electric load forecasting: evaluating the novel hierarchical neuro-fuzzy bsp model

Electric load forecasting: evaluating the novel hierarchical

neuro-fuzzy BSP model

Marley Maria B.R. Vellascoa,*, Marco Aurelio C. Pachecoa, Luiz Sabino Ribeiro Netob,Flavio J. de Souzac

aICA—Applied Computational Intelligence Laboratory, Department of Electrical Engineering/PUC-Rio,

Rua Marques de Sao Vicente, 225 Gavea, Rio de Janeiro, RJ 22453–000, BrazilbOperador Nacional do Sistema Eletrico, ONS, Rio de Janeiro, Brazil

cDepartment of Computer and Systems Engineering/UERJ, Rio de Janeiro, Brazil

Accepted 22 May 2003

Abstract

This paper introduces a new hybrid neuro-fuzzy model, called HNFB, and evaluates its performance in short-term load forecasting. To this

end, two Brazilian electric power companies were used as case studies. A total of three intelligent forecasting systems were tested and

compared: neural networks, neuro-fuzzy, and neural/neuro-fuzzy systems. As input variables, the experiments made use of historical load

series and of additional variables that influence the load behavior, such as the temperature, the comfort index and the consumption profile.

The results reveal the potential of the proposed neuro-fuzzy and neural/neuro-fuzzy models for load forecasting, when compared with neural

networks; the mean absolute percentage errors varied between 0.44 and 1.95%, depending on the case study at hand.

q 2004 Elsevier Ltd. All rights reserved.

Keywords: Neuro-fuzzy systems; Electric load forecasting; Binary space partitioning

1. Introduction

The load forecasting problem has been approached by

several authors and a variety of forecasting techniques

have been employed. Traditionally, statistical methods,

such as exponential smoothing, linear regression, and the

Box and Jenkins method have been applied more

frequently [1]. In the past few years, computational

intelligence techniques have also been applied success-

fully to the problem. The earliest works made use of

expert systems [2,3]; subsequent studies employed artifi-

cial neural nets (NNs). Recently, load forecasting began to

be tackled by fuzzy logic systems [4,5] and at present,

some works have employed neuro-fuzzy systems for

forecasting future monthly load values [6].

The use of NNs has proved to be quite efficient for load

forecasting and has led to the publication of a large number

of papers that deal with the subject [4,7–22]. NNs are able

to perform a nonlinear mapping of the load series, which

allows the extraction of more complex relationships. These

characteristics often make it possible to obtain more

accurate forecasts.

Neuro-Fuzzy systems [23] are among the most widely

studied hybrid systems nowadays because they associate the

advantages of two very popular modeling techniques—

Neural Networks [24] and Fuzzy Logic [25]. These systems

combine the learning capability of Artificial Neural Nets

with the power of linguistic interpretation offered by Fuzzy

Systems. One of the constraints presented by conventional

neuro-fuzzy systems is that they are restricted to work with a

low number of inputs. This limitation is related to the ‘curse

of dimensionality’ generated by the large number of rules

that results from the partitioning of the input space in the

form of a grid.1

0142-0615/03/$ - see front matter q 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/S0142-0615(03)00060-7

Electrical Power and Energy Systems 26 (2004) 131–142

www.elsevier.com/locate/ijepes

* Corresponding author. Tel.: þ55-21-3114-1630; fax: þ55-21-3114-

1232.

E-mail address: [email protected] (M.M.B.R. Vellasco).

1 A neuro-fuzzy system with five input variables, each with its universe of

discourse divided into 4 fuzzy sets, may obtain a total of 1024 rules (45). If

the number of inputs is raised to 20, and the same division of the universes

of discourse are used, the result is an unmanageable total of

1,099,511,627,776 rules ð420Þ:

http://www.elsevier.com/locate/ijepes

Most existing neuro-fuzzy systems, e.g. NEFPROX,

NEFCLASS [26] and ANFIS [27], make use of grid

partitioning, which significantly limits the total number of

possible variables to be dealt with in the model.

One way to minimize this problem is to make use of

recursive partitionings, such as Quadtree [28] and Binary

Space Partitioning (BSP) [29,30], which employ recursive

processes in their generation. By preserving the indepen-

dence of the input characteristics, these types of partitioning

maintain the interpretability of the model in a fuzzy rule

format. These two types of partitioning were used to create

two new Neuro-Fuzzy models: the HNFQ—Hierarchical

Neuro-Fuzzy Quadtree Model with Quadtree partitioning

[6]; and the HNFB—Hierarchical Neuro-Fuzzy BSP Model

with BSP partitioning.

This paper describes and evaluates the performance of

the new neuro-fuzzy HNFB model for hourly load

forecasting and compares the results with those obtained

by NNs. A total of three systems were tested and

compared—NNs, the Hierarchical Neuro-Fuzzy BSP

Model, and a hybrid system, called Hybrid Neural/Neuro-

Fuzzy Model for hourly (short-term) electric load forecast-

ing 24-steps ahead (1 day). In addition to the historical load

series, the systems also made use of temperature and load

consumption profile data.

The remaining of this paper has been organized as

follows: Section 2 contains an introduction to the neuro-

fuzzy HNFB model. Section 3 presents the load forecasting

problem and describes the parameters that influence the load

curve behavior. Section 4 describes the three systems that

have been developed, their respective architectures and

input variables, and the results obtained by each system.

Section 5 presents a comparative evaluation of the

performance of these systems and finally, Section 6 presents

the conclusions.

2. Hierarchical Neuro-Fuzzy BSP (HNFB) Model

2.1. BSP partitioning

BSP partitioning divides the space successively, in a

recursive way, into two regions. An example of such

partitioning, shown in Fig. 1(a), shows that, initially, the

space was divided into two parts in the vertical direction—

input variable x2 (for example, high and low).

In this example, the upper partition was subdivided in

two new partitions A and B, according to the horizontal

direction—variable x1: The inferior partition, in turn, was

subdivided successively in the horizontal and vertical route,

generating the partitions C, D, E and F. Fig. 1(b) shows each

final partition represented by letters in the BSP tree. Interior

knots represent the existing intermediate partitions.

BSP partitioning is flexible and minimizes the problem

of the exponential growth of rules, since it only creates new

rules locally, according to the training set. Its main

advantage is that it automatically builds its own structure.

This type of partitioning is considered recursive because it

uses recursive processes in its generation, which results in

models with hierarchy in their structure and, consequently,

hierarchical rules.

2.2. Basic neuro-fuzzy BSP (Binary Space Partitioning) cell

An HNFB (Hierarchical Neuro-Fuzzy BSP) cell is

actually a mini neuro-fuzzy system that performs binary

fuzzy partitioning of the input space. It generates a precise

(crisp) output after a defuzzification process. Fig. 2(a)

shows the cell’s defuzzification process and the concatena-

tion of the consequents. In this cell, x represents the input

variable, while r and m are the membership functions that

generate the antecedents of the two fuzzy rules. Fig. 2(b)

shows the representation of this cell in a simplified manner.

The linguistic interpretation of the mapping implemented

by the HNFB cell is given by the following set of rules:

Rule 1. If x [ r then y ¼ d1:

Rule 2. If x [ m then y ¼ d2:

Each rule corresponds to one of the two partitions

which are generated by BSP partitioning. When the inputs

occur in partition 1, it is rule 1 that has a higher firing

level. When they are incident to partition 2, it is rule 2

that has a higher firing level. Each partition can in turn be

subdivided into two parts by means of another HNFB cell.

The profiles of membership functions r and m are

Fig. 1. (a) BSP partitioning; (b) BSP tree referring to BSP partitioning.

Fig. 2. (a) Interior of the neuro-fuzzy BSP cell; (b) simplified neuro-fuzzy

BSP cell.

M.M.B.R. Vellasco et al. / Electrical Power and Energy Systems 26 (2004) 131–142132

presented by Eqs. (1) and (2).

mðxÞ ¼1

1 þ expð2xÞ: ð1Þ

rðxÞ ¼ 1 2 mðxÞ ð2Þ

The (crisp) output y of an HNFB cell is given by the

weighted average shown in Eq. (3).

y ¼rðxÞ £ d1 þ mðxÞ £ d2

rðxÞ þ mðxÞ: ð3Þ

Due to the fact that the membership function r is the

complement to 1 of the membership function m; the

output equation in the HNFB cell is simplified to

y ¼ rðxÞ £ d1 þ mðxÞ £ d2 ð4Þ

or

y ¼X2

i¼1

ai £ di: ð5Þ

where the ais symbolize the firing level of the rules and

are given by a1 ¼ rðxÞ; a2 ¼ mðxÞ:

Each di of Eq. (4) corresponds to one of the three possible

consequents below:

1. A singleton. The case where di ¼ constant;

2. A linear combination of the inputs: The case where di ¼Pnk¼0 wkxk:

where xk is the system’s kth input; the wk represent the

weights of the linear combination; and n is equal to the

total number of inputs. The w0 weight, with no input,

corresponds to a constant value (bias).

3. The output of a stage of a previous level: The case where

di ¼ yj; where yj represents the output of a generic cell j;

whose value is also calculated by Eq. (5).

2.3. HNFB architecture

An HNFB model may be described as a system that is

made up of interconnected HNFB cells. Fig. 3 shows an

HNFB system along with the respective partitioning of the

input space.

In this system, the initial partitions 1 and 2 (‘BSP 0’ cell)

have been subdivided; hence, the consequents of its rules are

the outputs of subsystem 1 and subsystem 2, respectively. In

turn, the latter has, as consequents, values d11; y12; d21 and

d22; respectively. Consequent y12 is the output of the

‘BSP 12’ cell. The output of the system in Fig. 3(a) is given

by Eq. (6).

y ¼a1ða11d11 þ a12ða121d121 þ a122d122ÞÞ

þ a2ða21d21 þ a22d22Þð6Þ

2.4. Learning algorithm

The HNFB system has a training algorithm based on the

gradient descent method [24] for learning the structure of

the model and consequently, the linguistic rules. The

parameters that define the profiles of the membership

functions of the antecedents and consequents are regarded

as the fuzzy weights of the neuro-fuzzy system. Thus, the dis

and parameters a and b are the fuzzy weights of the model.

In order to prevent the system’s structure from growing

indefinitely, a parameter, named decomposition rate ðdÞ;

was created. It is a dimensionless parameter and acts as a

limiting factor for the decomposition process.

3. Load series analysis

In order to perform good load forecasting, it is important

to analyze, not only the load series, but also other variables

that affect its behavior such as temperature. In addition, other

weather variables affect the load curve, such as, for instance,

humidity, luminosity and air pressure. There are also other

types of information that are very relevant to forecasting.

The load consumption profile (residential, commercial,

industrial, etc.) is an example, since different companies,

in particular in the Brazilian electric power sector, present

different profiles which influence load consumption. Most

authors, however, only make use of temperature combined

with load history in their studies [8,11,14,15]. There are also

papers whose authors perform load forecasting using only

temperature data as input for the NNs [16].

This work has investigated and analyzed several aspects

that affect the load behavior of two Brazilian utility

companies—the CPFL—Companhia Paulista de Forca e

Luz (Sao Paulo Light and Power Company) in Campinas,

and the LIGHT Company, in Rio de Janeiro, for the period

from 1996 to 1998. The main aspects that have been

considered here are

† Day of the week: Monday, Tuesday, Wednesday, etc.

† Season of the year: winter, summer, etc.

† Consumption profile: residential, commercial, industrial,

street lighting, etc.

The Sections 3.1–3.3 present a detailed analysis of each

one of these aspects with regard to the CPFL and LIGHT

companies.Fig. 3. (a) Example of an HNFB system. (b) input space partitioning of the

HNFB system.

M.M.B.R. Vellasco et al. / Electrical Power and Energy Systems 26 (2004) 131–142 133

3.1. Day of the week influence

Typically, the electric load presents a different type of

behavior for each day of the week (Fig. 4). On weekdays,

the behavior tends to be similar, while on Saturdays and

Sundays, it is quite different. Hence, when it is used as input

for a forecasting model, the information related to the day of

the week may influence the results [8,14]. In order to avoid

informing the type of day, the data may be separated

according to the identified load profiles and a prediction

model may be used for each type found. In his study [7],

Bakirtzis employs both of these techniques: informing the

day of the week as input for a NN; and using a NN for each

day of the week. Zebulum also makes use of the same

techniques but in the latter case, he organizes the days of the

week into four groups: one group for Sundays, a second

group for Saturdays, a third group for Mondays and a fourth

and last group that encompasses Tuesdays, Wednesdays,

Thursdays and Fridays [21,22].

It may also be observed that each of the companies has a

typical curve in which maximum (peak) consumption

occurs at different times of day. For example, in the

summer, Light’s peak consumption occurs in the afternoon

between 2 and 6 p.m., whereas in the case of the CPFL,

maximum consumption is observed between 5 and 10 p.m.

One method by which to improve the performance of hourly

forecasting consists of supplying information about the hour

of the day as an additional input to the model [21]. Authors

generally provide this type of information in the form of bit

codes [8,14,18,19,21,22].

Based on the behavior of the load curves that were

analyzed, this paper adopted a separate system for each day

of the week for all the intelligent load forecasting systems

that were developed.

3.2. Season of the year influence

Another important aspect regarding the behavior of the

load curve is the seasonal character of the series. Fig. 5

shows two curves of the Light Company for the same day of

the week (Wednesday), one in summertime and the other in

wintertime. It may be noticed that the profile of the winter

Fig. 4. Daily load curves in the week from 04/01/98 to 10/01/98 (summer) (a) CPFL; (b) Light.


load curve is similar to that of other companies, such as the

CPFL, for example, and that the peak occurs between 5 and

10 p.m., as is also observed in the large majority of the

companies that comprise Brazil’s electric power system.

However, in the summer, the curve behaves in quite a

different manner and presents two peak times (2–6 and 8–

12 p.m.), neither of which coincides with the normal peak of

other companies.

The seasonal aspect of the series may be treated similarly

to the series behavior with respect to the day of the week,

that is, information on the month may be provided at the

input of the model or a separate system may be used for each

season of the year. In Brazil, since the seasons of the year do

not present significant climatic differences, only two

seasons are considered for some regions: winter—compris-

ing the months of May through September, and summer—

covering the months of November through March. April and

October are considered transitional months.

Accordingly, for the models developed in this paper with

NNs, neuro-fuzzy and neural/neuro-fuzzy systems, the data

was separated into two seasons, and has therefore, made use

of two separate systems, one for wintertime and one for

summertime. The transitional months have not been

evaluated here.

3.3. Analysis of the consumption profile and other factors

The load consumed by an electric power company may

be separated into consumption classes, such as residential,

commercial, industrial, street lighting, losses, and others.

This consumption profile is the main factor in the difference

between the load curves of these companies. Therefore, it is

important to use it as information for the load forecasting

models. The Light and the CPFL companies provided these

profiles together with their hourly load histories and made it

possible to introduce this type of information in the NNs,

neuro-fuzzy and neural/neuro-fuzzy models that have been

tested in this paper.

Other factors that also affect electric power consump-

tion are

† Climatic factors: temperature, humidity, wind, lumin-

osity, comfort index;

† Economic factors: tariff structure, industrial activity,

economic growth;

† Social factors: vacation period, sports and cultural

events.

With regard to the factors mentioned above, it should be

pointed out that the economic and social factors are difficult

to analyze due to the absence of historical follow-ups and

are seldom used in load forecasting. Climactic factors, in

turn, are used more frequently [10], especially temperature

[7,9,11,12,14,16]. The reason that temperature is used so

frequently in load forecasting is that, for this variable, there

are more historical series available, normally, on a daily

(maximum and minimum), and, in some cases, on an hourly

basis. This does not apply to the other weather variables,

which are extremely difficult to have access to historical

data, when they are present. There are studies that consider

composing a comfort index based on weather data, which

would be very useful for load forecasting. The purpose of

this comfort index is to represent the degree of physical

comfort experienced by an individual under the weather

conditions to which he/she is exposed. The literature,

however, only contains studies of this type of index for use

in the area of civil engineering and, unfortunately, the index

is not suitable for use in time series forecasting.

In this paper, the tests with weather data have only made

use of historical temperature data, given the unavailability

of other types of weather data. The data were obtained for

the Light and the CPFL service areas. The temperature time

series for Rio de Janeiro was provided by the Light

Company and contains the hourly temperature information

at the International Airport for the 1996–1998 period. For

the Campinas region, since it was not possible to obtain

hourly temperature data, the daily data (maximum and

minimum temperatures) for the 1996 to 1998 period,

supplied by the IAC—Instituto Agronomico de Campinas

(Campinas Institute of Agronomy), were used.

A detailed description of the intelligent systems based on

neural networks, neuro-fuzzy and neural/neuro-fuzzy

models that were implemented and tested for hourly load

forecasting is provided below.

4. Intelligent forecasting systems

This section presents the three systems that are proposed

in this study: Neural Networks, the Hierarchical Neuro-

Fuzzy BSP Model (HNFB) and the Neural/Hierarchical

Neuro-Fuzzy System. In the Neural/Neuro-Fuzzy System,

the output of a neural network is one of the inputs of the

hierarchical neuro-fuzzy system. The NN that is used in this

case is the same one that has been used in the first system;

however, instead of receiving the past load data, the neuro-

fuzzy system receives the forecast that has been supplied by

Fig. 5. Light company load curves in winter and summer.


the neural network. The purpose of this third system is to use

the neuro-fuzzy model to adjust, based on the temperature

data and the consumption profile, the forecast performed by

the NN.

As has been mentioned in Section 2, the systems were

designed to perform hourly forecasts (multi-step, 24-hour

ahead) for two electric power companies. The systems thus

developed were separated according to the day of the week

and into winter and summer.

The case studies were carried out with the use of

historical load data (1996–1998), historical temperature

data and the consumption profiles of the two electric power

companies. The evaluation of the results was based on two

types of metrics: the Mean Absolute Percentage Error

(MAPE) and the U-Theil.

4.1. Neural networks

4.1.1. Model architecture

The model chosen for the neural network system was the

Multi-Layer Perceptron with the Backpropagation learning

algorithm [24]. The self-correlation of the data in the series

was analyzed and it was observed that the values that

presented the highest correlation with the value to be

predicted (1 h ahead load, lk) were the values of the two

previous hours (lk21 and lk22) and the value of the load at

the same hour of the forecast one week before ðlk2168Þ:

However, neural networks were also evaluated with the use

of the load value on the previous day, at the same instant k

for which the forecast is desired. In this manner, three input

configurations related to the historical series were evalu-

ated: the first one (Topology I), used only the load on the

previous week; the second (Topology II), used only the load

of the previous day; and the third (Topology III), used both

the loads of the previous day and of the previous week.

A few approximations were necessary to perform the

hourly load forecasting based on the consumption profile. In

the case of the Light Company, the hourly load curve was

analyzed for the residential and nonresidential (industrial,

commercial, etc.) classes. However, as Light was only able

to provide the load profile according to separate consump-

tion classes for a typical winter weekday, tests for the

summer were not performed for Light’s case. Though the

load profile refers to a weekday, this same profile was used

for analyzing Light’s weekends. As for the CPFL, the

consumption profile was divided into residential and

nonresidential classes, the latter being subdivided into

industrial and commercial. Since the load profile provided

by the CPFL did not specify what type of day the profile

applied to (weekday or weekend), this same profile was used

for all the days of the week in the case of the CPFL.

Table 1 presents a summary of the inputs used in each of

the three topologies, for each company.

All neural networks made use of the sigmoidal activation

function in the hidden layer and of a linear activation

function in the neuron of the output layer.

4.1.2. Case studies

In Light’s specific case, since the consumption profile

provided by the company was for a typical winter weekday,

it was not possible to run the cases for summer, as

mentioned in Section 4.1.1. In this case, data from the

periods May 1996 to October 1996, May 1997 to October

1997 and May 1998 to June 1998 were used in the training

process, and the forecasting tests were performed for the last

seven days of the month of June 1998. Each network was

trained in two 50,000-cycle stages. The training time for

each one of the two stages was of about three hours on a

Pentium II 350 MHz.

The networks defined for the CPFL were also trained in

two 50,000-cycle stages. The training time was of about

3 12

h. The load profile provided by the company was based

Table 1

Input configuration of the three topologies evaluated

Type of input Input configuration for both companies

Light CPFL

Load Series Topology I

Load value 1 h

before, lk21

Load value 1 h

before, lk21

Load value 2 h

before, lk22

Load value 2 h

before, lk22

Load value one

week before, lk2168

Load value one

week before, lk2168

Topology II

Load value 1 h

before, lk21

Load value 1 h

before, lk21

Load value 2 h

before, lk22

Load value 2 h

before, lk22

Load value on the

previous day, lk224

Load value on the

previous day, lk224

Topology III

Load value 1 h

before, lk21

Load value 1 h

before, lk21

Load value 2 h

before, lk22

Load value 2 h

before, lk22

Load value on the

previous day, lk224

Load value on the

previous day, lk224

Load value one week

before, lk2168

Load value one

week before, lk2168

Seasonal

(all topologies)

Forecasting month

coded in 4 bit

Forecasting month

coded in 4 bit

Forecasting hour

coded in 5 bit

Forecasting hour

coded in 5 bit

Climatological

(all topologies)

Hourly temperature Maximum temperature

of the day

Minimum temperature

of the day

Consumption Profile

(all topologies)

% Residential load

consumption

% Residential load

consumption

% Nonresidential load

consumption

% Commercial load

consumption

% Industrial load

consumption


on one day in July, but since CPFL’s load curve behaves

similarly in the winter and in the summer, the same profile

was used for both seasons. For the winter network, the data

employed for training are related to the periods between

May 1996 to September 1996, May 1997 to September 1997

and May 1998 to September 1998. The forecasts were made

for the last seven days of the month of September 1998. As

for CPFL’s summer network, the training data include the

periods from January 1996 to March 1996, November 1996

to March 1997, November 1997 to March 1998 and

November 1998. Forecasts were made for the seven days

of the period between 11/16/98 and 11/22/98.

Table 2 presents a summary of all the results obtained for

the Light Company in the winter. It may be noticed that, in

general, the networks that made use of Topology II

presented the best performances.

Likewise, Table 3 presents the results obtained for the

CPFL in winter. It may be observed that Topology I

obtained a better performance if the results for each day of

the week are compared. However, Topology III obtained a

better result on the average.

For the CPFL in the summer (Table 4), it may be noticed

that there is a balance between Topology I and Topology II

with a slight advantage for Topology II. For all three cases

(Light in winter and CPFL in winter and summer), it became

clear that Topology III only presents a better performance in

a limited number of situations.

4.2. Hierarchical neuro-fuzzy systems


This section describes how the new HNFB model—

Hierarchical Neuro-Fuzzy System with Binary Space

Partitioning (BSP)—presented in Section 2 may be applied

to hourly load forecasting.

In order to facilitate the comparison between the

performance of the neuro-fuzzy system and that of

the neural networks, the same inputs of Topology I and II

Table 2

Summary of the neural network results for the Light Company in winter

Day of the week Light, winter

Topology I Topology II Topology III

50,000 cycles 100,000 cycles 50,000 cycles 100,000 cycles 50,000 cycles 100,000 cycles

MAPE (%) U-Theil MAPE (%) U-Theil MAPE (%) U-Theil MAPE (%) U-Theil MAPE (%) U-Theil MAPE (%) U-Theil

Sunday 0.97 0.2298 1.58 0.3319 2.05 0.6727 6.25 0.6805 2.34 0.8131 2.51 0.7911

Monday 3.30 0.7520 2.99 0.6902 0.83 0.2573 1.22 0.3410 1.85 0.4488 1.22 0.3410

Tuesday 3.67 1.1308 3.34 1.0159 2.13 0.5717 1.93 0.5252 1.75 0.4908 1.75 0.4852

Wednesday 2.50 0.5950 3.98 0.9190 2.76 0.9961 2.22 0.7932 3.25 1.3000 2.22 0.7932

Thursday 3.74 1.0519 3.80 1.0707 3.37 1.0648 3.10 0.9989 3.06 0.9891 3.07 0.9635

Friday 1.57 0.4527 1.30 0.3633 1.13 0.3765 1.16 0.3761 1.66 0.4844 1.36 0.3889

Saturday 2.26 0.6646 2.45 0.7030 2.01 0.5752 2.07 0.5936 4.11 0.9064 4.21 0.9830

Average 2.57 0.696 2.78 0.728 2.04 0.645 2.56 0.6155 2.57 0.7760 2.33 0.6780

Table 3

Summary of the neural network results for the CPFL in winter

Day of

the week

CPFL, winter




Sunday 2.21 0.4630 3.91 0.7825 3.02 0.6062 2.38 0.5323 2.21 0.4630 3.05 0.6969

Monday 2.24 0.5819 1.96 0.5114 3.46 0.9557 1.46 0.4440 2.05 0.4677 1.71 0.3884

Tuesday 1.58 0.4524 1.47 0.4160 1.58 0.5187 1.54 0.3993 0.96 0.2527 1.00 0.2690

Wednesday 1.86 0.4640 2.42 0.5513 0.92 0.2714 0.73 0.2037 1.86 0.4640 2.42 0.5513

Thursday 2.38 0.5880 1.65 0.4218 3.78 0.9701 2.34 0.5687 1.25 0.3048 1.65 0.4218

Friday 1.64 0.5055 1.23 0.3361 2.06 0.6376 2.38 0.6778 1.73 0.4949 1.36 0.3978

Saturday 1.06 0.2618 1.03 0.2337 2.41 0.5467 1.99 0.4513 1.06 0.2618 1.34 0.3125

Average 1.85 0.4738 1.95 0.4647 2.46 0.6437 1.83 0.4681 1.59 0.3870 1.79 0.4339


of the neural nets were employed, since these were the

topologies that presented the best results. One different

aspect that needs to be pointed out is that the HNFB model

performs a normalization of the inputs internally. Hence, it

is not necessary, as it is in the case of the neural nets, to

normalize the load, temperature and load profile values, nor

is it necessary to code the month and the time in bits. This

causes the number of inputs to be reduced from 15 to 8 in the

case of the Light Company and from 17 to 10 in the case of

the CPFL.

A separate system was adopted for each day of the week,

as in the case of the neural network models. The HNFB

systems were also separated into winter and summer. The

forecasts were also multi-step, 24-steps ahead.

The HNFB model has a series of parameters that may be

adjusted for improving the system’s performance, such as:

the parameters of sigmoid functions; the sequence in which

the inputs are presented; and the decomposition rate, among

others. The different parameters were adjusted so that a

good performance would be obtained. The results presented

in Section 4.2.2 were obtained with the best parameter

configuration.

4.2.2. Case studies

The same three cases were tested with the HNFB models,

that is, Light Company in winter, CPFL in winter and CPFL

in summer, considering the input data sets related to

Topologies I and II of the NNs.

The average training time of the neuro-fuzzy system was

15 min, using the same Pentium II 350 MHz microcomputer

that was used for the test with the neural networks. The

training and testing data are also the same that were used in

the previous case.

Table 5 presents a summary of the results obtained for

all companies. Specifically for the case of Light Company

during the winter, it may be observed that the neuro-fuzzy

system with the Topology I dataset (including information

from the previous week) presented better results. In

addition, the results for the individual days of the week all

ranged between 1 and 2%. Topology II, in turn, also

obtained a good average error (1.58%), however, individu-

ally, the errors oscillated more with variations from 0.79 to

2.98%.

For the case of the CPFL in winter, also shown in Table 5,

once again a better result was obtained with the Topology I

Table 4

Summary of the neural network results for the CPFL in summer

Day of the week CPFL, summer




Sunday 8.91 2.1518 9.74 2.3837 6.72 1.5643 7.20 1.6862 8.91 2.1518 7.67 1.8251

Monday 3.07 0.7470 2.78 0.6942 5.18 1.4616 4.81 1.3816 6.73 1.7776 4.77 1.2147

Tuesday 1.72 0.5546 1.12 0.3633 2.64 0.8520 2.31 0.7532 2.48 0.7424 2.19 0.6507

Wednesday 1.73 0.5685 1.52 0.4961 1.51 0.5159 1.20 0.4175 1.96 0.6067 2.19 0.6558

Thursday 3.36 0.9400 3.21 0.9025 1.58 0.5297 1.44 0.4748 3.36 0.9400 2.22 0.5968

Friday 2.37 0.7813 1.90 0.6357 3.98 1.2985 2.48 0.8379 3.92 1.4153 4.15 1.4852

Saturday 1.78 0.5556 1.81 0.5557 1.47 0.4762 2.12 0.6115 1.78 0.5556 2.13 0.5447

Average 3.28 0.8998 3.15 0.8616 3.30 0.9568 3.08 0.8804 4.16 1.1699 3.62 0.9961

Table 5

Results (in %) obtained with the hierarchical neuro-fuzzy system

Day of the week Light, winter CPFL, winter CPFL, summer

Topology I Topology II Topology I Topology II Topology I Topology II

Sunday 1.94 2.98 0.37 0.72 0.88 0.96

Monday 1.65 0.79 0.56 1.02 0.97 0.71

Tuesday 1.01 0.80 0.34 0.87 0.97 0.92

Wednesday 1.34 1.57 0.27 0.44 1.68 0.91

Thursday 1.34 1.48 0.35 0.89 0.68 1.22

Friday 1.88 1.36 0.45 0.86 1.65 0.86

Saturday 1.30 2.05 0.73 0.74 0.56 1.16

Average 1.49 1.58 0.44 0.79 1.06 0.96


data. The errors for each day of the week were all below 1%

(from 0.27 to 0.73%) and the average was 0.44%. As for the

Topology II data, good results were obtained on the average

(0.79%), and individually, the errors ranged between 0.44

and 1.02%.

For the CPFL in the summer, it may be observed in

Table 5 that the neuro-fuzzy system with the Topology II

data presented a better performance with an average error of

0.96%, while the one with the Topology I data had an

average error of 1.06%.

4.3. Hybrid neural/neuro-fuzzy systems


This third model aims to evaluate the neuro-fuzzy system

as a tool for correcting a forecast provided by another

model. The main idea is to explore additional variables that

affect load behavior, such as temperature and consumption

profile, which are usually not crisp, in order to improve the

prediction performance of another model. To this end, the

neural network in Section 4.1 was selected as the predictor,

and the HNFB model was used to adjust the results of this

prediction.

In this new hybrid model, the HNFB system must be

retrained using the value predicted by the neural network,

instead of the past historical load values. As was the

case of the neural networks and the neuro-fuzzy systems,

the predictions were of the multi-step, 24-steps-ahead

type.

The tests for this third system were carried out only

with the NN with the configuration called Topology I,

that is, using information of the load on the previous

week as well as the two previous values of the load.

Instead of the past load values (previous hour, two hours

before and one week before), the HNFB model receives the

load forecasted by the neural network in addition to the

other Topology I inputs.

4.3.2. Case studies

In order to compare this model with the previous ones,

the same principles were employed, i.e.

† one system for each day of the week;

† different systems for winter and summer;

† the same data history for training, and;

† the same period assigned for forecasting.

The results obtained for all three cases—Light Company

in winter, CPFL in winter and CPFL in summer—are

presented in Table 6.

5. Comparison of performance

The neural network system presented good performance

for most of the cases tested. The results obtained for the

Saturdays and Sundays are atypical since the consumption

profile used was of a weekday. However, it may be observed

that the model may obtain better results if the appropriate

profile is employed. The same observation regarding the

consumption profile applies to the case of the CPFL in the

summer because the profile provided by the company was

obtained from a day in the month of July (winter). This fact

serves to justify the high errors found, especially in the

forecasting with the CPFL for a Sunday in summer.

The best results achieved for the Light Company were

obtained with Topology II (with the use of the load of the

previous day, Table 2). The reason for this lies in this

company’s load curve profile (predominantly residential) on

account of the fact that the temperature variation of the

previous day causes the previous day’s load to have greater

influence on the load to be predicted.

For the CPFL in winter, the best results per weekday

were obtained with Topology I (Table 3). Although few

results obtained by Topology III were better than those of

the other topologies, they were significantly lower in terms

of value and consequently, the average of the results was

better (1.59%).

Though the winter load profile was used for the CPFL

forecasts in the summer, the neural networks obtained good

results for the weekdays (Table 4). This indicates that if the

company’s load profile for the summer is employed, the

networks will perform even better.

Table 6

Results obtained with the hybrid neural/neuro-fuzzy system


U-Theil MAPE (%) Number of rules U-Theil MAPE (%) Number of rules U-Theil MAPE (%) Number of rules

Monday 0.6393 2.34 54 0.1532 0.85 105 0.0845 0.50 154

Tuesday 0.5214 2.06 11 0.0932 0.56 120 0.1551 0.57 158

Wednesday 0.4629 1.81 94 0.1193 0.66 52 0.0719 0.34 126

Thursday 0.6959 2.95 3 0.3564 1.99 21 0.1252 0.59 150

Friday 0.2055 0.89 194 0.1997 1.02 70 0.1929 0.84 108

Saturday 0.6746 2.49 98 0.2709 1.33 34 0.0754 0.41 143

Sunday 0.2349 1.11 3 0.1430 1.00 71 0.2221 1.20 99

Average 0.4906 1.95 – 0.1908 1.06 – 0.1324 0.64 –


As for training the networks, the results reveal that for

both companies in winter, when the appropriate load

profiles were employed, the training with 50,000 cycles

presented better results and that only in a few cases did

training with 100,000 cycles obtain a better performance.

The proposed hierarchical neuro-fuzzy system proved to

be capable of extracting those characteristics of the problem

that were present in the data and almost always obtained the

best results for the forecasts. A comparison of its results with

those obtained by the neural networks in the case of Light

reveals that the NNs only obtained a better result on Sunday

(an atypical case) and on Friday. As for the CPFL, the results

presented by the neuro-fuzzy system were much better than

those of the NNs for winter as well as for summer.

The hybrid neural/neuro-fuzzy model was tested with

the purpose of evaluating to what extent variables such

as the temperature and the consumption profile are able

to improve load forecasting. Though the results obtained

were good, in the case of the Light Company, for

the seven days of the week, only three days presented an

improvement by comparison with the results yielded by

the pure neural network system.

For the CPFL in winter, the neural/neuro-fuzzy model

was able to improve the forecast made by the NNs in

five days of the week.

In the summer, for CPFL, the model improved the

forecasts with regard to all days of the week. This shows

that the model was able to extract the information

contained in the temperature and load profile data even

though this profile corresponded to winter.

A comparison of the three models leads to the

observation that the hierarchical neuro-fuzzy model

obtained the best results when the data employed were

suitable for the case at hand. This is the case of the Light

Table 7

Comparison of the best results (in %) obtained with neural networks, neuro-fuzzy and neural/neuro-fuzzy models


Neural

networks

Neuro

-fuzzy

Neural/neuro

-fuzzy

Neural

networks

Neuro

-fuzzy

Neural/neuro

-fuzzy

Neural

networks

Neuro

-fuzzy

Neural/neuro

-fuzzy

Sunday 0.97 1.94 1.11 2.21 0.37 1.00 6.72 0.88 1.20

Monday 0.83 0.79 2.34 1.46 0.56 0.85 2.78 0.71 0.50

Tuesday 1.75 0.80 2.06 0.96 0.34 0.56 1.12 0.92 0.57

Wednesday 2.22 1.34 1.81 0.73 0.27 0.66 1.20 0.91 0.34

Thursday 3.06 1.34 2.95 1.25 0.35 1.99 1.44 0.68 0.59

Friday 1.13 1.36 0.89 1.23 0.45 1.02 1.90 0.86 0.84

Saturday 2.01 1.30 2.49 1.03 0.73 1.33 1.47 0.56 0.41

Average 1.71 1.27 1.95 1.27 0.44 1.06 2.38 0.79 0.64

Fig. 6. Comparison of daily load curves obtained with the hierarchical neuro-fuzzy system (Topology I) with the real data (a) light winter; (b) CPFL winter; (c)

CPFL summer.


Company in winter and of the CPFL in winter (Table 7)

as well. The neural/neuro-fuzzy model, in turn, attained a

better result when the data were not the best possible for

the case in question. The CPFL in summer is an example

of this because in addition to using a load profile that

was not quite suitable, it made use of daily (maximum

and minimum) temperature data when hourly data would

have been the ideal choice. The comparative results of

the CPFL in the summer are shown in Table 7.

Fig. 6 presents examples of forecasting load curves

compared with the real load data. All three graphs illustrate

curves obtained using the Hierarchical Neuro-Fuzzy System

with Topology I. Fig. 6(a) refers to Light in winter; Fig. 6(b)

to CPFL in winter and Fig. 6(c) to CPFL in summer.

6. Conclusions

The main objective of this paper was to introduce and

evaluate the performance of the hierarchical neuro-fuzzy

BSP—HNFB model for hourly load forecasting. In order to

attain this objective, three systems were designed and

tested: a system based on simple neural networks for the

purpose of establishing a comparison with the hybrid

methods; a hierarchical neuro-fuzzy system; and a hybrid

neural/neuro-fuzzy system, whose purpose was to evaluate

whether it was possible for a neuro-fuzzy system to improve

the result provided by a neural network.

In order to design a good forecasting model, it is of the

utmost importance to analyze the historical load series

previously, since it is this analysis that provides information

for defining the architecture of the model to be employed.

This type of analysis served as a basis for defining

parameters that were important for the topology of the

model, such as a system for each day of the week and

different systems for winter and summer. Additionally, this

analysis proved the importance of considering the load

profile according to consumption class. This information

was used as input for the models and caused the systems to

present better forecasting performances. This made it

possible to employ a similar forecasting system for

companies whose load behavior was markedly different.

According to the literature, the use of weather data has

proved to be a factor that strongly affects the performance of

load forecasting systems. However, the difficulties encoun-

tered in terms of obtaining such data reveal that the

companies in the electric power sector need to become

aware of the importance of collecting this type of data and of

producing a history that is more capable of representing the

behavior of weather variables in the service areas covered

by these companies. Due to the lack of this type of

information, the models used for the two companies were

slightly different, but this does not invalidate the compari-

son of the results among themselves. On the other hand, had

the data employed been equivalent with regard to

periodicity, the comparison of the results would surely

have been more elucidative.

With regard to the models that have been employed, the

results lead to the conclusion that all three have proved to be

applicable to load forecasting. The neural networks once

more demonstrated their forecasting capability and pre-

sented a good performance in their predictions. The

disadvantage is that neural networks require a long time

for training. Other neural network models, such as Bayesian

NNs, have also been employed, with better results than the

BackPropagation algorithm for monthly load forecasting.

However, the training time was even longer [20].

Based on the results obtained, the proposed hierarchical

neuro-fuzzy model has demonstrated that a better perform-

ance can be obtained with a hybrid intelligent system, with a

much faster training time. Lastly, the neural/neuro-fuzzy

system demonstrated that it was capable of extracting

knowledge based on the data that was supplied because it

managed to obtain a significant improvement in the

forecasts made by the NNs for the CPFL in the case of

summer, which had presented the worst performance among

all the cases that were tested with the neural networks.

Based on the good results obtained, extensions to this

work should occur in basically three directions: improving

the hybrid hierarchical neuro-fuzzy model with the use of a

greater variety of weather data provided at shorter intervals;

performing very short-term load forecasting (every 10 min);

and designing a generic load forecasting model for all the

electric power companies.

The first extension involves obtaining data related to

temperature, humidity, luminosity, air pressure and, if

possible, even to a comfort index, that are to be collected in

the service areas of each company in the electric power

sector at intervals of less than 1 h.

The second extension contemplates the growing demand

for the electric power sector to obtain load forecasts at

increasingly shorter intervals with the purpose of helping the

decision-making process of those responsible for meeting the

load demand. Forecasts of this type are essential because they

ensure that the operation will be coordinated in a safer

manner. This prevents the system from becoming unstable,

and therefore, generates a qualitative improvement in the

services provided to consumers.

The third and last extension involves plans to build a

product, a model with an automatic capacity to create its

own architecture, such the HNFB model, for any company

in the electric power sector. As input, the system would use

the weather database and parameters with the characteristics

of each company, as is the case of the consumption profile,

in addition to the historical series.

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