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Artificial intelligence techniques for solar energy and photovoltaic applications

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Artificial 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, insufficient 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 methodologies 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.
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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
Articial Intelligence
Techniques for Solar Energy
and Photovoltaic Applications
ABSTRACT
Articial 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, insufcient 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
377
Articial 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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Articial 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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Articial 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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Articial 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)
381
Articial 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):
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Articial 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 fuzzied.
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
difcult 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
Articial 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
384
Articial 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
385
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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
406
Articial 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
Articial 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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Articial 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)
409
Articial 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
Articial 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
411
Articial 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
Articial 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
Articial 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
Articial 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
Articial 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)
416
Articial 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
417
Articial 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