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Chapter 15

INTRODUCTION, REVIEW OF AI

TECHNIQUES

Intelligence is the ability to think, to imagine,

create, memorize, understand, recognize patterns,

make choices, adapt to change and learn from expe-

rience. Artificial intelligence is a human endeavor

to create a non-organic machine-based entity that

has all the above abilities of natural organic intelli-

gence. Hence it is known as ‘Artificial Intelligence’

(AI). AI emerged as a computer science discipline

in the mid1950s. Since then, it has produced a

number of powerful tools, many of which are

of practical use in engineering to solve difficult

problems normally requiring human intelligence.

Artificial Intelligence (AI) has been defined as the

Radian Belu

Drexel University, USA & Desert Research Institute, USA

Articial Intelligence

Techniques for Solar Energy

and Photovoltaic Applications

ABSTRACT

Articial intelligence (AI) techniques play an important role in modeling, analysis, and prediction of the

performance and control of renewable energy. The algorithms employed to model, control, or to predict

performances of the energy systems are complicated involving differential equations, large computer

power, and time requirements. Instead of complex rules and mathematical routines, AI techniques are

able to learn the key information patterns within a multidimensional information domain. Design,

control, and operation of solar energy systems require long-term series of meteorological data such as

solar radiation, temperature, or wind data. Such long-term measurements are often non-existent for most

of the interest locations or, wherever they are available, they suffer of a number of shortcomings (e.g.

poor quality of data, insufcient long series, etc.). To overcome these problems AI techniques appear to

be one of the strongest candidates. The chapter provides an overview of commonly used AI methodolo-

gies in solar energy, with a special emphasis on neural networks, fuzzy logic, and genetic algorithms.

Selected AI applications to solar energy are outlined in this chapter. In particular, methods using the

AI approach for the following applications are discussed: prediction and modeling of solar radiation,

seizing, performances, and controls of the solar photovoltaic (PV) systems.

DOI: 10.4018/978-1-4666-1996-8.ch015

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Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

study of how to make computers do things which

at the moment, people do better (Haugeland, 1985,

Rich and Knight, 1991). An Expert System (ES) is

a computer program that assimilates and reasons

with knowledge obtained from some expert(s)

with a view to solving problem(s) or giving ad-

vice. Thus expert systems are software packages

which translate human expertise into computer

programs. Portability of software makes the use

of expert systems very attractive where human

expertise is scarce or costly or is likely to be lost

through mobility. Applications of AI techniques to

power and renewable energy systems has been an

active area of research for over three decades and

significant successes have been achieved. Among

the AI techniques, artificial neural networks, fuzzy

logic, expert or knowledge based systems have

been the most successful.

AI techniques play an important role in model-

ing, analysis and prediction of the performance

and control of renewable energy processes. AI

techniques have been used to solve complicated

practical problems in various areas of engineer-

ing and technology and are become increasingly

popular. AI systems can be used as an alternative

way to tackle complex and ill-defined problems.

They can learn from examples, are fault tolerant

in the sense that they are able to handle noisy

and/or incomplete data, are able to deal with non-

linear problems, and once trained can perform

prediction and generalization at high speed. AI

systems have been used in diverse applications

in control, robotics, pattern recognition, forecast-

ing, power systems, manufacturing, optimization,

signal processing, or medical, and social sciences.

They are particularly useful in system modeling

such as in implementing complex mappings and

system identification. AI systems comprise areas

like, expert systems, artificial neural networks,

data mining, genetic algorithms, fuzzy logic and

various hybrid systems, combining two or more

techniques. Results presented in various papers,

are testimony to the potential of artificial intelli-

gence as a design tool in many areas of energy and

renewable energy engineering. For the modeling,

prediction of performance and control of renew-

able energy processes, analytic computer codes are

often used. The algorithms employed are usually

complicated involving the solution of complex

differential equations, requiring large computer

power and need a considerable amount of time

to give accurate predictions. Instead of complex

rules and mathematical routines, AI systems are

able to learn the key information patterns within

a multi-dimensional information domain.

The use of the AI techniques in the environ-

mental and renewable energy applications has

increased with recognition of its potential. Many

of the renewable energy problems are exactly

the types of problems, and issues for which AI

approach appears to be most applicable. In these

models of computation, attempts are made to

simulate the cognitive and sensory functions of the

human brain and to use this capability to represent

and manipulate knowledge in the form of patterns.

Based on these patterns, ANNs, for example,

model input-output functional relationships and

can make predictions about other combinations

of unseen inputs. The AI techniques have the

potential for making better, quicker and more

practical predictions than any of the traditional

methods. On the other hand, data from the renew-

able energy processes, being inherently noisy, are

a good candidate to be handled with AI systems.

In the following subsections of this chapter short

introduction to the AI techniques is presented, as

well as their advantages and disadvantages.

ARTIFICIAL NEURAL NETWORKS

Artificial Neural Networks (ANNs) are infor-

mation-processing systems inspired by models

formulated from the workings of the brain. An

ANN consists of interconnected layers of neurons

or processing elements. Information is passed

between these units along the interconnections.

Data is passed through the network from layer to

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Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

layer via synapses or connections, each of which

is characterised by a weight/strength of its own.

In addition an activation function is associated

to limit the amplitude of the output of a neuron

and is shown in Figure 1. To achieve the desired

relationship between the input and output of a

network, values must be derived for the connection

weights and the activation functions. The process

of this derivation is called supervised training.

ANNs while implemented on computers are not

programmed to perform specific tasks. Instead,

they are trained with respect to data sets until

they learn patterns used as inputs. Once they are

trained, new patterns may be presented to them

for prediction or classification. ANNs can auto-

matically learn to recognize patterns in data from

real systems or from physical models, computer

programs, or other sources. They can handle

many inputs and produce answers that are in a

form suitable for designers or further processing.

Multi-Layer Perceptron (MLP)

MLPs are perhaps the most common type of feed-

forward networks. Figure 2 shows an MLP which

has three layers: an input layer, an output layer

and a hidden layer. Neurons in input layer only

act as buffers for distributing the input signals x

to neurons in the hidden layer. An incoming con-

nection has two values associated with it an input

and a weight, as shown in Figure 1. The output of

the unit is a function of the summed value. The

processing units in an ANN are interconnected

by links (synapses) with weights.

The network has an input layer, an output

layer and any number of hidden layers (usually

one or two). A neuron is linked to all neurons in

the next layer, as shown in Figure 2.

Neuron x has n inputs and one output:

y x f w x

i i

i

n

( ) =

=

∑

0

(1)

where w0,..., wn are the input weights and f is the

non-linear activation function (Krishnamoorthy

and Rajeev, 1996; Pham and Liu, 1995), usually a

step function or a sigmoid. The step function output

is y = 1 if x ≥ 0, and 0 otherwise. The sigmoid

function, more commonly used, is asymptotic

about 0 and 1 and anti-symmetric about (0, 0.5):

f x x

( )

=+ −

1

1 exp( )β (2)

ANNs, while implemented on computer, are

not programmed to perform specific tasks. Instead,

they are trained with respect to data sets until they

learn patterns used as inputs. Once they are trained,

new pattern may be presented to them for predic-

tion or classification. ANNs are constructed in

layer connects to one or more hidden layers where

Figure 1. A simple processing element

Figure 2. An example of an artificial neural

network

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Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

the factual processing is performance through

weighted connections. Each neuron in the hidden

layer joins weighted connections. The results of

the processing are acquired from the output layer.

Learning in ANNs is achieved through particular

training algorithms which are expanded in accor-

dance with the learning laws, assumed to simulate

the learning mechanisms of biological systems

(Belu et al., 2003; Chen et al., 2008). However,

as an assembly of neurons, a neural network can

learn to perform complex tasks including pattern

recognition, system identification, trend predic-

tion and process control (Belu et al., 2003; Chen

et al., 2008; Kalogirou, 2001; Kalogirou, 2007).

Data are presented to the neural network via input

layer, while the output layer holds the response

of the network to the input. All hidden and output

neurons process their layer input by multiplying

each input by its weight (1), summing the prod-

ucts, and then processing the sum via activation

(transfer) function to generate a result. Informa-

tion flow is unidirectional in feed-forward ANNs,

with no cycles, but in both directions in feedback

ANNs so they have cycles, by which their states

evolves to equilibrium (Fuller, 2000; Kalogirou,

2001). In a multi-layer perceptron (MLP), perhaps

the most common type of feed-forward networks,

input signals are propagated in gradually modified

form in the forward direction, finally reaching

the output layer.

An important characteristic of the sigmoid

activation function (2) that it is differentiable

throughout its domain, which makes it suitable for

use in the conjunction with a learning algorithm

(the weight modification is done in propagation

to the negative gradient of the output). The error

for hidden layers is determined by propagating

back the error determined for the output layer;

hence the technique is named back-propagation.

During learning, the weights of the neurons are

optimised according to the Generalized Delta

Rule (GDR), which is the learning algorithm for

back-propagation MLP network. The error that is

minimized by the GDR is the sum of the squares

of the errors for all the output units, defined as:

E y o

P

k

Pk Pk

= −

( )

∑2 (3)

For weights’ modification of the output layer,

the direction in which the weights need to be

shifted is determined by the negative gradient of

Ep (3) with respect to the weight wkj. The

adjustments in the weight for each neuron is

the product of the error in the neuron’s output, the

gradient of the neuron’s output, the net input given

to the neuron and a learning rate parameter. The

weight’s modification in a hidden layer is done

in proportion to the gradient of Ep with respect

to the hidden layer weights. In this way, each

updated weight in a hidden layer is dependent

on all the error terms of the output layer. Thus,

the errors that could be exactly determined only

for the output layer are propagated back to the

hidden layers. MLP learning takes place under

supervision, and an important parameter that has

a controlling effect is the learning rate constant.

It decides the magnitude of changes to the con-

nection weights. A high learning rate constant has

the advantage of faster learning, but it may cause

the weights to bounce around error minima, thus

failing to learn properly. On the other hand, if the

learning rate constant is too small, the learning

may take a long time because of the slow descent

along the error surface, which may be favourable

as the network may find a better error minimum

and, hence, more accurate learning.

Radial Basis Function (RBF)

The RBF network is a type of network that is very

useful for pattern classification (Belu et al., 2003;

Tefler and Kadambe, 1992). Figure 3 shows the

structure of a RBF network consisting of three lay-

ers of neurons. The input layer neurons receive the

input pattern (x1 to xN). The hidden layer neurons

provide a set of activation functions that constitute

an arbitrary “basis” for the input patterns in the

input space to be expanded into the hidden space

by the way of nonlinear transformation. At the

input of each hidden neuron, the distance between

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Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

the centre of each activation or basis function and

the input vector is calculated. Applying the basis

function to this distance produces the output of the

hidden neuron. The RBF network outputs y1 to yp

are formed by the output layer neurons as weighted

sums of the hidden layer neuron activations (Chen

et al., 2008; Haykin, 1994). The basis function is

generally chosen to be a standard function which

is positive at its centre x =0, and then decreases

uniformly to zero on either side. A common choice

is the Gaussian distribution function. The output

of the RBF network yj is given by:

y w K x c

j ji

i

i

i

k

=−

=

∑σ

1

(4)

where wji is the weight of the hidden neuron i to

the output j, ci is the centre of the basis function

i, σi is the spread of the function, and K(x) is the

activation function.

The purpose of training an RBF network is to

determine the neuron weights wji, RBF centres

ci and spreads σi that enable the network to pro-

duce the correct outputs yj corresponding to the

input patterns x. The training of an RBF network

involves the minimization of an error function.

The error function defines the total difference

between the actual and desired output of the

network over a set of training patterns. Training

proceeds by presenting to the network a pattern

of known class taken from the training set. The

error component associated with that pattern is

the sum of the squared differences between the

desired and actual outputs of the network corre-

sponding to the presented pattern. The procedure

is repeated for all the patterns in the training set

and the error components for all the patterns are

summed to yield the value of the error function

for an RBF network with a given set of basis

function centres, spreads and neuron connection

weights (Pham et al., 2006).

FUZZY LOGIC

The concept of Fuzzy Logic (FL) was conceived

by Lotfi Zadeh (1965, 1972) a professor at the

University of California at Berkley, and pre-

sented not as a control methodology, but as a

way of processing data by allowing partial set

membership rather than crisp set membership or

non-membership. This approach to set theory was

not applied to control systems until the 70’s due to

insufficient small-computer capability prior to that

time. Professor Zadeh reasoned that people do not

require precise, numerical information input, and

yet they are capable of highly adaptive control.

If feedback controllers could be programmed to

accept noisy, imprecise input, they would be much

more effective and perhaps easier to implement.

In this context, FL is a problem-solving control

system methodology that lends itself to imple-

mentation in systems ranging from simple, small,

embedded micro-controllers to large, networked,

multi-channel PC or workstation-based data

acquisition and control systems. It can be imple-

mented in hardware, software, or a combination

of both. FL provides a simple way to arrive at a

Figure 3. Topology of an RBF network (adapted

from Chen et al., 2008)

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Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

definite conclusion based upon vague, ambiguous,

imprecise, noisy, or missing input information

Fuzzy logic is a form of multi-valued logic

derived from fuzzy set theory to deal with rea-

soning that is approximate rather than precise.

In contrast with “crisp logic”, where binary sets

have binary logic, fuzzy logic variables may have

a truth value that ranges between 0 and 1 and is

not constrained to the two truth values of classic

propositional logic (Zadeh, 1965). Furthermore,

when linguistic variables are used, these degrees

may be managed by specific functions. Fuzzy

logic is used mainly in control engineering. It is

based on fuzzy logic reasoning which employs

linguistic rules in the form of IF-THEN-ELSE

statements. Fuzzy logic and fuzzy control feature

a relative simplification of a control methodology

description. This allows the application of a “hu-

man language” to describe the problems and their

fuzzy solutions. In many control applications,

the model of the system is unknown or the input

parameters are highly variable and unstable. In

such cases, fuzzy controllers can be applied. These

are more robust and cheaper than conventional

PID controllers. It is also easier to understand and

modify fuzzy controller rules, which not only use

human operator’s strategy but, are expressed in

natural linguistic terms. FL offers several unique

features that make it a particularly good choice

for many control problems.

1. It is inherently robust since it does not re-

quire precise, noise-free inputs and can be

programmed to fail safely if a feedback sen-

sor quits or is destroyed. The output control

is a smooth control function despite a wide

range of input variations.

2. Since the FL controller processes user-

defined rules governing the target control

system, it can be modified and tweaked

easily to improve or drastically alter sys-

tem performance. New sensors can easily

be incorporated into the system simply by

generating appropriate governing rules.

3. FL is not limited to a few feedback inputs and

one or two control outputs, nor is it necessary

to measure or compute parameters’ change

rate in order to be implemented. Any sen-

sor data that provides some indication of a

system’s actions and reactions is sufficient,

allowing the use of imprecise and inexpen-

sive sensors thus keeping the overall system

cost and complexity low.

4. Because of the rule-based operation, any rea-

sonable number of inputs can be processed

and numerous outputs 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.

5. FL can control nonlinear systems that

would be difficult or impossible to model.

This opens doors for control systems that

would normally be deemed unfeasible for

automation.

Fuzzy systems (FS) use fuzzy sets to deal with

imprecise and incomplete data. In conventional

set theory an object is a member of a set or not,

but fuzzy membership takes any value between 0

and 1. Figure 4 shows the component of a typical

fuzzy loguic system. Fuzzification transforms

exact (crisp) input values into fuzzy membership

(Zadeh, 1965, Robert, 1995). Fuzzy models are

built on prior rules, combined with fuzzified data

by the fuzzy inference machine. The resulting

fuzzy output is transformed to a crisp number

(defuzzification). Techniques include maximum,

mean-of maximum and centroid defuzzification.

Figure 3 shows the components of a fuzzy system.

The development of fuzzy logic was motivated

by the need for a conceptual framework which

can address the issue of uncertainty and lexical

imprecision. Some of the essential characteristics

of fuzzy logic relate to the following (Yager, 1987):

382

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

• In fuzzy logic, exact reasoning is viewed

as a limiting case of approximate

reasoning;

• In fuzzy logic, everything is a matter of

degree;

• In fuzzy logic, knowledge is interpreted as a

collection of elastic or, equivalently, fuzzy

constraint on a collection of variables;

• Inference is viewed as a process of propa-

gation of elastic constraints

• Any logical system can be fuzzied.

There are two main characteristics of fuzzy

systems that give them better performance for

specific applications:

• Fuzzy systems are suitable for uncertain or

approximate reasoning, especially for the

system with a mathematical model that is

difcult to derive’

• Fuzzy logic allows decision making with

estimated values under incomplete or un-

certain information.

The ability of fuzzy logic systems to handle

vague or imprecise information represents one

of its main strengths over other AI techniques,

although they also are easy to understand and

apply. One of the main difficulties in developing

a fuzzy system is determining good membership

functions. Fuzzy systems have no learning capa-

bilities or memory. To overcome such limitations,

fuzzy modeling is often combined with other

techniques to form hybrid systems (Lakhmi and

Martin, 1998; Von Altrock, 1995; Tefler and Kad-

ambe, 1992). Fuzzy systems handle incomplete or

imprecise data in applications including function

approximation, classification or clustering, control

and prediction. Zadeh (1965, 1972) stated that the

attempts to automate various types of activities

from assembling hardware to medical diagnosis

have been impeded by the gap between the way

human beings reason and the way computers are

programmed. It attempts to incorporate the “rule

of thumb” approach generally used by human

beings for decision-making. Thus, fuzzy logic

provides an approximate but effective way of

describing the behavior of systems that are not

easy to describe precisely.

Fuzzy logic controllers, for example, are ex-

tensions of the common expert systems that use

production rules like “if-then” statements. With

fuzzy controllers, however, linguistic variables

like “tall” and “very tall” might be incorporated

in a traditional expert system. The result is that

fuzzy logic can be used in controllers that are

capable of making intelligent control decisions in

sometimes volatile and rapidly changing problem

Figure 4. The main components of a fuzzy system

383

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

environments. Fuzzy logic techniques have been

successfully applied in a number of applications

like, computer vision, decision-making and system

design including ANN training. The most exten-

sive use of fuzzy logic is in the area of control,

where examples include controllers for cement

kilns, braking systems, elevators, washing ma-

chines, hot water heaters, air-conditioners, video

cameras, rice cookers and photocopiers. Fuzzy

logic has been used for the solar radiation predic-

tion (Mellit et al., 2009) and for the development

of a solar tracking mechanism (Kalogirou, 2007).

GENETIC ALGORITHMS

A genetic algorithm (GA) is a stochastic process

that mimics the natural process of biological

evolution (Harp and Samad, 1991; Buckeles and

Petry, 1992). GA’s are inspired by the way living

organisms are adapted to the harsh environment,

i.e. by evolution and inheritance. The algorithms

imitate in the process, the evolution of population

by selecting only fit individuals for reproduction.

Therefore, a GA is an optimum search technique

based on the concepts of natural selection and

survival of the fittest. It works with a fixed-size

population of possible solutions of a problem,

called individuals, which are evolving in time.

GA’s find extensive applications in intelligent

search, machine learning and optimization prob-

lems. Problem states in a GA are denoted by

chromosomes, which are usually represented by

binary strings. A GA utilizes three principal genetic

operators (Buckeles, 1992; Forest, 1993; Kalogi-

rou, 2007). The initial population G(0) is gener-

ated randomly. Thereafter G(t) produces G(t+1)

through selection and reproduction (Buckeles,

1992). A proportion of the population is selected

to breed and produce new chromosomes, Selec-

tion is according to fitness of individual solutions,

i.e. proximity to a perfect solution (Forest, 1993),

most often by roulette selection and deterministic

sampling. Roulette selection randomly selects a

parent with probability computed from the fitness

fi of each individual (Kalogirou, 2007):

i

i

i

i

Ff

f

=∑ (5)

Reproduction is by genetic cross over and

mutation. Crossover produces offspring by

exchanging chromosome segments from two

parents. Mutation randomly changes part of one

parent’s chromosome. This occurs in frequently

and introduces new genetic material. Although

mutation plays a smaller part than crossover in

advancing the search, it is critical in maintaining

genetic diversity. If diversity is lost, evolution is

retarded or may stop. In steady-state GAs offspring

generated by the genetic operators, replace less

fitted members, resulting in higher average fit-

ness. Simple or generational algorithms replace

each entire generation (Forest, 1993). Selection

and reproduction are repeated until a stopping

criterion is met, e.g. all organisms are identical or

very similar, a given number of evaluations have

been completed, or maximum fitness has been

reached; evolution no longer yields better results.

GAs are computationally simple and robust,

and balance load and efficacy well (Forest, 1993).

This partly results from only examining fitness,

ignoring other information such as derivatives.

Genetic Algorithms treat the model as a black

box, an advantage when detailed information

is unavailable. An important strength of GAs is

implicit parallelism; a much larger number of

code sequences are indirectly sampled than are

actually tested by the GA. Unlike most stochastic

search techniques, which adjust a single solution,

GA keeps a population of solutions. Maintaining

several possible solutions reduces the probability

of reaching a false (local) optimum (Forest, 1993).

Therefore GAs can be very useful in searching

noisy and multimodal relations. However, the

latter may take a large computation time. In most

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Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

cases, Genetic Algorithms use randomization

in selection. They avoid picking only the best

individual and thus prevent the population from

converging to that individual. However, premature

convergence on a local optimum can occur if the

GA magnifies a small sampling error (Forest,

1993). If a very fit individual emerges early and

reproduces abundantly, early loss of diversity may

lead to convergence on that local optimum. GAs

are often used to optimize model parameters or

for resource management.

HYBRID SYSTEMS

Hybrid systems combine more than one of the

technologies introduced above, either as part of

an integrated method of problem solution, or to

perform a particular task that is followed by a

second technique, which performs some other task.

For the modeling, prediction of performance and

control of renewable energy processes, analytic

computer codes are often used. The algorithms

employed are usually complicated involving the

solution of complex differential equations. These

programs usually require large computer power

and need a considerable amount of time to give

accurate predictions. Instead of complex rules

and mathematical routines, artificial intelligence

systems are able to learn the key information

patterns within a multi-dimensional information

domain. On the other hand, in design, control and

operation of renewable energy systems, such as

PV or solar-thermal energy systems, a detailed

long-term series of meteorological data such as

solar radiation, temperature or wind data is nor-

mally required. The effort is to design and operate

systems that can make an efficient conversion and

utilization of these renewable energy resources.

However, one of the problems that designers of

such systems are often confronted with is the

acquisition or availability of sufficiently long

series of meteorological variables for direct uti-

lization. Such long-term measurements are often

non-existent for most of the interest locations

or, wherever they are available, they suffer of

a number of shortcomings (e.g. poor quality of

data, missing data, insufficient long series, etc.).

To overcome these problems AI techniques appear

to be one of the strongest candidates.

The increased popularity of Hybrid Intelligent

Systems (HIS) in recent years lies in the exten-

sive success of these systems in many real-world

complex problems. The main reason for this

success seems to be the synergy derived by the

computational intelligent components, such as

machine learning, FL, neural networks and GAs.

Each of these methodologies provides HS with

complementary reasoning and searching meth-

ods that allow the use of domain knowledge and

empirical data to solve complex problems (Harp

and Samand, 1991; Haykin, 1994; Von Altrock,

1995). Hybrid systems combine two or more AI

techniques (‘paradigm’) to gain strengths and

overcome weaknesses. HS combining FL, neural

networks, GAs, and ES are proving their effec-

tiveness in a wide variety of real-world problems.

There are three main types of hybrid systems

according to how the techniques are combined:

sequential, auxiliary and embedded (Lakhmi and

Martin, 1998). In a sequential hybrid, the first

paradigm passes its output to the second to generate

the output. In an auxiliary hybrid, the first para-

digm obtains some information from the second

to generate the output. In an embedded hybrid,

the two paradigms are contained in one another

(Lakhmi and Martin, 1998). The most common

hybrids are neuro-fuzzy systems, combining

ANNs and fuzzy systems. They are effective:

fast, efficient and easily designed, implemented

and understood (Chen et al. 2008; Fuller, 2000;

Kalogirou 2003). By combining them, the need

to prime fuzzy systems is reduced by learning

in ANNs. Fuzzy systems attenuate ‘noise’, from

which some ANNs suffer. Each AI technique has

capabilities and limitations, making its suitabil-

ity for environmental modeling specific to that

problem. On the other hand, one has to keep in

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Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

mid a hybrid system may retain the weaknesses

of both techniques and little of their strengths

(Kalogirou, 2007; Mellit, 2008). Hybrid tech-

niques also raise the problem of communication;

different representations have to be translated into

a common language. Another problem of hybrid

systems with learning is credit assignment (Tefler

and Kadambe, 1992). If one component cannot

distinguish changes caused by its own actions

from those due to others, penalties and rewards

will be in effective.

Fuzzy Neural Networks

Neural networks can be modified to incorporate

fuzzy techniques and produce a neural network

with improved performance. One approach is to

allow the fuzzy neural network to receive and

process fuzzy inputs. Another option is to add

layers on the front end of the network to fuzzify

crisp input data to the fuzzy neural processing

(Fuller, 2000; Tefler and Kadambe, 1992). The

fuzzy neuron is a fundamental concept used in

many approaches to integrate fuzzy and neural

technologies. In networks that map fuzzy input to

crisp output, nodes in every layer of the network

can have modified neurons. The input consists of

a set of fuzzy values, and the weights connecting

the node with nodes in the previous layer also

have fuzzy values. Input values and the weights

are each represented by membership functions.

A modified summation process is used to find

the product of the membership functions of the

fuzzy inputs and weights and then add the result-

ing membership functions to obtain another one

that represents the integration of weighted fuzzy

inputs to the node. A centroid operation on the

resultant can then be used to find a crisp value

for the output of the node. The computational

process envisioned for fuzzy neural systems is

as follows. It starts with the development of a

“fuzzy neuron” based on the understanding of

biological neuronal morphologies, followed by

learning mechanisms. This leads to the follow-

ing three steps in a fuzzy neural computational

process (Tefler and Kadambe, 1992):

• Development of fuzzy neural models moti-

vated by biological neurons,

• Models of synaptic connections which in-

corporates fuzziness into neural network,

• Development of learning algorithms (i.e.,

the method of adjusting the synaptic

weights).

Two possible models of fuzzy neural systems

are:

• In response to linguistic statements, the

fuzzy interface block provides an input

vector to a m layer neural network. The

neural network can be adapted (trained) to

yield the desired common outputs or deci-

sions (Figure 5a).

• A multi-layered neural network drives the

fuzzy inference mechanism (Figure 5b).

Wavelet and Neural Networks

Wavelet Neural Networks (WNNs) is an approach

towards the learning function. Wavelet networks,

combining the wavelet theory and neural networks,

utilize wavelets as the basic function to construct

a network. A wavelet function is a local function

and influences the network’s output only in some

local range. The WNN shows surprising effective-

ness in solving the conventional problems of poor

convergence or even divergence encountered in

other kinds of neural networks. The WNN consists

usually of three layers. The detailed description

of the calculation steps of WNN are explained in

Telfer and Kadambe (1992).

386

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

METEOROLOGICAL-BASED SOAR

RADIATION DATA ANALYSIS,

MODELING AND FORECASTING

Knowledge of the local solar radiation is essential

for the proper design of building energy systems,

solar energy systems and a good evaluation of

thermal environment within buildings (Davies and

McKay, 1982; Hsieh, 1986; Iqbal, 1983; Kalogi-

rou, 2009; Lu et al., 1998; Sherry and Justus, 1984;

Lewis, 1984). Solar radiation received at the flat

surface is the most important as far as designing

and operation of solar energy systems. All solar

energy applications require readily available,

site-oriented and long-term solar radiation data.

A typical solar radiation database comprises of

global, direct and diffuse solar irradiance, sunshine

duration and complementary data like cloud cover,

atmospheric turbidity, humidity, air temperature,

wind speed, etc (Davies and McKay, 1982; Hsieh,

1986; Iqbal, 1983; Kalogirou, 2009; Swartman

and Ogunlande, 1967). The best database would

be the long-term measured data at the site of the

proposed solar energy system. However, most of

these stations do not provide complete solar data

information, mainly due to the high costs for op-

eration and measuring instruments. For instance,

global radiation is the most frequently measured

parameter, while its two components (diffuse and

direct irradiance) are often not measured. This

limited spatial and temporal coverage of solar

radiation measurements dictates the need for the

development of the solar radiation models. Since

the direct (beam) irradiance is important in design-

ing solar energy systems, such as high-temperature

heat engines and high-intensity solar cells, em-

phasis is often put on modeling the beam (direct

radiation) component. There are two categories of

solar radiation models, available that predict the

beam component or sky component based on other

more readily measured quantities: a) parametric

models, and b) decomposition models.

Figure 5. a) The first model of fuzzy neural system, b) The second model of fuzzy neural system (adapted

from Fuller, 2000)

387

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

On the other hand, most of the solar radiation

applications involved tilted surfaces, requiring the

knowledge of both diffuse and direct components

of global radiation falling on a horizontal surface.

There are also a number of problems that may

arise during the measurement of the synoptic

and solar radiation. The most common causes of

the errors are related to the equipment and their

respective sensitivities. Another major cause of

errors is site operation conditions, such as instru-

ment proximity to shading elements, electrical

and magnetic field interferences, bird and insect

activity and weather elements. There is, therefore

a need to identify erroneous data and exclude

and correct them. In this regard, quality control

methodologies and procedures were developed

over the years, based on physical and statistical

tests to remove suspected outliers in the datasets.

The available datasets were used to fine tune the

proposed models.

When solar radiation data is unavailable, it is

possible to get reasonable accurate estimates us-

ing the proposed models which rely on alternative

synoptic information or on the measurement at

other locations. These models are also useful to

fill-in any gaps in the measured radiation datasets.

Over the years, various empirical models have

been developed for different geographical and

meteorological conditions.

The insulation available to a solar energy

system, such as a photovoltaic system with given

orientation and inclination depends on the local

climate and geographical location. To calculate

inclined insolation, it is necessary to know beam

and diffuse components of the global irradiance.

However, as most weather stations provide only

global irradiance data, a correlation developed

between the global and diffuse component using

measured values of these two quantities is used

to calculate the diffuse component of global

insolation. Correlated quantities can be divided

into four groups: daily global insolation and its

diffuse component; monthly mean daily global

insolation and its diffuse component; monthly

mean hourly global insolation and its diffuse

component; and hourly global insolation and its

diffuse component (Davies and McKay, 1982).

Solar radiation models may be categorized into

two groups: parametric models and decomposi-

tion models; parametric models require detailed

information of atmospheric conditions, whereas

decomposition models generally employ global

radiation to predict direct and diffuse components

(Davies and McKay, 1982). Wong and Chow

(2001) and Muneer et al. (2007) have presented

detailed reviews of these two kinds of models, as

well as in depth discussions of their characteristics

and performances. Several correlation models cor-

relating diffuse fraction (ratio of diffuse to global

radiation) and clearness index (ratio of horizontal

global radiation to extra-terrestrial radiation) have

been developed under various climatic conditions

(Wong and Chow, 2001). These correlations

are mostly latitude dependent (Lu et al. 1998).

Diffuse-global correlations have been developed

that include atmospheric effect such as dry bulb

temperature and relative humidity (Abdallah,

1994; Muneer, 2004; Muneer et al., 2007).

CONVENTIONAL MODELS

FOR SOLAR RADIATION

Most solar energy applications such as the simula-

tion of solar energy systems require, at the least,

knowledge of hourly values of solar radiation on a

tilted and arbitrarily oriented surface. Knowledge

of direct irradiance is important in applications

where the solar radiation is concentrated, either

to raise the temperature of the system, as in solar-

thermal energy technologies, or to increase the

electric current in solar cells, as in PV systems.

In the absence of direct irradiance data, this

component of solar radiation maybe estimated

using decomposition models. They calculate di-

rect irradiance from global solar irradiance on a

horizontal surface. These models are based on the

regressions between two dimensionless indices:

388

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

the clearness index, KT (horizontal global irradi-

ance/horizontal extra-terrestrial irradiance) and

the direct solar transmittance, kB (direct normal

irradiance/extra-terrestrial irradiance).

As we already mentioned in a previous section

of this chapter, there are two categories of solar

radiation models, available in the literature, that

predict the beam component of the based on other

more readily measured quantities: a) parametric

models, and b) decomposition models. Parametric

models require detailed information of atmo-

spheric conditions. Meteorological parameters

used as predictors include the type, amount, and

distribution of clouds or other observations, such

as the fractional sunshine, atmospheric turbidity

and precipitable water content (Angstrom, 1929;

Cartwright, 1993; Iqbal, 1978 and 1980; Kasten

and Czelpak, 1980; Machler and Iqbal, 1985;

Muneer and Saluja, 1985; Page, 1961; Rietveld,

1978; Trabea and Shaltout, 2000). One of the most

used models by the engineers and architects is

the ASHRAE algorithm (ASRE, 1999), while the

Iqbal model (1980) offers extra accuracy over more

conventional models as reviewed by Gueymard

(1993a, b). Development of correlation models

that predict the beam or sky radiation using other

solar radiation measurements is also possible.

Decomposition models usually use information

only on global radiation to predict the beam and

sky components. These relationships are usually

expressed in terms of the irradiations which are the

time integrals (usually over 1h) of the radiant flux

or irradiance. Decomposition models developed to

estimate direct and diffuse irradiance from global

irradiance data were found in the literature (Aki-

noglu and Ecevit, 1990; Almorox and Hontoria,

1967; Bahlel et al. 1987; Balirci, 2009; Caroll,

1985; Collaress-Pereiera and Rabl, 1979; Klucher,

1979; Liu and Jorda, 1960; Lewis, 1983; Roa at

al. 1984; Trabea and Shaltout, 2000).

There are several relationships that relate

the global radiation to other meteorological and

climatologic parameters such as sunshine hours,

air temperature, cloud coverage, and relative

humidity. The amount of solar energy per unit

time, at the mean distance from the sun, received

on the unit area perpendicular to the direction of

propagation of the solar radiation outside the at-

mosphere is called the solar constant, SC. When

the sun is closest to the earth, on January 3, the

solar constant is about 1400 W/m2, while when the

sun is farthest away, on July 4th, it is about 1330

W/m2, and the averages value adopted in 2000 by

the American Society of Testing and Materials is

1366.1 W/m2.

Parametric Models

One of the firs model developed to estimate direct

normal irradiance I0 (W/m2) described by

Iqbal (1980) is given by:

I E SC r o g w a0 0

0 9751= ⋅⋅.τ τ τ τ τ (6)

where the factor 0.9751 is included because the

spectral interval considered is 0.3-3 μm, E0 (di-

mensionless) is the eccentricity correction-factor

of the Earth’s orbit and is given by:

E01 00011 0 034221 0 00128

0 000719 2 0

= +

( )

+

( )

+

+

( )

+

. . cos . sin

. cos

Γ Γ

Γ.. sin( )000077 2Γ

(7)

The day angle Γ (radians) is given by:

Γ = −

21

365

πN (8)

where N is the day number of the year, ranging

from 1 on 1st January to 365 on 31ss December.

τr, τo, τg, τw, and τa (dimensionless) are the

Rayleigh, ozone, gas, water, and aerosol scattering

transmittances, respectively. The expressions for

computing these transmittances can be found in

(Igbal, 1983) or elsewhere in the literature.

389

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

A simpler procedure for solar radiation is ad-

opted in ASHARE (1999) and widely used in the

engineering and architectural communities. The

direct normal irradiance In (W/m2) is given by:

I C A B

n n

=

( )

⋅

( )

exp sec Φ (9)

where A (W/m2) is the apparent extraterrestrial

irradiance, which takes in account the variations

in the Sun-Earth distance (see Table 1 of Muneer

(2004)) for their values), and Φ is the zenith

angle (degrees). The variable B (dimensionless)

represents an overall broadband value of the

atmospheric attenuation coefficient for the basic

atmosphere of Threlkeld and Jordan (1958). Cn

(dimensionless) is the clearness number and

the map of Cn for the USA is provided in the

ASHARE handbook. Cn is the ratio of the direct

normal irradiance calculated with the local mean

clear-day water-vapor to the direct normal irradi-

ance calculated with water vapor according to the

basic atmosphere. Equation (8) was developed for

sea level conditions. It can be adapted for other

atmospheric pressures by:

I C A B p

p

n n

= ⋅

( )

⋅

( ) exp sec Φ0

(10)

where p (mbar) is the actual local air pressure

and p0 is the standard pressure (1013.25 mbar).

In the above equation, the term (p/p0)sec(Φ)

approximates to the air mass, with the assumptions

that the curvature of the Earth and the refraction

of air are negligible.

An all-sky broadband empirical algorithm,

the so-called Meteorological Radiation Model

(MRM), developed by Muneer et al. (2007) that

utilize dry and wet-bulb temperature or relative

humidity along with sunshine duration. The model

can estimate horizontal solar components (direct,

diffuse, and global irradiation on an hourly, daily,

or monthly basis and is an adaptation of the

Igbal model, discussed in the above paragraph.

Monthly average hourly and daily irradiance are

obtained via summing the long-term computed

and measured values. The correlation in this

model is given by:

DBR I

Ik

D

B

B

= = −

0 285211 1 00648

.. (11)

and

I SF SC

B r o g w a

=

( )

⋅ ⋅ τ τ τ τ τ (12)

finally

I I I

G B D

= + (13)

where ID is diffuse, IB is beam/direct, and IG is

global irradiation (W/m2), kB is beam clearness

index (dimensionless), and SF is sunshine fraction

(dimensionless). Interested reader can find the

full description if the model and the relationships

for the transmittances in (Iqbal, 1983; Kalogirou,

2009).

Kastern and Czplak (1980) developed an algo-

rithm (so-called Cloud-Cover Radiation Model or

CRN) capable of generating hour-by-hour global,

diffuse, and direct horizontal irradiance, by using

only cloud-cover data. In order to determine global

radiation IG from total cloud amount N in oktas,

the radiation under cloudless sky, IGc is required.

IGc depends on solar elevation angle a, and may be

obtained via the linear parametrization as given

by Kasten and Czeplak (1980):

I A B

Gc = ⋅

( )

−

()

sin sin α (14)

The ratio of global radiation IG for a given

cloud amount N (okta), to IGc has been shown to

be independent of the solar elevation α:

390

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

I

ICN

G

Gc

D

= −

18 (15)

The diffuse component is then calculated by

using estimated global irradiation from Equation

(12):

I

I

N

D

G

= +

0 3 0 7 8

2

. . (16)

The direct component will then be calculated

as the difference of global and diffuse irradiation.

The coefficients A, B, C, and D involved in this

model are fitted against the experimental data.

Muneer et al. (2007) fitted these coefficients for

UK locations.

Estimation of the Hourly Diffuse

Radiation on a Horizontal Surface

Using Decomposition Models

Values of global and diffuse radiations for indi-

vidual hours are essential for research and engi-

neering applications. Hourly global radiations

on horizontal surfaces are available for many

stations, but relatively few stations measure the

hourly diffuse radiation. Decomposition models

have, therefore, been developed to predict the

diffuse radiation using the measured global data.

The models are based on the correlations

between the clearness index KT (dimensionless)

and the diffuse fraction kd (dimensionless), dif-

fuse coefficient kD (dimensionless) or the direct

transmittance kB (dimensionless) where:

KI

IkI

IkI

IkI

I

T

G

d

d

G

D

D

B

B

= = = =

0 0 0

, , , ,

(17)

IG, IB, ID and I0 being the global, direct, diffuse

and extraterrestrial irradiances respectively, on a

horizontal surface (all in MJ/m2).

The relationships permitting the determina-

tion, for a horizontal surface, of the instantaneous

intensity of diffuse radiation on clear days, the

long-term average hourly and daily sums of diffuse

radiation, and the daily sums of diffuse radiation

for various categories of days of differing degrees

of cloudiness, with data from 98 localities in the

USA and Canada, were studied by Liu and Jordan

(1960). The transmission coefficient for total

radiation on a horizontal surface is given by the

intensity of total radiation (i.e. direct IB plus diffuse

ID) incident upon a horizontal surface IG divided

by the intensity of solar radiation incident upon a

horizontal surface outside the atmosphere of the

Earth I0. The correlation between the intensities of

direct and total radiations on clear days is given by:

k k

D B

= −0 271 0 2939. . (18)

since

KI I

Ik k

T

B D

B D

=+= +

0

(19)

then

k K

D T

= −0 384 0 416. . (20)

Following the work of Liu and Jordan (1960)

several researchers where involved in the de-

velopment of solar radiation models. Orgill and

Hollands (1977) using the clearness index only

developed a model to estimate diffuse radiation

fraction, based on the measurements of global and

radiation at Toronto, Canada. Erbs et al. (1982)

studied the same kind of correlations with data

from 5 stations, located in the Southern USA.

The data were of short duration, ranging from

1 to 4 years. In each station, hourly values of

normal direct irradiance and global irradiance

on a horizontal surface were registered. Diffuse

irradiance was obtained as the difference of these

391

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

quantities. Spencer (1982) studied the latitude

dependence on the mean daily diffuse radiation

with data from 5 stations in Australia. Reindl et al.

(1990) estimated the diffuse fraction kd using two

different models developed with measurements

of global and diffuse irradiance on a horizontal

surface registered at 5 locations in the USA and

Europe. Lam and Li (1993) studied the correla-

tion between global solar radiation and its direct

and diffuse components for Hong Kong with the

measured data in1991–1994. A hybrid correlation

model based on hourly measured data for the pre-

diction of hourly direct and diffuse components

from the global radiation for Hong Kong was

developed in their study.

Skartveit and Olseth (1987) showed that the

diffuse fraction depends also on other parameters

such as solar elevation, temperature and relative

humidity. Similar arguments were found in the

literature (Cartwright, 1993; Kasetn and Czelpak,

1980; Muneer and Saluja, 1985; Lui et al. 1998;

Machler and Iqbal, 1985). They estimated the

direct irradiance IB from the global irradiance Gt

and from the solar elevation angle, Φ for Bergen,

Norway, with the following equation:

IG

B

t

=−

( )

1ψ

sin( )Φ (21)

where ψ is a function of KT and the solar eleva-

tion angle, Φ (degrees). The model was validated

with data collected in Aas, Norway, Vancouver,

Canada and 10 other stations worldwide. Details

of this model can also be found in (Gueymard,

1993b; Lam and Li, 1993).

A quasi-physical model for converting hourly

global horizontal to direct normal insolation

proposed by Maxwell (1987) was reviewed by

Batlles et al. (2000). The model combines a clear

physical model with experimental fits for other

conditions. The direct irradiance IB is given by:

I I d d m d

B a

= − −

( )

()

0 4 5 6

ψexp (22)

where I0 is the extraterrestrial irradiance, is a

function of the air mass ma (dimensionless) and

is given by:

ψ= − + − +0 866 0 122 0 121 0 00065 0 000014

2 3 4

. . . . .m m m m

a a a a

(23)

and d4, d5 and d6 are functions of the clearness

index KT, determined form the experimental data.

Louche et al. (1991) used the clearness index KT

to estimate the transmittance of beam radiation kB.

The correlation was tested by using data collected

at Ajaccio, Corsica, France between 1981 and

1983. Vignola and McDaniels (1986) studied the

daily, 10-day and monthly average beam-global

correlations for 7 sites in Oregon and Idaho, USA.

The beam-global correlations vary with time of

year in a manner similar to the seasonal variations

exhibited by diffuse-global correlations.

Correlations of Average Daily Solar

Radiation with Hour of Sunshine and

Other Meteorological Parameters

The first correlation proposed for estimating the

monthly average daily global radiation is based

on the method of Angström (1929). The original

Angström-type regression equation related the

monthly average daily radiation to clear day ra-

diation in a given location and average fraction

of possible sunshine hours:

H

Ha b S

S

c

= +

0

(24)

A basic difficulty with Equation (7) lies in the

ambiguity of the terms S/Sc and Hc. Page (1961)

and other researchers (Abdallah, 1994; Bakirci,

392

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

2009; Batlles at al. 2000; Camps and Soler, 1995;

Garrison, 1985; Reidl et al. 1990) have modified

the method to base it on a horizontal surface rather

than on clear radiation (Gueymard 1993a):

H

Ha b S

S

0 0

= +

(25)

where H is the monthly average daily global radia-

tion, H0 the monthly average daily extraterrestrial

radiation, S the monthly average daily hours of

bright sunshine, So the monthly average day

length, and a and b are the empirical constants,

determined from the experimental data. The

monthly average daily extraterrestrial radiation on

a horizontal surface (H0) can be computed from

the following relationship:

H SC N

Ls

0

24 1 0 033 360

365

= +

( ) ( ) (

π

δ ω

.

cos cos cos cos c os

))

+

( )

2

360

2

360

πω πω δ

s s

sin sin sin( )L

(26)

where L is the local latitude, δ is the declination, Φ

is the zenith angle, and ωs is the mean sunrise hour

angle. The solar declination and the mean sunrise

hour angle are given by the following equations

(Gueymard 1993a; Orgill and Hollands, 1977):

δ=+

23 45 360 284

365

. sin ( )N (27)

and

ω δ

sarcos L= −

( )

tan( ) tan( ) (28)

here N is the Nth day of the year, counted from

January 1st of each year. The sunset hour angle

is also used to compute the maximum possible

sunshine hours S0, for a given month, from the

following equation:

Ss0

2

15

=

ω (29)

Lewis (1983) estimates monthly average daily

global radiation on a horizontal surface by the

following equation:

H a RH b

=

( )

(30)

where RH is the relative humidity, a and b empiri-

cal parameters.

Swartman and Ogulande (1967) proposed the

following models (31) and (32) for the global solar

radiation (GSR) prediction:

H a b S

ScRH= +

+

0

(31)

and

H a S

SRH

b

c

=

+

0

(32)

In the Equations (31) and 32) parameters a,

b, and c are empirical coefficients. The following

relationship (33) between the solar radiation and

sunshine hours was proposed by Almorox and

Hontoria (1967):

H a b exp S

S

= + ⋅

0

(33)

where a and b are empirical coefficients.

Bahlel et al. (1987) developed a 4-parameter

model for estimating the GSR:

H

Ha b S

ScS

SdS

S

0 0 0

2

0

3

= +

+

+

(34)

393

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

Again, parameters a, b, c and d are empirical

coefficients, fitted to the measured data.

Following equation has been proposed by Aki-

noglu and Ecevit (1990) for estimating the GSR:

H

Ha b S

ScS

S

0 0 0

2

= +

+

(35)

here a, b, and c are empirical coefficients, as in

the previous relationships.

Abdullah (1994) suggested the flowing model

(36) which includes the mainly daily temperature

in the global solar radiation estimate:

H

Ha b S

ScRH dT

0 0

= +

+ + (36)

where T is the daily mean air temperature and a-d

are empirical coefficients.

Trabea and Shaltout (2000) related the daily

global radiation to sunshine duration, relative

humidity, maximum air temperature, mean daily

vapor pressure and mean daily sea level pressure

to calculate H (37) at five stations in Egypt as

follows:

H

Ha b S

ScT dV eRH fP

0 0

= +

+ + +

max

(37)

where a, b, c, d, e, and f are regression coeffi-

cients, Tmax is the maximum air temperature, RH

is the relative humidity (%) and P is the ration

between mean sea level pressure and mean daily

vapor pressure (the ration of MSL to V). Recently,

Bakirci (2009) developed the following model

(Camps and Soler, 1995) for estimating the solar

radiation (38), using long-term measurements at

several locations in Turkey:

H a b S

Scexp S

S

= +

+

0 0

(38)

where a, b and c are empirical parameters.

On the other hand, the extraterrestrial solar

radiation, Gon measured on the plane normal to

the radiation on the Nth day of the year, varies

between the maximum and the minimum values

of the solar constant (SC) and can be calculated by

(Almorox and Hontoria, 1967; Davies and McKay,

1982; Klucher, 1979), using the Equation (39):

G SC N

on = ⋅ +

1 0 033 360

365

. (39)

On a surface parallel to the ground, the rate

of solar radiation, G0N, incident on this extrater-

restrial horizontal surface at a given time of the

year is given by:

G G

SC N

L coss

N on0

1 0 033 360

365

=

= ⋅ +

cos( )

[ . ( )]

[cos cos( ) cos cos( )

Φ

δ(( )

sin sin( )sin( )]

h

L+δ (40)

here h is the hour angle.

The total radiation, H0, incident on an extra-

terrestrial horizontal surface during a day can be

obtained by the integration of the Equation (40)

over a period from sunrise to sunset. To compute

the extraterrestrial radiation the Equation (40)

is integrated between hour angles, h1 and h2, so:

Ix S N

L h h

0

2

12 3600 1 0 033 360

365

= +

× −

π

δ

[ . ( )]

{cos cos( ) cos cos( ) cos( 11

2 1

180

)

[ ]sin sin( )sin( )}+−

( )

πδ

h h L (41)

It should be noted the limits h1 and h2 may

define any time period other than 1 h. A compre-

hensive list of definitions and terminology that

include those related to the solar radiation can be

found in (Davies and McKay, 1982; Iqbal, 1983)

or elsewhere in the literature. For example, the ir-

radiance (W/m2) is the rate of radiant energy falling

394

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

on a surface per unit of area of the surface, while

the irradiation (J/m2) is incident energy per unit

of area of a surface, obtained by integrating the

irradiance over a specific time interval. Specifi-

cally, for solar irradiance this is called insolation.

The solar radiation reaching the earth’s surface

is much lower than Gon because a large part of it

is scattered, reflected back out into the space, and

absorbed by the atmosphere. Some of the scattered

radiation, the so-called diffuse radiation reaches

the earth’s surface from the entire sky vault. The

solar heat coming directly through the atmosphere

is called direct or beam radiation. The insulation

received by a surface on a earth is the sum of

diffuse radiation and the normal component of

beam radiation. The solar heat at any pint on earth

depends on the ozone layer thickness, the distance

travelled through the atmosphere, the amount of

haze in the air, and the extent of the cloud cover.

The degree of attenuation of solar radiation travel-

ling through the earth’s radiation depends on the

length of the path and the characteristics of the

medium traversed. In solar radiation calculations,

one standard air mass is defined as the path’s length

traversed in reaching the sea level when the sun

is a zenith (the vertical point of the observation).

TERRESTRIAL RADIATION

To determine the long-term performances of a

solar system, the knowledge of the long-term

monthly average daily insulation data for that site

are required. Daily mean total solar radiation

(direct plus diffuse) incident on a horizontal sur-

face is available from various sources (radiation

maps, metrological service database). In these

sources, data, such as 24 h average temperature,

monthly average daily radiation on a horizontal

surface, H(MJ/m2∙d), and monthly average clear-

ness index, KTare given together with other

parameters. The monthly average clearness index

(42) is defined as:

T

K

H

H

=

0

(42)

where, H0is the monthly average daily total in-

solation on an extraterrestrial horizontal surface

(MJ/m2). The bar signifies a long-term average.

The values of H0 for each month function of

latitude can be found in Table 2.5 of Davies and

McKay, (1982).

To design or to predict the performance of

a solar energy system requires hourly values of

radiation. These types of data can be obtained,

using different correlations from the long-term

average daily radiation data, such as the Liu and

Jordan (1977) correlation or the Collarees-Pereira

(1979) correlation. The ration hourly total radia-

tion to daily radiation, using the Collarees-Pereira

correlation is given by (43):

r h h h

hh

SS

SS

SS

= +

[ ]

( )

−

( )

−

πα β π

24 2

360

cos( ) cos cos( )

sin cos( )hSS

(43)

here, hSS is the sunset hour angle (degrees), h is

the hour angle at the midpoint of each hour, and

the parameters α and β are given by (44) and (45):

α= + ⋅ −

( )

0 409 0 5016 60. . sin hSS (44)

β= − ⋅ −

( )

0 6609 0 4767 60. . sin hSS (45)

The solar collectors or PV panels are usually

installed at an angle to increase the amount of

radiation intercepted and to reduce reflection

and cosine losses. System designers need solar

radiation data on such tilted surfaces; measured

or estimated. Most of the time solar radiation

is available either for normal incidence or for

horizontal surfaces. The amount of insulation on

a surface at a given location for a given time de-

pends on the orientation and slope of the surface.

395

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

A flat surface absorbs beam (IBt), diffuse (IDt), and

ground-reflected (IGt) solar radiation, so the total

radiation is given by (46):

I I I I

t Bt Dt Gt

= + + (46)

The beam radiation on a tilted surface (see

Figure 6) is given by the following relationship:

I I

Bt Bn

=

( )

⋅cos θ (47)

While on a horizontal surface, it is given by:

I I

B Bn

=

( )

⋅cos Φ (48)

The beam radiation tilt factor is defined by the

(48) equation, as:

cos( )

cos( )

RI

I

B

Bt

B

= = θ

Φ (49)

There are several models to compute the solar

radiation on a tilted surface. The diffuse radiation

on a tilted surface, according to the isotropic

radiation model [51, 52] can be computed using:

I I

Dt D

=+

1

3

cos( )β (50)

Here ID is the diffuse radiation (ID = 2IR), and

IR is the diffuse sky radiation (W/m2∙rad). The

ground-reflected radiation on a tilted surface is

expressed as:

I I I

Gt G B D

= +

( )

−

( )

⋅ρβ1

2

cos cos

(51)

Combining (12), (13), (14) and (15), we get:

I R I I I I

t B B D G B D

= + +

+ +

( )

−

( )

1

3

1

2

cos( ) cos cos

βρβ

(52)

The total radiation on a horizontal surface, I, is

the sum of horizontal beam and diffuse radiation,

as shown in Equation (53):

I I I

B D

= + (53)

The isotropic sky model is the simplest model,

assuming that all diffuse radiation is uniformly

distributed over the sky and that the reflection

on the ground is diffuse. The model developed

by Kloucher (1979), takes into account the ho-

rizon brightening, and the effect of circumsolar

radiation, and the total irradiance on a tilted plane

(Hsieh, 1986) is given by:

I I R I K

K

t B B D t

t

= + ++

+

⋅[ ][ ( )]

[ ( ) ( )

cos cos( ) sin

cos sin

1

212

1

3

2 3

β β

βΦ]]

[ ]

( )

cos( )

+ +

⋅−

⋅

I I

B D

G

ρβ1

2

(54)

where KT is a clearness index given by:

Figure 6. Beam radiation on horizontal and tilted surfaces

396

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

KI

I I

T

D

B D

= − +

1

2

Under overcast skies, the clearness index is

0 and the model reduces to the isotropic model.

In the Hay-Davies (1980), the diffuse radiation

is composed of an isotropic and circumsolar

component, while the horizon brightening is not

taken into account. Reflection from the ground

is computed as in the isotropic mode. The total

irradiance (55) is computed by:

I I I R I A

I I

t B D B D

B D G

= +

( )

⋅ + −

( )

⋅+

( )

+

+ +

( )

−

11

2

1

cos cos

c

β

ρoos( )β

2

(55)

where represents the transmittance through atmo-

sphere for beam radiation.

The Reindl model (1990) takes also into ac-

count the horizon brightening, and the total ir-

radiance on a tilted surface can be calculated by:

I I I R I A

I

I I

I

t B D B D

B

B D

B

= + + − +

++

+ +

( ) cos cos( )

sin

(

( )[ ]

[ ( )]

11

2

12

3

β

β

IID) [ cos( )]ρβ1

2

−

(56)

Reflection on the ground is again as in the iso-

tropic model. Due to the inclusion of the horizon

brightening, Reindl (1990) model gives slightly

higher diffuse irradiance than the previous one.

INSULATION ON TILTED SURFACES

The amount of insulation on a terrestrial surface

at a given location and time depends on the ori-

entation and slope of the surface. Most of measured

radiation data are for either normal incidence or

horizontal, which need to be converted to radiation

on tilted surfaces. There are several empirical

relationships developed over the years for such

estimates. In the Liu and Jordan (1977) method

the diffuse and total radiation ratio for a horizon-

tal surface is expressed in terms of monthly clear-

ness index, KTas:

H

HK K

D

T T

= − −1 390 4 027 3 108 3

. . . (57)

Collares-Pereira and Rabl (1979) extended

previous model by considering the sunset hour

angle:

H

Hh

h

D

SS

SS

= + −

( )

−

− + −

( )

0 775 0 0065 90

0 505 0 00455 90 115

. .

. . cos πKKT−

( )

103

(58)

Interested readers can learn more about the

solar radiation models and estimate procedures

in the following review papers (Muneer, 2004;

Muneer et al. 2007) or elsewhere in the literature.

APPLICATION OF AI TECHNIQUES

FOR SOLAR RADIATION

PREDICTION AND MODELING

Meteorological data such as solar radiation, ambi-

ent temperature, relative humidity, wind speed,

clearness index and sunshine duration are accepted

as dependable and widely variable in renewable

energy sources. It is therefore required to be able

to formulate forecasting and estimation models of

these meteorological data. These data play a very

important role in solar energy systems. However,

in many cases these data are not available owing

to the high cost and complexity of the instrumen-

tation needed to record them. Solar energy is a

397

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

sustainable, safe and abundant energy resource

and therefore there are no restrictions of time

and space for its exploitation. Concerning the

exploitation of solar energy, it is divided into three

basic applications: passive solar systems, active

solar systems and photovoltaic systems (Figure

7). Passive and active solar systems exploit the

thermal energy of global solar irradiance, while

PV systems convert global solar irradiance to

electricity. Estimating global solar irradiance on

tilted surfaces is necessary as the majority of solar

energy systems are inclined according to the site

of installation and utilization. Moreover, beam and

diffuse components of global solar irradiance on

inclined surfaces are essential in order to calculate

the electric power of photovoltaic systems, design

solar thermal systems and to evaluate their long-

term average performance.

Despite the fact that many meteorological

stations measure global and diffuse irradiation

received on horizontal surfaces, the data on in-

clined surfaces are not available and are esti-

mated with several models, using the components

of global solar irradiance on horizontal surfaces.

It must be noted that the knowledge of the com-

ponents of global solar irradiance on horizontal

surfaces is essential for the prediction of global

solar irradiance on tilted surfaces, as it is difficult

to develop a simple model converting solar ir-

radiance received by the horizontal plane to that

arriving at an inclined area for two main reasons

(Wong and Chow, 2001): 1) Global solar irradi-

ance reaching at tilted surface includes irradiance

reflected from the surroundings; and 2) The view

angle of a tilted surface cuts out a limited solid

angle of the sky. This sky irradiation not only

depends on the tilt angle, on the azimuth of the

collector and on the solar elevation and azimuth

but also on the cloud conditions. The models for

predicting global solar irradiance on tilted sur-

faces are classified as isotropic and anisotropic.

The isotropic models (Bugler, 1977; Badescu,

2002; Koronakis, 1986; Liu and Jordan, 1960;

1962, Ma and Iqbal, 1983; Tian et al. 2002) pre-

dict the diffuse irradiance on a tilted surface,

assuming the uniformity of diffuse sky irradiance

over the sky dome. However, this theory is not

correct (Kalogirou, 2009) and therefore addi-

tional models, the so-called anisotropic models

were developed. In the anisotropic models con-

sider the sum of the anisotropy of the diffuse sky

irradiance in the circumsolar region (sky near the

solar disk) and the anisotropic diffuse component

for the rest of the sky dome.

Solar radiation data are accepted as dependable

and widely available renewable energy sources. It

is, therefore, necessary to formulate forecasting

and estimation models of these meteorological

data. These data play a very important role in PV-

systems sizing and design. The next sections of this

chapter deal with overviews of the applications of

various AI techniques in solar radiation estimation,

Figure 7. Basic applications of global solar irradiance (adapted from Behrang et al., 2010)

398

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

modeling and prediction. This includes modeling

of the monthly, daily and hourly solar radiation,

daily clearness index modeling, and insolation

forecasting and prediction. As we pointed out in

previous sections of this chapter, measurement

data may suffer of several drawbacks, such poor

quality data, not enough measurements, data gaps,

while the traditional modeling and forecasting

algorithms may be too complex and requiring

large computer resources. An alternative way to

avoid the above problems is to employ the AI

techniques and emphasis is given to their growing

use for data analysis and prediction, offering an

effective alternative to more traditional statistical

techniques.

ANN MODELS FOR SOLAR

RADIATION ESTIMATION,

PREDICTION, AND FORECASTING

Vergara-Dominguez et al. (1985) made one of

the first attempts, back in 1985 of the using an

automatic process to generate sand estimate daily

global solar radiation. However, one of the first

applications of a neural network for predicting

daily solar radiation was made by Elizondo et

al in 1994. Their neural network model predicts

solar radiation as a function of readily available

weather data and other environmental variables.

Four sites in the southeastern USA, i.e. Tifton,

GA, Clayton, NC, Gainesville, FL, and Quincy,

FL, were selected because of the existence of

long-term daily weather data sets which included

solar radiation. A combined total of 23 complete

years of weather data sets were used in this model.

The data sets were separated into 11 years for the

training data set and 12 years for the testing data

set. Daily observed values of minimum and maxi-

mum air temperature and precipitation, together

with daily calculated values for day-length and

clear sky radiation, were used as inputs for the

neural network model. Day-length and clear sky

radiation were calculated as a function of latitude,

day of year, solar angle, and solar constant. An

optimum momentum, learning rate, and number

of hidden nodes were determined for further use

in the development of the neural network model.

The neural network model was tested against the

independent data set. Root mean square error var-

ied from 2.92 to 3.64 MJ/m2 and the coefficient

of determination varied from 0.52 to 0.74 for the

individual years used to test the accuracy of the

model. Although this neural network model was

developed and tested for a limited number of sites,

the results suggest that it can be used to estimate

daily solar radiation when measurements of only

daily maximum and minimum air temperature and

precipitation are available.

Williams and Zazueta (1994, 1996) proposed

the use of feed-forward neural networks to estimate

the daily solar radiation. The authors used as inputs

other meteorological parameters such as precipita-

tion, temperature, clear sky radiation, day length

and day of the year. Mohandes et al. (1996) used

data from 41 collection stations in Saudi Arabia.

From these, the data for 31 stations were used to

train a neural network and the data for the other

10 for testing the network. The input values to

the network are latitude, longitude, altitude and

sunshine duration. The results for the testing sta-

tions obtained are within 16.4% and indicate the

viability of their approach for spatial modeling

of solar radiation. Alawi and Hinai (1998) have

used ANNs to predict solar radiation in areas not

covered by direct measurement instrumentation.

In this work, a novel approach using an artificial

neural network was used to develop a model for

analyzing the relationship between the Global

Radiation (GR) and climatological variables,

and to predict GR for locations not covered by

the model’s training data. The predicted global

radiation values for the different locations (for

different months) were then compared with the

actual values. The input data to the network are

the location, month, mean pressure, mean tem-

perature, mean vapor pressure, mean relative

humidity, mean wind speed and mean duration of

399

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

sunshine. The ANN model predicts solar radiation

with an accuracy of 93% and mean absolute error

of 7.3%. In addition, the model was also tested

to predict GR values for the Seeb location over a

12 months period. The monthly predicted values

of the ANN model compared to the actual GR

values for Seeb produced an accuracy of 95% and

a mean absolute percentage error of 5.43. Data for

these locations were not included as part of the

ANN training data. The results demonstrate the

generalization capability of this novel approach

over unseen data and its ability to produce accu-

rate estimates. A RBF network has been used for

prediction of daily solar radiation data in Algeria

by Guessoum et al., (1998).

A neural network approach for generating solar

radiation artificial series has been proposed by

Zufiria et al. (1999) to predict solar radiation for

Spain. Tog¢rul and Onat (1999) developed a model

for the estimation of the solar radiation based on

geographical and meteorological data in Elazige,

Turkey. In this study, the effect of geographical and

meteorological parameters on the monthly mean

global solar radiation was investigated. A multiple

linear regression was applied to six geographical

and meteorological data sets, which were monthly,

mean extraterrestrial radiation, the ratio of ‘bright

sunshine hours to the day-length, ambient and

soil temperatures, humidity and sine of declina-

tion angle. The global solar radiation estimated

from the models was compared with the 2-year

measurement data set. It has been determined that

these equations which express the 99th percentile

of the incident solar radiation, have a −9% devia-

tion from our measured values. Taken in account

that the mean error of the forecast insolation by the

single-stage neural network is about 30%, Kem-

moku et al. (1999) proposed a multistage ANN to

predict the insolation of the next day. The input

data to the network are the average atmospheric

pressure, predicted by another ANN and various

weather data of the previous day. A first-stage

neural network forecasts the average atmospheric

pressure of the next day from atmospheric pressure

data of the previous day. A second-stage neural

network forecasts the insolation level of the next

day from the average atmospheric pressure and

weather data of the previous day. A third-stage

neural network forecasts the insolation of the

next day from the insolation level and weather

data of the previous day. The results obtained

show a prediction accuracy of 20%. The authors

propose a multi-stage NN method for forecasting

the insolation of the next day. Figure 8 shows the

block diagram of the multi-stage NN used for

forecasting the insolation, proposed by Kemoku

et al. (1999). Meteorological data at Omaezaki,

Japan in 1988–1993 are used as input data, and the

insolations in 1994 are forecast. The insolations

forecast by the multi-stage and the single-stage

neural networks are compared with the measured

ones. The results show that the mean error reduces

from about 30% (by the single-stage) to about

20% (by the multi-stage).

Hontoria et al. (1999 and 2001a) improved

the generation of hourly solar radiation artificial

series using MLP neural networks. While, Hon-

toria et al. (2001b, 2002) applied an upgraded

recurrent MLP ANN, developed earlier for mod-

eling the solar radiation. This model consists of

the generation of synthetic series of hourly solar

irradiation. The model presented is based on the

capacity of the MLP for finding relations between

variables for which interrelation is unknown

explicitly. The information available can be in-

cluded progressively at the series generator at

different stages. Comparative study with other

solar irradiation synthetic generation methods

demonstrated the validity of the proposed model.

Mohandes et al. (1998) used RBF networks

(Figure 9) for modeling monthly mean daily values

of global solar radiation on horizontal surfaces

and compared its performance with that of a

MLP model and a classical regression model. The

proposed network employs as inputs the latitude,

longitude, altitude and sunshine duration for the

prediction of solar radiation values. Mohandes et

al. (2003) used solar radiation data from 41 sta-

400

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

Figure 8. Flowchart for insolation forecast using a multi-stage neural network (Adapted from Kemoku

et al., 1999)

Figure 9. A radial basis functions neural network (Adapted from Mohandes et al., 2003)

401

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

tions that are spread over the Kingdom of Saudi

Arabia, by using radial basis functions ANN. The

solar radiation data from 31 locations are used for

training the neural networks and the data from the

remaining 10 locations are used for testing the

estimated values. The testing data were not used

in the modeling or training of the networks to give

an indication of the performance of the system at

unknown locations. Results indicate the viability

of the radial basis for this kind of problem. The

authors believed that by adding new data would

further improve the models’ performances. This

is because the ANNs methods depend on learning

from examples. The method should be applicable

to any region, provided that samples of the so-

lar radiation data from locations of all types of

weather conditions are included in the training

process. That is these methods are not limited to

use in areas with solar conditions similar to Saudi

Arabia, only.

Mihalakakou et al. (2000) developed a total

solar radiation time series simulation model based

on ANN and applied in Athens. The model with

the least error was identified as a Neural Logic

Network that incorporated Logic Rules that pro-

duced an RMS error 4.9% lower than that of the

persistent approach. Sfetsos and Coonick (2000)

introduced a simple approach for the forecasting

of hourly solar radiation using various AI based

techniques (ANNs, ANFIS). They also investi-

gated other meteorological variables such as

temperature, wind speed, pressure. A comprehen-

sive discussion and review of the ANN applications

in the renewable energy systems applications was

published by Kalogirou (2001). Interested readers

are strongly encouraged to read this paper for in

depth presentation of the ANN applications in the

renewable energy systems. In this paper the author

presented various applications of the neural net-

works in renewable energy problems in a the-

matic rather than a chronological or any other

order. This includes the use of ANNs in solar

radiation and wind speed prediction, photovol-

taic systems, building services systems and load

forecasting and prediction.

A Radial Basis Functions (RBF) and Multi-

Layer Perception (MLP) methods to estimate solar

radiation, by using long-term data from eight sta-

tions in Oman was developed and implemented by

Drovlo et al. (2002). It is shown by these authors

that both the RBF and MLP models performed well

based on the root-mean-square error between the

observed and estimated solar radiations. However,

the RBF models are preferred since they require

less computing power and are more accurate. The

range of errors for the RBF networks was 0.83

to 10.08 MJ/m2/day, while the range of errors for

MLP networks was 1.01 to 9.41MJ/m2/day. As the

authors mentioned in this paper the model can be

used to estimate the solar radiation at any location

in Oman, with a proper training. Kalogirou et

al. (2002) used an ANN model for prediction of

maximum solar radiation. The prediction of solar

radiation is very important for many solar applica-

tions. Due to the very nature of solar radiation,

many parameters can influence both its intensity

and its availability and therefore it is difficult to

employ analytical methods for such predictions.

The input data that are used in their approach are

those which influence mostly the availability and

intensity of solar radiation, namely, the month,

day of month, Julian day, season, mean ambient

temperature and mean relative humidity (RH).

A multilayer recurrent architecture (considered

suitable for time series predictions) employing

the standard back-propagation learning algorithm

has been applied, here. Using the hourly records

for one complete year, the maximum value of

radiation and the mean daily values of temperature

and relative humidity (RH) were calculated. The

respective data for 11 months were used for the

training and testing of the network, whereas the

data for the remaining one month were used for

the validation of the network. The training of the

network was performed with adequate accuracy,

with a correlation coefficient between the actual

and the ANN predicted data of 0.9867. Also, the

402

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

sensitivity of the predictions to ±20% variation in

temperature and RH give correlation coefficients

of 0.9858 to 0.9875, which are considered satisfac-

tory. This is considered as an adequate accuracy

for such predictions.

ANN based models for estimation of monthly

mean daily and hourly values of solar global radia-

tion were proposed by Reddy and Manish (2003).

Solar radiation data from 11 stations spread over

India, round the year, have been used for train-

ing and testing the ANN. The results of the ANN

model have been compared with other empirical

regression models. The solar radiation estimations

by ANN were in good agreement with the actual

values and were superior to those of other avail-

able models. The maximum mean absolute relative

deviation of predicted hourly global radiation

tested is 4.07%. Their results indicate that the ANN

models are a promising candidate for evaluating

the solar global radiation potential at the places

where monitoring stations are not established.

The maximum mean absolute relative deviation of

predicted hourly global radiation tested is 4.07%.

Sozen et al. (2004a, 2004b) used an ANN for the

estimation of the solar potential of Turkey based

on geographical and meteorological data (latitude,

longitude, altitude, month, mean sunshine dura-

tion, and mean temperature). To train the neural

network, 3 year of the meteorological data (from

2000 to 2002) from 17 stations spread over Turkey

were used as training (11 stations) and testing (6

stations) data. The maximum mean absolute per-

centage error was found to be less than 6.7% and

the absolute fraction of variance (R2) values to be

about 99.9% for the testing stations. The trained

and tested ANN models showed greater accura-

cies for evaluating solar resource possibilities in

regions where a network of monitoring stations

has not been established in Turkey. The predicted

solar-potential values from the ANN were given in

the form of monthly maps. In later development

of these models, Sozen et al. (2005) used ANN to

forecast the solar potential of Turkey, to train the

neural network, meteorological data for 4 years

(2000–2003) and from 12 cities spread over Turkey

were used in this sturdy, nine stations as training

and three stations as testing data.

Mellit et al. (2004a, 2004c) used the RBF

networks for estimating total daily solar radiation

in Algeria data from measured daily sunshine du-

ration and temperature data. Soares et al. (2004)

used a neural network for modeling the hourly

diffuse solar radiation in the city of Sao Paulo,

Brazil. In this work, a perceptron neural-network

technique was applied to estimate hourly values

of the diffuse solar radiation, using as input the

global solar radiation and other meteorological

parameters measured from 1998 to 2001. ANN

verification was performed using the hourly mea-

surements of the diffuse solar radiation obtained

during 2002. The ANN was developed based on

both feature determination and pattern selection

techniques. The inclusion of the atmospheric

long-wave radiation as input improves the neural

network performance, while the inclusion of the

traditional meteorological parameters, like air

temperature and atmospheric pressure, are not

as important as long-wave radiation which acts

as a surrogate for cloud-cover information on

the regional scale. An objective evaluation has

shown that the diffuse solar radiation is better

reproduced by neural network synthetic series

than by a correlation model.

Hontoria et al. (2005a, 2005b) used a MLP

technique for developing solar radiation maps

for Spain. The inputs are the previous irradia-

tion, clearness index and the hour order number

of the KT. Figure 10 shows the proposed ANN

for clearness index prediction. To obtain a solar

radiation map it is necessary to know the solar

radiation of many points spread wide across the

area where the map is going to be drawn. In most

of the areas the data may not be available and

even where there are data they may be affected

by errors, data gaps, etc. In addition, to draw solar

radiation maps the number of points on the maps

(real sites) that it is necessary to work with makes

this problem difficult to solve. However, once the

403

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

MLP is trained a solar generation can be done in

all of the sites of the grid, which form the zone

map. This generation is simple and takes less time

than the same generation than classical methods

of solar generation. Their methodology is easily

extendible to other places.

A methodology for developing a simple theo-

retical model for calculating global insolation on

a horizontal surface was proposed by Elminir et

al. (2005). The input parameters to the model are

the latitude of the desired location and the amount

of total precipitable water content in the vertical

column at that location. Over the range of latitudes

covering most parts of India, the error is within

20% of the measured value. An ANN based fore-

casting of the mean monthly solar radiation in

Turkey was proposed by Adnan et al. (2005). The

proposed model has as inputs the geographical

coordinates, altitude, mean sunshine duration,

mean temperature and month. According to the

Figure 10. MLP architecture for clearness indexes prediction (Adapted from Hontoria et al., 2005a)

Figure 11. A single hidden-layer ANN for prediction solar radiation (Adapted from Adnan et al., 2005)

404

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

authors, the results indicate that the ANN model

seems promising for evaluating solar resource

potential at the places where there are no monitor-

ing stations in Turkey. Figure 11 shows the pro-

posed ANN for solar radiation forecasting. A

comparative study of Angstroms and ANN meth-

odologies in estimating global solar radiation on

horizontal surfaces in Cyprus was developed by

Tymvios et al. (2002, 2005). The ANN methodol-

ogy is a promising alternative to the traditional

approach for estimating global solar radiation,

especially in cases where radiation measurements

are not readily available.

Mellit et al. (2005b) proposed an ANN and

Markov transitions matrices (MTM) for prediction

of daily solar radiation and this model has been

applied for sizing a PV system at isolated sites.

The developed model can generate a sequence of

global solar radiation data using a minimum of

input data (latitude, longitude and altitude), es-

pecially in isolated sites. Using data collected at

60 meteorological stations in Algeria during

1991–2000, a data base and a typical meteoro-

logical year (TMY) have been built. A two steps

methodology was constructed. First, a neural

network has been trained based on 60 known

monthly solar radiation data from the TMY. The

neural network can generate the monthly solar

radiation data. Secondly, the data have been di-

vided by corresponding extraterrestrial value in

order to obtain the monthly clearness index values.

Based on these monthly clearness indexes and

using a library of MTM block the sequences of

daily clearness indexes were generated. Known

data were subsequently used to investigate the

accuracy of the prediction. Results obtained in-

dicate that the proposed model can successfully

be used for the estimation of the daily solar ra-

diation data for any locations in Algeria by using

as input the altitude, the longitude, and the latitude.

The model can be easily applied for any location

in the world. An application of sizing PV systems

in isolated sites has also been applied in order to

check the model’s validity.

López et al. (2005) proposed selection of input

parameters to model direct solar irradiance, which

is seldom measured by using an ANN and global

solar radiation measurements. The proposed ANN

methodology can be used in unfavorable condi-

tions, in terms of limited amount of available data,

performing successful results. In this work, the

Bayesian framework for ANN, named as automatic

Figure 12. ANN model used for the estimation of beam solar radiation (Adapted from Alam et al., 2006)

405

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

relevance determination method (ARD), was em-

ployed to obtain the relative relevance of a large

set of atmospheric and radiometric variables used

for estimating the hourly direct solar irradiance.

In addition, the authors tested the viability of this

novel technique applied to select the optimum

input parameters to the neural network. For that,

a multi-layer feed forward perceptron was trained

on these data. The results reflect the relative im-

portance of the inputs selected. Clearness index

and relative air mass were found to be the more

relevant input variables to the neural network, as

it was expected, proving the reliability of the ARD

method. The novel methodology can be used in

unfavorable conditions, in terms of limited amount

of available data, performing successful results.

The model was tested using radiometric data

measured at Desert Rock, USA, between 1989

and 1999. AI techniques, such as FL and neural

networks, have been used for estimating hourly

global radiation from satellite images (Zarzalejo

and Ramirez, 2005). The models have been fit-

ted to measured global irradiance data from 15

Spanish terrestrial stations.

Alam et al. (2006) proposed an ANN model

for estimating beam solar radiation. A new defined

parameter, known as Reference Clearness Index

(RCI), is introduced. Computation of monthly

mean daily beam solar radiation at normal inci-

dence has been carried out. According to the

authors, the results of the ANN model were com-

pared with measured data based on Root Mean

Square Error (RMSE) and Mean Bias Error

(MBE). It was found that RMSE in the ANN

model varies from 1.65% to 79% for the Indian

region. Figure 11 shows the proposed ANN ar-

chitecture used for estimating the beam solar

radiation.

Elminir et al. (2007) proposed an ANN model

to predict diffuse fraction in hourly and daily

scale (KD). An attempt was also done to describe

the ANN outputs in terms of first order polyno-

mials relating KD with clearness index (KT) and

sunshine fraction (S/S0). The procedure used here

was similar with one of (Zervas at al., 2008). If

care is taken in considering the corresponding

regional climatic differences, these correlations

can be generalized and transferred to other sites.

A comparison between the performances of the

ANN model with that of two linear regression

models has been reported. The results show that

the ANN model is more suitable to predict diffuse

fraction in hourly and daily scales than the regres-

sion models in the plain areas of Egypt. Turbidity

and water vapor, under cloudless conditions, are

important source of variability of the luminous

efficacy. Due to the complex functional relation-

ship between these atmospheric variables and the

luminous efficacy components, the derivation of

an on-local model considering all these physical

processes is nearly impossible if standard statisti-

cal techniques are employed.

To avoid this drawback, Iqdour and Zeronal

(2006) developed a MLP model to predict daily

solar radiation for Morocco. They applied Pollack-

Ribiere algorithm to train the neural network. The

agreement between the measured and predicted

daily solar radiation was excellent (see Figure

13 for details). The model can be easy applied to

other locations.

Lopez and Gueymard (2007) used ANN for

clear-sky solar luminous efficacy of direct, diffuse,

and global radiation estimates. In this purpose, a

detailed spectral radiation model (SMARTS) is

utilized to generate both illuminance and solar

radiation values covering a large range of atmo-

spheric conditions. Different input configurations

using combinations of atmospheric variables and

radiometric quantities were analyzed. Results

presented this paper shown that an ANN model

using direct and diffuse solar irradiance along

with precipitable water is able to accurately re-

produce the variations of the three components

of luminous efficacy caused by solar zenith angle

and the various atmospheric absorption and scat-

tering processes. The model developed in [46] is

considerably simpler than the SMARTS radiation

model it is derived from, but still can retain most

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Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

Figure 13. Measured and predicted daily radiation (Adapted from Iqdour and Zeronal, 2006)

Figure 14. Luminous efficacy components predicted by the SMARTS and ANN models for different tur-

bidity conditions (Lopez and Gueyamard, 2007, used with permission)

407

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

of its predicting power and versatility. The pro-

posed ANN model can thus be used worldwide,

avoiding the need of using detailed atmospheric

information or empirical models if radiometric

measurements and precipitable water data (or

temperature and relative humidity data) are avail-

able. Figure 14 displays the luminous efficacy

components predicted by the ANN model and

SMARTS versus solar zenith angle, for different

turbidity conditions. An excellent agreement

between the two models was found in this study.

Mubiru and Banda (2008) used ANN for es-

timating the monthly average daily global solar

irradiation on the horizontal surface in Uganda.

He model estimated the averaged daily solar ra-

diation by using weather station data: sunshine

duration, maximum temperature, cloud coverage,

and location parameters (latitude, longitude and

altitude). The comparison between the ANN and

empirical method emphasized the superiority of

the proposed ANN prediction model. Kratzenberg

et al. (2008) developed an ANN model to improve

the performances of the Numerical Weather Pre-

diction (NWP) model in forecasting daily solar

radiation. The NWP models have very low fore-

cast performance for the solar radiation. With the

intent to increase the performance of these mod-

els, their output variables are corrected, tradition-

ally with Model Output Statistic techniques. The

NWP model residuals, the forecasted weather

variable subtracted from the measured variable

are estimated. Even the corrected solar radiation

forecasts do presently not have satisfactory fore-

cast performance. In this work the solar radiation

is forecasted with the non-hydrostatic model

Advanced Regional Prediction System. This

model is providing its forecast weather variables

for a horizontal grid of (0.12 x 0.12)° resolution

with a sampling interval of 10 min. In their ap-

proach a novel high performance MOS technique

was developed, based on the Discrete Wavelet

Transformation (DWT) and ANNs. The daily

solar energy forecast by the presented method

reduces the RMSE from 25.5% to 9.06% for the

site Florianopolis, localized in the subtropical

south of Brazil. As shown in Figure 15 the pre-

sented ANN-based MOS model improves con-

siderably the output of the ARPS model simulation.

Measured air temperature and relative humid-

ity values, where used by Rehman and Mohandes

(2008) for the estimation of the global solar ra-

diation (GSR) in future time domain using articial

neural network method. The measurements used

in this study were collected between 1998 and

2002 for Abha city in Saudi Arabia. The estima-

tions of GSR were made using three combinations

of data sets namely: (i) day of the year and daily

maximum air temperatures inputs and GSR as

output, (ii) day of the year and daily mean air

temperatures inputs and GSR as output and (iii)

time day of the year, daily mean air temperature

and relative humidity as inputs and GSR as output.

The measured data between 1998 and 2001 were

used for training the neural networks while the

remaining 240 days’ data from 2002 as testing

data. The testing data were not used in training

the neural networks. Obtained results are showing

that neural networks are well capable of estimat-

ing GSR from temperature and relative humidity.

This can be used for estimating GSR for locations

where only temperature and humidity data are

available. A in depth and comprehensive review

of the AI technique applications was published

by Mellit (2008). In this paper the author presents

an overview of AI techniques for modeling, pre-

diction and forecasting of solar radiation data.

Published literature works, up to 2008 is pre-

sented and the potential of AI as a design tool for

prediction and forecasting of solar radiation data

is discussed. Additionally, the advantages of using

AI-based prediction solar radiation data in iso-

lated areas where there no instrument for the

measurement of this data, especially the param-

eters related to photovoltaic (PV) systems is also

discussed. Interested reader also can find a rich

bibliography in the Mellit and Kalogirou (2008)

review paper.

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Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

Jiang (2008) developed an artificial neural

network (ANN) model for estimating the monthly

mean daily diffuse solar radiation. Solar radiation

data from 9 stations having different climatic

conditions all over China were used in this study.

Data, collected during1995–2004 were used for

training and testing the ANN. Solar radiation data

from eight typical cities are used for training the

neural networks, while the data from the remaining

one location was used for testing the estimated

values. Estimated values were compared with

measured values in terms of mean percentage

error (MPE), mean bias error (MBE) and root

mean square error (RMSE). The results of the

ANN model have been compared with empirical

regression models to further test the ANN model.

A feed-forward back-propagation algorithm with

single hidden layer was used in this analysis.

The input variables are: the monthly mean daily

clearness index, and sunshine percentage, while

the output is monthly mean daily diffuse fraction.

The solar radiation estimations by ANN are in

good agreement with the actual values and are

superior to those of other available models. In

addition, ANN model was tested to predict the

same components for Zhengzhou station over the

Figure 15. Daily mean values of the forecasted versus the ground measured global solar radiation on

horizontal surface utilizing the ARPS model (left panel) and the ANN-based model (right panel) (Adapted

from Kratzenberg et al., 2008)

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Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

same period. Results indicate that ANN model

predicts the actual values for Zhengzhou with a

good accuracy of 94.81%. Data for Zhengzhou

are not included as a part of ANN training set.

Hence, these results demonstrate the generaliza-

tion capability of this approach and its ability to

produce accurate estimates.

The hourly solar radiation data collected during

the period August 1, 2005 July 30, 2006 from the

solar observation station in IkiEylul campus area

of Eskisehir region of Turkey was used by Hocao-

glu et al (2008) in a 2-D representation model of

the hourly solar radiation estimates. The model

provides a unique and compact visualization of the

data for inspection, and enables accurate forecast-

ing using image processing methods. Using the

hourly solar radiation data mentioned above, the

image model formed in raster scan form with rows

and columns corresponding to days and hours,

respectively. The results provide the necessary

correlation model and prediction directions for

obtaining the optimum prediction template for

forecasting. The 2-D forecasting performance is

tested through feed forward neural networks using

the same data. The optimal linear filters and ANN

models are compared in the sense of root mean-

square-error (RMSE). An ANN based model was

used by Boscha et al. (2008) to interpolate daily

solar radiation over the complex terrain in Spain.

Zervas et al. (2008) developed a ANN prediction

model of the global solar irradiance distribution on

horizontal surfaces. The approach was based on

neural network techniques and has been applied

to the meteorological database of NTUA Campus,

Athens, Greece.

Alam et al. (2009) used ANN models for es-

timating monthly mean hourly and daily diffuse

solar radiation. Solar radiation data from 10 Indian

stations, having different climatic conditions, all

over India have been used for training and testing

the ANN model. The coefficient of determination

(R2) for all the stations are higher than 0.85, in-

dicating strong correlation between diffuse solar

radiation and selected input parameters. The feed

Figure 16. ANN architecture for the prediction of diffuse solar radiation (Adapted from Alam et al., 2009)

410

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

forward back-propagation algorithm was used in

this analysis (see Figure 16). The neurons in the

input layer receive nine input signals representing

the latitude, longitude, altitude, time, month of the

year, air temperature, relative humidity, rainfall,

wind speed and net long wavelength. The output

layer consists of one output neuron representing

the diffuse solar radiation that is clearness index,

Kd. Results of ANN models have been compared

with the measured data on the basis of percentage

root-mean-square error (RMSE) and mean bias

error (MBE). The maximum value of RMSE in

ANN model is 8.8% in the prediction of

hourly diffuse solar radiation. The computation

of monthly mean daily diffuse solar radiation was

also carried out and the results were compared

with those of other empirical models. The ANN

model shows the maximum RMSE of 4.5% for

daily diffuse radiation, while for other empirical

models the same error is 37.4%, proving that the

ANN model performs better than empirical coun-

terparts.

An ANN-based model for prediction of solar

energy potential in Nigeria was developed by

Fadare (2009). Standard multi-layered, feed-

forward, back-propagation neural networks

with different architecture designed using neural

toolbox for MATLAB were used in this study.

Geographical and meteorological data of 195 cities

in Nigeria for period of 10 years (1983-1993) and

from the NASA geo-satellite database were used

for the training and testing the network. Meteoro-

logical and geographical data (latitude, longitude,

altitude, month, mean sunshine duration, mean

temperature, and relative humidity) were used as

inputs to the network, while the solar radiation

intensity was the output of the network. The results

shown that the correlation coefficients between

the ANN predictions and actual mean monthly

global solar radiation intensities for training and

testing data sets were higher than 90% suggesting

a high reliability of the model for evaluation of

solar radiation in locations where solar radiation

data are not available. The predicted solar radia-

tion values from the model were given in form of

monthly maps. Azadeh et al (2009) developed an

integrated ANN model for predicting solar global

radiation by using climatological variables, as

inputs. The proposed approach is particularly

useful for locations where no available measure-

ment equipment.

Seme et al (2009) was studied the prediction

of solar irradiation during the day. In order to

predict half hourly solar irradiation during the

day an artificial neural network is applied. The

artificial neural network was trained using error

back-propagation learning rule. Meteorological

data measured during three years in Slovenia were

used to form learning patterns. The trained artificial

neural network was tested with different patterns.

Some of them were new while the others were

used in the training procedure. The comparison of

measured and by the artificial neural network pre-

dicted daily distribution of solar irradiation shows

a very good agreement for the clear days. Mehleri

et al (2009) performed extensive comparisons of

various hourly slope irradiation models, found in

the literature, in order to select the most accurate

for the region of Athens. Finally, a neural network

model was developed to predict the global solar

irradiance on a tilted surface, using as input data

the total solar irradiance on a horizontal surface,

the extraterrestrial radiation, the solar zenith angle

and the solar incidence angle on a tilted plane. The

comparison with the aforementioned models has

shown that the neural network model, predicts

more realistically the total solar irradiance on

a tilted surface, as it performs better in regions

where the other models show under estimation or

over estimation in their calculations.

Rahimikhoob (2010) tested an ANN model

for the estimation of the global solar radiation as

a function of air temperature data in a semi-arid

environment. The ANNs (multilayer perceptron

type) were trained to estimate GSR as a function

of the maximum and minimum air temperature

and extraterrestrial radiation. The data used in the

network training were obtained from a historical

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Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

series (1994–2001) of daily climatic data collected

in weather station of Ahwaz located in Khuzestan

plain in the southwest of Iran. ANN-based models

for forecasting GSR on horizontal surfaces were

also developed and tested against conventional/

empirical GSR prediction models by Behrang et

al (2010). Daily mean air temperature, relative

humidity, sunshine hours, evaporation, and wind

speed values collected between 2002 and 2006

for Dezful city in Iran, were used in this study.

In order to consider the effect of each meteo-

rological variable on the daily GSR prediction

(the model output), six combinations of the input

variables were analyzed: a) day of the year, daily

mean air temperature and relative humidity; b)

day of the year, daily mean air temperature and

sunshine hours; c) day of the year, daily mean air

temperature, relative humidity and sunshine hours;

d) day of the year, daily mean air temperature,

relative humidity, sunshine hours and evaporation;

e) day of the year, daily mean air temperature,

relative humidity, sunshine hours and wind speed;

and f) day of the year, daily mean air temperature,

relative humidity, sunshine hours, evaporation

and wind speed. Multi-layer perceptron (MLP)

and radial basis function (RBF) neural networks

are applied for daily GSR modeling based on the

six proposed combinations of the input variables.

The measured data between 2002 and 2005 were

used to train the neural networks, while the data

for 214 days from 2006 were used to test the

models. The comparison of obtained results from

ANNs and several conventional GSR prediction

(CGSRP) models is shown higher performances

of the ANN-based models over the empirical ones.

The MLP architecture with day of the year, daily

mean air temperature, relative humidity, sunshine

hours and wind speed as inputs has the highest

accuracy of predictions, while the RBF model

with day of the year, daily mean air temperature

and sunshine hours, as inputs also is showing a

good accuracy.

FUZZY LOGIC AND HYBRID

APPROACHES TO MODEL AND

PREDICT SOLAR RADIATION

Sen (1998) used a FL approach for estimating solar

radiation from sunshine duration measurements.

A fuzzy logic algorithm for estimating the solar

irradiation from sunshine duration measurements

was proposed in this study. The main advantage

of fuzzy models is their ability to describe the

knowledge in a descriptive human-like manner in

the form of simple rules using linguistic variables

only. In this manner the classical Angstrom or any

other type of regression equations can be replaced

by a set of fuzzy rule bases. The fuzzy approach

was applied to predict solar irradiance for three

sites with monthly averages of daily irradiances

located in the western part of Turkey. The applica-

tion of the proposed fuzzy subsets and rule bases

is straightforward and easily to implement for any

of the irradiation and sunshine duration measure-

ments in any part of the world. Santamouris et al

(1999) developed three methods for analyzing and

modeling the global short wave radiation reaching

the earth’s surface. The estimation methods consist

of an atmospheric deterministic model and two

data-driven intelligent methods. The determinis-

tic method is a broad band atmospheric model,

developed for predicting the global and diffuse

solar radiation incident on the earth’s surface. The

intelligent data-driven methods are a new neural

network approach in which the hourly values of

global radiation for several years are calculated

and a new fuzzy logic method. The two data-driven

models, calculating the global solar radiation on

a horizontal surface, are based on measured data

of several meteorological parameters such as the

air temperature, the relative humidity, and the

sunshine duration. The three methods were tested

and compared using various sets of solar radiation

measurements collected at Athens, Greece. The

comparison of the three methods showed that

the proposed intelligent techniques can be suc-

cessfully used for the estimation of global solar

412

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

radiation during the warm period of the year, while

during the cold period the atmospheric determin-

istic model gives better estimations.

A fuzzy model of solar irradiance on inclined

surfaces has been developed by Gautman and

Kaushika (2002). The fuzzy model includes con-

cepts from earlier models, though unlike these,

it considers non-disjunctive sky categories. The

proposed model offers performance similar to that

of the models with the best results in the compara-

tive analysis of the literature, such as the Perez

model. The cloudiness index is defined, in this

study as the fraction of extraterrestrial radiation

that reaches the earth’s surface when the sky above

the location of interest is obscured by the cloud

cover. The cloud cover at the location of interest

during the jth time interval of a day is assumed

to follow the fuzzy random phenomenon. The

cloudiness index, therefore, is considered, here

as a fuzzy random variable that accounts for the

cloud cover at the location of interest during the

jth time interval of a day. A fuzzy based evaluation

model of the quality of the performance of the solar

radiation models was proposed by Bellocchi et al

(2002). Three modules were formulated reflecting

the magnitude of residuals (Accuracy), the corre-

lation estimates and measurements (Correlation),

and the presence or absence of patterns in the

residuals against independent variables (Pattern),

respectively. The Accuracy and Pattern modules

resulted from the aggregation of three (relative

root mean square error, modeling efficiency, and

t-Student probability) and two (pattern index vs.

day of the year and pattern index vs. minimum

air temperature) indices, respectively, while the

Correlation module was identified by a single

index (Pearson’s correlation coefficient). For each

index, two functions describing membership to the

fuzzy subsets Favorable (F) and Unfavorable (U)

have been defined. The expert system calculates

the modules according to both the membership

degree of the indices to the subsets F and U and

decision rules set. Then the modules are aggre-

gated into the indicator Irad. Sensitivity analysis

is presented, along with module and Irad scores

for some cases.

Solar irradiance is an extreme case of an

uncertain variable when measured on an hourly

or shorter time interval. Gomez and Casanovas

(2002) proposed a suitable model for estimating

the solar radiation data using FL random vari-

ables. The solar irradiance uncertainty is treated

in this study as a fuzzy uncertainty whilst other

variables are considered crisp. This approach is

robust as it does not rely on statistical assump-

tions, and it is a possible alternative to modeling

complex systems. This was one of the first at-

tempts, proposed to use a physical model of a

meteorological variable based on fuzzy numbers.

Previous rule-based fuzzy meteorological models

were only descriptive, and cannot be extrapolated

to non-measured cases. Compared with previous

non-fuzzy models of solar irradiance, this fuzzy

model shows an improved performance, and

when compared with experimental data, the per-

formance can be evaluated by fuzzy indices that

take into account the uncertainty of the data and

the model output. Gomez and Casanovas (2003)

proposed an updated model of the previous one

for estimating solar irradiation based on FL, ac-

cording to the authors the fuzzy model shows an

improved performance, and when compared with

experimental data.

Sen et al. (2004) developed a more efficient

model based on the fuzzy system architecture

for solar irradiation estimation from the sunshine

duration measurements than the conventional

empirical methods. Partial fuzzy modeling ac-

counts for the possible local nonlinearities in the

form of piece-wise linearization in this model.

The parameters estimation of such a fuzzy model

is achieved through the application of genetic

algorithm technique. The fuzzy part of the model

provides treatment of vague information about the

sunshine duration data whereas the genetic part

furnishes an objective and optimum estimation

procedure. The application of genetic-fuzzy model

as proposed in this article is presented for three

413

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

stations in Turkey and the results are compared

by ones from the previous classical approaches.

Rivington et al. (2006) conducted an extensive

evaluation of three models for the solar radiation

estimates, using data collected at 24 weather sta-

tions in the UK. Comparisons were made using

a fuzzy-logic based multiple-indices assessment

system (Irad) and tests of the temporal distribution

of mean errors. The conversion from sunshine

duration to solar radiation produces the best

overall estimates, but shows systematic seasonal

errors. The two air temperature based methods,

discussed in this study can be reliable alternatives

when only air temperature data are available. Their

study demonstrates the value and importance of

using a range of assessment methods to evaluate

model estimates.

Lah et al. (2006) applied fuzzy logic approach

to control and model daylight illuminance, Iqdour

and Zeronal (2006) proposed the investigation of

the use the fuzzy systems of Takagi Sugeno (TS)

for modeling the daily solar radiation data. The

Takagi-Sugeno models are non-linear techniques,

defined by a set of If- Then rules, each of which

establishes a local linear input-output relationship

between the variables of the model. The TS fuzzy

model is trained using data of daily solar radia-

tion recorded on a horizontal surface in Dakhla in

Morocco. The predicting results indicate that the

Takagi-Sugeno fuzzy model gives a good accuracy

of 96% and a root mean square error lower than 6%.

In addition, the performances of the identified TS

fuzzy model are then compared to a linear model

using the SOS techniques. The results show the

effectiveness of the nonlinear model. Paulescu et

al (2008) studied two models for solar radiation

attenuation in the atmosphere. The novelty consists

in using fuzzy logic algorithms for evaluating

atmospheric transmittances associated to the main

attenuators: Rayleigh scattering, aerosol extinc-

tion, ozone, water vapor and trace gas absorption.

The first model encompasses self-dependent

fuzzy modeling of each characteristic transmit-

tance, while the second one is a proper fuzzy

logic model for beam and diffuse atmospheric

transmittances. The results lead to the conclusion

that developing parametric models along the ways

of fuzzy logic is a viable alternative to classical

parameterization. Due to the heuristic nature of the

fuzzy model input–output map, it leads to more

flexibility in adapting to local climatic conditions.

Tulcan-Paulescu and Paulescu (2008) developed

a model for estimating daily global solar irradia-

tion from daily average air temperature based on

the Fuzzy sets theory for locations in Romania.

In addition to the presentation of a new mapping

technique, from the input to the output of the

model, an innovative approach for the tuning of

the fuzzy algorithm to fit a local meteo-climate

is proposed. Since air temperature-based solar

radiation models are strongly dependent on the

origin location, the adaptive method presented

here is designed as a tool for potential users to

either increase the application area or to devise

more precise local models. A critical assessment

of fuzzy model performances and limitations has

been conducted. The reported results demonstrated

the potential of modeling solar irradiation using

the fuzzy sets approach.

A Neuro-Fuzzy approach has been developed

for prediction of clearness index (KT) in isolated

sites for Algeria (Mellit and Guessoum, 2006). The

inputs of this model are the geographical coordi-

nates and the outputs are the mean monthly Kt. An

adaptive ANN and hybrid models for prediction

of daily solar radiation is proposed by Mellit et al.

(2004d, 2007a). The models combine ANN and

fuzzy logic (ANFIS). The input of these models is

the mean temperature and the sunshine duration.

Figure 17 illustrates the proposed ANFIS-model.

Mellit et al. (2007b) proposed a new model based

on neuro-fuzzy for predicting the sequences of

monthly clearness index and proposed it for gen-

erating solar radiation, which has been used for

the sizing of a PV-system. The authors proposed

a hybrid model for estimating sequences of daily

clearness index by using an ANFIS and Markov

chain; the proposed model has been used for

414

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

estimating the daily solar radiation. An applica-

tion of sizing a PV-system is presented based on

the data generated by this model. Badran et al

(2009) studied study the use of the fuzzy logic to

assess solar sites in Jordan and to decide which

sites should be given the highest priority with

respect to their benefits and costs. The criterion of

evaluation using fuzzy logic is based on different

parameters, i.e., solar resources, site capacity, site

accessibility, soil condition, water availability, grid

connection distance, land cost, land roughness, and

wind speed. This method seems very promising

for the solar site assessments.

APPLICATION OF NEURAL

NETWORKS AND MARKOV CHAINS

FOR SOLAR RADIATION

PREDICTION

Mellit et al. (2004c, 2005b, 2005c) proposed

simplified hybrid models for generating sequences

of total daily solar radiation; the proposed model

combines neural networks and Markov chains.

This model is called the ANN-MTM (Markov

Transition Matrix). The inputs of the proposed

model are the geographical coordinates while the

outputs are the daily total solar radiation. It can be

used for generating sequences of solar radiation

in the long term and it was applied for Algeria.

Figure 18 shows the hybrid configuration for

generating sequences of daily solar radiation data.

Cao and Cao (2005) developed a hybrid model for

forecasting sequences of total daily solar radiation,

which combines ANN with wavelet analysis. The

characteristic of this method is the pre-processing

Figure 17. The ANFIS-model used for estimating the irradiation from the mean temperature and the

sunshine duration (Adapted from Mellit et al., 2007a)

415

Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

of data using wavelet transformation, i.e., the

data sequence of solar irradiation is first mapped

onto several time-frequency domains and then

a recurrent Back-Propagation (BP) network is

established for each domain. According to the

authors, the results showed that the accuracy of

the method is more satisfactory than that of the

methods reported before (see Figure 18 for details).

Mellit (2006) also proposed an ANN with

Discrete Wavelet Transforms (DWTs) for time

series prediction. This model has been used for

prediction of solar radiation based on sunshine

duration and mean temperature. Cao and Cao

(2006) used neural network and wavelet analysis

for prediction of solar radiation. Mellit et al. (2006)

proposed an adaptive wavelet-network model for

forecasting daily total solar radiation. In this study,

several structures have been investigated for re-

solving the missing data problem. In this particu-

lar estimation process, the model consists of an

adaptive neural-network topology with the wave-

let transformation embedded in the hidden units.

The IIR synopsis network is used to create a

‘double’ local network architecture that provides

a computationally efficient method of training the

system and results in quick learning and fast

convergence.

An ANN fuzzy logic assisted model to forecast

solar irradiance was proposed by Cao and Lin

(2008). In general, the forecast models based

on ANN perform much better in accuracy than

many conventional prediction models. However,

a fact could not be neglected that most of such

existing ANN-based models have not yet satisfied

researchers and engineers in forecast precision

so far, and the generalization capability of these

networks needs further improving. Combining

the prominent dynamic characteristics of recur-

rent neural network with the enhanced ability

of wavelet neural network (WNN) in mapping

nonlinear functions, the authors proposed a diago-

nal recurrent wavelet neural network (DRWNN)

method to carry out fine forecasting of the hourly

global solar irradiance. Some additional steps,

e.g., using fuzzy technique to apply historical

information of cloud cover to sample data sets for

network training and the forecasted cloud cover

in weather program to network input for the ir-

radiation forecasting, were also adopted to help

enhancing forecast precision. The hourly irradi-

ance forecast is completed using the sample data

Figure 18. Block diagram of hybrid model ANN–MTM (Adapted from Mellit et al., 2005b)

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Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

set in Shanghai, China and comparisons between

irradiation models show that the DRWNN model

is definitely more accurate.

CONVENTIONAL METHODS

FOR PV SYSTEM SEIZING

Power output of a solar energy system varies

according to the irradiation and global system

functioning conditions. In any solar energy and PV

system, sizing represents an important part of the

system design. The optimal selection of the number

of solar cell panels, collector selection, the size of

the storage battery and the size of wind-generator

to be used for certain applications at a particular

site is an important economical task for electrifica-

tion of villages in rural areas, telecommunications,

refrigeration, water pumping, and water heating,

etc. Besides being an economic waste, an oversized

system can also adversely affect further utilization

of the solar cells and the pollution-free PV energy.

The estimation of the sizing parameters PV-array

area, useful capacity of battery, wind generator is

very useful to conceive an optimal PV systems

as well as conceiving an optimal and economic

PV systems particularly in isolated sites (Sahara

regions, small island archipelagos, remote areas in

developing nations, mountainous locations, rural

regions, etc.). In order to decide the size of any

solar energy conversion system, especially of the

stand-alone photovoltaic system, various methods

can be used. Over the years, several models have

been developed, simulating and sizing PV systems

using different operation strategies. Some are more

accurate than others and range from those known

as intuitive to others in which a detailed simulation

and analysis methods of the system is carried out

(numerical methods). Somewhere between these

two poles are the analytical methods that sacri-

fice certain accuracy in order to gain simplicity

in the calculations. Among these methods, there

are ones proposed, more than three decades by

Barra et al (1984), Bartoli et al. (1984), and Egido

and Lorenzo (1992). In all of these, accuracy is

achieved by using data from daily global irradia-

tion series. If this kind of data is not available,

the loss of accuracy is significant, or the method

cannot be used. Sidrach-de-Cardona and Mora

Lopez (1999) suggested an alternative method:

a multivariate qualitative model is proposed to

calculate the size of the stand-alone PV system,

using as input mean monthly irradiation values

and setting parameters.

The estimation of the excess of energy provided

by PV generators using the utilisability method was

developed by Liu and Jordan (1977). The excess

energy provided by PV systems for an installa-

tion having a constant load was also evaluated

by Klein (1978). Siegel et al. (1981) evaluated

the monthly average output, the excess of energy

and the storage capacity of the batteries. Evans

et al (1981) described a method to consider the

monthly average output of PV fields. All these

methods are based on the energy balance of the

systems studied to determine their storage capacity

and output. In the so-called numerical methods

employed to calculate the size of the PV system

for the various sites are based on the loss of load

probability method (LOLP). The data obtained

with this method is usually processed via mul-

tivariate regression linear analysis. The LOLP

method is based on the ideas proposed by Gordon

(1981), and Klein and Beckman (1987). LOLP is

defined as the dimensionless energy deficit, for

a PV system, carried out over a sufficiently long

period of time which allows us to fully characterize

the statistical nature of the solar irradiation. To

determine the array capacity and the battery sizes

for a specified LOLP, the long-term photovoltaic

behavior has been simulated and calculated daily.

The first step in this method is to calculate the solar

irradiation incident on the tilted surface, employ-

ing one of the methods presented in the previous

sections of this chapter. In order to simulate the

behavior of a PV system, a daily energy balance

is carried out each day

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Articial Intelligence Techniques for Solar Energy and Photovoltaic Applications

Other methods used to estimate the perfor-

mance of PV systems are based on the Loss of

Load Probability (LLP) technique, defined as the

ratio between the energy deficit and the energy

demand, both on the load, there are developed by

Bucciareli (1984), Klein and Beckman (1987),

Barra et al. (1994), and by Bartoli et al. (1984).

These analytical methods are simple to apply but

they are not general. On the other hand, the nu-

merical methods presented by Bucciarelli (1984),

Groumpos and Papageorgiou (1987), Graham et

al. (1988), Aguiar et al. (1988), Chapman (1990)

and Abouzahr (1991) present a good solution, but

these need a long period solar radiation data record.

Egido and Lorenzo (1992) reviewed methods

for computing capacity of PV arrays and battery

storage and suggested analytical model based

on LOLP, where it uses more complex methods

which allow the improvement of the precision of

the LLP calculation according to the dimension

of the PV-array area and the storage capacity. An

optimal method for the panel area of PV system

in relation to the static inverter practical results

has been developed by Keller and Affolter (1995).

A detailed evaluation of the sensitivity of a nu-

merical sizing method developed by Notton et

al. (1996), has shown that the influences of some

parameters on the sizing, i.e., simulation time step,

input and output power profile are very important.

It is therefore important to have knowledge of

the daily profile at least on an hourly basis. The

authors have highlighted that optimal solution

can be obtained if PV contributes for 75% of the

energy requirements.

The cost of electricity generated from a hybrid

PV system is also one of the decision-making pa-

rameters. Shrestha and Goel (1998) demonstrated

a method to find optimal combination of PV array

size and battery to meet the refrigeration load, by

using statistical models for both solar radiation

and the load. Mellit et al. (2005, 2008) developed

methods to design stand-alone PV systems, for

remote areas of Algeria based on mean monthly

clearness index and daily solar radiation data.

Benghanem (2002) has been developed a suitable

methodology based on LLP for sizing PV-system in

Algeria. Bhuiyan and Asgar (2003) optimized PV

battery system for Dhaka, Bangladesh with respect

to power output for different tilt and azimuth angle

for optimum performance of the system. Mellit

et al., (2004c) have presented a simplified meth-

odology for optimal sizing PV-system in Algeria

based on spatial interpolation method. Kaushika et

al. (2005) developed a computational scheme for

stand-alone solar PV