Short Term Load Forecasting Ann

8/6/2019 Short Term Load Forecasting Ann

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SHORT TERM LOAD FORECASTING

USING ARTIFICIAL NEURAL

NETWORKS AND FUZZY LOGIC

BY

K. Rithvik Prasad 07955A0203

G. Shravan Kumar 07955A0202

K. Priyanka 06951A0215

K.Naveen Kumar 06951A0213


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ACKNOWLEDGEMENT

The success accomplished in this project has been possible by the timely

help and guidance by many people. We wish to express our sincere and

heartfelt gratitude to those who have helped us in one way or other for

completion of our project.

We wish to express our propound sense of gratitude to Sri.P.Sridhar

Reddy for providing valuable guidance in successfully carrying out the project

work.

We have immense pleasure in expressing our thanks and deep sense of

gratitude to our guide Mrs.V.Naga Smitha, Department of Electrical and

Electronics engineering,

We would like to thank our Head of the Department, Prof. K.Manikyala

Rao for granting us permission and providing necessary facilities to work and

for his advice through out the course of the project .We would always be

grateful to him for his co-operation and kindness.

We would like to thank our beloved Principal, Prof. Dr G.POSHAL for his

valuable support in every aspect in making this project a success.


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Finally we express our sincere gratitude to all the faculty members of

EEE dept. our parents and our friends who contributed their valuable advice

and helped to complete the project successful


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INDEX

Abstract

Nomenclature

1. Introduction1.1.Back Ground

1.2..Importance of the load forecasting

1.3.The purpose of work

1.4..The structure of the work

2. Load forecasting2.1.The factors affecting the load

2.2..Properties of load curve

2.3.Types of load forecasting

2.3.1.Long term load forecasting

2.3.2.Medium term load forecasting

2.3.3.Short term load forecasting

2.4.Short term load forecasting techniques

2.4.1.Time series models

2.4.2.Multiple linear regression models

2.4.3.Stochastic models

2.4.4.State space models

2.4.5.ANN based load forecasting


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3.Fuzzy logic3.1.Introduction

3.2.Fuzzy inference system

3.2.1 .Main terms in fuzzy inference system4.Fuzzy logic module

4.1.Designing

4.1.1.Input variables

4.1.2.Rule base

4.1.3.Inference and defuzzification

5.Artificial neural network

5.1.Introduction

5.2.Training methods

5.3.Feed forward perceptron model

6. FL inference module with the base of Ann

7. Data of load and temperature

8. Load forecasting

9. Instructions used in program

10. STLF program

11. Results

12. Conclusion

13.Appendix

14. Reference


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ABSTRACT:

This project presents the approach to the short term load forecasting

using Artificial Neural Network (ANN) and Fuzzy Logic. Artificial Neural

Networks (AAN) have recently been receiving considerable attention and a large

number of publications concerning ANN-based short-term load forecasting

(STLF) have appeared in the literature. Along with this Fuzzy Logic , also a part

of Artificial Intelligence, is known to result in accurate predictions. In this

paper, a model using Fuzzy Logic with the help of an ANN system is used to

predict the load. There are a number of factors which affect the load, among

which, temperature plays a vital role. Here, we have analyzed the forecasting of

load with an added parameter of temperature.


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Introduction


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1.1. Back Ground:

Load forecasting is the one of the central function in power system

operations. The motivation for accurate forecasts lies in the nature of electricity

as a commodity and trading article. Electricity cannot be stored, which means

that for an electric utility the estimate of the future demand necessary in

managing the production and purchasing in an economically reasonable way.

Load forecasting methods can be divided into very short term, mid and

long term models according to the time span. In very short term load

forecasting the prediction time can be as short as a few minutes, while in the

long term forecasting it is from a few years up to several decades. This work

concentrates on short term load forecasting, where the prediction time varies

between a few hours and about one week.

Short term load forecasting (STLF) has been lately a very commonly addressed

problem in power system literature. One reason is that recent scientific innovations

have brought in new approaches to solve the problem. The development in computer

technology has broadened possibilities for these and other methods working and a real

time environment. Another reason may be that there is an international movement

towards greater competition in electricity markets.

Even if many forecasting procedures have been tested and proven successful,

none has achieved a strong stature as a generally applied method. A reason is that the

circumstances and requirements of a particular situation have a significant influence

on choosing the appropriate model. The results presented in the literature are usually

not directly comparable to each other.


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A majority of the recently reported approaches are based on Artificial Neural

Networks and Fuzzy logic (FL) systems have each yielded very encouraging results in

solving the problem of Short term load forecasting (STLF). Model combinations such

as fuzzy pre-processing of neural network inputs and fuzzy post processing of neural

networks outputs have yielded advances in reducing the forecasting error.

This project describes the development of a FL based model for STLF. The

developed model will provide a daily profile for 24-hour a head load forecast for normal

week days and holidays.

1.2. IMPORTANCE OF THE LOAD FORECASTING:

Load forecasting has always been important for planning and operational

decision conducted by 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 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.


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1.3. THE PURPOSE OF WORK:

This project studies the applicability ofFuzzy Logic model with a base of

Artificial Neural model on Short Term Load Forecasting. This model forecasts the load

for one whole day at a time. Testing is carried out on the real load data of Delhi

electric utility.

As there is need to forecast the load accurately at all spans, another goal is to

study the performance of the models for different lead times. Intuitively, it seems

possible that different models should be preferred for different time spans even within

the short term forecasting range.

The work provides the basis for an automatic forecasting application to be used in a

real-time environment.

There are some properties, which are considered important:

- The model should be automatic and able to adapt quickly to changes in the loadbehavior.

- The model is intended for use in many different cases. This means that generalityis desired.

- Updating the forecast with new available data should be possible. The hoursclosest to the forecasting time should always be forecast as accurately as possible.

- This model should be reliable. Even exceptional circumstances must not give riseto unreasonable forecasts.

- Outdoor temperature should be taken care of.- The model should be easily attachable to an energy management Different weather

conditions typical in Delhi, especially, large variation of system.


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- 1.4. THE STRUCTURE OF THE WORK:In first chapter a brief survey of previous work done on the STLF is discussed. It

concentrates on the subject of load forecasting in general, and needs and uses of the

Short Term Load Forecasting.

In the second chapter, first, the properties of the load curve of electric utility

and different factors affecting the load are discussed. Then possible approaches to the

problem are considered. The most popular conventional methods are briefly

introduced.

In third chapter discusses Fuzzy Logic (FL) models and their use in load

forecasting. First, a short general introduction to FL is given. Then, the most

popular network type, the Multi-Layer Perceptron network (MLP) is described.

The basic idea in applying MLP based methods to the problem at hand is given.

A literature survey on FL Short Term Load Forecasting models is carried out at

the end of the chapter. Finally, a description of the FL based hourly forecasting

for one week in different seasons by using different models is given. And it

Created by MAHEENis also explained the effect of the temperature on the load

forecasting.

In fourth chapter, FL based short term load forecasting is discussed, and

also discussed about the inputs to be chosen to FL for getting better

forecasting results.

In sixth chapter, conclusions and suggestions for further research are

given.


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Load Forecasting


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2.1 THE FACTORS AFFECTING THE LOAD:

Generally, the load of an electric utility is composed of very different

consumption units. A large part of the electricity is consumed by industrial

activities. Another part is of course used by private people in forms of heating,

lighting, cooking, laundry, etc. Also many services offered by society demand

electricity, for example street lighting, railway traffic etc.

Factors affecting the load depend on the particular consumption unit. The

industrial load is usually mostly determined by the level of the production. The

load is often quite steady, and it is possible to estimate its dependency on

different production levels. However, from the point of view of the utility selling

electricity, the industrial units usually add uncertainty in the forecasts. The

problem is the possibility of unexpected events, like machine breakdowns or

strikes, which can cause large unpredictable disturbances in the load level.

In the case of private people, the factors determining the load are much

more difficult to define. Each person behaves in his own individual way, and

human psychology is involved in each consumption decision. Many social and

behavioral factors can be found. For example, big events, holidays, even TV-

programs, affect the load. The weather is the most important individual factor;

the reason is largely being the electric heating of houses, which becomes more

intensive as the temperature drops.

As large part of the consumption is due to private people and other small

electricity customers, the usual approach in load forecasting is to concentrate


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on the aggregate load of the whole utility. This reduces the number of factors

that can be taken into account, the most important being.

In the short run, the meteorological conditions cause large variation in

this aggregated load. In addition to the temperature, also wind speed, cloud

cover, and humidity have an influence.

In the long run, the economic and demographic factors play the most

important role in determining the evolution of the electricity demand.

From the point of view of forecasting, the time factors are essential. By

these, various seasonal effects and cyclical behaviors (daily and weekly

rhythms) as well as occurrences of legal and religious holidays are meant.

The other factors causing disturbances can be classified as random

factors. These are usually small in the case of individual consumers, although

large social events and popular TV-programs add uncertainty in the forecasts.

Industrial units, on other hand, can cause relatively large disturbances.

Only Short Term Forecasting will be dealt in this project, and the time

span of the forecasts will not range further than about one week ahead.

Therefore, the economic and demographic factors will not be discussed.

The decision to combine all consumption units into one aggregate load

means that the forecasting rests largely on the past behavior of the load. Time

factors play the key role in the analysis of this work.


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2.2 PROPERTIES OF LOAD CURVE:

In this work, the load curve to be forecasted consists of hourly load

values, which are in reality hourly averages. This means that the load curve

can be seen as a time series of real numbers, each being the average load of

one hour. Although, the number of the observations is restricted to 24 per day,

the models studied can be applied with slight modifications to cases where the

interval between observations is shorter. The hourly electric load demand of a

Delhi electricity utility is used throughout this work as the test case. The

hourly temperature data from the influential district is also available. The data

of the months Aug 2009 are available, so the length of the data set is about 4

weeks. For a more thorough testing, load data of an even longer time period

would be preferred.

The load curve for different weeks shown in figure can be easily seen; in

the winter, the average load is about twice as high as in the summer. The

extent of this property is a special characteristic of Delhi's load conditions, and

is due to great differences between the weather conditions of different seasons

of the year.


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Figure2.1: load curve for one day

Figure2.2: load over the period one week

The weekly rhythm originates from the working day weekend rhythm

obeyed by most people. On working days social activities are at a higher level

than on Saturdays and Sundays, and therefore the load is also higher. The

series begins with five quite similar patterns, which are the load curves of


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Monday-Friday. Then two different patterns for Saturday and Sunday follow.

This same weekly pattern is then repeated.

2.3 TYPES OF LOAD FORECASTING:

Depending upon the period of forecast, the load forecast is of three types:

2.3.1 Long term Load forecast

2.3.2 Medium term Load forecast

2.3.3 Short-term load forecast.

The Long-term load forecast takes quite a long time to plan, install and

additional generating capacity.

In this we are presenting Short term Load forecast, which is important for

online control and security evaluation of a large system.

2.3.1 LONG TERM LOAD FORECASTING:

It takes quit a long time to plan, install and commission additional

generating capacity. Generally, system expansion planning starts with a

forecast of anticipated future load requirements. Proper long term forecasting is

necessary for optimal generation capacity expansion.

One method, used by many utilities, for long term, load forecasting is

extrapolation. This technique involves fitting trend curves to basic historical

data, adjusted to reflect the growth trend itself. Once the trend curve is known,

the forecast is found by evaluating the trend curve function at the desired

future point.


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Another technique for long term load forecasting is Correlation. This

technique relates system leads to various demographic and economic factors.

Typical factors like: population, employment, industrial licenses, appliance

saturation, weather data etc. are used in correlation techniques. However, the

forecasting the demographic and economic factors is rather difficult.

2.3.2 MEDIUM TERM LOAD FORECAST:

Medium term load forecast is just as important as Long term load

forecasting. The only difference is the time range. This type of forecast takes

the time period ranging from a couple of months to a year or so.

2.3.3 SHORT TERM LOAD FORECAST:

A precise short term load forecasting is essentially for monitoring and

controlling power system operation. The hourly load forecast with a lead-time up to

one week in advance is necessarily for online solution of scheduling problem. A 24-

hour load forecast is needed for successful operation of power plant. One hour forecast

is important for online time control and security evaluation of a large power system.

Short-term load forecasting techniques generally involve physical

decomposition of load into components. The load is decomposed into a daily

pattern reflecting the difference in activity level during the day. A weekly

pattern representing the day of the week effect on load is done. A trend

component concerning the seasonal growth in load and a weather sensitive

component reflecting the deviations in load due to weather fluctuations is also

considered. The random errors can be statistically analyzed to obtain a


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stochastic model for a error estimation. Thus, the expected hourly load forecast

is divided in to 5 components and can be written as:

Y (i, j). =ADP (j)+AWP (k, j)+WSC (i, j)+TR (i)+SEC (i, j)

Where

Y (i, j)=Load forecast for j th hour of i th day.

ADP (j)=Average daily load pattern at j th hour.

AWP (k, j)=Average weekly load pattern at j th hour and k th day of week.

(k=1,27)

WSC (i, j)=Weather sensitive component at j th hour of i th day

SEC (i, j)=Stochastic error component which is assumed to be normally

distributed.

TR (i)=Trend component of load on i th day.

The average daily pattern represents the hour of the day effect. It is an average

of the daily load pattern over an optimal number of past days. The average

weekly pattern reflects the day of week effect. It is calculated as the average of

the weekly cycles over a certain number of past weeks.

The weather sensitive components represent the changes in customer

requirements according to variations in weather conditions. Generally

temperature is considered as the only weather variable since data banks for

other weather variables like wind, humidity etc. are usually not available.


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The trend component includes three components: a long-term growth

trend, a short-term trend dependent on the economic cycle and a time of the

year pattern. The statistical error components represent error in estimate. The

standard deviation and variance are usually taken as error parameters.

2.4 SHORT TERM LOAD FORECASTING TECHNIQUES:

Load forecasting has been a central and an integral process in planning and

operation of electric utilities. Many techniques and approaches have been

investigated to tackle this problem in the last two decades. These are often

different in nature and apply different engineering considerations and

economic analysis. Some of the short-term loads forecasting techniques have

been listed below.

2.4.1 Time series models

2.4.2 Multiple Linear regression models

2.4.3 Stochastic models

2.4.4 State space models

2.4.5 ANN based load forecasting

2.4.1 Time Series models:

In the simplest form, a time series model takes the previous week's actual

load pattern as a model to predict the present week's load. Alternatively, a set

of load patterns is stored for typical weeks with different weather conditions.

These are then heuristically combined to create the forecast.


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More commonly, a time series model is of the form:

N

z(t)= a(i) f(t)+ v(t)2.1

i=1

Where the load at time t is expressed as a weighted sum of explicit time

functions, usually sinusoids with a period of 24 or 168. The coefficients a(i)are

slowly varying constants being usually estimated through a linear regression or

exponential smoothing. The modeling error v(t) is assumed to be white noise.

2.4.2 Regression models:

Regression models normally assume that the load can be divided into a

standard load component and a component linearly dependent on some

explanatory variables. The model can be written:

z(t)=b(t)+ )()()(1

ttyiaN

i

i I!

2.2

Where b (t) is the standard load, (t)is a white noise component, and yi(t) are

the independent explanatory variables. The most typical explanatory variables

are weather factors.

They model different consumer categories by separate regression models.

The load is divided into a rhythm component and a temperature dependent


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component. The rhythm component corresponds to the load of a certain hour

in the average temperature of the modeling period.

More complicated model variations have also been proposed. Some models use

earlier load values as explanatory variables in addition to external variables.

Regression models are among the oldest methods suggested for load

forecasting. They are quite insensitive to occasional disturbances in the

measurements. The easy implementation is another of its strengths. The serial

correlation, which is typical when regression models are used on time series,

can cause problems.

2.4.3 Stochastic models:

The method appears to be popular that has been applied and is still applied

to STLF in electric power industry. The load series y(t), is modeled as the

output form a linear filter that has a random series input, a(t) usually called

white noise as shown in figure.

Fig2.3. Load Time Series Modeling


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Depending on the characteristic of the linear filter, different models are

classified as Autoregressive (AR) process, Moving average (MA) process,

Autoregressive Moving Average (ARMA) process. This is a very popular class of

dynamic forecasting models.

The basic principle is that the load time series can first be transformed into

a stationary time series (i.e. invariant with respect to time) by a suitable

differencing. Then the remaining stationary series can be filtered into white

noise. The models assume that the properties of the time series remain

unchanged for the period used in model estimation, and all disturbances are

due to this white noise component contained in the identified process.

The stochastic time series models have many attractive features. First, the

theory of the models is well known and therefore it is easy to understand how

the forecast is composed. The properties of the model are easy to calculate; the

estimate for the variance of the white noise component allows the confidence

intervals for the forecasts to be created.

The model identification is also relatively easy. Established methods for

diagnostic checks are available. Moreover, the estimation of the model

parameters is quite straightforward, and the implementation is not difficult.

The weakness in the stochastic models is in the adaptability. In reality, the

load behavior can change quite quickly at certain parts of the year. While in

ARIMA models the forecast for a certain hour is in principle a function of all

earlier load values, the model cannot adapt to the new conditions very quickly,


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even if model parameters are estimated recursively. A forgetting factor can be

used to give more weight to the most recent behavior and thereby improve the

adaptability.

Another problem is the handling of the anomalous load conditions. If the

load behavior is abnormal on a certain day, this deviation from the normal

conditions will be reflected in the forecasts into the future. A possible solution

to the problem is to replace the abnormal load values in the load history by the

corresponding forecast values.

2.4.4 State-space models:

In the linear state-space model, the load at time tcan be written:

Z (t)=CTx (t),

Where

X (t+1)=Ax (t)+Bu (t)+w (t),

The state vector at time t is x (t), and u (t) is a weather variable based input

vector. w(t) is a vector of random white noise inputs. Matrices A, B, and the

vector C are assumed constants.

There exist a number of variations of the model. Some examples

can be found.

In fact, the basic state-space model can be converted into an ARIMA

model and vice versa, so there is no fundamental difference between the


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properties of the two model types. According to Gross and Galiana (1987), a

potential advantage over ARIMA models is the possibility to use prior

information in parameter estimation via Bayesian techniques. Yet, they point

out that the advantages are not very clear and more experimental comparisons

are needed.

2.4.5: EXPERT SYSTEMS MODELS:

Expert systems are heuristic models, which are usually able to take

both quantitative and qualitative factors into account. Many models of this type

have been proposed since the mid 1980's. A typical approach is to try to imitate

the reasoning of a human operator. The idea is then to reduce the analogical

thinking behind the intuitive forecasting to formal steps of logic.

A possible method for a human expert to create the forecast is to search in

history database for a day that corresponds to the target day with regard to the

day type, social factors and weather factors. Then the load values of this

similar day are taken as the basis for the forecast.

An expert system can thereby be an automated version of this kind of a

search process .On the other hand, the expert system can consist of a rule

base defining relationships between external factors and daily load shapes as

in Fuzzy Logic models.

The heuristic approach in arriving at solutions makes the expert systems

attractive for system operators; the system can provide the user with the line of

reasoning followed by the model.


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Some of the expert system models include Artificial Neural Network

(ANN) model, Fuzzy Logic (FL) model and the combination of both ANN-FL

models.


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FuzzyLogic


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3.1 INTRODUCTION:

Fuzzy logic is a form of evalued logic derived from fuzzy set theory to deal

with reasoning that is approximate rather than precise. In contrast with "crisp

logic", where binary sets have binary logic, the fuzzy logic variables may have a

membership value of not only 0 or 1 that is, the degree of truth of a

statement can range between 0 and 1 and is not constrained to the two truth

values of classic propositional logic. Furthermore, when linguistic variables are

used, these degrees may be managed by specific functions.

Fuzzy logic emerged as a consequence of the 1965 proposal of fuzzy set

theory by Lotfi Zadeh. Though fuzzy logic has been applied to many fields, from

control theory to artificial intelligence, it still remains controversial among most

statisticians, who prefer Bayesian logic, and some control engineers, who prefer

traditional two-valued logic

3.2 FUZZY INFERENCE SYSTEM:

Fuzzy inference is the process of formulating the mapping from a given

input to an output using fuzzy logic. The mapping then provides a basis from

which decisions can be made, or patterns discerned.

The process of fuzzy inference involves all of the pieces that are described in

the previous sections: Membership, Logical Operations, and If-Then Rules. You

can implement two types of fuzzy inference systems in the toolbox: Mamdani-

type and Sugeno-type. These two types of inference systems vary somewhat in

the way outputs are determined.


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3.2.1MAIN TERMS IN FUZZY INFERENCE SYSTEM: Fuzzification Membership function Rule base Inferencing Defuzzification

FIGURE 3.1: BLOCK DIAGRAM OF FUZZY INFERENCE SYSTEM


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a)FUZZIFICATION:The fuzzification comprises the process of transforming crisp values into grades of

membership for linguistic terms of fuzzy sets. The membership function is used to

associate a grade to each linguistic term.

b)MEMBERSHIP FUNCTIONS: 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.

Some features to note are:

y SHAPE - triangular is common, but bell, trapezoidal, haversine and,exponential have been used. More complex functions are possible but

require greater computing overhead to implement.

y HEIGHT or magnitude (usually normalized to 1)y WIDTH (of the base of function)y SHOULDERING (locks height at maximum if an outer function.

Shouldered functions evaluate as 1.0 past their center)

y CENTER points (center of the member function shape)


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y OVERLAP (N&Z, Z&P, typically about 50% of width but can be less).

FIGURE 3.2: MEMBERSHIP FUNCTIONS

Figure above, illustrates the features of the triangular membership function which is used in

this example because of its mathematical simplicity. Other shapes can be used but the triangular

shape lends itself to this illustration. The degree of membership (DOM) is determined by

plugging the selected input parameter(error or error-dot) into the horizontal axis and projecting

vertically to the upper boundary of the membership function(s).

c)RULE BASE:Fuzzy set theory defines fuzzy operators on fuzzy sets. The problem in applying

this is that the appropriate fuzzy operator may not be known. For this reason, fuzzy

logic usually uses IF-THEN rules, or constructs that are equivalent, such as fuzzy

associative matrices.

Rules are usually expressed in the form:

IFvariableISpropertyTHEN action.


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d)INFERENCING: The last step completed in the example in the last article was to

determine the firing strength of each rule. It turned out that rules 4, 5, 7, and

8 each fired at 50% or 0.5 while rules 1, 2, 3, 6, and 9 did not fire at all (0% or

0.0). The logical products for each rule must be combined or inferred (max-

min'd, max-dot'd, averaged, root-sum-squared, etc.) before being passed on to

the defuzzification process for crisp output generation. Several inference

methods exist.

The MAX-MIN method tests the magnitudes of each rule and selects the

highest one. The horizontal coordinate of the "fuzzy centroid" of the area under

that function is taken as the output. This method does not combine the effects

of all applicable rules but does produce a continuous output function and is

easy to implement.

The MAX-DOT or MAX-PRODUCT method scales each member function to

fit under its respective peak value and takes the horizontal coordinate of the

"fuzzy" centroid of the composite area under the function(s) as the output.

e) DEFUZZICATION:

The defuzzification of the data into a crisp output is accomplished by combining

the results of the inference process and then computing the "fuzzy centroid" of the

area. The weighted strengths of each output member function are multiplied by their

respective output membership function center points and summed. Finally, this area


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is divided by the sum of the weighted member function strengths and the result is

taken as the crisp output. One feature to note is that since the zero center is at zero,

any zero strength will automatically compute to zero. If the center of the zero function

happened to be offset from zero (which is likely in a real system where heating and

cooling effects are not perfectly equal), then this factor would have an influence.

ADVANTAGES OF FUZZY LOGIC:

FL offers several unique features that make it a particularly good

choice for many control problems.

It is inherently robust since it does not require precise, noise-free inputsand can be programmed to fail safely if a feedback sensor quits or is

destroyed. The output control is a smooth control function despite a wide

range of input variations.

Since the FL controller processes user-defined rules governing the targetcontrol system, it can be modified and tweaked easily to improve or

drastically alter system performance. New sensors can easily be

incorporated into the system simply by generating appropriate governing

rules.

FL is not limited to a few feedback inputs and one or two control outputs,nor is it necessary to measure or compute rate-of-change parameters in

order for it to be implemented. Any sensor data that provides some

indication of a system's actions and reactions is sufficient. This allows


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the sensors to be inexpensive and imprecise thus keeping the overall

system cost and complexity low.

Because of the rule-based operation, any reasonable number of inputscan be processed (1-8 or more) and numerous outputs (1-4 or more)

generated, although defining the rule base quickly becomes complex if

too many inputs and outputs are chosen for a single implementation

since rules defining their interrelations must also be defined. It would be

better to break the control system into smaller chunks and use several

smaller FL controllers distributed on the system, each with more limited

responsibilities.

FL can control nonlinear systems that would be difficult or impossible tomodel mathematically. This opens doors for control systems that would

normally be deemed unfeasible for automation.


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FuzzyL

ogicmodule


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4.1. DESIGNING:

The Fuzzy Inference systems, unlike neural networks, are applied to

peak load and through load forecasting only. The proposed technique for

implementing fuzzy logic based forecasting is:

Identification of the day of a certain week.

Forecast maximum and minimum temperature for that particular week

Listing the maximum temperature and peak load.

For the selected data, the relationship between the load and the temperature is

sent to the ANN model.

The following is the Fuzzy Logic module design consisting of two input variables, a

rule base, where the processing of the membership functions are done; and the output

variable.


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FIGURE 4.1: FUZZY LOGIC MODULE

4.1.1 INPUT VARIABLES:

There are two input variables used in terms of temperature, namely

Temperature 1 and Temperature 2. A more accurate fuzzy expert system can be

obtained by dividing the region into intervals. Each interval has its own membership

function. The intervals for the temperature forecasting errors are defined as follows.

Temperatures much lower than the forecasted value (VC)

Temperatures lower than the forecasted value (C)

Temperatures closer to the forecasted value (CMF)

Temperatures higher than the forecasted value (H)


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Temperatures much higher than the forecasted value (VH)

In this project the inputs to the Fuzzy logic Model are the following two sets of

temperature data.

FIGURE 4.2: INPUT VARIABLE (TEMPERATURE 1)


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FIGURE 4.3: INPUT VARIABLE (TEMPERATURE 2)

Where,

VC Very Cold

C Cold

CMF Comfortable

H Hot

VH Very Hot, for the membership functions

And,

NB Negative Big

NS Negative Small

ZE Zero


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PS Positive Small

PB Positive Big, for the rule base

4.1.2: RULE BASE

Here the rules are created according to the tables above which concern the

input variables. The rules are formed as,

IF condition AND condition THEN result.

So as a result of 5 membership functions for each input variable, there are on a

total, 25 rules. According to the variation in the temperature, the relationship is

formed between the temperature and the load. This, results in the formation of load

pattern, which is later utilized by an ANN model forecast the load.

4.1.3: INFERENCE AND DEFUZZIFICATION:

The rules are processed according to the ranges of the membership functions

and the output result is obtained. The result is the liaison between the temperature

and the load which is required for optimum load forecast. The method used to convert

fuzzy sets to crisp output set is the Centroid method of Defuzzification.


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Artificial NeuralNetworks


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5.1 INTRODUCTION:A neural network is an interconnected assembly of simple processing

elements known as neurons. The processing ability of the network is stored in

inter - unit connection strengths called weights obtained by a process of

learning from a set of training patterns.

It is a massively parallel distributed processor made up of neurons which

has a natural propensity for storing experiential knowledge and making it

available for use.

It resembles the brain in two respects,

Knowledge is acquired by the network from its environmentthrough a learning process.

Interneuron connection strengths known as synaptic weightsare used to store the acquired knowledge.

The Artificial Neural Networks are inspired from the human brain which

consists of structural constituents called neurons (nodes, units, processing

elements etc).

The human brain consists of 1010 to 1011 neurons, each of which is

connected to 104 neurons. These neurons communicate with each other by

means of electric impulses.


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FIGURE 5.1: ARTIFICIAL NEURAL NETWORKS

Neural networks can be classified as, single layered and multi layered

models.

y Single layered models: These networks contain only one layer of neurons,to which the input is given and an output is obtained.

FIGURE 5.2 - SINGLE LAYERED NEURAL NETWORK


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y Multi layered models: These networks have three or more layers. For models asthese, there are basically three layers namely, input layer, hidden layer and the

output layer.

FIGURE 5.3 - MULTI LAYERED NEURAL NETWORK

5.2: TRAINING METHODS

All neural network models after modeling must undergo training, and

there are three distinct classifications through which networks may be

trained.

Supervised training method: In this method, the network is made tolearn by providing an external teacher. Here a set of example pairs are

given (x,y), xX and yY, and the aim is to find a function f : XY in the

allowed class of functions that matches the examples. Tasks that fall

within the paradigm of supervised learning are pattern recognition (also


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known as classification) and regression (also known as function

approximation).

Unsupervised training method: In this method we are given some datax, and the cost function to be minimized can be any function of the data

x and the network's output, f. Here an external teacher is not used.

Tasks that fall within the paradigm of unsupervised learning are in

general estimation problems.

Reinforcement learning: It projects the learning aspects based on thenetworks actions and are represented either as good action or bad

action. Tasks that fall within the paradigm of reinforcement learning are

control problems, games and other sequential decision making tasks.

5.3 FEED FORWARD PERCEPTRON MODEL:

The original perceptron model was developed byFrank Rosenblatt in 1958. This

model consisted of three layers, (1) a retina that distributed the inputs to the second

layer, (2) association units that combine the inputs with weights and trigger a

threshold activation function which feeds to the output layer, (3) the output layer

which combines the values.

Multi-Layer Perceptron network is the most popular neural network type and

most of the reported neural network short-term load forecasting models are based on

it. The basic unit (neuron) of the network is a perceptron. This is a computation unit,

which produces its output by taking a linear combination of the input signals and by

transforming this by a function called activity function. The output of the perceptron as

a function of the input signals can thus be written:


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where

yis the output

xiare the input signals

wiare the neuron weights

qis the bias term (another neuron weight)

sis the activity function

Activation function: A function used to transform the activation level of a unit

(neuron) into an output signal. Typically, activation functions have a "squashing"

effect.

There are a wide range of activation functions. Some of the most important and widely

used functions are threshold function, sigmoid function, piecewise linear function and

hard limiter function.

Possible forms of the activity function are linear function, step function, logistic

function and hyperbolic tangent function.


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PERCEPTRON NEURAL NETWORK MODEL

FIGURE 5.4 - A PERCEPTRON NETWORK WITH THREE LAYERS

The MLP network consists of several layers of neurons. Each neuron in a

certain layer is connected to each neuron of the next layer. There are no feedback

connections. A three-layer MLP network is illustrated in figure 4.6

The most often used MLP-network consists of three layers: an input layer, one

hidden layer, and an output layer. The activation function used in the hidden layer is

usually nonlinear (sigmoid or hyperbolic tangent) and the activation function in the

output layer can be either nonlinear (a nonlinear-nonlinear network) or linear (a

nonlinear network).

Input Layer: A vector of predictor variable values (x1...xp) is presented to the input

layer. The input layer (or processing before the input layer) standardizes these values

so that the range of each variable is -1 to 1. The input layer distributes the values to

each of the neurons in the hidden layer. In addition to the predictor variables, there is


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a constant input of 1.0, called the biasthat is fed to each of the hidden layers; the bias

is multiplied by a weight and added to the sum going into the neuron.

Hidden Layer: Arriving at a neuron in the hidden layer, the value from each input

neuron is multiplied by a weight (wji), and the resulting weighted values are added

together producing a combined value uj. The weighted sum (uj) is fed into a transfer

function, , which outputs a value hj. The outputs from the hidden layer are

distributed to the output layer.

Output Layer: Arriving at a neuron in the output layer, the value from each hidden

layer neuron is multiplied by a weight (wkj), and the resulting weighted values are

added together producing a combined value vj. The weighted sum (vj) is fed into a

transfer function, , which outputs a value yk. The y values are the outputs of the

network.


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FL inference

Module with the

Base of ANN


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6.1 FUZZY LOGIC BASED INFERENCE SYSTEM:

Fig6.1: Block diagram ofFuzzy logic based interfaced system

DATA PROCESSING UNIT:

Here the entire raw data is continuously uploaded into a storage unit. This data is

the load with all the different variations and factors that affect the load.This is then

sent to the next block, which is the Preprocessing unit.


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PREPROCESSING DATA:

Here, the raw data sent from the processing unit, is preprocessed, or, made

ready with appropriate conditions and requirements, that are needed by the Fuzzy

Logic Module to work.

In this paper, the data is processed in terms of patterns of weeks. The entire load

which is sent, is divided into weeks and the load patterns are created. Also, the

temperature as an added parameter is segregated.

FUZZY LOGIC MODULE:

This is the heart of the entire process. Here, the FLM shows the relationship

between the load and the temperature as a parameter. It shows how the temperature

affects the variations in the load. Without this, the ANN model will be unable to give

accurate results. The rest of the process heavily depends on the values given by the

FLM. The following is the internal process of the FLM.


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FUZZIFICATION:

The fuzzification comprises the process of transforming crisp values into grades

of membership for linguistic terms of fuzzy sets. The membership function is used to

associate a grade to each linguistic term.

INPUT VARIABLES:

Both the variables are in terms of temperature and they are divided into 5

membership functions.

MEMBERSHIP FUNCTIONS:

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 input variables 5 membership functions are divided as very

cold(VC), cold(C), comfortable(COM), hot (H), very Hot (VH).

RULES:

Fuzzy set theory defines fuzzy operators on fuzzy sets. The problem in applying

this is that the appropriate fuzzy operator may not be known. For this reason, fuzzy

logic usually uses IF-THEN rules, or constructs that are equivalent, such as fuzzy

associative matrices.

Rules are usually expressed in the form:

IFvariableISpropertyTHEN action


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DEFUZZIFICATION:

The defuzzification of the data into a crisp output is accomplished by combining

the results of the inference process and then computing the "fuzzy centroid" of the

area. The weighted strengths of each output member function are multiplied by their

respective output membership function center points and summed. Finally, this area

is divided by the sum of the weighted member function strengths and the result is

taken as the crisp output. This crisp output is in the form of a relationship between

load and temperature.

Finally the output of the FLM is given to the ANN model


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Data ofLoad and

Temperature


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7.1 LOAD DATA

%august 2008(1 is Thursday)

aug=[2152 2021 1982 1995 1882 1968 2026 2032 2090 2287 2403 2403 2433 2513

2574 2466 2464 2512 2486 2555 2630 2712 2644 2587;

2554 2538 2434 2380 2325 2321 2266 2254 2184 2208 2251 2237 2229 2279 2405

2458 2457 2237 2268 2308 2430 2557 2532 2498;

2554 2538 2434 2380 2325 2321 2266 2254 2184 2208 2251 2237 2229 2279 2405

2458 2457 2237 2268 2308 2430 2557 2532 2498;

2417 2354 2336 2222 2225 2207 2133 2103 2206 2222 2542 2485 2115 1967 2040

2019 2088 2051 2186 2403 2276 2401 2332 2262;

2134 2029 1907 1719 1638 1569 1653 1711 1771 2016 1802 1863 1983 2032 2078

2109 2186 2197 2245 2332 2385 2346 2245 2230;

2148 2071 2068 2040 2008 1957 2029 2106 2130 2381 2382 2426 2299 2392 2451

2471 2499 2308 2151 2468 2509 2451 2447 2387;

2255 2199 2197 2085 2071 2108 2037 1874 1909 2077 2082 2100 2155 2236 1756

2164 2168 2199 2215 2250 2354 2430 2413 2292;

2116 2066 1978 1942 1847 1856 1941 2067 2150 2311 2446 2506 2449 2374 2433

2443 2489 2411 2411 2479 2518 2259 2453 2394;

2322 2225 2168 2272 2088 2253 2085 2092 2154 2262 2347 2309 2219 2198 2169

2213 2220 2180 2202 2426 2451 2495 2428 2351;


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2303 2223 2179 2105 2086 2095 2100 2177 2129 2151 2141 2164 2177 2197 2245

2335 2338 2324 2177 2197 2245 2335 2338 2324;

2340 2310 2270 2243 2213 2192 2133 2193 2228 2468 2458 2465 2506 2553 2590

2545 2498 2553 2561 2698 2700 2692 2709 2641;

2502 2468 2442 2424 2379 2293 2252 2295 2436 2587 2644 2515 2518 2587 2647

2595 2527 2539 2622 2608 2616 2690 2714 2615;

2560 2502 2457 2419 2442 2458 2388 2403 2431 2556 2597 2563 2571 2622 2680

2662 2640 2614 2607 2693 2524 2617 2700 2590;

2521 2513 2501 2415 2410 2430 2379 2383 2466 2605 2634 2450 2353 2298 2218

2351 2405 2305 2308 2449 2468 2574 2544 2461;

2301 2242 2242 2208 2118 2064 2459 2180 2309 2533 2535 2409 2518 2513 2626

2679 2707 2534 2571 2608 2592 2704 2711 2627;

2541 2510 2440 2389 2321 2304 2207 2158 2227 2391 2304 2212 2149 2051 2055

2116 2194 2146 2253 2379 2429 2469 2444 2340;

2227 2148 2117 2016 2010 2032 2004 2033 2070 2061 2148 2123 2116 2078 2123

2138 2200 2225 2244 2402 2476 2563 2498 2428;

2289 2204 2179 1958 2041 1885 2065 2105 2215 2415 2412 2325 2422 2447 2500

2597 2565 2478 2463 2519 2387 2393 2382 2412;

2335 2277 2209 2184 2138 2114 2134 2226 2288 2452 2 2579 2497 2554 2505

2481 2530 2644 2732 2695 2562;


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2452 2437 2357 2319 2280 2256 2222 2295 2229 2443 2544 2408 2441 2464 2471

2471 2547 2450 2499 2534 2524 2632 2657 2663;

2532 2443 2402 2337 2367 2327 2314 2269 2281 2503 2568 2534 2541 2511 2624

2747 2601 2384 2634 2640 2613 2665 2677 2677;

2618 2539 2474 2505 2373 2344 2289 2379 2418 2650 2710 2685 2676 2779 2773

2691 2640 2465 2421 2599 2584 2676 2490 2628;

2529 2513 2498 2390 2405 2279 2275 2317 2347 2620 2550 2515 2408 2478 2510

2576 2546 2453 2397 2414 2427 2479 2443 2389;

2304 2189 2186 2173 2115 2138 1963 2097 2124 2193 2191 2201 2120 2122 2052

2055 2099 2106 2094 2033 2324 2409 2400 2300;

2206 2187 2143 2109 2021 1984 1918 2062 1908 2244 2363 2311 2370 2314 2391

2228 2311 2292 2306 2439 2349 2414 2371 2266;

2140 2085 2046 1970 1988 1972 1944 2084 2156 2276 2425 2421 2221 2294 2209

2361 2407 2384 2400 2430 2432 2551 2533 2387;

2238 2216 2139 2058 2055 2039 2183 2116 2107 2406 2409 2403 2386 2408 2393

2506 2473 2381 2390 2466 2391 2428 2472 2322;

2257 2215 2205 2127 2070 2090 2130 2146 2343 2517 2559 2521 2263 2590 2575

2552 2529 2488 2263 2590 2575 2552 2529 2488;

2491 2408 2434 2371 2333 2311 2327 2300 2397 2509 2523 2515 2547 2543 2562

2627 2621 2628 2600 2737 2591 2745 2642 2545;


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2500 2487 2422 2376 2348 2326 2326 2191 2244 2475 2512 2578 2470 2486 2555

2569 2523 2517 2592 2570 2590 2563 2410 2416];

7.2 TEMPERATURE DATA:

T2=[58 60 64 61 61 69 68 72 69 61 68 69 69 69 61 69 69 68 69 65 59 59 63 65 70 62

58 63 62 62 69 69 69 65 66 64 72 77 85 75 70 72 75 74 71 79 75 72 76 75 74 79 80

74 75 80 78 81 83 84;

58 59 61 60 60 67 68 73 66 59 67 69 67 68 60 68 68 66 68 65 58 58 63 65 69 62

57 62 60 64 68 67 67 63 66 63 70 75 82 74 69 71 75 73 70 78 75 71 75 75 71 78 78

73 74 79 76 78 79 82;

57 58 60 59 59 65 67 73 64 59 64 68 66 66 60 67 70 63 64 65 57 57 62 63 68 62

57 60 59 63 68 66 66 61 64 62 70 74 83 72 68 71 74 71 68 78 74 69 72 76 70 74 76

70 74 78 74 76 78 80;

56 57 58 58 57 64 66 72 64 58 63 67 66 64 58 67 70 62 63 64 56 56 62 61 67 61

56 59 58 59 67 65 64 60 62 61 68 74 83 71 67 70 72 70 66 77 73 67 70 74 69 74 76

69 73 78 72 74 77 79;

55 57 57 57 57 63 64 71 64 58 62 64 66 63 56 64 69 61 62 64 55 55 60 60 66 60

55 56 57 58 66 64 64 60 61 60 66 74 80 70 65 68 71 70 66 76 70 66 68 72 68 74 74

68 72 76 71 73 75 77;

54 56 57 56 56 63 62 70 62 57 61 63 64 61 54 63 67 60 61 63 55 55 58 60 65 59

54 55 58 58 64 63 63 59 59 59 65 74 78 69 65 67 70 68 66 75 68 65 72 72 66 72 72

67 72 74 70 71 74 76;


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54 56 56 55 56 62 61 67 60 54 60 63 62 60 53 62 64 60 61 63 54 54 56 60 63 59

55 54 57 58 61 63 62 58 60 58 66 72 76 68 64 66 70 68 64 73 67 64 72 72 65 73 72

66 72 71 70 70 72 75;

55 55 59 55 55 61 60 67 60 52 59 62 61 60 53 60 65 58 60 61 54 54 56 60 62 58

54 54 55 56 60 61 62 57 60 60 64 70 74 69 63 66 68 64 63 73 67 62 72 72 64 73 72

64 70 69 69 69 71 74;

55 59 62 58 55 61 66 67 62 50 60 63 61 59 53 67 66 62 60 61 56 56 57 60 61 57

53 53 55 55 64 62 64 61 62 64 63 70 74 70 67 64 68 61 62 72 66 62 70 70 68 76 72

68 70 78 74 72 75 75;

59 63 65 62 62 62 70 71 66 60 64 64 61 58 52 72 68 66 64 66 61 61 56 60 60 60

58 58 60 60 70 66 70 64 68 72 66 79 76 76 69 64 68 62 62 71 65 61 74 72 74 78 74

72 72 82 78 78 83 79;

67 68 69 68 66 70 72 74 68 63 68 67 64 60 54 78 70 70 68 69 62 62 60 62 61 64

63 63 66 64 74 70 72 70 72 76 72 82 80 80 74 70 72 70 66 71 66 66 78 76 78 70 78

78 78 84 84 85 87 87;

71 71 72 72 71 74 75 77 70 66 72 72 70 66 58 83 74 76 72 70 63 63 62 67 64 68

68 66 70 70 78 75 75 74 74 83 76 89 83 83 78 73 77 74 71 73 69 70 80 80 82 74 82

80 80 88 88 88 90 89;

73 75 75 75 75 76 79 81 73 68 74 74 72 69 62 84 78 75 76 71 66 66 66 70 65 70

70 71 74 74 80 78 78 76 76 86 80 94 88 86 80 76 80 78 74 75 72 74 86 85 86 88 76

83 84 90 92 95 97 99;


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75 77 77 76 79 79 82 83 75 70 76 77 74 70 66 85 79 78 79 73 70 70 69 74 69 72

72 75 78 76 81 80 80 78 79 89 86 95 90 90 82 82 83 81 78 79 77 78 88 88 88 92 87

86 86 91 94 96 101 101;

78 78 80 79 81 82 84 83 76 70 79 80 78 71 67 85 80 79 80 76 72 72 71 78 71 72

74 78 79 78 82 82 80 80 82 91 90 98 92 94 86 85 85 84 83 83 82 85 90 90 88 96 88

87 86 92 95 98 103 102;

78 78 78 78 82 81 83 82 76 68 80 83 81 72 68 83 80 80 80 77 74 74 74 80 73 72

74 79 80 80 82 82 81 80 80 92 93 99 94 94 88 88 86 86 88 86 84 86 91 91 90 95 90

88 87 94 96 98 104 103;

78 77 77 77 81 80 82 80 76 68 80 83 82 73 70 80 80 79 80 79 76 76 73 82 74 72

76 79 80 78 81 82 80 81 80 91 94 99 94 94 87 88 87 88 90 87 83 88 92 92 90 94 90

88 87 96 94 98 104 104;

75 75 74 76 79 79 78 76 74 66 79 82 79 73 70 78 79 78 78 80 75 75 74 82 74 70

75 78 80 78 78 80 77 80 78 90 94 98 94 94 87 88 87 88 90 87 85 89 91 92 90 92 90

87 87 94 88 98 102 104;

71 72 70 70 73 76 76 75 72 64 78 80 76 73 69 75 75 76 76 79 74 74 73 81 74 67

74 76 78 78 75 78 74 77 75 86 93 96 93 92 86 86 86 85 90 87 85 90 90 91 89 90 88

86 86 93 89 97 101 101;

69 69 68 69 71 72 74 74 70 61 74 76 74 72 68 75 73 72 72 78 72 72 72 78 72 65

71 72 75 74 73 75 72 74 71 80 90 95 90 90 85 82 83 84 90 86 85 88 88 89 85 88 87

83 85 88 86 90 95 99;


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67 68 68 65 70 71 74 74 68 60 71 74 73 70 65 74 69 71 70 75 70 70 71 76 69 62

68 69 73 71 72 73 70 72 69 77 85 92 88 88 80 80 80 83 88 83 83 86 82 86 82 84 86

80 83 85 85 87 92 93;

66 67 66 62 69 70 73 73 67 60 70 72 72 66 63 73 68 70 69 73 67 67 68 74 67 60

67 67 70 69 72 73 68 70 66 76 82 89 84 86 79 77 78 78 84 81 81 82 81 84 80 83 82

79 80 84 85 86 91 92;

64 67 64 62 68 70 73 71 65 60 70 72 71 64 59 71 70 70 68 72 65 65 67 73 66 59

66 65 68 67 70 71 66 68 65 74 81 88 79 85 77 76 76 75 81 77 77 78 80 79 78 86 82

78 76 83 84 86 89 91;

62 66 62 65 67 69 71 70 64 59 69 71 70 62 58 70 69 69 67 71 64 64 66 73 64 59

65 62 66 66 69 70 65 67 64 72 78 87 77 84 75 76 76 75 83 76 75 76 78 78 79 80 78

77 74 80 84 86 88 89];


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Load Forecasting

using MATLAB


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8.1 DESIGNING OF THE PROGRAM:

The short term load forecasting program can be designed by using these

following steps:

y Selecting input variablesy Creating Fuzzy logic moduley Scaling the input variablesy Creating a new neural networky Selecting the training datay Evaluating the prediction performance

A. SELECTING NETWORK VARIABLES:Probably one of the most difficult tasks in the design of the

network structure is the selection of appropriate network inputs. Because the

dynamic behavior or the network is highly dependent on the chosen inputs, the

load has to exhibit a strong degree of statistical correlation with these

variables. It is also very important that the set of network inputs adequately

represents all the external factors influencing the system load. Thus, the

process of selecting the relevant network inputs has to be guided by an

intuitive knowledge of the various influencing factors, together with a careful

numerical validation of these assumptions.

Preventing weather patterns have a significant impact on the

nature of the load profile. Thus, the inclusion if weather variables in the


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network inputs can significantly improve the prediction performance. Typical

weather variables include temperature information (hourly, minimum,

maximum, average, etc.), humidity, rainfall, wind velocity, sky condition

indicators, and many more. The most important of these are the temperature

variables, representing the strongest correlation with weather-related load

variations. Temperature can, in general, also be measured to a higher degree of

accuracy relative to any of the other weather variables. Many of the forecasted

models proposed in the literature employ hourly-varying temperature variables

(27. S.T. Chen , D.C. Yu, and A.R.Moghaddamjo,Weather sensitive short term

load forecasting using nonfully connected artificial neural network, IEEE

Trans. On Power Systems, vol.7,pp.1098-1104, August 1992.

28. C.N.Lu, H.T.Wu, and S.VemuriNeural network based short term load

forecasting, IEEE Trans. On Power Systems, vol.8,pp.336-342, Feb1993.). This

holds practical limitations in the sense that any increase in performance

gained by using an hourly varying temperature variable, is offset by the lack of

accuracy in forecasting these values. A much more realistic model is one that

relies on temperature variables that are updated at a frequency of, at most,

once a day.

There is also very strong dependence of the load on time. The daily

load profile for a specific day retains essentially the same shape, having more

or less the same value for a given hour. These fluctuations are mostly

contributed to by localized (in time) weather effects. The properties of these

profiles also exhibit variations as a result of seasonal changes in the weather


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patterns. Thus, it is evident that the inclusion of time variables is essential if

the prediction accuracy is to be maximized. These include hour of the day, day

of the week, season of the year, etc.

The load shape is also influenced by a vast number of other external

influences. The magnitude of the induced load variation is dependent on the

system impact of the specific influence. For example, the brown-out of a

single 11 kVA domestic transformer may have a negligible effect on the nation-

wide load, where as the influence of a national holiday will be clearly visible.

Sometimes these effects can be quantified and presented to the network as an

additional input. In these cases the network forms an adequate internal

representation, linking the forecasted load to the specific external influence.

More often than not, such a simple technique does not suffice, due to the lack

of sufficient data pertaining to a specific external influence, and calls for

alternative modeling techniques for these situations (29.K.H.Kim, J.K.Park,

K.J.Hwang,and S.H.Kim, Implementation of hybrid short term load forecasting

systems using artificial neural networks and fuzzy expert systems, IEEE

Trans. On Power Systems, vol.10,pp.1534-1539, August 1995.).


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B. CREATING FUZZY LOGIC MODULE:

C. SCALING THE NETWORK VARIABLES:

Due to the nature of the sigmoidal transfer function, the outputs of

the neurons in the hidden layer , are limited to values between zero and one.

Thus, allowing large values for the neuron input variables will cause the

threshold function to be driven into saturation frequently, resulting in an

inability to train. In practice implementations this problem is solved by scaling

the network inputs and outputs to an appropriate range (usually between zero

and one).

Care has to be taken not to destroy vital relationships between

different network variables by the scaling techniques has employed. Thus, as a


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rule of thumb, if two network variables represent the same physical parameter

(e.g. temperature), albeit for different time instances or geographical locations,

they should be scaled according to the same strategy, using the same scaling

parameter.

D. CREATING A NEW NEURAL NETWORK:


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E. SELECTING THE TRAINING DATA:

Because the recurrent neural network forms its internal

representation relative to the training data, it is important that the selected

data closely match the circumstances of the time period to be predicted. From

a theoretical point of view, the best network generalization can be obtained by

using all of the training samples pertaining to a certain set of conditions. These

large data sets, however, often lead to practical difficulties during training. One

strategy to work around this problem is to be divide the forecasting in to a

number of sub problems, each to be solved by a different networks( e.g. one for

each day type). Each of the resulting networks is trained with as large a data

set as is practically possible. This allows the network to capture information

about the system states and important load trends that is simply not possible

with smaller training sets (due to under-representation) and each of the

individual networks can be optimized for the specific sub problem.

The moving window data selection strategy was proposed to reduce

the size of the training sets is required. In this approach the most recent data

(e.g. that for previous two weeks) is used to train the network for the required

lead-time prediction (mostly 24 hours to one week ahead). For each new

forecast the training data is different, and the network is subsequently

retrained. This method rests, of course, on the assumptions that the load is

relatively stationary within the selected time frame, and weather patterns (or

other external influences) are adequately represented by the training data. This

is not always the case, and one can intuitively conclude that the prediction


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performance will deteriorate as the lead time increase and rapidly changing

weather patterns (e.g. cold or warm fronts, seasonal transition effects, etc.) are

encountered.

F. EVALUATING THE PREDICTION PERFORMANCE:

The final step in the design procedure is the assessment of the

forecasting performance of the trained networks. This evaluation is typically

done by quantifying the prediction error obtained on an independent data set.

if training was successful, the networks will be able to generalize, resulting in a

high accuracy in the forecasting of unknown patterns(provided the training

data is sufficiently representative of the forecasting situation). Various error

metrics (distance measures) between the actual and forecasted load are

defined, but the one most commonly adopted by load forecasters, is the

absolute percentage error (APE), defined by

k

APEI =

ActualLoad

LoadForecastedActualLoad )( *100.

Where k is the time instant.


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Instructions used

in program


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1. In order to create a Perceptron model newff is used.

Newff: Create feed-forward back-propagation network

Syntax: net = newff(PR,[S1 S2...SNl],{TF1 TF2...TFNl},BTF,BLF,PF)

Description: newff(PR,[S1 S2...SNl],{TF1 TF2...TFNl},BTF,BLF,PF) takes several

arguments

PR - R x 2 matrix of min and max values for R input elements

Si - Size of ith layer, for Nl layers

Tfi - Transfer function of ith layer (default = 'tansig')

BTF - Backpropagation network training function (default = 'traingdx')

BLF - Backpropagation weight/bias learning

The transfer functions TFi can be any differentiable transfer function such as

tansig, logsig, or purelin.

The training function BTF can be any of the backpropagation training functions

such as trainlm, trainbfg, trainrp, traingd, etc

2. The Transfer Function used as biasing for the hidden layer is sigmoid

function

Tansig: Hyperbolic tangent sigmoid transfer function


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Description: tansig is a neural transfer function. Transfer functions calculate a

layer's output from its net input. tansig(N,FP) takes N and optional function

parameters,

N - S x Q matrix of net input (column) vectors

FP - Struct of function parameters (ignored)

And returns A, the S x Q matrix of N's elements squashed into [-1 1].

Graph and Symbol:

Figure 6.1

Syntax: A = tansig(N,FP)

3. The Transfer Function used as biasing for the output layer is linear transfer

funtion

Purelin: Linear transfer function

Graph and Symbol:


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Figure 6.2

Syntax: A = purelin(N,FP)

Description: purelin is a neural transfer function. Transfer functions calculate a

layer's output from its net input. purelin(N,FP) takes N and optional function

parameters,

N - S x Q matrix of net input (column) vectors

FP - Struct of function parameters (ignored)

And returns A, an S x Q matrix equal to N.

4. To train the ANN model train is used.

Train:Train neural network

Syntax: [net,tr,Y,E,Pf,Af] = train(net,P,T,Pi,Ai,VV,TV)

Description: train trains a network net according to net.trainFcn and

net.trainParam.

train(net,P,T,Pi,Ai,VV,TV) takes


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net Network

P - Network inputs

T - Network targets (default = zeros)

Pi - Initial input delay conditions (default = zeros)

Ai - Initial layer delay conditions (default = zeros)

VV - Structure of validation vectors (default = [])

TV - Structure of test vectors (default = [])

and returns

net - New network

tr - Training record (epoch and perf)

Y - Network outputs

E - Network errors

Pf - Final input delay conditions

Af - Final layer delay conditions

Algorithm:

train calls the function indicated by net.trainFcn, using the training parameter

values indicated by net.trainParam.

Typically one epoch of training is defined as a single presentation of all input

vectors to the network. The network is then updated according to the results of all


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those presentations. Where, epoch is the complete exposition of total data to the

neural network, all at the same time (at once).

Training occurs until a maximum number of epochs occur, the performance goal is

met, or any other stopping condition of the function net.trainFcn occurs.

5. In order to evaluate the percentage error, the mean error is found by using

mean

Mean: Average or mean value of array

Syntax: M = mean(A)

M = mean(A,dim)

Description: M = mean(A) returns the mean values of the elements along different

dimensions of an array.

If A is a vector, mean(A) returns the mean value of A.

If A is a matrix, mean(A) treats the columns of A as vectors, returning a row vector

of mean values.

If A is a multidimensional array, mean(A) treats the values along the first non-

singleton dimension as vectors, returning an array of mean values.

M = mean(A,dim) returns the mean values for elements along the dimension of A

specified by scalar dim. For matrices, mean(A,2) is a column vector containing the

mean value of each row.


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6. Grid on: Grid lines for 2-D and 3-D plots

Syntax: grid on

Description: The grid function turns the current axes' grid lines on and off.

grid on adds major grid lines to the current axes.


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STLF Program


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clc

clear all

close all

Tempdata;

august;

Load=aug';

Temp=febtemp;

%Temp=aug'

d=3;%corresponding to WEDNESDAY which was the day on 1st august 2001

for i=1:30

D(i)=d;

if(d~=7)

d=d+1;

else

d=1;

end

end

Tmax=max(Temp);


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Tmin=min(Temp);

for i=1:30

if(i==1)

fuzzinp(i,:)=[Tmax(i) Tmax(i)];

else

fuzzinp(i,:)=[Tmax(i) Tmax(i-1)];

end

end

sys=newfis('sysc');

sys=setfis(sys,'aggmethod','sum');

sys=addvar(sys,'input','temp1',[0 120]);

sys=addmf(sys,'input',1,'VC','trapmf',[0 0 20 40]);

sys=addmf(sys,'input',1,'CO','trimf',[20 40 60]);

sys=addmf(sys,'input',1,'CF','trimf',[40 60 80]);

sys=addmf(sys,'input',1,'HO','trimf',[60 80 100]);

sys=addmf(sys,'input',1,'VH','trapmf',[80 100 120 120]);


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sys=addvar(sys,'input','temp2',[0 120]);

sys=addmf(sys,'input',2,'VC','trapmf',[0 0 20 40]);

sys=addmf(sys,'input',2,'CO','trimf',[20 40 60]);

sys=addmf(sys,'input',2,'CF','trimf',[40 60 80]);

sys=addmf(sys,'input',2,'HO','trimf',[60 80 100]);

sys=addmf(sys,'input',2,'VH','trapmf',[80 100 120 120]);

sys=addvar(sys,'output','PLANT-OUT',[-1 1]);

sys=addmf(sys,'output',1,'NB','trapmf',[-1 -1 -.6 -.3]);

sys=addmf(sys,'output',1,'NS','trimf',[-.6 -.3 0]);

sys=addmf(sys,'output',1,'ZE','trimf',[-.3 0 .3]);

sys=addmf(sys,'output',1,'PS','trimf',[0 .3 .6]);

sys=addmf(sys,'output',1,'PB','trapmf',[.3 .6 1 1]);

rulelist=[1 1 3 1 1;1 2 4 1 1;1 3 5 1 1;1 4 3 1 1;1 5 1 1 1;2 1 2 1 1;2 2 3 1 1;2 3 4 1

1;2 4 2 1 1;2 5 1 1 1;3 1 1 1 1;3 2 2 1 1;3 3 3 1 1; 3 4 2 1 1; 3 5 1 1 1;4 1 3 1 1;4 2 4

1 1;4 3 4 1 1;4 4 3 1 1; 4 5 1 1 1;5 1 5 1 1;5 2 5 1 1;5 3 5 1 1; 5 4 5 1 1;5 5 3 1 1];

sys=addrule(sys,rulelist);


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Fuzz=evalfis(fuzzinp,sys);

FD=4;

FH=4;

for i=1:645

j=1;

inp(j,i)=D(FD);

j=j+1;

inp(j,i)=FH;

j=j+1;

inp(j,i)=Fuzz(FD);

j=j+1;

for k=1:3

for l=1:3

m=FH-l+1;

n=FD-k;

if(m


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end

inp(j,i)=Load(m,n);

j=j+1;

end

end

for k=1:3

for l=1:3

m=FH-l+1;

n=FD-k;

if(m


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j=j+1;

inp(j,i)=Tmin(FD-1);

out(i)=Load(FH,FD);

if(FH~=24)

FH=FH+1;

else

FH=1;

FD=FD+1;

end

end

%***************************************************************************%

inp((4:12),:)=inp((4:12),:)/2800;

inp((13:23),:)=inp((13:23),:)/100;

out=out/2800;

%net=newff(minmax(inp),[30 1],{'tansig' 'purelin'});

%net.trainParam.epochs =1000;

%net.trainParam.goal = 0;

%[net,tr]=train(net,inp,out);


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%save('augneurofuzzy1','net')

load('augneurofuzzy1')

testinp=inp(:,478:645);

yyauganntfl=sim(net,testinp)*2800;

figure(1)

k=1:168;

subplot(2,1,1)

plot(k,yyauganntfl,'r.',k,out(478:645)*2800,'b');

title('Actual Load Vs Forecasted Load in Mw for one week')

xlabel('Hours')

ylabel('Actual Load(-)-Forecasted Load (.) ')

grid on

errorwfl=out(478:645)*2800-yyauganntfl;

for i=1:168

percenterrorwfl(i)=errorwfl(i)/(out(i+477) *2800)*100;

end;

subplot(2,1,2)

plot(percenterrorwfl,'-')


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title('Percent Error Vs Hour of the Day for one week')

xlabel('Hours')

ylabel('Percent Error')

grid on

k=1:168;

disp('HOURS || ACTUAL LOAD || FORECASTED LOAD || ERROR || PERCENT

ERROR')

dataMfl=[k;out(478:645)*2800;yyauganntfl;errorwfl;percenterrorwfl]'

disp('Mean Error for one week=')

mean(percenterrorwfl)

figure(2)

k=1:24;

subplot(2,1,1)

plot(k,yyauganntfl(145:168),'r.',k,out(622:645) *2800,'b');

title('Actual Load Vs Forecasted Load in Mw for one day')

xlabel('Hours')

ylabel('Actual Load(-)-Forecasted Load (.) ')

grid on

errorDfl=out(622:645)*2800-yyauganntfl(145:168);


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for i=1:24

percenterrorDfl(i)=errorDfl(i)/(out(i+621) *2800)*100;

end;

subplot(2,1,2)

plot(percenterrorDfl,'k')

title('Percent Error Vs Hour of the Day for one day')

xlabel('Hours')

ylabel('Percent Error')

grid on

k=1:24;

disp('HOURS || ACTUAL LOAD || FORECASTED LOAD ONE DAY AHEAD || ERROR

|| PERCENT ERROR')

dataDfl=[k;out(49:72)*2800;yyauganntfl(49:72);errorDfl;percenterrorDfl]'

disp('Mean Error for one day ahead using fuzzy neural networks=')

mean(percenterrorDfl)


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Results


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LOAD CURVE and LOAD CURVE ERROR FOR A DAY


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LOAD CURVE and LOAD CURVE ERROR FOR A WEEK


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RESULT TABLE:

HOURS || ACTUAL LOAD || FORECASTED LOAD || ERROR || PERCENT

ERROR

dataMfl =1.0e+003 *

0.0010 2.3040 2.3040 0.0000 0.0000

0.0020 2.1890 2.1890 -0.0000 -0.0000

0.0030 2.1860 2.1860 -0.0000 -0.0000

0.0040 2.1730 2.1730 0.0000 0.0000

0.0050 2.1150 2.1150 -0.0000 -0.0000

0.0060 2.1380 2.1380 -0.0000 -0.0000

0.0070 1.9630 1.9630 -0.0000 -0.0000

0.0080 2.0970 2.0970 -0.0000 -0.0000

0.0090 2.1240 2.1240 0.0000 0.0000

0.0100 2.1930 2.1930 -0.0000 -0.0000

0.0110 2.1910 2.1910 -0.0000 -0.0000

0.0120 2.2010 2.2010 -0.0000 -0.0000

0.0130 2.1200 2.1200 0.0000 0.0000

0.0140 2.1220 2.1220 -0.0000 -0.0000


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0.0150 2.0520 2.0520 -0.0000 -0.0000

0.0160 2.0550 2.0550 0.0000 0.0000

0.0170 2.0990 2.0990 -0.0000 -0.0000

0.0180 2.1060 2.1060 -0.0000 -0.0000

0.0190 2.0940 2.0940 -0.0000 -0.0000

0.0200 2.0330 2.0330 -0.0000 -0.0000

0.0210 2.3240 2.3240 -0.0000 -0.0000

0.0220 2.4090 2.4090 -0.0000 -0.0000

0.0230 2.4000 2.4000 -0.0000 -0.0000

0.0240 2.3000 2.3000 -0.0000 -0.0000

0.0250 2.2060 2.2060 -0.0000 -0.0000

0.0260 2.1870 2.1870 0.0000 0.0000

0.0270 2.1430 2.1430 -0.0000 -0.0000

0.0280 2.1090 2.1090 -0.0000 -0.0000

0.0290 2.0210 2.0210 -0.0000 -0.0000

0.0300 1.9840 1.9840 -0.0000 -0.0000

0.0310 1.9180 1.9180 -0.0000 -0.0000

0.0320 2.0620 2.0620 -0.0000 -0.0000


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0.0330 1.9080 1.9080 -0.0000 -0.0000

0.0340 2.2440 2.2440 -0.0000 -0.0000

0.0350 2.3630 2.3630 0 0

0.0360 2.3110 2.3110 -0.0000 -0.0000

0.0370 2.3700 2.3700 0.0000 0.0000

0.0380 2.3140 2.3140 0.0000 0.0000

0.0390 2.3910 2.3910 -0.0000 -0.0000

0.0400 2.2280 2.2280 0.0000 0.0000

0.0410 2.3110 2.3110 -0.0000 -0.0000

0.0420 2.2920 2.2920 -0.0000 -0.0000

0.0430 2.3060 2.3060 0.0000 0.0000

0.0440 2.4390 2.4390 -0.0000 -0.0000

0.0450 2.3490 2.3490 0.0000 0.0000

0.0460 2.4140 2.4140 -0.0000 -0.0000

0.0470 2.3710 2.3710 -0.0000 -0.0000

0.0480 2.2660 2.2660 -0.0000 -0.0000

0.0490 2.1400 2.1400 -0.0000 -0.0000

0.0500 2.0850 2.0850 -0.0000 -0.0000


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0.0510 2.0460 2.0460 -0.0000 -0.0000

0.0520 1.9700 1.9700 -0.0000 -0.0000

0.0530 1.9880 1.9880 0.0000 0.0000

0.0540 1.9720 1.9720 0.0000 0.0000

0.0550 1.9440 1.9440 0.0000 0.0000

0.0560 2.0840 2.0840 -0.0000 -0.0000

0.0570 2.1560 2.1560 0.0000 0.0000

0.0580 2.2760 2.2760 -0.0000 -0.0000

0.0590 2.4250 2.4250 0.0000 0.0000

0.0600 2.4210 2.4210 0.0000 0.0000

0.0610 2.2210 2.2210 -0.0000 -0.0000

0.0620 2.2940 2.2940 -0.0000 -0.0000

0.0630 2.2090 2.2090 0 0

0.0640 2.3610 2.3610 0.0000 0.0000

0.0650 2.4070 2.4070 -0.0000 -0.0000

0.0660 2.3840 2.3840 -0.0000 -0.0000

0.0670 2.4000 2.4000 -0.0000 -0.0000

0.0680 2.4300 2.4300 0.0000 0.0000


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0.0690 2.4320 2.4320 0.0000 0.0000

0.0700 2.5510 2.5510 -0.0000 -0.0000

0.0710 2.5330 2.5330 -0.0000 -0.0000

0.0720 2.3870 2.3870 -0.0000 -0.0000

0.0730 2.2380 2.2380 0.0000 0.0000

0.0740 2.2160 2.2160 -0.0000 -0.0000

0.0750 2.1390 2.1390 -0.0000 -0.0000

0.0760 2.0580 2.0580 -0.0000 -0.0000

0.0770 2.0550 2.0550 0.0000 0.0000

0.0780 2.0390 2.0390 0.0000 0.0000

0.0790 2.1830 2.1830 0.0000 0.0000

0.0800 2.1160 2.1160 -0.0000 -0.0000

0.0810 2.1070 2.1070 -0.0000 -0.0000

0.0820 2.4060 2.4060 -0.0000 -0.0000

0.0830 2.4090 2.4090 -0.0000 -0.0000

0.0840 2.4030 2.4030 0.0000 0.0000

0.0850 2.3860 2.3860 -0.0000 -0.0000

0.0860 2.4080 2.4080 -0.0000 -0.0000


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0.0870 2.3930 2.3930 -0.0000 -0.0000

0.0880 2.5060 2.5060 -0.0000 -0.0000

0.0890 2.4730 2.4730 -0.0000 -0.0000

0.0900 2.3810 2.3810 -0.0000 -0.0000

0.0910 2.3900 2.3900 -0.0000 -0.0000

0.0920 2.4660 2.4660 -0.0000 -0.0000

0.0930 2.3910 2.3910 0.0000 0.0000

0.0940 2.4280 2.4280 -0.0000 -0.0000

0.0950 2.4720 2.4720 -0.0000 -0.0000

0.0960 2.3220 2.3220 -0.0000 -0.0000

0.0970 2.2570 2.2570 -0.0000 -0.0000

0.0980 2.2150 2.2150 -0.0000 -0.0000

0.0990 2.2050 2.2050 -0.0000 -0.0000

0.1000 2.1270 2.1270 -0.0000 -0.0000

0.1010 2.0700 2.0700 0.0000 0.0000

0.1020 2.0900 2.0900 -0.0000 -0.0000

0.1030 2.1300 2.1300 -0.0000 -0.0000

0.1040 2.1460 2.1460 -0.0000 -0.0000


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0.1050 2.3430 2.3430 -0.0000 -0.0000

0.1060 2.5170 2.5170 0.0000 0.0000

0.1070 2.5590 2.5590 -0.0000 -0.0000

0.1080 2.5210 2.5210 -0.0000 -0.0000

0.1090 2.2630 2.2630 -0.0000 -0.0000

0.1100 2.5900 2.5900 -0.0000 -0.0000

0.1110 2.5750 2.5750 -0.0000 -0.0000

0.1120 2.5520 2.5520 -0.0000 -0.0000

0.1130 2.5290 2.5290 -0.0000 -0.0000

0.1140 2.4880 2.4880 -0.0000 -0.0000

0.1150 2.2630 2.2630 -0.0000 -0.0000

0.1160 2.5900 2.5900 -0.0000 -0.0000

0.1170 2.5750 2.5750 -0.0000 -0.0000

0.1180 2.5520 2.5520 -0.0000 -0.0000

0.1190 2.5290 2.5290 -0.0000 -0.0000

0.1200 2.4880 2.4880 -0.0000 -0.0000

0.1210 2.4910 2.4910 0.0000 0.0000

0.1220 2.4080 2.4080 -0.0000 -0.0000


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0.1230 2.4340 2.4340 -0.0000 -0.0000

0.1240 2.3710 2.3710 -0.0000 -0.0000

0.1250 2.3330 2.3330 -0.0000 -0.0000

0.1260 2.3110 2.3110 -0.0000 -0.0000

0.1270 2.3270 2.3270 -0.0000 -0.0000

0.1280 2.3000 2.3000 -0.0000 -0.0000

0.1290 2.3970 2.3970 -0.0000 -0.0000

0.1300 2.5090 2.5090 0.0000 0.0000

0.1310 2.5230 2.5230 0.0000 0.0000

0.1320 2.5150 2.5150 -0.0000 -0.0000

0.1330 2.5470 2.5470 0.0000 0.0000

0.1340 2.5430 2.5430 -0.0000 -0.0000

0.1350 2.5620 2.5620 -0.0000 -0.0000

0.1360 2.6270 2.6270 -0.0000 -0.0000

0.1370 2.6210 2.6210 -0.0000 -0.0000

0.1380 2.6280 2.6280 -0.0000 -0.0000

0.1390 2.6000 2.6000 -0.0000 -0.0000

0.1400 2.7370 2.7370 -0.0000 -0.0000


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0.1410 2.5910 2.5910 -0.0000 -0.0000

0.1420 2.7450 2.7450 -0.0000 -0.0000

0.1430 2.6420 2.6420 -0.0000 -0.0000

0.1440 2.5450 2.5450 -0.0000 -0.0000

0.1450 2.5000 2.5000 -0.0000 -0.0000

0.1460 2.4870 2.4870 -0.0000 -0.0000

0.1470 2.4220 2.4220 -0.0000 -0.0000

0.1480 2.3760 2.3760 -0.0000 -0.0000

0.1490 2.3480 2.3480 -0.0000 -0.0000

0.1500 2.3260 2.3260 -0.0000 -0.0000

0.1510 2.3260 2.3260 -0.0000 -0.0000

0.1520 2.1910 2.1910 -0.0000 -0.0000

0.1530 2.2440 2.2440 -0.0000 -0.0000

0.1540 2.4750 2.4750 -0.0000 -0.0000

0.1550 2.5120 2.5120 0.0000 0.0000

0.1560 2.5780 2.5780 0.0000 0.0000

0.1570 2.4700 2.4700 -0.0000 -0.0000

0.1580 2.4860 2.4860 -0.0000 -0.0000


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0.1590 2.5550 2.5550 0.0000 0.0000

0.1600 2.5690 2.5690 -0.0000 -0.0000

0.1610 2.5230 2.5230 -0.0000 -0.0000

0.1620 2.5170 2.5170 0.0000 0.0000

0.1630 2.5920 2.5920 -0.0000 -0.0000

0.1640 2.5700 2.5700 -0.0000 -0.0000

0.1650 2.5900 2.5900 -0.0000 -0.0000

0.1660 2.5630 2.5630 0.0000 0.0000

0.1670 2.4100 2.4100 -0.0000 -0.0000

0.1680 2.4160 2.4160 -0.0000 -0.0000

Mean Error for one week = -2.1753e-013

HOURS || ACTUAL LOAD || FORECASTED LOAD ONE DAY AHEAD || ERROR ||

PERCENT ERROR

dataDfl = 1.0e+003 *

0.0010 2.0400 2.1400 -0.0000 -0.0000

0.0020 2.0080 2.0850 -0.0000 -0.0000

0.0030 1.9570 2.0460 -0.0000 -0.0000

0.0040 2.0290 1.9700 -0.0000 -0.0000

0.0050 2.1060 1.9880 -0.0000 -0.0000


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0.0060 2.1300 1.9720 -0.0000 -0.0000

0.0070 2.3810 1.9440 -0.0000 -0.0000

0.0080 2.3820 2.0840 -0.0000 -0.0000

0.0090 2.4260 2.1560 -0.0000 -0.0000

0.0100 2.2990 2.2760 -0.0000 -0.0000

0.0110 2.3920 2.4250 0.0000 0.0000

0.0120 2.4510 2.4210 0.0000 0.0000

0.0130 2.4710 2.2210 -0.0000 -0.0000

0.0140 2.4990 2.2940 -0.0000 -0.0000

0.0150 2.3080 2.

Documents

Short Term Load Forecasting Ann