Calculation of the intensity of solar radiation
Elyor Saitov
1
, Ortik Mamasaliyev
1
, Akhmedov Usmonjon
1
and Azimov Navruzbek
1
1
Tashkent University of Applied Sciences, Gavhar Str. 1, Tashkent 100149, Uzbekistan
(elyor.saitov, ortiqmamasaliyev)@gmail..ru
https://doi.org/10.5281/zenodo.10470990
Keywords:
Monitoring, Solar radiation, Wind characteristics, Meteorology, Pyrometer, Intensity, Anemometer, Weather
vane.
Abstract:
This paper of this work is the solar radiation of methods for calculating the intensity of solar radiation by
the analytical method and the method of coefficients. At the stage of developing a feasibility study for a solar
heating system project, the choice of a method for calculating the influx of solar radiation intensity is
important. As a result of the calculations, the graphs of the dependences of the total inflow of the specific heat
flux per 1 m
2
during the year were obtained, calculated using various methods. The calculations showed that
the amount of incoming heat calculated by various methods differs significantly.
1 INTRODUCTION
The solar power system seems to be very simple.
As in most other power supply systems from
autonomous sources, it has only 4 main components
the photovoltaic panels themselves, batteries, a
charge controller and an inverter that converts low-
voltage direct current to a household standard of 220
V
.
However, all elements must be coordinated with
each other. And if the components common to all
such systems (inverter, batteries, wires) are
considered on a separate page, then here I want to
consider components specific to photovoltaic systems
- photovoltaic panels (solar panels) and controllers for
them. But, of course, first of all, the most important
question is considered the choice of the power of solar
panels or, which in real life, with its inevitable
limitations in financial and material resources, is
much more relevant - how to determine what kind of
result can be expected from solar panels of one or
another nominal power , that is, is the game worth the
candle [1].
Unlike traditional energy sources, the operation of a
photovoltaic battery depends on both climatic and
technological factors. The whole set of factors that
affect the operation of a photovoltaic battery can be
divided into two groups:
1. Factors due to the design and manufacturing
technology of the photovoltaic array and the
photovoltaic installation, the angle of the photovoltaic
array in relation to the horizon, the characteristics of
the photovoltaic array, etc.
2. Climatic factors due to the impact of ambient solar
radiation on the output energy characteristics of a
photovoltaic battery. Such factors include solar
radiation, air temperature, air dustiness, humidity,
wind speed [2]. When designing a solar energy
system, it is necessary to take into account the
climatic features of the region where it is planned to
use a photovoltaic battery. For this, full-scale tests of
a photovoltaic battery were carried out with
simultaneous monitoring of atmospheric parameters.
Determination of the possibilities of the Sun. The
calculation of electricity needs for a particular mode
of its use is considered on a separate page. Now we
need to determine the possibilities of the Sun and,
before starting to invest our money and our time in
the creation of the system, solar radiation these
possibilities with their needs. The basis for
calculating expected energy production is data on the
power of solar radiation, taking into account weather
conditions. It is desirable that the data be for different
angles of the panel, at least for vertical and horizontal
orientation.
The most important issue is the choice of the angle
of the panel. Bearing in mind the possibility of year-
round use, an angle of 15° more than the geographical
latitude should be preferred (in addition, the greater
the slope, the less dust and snow will linger on the
panel). For Moscow, this is 70°, since I have the
opportunity to install a panel with a south orientation
at such an inclination (deviation from the south
direction by about 10 ° to the east is unprincipled).
By the way, if the winter use of solar panels is not
expected, they may well be placed on a wall or roof
slope oriented not to the south, but to the west or east,
and in this case it is better to increase the slope of the
panels along the solar radiation direction with the
optimal direction for summer or in general, install the
panels vertically, since in the morning and evening
the Sun is close to the horizon.
2 Materials and Methods
The purpose of this work is the solar radiation of
methods for calculating the intensity of solar radiation
by the analytical method and the method of
coefficients. Calculation of the intensity of solar
radiation by the method of coefficients. The intensity
of solar radiation, which enters the surface of any
spatial position every hour of daylight hours q
day.1
, is
determined by the formula:
𝛾 = |1 −
𝜂
1
𝜂
0
|
(1)
where q
day.1
is the intensity of solar radiation for
each hour of daylight hours;
P
A
is a coefficient that takes into account the
azimuth of the SC placement. P
s
is the SC position
coefficient for direct solar radiation (Table 1. [3]).
If the NC is oriented to the south, then the
coefficient PA =1.
Ps is the SC position coefficient for direct solar
radiation (Table 1. [4]).
A photo power plant (Fig. 1) consists of solar
modules, wind turbines, batteries, an inverter, a
controller, and other devices. When energy sources
(solar and wind power) are plentiful, the generated
power, after meeting the load demand, will charge the
battery. Table 1 shows a list of the main equipment
[5].
Table 1. Shows a list of the main equipment.
Determines the ratio of the intensity of direct solar
radiation, which enters the plane of southern
orientation, located at an angle
β
to the horizon, to the
intensity of direct solar radiation, which enters a
horizontal surface.
𝐼
𝑠
sop
is the intensity of direct solar radiation that
enters ahorizontal surface, W/m
2
;
𝐼
𝑑
sop
is the intensity of scattered solar radiation that
enters a horizontal surface,P
d
is the collector position
factor for diffuse solar radiation.
Data on
𝐼
𝑠
sop
and I
dsop
values for individual cities
are given in the appendix. In the absence of data, you
can use the approximate values of the hourly sums of
direct and diffuse solar radiation according to the
zoning map and weather data [6].
Calculation
of solar
radiation
intensity
analytically. In accordance with the methodology:
The magnitude of the intensity of solar radiation q,
W, incident on 1
m
2
of the inclined plane of the
surface surface in each hour of daylight hours, under
real conditions, is determined by the formula:
𝜂 = 𝑓𝑓
𝑗
𝑠𝑐
𝑈
𝑜𝑐
𝑊𝑆
(2)
then (2) can be written as
𝛾 = |1 −
𝑗
𝑠𝑐,1
𝑗
𝑠𝑐,0
|
where I
s
and I
d
are the specific heat flux, W/m
2
, of
direct and diffuse solar radiation incident on a
horizontal surface at latitude
ϕ
of a given area; these
data are given in climate reference books;
β
- is the angle between the considered plane and
the horizontal surface (i.e., the inclination of the solar
collector plane to the horizon);
δ
- declination, i.e., the angular position of the Sun
at solar noon relative to the plane of the equator,
depending on the time of year (positive value for the
northern hemisphere);
ω
- is the latitude of the area (positive for the
northern hemisphere);
γ
- is the azimuthal angle of the plane, i.e., the
deviation of the normal to the plane from the local
meridian (the south direction is taken as the reference
point, the deviation to the east is considered positive,
to the west - negative);
ω
- hour angle, equal to zero at noon for collectors
oriented to the south, in an hour the value of the hour
angle changes to 15 with a plus sign (from 12 o'clock
to the morning) or minus (from 12 to the evening).
For reservoirs whose orientation differs by an
azimuth angle r from the direction to the south, this
angle with its sign must be added to 180 °. To
determine solar radiation per hour of design
parameters, it is necessary to add 15°/2 = 7.5° to the
value of the hour angle of the start time of the
estimated hour, i.e. for example, for the time from 11
a.m. to 12 p.m., take the solar radiation value of the
hour angle as 1130.
Considering the above, the formula can be written
as:
ω
=180
0
+
γ
-15
0
t+7,5
0
δ
=23,45
∙
sin(360×384+n/262), (3)
where n is the ordinal number of the day of
theyear, as n is taken the number of solar radiation of
the settlement day of the month for I - XII months of
the year;
η
0
is a coefficient that takes into account real
cloudiness conditions
;
η
1
is a coefficient that takes into account the
degree of transparency of the atmosphere
(for
Simferopol
η
1
=1).
2.1
METHODS OF MODELING
SOLAR BATTERY
Thus, the intensity of the heat flow, determined by
formula (3), is a function of the season µ, time of day
τ
, tilt angle
β
and azimuth of the solar collector
τ
. It
depends on the specific heat flux, which brings with
it direct and diffuse solar radiation, which falls on the
horizontal plane at the latitude of the given area.
Table 1.
Methods of modeling solar battery.
№
Method
Explanation
1
Method for
calculating the
intensity of solar
radiation by the
method of coefficients
This technique will allow
you to calculate the intensity of
solar radiation that enters the
surface of any spatial
position every hour of daylight
hours.
2
Method for
calculating the
intensity of solar
radiation analytically
This technique will allow you
to calculate the magnitude of
the intensity of solar radiation
incident on 1 m
2
of an inclined
plane of the surface in every
hour of daylight hours, under
real conditions
Calculations were made according to formulas (1)
and (3) for the city of Simferopol for a surface
oriented to the south and plots of (Figure 1) were
plotted. and (Figure 2) dependence of solar radiation
inflow by (
Figure 1). The intensity of the incident
solar radiation per 1
m
2
of the surface at different
angles of inclination to the horizon. Calculation
according to the method [7].
Fegure 1:
Dependence of solar radiation inflow.
Figure 2: Intensity of the incident solar radiation per 1 m
2
of the surface at different angles of inclination to the
horizon.
Figure 2 the intensity of the incident solar radiation
per 1 m
2
of the surface at different angles of
inclination to the horizon. Calculation according to
the method [8].
Figure 3:
Solar radiation intensity for different tilt
angles.
Figures 3. Percentage of solar radiation intensity for
different tilt angles, calculated using various
methods.
Various variants of the analytical model of the
photocell are used to simulate the solar cell(SC) and
solar battery(SB). A generalized SC model and
several simplified versions of the model are
implemented, and the simulation results are analyzed.
It is shown that for photovoltaic applications, the
shunt resistance of solar cells is considered large
enough, and recombination in the region of the
volume charge is negligible [9, 10].
2.2
METHODS OF VAC
The simulation of the temperature characteristics of
the solar system based on the built-in PSpice model
of the diode is presented. This method of simulating
temperature effects does not take into account
changes in the photocurrent at different temperatures.
Simulations of SC for various levels of ionizing
cosmic radiation are performed [11, 12,13].
The SB model is presented and various cases of
battery shading are described. The positive role of
shunt diodes in SB is shown: they protect the battery
operation when one of the elements is completely
shaded, but reduce the output voltage of the system
(Figure 4), analysis of power loss and degradation of
the SB VAC during shading is quite a difficult task.
Modeling the effect of arbitrary shadows on the SB
characteristics makes it possible to estimate power
losses for various shading options [14, 15, 16]
a)
b)
a)
–
SB of 18 SC with shaded photocells and shunt diodes;
b)-comparison of the VAC of a partially shaded and non
shaded battery.
Figure 4: Modeling of solar battery shading [17].
The convenience of using the PS pice language
consists in the simplicity of describing the cases of
shading of SB and shunt diodes in the battery design.
The disadvantages of such a simulation language are
bulkiness, the need to adjust the source files to set
different environmental conditions, and the need to
first describe the library and then the schematic
components. This method of modeling does not allow
you to easily switch from a single SC to an arbitrary
SB configuration. To build a generalized SB model,
you need to use a different simulation environment
[18, 19, 20].
Analyzing the graph of the ratio of the total
monthly income of the specific heat flux per 1 m
2
,
calculated using various methods, we can see that for
an angle of inclination of 300, the percentage for the
period June November fluctuates within 25%, for
December, January-March about 45%, for April -
June 35%. For a slope angle of 450, the ratio during
the year is 40%. At an inclination angle of 600, the
ratio of the total monthly inflow of the specific heat
flux of 1
m
2
increases and amounts to 50% for
different months. With an inclination angle of 900 for
the summer months, the percentage varies from 5% to
20%, for the autumn, spring, winter periods - from
25% to 55% [21,22, 23].
The receiving area of the photovoltaic battery is
oriented once a month according to the angle of
inclination, which is determined by the formulas:
𝛽
𝑖
=
𝜑 − 𝛿
𝑖
(4)
where φ is the geographic latitude of the area,
degrees; δi - angle of declination of the Sun for a
given month, deg. The declination of the Sun on a
given day is determined by the Cooper formula (4).
According to formulas (4), the optimal monthly
angles of inclination of the photovoltaic battery for
the city of Tashkent are shown in Table 2. The
geographical latitude of the city of Tashkent is
41°15′52″. Optimum angle of inclination of the
photovoltaic battery to the horizontal plane by months
(degrees).
Table 2. The geographical latitude of the city of Tashkent
is 41°15′52″.
Month
Jan
Feb March Apr
May
June
July
Aug
Sep
Oct
Nov
Dec
57
49
41
33
25
18
25
33
41
49
57
64
The calculation shows that for the spring and
autumn equinoxes, the optimal angle of inclination is
equal to the value of the latitude of the region.
However,
in the operation of a photovoltaic array,
changing the orientation of the angle of inclination by
months gives rise to difficulties. thus, the choice of
the angle of inclination of the photovoltaic array is
carried out in seasonal variations (winter, spring,
autumn and summer) [24].
2.3.1 EQUATIONS
Knowing the insolation in this geographical
location, we find that the minimum energy of solar
radiation is typical for January and December. During
these two months, the declination of the Sun
(according to the analemma) is from -17.50 to -23.50.
Solar radiation the magnitude of the angle of
declination is determined through the solar radiation
of the arithmetic cosines of these angles:
𝑐𝑜𝑠𝛿
𝑐𝑝
=
cos(−17,5)+cos(−23,5)
2
(5)
whence δ
solar
radiation.
=21.1
0
The optimal angle of
inclination for the summer period;
𝛽
𝑎𝑛
.i
𝑛𝑐
= 41
0
−
(
−
20,7
0
) = 61,7
0
(6)
We will continue the calculations for the summer
period (June and July):
𝑐𝑜𝑠𝛿
𝑐𝑝
=
cos(23,5)+cos(18,5)
2
(7)
whence δ
solar
radiation.
=21.1
0
The optimal angle of
inclination for the summer period;
𝛽
𝑎𝑛
.i
𝑛𝑐
= 41
0
−
21,1
0
=9,9
0
(8)
Below is the installation of a photovoltaic battery
in terms of the angle of inclination to the horizontal
plane according to the seasons of the year in the
conditions of Tashkent.
Table 3. The optimal angle of inclination of the
photovoltaic array to the horizontal plane by seasons of the
year (deg.)
№ Winter
Spring and autumn
Summer
1.
~62
0
~41
0
~20
0
At the stage of developing a feasibility study
for a solar heating system project, the choice of a
method for calculating the influx of solar radiation
intensity is important. As a result of the
calculations, the graphs of the dependences of the
total inflow of the specific heat flux per 1 m
2
during the year were obtained, calculated using
various methods. The calculations showed that the
amount of incoming heat calculated by various
methods differs significantly.
CONCLUSIONS
A graph is given of the ratio of the values of the
results obtained, in percent. The values of the total
monthly inflow of the specific heat flux per 1 m
2
calculated by the analytical method take into
account such factors as: the transparency of the
atmosphere, the actual conditions of cloudiness,
the movement of the Sun during the day in the
celestial sphere, which have a significant impact
on the final results of the calculation.
In Uzbekistan, solar and wind resources are
monitored using automatic measurement systems.
Long- term averaged weather data allows you to
determine the optimal installation locations and
types of solar and wind power plants that work
effectively with such resources.
ACKNOWLEDGMENTS
The work was financially supported by the
Ministry of Innovative Development of the
Republic of Uzbekistan within the framework of
the project F-OT-2021-497 - “Development of the
scientific foundations for the creation of solar
cogeneration plants based on photovoltaic thermal
batteries”.
The authors express their gratitude to the
professors of Tashkent State Technical University
N.F.Zikrillayev and I.A. Yuldoshev for his
scientific and practical help in writing this article.
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