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0Descendants of Al-Farghani" electronic scientific
journal of Fergana branch of TATU named after
Muhammad al-Khorazmi. ISSN 2181-4252
Vol: 1 | Iss: 4 | 2024 year
Электронный научный журнал "Потомки Аль-
Фаргани" Ферганского филиала ТАТУ имени
Мухаммада аль-Хоразми ISSN 2181-4252
Том: 1 | Выпуск: 4 | 2024 год
Muhammad al-Xorazmiy nomidagi TATU
Farg‘ona filiali “Al-Farg‘oniy avlodlari”
elektron ilmiy jurnali ISSN 2181-4252
Tom: 1 | Son: 4 | 2024-yil
CREATING A MODEL OF THE FALL OF SOLAR ENERGY IN CERTAIN COORDINATES
Aliyev Ibratjon Xatamovich Researcher in the field of atomic nucleus and elementary particle physics, Director of the Scientific Research Institute "Physics of Resonant Nuclear Reactions" Presidium, Scientific Research Institute of Physics of Resonant Nuclear Reactions Margilan, Republic of Uzbekistan 151100, Republic of Uzbekistan, Fergana region, Margilan, Tinchlik str., 195/37 E-mail: [email protected], ORCID: https://orcid.org/0009-0000-4094-6704
Bilolov Inomjon Uktamovich Candidate of Pedagogical Sciences, Professor Department of Economics and Vocational Education, Faculty of Telecommunications Engineering and Vocational Education Ferghana, Republic of Uzbekistan 150118, Republic of Uzbekistan, Ferghana region, Ferghana city, Tadbirkorlar str., 162 E-mail: [email protected], ORCID: https://orcid.org/0000-0001-5022-7068
Abstract. In the course of this study, a mathematical model of solar activity was created at the specified coordinates for a certain time, with the development of an appropriate algorithm of action. In the course of the study, a function was created with respect to a spherical coordinate system based on an approximate model of the planet and its irradiation system. Subsequently, empirically obtained boundary conditions were set for the function, so that a certain general form was turned into a particular form in the class of linear functions.
|| Keywords: mathematical modeling, solar constant, functional dependence
INTRODUCTION
During the development of solar energy, it became possible to actively observe the growing need to consider the system for creating new renewable energy power plants, which include solar, wind, wave, BU and other systems [1-2; 4]. Each of them currently has a different degree of activity and creation algorithm. So, among such systems, solar panels deserve attention regarding their need to consider solar activity in the specified zone [3; 9].
Initially, it is necessary to take into account the concept of the solar constant, that is, the energy radiated from the Sun, which falls on a square meter [58; 11]. This parameter, calculated in W/m2, is a
constant and is valid on the Earth's surface at the equator during the vernal equinox or solstice [10]. Also, in addition, there are some additional empirical results that can be used, which as a result should create a common function in a spherical coordinate system of 3 variables, which will eventually make it possible to model solar activities in these coordinates, which is relevant.
MATERIALS AND METHODS
In the course of the study, methods of physical and mathematical modeling, analysis, empirical research were used, establishing the general form of the function with further substitution of boundary conditions and obtaining a particular form of the
https://al-fargoniy.uz/
"Descendants of Al-Farghani" electronic scientific
journal of Fergana branch of TATU named after
Muhammad al-Khorazmi. ISSN 2181-4252
Vol: 1 | Iss: 4 | 2024 year
Электронный научный журнал "Потомки Аль-
Фаргани" Ферганского филиала ТАТУ имени
Мухаммада аль-Хоразми ISSN 2181-4252
Том: 1 | Выпуск: 4 | 2024 год
Muhammad al-Xorazmiy nomidagi TATU
Farg‘ona filiali “Al-Farg‘oniy avlodlari”
elektron ilmiy jurnali ISSN 2181-4252
Tom: 1 | Son: 4 | 2024-yil
function. The experimental results were used as research materials.
RESEARCH
To model the described phenomenon, a spherical coordinate system is introduced, depending on the indicators of three variables, demonstrating the following parameters (1), while forming an equation of the form (2).
^1 — day, ф2 — latitude from 0 in the center, ф3 — deviation (—23.5,+23.5) (1)
%1Ф1 + *2<p2 + *3<р3 = E (2)
According to the empirical data obtained [1; 1011], the following statements have been established reliably:
1. At the equator at noon GMT in the waters of the Gulf of Guinea on January 1, when measured from 2013 to 2023, with a deviation of 23.497 degrees of the Earth's axis, an average energy value of 1,412 W/m2 was established;
2. In the specified coordinate "center of the world", when conducting similar measurements on July 1 during 2013-2023, an average energy value of 1,321 W/m2 was established.
3. On the territory of the Republic of Uzbekistan, namely on the territory of the city of Ferghana, the city of Margilan, the city of Tashkent, the city of Samarkand and some other coordinates of the corresponding observatories, observation posts and laboratories, an average value was obtained, set during the last observations from 2018-2023 at 350 W/m2 at noon on
According to the data obtained, a part of the function is formed and using the third statement, an equation is formed with the solution (4), as well as the general form of the function (5).
90x1 + 41x2 — 23.497x3 = 350 => = > x2 = —25.902422 (4)
E = 15.18(3)^ — 25.902422ф2 — 1.9364p3 (5)
The resulting function is complex-valued when switching to a real set, due to the representation of the graph relative to the Republic of Uzbekistan - 41 degrees north latitude in three-dimensional form (Fig. 1) and direct projection (Fig. 2).
Fig. 1. Three-dimensional modeling of the
Fig. 2. Projection of the graph relative to (5)
December 22 - the day of the winter solstices.
Based on what has been presented, it is
appropriate to present for the 2 initial cases a
formulation of the form (3).
(90x1 — 23,497x3 = 1 412 13
{90x1 + 23,497x3 = 1 321 > 180X1
= 2733 => {X1 = 1518(3)
x3 = —1.9364
(3)
The resulting formulations can indeed clearly show the system under study, taking into account the complex set, where it is possible for a function to participate while simultaneously in a spherical coordinate system.
RESULTS
In order to switch to the actual set, it became necessary to use experimental indicators again. The value stated by the devices, namely, luximeters, exposure meters, photometers and various types of
https://al-fargoniy.uz/
"Descendants of Al-Farghani" electronic scientific
journal of Fergana branch of TATU named after
Muhammad al-Khorazmi. ISSN 2181-4252
Vol: 1 | Iss: 4 | 2024 year
Электронный научный журнал "Потомки Аль-
Фаргани" Ферганского филиала ТАТУ имени
Мухаммада аль-Хоразми ISSN 2181-4252
Том: 1 | Выпуск: 4 | 2024 год
Muhammad al-Xorazmiy nomidagi TATU
Farg‘ona filiali “Al-Farg‘oniy avlodlari”
elektron ilmiy jurnali ISSN 2181-4252
Tom: 1 | Son: 4 | 2024-yil
solar cells showed the reduction of the type of function to the state (6).
(15.18(3)^! - 25.902422^ - 1.9364^3) - Е0 £’= - з - - -(6)
Where, £- — the average energy vaZue о/ 1
W
— 2, eauaZ to 1 360 .
m-
Thus, it is possible to move to the stage of direct three-dimensional modeling in a real set.
DISCUSSION
As a result of using the changes obtained, the function has changed, also making changes to the graph by projection relative to the time variable relative to different scales for readings on the scale of the whole day (Fig. 3) and year (Fig. 4).
Fig. 3. Time chart throughout the year
Fig. 4. Diagram by day throughout the year
Three-dimensional modeling of the modified system clearly shows the difference between the energy directed from the Sun and, with a known efficiency of the system, the possibility of generating indicators of actually generated energy. So, in the case of Figure 5, a simulated diagram is shown for the resulting function (6), taking into account all boundary conditions, which clearly shows the received capacities.
Fig. 5. Three-dimensional diagram of energy production
When considering in detail the efficiency of a solar battery, taking into account the use of crystalline or amorphous silicon, it is appropriate in the first case to take into account the laboratory efficiency of 56.4% and the empirically determined case of 24.6% in the case of crystalline silicon and 9.6% in the case of amorphous silicon. And since, based on the definition of efficiency, the ratio between the received and generated energy is represented, it is appropriate to create a graph of the generated power (Fig. 6).
Fig. 6. Three-dimensional diagram of energy generation
Due to this, it is clearly possible to see the obtained simulation results on the territory of the Republic of Uzbekistan (41 meridians).
ACKNOWLEDGMENTS
The authors are grateful to the researchers of the Ferghana Polytechnic Institute, namely Abdurakhmonov S. M., Ergashev S. F. and the researchers of Ferghana State University, namely 203
https://al-fargoniy.uz/
"Descendants of Al-Farghani" electronic scientific
journal of Fergana branch of TATU named after
Muhammad al-Khorazmi. ISSN 2181-4252
Vol: 1 | Iss: 4 | 2024 year
Электронный научный журнал "Потомки Аль-
Фаргани" Ферганского филиала ТАТУ имени
Мухаммада аль-Хоразми ISSN 2181-4252
Том: 1 | Выпуск: 4 | 2024 год
Muhammad al-Xorazmiy nomidagi TATU
Farg‘ona filiali “Al-Farg‘oniy avlodlari”
elektron ilmiy jurnali ISSN 2181-4252
Tom: 1 | Son: 4 | 2024-yil
Karimov B. H., Karimov Sh. T. and colleagues from the Research Institute of FPM at NU for their cooperation.
CONCLUSION
As a conclusion, it can be clearly noted that an organized study can later become a private model close to the analytical one. Or in the form of a discrete model, striving for the degree of analyticity of a physical and mathematical model for predicting the efficiency and energy indicators of solar activity in the specified coordinates.
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