SELF-ORGANIZING MAPS FOR CLASSIFICATION OF THE

RIO DE JANEIRO STATE CITIES BASED ON ELECTRICAL

ENERGY CONSUMPTION

Luiz Biondi Neto, Pedro Henrique Gouvêa Coelho

Faculty of Engineering (FEN), State University of Rio de Janeiro (UERJ), Rio de Janeiro, RJ, 20550-900, Brazil

João Carlos Soares de Mello, Lidia Angulo Meza

Fluminense Federal University (UFF)

Keywords: Self-Organizing Maps, Classification and Energy Management.

Abstract: The purpose of the present work is to classify the 31 cities of Rio de Janeiro State in Brazil based on their

energy consumption. The point is to search new criteria to cluster the users in order to establish, in a more

homogeneous way, indices of energy quality. Moreover, it aims to bring about a framework from which it

will be possible to determine the relative efficiency among the cities of all Brazilian states. Traditionally this

classification task is carried out using a statistical technique known as K-means, in which only five variables

are considered: the size of the main network in Kilometres, the offered power, the number of users, the

average monthly consumption and the covered area. This paper uses the Kohonen Self Organizing Maps

technique applied to 21 variables, including the residential, industrial, public and rural consumptions in

order to seek a better classification.

1 INTRODUCTION

The National Electrical Power Agency, ANEEL,

seeks to establish favorable conditions in such a way

that the Brazilian electrical energy market evolves in

harmony among the agents, for the benefit of the

society. ANEEL is the government energy

regulation agency responsible for guaranteeing

electrical energy quality, determined by a specific

index, and by establishing goals for each group of

energy users. Currently this quality index is checked

by two parameters: equivalent outage duration per

consumption unit that indicates the average number

of hours in which the user has no electric energy for

a period, usually a month, and the outage equivalent

frequency per consumption unity indicating how

many times, on average, there was an outage in the

unity (residential, commerce, industry etc).

(Tanure and Carvalho, 2000) uses the K-means

technique that requires, a priori, the desired number

K of clusters.

The statistical method K_Means, evaluates

initially classes by uniformly distributing them in

space and afterwards clustering class by class in an

iterative process using the minimum distance

technique (Tou and Gonzalez, 1974). In that way,

the more clustered the database is the better will be

the classification quality. So, the database will be

considered set up when the user defined number of

iterations is reached or when a previous established

change of class criterion is achieved (Anderberg,

1973).

Energy companies suggested new criteria for

clustering energy users in the advent of the ANEEL

agency creation in 2000. (Queiroz and Borba, 2001)

suggest a variable classification including a group

involving electrical network characteristics and

another one corresponding to variables strongly

related to energy consumption. Correlated

information on that matter can be found in

(Sperandio, Coelho and Queiroz, 2003) and (Ramos,

2000).

This work presents a new approach to cluster the

Rio de Janeiro (Brazil) state cities, using Kohonen

447

Biondi Neto L., Henrique Gouvêa Coelho P., Carlos Soares de Mello J. and Angulo Meza L. (2007).

SELF-ORGANIZING MAPS FOR CLASSIFICATION OF THE RIO DE JANEIRO STATE CITIES BASED ON ELECTRICAL ENERGY CONSUMPTION.

In Proceedings of the Ninth International Conference on Enterprise Information Systems - AIDSS, pages 447-450

DOI: 10.5220/0002392504470450

 SciTePress

map unsupervised algorithms (Kohonen, 2001)

where the previous specification of the number of

clusters is not required.

Unlike the Hebbian neural networks, in Kohonen

competitive and unsupervised learning neural

networks, only one output neuron remains active and

each neuron represents a model in the data state

space. In that case, no mapping or data input

classification is known before the training (Haykin,

1999). Clusters are developed in the training period

by means of similarity criteria indicating similar

features pattern clusters.

Each input neuron receives identical sets of input

information that compete each other in order to be

the winning neuron. In other words, each neuron

focus in a different area of the input space and its

output are used to generate the input space structure

(Haykin, 1999).

The software used in this work was Matlab 7.0

including the toolbox SOM (s

elf-organizing maps)

(Kohonen, Hynninen, Kangas, Laaksonen, 1996)

developed by Helsinki University of Technology.

2 PROBLEM DESCRIPTION AND

MODELLING

The problem is to classify the cities of Rio de

Janeiro state (Brazil) in groups of cities with similar

profiles as far as electrical energy demands are

concerned. There is no previous knowledge of such

classification nor there are no restrictions regarding

the number of desired clusters.

The database used in this application comprises

91 cities of the Rio de Janeiro state. The cities are

not listed by name but will identified by numbers

from 1 to 91

For each city there is a set of 21 variables

involving:

 Monthly consumption;

 Residential consumption;

 Industrial consumption;

 Commercial consumption;

 Rural consumption;

 Public illumination consumption;

 Public services consumption;

 Public power consumption;

 Self consumption;

 Overall or total consumption.

The data were treated statistically in the beginning

so as to avoid missing values, outliers and strongly

correlated values. In the end, it was possible to

achieve a data set represented by a matrix 91X21

that is not shown in this paper for the sake of space

optimization and readability.

The matrix is then set to be the input of the

competitive SOM yielding 21 inputs regarding the

variables corresponding to the 91 investigated cities.

3 RESULTS

Thirty SOM networks having grids of different

dimensions were tested in order to check the

clustering achieved by the Kohonen maps. A

hexagonal topology was used and a learning rate

varied from 0.01 to 0.1 with unity neighbourhood.

This paper presents the results of networks with

[6X6] grids, enabling up to 36 clusters and [3X3]

grids enabling up to 9 clusters.

Figure 1 shows a configuration for a [6X6] grid.

[6 x 6]

Figure 1: [6 X 6] Grid.

The results are the following:

Grid [6 x 6]

( 27 clusters were found )

Cluster #01

(26 cities): 02-04-14-17-18-21-22-

24-26-31-36-38-45-55-57-59-61-64-65-68-75-

78-82-83-86-89

Cluster #02

(07 cities): 20-28-32-43-44-53-70

Cluster #03

(04 cities): 05-77-80-88

Cluster #04

(03 cities): 03-39-46

Cluster #05

(01 cities): 48

Cluster #06

(01 cities): 60

Cluster #07

(05 cities): 10-19-23-76-79

Cluster #08

(06 cities): 35-52-63-66-81-90

Cluster #09

(02 cities): 33-41

Cluster #11

(03 cities): 09-15-74

Cluster #13

(06 cities): 06-11-42-71-73-84

Cluster #14

(02 cities): 50-51

Cluster #15

(01 cities): 30

Cluster #16

(04 cities): 01-12-29-85

Cluster #17

(01 cities): 54

Cluster #18

(01 cities): 49

Cluster #19

(03 cities): 13-40-69

ICEIS 2007 - International Conference on Enterprise Information Systems

448

Cluster #20

(01 cities): 87

Cluster #21

(03 cities): 07-37-62

Cluster #23

(02 cities): 25-72

Cluster #24

(01 cities): 47

Cluster #25

(03 cities): 27-34-58

Cluster #26

(01 cities): 56

Cluster #28

(01 cities: 08

Cluster #32

(01 cities): 16

Cluster #34

(01 cities): 91

Cluster #36

(01 cities): 67

In this case although cluster 01 comprises 26

cities, 12 clusters were found having only one city

and 03 clusters having 02 cities, suggesting

improvements.

The U-matrix, represented in Fig. 2, shows

Euclidian distances by means of a colour coding.

Grid [3 x 3]

(08 clusters were found)

Cluster #01

(06 cities): 09-16-29-37-48-62

Cluster #02

(05 cities): 08-15-54-60-74

Cluster #03

(01 cities): 91

Cluster #04

(10 cities): 01-03-07-12-30-39-46-

56-85-87

Cluster #05

(04 cities): 25-47-49-72

Cluster #06

(01 city): 67

Cluster #07

(55 cities): 02-04-05-06-10-11-13-

14-17-18-19-20-21-22-23-24-26-28-31-32-35-

36-38-42-43-44-45-50-51-52-53-55-57-59-61-

63-64-65-66-68-69-70-71-73-75-76-78-79-81-

82-83-84-86-89-90

Cluster #08

(09 cities): 27-33-34-40-41-58-77-

80-88

In [3 x 3] grid , Clusters #01, #02, #07, #13 e #14

of grid [6 x 6] are almost joined establishing cluster

07. The clusters #03, #09 and #25 of cluster [6 x 6],

also joined yielding cluster #08 of grid [3 x 3]. The

same occurs with clusters #04, #16 e #20 of grid [6

x 6], yielding cluster #04 of grid [3 x 3].

However there are still 2 clusters with only one

city. Figure 3 shows the U-matrix for a [3 x 3] grid.

Figure 4 depicts a comparison between residential and

rural consumption.

Finally Fig. 5 shows all variables involved in the

investigated case and allows an overview of the

clustering problem.

4 CONCLUSIONS

The Kohonen neural nets constitute a very efficient

method for clustering. The results were shown by

means of graphs which indicate easily the changes in

the groups occurring during the clustering formation.

Clustering is done within a large amount of data,

characterized by several variables in which many of

0.202

9.66

19.1

U-mat rix

Figure 2: U-Matrix for a [6X6] Grid.

0.181

1.72

3.25

U-matri x

Figure 3: U-Matrix for a [3X3] Grid.

44300

2.01e+006

3.98e+006

Resi denti al

619

7930

15200

Rural

Figure 4: Residential and Rural Consumption Compa-

rison.

SELF-ORGANIZING MAPS FOR CLASSIFICATION OF THE RIO DE JANEIRO STATE CITIES BASED ON

ELECTRICAL ENERGY CONSUMPTION

449

them show similarities. The results are presented in

2D maps.

The trouble in clustering the cities of Rio de

Janeiro (67) and Volta Redonda (91) was due to the

fact that both showed energy consumption above

average, making them different from the others. As a

matter of fact, Rio de Janeiro shows large energy

consumption in all variables except rural

consumption. Volta Redonda also shows this

characteristic in less volume but significantly in the

industrial energy consumption due to its steel

industry.

Although the results given by the Kohonen neural

nets showed a great deal of homogeneity in the

clustering formation, it is expected a classification

improvement if more variables are inserted such as

the city area, number of inhabitants and some

economical variable e. g. per capita income.

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U-mat rix JAN FEB MAR APR

MAY JUN JUL AUG SEP

OCT NOV DEC RESIDENTIAL INDUSTRIAL

COMMERCIAL RURAL P. ILLUMINATION P. SERVICES P. POWER

S. CONSUMPTION TOTAL

Figure 5: Overview of the Clustering Problem.

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