Char an 123456

Upload
charansingh 
Category
Documents

view
218 
download
0
Transcript of Char an 123456

8/9/2019 Char an 123456
1/49
Electrical Shortterm 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 Agra5
Session 2010

8/9/2019 Char an 123456
2/49
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

8/9/2019 Char an 123456
3/49
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

8/9/2019 Char an 123456
4/49
CERTIFICATE
I hereby to inform you that the PROJECT REPORT for the KISHORE VAIGYANIK
PROTSAHAN YOJANA 2010 titled Electrical ShortTerm 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

8/9/2019 Char an 123456
5/49
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
June2010 B.Sc.
ABSTRACT

8/9/2019 Char an 123456
6/49
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 offline
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 shortterm forecasts, shortterm forecasts, mediumterm
forecasts and longterm 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, dayahead shortterm 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.

8/9/2019 Char an 123456
7/49
35
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: shortterm
forecasts which are usually from one hour to one month, medium forecasts which are usually
from a month to a year, and longterm 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 13%. 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 socalled 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 socalled 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 2530 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

8/9/2019 Char an 123456
8/49
35
forecasting is vitally important for utilities. Shortterm 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
longterm forecasting are also more important than in a nonderegulated 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, socalled enduse and econometric
approach are broadly used for medium and longterm forecasting. A variety of methods,
which include the socalled similar day approach, various regression models, time series,
neural networks, statistical learning algorithms, fuzzy logic, and expert systems, have been
developed for shortterm 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:

8/9/2019 Char an 123456
9/49
35
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 hourlyload
demandforecasting. 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 knowledgebased expert system for the shortterm 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 shortterm load forecasting. Knowledge about the load and the
factors affecting it is extracted and represented in a parameterized rule base. This rule

8/9/2019 Char an 123456
10/49
35
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

8/9/2019 Char an 123456
11/49
35
be of 3layers or 4layers, the transfer function can be linear, nonlinear or a combination of
both. Also, the network can be either fully connected or nonfully 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 threelayer 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
nonfully 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 nonfully
connected ANN is more adaptive to respond to temperature changes. Moreover, [21]
presents a new approach to STLF which combines several subANNs 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 3layer ANN with suitable dimension is sufficient to approximate any continuous non
linear function [28]. The 4layer 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 [1530],
2. Historical and future (forecasted) temperatures [1527],3. Historical and future (forecasted) relative humidity [30]
4. Hour of day index [15],[21],[25],[31],

8/9/2019 Char an 123456
12/49
35
5. Day of week index [15],[21], [25],[31],
6. Windspeed 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 ( I1).[37] highlights that a multilayer perception with ( k1) hidden
neurons can realize arbitrary functions defined on a kelement 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],

8/9/2019 Char an 123456
13/49
35
[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, TuesdayThursday,
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];

8/9/2019 Char an 123456
14/49
35
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 shortterm 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 longterm 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 nonholidays because of their relative infrequent
occurrence. Weather conditions influence the load. In fact, forecasted weather Parameters is

8/9/2019 Char an 123456
15/49
35
the most important factors in shortterm 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
(temperaturehumidity 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 classbyclass 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, socalled enduse and econometric approach are broadly used for medium and long
term forecasting. A variety of methods, which include the socalled similar day approach,
various regression models, time series, neural networks, expert systems, fuzzy logic, and
statistical learning algorithms, are used for shortterm 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:

8/9/2019 Char an 123456
16/49
35
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 PennsylvaniaNew JerseyMaryland (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

8/9/2019 Char an 123456
17/49
35
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.

8/9/2019 Char an 123456
18/49
35
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 socalled 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 socalled 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 2530 years of historical data.

8/9/2019 Char an 123456
19/49
35
2.2 Classification of Short Term Load Forecasting Methods
2.2.1 SimilarDay 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,

8/9/2019 Char an 123456
20/49
35
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.

8/9/2019 Char an 123456
21/49
35
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 nonlinear
circuits that have the demonstrated capability to do nonlinear 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 bidirectional or unidirectional 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 preoperational training session. Artificial neural networks with
unsupervised learning do not require preoperational training. Bakirtzis et al. [1] developed an
ANN based shortterm load forecasting model for the Energy Control Center of the Greek
Public Power Corporation. In the development they used a fully connected threelayer feed
forward ANN and back propagation algorithm was used for training. Input variables include

8/9/2019 Char an 123456
22/49
35
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
multilayered feed forward ANN for shortterm 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

8/9/2019 Char an 123456
23/49
35
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 knowledgebased 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 BoxJenkins method. Rahman and Hazim [29] developed a site independent
technique for shortterm 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.

8/9/2019 Char an 123456
24/49
35
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 shortterm 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
shortterm load forecasting.

8/9/2019 Char an 123456
25/49
35
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 multivalued 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 blackwhite 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 subset of a more powerful type of logic known as fuzzy logic. The

8/9/2019 Char an 123456
26/49
35
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 nonmembership. 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.

8/9/2019 Char an 123456
27/49
35
1.Triangular 2.Trapmf
3.Gbellmf 4.Guassmf
5.Gauss2mf 6.Sigmf

8/9/2019 Char an 123456
28/49
35
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

8/9/2019 Char an 123456
29/49
35
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 tradeoff the
values is required. In classical logic we can pick the option whose worst is the least bad
(Maxmin) 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 (notbest) 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

8/9/2019 Char an 123456
30/49
35
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 Maxmin would choose all of them (all are 0 minimum) and Maxmax 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 Maxmin would choose B (0.33 minimum satisfaction) and Maxmax A (two 1s), a
compromise choice is provided by fuzzy reasoning (depending on your preference for
leastworst versus mostbest).
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

8/9/2019 Char an 123456
31/49
35
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 partsClass (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

8/9/2019 Char an 123456
32/49
35
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 ridgeshaped 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].

8/9/2019 Char an 123456
33/49
35
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

8/9/2019 Char an 123456
34/49
35
4.4.2 Membership function of The Days Maximum Temperature
4.4.3 Membership function of The Days Light Intensity

8/9/2019 Char an 123456
35/49
35

8/9/2019 Char an 123456
36/49
35
4.4.4 Membership function of The Days capacity
4.4.5 Membership function of The Season

8/9/2019 Char an 123456
37/49
35
4.4.6 Membership function of Rain
4.5 Fuzzy Rule Base

8/9/2019 Char an 123456
38/49
35
This is the part of fuzzy system where heuristic knowledge is stored in terms of IFTHEN
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 LightIntensity (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 LightIntensity (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 LightIntensity (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 LightIntensity (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).

8/9/2019 Char an 123456
39/49
35
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

8/9/2019 Char an 123456
40/49
35
Rule Window
Surface window

8/9/2019 Char an 123456
41/49
35
Graph of Days max. temp. V/s forecasted
Graph of Days minimum temp V/s forecasted load

8/9/2019 Char an 123456
42/49
35
Surface in between season ,day mini. Temp and forecasted load.

8/9/2019 Char an 123456
43/49
42
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 defuzzification. 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 ShortTerm
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
ShortTerm Load Forecasting, IEEE Transactions on Power Systems, vol. 13, no. 1,
pp. 725730, 1998.
[6] J.Y. Fan and J.D. McDonald, A RealTime Implementation of ShortTerm 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 ShortTerm 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 ShortTerm Load Forecasting Approach

8/9/2019 Char an 123456
45/49
42
using SelfOrganizing Fuzzy ARMAX Models, IEEE Transactions on Power
Systems, vol. 13, no. 1, pp. 2 17225, 1998.
[10] K.L. Ho, ShortTerm 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 SystemBased Technique, Electric Power Systems Research, vol. 39, no. 1,
pp. 161 169, 1996.
[12] S.E. Skarman and M. Georgiopoulous, ShortTerm 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 ShortTerm 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 NeuralNetworkBased 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 ShortTerm 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. 412449, 1991.
[19] T.S. Dillon, ShortTerm Load Forecasting Using an Adaptive Neural Network,
Electrical Power & Energy Systems, vol. 13, no. 1, pp.186191, 1991.
[20] M. Djukanvic, Unsupervised/Supervised Learning Concept for 24hour Load
Forecasting, IEE Proceedings C, vol. 140, no. 2, pp. 311318, 1993.
[21] K.Y. Lee and J. H. Park, ShortTerm Load Forecasting Using an Artificial neural
Network, IEEE Transactions on Power Systems, vol. 7, no. 1, pp. 124132, 1992.
[22] C.N. Lu, Neural Network Based Short Term Load Forecasting, IEEE Trans. on Power
Systems, vol. 8, no. 2, pp. 336341, 1993.
[23] M. Peng, N.F. Hubele and G.G. Karady, Advancement in the Application of Neural
Networks for ShortTerm Load Forecasting, IEEE Transactions on Power Systems, vol.
7, no. 1, pp. 250257, 1992.
[24] Y. Rui and P. Jin, The Modelling Method for ANNBased Forecaster, CDC' 94, China,
1994.
[25] D. Srinivasan, A Neural Network ShortTerm Load Forecaster, Electric Power
Research, vol. 28, no. 2, pp. 227234, 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. 141149, 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 ShortTerm Load
Forecasting System, IEEE Trans. on Power Systems, vol. 10, no. 2, pp. 254265,
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. 213218, 1993
[30] M. Daneshdoost, M. Lotfalian, G. Bumroonggit and J.P. Ngoy, Neural Network with
Fuzzy SetBased Classification for Short Term Load Forecasting , IEEE Transactions
on Power Systems, vol.13, no. 4, pp. 13861391, 1998,.
[31] T.W.S. Chow and C.T. Leung, Nonlinear Autoregressive Integrated Neural Network
Model for ShortTerm 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 19728, 1993.
[33] S.T. Chen, Weather Sensitive ShortTerm 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 HighOrder Neural
Networks, Proceedings, IEEE Second International Forum on the Applications of
Neural Networks to Power Systems, vol. 5, no. 1, pp. 801805,1993.
[35] J. Villiers, BackPropagation Neural Nets with One and Two Hidden Layers, IEEE
Trans. on Neural Networks, vol. 4, no. 1, pp. 136146, 1992.
[36] Y.Y. Hsu, Design of Artificial Neural Networks for ShortTerm Load
Forecasting, IEE Proc. C, vol. 138, no. 1, pp. 407418, 1991.

8/9/2019 Char an 123456
48/49
42
[37] V.V. Phansalkar, Analysis of the BackPropagation Algorithm with
Momentum, IEEE Transactions on Neural Networks, vol. 5, no. 1, pp. 505506, 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. 14147, 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. 103118, 1993.
[41] D. Srinivasan, A.C. Liew and C.S. Chang, Forecasting Daily Load Curves Using A
Hybrid FuzzyNeural Approach, IEE ProceedingsC, 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. 17801787, 1994.
[43] Y. Qiu, A Fuzzy Neural Network for Shortterm Load Forecasting, Proceedings of
the IEEE Transactions on Power systems, vol. 9, no. 2, pp. 17721780, 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. 1923, 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. 17601772, 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. 673675, 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. SMC18, no. 1, pp.4960, 1988.
[50] L. A. Zadeh, Fuzzy Sets, Inf. Control, vol. 8, no. 1, pp. 33 8353, 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.