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Electrical Short-term loadforecasting Using Fuzzy logic

Project ReportSubmitted in partial fulfillment of the requirements for the award

of KVPY.

ByCharan pratap singh

Under the supervision ofDr. Sonali Bhatnagar

Deptt. Of Physics and Comp. Sc.

Faculty of ScienceDEI, Dayalbagh Agra-5

Session 2010

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INDEX

CHAPTER 1 INTRODUCTION

1.1 Introduction

1.2 Literature review

1.2.1 Regression Methods

1.2.2 Time series

1.2.3 Expert system

1.2.4 Fuzzy logic

1.2.5 Neural network

1.2.6 Hybrid fuzzy neural approach

1.3 Important factors for load forecasting

1.4 Type of load forecast

CHAPTER 2 SHORT TERM LOAD FORECASTING

2.1 Introductions

2.2 Classifications of short term load forecasting methods

2.2.1 Similar day approach

2.2.2 Regression methods

2.2.3 Time Series

CHAPTER 3 LOAD FORECASTING TECHNIQUES

3.1 Short term load forecasting techniques

3.1.1 Neural Network

3.1.2 Expert System

3.1.3 Fuzzy Logic

3.1.4 Support Vector Machines

CHAPTER 4 SHORT TERM ELECTRIC LOAD FORECASTING

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USING FUZZY LOGIC

4.1 Fuzzy logic technique

4.2 Historical data and key factors

4.3 Fuzzyfication

4.4 Membership functions

4.5 Fuzzy Rule Base

4.6 Results

CHAPTER 5 CONCLUSIONS

REFERENCES

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CERTIFICATE

I hereby to inform you that the PROJECT REPORT for the KISHORE VAIGYANIK

PROTSAHAN YOJANA 2010 titled Electrical Short-Term load forecasting using

fuzzy logic projected by Charan Pratap singh has been carried out under my supervisiontowards partial fulfillment of the requirements for the award of KISHORE VAIGYANIKPROTSAHAN YOJANA 2010

Further to the best of my knowledge, the matter embodied in this work has not been

submitted for the award of any degree.

Dr. Sonali Bhatnagar

Deptt. Of Physics and Comp. Science

Faculty of Science, D.E.I., Dayalbagh

Agra, (U.P.)

Acknowledgement

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Knowledge is an infinite sphere of which the center is everywhere and circumference

nowhere.

Any small or big task cannot be accomplished without the help of connoisseurs.

I express my deepest sense of gratitude to the Most Revered, Chairman, Advisory Committee

of education, Dayalbagh for His guidance provided to us from time to time.

I have no words to express my deep sense of gratefulness and gratitude to the Dr. Sonali

Bhatnagar, Department of physics and Computer Science, Faculty of Science, D.E.I.,

without whose sustained motivation and guidance, this project would not have been

accomplished successfully.

Dayalbagh Charan Pratap Singh

June-2010 B.Sc.

ABSTRACT

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Today, its the need of developed and developing countries to consume electricity more

efficiently. Though developed countries do not want to waste electricity and developing

countries cannot waste electricity. Hence, the wise use of electricity is the need of hour. This

leads to the concept Load Forecasting. The short term load forecasting on daily basis.

Though this can be extended to hourly or half- hourly or real time load forecasting. Load

forecasting is an important component for power system energy management system.

Precise load forecasting helps the electric utility to make unit commitment decisions,

reduce spinning reserve capacity and schedule device maintenance plan properly. Besides

playing a key role in reducing the generation cost, it is also essential to the reliability of

power systems. The system operators use the load forecasting result as a basis of off-line

network analysis to determine if the system might be vulnerable. If so, corrective actions

should be prepared, such as load shedding, power purchases and bringing peaking units on

line. Load forecasting plays an important role in power system planning, operation and

control. Forecasting means estimating active loads at various load buses ahead of actual load

occurrence. Planning and operational applications of load forecasting requires a certain lead

time also called forecasting intervals. On the basis of lead time, load forecasts can be

divided into four categories: very short-term forecasts, short-term forecasts, medium-term

forecasts and long-term forecasts. The forecasts for different time horizons are important for

different operations within a utility company. Since in power systems the next days power

generation must be scheduled every day, day-ahead short-term load forecasting (STLF) is

a necessary daily task for power dispatch. Its accuracy affects the economic operation and

reliability of the system greatly. Under prediction of STLF leads to insufficient reserve

capacity preparation and, in turn, increases the operating cost by using expensive peaking

units. On the other hand, over prediction of STLF leads to the unnecessarily large reserve

capacity, which is also related to high operating cost.

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CHAPTER 1

INTRODUCTION

1.1Introduction

Accurate models for electric power load forecasting are essential to the operation and planning

of a utility company. Load forecasting helps an electric utility to make important decisions

including decisions on purchasing and generating electric power, load switching, and

infrastructure development. Load forecasts are extremely important for energy suppliers, ISOs,

financial institutions, and other participants in electric energy generation, transmission,

distribution, and markets. Load forecasts can be divided into three categories: short-term

forecasts which are usually from one hour to one month, medium forecasts which are usually

from a month to a year, and long-term forecasts which are longer than a year. The forecasts for

different time horizons are important for different operations within a utility company. The

natures of these forecasts are different as well. For example, for a particular region, it is

possible to predict the next day load with an accuracy of approximately 1-3%. However, it is

impossible to predict the next year peak load with the similar accuracy since accurate long-

term weather forecasts are not available. For the next year peak forecast, it is possible to

provide the probability distribution of the load based on historical weather observations. It is

also possible, according to the industry practice, to predict the so-called weather normalized

load, which would take place for average annual peak weather conditions or worse than

average peak weather conditions for a given area. Weather normalized load is the load

calculated for the so-called normal weather conditions which are the average of the weather

characteristics for the peak historical loads over a certain period of time. The duration of this

period varies from one utility to another. Most companies take the last 25-30 years of data.

Load forecasting has always been important for planning and operational decision conductedby utility companies. However, with the deregulation of the energy industries, load forecasting

is even more important. With supply and demand fluctuating and the changes of weather

conditions and energy prices increasing by a factor of ten or more during peak situations, load

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forecasting is vitally important for utilities. Short-term load forecasting can help to estimate

load flows and to make decisions that can prevent overloading. Timely implementations of

such decisions lead to the improvement of network reliability and to the reduced occurrences

of equipment failures and blackouts. Load forecasting is also important for contract

evaluations and evaluations of various sophisticated financial products on energy pricing

offered by the market. In the deregulated economy, decisions on capital expenditures based on

long-term forecasting are also more important than in a non-deregulated economy when rate

increases could be justified by capital expenditure projects. Most forecasting methods use

statistical techniques or artificial intelligence algorithms such as regression, neural networks,

fuzzy logic, and expert systems. Two of the methods, so-called end-use and econometric

approach are broadly used for medium- and long-term forecasting. A variety of methods,

which include the so-called similar day approach, various regression models, time series,

neural networks, statistical learning algorithms, fuzzy logic, and expert systems, have been

developed for short-term forecasting. As we see, a large variety of mathematical methods and

ideas have been used for load forecasting. The development and improvements of appropriate

mathematical tools will lead to the development of more accurate load forecasting techniques.

The accuracy of load forecasting depends not only on the load forecasting techniques, but also

on the accuracy of forecasted weather scenarios. Weather forecasting is an important topic

which is outside of the scope of this chapter.

1.2 Literature Review

The literature on the load forecasting and methods is much diversified and it is not possible to

complement them in the limited time span. Therefore, in this section, the literature on

Short term Load Forecasting is briefly revived. This literature review offers the

background for the thesis work. The published literature has been classified into six main

categories:

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1.2.1 Regression Methods

Engle et al. [1] presented several regression models for the next day load forecasting.

Their models incorporate deterministic influences such as holidays, stochastic influences

such as average loads, and exogenous influences such as weather. [2], [3], [4] and [5]

describe other applications of regression models applied to load forecasting.

1.2.2 Time Series

Time series method is based upon the assumption that the data has some internal structure such

as autocorrelation, trend or seasonal variation. Most commonly used classical time series

methods are ARMA (autoregressive moving average), ARIMA (autoregressive integrated

moving average), ARMAX (autoregressive moving average with exogenous variables), and

ARIMAX (autoregressive integrated moving average with exogenous variables). Fan

and McDonald [6] and Cho et al. [7] described implementations of ARIMAX models

for load forecasting. Fogel et al. [8] used an evolutionary programming (EP) approach to

identify the ARMAX model parameters for one day to one week ahead hourly-load-

demand-forecasting. The evolutionary programming is a method for simulating

evolution and constitutes a stochastic optimization algorithm. Yang and Huang [9]

proposed a fuzzy autoregressive moving average with exogenous input variables(FARMAX) for one day ahead hourly load forecasting.

1.2.3 Expert Systems

Ho et al. [10] proposed a knowledge-based expert system for the short-term load

forecasting of the Taiwan power system. Operators knowledge and the hourly

observation of system load over the past five years are employed to establish eleven day-

types. Weather parameters were also considered. Rahman and Hazim [11] developed a site-

independent technique for short-term load forecasting. Knowledge about the load and the

factors affecting it is extracted and represented in a parameterized rule base. This rule-

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based system is complemented by a parameter database that varies from site to site. The

technique is tested in different sites in the United States with low forecasting errors. The load

model, the rules and the parameters presented in the paper have been designed using no

specific knowledge about any particular site. Results can be improved if operators at a

particular site are consulted.

1.2.4 Fuzzy Logic

One of the advantages of the use of fuzzy logic is the absence of a need for a mathematical

model mapping inputs to outputs and the absence of a need for precise inputs. With such

generic conditioning rules, properly designed fuzzy logic systems can be very robust when

used for forecasting. Of course in many situations an exact output is needed. To produce such

precise outputs, defuzzification can be used after the logical processing of fuzzy inputs. [12],

[13] and [14] describe applications of fuzzy logic to load forecasting.

1.2.5 Neural Networks

The interest in applying neural networks to electric load forecasting began in 1990.

Artificial Neural Networks have parallel and distributed processing structures. They can be

thought of as a set of computing arrays consisting of series of repetitive uniform

processors placed on a grid. Learning is achieved by changing the interconnection

between the processors [15]. To date, there exist many types of ANNs which are

characterized by their topology and learning rules. As for the Short term TLF problem, the

BP network is the most widely used one. With the ability to approximate any continuous

nonlinear function, the BP network has extraordinary mapping (forecasting) Abilities. The

BP network is a kind of multilayer feed forward network, and the transfer function within the

network is usually a nonlinear function such as the sigmoid function. Neural Networks are

widely used for load forecasting, Fault diagnosis/Fault location, Economic load dispatch and

Security assessment etc. in the field of power systems [16]. The topology of BP network can

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be of 3-layers or 4-layers, the transfer function can be linear, nonlinear or a combination of

both. Also, the network can be either fully connected or non-fully connected. The BP network

structure is problem dependent, and a structure that is suitable for a given power system is not

necessarily suitable for another. The typical BP network structure for Short Term Load

Forecasting is a three-layer network, with the nonlinear sigmoid function as the transfer

function [17]-[18]. In addition to the typical sigmoid function, a linear transfer function from

the input layer directly to the output layer was proposed in [19] to account for linear

components of the load. Because fully connected BP networks need more training time a

non-fully connected BP model is proposed in [20], [21]. The reported results show that

although a fully connected ANN is able to capture the load characteristics, a non-fully

connected ANN is more adaptive to respond to temperature changes. Moreover, [21]

presents a new approach to STLF which combines several sub-ANNs together to give

better forecasting results. A recurrent high order neural network (RHONN) is also proposed

[22]. Due to its dynamic nature, the RHONN forecasting model is able to adapt quickly to

changing conditions such as important load variations or changes of the daily load pattern.

A 3-layer ANN with suitable dimension is sufficient to approximate any continuous non-

linear function [28]. The 4-layer structure is implemented and a load forecaster using this

structure was reported [23], [15], [25], [26].The BP network is a kind of array which can

realize nonlinear mapping from the inputs to the outputs. Therefore, the selection of input

variables of a load forecasting network is of great importance. Broadly, there are two

selection methods. One is based on experience [23], [15], [27], [19] and the other is based

on statistical analysis such as the ARIMA [21] and correlation analysis [25]. The input

variables are largely determined on engineering judgment and experience. In all, the input

variables can be classified into 6 main classes:

1. Historical loads [15-30],

2. Historical and future (forecasted) temperatures [15-27],3. Historical and future (forecasted) relative humidity [30]

4. Hour of day index [15],[21],[25],[31],

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5. Day of week index [15],[21], [25],[31],

6. Wind-speed and sky cover [20], [31],

7. Rainfall (Wet or dry day) [31].

The BP algorithm is widely used in STLF and has some good features such as, its ability to

easily accommodate weather variables, and its implicit expressions relating inputs and

outputs. However, the raining process is time consuming training process and it converges to

local minima. The research work has attributed the premature saturation as the major

reasons for these drawbacks [32]. A method to prevent premature saturation by the

appropriate selection of the initial weights is proposed in [33]. The BP algorithm with

momentum (BPM) converges much faster than the conventional BP algorithm [34]. In [27],

[35], it is shown that the use of the BPM in STLF significantly improves the training

process. The authors of [18] present extensive studies on the effects of factors such as the

learning step, the momentum factor to BPM. They proposed a learning algorithm for

adaptive training of neural networks. A learning algorithm motivated by the principle of

forced dynamic for the total error function is proposed in [36]. The rate of change of the

network weights is chosen such that the error function to be minimized is forced to decay in

a certain mode. An approach by updating the weights in direct proportion to total error is

proposed in [35]. With this, the periods of stagnation are much shorter and the possibility

of trapping in local minima is greatly reduced. Determination of the optimal number of

hidden neurons is a crucial issue. If it is too small, the network can not possess sufficient

information, and thus yields inaccurate forecasting results. On the other hand, if it is too large,

the training process will be very long [15]. The work in [32] discusses the number of

hidden neurons in binary value cases. In order to make the mapping between the output

value and input pattern for Iarbitrary learning patterns, the necessary and sufficient number

of hidden neurons is ( I-1).[37] highlights that a multilayer perception with ( k-1) hidden

neurons can realize arbitrary functions defined on a k-element set. Up to our knowledge, there

is no absolute criteria to determine the exact number of hidden neurons that will lead to an

optimal solution. Different numbers of hidden neurons are used in [12], [15], [20],

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[21].ANNs can only perform what they were trained to do. As for the case of STLF, the

selection of the training set is a crucial one. The criteria for selecting the training set is that

the characteristics of all the training pairs in the training set must be similar to those of the

day to be forecasted. To obtain good forecasting results, day type information must be taken

into account. There are two ways to do this. One way is to construct the different ANNs for

each day type, and feed each ANN with the corresponding day type training sets [22], [30].

The other is to use only one ANN but contain the day type information in the input variables

[15],[21],[28],. The former uses a number of relatively small size networks, while the later

has only one network of a relatively large size. A typical classification given in [15]

categorizes the historical loads into five classes. These are Monday, Tuesday-Thursday,

Friday, Saturday and Sunday/Public holiday. The work in [17], collects the data with

characteristics similar to the day being forecasted, and combines these data with the data from

the previous 5 days to form a training set. The conventional methods use observation and

comparison [15], [17], [19] and methods based on unsupervised ANN concepts and selects

the training set automatically [12], [20] are used for day type classification.

1.2.6 Hybrid Fuzzy Neural Approaches

Researchers have proposed several different ways to combine fuzzy logic with neuralnetworks techniques in order to improve the overall forecasting performance. They are

classified into five categories according to the method of combination:

Fuzzy logic system at the output stage of the neural network forecaster to

manipulate the output [38], [39], [40];

Fuzzy logic at the input stage of a neural network to preprocess the inputs [41],

[42], [43];

Integrated fuzzy neural network to create a fuzzy rule base from the historical

training data [44], [45];

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Separate fuzzy logic and neural network forecasters to forecast different

components of the load [46];

Fuzzy logic technique for the classification of huge training data into different

classes and neural network to forecast the load according to the classified training

data [30]

1.3 Important Factor for Load Forecasting

For short-term load forecasting several factors should be considered, such as time factors,

weather data, and possible customers classes. Generally following factor are mostly

considered.

Temperature

Day light intensity of cloud

Day type capacity

Season

Rain

Wind velocity

load

The medium- and long-term forecasts take into account the historical load and weather data,

the number of customers in different categories, the appliances in the area and their

characteristics including age, the economic and demographic data and their forecasts, the

appliance sales data, and other factors. The time factors include the time of the year, the day

of the week, and the hour of the day. There are important differences in load between

weekdays and weekends. The load on different weekdays also can behave differently. For

example, Mondays and Fridays being adjacent to Weekends, may have structurally different

loads than Tuesday through Thursday. This is particularly true during the summer time.

Holidays are more difficult to forecast than non-holidays because of their relative infrequent

occurrence. Weather conditions influence the load. In fact, forecasted weather Parameters is

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the most important factors in short-term load forecasts. Various weather variables could be

considered for load forecasting. Temperature and humidity are the most commonly used load

predictors. An electric load prediction survey published in [17] indicated that of the 22

research reports considered, 13 made use of temperature only, 3 made use of temperature and

humidity, 3 utilized additional weather parameters, And 3 used only load parameters. Among

the weather variables listed above, two composite weather Variable functions, the THI

(temperature-humidity index) and WCI (wind chill index), are broadly used by utility

companies. THI is a measure of summer heat discomfort and similarly WCI is cold stress in

winter. Most electric utilities serve customers of different types such as residential,

commercial, and industrial. The electric usage pattern is different for customers that belong to

different classes but is somewhat alike for customers within each class. Therefore, most

utilities distinguish load behavior on a class-by-class basis [32].

1.4 Type of Load Forecasting

Over the last few decades a number of forecasting methods have been developed. Two of the

methods, so-called end-use and econometric approach are broadly used for medium- and long-

term forecasting. A variety of methods, which include the so-called similar day approach,

various regression models, time series, neural networks, expert systems, fuzzy logic, and

statistical learning algorithms, are used for short-term forecasting. The development,

improvements, and investigation of the appropriate mathematical tools will lead to the

development of more accurate load forecasting techniques. Statistical approaches usually

require a mathematical model that represents load as function of different factors such as time,

weather, and customer class. The two important categories of such mathematical models are:

additive models and multiplicative models. They differ in whether the forecast load is the sum

(additive) of a number of components or the product (multiplicative) of a number of factors.

For example, Chen et al. [4] presented an additive model that takes the form of predicting load

as the function of four components:

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L =Ln +Lw+Ls +Lr,

where

L = total load,

Ln = the normal part of the load,

Lw = the weather sensitive part of the load

Ls = a special event component that create a substantial deviation from the usual load

pattern

Lr = a completely random term, the noise

Chen et al. [55] also suggested electricity pricing as an additional term that can be included in

the model. Naturally, price decreases/increases affect electricity consumption. Large cost

sensitive industrial and institutional loads can have a significant effect on loads. The study in[55] used Pennsylvania-New Jersey-Maryland (PJM) spot price data (as it related to Ontario

Hydro load) as a neural network input. The authors report that accurate estimates were

achieved more quickly with the inclusion of price data.A multiplicative model may be of the

form

L =Ln Fw Fs Fr,

Where

Ln = the normal (base) load

Fw =current weather

Fs =special events

Fr =random fluctuation

Fp =electricity pricing

Fw, Fs, andFr= the correction factors are positive numbers that can increase or decrease the

overall load. These corrections are based on current weather (Fw), special events (Fs), and

random fluctuation (Fr). Factors such as electricity pricing (Fp) and load growth (Fg) can also

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be included. Rahman presented a rule based forecast using a multiplicative model. Weather

variables and the base load associated with the weather measures were included in the model.

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CHAPTER 2

SHORT TERM LOAD FORECASTING

2.1 Introduction

Load forecasting plays an important role in power system planning, operation and control.

Forecasting is the study to estimate active loads ahead of actual load occurrence. Planning

and operational applications of load forecasting requires a certain lead time also called

forecasting intervals [47]. Accurate models for electric power load forecasting are

essential to the operation and planning of a utility company. Load forecasting helps an

electric utility to make important decisions including decisions on purchasing and

generating electric power, load switching, and infrastructure development. Load

forecasts are extremely important for energy suppliers, and other participants in electric

energy generation, transmission, distribution, and markets. The forecasts for different time

horizons are important for different operations within a utility company. For the next year

peak forecast, it is possible to provide the probability distribution of the load based on

historical weather observations. It is also possible, according to the industry practice, to

predict the so-called weather normalized load, which would take place for average annual

peak weather conditions or worse than average peak weather conditions for a given area.

Weather normalized load is the load calculated for the so-called normal weather conditions

which are the average of the weather characteristics for the peak historical loads over a

certain period of time. The duration of this period varies from one utility to another. Some

companies take the last 25-30 years of historical data.

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2.2 Classification of Short Term Load Forecasting Methods

2.2.1 Similar-Day Approach:

This approach is based on searching historical data for days within one, two, or three years

with similar characteristics to the forecast day. Similar characteristics include weather, day of

the week, and the date. The load of a similar day is considered as a forecast. Instead of a single

similar day load, the forecast can be a linear combination or regression procedure that can

include several similar days. The trend coefficients can be used for similar days in the previous

years

2.2.2 Regression Methods

Regression is the one of most widely used statistical techniques. For electric load forecasting

regression methods are usually used to model the relationship of load consumption and other

factors such as weather, day type, and customer class. Engle et al. [1] presented several

regression models for the next day peak forecasting. Their models incorporate deterministic

influences such as holidays, stochastic influences such as average loads, and exogenous

influences such as weather. References [1], [33], [17], [3] describe other applications of

regression models to loads forecasting.

2.2.3 Time Series

Time series methods are based on the assumption that the data have an internal structure, such

as autocorrelation, trend, or seasonal variation. Time series forecasting methods detect and

explore such a structure. Time series have been used for decades in such fields as economics,

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digital signal processing, as well as electric load forecasting. In particular, ARMA

(autoregressive moving average), ARIMA (autoregressive integrated moving average),

ARMAX (autoregressive moving average with exogenous variables), and ARIMAX

(autoregressive integrated moving average with exogenous variables) are the most often used

classical time series methods. ARMA models are usually used for stationary processes while

ARIMA is an extension of ARMA to no stationary processes. ARMA and ARIMA use the

time and load as the Only input parameters. Since load generally depends on the weather and

time of the day, ARIMAX is the most natural tool for load forecasting among the classical

time series models. Fan and McDonald [10] and Cho et al. [5] describe implementations of

ARIMAX models for load forecasting. Yang et al. [37] used evolutionary Programming (EP)

approach to identify the ARMAX model parameters for one day to one week ahead hourly

load demand forecast. Evolutionary programming [14] is a method for simulating evolution

and constitutes a stochastic optimization algorithm. Yang and Huang [43] proposed a fuzzy

autoregressive moving average with exogenous input variables (FARMAX) for one day ahead

hourly load forecasts.

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CHAPTER 3

SHORT TERM LOAD FORECASTING TECHNIQUE

3.1 Neural Networks

The use of artificial neural networks (ANN or simply NN) has been a widely studied electric

load forecasting technique since 1990 (see [22]). Neural networks are essentially non-linear

circuits that have the demonstrated capability to do non-linear curve fitting. The outputs of anartificial neural network are some linear or nonlinear mathematical function of its inputs. The

inputs may be the outputs of other network elements as well as actual network inputs. In

practice network elements are arranged in a relatively small number of connected layers of

elements between network inputs and outputs. Feedback paths are sometimes used. In applying

a neural network to electric load forecasting, one must select one of a number of architectures

(e.g. Hopfield, back propagation, Boltzmann machine), the number and connectivity of layers

and elements, use of bi-directional or uni-directional links, and the number format (e.g. binary

or continuous) to be used by inputs and outputs, and internally. The most popular artificial

neural network architecture for electric load forecasting is back propagation. Back propagation

neural networks use continuously valued functions and supervised learning. That is, under

supervised learning, the actual numerical weights assigned to element inputs are determined by

matching historical data (such as time and weather) to desired outputs (such as historical

electric loads) in a pre-operational training session. Artificial neural networks with

unsupervised learning do not require pre-operational training. Bakirtzis et al. [1] developed an

ANN based short-term load forecasting model for the Energy Control Center of the Greek

Public Power Corporation. In the development they used a fully connected three-layer feed

forward ANN and back propagation algorithm was used for training. Input variables include

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historical hourly load data, temperature, and the day of the week. The model can forecast load

profiles from one to seven days. Also Papalexopoulos et al. [21] developed and implemented a

multi-layered feed forward ANN for short-term system load forecasting. In the model three

types of variables are used as inputs to the neural network: season related inputs, weather

related inputs, and historical loads. Khotanzad et al. [13] described a load forecasting system

known as ANNSTLF. ANNSTLF is based on multiple ANN strategies that capture various

trends in the data. In the development they used a multilayer perception trained with the error

back propagation algorithm. ANNSTLF can consider the effect of temperature and relative

humidity on the load. It also contains forecasters that can generate the hourly temperature and

relative humidity forecasts needed by the system. An improvement of the above system was

described in [14]. In the new generation, ANNSTLF includes two ANN forecasters, one

predicts the base load and the other forecasts the change in load. The final forecast is computed

by an adaptive combination of these forecasts. The effects of humidity and wind speed are

considered through a linear transformation of temperature. As reported in [21], ANNSTLF was

being used by 35 utilities across the USA and Canada. Chen et al. [4] developed a three layer

fully connected feed forward neural network and the back propagation algorithm was used as

the training method. Their ANN though considers the electricity price as one of the main

characteristics of the system load. Many published studies use artificial neural networks in

conjunction with other forecasting techniques (such as with time series [7] regression trees

[20], or fuzzy logic [34]).

3.2Expert System

Rule based forecasting makes use of rules, which are often heuristic in nature, to do accurate

forecasting. Expert systems, incorporates rules and procedures used by human experts in the

field of interest into software that is then able to automatically make forecasts without human

assistance. Expert system use began in the 1960s for such applications as geological

prospecting and computer design. Expert systems work best when a human expert is available

to work with software developers for a considerable amount of time in imparting the experts

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knowledge to the expert system software. Also, an experts knowledge must be appropriate for

codification into software rules (i.e. the expert must be able to explain his/her decision process

to programmers). An expert system may codify up to hundreds or thousands of production

rules. Chow et al. [31] proposed a knowledge-based expert system for the short term load

forecasting of the Taiwan power system. Operators knowledge and the hourly observations of

system load over the past five years were employed to establish eleven day types. Weather

parameters were also considered. The developed algorithm performed better compared to the

conventional Box-Jenkins method. Rahman and Hazim [29] developed a site independent

technique for short-term load forecasting. Knowledge about the load and the factors affecting it

are extracted and represented in a parameterized rule base. This rule base is complemented by

a parameter database that varies from site to site. The technique was tested in several sites in

the United States with low forecasting errors. The load model, the rules, and the parameters

presented in the paper have been designed using no specific knowledge about any particular

site. The results can be improved if operators at a particular site are consulted.

3.3 Fuzzy Logic

fuzzy logic is a generalization of the usual boolean logic used for digital circuit design. 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. for instance a transformer load may be low,

medium and high. 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. of course in many situations an exact output (e.g.

the precise 12pm load) is needed. after the logical processing of fuzzy inputs, a

defuzzification process can be used to produce such precise outputs. references [25], [18],

[34] describe applications of fuzzy logic to electric load forecasting.

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3.4 Support Vector Machines

Support Vector Machines (SVMs) are a more recent powerful technique for solving

classification and regression problems. This approach was originated from Vapniks [35]

statistical learning theory. Unlike neural networks, which try to define complex functions of

the input feature space, support vector machines perform a nonlinear mapping (by using so-

called kernel functions) of the data into a high dimensional (feature) space. Then support

vector machines use simple linear functions to create linear decision boundaries in the new

space. The problem of choosing an architecture for a neural network is replaced here by the

problem of choosing a suitable kernel for the support vector machine [6]. Mohandes applied

the method of support vector machines for short-term electrical load forecasting. The author

compares its performance with the autoregressive method. The results indicate that SVMs

compare favorably against the autoregressive method. Chen et al. [2] proposed a SVM model

to predict daily load demand of a month. Their program was the winning entry of the

competition organized by the NITE network. Li and Fang [28] also used a SVM model for

short-term load forecasting.

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CHAPTER 4

SHORT TERM ELECTRIC LOAD FORECASTING BYFUZZY LOGIC TECHNIQUE

4.1 Overview of Fuzzy Logic Technique

According to Bauer et al [48],

"Fuzzy Logic is basically a multi-valued logic that allows intermediate values to be

defined between conventional evaluations like yes/no, true/false, black/white, etc. Notionslike rather warm or pretty cold can be formulated mathematically and processed by

computers."

According to Bart Kosko [49],

The facts were always fuzzy or vague or inexact. Science treated the gray or

fuzzy facts as if they were the black-white facts of math. Yet no one had put forth a single fact

about the world that was 100% true or 100% false. "Logic to most people relates to two state

thinking, the idea that the outcome can only be either true or false, 1 or 0, right or wrong.

This form of logic dates back to ancient Greece and is perfectly adequate to answer simple

questions in single dimensions, for example, if A is 1 and B is 0 what is A AND B? It can

be extended, as is done in Boolean algebra to more complex questions, as long as all the

parts can be described using the same restricted alphabet of two symbols. Such logic is a

deductive way of understanding consequences and a highly valuable intellectual technique

[50]. But this sort of logic is inadequate when we need to reason about variables that have

more than two values, or in cases where multiple incompatible variables are involved.

Yet we still need to make decisions in these cases, so how can we proceed? Bivalent, or

two states, logic is just a sub-set of a more powerful type of logic known as fuzzy logic. The

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concept of Fuzzy Logic (FL) was conceived by Zadeh and presented not as a control

methodology, but as a way of processing data by allowing partial set membership rather than

crisp set membership or non-membership. Zadeh reasoned that people do not require precise,

numerical information input, and yet they are capable of highly adaptive control [50], [51].

Fuzzy Sets

Fuzzy sets have membership properties defined between 0 and 1. This means that if we take

an attribute say 'red' we can express the colour of any particular apple as a position in this

fuzzy set. We may say for example that it is 30% red and thus has a fuzzy truth value (FTV) or

membership function of 0.3. The relation of FTV to actual values depends upon the desired

mapping from the real world to the normalized range 0 to 1, and this is arbitrary. The

membership function is a graphical representation of the magnitude of participation of

each input. It associates a weighting with each of the inputs that are processed, define

functional overlap between inputs, and ultimately determines an output response. The rules use

the input membership values as weighting factors to determine their influence on the fuzzy

output sets of the final output conclusion. Once the functions are inferred, scaled, and

combined, they are defuzzified into a crisp output which drives the system. There are

different membership functions associated with each input and output response.The

commonly used shape to describe the membership function is triangular, but bell, trapezoidal

and exponential can also be used. More complex functions are possible but require greater

computing overhead to implement. Fig.1 illustrates the different shapes of membership

functions commonly in use.

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1.Triangular 2.Trapmf

3.Gbellmf 4.Guassmf

5.Gauss2mf 6.Sigmf

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7.Dsigmf 8.Psigmf

9.Pigmf 10.Smf

Fuzzy logic is reasoning with fuzzy sets. Operations on fuzzy sets are similar to those of

standard logic but are differently defined [69]. Let us assume two FTVs to illustrate,

A(0.4) and B(0.7).

Union (the joined boundaries of the values): A

OR B = Maximum of the FTVs i.e., 0.7

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Intersection (the commonality between the values): A

AND B = Minimum of the FTVs i.e., 0.4

(again reducing to bivalent logic in the extremes)

Negation (the opposite of the value)

NOT A = 1 FTV A i.e., 0.6

(Once more this is simply an extension of normal logic)

If there is just one variable then decisions are easy, the option with the best value is selected,

but it is very difficult to deal with multiple variables where compromise or trade-off the

values is required. In classical logic we can pick the option whose worst is the least bad

(Max-min) or we could pick the option whose best is the highest (Max- max). In fuzzy

logic we rate each variable as a fuzzy truth value, giving 1 to the best option, 0 to the worst

and proportionate in between (we could alternatively rate them with respect to a theoretical or

practical minimum and maximum for the variable in question). A motoring example is

considered :

Table 4.1 A Motoring Example (Real Values)

Classical logic would set the best at 1 and rest (not-best) 0, i.e.:

Real Values Consumption mpg Max Speed mph Acceleration s

Car A 30 120 9

Car B 40 110 11

Car C 45 100 12

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Logic Values Consumption Max Speed Acceleration

Car A 0 1 1

Car B 0 0 0

Car C 1 0 0

Table 4.2 A Motoring Example (Logic Values)

Then Max-min would choose all of them (all are 0 minimum) and Max-max either A or C

(both have 1) - not much use as a method of choice.

Fuzzifying these values instead (where for Acceleration here low is good, so the minimum gets

the maximum marks) we get:

Fuzzy Values Consumption Max Speed Acceleration

Car A 0 1 1

Car B 0.66 0.5 0.33

Car C 1 0 0

Table 4.3 A Motoring Example (Fuzzy Values)

Here Max-min would choose B (0.33 minimum satisfaction) and Max-max A (two 1s), a

compromise choice is provided by fuzzy reasoning (depending on your preference for

least-worst versus most-best).

Fuzzy systems being inherently nonlinear however can deal with those situations hard to

formulate in traditional linear mathematical terms, and this includes complex nonlinear

machines and systems with multiple interrelated variables.

4.2Historical data and key factors

A good quality of historical data for input parameters for the last few years has been stored in

data base management system (DBMS) for accurate load forecasting. The system load is the

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sum of all the consumers load at the same time. The objective of system Load Forecasting

is to forecast the future system load. Good understanding of the system characteristics helps

to design reasonable forecasting models and select appropriate models in different situations.

Short term load forecasting mainly depends on the following conditions:

- Day capacity

- Weather conditions

- Day temperature

Though the day capacity can be defined as working day or non working day (weekend or

holiday). But as per this study weekend and holiday are put in the same category when no

work or negligible work is done. One more category as special day has been considered. This

is the category when work is done after regular 8 working hours of the day (means if work is

done for 9 Hrs. in a day shows one complete regular day and 1 Hr. of special day) or 9 Hrs. of

special day depending on the type of work. Overall working in an institute can be divided into

two parts-Class (Theory and Tutorials) and Practical Labs and workshops. The day capacity is

very much dependant on two factors:

- The type of work (either Theory or Practical)

- Day Elongation

So day capacity can be calculated as

DC= .. eqn.4.1

Where DC is Day Capacity, Ti is Evaluation Factor for the type of work and D is Elongation

of the day in eqn. (4.1). Two main factors have been defined to decide weather conditions

Cloudy and/or Rainy weather. Cloudy weather gives an important effect of the day light

intensity means more the clouds, lesser will be the day light intensity, more will be the

consumption of electricity. These factors somehow are related to days minimum temperature

and days maximum temperature. Actually, there can be a comparison between two working

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days with similar day capacity but different weather conditions; load consumed on both the

days will be different. This can also happen that for two days, one is working and other is non

working with different weather conditions, the load consumed is same.

4.3 Fuzzification

Fuzzy linguistic variables are used to represent various inputs as well as output parameters as

the member of fuzzy sets. In order to express the fuzziness of information, this paper makes an

arrangement of fuzzy subsets for different inputs and outputs in complete universe of discourse

as membership functions [9]. The relationship between several inputs and output may be non

linear but linear membership functions have been used for simplicity and only the membership

function for seasons is taken as ridge-shaped Membership functions such as gbell mf, gauss

mf, and gauss2mf.

The Days Minimum Temperature and Maximum Temperature are represented as fuzzy subset

[Very Low (VL), Low (L), Medium (M), High (H), and Very High (VH)].

The linguistic variables of Day Capacity as [Minimum (min), Very Low (VL), Low (L),Medium (M), High (H), Very High (VH), Maximum (max)].

The fuzzy subset for day capacity is [Very Low (VL), Low (L), Normal (N), High (H), Very

High (VH)].

The Seasons fuzzy subset is given with the names of season as [spring, summer, autumn,

winter].

The rain forecast has been given by fuzzy subset [No Rain, Drizzling, Normal Rain, Heavy

Rain].

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Similarly, the output factor load also has been assigned as fuzzy subset with membership

functions [Minimum (min), very low (VL), Low (L), medium (M), High (H), Very High (VH),

Maximum (max)].

INPUT Type of M.F. No. of M.F. Range of M.F.

Days mini. temperature Trimf 5 -5 to 35CDays max. temperature Trimf 5 5 to 50 C

Days light intensity of cloud Trimf 5 0 to 100 %

Day type capacity Trimf 7 0 to 1

Season Gauss2mf 4 0 to 350

Rain Trimf 4 0 to 1

OUTPUT Type of M.F. No. of M.F. Range of M.F.

Forecasted load Trimf 5 4000 to 10000 MHW

Table 4.4 Details of input and output M.F.

4.4 Membership Functions

Figure 2 FIS Editor Window

Fig 4.4.1 Membership function of The Days Minimum Temperature

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4.4.2 Membership function of The Days Maximum Temperature

4.4.3 Membership function of The Days Light Intensity

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4.4.4 Membership function of The Days capacity

4.4.5 Membership function of The Season

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4.4.6 Membership function of Rain

4.5 Fuzzy Rule Base

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This is the part of fuzzy system where heuristic knowledge is stored in terms of IF-THEN

Type Rules. The rule base is used to send information to fuzzy inference system (FIS) to

process through inference mechanism to numerically evaluate the information embedded in the

fuzzy rule base to get the output. The rules are like:

IF (MinTemp is M) and (MaxTemp is L) and (Day Light-Intensity (Clouds) is VH) and

(Season (Day Number) is SUMMER) and (Rain is NORMAL) THEN (Output Load is

H).

IF (Min Temp is H) and (Max Temp is H) and (Day Light-Intensity (Clouds) is L) and

(Season (Day Number) is AUTUMN) and (Rain is DRIZZLING) THEN (Output Load

is H).

IF (Min Temp is VL) and (Max Temp is VL) and (Day Light-Intensity (Clouds) is H)

and (Season (Day Number) is WINTER) and (Rain is NO_RAIN) THEN (Output Load

is MAX).

IF (Min Temp is H) and (Max Temp is H) and (Day Light-Intensity (Clouds) is L) and

(Season (Day Number) is SPRING) and (Rain is NO_RAIN) THEN (Output Load is

M).

IF (Day Type (Day Capacity) is MIN) and (Season (Day Number) is SUMMER)

THEN (Output Load is MIN).

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Figure4.5.1Rule editor window

4.6 Result

Fuzzy Logic technique approach to short term load forecasting is proposed in this project

report work. The daily load data from Dayalbagh and Dayalbagh Educational Institute

Dayalbagh Agra for different day types is used for load forecasting. DEIED USIC data is the

complete load demand of Dayalbagh and Dayalbagh Educational Institute taken from

Dayalbagh Electricity Deppt. USIC Dayalbagh , Agra. And finally as per the result. I make

the rules and find the following surface

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Rule Window

Surface window

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Graph of Days max. temp. V/s forecasted

Graph of Days minimum temp V/s forecasted load

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Surface in between season ,day mini. Temp and forecasted load.

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CHAPTER5

CONCLUSION

We can use fuzzy logic to forecast the load to some extent but there are inherent disadvantages

to the system because of the degree of freedom in selecting membership functions, method of

fuzzification and de-fuzzification. Such problems may be overcome by combining neural

network and fuzzy logic. The neural network optimizes the rule base. This involves the

training of the network to the historical data to determine the rules that contribute to a better

decision. The network also modifies the initial choice of the membership function to fit the

system. Some another technique are ANN and Genetic Algorithm. These types of Hybrid

expert systems are under research.

REFERENCES

[1] R.F. Engle, C. Mustafa and J. Rice, Modeling Peak Electricity Demand, Journal of

8/9/2019 Char an 123456

44/49

42

Forecasting, vol. 11, no. 3, pp. 241251, 1992.

[2] O. Hyde and P.F. Hodnett, An Adaptable Automated Procedure for Short-Term

Electricity Load Forecasting IEEE Transactions on Power Systems, vol. 12, no. 1,

pp. 8493, 1997.

[3] S. Ruzic, A. Vuckovic and N. Nikolic, Weather Sensitive Method for Short- Term

Load Forecasting in Electric Power Utility of Serbia, IEEE Transactions on Power

Systems, vol.18, no. 4, pp.15811586, 2003.

[4] T. Haida and S. Muto, Regression Based Peak Load Forecasting using a

Transformation Technique, IEEE Transactions on Power Systems, vol. 9, no. 4, pp.

17881794, 1994.

[5] W. Charytoniuk, M.S. Chen and P. Van Olinda, Nonparametric Regression Based

Short-Term Load Forecasting, IEEE Transactions on Power Systems, vol. 13, no. 1,

pp. 725730, 1998.

[6] J.Y. Fan and J.D. McDonald, A Real-Time Implementation of Short-Term Load

Forecasting for Distribution Power Systems, IEEE Transactions on Power

Systems, 9:988994, 1994.

[7] M.Y. Cho, J.C. Hwang and C.S. Chen, Customer Short-Term Load Forecasting by

using ARIMA Transfer Function Model, Proceedings of the International

Conference on Energy Management and Power Delivery, vol. 1, no. 1, pp.317 322,

1995.

[8] D.B. Fogel, An Introduction to Simulated Evolutionary Optimization, IEEE

Transactions on Neural Networks, vol. 5, no. 1, pp.314, 1994.

[9] H.T. Yang and C.M. Huang, A New Short-Term Load Forecasting Approach

8/9/2019 Char an 123456

45/49

42

using Self-Organizing Fuzzy ARMAX Models, IEEE Transactions on Power

Systems, vol. 13, no. 1, pp. 2 17225, 1998.

[10] K.L. Ho, Short-Term Load Forecasting of Taiwan Power System using A

Knowledge Based Expert System, IEEE Transactions on Power Systems, vol. 5, no.

1, pp. 1214 1221, 1990.

[11] S. Rahman and O. Hazim, Load Forecasting for Multiple Sites: Development of an

Expert System-Based Technique, Electric Power Systems Research, vol. 39, no. 1,

pp. 161 169, 1996.

[12] S.E. Skarman and M. Georgiopoulous, Short-Term Electrical Load Forecasting using a

Fuzzy ARTMAP Neural Network, Proceedings of SPIE, vol. 2, no. 1, pp.181191,1998\

[13] A.G. Bakirtzis, V. Petridis, S.J. Kiartzis, M.C. Alexiadis and A.H. Maissis, A

Neural Network Short-Term Load Forecasting Model for the Greek Power

System, IEEE Transactions on Power Systems, vol. 11, no. 1, pp. 858863, 1996.

[14] A.D. Papalexopoulos, S. Hao and T.M. Peng, An Implementation of a Neural

Network Based Load Forecasting Model for the EMS, IEEE Transactions on PowerSystems, vol. 9, no. 1, pp. 19561962, 1994.

[15] A. Khotanzad, R.A. Rohani, T.L. Lu, A. Abaye, M. Davis and D.J. Maratukulam,

ANNSTLFA Neural-Network-Based Electric Load Forecasting System, IEEE

Transactions on Neural Networks, vol. 8, no. 1, pp. 835846, 1997.

[16] Y. H. Song, A. Johns and R. Aggarwal, Computational Intellgence Applications to

Power System, Kluwer Academic Publishers, London.

[17] A. Khotanzad, R.A. Rohani and D. Maratukulam, ANNSTLF Artificial Neural

Network Short-Term Load ForecasterGeneration Three, IEEE Transactions on

Neural Networks, vol. 13, no. 2, pp. 14131422, 1998

8/9/2019 Char an 123456

46/49

42

[18] D.C. Park, Electric Load Forecasting using an Artificial Neural Network, IEEE

Transactions on Power Systems, vol. 6, no. 2, pp. 412-449, 1991.

[19] T.S. Dillon, Short-Term Load Forecasting Using an Adaptive Neural Network,

Electrical Power & Energy Systems, vol. 13, no. 1, pp.186-191, 1991.

[20] M. Djukanvic, Unsupervised/Supervised Learning Concept for 24-hour Load

Forecasting, IEE Proceedings -C, vol. 140, no. 2, pp. 311-318, 1993.

[21] K.Y. Lee and J. H. Park, Short-Term Load Forecasting Using an Artificial neural

Network, IEEE Transactions on Power Systems, vol. 7, no. 1, pp. 124-132, 1992.

[22] C.N. Lu, Neural Network Based Short Term Load Forecasting, IEEE Trans. on Power

Systems, vol. 8, no. 2, pp. 336-341, 1993.

[23] M. Peng, N.F. Hubele and G.G. Karady, Advancement in the Application of Neural

Networks for Short-Term Load Forecasting, IEEE Transactions on Power Systems, vol.

7, no. 1, pp. 250257, 1992.

[24] Y. Rui and P. Jin, The Modelling Method for ANN-Based Forecaster, CDC' 94, China,

1994.

[25] D. Srinivasan, A Neural Network Short-Term Load Forecaster, Electric Power

Research, vol. 28, no. 2, pp. 227-234, 1994.

[26] K.L. Ho, Short Term Load Forecasting using a Multilayer Neural Network with an

Adaptive Learning Algorithm, IEEE Transactions on Power Systems, vol. 7, no. 2,

pp. 141-149, 1992.

[27] H. Mori and N. Kosemura, Optimal Regression Tree Based Rule Discovery for Short-

Term Load Forecasting, Proceedings of IEEE Power Engineering Society Transmission

and Distribution Conference, vol. 2, no.1, pp. 421426, 2001.

8/9/2019 Char an 123456

47/49

42

[28] O. Mohammed, D. Park, R. Merchant, T. Dinh, C. Tong, A. Nazeem, J. Farah and C.

Draks Practical Experiences with an Adaptive Neural Network Short-Term Load

Forecasting System, IEEE Trans. on Power Systems, vol. 10, no. 2, pp. 254-265,

1995.

[29] B.S. Kermanshahi, Load Forecasting under Extreme Climatic Conditions,

Proceedings, IEEE Second International Forum on the Applications of Neural

Networks to Power Systems, vol. 5, no. 1, pp. 213-218, 1993

[30] M. Daneshdoost, M. Lotfalian, G. Bumroonggit and J.P. Ngoy, Neural Network with

Fuzzy Set-Based Classification for Short Term Load Forecasting , IEEE Transactions

on Power Systems, vol.13, no. 4, pp. 1386-1391, 1998,.

[31] T.W.S. Chow and C.T. Leung, Nonlinear Autoregressive Integrated Neural Network

Model for Short-Term Load Forecasting, IEE Proceedings on Generation,

Transmission and Distribution, vol. 143, no. 3, pp. 500 506, 1996.

[32] Y. Lee, An Analysis of Premature Saturation in Back Propagation Learning, Neural

Networks, vol. 6, no. 1, pp. 7 19-728, 1993.

[33] S.T. Chen, Weather Sensitive Short-Term Load Forecasting using Non Fully

Connected Artificial Neural Networks, IEEE Tranactions on Power Systems, 7: 1098-

1105, 1992.

[34] G.N. Kariniotakis, Load Forecasting using Dynamic High-Order Neural

Networks, Proceedings, IEEE Second International Forum on the Applications of

Neural Networks to Power Systems, vol. 5, no. 1, pp. 801-805,1993.

[35] J. Villiers, Back-Propagation Neural Nets with One and Two Hidden Layers, IEEE

Trans. on Neural Networks, vol. 4, no. 1, pp. 136-146, 1992.

[36] Y.Y. Hsu, Design of Artificial Neural Networks for Short-Term Load

Forecasting, IEE Proc. C, vol. 138, no. 1, pp. 407-418, 1991.

8/9/2019 Char an 123456

48/49

42

[37] V.V. Phansalkar, Analysis of the Back-Propagation Algorithm with

Momentum, IEEE Transactions on Neural Networks, vol. 5, no. 1, pp. 505-506, 1994.

[38] G. L.Torres, C.O. Traore, P.J. Lagace and D. Mukhedkar, A Knowledge

Engineering Tool for Load Forecasting, Proc. of the 33rd Midwest Symposium on

Circuits and Systems, vol. 1, no. 2, pp. 14-147, 1990.

[39] K H. Kim, J.K. Park, K.J. Hwang and S.H. Kim, Implementation of Hybrid Short-

term Load Forecasting System Using Artificial Neural Networks and Fuzzy Expert

Systems, IEEE Transactions on Power Systems, vol. 10, no. 3, pp. 1534- 1539, 1995.

[40] P.K. Dash, S. Dash, G. R. Krishna and S. Rahman, Forecasting of a Load Time Series

Using a Fuzzy Expert System and Fuzzy Neural Networks, International Journal ofEngineering Intelligent Systems, vol. 1, no. 1, pp. 103-118, 1993.

[41] D. Srinivasan, A.C. Liew and C.S. Chang, Forecasting Daily Load Curves Using A

Hybrid Fuzzy-Neural Approach, IEE Proceedings-C, vol. 141, no. 2, pp. 561- 567,

1994.

[42] D. Srinivasan, C.S. Chang and AC. Liew, Demand Forecasting Using Fuzzy Neural

Computation, With Special Emphasis on Weekend and Public Holiday Forecasting,

IEEE Transactions on Power Systems, vol. 9, no. 2, pp. 1780-1787, 1994.

[43] Y. Qiu, A Fuzzy Neural Network for Short-term Load Forecasting, Proceedings of

the IEEE Transactions on Power systems, vol. 9, no. 2, pp. 1772-1780, 1994.

[44] P.K. Dash, A.C. Liew and S. Rahman, Peak Load Forecasting using a Fuzzy Neural

Network, Electric Power Systems Research, vol. 32, no. 1, pp. 19-23, 1995.

[45] A.G. Bakirtzis, J.B. Theocharis, S.J. Kiatzis and K.J. Satios, Short Term Load

Forecasting Using Fuzzy Neural Networks, IEEE Transactions on Power

Systems, vol. 9, no. 2, pp. 1760-1772, 1994.

[46] H. Gottschalk, S. Heine, B. Fox and I. Neumann, Economic Operation of a Power

8/9/2019 Char an 123456

49/49

System with a Significant Amount of Controllable Load, Proceedings of the 29th

Universities Power Engineering Conference, vol. 2, no. 2, pp. 673-675, 1994.

[47] D.P. Kothari and I.J.Nagrath, Modern Power System Analysis, Tata McGraw Hill.

[48] C. Bauer and G. Viot, Fuzzy Logic Concepts and Constructs, AI Expert, pp. 26- 33,

1993.

[49] B. Kosko, Bidirectional Associative Memories, IEEE Transactions on Systems, Man

and Cybernetics, vol. SMC-18, no. 1, pp.49-60, 1988.

[50] L. A. Zadeh, Fuzzy Sets, Inf. Control, vol. 8, no. 1, pp. 33 8-353, 1965.

[51] C.L. Chang and R.C. Lee, Symbolic Logic and Mechanical Theorem Proving,

Academic Press, NY, 1973.

[52] T. N. Hung and A. W. Elbert, A First Course in Fuzzy Systems and Control, Prentice

Hall, 1999.