RBFNN Based Power Quality Issues Detection and Classification
using Wavelet-PSO
P. KANIRAJAN1
1Electrical and Electronics Engineering, NPR College of Engineering &Technology,
Natham, Dindigul,Tamilnadu, INDIA
Abstract: This paper introduces a new approach to detect and classify power quality disturbances in the power system
using Radial Basis Function Neural Networks (RBFNN) trained by Particle Swarm Optimization (PSO).Back
Propagation (BP) algorithm is the most frequently used for training, but it suffers from extensive computation and also
convergence speed is relatively slow. Feature mined through the wavelet is used for training. After training, the weight
obtained is used to classify the power quality issues. For classification, 8 types of disturbance are taken in to
explanation. The classification performance of RBFNN trained PSO algorithm is matched with BP algorithm. The
simulation result using PSO have significant improvement over BP methods in signal detection and classification.
Keywords: Power Quality, Radial basis function neural network, wavelet transformation,Back Propagation, Particle
Swarm Optimization
Received: October 29, 2022. Revised: May 11, 2023. Accepted: June 17, 2023. Published: July 18, 2023.
1. Introduction
The quality of electric power is more important
because one of the main problems the industries facing is
the falsification in electrical supply. The disturbance such
as voltage sag, swell with and without harmonics,
momentary interruption, harmonic distortion, notch,
flicker, spike and transients causing issues such as a
malfunction, uncertainty , short lifetimes, failure of
electrical equipments and so on. Switching off large load
and energization of large capacitor may affect voltage
swell. Whereas the faults leading to voltage sag or
momentary interruption, harmonic distortion and
notching in the voltage and current are initiated because
of the usage of solid state switching device and nonlinear
power electronically switched devices such as rectifier or
inverters . Transformer energization or capacitor
switching may cause transients. Flicker is formed because
of the furnaces and lightning strikes may lead to spikes.
In a power system, these issues need to be identified
in order to improve power quality (PQ). PQ event
identification is tough because it involves a wide range of
disturbance categories. Therefore, the decision
boundaries of event features may overlap. For these
reasons, the need of power quality analysis has been
strongly growing. Many techniques have been proposed
in the literature to identify and classify the events
envelope. Conventionally, probabilistic approach has
been used for time varying signals in a power quality
analysis, assuming that the power line disturbance
apparatuses vary too slowly to affect the accuracy of
logical process [1-3]. Another paper has suggested a
combination of spectral method with probabilistic
approach, also referred as evolutionary spectrum [4].
The Discrete Fourier Transforms (DFT), which is
computed via the Fast Fourier Transforms (FFT), is used
to extract the features in the waveforms. However, the
accuracy of the DFT algorithm is affected by the product
availability in the voltage waveform. Transient
characteristics of disturbances waveforms are discussed
in [5], since they pertain to signal analysis. This analytic
technique includes the Short-Time Fourier Transform
(STFT) which briefs time–frequency information related
to disturbance waveforms. However, the disturbance
signal cannot be adequately described in this transform,
due to fixed window size [6].
For this reason, S-Transform (ST) is often adopted as a
tool for signal analysis. The superior properties of the ST
are due to the fact that the modulating sinusoidal is fixed
with respect to the time axis, while the localizing scalable
Gaussian window dilates and translates. As a result, the
phase spectrum is absolute in the sense that it always
referred to the origin of the time axis, the fixed reference
point. ST is found to be superior [7].However, the
computational time is very large compared to Wavelet
Transform (WT), which is undesirable for on-line
applications. WT based approach, such as wavelet Multi-
resolution analysis (MRA), has been widely applied to
solve these issues [8].
Wavelet transform and multi-resolution analysis
provide a short window for high frequency components
and long window for low frequency components [9-11]
and hence, provides an excellent time frequency
resolution. This allows WT for analysis of signals with
localized disturbances components and also for
classifying low and high frequency power quality
problems. Using the properties of WT technique and the
features of the decomposed waveforms, along with ANN
algorithm [12-14], it is possible to extract important
information from a disturbing signal for to determine the
type of disturbance that caused. The energy of the
distorted signal will be partitioned at different resolution
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E-ISSN: 2769-2507
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levels in different ways depending on the event available.
The standard deviation can be considered as a measure of
energy signal with zero mean [15-19].
The classification of seven types of PQ disturbances
with self organizing learning array system considering 11
features, besides 22 families of wavelet are tested to
identify the best one for a better classification .
Classification of seven types of PQ events using wavelets
and Probabilistic Neural Network (PNN) is given in [20].
Energy distribution at 13 decomposition levels of wavelet
and time duration of each disturbance are taken as
features and applied to PNN for classification. If a large
number of features is considered, it may result in high
memory and computational overhead. Further, eleven
types of PQ events are also classified with the help of ST
and PNN using only four-dimensional feature sets for
training and testing. The computation time is also very
large compared to WT.
Considering all these matters related to detection and
classification of PQ events, a Radial Basis Function
Neural Network (RBFNN) classifier based on wavelet
transform trained by PSO algorithm is projected in this
work. BP algorithm is a straight forward algorithm which
is constructed on the steepest descent method. Backwards
calculating weight does not seem to be biologically
credible. Neurons synaptic weight modification do not
seems to work backward, and also in the design of
RBFNN trained by BP algorithm a set of system
variables which affect voltage utmost were selected as
RBFNN inputs, if the range of variation is increased, the
precision of the voltage estimation greatly suffers.
Furthermore, it suffers from extensive calculation and
therefore in most of the cases has a very slow
convergence speed. PSO can be a solution which models
the cognitive as well as the social behavior of a flock of
birds which are in search of food over an range [21].It
advances neural network in various aspects such as
learning algorithm, network connection weight and
construction.
Here, less number of features is required for actual
classification of 8 types of PQ events.The RBFNN-PSO
delivers accurate results even with inputs with under high
noisy conditions.
The performance of RBFNN-PSO is compared with
RBFNN-BP, to prove the solidity and accuracy of the
classification. The proposed method is tested with the
insertion of white noise in the signal. From the simulation
results, it is found that RBFNN-PSO classifies the PQ
event more successfully than the other well known BP
algorithm.
To summarize, the paper displays the power quality
problems classification using wavelet transformation and
RBFNN-PSO. First the work deals with wavelet
transformation and feature extraction from WT required
by the neural networks for training and for effective
classification of all the 8 types. Next the paper
pronounces the structure, results and discussion about
detection and classification of PQ events using RBFNN-
BP and similarly for RBFNN-PSO also. Finally, the
performance of RBFNN-PSO is assessed by simulation
and compared with well-known RBFNN-BP.
2. Wavelet Transforms
Wavelet transformation has the skill to analyze different
power quality disturbances in both time and frequency
domain. The wavelet transform is useful in mining
features of various power quality disturbances. Wavelet
analysis handles with expansion of functions in terms of a
set of basis function. However, wavelet analysis develops
functions not in terms of trigonometric polynomials, but
in terms of wavelets. Moreover, another important
property that the wavelet has is perfect reconstruction,
which is the process of reassembling a decomposed
signal into its original form without loss of
information.[1]
Scaling function and wavelet function are used as
construction blocks to decompose and construct the
signal at different resolution levels in MRA.
Representation of signals at various levels of resolution is
the vital goal of MRA. MRA consists of two filters in
each stage and they are low pass and high pass filters.
The resolution of the signal, which is a degree of the
amount of detail information in the signal, is improved by
the filtering operations, and the scale is changed by up-
sampling and down-sampling actions. Sub-sampling a
signal corresponds to reducing of the sampling rate, or
removing some of the samples from the signal. On the
other hand, upsampling a signal relates to increasing the
sampling rate of a signal by adding new samples to the
signal. MRA decomposition and reconstruction are
depicted in Fig.1 (a) and (b).
Fig.1 (a).Multi-resolution analysis decomposition (b) reconstruction
Assume a signal x[n], discrete time signal is dispersed
in 2 level. This signal is filtered into high frequency
constituent in level 1 by using a high pass filter (g(n)) and
low frequency constituents in level 2 by using a low pass
filter (h(n)). This signal is delivered through down
sampling and in MRA level 2.The components in level 1
International Journal of Electrical Engineering and Computer Science
DOI: 10.37394/232027.2023.5.12
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E-ISSN: 2769-2507
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Volume 5, 2023
are utilized as initial signals. These signals are sent
through high-pass filter and low-pass filter. The outputs
of filter can be expressed as in equation (1) and (2) as
follows.
(1)
(2)
g(n) is a high pass filter.
h(n) is a low-pass filter.
] and are the outputs of the high- pass
and low-pass filters, respectively. [2]
3. Wavelet Based Feature
Extraction
Power system consist of various kinds of electrical
disturbances such as sag, swell, momentary interruption,
voltage fluctuation, harmonics etc. and they are generated
by simulation using MATLAB code. The simulated
waveform shows the plot of amplitude of a given
magnitude in the time frequency coordinate system.
Voltage Sag: It occurs due to a fault or switching of
heavy loads. The amplitude of voltage drops by 10 to 90
percent of the rated value due to the sag situation as
shown in Fig.2 (b).
Voltage Swell: When the normal operating voltage
signals increases by 10 to 90 percent, it is known as
voltage swell and is, shown in Fig.2(c).In this way,
remaining classes are generated as shown in Fig.2(d) –
Fig.2(h) and simulated signals are handled through the
wavelet transform and represented by a set of
coefficients.
2 (3)
2 (4)
i= 1,2 …….l is the wavelet decomposition level from
level 1 to level l. N is the coefficients of detail (or)
approximate at each decomposition level. EDi is the
energy that is information level of the detail
decomposition for a level l and EAi is the energy of the
approximate at decomposition level l. In this way, the
wavelet based feature extraction for future analysis has
constructed for the following events from S1 to S8 [2].
S1 Normal
S2 Pure sag
S3 Pure swell
S4 Momentary interruption
S5 Voltage fluctuation
S6 Harmonics
S7 Transients
S8 Combination Events
Fig. 2 Various Electrical Signals (a). Normal Signal (b) Pure sag (c)
Pure swell (d) Momentary interruption (e) Voltage Fluctuaton (f)
Harmonics (g) Transients (h) Combination of Events
4. Radial Basis Function Neural
Network
Radial basis function neural network contains network
similar to back propagation network as shown in Fig. 3
with a hidden layer. RBFNN proves to be best for
classification work from result presented in [22].Each
hidden layer contains of smoothing factor and a
centroids . The distance between the input and the
centroid are normally calculated by the neurons. The
outputs for this particular networks are radial
symmetrical function of the distance [23].When is
nearer to value the output will be a strong one [1].
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DOI: 10.37394/232027.2023.5.12
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Volume 5, 2023
Fig. 3.Architecture of neural network
The mapping function in general form
(5)
The function is a radial symmetrical kernel function
calculated by M kernel units.
The Gaussian exponential function used in this work is
(6)
According to the training data set, centroid , constant
and have to be chosen appropriately.
5. Results and Disscussion for
Detection and Classification
Using RBFNN-BP
For training any neural network, backprobogation is
most commonly used technique, in which it back-
propagates its error during the training stage. Normally
neural networks train the input and expected output for
particular inputs. The sequential steps that carried out
for the detection and classification of power quality
disturbances is shown in Fig 4
Fig. 4.Back-Propagation Algorithm
The simulation of wavelet transformation with
RBFNN-BP for classification of 8 types of power quality
problems was simulated using MATLAB. Here,
amplitude, mean, standard deviation, mean absolute
deviation, median absolute deviation and energy are the
inputs to the RBFNN. Input signal for training is selected
by randomly at a time. The training is carried by setting
learning rate 0.01 and target error 0.001. Each network is
trained with 30 input data of each class and 100 data of
each class are taken in to account for testing. Centre and
weights are updated during every iteration after training
the RBFNN-BP, in this way new training input is given to
the network. The randomly selected signal from 100
signals of each power quality problem for various
orientations is used to test RBFNN-BP. The classification
result during testing is shown in Tables 1.The diagonal
elements are correctly classified events where as off
diagonal elements signifies the misclassification. The
overall accuracy of classification is the ratio of correctly
classified issues to that of the total number of issues. The
overall classification accuracy is 95.87% respectively.
Then the networks are trained and subsequently tested for
higher counts of classes with the same data.
TABLE I
CLASSIFDICATION RESULTS OF RBFNN-BP
6. Partical Swarm Optimization
This technique is one of the population based
optimization tool. To get the optimal solution, every
single solution ‘flies’ over the space . To check how close
they are, optimal is evaluated by using a fitness value
[21].
Particles may have cognitive and socialization. The
neural network weight matrix is reframed as an array to
form a particle, and then initialized randomly and
updated, according to the equation as (7) and (8).
(7)
Disturbances
S1
S S2
S4
S5
S6
S7
S8
S1
10
0
0
0
0
0
0
0
S2
2
98
0
0
0
0
0
S3
4
0
3
0
0
0
0
S4
0
0
98
0
2
0
0
S5
0
4
0
96
0
0
0
S6
4
0
0
0
94
0
2
S7
0
0
0
3
0
96
1
S8
0
0
1
2
0
5
92
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(8)
w, is inertia, cognitive and social acceleration
constant respectively [24].
pBest is the best solution that the particle has attained
and indicates the tendency to reproduce their
corresponding past behaviors. gBest is the best solution
that has attained so far by the specific particle in the
entire population, which indicates the tendency to follow
the achievement of others by the particles . Another
important factor is the maximum velocity Vmax ,
associated with PSO,which mainly fixes the resolution
with which the search space is searched. There may be
probabilities to fly past better solution by the particle if
the value is large and get trapped in the local optima if
the value is very small.
7. Results and Disscussion for
Detection and Classification
Using RBFNN-PSO
The PSO algorithm is somewhat different than any other
technique, rather than training a network PSO trains a
network of networks. It initializes all weights to random
values and starts training each other, on each pass, PSO
checks and compares networks fitness. Each network
comprises position and velocity. The position refers to
weight and the velocity refers to updating of neural
networks weights. Getting the best set of weight is the
main function of PSO. In RBFNN application, the fitness
value relates to a forward propagation and position vector
relates to the weight vector. The best and global best are
used to guide the particle new solution. Inputs are
amplitude, mean, standard deviation, mean absolute
deviation, median absolute deviation and energy. To
speed up the training process, the variables are
normalized. The purpose of having PSO in RBFNN is to
get the best set of weight. 80% of the generated inputs
were used for training and 20% were used for testing
purpose. For RBFNN-PSO with different initial weight, a
population of neural networks was created and sum of
square error in each iteration were calculated and
compared to find the best network in the neighborhood .If
minimum error required is attained, this weight is logged
to use it for testing, other wise again the algorithm is
applied to get the best weight and updating of weight i.e
position and velocity vector for all the networks. After
training the test signals are applied to estimate the
performance of the trained RBFNN-PSO. In this way the
randomly selected signals from 100 signals of each issue
is used to test RBFNN-PSO. The classification result
during testing is shown in Table 2, in these diagonal
elements are correctly classified PQ issues, and where as
off diagonal elements are misclassification.
TABLE II
CLASSIFDICATION RESULTS OF RBFNN-PSO
The overall accuracy results of classification is the ratio
of correctly classified events to that the of total number
of events. The overall classification is 98.25 %.
It is identified that RBFNN provides the best
classification results in this case.In training RBFNN-
PSO, the inputs for training are mostly noise free.
However, the signals in the real system will always have
some amount of noise. In order to test the potential and
robustness of RBFNN-PSO, the white noise, which has
random normal distribution, is added to normal signal to
test the performance of RBFNN-PSO under noisy
environment. The test results are shown in Table 3. As
seen from the simulation results, RBFNN-PSO is able to
detect and classify the power quality problems correctly
with more accuracy rate.
TABLE III
RESULTS OF CLASSIFICATION THE POWER QUALITY PEOBLEMS WITH
NOISE
8. Conclusion
In this paper, the application of wavelet transforms
combined with RBFNN and PSO, to detect and classify
Disturbances
S1
S S2
S4
S5
S6
S7
S8
S1
100
0
0
0
0
0
0
S2
0
95
0
0
3
0
0
S3
0
0
3
0
0
0
0
S4
0
2
98
0
0
0
0
S5
2
1
2
94
0
1
0
S6
0
0
0
0
98
0
2
S7
1
0
0
0
0
98
1
S8
0
0
0
4
0
0
94
Disturbances
S1
S S2
S4
S5
S6
S7
S8
S1
10
0
0
0
0
0
0
0
S2
2
98
0
0
0
0
0
S3
2
0
2
0
0
0
0
S4
0
0
98
0
1
0
0
S5
0
0
0
100
0
0
0
S6
0
2
0
0
98
0
0
S7
0
0
0
0
0
100
0
S8
0
0
0
3
0
0
96
International Journal of Electrical Engineering and Computer Science
DOI: 10.37394/232027.2023.5.12
P. Kanirajan
E-ISSN: 2769-2507
120
Volume 5, 2023
PQ disturbances is presented. Simulation is conducted
to exhibit the properties of WT-based MRA. The
feature extracted by wavelet is used as inputs to
RBFNN-BP. The classification accuracy of the RBFNN
network is improved, just by updating the weights with
cognitive as well as the social behavior of particles
along with a fitness value by PSO algorithm. The
performance of RBFNN-PSO is compared with initially
simulated results given by RBFNN-BP. The proposed
method stands as an evident that it can be used in any
online application.
Acknowledgements
The author would like to thank Management of NPR
College of Engineering and Technology, Natham
Dindigul for having given an opportunity to do research .
References
[1] Kanirajan, P & Suresh Kumar, V 2015, ‘Power
quality disturbances detection and classification
using wavelet and RBFNN’ In Applied Soft
Computing, Elsevier, Vol. 35, pp. 470-481.
[2] Kanirajan, P & Suresh Kumar, V ‘Wavelet - based
power quality disturbances detection and
classification using RBFNN and Fuzzy Logic’,
International Journal of Fuzzy Systems, Springer,
Vol.17 (4), pp.623-634.
[3] Kanirajan, P & Suresh Kumar, V 2015, ‘A wavelet
based data compression technique for power quality
events classification’, WSEAS Trans. on Power
system, Vol. 10, pp. 82-88
[4] Kanirajan P,Eswaran and V.Sureshkumar " An
Integrated Data Compression Using Wavelet and
Neural Network for Power Quality Disturbances"
Journal of Electrical Engineering vol.19(5), 2019.
[5] Kanirajan P,M.Joly and Eswaran " A Comparison of
Back propagation and PSO for training RBF Neural
Network for Wavelet based Detection and
Classification of Power Quality Disturbances "
Journal of Electrical Engineering “International
Journal of Signal Processing, Vol.6 2021.
[6] Chun-Yao Lee and Yi-Xing shen,“Optimal Feature
Selection for Power Quality Disturbances
Classification”, IEEE Trans.PowerDel.Vol.26.No.4.
pp.2342- 2351,Oct. 2000.
[7] W. Edward Reid, “Power Quality Issues – Standards
and Guidelines”, IEEE Trans. Industry
Applications,Vol.32.No.3 .pp.625-
632,May/June1996.
[8] A.Elmitwally;S.Farghal;M.Kandil;S.Abdelkader and
M.Elkateb, Proposed “wavelet-nerofuzzy combined
system for power quality violations detection and
diagnosis”, Pros.Inst.Elect.Eng.,Gen
,Transm,Distrib.,Vol.148.No.1.pp.15-20,Jan.2001.
[9] T.Mcconaghy,H.Lung,E.Bose;V.Vardan, “
Classifcaton of Audio radar sgnals using Radial
Basis Function Neural Networks”, IEEE Trans.
Inst. And Measurements,Vol.52.No.6.pp.1771-
1779, Dec.2003
[10] Chia-Hung Lina and Chia-Hao Wang, “Adaptive
Wavelet Networks for Power Quality Detection and
Discrimination in a Power system”, IEEE Trans.
PowerDel.Vol.21.No.3. pp.1106-1113,July 2006.
[11] S.Santoso.“Power quality assessment via wavelet
transform analysis,” IEEE Trans.Power Del.,
Vol.11.pp.924-930,Apr.1995.
[12] Gauda,M., Salama,M.A.,Sultam,M.R. and Chikhani
A.Y. “Power quality detection and classification
using wavelet multi-resolution signal
decomposition”, IEEE Trans.On Power
del.,Vol.14.pp.1469-1476,1999.
[13] Jaideva C. Goswami and Andrew K. Chan,
Fundamentals of wavelets: Theory, Algorithms,
and Applications John Wiley & Sons, 1999.
[14] InigoMonedero;Carlos Leon; Jorge Ropero; Antonio
Garcia and Jose Manuel Elena,“ Classification of
Electrical Disturbances in Real Time using Neural
Networks”, IEEE Trans. Power
Del.,Vol.22.No.3.pp.1288-1296,July2007
[15] Masoum; M.A.S, Jamali,S and Ghaftarzadeh,
N,“Detection and Classification of power quality
disturbances using discrete wavelet transform and
wavelet network”, IET Science,measurements &
technology.,Vol.4.pp.193-205, 2010.
[16] Z.L.Gaing, “Wavelet-Based neural network for
power disturbance recognition and classification”,
IEEE Trans.Power Del.,Vol.19.No.4.pp.1560-
1568.Oct.2004.
[17] S.Mishra; C.N.Bhende and B.K.Panigrahi,“Detection
and Classification of Power Quality Disturbances
using S-Transform and Probabilstic Neural
Networks”, IEEE Trans. Power Del.,
Vol.23.No.1.pp.280-286Jan.2008.
[18] A.Garcia-Perez and E. Cabal-Yepez,“Techniques
and methodologies for power quality analysis and
disturbances classification in power systems A
review”, IET Gener. Transm.Distrib. Vol.5.No.4.
Pp.519-529, Apr.2011.
[19] C. I. Chen, “Virtual Multifunction power quality
analyzer based on adaptive linear neural
network”,IEEE Trans.Ind.Electron ,
Vol.59.No.8.pp.3321-3329, Aug.2012.
[20] Prakash K.Ray; Soumy a R.Mohanty and
NandKishor, “Classification of Power Quality
Disturbances Dueto Environmental Characteristics in
Distributed Generation System”, IEEE Trans.on
sustainable energy.,Vol.4.No.2.pp.302-
313,Apr.2013.
[21] X.Hu, Y. Shi and R.Eberhart, “Recent advances in
Particle Swarm Optimization”, Proceedings of the
congress on Evolutionary Computation, Portland,
OR, USA, 1(2004), pp.90-97.
International Journal of Electrical Engineering and Computer Science
DOI: 10.37394/232027.2023.5.12
P. Kanirajan
E-ISSN: 2769-2507
121
Volume 5, 2023
[22] K.G Narendra; V.K.Stood; K. Khorasani and R.
Patel, “Application of Radial basis Function (RBF)
Neural Network for fault diagnosis in a
HVDCsystem”,IEEE Trans.on Power
Systems.,Vol.13.No.1.pp.177-183,Feb.1998.
[23] M. Chester, Neural Networks.A tutorial, London,
pp.50-66. Prentce hall,(1993)
[24] R.C.Eberhart and Y. Shi, “Particle swarm
Optimization Developments, Applications and
Resources”, Proceedngs of the 2001 Congress on
Evolutionary Computation, 1(2001), pp.81-86.
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