Research ArticleAssessment of Electrical Load in Water Distribution SystemsUsing Representative Load Profiles-Based Method

Gheorghe Grigoras

Power System Department Electrical Engineering Faculty ldquoGheorghe Asachirdquo Technical University of IasiBoulevard Dimitrie Mangeron No 21-23 700050 Iasi Romania

Correspondence should be addressed to Gheorghe Grigoras ghgrigorasyahoocom

Received 17 April 2014 Accepted 28 June 2014 Published 21 July 2014

Academic Editor Mamun B Ibne Reaz

Copyright copy 2014 Gheorghe Grigoras This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The problem of optimal management of a water distribution system includes the determination of the operation regime for eachhydrophore station The optimal operation of a water distribution system means a maximum attention to assess the demandsof the water with minimum electrical energy consumption The analysis of load profiles corresponding to a water distributionsystem can be the first step that water companies must make to assess the electrical energy consumption This paper presents anew method to assess the electrical load in water distribution systems taking into account the time-dependent evolution of loadsfrom the hydrophore stations The proposed method is tested on a real urban water distribution system showing its effectivenessin obtaining the electrical energy consumption with a relatively low computational burden

1 Introduction

Water and energy are critical resources that affect virtuallyall aspects of daily life A huge amount of electrical energyis necessary for the transportation treatment and distri-bution of water for drinking and industrial consumptionand for different internal technological processes of waterdistribution systems Water distribution systems are massiveconsumers of energy which is consumed in each of thestages of thewater production and supply chain starting frompumping the water to the water treatment plant followedby the treatment process while distributing the water viathe network In the Report Watergy by Alliance to SaveEnergy it has been asserted that 2-3 of the worldrsquos electricalenergy consumption is used to pump and treat water for civiland industrial supply [1] Energy costs constitute the largestexpenditure for nearly all water utilities worldwide and canconsume up to 65 percent of a water utilityrsquos annual operatingbudget [2] The energy requirements vary significantly fromcity to city depending on local factors such as topographylocation and quality of water sources pipe dimensions andconfigurations treatment standards required and the typesand numbers of consumers [1ndash8] Water industry decisionson operational strategies and technology selection can alsosignificantly influence electrical energy consumption [5] A

high electrical energy consumption may be due to variousreasons inefficient pump stations poor design installationor maintenance old pipes with high head loss bottlenecks inthe supply networks excessive supply pressure or inefficientoperation strategies of various supply facilities [2ndash4 9ndash16]

Energy-saving measures in water supply systems canbe realized in many ways from decreasing the volumeof water pumps (eg adjusting pressure zone boundaries)to reducing the price of energy (eg avoiding peak hourpumping and making effective use of storage tanks) orincreasing the efficiency of pumps (eg ensuring that pumpsare operating near their best efficiency point) These energy-saving measures often pay for themselves in months most dosowithin a year and almost all recover their costswithin threeyears Prolonging this enactment period would increase theinvestment required for long-term [11ndash16]

Utilities can further reduce energy costs by implementingon-line telemetry and control systems (SCADA) and bymanaging their energy consumption more effectively andimproving overall operations from water supply systems [2]The motivation for introducing such systems is due to thefollowing factors [2 9ndash15]

(i) operation of water supply systems which is in manycases becoming more complex with rising demands

Hindawi Publishing CorporationAdvances in Electrical EngineeringVolume 2014 Article ID 865621 10 pageshttpdxdoiorg1011552014865621

2 Advances in Electrical Engineering

incorporating water from a variety of sources andaging systems

(ii) high operating costs which justify investments toimprove efficiency

(iii) control and computer hardware and software whichare available and more reliable

(iv) the fact that as more computer control systems areinstalled there is more experience from which tolearn

Therefore a permanent policy for the reduction of elec-trical energy consumption not only involves the technicalimprovement in the water distribution system but alsorequires the use of software tools to facilitate the operationprocess Based on this concept a new approach is proposed inthe paper based on similarities that exist between daily loadprofiles of each hydrophore station from water distributionsystem and their grouping into representative clusters Byknowing the load profile water companies can simplify thedemand determination for their supply zone Thus they canprovide better and improved efficiency marketing strategies

Different techniques have been used in literature forthe classification and load profiling but most of them wereimplemented to solve the problems from power systemsTable 1 presents a synthesis of the solutions proposed inliterature depending on the type of technique

It can be seen that most techniques belong to ArtificialIntelligence (clustering data mining self-organizing mapsneural networks and fuzzy logic) and the number of ref-erences is higher after the year 2000 This aspect can beexplained by the fact that more and more information isbecoming available faster than ever before The impact is feltin the control and operation of the distribution and transportnetworks (electricity steam gas and water) Under thesecircumstances of momentous changes Artificial Intelligencehas the potential to play a more important role

This paper proposes an extension of profiling techniquesin the area of water distribution systems for the assessmentof electrical using on a hybrid algorithm The algorithmuses the K-means clustering method for obtaining of rep-resentative load profiles and a statistical approach for theassessment of the electrical load in the water distributionsystems The remainder of this paper is organized as followsIn Section 2 the K-means clustering method is presentedSection 3 presents the steps of process for obtaining ofrepresentative load profiles Section 4 presents the statisticalmethod for assessment of the electrical load in a waterdistribution system Section 5 presents the steps of proposedalgorithm Section 6 shows the results of testing the proposedmethod on a real system Finally Section 7 contains theconcluding remarks

2 119870-Means Clustering Method

TheK-means clustering is an algorithm to classify or to groupthe objects based on attributesfeatures into 119870 number ofgroups (119870 is positive integer number) The grouping is done

by minimizing the sum of squares of distances between dataand the corresponding cluster centroid [14 17ndash20]

min (119864) = min(119870

sum

119894=1

sum

119909isin119862119894

119889(119909 119911119894)2) (1)

where 119911119894is the center of cluster 119862

119894 while 119889(119909 119911

119894) is the

Euclidean distance between a point 119909 and 119911119894

Thus the criterion function 119864 attempts to minimize thedistance of each point from the center of the cluster to whichthe point belongs More specifically the algorithm begins byinitializing a set of 119870 cluster centers Then it assigns eachobject of the dataset to the cluster whose center is the nearestand recomputed the centers The process continues until thecenters of the clusters stop changing

The steps of the algorithm are the following [14 19ndash22]

Step 1 Choose119870 initial clusters centres 119911(0)1 119911(0)

2 119911

(0)

119870

Step 2 At the kth iterative step distribute the samples 119909among the119870 clusters using the relation

119909 isin 119862(119896)

119894if 119889 (119909 119911(119896)

119894) lt 119889 (119909 119911

(119896)

119895) 119894 = 1 2 119870 119894 = 119895

(2)

where 119862(119896)119894

denotes the set of samples whose cluster centre is119911(119896)

119894

Step 3 Compute the new cluster centres 119911(119896+1)119894

119894 =

1 2 119870 The new cluster centre is given by

119911(119896+1)

119894=1

119899119894

sum

119909isin119862(119896)

119894

119909 119894 = 1 2 119870 (3)

where 119899119894is the number of objects in cluster 119862(119896)

119894

Step 4 Repeat Steps 2 and 3 until convergence is achievedthat is until a pass through the training sample causes no newassignments

It is obvious in this algorithm that the final clusters willdepend on the initial cluster centers chosen and on the valuesof 119870

The optimal number of clusters 119870opt can be determinedusing the following algorithm [19ndash21]

(1) Determination of the maximum of clusters 119870max themaximum of clusters 119870max should be set to satisfycondition 2 le 119870max le radic119873 where 119873 is the clusteredobjects from database

(2) Use the K-means clustering method with given119870 (2 le 119870 le 119870max) for the set of objects fromdatabase

(3) According to the obtained clusters structure determi-nate partition quality is evaluated

(4) Increase the number of clusters to the 119870max to see ifK-means clustering method finds a better groupingof the data (to repeat Steps 2 and 3)

Advances in Electrical Engineering 3

Table 1 Synthesis of the literature techniques for classification andload profiling

Technique ReferencesBefore year 2000 After year 2000

Statistical [29ndash33] [34 35]Clustering [14 17 36ndash43]Data mining [44] [45ndash47]Self-organizing maps [17 36 37 48 49]Neural networks [33] [50ndash54]Fuzzy logic [11 34 39 50 51]

(5) Show number of clusters (119870opt) that have obtained theoptimal value of the silhouette global coefficient

Assessing the results of theK-means algorithm representsthe main subject of cluster validity In the process of clusteranalysis the following properties of clusters are being exam-ined density sizes and formof cluster separability of clustersrobustness of classification There are many approaches tocluster validation [17 20 23ndash27] but internal cluster vali-dation tests are more popular in practice of cluster analysisThe test based on the Silhouette Global Index calculationis one of the most used [20 23 24 28] This calculates thesilhouette width for each sample average silhouette width foreach cluster and overall average silhouette width for data setUsing this approach each cluster could be represented by aso-called silhouette which is based on the comparison of itstightness and separation Cluster validity checking is one ofthe most important issues in cluster analysis related to theinherent features of the data set under concern It aims atevaluating clustering results and the selection of the schemethat best fits the underlying data

3 Determination of RepresentativeLoad Profiles

The load profiling represents an alternative to the settlementbased on energy meters because in many countries in waterdistribution systems there is a lack of necessary metering andmonitoring systems to collect data The load diagram of thehydrophore stations is reconstructed using the normalizedload profile and their daily (monthly yearly depending onthe case) electrical energy consumption The time interval ofsampling load curve data can be one hour In this situationa load profile is represented by 24 load values throughoutthe day The shape of load profiles is influenced by the typeof hydrophore station and on the other hand by the typeof day or season of the year Because a large number ofload profiles regarding various water hydrophore stationscreate unnecessary problems in handling them they couldbe grouped into coherent groups seeing that some similar-ities exist between load profiles For this purpose the K-means clustering method is applied to classify profiles of thehydrophore stations into coherent groupsmdashrepresentativeload profiles (RLPs)

Each RLP is represented by a vector 119909119895= 119909119895ℎ ℎ =

1 119879 for 119895 = 1 119873 and the comprehensive set of

RLPs is contained in the set 119875 = 119909119895 119895 = 1 119873 The

time scale along the day is partitioned into 119879 time intervalsof duration Δ119905

ℎ for ℎ = 1 119879 Hourly values are used in

this paper to exemplify the application The variables used inthe calculations are assumed to be represented as constant(average) values within each time interval The clusteringprocess forms 119870 clusters corresponding to the hydrophorestations Further a RLP is assigned to each station

The algorithm is based on the load profiling process Themajor steps are as follows

(1) Measurements In this step a representative sample of theset of load profiles is identified the most relevant attributesare to be measured and the cadence for data collectionis defined Finally the collected data is gathered in a largedatabase

(2) Data Cleaning and Preprocessing In real problems likethis involving a large number of measurements spreadover a large geographic area and collecting data during aconsiderable period of time different kind of problems willaffect the quality of the database The most relevant andfrequent are communication problems outages failure ofmeters and irregular atypical behavior of some consumersThe result will be a very large database with problems likenoise missing values and outliers These data (after beingcleaned preprocessed and reduced) are used in clusteringprocess [43 55]

(3) Classification For realization of this classification the K-means clusteringmethod is usedThe normalized load profilefor each hydrophore station from the water distributionsystem is determined using a suitable normalizing factor (egenergy over the surveyed period)

119901119895ℎ=

119875119895ℎ

sumℎ119875119895ℎ

119895 = 1 119873 ℎ = 1 119879 (4)

where 119901119895ℎis normalized value [pu] 119875

119895ℎis actual value [kW]

sum119875119895ℎis the energy over the surveyed period [kWh] andN is

the total number of vectors 119909119895from database

(4) Determination of Representative Load Profiles Using theK-means clustering method the normalized load profiles arerefined so as to desist at the unrepresentative profiles Therepresentative load profile for each cluster is obtained byaveraging the normalized values for each hour These values(called the load factors) lead us to the representative loadprofiles corresponding to the active powers The load factorsfor each cluster are calculated with relation

119898119894

ℎ=

sum119899119894

119894=1119901119894

119895ℎ

119899119894 ℎ = 1 24 119894 = 1 119870 (5)

where 119899119894 represents the number of hydrophore stations fromcluster i

The signification of load factors 119898119894ℎ ℎ = 1 24

119894 = 1 119870 from relation (5) is the following these factors

4 Advances in Electrical Engineering

transform the electrical energy consumed by the mediummember of cluster 119894 in average power demanded by it

The representative load profiles can characterize verywell the operation mode of the water hydrophore stations(identified by the clusters obtained) related to the electricalenergy consumption

(5) Assignation Finally to each water hydrophore station ismade the assignation of a representative load profile

4 The Assessment of Electrical Load in WaterDistribution Systems

Theassessment of electrical load inwater distribution systemscan be made using an improved simulation method based onthe representative load profiles of hydrophore stations Themethod is based on the following hypotheses [30 31 56]

(i) The mean loads corresponding to a cluster ofhydrophore stations from the water distribution sys-tem in any hour during the analyzed period areapproximately proportional to the electrical energyconsumption of those stations

(ii) The loads for any hour during the analyzed periodhave a statistical distribution that can be regarded asnormal

Using these hypotheses the load estimation of a waterdistribution system at any hour ℎ = 1 24 is given by thefollowing formula

119875119878

ℎ=

119870

sum

119894=1

119873119894

HS sdot 119882119894

med sdot 119898119894

ℎ+ radic

119870

sum

119894=1

119873119894

HS sdot (119882119894

med sdot 120590119894

ℎ)2 [kW]

ℎ = 1 119879

(6)

where 119875119878ℎis the load of the water distribution system at

the hour h 119870 is the number of clusters corresponding tothe hydrophore stations from water distribution system119873119894HSis the number of the hydrophore stations from cluster i119882119894

med is the average energy consumption of the hydrophorestations from cluster i 119898119894

ℎis the average load factor of the

hydrophore stations from cluster i at the hour h 120590119894ℎis the

standard deviation for load factor from hydrophore stationscorresponding to cluster i

The standard deviations for each cluster are calculatedwith relation

120590119894

ℎ=radicsum119873119894

HS119895(119901119894

119895ℎminus 119898119894

ℎ)2

119873119894

HS ℎ = 1 119879 119894 = 1 119870

(7)

5 Algorithm for Assessment of Electrical Loadin Water Distribution Systems

The algorithm adopts a procedure composed of two calcula-tion stages

Input data

End

Electrical energy consumption assessment- Determination of number of stations in each cluster - Calculation of average electrical energy

consumption of water hydrophore stations in

- Calculation of the average load factor ofstations in each cluster

- Assessment of the electrical load from thewater distribution system

- Data cleaning and preprocessing

- Calculation of the normalised load profiles

- Assignation of the representative load profile to each hydrophore station in function by its type

Start

Clustering rarr representative load profiles

- Clustering process rarr representative load profiles

each cluster

Figure 1 Flow chart of the proposed method

(i) the use of a clustering technique (K-meansmethod) inthe first stage to determine the patterns of electricalload and determine a subset of representative loadprofiles to be processed by the second stage at eachiteration the clustering outcomes simplify the processof selecting a relatively small number of load profilescorresponding to hydrophore stations

(ii) the use of load simulation in the second stage thisapproach is based on a statistical method that consid-ers the loads for any hour during the analyzed periodhave a statistical distribution that can be regarded asnormalThe flow chart of the proposed method is shown inFigure 1

For a water distribution system the input informationrefers to the technical characteristics (rated power of the forcepumps rated water flow) and the hourly load patterns ofhydrophore stations

Advances in Electrical Engineering 5

0005

01015

02025

03035

04045

05

C2 C3 C4 C5 C6 C7 C8 C9

Silh

ouet

te g

loba

l coe

ffici

ent

Clusters

Figure 2The silhouette global coefficient for different values of thenumber of clusters

0 02 04 06 08 1

1

2

3

Silhouette value

Clus

ter

Figure 3 The silhouette plot for 119870opt = 3

51 Determination of Representative Load Profiles The loadprofile of each hydrophore station is normalized relatively tothe daily electrical energy consumption The normalizationis made in relation to daily electrical energy consumptionbecause it is always known This consumption is recordedwith meters placed in each hydrophore station The optimalnumber of clusters is obtained using the K-means cluster-ing algorithm presented in Section 2 Finally the silhouetteglobal coefficient is calculated to assess the partition qualityAfter aggregation of the normalized load profiles of eachcluster the representative profiles are determined and a RLPis assigned to each hydrophore station

52 The Assessment of Electrical Loads In the second stepof the study using information from clustering process(hourly average load factors average energy consumptionand standard deviation of load factors for each hydrophorestation from cluster 119894 119894 = 1 119870) and relation (6) thehourly loads of the analyzed water distribution system willbe obtained

The accuracy of the estimates is expressed depending onthe data available Thus if the actual value of the estimatedquantity is available (such as during method developmentand testing) the following quantity can be useful to verify themethod

MAPE =sum119879

ℎ=1(10038161003816100381610038161003816119875119878

ℎ real minus 119875119878

ℎ est10038161003816100381610038161003816119875119878

ℎ real)

119879sdot 100 (8)

Table 2 The technical characteristics of hydrophore stations fromwater distribution system

Type Number ofstations

Rated power[kW]

Rated waterflow [m3h]

I 3 3 times 22 24II 6 4 times 22 32III 11 4 times 4 64IV 13 3 times 55 96V 33 4 times 55 128VI 7 4 times 75 128

where 119875ℎ real and 119875ℎ est represent the real and estimated values

for the load of water distribution system at the hour ℎThe mean absolute percentage error (MAPE) from (8)

is dimensionless and thus it can be used to compare theaccuracy of the model on different data sets

6 Case Study

In order to show the characteristics of the proposed methodfor assessment of electrical energy consumption a real waterdistribution system with 119873 = 73 hydrophore stations isconsidered For this system the input information refers tothe technical characteristics (Table 2) and the hourly loadpatterns of the hydrophore stations

Thus in all stations three or four similar force pumpshaving the rated power between 22 and 75 kW are installedThe required water flow is delivered at a constant pressureby changing the frequency of the source supplying theelectrical engines of the force pumps The load patterns arerepresented by load profiles of the water hydrophore stationsThemeasurements of individual load profileswere performedusing an electronic meter A sensor and an electronic devicefor pulse counting anddata storage compose thismeterTheseprofiles were processed for the day when it registered themaximum load in the water distribution system The timeinterval is defined by taking hourly steps within a day (119879 = 24and Δ119905

ℎ= 1 hour)

The normalization of the load profiles was made inrelation to daily electrical energy consumption Further theoptimal number of clusters was determined using the algo-rithm described in Section 2 Getting started the maximumof clusters 119870max was calculated (119870max = radic119873 asymp 9) Thenfor the set of normalized active power profiles the K-meansclustering method with a given 119870 (2 le 119870 le 119870max) isused Finally the silhouette global coefficient is calculatedfor the assessment of partition Because the silhouette globalcoefficient has the highest value for 119870 = 3 this representsthe optimal solution for clustering process Figure 2 For thissolution the silhouette plot is presented in Figure 3

The characteristics of clusters (119901119862119894ℎand 120590119862119894

ℎ ℎ = 1 24

119894 = 1 3) are presented in Table 3 After aggregationof normalized load profiles of each cluster Figure 4 therepresentative profiles were determined Representative loadprofile for each cluster is obtained by averaging the valuesfor each hour represented by load factors 119901119862119894

ℎ 119894 = 1 3

6 Advances in Electrical Engineering

0 5 10 15 20 250

001002003004005006007008009

01

Time (hours)

Load

fact

or (p

u)

(a)

0 5 10 15 20 250

001002003004005006007008009

01

Time (hours)

Load

fact

or (p

u)

(b)

0 5 10 15 20 250

001002003004005006007008009

Time (hours)

Load

fact

or (p

u)

(c)

Figure 4 Clustering results with 3 clusters ((a) cluster C1 (b) cluster C2 (c) cluster C3)

Table 3 Hourly coefficients of representative load profiles

Hour 1199011198621

[pu]1199011198622

[pu]1199011198623

[pu]1205901198621

[pu]1205901198622

[pu]1205901198623

[pu]1 0026 0022 0033 00028 00053 000412 0023 0020 0031 00036 00043 000393 0021 0019 0030 00032 00040 000404 0022 0019 0030 00033 00036 000365 0022 0020 0031 00029 00042 000426 0026 0025 0035 00025 00044 000397 0036 0040 0041 00047 00040 000288 0050 0054 0047 00089 00072 000489 0054 0048 0045 00045 00055 0004810 0055 0048 0046 00062 00058 0004511 0053 0046 0044 00100 00036 0003312 0048 0043 0043 00040 00040 0002713 0051 0041 0042 00056 00028 0003714 0054 0041 0041 00064 00034 0003015 0051 0040 0041 00059 00028 0003716 0047 0044 0043 00047 00028 0002617 0046 0048 0045 00039 00045 0003018 0047 0055 0047 00072 00041 0004919 0046 0060 0050 00061 00058 0005720 0050 0063 0051 00067 00066 0005921 0056 0070 0056 00072 00077 0008222 0047 0058 0048 00076 00073 0005823 0039 0048 0043 00039 00049 0003724 0032 0030 0037 00030 00043 00037

Advances in Electrical Engineering 7

Table 4 Results of clustering process

Cluster Number of stations [] Type of stations119882med [kWh]

I II III IV V VI1198621 24 3288 4 2 11 7 41421198622 8 1233 3 5 1 28581198623 41 5479 1 6 11 22 3235Total 73 100 3 6 11 13 33 7 3411

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 5 Representative load profile for cluster C1

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 6 Representative load profile for cluster C2

Graphical representation of the representative load profilescorresponding to the three clusters obtained (C1 C2 and C3)is given in Figures 5 6 and 7

One hourly value from the representative load profilesdenotes the load of a water hydrophore station in per unit ofthe total average daily load of this station The hourly loadpattern can be employed to approximate the load pattern ofany water hydrophore station within the same cluster

The results of calculations carried out during the firststage of the clustering procedure are presented in Table 4

From Table 4 it can be seen that the most consistentclusters are C1 and C3 which together accounted for about85of the total load profiles of thewater hydrophore stationsIn terms of technical characteristics the water hydrophorestations from cluster C2 belong to types I and II (installedrated power is less than 88 kW) the stations from clustersC1 and C3 belong to types IIIndashVI (installed rated power is

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 7 Representative load profile for cluster C3

Table 5 Real and estimated hourly load of water distributionsystem

Hour 119875119878

real [kW] 119875119878

est [kW] Err []1 7105 7295 2682 6449 6695 3813 6350 6534 2904 6323 6519 3105 6514 6727 3266 7585 7861 3647 10744 10516 2128 12737 13096 2829 11880 12211 27910 11989 12357 30711 11529 11909 32912 10936 11326 35713 10622 10995 35114 10796 11044 23015 11015 10864 13716 10978 11311 30417 11428 11976 47918 12528 13013 38719 13702 14012 22620 13993 14500 36221 16531 16036 30022 13187 13624 33123 11154 11569 37224 8550 8794 285

between 16 and 30 kW) But in cluster C3 approximately 50percent of the total stations have an installed rated power by

8 Advances in Electrical Engineering

020406080

100120140160180

1 3 5 7 9 11 13 15 17 19 21 23

P (k

W)

Real powerEstimated power

Time (hours)

Figure 8 Real and estimated load profiles of the analyzed waterdistribution system

0

1

2

3

4

5

6

1 3 5 7 9 11 13 15 17 19 21 23

Estim

ated

erro

rs (

)

Time (hours)

Figure 9 Estimation errors obtained for hourly load of analyzedwater distribution system

22 kW In terms of the electrical energy consumption it canbe observed that the highest medium value is registered forcluster C1 and the lowest value is registered for cluster C2

In the second step of the study using information fromTables 3 and 4 and relation (6) the hourly loads of theanalyzed water distribution system were obtained Thus inTable 5 Figures 8 and 9 the real loads estimated loads andestimated errors are presented The estimation maximumerror is 479 and minimum error is 137 Global resultsshow that the value for MAPE is 311

Thismay be considered a very good result especially if wetake into account the arbitrariness inherent to loads behaviorand not all hydrophore stations have monitoring system

7 Conclusions

The investigation of combined actions which account forconnected water and electrical aspects allows improvingthe global efficiency of the water distribution systems andsupplying the consumers using the least possible amount ofwater and energy

In water distribution companies the system operatorpredicts the consumption for today and tomorrow based on

recent consumption trends weather forecasting day of theweek knowledge of future events and historical knowledgeof utility system performance This approach conducts at alarge percentage error (more than 5) for assessment of load

The proposed method is based on two stages in whichthe K-means clustering method and a load simulation tech-nique are exploited for estimation of the electrical energyconsumption The method based on the K-means clusteringalgorithm was used for determination of the representativeload profiles of the hydrophore stations A comparison ofobtained results using the proposed method with the realregistered data indicates an error by 311 which is very closeto the expected one by water companies (25ndash3) [57]

Results obtained demonstrate the ability of the proposedmethod to become the first step in an efficient managementof the water distribution systems On the one hand therepresentative load profiles can be used tomodel overall watercompany demands in a way that show how changes in use byone category affect the hourly load profiles for the system as awhole and on the other hand these profiles can contribute toa better understanding of the opportunities for linking water-efficiency and energy-efficiency programs

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] Alliance to Save Energy ldquoWhat watergy involvesrdquo 2014 httpwwwwatergynet

[2] P Boulos Z Wu C Orr M Moore P Hsiung and DThomasOptimal PumpOperation ofWaterDistribution SystemsUsing Genetic Algorithms H

2ONET-Users Guide MW Software

Consulting Dallas County Tex USA 2000[3] European Commission Directorate General for Environment

2013 httpeceuropaeuenvironmentwaterindex enhtm[4] A Anton and S Perju ldquoMonitoring the main parameters of a

water supply pumping station over ten yearsrdquo in Proceedings ofthe 6th International Conference on Hydraulic Machinery andHydrodynamics Timisoara Romania 2004

[5] S J Kenway A Priestley S Cook et al ldquoEnergy use in theprovision and consumption of urban water in Australia andNew Zealandrdquo Water for a Healthy Country National ResearchFlagship Report CSIRO 2008

[6] LHouseWater Supply Related ElectricityDemand inCaliforniaReport for California Energy Commission 2006

[7] R Goldstein and W Smith ldquoWater and sustainability USelectricity consumption for water supply amp treatmentmdashthe nexthalf centuryrdquo EPRI Report Electric Power Research InstitutePalo Alto Calif USA 2000

[8] I Pulido-Calvo and J C Gutierrez-Estrada ldquoSelection andoperation of pumping stations of water distribution systemsrdquoEnvironmental Research Journal vol 5 no 3 pp 1ndash20 2011

[9] K Feldman ldquoAspects of energy efficiency in water distributionsystemsrdquo inProceedings of the International Conference onWaterLoss pp 26ndash30 IWA Cape Town South Africa April 2009

Advances in Electrical Engineering 9

[10] G C Ionescu and D S Ionescu ldquoThe optimization of energyconsumption in water supply systemsrdquo Acta Electrotehnica vol46 pp 191ndash194 2005

[11] M Istrate and G Grigoras ldquoEnergy consumption estimationin water distribution systems using fuzzy techniquesrdquo Environ-mental Engineering and Management Journal vol 9 no 2 pp249ndash256 2010

[12] I Sarbu Energetic Optimization of the Water Distribution Sys-tems Publishing House of the Romanian Academy BucharestRomania 1997

[13] L Szychta ldquoEnergy consumption of water pumping for selectedcontrol systemsrdquo Electrical Power Quality and Utilization Jour-nal vol 12 pp 21ndash27 2006

[14] G Grigoras and M Istrate ldquoAn efficient clustering methodin evaluation of the electric energy consumption from waterhydrophore stationsrdquo International Review on Modelling andSimulations vol 4 no 2 pp 813ndash818 2011

[15] U Zessler and U Shamir ldquoOptimal operation of water dis-tribution systemsrdquo Journal of Water Resources Planning andManagement vol 115 no 6 pp 735ndash752 1989

[16] P Cutore A Campisano Z Kapelan C Modica and D SavicldquoProbabilistic prediction of urban water consumption using theSCEM-UA algorithmrdquo Urban Water Journal vol 5 no 2 pp125ndash132 2008

[17] G Chicco ldquoOverview and performance assessment of theclusteringmethods for electrical load pattern groupingrdquoEnergyvol 42 no 1 pp 68ndash80 2012

[18] A K Jain M N Murty and P J Flynn ldquoData clusteringa reviewrdquo httpdataclusteringcsemsuedupapersMSU-CSE-00-16pdf

[19] R Siddheswar and R Turi ldquoDetermination of number ofclusters in K-Means clustering and application in color imagesegmentationrdquo in Proceedings of the 4th International Confer-ence on Advanced in Pattern Recognition and Digital TechniquesCalcutta India 1999

[20] I Yatskiv and L Gusarova ldquoThe methods of cluster analysisresults validationrdquo in Proceedings of International ConferenceRelStat04 Riga Latvia 2004

[21] J Yu and Q Cheng ldquoThe upper bound of the optimal numberof clusters in fuzzy clusteringrdquo Science in China Series F vol 44pp 119ndash124 2001

[22] ldquoA tutorial on clustering algorithmsrdquo httphomedeipolimiitmatteuccClusteringtutorial html

[23] P J Rousseeuw ldquoSilhouettes a graphical aid to the interpreta-tion and validation of cluster analysisrdquo Journal of Computationaland Applied Mathematics vol 20 pp 53ndash65 1987

[24] M Halkidi Y Batistakis and M Vazirgiannis ldquoOn clusteringvalidation techniquesrdquo Journal of Intelligent Information Sys-tems vol 17 no 2-3 pp 107ndash145 2001

[25] M R Rezaee B P F Lelieveldt and J H C Reiber ldquoA newcluster validity index for the fuzzy C-meanrdquo Pattern RecognitionLetters vol 19 no 3-4 pp 237ndash246 1998

[26] P Berkhin ldquoSurvey of clustering data mining techniquesrdquo TechRep Accrue Software San Jose Calif USA 2002

[27] MHolgersson ldquoThe limited value of cophenetic correlation as aclustering criterionrdquo Pattern Recognition vol 10 no 4 pp 287ndash295 1978

[28] A D Gordon Classification Chapman amp Hall New York NYUSA 2nd edition 1999

[29] C G Carter-Brown ldquoLoad profile modeling for integratedenergy planningrdquo inProceedings of theDomestic Use of Electrical

Energy Conference pp 13ndash18 Cape Town South Africa April1999

[30] British Electricity Boards ldquoReport on the design of low voltageunderground networks for new housingrdquo ACE Report No 1051986

[31] British Electricity Boards ldquoReport on the computer programDEBUTE for the design of LV radial networks Part 1mdashgeneralconsiderations part 2mdashprogram user guiderdquo Tech Rep 1151988

[32] A Seppala Load research and load estimation in electricitydistribution [PhD thesis] Helsinki University of TechnologyEsbo Finland 1996

[33] J Nazarko and Z A Styczynski ldquoApplication of statisticaland neural approaches to the daily load profiles modelling inpower distribution systemsrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference pp 320ndash325 NewOrleans La USA May 1999

[34] Z Zakaria M N Othman and M H Sohod ldquoConsumerload profiling using fuzzy clustering and statistical approachrdquoin Proceedings of the 4th Student Conference on Researchand Development (SCOReD rsquo06) 274 p 270 IEEE SelangorMalaysia June 2006

[35] I H Yu J K Lee J M Ko and S I Kim ldquoA method forclassification of electricity demands using load profile datardquo inProceedings of the 4th Annual ACIS International Conference onComputer and Information Science (ICIS rsquo05) pp 164ndash168 JejuIsland South Korea July 2006

[36] G Chicco R Napoli and F Piglione ldquoComparisons amongclustering techniques for electricity customer classificationrdquoIEEE Transactions on Power Systems vol 21 no 2 pp 933ndash9402006

[37] G Chicco R Napoli and F Piglione ldquoApplication of clusteringalgorithms and self organising maps to classify electricitycustomersrdquo in Proceedings of the IEEE Bologna PowerTechConference vol 1 Bologna Italy June 2003

[38] D Gerbek S Gasperic and F Gubina ldquoComparison of differentclassification methods for the consumersrsquo load profile determi-nationrdquo in Proceedings of the 17th International Conference onElectricity Distribution Barcelona Spain 2003

[39] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI rsquo13) pp 1ndash6 Pitesti Romania June 2013

[40] N Mahmoudi-Kohan M P Moghaddam and S M BidakildquoEvaluating performance ofWFAK-means andmodified followthe leader methods for clustering load curvesrdquo in Proceedings ofthe IEEEPES Power Systems Conference and Exposition (PSCErsquo09) Seatle Wash USA March 2009

[41] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI 13) pp 1ndash6 Pitesti Romania June 2013

[42] A Mutanen M Ruska S Repo and P Jarventausta ldquoCustomerclassification and load profiling method for distribution sys-temsrdquo IEEE Transactions on Power Delivery vol 26 no 3 pp1755ndash1763 2011

[43] G Grigoras C Barbulescu G Cartina and D ComanesculdquoA comparative study regarding efficiency of the hierarchicalclustering techniques in typical load profiles determinationrdquoActa Electrotehnica vol 52 no 5 pp 184ndash188 2011

10 Advances in Electrical Engineering

[44] B D Pitt and D S Kirschen ldquoApplication of data miningtechniques to load profilingrdquo in Proceedings of the 21st IEEEInternational Conference Power Industry Computer ApplicationsSanta Clara Calif USA 1999

[45] S Ramos and Z Vale ldquoData mining techniques applicationin power distribution utilitiesrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Exposition pp 1ndash8 Chicago Ill USA April 2008

[46] V Figueiredo F Rodrigues Z Vale and J B Gouveia ldquoAnelectric energy consumer characterization framework based ondata mining techniquesrdquo IEEE Transactions on Power Systemsvol 20 no 2 pp 596ndash602 2005

[47] A H Nizar Z Y Dong and J H Zhao ldquoLoad profilingand data mining techniques in electricity deregulated marketrdquoin Proceedings of the IEEE Power Engineering Society GeneralMeeting (PES 06) Montreal Canada June 2006

[48] G J Tsekouras N D Hatziargyriou and E N Dialynas ldquoTwo-stage pattern recognition of load curves for classification ofelectricity customersrdquo IEEE Transactions on Power Systems vol22 no 3 pp 1120ndash1128 2007

[49] S V VerduMO Garcıa F J G Franco et al ldquoCharacterizationand identification of electrical customers through the use ofself-organizing maps and daily load parametersrdquo in Proceedingsof the IEEE PES Power System Conference and Exposition vol 2pp 899ndash906 Atlanta Ga USA 2004

[50] K L Lo and Z Zakaria ldquoElectricity consumer classificationusing artificial intelligencerdquo in Proceedings of the 39th Interna-tional Universities Power Engineering Conference Bristol UK2004

[51] D Gerbec S Gasperic I Smon and F Gubina ldquoDeter-mining the load profiles of consumers based on fuzzy logicand probability neural networksrdquo IEE Proceedings GenerationTransmission andDistribution vol 151 no 3 pp 395ndash400 2004

[52] D Gerbec S Gasperic I Smon and F Gubina ldquoAllocationof the load profiles to consumers using probabilistic neuralnetworksrdquo IEEE Transactions on Power Systems vol 20 no 2pp 548ndash555 2005

[53] M Sarlak T Ebrahimi and S S KarimiMadahi ldquoEnhancementthe accuracy of daily and hourly short time load forecastingusing neural networkrdquo Journal of Basic and Applied ScientificResearch vol 2 no 1 pp 247ndash255 2012

[54] H K Alfares and M Nazeeruddin ldquoElectric load forecastingLiterature survey and classification of methodsrdquo InternationalJournal of Systems Science vol 33 no 1 pp 23ndash34 2002

[55] L A Garcia-Escudero and A Gordaliza ldquoA proposal for robustcurve clusteringrdquo Journal of Classification vol 22 no 2 pp 185ndash201 2005

[56] Z Zisman and G Cartina ldquoApplication of fuzzy logic fordistribution system estimationrdquo in Proceedings of the 22ndSeminar on Fundamentals of Electrotechnics and Circuit TheoryUstron Poland May 1999

[57] L Jentgen H Kidder R Hill and S Conrad Water Con-sumption Forecasting to Improve Energy Efficiency of PumpingOperations Awwa Research Foundation 2007

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2 Advances in Electrical Engineering

incorporating water from a variety of sources andaging systems

(ii) high operating costs which justify investments toimprove efficiency

(iii) control and computer hardware and software whichare available and more reliable

(iv) the fact that as more computer control systems areinstalled there is more experience from which tolearn

Therefore a permanent policy for the reduction of elec-trical energy consumption not only involves the technicalimprovement in the water distribution system but alsorequires the use of software tools to facilitate the operationprocess Based on this concept a new approach is proposed inthe paper based on similarities that exist between daily loadprofiles of each hydrophore station from water distributionsystem and their grouping into representative clusters Byknowing the load profile water companies can simplify thedemand determination for their supply zone Thus they canprovide better and improved efficiency marketing strategies

Different techniques have been used in literature forthe classification and load profiling but most of them wereimplemented to solve the problems from power systemsTable 1 presents a synthesis of the solutions proposed inliterature depending on the type of technique

It can be seen that most techniques belong to ArtificialIntelligence (clustering data mining self-organizing mapsneural networks and fuzzy logic) and the number of ref-erences is higher after the year 2000 This aspect can beexplained by the fact that more and more information isbecoming available faster than ever before The impact is feltin the control and operation of the distribution and transportnetworks (electricity steam gas and water) Under thesecircumstances of momentous changes Artificial Intelligencehas the potential to play a more important role

This paper proposes an extension of profiling techniquesin the area of water distribution systems for the assessmentof electrical using on a hybrid algorithm The algorithmuses the K-means clustering method for obtaining of rep-resentative load profiles and a statistical approach for theassessment of the electrical load in the water distributionsystems The remainder of this paper is organized as followsIn Section 2 the K-means clustering method is presentedSection 3 presents the steps of process for obtaining ofrepresentative load profiles Section 4 presents the statisticalmethod for assessment of the electrical load in a waterdistribution system Section 5 presents the steps of proposedalgorithm Section 6 shows the results of testing the proposedmethod on a real system Finally Section 7 contains theconcluding remarks

2 119870-Means Clustering Method

TheK-means clustering is an algorithm to classify or to groupthe objects based on attributesfeatures into 119870 number ofgroups (119870 is positive integer number) The grouping is done

by minimizing the sum of squares of distances between dataand the corresponding cluster centroid [14 17ndash20]

min (119864) = min(119870

sum

119894=1

sum

119909isin119862119894

119889(119909 119911119894)2) (1)

where 119911119894is the center of cluster 119862

119894 while 119889(119909 119911

119894) is the

Euclidean distance between a point 119909 and 119911119894

Thus the criterion function 119864 attempts to minimize thedistance of each point from the center of the cluster to whichthe point belongs More specifically the algorithm begins byinitializing a set of 119870 cluster centers Then it assigns eachobject of the dataset to the cluster whose center is the nearestand recomputed the centers The process continues until thecenters of the clusters stop changing

The steps of the algorithm are the following [14 19ndash22]

Step 1 Choose119870 initial clusters centres 119911(0)1 119911(0)

2 119911

(0)

119870

Step 2 At the kth iterative step distribute the samples 119909among the119870 clusters using the relation

119909 isin 119862(119896)

119894if 119889 (119909 119911(119896)

119894) lt 119889 (119909 119911

(119896)

119895) 119894 = 1 2 119870 119894 = 119895

(2)

where 119862(119896)119894

denotes the set of samples whose cluster centre is119911(119896)

119894

Step 3 Compute the new cluster centres 119911(119896+1)119894

119894 =

1 2 119870 The new cluster centre is given by

119911(119896+1)

119894=1

119899119894

sum

119909isin119862(119896)

119894

119909 119894 = 1 2 119870 (3)

where 119899119894is the number of objects in cluster 119862(119896)

119894

Step 4 Repeat Steps 2 and 3 until convergence is achievedthat is until a pass through the training sample causes no newassignments

It is obvious in this algorithm that the final clusters willdepend on the initial cluster centers chosen and on the valuesof 119870

The optimal number of clusters 119870opt can be determinedusing the following algorithm [19ndash21]

(1) Determination of the maximum of clusters 119870max themaximum of clusters 119870max should be set to satisfycondition 2 le 119870max le radic119873 where 119873 is the clusteredobjects from database

(2) Use the K-means clustering method with given119870 (2 le 119870 le 119870max) for the set of objects fromdatabase

(3) According to the obtained clusters structure determi-nate partition quality is evaluated

(4) Increase the number of clusters to the 119870max to see ifK-means clustering method finds a better groupingof the data (to repeat Steps 2 and 3)

Advances in Electrical Engineering 3

Table 1 Synthesis of the literature techniques for classification andload profiling

Technique ReferencesBefore year 2000 After year 2000

Statistical [29ndash33] [34 35]Clustering [14 17 36ndash43]Data mining [44] [45ndash47]Self-organizing maps [17 36 37 48 49]Neural networks [33] [50ndash54]Fuzzy logic [11 34 39 50 51]

(5) Show number of clusters (119870opt) that have obtained theoptimal value of the silhouette global coefficient

Assessing the results of theK-means algorithm representsthe main subject of cluster validity In the process of clusteranalysis the following properties of clusters are being exam-ined density sizes and formof cluster separability of clustersrobustness of classification There are many approaches tocluster validation [17 20 23ndash27] but internal cluster vali-dation tests are more popular in practice of cluster analysisThe test based on the Silhouette Global Index calculationis one of the most used [20 23 24 28] This calculates thesilhouette width for each sample average silhouette width foreach cluster and overall average silhouette width for data setUsing this approach each cluster could be represented by aso-called silhouette which is based on the comparison of itstightness and separation Cluster validity checking is one ofthe most important issues in cluster analysis related to theinherent features of the data set under concern It aims atevaluating clustering results and the selection of the schemethat best fits the underlying data

3 Determination of RepresentativeLoad Profiles

The load profiling represents an alternative to the settlementbased on energy meters because in many countries in waterdistribution systems there is a lack of necessary metering andmonitoring systems to collect data The load diagram of thehydrophore stations is reconstructed using the normalizedload profile and their daily (monthly yearly depending onthe case) electrical energy consumption The time interval ofsampling load curve data can be one hour In this situationa load profile is represented by 24 load values throughoutthe day The shape of load profiles is influenced by the typeof hydrophore station and on the other hand by the typeof day or season of the year Because a large number ofload profiles regarding various water hydrophore stationscreate unnecessary problems in handling them they couldbe grouped into coherent groups seeing that some similar-ities exist between load profiles For this purpose the K-means clustering method is applied to classify profiles of thehydrophore stations into coherent groupsmdashrepresentativeload profiles (RLPs)

Each RLP is represented by a vector 119909119895= 119909119895ℎ ℎ =

1 119879 for 119895 = 1 119873 and the comprehensive set of

RLPs is contained in the set 119875 = 119909119895 119895 = 1 119873 The

time scale along the day is partitioned into 119879 time intervalsof duration Δ119905

ℎ for ℎ = 1 119879 Hourly values are used in

this paper to exemplify the application The variables used inthe calculations are assumed to be represented as constant(average) values within each time interval The clusteringprocess forms 119870 clusters corresponding to the hydrophorestations Further a RLP is assigned to each station

The algorithm is based on the load profiling process Themajor steps are as follows

(1) Measurements In this step a representative sample of theset of load profiles is identified the most relevant attributesare to be measured and the cadence for data collectionis defined Finally the collected data is gathered in a largedatabase

(2) Data Cleaning and Preprocessing In real problems likethis involving a large number of measurements spreadover a large geographic area and collecting data during aconsiderable period of time different kind of problems willaffect the quality of the database The most relevant andfrequent are communication problems outages failure ofmeters and irregular atypical behavior of some consumersThe result will be a very large database with problems likenoise missing values and outliers These data (after beingcleaned preprocessed and reduced) are used in clusteringprocess [43 55]

(3) Classification For realization of this classification the K-means clusteringmethod is usedThe normalized load profilefor each hydrophore station from the water distributionsystem is determined using a suitable normalizing factor (egenergy over the surveyed period)

119901119895ℎ=

119875119895ℎ

sumℎ119875119895ℎ

119895 = 1 119873 ℎ = 1 119879 (4)

where 119901119895ℎis normalized value [pu] 119875

119895ℎis actual value [kW]

sum119875119895ℎis the energy over the surveyed period [kWh] andN is

the total number of vectors 119909119895from database

(4) Determination of Representative Load Profiles Using theK-means clustering method the normalized load profiles arerefined so as to desist at the unrepresentative profiles Therepresentative load profile for each cluster is obtained byaveraging the normalized values for each hour These values(called the load factors) lead us to the representative loadprofiles corresponding to the active powers The load factorsfor each cluster are calculated with relation

119898119894

ℎ=

sum119899119894

119894=1119901119894

119895ℎ

119899119894 ℎ = 1 24 119894 = 1 119870 (5)

where 119899119894 represents the number of hydrophore stations fromcluster i

The signification of load factors 119898119894ℎ ℎ = 1 24

119894 = 1 119870 from relation (5) is the following these factors

4 Advances in Electrical Engineering

transform the electrical energy consumed by the mediummember of cluster 119894 in average power demanded by it

The representative load profiles can characterize verywell the operation mode of the water hydrophore stations(identified by the clusters obtained) related to the electricalenergy consumption

(5) Assignation Finally to each water hydrophore station ismade the assignation of a representative load profile

4 The Assessment of Electrical Load in WaterDistribution Systems

Theassessment of electrical load inwater distribution systemscan be made using an improved simulation method based onthe representative load profiles of hydrophore stations Themethod is based on the following hypotheses [30 31 56]

(i) The mean loads corresponding to a cluster ofhydrophore stations from the water distribution sys-tem in any hour during the analyzed period areapproximately proportional to the electrical energyconsumption of those stations

(ii) The loads for any hour during the analyzed periodhave a statistical distribution that can be regarded asnormal

Using these hypotheses the load estimation of a waterdistribution system at any hour ℎ = 1 24 is given by thefollowing formula

119875119878

ℎ=

119870

sum

119894=1

119873119894

HS sdot 119882119894

med sdot 119898119894

ℎ+ radic

119870

sum

119894=1

119873119894

HS sdot (119882119894

med sdot 120590119894

ℎ)2 [kW]

ℎ = 1 119879

(6)

where 119875119878ℎis the load of the water distribution system at

the hour h 119870 is the number of clusters corresponding tothe hydrophore stations from water distribution system119873119894HSis the number of the hydrophore stations from cluster i119882119894

med is the average energy consumption of the hydrophorestations from cluster i 119898119894

ℎis the average load factor of the

hydrophore stations from cluster i at the hour h 120590119894ℎis the

standard deviation for load factor from hydrophore stationscorresponding to cluster i

The standard deviations for each cluster are calculatedwith relation

120590119894

ℎ=radicsum119873119894

HS119895(119901119894

119895ℎminus 119898119894

ℎ)2

119873119894

HS ℎ = 1 119879 119894 = 1 119870

(7)

5 Algorithm for Assessment of Electrical Loadin Water Distribution Systems

The algorithm adopts a procedure composed of two calcula-tion stages

Input data

End

Electrical energy consumption assessment- Determination of number of stations in each cluster - Calculation of average electrical energy

consumption of water hydrophore stations in

- Calculation of the average load factor ofstations in each cluster

- Assessment of the electrical load from thewater distribution system

- Data cleaning and preprocessing

- Calculation of the normalised load profiles

- Assignation of the representative load profile to each hydrophore station in function by its type

Start

Clustering rarr representative load profiles

- Clustering process rarr representative load profiles

each cluster

Figure 1 Flow chart of the proposed method

(i) the use of a clustering technique (K-meansmethod) inthe first stage to determine the patterns of electricalload and determine a subset of representative loadprofiles to be processed by the second stage at eachiteration the clustering outcomes simplify the processof selecting a relatively small number of load profilescorresponding to hydrophore stations

(ii) the use of load simulation in the second stage thisapproach is based on a statistical method that consid-ers the loads for any hour during the analyzed periodhave a statistical distribution that can be regarded asnormalThe flow chart of the proposed method is shown inFigure 1

For a water distribution system the input informationrefers to the technical characteristics (rated power of the forcepumps rated water flow) and the hourly load patterns ofhydrophore stations

Advances in Electrical Engineering 5

0005

01015

02025

03035

04045

05

C2 C3 C4 C5 C6 C7 C8 C9

Silh

ouet

te g

loba

l coe

ffici

ent

Clusters

Figure 2The silhouette global coefficient for different values of thenumber of clusters

0 02 04 06 08 1

1

2

3

Silhouette value

Clus

ter

Figure 3 The silhouette plot for 119870opt = 3

51 Determination of Representative Load Profiles The loadprofile of each hydrophore station is normalized relatively tothe daily electrical energy consumption The normalizationis made in relation to daily electrical energy consumptionbecause it is always known This consumption is recordedwith meters placed in each hydrophore station The optimalnumber of clusters is obtained using the K-means cluster-ing algorithm presented in Section 2 Finally the silhouetteglobal coefficient is calculated to assess the partition qualityAfter aggregation of the normalized load profiles of eachcluster the representative profiles are determined and a RLPis assigned to each hydrophore station

52 The Assessment of Electrical Loads In the second stepof the study using information from clustering process(hourly average load factors average energy consumptionand standard deviation of load factors for each hydrophorestation from cluster 119894 119894 = 1 119870) and relation (6) thehourly loads of the analyzed water distribution system willbe obtained

The accuracy of the estimates is expressed depending onthe data available Thus if the actual value of the estimatedquantity is available (such as during method developmentand testing) the following quantity can be useful to verify themethod

MAPE =sum119879

ℎ=1(10038161003816100381610038161003816119875119878

ℎ real minus 119875119878

ℎ est10038161003816100381610038161003816119875119878

ℎ real)

119879sdot 100 (8)

Table 2 The technical characteristics of hydrophore stations fromwater distribution system

Type Number ofstations

Rated power[kW]

Rated waterflow [m3h]

I 3 3 times 22 24II 6 4 times 22 32III 11 4 times 4 64IV 13 3 times 55 96V 33 4 times 55 128VI 7 4 times 75 128

where 119875ℎ real and 119875ℎ est represent the real and estimated values

for the load of water distribution system at the hour ℎThe mean absolute percentage error (MAPE) from (8)

is dimensionless and thus it can be used to compare theaccuracy of the model on different data sets

6 Case Study

In order to show the characteristics of the proposed methodfor assessment of electrical energy consumption a real waterdistribution system with 119873 = 73 hydrophore stations isconsidered For this system the input information refers tothe technical characteristics (Table 2) and the hourly loadpatterns of the hydrophore stations

Thus in all stations three or four similar force pumpshaving the rated power between 22 and 75 kW are installedThe required water flow is delivered at a constant pressureby changing the frequency of the source supplying theelectrical engines of the force pumps The load patterns arerepresented by load profiles of the water hydrophore stationsThemeasurements of individual load profileswere performedusing an electronic meter A sensor and an electronic devicefor pulse counting anddata storage compose thismeterTheseprofiles were processed for the day when it registered themaximum load in the water distribution system The timeinterval is defined by taking hourly steps within a day (119879 = 24and Δ119905

ℎ= 1 hour)

The normalization of the load profiles was made inrelation to daily electrical energy consumption Further theoptimal number of clusters was determined using the algo-rithm described in Section 2 Getting started the maximumof clusters 119870max was calculated (119870max = radic119873 asymp 9) Thenfor the set of normalized active power profiles the K-meansclustering method with a given 119870 (2 le 119870 le 119870max) isused Finally the silhouette global coefficient is calculatedfor the assessment of partition Because the silhouette globalcoefficient has the highest value for 119870 = 3 this representsthe optimal solution for clustering process Figure 2 For thissolution the silhouette plot is presented in Figure 3

The characteristics of clusters (119901119862119894ℎand 120590119862119894

ℎ ℎ = 1 24

119894 = 1 3) are presented in Table 3 After aggregationof normalized load profiles of each cluster Figure 4 therepresentative profiles were determined Representative loadprofile for each cluster is obtained by averaging the valuesfor each hour represented by load factors 119901119862119894

ℎ 119894 = 1 3

6 Advances in Electrical Engineering

0 5 10 15 20 250

001002003004005006007008009

01

Time (hours)

Load

fact

or (p

u)

(a)

0 5 10 15 20 250

001002003004005006007008009

01

Time (hours)

Load

fact

or (p

u)

(b)

0 5 10 15 20 250

001002003004005006007008009

Time (hours)

Load

fact

or (p

u)

(c)

Figure 4 Clustering results with 3 clusters ((a) cluster C1 (b) cluster C2 (c) cluster C3)

Table 3 Hourly coefficients of representative load profiles

Hour 1199011198621

[pu]1199011198622

[pu]1199011198623

[pu]1205901198621

[pu]1205901198622

[pu]1205901198623

[pu]1 0026 0022 0033 00028 00053 000412 0023 0020 0031 00036 00043 000393 0021 0019 0030 00032 00040 000404 0022 0019 0030 00033 00036 000365 0022 0020 0031 00029 00042 000426 0026 0025 0035 00025 00044 000397 0036 0040 0041 00047 00040 000288 0050 0054 0047 00089 00072 000489 0054 0048 0045 00045 00055 0004810 0055 0048 0046 00062 00058 0004511 0053 0046 0044 00100 00036 0003312 0048 0043 0043 00040 00040 0002713 0051 0041 0042 00056 00028 0003714 0054 0041 0041 00064 00034 0003015 0051 0040 0041 00059 00028 0003716 0047 0044 0043 00047 00028 0002617 0046 0048 0045 00039 00045 0003018 0047 0055 0047 00072 00041 0004919 0046 0060 0050 00061 00058 0005720 0050 0063 0051 00067 00066 0005921 0056 0070 0056 00072 00077 0008222 0047 0058 0048 00076 00073 0005823 0039 0048 0043 00039 00049 0003724 0032 0030 0037 00030 00043 00037

Advances in Electrical Engineering 7

Table 4 Results of clustering process

Cluster Number of stations [] Type of stations119882med [kWh]

I II III IV V VI1198621 24 3288 4 2 11 7 41421198622 8 1233 3 5 1 28581198623 41 5479 1 6 11 22 3235Total 73 100 3 6 11 13 33 7 3411

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 5 Representative load profile for cluster C1

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 6 Representative load profile for cluster C2

Graphical representation of the representative load profilescorresponding to the three clusters obtained (C1 C2 and C3)is given in Figures 5 6 and 7

One hourly value from the representative load profilesdenotes the load of a water hydrophore station in per unit ofthe total average daily load of this station The hourly loadpattern can be employed to approximate the load pattern ofany water hydrophore station within the same cluster

The results of calculations carried out during the firststage of the clustering procedure are presented in Table 4

From Table 4 it can be seen that the most consistentclusters are C1 and C3 which together accounted for about85of the total load profiles of thewater hydrophore stationsIn terms of technical characteristics the water hydrophorestations from cluster C2 belong to types I and II (installedrated power is less than 88 kW) the stations from clustersC1 and C3 belong to types IIIndashVI (installed rated power is

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 7 Representative load profile for cluster C3

Table 5 Real and estimated hourly load of water distributionsystem

Hour 119875119878

real [kW] 119875119878

est [kW] Err []1 7105 7295 2682 6449 6695 3813 6350 6534 2904 6323 6519 3105 6514 6727 3266 7585 7861 3647 10744 10516 2128 12737 13096 2829 11880 12211 27910 11989 12357 30711 11529 11909 32912 10936 11326 35713 10622 10995 35114 10796 11044 23015 11015 10864 13716 10978 11311 30417 11428 11976 47918 12528 13013 38719 13702 14012 22620 13993 14500 36221 16531 16036 30022 13187 13624 33123 11154 11569 37224 8550 8794 285

between 16 and 30 kW) But in cluster C3 approximately 50percent of the total stations have an installed rated power by

8 Advances in Electrical Engineering

020406080

100120140160180

1 3 5 7 9 11 13 15 17 19 21 23

P (k

W)

Real powerEstimated power

Time (hours)

Figure 8 Real and estimated load profiles of the analyzed waterdistribution system

0

1

2

3

4

5

6

1 3 5 7 9 11 13 15 17 19 21 23

Estim

ated

erro

rs (

)

Time (hours)

Figure 9 Estimation errors obtained for hourly load of analyzedwater distribution system

22 kW In terms of the electrical energy consumption it canbe observed that the highest medium value is registered forcluster C1 and the lowest value is registered for cluster C2

In the second step of the study using information fromTables 3 and 4 and relation (6) the hourly loads of theanalyzed water distribution system were obtained Thus inTable 5 Figures 8 and 9 the real loads estimated loads andestimated errors are presented The estimation maximumerror is 479 and minimum error is 137 Global resultsshow that the value for MAPE is 311

Thismay be considered a very good result especially if wetake into account the arbitrariness inherent to loads behaviorand not all hydrophore stations have monitoring system

7 Conclusions

The investigation of combined actions which account forconnected water and electrical aspects allows improvingthe global efficiency of the water distribution systems andsupplying the consumers using the least possible amount ofwater and energy

In water distribution companies the system operatorpredicts the consumption for today and tomorrow based on

recent consumption trends weather forecasting day of theweek knowledge of future events and historical knowledgeof utility system performance This approach conducts at alarge percentage error (more than 5) for assessment of load

The proposed method is based on two stages in whichthe K-means clustering method and a load simulation tech-nique are exploited for estimation of the electrical energyconsumption The method based on the K-means clusteringalgorithm was used for determination of the representativeload profiles of the hydrophore stations A comparison ofobtained results using the proposed method with the realregistered data indicates an error by 311 which is very closeto the expected one by water companies (25ndash3) [57]

Results obtained demonstrate the ability of the proposedmethod to become the first step in an efficient managementof the water distribution systems On the one hand therepresentative load profiles can be used tomodel overall watercompany demands in a way that show how changes in use byone category affect the hourly load profiles for the system as awhole and on the other hand these profiles can contribute toa better understanding of the opportunities for linking water-efficiency and energy-efficiency programs

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] Alliance to Save Energy ldquoWhat watergy involvesrdquo 2014 httpwwwwatergynet

[2] P Boulos Z Wu C Orr M Moore P Hsiung and DThomasOptimal PumpOperation ofWaterDistribution SystemsUsing Genetic Algorithms H

2ONET-Users Guide MW Software

Consulting Dallas County Tex USA 2000[3] European Commission Directorate General for Environment

2013 httpeceuropaeuenvironmentwaterindex enhtm[4] A Anton and S Perju ldquoMonitoring the main parameters of a

water supply pumping station over ten yearsrdquo in Proceedings ofthe 6th International Conference on Hydraulic Machinery andHydrodynamics Timisoara Romania 2004

[5] S J Kenway A Priestley S Cook et al ldquoEnergy use in theprovision and consumption of urban water in Australia andNew Zealandrdquo Water for a Healthy Country National ResearchFlagship Report CSIRO 2008

[6] LHouseWater Supply Related ElectricityDemand inCaliforniaReport for California Energy Commission 2006

[7] R Goldstein and W Smith ldquoWater and sustainability USelectricity consumption for water supply amp treatmentmdashthe nexthalf centuryrdquo EPRI Report Electric Power Research InstitutePalo Alto Calif USA 2000

[8] I Pulido-Calvo and J C Gutierrez-Estrada ldquoSelection andoperation of pumping stations of water distribution systemsrdquoEnvironmental Research Journal vol 5 no 3 pp 1ndash20 2011

[9] K Feldman ldquoAspects of energy efficiency in water distributionsystemsrdquo inProceedings of the International Conference onWaterLoss pp 26ndash30 IWA Cape Town South Africa April 2009

Advances in Electrical Engineering 9

[10] G C Ionescu and D S Ionescu ldquoThe optimization of energyconsumption in water supply systemsrdquo Acta Electrotehnica vol46 pp 191ndash194 2005

[11] M Istrate and G Grigoras ldquoEnergy consumption estimationin water distribution systems using fuzzy techniquesrdquo Environ-mental Engineering and Management Journal vol 9 no 2 pp249ndash256 2010

[12] I Sarbu Energetic Optimization of the Water Distribution Sys-tems Publishing House of the Romanian Academy BucharestRomania 1997

[13] L Szychta ldquoEnergy consumption of water pumping for selectedcontrol systemsrdquo Electrical Power Quality and Utilization Jour-nal vol 12 pp 21ndash27 2006

[14] G Grigoras and M Istrate ldquoAn efficient clustering methodin evaluation of the electric energy consumption from waterhydrophore stationsrdquo International Review on Modelling andSimulations vol 4 no 2 pp 813ndash818 2011

[15] U Zessler and U Shamir ldquoOptimal operation of water dis-tribution systemsrdquo Journal of Water Resources Planning andManagement vol 115 no 6 pp 735ndash752 1989

[16] P Cutore A Campisano Z Kapelan C Modica and D SavicldquoProbabilistic prediction of urban water consumption using theSCEM-UA algorithmrdquo Urban Water Journal vol 5 no 2 pp125ndash132 2008

[17] G Chicco ldquoOverview and performance assessment of theclusteringmethods for electrical load pattern groupingrdquoEnergyvol 42 no 1 pp 68ndash80 2012

[18] A K Jain M N Murty and P J Flynn ldquoData clusteringa reviewrdquo httpdataclusteringcsemsuedupapersMSU-CSE-00-16pdf

[19] R Siddheswar and R Turi ldquoDetermination of number ofclusters in K-Means clustering and application in color imagesegmentationrdquo in Proceedings of the 4th International Confer-ence on Advanced in Pattern Recognition and Digital TechniquesCalcutta India 1999

[20] I Yatskiv and L Gusarova ldquoThe methods of cluster analysisresults validationrdquo in Proceedings of International ConferenceRelStat04 Riga Latvia 2004

[21] J Yu and Q Cheng ldquoThe upper bound of the optimal numberof clusters in fuzzy clusteringrdquo Science in China Series F vol 44pp 119ndash124 2001

[22] ldquoA tutorial on clustering algorithmsrdquo httphomedeipolimiitmatteuccClusteringtutorial html

[23] P J Rousseeuw ldquoSilhouettes a graphical aid to the interpreta-tion and validation of cluster analysisrdquo Journal of Computationaland Applied Mathematics vol 20 pp 53ndash65 1987

[24] M Halkidi Y Batistakis and M Vazirgiannis ldquoOn clusteringvalidation techniquesrdquo Journal of Intelligent Information Sys-tems vol 17 no 2-3 pp 107ndash145 2001

[25] M R Rezaee B P F Lelieveldt and J H C Reiber ldquoA newcluster validity index for the fuzzy C-meanrdquo Pattern RecognitionLetters vol 19 no 3-4 pp 237ndash246 1998

[26] P Berkhin ldquoSurvey of clustering data mining techniquesrdquo TechRep Accrue Software San Jose Calif USA 2002

[27] MHolgersson ldquoThe limited value of cophenetic correlation as aclustering criterionrdquo Pattern Recognition vol 10 no 4 pp 287ndash295 1978

[28] A D Gordon Classification Chapman amp Hall New York NYUSA 2nd edition 1999

[29] C G Carter-Brown ldquoLoad profile modeling for integratedenergy planningrdquo inProceedings of theDomestic Use of Electrical

Energy Conference pp 13ndash18 Cape Town South Africa April1999

[30] British Electricity Boards ldquoReport on the design of low voltageunderground networks for new housingrdquo ACE Report No 1051986

[31] British Electricity Boards ldquoReport on the computer programDEBUTE for the design of LV radial networks Part 1mdashgeneralconsiderations part 2mdashprogram user guiderdquo Tech Rep 1151988

[32] A Seppala Load research and load estimation in electricitydistribution [PhD thesis] Helsinki University of TechnologyEsbo Finland 1996

[33] J Nazarko and Z A Styczynski ldquoApplication of statisticaland neural approaches to the daily load profiles modelling inpower distribution systemsrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference pp 320ndash325 NewOrleans La USA May 1999

[34] Z Zakaria M N Othman and M H Sohod ldquoConsumerload profiling using fuzzy clustering and statistical approachrdquoin Proceedings of the 4th Student Conference on Researchand Development (SCOReD rsquo06) 274 p 270 IEEE SelangorMalaysia June 2006

[35] I H Yu J K Lee J M Ko and S I Kim ldquoA method forclassification of electricity demands using load profile datardquo inProceedings of the 4th Annual ACIS International Conference onComputer and Information Science (ICIS rsquo05) pp 164ndash168 JejuIsland South Korea July 2006

[36] G Chicco R Napoli and F Piglione ldquoComparisons amongclustering techniques for electricity customer classificationrdquoIEEE Transactions on Power Systems vol 21 no 2 pp 933ndash9402006

[37] G Chicco R Napoli and F Piglione ldquoApplication of clusteringalgorithms and self organising maps to classify electricitycustomersrdquo in Proceedings of the IEEE Bologna PowerTechConference vol 1 Bologna Italy June 2003

[38] D Gerbek S Gasperic and F Gubina ldquoComparison of differentclassification methods for the consumersrsquo load profile determi-nationrdquo in Proceedings of the 17th International Conference onElectricity Distribution Barcelona Spain 2003

[39] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI rsquo13) pp 1ndash6 Pitesti Romania June 2013

[40] N Mahmoudi-Kohan M P Moghaddam and S M BidakildquoEvaluating performance ofWFAK-means andmodified followthe leader methods for clustering load curvesrdquo in Proceedings ofthe IEEEPES Power Systems Conference and Exposition (PSCErsquo09) Seatle Wash USA March 2009

[41] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI 13) pp 1ndash6 Pitesti Romania June 2013

[42] A Mutanen M Ruska S Repo and P Jarventausta ldquoCustomerclassification and load profiling method for distribution sys-temsrdquo IEEE Transactions on Power Delivery vol 26 no 3 pp1755ndash1763 2011

[43] G Grigoras C Barbulescu G Cartina and D ComanesculdquoA comparative study regarding efficiency of the hierarchicalclustering techniques in typical load profiles determinationrdquoActa Electrotehnica vol 52 no 5 pp 184ndash188 2011

10 Advances in Electrical Engineering

[44] B D Pitt and D S Kirschen ldquoApplication of data miningtechniques to load profilingrdquo in Proceedings of the 21st IEEEInternational Conference Power Industry Computer ApplicationsSanta Clara Calif USA 1999

[45] S Ramos and Z Vale ldquoData mining techniques applicationin power distribution utilitiesrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Exposition pp 1ndash8 Chicago Ill USA April 2008

[46] V Figueiredo F Rodrigues Z Vale and J B Gouveia ldquoAnelectric energy consumer characterization framework based ondata mining techniquesrdquo IEEE Transactions on Power Systemsvol 20 no 2 pp 596ndash602 2005

[47] A H Nizar Z Y Dong and J H Zhao ldquoLoad profilingand data mining techniques in electricity deregulated marketrdquoin Proceedings of the IEEE Power Engineering Society GeneralMeeting (PES 06) Montreal Canada June 2006

[48] G J Tsekouras N D Hatziargyriou and E N Dialynas ldquoTwo-stage pattern recognition of load curves for classification ofelectricity customersrdquo IEEE Transactions on Power Systems vol22 no 3 pp 1120ndash1128 2007

[49] S V VerduMO Garcıa F J G Franco et al ldquoCharacterizationand identification of electrical customers through the use ofself-organizing maps and daily load parametersrdquo in Proceedingsof the IEEE PES Power System Conference and Exposition vol 2pp 899ndash906 Atlanta Ga USA 2004

[50] K L Lo and Z Zakaria ldquoElectricity consumer classificationusing artificial intelligencerdquo in Proceedings of the 39th Interna-tional Universities Power Engineering Conference Bristol UK2004

[51] D Gerbec S Gasperic I Smon and F Gubina ldquoDeter-mining the load profiles of consumers based on fuzzy logicand probability neural networksrdquo IEE Proceedings GenerationTransmission andDistribution vol 151 no 3 pp 395ndash400 2004

[52] D Gerbec S Gasperic I Smon and F Gubina ldquoAllocationof the load profiles to consumers using probabilistic neuralnetworksrdquo IEEE Transactions on Power Systems vol 20 no 2pp 548ndash555 2005

[53] M Sarlak T Ebrahimi and S S KarimiMadahi ldquoEnhancementthe accuracy of daily and hourly short time load forecastingusing neural networkrdquo Journal of Basic and Applied ScientificResearch vol 2 no 1 pp 247ndash255 2012

[54] H K Alfares and M Nazeeruddin ldquoElectric load forecastingLiterature survey and classification of methodsrdquo InternationalJournal of Systems Science vol 33 no 1 pp 23ndash34 2002

[55] L A Garcia-Escudero and A Gordaliza ldquoA proposal for robustcurve clusteringrdquo Journal of Classification vol 22 no 2 pp 185ndash201 2005

[56] Z Zisman and G Cartina ldquoApplication of fuzzy logic fordistribution system estimationrdquo in Proceedings of the 22ndSeminar on Fundamentals of Electrotechnics and Circuit TheoryUstron Poland May 1999

[57] L Jentgen H Kidder R Hill and S Conrad Water Con-sumption Forecasting to Improve Energy Efficiency of PumpingOperations Awwa Research Foundation 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Electrical and Computer Engineering

Journal of

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SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

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DistributedSensor Networks

International Journal of

Advances in Electrical Engineering 3

Table 1 Synthesis of the literature techniques for classification andload profiling

Technique ReferencesBefore year 2000 After year 2000

Statistical [29ndash33] [34 35]Clustering [14 17 36ndash43]Data mining [44] [45ndash47]Self-organizing maps [17 36 37 48 49]Neural networks [33] [50ndash54]Fuzzy logic [11 34 39 50 51]

(5) Show number of clusters (119870opt) that have obtained theoptimal value of the silhouette global coefficient

Assessing the results of theK-means algorithm representsthe main subject of cluster validity In the process of clusteranalysis the following properties of clusters are being exam-ined density sizes and formof cluster separability of clustersrobustness of classification There are many approaches tocluster validation [17 20 23ndash27] but internal cluster vali-dation tests are more popular in practice of cluster analysisThe test based on the Silhouette Global Index calculationis one of the most used [20 23 24 28] This calculates thesilhouette width for each sample average silhouette width foreach cluster and overall average silhouette width for data setUsing this approach each cluster could be represented by aso-called silhouette which is based on the comparison of itstightness and separation Cluster validity checking is one ofthe most important issues in cluster analysis related to theinherent features of the data set under concern It aims atevaluating clustering results and the selection of the schemethat best fits the underlying data

3 Determination of RepresentativeLoad Profiles

The load profiling represents an alternative to the settlementbased on energy meters because in many countries in waterdistribution systems there is a lack of necessary metering andmonitoring systems to collect data The load diagram of thehydrophore stations is reconstructed using the normalizedload profile and their daily (monthly yearly depending onthe case) electrical energy consumption The time interval ofsampling load curve data can be one hour In this situationa load profile is represented by 24 load values throughoutthe day The shape of load profiles is influenced by the typeof hydrophore station and on the other hand by the typeof day or season of the year Because a large number ofload profiles regarding various water hydrophore stationscreate unnecessary problems in handling them they couldbe grouped into coherent groups seeing that some similar-ities exist between load profiles For this purpose the K-means clustering method is applied to classify profiles of thehydrophore stations into coherent groupsmdashrepresentativeload profiles (RLPs)

Each RLP is represented by a vector 119909119895= 119909119895ℎ ℎ =

1 119879 for 119895 = 1 119873 and the comprehensive set of

RLPs is contained in the set 119875 = 119909119895 119895 = 1 119873 The

time scale along the day is partitioned into 119879 time intervalsof duration Δ119905

ℎ for ℎ = 1 119879 Hourly values are used in

this paper to exemplify the application The variables used inthe calculations are assumed to be represented as constant(average) values within each time interval The clusteringprocess forms 119870 clusters corresponding to the hydrophorestations Further a RLP is assigned to each station

The algorithm is based on the load profiling process Themajor steps are as follows

(1) Measurements In this step a representative sample of theset of load profiles is identified the most relevant attributesare to be measured and the cadence for data collectionis defined Finally the collected data is gathered in a largedatabase

(2) Data Cleaning and Preprocessing In real problems likethis involving a large number of measurements spreadover a large geographic area and collecting data during aconsiderable period of time different kind of problems willaffect the quality of the database The most relevant andfrequent are communication problems outages failure ofmeters and irregular atypical behavior of some consumersThe result will be a very large database with problems likenoise missing values and outliers These data (after beingcleaned preprocessed and reduced) are used in clusteringprocess [43 55]

(3) Classification For realization of this classification the K-means clusteringmethod is usedThe normalized load profilefor each hydrophore station from the water distributionsystem is determined using a suitable normalizing factor (egenergy over the surveyed period)

119901119895ℎ=

119875119895ℎ

sumℎ119875119895ℎ

119895 = 1 119873 ℎ = 1 119879 (4)

where 119901119895ℎis normalized value [pu] 119875

119895ℎis actual value [kW]

sum119875119895ℎis the energy over the surveyed period [kWh] andN is

the total number of vectors 119909119895from database

(4) Determination of Representative Load Profiles Using theK-means clustering method the normalized load profiles arerefined so as to desist at the unrepresentative profiles Therepresentative load profile for each cluster is obtained byaveraging the normalized values for each hour These values(called the load factors) lead us to the representative loadprofiles corresponding to the active powers The load factorsfor each cluster are calculated with relation

119898119894

ℎ=

sum119899119894

119894=1119901119894

119895ℎ

119899119894 ℎ = 1 24 119894 = 1 119870 (5)

where 119899119894 represents the number of hydrophore stations fromcluster i

The signification of load factors 119898119894ℎ ℎ = 1 24

119894 = 1 119870 from relation (5) is the following these factors

4 Advances in Electrical Engineering

transform the electrical energy consumed by the mediummember of cluster 119894 in average power demanded by it

The representative load profiles can characterize verywell the operation mode of the water hydrophore stations(identified by the clusters obtained) related to the electricalenergy consumption

(5) Assignation Finally to each water hydrophore station ismade the assignation of a representative load profile

4 The Assessment of Electrical Load in WaterDistribution Systems

Theassessment of electrical load inwater distribution systemscan be made using an improved simulation method based onthe representative load profiles of hydrophore stations Themethod is based on the following hypotheses [30 31 56]

(i) The mean loads corresponding to a cluster ofhydrophore stations from the water distribution sys-tem in any hour during the analyzed period areapproximately proportional to the electrical energyconsumption of those stations

(ii) The loads for any hour during the analyzed periodhave a statistical distribution that can be regarded asnormal

Using these hypotheses the load estimation of a waterdistribution system at any hour ℎ = 1 24 is given by thefollowing formula

119875119878

ℎ=

119870

sum

119894=1

119873119894

HS sdot 119882119894

med sdot 119898119894

ℎ+ radic

119870

sum

119894=1

119873119894

HS sdot (119882119894

med sdot 120590119894

ℎ)2 [kW]

ℎ = 1 119879

(6)

where 119875119878ℎis the load of the water distribution system at

the hour h 119870 is the number of clusters corresponding tothe hydrophore stations from water distribution system119873119894HSis the number of the hydrophore stations from cluster i119882119894

med is the average energy consumption of the hydrophorestations from cluster i 119898119894

ℎis the average load factor of the

hydrophore stations from cluster i at the hour h 120590119894ℎis the

standard deviation for load factor from hydrophore stationscorresponding to cluster i

The standard deviations for each cluster are calculatedwith relation

120590119894

ℎ=radicsum119873119894

HS119895(119901119894

119895ℎminus 119898119894

ℎ)2

119873119894

HS ℎ = 1 119879 119894 = 1 119870

(7)

5 Algorithm for Assessment of Electrical Loadin Water Distribution Systems

The algorithm adopts a procedure composed of two calcula-tion stages

Input data

End

Electrical energy consumption assessment- Determination of number of stations in each cluster - Calculation of average electrical energy

consumption of water hydrophore stations in

- Calculation of the average load factor ofstations in each cluster

- Assessment of the electrical load from thewater distribution system

- Data cleaning and preprocessing

- Calculation of the normalised load profiles

- Assignation of the representative load profile to each hydrophore station in function by its type

Start

Clustering rarr representative load profiles

- Clustering process rarr representative load profiles

each cluster

Figure 1 Flow chart of the proposed method

(i) the use of a clustering technique (K-meansmethod) inthe first stage to determine the patterns of electricalload and determine a subset of representative loadprofiles to be processed by the second stage at eachiteration the clustering outcomes simplify the processof selecting a relatively small number of load profilescorresponding to hydrophore stations

(ii) the use of load simulation in the second stage thisapproach is based on a statistical method that consid-ers the loads for any hour during the analyzed periodhave a statistical distribution that can be regarded asnormalThe flow chart of the proposed method is shown inFigure 1

For a water distribution system the input informationrefers to the technical characteristics (rated power of the forcepumps rated water flow) and the hourly load patterns ofhydrophore stations

Advances in Electrical Engineering 5

0005

01015

02025

03035

04045

05

C2 C3 C4 C5 C6 C7 C8 C9

Silh

ouet

te g

loba

l coe

ffici

ent

Clusters

Figure 2The silhouette global coefficient for different values of thenumber of clusters

0 02 04 06 08 1

1

2

3

Silhouette value

Clus

ter

Figure 3 The silhouette plot for 119870opt = 3

51 Determination of Representative Load Profiles The loadprofile of each hydrophore station is normalized relatively tothe daily electrical energy consumption The normalizationis made in relation to daily electrical energy consumptionbecause it is always known This consumption is recordedwith meters placed in each hydrophore station The optimalnumber of clusters is obtained using the K-means cluster-ing algorithm presented in Section 2 Finally the silhouetteglobal coefficient is calculated to assess the partition qualityAfter aggregation of the normalized load profiles of eachcluster the representative profiles are determined and a RLPis assigned to each hydrophore station

52 The Assessment of Electrical Loads In the second stepof the study using information from clustering process(hourly average load factors average energy consumptionand standard deviation of load factors for each hydrophorestation from cluster 119894 119894 = 1 119870) and relation (6) thehourly loads of the analyzed water distribution system willbe obtained

The accuracy of the estimates is expressed depending onthe data available Thus if the actual value of the estimatedquantity is available (such as during method developmentand testing) the following quantity can be useful to verify themethod

MAPE =sum119879

ℎ=1(10038161003816100381610038161003816119875119878

ℎ real minus 119875119878

ℎ est10038161003816100381610038161003816119875119878

ℎ real)

119879sdot 100 (8)

Table 2 The technical characteristics of hydrophore stations fromwater distribution system

Type Number ofstations

Rated power[kW]

Rated waterflow [m3h]

I 3 3 times 22 24II 6 4 times 22 32III 11 4 times 4 64IV 13 3 times 55 96V 33 4 times 55 128VI 7 4 times 75 128

where 119875ℎ real and 119875ℎ est represent the real and estimated values

for the load of water distribution system at the hour ℎThe mean absolute percentage error (MAPE) from (8)

is dimensionless and thus it can be used to compare theaccuracy of the model on different data sets

6 Case Study

In order to show the characteristics of the proposed methodfor assessment of electrical energy consumption a real waterdistribution system with 119873 = 73 hydrophore stations isconsidered For this system the input information refers tothe technical characteristics (Table 2) and the hourly loadpatterns of the hydrophore stations

Thus in all stations three or four similar force pumpshaving the rated power between 22 and 75 kW are installedThe required water flow is delivered at a constant pressureby changing the frequency of the source supplying theelectrical engines of the force pumps The load patterns arerepresented by load profiles of the water hydrophore stationsThemeasurements of individual load profileswere performedusing an electronic meter A sensor and an electronic devicefor pulse counting anddata storage compose thismeterTheseprofiles were processed for the day when it registered themaximum load in the water distribution system The timeinterval is defined by taking hourly steps within a day (119879 = 24and Δ119905

ℎ= 1 hour)

The normalization of the load profiles was made inrelation to daily electrical energy consumption Further theoptimal number of clusters was determined using the algo-rithm described in Section 2 Getting started the maximumof clusters 119870max was calculated (119870max = radic119873 asymp 9) Thenfor the set of normalized active power profiles the K-meansclustering method with a given 119870 (2 le 119870 le 119870max) isused Finally the silhouette global coefficient is calculatedfor the assessment of partition Because the silhouette globalcoefficient has the highest value for 119870 = 3 this representsthe optimal solution for clustering process Figure 2 For thissolution the silhouette plot is presented in Figure 3

The characteristics of clusters (119901119862119894ℎand 120590119862119894

ℎ ℎ = 1 24

119894 = 1 3) are presented in Table 3 After aggregationof normalized load profiles of each cluster Figure 4 therepresentative profiles were determined Representative loadprofile for each cluster is obtained by averaging the valuesfor each hour represented by load factors 119901119862119894

ℎ 119894 = 1 3

6 Advances in Electrical Engineering

0 5 10 15 20 250

001002003004005006007008009

01

Time (hours)

Load

fact

or (p

u)

(a)

0 5 10 15 20 250

001002003004005006007008009

01

Time (hours)

Load

fact

or (p

u)

(b)

0 5 10 15 20 250

001002003004005006007008009

Time (hours)

Load

fact

or (p

u)

(c)

Figure 4 Clustering results with 3 clusters ((a) cluster C1 (b) cluster C2 (c) cluster C3)

Table 3 Hourly coefficients of representative load profiles

Hour 1199011198621

[pu]1199011198622

[pu]1199011198623

[pu]1205901198621

[pu]1205901198622

[pu]1205901198623

[pu]1 0026 0022 0033 00028 00053 000412 0023 0020 0031 00036 00043 000393 0021 0019 0030 00032 00040 000404 0022 0019 0030 00033 00036 000365 0022 0020 0031 00029 00042 000426 0026 0025 0035 00025 00044 000397 0036 0040 0041 00047 00040 000288 0050 0054 0047 00089 00072 000489 0054 0048 0045 00045 00055 0004810 0055 0048 0046 00062 00058 0004511 0053 0046 0044 00100 00036 0003312 0048 0043 0043 00040 00040 0002713 0051 0041 0042 00056 00028 0003714 0054 0041 0041 00064 00034 0003015 0051 0040 0041 00059 00028 0003716 0047 0044 0043 00047 00028 0002617 0046 0048 0045 00039 00045 0003018 0047 0055 0047 00072 00041 0004919 0046 0060 0050 00061 00058 0005720 0050 0063 0051 00067 00066 0005921 0056 0070 0056 00072 00077 0008222 0047 0058 0048 00076 00073 0005823 0039 0048 0043 00039 00049 0003724 0032 0030 0037 00030 00043 00037

Advances in Electrical Engineering 7

Table 4 Results of clustering process

Cluster Number of stations [] Type of stations119882med [kWh]

I II III IV V VI1198621 24 3288 4 2 11 7 41421198622 8 1233 3 5 1 28581198623 41 5479 1 6 11 22 3235Total 73 100 3 6 11 13 33 7 3411

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 5 Representative load profile for cluster C1

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 6 Representative load profile for cluster C2

Graphical representation of the representative load profilescorresponding to the three clusters obtained (C1 C2 and C3)is given in Figures 5 6 and 7

One hourly value from the representative load profilesdenotes the load of a water hydrophore station in per unit ofthe total average daily load of this station The hourly loadpattern can be employed to approximate the load pattern ofany water hydrophore station within the same cluster

The results of calculations carried out during the firststage of the clustering procedure are presented in Table 4

From Table 4 it can be seen that the most consistentclusters are C1 and C3 which together accounted for about85of the total load profiles of thewater hydrophore stationsIn terms of technical characteristics the water hydrophorestations from cluster C2 belong to types I and II (installedrated power is less than 88 kW) the stations from clustersC1 and C3 belong to types IIIndashVI (installed rated power is

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 7 Representative load profile for cluster C3

Table 5 Real and estimated hourly load of water distributionsystem

Hour 119875119878

real [kW] 119875119878

est [kW] Err []1 7105 7295 2682 6449 6695 3813 6350 6534 2904 6323 6519 3105 6514 6727 3266 7585 7861 3647 10744 10516 2128 12737 13096 2829 11880 12211 27910 11989 12357 30711 11529 11909 32912 10936 11326 35713 10622 10995 35114 10796 11044 23015 11015 10864 13716 10978 11311 30417 11428 11976 47918 12528 13013 38719 13702 14012 22620 13993 14500 36221 16531 16036 30022 13187 13624 33123 11154 11569 37224 8550 8794 285

between 16 and 30 kW) But in cluster C3 approximately 50percent of the total stations have an installed rated power by

8 Advances in Electrical Engineering

020406080

100120140160180

1 3 5 7 9 11 13 15 17 19 21 23

P (k

W)

Real powerEstimated power

Time (hours)

Figure 8 Real and estimated load profiles of the analyzed waterdistribution system

0

1

2

3

4

5

6

1 3 5 7 9 11 13 15 17 19 21 23

Estim

ated

erro

rs (

)

Time (hours)

Figure 9 Estimation errors obtained for hourly load of analyzedwater distribution system

22 kW In terms of the electrical energy consumption it canbe observed that the highest medium value is registered forcluster C1 and the lowest value is registered for cluster C2

In the second step of the study using information fromTables 3 and 4 and relation (6) the hourly loads of theanalyzed water distribution system were obtained Thus inTable 5 Figures 8 and 9 the real loads estimated loads andestimated errors are presented The estimation maximumerror is 479 and minimum error is 137 Global resultsshow that the value for MAPE is 311

Thismay be considered a very good result especially if wetake into account the arbitrariness inherent to loads behaviorand not all hydrophore stations have monitoring system

7 Conclusions

The investigation of combined actions which account forconnected water and electrical aspects allows improvingthe global efficiency of the water distribution systems andsupplying the consumers using the least possible amount ofwater and energy

In water distribution companies the system operatorpredicts the consumption for today and tomorrow based on

recent consumption trends weather forecasting day of theweek knowledge of future events and historical knowledgeof utility system performance This approach conducts at alarge percentage error (more than 5) for assessment of load

The proposed method is based on two stages in whichthe K-means clustering method and a load simulation tech-nique are exploited for estimation of the electrical energyconsumption The method based on the K-means clusteringalgorithm was used for determination of the representativeload profiles of the hydrophore stations A comparison ofobtained results using the proposed method with the realregistered data indicates an error by 311 which is very closeto the expected one by water companies (25ndash3) [57]

Results obtained demonstrate the ability of the proposedmethod to become the first step in an efficient managementof the water distribution systems On the one hand therepresentative load profiles can be used tomodel overall watercompany demands in a way that show how changes in use byone category affect the hourly load profiles for the system as awhole and on the other hand these profiles can contribute toa better understanding of the opportunities for linking water-efficiency and energy-efficiency programs

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] Alliance to Save Energy ldquoWhat watergy involvesrdquo 2014 httpwwwwatergynet

[2] P Boulos Z Wu C Orr M Moore P Hsiung and DThomasOptimal PumpOperation ofWaterDistribution SystemsUsing Genetic Algorithms H

2ONET-Users Guide MW Software

Consulting Dallas County Tex USA 2000[3] European Commission Directorate General for Environment

2013 httpeceuropaeuenvironmentwaterindex enhtm[4] A Anton and S Perju ldquoMonitoring the main parameters of a

water supply pumping station over ten yearsrdquo in Proceedings ofthe 6th International Conference on Hydraulic Machinery andHydrodynamics Timisoara Romania 2004

[5] S J Kenway A Priestley S Cook et al ldquoEnergy use in theprovision and consumption of urban water in Australia andNew Zealandrdquo Water for a Healthy Country National ResearchFlagship Report CSIRO 2008

[6] LHouseWater Supply Related ElectricityDemand inCaliforniaReport for California Energy Commission 2006

[7] R Goldstein and W Smith ldquoWater and sustainability USelectricity consumption for water supply amp treatmentmdashthe nexthalf centuryrdquo EPRI Report Electric Power Research InstitutePalo Alto Calif USA 2000

[8] I Pulido-Calvo and J C Gutierrez-Estrada ldquoSelection andoperation of pumping stations of water distribution systemsrdquoEnvironmental Research Journal vol 5 no 3 pp 1ndash20 2011

[9] K Feldman ldquoAspects of energy efficiency in water distributionsystemsrdquo inProceedings of the International Conference onWaterLoss pp 26ndash30 IWA Cape Town South Africa April 2009

Advances in Electrical Engineering 9

[10] G C Ionescu and D S Ionescu ldquoThe optimization of energyconsumption in water supply systemsrdquo Acta Electrotehnica vol46 pp 191ndash194 2005

[11] M Istrate and G Grigoras ldquoEnergy consumption estimationin water distribution systems using fuzzy techniquesrdquo Environ-mental Engineering and Management Journal vol 9 no 2 pp249ndash256 2010

[12] I Sarbu Energetic Optimization of the Water Distribution Sys-tems Publishing House of the Romanian Academy BucharestRomania 1997

[13] L Szychta ldquoEnergy consumption of water pumping for selectedcontrol systemsrdquo Electrical Power Quality and Utilization Jour-nal vol 12 pp 21ndash27 2006

[14] G Grigoras and M Istrate ldquoAn efficient clustering methodin evaluation of the electric energy consumption from waterhydrophore stationsrdquo International Review on Modelling andSimulations vol 4 no 2 pp 813ndash818 2011

[15] U Zessler and U Shamir ldquoOptimal operation of water dis-tribution systemsrdquo Journal of Water Resources Planning andManagement vol 115 no 6 pp 735ndash752 1989

[16] P Cutore A Campisano Z Kapelan C Modica and D SavicldquoProbabilistic prediction of urban water consumption using theSCEM-UA algorithmrdquo Urban Water Journal vol 5 no 2 pp125ndash132 2008

[17] G Chicco ldquoOverview and performance assessment of theclusteringmethods for electrical load pattern groupingrdquoEnergyvol 42 no 1 pp 68ndash80 2012

[18] A K Jain M N Murty and P J Flynn ldquoData clusteringa reviewrdquo httpdataclusteringcsemsuedupapersMSU-CSE-00-16pdf

[19] R Siddheswar and R Turi ldquoDetermination of number ofclusters in K-Means clustering and application in color imagesegmentationrdquo in Proceedings of the 4th International Confer-ence on Advanced in Pattern Recognition and Digital TechniquesCalcutta India 1999

[20] I Yatskiv and L Gusarova ldquoThe methods of cluster analysisresults validationrdquo in Proceedings of International ConferenceRelStat04 Riga Latvia 2004

[21] J Yu and Q Cheng ldquoThe upper bound of the optimal numberof clusters in fuzzy clusteringrdquo Science in China Series F vol 44pp 119ndash124 2001

[22] ldquoA tutorial on clustering algorithmsrdquo httphomedeipolimiitmatteuccClusteringtutorial html

[23] P J Rousseeuw ldquoSilhouettes a graphical aid to the interpreta-tion and validation of cluster analysisrdquo Journal of Computationaland Applied Mathematics vol 20 pp 53ndash65 1987

[24] M Halkidi Y Batistakis and M Vazirgiannis ldquoOn clusteringvalidation techniquesrdquo Journal of Intelligent Information Sys-tems vol 17 no 2-3 pp 107ndash145 2001

[25] M R Rezaee B P F Lelieveldt and J H C Reiber ldquoA newcluster validity index for the fuzzy C-meanrdquo Pattern RecognitionLetters vol 19 no 3-4 pp 237ndash246 1998

[26] P Berkhin ldquoSurvey of clustering data mining techniquesrdquo TechRep Accrue Software San Jose Calif USA 2002

[27] MHolgersson ldquoThe limited value of cophenetic correlation as aclustering criterionrdquo Pattern Recognition vol 10 no 4 pp 287ndash295 1978

[28] A D Gordon Classification Chapman amp Hall New York NYUSA 2nd edition 1999

[29] C G Carter-Brown ldquoLoad profile modeling for integratedenergy planningrdquo inProceedings of theDomestic Use of Electrical

Energy Conference pp 13ndash18 Cape Town South Africa April1999

[30] British Electricity Boards ldquoReport on the design of low voltageunderground networks for new housingrdquo ACE Report No 1051986

[31] British Electricity Boards ldquoReport on the computer programDEBUTE for the design of LV radial networks Part 1mdashgeneralconsiderations part 2mdashprogram user guiderdquo Tech Rep 1151988

[32] A Seppala Load research and load estimation in electricitydistribution [PhD thesis] Helsinki University of TechnologyEsbo Finland 1996

[33] J Nazarko and Z A Styczynski ldquoApplication of statisticaland neural approaches to the daily load profiles modelling inpower distribution systemsrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference pp 320ndash325 NewOrleans La USA May 1999

[34] Z Zakaria M N Othman and M H Sohod ldquoConsumerload profiling using fuzzy clustering and statistical approachrdquoin Proceedings of the 4th Student Conference on Researchand Development (SCOReD rsquo06) 274 p 270 IEEE SelangorMalaysia June 2006

[35] I H Yu J K Lee J M Ko and S I Kim ldquoA method forclassification of electricity demands using load profile datardquo inProceedings of the 4th Annual ACIS International Conference onComputer and Information Science (ICIS rsquo05) pp 164ndash168 JejuIsland South Korea July 2006

[36] G Chicco R Napoli and F Piglione ldquoComparisons amongclustering techniques for electricity customer classificationrdquoIEEE Transactions on Power Systems vol 21 no 2 pp 933ndash9402006

[37] G Chicco R Napoli and F Piglione ldquoApplication of clusteringalgorithms and self organising maps to classify electricitycustomersrdquo in Proceedings of the IEEE Bologna PowerTechConference vol 1 Bologna Italy June 2003

[38] D Gerbek S Gasperic and F Gubina ldquoComparison of differentclassification methods for the consumersrsquo load profile determi-nationrdquo in Proceedings of the 17th International Conference onElectricity Distribution Barcelona Spain 2003

[39] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI rsquo13) pp 1ndash6 Pitesti Romania June 2013

[40] N Mahmoudi-Kohan M P Moghaddam and S M BidakildquoEvaluating performance ofWFAK-means andmodified followthe leader methods for clustering load curvesrdquo in Proceedings ofthe IEEEPES Power Systems Conference and Exposition (PSCErsquo09) Seatle Wash USA March 2009

[41] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI 13) pp 1ndash6 Pitesti Romania June 2013

[42] A Mutanen M Ruska S Repo and P Jarventausta ldquoCustomerclassification and load profiling method for distribution sys-temsrdquo IEEE Transactions on Power Delivery vol 26 no 3 pp1755ndash1763 2011

[43] G Grigoras C Barbulescu G Cartina and D ComanesculdquoA comparative study regarding efficiency of the hierarchicalclustering techniques in typical load profiles determinationrdquoActa Electrotehnica vol 52 no 5 pp 184ndash188 2011

10 Advances in Electrical Engineering

[44] B D Pitt and D S Kirschen ldquoApplication of data miningtechniques to load profilingrdquo in Proceedings of the 21st IEEEInternational Conference Power Industry Computer ApplicationsSanta Clara Calif USA 1999

[45] S Ramos and Z Vale ldquoData mining techniques applicationin power distribution utilitiesrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Exposition pp 1ndash8 Chicago Ill USA April 2008

[46] V Figueiredo F Rodrigues Z Vale and J B Gouveia ldquoAnelectric energy consumer characterization framework based ondata mining techniquesrdquo IEEE Transactions on Power Systemsvol 20 no 2 pp 596ndash602 2005

[47] A H Nizar Z Y Dong and J H Zhao ldquoLoad profilingand data mining techniques in electricity deregulated marketrdquoin Proceedings of the IEEE Power Engineering Society GeneralMeeting (PES 06) Montreal Canada June 2006

[48] G J Tsekouras N D Hatziargyriou and E N Dialynas ldquoTwo-stage pattern recognition of load curves for classification ofelectricity customersrdquo IEEE Transactions on Power Systems vol22 no 3 pp 1120ndash1128 2007

[49] S V VerduMO Garcıa F J G Franco et al ldquoCharacterizationand identification of electrical customers through the use ofself-organizing maps and daily load parametersrdquo in Proceedingsof the IEEE PES Power System Conference and Exposition vol 2pp 899ndash906 Atlanta Ga USA 2004

[50] K L Lo and Z Zakaria ldquoElectricity consumer classificationusing artificial intelligencerdquo in Proceedings of the 39th Interna-tional Universities Power Engineering Conference Bristol UK2004

[51] D Gerbec S Gasperic I Smon and F Gubina ldquoDeter-mining the load profiles of consumers based on fuzzy logicand probability neural networksrdquo IEE Proceedings GenerationTransmission andDistribution vol 151 no 3 pp 395ndash400 2004

[52] D Gerbec S Gasperic I Smon and F Gubina ldquoAllocationof the load profiles to consumers using probabilistic neuralnetworksrdquo IEEE Transactions on Power Systems vol 20 no 2pp 548ndash555 2005

[53] M Sarlak T Ebrahimi and S S KarimiMadahi ldquoEnhancementthe accuracy of daily and hourly short time load forecastingusing neural networkrdquo Journal of Basic and Applied ScientificResearch vol 2 no 1 pp 247ndash255 2012

[54] H K Alfares and M Nazeeruddin ldquoElectric load forecastingLiterature survey and classification of methodsrdquo InternationalJournal of Systems Science vol 33 no 1 pp 23ndash34 2002

[55] L A Garcia-Escudero and A Gordaliza ldquoA proposal for robustcurve clusteringrdquo Journal of Classification vol 22 no 2 pp 185ndash201 2005

[56] Z Zisman and G Cartina ldquoApplication of fuzzy logic fordistribution system estimationrdquo in Proceedings of the 22ndSeminar on Fundamentals of Electrotechnics and Circuit TheoryUstron Poland May 1999

[57] L Jentgen H Kidder R Hill and S Conrad Water Con-sumption Forecasting to Improve Energy Efficiency of PumpingOperations Awwa Research Foundation 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Shock and Vibration

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Civil EngineeringAdvances in

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Electrical and Computer Engineering

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SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 Advances in Electrical Engineering

transform the electrical energy consumed by the mediummember of cluster 119894 in average power demanded by it

The representative load profiles can characterize verywell the operation mode of the water hydrophore stations(identified by the clusters obtained) related to the electricalenergy consumption

(5) Assignation Finally to each water hydrophore station ismade the assignation of a representative load profile

4 The Assessment of Electrical Load in WaterDistribution Systems

Theassessment of electrical load inwater distribution systemscan be made using an improved simulation method based onthe representative load profiles of hydrophore stations Themethod is based on the following hypotheses [30 31 56]

(i) The mean loads corresponding to a cluster ofhydrophore stations from the water distribution sys-tem in any hour during the analyzed period areapproximately proportional to the electrical energyconsumption of those stations

(ii) The loads for any hour during the analyzed periodhave a statistical distribution that can be regarded asnormal

Using these hypotheses the load estimation of a waterdistribution system at any hour ℎ = 1 24 is given by thefollowing formula

119875119878

ℎ=

119870

sum

119894=1

119873119894

HS sdot 119882119894

med sdot 119898119894

ℎ+ radic

119870

sum

119894=1

119873119894

HS sdot (119882119894

med sdot 120590119894

ℎ)2 [kW]

ℎ = 1 119879

(6)

where 119875119878ℎis the load of the water distribution system at

the hour h 119870 is the number of clusters corresponding tothe hydrophore stations from water distribution system119873119894HSis the number of the hydrophore stations from cluster i119882119894

med is the average energy consumption of the hydrophorestations from cluster i 119898119894

ℎis the average load factor of the

hydrophore stations from cluster i at the hour h 120590119894ℎis the

standard deviation for load factor from hydrophore stationscorresponding to cluster i

The standard deviations for each cluster are calculatedwith relation

120590119894

ℎ=radicsum119873119894

HS119895(119901119894

119895ℎminus 119898119894

ℎ)2

119873119894

HS ℎ = 1 119879 119894 = 1 119870

(7)

5 Algorithm for Assessment of Electrical Loadin Water Distribution Systems

The algorithm adopts a procedure composed of two calcula-tion stages

Input data

End

Electrical energy consumption assessment- Determination of number of stations in each cluster - Calculation of average electrical energy

consumption of water hydrophore stations in

- Calculation of the average load factor ofstations in each cluster

- Assessment of the electrical load from thewater distribution system

- Data cleaning and preprocessing

- Calculation of the normalised load profiles

- Assignation of the representative load profile to each hydrophore station in function by its type

Start

Clustering rarr representative load profiles

- Clustering process rarr representative load profiles

each cluster

Figure 1 Flow chart of the proposed method

(i) the use of a clustering technique (K-meansmethod) inthe first stage to determine the patterns of electricalload and determine a subset of representative loadprofiles to be processed by the second stage at eachiteration the clustering outcomes simplify the processof selecting a relatively small number of load profilescorresponding to hydrophore stations

(ii) the use of load simulation in the second stage thisapproach is based on a statistical method that consid-ers the loads for any hour during the analyzed periodhave a statistical distribution that can be regarded asnormalThe flow chart of the proposed method is shown inFigure 1

For a water distribution system the input informationrefers to the technical characteristics (rated power of the forcepumps rated water flow) and the hourly load patterns ofhydrophore stations

Advances in Electrical Engineering 5

0005

01015

02025

03035

04045

05

C2 C3 C4 C5 C6 C7 C8 C9

Silh

ouet

te g

loba

l coe

ffici

ent

Clusters

Figure 2The silhouette global coefficient for different values of thenumber of clusters

0 02 04 06 08 1

1

2

3

Silhouette value

Clus

ter

Figure 3 The silhouette plot for 119870opt = 3

51 Determination of Representative Load Profiles The loadprofile of each hydrophore station is normalized relatively tothe daily electrical energy consumption The normalizationis made in relation to daily electrical energy consumptionbecause it is always known This consumption is recordedwith meters placed in each hydrophore station The optimalnumber of clusters is obtained using the K-means cluster-ing algorithm presented in Section 2 Finally the silhouetteglobal coefficient is calculated to assess the partition qualityAfter aggregation of the normalized load profiles of eachcluster the representative profiles are determined and a RLPis assigned to each hydrophore station

52 The Assessment of Electrical Loads In the second stepof the study using information from clustering process(hourly average load factors average energy consumptionand standard deviation of load factors for each hydrophorestation from cluster 119894 119894 = 1 119870) and relation (6) thehourly loads of the analyzed water distribution system willbe obtained

The accuracy of the estimates is expressed depending onthe data available Thus if the actual value of the estimatedquantity is available (such as during method developmentand testing) the following quantity can be useful to verify themethod

MAPE =sum119879

ℎ=1(10038161003816100381610038161003816119875119878

ℎ real minus 119875119878

ℎ est10038161003816100381610038161003816119875119878

ℎ real)

119879sdot 100 (8)

Table 2 The technical characteristics of hydrophore stations fromwater distribution system

Type Number ofstations

Rated power[kW]

Rated waterflow [m3h]

I 3 3 times 22 24II 6 4 times 22 32III 11 4 times 4 64IV 13 3 times 55 96V 33 4 times 55 128VI 7 4 times 75 128

where 119875ℎ real and 119875ℎ est represent the real and estimated values

for the load of water distribution system at the hour ℎThe mean absolute percentage error (MAPE) from (8)

is dimensionless and thus it can be used to compare theaccuracy of the model on different data sets

6 Case Study

In order to show the characteristics of the proposed methodfor assessment of electrical energy consumption a real waterdistribution system with 119873 = 73 hydrophore stations isconsidered For this system the input information refers tothe technical characteristics (Table 2) and the hourly loadpatterns of the hydrophore stations

Thus in all stations three or four similar force pumpshaving the rated power between 22 and 75 kW are installedThe required water flow is delivered at a constant pressureby changing the frequency of the source supplying theelectrical engines of the force pumps The load patterns arerepresented by load profiles of the water hydrophore stationsThemeasurements of individual load profileswere performedusing an electronic meter A sensor and an electronic devicefor pulse counting anddata storage compose thismeterTheseprofiles were processed for the day when it registered themaximum load in the water distribution system The timeinterval is defined by taking hourly steps within a day (119879 = 24and Δ119905

ℎ= 1 hour)

The normalization of the load profiles was made inrelation to daily electrical energy consumption Further theoptimal number of clusters was determined using the algo-rithm described in Section 2 Getting started the maximumof clusters 119870max was calculated (119870max = radic119873 asymp 9) Thenfor the set of normalized active power profiles the K-meansclustering method with a given 119870 (2 le 119870 le 119870max) isused Finally the silhouette global coefficient is calculatedfor the assessment of partition Because the silhouette globalcoefficient has the highest value for 119870 = 3 this representsthe optimal solution for clustering process Figure 2 For thissolution the silhouette plot is presented in Figure 3

The characteristics of clusters (119901119862119894ℎand 120590119862119894

ℎ ℎ = 1 24

119894 = 1 3) are presented in Table 3 After aggregationof normalized load profiles of each cluster Figure 4 therepresentative profiles were determined Representative loadprofile for each cluster is obtained by averaging the valuesfor each hour represented by load factors 119901119862119894

ℎ 119894 = 1 3

6 Advances in Electrical Engineering

0 5 10 15 20 250

001002003004005006007008009

01

Time (hours)

Load

fact

or (p

u)

(a)

0 5 10 15 20 250

001002003004005006007008009

01

Time (hours)

Load

fact

or (p

u)

(b)

0 5 10 15 20 250

001002003004005006007008009

Time (hours)

Load

fact

or (p

u)

(c)

Figure 4 Clustering results with 3 clusters ((a) cluster C1 (b) cluster C2 (c) cluster C3)

Table 3 Hourly coefficients of representative load profiles

Hour 1199011198621

[pu]1199011198622

[pu]1199011198623

[pu]1205901198621

[pu]1205901198622

[pu]1205901198623

[pu]1 0026 0022 0033 00028 00053 000412 0023 0020 0031 00036 00043 000393 0021 0019 0030 00032 00040 000404 0022 0019 0030 00033 00036 000365 0022 0020 0031 00029 00042 000426 0026 0025 0035 00025 00044 000397 0036 0040 0041 00047 00040 000288 0050 0054 0047 00089 00072 000489 0054 0048 0045 00045 00055 0004810 0055 0048 0046 00062 00058 0004511 0053 0046 0044 00100 00036 0003312 0048 0043 0043 00040 00040 0002713 0051 0041 0042 00056 00028 0003714 0054 0041 0041 00064 00034 0003015 0051 0040 0041 00059 00028 0003716 0047 0044 0043 00047 00028 0002617 0046 0048 0045 00039 00045 0003018 0047 0055 0047 00072 00041 0004919 0046 0060 0050 00061 00058 0005720 0050 0063 0051 00067 00066 0005921 0056 0070 0056 00072 00077 0008222 0047 0058 0048 00076 00073 0005823 0039 0048 0043 00039 00049 0003724 0032 0030 0037 00030 00043 00037

Advances in Electrical Engineering 7

Table 4 Results of clustering process

Cluster Number of stations [] Type of stations119882med [kWh]

I II III IV V VI1198621 24 3288 4 2 11 7 41421198622 8 1233 3 5 1 28581198623 41 5479 1 6 11 22 3235Total 73 100 3 6 11 13 33 7 3411

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 5 Representative load profile for cluster C1

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 6 Representative load profile for cluster C2

Graphical representation of the representative load profilescorresponding to the three clusters obtained (C1 C2 and C3)is given in Figures 5 6 and 7

One hourly value from the representative load profilesdenotes the load of a water hydrophore station in per unit ofthe total average daily load of this station The hourly loadpattern can be employed to approximate the load pattern ofany water hydrophore station within the same cluster

The results of calculations carried out during the firststage of the clustering procedure are presented in Table 4

From Table 4 it can be seen that the most consistentclusters are C1 and C3 which together accounted for about85of the total load profiles of thewater hydrophore stationsIn terms of technical characteristics the water hydrophorestations from cluster C2 belong to types I and II (installedrated power is less than 88 kW) the stations from clustersC1 and C3 belong to types IIIndashVI (installed rated power is

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 7 Representative load profile for cluster C3

Table 5 Real and estimated hourly load of water distributionsystem

Hour 119875119878

real [kW] 119875119878

est [kW] Err []1 7105 7295 2682 6449 6695 3813 6350 6534 2904 6323 6519 3105 6514 6727 3266 7585 7861 3647 10744 10516 2128 12737 13096 2829 11880 12211 27910 11989 12357 30711 11529 11909 32912 10936 11326 35713 10622 10995 35114 10796 11044 23015 11015 10864 13716 10978 11311 30417 11428 11976 47918 12528 13013 38719 13702 14012 22620 13993 14500 36221 16531 16036 30022 13187 13624 33123 11154 11569 37224 8550 8794 285

between 16 and 30 kW) But in cluster C3 approximately 50percent of the total stations have an installed rated power by

8 Advances in Electrical Engineering

020406080

100120140160180

1 3 5 7 9 11 13 15 17 19 21 23

P (k

W)

Real powerEstimated power

Time (hours)

Figure 8 Real and estimated load profiles of the analyzed waterdistribution system

0

1

2

3

4

5

6

1 3 5 7 9 11 13 15 17 19 21 23

Estim

ated

erro

rs (

)

Time (hours)

Figure 9 Estimation errors obtained for hourly load of analyzedwater distribution system

22 kW In terms of the electrical energy consumption it canbe observed that the highest medium value is registered forcluster C1 and the lowest value is registered for cluster C2

In the second step of the study using information fromTables 3 and 4 and relation (6) the hourly loads of theanalyzed water distribution system were obtained Thus inTable 5 Figures 8 and 9 the real loads estimated loads andestimated errors are presented The estimation maximumerror is 479 and minimum error is 137 Global resultsshow that the value for MAPE is 311

Thismay be considered a very good result especially if wetake into account the arbitrariness inherent to loads behaviorand not all hydrophore stations have monitoring system

7 Conclusions

The investigation of combined actions which account forconnected water and electrical aspects allows improvingthe global efficiency of the water distribution systems andsupplying the consumers using the least possible amount ofwater and energy

In water distribution companies the system operatorpredicts the consumption for today and tomorrow based on

recent consumption trends weather forecasting day of theweek knowledge of future events and historical knowledgeof utility system performance This approach conducts at alarge percentage error (more than 5) for assessment of load

The proposed method is based on two stages in whichthe K-means clustering method and a load simulation tech-nique are exploited for estimation of the electrical energyconsumption The method based on the K-means clusteringalgorithm was used for determination of the representativeload profiles of the hydrophore stations A comparison ofobtained results using the proposed method with the realregistered data indicates an error by 311 which is very closeto the expected one by water companies (25ndash3) [57]

Results obtained demonstrate the ability of the proposedmethod to become the first step in an efficient managementof the water distribution systems On the one hand therepresentative load profiles can be used tomodel overall watercompany demands in a way that show how changes in use byone category affect the hourly load profiles for the system as awhole and on the other hand these profiles can contribute toa better understanding of the opportunities for linking water-efficiency and energy-efficiency programs

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] Alliance to Save Energy ldquoWhat watergy involvesrdquo 2014 httpwwwwatergynet

[2] P Boulos Z Wu C Orr M Moore P Hsiung and DThomasOptimal PumpOperation ofWaterDistribution SystemsUsing Genetic Algorithms H

2ONET-Users Guide MW Software

Consulting Dallas County Tex USA 2000[3] European Commission Directorate General for Environment

2013 httpeceuropaeuenvironmentwaterindex enhtm[4] A Anton and S Perju ldquoMonitoring the main parameters of a

water supply pumping station over ten yearsrdquo in Proceedings ofthe 6th International Conference on Hydraulic Machinery andHydrodynamics Timisoara Romania 2004

[5] S J Kenway A Priestley S Cook et al ldquoEnergy use in theprovision and consumption of urban water in Australia andNew Zealandrdquo Water for a Healthy Country National ResearchFlagship Report CSIRO 2008

[6] LHouseWater Supply Related ElectricityDemand inCaliforniaReport for California Energy Commission 2006

[7] R Goldstein and W Smith ldquoWater and sustainability USelectricity consumption for water supply amp treatmentmdashthe nexthalf centuryrdquo EPRI Report Electric Power Research InstitutePalo Alto Calif USA 2000

[8] I Pulido-Calvo and J C Gutierrez-Estrada ldquoSelection andoperation of pumping stations of water distribution systemsrdquoEnvironmental Research Journal vol 5 no 3 pp 1ndash20 2011

[9] K Feldman ldquoAspects of energy efficiency in water distributionsystemsrdquo inProceedings of the International Conference onWaterLoss pp 26ndash30 IWA Cape Town South Africa April 2009

Advances in Electrical Engineering 9

[10] G C Ionescu and D S Ionescu ldquoThe optimization of energyconsumption in water supply systemsrdquo Acta Electrotehnica vol46 pp 191ndash194 2005

[11] M Istrate and G Grigoras ldquoEnergy consumption estimationin water distribution systems using fuzzy techniquesrdquo Environ-mental Engineering and Management Journal vol 9 no 2 pp249ndash256 2010

[12] I Sarbu Energetic Optimization of the Water Distribution Sys-tems Publishing House of the Romanian Academy BucharestRomania 1997

[13] L Szychta ldquoEnergy consumption of water pumping for selectedcontrol systemsrdquo Electrical Power Quality and Utilization Jour-nal vol 12 pp 21ndash27 2006

[14] G Grigoras and M Istrate ldquoAn efficient clustering methodin evaluation of the electric energy consumption from waterhydrophore stationsrdquo International Review on Modelling andSimulations vol 4 no 2 pp 813ndash818 2011

[15] U Zessler and U Shamir ldquoOptimal operation of water dis-tribution systemsrdquo Journal of Water Resources Planning andManagement vol 115 no 6 pp 735ndash752 1989

[16] P Cutore A Campisano Z Kapelan C Modica and D SavicldquoProbabilistic prediction of urban water consumption using theSCEM-UA algorithmrdquo Urban Water Journal vol 5 no 2 pp125ndash132 2008

[17] G Chicco ldquoOverview and performance assessment of theclusteringmethods for electrical load pattern groupingrdquoEnergyvol 42 no 1 pp 68ndash80 2012

[18] A K Jain M N Murty and P J Flynn ldquoData clusteringa reviewrdquo httpdataclusteringcsemsuedupapersMSU-CSE-00-16pdf

[19] R Siddheswar and R Turi ldquoDetermination of number ofclusters in K-Means clustering and application in color imagesegmentationrdquo in Proceedings of the 4th International Confer-ence on Advanced in Pattern Recognition and Digital TechniquesCalcutta India 1999

[20] I Yatskiv and L Gusarova ldquoThe methods of cluster analysisresults validationrdquo in Proceedings of International ConferenceRelStat04 Riga Latvia 2004

[21] J Yu and Q Cheng ldquoThe upper bound of the optimal numberof clusters in fuzzy clusteringrdquo Science in China Series F vol 44pp 119ndash124 2001

[22] ldquoA tutorial on clustering algorithmsrdquo httphomedeipolimiitmatteuccClusteringtutorial html

[23] P J Rousseeuw ldquoSilhouettes a graphical aid to the interpreta-tion and validation of cluster analysisrdquo Journal of Computationaland Applied Mathematics vol 20 pp 53ndash65 1987

[24] M Halkidi Y Batistakis and M Vazirgiannis ldquoOn clusteringvalidation techniquesrdquo Journal of Intelligent Information Sys-tems vol 17 no 2-3 pp 107ndash145 2001

[25] M R Rezaee B P F Lelieveldt and J H C Reiber ldquoA newcluster validity index for the fuzzy C-meanrdquo Pattern RecognitionLetters vol 19 no 3-4 pp 237ndash246 1998

[26] P Berkhin ldquoSurvey of clustering data mining techniquesrdquo TechRep Accrue Software San Jose Calif USA 2002

[27] MHolgersson ldquoThe limited value of cophenetic correlation as aclustering criterionrdquo Pattern Recognition vol 10 no 4 pp 287ndash295 1978

[28] A D Gordon Classification Chapman amp Hall New York NYUSA 2nd edition 1999

[29] C G Carter-Brown ldquoLoad profile modeling for integratedenergy planningrdquo inProceedings of theDomestic Use of Electrical

Energy Conference pp 13ndash18 Cape Town South Africa April1999

[30] British Electricity Boards ldquoReport on the design of low voltageunderground networks for new housingrdquo ACE Report No 1051986

[31] British Electricity Boards ldquoReport on the computer programDEBUTE for the design of LV radial networks Part 1mdashgeneralconsiderations part 2mdashprogram user guiderdquo Tech Rep 1151988

[32] A Seppala Load research and load estimation in electricitydistribution [PhD thesis] Helsinki University of TechnologyEsbo Finland 1996

[33] J Nazarko and Z A Styczynski ldquoApplication of statisticaland neural approaches to the daily load profiles modelling inpower distribution systemsrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference pp 320ndash325 NewOrleans La USA May 1999

[34] Z Zakaria M N Othman and M H Sohod ldquoConsumerload profiling using fuzzy clustering and statistical approachrdquoin Proceedings of the 4th Student Conference on Researchand Development (SCOReD rsquo06) 274 p 270 IEEE SelangorMalaysia June 2006

[35] I H Yu J K Lee J M Ko and S I Kim ldquoA method forclassification of electricity demands using load profile datardquo inProceedings of the 4th Annual ACIS International Conference onComputer and Information Science (ICIS rsquo05) pp 164ndash168 JejuIsland South Korea July 2006

[36] G Chicco R Napoli and F Piglione ldquoComparisons amongclustering techniques for electricity customer classificationrdquoIEEE Transactions on Power Systems vol 21 no 2 pp 933ndash9402006

[37] G Chicco R Napoli and F Piglione ldquoApplication of clusteringalgorithms and self organising maps to classify electricitycustomersrdquo in Proceedings of the IEEE Bologna PowerTechConference vol 1 Bologna Italy June 2003

[38] D Gerbek S Gasperic and F Gubina ldquoComparison of differentclassification methods for the consumersrsquo load profile determi-nationrdquo in Proceedings of the 17th International Conference onElectricity Distribution Barcelona Spain 2003

[39] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI rsquo13) pp 1ndash6 Pitesti Romania June 2013

[40] N Mahmoudi-Kohan M P Moghaddam and S M BidakildquoEvaluating performance ofWFAK-means andmodified followthe leader methods for clustering load curvesrdquo in Proceedings ofthe IEEEPES Power Systems Conference and Exposition (PSCErsquo09) Seatle Wash USA March 2009

[41] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI 13) pp 1ndash6 Pitesti Romania June 2013

[42] A Mutanen M Ruska S Repo and P Jarventausta ldquoCustomerclassification and load profiling method for distribution sys-temsrdquo IEEE Transactions on Power Delivery vol 26 no 3 pp1755ndash1763 2011

[43] G Grigoras C Barbulescu G Cartina and D ComanesculdquoA comparative study regarding efficiency of the hierarchicalclustering techniques in typical load profiles determinationrdquoActa Electrotehnica vol 52 no 5 pp 184ndash188 2011

10 Advances in Electrical Engineering

[44] B D Pitt and D S Kirschen ldquoApplication of data miningtechniques to load profilingrdquo in Proceedings of the 21st IEEEInternational Conference Power Industry Computer ApplicationsSanta Clara Calif USA 1999

[45] S Ramos and Z Vale ldquoData mining techniques applicationin power distribution utilitiesrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Exposition pp 1ndash8 Chicago Ill USA April 2008

[46] V Figueiredo F Rodrigues Z Vale and J B Gouveia ldquoAnelectric energy consumer characterization framework based ondata mining techniquesrdquo IEEE Transactions on Power Systemsvol 20 no 2 pp 596ndash602 2005

[47] A H Nizar Z Y Dong and J H Zhao ldquoLoad profilingand data mining techniques in electricity deregulated marketrdquoin Proceedings of the IEEE Power Engineering Society GeneralMeeting (PES 06) Montreal Canada June 2006

[48] G J Tsekouras N D Hatziargyriou and E N Dialynas ldquoTwo-stage pattern recognition of load curves for classification ofelectricity customersrdquo IEEE Transactions on Power Systems vol22 no 3 pp 1120ndash1128 2007

[49] S V VerduMO Garcıa F J G Franco et al ldquoCharacterizationand identification of electrical customers through the use ofself-organizing maps and daily load parametersrdquo in Proceedingsof the IEEE PES Power System Conference and Exposition vol 2pp 899ndash906 Atlanta Ga USA 2004

[50] K L Lo and Z Zakaria ldquoElectricity consumer classificationusing artificial intelligencerdquo in Proceedings of the 39th Interna-tional Universities Power Engineering Conference Bristol UK2004

[51] D Gerbec S Gasperic I Smon and F Gubina ldquoDeter-mining the load profiles of consumers based on fuzzy logicand probability neural networksrdquo IEE Proceedings GenerationTransmission andDistribution vol 151 no 3 pp 395ndash400 2004

[52] D Gerbec S Gasperic I Smon and F Gubina ldquoAllocationof the load profiles to consumers using probabilistic neuralnetworksrdquo IEEE Transactions on Power Systems vol 20 no 2pp 548ndash555 2005

[53] M Sarlak T Ebrahimi and S S KarimiMadahi ldquoEnhancementthe accuracy of daily and hourly short time load forecastingusing neural networkrdquo Journal of Basic and Applied ScientificResearch vol 2 no 1 pp 247ndash255 2012

[54] H K Alfares and M Nazeeruddin ldquoElectric load forecastingLiterature survey and classification of methodsrdquo InternationalJournal of Systems Science vol 33 no 1 pp 23ndash34 2002

[55] L A Garcia-Escudero and A Gordaliza ldquoA proposal for robustcurve clusteringrdquo Journal of Classification vol 22 no 2 pp 185ndash201 2005

[56] Z Zisman and G Cartina ldquoApplication of fuzzy logic fordistribution system estimationrdquo in Proceedings of the 22ndSeminar on Fundamentals of Electrotechnics and Circuit TheoryUstron Poland May 1999

[57] L Jentgen H Kidder R Hill and S Conrad Water Con-sumption Forecasting to Improve Energy Efficiency of PumpingOperations Awwa Research Foundation 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Advances in Electrical Engineering 5

0005

01015

02025

03035

04045

05

C2 C3 C4 C5 C6 C7 C8 C9

Silh

ouet

te g

loba

l coe

ffici

ent

Clusters

Figure 2The silhouette global coefficient for different values of thenumber of clusters

0 02 04 06 08 1

1

2

3

Silhouette value

Clus

ter

Figure 3 The silhouette plot for 119870opt = 3

51 Determination of Representative Load Profiles The loadprofile of each hydrophore station is normalized relatively tothe daily electrical energy consumption The normalizationis made in relation to daily electrical energy consumptionbecause it is always known This consumption is recordedwith meters placed in each hydrophore station The optimalnumber of clusters is obtained using the K-means cluster-ing algorithm presented in Section 2 Finally the silhouetteglobal coefficient is calculated to assess the partition qualityAfter aggregation of the normalized load profiles of eachcluster the representative profiles are determined and a RLPis assigned to each hydrophore station

52 The Assessment of Electrical Loads In the second stepof the study using information from clustering process(hourly average load factors average energy consumptionand standard deviation of load factors for each hydrophorestation from cluster 119894 119894 = 1 119870) and relation (6) thehourly loads of the analyzed water distribution system willbe obtained

The accuracy of the estimates is expressed depending onthe data available Thus if the actual value of the estimatedquantity is available (such as during method developmentand testing) the following quantity can be useful to verify themethod

MAPE =sum119879

ℎ=1(10038161003816100381610038161003816119875119878

ℎ real minus 119875119878

ℎ est10038161003816100381610038161003816119875119878

ℎ real)

119879sdot 100 (8)

Table 2 The technical characteristics of hydrophore stations fromwater distribution system

Type Number ofstations

Rated power[kW]

Rated waterflow [m3h]

I 3 3 times 22 24II 6 4 times 22 32III 11 4 times 4 64IV 13 3 times 55 96V 33 4 times 55 128VI 7 4 times 75 128

where 119875ℎ real and 119875ℎ est represent the real and estimated values

for the load of water distribution system at the hour ℎThe mean absolute percentage error (MAPE) from (8)

is dimensionless and thus it can be used to compare theaccuracy of the model on different data sets

6 Case Study

In order to show the characteristics of the proposed methodfor assessment of electrical energy consumption a real waterdistribution system with 119873 = 73 hydrophore stations isconsidered For this system the input information refers tothe technical characteristics (Table 2) and the hourly loadpatterns of the hydrophore stations

Thus in all stations three or four similar force pumpshaving the rated power between 22 and 75 kW are installedThe required water flow is delivered at a constant pressureby changing the frequency of the source supplying theelectrical engines of the force pumps The load patterns arerepresented by load profiles of the water hydrophore stationsThemeasurements of individual load profileswere performedusing an electronic meter A sensor and an electronic devicefor pulse counting anddata storage compose thismeterTheseprofiles were processed for the day when it registered themaximum load in the water distribution system The timeinterval is defined by taking hourly steps within a day (119879 = 24and Δ119905

ℎ= 1 hour)

The normalization of the load profiles was made inrelation to daily electrical energy consumption Further theoptimal number of clusters was determined using the algo-rithm described in Section 2 Getting started the maximumof clusters 119870max was calculated (119870max = radic119873 asymp 9) Thenfor the set of normalized active power profiles the K-meansclustering method with a given 119870 (2 le 119870 le 119870max) isused Finally the silhouette global coefficient is calculatedfor the assessment of partition Because the silhouette globalcoefficient has the highest value for 119870 = 3 this representsthe optimal solution for clustering process Figure 2 For thissolution the silhouette plot is presented in Figure 3

The characteristics of clusters (119901119862119894ℎand 120590119862119894

ℎ ℎ = 1 24

119894 = 1 3) are presented in Table 3 After aggregationof normalized load profiles of each cluster Figure 4 therepresentative profiles were determined Representative loadprofile for each cluster is obtained by averaging the valuesfor each hour represented by load factors 119901119862119894

ℎ 119894 = 1 3

6 Advances in Electrical Engineering

0 5 10 15 20 250

001002003004005006007008009

01

Time (hours)

Load

fact

or (p

u)

(a)

0 5 10 15 20 250

001002003004005006007008009

01

Time (hours)

Load

fact

or (p

u)

(b)

0 5 10 15 20 250

001002003004005006007008009

Time (hours)

Load

fact

or (p

u)

(c)

Figure 4 Clustering results with 3 clusters ((a) cluster C1 (b) cluster C2 (c) cluster C3)

Table 3 Hourly coefficients of representative load profiles

Hour 1199011198621

[pu]1199011198622

[pu]1199011198623

[pu]1205901198621

[pu]1205901198622

[pu]1205901198623

[pu]1 0026 0022 0033 00028 00053 000412 0023 0020 0031 00036 00043 000393 0021 0019 0030 00032 00040 000404 0022 0019 0030 00033 00036 000365 0022 0020 0031 00029 00042 000426 0026 0025 0035 00025 00044 000397 0036 0040 0041 00047 00040 000288 0050 0054 0047 00089 00072 000489 0054 0048 0045 00045 00055 0004810 0055 0048 0046 00062 00058 0004511 0053 0046 0044 00100 00036 0003312 0048 0043 0043 00040 00040 0002713 0051 0041 0042 00056 00028 0003714 0054 0041 0041 00064 00034 0003015 0051 0040 0041 00059 00028 0003716 0047 0044 0043 00047 00028 0002617 0046 0048 0045 00039 00045 0003018 0047 0055 0047 00072 00041 0004919 0046 0060 0050 00061 00058 0005720 0050 0063 0051 00067 00066 0005921 0056 0070 0056 00072 00077 0008222 0047 0058 0048 00076 00073 0005823 0039 0048 0043 00039 00049 0003724 0032 0030 0037 00030 00043 00037

Advances in Electrical Engineering 7

Table 4 Results of clustering process

Cluster Number of stations [] Type of stations119882med [kWh]

I II III IV V VI1198621 24 3288 4 2 11 7 41421198622 8 1233 3 5 1 28581198623 41 5479 1 6 11 22 3235Total 73 100 3 6 11 13 33 7 3411

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 5 Representative load profile for cluster C1

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 6 Representative load profile for cluster C2

Graphical representation of the representative load profilescorresponding to the three clusters obtained (C1 C2 and C3)is given in Figures 5 6 and 7

One hourly value from the representative load profilesdenotes the load of a water hydrophore station in per unit ofthe total average daily load of this station The hourly loadpattern can be employed to approximate the load pattern ofany water hydrophore station within the same cluster

The results of calculations carried out during the firststage of the clustering procedure are presented in Table 4

From Table 4 it can be seen that the most consistentclusters are C1 and C3 which together accounted for about85of the total load profiles of thewater hydrophore stationsIn terms of technical characteristics the water hydrophorestations from cluster C2 belong to types I and II (installedrated power is less than 88 kW) the stations from clustersC1 and C3 belong to types IIIndashVI (installed rated power is

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 7 Representative load profile for cluster C3

Table 5 Real and estimated hourly load of water distributionsystem

Hour 119875119878

real [kW] 119875119878

est [kW] Err []1 7105 7295 2682 6449 6695 3813 6350 6534 2904 6323 6519 3105 6514 6727 3266 7585 7861 3647 10744 10516 2128 12737 13096 2829 11880 12211 27910 11989 12357 30711 11529 11909 32912 10936 11326 35713 10622 10995 35114 10796 11044 23015 11015 10864 13716 10978 11311 30417 11428 11976 47918 12528 13013 38719 13702 14012 22620 13993 14500 36221 16531 16036 30022 13187 13624 33123 11154 11569 37224 8550 8794 285

between 16 and 30 kW) But in cluster C3 approximately 50percent of the total stations have an installed rated power by

8 Advances in Electrical Engineering

020406080

100120140160180

1 3 5 7 9 11 13 15 17 19 21 23

P (k

W)

Real powerEstimated power

Time (hours)

Figure 8 Real and estimated load profiles of the analyzed waterdistribution system

0

1

2

3

4

5

6

1 3 5 7 9 11 13 15 17 19 21 23

Estim

ated

erro

rs (

)

Time (hours)

Figure 9 Estimation errors obtained for hourly load of analyzedwater distribution system

22 kW In terms of the electrical energy consumption it canbe observed that the highest medium value is registered forcluster C1 and the lowest value is registered for cluster C2

In the second step of the study using information fromTables 3 and 4 and relation (6) the hourly loads of theanalyzed water distribution system were obtained Thus inTable 5 Figures 8 and 9 the real loads estimated loads andestimated errors are presented The estimation maximumerror is 479 and minimum error is 137 Global resultsshow that the value for MAPE is 311

Thismay be considered a very good result especially if wetake into account the arbitrariness inherent to loads behaviorand not all hydrophore stations have monitoring system

7 Conclusions

The investigation of combined actions which account forconnected water and electrical aspects allows improvingthe global efficiency of the water distribution systems andsupplying the consumers using the least possible amount ofwater and energy

In water distribution companies the system operatorpredicts the consumption for today and tomorrow based on

recent consumption trends weather forecasting day of theweek knowledge of future events and historical knowledgeof utility system performance This approach conducts at alarge percentage error (more than 5) for assessment of load

The proposed method is based on two stages in whichthe K-means clustering method and a load simulation tech-nique are exploited for estimation of the electrical energyconsumption The method based on the K-means clusteringalgorithm was used for determination of the representativeload profiles of the hydrophore stations A comparison ofobtained results using the proposed method with the realregistered data indicates an error by 311 which is very closeto the expected one by water companies (25ndash3) [57]

Results obtained demonstrate the ability of the proposedmethod to become the first step in an efficient managementof the water distribution systems On the one hand therepresentative load profiles can be used tomodel overall watercompany demands in a way that show how changes in use byone category affect the hourly load profiles for the system as awhole and on the other hand these profiles can contribute toa better understanding of the opportunities for linking water-efficiency and energy-efficiency programs

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] Alliance to Save Energy ldquoWhat watergy involvesrdquo 2014 httpwwwwatergynet

[2] P Boulos Z Wu C Orr M Moore P Hsiung and DThomasOptimal PumpOperation ofWaterDistribution SystemsUsing Genetic Algorithms H

2ONET-Users Guide MW Software

Consulting Dallas County Tex USA 2000[3] European Commission Directorate General for Environment

2013 httpeceuropaeuenvironmentwaterindex enhtm[4] A Anton and S Perju ldquoMonitoring the main parameters of a

water supply pumping station over ten yearsrdquo in Proceedings ofthe 6th International Conference on Hydraulic Machinery andHydrodynamics Timisoara Romania 2004

[5] S J Kenway A Priestley S Cook et al ldquoEnergy use in theprovision and consumption of urban water in Australia andNew Zealandrdquo Water for a Healthy Country National ResearchFlagship Report CSIRO 2008

[6] LHouseWater Supply Related ElectricityDemand inCaliforniaReport for California Energy Commission 2006

[7] R Goldstein and W Smith ldquoWater and sustainability USelectricity consumption for water supply amp treatmentmdashthe nexthalf centuryrdquo EPRI Report Electric Power Research InstitutePalo Alto Calif USA 2000

[8] I Pulido-Calvo and J C Gutierrez-Estrada ldquoSelection andoperation of pumping stations of water distribution systemsrdquoEnvironmental Research Journal vol 5 no 3 pp 1ndash20 2011

[9] K Feldman ldquoAspects of energy efficiency in water distributionsystemsrdquo inProceedings of the International Conference onWaterLoss pp 26ndash30 IWA Cape Town South Africa April 2009

Advances in Electrical Engineering 9

[10] G C Ionescu and D S Ionescu ldquoThe optimization of energyconsumption in water supply systemsrdquo Acta Electrotehnica vol46 pp 191ndash194 2005

[11] M Istrate and G Grigoras ldquoEnergy consumption estimationin water distribution systems using fuzzy techniquesrdquo Environ-mental Engineering and Management Journal vol 9 no 2 pp249ndash256 2010

[12] I Sarbu Energetic Optimization of the Water Distribution Sys-tems Publishing House of the Romanian Academy BucharestRomania 1997

[13] L Szychta ldquoEnergy consumption of water pumping for selectedcontrol systemsrdquo Electrical Power Quality and Utilization Jour-nal vol 12 pp 21ndash27 2006

[14] G Grigoras and M Istrate ldquoAn efficient clustering methodin evaluation of the electric energy consumption from waterhydrophore stationsrdquo International Review on Modelling andSimulations vol 4 no 2 pp 813ndash818 2011

[15] U Zessler and U Shamir ldquoOptimal operation of water dis-tribution systemsrdquo Journal of Water Resources Planning andManagement vol 115 no 6 pp 735ndash752 1989

[16] P Cutore A Campisano Z Kapelan C Modica and D SavicldquoProbabilistic prediction of urban water consumption using theSCEM-UA algorithmrdquo Urban Water Journal vol 5 no 2 pp125ndash132 2008

[17] G Chicco ldquoOverview and performance assessment of theclusteringmethods for electrical load pattern groupingrdquoEnergyvol 42 no 1 pp 68ndash80 2012

[18] A K Jain M N Murty and P J Flynn ldquoData clusteringa reviewrdquo httpdataclusteringcsemsuedupapersMSU-CSE-00-16pdf

[19] R Siddheswar and R Turi ldquoDetermination of number ofclusters in K-Means clustering and application in color imagesegmentationrdquo in Proceedings of the 4th International Confer-ence on Advanced in Pattern Recognition and Digital TechniquesCalcutta India 1999

[20] I Yatskiv and L Gusarova ldquoThe methods of cluster analysisresults validationrdquo in Proceedings of International ConferenceRelStat04 Riga Latvia 2004

[21] J Yu and Q Cheng ldquoThe upper bound of the optimal numberof clusters in fuzzy clusteringrdquo Science in China Series F vol 44pp 119ndash124 2001

[22] ldquoA tutorial on clustering algorithmsrdquo httphomedeipolimiitmatteuccClusteringtutorial html

[23] P J Rousseeuw ldquoSilhouettes a graphical aid to the interpreta-tion and validation of cluster analysisrdquo Journal of Computationaland Applied Mathematics vol 20 pp 53ndash65 1987

[24] M Halkidi Y Batistakis and M Vazirgiannis ldquoOn clusteringvalidation techniquesrdquo Journal of Intelligent Information Sys-tems vol 17 no 2-3 pp 107ndash145 2001

[25] M R Rezaee B P F Lelieveldt and J H C Reiber ldquoA newcluster validity index for the fuzzy C-meanrdquo Pattern RecognitionLetters vol 19 no 3-4 pp 237ndash246 1998

[26] P Berkhin ldquoSurvey of clustering data mining techniquesrdquo TechRep Accrue Software San Jose Calif USA 2002

[27] MHolgersson ldquoThe limited value of cophenetic correlation as aclustering criterionrdquo Pattern Recognition vol 10 no 4 pp 287ndash295 1978

[28] A D Gordon Classification Chapman amp Hall New York NYUSA 2nd edition 1999

[29] C G Carter-Brown ldquoLoad profile modeling for integratedenergy planningrdquo inProceedings of theDomestic Use of Electrical

Energy Conference pp 13ndash18 Cape Town South Africa April1999

[30] British Electricity Boards ldquoReport on the design of low voltageunderground networks for new housingrdquo ACE Report No 1051986

[31] British Electricity Boards ldquoReport on the computer programDEBUTE for the design of LV radial networks Part 1mdashgeneralconsiderations part 2mdashprogram user guiderdquo Tech Rep 1151988

[32] A Seppala Load research and load estimation in electricitydistribution [PhD thesis] Helsinki University of TechnologyEsbo Finland 1996

[33] J Nazarko and Z A Styczynski ldquoApplication of statisticaland neural approaches to the daily load profiles modelling inpower distribution systemsrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference pp 320ndash325 NewOrleans La USA May 1999

[34] Z Zakaria M N Othman and M H Sohod ldquoConsumerload profiling using fuzzy clustering and statistical approachrdquoin Proceedings of the 4th Student Conference on Researchand Development (SCOReD rsquo06) 274 p 270 IEEE SelangorMalaysia June 2006

[35] I H Yu J K Lee J M Ko and S I Kim ldquoA method forclassification of electricity demands using load profile datardquo inProceedings of the 4th Annual ACIS International Conference onComputer and Information Science (ICIS rsquo05) pp 164ndash168 JejuIsland South Korea July 2006

[36] G Chicco R Napoli and F Piglione ldquoComparisons amongclustering techniques for electricity customer classificationrdquoIEEE Transactions on Power Systems vol 21 no 2 pp 933ndash9402006

[37] G Chicco R Napoli and F Piglione ldquoApplication of clusteringalgorithms and self organising maps to classify electricitycustomersrdquo in Proceedings of the IEEE Bologna PowerTechConference vol 1 Bologna Italy June 2003

[38] D Gerbek S Gasperic and F Gubina ldquoComparison of differentclassification methods for the consumersrsquo load profile determi-nationrdquo in Proceedings of the 17th International Conference onElectricity Distribution Barcelona Spain 2003

[39] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI rsquo13) pp 1ndash6 Pitesti Romania June 2013

[40] N Mahmoudi-Kohan M P Moghaddam and S M BidakildquoEvaluating performance ofWFAK-means andmodified followthe leader methods for clustering load curvesrdquo in Proceedings ofthe IEEEPES Power Systems Conference and Exposition (PSCErsquo09) Seatle Wash USA March 2009

[41] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI 13) pp 1ndash6 Pitesti Romania June 2013

[42] A Mutanen M Ruska S Repo and P Jarventausta ldquoCustomerclassification and load profiling method for distribution sys-temsrdquo IEEE Transactions on Power Delivery vol 26 no 3 pp1755ndash1763 2011

[43] G Grigoras C Barbulescu G Cartina and D ComanesculdquoA comparative study regarding efficiency of the hierarchicalclustering techniques in typical load profiles determinationrdquoActa Electrotehnica vol 52 no 5 pp 184ndash188 2011

10 Advances in Electrical Engineering

[44] B D Pitt and D S Kirschen ldquoApplication of data miningtechniques to load profilingrdquo in Proceedings of the 21st IEEEInternational Conference Power Industry Computer ApplicationsSanta Clara Calif USA 1999

[45] S Ramos and Z Vale ldquoData mining techniques applicationin power distribution utilitiesrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Exposition pp 1ndash8 Chicago Ill USA April 2008

[46] V Figueiredo F Rodrigues Z Vale and J B Gouveia ldquoAnelectric energy consumer characterization framework based ondata mining techniquesrdquo IEEE Transactions on Power Systemsvol 20 no 2 pp 596ndash602 2005

[47] A H Nizar Z Y Dong and J H Zhao ldquoLoad profilingand data mining techniques in electricity deregulated marketrdquoin Proceedings of the IEEE Power Engineering Society GeneralMeeting (PES 06) Montreal Canada June 2006

[48] G J Tsekouras N D Hatziargyriou and E N Dialynas ldquoTwo-stage pattern recognition of load curves for classification ofelectricity customersrdquo IEEE Transactions on Power Systems vol22 no 3 pp 1120ndash1128 2007

[49] S V VerduMO Garcıa F J G Franco et al ldquoCharacterizationand identification of electrical customers through the use ofself-organizing maps and daily load parametersrdquo in Proceedingsof the IEEE PES Power System Conference and Exposition vol 2pp 899ndash906 Atlanta Ga USA 2004

[50] K L Lo and Z Zakaria ldquoElectricity consumer classificationusing artificial intelligencerdquo in Proceedings of the 39th Interna-tional Universities Power Engineering Conference Bristol UK2004

[51] D Gerbec S Gasperic I Smon and F Gubina ldquoDeter-mining the load profiles of consumers based on fuzzy logicand probability neural networksrdquo IEE Proceedings GenerationTransmission andDistribution vol 151 no 3 pp 395ndash400 2004

[52] D Gerbec S Gasperic I Smon and F Gubina ldquoAllocationof the load profiles to consumers using probabilistic neuralnetworksrdquo IEEE Transactions on Power Systems vol 20 no 2pp 548ndash555 2005

[53] M Sarlak T Ebrahimi and S S KarimiMadahi ldquoEnhancementthe accuracy of daily and hourly short time load forecastingusing neural networkrdquo Journal of Basic and Applied ScientificResearch vol 2 no 1 pp 247ndash255 2012

[54] H K Alfares and M Nazeeruddin ldquoElectric load forecastingLiterature survey and classification of methodsrdquo InternationalJournal of Systems Science vol 33 no 1 pp 23ndash34 2002

[55] L A Garcia-Escudero and A Gordaliza ldquoA proposal for robustcurve clusteringrdquo Journal of Classification vol 22 no 2 pp 185ndash201 2005

[56] Z Zisman and G Cartina ldquoApplication of fuzzy logic fordistribution system estimationrdquo in Proceedings of the 22ndSeminar on Fundamentals of Electrotechnics and Circuit TheoryUstron Poland May 1999

[57] L Jentgen H Kidder R Hill and S Conrad Water Con-sumption Forecasting to Improve Energy Efficiency of PumpingOperations Awwa Research Foundation 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Advances in Electrical Engineering

0 5 10 15 20 250

001002003004005006007008009

01

Time (hours)

Load

fact

or (p

u)

(a)

0 5 10 15 20 250

001002003004005006007008009

01

Time (hours)

Load

fact

or (p

u)

(b)

0 5 10 15 20 250

001002003004005006007008009

Time (hours)

Load

fact

or (p

u)

(c)

Figure 4 Clustering results with 3 clusters ((a) cluster C1 (b) cluster C2 (c) cluster C3)

Table 3 Hourly coefficients of representative load profiles

Hour 1199011198621

[pu]1199011198622

[pu]1199011198623

[pu]1205901198621

[pu]1205901198622

[pu]1205901198623

[pu]1 0026 0022 0033 00028 00053 000412 0023 0020 0031 00036 00043 000393 0021 0019 0030 00032 00040 000404 0022 0019 0030 00033 00036 000365 0022 0020 0031 00029 00042 000426 0026 0025 0035 00025 00044 000397 0036 0040 0041 00047 00040 000288 0050 0054 0047 00089 00072 000489 0054 0048 0045 00045 00055 0004810 0055 0048 0046 00062 00058 0004511 0053 0046 0044 00100 00036 0003312 0048 0043 0043 00040 00040 0002713 0051 0041 0042 00056 00028 0003714 0054 0041 0041 00064 00034 0003015 0051 0040 0041 00059 00028 0003716 0047 0044 0043 00047 00028 0002617 0046 0048 0045 00039 00045 0003018 0047 0055 0047 00072 00041 0004919 0046 0060 0050 00061 00058 0005720 0050 0063 0051 00067 00066 0005921 0056 0070 0056 00072 00077 0008222 0047 0058 0048 00076 00073 0005823 0039 0048 0043 00039 00049 0003724 0032 0030 0037 00030 00043 00037

Advances in Electrical Engineering 7

Table 4 Results of clustering process

Cluster Number of stations [] Type of stations119882med [kWh]

I II III IV V VI1198621 24 3288 4 2 11 7 41421198622 8 1233 3 5 1 28581198623 41 5479 1 6 11 22 3235Total 73 100 3 6 11 13 33 7 3411

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 5 Representative load profile for cluster C1

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 6 Representative load profile for cluster C2

Graphical representation of the representative load profilescorresponding to the three clusters obtained (C1 C2 and C3)is given in Figures 5 6 and 7

One hourly value from the representative load profilesdenotes the load of a water hydrophore station in per unit ofthe total average daily load of this station The hourly loadpattern can be employed to approximate the load pattern ofany water hydrophore station within the same cluster

The results of calculations carried out during the firststage of the clustering procedure are presented in Table 4

From Table 4 it can be seen that the most consistentclusters are C1 and C3 which together accounted for about85of the total load profiles of thewater hydrophore stationsIn terms of technical characteristics the water hydrophorestations from cluster C2 belong to types I and II (installedrated power is less than 88 kW) the stations from clustersC1 and C3 belong to types IIIndashVI (installed rated power is

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 7 Representative load profile for cluster C3

Table 5 Real and estimated hourly load of water distributionsystem

Hour 119875119878

real [kW] 119875119878

est [kW] Err []1 7105 7295 2682 6449 6695 3813 6350 6534 2904 6323 6519 3105 6514 6727 3266 7585 7861 3647 10744 10516 2128 12737 13096 2829 11880 12211 27910 11989 12357 30711 11529 11909 32912 10936 11326 35713 10622 10995 35114 10796 11044 23015 11015 10864 13716 10978 11311 30417 11428 11976 47918 12528 13013 38719 13702 14012 22620 13993 14500 36221 16531 16036 30022 13187 13624 33123 11154 11569 37224 8550 8794 285

between 16 and 30 kW) But in cluster C3 approximately 50percent of the total stations have an installed rated power by

8 Advances in Electrical Engineering

020406080

100120140160180

1 3 5 7 9 11 13 15 17 19 21 23

P (k

W)

Real powerEstimated power

Time (hours)

Figure 8 Real and estimated load profiles of the analyzed waterdistribution system

0

1

2

3

4

5

6

1 3 5 7 9 11 13 15 17 19 21 23

Estim

ated

erro

rs (

)

Time (hours)

Figure 9 Estimation errors obtained for hourly load of analyzedwater distribution system

22 kW In terms of the electrical energy consumption it canbe observed that the highest medium value is registered forcluster C1 and the lowest value is registered for cluster C2

In the second step of the study using information fromTables 3 and 4 and relation (6) the hourly loads of theanalyzed water distribution system were obtained Thus inTable 5 Figures 8 and 9 the real loads estimated loads andestimated errors are presented The estimation maximumerror is 479 and minimum error is 137 Global resultsshow that the value for MAPE is 311

Thismay be considered a very good result especially if wetake into account the arbitrariness inherent to loads behaviorand not all hydrophore stations have monitoring system

7 Conclusions

The investigation of combined actions which account forconnected water and electrical aspects allows improvingthe global efficiency of the water distribution systems andsupplying the consumers using the least possible amount ofwater and energy

In water distribution companies the system operatorpredicts the consumption for today and tomorrow based on

recent consumption trends weather forecasting day of theweek knowledge of future events and historical knowledgeof utility system performance This approach conducts at alarge percentage error (more than 5) for assessment of load

The proposed method is based on two stages in whichthe K-means clustering method and a load simulation tech-nique are exploited for estimation of the electrical energyconsumption The method based on the K-means clusteringalgorithm was used for determination of the representativeload profiles of the hydrophore stations A comparison ofobtained results using the proposed method with the realregistered data indicates an error by 311 which is very closeto the expected one by water companies (25ndash3) [57]

Results obtained demonstrate the ability of the proposedmethod to become the first step in an efficient managementof the water distribution systems On the one hand therepresentative load profiles can be used tomodel overall watercompany demands in a way that show how changes in use byone category affect the hourly load profiles for the system as awhole and on the other hand these profiles can contribute toa better understanding of the opportunities for linking water-efficiency and energy-efficiency programs

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] Alliance to Save Energy ldquoWhat watergy involvesrdquo 2014 httpwwwwatergynet

[2] P Boulos Z Wu C Orr M Moore P Hsiung and DThomasOptimal PumpOperation ofWaterDistribution SystemsUsing Genetic Algorithms H

2ONET-Users Guide MW Software

Consulting Dallas County Tex USA 2000[3] European Commission Directorate General for Environment

2013 httpeceuropaeuenvironmentwaterindex enhtm[4] A Anton and S Perju ldquoMonitoring the main parameters of a

water supply pumping station over ten yearsrdquo in Proceedings ofthe 6th International Conference on Hydraulic Machinery andHydrodynamics Timisoara Romania 2004

[5] S J Kenway A Priestley S Cook et al ldquoEnergy use in theprovision and consumption of urban water in Australia andNew Zealandrdquo Water for a Healthy Country National ResearchFlagship Report CSIRO 2008

[6] LHouseWater Supply Related ElectricityDemand inCaliforniaReport for California Energy Commission 2006

[7] R Goldstein and W Smith ldquoWater and sustainability USelectricity consumption for water supply amp treatmentmdashthe nexthalf centuryrdquo EPRI Report Electric Power Research InstitutePalo Alto Calif USA 2000

[8] I Pulido-Calvo and J C Gutierrez-Estrada ldquoSelection andoperation of pumping stations of water distribution systemsrdquoEnvironmental Research Journal vol 5 no 3 pp 1ndash20 2011

[9] K Feldman ldquoAspects of energy efficiency in water distributionsystemsrdquo inProceedings of the International Conference onWaterLoss pp 26ndash30 IWA Cape Town South Africa April 2009

Advances in Electrical Engineering 9

[10] G C Ionescu and D S Ionescu ldquoThe optimization of energyconsumption in water supply systemsrdquo Acta Electrotehnica vol46 pp 191ndash194 2005

[11] M Istrate and G Grigoras ldquoEnergy consumption estimationin water distribution systems using fuzzy techniquesrdquo Environ-mental Engineering and Management Journal vol 9 no 2 pp249ndash256 2010

[12] I Sarbu Energetic Optimization of the Water Distribution Sys-tems Publishing House of the Romanian Academy BucharestRomania 1997

[13] L Szychta ldquoEnergy consumption of water pumping for selectedcontrol systemsrdquo Electrical Power Quality and Utilization Jour-nal vol 12 pp 21ndash27 2006

[14] G Grigoras and M Istrate ldquoAn efficient clustering methodin evaluation of the electric energy consumption from waterhydrophore stationsrdquo International Review on Modelling andSimulations vol 4 no 2 pp 813ndash818 2011

[15] U Zessler and U Shamir ldquoOptimal operation of water dis-tribution systemsrdquo Journal of Water Resources Planning andManagement vol 115 no 6 pp 735ndash752 1989

[16] P Cutore A Campisano Z Kapelan C Modica and D SavicldquoProbabilistic prediction of urban water consumption using theSCEM-UA algorithmrdquo Urban Water Journal vol 5 no 2 pp125ndash132 2008

[17] G Chicco ldquoOverview and performance assessment of theclusteringmethods for electrical load pattern groupingrdquoEnergyvol 42 no 1 pp 68ndash80 2012

[18] A K Jain M N Murty and P J Flynn ldquoData clusteringa reviewrdquo httpdataclusteringcsemsuedupapersMSU-CSE-00-16pdf

[19] R Siddheswar and R Turi ldquoDetermination of number ofclusters in K-Means clustering and application in color imagesegmentationrdquo in Proceedings of the 4th International Confer-ence on Advanced in Pattern Recognition and Digital TechniquesCalcutta India 1999

[20] I Yatskiv and L Gusarova ldquoThe methods of cluster analysisresults validationrdquo in Proceedings of International ConferenceRelStat04 Riga Latvia 2004

[21] J Yu and Q Cheng ldquoThe upper bound of the optimal numberof clusters in fuzzy clusteringrdquo Science in China Series F vol 44pp 119ndash124 2001

[22] ldquoA tutorial on clustering algorithmsrdquo httphomedeipolimiitmatteuccClusteringtutorial html

[23] P J Rousseeuw ldquoSilhouettes a graphical aid to the interpreta-tion and validation of cluster analysisrdquo Journal of Computationaland Applied Mathematics vol 20 pp 53ndash65 1987

[24] M Halkidi Y Batistakis and M Vazirgiannis ldquoOn clusteringvalidation techniquesrdquo Journal of Intelligent Information Sys-tems vol 17 no 2-3 pp 107ndash145 2001

[25] M R Rezaee B P F Lelieveldt and J H C Reiber ldquoA newcluster validity index for the fuzzy C-meanrdquo Pattern RecognitionLetters vol 19 no 3-4 pp 237ndash246 1998

[26] P Berkhin ldquoSurvey of clustering data mining techniquesrdquo TechRep Accrue Software San Jose Calif USA 2002

[27] MHolgersson ldquoThe limited value of cophenetic correlation as aclustering criterionrdquo Pattern Recognition vol 10 no 4 pp 287ndash295 1978

[28] A D Gordon Classification Chapman amp Hall New York NYUSA 2nd edition 1999

[29] C G Carter-Brown ldquoLoad profile modeling for integratedenergy planningrdquo inProceedings of theDomestic Use of Electrical

Energy Conference pp 13ndash18 Cape Town South Africa April1999

[30] British Electricity Boards ldquoReport on the design of low voltageunderground networks for new housingrdquo ACE Report No 1051986

[31] British Electricity Boards ldquoReport on the computer programDEBUTE for the design of LV radial networks Part 1mdashgeneralconsiderations part 2mdashprogram user guiderdquo Tech Rep 1151988

[32] A Seppala Load research and load estimation in electricitydistribution [PhD thesis] Helsinki University of TechnologyEsbo Finland 1996

[33] J Nazarko and Z A Styczynski ldquoApplication of statisticaland neural approaches to the daily load profiles modelling inpower distribution systemsrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference pp 320ndash325 NewOrleans La USA May 1999

[34] Z Zakaria M N Othman and M H Sohod ldquoConsumerload profiling using fuzzy clustering and statistical approachrdquoin Proceedings of the 4th Student Conference on Researchand Development (SCOReD rsquo06) 274 p 270 IEEE SelangorMalaysia June 2006

[35] I H Yu J K Lee J M Ko and S I Kim ldquoA method forclassification of electricity demands using load profile datardquo inProceedings of the 4th Annual ACIS International Conference onComputer and Information Science (ICIS rsquo05) pp 164ndash168 JejuIsland South Korea July 2006

[36] G Chicco R Napoli and F Piglione ldquoComparisons amongclustering techniques for electricity customer classificationrdquoIEEE Transactions on Power Systems vol 21 no 2 pp 933ndash9402006

[37] G Chicco R Napoli and F Piglione ldquoApplication of clusteringalgorithms and self organising maps to classify electricitycustomersrdquo in Proceedings of the IEEE Bologna PowerTechConference vol 1 Bologna Italy June 2003

[38] D Gerbek S Gasperic and F Gubina ldquoComparison of differentclassification methods for the consumersrsquo load profile determi-nationrdquo in Proceedings of the 17th International Conference onElectricity Distribution Barcelona Spain 2003

[39] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI rsquo13) pp 1ndash6 Pitesti Romania June 2013

[40] N Mahmoudi-Kohan M P Moghaddam and S M BidakildquoEvaluating performance ofWFAK-means andmodified followthe leader methods for clustering load curvesrdquo in Proceedings ofthe IEEEPES Power Systems Conference and Exposition (PSCErsquo09) Seatle Wash USA March 2009

[41] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI 13) pp 1ndash6 Pitesti Romania June 2013

[42] A Mutanen M Ruska S Repo and P Jarventausta ldquoCustomerclassification and load profiling method for distribution sys-temsrdquo IEEE Transactions on Power Delivery vol 26 no 3 pp1755ndash1763 2011

[43] G Grigoras C Barbulescu G Cartina and D ComanesculdquoA comparative study regarding efficiency of the hierarchicalclustering techniques in typical load profiles determinationrdquoActa Electrotehnica vol 52 no 5 pp 184ndash188 2011

10 Advances in Electrical Engineering

[44] B D Pitt and D S Kirschen ldquoApplication of data miningtechniques to load profilingrdquo in Proceedings of the 21st IEEEInternational Conference Power Industry Computer ApplicationsSanta Clara Calif USA 1999

[45] S Ramos and Z Vale ldquoData mining techniques applicationin power distribution utilitiesrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Exposition pp 1ndash8 Chicago Ill USA April 2008

[46] V Figueiredo F Rodrigues Z Vale and J B Gouveia ldquoAnelectric energy consumer characterization framework based ondata mining techniquesrdquo IEEE Transactions on Power Systemsvol 20 no 2 pp 596ndash602 2005

[47] A H Nizar Z Y Dong and J H Zhao ldquoLoad profilingand data mining techniques in electricity deregulated marketrdquoin Proceedings of the IEEE Power Engineering Society GeneralMeeting (PES 06) Montreal Canada June 2006

[48] G J Tsekouras N D Hatziargyriou and E N Dialynas ldquoTwo-stage pattern recognition of load curves for classification ofelectricity customersrdquo IEEE Transactions on Power Systems vol22 no 3 pp 1120ndash1128 2007

[49] S V VerduMO Garcıa F J G Franco et al ldquoCharacterizationand identification of electrical customers through the use ofself-organizing maps and daily load parametersrdquo in Proceedingsof the IEEE PES Power System Conference and Exposition vol 2pp 899ndash906 Atlanta Ga USA 2004

[50] K L Lo and Z Zakaria ldquoElectricity consumer classificationusing artificial intelligencerdquo in Proceedings of the 39th Interna-tional Universities Power Engineering Conference Bristol UK2004

[51] D Gerbec S Gasperic I Smon and F Gubina ldquoDeter-mining the load profiles of consumers based on fuzzy logicand probability neural networksrdquo IEE Proceedings GenerationTransmission andDistribution vol 151 no 3 pp 395ndash400 2004

[52] D Gerbec S Gasperic I Smon and F Gubina ldquoAllocationof the load profiles to consumers using probabilistic neuralnetworksrdquo IEEE Transactions on Power Systems vol 20 no 2pp 548ndash555 2005

[53] M Sarlak T Ebrahimi and S S KarimiMadahi ldquoEnhancementthe accuracy of daily and hourly short time load forecastingusing neural networkrdquo Journal of Basic and Applied ScientificResearch vol 2 no 1 pp 247ndash255 2012

[54] H K Alfares and M Nazeeruddin ldquoElectric load forecastingLiterature survey and classification of methodsrdquo InternationalJournal of Systems Science vol 33 no 1 pp 23ndash34 2002

[55] L A Garcia-Escudero and A Gordaliza ldquoA proposal for robustcurve clusteringrdquo Journal of Classification vol 22 no 2 pp 185ndash201 2005

[56] Z Zisman and G Cartina ldquoApplication of fuzzy logic fordistribution system estimationrdquo in Proceedings of the 22ndSeminar on Fundamentals of Electrotechnics and Circuit TheoryUstron Poland May 1999

[57] L Jentgen H Kidder R Hill and S Conrad Water Con-sumption Forecasting to Improve Energy Efficiency of PumpingOperations Awwa Research Foundation 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Advances in Electrical Engineering 7

Table 4 Results of clustering process

Cluster Number of stations [] Type of stations119882med [kWh]

I II III IV V VI1198621 24 3288 4 2 11 7 41421198622 8 1233 3 5 1 28581198623 41 5479 1 6 11 22 3235Total 73 100 3 6 11 13 33 7 3411

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 5 Representative load profile for cluster C1

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 6 Representative load profile for cluster C2

Graphical representation of the representative load profilescorresponding to the three clusters obtained (C1 C2 and C3)is given in Figures 5 6 and 7

One hourly value from the representative load profilesdenotes the load of a water hydrophore station in per unit ofthe total average daily load of this station The hourly loadpattern can be employed to approximate the load pattern ofany water hydrophore station within the same cluster

The results of calculations carried out during the firststage of the clustering procedure are presented in Table 4

From Table 4 it can be seen that the most consistentclusters are C1 and C3 which together accounted for about85of the total load profiles of thewater hydrophore stationsIn terms of technical characteristics the water hydrophorestations from cluster C2 belong to types I and II (installedrated power is less than 88 kW) the stations from clustersC1 and C3 belong to types IIIndashVI (installed rated power is

0001002003004005006007008

1 3 5 7 9 11 13 15 17 19 21 23Time (hours)

Load

fact

or (p

u)

Figure 7 Representative load profile for cluster C3

Table 5 Real and estimated hourly load of water distributionsystem

Hour 119875119878

real [kW] 119875119878

est [kW] Err []1 7105 7295 2682 6449 6695 3813 6350 6534 2904 6323 6519 3105 6514 6727 3266 7585 7861 3647 10744 10516 2128 12737 13096 2829 11880 12211 27910 11989 12357 30711 11529 11909 32912 10936 11326 35713 10622 10995 35114 10796 11044 23015 11015 10864 13716 10978 11311 30417 11428 11976 47918 12528 13013 38719 13702 14012 22620 13993 14500 36221 16531 16036 30022 13187 13624 33123 11154 11569 37224 8550 8794 285

between 16 and 30 kW) But in cluster C3 approximately 50percent of the total stations have an installed rated power by

8 Advances in Electrical Engineering

020406080

100120140160180

1 3 5 7 9 11 13 15 17 19 21 23

P (k

W)

Real powerEstimated power

Time (hours)

Figure 8 Real and estimated load profiles of the analyzed waterdistribution system

0

1

2

3

4

5

6

1 3 5 7 9 11 13 15 17 19 21 23

Estim

ated

erro

rs (

)

Time (hours)

Figure 9 Estimation errors obtained for hourly load of analyzedwater distribution system

22 kW In terms of the electrical energy consumption it canbe observed that the highest medium value is registered forcluster C1 and the lowest value is registered for cluster C2

In the second step of the study using information fromTables 3 and 4 and relation (6) the hourly loads of theanalyzed water distribution system were obtained Thus inTable 5 Figures 8 and 9 the real loads estimated loads andestimated errors are presented The estimation maximumerror is 479 and minimum error is 137 Global resultsshow that the value for MAPE is 311

Thismay be considered a very good result especially if wetake into account the arbitrariness inherent to loads behaviorand not all hydrophore stations have monitoring system

7 Conclusions

The investigation of combined actions which account forconnected water and electrical aspects allows improvingthe global efficiency of the water distribution systems andsupplying the consumers using the least possible amount ofwater and energy

In water distribution companies the system operatorpredicts the consumption for today and tomorrow based on

recent consumption trends weather forecasting day of theweek knowledge of future events and historical knowledgeof utility system performance This approach conducts at alarge percentage error (more than 5) for assessment of load

The proposed method is based on two stages in whichthe K-means clustering method and a load simulation tech-nique are exploited for estimation of the electrical energyconsumption The method based on the K-means clusteringalgorithm was used for determination of the representativeload profiles of the hydrophore stations A comparison ofobtained results using the proposed method with the realregistered data indicates an error by 311 which is very closeto the expected one by water companies (25ndash3) [57]

Results obtained demonstrate the ability of the proposedmethod to become the first step in an efficient managementof the water distribution systems On the one hand therepresentative load profiles can be used tomodel overall watercompany demands in a way that show how changes in use byone category affect the hourly load profiles for the system as awhole and on the other hand these profiles can contribute toa better understanding of the opportunities for linking water-efficiency and energy-efficiency programs

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] Alliance to Save Energy ldquoWhat watergy involvesrdquo 2014 httpwwwwatergynet

[2] P Boulos Z Wu C Orr M Moore P Hsiung and DThomasOptimal PumpOperation ofWaterDistribution SystemsUsing Genetic Algorithms H

2ONET-Users Guide MW Software

Consulting Dallas County Tex USA 2000[3] European Commission Directorate General for Environment

2013 httpeceuropaeuenvironmentwaterindex enhtm[4] A Anton and S Perju ldquoMonitoring the main parameters of a

water supply pumping station over ten yearsrdquo in Proceedings ofthe 6th International Conference on Hydraulic Machinery andHydrodynamics Timisoara Romania 2004

[5] S J Kenway A Priestley S Cook et al ldquoEnergy use in theprovision and consumption of urban water in Australia andNew Zealandrdquo Water for a Healthy Country National ResearchFlagship Report CSIRO 2008

[6] LHouseWater Supply Related ElectricityDemand inCaliforniaReport for California Energy Commission 2006

[7] R Goldstein and W Smith ldquoWater and sustainability USelectricity consumption for water supply amp treatmentmdashthe nexthalf centuryrdquo EPRI Report Electric Power Research InstitutePalo Alto Calif USA 2000

[8] I Pulido-Calvo and J C Gutierrez-Estrada ldquoSelection andoperation of pumping stations of water distribution systemsrdquoEnvironmental Research Journal vol 5 no 3 pp 1ndash20 2011

[9] K Feldman ldquoAspects of energy efficiency in water distributionsystemsrdquo inProceedings of the International Conference onWaterLoss pp 26ndash30 IWA Cape Town South Africa April 2009

Advances in Electrical Engineering 9

[10] G C Ionescu and D S Ionescu ldquoThe optimization of energyconsumption in water supply systemsrdquo Acta Electrotehnica vol46 pp 191ndash194 2005

[11] M Istrate and G Grigoras ldquoEnergy consumption estimationin water distribution systems using fuzzy techniquesrdquo Environ-mental Engineering and Management Journal vol 9 no 2 pp249ndash256 2010

[12] I Sarbu Energetic Optimization of the Water Distribution Sys-tems Publishing House of the Romanian Academy BucharestRomania 1997

[13] L Szychta ldquoEnergy consumption of water pumping for selectedcontrol systemsrdquo Electrical Power Quality and Utilization Jour-nal vol 12 pp 21ndash27 2006

[14] G Grigoras and M Istrate ldquoAn efficient clustering methodin evaluation of the electric energy consumption from waterhydrophore stationsrdquo International Review on Modelling andSimulations vol 4 no 2 pp 813ndash818 2011

[15] U Zessler and U Shamir ldquoOptimal operation of water dis-tribution systemsrdquo Journal of Water Resources Planning andManagement vol 115 no 6 pp 735ndash752 1989

[16] P Cutore A Campisano Z Kapelan C Modica and D SavicldquoProbabilistic prediction of urban water consumption using theSCEM-UA algorithmrdquo Urban Water Journal vol 5 no 2 pp125ndash132 2008

[17] G Chicco ldquoOverview and performance assessment of theclusteringmethods for electrical load pattern groupingrdquoEnergyvol 42 no 1 pp 68ndash80 2012

[18] A K Jain M N Murty and P J Flynn ldquoData clusteringa reviewrdquo httpdataclusteringcsemsuedupapersMSU-CSE-00-16pdf

[19] R Siddheswar and R Turi ldquoDetermination of number ofclusters in K-Means clustering and application in color imagesegmentationrdquo in Proceedings of the 4th International Confer-ence on Advanced in Pattern Recognition and Digital TechniquesCalcutta India 1999

[20] I Yatskiv and L Gusarova ldquoThe methods of cluster analysisresults validationrdquo in Proceedings of International ConferenceRelStat04 Riga Latvia 2004

[21] J Yu and Q Cheng ldquoThe upper bound of the optimal numberof clusters in fuzzy clusteringrdquo Science in China Series F vol 44pp 119ndash124 2001

[22] ldquoA tutorial on clustering algorithmsrdquo httphomedeipolimiitmatteuccClusteringtutorial html

[23] P J Rousseeuw ldquoSilhouettes a graphical aid to the interpreta-tion and validation of cluster analysisrdquo Journal of Computationaland Applied Mathematics vol 20 pp 53ndash65 1987

[24] M Halkidi Y Batistakis and M Vazirgiannis ldquoOn clusteringvalidation techniquesrdquo Journal of Intelligent Information Sys-tems vol 17 no 2-3 pp 107ndash145 2001

[25] M R Rezaee B P F Lelieveldt and J H C Reiber ldquoA newcluster validity index for the fuzzy C-meanrdquo Pattern RecognitionLetters vol 19 no 3-4 pp 237ndash246 1998

[26] P Berkhin ldquoSurvey of clustering data mining techniquesrdquo TechRep Accrue Software San Jose Calif USA 2002

[27] MHolgersson ldquoThe limited value of cophenetic correlation as aclustering criterionrdquo Pattern Recognition vol 10 no 4 pp 287ndash295 1978

[28] A D Gordon Classification Chapman amp Hall New York NYUSA 2nd edition 1999

[29] C G Carter-Brown ldquoLoad profile modeling for integratedenergy planningrdquo inProceedings of theDomestic Use of Electrical

Energy Conference pp 13ndash18 Cape Town South Africa April1999

[30] British Electricity Boards ldquoReport on the design of low voltageunderground networks for new housingrdquo ACE Report No 1051986

[31] British Electricity Boards ldquoReport on the computer programDEBUTE for the design of LV radial networks Part 1mdashgeneralconsiderations part 2mdashprogram user guiderdquo Tech Rep 1151988

[32] A Seppala Load research and load estimation in electricitydistribution [PhD thesis] Helsinki University of TechnologyEsbo Finland 1996

[33] J Nazarko and Z A Styczynski ldquoApplication of statisticaland neural approaches to the daily load profiles modelling inpower distribution systemsrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference pp 320ndash325 NewOrleans La USA May 1999

[34] Z Zakaria M N Othman and M H Sohod ldquoConsumerload profiling using fuzzy clustering and statistical approachrdquoin Proceedings of the 4th Student Conference on Researchand Development (SCOReD rsquo06) 274 p 270 IEEE SelangorMalaysia June 2006

[35] I H Yu J K Lee J M Ko and S I Kim ldquoA method forclassification of electricity demands using load profile datardquo inProceedings of the 4th Annual ACIS International Conference onComputer and Information Science (ICIS rsquo05) pp 164ndash168 JejuIsland South Korea July 2006

[36] G Chicco R Napoli and F Piglione ldquoComparisons amongclustering techniques for electricity customer classificationrdquoIEEE Transactions on Power Systems vol 21 no 2 pp 933ndash9402006

[37] G Chicco R Napoli and F Piglione ldquoApplication of clusteringalgorithms and self organising maps to classify electricitycustomersrdquo in Proceedings of the IEEE Bologna PowerTechConference vol 1 Bologna Italy June 2003

[38] D Gerbek S Gasperic and F Gubina ldquoComparison of differentclassification methods for the consumersrsquo load profile determi-nationrdquo in Proceedings of the 17th International Conference onElectricity Distribution Barcelona Spain 2003

[39] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI rsquo13) pp 1ndash6 Pitesti Romania June 2013

[40] N Mahmoudi-Kohan M P Moghaddam and S M BidakildquoEvaluating performance ofWFAK-means andmodified followthe leader methods for clustering load curvesrdquo in Proceedings ofthe IEEEPES Power Systems Conference and Exposition (PSCErsquo09) Seatle Wash USA March 2009

[41] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI 13) pp 1ndash6 Pitesti Romania June 2013

[42] A Mutanen M Ruska S Repo and P Jarventausta ldquoCustomerclassification and load profiling method for distribution sys-temsrdquo IEEE Transactions on Power Delivery vol 26 no 3 pp1755ndash1763 2011

[43] G Grigoras C Barbulescu G Cartina and D ComanesculdquoA comparative study regarding efficiency of the hierarchicalclustering techniques in typical load profiles determinationrdquoActa Electrotehnica vol 52 no 5 pp 184ndash188 2011

10 Advances in Electrical Engineering

[44] B D Pitt and D S Kirschen ldquoApplication of data miningtechniques to load profilingrdquo in Proceedings of the 21st IEEEInternational Conference Power Industry Computer ApplicationsSanta Clara Calif USA 1999

[45] S Ramos and Z Vale ldquoData mining techniques applicationin power distribution utilitiesrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Exposition pp 1ndash8 Chicago Ill USA April 2008

[46] V Figueiredo F Rodrigues Z Vale and J B Gouveia ldquoAnelectric energy consumer characterization framework based ondata mining techniquesrdquo IEEE Transactions on Power Systemsvol 20 no 2 pp 596ndash602 2005

[47] A H Nizar Z Y Dong and J H Zhao ldquoLoad profilingand data mining techniques in electricity deregulated marketrdquoin Proceedings of the IEEE Power Engineering Society GeneralMeeting (PES 06) Montreal Canada June 2006

[48] G J Tsekouras N D Hatziargyriou and E N Dialynas ldquoTwo-stage pattern recognition of load curves for classification ofelectricity customersrdquo IEEE Transactions on Power Systems vol22 no 3 pp 1120ndash1128 2007

[49] S V VerduMO Garcıa F J G Franco et al ldquoCharacterizationand identification of electrical customers through the use ofself-organizing maps and daily load parametersrdquo in Proceedingsof the IEEE PES Power System Conference and Exposition vol 2pp 899ndash906 Atlanta Ga USA 2004

[50] K L Lo and Z Zakaria ldquoElectricity consumer classificationusing artificial intelligencerdquo in Proceedings of the 39th Interna-tional Universities Power Engineering Conference Bristol UK2004

[51] D Gerbec S Gasperic I Smon and F Gubina ldquoDeter-mining the load profiles of consumers based on fuzzy logicand probability neural networksrdquo IEE Proceedings GenerationTransmission andDistribution vol 151 no 3 pp 395ndash400 2004

[52] D Gerbec S Gasperic I Smon and F Gubina ldquoAllocationof the load profiles to consumers using probabilistic neuralnetworksrdquo IEEE Transactions on Power Systems vol 20 no 2pp 548ndash555 2005

[53] M Sarlak T Ebrahimi and S S KarimiMadahi ldquoEnhancementthe accuracy of daily and hourly short time load forecastingusing neural networkrdquo Journal of Basic and Applied ScientificResearch vol 2 no 1 pp 247ndash255 2012

[54] H K Alfares and M Nazeeruddin ldquoElectric load forecastingLiterature survey and classification of methodsrdquo InternationalJournal of Systems Science vol 33 no 1 pp 23ndash34 2002

[55] L A Garcia-Escudero and A Gordaliza ldquoA proposal for robustcurve clusteringrdquo Journal of Classification vol 22 no 2 pp 185ndash201 2005

[56] Z Zisman and G Cartina ldquoApplication of fuzzy logic fordistribution system estimationrdquo in Proceedings of the 22ndSeminar on Fundamentals of Electrotechnics and Circuit TheoryUstron Poland May 1999

[57] L Jentgen H Kidder R Hill and S Conrad Water Con-sumption Forecasting to Improve Energy Efficiency of PumpingOperations Awwa Research Foundation 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Advances in Electrical Engineering

020406080

100120140160180

1 3 5 7 9 11 13 15 17 19 21 23

P (k

W)

Real powerEstimated power

Time (hours)

Figure 8 Real and estimated load profiles of the analyzed waterdistribution system

0

1

2

3

4

5

6

1 3 5 7 9 11 13 15 17 19 21 23

Estim

ated

erro

rs (

)

Time (hours)

Figure 9 Estimation errors obtained for hourly load of analyzedwater distribution system

22 kW In terms of the electrical energy consumption it canbe observed that the highest medium value is registered forcluster C1 and the lowest value is registered for cluster C2

In the second step of the study using information fromTables 3 and 4 and relation (6) the hourly loads of theanalyzed water distribution system were obtained Thus inTable 5 Figures 8 and 9 the real loads estimated loads andestimated errors are presented The estimation maximumerror is 479 and minimum error is 137 Global resultsshow that the value for MAPE is 311

Thismay be considered a very good result especially if wetake into account the arbitrariness inherent to loads behaviorand not all hydrophore stations have monitoring system

7 Conclusions

The investigation of combined actions which account forconnected water and electrical aspects allows improvingthe global efficiency of the water distribution systems andsupplying the consumers using the least possible amount ofwater and energy

In water distribution companies the system operatorpredicts the consumption for today and tomorrow based on

recent consumption trends weather forecasting day of theweek knowledge of future events and historical knowledgeof utility system performance This approach conducts at alarge percentage error (more than 5) for assessment of load

The proposed method is based on two stages in whichthe K-means clustering method and a load simulation tech-nique are exploited for estimation of the electrical energyconsumption The method based on the K-means clusteringalgorithm was used for determination of the representativeload profiles of the hydrophore stations A comparison ofobtained results using the proposed method with the realregistered data indicates an error by 311 which is very closeto the expected one by water companies (25ndash3) [57]

Results obtained demonstrate the ability of the proposedmethod to become the first step in an efficient managementof the water distribution systems On the one hand therepresentative load profiles can be used tomodel overall watercompany demands in a way that show how changes in use byone category affect the hourly load profiles for the system as awhole and on the other hand these profiles can contribute toa better understanding of the opportunities for linking water-efficiency and energy-efficiency programs

Conflict of Interests

The author declares that there is no conflict of interestsregarding the publication of this paper

References

[1] Alliance to Save Energy ldquoWhat watergy involvesrdquo 2014 httpwwwwatergynet

[2] P Boulos Z Wu C Orr M Moore P Hsiung and DThomasOptimal PumpOperation ofWaterDistribution SystemsUsing Genetic Algorithms H

2ONET-Users Guide MW Software

Consulting Dallas County Tex USA 2000[3] European Commission Directorate General for Environment

2013 httpeceuropaeuenvironmentwaterindex enhtm[4] A Anton and S Perju ldquoMonitoring the main parameters of a

water supply pumping station over ten yearsrdquo in Proceedings ofthe 6th International Conference on Hydraulic Machinery andHydrodynamics Timisoara Romania 2004

[5] S J Kenway A Priestley S Cook et al ldquoEnergy use in theprovision and consumption of urban water in Australia andNew Zealandrdquo Water for a Healthy Country National ResearchFlagship Report CSIRO 2008

[6] LHouseWater Supply Related ElectricityDemand inCaliforniaReport for California Energy Commission 2006

[7] R Goldstein and W Smith ldquoWater and sustainability USelectricity consumption for water supply amp treatmentmdashthe nexthalf centuryrdquo EPRI Report Electric Power Research InstitutePalo Alto Calif USA 2000

[8] I Pulido-Calvo and J C Gutierrez-Estrada ldquoSelection andoperation of pumping stations of water distribution systemsrdquoEnvironmental Research Journal vol 5 no 3 pp 1ndash20 2011

[9] K Feldman ldquoAspects of energy efficiency in water distributionsystemsrdquo inProceedings of the International Conference onWaterLoss pp 26ndash30 IWA Cape Town South Africa April 2009

Advances in Electrical Engineering 9

[10] G C Ionescu and D S Ionescu ldquoThe optimization of energyconsumption in water supply systemsrdquo Acta Electrotehnica vol46 pp 191ndash194 2005

[11] M Istrate and G Grigoras ldquoEnergy consumption estimationin water distribution systems using fuzzy techniquesrdquo Environ-mental Engineering and Management Journal vol 9 no 2 pp249ndash256 2010

[12] I Sarbu Energetic Optimization of the Water Distribution Sys-tems Publishing House of the Romanian Academy BucharestRomania 1997

[13] L Szychta ldquoEnergy consumption of water pumping for selectedcontrol systemsrdquo Electrical Power Quality and Utilization Jour-nal vol 12 pp 21ndash27 2006

[14] G Grigoras and M Istrate ldquoAn efficient clustering methodin evaluation of the electric energy consumption from waterhydrophore stationsrdquo International Review on Modelling andSimulations vol 4 no 2 pp 813ndash818 2011

[15] U Zessler and U Shamir ldquoOptimal operation of water dis-tribution systemsrdquo Journal of Water Resources Planning andManagement vol 115 no 6 pp 735ndash752 1989

[16] P Cutore A Campisano Z Kapelan C Modica and D SavicldquoProbabilistic prediction of urban water consumption using theSCEM-UA algorithmrdquo Urban Water Journal vol 5 no 2 pp125ndash132 2008

[17] G Chicco ldquoOverview and performance assessment of theclusteringmethods for electrical load pattern groupingrdquoEnergyvol 42 no 1 pp 68ndash80 2012

[18] A K Jain M N Murty and P J Flynn ldquoData clusteringa reviewrdquo httpdataclusteringcsemsuedupapersMSU-CSE-00-16pdf

[19] R Siddheswar and R Turi ldquoDetermination of number ofclusters in K-Means clustering and application in color imagesegmentationrdquo in Proceedings of the 4th International Confer-ence on Advanced in Pattern Recognition and Digital TechniquesCalcutta India 1999

[20] I Yatskiv and L Gusarova ldquoThe methods of cluster analysisresults validationrdquo in Proceedings of International ConferenceRelStat04 Riga Latvia 2004

[21] J Yu and Q Cheng ldquoThe upper bound of the optimal numberof clusters in fuzzy clusteringrdquo Science in China Series F vol 44pp 119ndash124 2001

[22] ldquoA tutorial on clustering algorithmsrdquo httphomedeipolimiitmatteuccClusteringtutorial html

[23] P J Rousseeuw ldquoSilhouettes a graphical aid to the interpreta-tion and validation of cluster analysisrdquo Journal of Computationaland Applied Mathematics vol 20 pp 53ndash65 1987

[24] M Halkidi Y Batistakis and M Vazirgiannis ldquoOn clusteringvalidation techniquesrdquo Journal of Intelligent Information Sys-tems vol 17 no 2-3 pp 107ndash145 2001

[25] M R Rezaee B P F Lelieveldt and J H C Reiber ldquoA newcluster validity index for the fuzzy C-meanrdquo Pattern RecognitionLetters vol 19 no 3-4 pp 237ndash246 1998

[26] P Berkhin ldquoSurvey of clustering data mining techniquesrdquo TechRep Accrue Software San Jose Calif USA 2002

[27] MHolgersson ldquoThe limited value of cophenetic correlation as aclustering criterionrdquo Pattern Recognition vol 10 no 4 pp 287ndash295 1978

[28] A D Gordon Classification Chapman amp Hall New York NYUSA 2nd edition 1999

[29] C G Carter-Brown ldquoLoad profile modeling for integratedenergy planningrdquo inProceedings of theDomestic Use of Electrical

Energy Conference pp 13ndash18 Cape Town South Africa April1999

[30] British Electricity Boards ldquoReport on the design of low voltageunderground networks for new housingrdquo ACE Report No 1051986

[31] British Electricity Boards ldquoReport on the computer programDEBUTE for the design of LV radial networks Part 1mdashgeneralconsiderations part 2mdashprogram user guiderdquo Tech Rep 1151988

[32] A Seppala Load research and load estimation in electricitydistribution [PhD thesis] Helsinki University of TechnologyEsbo Finland 1996

[33] J Nazarko and Z A Styczynski ldquoApplication of statisticaland neural approaches to the daily load profiles modelling inpower distribution systemsrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference pp 320ndash325 NewOrleans La USA May 1999

[34] Z Zakaria M N Othman and M H Sohod ldquoConsumerload profiling using fuzzy clustering and statistical approachrdquoin Proceedings of the 4th Student Conference on Researchand Development (SCOReD rsquo06) 274 p 270 IEEE SelangorMalaysia June 2006

[35] I H Yu J K Lee J M Ko and S I Kim ldquoA method forclassification of electricity demands using load profile datardquo inProceedings of the 4th Annual ACIS International Conference onComputer and Information Science (ICIS rsquo05) pp 164ndash168 JejuIsland South Korea July 2006

[36] G Chicco R Napoli and F Piglione ldquoComparisons amongclustering techniques for electricity customer classificationrdquoIEEE Transactions on Power Systems vol 21 no 2 pp 933ndash9402006

[37] G Chicco R Napoli and F Piglione ldquoApplication of clusteringalgorithms and self organising maps to classify electricitycustomersrdquo in Proceedings of the IEEE Bologna PowerTechConference vol 1 Bologna Italy June 2003

[38] D Gerbek S Gasperic and F Gubina ldquoComparison of differentclassification methods for the consumersrsquo load profile determi-nationrdquo in Proceedings of the 17th International Conference onElectricity Distribution Barcelona Spain 2003

[39] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI rsquo13) pp 1ndash6 Pitesti Romania June 2013

[40] N Mahmoudi-Kohan M P Moghaddam and S M BidakildquoEvaluating performance ofWFAK-means andmodified followthe leader methods for clustering load curvesrdquo in Proceedings ofthe IEEEPES Power Systems Conference and Exposition (PSCErsquo09) Seatle Wash USA March 2009

[41] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI 13) pp 1ndash6 Pitesti Romania June 2013

[42] A Mutanen M Ruska S Repo and P Jarventausta ldquoCustomerclassification and load profiling method for distribution sys-temsrdquo IEEE Transactions on Power Delivery vol 26 no 3 pp1755ndash1763 2011

[43] G Grigoras C Barbulescu G Cartina and D ComanesculdquoA comparative study regarding efficiency of the hierarchicalclustering techniques in typical load profiles determinationrdquoActa Electrotehnica vol 52 no 5 pp 184ndash188 2011

10 Advances in Electrical Engineering

[44] B D Pitt and D S Kirschen ldquoApplication of data miningtechniques to load profilingrdquo in Proceedings of the 21st IEEEInternational Conference Power Industry Computer ApplicationsSanta Clara Calif USA 1999

[45] S Ramos and Z Vale ldquoData mining techniques applicationin power distribution utilitiesrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Exposition pp 1ndash8 Chicago Ill USA April 2008

[46] V Figueiredo F Rodrigues Z Vale and J B Gouveia ldquoAnelectric energy consumer characterization framework based ondata mining techniquesrdquo IEEE Transactions on Power Systemsvol 20 no 2 pp 596ndash602 2005

[47] A H Nizar Z Y Dong and J H Zhao ldquoLoad profilingand data mining techniques in electricity deregulated marketrdquoin Proceedings of the IEEE Power Engineering Society GeneralMeeting (PES 06) Montreal Canada June 2006

[48] G J Tsekouras N D Hatziargyriou and E N Dialynas ldquoTwo-stage pattern recognition of load curves for classification ofelectricity customersrdquo IEEE Transactions on Power Systems vol22 no 3 pp 1120ndash1128 2007

[49] S V VerduMO Garcıa F J G Franco et al ldquoCharacterizationand identification of electrical customers through the use ofself-organizing maps and daily load parametersrdquo in Proceedingsof the IEEE PES Power System Conference and Exposition vol 2pp 899ndash906 Atlanta Ga USA 2004

[50] K L Lo and Z Zakaria ldquoElectricity consumer classificationusing artificial intelligencerdquo in Proceedings of the 39th Interna-tional Universities Power Engineering Conference Bristol UK2004

[51] D Gerbec S Gasperic I Smon and F Gubina ldquoDeter-mining the load profiles of consumers based on fuzzy logicand probability neural networksrdquo IEE Proceedings GenerationTransmission andDistribution vol 151 no 3 pp 395ndash400 2004

[52] D Gerbec S Gasperic I Smon and F Gubina ldquoAllocationof the load profiles to consumers using probabilistic neuralnetworksrdquo IEEE Transactions on Power Systems vol 20 no 2pp 548ndash555 2005

[53] M Sarlak T Ebrahimi and S S KarimiMadahi ldquoEnhancementthe accuracy of daily and hourly short time load forecastingusing neural networkrdquo Journal of Basic and Applied ScientificResearch vol 2 no 1 pp 247ndash255 2012

[54] H K Alfares and M Nazeeruddin ldquoElectric load forecastingLiterature survey and classification of methodsrdquo InternationalJournal of Systems Science vol 33 no 1 pp 23ndash34 2002

[55] L A Garcia-Escudero and A Gordaliza ldquoA proposal for robustcurve clusteringrdquo Journal of Classification vol 22 no 2 pp 185ndash201 2005

[56] Z Zisman and G Cartina ldquoApplication of fuzzy logic fordistribution system estimationrdquo in Proceedings of the 22ndSeminar on Fundamentals of Electrotechnics and Circuit TheoryUstron Poland May 1999

[57] L Jentgen H Kidder R Hill and S Conrad Water Con-sumption Forecasting to Improve Energy Efficiency of PumpingOperations Awwa Research Foundation 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Advances in Electrical Engineering 9

[10] G C Ionescu and D S Ionescu ldquoThe optimization of energyconsumption in water supply systemsrdquo Acta Electrotehnica vol46 pp 191ndash194 2005

[11] M Istrate and G Grigoras ldquoEnergy consumption estimationin water distribution systems using fuzzy techniquesrdquo Environ-mental Engineering and Management Journal vol 9 no 2 pp249ndash256 2010

[12] I Sarbu Energetic Optimization of the Water Distribution Sys-tems Publishing House of the Romanian Academy BucharestRomania 1997

[13] L Szychta ldquoEnergy consumption of water pumping for selectedcontrol systemsrdquo Electrical Power Quality and Utilization Jour-nal vol 12 pp 21ndash27 2006

[14] G Grigoras and M Istrate ldquoAn efficient clustering methodin evaluation of the electric energy consumption from waterhydrophore stationsrdquo International Review on Modelling andSimulations vol 4 no 2 pp 813ndash818 2011

[15] U Zessler and U Shamir ldquoOptimal operation of water dis-tribution systemsrdquo Journal of Water Resources Planning andManagement vol 115 no 6 pp 735ndash752 1989

[16] P Cutore A Campisano Z Kapelan C Modica and D SavicldquoProbabilistic prediction of urban water consumption using theSCEM-UA algorithmrdquo Urban Water Journal vol 5 no 2 pp125ndash132 2008

[17] G Chicco ldquoOverview and performance assessment of theclusteringmethods for electrical load pattern groupingrdquoEnergyvol 42 no 1 pp 68ndash80 2012

[18] A K Jain M N Murty and P J Flynn ldquoData clusteringa reviewrdquo httpdataclusteringcsemsuedupapersMSU-CSE-00-16pdf

[19] R Siddheswar and R Turi ldquoDetermination of number ofclusters in K-Means clustering and application in color imagesegmentationrdquo in Proceedings of the 4th International Confer-ence on Advanced in Pattern Recognition and Digital TechniquesCalcutta India 1999

[20] I Yatskiv and L Gusarova ldquoThe methods of cluster analysisresults validationrdquo in Proceedings of International ConferenceRelStat04 Riga Latvia 2004

[21] J Yu and Q Cheng ldquoThe upper bound of the optimal numberof clusters in fuzzy clusteringrdquo Science in China Series F vol 44pp 119ndash124 2001

[22] ldquoA tutorial on clustering algorithmsrdquo httphomedeipolimiitmatteuccClusteringtutorial html

[23] P J Rousseeuw ldquoSilhouettes a graphical aid to the interpreta-tion and validation of cluster analysisrdquo Journal of Computationaland Applied Mathematics vol 20 pp 53ndash65 1987

[24] M Halkidi Y Batistakis and M Vazirgiannis ldquoOn clusteringvalidation techniquesrdquo Journal of Intelligent Information Sys-tems vol 17 no 2-3 pp 107ndash145 2001

[25] M R Rezaee B P F Lelieveldt and J H C Reiber ldquoA newcluster validity index for the fuzzy C-meanrdquo Pattern RecognitionLetters vol 19 no 3-4 pp 237ndash246 1998

[26] P Berkhin ldquoSurvey of clustering data mining techniquesrdquo TechRep Accrue Software San Jose Calif USA 2002

[27] MHolgersson ldquoThe limited value of cophenetic correlation as aclustering criterionrdquo Pattern Recognition vol 10 no 4 pp 287ndash295 1978

[28] A D Gordon Classification Chapman amp Hall New York NYUSA 2nd edition 1999

[29] C G Carter-Brown ldquoLoad profile modeling for integratedenergy planningrdquo inProceedings of theDomestic Use of Electrical

Energy Conference pp 13ndash18 Cape Town South Africa April1999

[30] British Electricity Boards ldquoReport on the design of low voltageunderground networks for new housingrdquo ACE Report No 1051986

[31] British Electricity Boards ldquoReport on the computer programDEBUTE for the design of LV radial networks Part 1mdashgeneralconsiderations part 2mdashprogram user guiderdquo Tech Rep 1151988

[32] A Seppala Load research and load estimation in electricitydistribution [PhD thesis] Helsinki University of TechnologyEsbo Finland 1996

[33] J Nazarko and Z A Styczynski ldquoApplication of statisticaland neural approaches to the daily load profiles modelling inpower distribution systemsrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference pp 320ndash325 NewOrleans La USA May 1999

[34] Z Zakaria M N Othman and M H Sohod ldquoConsumerload profiling using fuzzy clustering and statistical approachrdquoin Proceedings of the 4th Student Conference on Researchand Development (SCOReD rsquo06) 274 p 270 IEEE SelangorMalaysia June 2006

[35] I H Yu J K Lee J M Ko and S I Kim ldquoA method forclassification of electricity demands using load profile datardquo inProceedings of the 4th Annual ACIS International Conference onComputer and Information Science (ICIS rsquo05) pp 164ndash168 JejuIsland South Korea July 2006

[36] G Chicco R Napoli and F Piglione ldquoComparisons amongclustering techniques for electricity customer classificationrdquoIEEE Transactions on Power Systems vol 21 no 2 pp 933ndash9402006

[37] G Chicco R Napoli and F Piglione ldquoApplication of clusteringalgorithms and self organising maps to classify electricitycustomersrdquo in Proceedings of the IEEE Bologna PowerTechConference vol 1 Bologna Italy June 2003

[38] D Gerbek S Gasperic and F Gubina ldquoComparison of differentclassification methods for the consumersrsquo load profile determi-nationrdquo in Proceedings of the 17th International Conference onElectricity Distribution Barcelona Spain 2003

[39] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI rsquo13) pp 1ndash6 Pitesti Romania June 2013

[40] N Mahmoudi-Kohan M P Moghaddam and S M BidakildquoEvaluating performance ofWFAK-means andmodified followthe leader methods for clustering load curvesrdquo in Proceedings ofthe IEEEPES Power Systems Conference and Exposition (PSCErsquo09) Seatle Wash USA March 2009

[41] G Grigoras M Istrate and F Scarlatache ldquoElectrical energyconsumption estimation in water distribution systems using aclustering based methodrdquo in Proceedings of the InternationalConference on Electronics Computers and Artificial Intelligence(ECAI 13) pp 1ndash6 Pitesti Romania June 2013

[42] A Mutanen M Ruska S Repo and P Jarventausta ldquoCustomerclassification and load profiling method for distribution sys-temsrdquo IEEE Transactions on Power Delivery vol 26 no 3 pp1755ndash1763 2011

[43] G Grigoras C Barbulescu G Cartina and D ComanesculdquoA comparative study regarding efficiency of the hierarchicalclustering techniques in typical load profiles determinationrdquoActa Electrotehnica vol 52 no 5 pp 184ndash188 2011

10 Advances in Electrical Engineering

[44] B D Pitt and D S Kirschen ldquoApplication of data miningtechniques to load profilingrdquo in Proceedings of the 21st IEEEInternational Conference Power Industry Computer ApplicationsSanta Clara Calif USA 1999

[45] S Ramos and Z Vale ldquoData mining techniques applicationin power distribution utilitiesrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Exposition pp 1ndash8 Chicago Ill USA April 2008

[46] V Figueiredo F Rodrigues Z Vale and J B Gouveia ldquoAnelectric energy consumer characterization framework based ondata mining techniquesrdquo IEEE Transactions on Power Systemsvol 20 no 2 pp 596ndash602 2005

[47] A H Nizar Z Y Dong and J H Zhao ldquoLoad profilingand data mining techniques in electricity deregulated marketrdquoin Proceedings of the IEEE Power Engineering Society GeneralMeeting (PES 06) Montreal Canada June 2006

[48] G J Tsekouras N D Hatziargyriou and E N Dialynas ldquoTwo-stage pattern recognition of load curves for classification ofelectricity customersrdquo IEEE Transactions on Power Systems vol22 no 3 pp 1120ndash1128 2007

[49] S V VerduMO Garcıa F J G Franco et al ldquoCharacterizationand identification of electrical customers through the use ofself-organizing maps and daily load parametersrdquo in Proceedingsof the IEEE PES Power System Conference and Exposition vol 2pp 899ndash906 Atlanta Ga USA 2004

[50] K L Lo and Z Zakaria ldquoElectricity consumer classificationusing artificial intelligencerdquo in Proceedings of the 39th Interna-tional Universities Power Engineering Conference Bristol UK2004

[51] D Gerbec S Gasperic I Smon and F Gubina ldquoDeter-mining the load profiles of consumers based on fuzzy logicand probability neural networksrdquo IEE Proceedings GenerationTransmission andDistribution vol 151 no 3 pp 395ndash400 2004

[52] D Gerbec S Gasperic I Smon and F Gubina ldquoAllocationof the load profiles to consumers using probabilistic neuralnetworksrdquo IEEE Transactions on Power Systems vol 20 no 2pp 548ndash555 2005

[53] M Sarlak T Ebrahimi and S S KarimiMadahi ldquoEnhancementthe accuracy of daily and hourly short time load forecastingusing neural networkrdquo Journal of Basic and Applied ScientificResearch vol 2 no 1 pp 247ndash255 2012

[54] H K Alfares and M Nazeeruddin ldquoElectric load forecastingLiterature survey and classification of methodsrdquo InternationalJournal of Systems Science vol 33 no 1 pp 23ndash34 2002

[55] L A Garcia-Escudero and A Gordaliza ldquoA proposal for robustcurve clusteringrdquo Journal of Classification vol 22 no 2 pp 185ndash201 2005

[56] Z Zisman and G Cartina ldquoApplication of fuzzy logic fordistribution system estimationrdquo in Proceedings of the 22ndSeminar on Fundamentals of Electrotechnics and Circuit TheoryUstron Poland May 1999

[57] L Jentgen H Kidder R Hill and S Conrad Water Con-sumption Forecasting to Improve Energy Efficiency of PumpingOperations Awwa Research Foundation 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Advances in Electrical Engineering

[44] B D Pitt and D S Kirschen ldquoApplication of data miningtechniques to load profilingrdquo in Proceedings of the 21st IEEEInternational Conference Power Industry Computer ApplicationsSanta Clara Calif USA 1999

[45] S Ramos and Z Vale ldquoData mining techniques applicationin power distribution utilitiesrdquo in Proceedings of the IEEEPESTransmission and Distribution Conference and Exposition pp 1ndash8 Chicago Ill USA April 2008

[46] V Figueiredo F Rodrigues Z Vale and J B Gouveia ldquoAnelectric energy consumer characterization framework based ondata mining techniquesrdquo IEEE Transactions on Power Systemsvol 20 no 2 pp 596ndash602 2005

[47] A H Nizar Z Y Dong and J H Zhao ldquoLoad profilingand data mining techniques in electricity deregulated marketrdquoin Proceedings of the IEEE Power Engineering Society GeneralMeeting (PES 06) Montreal Canada June 2006

[48] G J Tsekouras N D Hatziargyriou and E N Dialynas ldquoTwo-stage pattern recognition of load curves for classification ofelectricity customersrdquo IEEE Transactions on Power Systems vol22 no 3 pp 1120ndash1128 2007

[49] S V VerduMO Garcıa F J G Franco et al ldquoCharacterizationand identification of electrical customers through the use ofself-organizing maps and daily load parametersrdquo in Proceedingsof the IEEE PES Power System Conference and Exposition vol 2pp 899ndash906 Atlanta Ga USA 2004

[50] K L Lo and Z Zakaria ldquoElectricity consumer classificationusing artificial intelligencerdquo in Proceedings of the 39th Interna-tional Universities Power Engineering Conference Bristol UK2004

[51] D Gerbec S Gasperic I Smon and F Gubina ldquoDeter-mining the load profiles of consumers based on fuzzy logicand probability neural networksrdquo IEE Proceedings GenerationTransmission andDistribution vol 151 no 3 pp 395ndash400 2004

[52] D Gerbec S Gasperic I Smon and F Gubina ldquoAllocationof the load profiles to consumers using probabilistic neuralnetworksrdquo IEEE Transactions on Power Systems vol 20 no 2pp 548ndash555 2005

[53] M Sarlak T Ebrahimi and S S KarimiMadahi ldquoEnhancementthe accuracy of daily and hourly short time load forecastingusing neural networkrdquo Journal of Basic and Applied ScientificResearch vol 2 no 1 pp 247ndash255 2012

[54] H K Alfares and M Nazeeruddin ldquoElectric load forecastingLiterature survey and classification of methodsrdquo InternationalJournal of Systems Science vol 33 no 1 pp 23ndash34 2002

[55] L A Garcia-Escudero and A Gordaliza ldquoA proposal for robustcurve clusteringrdquo Journal of Classification vol 22 no 2 pp 185ndash201 2005

[56] Z Zisman and G Cartina ldquoApplication of fuzzy logic fordistribution system estimationrdquo in Proceedings of the 22ndSeminar on Fundamentals of Electrotechnics and Circuit TheoryUstron Poland May 1999

[57] L Jentgen H Kidder R Hill and S Conrad Water Con-sumption Forecasting to Improve Energy Efficiency of PumpingOperations Awwa Research Foundation 2007

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of