short-term load forecasting using generalized regression and probabilistic neural networks in the...

M.M. Tripathi is Senior DesignEngineer in DOEACC Society

Gorakhpur Centre, Gorakhpur (UttarPradesh), India. He has also workedas Engineer-SC with the Institute for

Plasma Research in Gandhinagar.His research interests include

artificial neural networks and fuzzy-neural applications in power system

problems, application of real-timecontrol in power systems, and powersystem restructuring. He received his

B.Tech. degree from M.M.M.Engineering College, Gorakhpur, in

1994. Presently he is pursuing Ph.D.work from U.P. Technical University

in Lucknow.

K.G. Upadhyay is a faculty memberin the Department of Electrical

Engineering of M.M.M. EngineeringCollege in Gorakhpur. His research

interests include power systemsoperation and control, FACTS, and

deregulation. He received hisM.Tech. and Ph.D. degrees from IITDelhi, and U.P. Technical University

in Lucknow in 1989 and 2002,respectively.

S.N. Singh is Professor in theDepartment of Electrical

Engineering of I.I.T. Kanpur. Hisresearch interests include power

system restructuring, FACTS, powersystem optimization and control,security analysis, artificial neural

networks and fuzzy/neuralapplications in power system

problems, and transient stability.

24 1040-6190/$–see front matter # 2008 Else

Short-Term Load ForecastingUsing Generalized Regressionand Probabilistic NeuralNetworks in the ElectricityMarket

For the economic and secure operation of power systems, aprecise short-term load forecasting technique is essential.Modern load forecasting techniques – especially artificialneural network methods – are particularly attractive, asthey have the ability to handle the non-linear relationshipsbetween load, weather temperature, and the factorsaffecting them directly. A test of two different ANN modelson data from Australia’s Victoria market is promising.

M.M. Tripathi, K.G. Upadhyay and S.N. Singh

I. Introduction

Short-term load forecasting,

which plays an important role in

the economic and secure

operation of the power system,

is always a concern of power

system operators.1 Reasonably

accurate short-term load

forecasting has become a

challenging issue in the ongoing

deregulation of electricity sector

vier Inc. All rights reserved., doi:/10.1016/j.

where load demand is greatly

influenced by electricity prices

which change hourly or half-

hourly depending on the market

structure and rules. With accurate

forecasted load, on the one hand,

the market operators can operate

the system in an economical

manner; on the other hand,

utilities can optimize their

resources for better profit. Load

forecasting in a power system can

tej.2008.09.016 The Electricity Journal

http://dx.doi.org/10.1016/j.tej.2008.09.016

N

normally be segregated into three

categories:

� Short-term forecasting of up

to a few minutes ahead,

� Forecasting with a lead time

of up to a few days ahead,

� Long-term forecasting of the

power system.

Artificial neuralnetworks havebeen applied tomany areas of powersystem analysis,operation, andcontrol problems.

M any conventional

methods are available for

short-term forecasting, including

the time-of-day method,

regression methods, stochastic

time-series methods, and state-

space methods. Also available are

techniques based on artificial

intelligence (AI) such as expert

system-based methods. These

existing methods are capable of

forecasting short-term load but

suffer from several limitations.

Moreover, very few works

reported in the literature take care

of price as an input signal in

forecasting the load.

In recent years, artificial neural

networks (ANNs) have been

applied to many areas of power

system analysis, operation, and

control problems. These include

load forecasting,2 static and

dynamic security assessment,

dynamic load modeling, and

alarm processing and fault

diagnosis.3 The availability of

historical load data on the utility

databases makes this area highly

suitable for ANN implementation.

ANNs are able to learn the

relationship among past, current,

and future variables and loads

combining both time series and

regression approaches. As is the

case with the time series approach,

the ANN traces previous load

patterns and predicts (i.e.,

ovember 2008, Vol. 21, Issue 9 1040-6190/$–

extrapolates) a load pattern using

recent load data. It can also use

weather information for modeling.

The ANN is able to perform non-

linear modeling and adaptation. It

does not need assumption of any

functional relationship between

load and weather variables in

advance.

Modern load forecasting

techniques have been developed,

recently, showing encouraging

results. Among them, ANN

methods are particularly

attractive as they have the ability

to handle the non-linear

relationships between load and

the factors affecting it directly.4

ANN can perform better than

traditional methods, especially

during rapidly changing weather

conditions. Also the short time

required for their development

has made ANN-based load

forecasting models a very

attractive alternative.

T he most important input

variables, which affect load

forecasting, are weather

temperature and price, as there is

a strong correlation between them

and load. The Radial Basis

see front matter # 2008 Elsevier Inc. All rights

Function Network (RBFN) seems

to be very useful in short-term

load forecasting.5,6

In this article, two different

ANN models, the generalized

regression neural network

(GRNN) and probabilistic neural

network (PNN), have been used

for short-term load forecasting

using hour and day indicators,

weather temperature data, and

pricing signal as inputs. The

proposed approach is tested on

publicly available data of the

Victorian electricity market from

the Australian National

Electricity Market Management

Company (NEMMCO) Web site.

The results show that mean

absolute percentage error

(MAPE) in load forecasting is

reasonable; however, the results

obtained with GRNN are superior

to those using PNN.

II. Short-Term LoadForecasting Methods

The system load to be

forecasted is a random non-

stationary process composed of

thousands of individual

components. Therefore, the range

of possible approaches to the load

forecasting is wide. Some of the

most popular methods are

discussed below.

A. Time-of-day method

In the simplest form, a time-of-

day method takes the previous

week’s actual load pattern as a

model to predict the load of the

present week. Alternatively, a set

reserved., doi:/10.1016/j.tej.2008.09.016 25


26

of load patterns is stored for

typical weeks with different

weather conditions.7 These are

then heuristically combined to

create the forecast.

B. Regression method

The weaknessin the stochastic

models is in theiradaptability,

since loadbehavior can change

quite quickly.

Regression models, normally,

assume that the load can be

divided into a standard load

component and a component

linearly dependent on some

explanatory variables. The most

typical explanatory variables are

weather factors. A typical

regression model has been used by

Rasanen and Ruusunen.8 The load

is divided into a rhythm

component and a temperature-

dependent component. The

rhythm component corresponds

to the load of a certain hour in the

average temperature of the

modeling period. More

complicated model variations

have also been proposed. Some

models use earlier load values as

explanatory variables in addition

to external variables.9 Regression

methods are among the oldest

methods suggested for load

forecasting. They are quite

insensitive to occasional

disturbances in the measurements.

The easy implementation is the

strength of this method. The serial

correlation, which is typical when

regression models are used on

time series, can cause problems.

C. Stochastic time-series

methods

This is a very popular class of

dynamic forecasting models.10

1040-6190/$–see front matter # 2008 Els

There are many names

encountered in the literature for

the class, such as ARMA

(autoregressive–moving

average) models, ARIMA

(integrated autoregressive–

moving average) models, Box-

Jenkins method, and linear time-

series models. A general

treatment of the model type can

be found in Pindyck and

Rubenfeld.11 The basic principle

is that the load time series can

first be transformed into a

stationary time series (i.e.,

invariant with respect to time) by

a suitable differencing. Then the

remaining stationary series can

be filtered into white noise. The

methods assume that the

properties of the time series

remain unchanged for the period

used in model estimation, and all

disturbances are due to this

white noise component

contained in the identified

process.

T he basic ARIMA model is

not by itself suitable for

describing the load time series,

since the load series incorporates

seasonal variation. Therefore, the

evier Inc. All rights reserved., doi:/10.1016/j.

differencing with the period of

seasonal variation is required.

The model then obtained is called

a seasonal ARIMA (SARIMA)

model.

A n external input variable,

such as temperature in the

case of load time series, can also

be included in the model. Such a

variant of the ARIMA model is

called an ARIMAX model.

The ARIMA model includes

both, the seasonal variation and

external variable, and is

sometimes called a SARIMAX

model.

The stochastic time-series

models have many attractive

features. First, the theory of the

models is well known and

therefore it is easy to understand

how the forecast is composed.

The properties of the model are

easy to calculate; the estimate for

the variance of the white noise

component allows the confidence

intervals for the forecasts to be

created. The model identification

is also relatively easy.

Established methods for

diagnostic checks are available.

Moreover, the estimation of the

model parameters is quite

straightforward and the

implementation is not difficult.

The weakness in the stochastic

models is in their adaptability. In

reality, load behavior can change

quite quickly in certain parts of

the year. While in ARIMA

models the forecast for a certain

hour is in principle a function of

all earlier load values, the model

cannot adapt to the new

conditions very quickly, even if

model parameters are estimated



N

recursively. A forgetting factor

can be used to give more weight

to the most recent behavior and

thereby improve the

adaptability. Another problem is

the handling of the anomalous

load conditions. If the load

behavior is abnormal on a certain

day, this deviation from the

normal conditions will be

reflected in forecasts into the

future. A possible solution to the

problem is to replace the

abnormal load values in the load

history by the corresponding

forecast values.
One possibilityis to classify D. State-space method
neural networkmodels on thebasis of thelearningprinciple.

There exist a number of

variations of the state-space

model. Some examples can be

found in Camp and Ruiz.12 In fact,

the basic state-space model can be

converted into an ARIMA model

and vice versa, so there is no

fundamental difference between

the properties of the two model

types. According to Gross and

Galiana, a potential advantage

over ARIMA models is the

possibility to use a priori

information in parameter

estimation via Bayesian

techniques.13 It is also pointed out

that the advantages are not very

clear and more experimental

comparisons are needed.

E. Expert systems

Expert systems are heuristic

models, which are usually able to

take both quantitative and

qualitative factors into account.

Many models of this type have


been proposed since the mid-

1980s. A typical approach is to try

to imitate the reasoning of a

human operator. The idea is then

to reduce the analogical thinking

behind the intuitive forecasting to

formal steps of logic.14 A possible

method for a human expert to

create the forecast is to search in

history database for a day that

corresponds to the target day with

regard to the day type, social

factors, and weather factors. Then

the load values of this similar day

are taken as the basis for the

forecast. An expert system can

thereby be an automated version

of this kind of a search process.15

On the other hand, the expert

system can consist of a rule base

defining relationships between

external factors and daily load

shapes. Recently, a popular

approach has been used to

develop rules on the basis of

fuzzy logic.16 The heuristic

approach in arriving at solutions

makes the expert systems

attractive for system operators

where the system can provide the

user with the line of reasoning

followed by the model.17


III. Neural-Network-Based Load Forecasting

Neural networks, also known

as artificial neural networks

(ANNs), are inspired by

biological nervous systems.

ANNs are composed of many

computing elements, usually

denoted as neurons, working in

parallel. The elements are

connected by synaptic weights,

which are allowed to adapt

through a learning process.

Neural networks can be

interpreted as adaptive machines,

which can store knowledge

through the learning process. The

research in the field has a history

of many decades, but after a

diminishing interest in the 1970s,

a massive growth started in the

early 1980s. Today, neural

networks have applications, for

example, in pattern recognition,

identification, speech recognition,

vision, classification, and control

and power systems application

problems.

T here are many types of

neural network models,

which can be categorized in many

ways. One possibility is to classify

them on the basis of the learning

principle. A neural network uses

either supervised or

unsupervised learning. In

supervised learning, the network

is provided with example cases

and desired responses. The

network weights are then adapted

in order to minimize the

difference between network

outputs and desired outputs. In

unsupervised learning the

network is given only input



Figure 1: Load and Price Changes during the Day

able 1: Correlation Factor betweenoad and Historical Price

pain Australia PJM

.8993 0.8517 0.9397

28

signals, and the network weights

change through a predefined

mechanism, which usually

groups the data into clusters

of similar data. The most

common network type using

supervised learning is a feed-

forward (signal transfer) network.

The most popular of all neural

networks, the Multi-Layer

Perceptron network (MLP), is of

this type.

I nterest in using ANNs for

forecasting has led to a

tremendous surge in research

activities in the past decade. They

can achieve complicated input–

output mappings without explicit

programming and extract

relationships (both linear and

non-linear) between data sets

presented during a learning

process. ANNs are massively

parallel, so that, in principle, they

are able to respond with high

speed. Furthermore, the

redundancy of their

interconnections ensures

robustness and fault tolerance,

and they can be designed to self

adapt and learn.18 The ANN

models are used in many power

system applications, with short-

term forecasting being one of the

most typical areas. Most of the

suggested models use MLP

networks.19 MLP forecasters,

models based on unsupervised

learning, have been suggested for

load forecasting.20 The purpose of

these models can be the

classification of the days into

different day types, or choosing

the most appropriate days in the

history to be used as the basis for

the actual load forecasting.


IV. Input Selection forANN

The most important work in

building an ANN load forecasting

model is the selection of input

variables. There is no general rule

that can be followed in this

process. It depends on

engineering judgment and

experience and is carried out

almost entirely by trial and error.

However, some statistical

analysis can be very helpful in

determining which variables have

significant influence on the

system load.

The factors affecting the load

forecasting can be represented as

L ¼ fðday;weather; special;

price; randomÞ

where f(�) is a highly non-linear

function.

I n general, variables like

hour and day indicators,

weather-related inputs

(temperature), and historical

loads are used as inputs to the

neural network. Some new


variables like price can be more

important input in load

forecasting. In load forecasting

modeling, interdependence

between price and load can be the

deciding factor. This will be

reflected in pricing patterns of the

market. The price–load

relationship is neither linear nor

stationary in time but price–load

relationship may be relatively

stable over shorter periods of

time. Volatile electricity prices in

power markets are a new

phenomenon and this needs a

reliable solution. Since the

relationship between electricity

price and load is complex and

dynamic, further research is

needed to study how different

customers’ price response

characteristics and locations affect

the load forecasting. It is clear

from Figure 1 and Table 1 that

TL

S

0



N

there is a strong correlation

between load and price; hence,

price will be a major deciding

factor for load forecasting. This is

why in this analysis only price

with hour and day indicators has

been taken as input.

V. Proposed NeuralNetwork Models forLoad Forecasting

Figure 2: Generalized Regression Neural Network (GRNN)
The well-known Radial Basis
Function Network (RBFN) having

special features is used here as a

primary test in this application.

An RBFN consists of two layers, a

hidden layer with non-linear

neurons and an output layer with

linear neurons. Thus the

transformation from the input

space to the hidden unit space is

non-linear whereas the

transformation from the hidden

unit space to the output space is

linear. Two types of well-known

RBFNs, which have several merits

over other ANN models, have

been used in this work for load

forecasting.

A. Generalized Regression

Neural Network

G eneralized Regression

Neural Network (GRNN)

is a new kind of neural

network that Donald F. Specht

put forward in 1991. At present,

this neural network has found

applications in system

distinguishing, prediction, and

the like.

The architecture for the

GRNN is similar to the radial


basis network, but has a

slightly different second layer.

The first layer has as many

neurons as there are input/target

vectors. Each neuron’s weighted

input is the distance between the

input vector and its weight

vector. Each neuron’s net input is

the product of its weighted input

with its bias. Each neuron’s

output is its net input passed

through radial basis layer. The

second layer also has as many

neurons as input/target vectors.

A larger spread (distance) leads

to a large area around the input

vector where layer 1 neurons will

respond with significant outputs.

Therefore, if the spread is small

the radial basis function is

very steep so that the neuron

with the weight vector closest

to the input will have a much

larger output than other

neurons. The network will

tend to respond with the target

vector associated with the

nearest design input vector.

As the spread gets larger, the

radial basis function’s slope


gets smoother and several

neurons may respond to an

input vector. The network

then acts like it is taking a

weighted average among target

vectors whose design input

vectors are closest to the new

input vector. As the spread gets

larger, more and more neurons

contribute to the average with

the result that the network

function becomes smoother

(Figure 2).

B. Probabilistic neural

network

Probabilistic neural network is

a kind of radial basis network

suitable for classification

problems.21 The probabilistic

neural network (PNN) constitutes

an alternative approach for class

conditional density estimation. It

is an RBF-like neural network

adapted to provide output values

corresponding to the class

conditional densities. Since the

network is RBF, the components

(hidden units) are shared among



Figure 4: The ANN Model Used in this Application

Figure 3: Probabilistic Neural Network (PNN)

30

classes and each class conditional

density is evaluated using not

only the corresponding class data

points (as in the case of separate

mixtures) but also all the available

data points. Probabilistic neural

networks can be used for

classification problems. When an

input is presented, the first layer

computes distances from the

input vector to the training input

vectors, and produces a vector

whose elements indicate how

close the input is to a training

input. The second layer sums

these contributions for each class

of inputs to produce as its net

output vector of probabilities.

Finally, a complete transfer

function on the output of the

second layer picks the maximum

of these probabilities, and

produces a 1 for that

class and a zero for the other

classes.

A n example of a

probabilistic neural

network is shown in Figure 3.

It has three layers. The network

contains an input layer, which

has as many elements as there

are separable parameters needed

to describe the objects to be

classified. It has a pattern layer,

which organizes the training set


such that an individual

processing element represents

each input vector. It contains an

output layer, called the

summation layer, which has as

many processing elements as

there are classes to be

recognized. Each element in

this layer combines via

processing elements within the

pattern layer, which relate to the

same class and prepares that

category for output. The transfer

function is radial basis function

for the first layer and is

competitive function for the


second layer. Only the first layer

has biases.

VI. ANN Training: Dataand Algorithm

GRNN and PNN, which were

used for forecasting short-term

load, in this article were tested

on publicly available data from

the NEMMCO Web site to

forecast electricity prices and

loads for the Victorian electricity

market in Australia. The

Australian National Electricity

Market (NEM) is the deregulated

electricity supply industry

covering Victoria, New South

Wales, Queensland, South

Australia, and the Australian

Capital Territory. The data of

2006 is divided into several

windows where half of them

(non-consecutive ones) are used

for training and the other half is

used for testing the ANN.



Figure 5: Output Compared to Actual Load Using GRNN

N

More precisely, for each month,

the first week and the third

week are used for training,

while the second and fourth

weeks are left for testing the

ANN. Training was done for

all the data windows at the

same time; i.e., the same ANN

is trained to be used at any

time during the year. All

inputs and outputs are

normalized before training.

Cross-correlation between load

and price is found and only those

price inputs were considered

which are best correlated. The

inputs to the ANN as shown in

Figure 4 are:

� H(k) hour indicator

� D(k) day indicator

� P(k) Price at hour k

� P(k � 1/2) Price at 30 min-

utes before hour k

� P(k + 1/2) Price at 30 min-

utes after hour k

� P(k � 1) Price at 60 minutes

before hour k

� P(k � 1) Price at 60 minutes

before hour k

� T(max) Maximum tempera-

ture of the day

� T(min) Minimum tempera-

ture of the day

VII. Simulation andResults

Figure 6: Output Compared to Actual Load Using PNN

The algorithm resulted in a

very fast training due to its

special features as explained in

the previous sections and the

error was significantly reduced

to very low value. Then the

performance of the developed

ANN model for load profile


forecasting was tested using

windows of data that were not

included in the training set. The

forecasted hourly load for the

several days was estimated but

due to limited space, only two

cases are presented here which

gave more error in the


prediction. Figures 5 and 6 show

the actual and forecasted load for

Jan. 17, 2006, with GRNN and

PNN. It is clear from the results

that forecasted load patterns are

similar to the actual one. The

percentage error in load

forecasting by GRNN and PNN



Figure 7: Error in Load Forecasting Using GRNN

able 2: MAPE (%) in Case of BothRNN and PNN

MAPE (%)

ay PNN GRNN

unday 8.94 2.72

onday 9.51 2.63

uesday 2.96 2.34

ednesday 6.79 3.64

hursday 9.07 4.00

riday 2.23 1.80

aturday 3.98 2.86

32

methods is shown in Figures 7

and 8, respectively.

ANN performance is checked

with the mean absolute

percentage error (MAPE) as

Figure 8: Error in Load Forecasting Using PN


defined below:

MAPEð%Þ ¼ 1

N

XN

i¼1

LiF � Li

A

��

LiA

� 100 (2)

N


TG

D

S

M

T

W

T

F

S

tej.2008.09.016 The Electricity Journ

where LA and LF are the

actual and forecasted load,

respectively. N is the number of

hours.

T he maximum error in

load forecasting is 7.62

percent and 6.45 percent in the

GRNN and PNN models,

respectively, which can be

seen from Figures 7 and 8.

Comparison of mean absolute

percentage error (MAPE) in the

case of both GRNN and PNN is

given in Table 2. The maximum

value of MAPE is 4.0 percent in

the case of GRNN whereas it is

9.51 percent in the case of PNN

during different days of the week.

From Table 2, it can be seen that

the performance of GRNN is

better than PNN.

A comparison of different

methods used for load

forecasting in recent years has

been done as shown in Table 3.

The data has been collected

from various published

literatures.22 The market

considered in all the cases is

different. It is clear from the table

that average MAPE (avg. MAPE)

for GRNN is better than all the

methods.

al


Table 3: Comparison of MAPE (%) Using Different Methods for Load Forecasting inRecent Years

Methods Max. MAPE Min. MAPE Avg. MAPE

GRNN 3.14 0.14 1.85

PNN 11.30 4.27 8.24

MLP 3.15 0.80 2.43

Back Propagation 3.48 0.73 2.10

ANN-Fuzzy 4.28 1.00 2.00

Multi-stage ANN-STLF 6.39 2.81 4.85

SOM-SVM Hybrid 2.68 1.34 2.06

GA 2.75 0.7 2.43

LAVF 3.89 1.69 2.79

LS 11.5 3.76 7.63

Back Propagation 3.27 1.73 2.53

SVM 6.10 1.50 2.71

Dual-SVM Hybrid 3.62 1.21 2.10

ARMA 10.34 1.53 4.77

Recurrent ANN 4.10 1.39 2.08

N

VIII. Conclusion

Load forecasting in the

emerging electricity market

plays a very important role for

the economic and secure

operation of power systems.

ANN methods are particularly

attractive in the case of load

forecasting as they have the

ability to handle the non-linear

relationships between load and

the factors affecting it directly.

Volatile electricity price in power

markets is a major input for load

forecasting using ANN. In this

article, two types of neural

networks, known as generalized

regression neural network

(GRNN) and probabilistic neural

network (PNN), have been used.

The results show the

effectiveness of the proposed

model, as the forecasted load is

very close to the actual load. The

maximum error in load


forecasting is 7.62 percent and

6.45 percent in the GRNN and

PNN models, respectively,

whereas the maximum value of

MAPE is 4.0 percent in the case

of GRNN and 9.51 percent in the

case of PNN during different

days of the week. It is also clear

from the comparison of all other

methods used for load

forecasting in recent years that

avg. MAPE for GRNN is 1.85

percent, which is better than all

other methods.&

Endnotes:

1. G. Gross and F.D. Galiana, Short-Term Forecasting, Proceedings of IEEE,75(12), 1987, at 1558–73.

2. D.C. Park, M.A. El-Sharakawi andRi Marks II, Electric Load ForecastingUsing Artificial Neural Networks, IEEETRANS. POWER SYS., 6(2), 1991, at 442–449.

3. N. Kandil, V.K. Sood, K. Khorasaniand R.V. Patel, Fault Identification in


an AC–DC Transmission SystemUsing Neural Networks, IEEE TRANS.POWER SYS., 7(2), 1992, at 812–9.

4. Nahil Kandil, R. Wamkeue, M.Saad and S. Georges, An EfficientApproach for Short-Term LoadForecasting Using Artificial NeuralNetworks, J. ELEC. POWER & ENERGY

SYS., 28 (2006): 525-530.

5. D.K. Ranaweera, N.F. Hubele andA.D. Papalexopoulos, Application ofRadial Basis Function Neural NetworkModel for Short Term LoadForecasting, IEE PROC. GENERATION,TRANSMISSION & DISTRIBUTION, Vol. 142,No. 1, Jan. 1995.

6. C. Constantinopoulos and A. Likas,An Incremental Training Method for theProbabilistic RBF Network, IEEE TRANS.ON NEURAL NETWORKS, Vol. 17, No. 4,July 2006.

7. Gross and Galiana, supra note 1.

8. M Rasanen and J Ruusunen,Verkoston Tilan Seurantamittauksillaja Kuormitusmalleilla, ResearchReport B17, Systems AnalysisLaboratory, Helsinki Univ. ofTechnology (in Finnish).

9. Id.

10. M.T. Hagan and S.M. Behr, TheTime Series Approach to Short Term LoadForecasting, IEEE TRANS. ON POWER SYS.,Vol. PWRS-2, No. 3, Aug. 1987, at785-791.

11. R.S. PINDYCK AND D.L. RUBINFELD,

ECONOMETRIC MODELS AND ECONOMIC

FORECASTS (Singapore: McGraw-Hill,1981).

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34

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22. These include P. Mandal, T.Senjyu, N. Urasaki and T. Funabashi,A Neural Network Based Several-Hour-Ahead Electric Load Forecasting UsingSimilar Days Approach, ELEC. POWER &ENERGY SYS. 28 (2006) at 373; P. Mandal,T. Senjyu and T. Funabashi, NeuralNetworks Approach to Forecast SeveralHour Ahead Electricity Prices and Loadsin a Deregulated Market, ENERGY

CONVERSION & MGMT. 47 (2006) at 2128–2142; P.K. Dash, A.C. Liew andS.Rahman, Fuzzy Neural Network andFuzzy Expert System for Loads

the emerging electricity market plays a very i


Forecasting, 114 IEEE PROCEEDINGS –GENERATION, TRANSMISSION &DISTRIBUTION, Vol. 143, No. 1, Jan. 1996;K. Methaprayoon, W.J. Lee, S.Rasmiddatta, J. Liao and R. Ross,Multi-Stage Artificial Neural NetworkShort-Term Load Forecasting Engine withFront-End Weather Forecast, 1-4244-0336-7/2006 IEEE; S. Fan and L. Chen,Short-Term Load Forecasting Based on anAdaptive Hybrid Method, 392 IEEETRANSACTIONS POWER SYS., Vol. 21, No.1, Feb. 2006; K.M. EL-Naggar and K.A.Al-Rumaih, Electric Load ForecastingUsing Genetic Based Algorithm, OptimalFilter Estimator and Least Error SquaresTechnique: Comparative Study,PROCEEDINGS OF WORLD ACAD. OF SCI.,ENG’G. & TECH., Vol. 6, June 2005; G.A.Adepoju, S.O.A. Ogunjuyigbe andK.O. Alawode, Application of NeuralNetwork to Load Forecasting in NigerianElectrical Power System, PACIFIC J. OF

SCI. & TECH. 8(1) 2007, at 68-72; L. Ao,Y. Wang, Q. Zhang, Application of aHybrid Model on Short-Term LoadForecasting Based on Support VectorMachines (SVM), NEW ZEALAND J.AGRICULTURAL RES. 2007, Vol. 50, at567–572; and A.K. Topalli, I. Erkmenand I. Topalli, Intelligent Short-TermLoad Forecasting in Turkey, ELEC.POWER & ENERGY SYS. 28 (2006),at 437–447.

mportant role.



short-term load forecasting using generalized regression and probabilistic neural networks in the...

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