WFB2009
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
WFB2009
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.
WFB2009
Procedure to identify typical load profiles
0 50 1000
1000
2000
3000
4000
1
0 50 100200
400
600
800
2
0 50 1000
2000
4000
6000
3
0 50 100200
400
600
800
4
0 50 1000
20
40
60
80
5
0 50 1000
1000
2000
3000
4000
6
0 50 1000
50
100
7
0 50 1000
500
1000
1500
8
0 50 1000
500
1000
1500
9
0 50 100200
400
600
800
10
0 50 1000
50
100
150
11
0 50 1000
500
1000
12
0 50 1000
500
1000
13
0 50 100200
400
600
800
14
0 50 1000
200
400
600
800
15
0 50 1000
200
400
600
800
16
0 50 1000
200
400
600
17
0 50 1000
20
40
60
18
0 5 1 0 1 5 2 0 2 50
0 . 5
1
1 . 5
2
2 . 5
3
3 . 5
0 5 1 0 1 5 2 0 2 50
0 . 2
0 . 4
0 . 6
0 . 8
1
1 . 2
1 . 4
1 . 6
1 . 8
2
0 5 1 0 1 5 2 0 2 50
0 . 5
1
1 . 5
2
2 . 5
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.
WFB2009
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.
WFB2009
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.
WFB2009
SNACC Program (1991)
““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.
WFB2009
SNACC Program (1991)
�� 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
WFB2009
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.
WFB2009
TARDIST program (1998)
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
WFB2009
TARDIST program (1998)
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
WFB2009
TARDIST program (1998)
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).
WFB2009
TARDIST program (1998)
The software shows the load curves classified in eachcluster.
SELECIONAAGRUPAMENTOS
VER 1 OU 2GRÁFICOS
OneOne clustercluster TwoTwo clustersclusters
WFB2009
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.
WFB2009
ANATIPO Program (2005)
Sample of customers or electric power transformers
CustomerCustomer codecode CustomerCustomer namenameFile File withwith loadload curve curve
measurementmeasurement
AnnualAnnualconsumptionconsumption((MWhMWh))
DataDatainputinputformform
WFB2009
load curve measurement file
(text format)
Sample points
Reading load curve measurements
ANATIPO Program (2005)
WFB2009
load curve measurement file
Saturday andSunday
measurements
workdaysmeasurements
Reading load curve measurements
ANATIPO Program (2005)
WFB2009
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
ANATIPO Program (2005)
WFB2009
Automatic selection of the representative load curves of each measurement file
0
2
4
6
8
10
12
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96
Tempo (intervalo de 15 minutos)
kW
0
2
4
6
8
10
12
14
16
Tempo (intervalo de 15 minutos)
0
2
4
6
8
10
12
Tempo (int ervalo de 15 minut os)
0
2
4
6
8
10
12
Tempo ( intervalo de 15 minutos)
0
2
4
6
8
10
12
14
Tempo ( int ervalo de 15 minut os)
0
2
4
6
8
10
12
Tempo ( intervalo de 15 minutos)
0
2
4
6
8
10
12
Tempo (inter valo de 15 minutos)
Sunday
Saturday
workdays
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
0
2
4
6
8
10
12
1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93
Tempo (Intervalo de 15 minutos)
kW
domingosábadosegunda
The three representative loadcurves for a customer: workday,
Saturday and Sunday
AutomaticAutomatic selectionselection
ANATIPO Program (2005)
ThisThis procedureprocedure is is appliedapplied automaticallyautomatically
to to eacheach loadload curve curve measurementmeasurement filefile
WFB2009
Identification of the load curves with abnormal consumptions
0
2
4
6
8
10
12
Tempo (int ervalo de 15 minut os)
0
2
4
6
8
10
12
Tempo ( intervalo de 15 minutos)
0
2
4
6
8
10
12
14
Tempo ( int ervalo de 15 minut os)
0
2
4
6
8
10
12
Tempo ( intervalo de 15 minutos)
0
2
4
6
8
10
12
Tempo (inter valo de 15 minutos)
workdays
Consumption
Consumptiondistribution
distribution(kWh)
(kWh)
medianmedian
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)
ANATIPO Program (2005)
TheseThese loadload curves curves are are notnot consideredconsideredin in thethe averageaveragecomputationcomputation
TheseThese loadload curves curves are are notnot consideredconsideredin in thethe averageaveragecomputationcomputation
WFB2009
0 5 0 1 0 00
1 0 0 0
2 0 0 0
3 0 0 0
4 0 0 0
1
0 5 0 1 0 02 0 0
4 0 0
6 0 0
8 0 0
2
0 5 0 1 0 00
2 0 0 0
4 0 0 0
6 0 0 0
3
0 5 0 1 0 02 0 0
4 0 0
6 0 0
8 0 0
4
0 5 0 1 0 00
2 0
4 0
6 0
8 0
5
0 5 0 1 0 00
1 0 0 0
2 0 0 0
3 0 0 0
4 0 0 06
0 5 0 1 0 00
5 0
1 0 0
7
0 5 0 1 0 00
5 0 0
1 0 0 0
1 5 0 0
8
0 5 0 1 0 00
5 0 0
1 0 0 0
1 5 0 0
9
0 5 0 1 0 02 0 0
4 0 0
6 0 0
8 0 0
10
0 5 0 1 0 00
5 0
1 0 0
1 5 0
11
0 5 0 1 0 00
5 0 0
1 0 0 0
12
0 5 0 1 0 00
5 0 0
1 0 0 0
13
0 5 0 1 0 02 0 0
4 0 0
6 0 0
8 0 0
14
0 5 0 1 0 00
2 0 0
4 0 0
6 0 0
8 0 0
15
0 5 0 1 0 00
2 0 0
4 0 0
6 0 0
8 0 0
16
0 5 0 1 0 00
2 0 0
4 0 0
6 0 0
17
0 5 0 1 0 00
2 0
4 0
6 0
18
Set of workdays
representativeload curves
The usercan
choiceK-Means,
Ward,or FCM
centroidscentroids
Cluster Cluster analysisanalysis
ANATIPO Program (2005)
WFB2009
User can move a load curve from one cluster to another
ANATIPO Program (2005)
WFB2009
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
∑=
−=k
jj ccBSS
1
2
2
211 1
2min jj
k
j
n
iji
mij ccncxuCS −⋅−=∑∑
= =
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
∑∑= =
−=k
j
n
iji
j
cxWSS1 1
2
ANATIPO Program (2005)
WFB2009
The main result is a worksheet with the typical load profiles
ANATIPO Program (2005)
Excel Excel worksheetworksheetreadyready to to bebe usedusedin in thethe distributiondistributiontarifftariff computationcomputation
WFB2009
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.
WFB2009
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.
WFB2009
José Francisco Moreira José Francisco Moreira PessanhaPessanha (([email protected]@cepel.br))
Luiz da Costa Luiz da Costa LaurencelLaurencel ([email protected])([email protected])