Assessing power quality of power system using FICA algorithm

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: [email protected], 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. 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 Distribution, 4 (7) (2010) 810-823. http://dx.doi.org/10.1049/iet-gtd.2009.0479 [2] A. Bracale, P. Caramia, G. Carpinelli, A. Russo, P. Verde, Site and System Indices for Power-Quality Characterization of Distribution Networks With Distributed Generation, IEEE Trans. Power Del, 26 (3) (2011). http://dx.doi.org/10.1109/TPWRD.2011.2112381 [3] M. Liang, Y. Liu, A New Method on Power Quality Comprehensive Evaluation, The Ninth International Conference on Electronic Measurement and Instruments (ICEMI): (2009) 1057-1060. [4] T. Lin, A. Domijan, On power quality indices and real time measurement, IEEE Trans. Power Del, 20 (4) (2005) 2552-2562. http://dx.doi.org/10.1109/TPWRD.2005.852333 [5] H. M. S. C. Herath, V. J. Gosbell, S. Perera, Power quality (PQ) survey reporting: discrete disturbance limits, IEEE Trans. Power Del, 20 (2) (2005) 851-858. http://dx.doi.org/10.1109/TPWRD.2005.844257 [6] M. I. Marei, E. F. El-Saadany, M. M. A. Salama, A Flexible DG Interface Based on a New RLS Algorithm for Power Quality Improvement, IEEE system journal 6(1) (2012). http://dx.doi.org/10.1109/JSYST.2011.2162930 [7] S. R. Naidu, G. V. Andrade, E. G. Costa, Voltage Sag Performance of a Distribution System and Its Improvement, IEEE Trans. Industry applications, 48 (1) (2012). http://dx.doi.org/10.1109/TIA.2011.2175885 [8] S. Lee, J. W. Park, G. Kumar, New Power Quality Index in a Distribution Power System by Using RMP Model, IEEE Trans. Industry applications, 46 (3) (2010). http://dx.doi.org/10.1109/TIA.2010.2045214 [9] L. Qian, D. A. Cartes, H. Li, An improved adaptive detection method for power quality improvement, IEEE Trans. Industry applications, 44 (2) (2008) 525-533. http://dx.doi.org/10.1109/TIA.2008.916740

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