FinalReport

OPTIMAL SYSTEM OPERATION
FINAL REPORT
Name:
Oswaldo Guerra Gomez

2
OPTIMAL SYSTEM OPERATION
FINAL REPORT
Name:
Oswaldo Guerra Gomez
Student Number:
340672
Supervisor names:
Mr. Nguyen Trung Thang
Mr. Jan Bollen
Version:
1.0
27 December 2016
Saxion University of Applied Sciences
Enschede, Netherlands

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Foreword
A special thanks goes to Mr. Jan Bollen for giving me the opportunity to come to Vietnam and
be able to do an interesting project. Also a special thanks to Mr. Nguyen Trung Thang and Mr.
Ly for guiding me during this hard and very interesting project in Vietnam.
This project has given me new and relevant knowledge that I can apply in my future job or
future innovations. This project is about one of the biggest problems nowadays. Economical
load dispatch is a powerful problem affecting the economy and ecology every day. By having
the opportunity to learn about this topic and trying to improve it, brings me joy to be able to
contribute to future innovations.
As last, a special thanks goes to the university of Ton Duc Thang for offering me their
instruments and facilities to be able to work on the project.

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Summary
For many years economic load dispatch (ELD) is a worldwide problem and has been broadly
studied in power system operation in late decades. The main aim of economical dispatch
problem is to minimize the total cost of generating real power, while satisfying the load and the
losses in transmission link.
After many years of research a new nature-inspired metaheuristic has been created to solve this
serious problem called Flower Pollination Algorithm(FPA)
From the biological evolution point of view, the objective of the flower pollination is
the survival of the fittest and the optimal reproduction of plants in terms of numbers as well as
most fittest.
The project is based on programming this new nature-inspired metaheuristic with the help of
the program MATLAB to help us with ELD problem. Before programming this nature-inspired
metaheuristic an analysis has been done with the help of flowcharts and pseudo codes in order
to understand its function. After programming the Flower Pollination Algorithm a test has been
done in order to prove that it works and that its effectiveness is higher than other algorithms
like Cuckoo Search Algorithm or fuzzy logic controlled genetic algorithm. Flower Pollinations
Algorithm proved that it is more accurate in finding the global optima solution including a low
execution time in comparison with other algorithms like CSA and FCGA.
In addition a documentary has been done about Vietnam. The purpose of this documentary is
to give a short overview of the beauty of the people, culture and nature in Vietnam. Vietnam is
not so popular in comparison to other countries and my purpose is to show Saxion university
of Applied Sciences the beauty of Vietnam.

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Content
FOREWORD 3
SUMMARY 4
ABBREVIATIONS 6
GLOSSARY 6
FIGURE LIST 7
TABLE LIST 7
1. INTRODUCTION 8
1.1. BACKGROUND OF ASSIGNMENT 8
1.2. PURPOSE OF ASSIGNMENT 9
1.3. SCOPE OF WORK 9
1.4. APPROACH AND METHODOLOGY 10
1.5. OUTLINE OF REPORT 10
2. ALGORITHMS 11
2.1. HISTORY 11
2.2. FLOWER POLLINATION ALGORITHM 17
2.2.1. PSEUDO CODE 19
2.2.2. FLOWCHART 22
2.2.3. TEST FUNCTION 23
2.3. EXECUTION OF ASSIGNMENT 24
2.3.1. PROBLEM FORMULATION 24
2.3.2. IMPLEMENTATION OF FPA FOR ELD PROBLEMS 25
2.3.3. EXECUTION OF FPA METHOD 27
2.4. RESULTS 28
2.5. CONCLUSION 36
3. VIETNAM 37
3.1. COUNTRY 37
3.2. PEOPLE 37
3.3. RELIGION 38
3.4. WONDERS IN VIETNAM 39
4. REFLECTION 41
4.1. COMPANY 41
4.2. OWN DEVELOPMENT TECHNICAL AND SOCIAL 41
4.3. OWN FUTURE 41
5. REFERENCES 42

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Abbreviations
Abbreviation Description
ELD Economic Load Dispatch
Number of population
Power output
P Total system load demand
P Total transmission loss
P Total system load demand
P Total transmission loss
S Spinning reserve of unit i
S , Maximum spinning reserve contribution of unit i
S Total system spinning reserve requirement
flower or a pollen gamete
t Step
ith
pollen
∗ Current best solution
L Strength of the pollination
Solution of a plant
Solution of a plant
ɛ Randomized between 0 and 1
Switch probability
Glossary
Glossary Definition
Non linear In physical sciences, a nonlinear system is a system in which the
output is not directly proportional to the input.
Multimodal having or involving several modes, modalities, or maxima
Metaheuristic metaheuristic is a higher-level procedure designed to find, generate,
or select a search algorithm that may provide a sufficiently good
solution to an optimization problem, especially with incomplete or
imperfect information or limited computation capacity.
MATLAB a multi-paradigm numerical computing environment and fourth-
generation programming language. A proprietary programming
language developed by MathWorks. MATLAB
allows matrix manipulations, plotting of functions and data,
implementation of algorithms, creation of user interfaces, and
interfacing with programs written in other languages,
including C, C++, C#, Java, Fortran and Python.

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Figure list
Figure No. Definition
Figure 1 SOS flowchart
Figure 2 Flower Pollination
Figure 3 FPA flowchart
Figure 4 probability switch
Figure 5 Determining the best P for PD 800MW
Figure 6 Fitness convergence characteristic 800MW
Table list
Figure No. Definition
Table 1 Comparison of algorithm performance in terms of number of iterations
Table 2 Result obtained by FPA for the 6 unit system for load demand of 800
MW with different values of p. 300 iterations
Table 5 Tested 800MW load demand
Table 14 All official tested units

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1. Introduction
This chapter describes the background of the assignment along with the purpose.
Also the scope of the work and outline of the report will be described
1.1. Background of assignment
This section describes the occasion, competitions and learning objectives of this project. Also
information about the Mentor & Supervisor and the assignment can be found here.
Occasion:
This project is part of a 3rd
year subject called “minor”. Minor is a specialization phase in the
career Electric & Electronical Engineering at Saxion University of Applied Sciences. In this
phase the student has to specialize himself in a unique direction of Electric & Electronical
Engineering.
A combination of different backgrounds, skills and experiences will be applied by the student
in a project to help him specialize in a unique direction. This project will take 5 months in total.
This project is led by the 3rd
year student Oswaldo Junior Guerra Gomez with the guidance
of the mentor Dr.Nguyen Trung Thang and the supervisor Dr.Jan Bollen.
The contact information of the student and supervisors can be found under section “Reflection”
with all the necessary information.
This specialization project is taken place in the university of Ton Duc Thang in Ho Chi Minh
City, Vietnam.
The basic principle of this project is about the economical load dispatch. The main aim in the
economic dispatch problem is to minimize the total cost of generating real power (production
cost) at various station while satisfying the loads and the losses in the transmission links.
In this project I have to analyze and learn many algorithms to be able to choose the best one
(effective and simple) to apply in this situation, for achieving this goal
For this basic knowledge from previous modules, essential courses are:
● Communication Skills
● Programming MATLAB
● Mathematics
● Power system engineering
The project is divided into 5 categories:
1. Analyzing and researching different types of algorithms
2. Selecting the most simple and effective algorithm
3. Analyzing the chosen algorithm
4. Testing and documenting the chosen algorithm
5. Applying it in to the real world

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1.2. Purpose of assignment
Economic Load Dispatch (ELD) problem is a standout amongst the most well-known and
critical problem and has been broadly studied in power system operation in late decades. The
main aim of economical dispatch problem is to minimize the total cost of generating real power,
in other words the production cost, while satisfying the load and the losses in transmission link
[1].
For many years fossil fuels have been used to generate electricity. According to studies 67% of
electricity is being generated by fossil fuels sources around the whole world. Majority of fossil
fuel usage for the generation of electricity is coal and gas [2].
Countries with the highest consumption percentage of fossil fuel are USA and China.
That means if by applying some algorithms that can help optimize the system while keeping
the cost at a minimum, a lot of revenue can be saved [2].
Consumers need to pay an appropriate price for what they are consuming, which are very high
especially in fossil fuel plants, so economic dispatch can help sparing a significant amount of
income [3].
1.3. Scope of work
To not over expand the project and to finish the project on time, we will add some boundaries
during the research. In this chapter we will name the boundaries.
Economic load dispatch is a very complex problem. There are many factors that affect the
problem. To keep everything between boundaries, we will consider only some parts of the
problem.
One of the most important is considering the power balance constraint. Constraints are the need
to maintain a power balance, and that the flow on any line must not exceed its capacity. The
total power generated from a set of available units must satisfy the total demand and system
power losses.
The total power generated from a set of available units must satisfy the total demand and system
power losses. So as just said, we also have to consider power loss. The power losses depend on
the flows in the branches and thus on the net injections.
We also have to consider a minimum and maximum output power. This is really important for
making boundaries for the system. Having an idea of what are the goals the user wants to reach
for the output power during improving economical load dispatch.
One of the factors we don’t consider is the frequency and voltage. These two factors are mainly
taken in account for power quality. Power quality mainly focuses in maintaining the near
sinusoidal waveform of power distribution bus voltages and currents at rated magnitude and
frequency and this is very relevant for the transmission lines. Since our main concern is to
improve the of a power unit, we do not focus in the power quality.
Because of the big amount of thermal power plants and simplicity, we consider in this research
the presence of only thermal power plants.

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1.4. Approach and methodology
In many design applications in engineering and industry, we have to try to find the
optimal solution to a given problem under highly complex constraints. Such constrained
optimization problems are often highly nonlinear. To be able to find the optimal solution is very
difficult, challenging and sometimes impossible due the complexity of its constraints.
Most conventional optimization do not work well for problems with nonlinearity and
multimodality.
Methods nowadays is to use nature-inspired metaheuristic algorithms to approach such difficult
problems, and it has been shown that metaheuristics are surprisingly very efficient. For this
reason, the literature of metaheuristics has expanded tremendously[4,5]. Up to now, researchers
have only use a very limited characteristics inspired by nature, and there is room for more
algorithm development.
In this paper, we will propose an algorithm based on the flower pollination process of flowering
plants.
From the biological evolution point of view, the objective of the flower pollination is
the survival of the fittest and the optimal reproduction of plants in terms of numbers as well as
most fittest. The main idea of flower pollination is to achieve optimal reproduction of the
flowering plants. Therefore, this can inspire to design new optimization algorithm. The basic
idea of flower pollination in the context of bees and clustering was investigated before [6], but
in this paper, we will rewrite flower pollination algorithm characteristics for simplicity and to
improve the optimization, efficiency and execution time.
1.5. Outline of report
In this paper, we will review a new algorithm based on the flower pollination process of
flowering plants.
We will first briefly have a look at the history of metaheuristic algorithms. Trying to have a
basic idea how algorithms started and the different types of existing algorithms. The idea of
this is to gain some basic knowledge of algorithms and learn from the drawbacks of existing
algorithms so we can avoid them for our own algorithm.
Then we will review the main characteristics of flower pollination, and thus idealize these
characteristics into four rules. We will then use them to develop a flower pollination algorithm
(FPA), or the flower algorithm. An analysis has to be done using flowcharts and pseudo codes
in order to understand FPA and prevent any misunderstandings.
Then, we validate it using a set of well-known test functions and design benchmark. We analyze
the simulations and make comparison of its performance with 2 fuzzy logic controlled genetic
algorithm (FCGA), (CGA) and Cuckoo Search Algorithm (CSA).
Finally, we discuss further topics for rewriting this algorithm for simplicity and further
improvements.

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2. Algorithms
2.1. History
So far a large number of techniques using mathematical programming have been widely applied
for solving these problems. The most utilized ones are called deterministic algorithms namely:
 Dynamic programming (DP)[7]
 Newton’s method [7]
 Lambda iteration method [8]
 Gradient method [9]
 Linear programming (LP) [10]
 Lagrangian relaxation algorithm [11]
Most of these deterministic methods focused on the systems with simple constraints and
differential objective function where nonlinear constraints and valve point loading effects were
not considered[12].
For example, the inventors of Newton’s method, created a simple fuel cost function, for solving
the ELD problem but with only linear constraints. The problem was that is not applicable for
realistic representation. After Newton’s method, a representation of the generation cost function
for fossil fuel fired plant was introduced, and it was more realistic because a quadratic function
and valve points effects in a thermal unit were considered[13].
The characteristic of the ELD problem becomes more complicated as generating units can be
supplied with multiple fuel (MF) sources (such as gas and oil) to produce electricity or each
generating unit has to satisfy its own physical constraints including limits on generation,
prohibited operating zones and system spinning reserve constraint[14,15].
These methods can be only applicable to thermal units where the cost function is represented
by a simple quadratic function and the valve-effect are neglected[16].
Other modern methods called metaheuristic algorithms have been recently applied for solving
ELD problems:
 Differential evolution (DE)
 Evolutionary programming (EP) (mutation and crossover and selection)[17,18]
 Genetic algorithm (GA) [19-21]
 Simulated annealing
These methods are considered as the fastest and advanced algorithms because of their inherent
parallel search technique.
These algorithms are advantageous because it possess good properties like [4]:
 global search capability
 Robust
 Effective constraints handling capacity
 Reliable performance
 Minimum information requirement

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These good properties makes it a potential choice for solving ELD problems in realistic
situations. These 3 algorithms excluding Simulated Annealing Algorithm consist of three main
operators to be able to function, namely[22]:
1. Mutation
2. Crossover
3. Selection
Mutation
In simple terms, mutation may be defined as a small random tweak in the chromosome, to get
a new solution. It is used to maintain and introduce diversity in the genetic population and is
usually applied with a low probability. If the probability is very high, the GA gets reduced to
a random search. Mutation is the part of the GA which is related to the “exploration” of the
search space.
Crossover
The crossover operator is analogous to reproduction and biological crossover. In this more
than one parent is selected and one or more off-springs are produced using the genetic material
of the parents. Crossover is usually applied in a GA with a high probability.
Selection
The Selection Policy determines which individuals are to be kicked out and which are to be
kept in the next generation. It is crucial as it should ensure that the fitter individuals are not
kicked out of the population, while at the same time diversity should be maintained in the
population
GA is the method early applied for solving optimization problems in engineering field,
especially in electrical engineering. . GA still suffers several disadvantages such as
prematurely converge in local optima and long execution time. Prematurely converging means
that the convergence will be so fast that it finds local minimum instead of the global optima.
This happens because local minimum is easier to find than the global minimum.
SA is a better probabilistic approach which is applicable for finding global optima of a cost
function that may possess several local minima but it converges slower than then GA and EP
DE is more popular because of its simple and compact structure with few control parameter.
The DE method can be considered as a more powerful method than the others since it can
obtain better solution quality with shorter computation time for optimization problems and this
method has been widely used in power system optimization problems in power systems.

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But faster convergence does not mean a higher percentage of finding the global optima. Most
algorithms suffers from this drawback of premature convergence. The only way of overcoming
this drawback is by increasing a larger population. However, this will lead to time consuming
to estimate the global optima.
A new method has been created named Hopfield neural network (HNN). It is a method
focusing on the minimization of its energy function. HNN is efficient and applicable for large
scale system. But as mentioned before, it may require long computation time and may also
converge to local minimum solution instead of the global minimum solution[23, 24].
Particle swam optimization (PSO) is another algorithm created in 1995 by Kennedy and
Eberhart. PSO shares many similarities with evolutionary computation techniques such as
Genetic Algorithms (GA). The system is initialized with a population of random solutions and
searches for optima by updating generations. However, unlike GA, PSO has no evolution
operators such as crossover and mutation. In PSO, the potential solutions, called particles, fly
through the problem space by following the current optimum particles[25, 26].
Each particle keeps track of its coordinates in the problem space which are associated with the
best solution (fitness) it has achieved so far. (The fitness value is also stored.) This value is
called pbest. Another "best" value that is tracked by the particle swarm optimizer is the best
value, obtained so far by any particle in the neighbors of the particle. This location is
called lbest. when a particle takes all the population as its topological neighbors, the best value
is a global best and is called gbest. However, the performance of the traditional PSO greatly
depends on its parameters and it often suffers from the problem of being trapped in local optima.
Harmony search is a music-based metaheuristic optimization algorithm. It was inspired by the
observation that the aim of music is to search for a perfect state of harmony. This harmony in
music is analogous to find the optimality in an optimization process. Again, the HS can get the
premature convergence in the performance[27].
Biogeography is the study of the geographical distribution of biological organisms. The
mathematics of biogeography inspired the development of a new algorithm: biogeography-
based optimization (BBO)[28].

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As it can be seen, each method that has been mentioned has their advantage and disadvantage
to solve ELD problems. Many researchers tried to combine many different algorithms to exploit
the advantages, expand the searching capability and increase the efficiency. These combined
algorithms are called hybrid algorithms. Most well-known hybrid algorithms are:
 Hybrid GA-PS-SQP algorithm [29]
 Hybrid stochastic search (HSS) [30]
 Hybrid genetic algorithm [31]
These hybrid algorithms can perform better than other mentioned algorithms, but they suffer
from difficulty of selecting many controllable parameters.
Many new and improved algorithms have been develop for solving ELD problem. One of the
most popular ones are Cuckoo Search Algorithm (CSA) and its improved version One Rank
Cuckoo Search Algorithm(ORCSA).
Cuckoo search is an optimization algorithm developed by Xin-she Yang and Suash Deb in
2009. It was inspired by the obligate brood parasitism of some cuckoo species by laying their
eggs in the nests of other host birds (of other species). Some host birds can engage direct
conflict with the intruding cuckoos. For example, if a host bird discovers the eggs are not their
own, it will either throw these alien eggs away or simply abandon its nest and build a new nest
elsewhere[32].
Cuckoo search (CS) uses the following representations:
Each egg in a nest represents a solution, and a cuckoo egg represents a new solution. The aim
is to use the new and potentially better solutions (cuckoos) to replace a not-so-good solution in
the nests. In the simplest form, each nest has one egg. The algorithm can be extended to more
complicated cases in which each nest has multiple eggs representing a set of solutions[32].
CS is based on three idealized rules:
1. Each cuckoo lays one egg at a time, and dumps its egg in a randomly chosen nest;
2. The best nests with high quality of eggs will carry over to the next generation;
3. The number of available hosts nests is fixed, and the egg laid by a cuckoo discovered
by the host bird with a probability. Discovering operate on some set of worst nests, and
discovered solutions dumped from farther calculations.
After improving the cuckoo search, the One Rank Cuckoo Search Algorithm became more
effective than any other algorithm[33,34].

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After a year a new algorithm considered better then Cuckoo Search algorithm or ORCSA was
created. The Symbiotic Organism Search Algorithm (SOS) and its modified version (MSOS)
made in 2014. The nature-inspired philosophy of SOS algorithm is analogous to the interactive
behavior among organisms in nature. Organisms in the real world rarely live in isolation due to
dependence on other species for sustenance and survival. In general, organisms develop
symbiotic relationships as a strategy to adapt to changes in their environment[35].
This new algorithm depends on 3 essential cycles to be able to function, called[36]:
 Mutualism phase
 Commensalism phase
 Parasitism phase
By performing this three phases, SOS attempts to move a population, called an ecosystem of
possible solutions, to promising areas of the search space during the search for the optimal
solution.
Mutualism phase
This relationship category describes the symbiotic relationship between two different species
that benefit mutually from that relationships. Bees fly amongst flowers, gathering nectar to turn
into honey. While this activity benefits bees, it also benefits flowers because pollen distribution
is a side effect of this process.
Commensalism phase
in which one benefits and the other is unaffected or neutral. The remora attaches itself to the
shark and eats food leftovers, thus receiving a benefit. The shark is unaffected by remora fish
activities and receives minimal, if any, benefit from the relationship
Parasitism phase
in which one benefits and the other is actively harmed. The plasmodium parasite uses its
relationship with the anopheles mosquito to pass between human hosts. While the parasite
thrives and reproduces inside the human body, its human host suffers malaria and may die as
a result.

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Figure 1 SOS flowchart
Based on the test result comparisons, researchers have concluded that the MSOS was superior
to CCSA and ORCSA; however, the conclusion should be reevaluated because the execution
time for obtaining optimal solution from MSOS is higher than that from CCSA and
ORCSA[35].
After these interesting research and studies many other algorithms have been recently created,
because the ELD problem with different constraints and large scale have attracted more and
more attention from researchers. For example:
 Teaching-learning-based Optimization
 Oppositional Real Coded Chemical Reaction Optimization
 Species-based Quantum Particle Swarm Optimization
 Cross Entropy Method with Sequential Quadratic Programming
 Traverse Search Method
 Oppositional Invasive Weed Optimization
 Improved Differential Evolution
 Immune Algorithm with Power Redistribution
 Colonial Competitive Differential Evolution
 Chaotic Bat Algorithm
 Exchange Market Algorithm
 Combination of Continuous GreedyRandomized Adaptive Search Procedure Algorithm
And many others….

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2.2. Flower Pollination Algorithm
In this paper, we will propose a new algorithm based on the flower pollination process of
flowering plants. Flower pollination algorithm (FPA) is a metaheuristic algorithm that was
developed by Xin-She Yang (2012), based on the pollination process of flowering plants. From
the biological evolution point of view, the objective of the flower pollination is the survival of
the fittest and the optimal reproduction of plants in terms of numbers as well as most fittest.
This is in fact an optimization process of plant species [37].
Pollination is the process by which pollen is transferred to the female reproductive organs of a
plant, thereby enabling fertilization to take place. Like all living organisms, seed plants have a
single major goal: to pass their genetic information on to the next generation. The reproductive
unit is the seed, and pollination is an essential step in the production of seeds in
all spermatophytes (seed plants) [38].
There are two types of pollination, namely:
 Self-pollination
Type of pollination which occurs in a single plant either in two ways: within the same
flower (also called intra floral pollination) or between two flowers
 Cross-pollination
Transfer of pollen from the anther in a flower in one plant to the stigma in a separate
flower in another plant. Cross-pollination, therefore, necessarily involves two flowers
and two plants.
There are 2 types of pollinators, namely:
 Abiotic
Refers to situations where pollination is mediated without the involvement of other
organisms. The abiotic pollinators are the wind and water, the latter with a limited
occurrence to a few aquatic plants[39].
 Biotic
Organisms that carry or move the pollen grains from the anther of one flower to the
receptive part (stigma) of another. Such as insects, birds, bats and other animals. In fact,
some flowers and insects have co-evolved into a very specialized flower-pollinator
partnership[39]. For example, some flowers can only attract and can only depend on a
specific species of insects. This will maximize the transfer of flower pollen to the same
or conspecific plants, and thus maximizing the reproduction of the same flower
species(flower constancy) [37].

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Figure 2 Flower Pollination
Now we can idealize the above characteristics of pollination process, flower constancy and
pollinator behavior as the following rules [37]:
1. Biotic and cross-pollination are considered as global pollination process with pollen
carrying pollinators performing Lévy flights.
2. Abiotic and self-pollination are considered as local pollination.
3. Flower constancy can be considered as the reproduction probability is proportional to
the similarity of two flowers involved.
4. Local pollination and global pollination is controlled by a switch probability p ∈ [0, 1].
Due to the physical proximity and other factors such as wind, local pollination can have
a significant fraction p in the overall pollination activities.

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In the real world, a plant has multiple flowers and the flower patches release a lot of pollen
gametes. For simplicity, it is assumed that each plant has one flower producing a single pollen
gamete. Due to this simplicity, a solution ( ) in the present optimization problem is equal to a
flower or a pollen gamete. For multi-objective optimization problems, multiple pollen gametes
can be considered.
In the flower pollination algorithm, there are two key steps involving global and
local pollination. In the global pollination step, the first and third rules are used
together to find the solution of the next step ( ) using the values from the
previous step (step t) defined as . Global pollination is formulized in Eq.(1) [40]
1
( *)t t t
i i iX X L X g
   (1)
The subscript i represents the ith
pollen (or flower) and Eq. (1) is applied for the
pollen of the flowers. g* is the current best solution. Since insects may move over a long
distance with various distance steps, we can use a Lévy flight to mimic this characteristic
efficiently [1]. That is, we draw L > 0 from a Levy distribution.
1
( )sin( )
12 *
T
L
s 

 
 
 (2)
The second rule is used for local pollination with the fourth rule about flower constancy. The
new solution is generated with random walks as seen in Eq. (3).
1
( )t t t t
i i j kX X X X
   (3)
where and are solutions of different plants. ε is randomized combination of .
According to the fourth rule, a switch probability (p) is used in order to choose the
type of pollination which will control the optimization process in iterations[40].
2.2.1. Pseudo Code
Flower Pollination Algorithm (FPA)
Objective min or max ( ), = ( , , … ) using matrices
Set control parameters: Np, , , PD and data
Initialize a population of n flowers/pollen gametes with random solutions
Generate a using formula = + ( − ) ∗ (2,n)
Calculate objective function and find best solution g* in the initial population
Define a switch probability ɛ[0,1]
while ( < )
if rand(1,n)<p
logic=1
draw a (d-dimensional) step vector L from a Lévy distribution
else
logic=0
Draw ɛ from a uniform distribution in |[0,1]
end if
The formula (Global*logic)+(Local*(1-logic)) will be applied
= ( + ( − g ∗) ∗ ) + ( + ɛ ( − ) ∗ (1 − Logic))
Evaluate new solution
If new solutions are better, update them in the population
Find the current best solution g*
end while
Output min_cost, max_cost, aver_cost, std_ved and aver_time

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Step 1
In this phase the user has to set the control parameters. Define the number of population, the
desired iterations, probability switch, load demand and all data about the units. The data
contains all information about the units, for example their max/min input power or the maxx or
minx . For the probability switch the user has to choose a value between 0 and 1.
Step 2
After entering all parameters and data, will be generated using the formula
min max min( )*i ix x x x rand   (4)
After generating we substitute it in the objective function ( ). The objective function
depends on the system the user is working with. If it is for a hydropower plant, the objective
function will be totally different than from a thermal power plant.
After getting we have to choose the current best solution (g*). The current best solution is
considered the with the lowest value.
For preventing confusion in the MATLAB code, we rename the variables and to _
and _ and these will be the variables that will be used when entering the loop.
After this we reset the counters back to 1 in order for the next run to work properly.
Step 3
In this phase the user has already chosen a value for the probability switch. is a value between
0 and 1. According to researches 0.8 is the best value for a , but of course it depends on the
type of system, load demand and amount of iterations.
A logic function has been created. Logic function is just a series of 0’s and 1’s. The amount of
1’s and 0’s depends on the number of population and the value of the probability switch.
log (1, )pic rand N p  (5)
The dimension of the matrix rand depends on the number of population. MATLAB will choose
a random number, if rand is smaller than then you will have 1’s, otherwise only 0’s.
A new will be generated according to this formula
*log *(1 log )ix Global ic Local ic   (6)
If is equal to 1, then global pollination will take place.
1
( *)t t t
i i iX X L X g
   (7)
If is equal to 0 then local pollination will take place.
1
( )t t t t
i i j kX X X X
   (8)
Because of working with matrices, all population will be calculated in this step. By making a
modification in this step and also working with matrices, the execution time will be shorter.

21
With a small number of population, the benefits will not be seen. But in the moment of
introducing a big amount of population, this improved algorithm will be really useful.
Step 4
In this phase the user has already chosen the number of population. Depending on the number
of population the user can proceed to the next step. If all population are not satisfied, then the
program will go back to step 3 and run the same process for each population until all of them
are satisfied.
Step 5
In this phase we introduce the penalizing method. In step 1 the user already chose a value for
minx or maxx . If newx is bigger than maxx , we penalize it and put it equal to maxx . if newx is smaller
than minx , then we penalize it and put it equal to maxx . this method is being used to keep the
process between boundaries.
Thus if maxx =10 and newx =15, then we penalize it and the new answer will be newx =10
Step 6
In this phase the program calculates the new fittest function and a comparison will be made.
The comparison will be held between the new fittest result ( ) and the old fittest result
( _ ). Same process with the new global best result ( newx ) and the old global best result
( _ ).
After this a selection will be made between the old and new result. The objective fittest result
with the lowest value is considered the best one. The other results are not relevant anymore so
it will be deleted. After this process the new result will remain in the loop.
Step 7
In this phase the user has already chosen the number of iteration. If each steps are satisfied, the
program has to repeat the same process again according to the number of iteration chosen by
the user. The higher the amount of iterations, the more accurate the answer will be. But also the
higher the amount of iteration, the longer the execution time will be. So the user has to be
careful with choosing the number of iterations
Step 8
This phase is the end result. Here the program will show the user the end result. Depending on
the number of population, number of iterations and parameters, the end result will be different.
The purpose of the end result is to show the user the minimum cost he should invest on
generating real power while satisfying the loads and the losses in the transmission links. Also
the execution time will be shown in order to show if the algorithm is efficient enough in
comparison to others algorithms and max cost, average cost and standard deviation.

22
2.2.2. Flowchart
Set control parameters:
Np, , , PD
and data
rand<p
True
False
Global pollination
+ ( − g ∗)
Local pollination
+ ɛ ( − )
True
i=i+1
Show min_cost, max_cost, aver_cost,
std_ved and aver_time
G=Gmax
False
False
STOP
G=G+1
i > Np
True
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Figure 3 FPA flowchart
- Generate
- Calculate fittest function
- Choose Xbest and Gbest
- _ =
- _ =
- Set counter G and i= 1
Initialize population
Penalizing:
Xnew(Xnew>Xmax)=Xmax(Xnew>Xmax)
Xnew(Xnew<Xmin)=Xmin(Xnew<Xmin)
- Calculate fittest function
- Compare _ with
- Compare _ with
- Choose Xbest_new and
Fbest_new
Step 7
Step 8

23
2.2.3. Test function
Xin-she Yang used several functions to test it with Flower Pollination algorithm to measure its
effectiveness. In order to measure its effectiveness, he compared the results with Genetic
Algorithm(GA) and Particle Swarm Optimization Algorithm(PSO).
The functions used for testing are:
 The Ackley function can be written as [43]
 De Jong’s functions is the so-called sphere function [43]
 Easom’s function [43]
 Griewangk’s function [43]
 Michaelwicz’s function [43]
 Rastgrin’s function [43]
 Rosenbrock’s function [43]
 Schwefel’s function [43]
 Yang’s forest-like function [43]
 Shubert’s function [43]
Functions GA PSO FPA
Michalewicz (d=16) 89325±7914(95%) 6922±537(98%) 3341±649(100%)
Rosenbrock (d=16) 55723±8901(90%) 32756±5325(98%) 5532±1464(100%)
De Jong (d=256) 25412±1237(100%) 17040±1123(100%) 4245± 545(100%)
Schwefel (d=128) 227329±7572(95%) 14522±1275(97%) 6851± 448(100%)
Ackley (d=128) 32720±3327(90%) 23407±4325(92%) 3357± 968(100%)
Rastringin 110523±5199(77%) 79491±3715(90%) 10840± 2689(100%)
Easom 19239±3307(92%) 17273±2929(90%) 4017±982(100%)
Griewank 70925±7652(90%) 55970±4223(92%) 4918± 1429(100%)
Yang (d=16) 27923±3025(83%) 14116±2949(90%) 4254± 1839(100%)
Shubert (18 minima) 54077±4997(89%) 23992±3755(92%) 9271± 1758(100%)
Three algorithms have been used to find the optimal solution with a given tolerance 10 .
For each algorithm, 100 iteration have been run using a population size of Np=25 and p=0.8
for FPA, crossover probability 0.95 and mutation probability 0.95 and mutation probability
0.05 for GA, and learning parameters 2 for PSO. The results are summarized in table 1.
In the table, the results are provided as mean ± standard deviation (success rate). For example,
3341 ± 649(100%) means that mean number iterations is 3341 with one standard deviation of
649 and a success rate of 100%. The total number of function evaluations is n times the mean
number of iterations. For example, the number of iterations is 3341 in the table, so the total
number of function evaluations is 3341n = 3341 × 25 = 83525.
Table 1: Comparison of algorithms performance in terms of number of iterations

24
2.3. Execution of assignment
This chapter will explain how the assignment will be executed. Firstly, a mathematical
explanation will be given in order to understand to theory, then a small background of the
assignment will be given with information about each step taken in order to reach the global
optima solution.
2.3.1. Problem formulation
The objective of the ELD problem is to minimize the total cost of thermal units as follows:
1
( )
N
i i
i
MinF F P

  (9)
Where i represents the number of power unit.
In the classical ELD problem, the fuel cost of each generating unit is expressed as a quadratic
function of its power output, as the generating units can only use one fuel option or multiple
fuel options to generate electricity and the valve point effects considered.
The fuel cost function is given as:
2
,min( ) | *sin( *( ))i i i i i i i i i i iF P a b P c P e f P P     (10)
Subject to
Power balance constraint: The total power generated from a set of available units must satisfy
the total load demand and system power losses:
1
0
N
i D L
i
P P P

   (11)
where power loss is calculated using Kron’s formula:
0 00
1 1 1
N N N
L i ij j i i
i j i
P PB P B P B
  
    (12)
Generator capacity limits: The real power output of thermal units should be in their range
between the minimum limit and maximum limits:
,min ,maxi i iP P P  (13)

25
2.3.2. Implementation of FPA for ELD problems
Handling power balance constraint
The slack variable technique is used in this paper for handling equality constraints i.e. power
balance constraint. The slack variable technique is a way to guarantee that the equality
constraint is always satisfied where a slack variable is calculated based on the other variables
from the equality constraint. In this paper, the first generating unit is chosen as the slack variable
so that the sum of power output from the slack unit and the rest of ones equals to the load
demand plus power losses in transmission lines. Therefore, suppose the power output of the N-
1 generating units from 2 to N is known, the power output of the slack unit 1 is calculated based
on (11) as follows:
1
2
N
D L i
i
P P P P

    (14)
The power loss equation in (12) is rewritten with respect to an unknown variable of by 1P as:
11 1 1 01 1 0 00
2 2 2 2
² (2 )
N N N N
L i i i ij j i i
i i j i
P B P B P B P PB P B P B
   
        (15)
Substituting LP in (15) into (14), a quadratic equation is obtained:
1 1* ² * 0A P B P C   (16)
Where the coefficients A, B and C are determined by:
11A B (17)
1 01
2
2 1
N
i i
i
B B P B

   (18)
0 00
2 2 2 2
N N N N
i ij j i i D i
i j i i
C PB P B P B P P
   
       (19)
The power output of the slack unit with positive value is chosen between the two roots obtained
by solving second order Eq.(16) as below:
1
² 4
2
B B AC
P
A
  
 , where ² 4 0B AC  (20)
As a result , the equality constraint (11) is easily maintained due the slack unit
Initialization
For implementation of FPA method to the problem, there are pN flower in the population
where each flower represented by dX (d=1,…. pN ) containing thermal unit 2- 1N those are

26
,si dP (i=2,… 1N ). The thermal unit generation satisfying ,min ,m, ,maxsi si d siP P P  are randomly
initialized as follows.
, ,min ,max ,min*( );i d i i i iP P rand P P   i=2,….,N (21)
Where irand is a random number between [0,1]. Each flower corresponding to a solution needs
to be evaluated to improve obtained solution after each iteration. Therefore, the evaluation is
performed based on fitness function defined as below.
lim
, 1
1
( ) *( )²
N
d i di s i d
i
FT F X K P P

   (22)
Where sK is a penalty factors for the slack unit and spinning reserve constraint, respectively;
,i dP is the power output of the slack thermal unit 1 corresponding to flower d in the population.
The limit of the slack thermal unit 1 in (22) has not been predetermined but used to penalize
the invalid flower for handling equality constraints. The limit is obtained by:
Global search
If the random number chosen by MATLAB is smaller than the probability switch, then global
search will take place
1
( *)t t t
i i iX X L X g
   (23)
The subscript i represents the ith
pollen (or flower) and Eq. (23) is applied for the
pollen of the flowers. g* is the current best solution. Since insects may move over a long
distance with various distance steps, we can use a Lévy flight to mimic this characteristic
efficiently [1]. That is, we draw L > 0 from a Levy distribution.
Local search
If the random number chosen by MATLAB is bigger than the probability switch, then global
search will take place
1
( )t t t t
i i j kX X X X
   (24)
where and are solutions of different plants. ε is randomized combination of .
According to the fourth rule, a switch probability (p) is used in order to choose the
type of pollination which will control the optimization process in iterations.
Stopping criterion
In the FPA method, the stopping criterion for the algorithm is based on the maximum number
of iterations. The algorithm is terminated as the maximum number of iterations is reached
Selection of parameters
The most important parameter of the FPA method is the probability switch p which has a great
effect on the final solution. This parameter should be tuned for each system since it is a number
in the range [0,1] and there are no criteria for a proper selection of this parameter. Therefore,
the effect of p on the final solution by the FPA method for each test system will be analyzed
with the value of p varying from 0.1 to 0,9 with step size of 0.1 to obtain the most suitable value
for each system.

27
2.3.3. Execution of FPA method
The assignment will be executed in an university environment. The student has the duty to re-
write the FPA code in to a more simple and effective way. After accomplishing this, the student
will receive realistic data of a 6 unit thermal power plant, where it has to be run by the FPA
code made by the student. This 6 unit data have been tested before with 2 fuzzy logic controlled
genetic algorithm (FCGA)[51], (CGA) [51] and Cuckoo Search Algorithm (CSA). so the
global optima solution are known already.
The mentor will show the global optimal solution and the student has to accurately reach this
minimum solution with the Re-written FPA code.
In order to get the best global optima result when running the code, the user has to follow these
3 key steps:
 Selection of parameter
 Standard deviation
 Iteration
Selection of parameter
The probability switch is an important factor in the FP algorithm. This determines if the solution
will be global or local.
MATLAB will choose a random number, if the random value is lower than the chosen p value,
then global pollination will take place, otherwise local pollination.
In order to determine the best p value, a modification in the code has to take place. The idea is
to run the code 10 times testing each p from 0 to 1 with steps of 0.1
p=0;
for run_p=1:10
p=p+0.1;
end
Figure 4 Probability switch

28
After getting 10 runs, the p that shows the most accurate global optima result will be the most
efficient p to be used in this problem.
Standard deviation
Standard deviation is a measure that is used to quantify the amount of variation or dispersion of
a set of data values. A low standard deviation indicates that the data points tend to be close to
the mean of the set, while a high standard deviation indicates that the data points are spread out
over a wider range of values[50]. Thus the lower the standard deviation of a global minimum,
the most accurate it is.
0.5
(cos _ cos )²
_ ( )
max_
t aver t
std dev
run


 (26)
Standard deviation is being used when there are many global results with the same value. The
only way to choose the most efficient global minimum, is by analyzing the standard deviation
and choosing the lowest one.
Iteration
The lower the iteration, the lower the execution time. If the execution time is small the faster
the algorithm works, thus it becomes more efficient. When working with a big size population
the execution time becomes an important factor. But a drastic low iteration means that the global
answer might not be accurate enough. That is why a test has to be done in order to choose the
right amount of iteration that maintain the execution time low and accuracy high.
2.4. Results
This chapter shows all the results gotten from the FP algorithm. The mentor has given the
student 3 different 6 unit system with load demands of 800MW, 1200MW and 1800MW. All 3
should be tested in order to choose the proper p, iteration and accurate global minimum.
These units has been already tested before with 2 fuzzy logic controlled genetic algorithm
(FCGA)[51], (CGA) [51] and Cuckoo Search Algorithm (CSA). Thus the global optima results
are already known. Now it is time to test the 3 different 6 unit systems with the Flower
Pollination Algorithm.
Several runs have been made but only three of them are shown to see the behavior of the system.
Firstly the probability p will be tuned in the range from 0.1 to 0.9 with a step of 0.1 then we
start with the max iteration, where the global optimal result is accurate but the execution time
is really high. Then we decrease the iteration till the global optima value is maintained, if the
global optima increases then we stop decreasing the iterations and this will be the official global
optima result.
In order to show the reader the best result in a 1 run, I black bolded the row with best result.
During the execution of the assignment 6 important factors are shown in order to make a
selection of the best result, namely probability switch, minimum cost (global optima),
maximum cost, standard deviation, average time (CPU time)

29
6 unit system with load demand of 800MW
P MIN_COST
($/H)
AVER_COST
($/H)
MAX_COST
($/H)
STD_VER
($/H)
AVER_TIME
($/H)
0.1 8227.0968 8227.1652 8228.1006 0.147 0.025
0.2 8227.0968 8227.1298 8227.4877 0.0718 0.0227
0.3 8227.0968 8227.1274 8227.4733 0.0635 0.0227
0.4 8227.0968 8227.1248 8227.5035 0.0683 0.022
0.5 8227.0969 8227.123 8227.6058 0.0619 0.0206
0.6 8227.0974 8227.1252 8227.3155 0.0373 0.0228
0.7 8227.0986 8227.157 8227.465 0.066 0.0244
0.8 8227.1082 8227.2355 8227.7955 0.1197 0.0211
0.9 8227.1369 8227.6109 8229.0209 0.435 0.0213
1 8227.1382 8233.6439 8270.2216 7.3359 0.0214
P MIN_COST
($/H)
AVER_COST
($/H)
MAX_COST
($/H)
STD_VER
($/H)
AVER_TIME
(S)
0.1 8227.097 8227.3057 8232.3526 0.6357 0.013
0.2 8227.0976 8227.1969 8227.8556 0.1671 0.0116
0.3 8227.0984 8227.1702 8227.7952 0.1001 0.0113
0.4 8227.1002 8227.1935 8227.6074 0.1141 0.0123
0.5 8227.0982 8227.2982 8228.4778 0.2573 0.0123
0.6 8227.1134 8227.3356 8229.4048 0.2669 0.0117
0.7 8227.1289 8227.5756 8232.8279 0.6616 0.0113
0.8 8227.134 8228.0984 8232.7449 1.0948 0.0113
0.9 8227.1023 8229.3448 8245.8838 3.0044 0.0117
1 8227.1699 8241.9782 8371.6965 18.3271 0.0116
P MIN_COST
($/H)
AVER_COST
($/H)
MAX_COST
($/H)
STD_VER
($/H)
AVER_TIME
($/H)
0.1 8227.1032 8227.5616 8229.939 0.5297 0.0089
0.2 8227.1319 8227.8351 8232.5882 0.8973 0.0075
0.3 8227.1128 8227.9364 8243.6002 1.7184 0.008
0.4 8227.1271 8228.0402 8230.4628 0.8436 0.0073
0.5 8227.1305 8228.7377 8243.9592 2.5032 0.0072
0.6 8227.161 8228.7888 8240.786 2.0618 0.0069
0.7 8227.2143 8230.0134 8244.3823 3.4533 0.0067
0.8 8227.4802 8231.5958 8261.0997 5.6255 0.0069
0.9 8227.2654 8234.2135 8263.1565 7.6042 0.0066
1 8227.8939 8243.3298 8301.3018 13.8535 0.007
Table 2 Result obtained by FPA for the 6 unit system for load demand of 800MW with different values of p.
300 iterations
175 iterations
100 iterations

30
As observed from the tables 2, 3 and 4 the best solution for the 800 MW load demand is obtained
at p= 0.1 and the most global iteration is reached at 100
As seen in table 5 the CSA and FPA algorithms have the same global minimum result. As
observed the cpu time for FPA is nearly 1600 times faster than the CGAs and 4 times faster
than CSA. This is a big advantage for the FPA when working with a big size population.
Figure 6 Fitness convergence characteristic 800MW Figure 5 Determining the best p
Figure 6 shows the fitness convergence characteristic of this system. When the iteration is
between 10 and 20 it is far away from the global optima. As soon as the iteration is increased
to 100 it remains stable in global minimum zone. Thus at 100 is the most efficient iteration to
use in this system.
8226.6000
8226.8000
8227.0000
8227.2000
8227.4000
8227.6000
8227.8000
8228.0000
0.10.20.30.40.50.60.70.80.9 1
FitnessFunction($)
p
Determining the best P
LOAD DEMAND ALGORITHM COST
($/H)
CPU TIME
(S)
800 CGAs 8232.89 14.46
800 FCGAs 8231.03 5.62
800 CSA 8227.100 0.031
800 FPA 8227.100 0.0089

31
P MIN_COST
($/H)
AVER_COST
($/H)
MAX_COST
($/H)
STD_VER
($/H)
AVER_TIME
(S)
0.1 11477.0899 11477.0936 11477.1457 0.0093 0.0164
0.2 11477.0899 11477.0919 11477.1343 0.0048 0.0141
0.3 11477.0899 11477.0928 11477.1425 0.0065 0.0142
0.4 11477.09 11477.0927 11477.1328 0.0048 0.0139
0.5 11477.0899 11477.095 11477.1525 0.0076 0.0142
0.6 11477.0901 11477.0975 11477.1367 0.0073 0.0144
0.7 11477.0902 11477.1025 11477.1466 0.0109 0.0152
0.8 11477.0916 11477.1131 11477.1833 0.0174 0.0144
0.9 11477.0911 11477.1403 11477.7967 0.0736 0.0139
1 11477.096 11478.431 11495.25 3.15 0.014
P MIN_COST
($/H)
AVER_COST
($/H)
MAX_COST
($/H)
STD_DEV
($/H)
AVER_TIME
(S)
0.1 11477.0899 11477.0941 11477.1614 0.0091 0.0172
0.2 11477.0899 11477.0936 11477.1422 0.006 0.0144
0.3 11477.09 11477.0942 11477.1363 0.0058 0.0136
0.4 11477.0902 11477.0954 11477.1143 0.005 0.0144
0.5 11477.0901 11477.0982 11477.1287 0.0073 0.0142
0.6 11477.0901 11477.1064 11477.1953 0.0173 0.0144
0.7 11477.0904 11477.1178 11477.3481 0.0317 0.0142
0.8 11477.0939 11477.132 11477.2132 0.0283 0.0138
0.9 11477.0918 11477.1922 11478.1787 0.137 0.0138
1 11477.099 11478.27 11495.666 2.452 0.016
P MIN_COST
($/H)
AVER_COST
($/H)
MAX_COST
($/H)
STD_VER
($/H)
AVER_TIME
($/H)
0.1 11477.09 11477.0975 11477.1437 0.0105 0.0187
0.2 11477.0902 11477.0986 11477.1572 0.0098 0.015
0.3 11477.0912 11477.1027 11477.1487 0.0124 0.0134
0.4 11477.0904 11477.1049 11477.1621 0.0153 0.0144
0.5 11477.0911 11477.1158 11477.1817 0.0216 0.0156
0.6 11477.0904 11477.1255 11477.3103 0.0359 0.0163
0.7 11477.091 11477.1384 11477.2481 0.0359 0.0148
0.8 11477.0935 11477.174 11477.4322 0.0627 0.0161
0.9 11477.0901 11477.2412 11477.7886 0.1378 0.015
1 11477.11 11478.389 11489.305 1.963 0.013
Table 6 Result obtained FPA for the 6 unit system for load demand of 1200MW with different values of p.
200 iterations
Table 7 Result obtained FPA for the 6 unit system for load demand of 1200MW with different values of p
175 iterations
Table 8 Result obtained FPA for the 6 unit system for load demand of 1200MW with different values of p
150 iterations

32
As observed from the tables 6, 7 and 8 the best solution for the 1200 MW load demand is
obtained at p= 0.2 and the global iteration is reached at 175. As seen in table 8 that both p=0.1
and p=0.2 have the same minimum cost. To select the global optima result we have to analyze
the standard deviation. As shown p=0.2 has the lowest standard deviation. Thus p=0.2 is the
global optima result. In table 8 and 9 it can be clearly seen that the global minimum has changed
from 11477.0899 to 11477.0900. As mentioned before, the global optima is the lowest
minimum cost in the system. Thus, it is concluded that the global optima is reached at 175
iteration instead of 150 iteration
Figure 7 Determining the best P
11477.0850
11477.0900
11477.0950
11477.1000
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
FitnessFunction($)
P
LOAD DEMAND ALGORITHM COST
($/H)
CPU TIME
(S)
1200 CGAs 11493.74 17.83
1200 FCGAs 11480.03 7.43
1200 CSA 11477.09 0.031
1200 FPA 11477.0899 0.0144

33
P MIN_COST
($/H)
AVER_COST
($/H)
MAX_COST
($/H)
STD_VER
($/H)
AVER_TIME
(S)
0.1 16579.3339 16579.3363 16579.3543 0.0039 0.0209
0.2 16579.3339 16579.3358 16579.3503 0.003 0.0206
0.3 16579.3339 16579.3354 16579.3577 0.003 0.0197
0.4 16579.3339 16579.3352 16579.3493 0.0022 0.0197
0.5 16579.3339 16579.3353 16579.3467 0.0021 0.02
0.6 16579.3339 16579.3352 16579.3418 0.0013 0.02
0.7 16579.334 16579.3361 16579.3453 0.002 0.0206
0.8 16579.3345 16579.3382 16579.3521 0.003 0.0198
0.9 16579.3347 16579.3436 16579.3893 0.0085 0.0206
1 16579.3346 16579.4853 16583.6409 0.5201 0.0195
P MIN_COST
($/H)
AVER_COST
($/H)
MAX_COST
($/H)
STD_VER
($/H)
AVER_TIME
($/H)
0.1 16579.334 16579.3387 16579.3767 0.0074 0.0159
0.2 16579.3341 16579.3372 16579.3536 0.004 0.0134
0.3 16579.3341 16579.3369 16579.3514 0.0027 0.0138
0.4 16579.3341 16579.3376 16579.3464 0.0027 0.0123
0.5 16579.3347 16579.339 16579.3488 0.003 0.0133
0.6 16579.3345 16579.3401 16579.3515 0.0035 0.0127
0.7 16579.3348 16579.3433 16579.3595 0.0052 0.0127
0.8 16579.3348 16579.3489 16579.3901 0.0103 0.0127
0.9 16579.3369 16579.356 16579.4153 0.0137 0.0136
1 16579.3411 16579.8131 16588.8801 1.3262 0.0133
P MIN_COST AVER_COST MAX_COST STD_VER AVER_TIME
0.1 16579.33 16579.3386 16579.3953 0.0074 0.0141
0.2 16579.3342 16579.3385 16579.358 0.0045 0.0116
0.3 16579.3341 16579.3377 16579.3539 0.0031 0.0114
0.4 16579.3342 16579.3393 16579.3508 0.0038 0.0116
0.5 16579.3348 16579.3409 16579.3722 0.0063 0.0119
0.6 16579.3345 16579.3437 16579.3823 0.0073 0.0117
0.7 16579.3347 16579.3469 16579.384 0.0085 0.0116
0.8 16579.3376 16579.3526 16579.4089 0.014 0.0114
0.9 16579.3357 16579.3622 16579.4941 0.0224 0.0116
1 16579.3376 16579.9036 16587.4535 1.1445 0.0116
Table 10 Result obtained by FPA for the 6 unit system for load demand of 1800 MW with different values
of p. 300 iterations

34
As observed from the tables 10, 11 and 12 the best solution for the 1800 MW load demand is
obtained at p= 0.1 and the most global iteration is reached at 175.
As seen in table 13 CSA and FPA algorithms have the same minimum cost. As observed the
cpu time for FPA is nearly 4.4 times faster than the CSA. This is a big advantage for the FPA
when working with a big size population.
LOAD DEMAND ALGORITHM COST($/H) CPU TIME (S)
1800 CGAs 16589.05 19.66
1800 FCGAs 16585.85 10.44
1800 CSA 16579.33 0.062
1800 FPA 16579.330 0.0141
Figure 9 Determining the best P
16579.332
16579.333
16579.334
16579.335
16579.336
16579.337
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
FitnessFunction($)
P

35
Algorithm Load
(MW)
Unit 1
(MW)
Unit 2
(MW)
Unit 3
(MW)
Unit 4
(MW)
Unit 5
(MW)
Unit 6
(MW)
Cost
($/h)
Cpu
(s)
CGAs[51] 800 109.1700 104.0800 52.0400 305.0500 114.8300 114.8300 8232.8900 14.46
FCGAs[51] 800 104.8900 102.8700 51.7400 314.1800 113.1600 113.1600 8231.0300 5.62
CSA[35] 800 100.0030 100.0000 50.0000 305.6251 122.0105 122.3613 8227.1000 0.031
FPA[37] 800 100.1134 100.1134 100.1134 100.1134 100.1134 100.1134 8227.1000 0.0089
CGAs[51] 1200 142.5500 117.8000 58.9000 515.2000 182.7800 182.7800 11493.7400 17.83
FCGAs[51] 1200 131.5000 129.0500 52.0800 494.0800 200.6100 200.6100 11480.0300 7.43
CSA[35] 1200 123.7606 117.6874 50.0000 448.4274 230.0625 230.0621 11477.0900 0.031
FPA[37] 1200 123.3139 117.3859 50.0000 449.0058 230.1501 230.1444 11477.0899 0.0144
CGAs[51] 1800 222.4200 190.7300 95.3600 555.6300 367.9200 367.9200 16589.0500 19.66
FCGAs[51] 1800 250.4900 215.4300 109.9200 572.8400 325.6600 325.6600 16585.8500 10.44
CSA[35] 1800 248.0009 217.7156 75.1775 588.0389 335.5298 335.5372 16579.3300 0.062
FPA[37] 1800 247.8072 217.9266 75.2741 588.0123 335.9418 335.0380 16579.3300 0.0141
Table 14 All official tested units

36
2.5. Conclusion
In this paper, a Flower Pollination Algorithm has been implemented for solving environmental
economic load dispatch. FPA is a meta-heuristic algorithm with the advantage of few control
parameters. The effectiveness of FPA is tested on a systems with several cases of dispatches
and loads. The optimal solution from FPA compared to that from other methods has indicated
that FPA is a very efficient method for solving EELD problem.
The factors that indicate that the effectiveness of Flower Pollination is higher than the other
algorithms are namely:
 Minimum cost
 Cpu time
As seen in table 14, in each load demand category FPA has the lowest cost. In this case it might
be around 15$ cheaper in comparison with CGA. It does not seem a lot. But when working with
a big size population and big load demands, the difference will increase drastically
As seen in table 14, FPA is the best algorithm. What indicates that FPA is more effective than
other algorithms is the cpu time. As calculated it seems that FPA is 4 times faster than CSA and
1400 times faster than CGA. The cpu time difference between CSA and FPA might be a few
milli second but when working with a big size population, this difference will increase
drastically
Therefore, the FPA can be a very favorable method for solving ELD problems

37
3. Vietnam
3.1. Country
Vietnam is a country well known because of its history. The one that features in most foreigners
mind is known as “the American War” (1961 to 1975). These years were really disastrous,
millions of people died and most of the countryside was destroyed, slowing the country’s
economic development for years afterwards.
Vietnam is now country a country at peace, for the majority of the population the war years are
behind and most of them are striving every day for a better economic prosperity, future and
education[44].
An estimated population of just over 90 million makes it the world’s 13th
most populous country
and 8th
most populous Asian country. Most people are Vietnamese but some 20% are ethnic
Chinese, Khmers, Chams are one of 54 ethno-linguistic groups collectively known as hill tribe
people. While Vietnam is nominally Buddhist nation, there are other religions providing
spiritual guidance to the citizens[45].
Vietnam is known as the “Socialist Republic of Vietnam”. The Socialist Republic of Vietnam,
along with China, Cuba, and Laos, is one of the world's four remaining one-party socialist
states officially communist.
The country has a president (Tran Dai Quang) as its head and is a single party
(the Communist Party of Vietnam) socialist republic with a prime minister
(Nguyen Xuan Phuc) as head of the government. The capital of Vietnam is Hanoi but Ho Chi
Minh City has the largest population and the country’s economic powerhouse. The currency is
the Vietnamese Dong and the official language is Vietnamese[44].
3.2. People
Vietnam’s population exceeds 90 million. The majority of the population belongs to Viet or
Kinh groups but another 54 ethnic groups call Vietnam home. These include Chinese, Thai,
Dao, Tay, Nung Hmong, Khmer, Cham, Jarai, Bahnar and Ede, Black Thai and Brau[44].
Vietnam is one of the most crowded countries in the world with population densities exceeding
200 per km².
Vietnam’s currency is called Vietnamese dong. 1€ is about 24000 dong. With 40€ you can
become a Vietnamese millionaire easily. Vietnam is very cheap and many people are selling in
the streets offering many varieties of foods or souvenirs. A lunch in Ho Chi Minh city can cost
around 20.000VND to 40.000VND.
The national dress for girls and woman is the ao dai, a high neck, fitted tunic slit to the waist
over loose silk pants, that resembles the Chinese qi pao. In Ton Duc Thang university all female
students have to wear a ao dai every Monday and Thursday. The tunic has a pink color and the
pants are white. Very beautiful and gives an elegant touch[44].

38
In the beginning of October I went for vacation to the north-west of Vietnam. Sapa is a beautiful
mountainous part of Vietnam. Where many high old mountains can be seen and many rivers
were born. Sapa is one of the best places to see colorful hill tribe communities, such as the
Black Hmong, Flower Hmong and Red Dao.
The tribe that I saw was the Black Hmong and was easily to identified because of their black
linen inner clothing over which is worn a colorful skirt, apron and leggings.
Vietnam’s Hmong community is estimated to be 500,00 and one of the country’s largest ethnic
groups. Most of the Black Hmong wear big silver jewelry and large earrings. Most of these
ethnic groups migrated from China many years ago. These ethnic groups consider Vietnam
their home and nationality[45].
Approximately 60% of the population is still employed in the agriculture, fishing and forestry
sector of the economy and some 25% of the country is under agriculture production. Vietnam
is well known because of its production and export[44].
Top exportation products are:
 Rice
 Rubber
 Coffee
 Fishing
Vietnam is the world’s fifth largest producer of rice but the second largest exporter of grain.
Most rice is grown as wet rice while some in the uplands is dry production.
Vietnam is also the world’s biggest coffee exporter after Brazil.
Rubber is also a very important source in Vietnam. Vietnam is the world’s fifth largest producer
of rubber and fourth largest exporter. 50% of the production takes place in the south of Vietnam.
Fishing is an important source of income in Vietnam. The country is located along the coast
where there are many good locations to fish. Large nest are thrown in water in the water, then
dropped over the surface to entrap anything below. The typical Vietnamese boats used are
called “thung chai” made from bamboo for operating close to shore or along rivers[45].
3.3. Religion
Vietnam is a multi-religious country. Because of its history, there are many western and eastern
countries that were a big influence to Vietnam. According to an analysis by the Pew Research
Center, in 2010 about 45.3% of the Vietnamese adhere to indigenous religions, 16.4%
to Buddhism, 8.2% to Christianity, 0.4% to other faiths, and 29.6% of the population isn't
religious[45].
Buddhism in Vietnam as practiced by the Vietnamese is mainly of the Mahayana tradition.
Buddhism may have first come to Vietnam as early as the 3rd or 2nd century BCE from South
Asia or from China in the 1st or 2nd century CE. Vietnamese Buddhism has had a symbiotic
relationship with certain elements of Taoism, Chinese spirituality, and the Vietnamese folk
religion. 6.8 million people in Vietnam are practicing Buddhists[45].
Catholicism was introduces by French missionaries in the 16th
century and has over six million
followers in Vietnam. Here in Ho Chi Minh city there is a big cathedral built in 1877 with the
typical French structure and very well-known[45].

39
Approximately 1% of the population is Muslim. Islam was introduces to Vietnam by early Arab
traders journeyed to china in the early 7th
century[45].
Confucianism is a way of life taught by Confucius in the 6th–5th century BCE. Sometimes
viewed as a philosophy, sometimes as a religion, Confucianism is perhaps best understood as
an all-encompassing humanism that neither denies nor slights heaven. Confucianism has been
followed by the Chinese for more than two millennia.
It has deeply influenced spiritual and political life in China; its influence has also extended to
Korea, Japan, and Vietnam. East Asians may profess themselves to be Shintoists, Taoists,
Buddhists, Muslims, or Christians - but seldom do they cease to be Confucians[45].
Cao Dai (or Caodaism) is a syncretist Vietnamese religious movement with a strongly
nationalist political character. Cao Dai draws upon ethical precepts from Confucianism, occult
practices from Taoism, theories of karma and rebirth from Buddhism, and a hierarchical
organization (including a pope) from Roman Catholicism. Its pantheon of saints includes such
diverse figures as the Buddha, Confucius, Jesus Christ, Muhammad, Pericles, Julius Caesar,
Joan of Arc, Victor Hugo, and Sun Yat-sen.
0.8 million people practice Caodaism in Vietnam[44].
3.4. Wonders in Vietnam
Ha long Bay, descending from Dragon Bay is a UNESCO World Heritage Site and popular
travel destination in Quang Ninh Province, Vietnam. Halong is located 160 km east of the
capital Hanoi. Ha Long Bay has an area of around 1,553 km2
, including 1,960–2,000 islets,
most of which are limestone[46].
The core of the bay has an area of 334 km2
with a high density of 775 islets. The limestone in
this bay has gone through 500 million years of formation in different conditions and
environments. The evolution of the karst in this bay has taken 20 million years under the impact
of the tropical wet climate[46].
Halong Bay’s topography indicates that the area was once inundated by a sea. These rocks are
rich in mineral calcite and has evolved for millions of years from the accumulation of the
skeletal fragments of marine organism, such as corals. As the large limestone blocks weather ,
the tops of these islands become rounded and within the rocks, water erodes along cracks and
fault lines to create caves, caverns and grottoes[44].
Sa Pa District is in Lao Cai Province, northwest Vietnam, 380 km northwest of Hanoi close to
the border with China. The Hoang Lien Son range of mountains dominates the district, which
is at the eastern extremity of the Himalayas. This range includes Vietnam's highest mountain,
Fan Si Pan, at a height of 3143 m above sea level. Located in the south-west of Sapa, Dien Bien
Phu was the scene of a fierce and famous battle between French and local Viet Minh forces in
1954.
In addition, other mountains like Aurora & J (where the sun appears at sunrise) complete a very
steep terrain. The town of Sa Pa lies at an elevation of about 1500 meters (4,921 feet) elevation.
The climate is moderate and rainy in summer (May—August), and foggy and cold with
occasional snowfalls in winter [47].

40
Son Doong cave is world's largest cave, located in Quang Binh province, Vietnam. It is found
by a local man named Ho Khanh in 1991 and was recently discovered in 2009 by British cavers,
led by Howard Limbert. The name "Son Doong" cave means "mountain river cave", It was
created 2-5 million years ago by river water eroding away the limestone underneath the
mountain Where the limestone was weak, the ceiling collapsed creating huge skylights[48].
According to the Limberts, the main Son Doong cave passage is the largest known cave passage
in the world by volume – 38.4×106
cubic meters. It is more than 5 kilometers long, 200 meters
(660 ft) high and 150 meters (490 ft) wide. Its cross-section is believed to be twice that of the
next largest passage, in Deer Cave, Malaysia. The cave runs for approximately 9 kilometers
(5.6 mi) and is punctuated by 2 large dolines, which are areas where the ceiling of the cave has
collapsed. The dolines allow sunlight to enter sections of the cave and has resulted in the growth
of trees as well as other vegetation.
Ho Chi Minh city is not a wonder of Vietnam. But I would like to give some information about
the city where I lived for 5 months.
Ho Chi Minh City formerly named and still also referred to as is the largest city in Vietnam.
Under the name Saigon, it was the capital of the French colony of Cochin china and later of the
independent republic of South Vietnam 1955–75[49].
It’s a city with a fast economically grow, re-energized and revitalized city of over 9 million
residents. Once the capital of south Vietnam tanks crushed the gates of the independence Palace
to end the war and reunify the nation now seems a long while ago[46].
Ho Chi Minh is well-known as the city that never sleeps. There are many varieties of shops,
food and people. It is really easy to start a business so that is the main reason for the varieties
of things to do in the city. There are also many museums that reflects the war that once marked
this country. Also many skyscrapers and pagoda’s. There is approximately 7.5 million
motorbikes in Ho Chi Minh.
The city has a tropical climate, specifically a tropical wet and dry climate, with an average
humidity of 78–82%. The year is divided into two distinct seasons. The rainy season, with an
average rainfall of about 1,800 millimeters (71 in) annually (about 150 rainy days per year),
usually begins in May and ends in late October. The dry season lasts from December to
April. The average temperature is 28 °C (82 °F), with little variation throughout the year[48].

41
4. Reflection
4.1. Company
Dai Hoc Ton Duc Thang is a university located in District 7, Ho Chi Minh city, Vietnam. The
university was founded in 1997. The University provide basic to university-level of 24
specialties, including: law, technology, techniques, social sciences, economics, business,
foreign languages, arts.
Ton Duc Thang university has approximately 22500 students including some international
students from Laos, Cambodia, Japan Korea and France.
This project has been guided by Mr. Thang T. Nguyen and Mr. Pham Huu Lý and supervised
by Mr. Jan Bollen
Contact info
ME. Thang T. Nguyen;
Faculty of electrical and electronics engineering&
Power system optimization research group;
Ton Duc Thang University;
19 Nguyen Huu Tho, District 7, Ho Chi Minh City, Vietnam;
Email:nguyentrungthang@tdt.edu.vn
Mr. Jan Bollen
Coordinator internship Electrical and Electronic Engineering (EEE)
Member examination board Electrical and Electronic Engineering (EEE)
Saxion | University of Applied Sciences | School of Life Science, Engineering & Design
M.H. Tromplaan 28 | Postbox 70.000, 7500 KB Enschede | The Netherlands | Room W2.28
T: +31 53 4871281 | M: +31 6 15241386 | Mail, j.w.bollen@saxion.nl | Skype, janbollen.nl
4.2. Own development technical and social
This project has taught many things about economic problems nowadays and how to solve them
or how to minimize the damages. The teachers have taken a lot of their time and patience to
teach me how to analyze a problem and how to program. One of my weak points is
programming and thanks to the teachers a have improved my skills in programming. Not only
with programming but also with self-discipline and methods on how to research on the topic
without over expanding it. How to keep everything between boundaries to not spent a lot of
time on one problem. In other words how to plan everything very efficiently.
Coming to Vietnam and studying in Ton Duc Thang university has been an amazing experience.
Apart from learning about power system optimization I have also learn about new mentalities,
culture, traditions, lifestyles, religion and many more things. Also how to interact with people
that see life with another perspective than me. Coming to Vietnam has open my mind and has
brought a lot of knowledge. Vietnam is totally different from where I was born and raised, it
has been a challenge but I am really grateful for that.
4.3. Own future
I consider myself very skilled and talented in interacting with people. In the future I see myself
working on the business side of electrical engineering. More like representing a company
abroad. I am very good at persuading costumers to be interested in something I am selling or
offering. Programming is not my strongest point or my biggest interest, but it has taught me

42
many good things that might help me in the future. Having experience about the software side
of electrical engineering has expand my knowledge. After this project I am thinking about
combining software and interaction knowledge to bring business tactics to another level.
5. References
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