Chapter 1: INTRODUCTION - Department of Electrical...

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Chapter 1: INTRODUCTION

1.1: Overview

A reliable and continuous supply of electrical energy is necessary for the functioning of

today’s complex society. Because of the combination of increasing consumption and

obstruction of various kinds, and the extension of existing electrical transmission

networks and these power systems are operated closer and closer to their limits. It is

known for all that electrical energy cannot be stored efficiently, due to this factor that the

electrical load could be controlled by utilities only to a very small extend. The electric

load forecast is an important topic for power generation and transmission. This project is

based on the long term electric load forecasting using artificial intelligent techniques-

NEURAL NETWORKS. For comparison and performance evaluation forecasted electric

load based on econometric model from the Kenya Power And lighting company was

used.

Long term load forecasting is the prediction of future electric load demand for the

next 20 years. Because of the long duration of this forecast, it is much more difficult to

forecast off-peak load demand and so the main emphasis is on the annual peak system

load. Long term electric load forecasting is essential in determining the load growth in a

particular country. The peak load forecasted helps the power utilities in establishing

whether upgrades of a particular network need to be performed. The capacity in terms of

electrical power in that area may be exceeded thus making long term electric load

forecasting a key factor in planning of a utility. The key contribution of forecasters is

their knowledge of electricity consumers and understanding of the way they use

electricity and other competing energy forms. This problem gains special aspect in

developing countries such as Kenya, because of the high demand growth rate as well as

the wide differences in the modes and levels of consumption in the various regions in the

country.

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Recently (June 6th 2008) the Kenyan Government launched an economic

blueprint dubbed “Kenya vision 2030” whose key aim is to put in place measures to

accelerate economic growth in the country.

1.2 Objectives of the project

In order to plan efficient operation and economical capital expansion of deregulated

electrical markets, the market owners should be able to anticipate the need of power

delivery, how much power must be delivered and where and when it will be needed. The

main objective of this project is to perform electric load forecast up to 2030.

The specific objectives of this project are:

• Capture data on various input variables

• Pre-process the data

• Create the Neural Network

• Train the Neural Network

• Test the Neural Network.

• Perform electric load forecast for each particular year from 2009

up to 2030

This project makes an estimate of the electric needs of Kenya by the year 2030.

The data generated as a result will be useful in future generation planning for the

country either from hydroelectricity or alternative sources of power. Therefore, load

forecast applications are of great importance. This information can be provided only by

electric load forecasting. Nowadays the load forecasting is done using ARTIFICIAL

NEURAL NETWORKS.

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1.3: Plan of development

The following describes the layout of the thesis:

Chapter 2: This chapter contains a general discussion of load forecasting as well as

discussion of the factors that affect load demand. Artificial intelligent techniques-Neural

networks used for the load forecasting procedure are also discussed.

Chapter 3: The proposed AI technique (i.e. Artificial Neural Networks) is discussed in

detail. This chapter describes the components of an artificial neural network and explains

how they function.

Chapter 4: A long term electric load forecasting model based on ANN is developed and

for comparative purposes, K.P.L.Cs Econometric forecasted data is used. The simulation

results from these two models are analyzed and compared.

Chapter 5: Conclusions and recommendations based on the results obtained in chapter

four are made. An opportunity for further work is also proposed in this chapter.

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Chapter 2: LITERATURE REVIEW

2.1 LOAD FORECASTING

Load forecasting is the prediction of future electrical demand. It is important since

electrical power generation requires efficient management. This is because the power

generated needs to be equal to that consumed. For the Kenyan power generating

companies to meet the requirements, it is necessary to predict or forecast the future

Electrical load requirements. The term load forecasting refers to the projected load

requirement determined using past knowledge to define future load in sufficient

quantitative detail [1]. Demand electric load prediction is an important aspect in

electricity planning [2] of electric utilities. It is a means of knowing how much power to

schedule for the future demand, useful in drawing up a feasibility report for power plants

and is also useful in determining whether the current capacity of the power stations or

sub-stations of a service area will be exceeded. The latter is usually determined when

the load demand is forecasted for a period longer than a year.

Load forecasting can be categorized into three important parts namely:

I. Short-term load forecasting.

II. Medium-term load forecasting.

III. Long-term load forecasting

In short-term load forecasting refers to a few minutes to a week forecast of electrical

demand. Medium-term load forecasting is usually from a week to a year ahead whilst

long-term load forecasting is for a longer duration which is from a year up to 20 years.

The forecast period mentioned above is not a definite period, some literature mention

that medium term is the period from six months to a year, and some say it is from a year

to five years into the future. The period varies from utility to utility and so for the

purpose of this project, a period from a week to less than a year will be referred to as

medium-term electric load forecasting.

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The following section discuses the three types of forecasting:

2.1.1 SHORT TERM LOAD FORECASTING

The term short implies that forecast can be done for every hour, day, and week.

The forecast value is usually the total system load demand as well as the values of the

system load at different times of the day. Short-term load forecasting (STLF) is essential

for the economic generation dispatch of power systems. This means that power

generation can be planned according to the forecasted value decreasing the risk of

equipment failures such as transformer and transmission lines. The possibility of

blackouts occurring is also reduced as well as losses in revenue of power utilities.

The key objectives of this forecast are as follows:

• Provide load prediction for the basic generation scheduling.

• Supply timely dispatcher information based on the load predictions.

• Assist with the assessment of the security of the system at any particular time,

thereby improving the network reliability.

Short-term load forecasting helps to improve system reliability in that the system load

forecast that can be generated using short-term load forecasting is essential for the off-

line network analysis function, and for the detection of future conditions under which the

power system may be vulnerable. This helps the dispatcher to make informed decisions

and take the necessary actions. These actions may compromise of bringing peaking units

online load forecasting scheduling, switching operations so that the reliability of the

system is no hindered.

2.1.2: MEDIUM TERM LOAD FORECASTING

Medium –term load forecasting is predictions of demand for a week to a year in

the future. It is necessary for the maintenance and network development work performed

by power utilities. It involves the forecasting of systems load and sometimes bulk power

interchange levels. Peak load demand is the main focus in this forecast but off-peak

demand is also forecasted.

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2.1.3: LONG TERM LOAD FORECASTING

This type of forecast is for much longer duration into the future. The forecast

period may last up to twenty years. Because of long duration of this forecast, it is much

more difficult to forecast off-peak load demand and so the main emphasis is on the

annual peak system load.

Long-term load forecasting is essential in determining the load growth of a particular

area. The peak load forecasted helps the power utilities in establishing whether upgrades

of particular networks need to be performed. The capacity in terms of electrical power in

that area may be exceeded thus making long term forecast, a key factor in planning

operations of a utility.

2.2 DISCUSSION OF LOAD FORECASTING

Load forecasting as a whole is a technique necessary for the reliability and adequate

functioning of the power system network. Each type of load forecast is essential. The

objective is to obtain an accurate load forecast but sometimes this is not always the case.

The subject of electric load forecasting accuracy will be discussed further at a later stage.

There are a number of factors affecting electric load demand that need to be considered

when trying to formulate a model for any of the three types of load forecasting. The

factors affecting each type of load forecast are different and they vary from utility to

utility as it is the utility that decides on the importance or the relevance of that particular

factor.

This leads to a discussion on the types of factors affecting electric load demand and the

types of load forecasts.

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2.3 FACTORS AFFECTING ELECTRIC LOAD

Before a load forecast model can be developed, the forecaster needs to determine the

factors that affect the electric load demand in the particular areas that need to be

forecasted.

The factors that need to be considered are:

• Time of the day

• Day of the week

• Time of the year (including seasons, holidays, etc)

• Weather

• Customer class

• Demographic factors (Population, housing)

• Macroeconomic factors (GDP, CPI, HSI)

Customer classing is the division of load demand into groups that utilize power in the

same manner. This means that the load demand can be broken down into classes namely;

residential (domestic), commercial (banks, hotels, schools, etc), Industrial (sugar milling

companies, paper mills), mining (e.g. cement manufacturing plants), agricultural and

transport. The customer class defines the load profile, for example the power demand for

a residential class is not the same as that of an industrial class. Industries may require

more power because of equipment such as heavy duty motors that they use whereas the

appliances used by those of residential class do not draw as much power.

Other factors that affect electric load forecast are as follows

• Historical electric load

• Appliance sales

• Price of electricity

• Number of customers in the class

• The economic as well as demographic data.

These usually affect the medium and long-term forecasts.

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The following are regarded as the most important factors.

1. WEATHER

Weather factors are as follows: Wind speed (this defines how cold people feel),

temperature, humidity, cloud cover and rainfall. There is a varying of load demand from

season to season influenced by the change in weather temperature; for example in Kenya

the load demand in summer is not as high as in winter because of increase in

temperature. In winter, people start using heating appliances in order to keep warm.

Lights come on earlier for a much longer period than in summer as the sun sets at an

earlier time.

There is a shift in the load peak-time as a result. It is difficult to incorporate weather

factors in the long-term forecasts because it is continually changing and there are no

long-term weather forecasts available. Short term forecasts take weather forecasts into

great considerations because they affect the daily load profile and this is necessary for

accurate forecasting. Medium-term electric load forecasting take weather into

consideration and the seasonal effects are accounted for in the model.

We can find that not all weather factors are important. Some are typically random during

a period of time, such as wind speed and thunderstorms. Also some factors are

interrelated. Among all those factors, temperature is the most important because it has

direct influence on many kind of electrical consumption, such as air conditioner, heater

and refrigerator. However, the leading weather influential factor for specific consumer

may be different.

2. ELECTRICITY PRICING

In general, this is a factor that has not been greatly used in the forecasting of load. Very

few models include this factor; because electricity prices vary depending on place and

time and consumers can adjust their consumption behavior according to the price of the

electricity.

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3. ECONOMICAL OR ENVIROMENTAL

The economy has an effect on the electric demand patterns. The general trend has an

effect on the increase or decline of electricity consumed. This includes levels of

industrial growth activities, changes of farming sector, emergency of new industry,

service area demographics (rural, residential), Economic trends (recession or expansion),

demand side load management.

4. UNFORSEEABLE RANDOM EVENTS

In Kenya random events are inevitable. This includes recurrent post elections violence,

widespread of strikes, start or stop of large loads (steel mill, factory reviving and

furnaces), sporting events and popular televisions shows and recording and also shut-

down of industrial facility.

2.4: DISCUSSION OF ARTIFICIAL INTELLIGENCE TECHNIQUES

The electric load forecasting is a problem that is difficult to deal with because of the

nonlinear and random behavior of system loads as well as other factors that may

influence the demand. The artificial intelligent techniques are effective to a certain

extend. The main disadvantage of these techniques is their inability to incorporate and

handle this random-like behavior of system loads. Moreover, because of the

developments in technology, economic growth, past trends, causes the classical methods

to produce incorrect predictions which may have a negative effect on the power utilities.

A need that requires models to be able to adapt quickly to the changing environment and

be able to learn on their own without human assistance arises. Methods with improved

accuracies that can be updated without interfering with the rest of the system, and can

incorporate as many input parameters as possible without failing to converge become a

necessity. Various research programs have been undertaken in order to find solutions to

these problems and one of the result was Artificial Intelligent techniques (NEURAL

NETWORKS)

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AITs are unconventional ways of solving classes of problems. A number of artificial

intelligent techniques have been developed over the past century and their applications

are global. They are able to use human knowledge to create solutions to problems. This

type of knowledge is stored in knowledge basis such as the expert systems. They are able

to gain experience over time and are able to handle uncertainty in information very well

like the fuzzy logic system.

2.4.1: ARTIFICIAL NEURAL NETWORKS

ANNs have been used since 1990 and have been studied intensively as a tool to be used

for electric load forecasting. Essentially, a neural network is a non-linear circuit that is

capable of doing non-linear curve fitting. It is an information processing paradigm that

was inspired by the way the biological systems of humans such as the brain processes

information.

The human brain is made up of neurons, which are interconnected by dendrites and

collect information via the connection. All the neurons in the brain work in unison to

make sure that all the information that is received is processed as efficiently and as

accurately as possible. Therefore, the artificial neurons try to simulate this kind of

behavior displayed by the real neurons in the brain.

ANNs learn by example much like the human brain. They are configured for particular

classes of problems or applications through a learning process.

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2.4.2: SYSTEM STRUCTURE

AANs are made up of simple and highly interconnected processing elements (PE) called

neurons. An illustration of a neuron and its mathematical model is shown bellow:

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Figure 2.1: Structure of a neuron [10]

The mathematical model is of the form:

Oj = fi∑ (wjk*xk) (2.1)

Where

Oj: output of the neuron

fi : transfer function called a sigmoid that is differential and non-decreasing; it is in the

form of an “S” shape

wjk : weighting functions that are adjustable and represent the strength of the connection

between the input data and output.

xk : input to the neuron.

Figure 2.2 below shows the interconnectivity of a neural network. The network is made

up of interconnected neurons in a layer configuration.

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The first two layers are known as the hidden layers and the last layer is the output.

Figure 2.2: artificial neural network structure [4]

The figure above uses a topology called feed-forward. Feed-forward is basically the

structure where the input signals is propagated in one way from input neuron via a

hidden layer to the output. These are straight forward artificial neural networks as they

associate the input to the output very easily.

Another type of ANN is the feedback ANN. These networks can have signals travelling

in both directions within the network. Feedback networks are dynamic and their status is

always changing until an equilibrium point is reached. They can become very

complicated but are regarded as very powerful networks. They are also regarded as

recurrent networks.

2.4.3: THE LEARNING REGIME

There are two types of training or learning regimes used for ANNs; namely supervised

and unsupervised learning. Supervised learning is the process where each output unit is

told what desired response to the input signal is should be. An important issue with

regards to supervised learning is the problem of error convergence. The objective is to

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minimize the error between the desired and computed values. Therefore weighting

functions which minimize these errors need to be developed.

A training system called back propagation falls under the supervised learning section. It

is most commonly used for the training period of the ANN. Its basic procedure is as

follows [7]: a training sample is provided to the network, the outputs are calculated for

given inputs in the forward direction, thereafter in the backward motion, the errors at the

output layer are propagated backwards to the input layer. The weights are adjusted for

each neuron and an algorithm is implemented that finds the weighting functions that

minimize the error.

The next is the unsupervised learning system. Unsupervised learning is based upon the

local information that is provided and there are no actual target outputs. The weights are

changed in response to the network inputs. A set of data inputs are taken and the neural

network treats this data as a random variables. The network then uses this information to

determine the properties and then produce a solution.

2.4.4: APPLICATION TO LOAD FORECASTING

In applying the ANN to load forecasting, the forecaster needs to choose one of the

architectures such as back propagation as well as the number and connectivity of the

layers. He/she needs to be able to decide whether to use feed-forward, recurrent

networks; and the training period and the data required for the learning regime. This kind

of structure has been used by a number of forecasters. The ANN model has received

much recognition with respect to the problem of long-term electric load forecasting. The

success of an ANN method lies in its ability to learn and adapt to the changing

environment.

The following lists the advantages and disadvantages associated with this technique.

Advantages

• ANN systems are fast and robust.

• Possesses a good learning ability.

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• Capable of adapting to the data.

• Appropriate for non-linear modeling.

• Does not require a mathematical model of the load

Disadvantages

• The forecaster needs to be able to select the optimum configuration from many

options available.

• Results are always generated even though the input data may be unreasonable.

• Needs to choose a training methodology

• ANNs are not able to explain the decisions that are made within the neural

networks

2.4.5: ACCURACY OF LOAD FORECASTS

The most important aspect of electric load forecasting method is its accuracy. The model

needs to be able to project the future demand as accurately as possible so that the risk of

losing revenue for electric utilities is minimized as well as the cost of generating

electricity; there is no standard set for forecasts because of the uncertainties that come

with predicting future load.

Forecasting accuracy depends on the quality and quantity of the historical data used the

validity of the forecaster’s assumptions, and the accuracy of the demand-influencing

factors such as weather, income, prices etc [9]. It is common to measure the model

accuracy statistically in terms of the standard deviation of the forecast error [5].

The accuracy may then be measured by this formula:

error = (2.2)

Where

a(t): actual (measured) demand at time t

f(t) : forecasted demand at time t

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The assumption made is that the mean e=0. The variance is calculated by taking the

mean of e. the standard deviation is the square root of this variance. If the error analysis

does not provide a convincing situation, the model has to be re-evaluated.

The foundations of load forecasting have been established. This thesis focuses on the

problem of long-term load forecasting with the use of neural networks. The knowledge

obtained in this section will be used to create a model that will be able to perform as

required.

For comparison purposes electric load forecasted data using econometric model was

obtained. Here is brief discussion on how the Kenya power and lighting company

performed the Econometric electric load forecast.

2.5: ECONOMETRIC MODEL

This method incorporates statistics, economics and mathematical theory in order to

forecast the electricity demand. The approach estimates the relationships between

energy consumption and factors influencing consumption [3]. It is a combination of the

end-use and trend analysis methods but it does not take on the assumption used in

trending that future demand can be predicted based on past demand. Unlike the end-use

model, it allows the variation of the relationships between the end-use and the amount of

electrical power received by consumers.

Complex mathematical equations are used to show past relationships between demand

and the demand-affecting factors [9]. The equation can show whether these factors

decrease or increase the demand as well as the percentage increase or decrease.

The equation is then tested for its reliability and accurate representation of past data.

Thereafter, projected values of the factors (price, population etc) are put into the

equation and a forecast is made. In this method past electricity consumption data was

used and GDP growth was established and regression method was used to obtain the

electricity demand for the consecutive years.

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Advantages

• Shows how and why electricity increases or decreases.

• Provides detailed information about the future levels of electricity demand.

• Provides separate forecasts for residential, commercial and industrial demand.

• Flexible and useful for analyzing load growth under different scenarios [9]

Disadvantages

• Large changes in demand affecting factors are not accounted for.

• In order for the forecast to be accurate, the factors influencing the electricity

demand need to be in the same forecast period as in the past.

• It is only as accurate as the forecasts of the factors which influence the demand.

• The econometric forecast works better for larger areas than small areas i.e. at

regional (for example in Kenya, the entire Nairobi south is a region) or national

level (entire Kenyan country) because of the extensive data needed to formulate

the model.

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Chapter 3: ARTIFICIAL NEURAL NETWORKS

This chapter presents a detailed description of the components that make up an Artificial

Neural network and how they function. Before this is explained, a brief history of how

and when these neural networks were developed will be discussed.

3.1 INTRODUCTION TO ARTIFICIAL NEURAL NETWORKS

ANNS are models that were developed based on the structure of the brain. The idea was

that the brain learns by experience and so the scientist at the time wanted to develop

something that will use this ability to learn. The neural cell in the brain was discovered

in 1836 [4]. An organism does not seem to regenerate itself and has the ability to provide

the human with the power to remember and think.

The neuron is a complex organism and biological research is still ongoing in terms of its

functions. It consists of many parts as is illustrated in the figure below.

Figure 3.1: Diagram of neuron in the human brain [6]

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They are able to convey information amongst themselves through electrochemical

pathways called the synapse. All these neurons have specific tasks to perform and belong

to different classes but they work together to bring about coherent output. In analogy to

the brain, the artificial neuron was developed by McCulloth and Pitts. A simple neuron

structure as shown in the figure below

Figure 3.2: Artificial neuron and its components [6]

It works in a more simplistic way as compared to the real neuron. A real neuron receives

input signals from different types of sources, combines them in a generally non-linear

manner, and then produces the result. The artificial neuron behaves in much the same

way but the difference is that the function is known whereas the biological neuron’s

processing system is known.

3.2 DESCRIPTION OF NEURAL NETWORK COMPONENTS

As mentioned in previous chapters, an ANN is a system made up of a number of

interconnected neurons. They are useful in producing solutions to specific complex

problems. ANNs are based on biology in particular the interactions between the neurons

in the brain and the processing strategy and the results produced. This section describes

the major components of an artificial neuron. The following information as well as the

sections in the rest of this chapter [11]

Weighting functions: A neuron may receive a number of input signals at the same time.

Each input has a weighting of a magnitude that causes the input to have an impact on the

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summation function of the processing element depending on the strength of the

connection between the input and the neuron. The weights perform the same function as

the synapses that connect the neurons in the brain. In both cases, some inputs are made

more important than others are so that they have a greater effect on the processing

element as they combine to produce a neural response [11]. The weights are adaptive

coefficients that can be increased or decreased where necessary. This occurs during the

training regime as mentioned earlier.

Summation function: This component performs the weighted summation of the various

inputs received by neuron. The inputs are corresponding weights are represented as

vectors and so the dot product of these two vectors result in the total input signal.

Transfer function: The output of the summation function is then taken by the transfer

function. This transfer function transforms the summation output into a working output.

There is a certain threshold set by the transfer function that the summation output can be

compared to determine the neural output. Transfer functions that are used are:

• Hard limiter

• Ramping function

• Sigmoid functions

If the sum is greater than the threshold, the neuron generates a signal. However if the

sum is less then no signal is generated.

Hard limiter: This function as illustrated in the figure above has limits between minus

one and positive one. This means that the output is either a minus one or one for a given

input. The threshold can also be between zero and one.

• Ramping function: The input to the function is mirrored for a certain

range and thereafter a hard limit is enforced.

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In figure 3.3, the input is the same as the output for the range between

zero and one and thereafter the output is clipped to a maximum value of

one

• Sigmoid function: A sigmoid function is an “S” shaped function that is

continuous, differentiable, and non-decreasing and its derivative has the

same properties. There are two types of sigmoid commonly used in ANN

architecture namely the hyperbolic tangent as well as the logistic function.

The logistic function has outputs ranging from zero to one whereas the

hyperbolic one has outputs from minus one to positive one.

The transfer functions that are usually used are shown in the figure below.

Figure 3.3: Sample transfer functions [11]

3.3: SCALING AND LIMITING:

The result from the transfer function may be passed through further scaling limiting

processes. The output from the transfer function is multiplied by a certain scale factor

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and then an offset may be added. This decision rests with the designer. Limiting this

output ensures that it does not exceed any specified upper and lower bounds.

Output function: Each neuron produces an output after the scaling and limiting of the

original output from the transfer function. The neuron outputs a signal to many output

neurons. A phenomenon known as competition is sometimes used at this stage (not all

network topologies use this technique). The result of the transfer function is modified to

include an element of competitiveness between the neurons. The neurons are allowed to

compete with each other thereby inhibiting other neurons unless they have the greater

strength. Competition can occur at one or two levels. First, competition determines

which artificial neuron will be active or provide an output. Second, competitive inputs

help to determine which processing element will participate in the learning or

adaptation process [11].

Error function: The difference between the actual output and the desired output is

calculated, the raw error. It is then taken into an error function and then propagated

backwards to a previous layer. The error is usually multiplied against each of the

incoming connection weights to modify them before the learning cycle.

Learning function: This function is used to modify the weights of the inputs of every

neuron according to the errors propagated backwards as well as according to some other

neural based algorithm. This process is done until a desired result is obtained and is

known as the adaptation or the learning mode. There are two types of learning modes as

stated earlier namely supervised an unsupervised learning. These will be discussed in the

next section.

3.4 ANN TRAINING

It was mentioned earlier that weights for the inputs needed to be found so that the

desired outputs can be obtained. In order for this to occur, the ANN needs to undergo

some for of training where it learns and discovers relationships between certain input

parameters. Because of this, the ANN is able to modify the weights so that the expected

result is achieved with a little room for error. It does so by using two learning methods,

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namely supervised and unsupervised learning. The learning methods try to minimize the

errors of all the neurons by modifying the weights until the level of accuracy in the

network is acceptable.

3.4.1 SUPERVISED LEARNING

This type of learning mode was discussed briefly in section two. With this kind of

learning, the ANN needs to be trained before it can be able to solve any problems. Input

and output data (training data) is given to the network during the training stage. For each

input, there needs to be a corresponding output. A very careful selection of input data is

required as the ANN will discover relationships between input parameters and thus use

this as a standard when actual data is presented during the validation stage. Training sets

need to be fairly large and inclusive of every situation because as mentioned above, the

network needs all this information so that it can be able to learn all features and

relationships that are important.

The output obtained by the neural network is compared to the desired output. The

difference between the two is then propagated backwards into the network. The weights

are initially set to some random numbers and then they are modified iteratively during

the learning process according to the error difference.

When the desired accuracy is reached, the network is presented with data it has not seen

before and the performance level is monitored. If the performance is not satisfactory, the

training session continues. This testing is critical to ensure that the network has not

simply memorized a given set of data but has learning the general patterns involved

within an application [11]

3.4.2 UNSUPERVISED LEARNING

In unsupervised learning, the network is trained without any external help. This means

that the data is presented to the network consists of only the input values. There is no

target vector for the outputs. The weights are adjusted by the network by monitoring its

internal performance. The network looks for trends in the input signals and makes

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changes according to its function. The ideal behind this kind of learning is that the output

or consequence of doing something is unknown.

An input is presented but the outcome is unknown and so the network needs to train

itself to find any similarities among the inputs so that it can be able to produce a

reasonable result.

This training correlates in a way to human activity. One might be faced with a situation

(for example a mathematical or engineering problem) that one has never encountered

before and an outcome is required. So that person goes out and performs some kind of

research and looks at the information that has been presented (training) and then makes

an informed decision.

However, unsupervised learning is a subject that is still being researched and not been

widely implemented.

3.4.3 LEARNING RATES

A learning rate defines how long it will take to train the network. The slower the ANN

learns the more time spent, the faster the learning rate the more the network will not be

able to make the fine discriminations required to reach the desired accuracy. Factors like

the size of the network, architecture type, type of learning rule and desired accuracy need

to be considered when coming up with a learning rate. The learning rate is usually a

positive number between zero and one.

If it is bigger than one, the learning algorithm may overshoot in correcting the weights

whereas if it is very small, it may not be quick enough to correct the errors and may lead

to convergence problems.

3.4.4 LEARNING RULES

The first learning rule was developed by Donald Hebb in 1949 and it is known as

Hebb’s rule. His rule states that “If a neuron receives an input from another neuron, and

if both are highly active (mathematically have the same sign), the weight between the

neurons should be strengthened.”

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The next rule to be developed was the Hopfield law, which is similar to Hebb’s rule, but

the difference is that the magnitude of the strengthening is specified.

It says that “If the desired output and the input are both either active or inactive,

increment the connection weight by the learning rate, otherwise decrement the weight by

the learning rate.”

The delta rule is a rule that has been implemented widely in the ANN application to

load forecasting. It is a further variation of Hebb’s rule. The principle behind is that the

strengths of the input connections have to be continuously modified in order to reduce

the difference (delta) between the target output and the actual output value of the neuron.

It changes the weights in a way that minimizes the mean square error of the network. It

works as follows:

1. The delta error in the output layer is transformed by the derivative of the

transfer function.

2. The result is taken by the previous layer to adjust the connection weights.

3. This error is propagated into other previous layers one at a time.

4. The error reaches the input layer and the weights are adjusted.

5. The training procedure is repeated until the accuracy is acceptable.

In mathematical terms, the following equations are used for the delta rule:

(3.1)

represents the error term.

For a neuron j with a transfer (activation) function given by g(x) the delta rule for its ith

weight wji is given by

∆wji =α (tj – yj)g’(h)xj (3.2)

Where

α: learning rate

25

g(x): transfer function

tj : target output

yj : actual output

xj : ith input

hj =∑xjwji (3.3

yj = g(hj) (3.4)

A network type called Feed-forward; back-propagation derives its name from this

method of calculating the error term. This network is most commonly applied to the

problem of load forecasting and is the subject of discussion in the next section.

3.4.5: NETWORK SELECTION

There exists a variety of networks in the ANN architecture. Each network type is specific

to a certain class of problems. The table overleaf illustrates some of the applications or

problem types for which neural networks are used. There are five categories:

1. Prediction

2. Classification

3. Data association

4. Data conceptualization

5. Data filtering

26

Table 3.1: shows applications and problems solved using neural networks

Network type Networks Use for networks

Prediction -Back propagation

-Delta bar delta

-Extended delta bar delta

-Directed random search

-Higher order neural networks

-Self organizing map into

Back-propagation

-Use input to predict some

output (e.g. pick the best

stocks in the stock market,

predict the weather, identify

people with cancer risks)

Classification -Learning vector quantization

-Counter-propagation

_probabilistic neural network

Use input values to determine

the classification (e.g. is the

input the letter A, is the blob

of video data a plane and

what kind of plane it is)

Data Association -Hopfield

-Boltzmann machine

-Hamming network

-Bidirectional associative

memory

-spatial-temporal pattern

recognition

Like classification but it also

recognizes data that contains

errors (e.g. not only identify

the characters that were

scanned but also identify

when the scanner wasn’t

working properly)

Data conceptualization -Adaptive resonance network

-Self organizing map

Analyze the inputs so that

grouping relationships can be

inferred (e.g. extract from a

data base the names of those

most likely to buy a particular

product)

Data Filtering -Recirculation Smooth an input signal (e.g.

take the noise out of a

telephone signal)

27

Since this project is about electric load forecasting, which is a form of predicting

the future, the network that is most commonly used in this problem will be

discussed.

3.4.6: FEEDFORWARD, BACK-PROPAGATION

The feed-forward, back-propagation architecture was developed in the 1970’s by

several people namely Werbor, Parker, Hinton, Rumelhalt and Williams. Their

theories were developed independently from each other. By generalizing the delta

rule to multiply layer networks and non-linear differentiable functions, the back

propagation rule was created [8].

This architecture is the most popular, effective, and easy to learn model for

complex problems such as load forecasting. Its greatest strength is in non-linear

solutions to ill defined problems [6]

A typical network of this nature consists of one hidden layer and an output layer.

This is shown on the figure below.

Figure 3.4: Typical layout of a feed-forward network [12]

Training inputs are applied to the input layer and the target outputs are compared to the

outputs at the final layer. During the learning regime, a forward movement is made

28

though the network with the information moving from input layer through the hidden

layer and finally to the output layer, hence the name feed-forward.

The difference between the target and computed outputs (error term) are then propagated

backwards to the previous layers. This is usually modified by the derivative of the

transfer function and the connection weights are normally adjusted by the Delta rule.

The back-propagation rule is best descried by a worked example. Consider a two-layer

feed- forward network with a set of n inputs as illustrated in figure below.

Figure 3.5: Two layer feed-forward network.

Given a set of input i and j hidden layer neurons as well as k output layer neurons, the

hidden layer receives the following signal input

hj= ∑xiwji (3.5)

and produces an output that has been transformed by the transfer function which in this

case we will take as sigmoid or logistic function of the form

(3.6)

The output of a single hidden layer neuron is the following

29

fj = g(hj) (3.7)

This is then multiplied by the weight connecting the hidden layer to the output neurons.

yk = g(∑ (wjk*fj)) = g(vk) (3.8)

is the final output of a neuron k at the output layer.

For the hidden to output neurons the change in weight is calculated by

∆wjk=α (∑(tk – yk)g’(vk)fj (3.9)

Where α is the learning rate.

For the input to the hidden connections, the task becomes more difficult and partial

derivatives of the error term need to be used. The partial derivative of the error function

(equation 3.1) with respect to the weight connections between the input and the hidden

layer needs to be performed.

∆wji = α (using chain rule) (3.10)

=α∑k(tk – yk)g’(vk)g’(hj)xi (3.11)

The final step is to add the changes to the original weights

Wijnew = wij

old + ∆wij (3.12)

Wjknew =wjk

old + wjk (3.13)

There are many other variations of the back-propagation rule such as the back-

propagation with momentum. This was developed so that the learning of the network

may become faster causing it to converge as it was discovered that the network

sometimes did not converge using the standard algorithm. The error function or delta

weight is modified so that a portion of the previous delta weight is fed through to the

30

current delta weight. Therefore, a momentum coefficient mc that ranges between zero

and one is used in the delta equation.

∆ w = ∆w +mc*∆wprev (3.14)

A different viewpoint concerning the supervised training of a network is taken when the

training is approached as a problem in numerical optimization. The Scaled Conjugate

Gradient (SCG) method, which is a member of the Conjugate Gradient Method CGM)

family, is a training algorithm that is used in conjunction with back-propagation. This is

done in order to increase the computational speed of the training. Despite the standard

back-propagation method being given a momentum factor, convergence for large-scale

networks does not occur optimally.

The CGM is a general-purpose second order technique that helps to minimize the goal

(error) function of certain variables. Second order means that the function uses second

derivatives in the goal functions whereas the back-propagation method uses first

derivatives. CGMs are much like the back-propagation method in that they iterate until

the minimum is reached. The difference is that the back-propagation iterates down a

gradient while the method can be found in the appendix.

3.5 LOAD FORECASTING USING ANN

The following feature of an ANN network are regarded as most important when wanting

to apply this kind of technique for load forecasting

• Network structure

• Learning rule used for training

• Choice of input variables

• Learning rate

Network structure: This is important as the designer needs to decide on the number of

layers he/she is going to use. The most commonly used is the three-layer feed-forward

network because of its great ability to map non-linear functions [6] the three layer

31

network will be divided such that the first, second and third layers constitute the input,

hidden and output layers.

The number of hidden layers is also a critical decision because if the system contains

many hidden layers, there is a high chance that the data will only be memorized and a

pattern will not be found. The models encountered for the short-term load forecasting

problem use one or two hidden layers. The choice of the number of hidden layers

depends on the complexity of the problem at hand. The output layer can have as many

output neurons as the designer wishes.

In the case of hourly load forecasting, there are 24 hours in a day and so the designer

may want an output for each hour of the day or one output stating the total system load

for the next day.

Choice of input variables: load forecasting models are different for each power utility.

This is because there is no standard that dictates which variables to use when developing

a model for load forecasting. The choice of inputs lies with the designer. Input variables

such as weather, the previous year’s load and weather characteristics (this includes the

temperature and precipitation) to name a few may be used. The knowledge about the

kind of stimuli that influence the load needs to be known to make an informed decision

on the type of input variables to choose.

Learning rule: it is important to choose the correct learning rule for a specific

application. In load forecasting, the back-propagation method is widely used and has

been proven to produce effective results. Another aspect of the learning rule is the

accuracy that the network is to reach. This accuracy needs to be predefined by the

designer so that the network can be trained until it reaches that level of performance.

Learning rate: As discussed previously, this factor is important and defines the duration

of the training period. This number should be chosen carefully so that there is no

overshooting in correcting errors and that the network does not overstep the predefined

error goal.

32

When the above decisions are made, what is left is to train the network. Once the desired

error goal has been reached, actual data can be presented to the ANN so that it can

perform a load forecast. The performance of the ANN can be then be monitored by the

following measures [7]:

• Mean absolute percentage error

Є = *100 (3.15)

• Root mean square error (RMSE)

α = (3.16)

• Average (mean) error

e = ( ) (3.16)

Note: Xt and Xf are the target and forecasted outputs respectively.

33

CHAPTER 4: LONG TERM LOAD FORECASTING BASED ON VISION 2030

4.1: FORECAST MODEL

This section presents an ANN-based model that was developed as a solution to

specification, based on the literature that was reviewed. For comparative purposes data

from K.P.L.C (forecasted) data was obtained. The first two sections describe the

procedures used in to develop the models starting with ANN .Results from two models

are then analyzed and compared

The data used in the model to train the Neural Networks are:

1. Historical electric load demand

2. Historical G.D.P

3. Population growth

4. Weather data

4.2 DEVELOPMENT OF THE ANN MODEL

The section describes the procedures and guidelines that were used in formulating this

model. Below is a diagram of the steps that are taken in developing a model for load

forecasting.

Fig 4.1: Stages involved in developing a load forecasting model

According to fig 4.1, the first step in developing a load forecasting model is to decide on

the objectives of the model.

34

The objectives of this forecasting model are:

• Perform a long-term electric load forecast for the next 20 years

• Create an automated forecasting system

• Develop a forecasting tool that considers weather, historical electric load

data, G.D.P and Housing as inputs

From fig 4.1;

Ø Model formulation/selection: This type of model needs to be decided on this

stage i.e. hourly, weekly or yearly forecast. The year type are also developed

according to the information provided and engineer’s discretion. The year

objectives of the forecast need to be clarified in this stage so that the engineer can

proceed to the next.

Ø Identification: The most important parameters of the model are identified. The

parameters include historical electric load, G.D.P, housing, weather data etc

Ø Validation: This is the stage where the model will be tested to see whether it

performed as required. The performance of the model is checked here as well

and if it does not conform, then the model will have to be re-evaluated and

either additional parameters will have to be added so that better accuracy can

be achieved.

Ø Use for forecasting: This is the final stage after the validation procedure has been

performed. The model can be used for the actual forecasting of the load.

4.3 PROPOSED MODEL

It was decided to develop a fully connected 3 layer feed-forward, back

propagation network because of its ability to approximate non-linear functions. A fully

connected network means that each neuron receives information from every input

variable.

35

A simplified structure of the network is shown in figure. 4.2. below.

Figure 4 .2: simplified structure 3-layer feed forward network.

The network has three layers, namely the first hidden layer, the second hidden layer and

the output layer. The input vector contains the variables that are required to perform the

forecast. The identification of these parameters is discussed in the next section.

4.3.1 IDENTIFICATION OF PARAMETERS

Carrying out an analysis of input variables consists in studying the contribution of each

variable to the result of the forecasting model. The input variables were chosen

according to the specification in chapter 2 (section 3). Two three – layer neural network

models were developed. The first model had an input vector that consisted of 56

variables. The second model had 60 variables. ANN inputs and outputs for he two

models are described in table 4.1

36

Table 4.1: ANN inputs and outputs

Model one Model two

1-48 -previous 10 years

half-year load

demand

1-55 -Same as model one

49-50 -Previous years

housing trend

56 -hourly salary index

51-52 -Previous years

GDP

57-59 -same as model one

53-55 -Previous year

minimum and

maximum weather

forecast

60 -Same as model one

56 -Previous year

population

The first hidden layer is the same size as the number of inputs, that is, the number of

neurons corresponds to the number of inputs. Model one has 56 neurons whilst the

second model has 58 neurons in their respective first hidden layer. The number of output

neurons equals to the number of half - months in a year. Both models have 20 neurons in

the second hidden layer. The transfer function chosen for these layers are the tangent

sigmoid functions; fig 4.3. The output layer has neurons with a linear activation function

so that the outputs can take on any value. It is suggested that the number of hidden

neurons was chosen using the guideline and through experimentation with different

number of neurons as will be discussed in the validation phase.

37

Fig. 4.3 Sigmoid activation function [11]

The network structure for model one is shown in fig. 4.4. Model two is an extension of

model one. This model was created in order to see the effect of the inclusion of

population as a parameter in the forecast. Most authors usually include historical electric

load data and G.D.P as their input variables.

38

Figure 4.4: Network structure

4.4 PRE-PROCESSING OF INPUT DATA

The data used in the training and validation phases was obtained from the KENYA

POWER AND LIGHTING COMPANY. Yearly half-load data for the years 1998 to

2008 were obtained. The 1998-2004 data was used to train the neural network system

and the 2005-2008 data was used for testing the network. G.D.P data for the period

1998-2007 was obtained from the Kenya bureau of statistics. The data that was obtained

could not be used in its actual form because the ANN model has activation functions that

work optimally in a small range such as from minus two to two. See fig. 4.3. Therefore

all load and G.D.P had to be pre-processed.

39

Table 4.2: 1nput parameter values

ELECTRIC DEMAND/%GDP GROWTH RATE

YEAR

DEMAND

(GWh)

%GDP

GROWTH POPULATION(10^6)

1998 4050 1.7526 10

1999 4127 1.3716 12

2000 4374 1.0668 15

2001 4637 1.143 20

2002 4915 2.3622 25

2003 5210 3.3528 30

2004 5722 4.191 35

2005 5854 5 37

2006 6504 6.1 39

2007 6600 6.5 42

2008 6604.5 6.5 45

4.4.1: SCALING LOAD DATA

The pre-processing of the yearly half load data was done using

Xni=(XI-X’)/αI (4.1)

Where

Xni : scaled input of year I,

Xi : Half-year load demand,

40

X’i: Average load demand,

αi: Standard deviation

This scaling scheme was used on all data from the year 1998 to 2008

4.4.2: NORMALIZING WEATHER DATA

It was suggested by Dr. WEKESA that the maximum and minimum temperature be

normalized by dividing both by 33o this is the absolute temperature that NAIROBI

receives.

The year type was represented as a number with 2010 being 0.1 and 2030 as 1 as done in

reference [13]

4.5: VALIDATION OF THE MODEL

A Netlab Toolbox, designed by Ian T Nabney [34], containing Matlab files (M-files) on

neural networks was used to build, train, and test the proposed models. However, the

toolbox only contained a two-layer feed-forward network. A MATLAB code was

developed to enhance a three-layer neural network. The proposed model is a three-layer

network. The relevant M-files had to be extended in order to create the three-layer

network structure as required

41

As seen if figure below once the network was created the pre-processed training data

was presented to the network.

Figure 4.5: shows how to creat the resolution level for training the neural netwok

As seen from above you select the resolution level of your choice for testing. For the

training of the neural network, enter the amount of years you are using for the training of

the network. The training data used was from 1998 to the year 2008, as shown in the

figure below.

Figure 4.6: shows number of years selected for neural network training.

42

For the 7 years you select data for a particular year for the testing as shown in the figure

below.

Figure 4.7: shows the year data selection for the testing of the neural network

Once you finish entering scaling the historical load data, normalized G.D.P and the

historical population, you repeat the same for every year from 1998 to 2008. Then now

you can select one of the options:

• Create new neural network

• Perform load forecasting demand.

• Quit session

As shown in the figure below,

Figure 4.8: shows selection of options (create new Neural Networks, perform

forecasting of load demand or Quit session).

43

Now the neural network is already created, trained, tested and ready for electric

load forecasting.

4.5.1: SIMULATION RESULTS

The following presents the forecast that were generated by the neural network and the

econometric results developed by K.P.L.C model. The performance of the neural

network is judged based on the K.P.L.C model. The figure below shows the electric load

forecast for the next 22 years (that is, 2008 to 2030)

Figure 4.9: ANN output results(forecasted load for 2009-2030)

Given the results from the simulation of the neural network and the K.P.LC’s

econometric model results comparison had to be made to establish the best suited model

for long-term electric load forecasting.

44

4.5.2: COMPARISON BETWEEN ANN AND K.P.L.C MODEL

The tool developed by K.P.LC engineers was used to forecast the next 30 years. As

shown in the table 4.2 below K.P.L.C forecast has the same load profile as the ANN load

which is good. In figure 4.3, as the year’s proceeds the difference between the ANN and

K.P.LC econometric model become large. This is because the ANN tool has adjustment

factors which affect the forecast. By adjusting these factors and checking the graph of

the resulting forecast against the K.P.LC load, are obtained

Table 4.3: ANN and K.P.L.C forecasted results

YEAR

ANN

FORECAST

KPLC

FORECAST

2009 7118 7004.9

2010 7626 7461.8

2011 8176 7983.1

2012 8766 8578

2013 9395 9256.7

2014 10070 10031.1

2015 10780 10914.7

2016 11530 11922.9

2017 12320 13073.3

2018 13160 14385.8

2019 14040 15883.4

2020 14960 17592.2

2021 15920 19541.9

2022 16930 21760.5

2023 17980 24304.5

2024 19070 27201

2025 20210 30505.4

2026 21390 34276.1

2027 22610 38578.2

2028 23890 43487

2029 25200 49087.8

2030 26560 55478.4

45

It can be seen that in the figure 4.4, ANN approximates the K.P.L.C forecasted load

better for the next ten years,then K.P.LC forecast shoots up exponentially. The K.P.L.C

this is higher than expected by the ANN. The consequnce of high forecasting is that the

generation that will be scheduled will be low and will not be able to meet the load

demand for that particular year. This can cause the overloading of transmission lines and

transformers in severe cases, cause a blackout.

As shown in the figure below, ANN is more superior tool. Ths is because ANN is a

automated forecasting tool that does not require manual updating of input data. Errors

that may be caused by human interference are minimal in ANN whereas in K.P.L.C

econometric model this may lead to unfavourable results.

Figure 4.10: ANN and K.P.L.C results

46

Chapter 5: CONCLUSION AND RECOMMENDATIONS

This project presents a model that forecast on a long-term basis; for the next 20 years

ahead according to the specification discussed in the project, ANN based long-term load

forecasting method that use a three-layer feed forward neural network and a scaled

conjugate back-propagation training algorithm are presented in this project. The model

considers historical load data, population, G.D.P and weather conditions. For

comparative purposes as well as to deduce whether ANN produces effective results,

K.P.L.C forecasted results were used. The difference in the forecasted results is

accounted for by the fact that K.P.L.C econometric methods are not able to detect and

determine the relationship between load affecting factors and the load demanded. The

ANN model performs much better than the econometric model because it is able to learn

from the training data, the relationship between certain variables and their effects on the

load demand thereby making relatively accurate predictions. In order to get accurate

predictions, the data should be trained. Increasing the number of training cycles has an

improving effect on the forecasting errors. However, if a network is over-trained, the

results may be unfavorable.

When comparing the ANN and K.P.L.C econometric models, it is concluded that

inclusion of more load affecting variables increases the accuracy of the forecasts, hence

proving that ANN is more superior. It can thus be concluded that Artificial Intelligent

Techniques such as Neural Networks in particular, are better suited for long-term electric

load forecasts than classical methods (that is, econometric method used by K.P.L.C). The

approach to long-term electric load forecasting used in this project should therefore be

considered by the Kenya Power and Lighting Company for further development as an

operational tool.

47

Based on these conclusions, the following is recommended:

• Artificial Intelligent-based techniques, ANN in particular, must be implemented

for long-term electric load forecast for the Kenya Power and Lighting

Company.

• More load affecting variables, Hourly salary index and electric pricing in

particular should be investigated and used as input variables to the model to

improve forecasting accuracy. These two are specified because of the current

growth of unemployment in Kenya.

• Investigate ways of normalizing the weather variables as this may affect the

output of the forecast.

• Use a high processing computer for the development of the ANN model.

Further work

Due to the unreliability of the weather forecasts an ANN based weather forecasting

model can be developed for the ANN-based long-term load forecasting model.

Chaos years (as experienced during and after last general elections), holidays their

respective input variables were discarded: in reality it cannot be done. Therefore, an

ANN-based or other AI-based short-term and medium-term for holidays can be

developed so that all years can be covered when forecasting.

48

APPENDICES

%File name: nprogram.m

%Description: This file reads the data from its source into their respective arrays.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Clear command screen and variables

clc;

clear;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%user desired resolution level (Tested: resolution = 2 is best)

level = menu('Enter desired resolution level: ', '1',...

'2 (Select this for testing)', '3', '4');

switch level

case 1, resolution = 1;




end

msg = ['Resolution level to be used is ', num2str(resolution)];

disp(msg);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% user desired amount of data to use

data = menu('Choose amount of data to use: ', '1 year', '2 years', '3 years', '4 years',...

'5 years', '6 years', '7 years (Select this for testing)');

switch data

case 1, dataPoints = 4050; %1 year = 4050 points

case 2, dataPoints = 4127; %2 years = 4127 points

49






end

msg = ['No. of data points to be used is ', num2str(dataPoints)];

disp(msg);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Menu for data set selection

select = menu('Use QLD data of: ', '1998',...

'1999', '2000 (Select this for testing)', '2001', '2002');

switch select

case 1, demandFile = 'DATA1998_QLD1';





end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Plot the original demand data signal

figure (1);

subplot(resolution + 2, 1, 1); plot(1: dataPoints)

legend('Demand Original');

title('QLD Demand Data Signal');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Function here allows repetitive options to,

50

% 1) Create new NNs, 2) Retrain the existing NNs,

% 3) Perform load demand forecasting and 4) Quit session

while (1)

choice = menu('Please select one of the following options: ',...

'CREATE new Neural Networks',...

'Perform FORECASTING of load demand', 'QUIT session...');

switch choice

case 1, scheme = '1';




end

%If scheme is 'c', call <nCreate> to create new NNs, train them then perform forecast

if(scheme == '1')

nCreate;

end

%If scheme is 'r', call <nRetrain> to retrain the existing NNs

if(scheme == '2')

nRetrain;

end

%If scheme is 'f', call <nForecast> to load the existing NN model

if(scheme == '3')

nForecast;

end

%If scheme is 'e', verifies and quit session if ’yes’ is selected else continue

if(scheme == '4')

button = questdlg('Quit session?', 'Exit Dialog','Yes','No','No');

51

switch button

case 'Yes', disp(' ');

disp('Session has ended!!');

disp(' ');

break;

case 'No', quit cancel; e As seen if figure below once the network was created the pre-processed training data was presented to the network.

end

end

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%File name : ncreate.m

%Description: This file prepares the input & output data for the NNs. It creates then trains the

NNs to mature them.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Clear command screen and set target demand output to start at point 2

clc;

targetStartAt = 2;

disp('Program will now CREATE a Neural Network for training and forecasting...');

disp(' ');

disp('To capture the pattern of the signal, the model is ')

disp('set to accept dataPoints x 2 sets of training examples; ');

disp('1 set of demand + 1 sets of gdp. ');

disp(' ');

disp('The normalised demand data <point 2>, is to be taken as the ')

disp('output value for the first iteration of training examples. ');

52

disp(' ');

disp('Press ENTER key to continue...');

pause;

%Clear command screen then prompt for no. of training cycles

%For current program, 1 cycle = user set no. of iterations (ie: dataPoints)

clc;

cycle = input('Input the number of training cycles: ');

numOfTimes = resolution + 1;

%Creating and training the NNs for the respective

%demand and gdp coefficient signals

for x = 1: numOfTimes

%Clearing variables

clear targetDemand;

clear inputs;

clear output;

clc;

if(x == 1)

neuralNetwork = ['Neural network settings for approximation level ',

num2str(resolution)];

else

neuralNetwork = ['Neural network settings for detail level ', num2str(x - 1)];

end

disp(neuralNetwork);

disp(' ');

%Set no. of input nodes and hidden neurons for the

%respective demand and price coefficient signal

numOfInputs = 2;

53

inputValue = ['Number of neural network INPUT units is set at ', num2str(numOfInputs)];

disp(inputValue);

disp(' ');

numOfOutput = 1;

outValue = ['Output is set to ', num2str(numOfOutput)];

disp(outValue);

disp(' ');

numOfHiddens = input('Enter the no. of HIDDEN units for the NN hidden : ');

hiddenValue = ['Number of neural network HIDDEN units is set at ',

num2str(numOfHiddens)];

disp(hiddenValue);

disp(' ');

%Setting no. of training examples

trainingLength = dataPoints;

%Set target outputs of the training examples

if(x == 1)

targetDemand = normDemand(targetStartAt: 1 + trainingLength);

else

targetDemand = normDemandDetail(x - 1, targetStartAt: 1 + trainingLength);

end

%Preparing training examples

%Setting training i/ps to be 2 with user defined no. of iterations (dataPoints)

y = 0;

while y < trainingLength

if(x == 1)

inputs(1, y + 1) = normDemand(y + 1);

54

inputs(2, y + 1) = normgdp(y + 1);

else

inputs(1, y + 1) = normDemandDetail(x - 1, y + 1);

inputs(2, y + 1) = normgdpDetail(x - 1, y + 1);

end

output(y + 1, :) = targetDemand(y + 1);

y = y + 1;

end

inputs = (inputs’);

%Setting no. of training cycles

[ni, np] = size(targetDemand);

% <== [ni, np] tells the NN how long is 1 cycle;

size(targetDemand)

clear nn;

%Create new neural network for respective coefficient signal

%NET = MLP(NIN, NHIDDEN, NOUT, FUNC)

nn = mlp(numOfInputs, numOfHiddens, numOfOutput, 'linear');

%NN options

options = zeros(1, 18);

options(1) = 1;

%Provides display of error values

options(14) = cycle * ni * np;

%Training the neural network

%netopt(net, options, x, t, alg);

nn = netopt(nn, options, inputs, output, 'scg');

%Save the neural network

55

filename = ['nn', num2str(x)];

save(filename, 'nn');

disp(' ');

msg = ['Neural network successfully CREATED and saved as => ', filename];

disp(msg);

if(x < 3)

disp(' ');

disp('Press ENTER key to continue training the next NN...');

else

disp(' ');

disp('Model is now ready to forecast!!');

disp(' ');


end

pause;

end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%File name : nforecast.m

%Description : This file loads the trained NNs for load forecasting and recombines the predicted

outputs from the NNs to form the final predicted load series.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Clear command screen and variables

clc;

clear forecastResult;

clear actualDemand;

clear predicted;

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clear actualWithPredicted;

disp('Neural networks loaded, performing electricity demand forecast...');

disp(' ');

pointsAhead = input('Enter no. of points to predict (should be < 5755): ');


%Predict coefficient signals using respective NNs

for x = 1 : numOfTimes

%Loading NN


clear nn

load(filename);

clear in;

numOfInputs = nn.nin;

y = 0;

%Preparing details to forecast

while y < pointsAhead

if(x == 1)

propData(1, y + 1) = normDemand(y + 1);

propData(2, y + 1) = normgdp(y + 1);

else

propData(1, y + 1) = normDemandDetail(x - 1, y + 1);

propData(2, y + 1) = normgdpDetail(x - 1, y + 1);

end

y = y + 1;

end

if(x == 1)

forecast = mlpfwd(nn, propData') * maxDemand;

57

else

forecast = mlpfwd(nn, propData') * maxDemandDetail(x - 1) - 4000;

end

forecastResult(x, :) = forecast';

end

%For debugging

% forecastResult

actualDemand = tDemandArray(2: 1 + pointsAhead);

predicted = sum(forecastResult, 1)';

%Calculating Mean Absolute Error

AbsError = abs(actualDemand - predicted(1: pointsAhead)) ./ actualDemand;

msg = ['Mean Absolute Error = ', num2str(mean(AbsError(1: pointsAhead))), ' !!'];

disp(' ');

disp(msg);

%Plot actual time series against predicted result

figure(3)

actualWithPredicted(:, 1) = actualDemand;

actualWithPredicted(:, 2) = predicted(1: pointsAhead);

plot(actualWithPredicted);

graph = ['Mean Absolute Error = ', num2str(mean(AbsError))];

title(graph);

legend('Actual', 'Forecasted');

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%File name : nretrain.m

%Description : This file loads the existing NNs and trains them again.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clc;

58

%Prompt for the starting point for training

disp('Program will now RETRAIN the Neural Networks ')

disp('with the SAME intial data series again...');

disp(' ');

disp('To capture the pattern of the signal, the model is ')

disp('set to accept dataPoints x 2 sets of training examples; ');

disp('1 set of demand + 1 sets of gdp. ');

disp(' ');

disp('The normalised demand data <point 2>, is to be taken as the ')

disp('output value for the first iteration of training examples. ');

disp(' ');

msg = ['Data points to be used for reTraining the NNs is from 1 to ',...

num2str(dataPoints)];

disp(msg);

disp(' ');


pause;

%Clear command screen

clc;

%Prompt for no. of training cycles

%For current program, 1 cycle = user set no. of iterations (i.e.: dataPoints)

cycle = input('Input number of cycles to retrain the NNs: ');


%Loading existing NNs for training

for x = 1: numOfTimes

%Re-initialising variables

clear targetDemand;

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clear inputs;

clear output;

clc;

%Loading NN for the respective demand and temperature coefficient signals


clear nn

load(filename);

%Getting the size of NN

numOfInputs = nn.nin;

numOfHiddens = nn.nhidden;

numOfOutput = 1;

%Setting length of reTraining examples

targetStartAt = 2;

%Set target outputs of the training examples

if(x == 1)

targetDemand = normDemand(targetStartAt: 1 + targetLength);

else

targetDemand = normDemandDetail(x - 1, targetStartAt: 1 + targetLength);

end

%Preparing training examples

%Setting training i/ps to be 2 with user set no. of iterations (dataPoints)

y = 0;

while y < reTrainLength

if(x == 1)

inputs(1, y + 1) = normDemand(y + 1);

inputs(2, y + 1) = normgdp(y + 1);

else

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inputs(1, y + 1) = normDemandDetail(x - 1, y + 1);

inputs(2, y + 1) = normgdpDetail(x - 1, y + 1);

end

output(y + 1, :) = targetDemand(y + 1);

y = y + 1;

end

inputs = (inputs');

%Setting no. of training cycles

[ni, np] = size(targetDemand);

% <== [ni, np] tells the NN how long is 1 cycle;

size(targetDemand)

%With reference to line 106

%NN options

options = zeros(1, 18);

options(1) = 1;

%Provides display of error values

options(14) = cycle * ni * np;

%Training the neural network

%netopt(net, options, x, t, alg);

nn = netopt(nn, options, inputs, output, 'scg');

%Save the neural network


save(filename, 'nn');

disp(' ');

msg = ['Neural network => ', filename, ' <= successfully RETRAINED and saved!!'];

disp(msg);

if(x < 3)

61

disp(' ');

disp('Press ENTER key to continue training the next NN...');

else

disp(' ');

disp('Model is now ready to forecast again!!');

disp(' ');


end

pause;

end

% Here is the electric load data from 1998 to 2008.

% Time interval

t = (1998:1:2008)';

% electric load

e = [4050 4127 4374 4437 4615 ...

4810 5222 5454 5804 6300 6604.5]';

% Plot

plot(t, e,'bo');

axis([1998 2030 4000 34000]);

title('electric load. 1998-2030');

ylabel('Gwh');

% what is your guess for the electric load in the year 2020?

% Let's fit the data with a polynomial in t and use it to extrapolate to t = 2010. The coefficients in the polynomial are obtained by solving a linear system of equations involving a 11-by-11 Vandermonde matrix, whose elements

62

are powers of scaled time,

A(i,j) = s(i)^(n-j);

n = length(t);

s = (t-2004)/5;

A = zeros(n);

A(:,end) = 1;

for j = n-1:-1:1, A(:,j) = s .* A(:,j+1); end

% The coefficients c for a polynomial of degree d that fits the data e are obtained by solving a linear system of equations involving the last d+1 columns of the Vandermonde matrix:

A(:,n-d:n)*c ~= e

% If d is less than 10, there are more equations than unknowns and a least squares solution is appropriate. If d is equal to 10, the equations can be solved exactly and the polynomial actually interpolates the data. In either case, the system is solved with MATLAB's backslash operator. Here are the coefficients for the cubic fit.

c = A(:,n-3:n)\e

% Now we evaluate the polynomial at every year from 1998 to 2010-2030 and plot the results.

v = (1998:2030)';

x = (v-2004)/5;

w = (2020-2004)/5;

y = polyval(c,x);

z = polyval(c,w);

hold on

plot(v,y,'k-');

plot(2020,z,'ks');

text(2020,z+15,num2str(z));

hold off

v = (1998:2030)';

63

x = (v-2004)/5;

w = (2030-2004)/5;

y = polyval(c,x);

z = polyval(c,w);

hold on

plot(v,y,'k-');

plot(2030,z,'ks');


hold off

v = (1998:2030)';

x = (v-2004)/5;

w = (2020-2004)/5;

y = polyval(c,x);

z = polyval(c,w);

hold on

plot(v,y,'k-');

plot(2020,z,'ks');


hold off

v = (1998:2030)';

x = (v-2004)/5;

w = (2028-2004)/5;

y = polyval(c,x);

z = polyval(c,w);

hold on

plot(v,y,'k-');

plot(2028,z,'ks');

64


hold off

v = (1998:2030)';

x = (v-2004)/5;

w = (2026-2004)/5;

y = polyval(c,x);

z = polyval(c,w);

hold on

plot(v,y,'k-');

plot(2026,z,'ks');


hold off

v = (1998:2030)';

x = (v-2004)/5;

w = (2024-2004)/5;

y = polyval(c,x);

z = polyval(c,w);

hold on

plot(v,y,'k-');

plot(2024,z,'ks');


hold off

v = (1998:2030)';

x = (v-2004)/5;

w = (2022-2004)/5;

y = polyval(c,x);

z = polyval(c,w);

65

hold on

plot(v,y,'k-');

plot(2022,z,'ks');


hold off

v = (1998:2030)';

x = (v-2004)/5;

w = (2015-2004)/5;

y = polyval(c,x);

z = polyval(c,w);

hold on

plot(v,y,'k-');

plot(2015,z,'ks');


hold off

v = (1998:2030)';

x = (v-2004)/5;

w = (2018-2004)/5;

y = polyval(c,x);

z = polyval(c,w);

hold on

plot(v,y,'k-');

plot(2018,z,'ks');


hold off

v = (1998:2030)';

x = (v-2004)/5;

66

w = (2013-2004)/5;

y = polyval(c,x);

z = polyval(c,w);

hold on

plot(v,y,'k-');

plot(2013,z,'ks');


hold off

v = (1998:2030)';

x = (v-2004)/5;

w = (2010-2004)/5;

y = polyval(c,x);

z = polyval(c,w);

hold on

plot(v,y,'k-');

plot(2010,z,'ks');


hold off

% code is used to give the forecasted electric load based on vision 2030

% years when electric load is forecasted

Yr (1-22) = (2009-2030)

% electric load demand in GWh obtained using M.file.r.m

e0=6644

e1=7118

e2=7677.3939

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e3=8176

e4=8766

e5=9395

e6=1.007e+004

e7=1.078 e+004

e8=1.153 e+004

e9=1.232 e+004

e10=1.316 e+004

e11=1.404 e+004

e12=1.496 e+004

e13=1.592 e+004

e14=1.693 e+004

e15=1.798 e+004

e16=1.907 e+004

e17=2.2021 e+004

e18=2.139 e+004

e19=2.261 e+004

e20=2.389 e+004

e21=2.52 e+004

e22=2.656 e+004.

68

REFERENCES

[1] Singh A, Kalra P.K, Emmanuel, “Point of view of knowledge based systems for load

forecasting”, Symposium on expert systems application to power systems, 1998, pp 7~1-

7~4.

[2] Taylor W. J, McSharry E.P, de Menezes M.L, “A comparison of univariate methods

used for forecasting electricity demand up to a year ahead”, International Journal of

Forecasting,2006, Vol.22, pp 1-16

[3] Feinberg E.A, Genethliou D, “Chapter 12 Load Forecasting”, Applied mathematics

for power systems, pp 269-282

[4] Galkin I, “Crash introduction to artificial neural networks” found on

http://ulcal.uml.edu/~iag/CS/intro-to-ANN.html

[5] Galiana F.D, Gross G, ”long term load forecasting”, Proceedings of the IEEE, 1987,

Vol. 75 No.12, pp 1558-1573

[6] http://www.cs.nott.ac.uk/~gxk/courses/g5aiai/006neural/networks/neural-

networks.html

[7] Singh A, Chen H, Canizares A.C, “ANN-based short term load forecasting in

electricity markets”, Proceedings of the IEEE power engineering society transmission

and distribution conference, 2001, pp2:411-415

[8] Komane T, “Short term peak load forecasting using neural networks”, Department of

Electrical Engineering, University of Cape Town, 2001

[9] EM 1110-2-1701,”Appendix B load forecasting methods”, 1985, pp B-1-B-5 found

on

http://www.usace.army.mil/publications/eng-manuals/em1110-21701/a-b.pdf

[10] http://www.cee.hw.ac.uk/~alison/ai3notes/subsection 2 5 2 1.htm, Expert system

architecture

http://ulcal.uml.edu/~iag/CS/intro-to-ANN.html

http://www.cs.nott.ac.uk/~gxk/courses/g5aiai/006neural/networks/neural-networks.html

http://www.cs.nott.ac.uk/~gxk/courses/g5aiai/006neural/networks/neural-networks.html

http://www.usace.army.mil/publications/eng-manuals/em1110-21701/a-b.pdf

http://www.cee.hw.ac.uk/~alison/ai3notes/subsection 2 5 2 1.htm

69

[11] Anderson D, McNeil G, “Artificial neural networks technology”, A DACS State-of-

the Art Report, Data & Analysis Center for Software, 1990, pp 1-35

[12] stergiou C, Siganos D, “Neural Networks” found on

http://www.doc.ic.ac.uk/~nd/surprise 96/journals /vol4/cs11/report.html

[13] Khothanzad A, Hwang R.C, Abaye A, Maratukulam D, “An adaptive modular

artificial neural network yearly load forecaster and its implementation at electric utilities

”, IEEE transactions on power systems, Vol. 10, NO. 3, 1995, pp1716-1722

[14] Netlab Toolbox, help files, © Ian T Nabney (1996-2001),

www.ncrg.aston.uk/netlab/index.php

http://www.doc.ic.ac.uk/~nd/surprise 96/journals /vol4/cs11/report.html

70

Bibliography

1 Matlab (7.0) Neural Network Toolbox. © Mark Beale (1992-2004), the

Mathworks Inc.

2 www.planning.go.ke

3 www.hdropower-dams.com

http://www.planning.go.ke/

http://www.hdropower-dams.com/

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