Clustering Electric Load Curves: The Brazilian Experience · José Francisco Moreira Pessanha...

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José Francisco Moreira José Francisco Moreira PessanhaPessanha (CEPEL / UERJ) [email protected] (CEPEL / UERJ) [email protected]

Luiz da Costa Luiz da Costa LaurencelLaurencel (UERJ / UFF) [email protected](UERJ / UFF) [email protected]

Clustering Electric Load Curves:

The Brazilian Experience

Workshop Franco-Brasileiro

sobre Mineração de Dados

Workshop Franco-Brésilien sur

la Fouille des Données

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Introduction

� The Brazilian electric power sector adopts tariffs based on marginal cost pricing since 1980.

� The electricity tariffs are calculated by a methodology, whose origin is the Electricitéde France (EDF) and the French 'marginaliste' economists like Allais and Boiteux.

� In this methodology, an important step is the identification of a few typical daily load profiles from a set of electric load curves measurements on a sample of customers.

� These profiles represent patterns of energy use of different class of customers e.g. residential, commercial, industrial, rural, public lighting, public administration etc.

� The standard way to identify the typical load profile from a sample of load curves is to perform a clustering of the representative workday load curves. The centroid of each cluster defines a typical load profile.

� This work presents a brief history about the softwares for identifying of typical daily load profiles developed in the Brazilian electric power sector.

� In order to tell this history we present the features of three softwares that have been used by the Brazilian electric distribution utilities.

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Procedure to identify typical load profiles

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ClusteringTechnique

Sample of workday

representativeload curves

3 clusters 3 typical load profiles

4) Apply a clustering technique to group customers with similar workday load curves (each daily curve has 96 points). After that, take the typical load profiles fromeach cluster

5) Derive typical load profiles for the entire population

3) Examine the load curve measurement (kW) of eachcustomer in order to identify its three representativeload curves (workday, Saturday and Sunday)

LoadLoad curve curve measurementmeasurement

workdayworkday SaturdaySaturday SundaySunday

1) Select a sample of customers (or power transformers)

2) Get a load curve measurement from each customer

The load curves measures cover a period of two weeks, where the demand is recorded every 15 minutes by recording meters installed at each point in the sample.

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Softwares for identifying of typical load profiles developed in the Brazilian electric power sector

• SNACC (1991)Sistema Nacional de Avaliação do Comportamento da CargaNational system of evaluation of the load behavior

• TARDIST (1998)Programa para cálculo dos custos marginais de fornecimento e tarifas de uso da distribuiçãoComputational program for computing the supply marginal costs and distribution tariffs

• ANATIPO (2005)Sistema computacional para construção de tipologias de curvas de cargaSoftware for building typical load curves

We select a representative sample of three softwares for identifying of typical load profiles used in the Brazilian electric power sector.

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SNACC Program (1991)

It was the first software for clustering loadcurves developed in theBrazilian power sector.

It was developed by the National Department of Waters and Electric Power (DNAEE).

DNAEE was officially closed upon the establishment of theBrazilian ElectricityRegulatory Agency (ANEEL).

The SNACC employs the methods of cluster analysis p rogrammed in two computational routines in Fortran brought from the Electricité de France (EDF): NUDYC (nuées dynamique ) and DESCR2 (Ward method). • Molliere, M. Um ensemble de modules de classification automatique et de modules explicatifs associes, Note EDF, Direction des etudes et Recherches nº HI 2818/02, 1978.• BRASIL, Ministério das Minas e Energia, DNAEE, Eletrobrás, Empresas Concessionárias de Energia Elétrica, Nova Tarifa de Energia Elétrica: metodologia e aplicação, DNAEE, Brasília,1985.

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““Module NUDYC”Module NUDYC”NuéesNuées dynamiquesdynamiques

““Module de Module de DescriptionDescription etet classificationclassificationhiérarchiquehiérarchique ascendente (DESCR2)”ascendente (DESCR2)”

WardWard methodmethod

Set of Set of workdayworkday loadload curves curves ((eacheach loadload curve curve hashas 96 96 pointspoints andand

representsrepresents a a customercustomer))

TypicalTypical loadload profilesprofiles

formes fortesformes fortes

Diday, E. Une nouvelle méthode em classificationautomatique et reconnaissance des formes. Laméthode des nuées dynamiques. Revue de statistiqueAppliquée, 1971, vol. XIV nº 2. Institut de Statistique. Université de Paris.

The NUDYC and DESCR2 routines are executed sequenti ally: first the typical workday load curves are clustered by the “nuées dynamique“ programmed in the NUDYC routine, then the formes fortes are clustered by the Ward method programmed in the DESCR2 routine.

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�� GraphicalGraphical outputsoutputs are are veryvery usefuluseful for for thetheloadload curve curve analysisanalysis , , butbut thethe SNACC does SNACC does notnotshow show graphsgraphs of of loadload curve curve measurementsmeasurementsandand typicaltypical loadload profilesprofiles . .

�� The identification of the typical profiles requests a visual anaThe identification of the typical profiles requests a visual ana lysis of lysis of a large number of load curve measurements. It is th e heaviest woa large number of load curve measurements. It is th e heaviest wo rk rk stage and the stage and the mainmain criticalcritical stepstep in in thethe computationcomputation of of distributiondistributiontariffstariffs ..

�� In In orderorder to to overcomeovercome thisthis deficiencydeficiency , in 1998 , in 1998 thethe BrazilianBrazilian ElectricElectricPowerPower ResearchResearch CenterCenter (Cepel) (Cepel) developeddeveloped thethe TARDIST TARDIST programprogram

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TARDIST program (1998)

Software developed by the Brazilian Electric Power Research Center (Cepel) to compute the distribution tariff framework based onmarginal cost.

TARDIST also has a module to build typicalload profiles, but it has a friendly user interface.

The software is used by the Brazilian Electricity Regulatory Agency (ANEEL) to set the distribution tariff.

Pessanha, J.F.M., Huang, J.L.C., Pereira, L.A.C., Passos Júnior, R., Castellani, V.L.O. Metodologia e sistema computacional para cálculo das tarifas de uso dos sistemas de distribui»cão, XXXVI SBPO, São João delRey - MG,2004.

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Input data:Input data:� List of costumers and electric power transformers in the sample.� Load curves measurements files (Excel or text format) for each sample point� Annual energy demand (MWh) for each consumption class and energy flows(MWh) among the voltage levels.

load curve measurement file

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The friendly user interface shows the load The friendly user interface shows the load curves registered in each measurement file.curves registered in each measurement file.

Based on a pictorial analysis any user can Based on a pictorial analysis any user can select the select the three typical days (a workday, a three typical days (a workday, a Saturday and a Sunday) of Saturday and a Sunday) of each measurement each measurement file.file.

measurementmeasurement

workdayworkday SaturdaySaturday SundaySunday

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TARDIST employs only the Ward method to cluster the workdays loaTARDIST employs only the Ward method to cluster the workdays loa d d curves. curves.

The user can change the clusters' The user can change the clusters' composition, in order to correct any composition, in order to correct any misclassification made during the misclassification made during the clustering process. clustering process.

TARDIST shows the following results TARDIST shows the following results useful to set the number of cluster useful to set the number of cluster (typical load profiles):(typical load profiles):

�� Load profiles plots for each clusterLoad profiles plots for each cluster�� Share (%) of each cluster in the energy Share (%) of each cluster in the energy consumptionconsumption�� Within Sum Squares (WSS) and Within Sum Squares (WSS) and Between Sum Square (BSS).Between Sum Square (BSS).

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The software shows the load curves classified in eachcluster.

SELECIONAAGRUPAMENTOS

VER 1 OU 2GRÁFICOS

OneOne clustercluster TwoTwo clustersclusters

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ANATIPO Program (2005)

Software developed by Cepel to Cosern (Companhia Ener gética do Rio Grande do Norte) in its R&D Program.

Purpose: To identify typical load profiles from a s ample of load curves measurements.

Main characteristics:

� Import load curve measurements (kW) from files in t ext format orExcel worksheet

� Routine for automatic identification of the typical workday, Saturday and Sunday curves of each measurement file

� Allows data analysis through graphics and reports

� Three clustering techniques: Ward, k-Means and Fuzz y Clustering Method (FCM)

� User friendly graphical interface

� Output reports (text format and Excel)

Pessanha, J.F.M., Castellani, V.L.O., Araújo, A.L.A. Uma nova ferramenta computacional para construção de tipologias de curva de carga, X SEPOPE, Florianópolis - SC,2006.

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Sample of customers or electric power transformers

CustomerCustomer codecode CustomerCustomer namenameFile File withwith loadload curve curve

measurementmeasurement

AnnualAnnualconsumptionconsumption((MWhMWh))

DataDatainputinputformform

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(text format)

Sample points

Reading load curve measurements


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Saturday andSunday

measurements

workdaysmeasurements

Reading load curve measurements


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Saturday and Sunday measurements

Workday measurements

The three representative load curves : workday, Saturday and Sunday

Identify the typicalSaturday load curve

SaturdaySaturday

SundaySunday

MondayMonday TuesdayTuesday

WednesdayWednesday ThursdayThursday

Identify the typicalworkday load curve

Identify the typicalSunday load curve

Two modes to select the three representative load curves from measurement files: • non-automatic (pictorial analysis of each measurement)• automatic


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Automatic selection of the representative load curves of each measurement file

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1 - Delete the bad data (outage service andabnormal powerconsumption)

2 - Compute three averagecurves (Sunday, Saturdayand workday)

3 – Choice the three curves near to the average curves

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The three representative loadcurves for a customer: workday,

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AutomaticAutomatic selectionselection


ThisThis procedureprocedure is is appliedapplied automaticallyautomatically

to to eacheach loadload curve curve measurementmeasurement filefile

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Identification of the load curves with abnormal consumptions

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Consumption

Consumptiondistribution

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LowerLower boundbound (LB)(LB)

UpperUpper boundbound (UB)(UB)

25% 25% percentilepercentile (Q1)(Q1)

75% 75% percentilepercentile (Q3)(Q3)

Abnormal Abnormal consumptionconsumption

Abnormal Abnormal consumptionconsumption

Box plot

LB = Q1 LB = Q1 –– 1.5*(Q31.5*(Q3--Q1)Q1)

UB = Q3 + 1.5*(Q3UB = Q3 + 1.5*(Q3--Q1)Q1)


TheseThese loadload curves curves are are notnot consideredconsideredin in thethe averageaveragecomputationcomputation

TheseThese loadload curves curves are are notnot consideredconsideredin in thethe averageaveragecomputationcomputation

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Cluster Cluster analysisanalysis


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User can move a load curve from one cluster to another


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BSS = BSS = BetweenBetween sumsum squaressquares

WSS = WSS = WithinWithin sumsum squaressquares

%BSS = BSS / (WSS + BSS)%BSS = BSS / (WSS + BSS)

%WSS = WSS / (WSS + BSS)%WSS = WSS / (WSS + BSS)

Output report with statistics to set the number of clusters

∑=

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The ideal number of clusters minimizes the compacity and separationmeasure (CS)

k = k = numbernumber of clusters x = of clusters x = loadload curve c= cluster curve c= cluster centroidcentroidn = n = numbernumber of of objectsobjects ((loadload curves) u = curves) u = membershipmembership functionfunctionm = m = degreedegree of of fuzzyficationfuzzyfication (m=1 for (m=1 for crispcrisp methodsmethods kk--MeansMeans andand WardWard))

NumberNumber of of clustersclusters BSSBSS%WSS%WSS%BSS%BSSCSCS

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The main result is a worksheet with the typical load profiles


Excel Excel worksheetworksheetreadyready to to bebe usedusedin in thethe distributiondistributiontarifftariff computationcomputation

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Conclusions

The softwares for identifying typical load profiles deve loped in theBrazilian electric power sector are based on the French tr adition, specially from the EDF’s experience.

Most of the studies carried out in the Brazilian electric ity distributionutilities have been used statistics techniques (Ward metho d, k-Means orthe “ Nuées dynamiques ”) to obtain the typical load profiles. For example, the statistics techniques have been used in the tariff revi sion process.

However it is possible to find few studies that use Self- Organizing Map(SOM) in order to get the typical load profiles. Most of these studies havebeen used the Matlab Neural Network Toolbox. The challeng e remains to develop a software based on SOM like “ Courboscope ” (Debregeas & Hebrail, 1998) developed by the EDF’s R&D Division.

Debrégeas, A., Hébrail G. (1998). Interactive Interpretation of Kohonen Maps Applied To Curves, In KDD’98, Proceedings of the 4th International Conference on Knowledge Discovery and Data Mining, New-York, pp.179-183, AAAI Press.

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References

1) BRASIL, Ministério das Minas e Energia, DNAEE, Eletrobrás, Empresas Concessionárias de Energia Elétrica, Nova Tarifa de Energia Elétrica: metodologia e aplicação, DNAEE, Brasília,1985.

2) Boiteux, M. La tarification dês demandes en pointe: application de la théorie de la vente au coût marginal, Revue générale d l’electricité, 1949.

3) Bouroche, J.M, Saporta, G., L’analyse dês données, PUF, 9e édition, Paris, 2005.

4) Debrégeas, A., Hébrail G. (1998). Interactive Interpretation of Kohonen Maps Applied To Curves, In KDD’98, Proceedings of the 4th InternationalConference on Knowledge Discovery and Data Mining, New-York, pp.179-183, AAAI Press.

5) Diday, E. Une nouvelle méthode em classification automatique et reconnaissance des formes. La méthode des nuées dynamiques. Revue de statistiqueAppliquée, 1971, vol. XIV nº 2. Institut de Statistique. Université de Paris.

6) Hébrail, G. Practical data mining in a large utility company, Revue Questiio (Quaderns d’Estadistica i Investigacio Operativa), Vol.25, N.3, pp.509-520, 2001.

7) Lebart, L.; Piron, M.; Morineau, A. Statistique exploratoire multidimensionnelle, 3e édition, DUNOD, Paris, 2000.

8) Jain, J.S.R., Sun C.T., Mizutani, E. Neuro-Fuzzy and Soft Computing: a computational approach to learning and machine intelligence, Prentice Hall Inc, 1997.

9) Molliere, M. Um ensemble de modules de classification automatique et de modules explicatifs associes, Note EDF, Direction des etudes et Recherchesnº HI 2818/02, 1978.

10) Pessanha, J.F.M., Huang, J.L.C., Pereira, L.A.C., Passos Júnior, R., Castellani, V.L.O. Metodologia e sistema computacional para cálculo das tarifas de uso dos sistemas de distribui»cão, XXXVI SBPO, São João del Rey - MG,2004.

11) Pessanha, J.F.M., Castellani, V.L.O., Araújo, A.L.A. Uma nova ferramenta computacional para construção de tipologias de curva de carga, X SEPOPE, Florianópolis - SC,2006.

12) Pessanha, J.F.M., Laurencel, L.C., Souza, R.C. Kohonen Map to build load curve types, XXXVI SBPO, São João Del Rey, Brasil, 2004.

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José Francisco Moreira José Francisco Moreira PessanhaPessanha (([email protected]@cepel.br))

Luiz da Costa Luiz da Costa LaurencelLaurencel ([email protected])([email protected])

Clustering Electric Load Curves: The Brazilian Experience · José Francisco Moreira Pessanha...

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