
0.6
Target
Outp
ut ~= 1
.1*T
arg
et + -0.0
45
Test: R=0.99923
Data
Fit
Y = T
0.2 0.4 0.6 0.8
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Target
Outp
ut ~= 1
*Targ
et + -0.0
063
All: R=0.99914
Data
Fit
Y = T
Fig 4.14: Error histogram for fault locator using voltage and current values in zone 2
Fig 4.15: Regression fit for Fault Locator using Voltage and Current Values on Zone 3
64
4.3.1 Discussion of Plots from A.N.N. Fault Locator
Fig 4.7-4.16 are plots of error histogram and regression plots result from the algorithm
carried out using A.N.N. to locate faults. Regression plot is a plot used to validate the
network after training is done. It shows the relationship between outputs of the A.N.N. and
target output fed to the network. The solid line represents the best linear regression fit
between output and targets. The R value of 1 shows a perfect linear relationship. Fig 4.8,
4.10, 4.11, 4.13, 4.15 shows R values within 0.995-0.999 which means an excellent result is
obtained from validating the trained network. Fig 4.7, 4.9, 4.12, 4.14 and 4.16 are plots of
error histogram. This graph plots instances versus errors. The error for each training,
validation and test data sample are all below 0.002, the zero errors occurs for the highest
amongst other errors showing lots of inputs are validated. Fig 4.12b is a plot of voltage and
current input signals versus estimated output derived from the A.N.N. fault locator algorithm,
the estimated output are locations function of distances in Km.
0
5
10
15
Error Histogram with 20 Bins
Insta
nces
Errors = Targets - Outputs
-0.0
2413
-0.0
2064
-0.0
1714
-0.0
1365
-0.0
1015
-0.0
0666
-0.0
0316
0.0
00331
0.0
03825
0.0
0732
0.0
1081
0.0
1431
0.0
178
0.0
213
0.0
2479
0.0
2829
0.0
3178
0.0
3528
0.0
3877
0.0
4227
Training
Validation
Test
Zero Error
Fig 4.16: Error histogram for fault locator using voltage and current values on zone 3
65
4.4 Simulation Results for Fault Classification via Self Organizing Map Function
0 2 4 6 8 10-1
0
1
2
3
4
5
6
7
8
9
1 0 1 2 2 2 2 1 2 2 2
0 1 1 1 2 2 3 1 1 1 6
1 2 0 0 3 2 4 3 1 1 3
0 1 2 0 2 2 2 2 1 2 1
1 3 0 1 1 0 2 1 2 1 2
3 0 1 0 0 1 5 4 1 1 1
1 1 0 2 2 4 4 1 2 2 1
1 2 1 5 3 5 0 1 3 2 4
4 1 1 1 3 1 2 0 5 2 2
1 1 2 3 1 1 2 1 0 3 2
3 5 2 3 4 4 4 1 4 0 1
Hits
0 2 4 6 8 10-1
0
1
2
3
4
5
6
7
8
9
SOM Neighbor Weight Distances
Fig 4.17: plot of S.O.M Sample Hits
Fig 4.18: plot of S.O.M Neighbour weight distances
66
4.4.1 Discussion of Results of Fault Classification via Self Organising Map Function
Fig 4.17 shows a sample hit plot. This plot shows how many samples fall into each clusters
which represents different fault classes. It can be viewed that there are four major clusters
from the plot. Each cluster represent four fault types (L-G, L-L, LLL, LLLG) Faults. Fig 4.18
shows the neighbour weight distance plot consisting of 100 neurons with bright colours
between the neurons whose clusters are similar and dark clusters which are farther apart. The
neighbour weight distance in fig 4.18 shows major bright colours showing similarity between
A-G, B-G, C-G faults since this clusters have little difference in their fault values after
simulation. This is also extended to A-B-G, A-C-G, B-C-G faults as their clusters are closely
related since they fall within double line to ground (LLG) Faults. The dark features shows
few input samples that are not properly classified. Fig 4.19 is a plot of the self-organising
map input planes confirming the observation made in the neighbour weight planes;
demonstrating input samples dependent on another.
0 5 10
0
2
4
6
8
Weights from Input 1
0 5 10
0
2
4
6
8
Weights from Input 2
0 5 10
0
2
4
6
8
Weights from Input 3
0 5 10
0
2
4
6
8
Weights from Input 4
0 5 10
0
2
4
6
8
Weights from Input 5
0 5 10
0
2
4
6
8
Weights from Input 6
Fig 4.19: plot of S.O.M input planes
67
4.5 Simulation Results for Adaptive Auto-Reclosure Scheme
The example fault waveforms are generated via the Matlab Simulink to model the behaviour
of transmission line. In the simulation, transient and permanent faults are simulated.
Transient faults are simulated using a realistic arc model, in particular the secondary arc
model which develops once the faulted phase line breakers have opened. In simulation of
permanent faults, fault arc resistances between (200-250) ohms is used. In any fault study,
voltages and currents seen at the end of a faulted line depends on a number of different
system parameters as discussed in the previous chapter. Fig 4.20 and 4.21 shows a transient
and permanent fault time series for the 330kV system generated using Matlab Simulink. At
point 1 on fig 4.20, the transient arcing fault occurs. The circuit breaker closes at point 2 and
the secondary arc begins, which eventually extinguishes leaving a plain permanent sinusoid.
In fig 4.21, the same sequence occurs except the resistance of the fault is fixed. After point 2,
the CB operates and after a short period of transients, a bare sinusoid occurs. From the
figures, the post arcing period are both plain sinusoids but belong to different classes in the
problem space. To distinguish these classes, a feed forward network is designed as a pattern
classifier to distinguish the classes; the output of this network is fed into another A.N.N
pattern classifier network to implement reclosing. Reclosing is done if the A.N.N deems the
fault to be transient.
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-5000
0
5000
Ub: Three-Phase Fault/Fault A
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-5000
0
5000
Ub: Three-Phase Fault/Fault B
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-5000
0
5000
Ub: Three-Phase Fault/Fault C
Fig 4.20 Transient fault waveform, A-G fault, fault resistance 30ohm, Distance
1 2 Secondary Arc
68
The results presented here are results of the neural network pattern classifier. First the
network is trained to act as a fault phase detector/ selector then the second neural network
works as a fault classifier, in the sense that it classifies the fault into two classes; transient or
permanent fault which informs the decision on whether or not to reclose.
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-5000
0
5000
Ub: Three-Phase Fault/Fault A
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-5000
0
5000
Ub: Three-Phase Fault/Fault B
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
-5000
0
5000
Ub: Three-Phase Fault/Fault C
1 2
1
2
13
46.4%
0
0.0%
100%
0.0%
0
0.0%
15
53.6%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Output Class
Training Confusion Matrix
1 2
1
2
4
66.7%
0
0.0%
100%
0.0%
0
0.0%
2
33.3%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Output Class
Validation Confusion Matrix
1 2
1
2
3
50.0%
0
0.0%
100%
0.0%
0
0.0%
3
50.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Output Class
Test Confusion Matrix
1 2
1
2
20
50.0%
0
0.0%
100%
0.0%
0
0.0%
20
50.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Output Class
All Confusion Matrix
Fig 4.22 confusion matrix for fault classifier using voltage and current values
Fig 4.21 Permanent Fault Waveform of A-G Fault Resistance 200ohm, Distance 88Km
1 2
69
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
True Positive Rate
Training ROC
Class 1
Class 2
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
True Positive Rate
Validation ROC
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
True Positive Rate
Test ROC
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
True Positive Rate
All ROC
1 2
1
2
13
46.4%
0
0.0%
100%
0.0%
0
0.0%
15
53.6%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut Cla
ss
Training Confusion Matrix
1 2
1
2
3
50.0%
0
0.0%
100%
0.0%
0
0.0%
3
50.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut Cla
ss
Validation Confusion Matrix
1 2
1
2
4
66.7%
0
0.0%
100%
0.0%
0
0.0%
2
33.3%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut Cla
ss
Test Confusion Matrix
1 2
1
2
20
50.0%
0
0.0%
100%
0.0%
0
0.0%
20
50.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut Cla
ss
All Confusion Matrix
Fig 4.23: Receiver operating characteristics for fault classifier using voltage and current values
Fig 4.24: Confusion Matrix for fault classifier using voltage and current values
70
4.5.1 Discussion of Results for Adaptive Fault Classifier Plots
Fig 4.22-4.25 are plots of neural network fault detector and adaptive fault classifier (transient
and permanent faults). The figures are plots of confusion matrix and receiver operating
characteristics. As explained in section 4.2, the confusion matrix in this plot of fig 4.22 and
4.24 shows green squares all with 100% values thus the algorithm created works well as a
fault detector. The receiver operating characteristics plot of fig 4.23 and 4.25 shows a perfect
line, no deviation between the A.N.N. output and target outputs fed to the network. The
straight line is also an indication 100% specificity and 100% sensitivity of the adaptive fault
classifier.
4.6 Testing the Neural Network Fault Detection Algorithm
Once the neural network has been trained, its performance is tested by taking three factors
into consideration. The first is the plot of confusion matrix. The confusion matrices for
training, testing, and validation, and the three kinds of data combined[27]. The network
outputs are very accurate, as you can see by the high numbers of correct responses in the
green squares and the low numbers of incorrect responses in the red squares as shown in fig
4.26.
The second factor is the plot of the receiver operating characteristics. The coloured lines in
each axis represent the ROC curves. The ROC curve is a plot of the true positive rate
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
Tru
e P
ositive R
ate
Training ROC
Class 1
Class 2
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
Tru
e P
ositive R
ate
Validation ROC
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
Tru
e P
ositive R
ate
Test ROC
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
Tru
e P
ositive R
ate
All ROC
Fig 4.25: Receiver operating characteristics plot for adaptive reclosure scheme using voltage and current values
71
(sensitivity) versus the false positive rate (1 - specificity) as the threshold is varied. A perfect
test from fig 4.29 show points in the upper-left corner, with 100% sensitivity and 100%
specificity.
The third test would be to use new data set different from the ones used in the training of the
fault detection network. The new data set was gotten from a different model; 132kV with
different parameters to input fresh set of values to the 330kV neural network algorithm.
1 2 3
1
2
3
14
34.1%
00.0%
00.0%
100%
0.0%
0
0.0%
1434.1%
00.0%
100%
0.0%
0
0.0%
12.4%
1229.3%
92.3%
7.7%
100%
0.0%
93.3%
6.7%
100%
0.0%
97.6%
2.4%
Target Class
Outp
ut Class
Training Confusion Matrix
1 2 3
1
2
3
4
44.4%
00.0%
00.0%
100%
0.0%
0
0.0%
333.3%
00.0%
100%
0.0%
0
0.0%
00.0%
222.2%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut Class
Validation Confusion Matrix
1 2 3
1
2
3
222.2%
00.0%
0
0.0%
100%
0.0%
00.0%
333.3%
0
0.0%
100%
0.0%
00.0%
00.0%
4
44.4%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut Class
Test Confusion Matrix
1 2 3
1
2
3
2033.9%
00.0%
0
0.0%
100%
0.0%
00.0%
2033.9%
0
0.0%
100%
0.0%
00.0%
11.7%
18
30.5%
94.7%
5.3%
100%
0.0%
95.2%
4.8%
100%
0.0%
98.3%
1.7%
Target Class
Outp
ut Class
All Confusion Matrix
Fig 4.26 Confusion matrix plot for testing fault detector using current values
72
10-2
10-1
100
gra
die
nt
Gradient = 0.022603, at epoch 28
0 5 10 15 20 250
2
4
6
val fa
il
28 Epochs
Validation Checks = 6, at epoch 28
0
20
40
60
80
100
120
140
160
Error Histogram with 20 Bins
Insta
nces
Errors = Targets - Outputs
-0.7
26
-0.6
432
-0.5
604
-0.4
776
-0.3
948
-0.3
12
-0.2
292
-0.1
464
-0.0
6359
0.0
1921
0.1
02
0.1
848
0.2
676
0.3
504
0.4
332
0.5
16
0.5
988
0.6
816
0.7
644
0.8
472
Training
Validation
Test
Zero Error
Fig 4.27 Plot of training state for testing fault detector using current values
Fig 4.28 Error histogram for testing fault detector using current values
73
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
Tru
e P
ositiv
e R
ate
Training ROC
Class 1
Class 2
Class 3
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
Tru
e P
ositiv
e R
ate
Validation ROC
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
Tru
e P
ositiv
e R
ate
Test ROC
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
Tru
e P
ositiv
e R
ate
All ROC
10-10
10-5
100
gra
die
nt
Gradient = 7.5004e-07, at epoch 39
0 5 10 15 20 25 30 350
0.5
1
val fa
il
39 Epochs
Validation Checks = 0, at epoch 39
Fig 4.29 Receiver operating characteristics for testing fault detector using current values
Fig 4.30 Plot of training state for testing fault detector using voltage and current values
74
0
20
40
60
80
100
120
140
160
180
Error Histogram with 20 Bins
Insta
nces
Errors = Targets - Outputs
-0.0
099
-0.0
0886
-0.0
0782
-0.0
0678
-0.0
0573
-0.0
0469
-0.0
0365
-0.0
0261
-0.0
0156
-0.0
0052
0.0
00522
0.0
01565
0.0
02607
0.0
0365
0.0
04692
0.0
05735
0.0
06777
0.0
0782
0.0
08862
0.0
09905
Training
Validation
Test
Zero Error
1 2 3
1
2
3
17
41.5%
0
0.0%
0
0.0%
100%
0.0%
0
0.0%
14
34.1%
0
0.0%
100%
0.0%
0
0.0%
0
0.0%
10
24.4%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut Class
Training Confusion Matrix
1 2 3
1
2
3
1
11.1%
0
0.0%
0
0.0%
100%
0.0%
0
0.0%
1
11.1%
0
0.0%
100%
0.0%
0
0.0%
0
0.0%
7
77.8%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut Class
Validation Confusion Matrix
1 2 3
1
2
3
2
22.2%
0
0.0%
0
0.0%
100%
0.0%
0
0.0%
5
55.6%
0
0.0%
100%
0.0%
0
0.0%
0
0.0%
2
22.2%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut Cla
ss
Test Confusion Matrix
1 2 3
1
2
3
20
33.9%
0
0.0%
0
0.0%
100%
0.0%
0
0.0%
20
33.9%
0
0.0%
100%
0.0%
0
0.0%
0
0.0%
19
32.2%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
100%
0.0%
Target Class
Outp
ut Cla
ss
All Confusion Matrix
Fig 4.31 Error histogram for testing fault detector using voltage and current values
Fig 4.32 Confusion matrix for testing fault detector using voltage and current values
75
4.6.1 Discussion of Test Results of A.N.N. Fault Detector Algorithm
Figures 4.26-4.32 show plots of simulation results for tests carried out on a 132kV Network
model using the A.N.N. fault detection algorithm designed for 330kV network. The inputs of
the pre-processed fault voltages and currents are now the new samples generated from the
132kV simulation also carried out on Matlab Simulink environment. The green boxes of fig
4.26 and 4.32 are all in the region of 90%-100% value showing good classification. Fig 4.27
and 4.30 shows training state plot generated after running the algorithm on the 132kV
network. Fig 4.27 shows several failed values for different iterations, at iterations 11-16
errors from 1-5 is observed. Iterations 21-30 show error in the range of 1-6. Fig 4.30 is
different because the input samples are of current and voltage values. The only error observed
occur at iteration 6.
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
True Positive Rate
Training ROC
Class 1
Class 2
Class 3
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
True Positive Rate
Validation ROC
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
True Positive Rate
Test ROC
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
True Positive Rate
All ROC
Fig 4.33 Confusion matrix for testing fault detector using voltage and current values
76
4.7 Test Results for Neural Network Fault Location Algorithm
10-20
100
1020
gra
die
nt
Gradient = 1.6281e-11, at epoch 43
10-10
10-5
100
mu
Mu = 1e-10, at epoch 43
0 5 10 15 20 25 30 35 400
2
4
val fa
il
43 Epochs
Validation Checks = 0, at epoch 43
0
2
4
6
8
10
12
14
16
Error Histogram with 20 Bins
Instances
Errors = Targets - Outputs
-0.01952
-0.01403
-0.00855
-0.00306
0.002431
0.00792
0.01341
0.0189
0.02438
0.02987
0.03536
0.04085
0.04634
0.05183
0.05731
0.0628
0.06829
0.07378
0.07927
0.08476
Training
Validation
Test
Zero Error
Fig 4.34 Training state results for testing fault locator using current values
Fig 4.35 Error Histogram for testing fault detector using current values
77
0.1 0.2 0.3 0.4 0.5 0.6
0.1
0.2
0.3
0.4
0.5
0.6
Target
Outp
ut ~= 1*T
arg
et + 4.1e-13
Training: R=1
Data
Fit
Y = T
0.1 0.2 0.3 0.4 0.5 0.6
0.1
0.2
0.3
0.4
0.5
0.6
Target
Outp
ut ~= 1*T
arg
et + -0.0039
Validation: R=0.99998
Data
Fit
Y = T
0.1 0.2 0.3 0.4 0.5 0.6
0.1
0.2
0.3
0.4
0.5
0.6
Target
Outp
ut ~= 0.75*T
arg
et + 0.086
Test: R=0.99983
Data
Fit
Y = T
0.1 0.2 0.3 0.4 0.5 0.6
0.1
0.2
0.3
0.4
0.5
0.6
Target
Outp
ut ~= 0.97*T
arg
et + 0.012
All: R=0.9948
Data
Fit
Y = T
10-10
10-5
100
gra
die
nt
Gradient = 5.9533e-09, at epoch 5
10-10
10-5
100
mu
Mu = 1e-08, at epoch 5
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50
1
2
val fa
il
5 Epochs
Validation Checks = 2, at epoch 5
Fig 4.36 Regression plot for testing fault locator using current values
Fig 4.37 Training state plot for testing fault locator using voltage and current values
78
0
1
2
3
4
5
6
7
8
9
Error Histogram with 20 Bins
Insta
nces
Errors = Targets - Outputs
-0.0
8835
-0.0
8291
-0.0
7746
-0.0
7202
-0.0
6658
-0.0
6113
-0.0
5569
-0.0
5024
-0.0
448
-0.0
3936
-0.0
3391
-0.0
2847
-0.0
2302
-0.0
1758
-0.0
1214
-0.0
0669
-0.0
0125
0.0
04195
0.0
09639
0.0
1508
Training
Validation
Test
Zero Error
0.2 0.4 0.6
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Target
Output ~= 1*Target + 0.0017
Training: R=0.99994
Data
Fit
Y = T
0.2 0.4 0.6
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Target
Output ~= 1.1*Target + -0.015
Validation: R=0.99893
Data
Fit
Y = T
0.2 0.4 0.6
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Target
Output ~= 0.91*Target + 0.11
Test: R=0.9999
Data
Fit
Y = T
0.2 0.4 0.6
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Target
Output ~= 0.99*Target + 0.018
All: R=0.9899
Data
Fit
Y = T
Fig 4.38: Error histogram for testing fault locator using voltage and current values
Fig 4.39 Regression plot after testing fault locator using voltage and current values
79
4.7.1 Discussion of Simulation Results from Testing Fault Location Algorithm
Fig 4.34-4.37 are training state plots for testing the fault location algorithm designed for the
330kV network model on a different 132kV model. In fig 4.37, the error values are present
only at numbers 4 & 5 iterations. The number of iterations shows how many iterations before
convergence is obtained. The speed of convergence of the neural network training depends on
the accuracy of the input values as well as the adherence of this values to normalization
constraint of neural network architecture. The error histogram of fig 4.38 shows extremely
low error value for all instances of training, validation and testing.
4.8 Tests Results for Neural Network Fault Classification Algorithm
The fault classification neural network is a clustering problem carried out through the self-
organized map, a competitive layer algorithm. 11 cases of different fault types are used as
input to the network. As discussed in the previous chapter, self-organized map function
classifies the input data unsupervised i.e. without target data by recognizing similarities in
input patterns. The training results show the S.O.M network classified the entire fault data
into four different classes (LG, LL, LLG, LLL, and LLLG). Although five varying fault
classes, it can be deduced from the results that the S.O.M network classified LLL and LLLG
fault into the same class. To test the trained S.O.M network, new sets of data from a different
zone2 of a 132kV network is utilized. The results are presented in figures below.
0 2 4 6 8 10-1
0
1
2
3
4
5
6
7
8
9
SOM Neighbor Weight Distances
Fig 4.40 SOM Neighbour Weight Distances for testing fault classifier
80
0 5 10
0
2
4
6
8
Weights from Input 1
0 5 10
0
2
4
6
8
Weights from Input 2
0 5 10
0
2
4
6
8
Weights from Input 3
0 5 10
0
2
4
6
8
Weights from Input 4
0 5 10
0
2
4
6
8
Weights from Input 5
0 5 10
0
2
4
6
8
Weights from Input 6
0 2 4 6 8 10-1
0
1
2
3
4
5
6
7
8
9
1 3 1 0 5 2 4 4 3 1 1
1 1 1 0 5 2 0 5 5 1 2
4 2 0 0 0 0 0 4 1 1 4
1 0 5 2 2 4 2 2 2 2 4
0 0 0 0 2 1 2 0 0 1 0
1 2 2 1 0 2 0 4 2 2 4
4 1 0 0 3 5 4 6 2 2 1
5 3 2 1 1 1 0 0 1 2 2
1 1 0 2 1 0 2 5 2 2 1
0 2 2 0 2 2 0 0 2 1 2
3 5 2 0 2 1 3 2 2 4 3
Hits
Fig 4.41 SOM Input Planes for Fault Classifier
Fig 4.42 Sample hits plots for testing fault classifier
81
Fig 4.41 shows the self-organised map planes with combination of dark and bright colour
pigments showing interdependence of different fault types on each other. A-G, B-G, C-G
faults for example have fault voltage and current values that do not vary over a wide range.
Fig 4.42 shows the sample hit plot showing distribution of fault data samples into 6 clusters.
It is observed that 1-4 clusters occur frequently. This implies that most of the input samples
fall within this clusters consequently proving the algorithm is able to classify faults for other
networks successfully. Fig 4.43 shows the confusion matrix for test carried out on adaptive
reclosure scheme. All green features possess 100% values. The receiver operating
characteristics of fig 4.44 shows a perfect line connecting the output and target class, no
deviation whatsoever is observed. This proves that the algorithm is able to determine
reclosing decision at 100% specificity and 100% sensitivity.
1 2
1
2
14
100%
0
0.0%
100%
0.0%
0
0.0%
0
0.0%
NaN%
NaN%
100%
0.0%
NaN%
NaN%
100%
0.0%
Target Class
Outp
ut Cla
ss
Training Confusion Matrix
1 2
1
2
3
100%
0
0.0%
100%
0.0%
0
0.0%
0
0.0%
NaN%
NaN%
100%
0.0%
NaN%
NaN%
100%
0.0%
Target Class
Outp
ut Class
Validation Confusion Matrix
1 2
1
2
3
100%
0
0.0%
100%
0.0%
0
0.0%
0
0.0%
NaN%
NaN%
100%
0.0%
NaN%
NaN%
100%
0.0%
Target Class
Outp
ut Class
Test Confusion Matrix
1 2
1
2
20
100%
0
0.0%
100%
0.0%
0
0.0%
0
0.0%
NaN%
NaN%
100%
0.0%
NaN%
NaN%
100%
0.0%
Target Class
Outp
ut Class
All Confusion Matrix
Fig 4.43 Confusion matrix for test on adaptive reclosure scheme
82
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
Tru
e P
ositiv
e R
ate
Training ROC
Class 1
Class 2
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
Tru
e P
ositiv
e R
ate
Validation ROC
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
Tru
e P
ositiv
e R
ate
Test ROC
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
False Positive Rate
Tru
e P
ositiv
e R
ate
All ROC
Zones Current Values Voltage and current
Values
Hidden
Layers
CE %E CE %E
Zone 1 10 1.81358e-0 0 4.41113e-0 0
5.46648e-0 0 12.56130e-0 0
5.37691e-0 0 12.78173e-0 0
Zone 2 15 1.25726e-0 0 3.92247e-0 0
3.01199e-0 0 10.62411e-0 0
3.07638e-0 0 13.93316e-0 0
Zone 3 31 1.32389e-0 4.76e-0 2.19115e-0 2.38e-0
3.53742e-0 0 5.35857e-0 0
3.70216e-0 11.1e-0 5.31707e-0 0
Fig 4.44 Receiver operating characteristics for test on adaptive reclosure scheme
Table 4.1 performance table for fault detector neural network
83
Zones Current Values Voltage and current
Values
Data
Divisions
Hidden
Layers
CE %E CE %E
Zone 1 10 1.73761e-0 0 2.38956e-0 0 Training
2.44491e-0 0 6.75411e-0 0 Validating
2.56877e-0 0 6.68094e-0 0 Testing
Figure 4.1 shows a table of cross entropy C.E and percentage error %E of A.N.N. fault
detector scheme for zone 1-3. The number of neurons in the hidden layers were randomly
chosen based on trial and error methods during training procedures. These layers work like a
conduit between the input and output layer of the neural network architectural design. Each
zone has corresponding C.E. and %E values. The C.E column have three separate rows;
training, validating, and testing columns respectively. Training column covers dataset
presented to the network during training and how well the network is adjusted to its error.
Minimizing cross entropy error results in good classification, lower values are better, zero
means no error. Percentage error represents fractions of samples misclassified. The values
presented for each zone in the C.E column are all low values. It is observed that cross entropy
values for zone 1 and 2 using voltage and current values are a bit higher compared to current
values alone. For all zones 0% error is mostly obtained except the training data column for
zone 3 where 2.83% is observed. Tables 4.2 and 4.3 are performance tables for adaptive fault
classifier and adaptive reclosing; the cross entropy values and %E values show low values of
0%. Zone 2 records C.E of 10.77542 in the testing column under voltage and current values
used as input samples still well within acceptable limit for cross entropy values
Zones Current Values Voltage and current
Values
Data
Divisions
Hidden
Layers
CE %E CE %E
Zone 1 20 1.49311e-0 0 2.16318e-0 0 Training
5.14771e-0 0 6.96687e-0 0 Validating
5.23641e-0 0 7.17856e-0 0 Testing
Zone 2 25 2.94365e-0 0 3.62898e-0 0 Training
7.760704e-
0
0 10.72542e-0 0 Validating
8.60164e-0 0 11.37871e-0 0 Testing
Zone 3 30 2.57941e-0 4.76e-0 2.91388e-0 2.38e-0 Training
7.52102e-0 0 8.36907e-0 0 Validating
7.48334e-0 11.1e-0 8.29864e-0 0 Testing
Table 4.2 Performance table for adaptive fault classifier neural network
Table 4.3: Performance Table for Adaptive Reclosure Scheme Network
84
Fig 4.4 is the performance table for the fault locator algorithm simulated. The columns show
mean squared error and regression values. Mean square error is the average squared
difference between outputs and targets if the mean square error is zero then no error occurs. R
represents regression values measuring correlation between output and target. An R value of
1 means a close linear relationship. Zero means random relationship. These columns have
rows for training, validation and testing. The regression values for all the three zones are well
close to 1. Low values for M.S.E in the range from 1-7 is observed. The highest values are
observed in zone 2.
.
Zones Current Values Voltage and current
Values
Data
Divisions
Hidden
Layers
M.S.E R M.S.E R
Zone 1 10 3.53331e-0 0.999796 4.02650e-6 0.99977 Training
1.07993e-0 0.999999 7.20332e-4 0.98151 Validating
1.10549e-0 0.9994 6.754441e-5 0.999281 Testing
Zone 2 14 7.54288e-0 0.993357 2.40135e-6 0.999978 Training
3.24661e-0 0.999172 6.94280e-4 0.99949 Validating
7.24130e-0 0.99406 1.64933e-2 0.994971 Testing
Zone 3 22 2.47634e-8 0.99999 2.09400e-6 0.99984 Training
3.80027e-4 0.99456 6.36174e-4 0.99685 Validating
1.42481e-4 0.999603 2.29223e-3 0.994046 Testing
Table 4.4: Performance Table for Fault Locator Neural Network
85
Actual Output Network Output
A B C ®7 ®9 ®:
1 0 0 0.99797 0.0021983 3.4255e-07
1 0 0 0.99862 0.00031272 5.7421e-07
1 0 0 0.99892 6.6702e-05 1.4445e-06
1 0 0 0.99905 1.3048e-05 3.1301e-06
0 1 0 0.004136 0.97556 4.848e-05
0 1 0 0.0020006 0.98146 7.6016e-06
0 1 0 0.0013137 0.98091 5.0511e-07
0 1 0 0.00093317 0.97866 4.4615e-08
0 0 1 7.9193e-05 0.0013349 1
0 0 1 3.1191e-05 0.0014288 1
0 0 1 1.929e-05 0.00066873 1
0 0 1 6.851e-06 0.00034928 1
Table 4.5 Output of Trained Faulted Phase Detector Network using Current Values only for Zone 1
86
Actual Output Network Output
A B C ®7 ®9 ®:
1 0 0 1 3.187e-09 2.9406e-11
1 0 0 1 5.2048e-09 7.296e-18
1 0 0 1 4.6853e-09 4.96e-16
1 0 0 1 2.9435e-09 4.7864e-15
0 1 0 2.2993e-14 1 1.0785e-15
0 1 0 5.2404e-10 1 2.3859e-13
0 1 0 1.3103e-09 1 4.7025e-12
0 1 0 3.9816e-09 1 2.4605e-11
0 0 1 1.0566e-08 4.5532e-7 1
0 0 1 2.7311e-19 4.0572e-7 1
0 0 1 8.6396e-19 8.6091e-8 1
0 0 1 3.4763e-18 9.1578e-09 1
Table 4.6 Output of Trained Faulted Phase Detector Network using Current & Voltage Values for Zone
1 onfor zone 1
87
Actual Output Network Output
A B C ®7 ®9 ®:
1 0 0 1 1.3992e-08 9.0419e-7
1 0 0 1 1.4023e-08 7.1044e-8
1 0 0 1 1.4487e-08 2.9234e-8
1 0 0 1 1.4017e-08 2.0501e-8
0 1 0 2.2033e-10 1 7.5956e-11
0 1 0 6.6657e-11 1 3.756e-9
0 1 0 9.2096e-11 1 3.6956e-6
0 1 0 6.4726e-08 1 5.5874e-9
0 0 1 4.6128e-11 5.2934e-9 1
0 0 1 1.5756e-10 4.7686e-7 1
0 0 1 7.3582e-10 1.8523e-6 1
0 0 1 4.2926e-9 1.6599e-07 1
Table 4.7 Output of Trained Fault Phase Detector Network Using Current Values only for Zone 2
88
Actual Output Network Output
A B C ®7 ®9 ®:
1 0 0 1 4.9113e-13 7.671e-7
1 0 0 1 3.1197e-13 1.502e-7
1 0 0 1 8.5553e-14 8.8122e-8
1 0 0 1 4.5722e-14 5.0125e-7
0 1 0 4.0768e-13 1 2.4829e-9
0 1 0 1.711e-13 1 7.2075e-9
0 1 0 2.1219e-12 1 5.6725e-6
0 1 0 1.5122e-08 1 1.7028e-7
0 0 1 1.6831e-7 4.7491e-9 1
0 0 1 8.8786e-8 4.1184e-7 1
0 0 1 1.5212e-8 3.4071e-6 1
0 0 1 3.5697e-8 4.8571e-07 1
Table 4.8 Output of Trained Fault Phase Detector Network using Voltage & Current values for Zone 2
222222
89
Actual Output Network Output
A B C ®7 ®9 ®:
1 0 0 1 5.0387e-8 3.0117e-9
1 0 0 1 1.2102e-8 5.2331e-9
1 0 0 1 9.7796e-9 4.7442e-9
1 0 0 1 6.0627e-9 1.0761e-8
0 1 0 6.4083e-8 1 5.1838e-11
0 1 0 3.0927e-8 1 3.2455e-9
0 1 0 5.3297e-8 1 7.2582e-7
0 1 0 6.9285e-07 1 1.9416e-8
0 0 1 9.1997e-9 2.1645e-8 1
0 0 1 7.6195e-9 6.0341e-9 0.99997
0 0 1 5.4824e-9 4.3582e-9 1
0 0 1 3.5571e-9 1.1723e-08 0.99999
Table 4.9 Output of Trained Fault Phase Detector Network Using Current values for Zones 3
90
Actual Output Network Output
A B C ®7 ®9 ®:
1 0 0 1 7.2344e-13 6.2369e-10
1 0 0 1 4.7142e-13 3.8236e-9
1 0 0 1 4.2928e-13 1.3729e-8
1 0 0 1 1.6309e-12 7.234e-8
0 1 0 9.6231e-8 1 2.0559e-7
0 1 0 2.277e-10 1 4.9453e-8
0 1 0 4.9739e-10 1 3.2428e-8
0 1 0 4.7967e-08 1 9.0871e-9
0 0 1 6.3113e-11 9.0798e-8 1
0 0 1 3.9469e-11 1.9304e-8 1
0 0 1 5.2518e-11 2.9428e-9 1
0 0 1 1.1796e-10 2.2532e-09 1
Table 4.5 is a comparison of target values against A.N.N. output values using just pre-
processed fault current values generated from the 330kV network model used for this
research as input samples. The value ‘1’ represents presence of fault while ‘0’ represents no
fault. The first three columns represents phase A, B, and C while m[¯, m[° , m[± which are the
A.N.N fault detector on phase A, B, C is represented in the next three columns. table 4.5 and
4.6 are comparisons made for zone 1. Although the results are accurate, an improved
accuracy by 13.8% is recorded when voltage and current values is used to train the neural
network for fault detection. Tables 4.7 and 4.8 represent comparisons for zone 2. For this
cases expressed in tables 4.7 and 4.8, an improvement of 11% is observed when voltage and
current values is used as input samples. Fault detection comparison in fig 4.9 and 4.10
records an improvement of 12% using voltage and current values as input samples to train the
network. A particular threshold will be used when programming the numerical relays using
this A.N.N. algorithm generated for fault detection. 0.95-1 to represent presence of fault and 1!A − 1!B to represent no fault present.
Table 4.10 Output of Trained Faulted Phase Detector network using Voltage & Current Values only for Zones 3
91
Actual
Output*1000(Km)
²³´(current and
voltage)*1000(Km)
²³µ(¶·¸¸¹º» ¼´½·¹¾)∗ ¿ÀÀÀ(ÁÂ)
0.05 0.051309 0.050606
0.07 0.085325 0.070551
0.14 0.22596 0.14016
0.24 0.23915 0.23999
0.28 0.27906 0.29259
0.32 0.32012 0.31994
0.36 0.359 0.35965
0.4 0.39664 0.39937
0.44 0.42937 0.42314
0.48 0.46694 0.47963
0.5 0.48241 0.50312
0.52 0.50179 0.52813
0.54 0.52526 0.54537
0.57 0.55805 0.55805
0.59 0.57383 0.57383
0.62 0.60576 0.60576
0.63 0.61758 0.61758
0.64 0.63387 0.63381
0.66 0.65076 0.65076
0.68 0.66801 0.66801
Table 4.11 Comparison of Estimated and Target Output of Fault Locator Zone 2
92
Actual
Output*1000(Km)
²³´(current and
voltage)*1000(Km)
²³µ(¶·¸¸¹º» ¼´½·¹¾)*1000(Km)
0.04 0.039793 0.040474
0.1 0.10177 0.10039
0.12 0.08832 0.12038
0.15 0.14779 0.15274
0.18 0.17507 0.22142
0.2 0.16586 0.1848
0.25 0.23392 0.31858
0.35 0.34142 0.34378
0.38 0.37241 0.36593
0.4 0.39245 0.44087
0.42 0.41428 0.48579
0.5 0.50611 0.51579
0.52 0.52147 0.53286
0.58 0.58264 0.49158
0.62 0.61711 0.62025
0.68 0.68339 0.7066
0.72 0.72072 0.72939
0.75 0.71613 0.75077
0.78 0.79574 0.80137
0.82 0.82133 0.82958
Table 4.12: Comparison of Estimated and Target Output of Fault Locator Zone 1
93
Actual
Output*1000(Km)
²³´(current and
voltage)*1000(Km)
²³µ(¶·¸¸¹º» ¼´½·¹¾)*1000(Km)
0.04 0.040034 0.03989
0.10 0.099974 0.099728
0.12 0.11998 0.075985
0.15 0.13064 0.14958
0.18 0.17999 0.17955
0.20 0.21801 0.19958
0.25 0.24782 0.24924
0.30 0.29998 0.29212
0.35 0.36455 0.34928
0.40 0.39985 0.39948
0.45 0.47458 0.47588
0.50 0.50692 0.51179
0.55 0.54991 0.54946
0.60 0.59955 0.60012
0.65 0.65017 0.65287
0.70 0.6998 0.70414
0.75 0.75001 0.74979
0.80 0.80008 0.801
0.85 0.85014 0.85039
0.95 0.9499 0.95038
Table 4.11 and tables 4.12-4.13 are tables of comparisons of target output in kilometres
separated by 10km interval until the maximum distance for each zone is reached i.e. zone 1
68km, zone 2 68km and zone 3 95km as well as A.N.N. output using either current or
Table 4.13 Comparison of Estimated and Target Output of Fault Locator Zone 3
94
current and voltage input samples. The values obtained with current and voltage values are
closer to the target output compared to using just current values. Tables 4.11-4.13 are output
tables highlighting the fault location algorithm scheme. Tables 4.11-4.13 further elucidates
the mean square error and regression values in fig 4.4 which proves the fault location
algorithm works effectively. Numerical calculation is done based on the output plot of fig
4.12b to determine the speed of response of the A.N.N. fault locator;
To test the speed of operation of the neural network fault locator, the following assessment is
carried out; fig 3.9 shows a plot of A-G fault at 50Km with fault resistance of 30ohm, it is
observed that the fault inception time is 0.00875s. Another plot showing the output (distance
in Km against instances of data input) shown in fig 4.12b reveals that at 50Km, the fault
locator output estimates 50.611Km at sample no.12 with sampling time 5e-5s. It is important
to note that this calculation is carried out based on the neural network designed with both
voltage and current signals on phases A, B, C making six samples in all by re-ordering of
data in matrix. The above deductions are used to perform the following calculations:
Fault inception time = 0.00875s
Fault located at sample no.12= 12*6(consecutive samples)*5e-5s=3.6e-3
Time of operation = 0.00875 – 0.0036 = 0.00515s
95
Target Values Estimated Values
1 0 0.99998 0.0040611
1 0 0.99978 0.0016642
1 0 0.99957 0.0093235
1 0 0.99898 0.054378
1 0 0.99773 0.078368
1 0 0.99598 0.091319
1 0 0.98456 0.002456
1 0 0.93917 0.000065489
1 0 0.93967 0.0021379
1 0 0.93976 0.011087
1 0 0.95069 0.050172
0 1 1.8854e-05 0.99594
0 1 0.00022104 0.99834
0 1 0.00043285 0.99068
0 1 0.0010199 0.94562
0 1 0.0022676 0.92163
0 1 0.0040226 0.90868
0 1 0.015444 0.99754
0 1 0.060829 0.99993
0 1 0.060333 0.99786
0 1 0.060237 0.98891
The table 4.14 shows the adaptive fault classifier where ‘1’ represents transient fault ‘0’
represents permanent fault. The output of the adaptive classifier in fig 4.43 and 4.44 as well
as table 4.3 is used to determine the necessary reclose command that is whether or not to
reclose. The table is grouped with the first ten rows having the transient and permanent fault
classifier while the next ten rows the classifier is reversed having permanent fault first before
transient fault. The estimated output for each shows the A.N.N. adaptive classifier is able to
track the target output fed to it. For the first ten cases, if a transient fault occurs, the reclose
operation is issued, if the pattern classifier senses another fault peradventure a permanent
fault is sensed, the command to break the circuit is issued. The next ten rows is used if the
A.N.N. classifier senses a permanent fault, the do not reclose command is issued until the
fault dissipates then the circuit is reconnected. According to the time plot of the transient and
permanent fault simulated in fig 4.20 and 4.21, the time it takes for a transient fault to
dissipate is 0.1s while for a permanent fault it takes 0.14s. After 0.14s, the reclose command
is then issued to reconnect the break circuit
Table 4.14: Adaptive Fault Classifier for Transient or permanent Fault
96
CHAPTER FIVE
CONCLUSION AND RECOMMENDATION
Conclusion
This research work describes the application of artificial neural networks to fault detection,
fault location, fault classification. The design process and test results proves the successful
adaptation of neural network to varied fault conditions as well as system parameters on the
Benin, Onistha, and New Haven transmission network modelled on MATLAB SIMULINK.
It also shows the A.N.N’s immunity to noise, D.C offset or harmonics in the voltage/current
waveform hence the possibility of relay non-reach/over-reach is minimized. The adaptive
reclosure scheme has proven to be a good example for system protection, although not yet
existing on the Nigerian power system thus the minimum field data available. The input
utilized for these networks are generally simulated notwithstanding the test proves real time
implementation will be successful. The results from this work show for the fault location
algorithm, on average an improved accuracy of 12% is obtained when voltage and current
values are used as inputs to the neural network compared to using only current values as input
samples. Also, successful combination of two neural networks, one to classify the fault type
(transient or permanent); the time evaluated to clear a transient fault is 0.1s while the time to
clear permanent fault is 0.14s and using this output determine or adapt the reclosing time to
ensure successful reclosure. The speed of operation of the fault locator is evaluated as 3.6ms
when A.N.N. is applied compared to the distance relay time of response of the existing
protection which is 0.350s as recorded in the relay data obtained from the New Haven
Transmission station shown in appendix B. This proves the neural fault locator locates faults
faster.
Recommendations
Some notable recommendations from this work to power system engineers and relevant
authorities are as follows:
The self-organised neural network can be used in conjunction with K-means
clustering as well as fuzzy K-nearest neighbour (K-NN) algorithm can be used to
substitute the error back propagated pattern classifier due to convergence issues.
The adaptive auto reclosing scheme applied in this research is based on the theory of
single pole auto reclosure technique. The three pole technique although not popular in
many power systems establishment can also be adapted using artificial intelligence
tools.
Another enhanced protection scheme that I recommend to be investigated using
artificial neural network is the adaptive distance protection.
97
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