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A Comparative Study of Power Distribution Over
voltages Classification Using feed forward ArtificialNeural Networks and General Regression Neural
Networks Pascal Dieu Seul Assala, Haoyong Chen
#
South China University of Technology , Guangzhou , 510641 PR-China School of Electric Power
Abstract- Power outages due to overvoltage and following damages affect a large part of
power distribution networks. A right identification system for the overvoltage can help in
fast intervention and shorten the outage duration. In the present work, authors present a
comparative study of distribution overvoltage identification. The study is conducted with
data simulated from ATP-EMTP with a network designed from data of real case studies
conducted on 10kV distribution network of the city of Qingyuan electrified by the China
Southern Power Grid. The comparison study is conducted with data from time domain
analysis and Wavelet Packet Decomposition (WPD) analysis. Two identification tools are
used: the General Regression Neural Network (GRNN) and the Feed forward Artificial
Neural Network (FANN). Training and identification performances are compared at the
end of the study bringing out some specificities of the two identification tools regarding
identifications of the direct strike lightning overvoltages, temporary overvoltages and
capacitor bank energization overvoltages.
Keywords: Power distribution, neural networks, over voltages, wavelet packet
decomposition
# Corresponding AuthorE-mail : [email protected]
I. INTRODUCTION
Overvoltage in power distribution system
is the first cause of damage in electronics
[1]. A power outage is also a phenomenon
induced by distribution overvoltage events.
In order to protect a sub-network, a
protection relay will trigger to stop the
energy generated from the surge event to
flow towards the protected area. This
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triggering will sometimes be repeated in a
sequence to attempt to re-energize the
protected area until the surge is detected to
delay longer and, therefore, the protection
apparatus will definitely shut down the
protected network area awaiting for the
distribution network response team to
manually come to inspect the possible
causes and ensure the security of the
affected network prior to the next
energization balanced study of overvoltage
identification between the most used
pattern recognition tool the FANN and the
GRNN a new generation of neural
networks (NN) introduced by Specht [2]
belonging to the probabilistic neural
networks (PNN) family.
Regardless of the source provoking the
event, over voltages are harmful to power
network system lines and can cause
insulator breakdown and can decrease
magnetic circuit quality. In a power
transformer, this will bring a loud noise
and higher Foucault currents circulating in
the magnetic circuit leading to transformer
heating. Voltage surge will often cause
equipment damage, maloperation of
protective devices and even loss of human
life. In the area of power quality, several
research works have been done providing
very good results for overvoltage
classification. The short-time Fourier
transform (STFT) [3] is a deterministic
versus statistical method analysis [4], a
covariance analysis [5]. Support vector
machine (SVM) theory used for
classification is combined with wavelet
transform (WT) method [6] and has also
been associated with S-transform as a
discrimination tool [7]. ANN pattern
recognition capabilities have been used in
Ref. [8]. In Ref. [9], ANN is combined
with the Fisher discriminant function
(FDF).
At present, overvoltage classification
works have gained a lot of attention from
the researchers and many research works
have brought about many advances in the
area. GRNN and FANN capabilities are
used with different datasets simulated on
ATP based on a real-world distribution
system of Qingyuan city, which is a part of
China’s Southern Power Grid. Processed
samples are generated from time domain
and time-frequency domain analysis of
simulated data. Results obtained highlight
the advantages and specific aspects of
using GRNN and FANN for applications
of overvoltage classification.
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1.Wavelet Packet Decomposition
Wavelet packet decomposition (WPD)theory emerges from wavelet signal
processing. It was introduced by
Coifmanand Wickerhauser [10]. WPD
gives a more complete signal time
frequency analysis compared to the
discrete wavelet transform (DWT). The
DWT recursively processes a signal using
the pyramid algorithm [11]. In DWT, the
discrete signal of length N to be processed
is sent to two mirror filters. The output of
the low-pass filter consists of N /2 wavelet
coefficients ar ={a
r
1,a
r
2,a
r
3,....a
r
( N /2)!1}
being the approximation of the signal at
scale r of wavelet signal analysis. The
high-pass filter outputs the detail
coefficients d r ={d
r
1,d
r
2,d
r
3,....d
r
( N /2)!1} at
the resolution level r . The difference
between WPD and DWT is that the DWT
will only use the wavelet coefficients for
processing from one resolution level to
another while the WPD will use both low-
pass and high-pass filters’ output. This
gives a full signal sub-band representation.
FigureFig! # presents the pyramidal
processing of WPD. Shannon wavelet
packets with low-pass filter " and high
pass filter # from Ref. [11] as in Eqs. (1) &
(2) respectively are used in the present
study.
Fig. 1: Wavelet Packet Decomposition
Tree.
2. Feedforward Artificial Neural
Networks
A feed forward artificial neural network
(FANN) is a type of classic artificial
neural networks (ANN) that are based on
the first model of human neuron presented
by McCulloch and Pitts. The artificial
neuron in the model used on FANN is a
mathematical unit built on a set of inputs, a
summation unit, an activation function and
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an output. Mathematically, a neuron is
presented as modeled in Eq. (3),where X is
the neuron with number of n inputs and
one output y(X), g is the activation
function; it computes the neuron output
based on the net function Netf that is
mathematically modeled in Eq. (4). The
sigmoid activation function is presented in
Eq. (5).
In FANN, a neuron located in layer L$
only sends information to neurons located
at layer L$+1 and only receives signals
from neurons of layer L$!1 [12]. Three-
layer FANNs are very powerful tools for
pattern recognition that can be used to
implement a wide range of real life
applications requiring a decision-making
[13]. The network in this study is a three-
layer FANN. Training algorithm and
network information are as presented in
Table 1. A three-layer FANN at its first
layer (also called input layer) will receive
an input pattern of the overvoltage data to
be identified; the hidden layer is made of
neurons, each of them computes its output
independently of others of the same layer.
The output layer in our case is a unique
neuron that outputs the identified type best
matching the input pattern.
Table 1: Basic Characteristics of the FANN.
The mathematical expression of Sigmoid
activation function is presented in Eq. (5).
3. General Regression Neural
Networks
Firstly developed by Specht [2], a GRNN
is a type of probabilistic neural network.
For a known joint probability density
function f ( x, y), the regression of y gives an
input X as presented in Eq. (6). X is a
vector of size p; p%1.
Element Value and details
Activation function
Sigmoid
1
Topology Feedforward
multilaye perceptron
Number of layers 3
Learning type and
algorithm
Supervised, LMS
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f ( x, y) in the ongoing overvoltage
identification study is unknown. Assuming
that the first partial derivative of f is small
at any x and the underlying density is
continuous, as stipulated in Ref. [2], for
our GRNN, neurons will use the third
activation function in table 1 of Ref. [14]
for computing the probability estimator of
f ( X ,Y ) presented in Eq. (7).
Combining Eqs. (6) & (7) and calculating
different integration yields to the generic
model of GRNN. (Eq. (5) in Ref. [2])
presents the mathematical model. In regard
to the work conducted in the present paper,
the model (Eq. (9) in Ref. [2]) presented in
Eq. (8) has been chosen.
&(X)=
!i=1
m
Aiexp
"#$
%&'
! D2
i
2'2
!i=1
m B
iexp
"
#$
%
&'
! D2
i
2'2
(8)
Where, D2i =( X ! X i)T ( X ! X i).
In Eq. (8), Ai and B
i are defined following
Eq. (9). Ai & B
i are updated during the
clustering process each time a training
sample that belongs to the group
represented by the cluster center is
processed during the training. When a
training sample difference from all the
cluster centers is greater than a predefined
limit r , it becomes a new cluster center.
4. Data Construction
4.1. Overvoltage Types
Three types of over voltages have been
selected to support the undergoing study:
the direct strike lightning surge, the
temporary overvoltage and the capacitor
bank energization overvoltage.
Direct Strike Lightning Overvoltage:
The most devastating overvoltage type in
power distribution lines is the lightning
overvoltage. It can affect the power
network by inducing overvoltage or a
direct strike on a power cable. For both
cases, the resulting overvoltage is usually
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of very high amplitude, a steep front, and
low energy. The power distribution
network modeled on ATP for running the
simulations is a three-phase overhead
network without protection cable. For that,
only the direct strike lightning surge has
been taken into account for analysis. When
lightning strikes on the overhead cable, the
voltage is raised from the normal 10!15kV
to several MV. The adjacent lines are also
affected and some effect isdepicted in Fig.
Fig. 2.
Fig. 2: Overvoltage Resulting from a
Lightning Direct Strike on Phase C of the
Overhead Line.
The voltage of the phase at which
lightning directly strikes embeds the
impulses with the highest amplitude at the
striking instant; the waveform is rapidly
damped in the following 5ms. The
adjacent phases are affected in a different
way. Figure 2 shows two differences
in the time domain analysis that will be
used in the next stage of our work for
online detection of lightning strike
overvoltage. In the first 3 ms, the voltage
of the struck phase will be directly damped
after the lightning strike while adjacent
phases will present some few peaks at the
highest amplitude before being damped.
Figure 3 shows a typical lightning impulse
recorded in one phase.
Fig. 3: Measured Lightning Impulse
Waveform.
Temporary Overvoltage: Temporary
overvoltage isthe result of phase-to-ground
fault clearance. A temporary overvoltage
can provoke rising voltage waveform up to
2.5 p.u. of the host distribution network
voltage amplitude [15]. A typical
temporary overvoltage resulting from
Phase B to ground fault clearance is shown
in Figure 4.
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Fig.4: Temporary Overvoltage Waveform
in a Three-Phase Overhead Distribution
Network.
The bold dot on the plot in Figure 4
materializes the instant at which the phase-
to-ground default appears and the high
increase of voltage appears from the
instant at which the default is cleared.
Capacitor Bank Energization
Overvoltage: The principal use of
capacitor banks in power distribution
networks is to improve the power factor.
This is done by providing the reactive
energy Q consumed by a load using a
source different from the power generator
or the distribution transformer. The
capacitor bank can be located at different
points in the network chosen taking into
account cable characteristics and the
amount of reactive power to be produced.
Among three types of overvoltages under
study, the capacitor bank energization
overvoltage is the type that lasts longer
and produces lower peaks in the
waveform. The amplitude of capacitor
bank energization overvoltage depends on
the host network voltage level at the time
of energization and the initial charge of the
capacitor. An overvoltage resulting from
energization of the capacitor bank initially
discharged with line voltage above 90% of
the maximum value is presented in Figure
5.
Fig. 5: Waveform of Capacitor Bank
Energization Overvoltage.
4.2. Time Domain Analysis
In the time domain analysis, data used for
identification are recorded from three
nodes in the network following the
description in Ref. [16]. A vector is built
from the same phases’ signal propagated
to each of the three recorders installed on
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the network. The three data sets calculated
are then concatenated to build an input
vector for the specific overvoltage. The
seven parameters calculated at a recorder
for a specific phase as proposed in Ref.
[16] are presented below from Eqs. (10) to
(16).
ST is the sampling period, t 0 the time at
which the overvoltage occurs and T the
considered period of the overvoltage
waveform for the time domain analysis.
1. Rising time from occurrence to 20% of
maximum value calculated in t 0
to t 1
interval:
R02=t 1!t 0 (10)
2. Rising time from 20 to 90% of the
maximum value calculated in t 1 to t
2
interval:
R09=t 2!t
1 (11)
3. Time from occurrence to falling down
to half of its maximum value:
TTH=t 5!t
0 (12)
4. Absolute rising slope from 20% to
maximum value:
ARS=max(A)*0.8
(t 3!t
0 )
(13)
5. The form factor of the signal:
FF= RMS(A)
Mean(A) (14)
Mean(A) stands for the average value of
the signal. RMS(A) and Mean(A)
calculated over the studied period T
bounded by t 0 & t 5.
6. The ripple factor of the signal:
RF=max( A)!min( A)
Mean( A) (15)
7. The signals’ peak time ratio over its
period:
PTR=t 4!t 2TTH
(16)
4.3. Frequency Band Analysis
The spectral analyses of the three types of
overvoltages under study are the guides for
the choice of frequency bands of the
signals to be retained as parameters for
identification. Figures 6-8 depict the
spectrum of a direct strike overvoltage, a
temporary overvoltage and a capacitor
bank energization overvoltage
respectively.
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Fig. 6: Direct Strike Lightning
Overvoltage Spectrum.
Fig. 7: Temporary Overvoltage Spectrum.
Fig. 8: Capacitor Bank Energization
Overvoltage Spectrum.
The second and third stages of the analysis
in the present work use data provided by
WPD analysis.
In the second stage, signals are grouped
into 1 kHz bandwidth frequency groups
and their energy will be calculated.
Harmonics number 1 and 2 are excluded in
the first group of 1 kHz frequency
bandwidth. Every recorder will be
processed and 10 parameters computed
and concatenated with those from other
two recorders to build a 30-element input
vector for every overvoltage sample.
The choice of data in the third stage is
performed as follows:
Looking back at Figures 6 – Figure 8, it
appears that a right choice of few
parameters can be performed to obtain a
better classification results for a pattern
recognition tool. Keeping the original
WPD with sub-band groups of 1 kHz
bandwidth, the spectral analysis shows that
signals of the first, the third the seventh
and the tenth groups have significant
information that can be used to classify the
three types of over-voltages under study.
This last step will give performances of the
FANN and GRNN in classification using
rightly chosen classification input data’s.
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Data analyzed in the present work are
sampled at 500 kHz, analysis and further
signal processing are performed under
Matlab. The comparative study is
conducted under three categories of inputs.
From time domain analysis, data formally
used for internal and external overvoltage
classification will be used for the first level
of evaluation. It is obvious that the
obtained results will be far lower than
those obtained with the internal and
external classification in Ref. [16]. The
main objective in this part will be to
collect some information about the
adaptability of two types of neural
networks in classification with a non-
accurate choice of input data’s.
The second stage of the analysis will be
dedicated to the frequency band analysis
of different inputs. Simulated data’s will
be processed with the WPD and specific
sub-bands will be considered for building
input data for classification. The goal inthis second part will be to evaluate the
neural network performances with a larger
input vectors.
The third stage will be about the
evaluation of classification performances
using input vector characteristics that are
also based on the precedent figures. Data
are obtained from WPD analysis, the
energy of selected frequency bands will be
calculated to serve as elements of every
input vector. In this case, input vector
elements are not normalized. An extra
evaluation is performed with data of the
third stage normalized to p.u. of
100(V max the line-to-ground peak
voltage.
A discussion from the previously
mentioned cases will follow in Sec. 7 to
bring out specific information about the
conducted comparative study.
5. Performance Evaluation
As stipulated in Sec.5.3, the analysis is
performed with three types of over-
voltages analyzed in frequency domain
and in wavelet sub-band decomposition
domain. The results are evaluated in time
spent for training the NN for different
sizes of input data on the same computer
and the ratio of right identified input data
over the total test data available. The
complete comparison results are presented
in Table 2.
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Table 2: Table of Performance Details.
1. GRNN built on smoothing parameter
'=0.0701 and 46 cluster centers.
2. GRNN built on smoothing parameter
'=0.147 and 61 cluster centers.
3. GRNN built on smoothing parameter
'=0.0204 and 61 cluster centers.
4. GRNN built on smoothing parameter
'=0.0204 and 18 cluster centers; data
normalized to p.u. of 100(V m
ax the line-
to-ground peak voltage.
6. Discussion
With regard to the study carried out in the
present paper, there are some observations
that can be obtained from interpreting the
obtained results. At the first sight, we can
confirm with Ref. [14] that regardless of
the output performance, training GRNN is
hundreds of times faster than training
FANN for the same type and amount of
training data.
The GRNN performs best for normalized
input vectors; the FANN despite the time
taken for training can provide a better
output performance for raw data non-
normalized and regardless of the size of
the input. Normalizing input data is very
crucial for improving the performance of
GRNN
II. CONCLUSION
In the present paper, authors have focused
the study on enlightening some usage tips
of the GRNN and FANN. GRNN is
Input NN Inpu
t
Trai
ning
Training Test Ident
ificat
ion
data
type
type vecto
r size
samp
les
time (s) samp
les
Resu
lts
(%)
Time
domain
FANN 21 54 0.734571 142 54.22
GRNN 1 21 54 0.0281182 142 98.6
WPD FANN 30 61 4.862906 163 75.5
GRNN 2 30 61 0.023164 163 65
FANN 12 61 2.013288 163 81.12
GRNN 3 12 61 0.032108 163 69.5
FANN 4 12 61 2.1602197
0
163 83.11
GRNN 4 12 61 0.0100708 163 91.21
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relatively new to the public and is not yet
widely used as FANNs are well known for
their speed in processing despite the
memory size used to store a complete
trained GRNN that is evaluated to be far
higher than the required memory for
storing the FANN. FANN appears to
behave better in case of non-normalized
data or input data vectors that have a high
variance between equivalent elements.
Adjusting the parameter r in Section 4 for
evaluation of D2
i or modifying the
minimum required output error does not
significantly improve the performance of
GRNN.
FANN and GRNN are both good tools for
autonomous decision making applications ,
although the GRNN performance
outperforms the FANN’s, the FANN can
still be an indicated tool for data cases
where normalization of inputs cannot help
reduce the first partial derivative of inputs
to model suitable data for better
performance of GRNN.
III. ACKNOWLEDGMENT
This work was supported in part by National
Natural Science Foundation of China
(51177049) and by National Science Fund for
Excellent Young Scholars (51322702).
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