Neurofuzzy system for short term Electric Load forecasting

JOURNAL OF COMPUTER SCIENCE AND ENGINEERING, VOLUME 15, ISSUE 2, OCTOBER 2012

© 2012 JCSE www.Journalcse.co.uk

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Neurofuzzy system for short term Electric Load forecasting

Oyedoja, kayode. O., Olanloye, D. Odunayo., and Obiyemi, Obiseye. O

Abstract

Load forecasting models are used to predict the load consumption demand in order to increase or decrease

the power generated and thus minimize the operating costs of producing electricity. Besides conventional

classical models, models based on artificial intelligence have been proposed in the literature. This study

presents a short term electric load forecasting model using an adaptive neurofuzzy inference system

(ANFIS). The input-output pairs used are historical electricity load measure on hourly bases for a week

period during various seasons of the year. Results and forecasting performance obtained revealed the

effectiveness of the proposed approach and shows that it is possible to build a high accuracy model with

less historical data using a hybrid artificial intelligence network that integrates neural network and fuzzy

logic.

Keywords: Short term load forecasting, ANFIS, Matlab, neural network, fuzzy logic

Oyedoja, K.O is with the Technical Education Department,

Emmanuel Alayande College of Education, Oyo,

Oyo state, Nigeria.

Olanloye, D.O is with the Department of Computer Science,

Emmanuel Alayande College of Education, Oyo, Oyo state,

Nigeria.

Obiyemi, O.O is with the Electrical/Electronic Engineering Department, Osun State University, Osogbo, Nigeria.

1. INTRODUCTION

Load forecasting is a central and integral process

in the planning and operation of electric utilities.

It involves the accurate prediction of both the

magnitudes and geographical locations of

electric load over the different periods (usually

hours) of the planning horizon. The basic

quantity of interest in load forecasting is

typically the hourly total system load,

forecasting load is also concerned with the

prediction of hourly, daily, weekly and

monthlyvalues ofthe system load, peak system

load and the system energy[1]. Load forecasting

can also be classified in terms of the planning

horizon’s duration [2] up to 1 day for short term

load forecasting (STLF), 1 day to 1 year for

medium term load forecasting (MTLF), and 1-

10years for long term load forecasting (LTLF).

Accurate load forecasting holds a great saving

potential for electric utility corporations.

Savings are realized when load forecasting is

used to control operations and decisions such as

dispatch, unit commitment, fuel allocation and

off line network analysis [3]. The accuracy of

load forecasts has a significant effect on power

system operations, as economy of operations and

control of power systems maybe quite sensitive

to forecasting errors. Load forecasting resulted

in increase positive and negative operating cost

errors [4].



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Based on their capabilities to approximate the

non linear continuous functions, to identify

complex systems, recognize and solving

optimization tasks e.t.c, neutral network, fuzzy

logic and neurofuzzy approaches have been

successfully applied in several scientific and

engineering fields. In power system planning

however, several model based on neutral

network have been proposed for short term

electric load forecasting, they enhanced their

ability to learn and construct a highly non linear

mapping throughout a set of input-output data

pair [5,6]. The work of [7] focused on the

application of non linear system identification

technique for short term load forecasting. They

used fixed size least squares support vector

machines for non linear estimation in WARX

model.

Artificial neutral network model for short term

load forecasting provide errors when there are

speedy fluctuations in load and temperature. To

overcome difficulties and to have a good model,

fuzzy adaptive inference and similarity which

takes into account the effect of humidity and

temperature have been employed [8]. In this

approach, fuzzy adaptive inference is employed

to adjust the load curves on selected similar days

and results obtained show a good prediction with

a small mean absolute percentage error (MAPE).

Hybrid intelligent system takes advantage of

neutral networks and fuzzy logic have been used

to forecast medium and long term energy

demand of a complicated electrical system [9].

With the proposed approach, the authors try to

search recurrent relationships in historical data

that allows the prediction of energy demand for

certain number of years. This paper considers in

particular, the application of intelligent system

to the modeling and forecasting of short term

load,with reference to hourly, weekly and annual

load data. With the emergence of new de-

regulated electricity markets, forecasting of

electricity unit price has also become an

important application for intelligent system [10].

Though price forecasting is not the focus of this

paper, the study is however aims to model and

forecast short term load using adaptive

neurofuzzy inference system in Matlab

environment.

This paper is organized in three parts. Part 2

presents a brief study of manual, statistical and

artificial intelligence approaches used for load

forecasting. Adaptive Neurofuzzy Inference

System [ANFIS] structure is presented in part 3.

Results of proposed model structure for load

forecasting of weekly load consumption and

discussion are shown in part 4 followed by the

conclusion of the research.

2.0 APPROACHES TO LOAD

FORECASTING

There are three major approaches to load

forecasting, these include manual, statistical and

artificial intelligence.

2.1 MANUAL APPROACH

This is the approach in which the operator uses

his or her experience and intuition to obtain a

good guess of the load demand. This approach is

inefficient, non effective and time taking; it is

prone to too much error. These limitations

render this method not appropriate for load

forecasting.

2.2 STATISTICAL APPROACH

This is the approach that depends largely on

historical data of electric load consumption. This

approach usually requires a mathematical model

that represents load as function of different

factors such as time of the day, weather and

customer class. It involves the use of historical

data and produces instant result. Statistical

packages are readily available, although

expensive. The historical data used by this

approach may not always be available especially

in the developing countries. Load behavior

experiences sudden change which statistical

method cannot always cope with. Therefore, this

approach is not most appropriate for use in

STELF. Statistical approach includes multiple

linear regression (MPL), adaptive models,

general exponential smoothing, stochastic time

series and state space methods.

2.3 ARTIFICIAL INTELLIGENCE (AI)

APPROACH



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Artificial intelligence approach tends to be

flexible and can handle complexity and non

linearity. In this paper, this approach is

subdivided into four major parts. AI approach

includes the expert system, neural network,

genetic algorithm and fuzzy logic.

2.3.1 EXPERT SYSTEM

These methods incorporate rules and procedures

used by experts. Expert systems are heuristic

models, which can usually take into account

quantitative and qualitative factors in software

which will then automatically be able to predict

without human assistance. Several techniques

were proposed since the 80s. A typical approach

is to try to emulate the reasoning of a human

operator. One possible method for creating a

human expert prediction is to search the

historical database on the day that best fits the

target day, taking account of factors that

characterize it. The values of the corresponding

load recorded to date are then taken as the basis

for forecasting [11,12,13,14]. An expert system

can be an automated version of this kind of

research process. Moreover, the expert system

can refine its results taking more explicitly,

taking into account external factors and daily

usage patterns.

2.3.2 NEURAL NETWORK

Based on learning strategies, neural network

methods for load forecasting can be classified

into two groups. The first one is a supervised

neural network that adjusts its weights according

to the error between pre-tested and desired

output. The second are methods based on

unsupervised learning algorithm. Generally,

methods based on supervised learning algorithm

like a feed forward multilayer perception are

used [15, 16].

2.3.3 GENETIC ALGORITHM

Genetic algorithms (GAs) have recently

received much attention as robust stochastic

search algorithms for various problems [17].

This class of methods is based on the

mechanism of natural selection and natural

genetics which combines the notion of survival

of the fittest, random and yet structured search

and parallel evaluation of the points in the

search space. GA accommodate all the facets of

soft computing, namely uncertainty,

imprecision, non-linearity, and robustness. GA

can be used to provide a good set of initial

weights for the Neural Network (NN), or can be

used to fully train the NN or to find the optimal

network structure [18]

2.3.4 FUZZY LOGIC

Fuzzy logic is a generalization of the usual

Boolean logic used for digital circuit design

[19]. An input under Boolean logic takes on a

truth-value of “0” or “1”. Under fuzzy logic an

input has associated with it a certain qualitative

ranges. Fuzzy logic allows one to (logically)

deduce outputs from fuzzy inputs. In this sense,

fuzzy logic is one of a number of techniques for

mapping inputs to outputs (i.e. curve fitting).

Among the advantages of fuzzy logic are the

absence of a need for a mathematical model

mapping inputs to outputs and the absence of a

need for precise (or even noise free) inputs. With

such generic conditioning rules, properly

designed fuzzy logic systems can be very robust

when used for forecasting.

3 NEUROFUZZY MODEL

Neurofuzzy modeling refers to the way of

applying various learning techniques developed

in the neural network literature to fuzzy

inference system (FIS). The basic structure of a

FIS is shown in Fig. 1 which consists of three

conceptual components: A rule base, which

contains a selection of fuzzy rules; a database

which defines the membership function (MF)

used in the fuzzy rules; and a reasoning

mechanism, which performs the inference

procedure upon the rules and a given condition

to derive a reasonable output conclusion. A FIS

implements a nonlinear mapping from its input

space to an output space. A FIS can utilize

human expertise by storing its essential

components in a rule base and database, and

perform fuzzy reasoning to infer the overall

output value. The derivation of if-then rules and

corresponding membership functions depends

heavily on the prior knowledge of the system



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under consideration. However there is no

systematic way to transform the experience of

the knowledge of human experts to the

knowledge base of a FIS. On the other hand,

artificial neural network [ANN] learning

mechanisms do not rely on human expertise.

Because of the highly parallel structure of an

ANN, it is hard to extract structured knowledge

from either the weights or the configuration of

the ANN. The weights of the ANN represent the

coefficients of the hyperplane that partitions the

input space into two regions with different

output values. If one can visualize the

hyperplane structure from the training data then

the subsequent learning procedures in an ANN

can be reduced. On the contrary, a prior

knowledge is usually obtained from the human

experts and it is most appropriate to express the

knowledge as a fuzzy if-then rules.

To a large extent, the drawbacks of these two

approaches seem to be complementary.

Therefore it is possible to consider building an

integrated system combining the concept of FIS

and ANN modeling. A common way to apply a

learning algorithm to a FIS is to represent it in a

special ANN architecture. However the

conventional ANN learning algorithms (e.g

gradient descent) cannot be applied directly to

such a system as the function of the inference

system or by not using the standard neural

leaning algorithm. In this paper a class of

adaptive networks [20] that act as a fundamental

framework for adaptive fuzzy inference system

is employed. The procedure of developing a FIS

using the framework is called adaptive

neurofuzzy inference system (ANFIS).

Fig. 1: Fuzzy inference system

3.1 Adaptive Neuro-Fuzzy

Inference System (ANFIS)

The selection of a FIS is the major concern

while designing an ANFIS to model a specific

target system. Various types of FIS are reported

in the literature [21,22,23] and each is

characterized by their consequent parameters

only. The current work used a Takagi-Sugeno-

Kang fuzzy (TSK) inference system [23] since

the conclusion of a fuzzy rule is constituted by a

weighted linear combination, and parameters

can be estimated by a simple least squares error

method.

Knowledge Base INPUT

rule base database OUTPUT

defuzzification

interface

Fuzzification

interface

decision making unit



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Fig .2 The general ANFIS architecture

Consider that the FIS has two inputs x1

and x2

and one output y. Fig.2 shows an ANFIS

architecture when each input (x1

and x2 ) is

assigned two membership functions. For the first

order TSK model, a typical rule set with two

fuzzy if-then rules can be expressed as:

121111

1211 ), ( ) ( :1

rxqxpfTHEN

BisxANDAisxIFRule

(1)

222121

2221 ), ( ) ( :2

rxqxpfTHEN

BisxANDAisxIFRule

(2)

where A1, A

2and B

1, B

2are the membership

functions for the input x1and x

2 respectively.p

1,

q1, r

1and p

2, q

2, r

2are the parameters of the

output function. The functioning of the ANFIS

is as follows [24,25]

Layer 1: Calculate Membership Value for

Premise Parameter Every node in this layer produces membership

grades of an input parameter. The node output

4 ,3for )(

or 2 ,1for )(

12,

1,

ixO

ixO

Biil

Aiil

(3)

where x1(or x

2) is the input to the node i; A

i(or B

i-

2) is a linguistic fuzzy set associated with this

node. O1,i

is the membership functions (MFs)

grade of a fuzzy set and it specifies the degree to

which the given input x1(or x

2) satisfies the

quantifier. MFs can be functions that are

Gaussian, generalized bell shaped, triangular and

trapezoidal shaped functions. A generalized bell

shaped function can be selected within this MFs

and it is described as:

bi

i

i

Ai

a

cX

X2

1

1

1

1)(

(4)

where ai, b

i, c

i are the parameter sets which

changes the shapes of the membership function

degree with maximum value equal to 1 and

minimum value equal to 0.

Layer 2: Firing Strength of Rule Every node in this layer, labeled Π, whose

output is the product of all incoming signals:

2,1 for )()( 1 1 ,2 ixxwO BiAiii (5)



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Layer 3: Normalize Firing Strength

The ith

node of this layer, labeled N, calculates

the normalized firing strength as,

2 ,1 21

_

,2

iww

WWO i

ii (6)

Layer 4: Consequent Parameters

Every node i in this layer is an adaptive node

with a node function,

)( 21

__

1,4 iiiii rxqxpWfWO (7)

where i is the normalized weighting factor of the

iwth

rule, fi is the output of the i

th

rule and pi, qi

and riare the consequent parameter sets.

Layer 5: Overall Output

The single node in this layer is a fixed node

labeled Σ, which computes the overall output as

the summation of all incoming signals:

ii

iii

iiiiW

fWfWO

_

,5 output Overall (8)

ANFIS requires a training data set of desired

input/output pair (x1, x

2…x

m, y) depicting the

target system to be modeled. ANFIS adaptively

maps the inputs (x1, x

2…x

m) to the outputs (y)

through MFs, the rule base and the related

parameters emulating the given training data set.

It starts with initial MFs, in terms of type and

number, and the rule base that can be designed

intuitively. ANFIS applies a hybrid learning

method for updating the FIS parameters. It

utilizes the gradient descent approach to fine-

tune the premise parameters that define MFs. It

applies the least-squares method to identify the

consequent parameters that define the

coefficients of each output equation in the

Sugeno-type fuzzy rule base. The training

process continues till the desired number of

training steps (epochs) or the desired root mean

square error (RMSE) between the desired and

the generated output is achieved. In addition to

the training data, the validation data are also

optionally used for checking the generalization

capability of FIS.

4.0 SHORT TERM LOAD

FORECASTING WITH ANFIS

Datasets for power load consumption measured

hourly for weeks were obtained for different

seasons of the year. Fig. 3 shows a sample plot

of a data series. The power demand shows some

fluctuation during each day, depicting that the

demand during weekends is different from

workdays. For a good prediction of load series,

building of a model must take into account the

monthly and seasonal variations as well as

various factors affecting the load such as

weather fluctuation.



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Fig.3: Load data measured hourly for a week

In order to model the weekly data series, we use

an ANFIS network with six inputs and one

output as shown in Fig. 4. The inputs are directly

extracted from the normalized weekly data

series y(t) such that:

)]([Output

)]6(),5(

)4(),3(),2(),1([Input

ty

tyty

tytytyty

Fig.4: Schematic structure of the ANFIS network



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Fig.5: Fan-out diagram of the ANFIS network

Fig. 5 shows the fan-out diagram of the ANFIS

network model. Datasets were selected and

grouped into training, testing and checking data

sets. Each data sets consists of 160 input/output

pairs. Figure 6 below show the training data sets.

Fig.6: Training data set Fig.7: Training error

The ANFIS network was trained for various

numbers of epochs, with loaded training dataset.

Fig. 7,show the error value as the training

proceeds. The error value reduces as the number

of epoches increases.The trained network is then

tested with testing data sets. The result of the

testing is shown in Fig. 8. It confirms the

acceptability of the ANFIS model as suitable for



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short term load forecasting at hourly rate. Fig. 9

shows the final input membership function

combination rules used by the trained

network.The final membership function for each

output is shown in Fig. 10. Fig. 11,shows a 3-D

surface

Fig.8: Result of test on the trained network

visualization of the membership function

combination rules between some inputs.

5.0 Conclusion.

In this sudy, we have built a short term electric

load consumption forecasting model using

Adaptive NeurofuzzyInference System

(ANFIS). The obtained model has been tested

with testing and checking data sets and the

results has proven the acceptability of the model

for hourly forecasts. The model needs to be

tested on-line and tuned to seasonal and weather

conditions.

Fig.9: Rules for the trained network.



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Fig. 10: Membership functions of the trained

network



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Fig. 11: Rule surfaces

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AUTHOR’S PROFILE

Oyedoja, K.O. received is

B.Eng., M.Eng., in Electrical

Engineering from University

of Ilorin, Nigeria, Msc in

Industrial and Production

Engineering from University

of Ibadan, Nigeria,

respectively. At present, he

is with the Department of Technical Education,

EACOED, Oyo, Oyo State, Nigeria and working

towards his Ph.D. His research interests are

Artificial intelligent, Digital signal Processing,

Neural Network, fuzzy logic, Matlab, etc.

Olanloye, D.O. received is

B.sc in Computer Science

from University of

Agriculture,Abeokuta and

Msc in Computer Science

from Nnabiazkwe

University,Akwa

respectively. At present, he is with the

Department of Computer Science, EACOED,

Oyo, Oyo State, Nigeria and working towards

his PhD. His research interests are Artificial

intelligent, Neural Network, fuzzy logic, Matlab,

etc.

Obiyemi O.O. received the

B.Eng. and M.Eng. Degrees in

Electrical Engineering from the

University of Ilorin, Nigeria in

2006 and 2010 respectively. He

joined the Department of

Electrical and Electronic Engineering, Osun

State University in 2010 and He is currently

working towards the Ph.D degree from the

Department of Electrical and Electronic

Engineering, University of Ilorin, Nigeria.

Neurofuzzy system for short term Electric Load forecasting

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