Optimal utilization of electrical energy from power plants based on final energy consumption using gravitational search algorithm
Purpose. Energy consumption is a standard measure to evaluate the progress and quality of life in a country. When used properly and logically it could be cause of progress in science, technology and welfare of the people in any country and otherwise irreparable economic losses and economic gross r...
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irk-123456789-1479492019-02-17T01:24:32Z Optimal utilization of electrical energy from power plants based on final energy consumption using gravitational search algorithm Montazeri, Z. Niknam, T. Електричні станції, мережі і системи Purpose. Energy consumption is a standard measure to evaluate the progress and quality of life in a country. When used properly and logically it could be cause of progress in science, technology and welfare of the people in any country and otherwise irreparable economic losses and economic gross recession would happen. And finally, the quantity of energy consumption per GDP will increase day by day. Electrical energy, as the most prominent type of energy, is very important. In this article based on a different approach, according to the final consumption of electric energy, a proper economic planning in order to supply electrical energy is submitted. In this programming, the details of final energy consumption, will replace with the information of power network, by considering the network efficiency and power plants. Operation of power plants is based on the energy optimization entranced to a plant. By using the proposed method and gravitational search algorithm, the total cost of electrical energy can be minimized. The results of simulation and numerical studies show better convergence of gravitational search algorithm in comparison with other existing methods in this area. Цель. Энергопотребление является стандартной мерой для оценки прогресса и качества жизни в стране. Правильное и обоснованное ее использование может привести к прогрессу в науке, технике и благосостоянии людей в любой стране, в противном случае произойдут непоправимые экономические потери и падение валового внутреннего продукта. И, наконец, количество потребленной энергии на единицу ВВП будет возрастать с каждым днем. Электрическая энергия, как основной вид энергии, является весьма важной. В данной статье, основываясь на различных подходах, в соответствии с конечным потреблением электрической энергии, представлено соответствующее экономическое планирование подачи электроэнергии. При этом, подробности конечного потребления энергии заменяются информацией о сети электроснабжения, учитывая эффективность сети и электростанций. Работа электростанций основана на оптимизации энергии, производимой ею. Используя предложенный метод и алгоритм гравитационного поиска, можно минимизировать общую стоимость электрической энергии. Результаты моделирования и численных исследований показывают лучшую сходимость алгоритма гравитационного поиска по сравнению с другими существующими методами в данной области. 2018 Article Optimal utilization of electrical energy from power plants based on final energy consumption using gravitational search algorithm / Z. Montazeri, T. Niknam // Електротехніка і електромеханіка. — 2018. — № 4. — С. 70-73. — Бібліогр.: 17 назв. — англ. 2074-272X DOI: https://doi.org/10.20998/2074-272X.2018.4.12 http://dspace.nbuv.gov.ua/handle/123456789/147949 621.3 en Електротехніка і електромеханіка Інститут технічних проблем магнетизму НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| topic |
Електричні станції, мережі і системи Електричні станції, мережі і системи |
| spellingShingle |
Електричні станції, мережі і системи Електричні станції, мережі і системи Montazeri, Z. Niknam, T. Optimal utilization of electrical energy from power plants based on final energy consumption using gravitational search algorithm Електротехніка і електромеханіка |
| description |
Purpose. Energy consumption is a standard measure to evaluate the progress and quality of life in a country. When used properly
and logically it could be cause of progress in science, technology and welfare of the people in any country and otherwise
irreparable economic losses and economic gross recession would happen. And finally, the quantity of energy consumption per
GDP will increase day by day. Electrical energy, as the most prominent type of energy, is very important. In this article based on a
different approach, according to the final consumption of electric energy, a proper economic planning in order to supply
electrical energy is submitted. In this programming, the details of final energy consumption, will replace with the information of
power network, by considering the network efficiency and power plants. Operation of power plants is based on the energy
optimization entranced to a plant. By using the proposed method and gravitational search algorithm, the total cost of electrical
energy can be minimized. The results of simulation and numerical studies show better convergence of gravitational search
algorithm in comparison with other existing methods in this area. |
| format |
Article |
| author |
Montazeri, Z. Niknam, T. |
| author_facet |
Montazeri, Z. Niknam, T. |
| author_sort |
Montazeri, Z. |
| title |
Optimal utilization of electrical energy from power plants based on final energy consumption using gravitational search algorithm |
| title_short |
Optimal utilization of electrical energy from power plants based on final energy consumption using gravitational search algorithm |
| title_full |
Optimal utilization of electrical energy from power plants based on final energy consumption using gravitational search algorithm |
| title_fullStr |
Optimal utilization of electrical energy from power plants based on final energy consumption using gravitational search algorithm |
| title_full_unstemmed |
Optimal utilization of electrical energy from power plants based on final energy consumption using gravitational search algorithm |
| title_sort |
optimal utilization of electrical energy from power plants based on final energy consumption using gravitational search algorithm |
| publisher |
Інститут технічних проблем магнетизму НАН України |
| publishDate |
2018 |
| topic_facet |
Електричні станції, мережі і системи |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147949 |
| citation_txt |
Optimal utilization of electrical energy from power plants based on final energy consumption using gravitational search algorithm / Z. Montazeri, T. Niknam // Електротехніка і електромеханіка. — 2018. — № 4. — С. 70-73. — Бібліогр.: 17 назв. — англ. |
| series |
Електротехніка і електромеханіка |
| work_keys_str_mv |
AT montazeriz optimalutilizationofelectricalenergyfrompowerplantsbasedonfinalenergyconsumptionusinggravitationalsearchalgorithm AT niknamt optimalutilizationofelectricalenergyfrompowerplantsbasedonfinalenergyconsumptionusinggravitationalsearchalgorithm |
| first_indexed |
2025-07-11T03:11:53Z |
| last_indexed |
2025-07-11T03:11:53Z |
| _version_ |
1837318555226341376 |
| fulltext |
Електричні станції, мережі і системи
70 ISSN 2074-272X. Електротехніка і Електромеханіка. 2018. №4
© Z. Montazeri, T. Niknam
UDC 621.3 doi: 10.20998/2074-272X.2018.4.12
Z. Montazeri, T. Niknam
OPTIMAL UTILIZATION OF ELECTRICAL ENERGY FROM POWER PLANTS
BASED ON FINAL ENERGY CONSUMPTION USING GRAVITATIONAL SEARCH
ALGORITHM
Purpose. Energy consumption is a standard measure to evaluate the progress and quality of life in a country. When used properly
and logically it could be cause of progress in science, technology and welfare of the people in any country and otherwise
irreparable economic losses and economic gross recession would happen. And finally, the quantity of energy consumption per
GDP will increase day by day. Electrical energy, as the most prominent type of energy, is very important. In this article based on a
different approach, according to the final consumption of electric energy, a proper economic planning in order to supply
electrical energy is submitted. In this programming, the details of final energy consumption, will replace with the information of
power network, by considering the network efficiency and power plants. Operation of power plants is based on the energy
optimization entranced to a plant. By using the proposed method and gravitational search algorithm, the total cost of electrical
energy can be minimized. The results of simulation and numerical studies show better convergence of gravitational search
algorithm in comparison with other existing methods in this area. References 17, tables 2, figures 4.
Key words: gravitational search algorithm, energy, electrical energy, economic distribution, final energy consumption.
Цель. Энергопотребление является стандартной мерой для оценки прогресса и качества жизни в стране. Правильное и
обоснованное ее использование может привести к прогрессу в науке, технике и благосостоянии людей в любой стране, в
противном случае произойдут непоправимые экономические потери и падение валового внутреннего продукта. И,
наконец, количество потребленной энергии на единицу ВВП будет возрастать с каждым днем. Электрическая энергия,
как основной вид энергии, является весьма важной. В данной статье, основываясь на различных подходах, в
соответствии с конечным потреблением электрической энергии, представлено соответствующее экономическое
планирование подачи электроэнергии. При этом, подробности конечного потребления энергии заменяются
информацией о сети электроснабжения, учитывая эффективность сети и электростанций. Работа электростанций
основана на оптимизации энергии, производимой ею. Используя предложенный метод и алгоритм гравитационного
поиска, можно минимизировать общую стоимость электрической энергии. Результаты моделирования и численных
исследований показывают лучшую сходимость алгоритма гравитационного поиска по сравнению с другими
существующими методами в данной области. Библ. 17, табл. 2, рис. 4.
Ключевые слова: алгоритм гравитационного поиска, энергия, электрическая энергия, экономическое распределение,
конечное потребление энергии.
Introduction. The energy consumption trend in
recent years has been very rapid and worrying. This
process in developing countries, especially Iran has been
much higher than the global average. The continuation of
energy supply and ensuring long-term access to resources,
needs a comprehensive energy plan, and therefore the
energy planning is the undeniable necessities of
economic, national and strategic in a country. One of the
key topics that is discussed in the context of energy
planning, is the economic distribution of electrical energy.
Economic dispatch problem using Tucker-Cohen is
performing well and appropriate economic status is
determined. When these conditions are met, all the
plants that are in circuit, with the exception of plants
that can effectively inject their maximum power into the
network, due to their amount of fuel are loaded [1].
Economic dispatch methods can be placed in two groups
of analytical methods and intelligent systems. One of the
most famous and oldest analytical methods, is Lagrange
method [2]. Including the intelligent systems, can note
the optimization of the application of innovative
methods in economic dispatch and entrance of plant into
the circuit [3].
Despite the research conducted on the economic
dispatch and as a result, the problem of entrancing the
plant into the circuit, most of these studies has been
appropriated by electric power consumer's expectations.
In this paper a different approach with regard to the
undeniable importance of energy, is presented in the field
of economic distribution with needs of consumers. In
describing this new and different expression, according to
the final consumption of electric energy, economic
distribution of this energy consumption will be
established by power plants. And then based on different
power plants efficiency, input energy requirements of
power plants, is planned and optimized.
In this paper, first in the second part, definition and
discussion of how to formulate economic distribution of
energy is expressed. Then, in the third part gravitational
search algorithm is presented. The fourth part of the
article is devoted to the application of gravitational search
algorithm in the context of economic distribution. In the
fifth part the simulation results are given and finally in the
sixth part of the article summary is expressed.
Problem statement and formulation. The cost of
electrical power distribution for the whole system is equal
to the sum of Costs of different units [4]. The basic
operation of the system is that the total output powers
must be equal to the total load [5]. In this case the
economic dispatch is expressed by relations:
;
1
N
i
iiT PFF (1)
N
i
iR PP
1
,0 (2)
ISSN 2074-272X. Електротехніка і Електромеханіка. 2018. №4 71
where FT is the total cost of the operation from the
system, N is the number of power plants, Pi is the share of
i-th power plant from the total demand, and Fi(Pi), is the
cost of power plants, in order to generating power P.
Ø indicating the fundamental issue PR, is the total
demand.
It should be noted that each plant is able to operate
in the range of its unique ability to inject power. This
range of capability is expressed as:
max.min. iii PPP , (3)
where Pi.min and Pi.max respectively, are the minimum and
maximum power injection at the i-th power plant.
Expressions (1) and (2) show the overview of the
economic distribution of electric power, we intend to
extend this relation into the energy definition domain. So,
in the new expression, ER replacing with PR and we define
total electric energy demand based on final consumption
of electrical energy. Therefore, this new attitude we try to
provide electrical energy demand in a way to reduce the
rate of its costs. The subject that expressed in fact is an
optimization problem with a constraint which can be
solved with optimization existing methods. However
analytical methods such as Lagrange method solve this
issue, but in the complex systems and real great,
especially when considering the losses and efficiency of
the network and in fact nonlinear problem, becomes more
with computational complexity. In these situations,
evolutionary optimization algorithms, represent their
ability to well solve such issues. Various evolutionary
optimization algorithms have been proposed and
introduced by various authors [6-10].
Gravitational search algorithm. Considering the
extent and complexity of the issues and the importance of
speed to get answers, other classical optimization
methods, do not have ability to solve many issues, and
instead of searching of comprehensive space, random
search algorithms are used to define the problem. This has
led to the use of heuristic search algorithm (intuitive or
initiatives) which have grown substantially in recent years
[6-10]. Heuristic algorithms have demonstrated their high
ability in many fields of science such as transport [11],
bioinformatics [12], data mining [13], physical chemistry
[14], electronics [15] and other related fields. The
achievement of an appropriate mathematical model to the
process of searching for innovative methods, is very hard
and even impossible [13]. Therefore, this type of
algorithms, can be named as «black boxes» optimization
algorithms [16].
According to the gravity law each mass perceived
location and status of other masses through the law of
gravitational attraction. Therefore, this force can be used
as a tool for information exchange. The optimum detector
designed to solve the optimization problem can be used,
which each answer can be defined as a position in space
and its similarity to the other solutions can be expressed
as a distance. The rate of masses is determined according
to the objective function [17].
However, imagine the system as a set of m object.
The position of each object is a point in space which is an
answer of the problem. In (4), the position of dimension d
of the object i is shown with d
ix
n
i
d
iii xxxX ,...,,...,1 . (4)
At first, randomly the initial position of the objects,
is define in the space of problem definition, these objects
due to the forces which exert to each other proceed
towards the answer of the problem.
In this system at time t to mass i from mass j in the
direction of dimension d force equal to tF d
ij is
imported. Mgj is gravitational mass of mass j, G(t) is the
gravitational constant in time t and Rij is the distance
between the two objects j and i. Euclidean distance is
used to determine the distance between the objects. is a
very small number
;txtx
tR
tMtG
tF d
i
d
j
ij
gjd
ij
(5)
2
tXtXtR jiij . (6)
Force on object j in the direction of dimension d at
the time t, tF d
i , is calculated according to (7). In this
equation, r1 is a random number with uniform distribution
in [0-1]
.
,1
1 tFrtF d
ij
m
ijj
d
i
(7)
Acceleration of object i in the direction of dimension
d at time t is shown with tad
i and inertial mass of object
i is shown with Mi1(t)
.
1 tMi
tF
ta
d
id
i (8)
In this case we have:
;1 2 tatVrtV d
i
d
i
d
i (9)
,11 tVtxtx d
i
d
i
d
i (10)
where r1 and r2 are uniformly-distributed random
numbers in [0-1] which have been used to maintain the
random search. d
iV is speed of dimension d from object i.
Relationship (5) to (10), will repeat until the
convergence condition is established.
Problem solving of economic distribution using
gravitational search algorithm. Distribution of electrical
energy, is a non-linear problem and due to high provisions
has a very high complexity. For this reason, the usual
methods for solving this problem are faced with many
problems, and either are not able to solve this problem or
solve the problem with many hardships. For these reasons
described in this article gravitational search algorithm is
used to solve nonlinear problems which is very efficient.
Electric energy demand is equal to ER. In the period
studied, power plants which are available assumed to be
constant, so each of these power plants, are at their least
production. Different power plants according to the
structure have different efficiencies. When the economic
distribution of electrical energy is concerned, this fully
shows. Thus, only the desired power generation is not
considered, but the total final consumption of energy that
needed to provide electric energy is optimized. In other
words, for effective optimization is done.
72 ISSN 2074-272X. Електротехніка і Електромеханіка. 2018. №4
We introduce the network efficiency with and
efficiency of different power plants with i for n, i = 1, 2,…
;RRL EE (11)
,
1
n
i
iiRL EE (12)
where ERL is the energy demand of the power plant due to
final energy consumption and efficiency of the network
and Ei is the input energy required to i-th power plant.
The simulation is done in time domain, so, the mean
power and electric power, are the same.
Simulations and results. The simulation is performed
based on a specific system in accordance with Table 1.
Values of a, b and c related to the input data of costs of
power plant operation that is used to calculate the relation
,2 cbPaPPF iiii (13)
where Fi is the operating costs, and Pi is the amount of
i-th power plant output power.
Table 1
Information about power system plants
unit Pmin(MW) Pmax(MW) a b c
1 150 455 0.00048 19.16 1000 30
2 150 455 0.00031 26.17 970 45
3 20 130 0.002 16.6 700 32
4 20 130 0.00211 16.5 680 35
5 25 162 0.00398 19.7 450 28
6 20 80 0.007 22.26 370 27
7 25 85 0.00079 27.74 480 30
8 10 55 0.004 25.92 660 35
9 10 55 0.00222 27.27 665 33
10 10 55 0.002 27.79 670 33
It assumed that ER is equal to 1500 kWh, if the
efficiency of the network is equal to 75 %, so the demand
from the power plant ERL will be 2000 kWh. Performance
of the gravity algorithm, was compared with genetic
algorithm and particle population algorithm, the results of
the implementation of the three algorithms are shown in
Table 2.
Table 2
The simulation results of the studied power system
GA PSO GSA
The best answer 70492.205 70526.659 70785.216
Average of answers 70546.156 70574.379 70837.164
The worst answer 70913.142 71052.215 71356.184
To evaluate the proposed method, gravitational
algorithm, genetic algorithm and particle swarm
algorithm in solving the problem of finding the minimum
of economic distribution problem, have been
implemented under the same conditions. For n = 30, and
population size equal to 50, the results for 1500 times
iteration is given in Table 2. And for comparison, the
fitness average and the best answer which so far has been
observed are calculated. These parameters were
calculated for 20 times for the implementation of the
stand-alone application and middle of the results is
obtained. The results of gravitational algorithm show
better performance. In the PSO simulation, relation (14) is
used for updating the particles velocity in this relation,
c1 = c2 = 2, and w decreases linearly from 0.9 to 0.2. In
this relation d
iV (t), is velocity of particle i in d dimension
in time t, and r1 and r2 are random numbers uniformly
distributed between zero and one. Also gbest is the best
position that has been found by the community, pbesti is
the best position that particle i so far has been accessed
.
1
22
11
tXtgtrc
tVtptrctVtwtV
d
i
d
besti
d
i
d
ibesti
d
i
d
i
(14)
In order to evaluate the results of the presented
objective function optimization, this case is shown in the
Table 2. As seen in Table 2, gravitational search
algorithm has more acceptable performance and results
than GA and PSO algorithms. The results demonstrate the
convergence of the GSA algorithm compared to RGA and
PSO algorithms.
In order to evaluate the progress of the optimization
process, in Fig. 1 to Fig.3 the accomplishing pattern of the
optimal solution for gravitational, particle population and
genetics algorithms is drawn. Also, in order to have a
proper comparison of the performance for these
algorithms, the achieving pattern of these algorithms for
optimal solution are shown in Fig. 4, simultaneously.
Fig. 1. Accomplishing pattern of the optimal solution
by GSA algorithm
Fig. 2. Accomplishing pattern of the optimal solution
by PSO algorithm
Fig. 3. Accomplishing pattern of the optimal solution
by GA algorithm
ISSN 2074-272X. Електротехніка і Електромеханіка. 2018. №4 73
Fig. 4. The comparison of the evolutionary algorithms GSA,
PSO and GA to achieve the optimal solution
Conclusion. Electrical energy is very important, and
therefore it is important to minimize the energy costs. In a
new approach in this paper, according to the final
consumption of electric energy and efficiency of power
system planets and network, the economic distribution of
electrical energy is created. In this regard, according to
the non-linear nature of the problem, evolutionary
algorithms have been used. The results of the simulation
show the well performance of gravity algorithm in
compare to other algorithms.
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Received 14.03.2018
Zeinab Montazeri1, Candidate of Power Engineering,
M.Sc. Student,
Taher Niknam1, Doctor of Power Engineering, Professor,
1 Department of Electrical Engineering,
Islamic Azad University of Marvdasht,
Marvdasht, I.R. Iran.
phones +989171128689, +989171876173
e-mail: Z.montazeri2002@gmail.com, niknam@sutech.ac.ir
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