Mathematical Modeling and Planning of Energy Production using a
Neural Network
EKATERINA GOSPODINOVA
Department of Electronics, Automation and Information Technologies - Sliven,
Technical University of Sofia,
BULGARIA
Abstract: - This paper examines the investigation and optimization of existing approaches for the efficient
deployment of renewable energy-based power generation facilities and a genetic algorithm for predicting the
operating mode with the help of efficient deployment of production facilities. The developed genetic algorithm
model is based on the use of a radial basic neural network. As a result of these neural networks, it becomes
possible to minimize the cost of data processing time and use them in solving technical and economic problems
that require high-speed processing. The proposed approach allows for obtaining the most accurate and justified
option for the deployment of renewable energy sources to solve the problem of active power reserves and
allows for forecasting with an error of no more than 20%.
Key-Words: - Genetic algorithms, renewable energy, Neural Networks, mathematical modeling, power
reserves.
Received: July 8, 2022. Revised: January 11, 2023. Accepted: February 17, 2023. Published: March 21, 2023.
1 Introduction
One of the main problems with multilayer
perceptrons and neural networks is training them
with a level of difficulty above average. One
example of this is figuring out how renewable
energy systems will work with the help of modeling
and neural network training so that production
facilities can be put in the best places. This is a
complex process, where first you need to decide on
the type of network, the structure of the network
layers and neurons in them, inputs and outputs, and
prepare the data. Then it is necessary to train the
network, that is, to select the connection coefficients
between neurons, to be verified in the validation set
and in a real working environment. A modern
approach to the search for the structure of a neural
network and its training is the use of genetic
algorithms. They are able to find solutions in the
almost complete absence of assumptions about the
nature of the function under study when solving
integer or combinatorial prediction problems.
Genetic algorithms (GA) are closely related to
the biological process and evolution, which can be
seen as a process of constant optimization of
species, with natural selection as the main guide.
The advantages of genetic algorithms are as follows:
GAs can work with high-dimensional and unordered
data and be used for a wide range of problems,
including problems with a changing environment.
Their main advantage is that they can be used for
complex, informal tasks for which there are no
special methods, [1].
At the same time, the development of the
planet's energy infrastructure faces serious
challenges. They are increasingly the subject of
international discussion forums related to the growth
of the world population, the improvement of living
standards, the regulatory requirements for reducing
environmental pollution, reducing the use of
resources from organic fuels, etc. On a global scale,
an increase in responsibility for the protection of the
earth's resources and the transition to "green
consumption" and "green economies" is being
initiated. Using renewable energy sources and
integrating them into the energy grid offer crucial
prospects for the growth of the future innovation
economy. For the formulation of energy policies and
the monitoring of their impact on the economy, the
availability of detailed and high-quality energy
statistics, the development of analysis and forecasts
for the state, and trends and regularities in the use of
solar, wind, and other energies are of great
importance. The significance of scientific research
on the issues surrounding the use of renewable
energy sources, as well as the state and dynamics of
those sources, is determined by all of this, [2], [3].
With a significant share in solving this task is the
effective deployment of renewable energy
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.5
Ekaterina Gospodinova
E-ISSN: 2224-350X
39
Volume 18, 2023
generation facilities, which is related to the
problems of placing and planning the modes of
operation determined by the rules of technological
operation and are based on the formation of long-
term and short-term energy and electricity balance
sheets, [4], [5].
Additionally, the task of building facilities for
power plants with a significant proportion of
renewable energy is directly related to the issue of
forecasting the generation of electric power, as the
absence of accurate predictions of renewable energy
sources necessitates the constant maintenance of a
full reserve of active power in the power system,
which necessitates the inclusion of additional
production in non-economic modes and complicates
the process of forming new power plants, [6]. The
problems of short-term forecasting of electricity
production provide technological control, electricity
mode planning, and continuous supply to
consumers, technically and economically.
The data led the authors to conclude that applied
mathematics has a recent trend toward using bio-
inspired methods, [7], [8]. The main characteristic
of this tendency is the reproduction of the
evolutionary processes of nature in technical
systems. The genetic algorithm (GA) is one of the
most well-liked bio-inspired techniques. It should be
noted that it utilizes encoded input parameters, a
collection of potential solutions to a given issue, and
uses the objective function's value to assess the
effectiveness of potential optimization problem
solutions, as opposed to many traditional
algorithms, which base their operations on the
evaluation of the objective function. The foundation
of GAs is the use of probabilistic, as opposed to
deterministic, methods to address optimization
issues. There are other challenges, such as the need
to choose the ideal population size, which can be
challenging for complex issues, to reduce the
computational and temporal expenses of executing
the genetic algorithm. By appropriately configuring
the optimization process and selecting the
appropriate values for the chance of mutation,
crossover, an effective chromosomal coding
method, a structure, and a fitness function
calculation method, many of the defects that are
now present are eradicated.
The article goes on to offer articles that use
genetic algorithms to solve the issue of deciding
where and how powerfully to place generating
facilities in the electric network. In addition to other
mathematical techniques, linear and non-linear
optimization techniques are applied. An analytical
method to establish the ideal generating power
based on a power loss sensitivity analysis has been
developed by [9]. Their strategy is based on a
standard that seeks to reduce distribution network
electricity losses. The distribution system of the
Australian island of Tasmania is used to test the
proposed strategy. However, it assumes an even
distribution of the load along the length of the
feeder of the radial distribution system. All loads are
also assumed to have the same power factor. These
factors limit the application of the authors' proposed
method for practical purposes.
[10], analyzed the increase in power loss as a
function of the change in the active power injection
sensitivity factor. This coefficient was used to
determine a node that is optimal in terms of
reducing generational placement losses. The authors
determine the ideal value of the output-producing
power by equating this coefficient to zero. The
location of the generator unit is determined by
enumeration. One of the main disadvantages of the
proposed algorithm is the duration of searching for
the optimal location. Moreover, in such a problem
formulation, only the optimization of location and
power selection for a single generator is considered.
[11], solved the location and generated a power
optimization problem using GA. They consider two
scenarios. In the first one, the usual principles of
construction of the distribution systems are
preserved since the flow of electricity from the plant
in normal mode is directed to the user. In the second
scenario, reverse flow to the head is allowed. The
power loss function of the radial distribution
network is the objective function that needs to be
minimized.
The challenge of integrating generation sources
into a network was formulated by [12] using the
multi-criteria electronic constraints technique, and it
was resolved using GA. The suggested algorithm
separates the optimization task's criteria into one
dominant and several auxiliary criteria. The
optimization is performed according to the dominant
criterion, while the auxiliary ones are taken into
account in the form of constraints with a preset
tolerance. In today's market environment, due to the
presence of many interested parties, this approach
may be of limited use and lead to biased results.
In the studies of [13], the problem of choosing the
number, type, and location of production
installations in the distribution network and the
composition of the working equipment in different
operating situations is formulated and solved. As an
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.5
Ekaterina Gospodinova
E-ISSN: 2224-350X
40
Volume 18, 2023
objective function, the author uses a multiparameter
cost function resulting from the introduction of a
production facility into the distribution system. A
standard GA was used throughout the study. The
author proved that the use of GA to solve this
problem is efficient and allows the obtaining of the
required solution in a shorter time.
The earliest research in the field of optimization
of the performance of photovoltaic installations
refers to the works of various scientists, [14], [15].
The writers take into account installations that are
running in parallel and autonomous modes.
Operating costs and the dependability of the power
supply to consumers serve as the primary criteria.
The study's findings led the authors to list
several benefits of small power plants operating in
parallel. In most of the works described, the
problems of finding the optimal location and power
have been solved sequentially. This is due to the
complexity of the task. The placement problem
combines both discrete and continuous variables and
is non, [1] linear, which poses great difficulties for
most traditional mathematical methods.
For the solved problem of choosing the location,
region, installed capacity, and type of generating
facilities based on renewable energy systems (RES),
it is advisable to highlight the following advantages
of using GA: they are insensitive to the quality of
the initial approximation of the problem solution
and have in their structure means to overcome the
local extrema of the objective function; in the
presented formulation, the problem of deployment
of generating capacities based on RES is a discrete
optimization problem with a large dimension and
the presence of logical variables; the direct
calculation of the objective function in addition to
the logical operators in the presented problem
allows to integrate an additional external software
module for calculation, [16], [17].
The goal of this study is to evaluate and
improve current methods for predicting how RES
will work in the short term and choosing a good site
by using a neural network and machine learning. To
reach this goal, a review of the most common
positioning techniques and strategies was done. We
developed a mathematical model and trained a
neural network with hierarchical GA structures.
2 An Approach to Energy Analysis
Supply of Territories based on RES
To provide a solution to the efficiency issue and
compare potential options for project
implementation, the analysis of the issues related to
the development of generating capacities and the
optimal deployment of production facilities based
on the use of RES was conducted using evolutionary
methods based on geographical and technological
zoning maps. Solving the territorial planning
problem requires the collection of the following
initial information: data from schemes and programs
for the development of the energy complex;
structure and composition of the installed capacity
of power plants; dynamics and forecast of electricity
and power consumption; maps and schemes of
electrical networks 110 kV and higher; and a target
indicator for RES development, % (MW), [18],
[19].
Data on the load on the electrical network in the
area, including the power of central transformers
(CP), MVA; a load at the substation according to
control measurements; transmission capacity of the
connection 110–220 kV, MW; averaged data on the
energy potential of RES; average solar radiation
energy for the period, kWh/m2; map of average
annual wind speed, m/s; volumes of forest industry
waste, million m3; technical and cost characteristics
of renewable energy facilities; specific price of 1
kW of installed power, rub / kW; the price of these
connections depending on the exchange rate;
average annual maintenance costs.
The foundation for optimizing the territorial
deployment of manufacturing facilities using
renewable energy sources is a map of technological
and geographical zoning. The source data's
cartographic representation is linked to a latitude-
longitude grid. As a method for qualitative and
quantitative assessment of the usefulness of setting a
generating object, the method of hierarchies was
chosen, allowing a comparative assessment of the
options for the following groups of parameters: a
group of technical parameters; a group of economic
parameters; a group of environmental parameters.
The system for evaluating the degree of
usefulness of decisions is based on a single scale of
Saaty from 1 to 9 points, where 1 corresponds to
maximum usefulness and 9 to zero usefulness for all
groups of parameters. Estimates of utility with
possible solutions are presented in Table 1. The
assignment of object j according to the considered
parameter I to this or another state is determined by
the ratio between the values of the parameter Yijt
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.5
Ekaterina Gospodinova
E-ISSN: 2224-350X
41
Volume 18, 2023
and the threshold values. Such transformations are
performed according to the rules described in Table
1, [20], [21].
Table 1. Single scale of Saaty
nothing of
value
Ratio of
normalized
parameter values
Evaluation
Maximum
utility 0 and -1
1
Objective
utility level 1
0<
2
Objective
utility levels 2
<
3
Objective
utility levels 3
<
4
Compromised
utility
<
5
Subjective
usefulness
level 1
<
6
Subjective
usefulness
levels 2
<
7
Subjective
usefulness
levels 3
<
8
Zero utility
9
A group of technical parameters: Available power
αp:
, (1)
where is the available power. This parameter
takes a value of 0 with respect to the object j(x, y) if
the current of any line Ip connected to the energy
center k(x, y), in mode N-1, does not exceed the
permissible value on Ipv; the value of 1 if the current
of any line Ip does not exceed the emergency
tolerance value Ietv; otherwise, it is determined by the
ratio Ip/Ietv.
Limited to the power of the force center :
, (2)
The parameter takes the value 0 if the limited power
of the transformer for k(x,y) is provided.
Otherwise, it is determined by the ratio of the power
set Pset to the limited power .
Ensuring the required voltage level in the network:
The parameter assumes the value 0 if, as a result of
the calculation of the established state with
generating object j(x, y), the voltage deviation Uk is
more than 5% of the nominal value; if it is less than
5%, the value is 1.
, (3)
Influence on active power losses ∆:
(4)
The parameter is determined by the ratio of
total power losses in the circuit with the
generated object/,
km, and in
the output circuit
.
A group of economic parameters. Investments
γ:
The evaluation of the specific capital
investment k in the construction of a production
facility j(x,y) was carried out on the basis of
RES and is determined by the ratio:
(5)
Payback period γc. The parameter estimates the
period of time for the return of the initial
investments in the construction of the generating
object j(x, y) and takes the value c 15 if the term Tc
is a payback period exceeding 15 years, otherwise -
0. The calculation is based on RES data, includes
land acquisition, and cost of electricity, and is
calculated as follows:
(6)
Group of harmful substances εj. Noise N and
vibration V: The parameter, which takes the value 1
in the event of an increase in harmful substance
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.5
Ekaterina Gospodinova
E-ISSN: 2224-350X
42
Volume 18, 2023
emissions and 0 in all other cases, is defined based
on the estimation of the reduction of pollutant
emissions into the atmosphere in thousands of tons.
After determining the estimates for individual
parameters for object j, an estimate for groups of
parameters n is formed, which is calculated as a
weighted average normalized estimate.
(7)
Similar to (7), after determining the ratings for
groups jn in accordance with the proposed scale
(Table 1), the final utility rating e Zj for all groups
of parameters for the implementation of a RES-
based production project.
.
/
(8)
Optimal options for deploying RES-generating
capacities in a given region are implemented based
on a genetic algorithm, the function of which is the
final utility result Zj for all groups of parameters
[22], [23].
3 Mathematical Model and the
Genetic Algorithm
Based on the idea that the template H is a specific
subset of genetic strings and Holland's theorem,
which allows one to establish a relationship between
the number of strings belonging to mt(H) in the
current evolution level and the number of strings
belonging to mt+1(H) in the next evolution level in
the form of a useful working ratio, it is possible to
estimate the speed and stability of the adaptation
process in artificial populations of the genetic
algorithm:
(9)
where mt(H) is the current value of the average
survival according to the template,
is the
observed value of the average survival,
and is an
event consisting of the fact that the template H will
be destroyed as a result of the joint action of genetic
operators; in other words,
, (10)
Where
is an event consisting of the fact that
the template H will be destroyed as a result of the
execution of a genetic operator. Using the
provisions of the theory of individual survival
allows the identification of the main shortcomings
of genetic search methods and shows the need to
develop GA using different evolutionary models
when solving global extremum search problems.
There are ways to make it easier to use genetic
algorithms to find the global extrema of objective
functions when solving problems. A dominant
genetic algorithm was developed based on a
mathematical model. It has been demonstrated that
encoding information as binary code with strings
might enhance GA performance, particularly when
utilizing gray codes. Nevertheless, in this situation,
it is difficult to decrease the time required to encode
and decode binary data. One solution to this
problem is linear codes, which include gray codes
when using the neural network apparatus.
Let a linear code (n, k) forming vectors that are
elements of the field GF(2n) be given in the form of
a generating matrix:
(11)
For a given set A, a matrix can be constructed:
A=
(12)
whose elements are elements of vectors αkA, [24].
The created neural network consists of k neurons, a
distribution input layer, and m radial neurons input;
the links between the elements of the hidden layer
establish the center of the radial function for each
element.
, (13)
where is the Euclidean norm (the
Hamming distance is permissible), α1c is a vector
serving as the centroid, and the constant σ
determines the width of the curve; it is suggested
that the value be chosen to satisfy the inequality
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.5
Ekaterina Gospodinova
E-ISSN: 2224-350X
43
Volume 18, 2023
. The centroids of the radial neurons
coincide with the code words of set A:
The output layer of the neural network
consists of n neurons, and the weighted summation
of the signals of the hidden layer is performed with
subsequent transformation of the activation
function, [25].
, (14)
The following equation can be used to determine the
weight matrix of the neural network's output layer,
whose element indicates the strength of the synaptic
connection between a neuron from the hidden layer
and the j-th neuron from the output layer:
, (15)
where A is the code word matrix (4), and G is the
linear code-generating matrix. The offset value of
all output neurons in the output layer is bi=-1/2, j=1,
n. Let the values of the allelic genes and the locus
dominance trait form a cluster
, with a
score value of
,
, (16)
which shows how the inputs and outputs of the
majority of elements depend on each other.
The set of genetic operators in the developed
majority genetic algorithm is determined, the
performance characteristics of the selected genetic
operators are shown, and their destructive properties
are evaluated from the point of view of the theory of
the survival of individuals based on how they affect
the value of the growth factor.
[1-P.SH] (17)
For the Majority Genetic Algorithm, we consider
multiple genetic operators Ω, which consist of a
crossing operator ς and a mutation operator ψ. In
this case, for the growth factor from equations 10
and 17, we get:
[(1-P])(1-P|], (18)
where P is the probability of destruction of the
template and H, P. | is the probability of
destruction of the template H due to the influence of
mutations, the probability of pattern destruction H.
The estimate of the probability of pattern
destruction is determined by the ratio:
P])
, (19)
where P is the probability of crossing execution
σ(H) is the order of the pattern H.
Estimates of the likelihood of template destruction
due to mutations were made, and the formula can be
used to measure how well the proposed models of
how mutations happen work in most genetic
algorithms:
P|=, (20)
where Pm is the mutation probability.
It was found that if the gene
can be changed by
mutation with frequency
and the gene
with
probability
, and the point mutations of the genes
are independent, then the probability to destroy the
template is:
P|=
, (21)
when
.
The lowest value of P|is reached when
=0.
The developed mathematical model of the non-free
mutation process proves that the use of non-free
mutation algorithms allows minimizing and even
eliminates the influence of mutations; in other
words, equality is achieved.
P|= (22)
as a result of which it is possible to provide the
maximum values of the studied data without
abandoning the mutation operator.
The mean relative prediction error is
, (23)
where d is the actual value of the predicted quote; y
is the prediction of the neural network; and S is the
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.5
Ekaterina Gospodinova
E-ISSN: 2224-350X
44
Volume 18, 2023
number of examples in the validation sample.
Single-output neural networks are commonly used
for prediction.
3 Results of Neural Network Research
Using the genetic algorithm that was made, tests
were done and the results were analyzed to figure
out how renewable energy power plants would
work. They confirm the reliability and significance
of the theoretical results. The neural network
training procedure was performed with intermodal
alpha activation functions, then for single-layer and
multi-layer neural networks with threshold
activation functions. In all three cases, the effective
application of GA to train prior neural networks is
confirmed.
Some of the best things about the genetic algorithm
are that it is good at solving discrete problems, it
doesn't care much about how accurate the first
approximation is, and it lets you figure out the
objective function right away. Zoning was done in
accordance with the energy potential of the RES for
the calculations made on the Sliven region's land. In
the plan of an equivalent electrical network with a
voltage of 110 kV or higher, 32 energy centers
connected to neighboring municipalities are taken
into account. The volume of the primary
interregional transmissions accounts for the 220 kV
electrical network. The following RES-based
production capacity was examined during the
forecasting process for a specific territory: wind
farms, power plants, and photovoltaic stations. The
use of the genetic algorithm led to the ranking of
several possibilities for the development of RES-
based production in accordance with the type of
primary energy carrier. Table 2 displays the options
with the highest level of compliance.
Table 2. Level of compliance according to type of
primary energy carrier
P
MWt
Location
Technical
parameters
Economic
parameters
Environmental
Parameters
10
Sliven
0,68
0,83
0,00
50
Yambol
0,49
0,85
0,00
20
Kotel
0,61
0,83
0,00
15
Nova Zagora
0,65
0,48
1,00
20
Meden
Kladenec
0,38
0,48
1,00
30
Kaloyanovo
0,62
0,62
1,00
25
Katunishte
0,78
0,67
0,80
28
Samoilovo
0,65
0,74
0,00
After looking into the results of RES-based
optimization of the type, installed capacity, and
location of production facilities, the following was
found: expanding the production facilities' capacity,
distributing the supplies while the network is empty,
and cutting down the load on the lines by up to
40%; The transformer power value of the power
centers under consideration typically sets a limit on
the installed power that results; the energy regions
with the highest levels of economic activity—as
measured by an increase in load over a five-year
horizon—are the most suitable locations for RES-
based power generation. Figure 1 shows how the
options' usefulness is illustrated.
The last stage certifying the reliability of the
obtained results is shown in Figure 2, a histogram of
the error representing a comparison between the
testing and training processes.
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.5
Ekaterina Gospodinova
E-ISSN: 2224-350X
45
Volume 18, 2023
Fig. 1: Parameterized utility evaluation.
Fig. 2: Error histogram.
In Figure 3 a graphical comparison is made between
real input data and output prediction results of the
neural network. The comparison is made for the
entire investigated time interval. In the conducted
research, with the parameters and settings set in this
way, the obtained estimated results for power
generation from RES are as close as possible to the
real ones, in percentage ratio the deviation from the
actual values is 10.13%.
Fig. 3: Comparison between Energyand Neuron
Energy.
4 Conclusion
This study is all about analyzing and making a
mathematical model and algorithm to improve the
efficiency of energy supply to areas that use
renewable energy sources and are connected to a
parallel energy system. The model was made to
optimize the placement of production facilities
based on maps for technological zoning. It worked
well when the electricity system in the Sliven region
was analyzed as an example. The importance is
explained, and the need to make GAs using different
models of evolution and study how adaptation
works are shown. A genetic algorithm has been
developed for which the rules of gene expression are
built according to the majority principle, which
makes it possible to simplify its hardware and
software implementation. Its use allowed us to
investigate the impact of natural resources on
performance evaluation and to predict suitable
locations for generating RES-based capacities. The
GA performance analysis performed confirmed the
theoretical results from which simulation models
were built. Based on the results of the simulation
modeling, a conclusion is made about the increase
in the efficiency of the search for extremes due to
the application of the developed algorithm in
solving optimization problems. The effective
application of GA is shown in the example of
solving the neural network training problem.
Acknowledgment:
The authors would like to thank the Research and
Development Sector at the Technical University of
Sofia for the financial support.
References:
[1] Ayamolowo, O. J., Manditereza, P. T. &
Kusakana, K., Optimal planning of
Renewable energy generators in modern
power grid for enhanced system inertia,
Technology and Economics of Smart Grids
and Sustainable Energy, volume 7, Article
number: 33, 2022.
[2] De Caro, F., Collin A. J. & Vaccaro A.,
Evaluation of Classification Models for
Forecasting Critical Voltage Events in Power
Systems, Technology and Economics of Smart
Grids and Sustainable Energy, volume 8,
Article number:1, 2022.
[3] Mollov, Y., Energy production from
renewable sources in the Republic of Bulgaria
– situation and trends, Modern engineering
and innovative technologies, International
scientific conference "World Science and
Technology Trends, SWorld, issue 2, vol. 1,
2019, pp. 48-52. ISSN 2567-5273, November,
Germany.
[4] Ibrahim, A., Aboelsaud R. & Obukhov, S.,
Application of Cuckoo Search Algorithm for
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.5
Ekaterina Gospodinova
E-ISSN: 2224-350X
46
Volume 18, 2023
Global Maximum Power Point Tracking of
PV under Partial Shading, 1st IEEE
International Youth Conference on Radio
Electronics, Electrical and Power
Engineering, Moscow, March 14-15, 2019.
[5] Obukhov, S., Ibrahim, A. Al-Sumaiti. A. &
Rboelsaud, R., Optimal performance of
dynamic particle swarm optimization based
maximum power trackers for stand-alone PV
system under partial shading conditions,
IEEE, DOI: 2966430, 2020.
[6] Khakhar, D., The National Centre for
Photovoltaic Research and Education,
Jawaharlal Nehru National Solar Mission of
the Government of India,2020.
[7] Barkhordar, Z., Investigating the cost-
effective energy efficiency practices with
mitigated rebound: the case of energy
intensive industries, International Journal of
Sustainable Energy Planning and
Management, Vol.35, 2022,
https://doi.org/10.54337/ijsepm.vol35.
[8] Tailor, R., Beña, L., Conka Z. & Kolcun, M.,
Design of Management Systems for Smart
Grid, In Proceedings of the 2021 Selected
Issues of Electrical Engineering and
Electronics (WZEE), Rzeszow, Poland, 2021.
[9] Jurasz, J., Canales Kies, F.A., Guezgouz M. &
Beluco, A., A review on the complementarity
of renewable energy sources: Concept,
metrics, application and future research
directions, Solar Energy, № 195., 2022, рр.
703-724 (doi: 10.1016/j.solener.).
[10] Siregar, Y., Ranking of energy sources for
sustainable electricity generation in Indonesia:
A participatory multi-criteria analysis,
International Journal of Sustainable Energy
Planning and Management, Vol.35, 2022,
DOI: https://doi.org/10.54337/ijsepm.vol35.
[11] Chiang, M., Huang, S., Hsiao, T. Zhan T. &
Hou, J., Optimal Sizing and Location of
Photovoltaic Generation and Energy Storage
Systems in an Unbalanced Distribution
System, MDPI Energies, 2022,
https://doi.org/10.3390/en15186682.
[12] Kanth, D., Lalita M. and Babu, P., Siting &
Sizing of Dg for Power Loss & Thd
Reduction, Voltage Improvement Using Pso
& Sensitivity Analysis, International Journal
of Engineering Research and Development, e-
ISSN: 2278-067X, p-ISSN: 2278-800X,
www.ijerd.com, Volume 9, Issue 6, 2013, pp.
01-07.
[13] Khan B. & Singh, P., Optimal Power Flow
Techniques under Characterization of
Conventional and Renewable Energy Sources:
A Comprehensive Analysis, Journal of
Engineering, Volume 2017,
https://doi.org/10.1155/2017/9539506.
[14] Georgieva, P., GENETIC ALGORITHMS AS
A TOOL FOR SOLVING OPTIMIZATION
PROBLEMS, Computer Sciences and
Communications, Volume 2, No. 3, BSU,
Burgas, 2022.
[15] Lenarczyk, A., Jaskólski M. & Bućko, P., The
Application of a Multi-Criteria Decision-
Making for Indication of Directions of the
Development of Renewable Energy Sources
in the Context of Energy Policy, MDPI
Energies, 15(24), 9629, 2022,
https://doi.org/10.3390/en15249629.
[16] Hassan, A., Sun Y. & Wang, Z., Optimization
techniques applied for optimal planning and
integration of renewable energy sources based
on distributed generation: Recent trends,
Cogent Engineering, Volume 7, Issue 1,
2020,
https://doi.org/10.1080/23311916.2020.17663
94.
[17] Bhatti J. & Making, H., The World More
Sustainable: Enabling Localized Energy
Generation and Distribution on Decentralized
Smart Grid Systems, World Journal of
Engineering and Technology, № 6, 2018, рр.
350-382, (doi: 10.4236/wjet.2018.62022).
[18] Burger, C., Froggatt, A., Mitchell C. &
Weinmann, J., Decentralised Energy: A
Global Game Changer, Ubiquity Press:
Berkeley, CA, USA, 2020.
[19] Kirgizov, A., Expert system application for
reactive power compensation in isolated
electric power systems, Electr. Comput. Eng.,
Vol. 11, № 5, 2021 pр. 3682-3691 (doi:
10.11591/ijece.v11i5. pp3682-3691).
[20] Eroshenko, S.A., Manusov, V.Z., Matrenin,
P.V., Igumnova E.A. & Nesterenko, G.B.,
Comparison study of wind flow velocity
short-term forecasting methods based on
adaptive models and neural networks,
International Journal of Advanced Science
and Technology, 29 (8 Special Issue), 2020,
pp. 2108-2115.
[21] Eroshenko S. and Khalyasmaa A.I., The
improvement of distributed generation
integration efficiency, In: 11th IEEE
International Conference on Compatibility,
Power Electronics and Power Engineering –
CPE-POWERENG, 2017, pp. 94-99. DOI:
10.1109/CPE.2017.7915151.
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.5
Ekaterina Gospodinova
E-ISSN: 2224-350X
47
Volume 18, 2023
[22] Eroshenko S. and Khalyasmaa A.I.,
Intelligent model of decision support system
of distributed generation integration, IEEE
International Conference on Software
Engineering and Service Science – ICSESS,
2017, pp. 79-82. DOI:
10.1109/ICSESS.2017.8342868
[23] Eroshenko, S., Manusov, V. Z., Makarov I. S.
& Dmitrev, S.A., Training sample
dimensions impact on artificial neural
network optimal structure, 12th International
Conference on Environment and Electrical
Engineering, 2013, pp. 156-159. DOI:
10.1109/EEEIC.2013.6549608.
[24] Xiaofeng Q. and Palmieti, F., Theoretical
analysis of evolutionary algorithms an infinite
population size in continuous space. Parts
1,11 IEEE Trans, on Neural Networks, Vol.5,
No.l, 102-130, 2014.
[25] Michalewicz, Z., Genetic Algorithms + Data
Structures = Evolutionary Programs,
Springer-Verlag, Al Series, New York, 1992.
WSEAS TRANSACTIONS on POWER SYSTEMS
DOI: 10.37394/232016.2023.18.5
Ekaterina Gospodinova
E-ISSN: 2224-350X
48
Volume 18, 2023
Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
The author contributed in the present research, at all
stages from the formulation of the problem to the
final findings and solution.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
Conflict of Interest
The author has no conflict of interest to declare that
is relevant to the content of this article.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
The authors would like to thank the Research and
Development Sector at the Technical University of
Sofia for the financial support.
