-
A data mining method for obtaining global power quality
index
Sara Nourollah Department of Electrical and Computer
Engineering
Isfahan University of Technology Isfahan, Iran
[email protected]
Mehdi Moallem Department of Electrical and Computer
Engineering
Isfahan University of Technology Isfahan, Iran
[email protected]
Abstract-The new development in power system such as
restructuring and competetive electricity market make power quality
an important factor in competition. However, to find a measure for
power quality evaluation is very difficult due to many indices
involved in power quality standards. For this reason, obtaining a
single quantitative index based on the standard measurements has
been a new challenge in recent researches. Data mining methods are
required for this purpose due to the large amount of data obtained
from power quality measurements. In this paper, a data mining
method is proposed to determine a global index for power quality.
The continuous and discrete indices of power quality are considered
and the Unified Power Quality Index (UPQI) is presented for each
power quality index, based on the method of incorporation and
normalization. The indices normalized and classified. The power
quality level of each distribution site is determined by the Fast
Independent Component Analysis (Fast-ICA) algorithm. The power
quality measurements of 313 distribution sites in Iran are used to
classify the indices for different type of loads in the
distribution system.
Key Words-Power Quality, Data Mining, Fast-ICA,
Classification.
I. INTRODUCTION In the past two decades, the electric power
quality
has become very important for several reasons such as the
increase nonlinear loads such as arc and power electronic loads,
expansion of the sensitive loads such as computers and
microprocessors, expansion of the interconnected power networks,
renewing the structure in the electric industry and providing the
competitive electric market. Power quality mainly includes voltage
quality of supply and emission limit of the load currents. The
former is to evaluate the effects of supply voltage on customers
and loads, and the latter is to indicate the disturbances of load
to the
grid and other customers [1]. To adapt the request of market,
such as complete assessing of power quality, amending the price of
power and finally realizing higher price for higher quality, the
traditional power quality evaluation could be more extensive in
meaning, more integrated in framework and more realizable in
characterization [1]. The disturbances of power quality and their
negative effects on the power system can be evaluated by the power
quality indices. Many studies have been carried out to determine
the power quality disturbances and to introduce the effective
indices for explaining their features. Some of these studies are as
follows: Improved-ICA [2], Fuzzy Clustering Analysis [3],
presenting a method based on the s-transform [4], a method based on
the fuzzy-wavelet transform [5], a method for obtaining a global
index of discrete disturbances [6], introducing the new indices of
power quality [7].
To study power quality of distribution sites needs to collect
and assessment many different data, related to the types of power
quality indices. The measured data are not in a suitable form to
present the power quality condition of a site or a special area.
Although considerable endeavors have been already performed to
define the different kinds of power quality disturbances and their
indices, it is less tried to determine a specific framework for
determining a global power quality index.
In this paper, a data mining method is proposed for defining the
global power quality index. The continuous and discrete phenomena
of power quality, indices and their limitations are firstly
introduced. In part 4, a normalization and incorporation method of
recorded indices is presented to evaluate the annual index of each
power quality indices. In part 5, the
-
power quality indices are linearly classified from the best to
worst levels. In part 6, the FAST-ICA algorithm and its application
are described in order to determine a global power quality index
for each distribution site is discussed. In part VII, the power
quality of a real distribution system is evaluated by the measured
data of 313 sites, based on the type of load.
II. DESCRIPTION OF THE METHOD
After measuring single indices of power quality for obtaining
two global indices of power quality, there are five step which
should be followed:
1. Introduce continuous and discrete phenomena of power quality
and their limitations.
2. Normalize and incorporate recorded indices to evaluate the
annual index of each power quality indices.
3. Classify the power quality indices linearly from the best to
worst levels.
4. Implement the Fast-ICA algorithm in order to determine weight
matrix (w) and then distance index for each distribution site.
5. Evaluate two global indices for six type of loads.
III. POWER QUALITY PHENOMENA AND THEIR INDICES
Since years ago, some of the measurable parameters have been
accepted as the power quality phenomena. These parameters determine
the power quality level in the monitoring point. The national and
international standards define limitations for these parameters.
The power quality phenomena are divided to two continuous and
discrete groups. Some of the most important phenomena are shown in
Fig. 1 [8].
For any continuous power quality phenomena, an index is
presented in various standards that their recommended limits
according to Iran Power Industry Standards-Power Quality (IPIS) for
20 KV are presented in Table I.
Fig. 1 Power quality phenomena and their classification
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TABLE I. Recommended limits of continuous disturbances according
to IPIS for 20 KV
V_div% Pf THDv% THDi% I_unbal% V_unbal% F_div Plt Pst Index
5 0.9 5 5 8 2 0.6 0.7 0.9 Limit
In general, there are few methods for defining the discrete
power quality indices and no international standard has been still
presented. 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.
One of the most common methods of evaluating the discrete power
quality phenomena is using voltage tolerance curves that are plots
of equipment maximum acceptable voltage deviation versus time
duration for acceptable operation. The most famous of these curves
are Computer and Business Equipment Manufactors Association (CBEMA)
and Information Technology Industry Council (ITIC) curves. In [9],
the RPM index is presented, based on the CBMA graph. In [9]
deficiencies of RPM index are mentioned and better method of least
squares was applied to the log plot of CBEMA/ITIC curves. According
to this method, an index named Contour Number (CN) in equation (1)
is calculated for each point of the graph in Fig. 2.
11
/
=
ITICCBMAVVCN (1)
,where VCBMA/ITIC is calculated based on equation (2), (3),
(4):
=
22.11
0035.086.0)(t
tV SagCBEMA (2)
+=
48.11
000295.006.1)(t
tV SwellCBEMA (3)
+=
014.11
.00076.02.1)(
ttV transOsITIC (4)
For any discrete phenomenon, permissible limits of CN index
based on recorded data in 9 European countries and method given in
[9] are presented in Table II. In this method, the indices are
generated by the number of events in each region of CBEMA curve
using UNIPEDE DISDIP survey results and Electric Power Research
Institute DPQ project data and weighting them in each region
[9].
TABLE II. permitted limits of CN
CN_Os.transient CN_swell CN_sag Index
1 5 4 Limit
Fig. 2 CBEMA and ITIC curve fittings for different discrete
disturbance types (i.e., voltage sags, swells, and transients)
[9].
IV. COMPUTING THE ANNUAL INDICES OF A DISTRIBUTION SITE
During a year, a distribution site is frequently studied and its
power quality indices are calculated and recorded. The recorded
data are not in a suitable form to show the power quality status of
site. Therefore, it requires to present a method for this problem.
The following method is based on the normalization and
incorporation procedure of recorded indices during a year.
-
A. Normalization
In order to normalize, each recorded index is divided to its
permitted amount. For example, the permitted amount of Pst index is
0.9. 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 permitted value is 1.
B. Incorporation
For 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 standards are not suitable, and a better standard is
presented. There is a need for a single number, which we call the
Unified Power Quality Index (UPQI), to summarise the overall level
of PQ disturbances. The maximum and average method and proposed
method are compared in Table III. The presented values in the table
consist of the measured samples of an index for 3 distribution
sites. The Power Quality Index(PQI) average equals the average
value and the PQImaximum equals the maximum value in the annual
recorded value of index. As it is presented in table 3, the
recorded values of site 1 are all in their permitted limits and
there is no problem with the power quality. Nevertheless, the
PQIaverage value of site 1 is more than site 3, while one of the
recorded value of site 3 is more than the permitted limit.
Therefore, the average value is not a suitable standard for
incorporation. In addition, the PQImaximum value of site 2 and site
3 are equal, while three recorded value of site 2 are more than the
permitted limits, and site 3 has only an unpermitted value and it
is in a better status. So, the maximum value is also not a suitable
standard for incorporation. In this paper, it is suggested that the
UPQI value is applied for incorporation. This index is computed
according to the following instructions:
1) If all the recorded value are less than 1, the UPQI value
equals the maximum of recorded values which indicates the greatest
probability of its 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 that
the trepass values is index value minus 1. If an index is less than
1, the trepass value is zero.
As it is shown in Table III, UPQI value of site 2 is less than
site 3 and UPQI value of site 3 is less than site 1 that its
reliability is accordant with intuition.
TABLE III. Comparing of average, maximum and proposed
methods.
3 2 1 Site
Samples
0.5 1.2 0.8 First sample
0.1 0.6 0.7 Second sample
0.4 1.4 0.8 Third sample
1.4 1.4 0.8 Fourth sample
0.6 1.1 0.8 PQIavarage
1.4 1.4 0.8 PQImaximum
1.1 1.4 0.8 UPQI
V. CLASSIFICATION
After computing the UPQI indices for each power quality index
and distribution site, the recorded data are reduced by classifying
them in their permitted and unpermitted area in order to change the
data into a set of coherent and useful data. The procedure is that
the power quality indices are linearly classified according to
their maximum of permitted level. The permitted maximum of each
phenomenon is in class 3. The classes 1, 2 and 3 are the permitted
areas and the classes 4, 5, 6 and 7 are the unpermitted areas of
power quality phenomena. When the classification level becomes
closer from class 1 to class 7, the quality level of phenomena is
reduced. In Table IV, numbering the classes is presented based on
their quality expression. Now this question is put forward that in
which level of power quality, a distribution site with the various
power quality indices is classified. In the next section, the ICA
algorithm is proposed to solve this problem. Table V shows the
classification levels of the normalized power quality
-
indices. This classification is performed by studying and
examining more than a hundred of measured points in Iran.
TABLE IV. Numbering the classes based on their quality
expression.
Excellent Class 1 Very good Class 2
Good Class 3 Medium Class 4
Bad Class 5 Very bad Class 6
Terrible Class 7
VI. FAST-ICA ALGORITHM
The ICA algorithm is a known method for finding the hidden
structure of data. In linear position, the ICA model is as
below:
wsx =
(5)
where x is the data matrix and w is the hidden structure of
data. There are various methods for computing the matrix w such as
FAST-ICA algorithm which estimates the matrix w by the following
equations:
(6) { } { }wxwgExwgxEw TT ).().(. ( ) ( ) 3343 ,4
1 yygyyg == (7)
The steps of implementing the FAST-ICA algorithm are as
follows:
1. The x data are transformed such that they have
zero mean and preprocessed by whitening .
2. An initial unit norm vector w is chosen randomly.
3. The functions g, g are calculated according to
equations (7).
4. The w is updated according to equation (6).
5. The w is again normalized to have unit norm.
6. The steps 3, 4, 5 are repeated until the convergence.
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 is presented as blow.
By implementing the FAST-ICA algorithm, the matrix w is computed in
dimensions 112. With
TABLE V. Classifying the limit of changes of 12 power quality
phenomena.
Class 7 Class 6 Class 5 Class 4 Class 3 Class 2 Class 1
9 7 5 3 1 0.66 0.33 V_dev
5 4 3 2 1 0.66 0.33 THDv
7.5 4.75 3.5 2.25 1 0.66 0.33 THDi
5 2.5 2 1.5 1 0.66 0.33 V_unbal
7.5 4.75 3.5 2.25 1 0.66 0.33 I_unbal
5 1.5 1.33 1.16 1 0.66 0.33 F_dev
10 4 3 2 1 0.66 0.33 Pf
5.55 2 1.66 1.33 1 0.66 0.33 Pst
5.72 2.29 1.86 1.43 1 0.66 0.33 Plt
10 3.4 2.6 1.8 1 0.66 0.33 CN_Swell 10 4 3 2 1 0.66 0.33 CN_Sag
10 4 3 2 1 0.66 0.33 CN_Trans
-
=
0.100.0110.0 00.90.0100.550.750.700.500.572.555.500.440.34.00
00.700.400.475.475.450.250.129.200.200.360.23.00
00.500.300.350.350.300.233.186.166.100.280.12.00
00.300.250.125.225.250.116.143.133.100.100.11.00
00.100.100.100.100.100.100.100.100.1
0.66 0.660.66 0.660.660.660.660.660.660.660.660.660.330.330.33
0.330.330.330.330.330.330.330.3333.00.140.560.04
1.50.610.431.000.410.250.530.821.000.060.180.121.001.000.391.150.550.160.450.480.150.061.770.331.001.610.131.001.000.150.830.330.120.210.510.30.641.000.761.070.240.180.3980.851.000.380.571.372.001.020.440.990.660.370.4590.961.000.110.021.120.720.170.280.430.490.220.4830.340.120.440.341.531.130.520.681.000.510.290.4330.360.120.180.430.320.850.880.541.020.410.150.4090.981.000.120.141.111.020.410.591.080.510.20.4170.440.14
X
using these weighting coefficients, the close degree of any
class or site of matrix X can be calculated, according to the
Euclidean space distance method. First, the virtual optimal and
worst points of indicators are obtained as:
{ }{ }
12,...2,13131
12,...2,13131
max
max
=
=
+
=
=
ji
ijj
ji
ijj
xr
xr
(8)
Then, the Euclidean distance of samples are calculated by best
point (d+) and the worst point (d-) based on equation (9):
(9)
=
=
++
=
=
m
jjijji
m
jjijji
rxWd
rxWd
1
2
1
2
)(
)(
where m=12 and i=1,2,,17. Finally, close degree (Ci) is obtained
as:
+
+=
ii
ii dd
dC
(10)
If Ci is closer to zero, the position of that point is better.
The indices C1 to C10 are related to 10 measured site and C11 to
C17 are related to 7 defined classes. For each site, the Ci is
calculated and set in a class that its Ci is closer to. Therefore,
all the measured sites are qualitatively classified.
VII. RESULT AND DISCUSSION
In this section, the power quality status is examined for each
type of loads in a real distribution system. Here, the measured
data of 313 distribution sites are evaluated in 4 provinces
Isfahan, Qazvin, Khuzestan and Kurdistan. The measured sites are
divided in to 6 groups as follows:
Group 1: metallic and casting industry.
Group 2: textile industry.
Group 3: nutritional and chemical industry.
Group 4: nonmetallic and stonework industry.
Group 5: residential, public and hospital.
Group 6: mixed load.
In Table VI, the number of points, related to each type of load
is shown.
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TABLE VI. Number of measured points related to each type of
load.
Number of measured points Type of load 73 metallic and casting
industry 17 textile industry 31 nutritional and chemical industry
65 nonmetallic and stonework industry 47 residential, public and
hospital 81 mixed load
There are two global indices defined with names of Supply side
Power Performance Index (SPPI) and Load side Power Performance
Index (LPPI). SPPI shows effect of six voltage power quality
indices and LPPI shows effect of three current power quality
indices. In each class, The redundancy percentage of twelve indices
is calculated for different load types. For instance, the bar graph
of redundancy percentage for metallic and casting industry, related
to three current indices are shown in Fig. 3.
Fig. 3 The bar graph of redundancy percentage for metallic and
casting industry, related to three current indices.
In each class, the redundancy percentage of global power quality
indices is calculated for different load types. According to
results, the class related to the greatest redundancy percentage
for each type of loads, are presented in Table VII.
TABLE VII. The class related to the greatest redundancy
percentage for each type of loads
Group1 Group2 Group3 Group4 Group5 Group6 SPPI 3 2 2 2 3 2 LPPI
4 3 3 4 3 3
VIII. CONCLUTION
In this paper, a method is presented to obtain two power quality
global indices for the recorded data. In
this method, the recorded data were normalized, incorporated and
classified. Then, the power quality level of several distribution
sites was evaluated, based on the type of load and position in the
distribution system.In the view point of the type of loads, it can
be noted that the nonmetallic and stonework industry has the best
level according to the global power quality index In all types of
loads, four index have the best quality with compared to other
indices: voltage unbalance, total harmonic distortion, voltage
swell and transients.
REFERENCES
[1] A. Salarvand, B. Mirzaeian, M. Moallem, Obtaining a
quantitative index for power quality evaluation in competitive
electricity market, IET Journal, Generation Transmission and
DistributionVol. 4, lss. 7, pp. 810-823, 2010.
[2] Mei Liang, Yongqiang Liu, A New Method on Power Quality
Comprehensive Evaluation, The Ninth International Conference on
Electronic Measurement and Instruments (ICEMI), pp. 1057-1060,
2009.
[3] G. Yang and G. Wen, A device for power quality monitoring
based on ARM and DSP, Industrial Electronics and Applications,
2006.
[4] Y. Jia, Z. Y. He and T. L. Zang, S-transform Based Power
Quality Indices for Transient Disturbances, IEEE Trans. Power
Delivery, Vol. 19, No. 1, pp. 323-330, Jan. 2010.
[5] W. Morsi, M. El-Hawary, Fuzzy-Wavelet-Based Electric Power
Quality Assessment of Distribution Systems Under Stationary and
Nonstationary Disturbances, IEEE Trans. Power Delivery, Vol. 24,
No. 4, pp.2099-2106, Oct. 2009.
[6] G. Carpinelli, P. Caramia, P. Varilone, R. Chiumeo, I.
Mastrandrea, A Global Index for Discrete Voltage Disturbances,
IEEE, International Conference on Electrical Power Quality and
Utilization(EPQU), Spain, pp. 1-5, 2007.
[7] C. Capua, S. D. Falco, A. Liccardo, E. Romeo, Improvement of
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[8] IEEE Recommended Practice for Monitoring Electric Power
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[9] M. Fleming, Predicting power quality, Power Transmis.
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