Advanced Computational Techniques in Electromagnetics 2014 (2014) 1-20
Available online at www.ispacs.com/acte
Volume 2014, Year 2014 Article ID acte-00183, 20 Pages
doi:10.5899/2014/acte-00183
Research Article
Assessing power quality of power system using FICA algorithm
S. Nourollah1*, A. Zargari1
(1) Department of Electrical and Computer Engineering, Qazvin Islamic Azad University
Copyright 2014 © S. Nourollah and A. Zargari. This is an open access article distributed under the Creative
Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium,
provided the original work is properly cited.
Abstract
The new developments in power system such as restructuring and competitive electricity market make
power quality (PQ) an important factor in competition. However, finding a measure for PQ evaluation is
very difficult due to many indices involved in PQ measurement. For this reason, obtaining a single
quantitative index based on the standard measurements has been a new challenge in recent researches. In
this paper, a data mining method is proposed to determine global indices for PQ. The continuous and
discrete indices of PQ are considered and a Unified Power Quality Index (UPQI) is presented for each PQ
index, based on the method of incorporation and normalization. The indices are normalized and classified.
Then, the global PQ index of each distribution site is determined by the Fast Independent Component
Analysis (FICA) algorithm. In this approach, the PQ measurements of 313 real distribution sites are used
to assess and classify the indices for different type of loads in the real distribution system. The results
show the capability of this method to obtain an accurate measure for PQ evaluation. In this method, the
convergence rate is very fast. Also for evaluating the accuracy of the proposed algorithm, an intelligent
method based on artificial neural network (ANN) and fuzzy logic to obtain a global index for PQ
assessment are implemented that the comparing between this two method show that the proposed method
is stronger and proper than the intelligent method. This method can be extended for many distribution
sites.
Keywords: Global index, Fuzzy Logic, Independent Component Analysis, Power Quality.
1 Introduction
In the past two decades, the electrical power has become very important in many sectors (e.g. textile,
metal and casting industry, residential and electricity market). The electric power quality (PQ) has become
very important for several reasons such as rapid increase of nonlinear loads and sensitive loads at the same
time, restructuring of the electric power industry and establishing the competitive electricity market
(Salarvand et al. 2010 [1]; Bracale et al. 2011 [2]; Liang et al. 2009 [3]). Also all phenomena of PQ must
be characterized and qualified to appraise system performance. The disturbances of PQ and their negative
* Corresponding Author. Email address: S_Nourollah@sbu.ac.ir, Tel: +982129904105
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effects on the power system can be evaluated by the PQ indices. Because of having different power quality
indices with has no concept unless they are combined into global value that could represent them. In the
other hand, to study PQ of distribution sites needs to collect and assess large amount of data, related to
different types of PQ indices. The measured data are not in a suitable form to present the PQ condition of a
site or a special area (Salarvand et al. 2010 [1]; Bracale et al. 2011 [2]). The phenomena of PQ are
classified into two main types, “continuous” type and “discrete” type. The continuous phenomena include
some of voltage indices; e.g. flicker (Plt, Pst), unbalance and harmonics. The discrete types are voltage
sag, swell and transient that occur non-periodically and the iteration, date and time of their occurrence are
recorded (Lin et al. 2005) [4]. Although considerable endeavors have been already performed to define the
different kinds of PQ disturbances and their indices, it is less tried to determine a specific framework for
determining a global PQ index. Generally, there is a need to obtain a global index for comprehensive
assessing of voltage and current quality and characterizing the all level of them (Salarvand et al. 2010) [1].
A global index reduces the huge amount of measured data in distributed sites. Also, the level of PQ of each
discrete disturbance is obtained over the desired period with a single quantitative index that this is
explained in this paper. Many studies have been carried out to determine the PQ disturbances and to
introduce the effective indices for explaining their features. Paper (Herath et al. 2005) [5] discusses about
three disturbances, voltage sag, swell and transient. In there, a method based on disturbance severity
indicator (DSI) proportional to the customer complaint (CC) rate is proposed that it characterizes these
phenomena and their suitable limits. In order to improve the PQ of distributed systems, in (Mostafa et al.
2012) [6], a method based on flexible distributed generation (FDG) and a recursive least square (RLS)
algorithm is proposed. The FDG method decreases and mitigates harmonics and voltage flicker. Also the
power factor and the voltage unbalance, in the point of common coupling (PCC), are tuned and the RLS
algorithm estimates the voltage phase angle. Based on the method given in (Salarvand et al. 2010) [1], two
global PQ indices for both load and supply sides, with cost coefficient, are presented that they determine
the level of PQ in some real sites. In this method, artificial neural network is used. In (Naidu et al. 2012)
[7], a method based on the Monte-Carlo procedure, for estimating the number of unacceptable voltage sags
in the distribution systems, is proposed. Also the transmission lines and distribution feeders identify the
critical sags in each load bus. A method of PQ evaluation is given in (Liang et al. 2009 [3]) that using
improved independent component analysis, some of voltage PQ indices can be analyzed. Mainly, the
hidden structure of data can be found and eventually these phenomena are numerically expressed. The
nonlinear harmonic loads of the distribution system generate voltage and current harmonics. In (Lee et al.
2010 [8]; Qian et al. 2008 [9]; Lee et al. 2008 [10]) the methods for detecting and cancelling the harmful
harmonics of nonlinear loads in power systems are introduced that they are effective in improving PQ. In
(Lee et al. 2010) [8], a new PQ index (PQI) is defined that the total harmonic distortion (THD) and the
electric load composition rate (LCR) are effective on it. This method appraises the harmonic pollution rate
in each distribution system, the transient disturbances and their impacts on the main grid are assessed by
employing the S-transform method. Then by probabilistic neural network, all of them are classified in
eleven classes, in (Mishra et al. 2008 [11]; Jia et al. 2010 [12]). Reference (Morsi et al. 2009) [13] Studies
on some PQ indices, e.g. PF, THDv and THDi. Based on the wavelet packet transform, it defines a global
index for assessing the PQ of system and then using fuzzy systems, the new PQI in both load side and
supply side is numerically expressing. For discrete disturbances, based on discrete severity indicators
(DSI), a global index is defined in (Carpinelli et al. 2007) [14]. This index is assessed in two modes. In the
first mode, without disturbances, difference of ideal and real voltage value is evaluated but in another one,
by the variations of some conventional PQ indices, voltage quality in supply side is determined. In (Lee et
al. 2004 [15]; Lee et al. 2009 [16]), Voltage sag index and its effects on loads is evaluated. In (Lee et al.
2004) [15], two indices, load drop index (LDI) and load drop cost (LDC), is defined. These can evaluate
the impacts and interruptions of voltage sags on customers. LDI and LDC are calculated by CBEMA and
ITIC curves, IEEE standard 1159, voltage estimation, cost data and load types. Also in (Lee et al. 2009)
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[16], for assessing the uncertainties, reliability and voltage sag indices are combined and define one new
index. In there, also a cost index is proposed that it determines the penalty value for each consumer. The
Adaptive Prony method as a signal processing approach for assessing PQ disturbances is introduced in
(Andreotti et al. 2009) [17]. This method can follow fast changes of the PQ. For voltage sags detection, a
method is introduced in (Capua et al. 2005) [18] that it modifies three new PQ indices presented in (Capu
et al. 2004) [19], with presence of uncertainties in grid. This technique can make drastic accordance
between numeric index and cost value. All of these methods assess the effects of PQ indices in the network
for improving the electrical PQ in power systems.
In this paper, a data mining method is proposed for defining a global PQ index. At the first, the continuous
and discrete phenomena of PQ, standard indices, and their limitations are introduced. In part 4, a
normalization and incorporation method of recorded indices is presented to evaluate the annual index for
each PQ index. In part 5, the twelve PQ indices are classified from in seven classes and each class gives a
fuzzy expression. In part 6, the FICA algorithm and its application are described in order to determine a
global PQ index for each distribution site. In part 7, the PQ of a real distribution system is evaluated using
proposed method. In part 8, the proposed method is compared with another method and FICA properties
are presented and eventually conclusion is given.
2 Description of the method
After measuring standard single indices of PQ of the site, for obtaining two global indices of PQ, there
are five steps which should be followed:
1. Introduce qualified and disqualified regions of Continuous and discrete PQ phenomena and their limits
according to PQ standards.
2. Normalize and incorporate recorded indices to evaluate the annual index for each PQ index.
3. Define several classes with fuzzy expression.
4. Determine range of variations each PQ index in each class.
5. Implement the FICA algorithm in order to determine weight matrix (w).
6. Calculate distance and correlation indices for each distribution site.
7. Evaluate two global indices for six types of load.
3 Classification of PQ phenomena and determination of their permissible limits
PQ phenomena are divided into two continuous and discrete groups. Some of the most important
phenomena are shown in Fig. 1 (IEEE Std. 1159-1995, 1995 [20]; Golkar, 2004 [21]; Dugan et al. 2002
[22]).
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Power Quality
Phenomena
Continuous Phenomena
Discrete Phenomena
Voltage Sag
V_unbal
Voltage Fliker
(plt,pst)
F_dev
THDv
V_dev
Voltage Swell
I_unbal
Transient
THDi
PF
Figure 1: PQ phenomena and their classification
For each continuous PQ phenomena, an index is presented in various standards with their permissible
limits. The recommended limits according to Iran Power Industry Standards (IPIS) PQ limits for 20 KV
network are given in Table 1, (IPIS, 2002) [23]:
Table 1: Recommended limits of continuous disturbances according to IPIS for 20 KV network
Index
Pst
Plt
F_dev
V_unbal%
I_unbal%
THDi%
THDv%
Pf
V_dev%
Limit
0.9
0.7
0.6
2
8
5
5
0.9
5
Generally, there are few methods for defining the discrete PQ indices and their limits (ESKOM, 1996 [24];
CPQ Std. DS 327, 1997 [25]). Some of these methods provide a count of event frequency and duration, the
undelivered energy during events or the cost and severity of the disturbances (Bollen et al. 2003 [26];
Thallam, 2001[27]; Thallam et al. 2000 [28]).
One of the most common methods of evaluating the discrete PQ phenomena is using voltage tolerance
curves that are plots of equipment maximum acceptable voltage deviation versus time for acceptable
operation. The most famous of these curves are Computer and Business Equipment Manufactor’s
Association (CBEMA) and Information Technology Industry Council (ITIC) curves. In (Fleming, 2000)
[29], the RPM index is presented, based on the CBEMA graph. In (Fleming, 2000 [29]; Herath et al. 2003
[30]; Gosbell et al. 2002 [31]) deficiencies of RPM index are mentioned and better method of Least
Squares (LS) is applied to the log plot of CBEMA/ITIC curves. According to this method, an index named
Contour Number (CN) in equation (3.1) is calculated for each point of the graph in Fig. 2:
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Figure 2: CBEMA and ITIC curve fittings for different discrete disturbance types (i.e. voltage sags, swells, and
transients)
CN 
V 1
(3.1)
VCBEMA / ITIC  1
where VCBEMA/ITIC is calculated based on equation (3.2), (3.3) and (3.4):
 1 


 0.0035   1.22 
VCBEMA Sag (t )  0.86  

 t 
(3.2)
 1 


 0.000295   1.48 
VCBEMA Swell (t )  1.06  

t




1
(3.3)


 0.00076   1.014 
V ITIC Os.trans (t )  1.2  

t


(3.4)
For any discrete phenomenon, permissible limits of CN index based on recorded data in 9 European
countries and method given in (Fleming, 2000) [29] are presented in Table 2. In this method, the indices
are generated by the number of events in each region of CBEMA curve using UNIPEDE DISDIP survey
(IEC 61000-2-8, 2002) [32] results and Electric Power Research Institute (EPRI) DPQ project data (Dorr,
1995) [33].
Index
Limit
Table 2: Permitted limits of CN
CN_sag
CN_swell
CN_Os.transient
4
5
1
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4 Computing the annual indices for a distribution site:
During a year, a distribution site is frequently studied and its PQ indices are measured and recorded. The
recorded data are not in a suitable form to show the PQ status of site. Therefore, it requires obtaining a
method for this problem. The following method is based on the normalization and incorporation procedure
of recorded indices during a year.
4.1. Normalization
In order to normalize, each recorded index is divided by its standard permissible interval of variation. For
example, the permissible value of Pst index is 0.9 for 20kv network. If the recorded value for the Pst index
is 0.8, its normalized value will be 0.89. So, the final indices obtained by normalizing, have a simple
feature that their maximum value is always 1.
4.2. Incorporation
In incorporation procedure, the recorded and normalized indices of each index during a year are
incorporated in a way that a suitable annual standard is obtained for each index. Generally, the average or
maximum value is used for incorporation. But it is shown that these methods are not suitable, and a better
method is presented here. There is a need for a single quantity, which we call the Unified PQ Index
(UPQI). The maximum and average method and proposed method are compared in Table 3. The presented
values in the table consist of the measured samples of an index for 3 distribution sites. The Average PQ
Index (APQI) equals the average value and the Maximum PQ Index (MPQI) equals the maximum value in
the annual recorded values of index.
In Table 3, all recorded samples were normalized. As it is presented in Table 3, all recorded samples of site
1 are within standard limits. Nevertheless, the APQI value of site 1 is more than site 3, while one of the
recorded samples of site 3 is more than the permitted limit. Therefore, the average value is not a suitable
measure. In addition, the MPQI value of site 2 and site 3 are equal, while three recorded indices of site 2
are more than the permitted limits, and site 3 has only one over limit value and it is in a better PQ status.
So, the maximum value is not a suitable measure for inclusion too.
Table 3: Comparison of average, maximum and proposed methods
Site
samples
First sample
Second sample
Third sample
Fourth sample
APQI
MPQI
UPQI
1
2
3
0.8
0.7
0.8
0.8
0.8
0.8
0.8
1.2
0.6
1.4
1.4
1.1
1.4
1.4
0.5
0.1
0.4
1.4
0.6
1.4
1.1
In this paper, the UPQI measure is used in our calculation. This index is computed based on the following
assumptions:
1) If all the recorded values are less than 1, the UPQI value equals the maximum of recorded values which
indicates the greatest effect on the power system’s customers.
2) If some of the recorded values are more than 1, the UPQI value equals the addition of 1 with average of
trepass values. If a sample value is more than 1, the trespass value equals sample value minus 1 and if a
sample value is less than 1, the trepass value is zero.
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As it is shown in Table 3, UPQI value of site 2 is less than site 3 and UPQI value of site 3 is less than site
1 that it is more reasonable than two other measures.
5 Classification of the variation range of PQ phenomena and Determination of their fuzzy
expression
In this section, the range of variations of PQ phenomena is divided to seven levels or classes as Table 4.
Class 1 is the best class and class 7 is the worst. The maximum qualified value of each phenomenon is in
class 3. So, classes 1, 2, and 3 are in the permissible region and the classes 4, 5, 6, and 7 are in the
impermissible region. In Table 5, the quality of each class is presented by a fuzzy expression.
Table 4: Classification of the variation range of twelve PQ phenomena
V_dev
THDv
THDi
V_unbal
I_unbal
F_dev
Pf
Pst
Plt
CN_Swell
CN_Sag
CN_Trans
Class 1
[0 1.66]
[0 1.66]
[0 2.66]
[0 0.66]
[0 2.66]
[0 0.2]
[0.966 1]
[0 0.3]
[0 0.23]
[0 1.66]
[0 1.33]
[0 1.33]
Class 2
[1.66 3.33]
[1.66 3.33]
[2.66 5.33]
[0.66 1.33]
[2.66 5.33]
[0.2 0.4]
[0.933 0.966]
[0.3 0.6]
[0.23 0.46]
[1.66 3.33]
[1.33 2.66]
[1.33 2.66]
Class 3
[3.33 5]
[3.33 5]
[5.33 8]
[1.33 2]
[5.33 8]
[0.4 0.6]
[0.9 0.933]
[0.6 0.9]
[0.46 0.7]
[3.33 5]
[2.66 4]
[2.66 4]
Class 4
[5 15]
[5 10]
[8 18]
[2 3]
[8 18]
[0.6 0.7]
[0.8 0.9]
[0.9 1.2]
[0.7 1]
[5 9]
[4 8]
[4 8]
Class 5
[15 25]
[10 15]
[18 28]
[3 4]
[18 28]
[0.7 0.8]
[0.7 0.8]
[1.2 1.5]
[1 1.3]
[9 13]
[8 12]
[8 12]
Class 6
[25 35]
[15 20]
[28 38]
[4 5]
[28 38]
[0.8 0.9]
[0.6 0.7]
[1.5 1.8]
[1.3 1.6]
[13 17]
[12 16]
[12 16]
Class 7
[35 45]
[20 25]
[38 60]
[5 10]
[38 60]
[0.9 3]
[0 0.6]
[1.8 5]
[1.6 4]
[17 50]
[16 50]
[16 50]
Table 5: Fuzzy expression of the quality of classes
Number of Class
Class 1
Class 2
Class 3
Class 4
Class 5
Class 6
Class 7
Fuzzy Expression
Excellent
Very good
Good
Medium
Bad
Very bad
Terrible
Now, this question is put forward that in which level of PQ, a distribution site with the various PQ indices
is classified. In the next section, the FICA algorithm is proposed to answer this question.
6 FICA algorithm
Fast Independent Component Analysis (FICA) is a very general-purpose statistical technique in which
observed random data are linearly transformed into components that are maximally independent from each
other, and simultaneously have “interesting” distributions. The FICA is nominated as: given a set of
( ), that are generated by linear mix of a group of source
observed signals (random), ( ) ( ) …,
( ), and t represents the time or sample labeling
signals (independent component), ( ) ( )
(Hyvarinen, 1999 [34]; Hyvarinen et al. 2001 [35]).
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x 1 (t) = k 11 s1 (t) + k 12 s 2 (t) + …+ k 1m s m (t)
x 2 (t) = k 21 s1 (t) + k 22 S 2 (t) + …+ k 2m S m (t)
x m (t) = k m1 s1 (t) + k m2 s 2 (t) + …+ k mm s m (t)
These can be expressed ( )
weight matrix,
. So:
( ) Where
(6.5)
is the mixed coefficient matrix. We need to find a
Z = K -1 X = W T X = S
(6.6)
W = [w 1 , w 2 , …, w m ]T
(6.7)
Using a fixed point iterative algorithm, FICA mainly detects the maximum Non-Gaussianity of
or
till the unit vector W (weight vector) is found.
It should be noted that the Gaussian value of each vector comprises the biggest data entropy. So, the
Gaussianity of the separated signals is measured. For measuring the Gaussianity of signal needs to
negative entropy. Negative entropy is given by:
J(Z) = H(Zgauss ) - H(Z)
(6.8)
Where
H ( Z )   p z ( ) log( p z ( )) d
(6.9)
shows gaussian value of vector Z. it’s important that the covariance matrices of vectors Z and
are similar and if vector Z has gaussian distribution then negative entropy will be zero otherwise it
will be nonnegative. ( ) shows probability density in which it is often indescribable. So, negative
entropy must be calculated approximately by:
J(Z)  [ E{g(Z) } - E{g(Z gauss ) }]2
(6.10)
Where E means expected value and g is a non quadratic that it’s approximated by equations (6.11), (6.12)
and (6.13):
g(r) =
1 4
r
4
(6.11)
r2
)
2
(6.12)
g(r) = log (coshr)
(6.13)
g(r) = -exp (
Negative entropy must be maximized. Based on the central limit theorem, it means to maximize ( ) or
* ( )+. Eventually, the iterative equation of FICA is:
W(t + 1)  E{X g(W T (t) X) } - E{g ' (W T (t)X)}W(t)
(6.14)
And then weight matrix must be normalized.
W* =
W(t + 1)
|| W(t + 1) ||
(6.15)
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Symmetrical orthogonalization is done by:
W  (WW T ) -0.5 W
(6.16)
This process must be iterated until the weight matrix (W) converges.
So the steps for implementation of the FAST-ICA algorithm can be described as follows:
1. The matrix data, x, is transformed such that it has zero mean.
2. An initial unit norm vector w is chosen randomly.
3. The function g is calculated by equations (6.11), (6.12) or (6.13).
4. W is updated by equation (6.14).
5. W is normalized again to have unit norm by equation (6.15).
6. Symmetrical orthogonalization is done by equation (6.16).
7. Steps 3, 4, 5 and 6 are repeated until w converges.
By implementation of the FICA algorithm, the matrix W can be computed. Using these weighting
coefficients and the Euclidean distance method, the correlation of all classes and sites ( C i ) can be
calculated. First, the virtual optimal and worst points of indicators are obtained as:
 
r j  max xij ,
r j  max xij , i  1,2,..., n
(6.17)
i  1,2,..., n
Where h , p and n are number of classes, sites and PQ indices respectively. Then, the Euclidean distance
of samples are calculated using best point, d+, and the worst point, d-, based on equation (6.18):
d i
p
 W j ( xij  r j ) 2

, i  1,2,..., ( p  h) , j  1,2,.., n
j 1
d i 
p
(6.18)
 W j ( xij  r j ) 2
, i  1,2,..., ( p  h) , j  1,2,.., n
j 1
Finally, correlation ( C i ) is obtained as:
Ci 
d i
d i  d i
, i  1,2,..., ( p  h)
(6.19)
The value of C i is between 0 to 1, it should be mentioned that the best PQ for the site number i will
happen in C i equal to zero. By equation (6.19) C i will be calculated for all sites and according to value of
C i for each site, classification will be done. The procedure of proposed method is given in Fig. 3.
For example, in order to use the ICA algorithm for determining the quality level of 10 measured sites in
the 20KV distribution system of Isfahan province, the data matrix, x, can be presented as:
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Pst
Samples of site1 to site 10
limits of class 1 to class 7
0.14
1.00

0.12

0.12
1.00

1.00
0.12

0.15
X 
1.00

0.33

0.66
1.00

1.33
1.66

2.00
5.55

Plt
0.44
0.98
0.36
0.34
0.96
0.85
0.33
0.48
0.82
0.33
0.66
1.00
1.43
1.86
2.29
5.72
F_div V_un
0.417
0.409
0.433
0.483
0.459
0.398
0.83
0.45
0.53
0.33
0.66
1.00
1.16
1.33
1.50
5.00
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I_un
0.2 0.51
0.15 0.41
0.29 0.51
0.22 0.49
0.37 0.66
0.18 0.24
0.15 1.00
0.16 0.55
0.25 0.41
0.33 0.33
0.66 0.66
1.00 1.00
1.50 2.25
2.00 3.50
2.50 4.75
5.00 7.50
THDi
THDv
1.08 0.59
1.02 0.54
1.00 0.68
0.43 0.28
0.99 0.44
1.07 0.76
1.00 0.13
1.15 0.39
1.00 0.43
0.33 0.33
0.66 0.66
1.00 1.00
2.25 1.50
3.50 3.00
4.75 4.00
7.50 5.00
Pf
0.41
0.88
0.52
0.17
1.02
1.00
1.61
1.00
0.61
0.33
0.66
1.00
2.00
3.00
4.00
10.0
V_div CN_sag CN_swell CN_trans
1.02
0.85
1.13
0.72
2.00
0.64
1.00
1.00
1.5
0.33
0.66
1.00
3.00
5.00
7.00
9.00
1.11
0.32
1.53
1.12
1.37
0.3
0.33
0.12
0.04
0.33
0.66
1.00
2.00
3.00
4.00
10.0
0.14 0.12
0.43 0.18
0.34 0.44

0.02 0.11
0.57 0.38

0.51 0.21
1.77 0.06

0.18 0.06
0.56 0.14

0.33 0.33

0.66 0.66 
1.00 1.00 

1.80 2.00
2.60 3.00 

3.40 4.00
10.0 10.0 
Figure 3: Flowchart of proposed method
7 Result and Discussion
In this section, the PQ level is examined for several types of load in a real distribution system. The
measured data of 313 distribution sites are evaluated in 4 provinces of Isfahan, Qazvin, Khuzestan, and
Kurdistan. The measured sites are divided into 6 load groups as follows:
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Group 1: Metal and casting industry
Group 2: Textile industry
Group 3: Food and chemical industry
Group 4: Nonmetal and stonework industry
Group 5: Residential, public, and hospital
Group 6: Mixed load
Table 6 is shown the number of points related to each type of load.
Table 6: Number of measured sites related to each type of load
Group
Type of load
Number of measured points
1
metal and casting industry
73
2
textile industry
17
3
food and chemical industry
31
4
nonmetal and stonework industry
65
5
residential, public and hospital
47
6
mixed load
80
There are two defined global PQ indices; Supply side Power Performance Index (SPPI) and Load side
Power Performance Index (LPPI). According to the definition, SPPI shows effect of six voltage PQ indices
and LPPI shows effect of three current PQ indices.
7.1. Twelve single power quality indices for different load types
In each class, the frequency percentage of twelve indices is calculated for different load types. For
instance, the bar graphs of frequency percentage for metal and casting industry are shown in Fig. 4 to Fig.
6:
70
60
PF
50
I_unbalance
40
THDi
30
20
10
0
class 1 class 2 class 3 class 4 class 5 class 6 class 7
Figure 4: Bar graph of frequency percentage for current indices of metal and casting industry
It should to be mentioned that classes 1, 2 and 3 are in the permissible region and the classes 4, 5, 6, and 7
are in the impermissible region. As shown in fig. 4, I_unbalance for 96% of sites of metal and casting
industry are in permissible region, also are 82% for PF, and 68% for THDi.
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100
90
80
70
60
50
40
30
20
10
0
THDv
V_deviation
V_unbalance
Frequency
Pst
Plt
class 1
class 2
class 3
class 4
class 5
class 6
class 7
Figure 5: Bar graph of frequency percentage for voltage indices of metal and casting industry
As shown in Fig. 5, all voltage indices except flicker indices (Plt & Pst) are in the permissible region. Also
for discrete indices, the transient index has the best quality (Fig. 6).
100
90
80
Swell
70
Sag
60
Transient
50
40
30
20
10
0
class 1
class 2
class 3
class 4
class 5
class 6
class 7
Figure 6: Bar graph of frequency percentage for discrete indices of metal and casting industry
7.2. Two global power quality indices for different load types
In each class, the frequency percentage of global power quality indices, LPPI and SPPI, are calculated for
different load types that are shown in Fig. 7 and Fig. 8:
Metal and
Casting
100
Textile
80
60
40
food and
chemical
Nonmetal and
Stonwork
20
0
Residential,
Public and
Hospital
Figure 7: Bar graph of frequency percentage of SPPI index for all industries
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The summarization of Bar graph of frequency percentage of SPPI index for all industries in Fig. 7 is
presented in Table 7. The Textile group has the maximum percentage equal to 85.71% in the permissible
region and the Metal and Casting group have the minimum percentage equal to 40%.
Class7
0
0
0
0
0
0
Class6
0
0
4%
0
0
0
Table 7: Frequency percentage of SPPI index for all industries
Class5
Class4
Class3
Class2 Class1
SPPI
0
60%
40%
0
0
Metal and Casting industry
0
14.3%
85.71%
0
0
Textile industry
4%
40%
52%
0
0
Food and Chemical industry
0
38.1%
61.1%
0
0
Nonmetal and Stonework industry
0
53.65% 46.34%
0
0
Residential, Public and Hospital
1.58% 21.42%
77%
0
0
mixed load
Metal and Casting
Textile
100
90
80
70
60
50
40
30
20
10
0
food and chemical
Nonmetal and
Stonwork
Residential, Public
and Hospital
Terrible
Bad
Very Bad
Good
Medium
Exellent
Very Good
Mixed load
Figure 8: Bar graph of frequency percentage of LPPI index for all industries
The summarization of Bar graph of frequency percentage of LPPI index for all industries in Fig. 8 is
presented in Table 8. The Food and Chemical group have the maximum percentage equal to 92% in the
permissible region and the Metal and Casting group have the minimum percentage equal to 60%.
Table 8: Frequency percentage of LPPI index for all industries
Class7
0
0
0
0
0
0
Class6
0
0
0
0
0
0
Class5
12%
0
0
9.52%
0
1.6%
Class4
28%
14.3%
8%
4.76%
9.75%
12.7%
Class3
52%
71.4%
52%
71.43%
63.41%
51.58%
Class2
8%
14.3%
36%
14.3%
21.95%
33.33%
Class1
0
0
4%
0
4.8%
0.8%
LPPI
Metal and Casting industry
Textile industry
Food and Chemical industry
Nonmetal and Stonework industry
Residential, Public and Hospital
mixed load
According to Fig. 7 and Fig. 8, the class related to the greatest percentage for each type of load is
presented in Table 9.
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Table 9: The class related to the greatest percentage for each type of load
Group
metallic
and casting
industry
Global index
SPPI
Good
LPPI
Good
textile
industry
food and
chemical
industry
nonmetallic
and stonework
industry
residential,
public and
hospital
mixed load
Very
Good
Good
Very
Good
Good
Very Good
Good
Very Good
Good
Good
Good
8 Intelligent algorithm: Artificial neural network (ANN) and fuzzy logic
In this section, for evaluating the obtained results by FICA algorithm, intelligent methods like ANNs and
fuzzy logic will be employed and collation of these results shows the capability and the advantages of the
FICA algorithm for the obtaining global PQ Indices.
At the first, variations domain of discrete and continuous indices is determined and each PQ index is
classified into permissible and impermissible regions according to PQ standards. In this step, several
points from qualified and disqualified regions from ideal data are choose for training the three-layer MLP
neural network that we know its output experimentally. The output of ANN is a number between 0 till 280.
After train the neural network, the output results enter into fuzzy logic block for take fuzzy expression.
The schematic of three-layer MLP neural network and fuzzy logic system are given in Fig. 9 and Fig. 10,
respectively. This fuzzy definition will create seven classes as Q1…Q7 which class1 (Q1) means the best
quality and class7 (Q7) means the worst quality. The procedure of this method is shown Fig. 11.
Figure 9: Three-layer MLP neural network
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Figure 10: Fuzzy logic system
In Table 10 and 11, the results of two methods are compared with the experimental results. Table 10
implies that 73% of results of the proposed method for LPPI are equal to the experimental results and just
60% of results of second method are equal to the experimental results and also Table 11 implies that 80%
of results of the proposed method for SPPI are equal to the experimental results and just 66% of results of
second method are equal to the experimental results.
FICA algorithm has properties as:
1. Fast convergence.
2. The FICA is statistical method and doesn’t have step size parameters. So, it is easy to use.
3. Unlike many algorithms, FICA can directly find independent components for each distribution even if
the probability distribution function isn’t available.
3. The nonlinearity function (NF) has some equations. So, by selecting an appropriate NF, the outcome of
algorithm can be optimized.
4. The FICA doesn’t need large physical memory.
Therefore, the FICA algorithm is better and stronger than ANN algorithm. The map of some real sites in
the network is shown in Fig. 12.
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Table 10: The comparison of three sets of results for LPPI in ten real distribution sites
LPPI-FICA
LPPI-ANN
LPPI-XPRIMENTAL
Site
Bad
Very bad
Bad
Site 1
Good
Good
Good
Site 2
Very bad
Bad
Very bad
Site 3
Medium
Good
Medium
Site 4
Very bad
Very bad
Bad
Site 5
Very bad
Very bad
Very bad
Site 6
Very bad
Bad
Bad
Site 7
Medium
Medium
Medium
Site 8
Terrible
Terrible
Terrible
Site 9
Terrible
Very bad
Terrible
Site 10
Excellent
Excellent
Excellent
Site 11
Very bad
Very bad
Very bad
Site 12
Good
Good
Good
Site 13
Very good
Very good
Medium
Site 14
Bad
Bad
Very bad
Site 15
Table 11: The comparison of three sets of results for SPPI in ten real distribution sites
SPPI-FICA
Very bad
Very good
Medium
Medium
Bad
Medium
Bad
Very good
Good
Very bad
Very good
Very good
Good
Medium
Medium
SPPI-ANN
Bad
Excellent
Medium
Medium
Bad
Medium
Very bad
Very good
Good
Terrible
Very good
Excellent
Good
Medium
Bad
SPPI - EXPRIMENTAL
Bad
Very good
Good
Medium
Bad
Medium
Very bad
Very good
Good
Very bad
Very good
Very good
Good
Medium
Medium
Site
Site 1
Site 2
Site 3
Site 4
Site 5
Site 6
Site 7
Site 8
Site 9
Site 10
Site 11
Site 12
Site 13
Site 14
Site 15
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Figure 11: The procedure of intelligent method
Figure 12: An example of real site in the network
9 Conclusion
In this paper, Fast-ICA method is presented to obtain two PQ global indices for the measured data. To
use this method, the recorded data are normalized, incorporated, and classified. Then, the PQ level of
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several distribution sites are evaluated, based on the type of load and position in the distribution system.
For different types of loads, it can be noted that the nonmetal and stonework industry has the best level
based on the calculated global PQ index. In all types of loads, four indices have better quality as compared
to other indices: voltage unbalance, total harmonic distortion, voltage swell and transients. The global
indices can be used for site PQ evaluation for the cost or penalty on the customers for their PQ emissions
to the network and vice versa. For geographical position in the distribution system, it is noticed that the
customers of a site do not necessarily have a similar index with neighboring customers and sudden
changes or in other words, non gradual changes can happen in the same neighborhood.
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