American Journal of Applied Science and Technology
156
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VOLUME
Vol.05 Issue 05 2025
PAGE NO.
156-169
10.37547/ajast/Volume05Issue05-33
Development of A Mathematical Model for
Substantiating the Energy Efficiency of a Heating-
Cooling Device
Doniyor Tursunov Abdusalimovich
Fergana state technical univercity, Uzbekistan
Received:
31 March 2025;
Accepted:
29 April 2025;
Published:
31 May 2025
Abstract:
This article considers the methodology for achieving efficiency by replacing the existing device scheme in
the heating and cooling system of buildings with a new proposed structure scheme. In this case, using the created
mathematical expression, its characteristics are obtained using the Matlab program and its validation is checked,
and based on them, the device operation algorithm is created and the structural scheme of the device is developed.
Keywords:
System, function, scheme, Laplace transform, validation, characteristic, matlab.
Introduction:
The issues of energy efficiency of microclimate
systems in socially important buildings in the world
are currently considered one of the most urgent tasks
of science and practice, and such research is of great
importance from the point of view of energy saving.
Because systems for optimizing human life include
energy-intensive subsystems such as heating,
ventilation, air conditioning, cold and hot water
supply, etc. The total final (useful) consumption of
electricity worldwide (179 countries) for 2020-2021
was 2.3734 billion kWh. By 2020, total useful
consumption had increased by 5.5% compared to
1992. The largest increase in electricity consumption
in 2021 compared to 1992 was in Asia and Oceania -
up to 5.1 times. Currently, "50-55% of electricity
consumption is spent on heating and cooling
buildings." Particular attention is paid to minimizing
energy costs for existing facilities of these
subsystems, as well as making optimal decisions
when designing them.
A number of studies are being conducted around the
world to introduce energy-saving devices into the
heating and cooling systems of buildings, to manage
them using environmentally friendly and modern
devices, and to avoid using traditional electricity
supplies as much as possible. Based on this, one of the
urgent tasks is to increase the energy efficiency of
economic sectors and the social sphere in the heating
and cooling systems of buildings, to widely introduce
energy-saving technologies and renewable energy
sources.
Therefore, job creation and rational use of resources
can help reduce some of the social costs. Our country
is well positioned to take advantage of these
opportunities..
Based on this, a number of decisions and decrees are
being adopted and tasks are being set in our country
to implement a number of changes in this regard.
Taking into account these tasks, one of the important
issues is the production of new devices for the
heating and cooling system of socially important
buildings using solar energy, the creation of improved
resource-saving technologies, the optimization of
energy saving issues in heating and cooling buildings,
and thereby increasing energy and economic
efficiency.
METHODOLOGY
Development of the device scheme. Before
developing the device scheme, we need to consider
the scheme of the existing heating and cooling device
[1]. In Figure 1, we can see that the complexity of the
existing device circuit and its high energy
consumption due to the location of high-power
elements in it, and in turn, when the energy
consumption increases, it can cause overloading of
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the transformers. In addition, its compressor unit is
installed outside the room where the device is
installed, which causes it to emit loud noise and
damage the external facade of the building.
Figure 1: Structural diagram of the existing device
The above-mentioned principles served as the basis
for developing an energy-saving and efficient device
scheme in the power system. Due to the low-power
elements in the device and the use of a Peltier
element for cooling, there is no external block and
high energy consumption in it [2]. In turn, the energy-
efficient device prevents overloading of transformers
during periods of high consumption.
The device's power supply converts the signal from
the network into 12 V, which is necessary for the
cooling system to operate, and 220 V, which is
necessary for the heating system to operate.
The control board is one of the main components of
the device, which controls the device's on-off,
temperature control, switching of the heating and
cooling system, and the signals from the remote
control element. It also regulates and controls the
device when it reaches the desired temperature limit
based on the signal from the thermostat [3].
It can also be said that the device itself, depending on
the changes in its functions, i.e., temperature changes
or mode changes, displays them through the segment
in which the device is installed.
Figure 2 shows the structural diagram of the device.
Figure 2: Structural diagram of the proposed device
In heating and cooling systems, two different
temperatures are set for the device to ensure
meteorological conditions in the room, that is, in the
cooling mode of the device, when the set value of the
room temperature “t
1
” is less than or equal to the
operating temperature of the device “t
0
”, the dev
ice
remains in a stable state. Similarly, in the heating
mode, when the set value of the room temperature
“t
1
” is greater than or equal to the operating
temperature of the device “t
0
”, the device returns to
a stable state. This is done by correctly directing the
signal from the temperature sensor of the control
board to the switch that regulates the device modes.
The circuit shown in Figure 1 is a program written on
the Arduino C++ software on the mainboard for the
device to operate, and it is the main element that
regulates and controls all modes of the device.
Developing the device transfer function. Based on the
time-related relationships between power and
energy of the system, we express the transfer
function as follows:
P
3
(t) =
k
inv.f.i.k
P
0
t
0
+P
4
t
4
+k
ak.f.i.k
P
2
t
2
−P
1
t
1
t
3
(1)
Using the Laplace transform:
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By taking the Laplace transform of the time function,
we express the transfer function as follows:
P
3
(s) =
k
inv.f.i.k
P
0
(s)+P
4
(s)+k
ak.f.i.k
P
2
(s)−P
1
(s)
t
3
(s)
(2)
Final transfer function:
The transfer function is the basic mathematical model
for controlling power distribution and energy
efficiency in an energy-
efficient system of the “Climat
control” device:
G(s) =
P
3
(s)
P
0
(s),P
4
(s),P
2
(s),P
1
(s)
=
k
inv.f.i.k
+k
ak.f.i.k
−1
t
3
(s)
(3)
Figure 3: Transmission function
According to international statistics, primary fuel
energy sources are decreasing today. This requires
the use of renewable energy sources, while the issues
of saving existing energy sources, their rational use,
and the introduction of energy-saving technologies
are relevant today. In particular, the use of renewable
energy sources is of great importance in the use of
energy-saving devices in the heating and cooling
systems of socially important buildings. In addition,
the use of autonomous energy sources in the
implementation of such technologies will reduce the
observed overloads, voltage asymmetry and non-
sinusoidality, reactive power deficiency and a number
of other abnormal modes in the power system.
One of the main criteria in building design is to
accurately calculate the capacity of the heating and
cooling systems of socially important buildings, the
amount of electricity consumed during maximum and
minimum load times (for the coldest and hottest
times of the year).
This section discusses the improvement of the
mathematical expression of modern automatic room
climate control devices to achieve energy savings and
thereby energy efficiency by using renewable energy
sources (solar energy) rather than traditional
electricity sources for the electricity they consume.
The mathematical expression of the working scheme
of the improved "Climat control" device proposed
above was based on the law of conservation of
energy, the photoelectric effect, thermodynamic
processes, heat exchange processes, electrostatic
and electrodynamic laws.
We use solar energy as our primary energy source,
but the power received during the day and the power
received throughout the year are variable, that is, it is
not possible to obtain constant power. Therefore,
when obtaining electricity from solar energy, we
calculate the power obtained using a solar
photovoltaic panel based on the following conditions.
a) The intensity of the sun is assumed to be constant
throughout each season. ( Spring:
ye
0
= 1330 Vt/
m
2
; Summer:
ye
0
= 1380 Vt/m
2
; Winter:
ye
0
=
1320 Vt/m
2
; Autumn:
ye
0
= 1350 Vt/m
2
;) [47].
e
0
= ∫ e
1
(1)dx = const
ω
0
;
[
Vt/m
2
]
(4)
Where,
ω −
angular velocity
ye
1
−
instantaneous value of the solar constant
b) The average operating time of a solar photovoltaic panel is assumed to be the same for each season.
s) Solar photovoltaic panel statically clamped [86].
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Figure 4: Static positioning of solar photovoltaic panels
Figure 5: Sunlight falling on a solar photovoltaic panel
The active power generated by a solar photovoltaic panel during the day is generally as follows:
P
0
= ∫ P
t
dt
t
2
t
1
; [Vt]
(5)
Where,
t
1
−
start time;
t
2
−
end time;
P
t
−
instantaneous value of power over time
If we take into account the change in the angle of incidence of the sun on the photovoltaic panel during the day,
and express the power in terms of the solar constant and the surface area of the photovoltaic panel, we obtain
the following expression.
P
t
= e
0
S ∫ sin (ωt)dt
t
0
; [Vt]
(6)
Where,
S −
solar photovoltaic panel surfacing surface,
ω =
2π
T
f
;
Figure 6: Active power graph used from the grid and solar photovoltaic panels during the day (not taking into
account sudden changes in weather)
T
f
= t
1
− t
2
;
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T
f
- solar panel daily operating time.
Let's consider the power distribution according to the following principle diagram.
Since the power management inverter does not store power or energy, we can write the following relationship:
Figure 7: Schematic diagram for selecting the power of a solar panel for a device
1)
Considering the inverter F.I.K, then according to the above principle diagram, we can write the following
relationships in terms of power and energy flows.
k
f.i.k
(P
0
+ P
2
+ P
4
) − (P
3
+ P
1
) = 0
;
(7)
Where,
k
f.i.k
−
inverter efficiency;
R
0
−
the active power generated by the solar panel;
P
1
−
active power
flowing from the inverter to the battery;
P
2
−
active power output from the battery;
P
3
−
active power output
from the inverter to the device;
P
4
−
active power entering the inverter from the power grid.
If we calculate the active power coming out of the inverter here, it looks like this.
P
3
= k
f.i.k
(P
0
+ P
4
+ P
2
) − P
1
; [Vt]
(7.1)
k
f.i.k
(W
0
+ W
2
+ W
4
) − (W
3
+ W
1
) = 0
;
(8)
Where,
W
0
−
energy generated by the solar panel;
W
1
−
energy flowing from the inverter to the battery;
W
2
−
energy released from the battery;
W
3
−
energy flowing from the inverter to the device;
W
4
−
energy entering
the inverter from the electrical grid.
2)
The battery can store maximum energy depending on its capacity, and for long-term operation, this
energy is not fully used, that is, it has a minimum value. Accordingly, the device can use the energy between the
minimum value and the maximum value.
W
2
= W
2min
÷ W
2max
; [
kVt ∙ hour
]
(9)
Where,
W
2min
−
the minimum usable energy of the battery;
W
2max
−
maximum usable energy of the battery.
According to condition 2, we can write the same relationship for power.
P
2
= P
2min
÷ P
2max
; [Vt]
(10)
Where,
R
2min
−
minimum usable active capacity of the battery;
R
2max
−
maximum usable active capacity of
the battery
If we calculate the energy consumed by the device from expression (2.8), we get the following expression:
W
3
= k
f.i.k
(W
0
+ W
4
+ W
2
) − W
1
; [
kVt ∙ hour]
(11)
P =
W
t
; [Vt]
(12)
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According to expressions (2.11) and (2.12) and the above 3 conditions, we obtain the equation of the device
power dependence on time depending on the device operating time:
P
3
′
t
3
′
= k
f.i.k
(P
0
t
0
+ P
4
t
4
+ P
2min
t
2min
) − P
1
t
1
[Vt]
(13)
Where,
t
0
−
The actual power generated by the solar panel is operating time.
t
1
−
Active power output from the inverter to the battery operating time;
t
2min
−
minimum time of active
power output from the battery;
t
3
−
Active power output from the inverter to the device operating time;
t
4
−
The operating time of the active power entering the inverter from the power grid.
P
3
′′
t
3
′′
= k
f.i.k
(P
0
t
0
+ P
4
t
4
+ P
2max
t
2max
) − P
1
t
1
[Vt]
(14)
Where,
t
0
′
−
the operating time of the active power generated by the solar panel according to condition 3;
t
1
′
−
The operating time of the active power output from the inverter to the battery according to condition 3;
t
2max
′
−
Maximum time of active power output from the battery according to 3 condition;
t
3
′
−
The operating
time of the active power output from the inverter to the device according to 3 condition;
t
4
′
−
The operating
time of the active power entering the inverter from the power grid according to 3 condition.
If we take into account the F.I.K of the battery, then equations (2.13) and (2.14) take the following form:
P
3
= (k
inv.f.i.k
(P
0
t
0
+ P
4
t
4
+ k
ak.fik
P
2min
t
2min
) − P
1
t
1
)/t
3
[Vt]
(15)
𝑃
3
′
= (𝑘
𝑖𝑛𝑣.𝑓.𝑖.𝑘
(𝑃
0
𝑡
0
′
+ 𝑃
4
𝑡
4
′
+ 𝑘
𝑎𝑘.𝑓𝑖𝑘
𝑃
2𝑚𝑎𝑥
𝑡
2𝑚𝑎𝑥
′
) − 𝑃
1
𝑡
1
′
)/𝑡
3
′
[Vt]
(16)
Where,
𝑘
𝑖𝑛𝑣.𝑓.𝑖.𝑘
−
the inverter efficiency coefficient (taken to be equal to k
f.i.k
);
𝑘
𝑎𝑘.𝑓.𝑖.𝑘
−
accumulator
efficiency.
Figure 8: Input and output quantities when obtaining a mathematical representation of the proposed device
When the heating system is turned on, the power consumed by the device becomes equal to the heating power.
All the elements necessary for heating start working. Therefore, the following relationship is valid:
𝑅
ℎ𝑒𝑎𝑡.0
= 𝑅
3
; [Vt]
(17)
However, since the heating system consists of several elements, some of the power is wasted in the circuit of
these elements. We can determine this by the following expression.
𝑅
ℎ𝑒𝑎𝑡
= 𝑘
𝑖𝑐
𝑅
ℎ𝑒𝑎𝑡.0
;
[Vt]
(18)
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Where,
𝑘
𝑖𝑐
−
power loss coefficient in the heating system.
In turn, since power and energy are related through time, energy is also wasted, and the energy spent on
heating per unit time is defined by the following expression based on the law of conservation of energy.
𝑊
ℎ𝑒𝑎𝑡
= 𝑅
ℎ𝑒𝑎𝑡
𝑡
𝑖𝑐
; [
𝑘𝑉𝑡 ∙ 𝑠𝑜𝑎𝑡
]
(19)
Where,
𝑡
𝑖𝑐
−
heating time.
The energy obtained for heating is introduced into the room using convection, and the required amount of heat
is needed to reach the set temperature.
𝑄
0
= 𝑊
ℎ𝑒𝑎𝑡
𝑛
; [J]
(20)
Where,
𝑛 −
the required portion of heat, which characterizes the time taken for heating in this case. According
to the heat balance equation, we derive the following expression.
𝑄
ℎ𝑒𝑎𝑡.𝑒𝑓𝑓
= 𝑘
ℎ𝑒𝑎𝑡.𝑓.𝑖.𝑘
𝑄
0
= 𝑐𝑚(𝑇
2
− 𝑇
1
)
; [J]
(21)
Where,
𝑚 −
mass;
𝑘
ℎ𝑒𝑎𝑡.𝑓.𝑖.𝑘
−
heating efficiency;
𝑇
1
−
outside temperature;
𝑇
2
−
required temperature;
𝑠 −
the specific heat capacity of air, which is related to the parameters of the room volume and air density as
follows.
𝑚 = 𝜌 ∙ 𝑎 ∙ 𝑏 ∙ ℎ
; [kg]
(21.1)
Where,
𝜌 −
air density;
𝑎 𝑎𝑛𝑑 𝑏 –
room sides;
ℎ −
room height.
Taking into account expressions (2.21) and (2.21.1), we calculate the amount of useful heat used for heating as
follows.
𝑄
ℎ𝑒𝑎𝑡.𝑒𝑓𝑓
= 𝑐𝜌𝑎𝑏ℎ(𝑇
2
− 𝑇
1
)
; [J]
(22)
If
𝑃
0
= 𝑃
𝑎
,
𝜌 = 1.29 𝑘𝑔/𝑚
3
;
𝑊
𝑒𝑙.𝑒𝑛
= 𝑅
3
𝑡
𝑖𝑠
; [
𝑘𝑉𝑡 ∙ ℎ𝑜𝑢𝑟
]
23)
Using expression (2.17), the electrical power is found by the following expression:
𝑊
𝑒𝑙.𝑒𝑛
= 𝑅
ℎ𝑒𝑎𝑡.0
𝑡
𝑖𝑐
;
[
𝑘𝑉𝑡 ∙ ℎ𝑜𝑢𝑟
]
(24)
Using expression (2.18), we can reduce the electrical energy to the following expression.
𝑊
𝑒𝑙.𝑒𝑛
=
𝑅
ℎ𝑒𝑎𝑡
𝑘
𝑖𝑐
𝑡
𝑖𝑐
; [
𝑘𝑉𝑡 ∙ ℎ𝑜𝑢𝑟
]
(25)
Using expressions (2.19) and (2.20), we define the electrical power in the following form.
𝑊
𝑒𝑙.𝑒𝑛
=
𝑊
𝑖𝑠𝑖𝑡
𝑡
𝑖𝑠
𝑘
𝑖𝑠
𝑡
𝑖𝑠
=
𝑄
0
𝑘
𝑖𝑠
; [kJ]
(26)
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Using expressions (2.21) and (2.22), we express the electrical power through the following expression.
𝑊
𝑒𝑙.𝑒𝑛
=
𝑄
ℎ𝑒𝑎𝑡.𝑒𝑓𝑓
𝑘
ℎ𝑒𝑎𝑡.𝑓.𝑖.𝑘
𝑘
𝑖𝑐
=
𝑐𝜌𝑎𝑏ℎ(𝑇
2
−𝑇
1
)
𝑘
ℎ𝑒𝑎𝑡.𝑓.𝑖.𝑘
𝑘
𝑖𝑐
; [kJ]
(27)
So we define electrical energy by the following expression.
𝑊
𝑒𝑙.𝑒𝑛
=
𝑐𝜌𝑎𝑏ℎ(𝑇
2
−𝑇
1
)
𝑘
ℎ𝑒𝑎𝑡.𝑓.𝑖.𝑘
𝑘
𝑖𝑐
; [kJ]
(28)
When the cooling system starts, the power consumed by the device becomes equal to the cooling capacity. All
the elements necessary for cooling start working. Therefore, the following relationship is valid.
𝑅
𝑐𝑜𝑜𝑙.0
= 𝑃
3
′
; [Vt]
(29)
However, since the cooling system consists of several elements, some of the power is wasted in the chain of
these elements. We can determine this by the following expression.
𝑅
𝑠𝑜𝑣
= 𝑘
𝑠𝑜𝑣
𝑅
𝑠𝑜𝑣.0
; [Vt]
(30)
Where,
𝑘
𝑐𝑜𝑜𝑙
−
power dissipation coefficient in the cooling system.
In turn, since power and energy are related through time, energy is also wasted, and the energy lost per unit
time for cooling is defined by the following expression based on the law of conservation of energy.
𝑊
𝑐𝑜𝑜𝑙
= 𝑅
𝑐𝑜𝑜𝑙
𝑡
𝑐𝑜𝑜𝑙
; [
𝑘𝑉𝑡 ∙ ℎ𝑜𝑢𝑟
]
(31)
Where,
𝑡
𝑐𝑜𝑜𝑙
−
cooling time.
The energy obtained for cooling is introduced into the room using convection and the required amount of heat
is needed to reach the set temperature.
𝑄
0
= 𝑊
𝑐𝑜𝑜𝑙
𝑛
; [J]
(32)
Where,
𝑛 −
the required portion of cold, which characterizes the time taken for cooling in this case. According
to this balance equation, we derive the following expression.
𝑄
𝑐𝑜𝑜𝑙.𝑒𝑓𝑓
= 𝑘
𝑐𝑜𝑜𝑙.𝑓.𝑖.𝑘
𝑄
0
= 𝑐𝑚(𝑇
1
− 𝑇
2
)
; [J]
(33)
Where,
𝑚 −
mass;
𝑘
𝑐𝑜𝑜𝑙.𝑓.𝑖.𝑘
−
cooling efficiency;
𝑇
1
−
outside temperature;
𝑇
2
−
required temperature;
𝑠 −
the specific heat capacity of air, which is related to the parameters of the room volume and air density as
follows.
Taking into account expressions (2.33) and (2.21.1), we calculate the amount of useful cold used for cooling as
follows.
𝑄
𝑐𝑜𝑜𝑙.𝑒𝑓𝑓
= 𝑐𝜌𝑎𝑏ℎ(𝑇
1
− 𝑇
2
)
; [J]
(34)
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If
𝑃
0
= 𝑃
𝑎
,
𝜌 = 1.29 𝑘𝑔/𝑚
3
; s- specific heat capacity of air;
𝑊
𝑒𝑙.𝑒𝑛
= 𝑅
3
𝑡
𝑐𝑜𝑜𝑙
; [
𝑘𝑉𝑡 ∙ ℎ𝑜𝑢𝑟
]
(35)
Using expression (2.29), the electric power is found by the following expression.
𝑊
𝑒𝑙.𝑒𝑛
= 𝑅
𝑐𝑜𝑜𝑙.0
𝑡
𝑐𝑜𝑜𝑙
; [
𝑘𝑉𝑡 ∙ ℎ𝑜𝑢𝑟
]
(36)
Using expression (2.30), we can reduce the electrical power to the following expression.
𝑊
𝑒𝑙.𝑒𝑛
=
𝑅
𝑐𝑜𝑜𝑙
𝑘
𝑐𝑜𝑜𝑙
𝑡
𝑐𝑜𝑜𝑙
; [
𝑘𝑉𝑡 ∙ ℎ𝑜𝑢𝑟
]
(37)
Using expressions (2.31) and (2.32), we define the electrical power in the following form.
𝑊
𝑒𝑙.𝑒𝑛
=
𝑊
𝑐𝑜𝑜𝑙
𝑡
𝑐𝑜𝑜𝑙
𝑘
𝑐𝑜𝑜𝑙
𝑡
𝑐𝑜𝑜𝑙
=
𝑄
0
𝑘
𝑐𝑜𝑜𝑙
; [kJ]
(38)
Using expressions (2.33) and (2.34), we express the electric energy by the following expression.
𝑊
𝑒𝑙.𝑒𝑛
=
𝑄
𝑐𝑜𝑜𝑙.𝑒𝑓𝑓
𝑘
𝑐𝑜𝑜𝑙.𝑓.𝑖.𝑘
𝑘
𝑐𝑜𝑜𝑙
=
𝑐𝜌𝑎𝑏ℎ(𝑇
1
−𝑇
2
)
𝑘
𝑐𝑜𝑜𝑙.𝑓.𝑖.𝑘
𝑘
𝑐𝑜𝑜𝑙
; [kJ]
(39)
Thus, we determine the amount of electricity consumed using the following expression.
𝑊
𝑒𝑙.𝑒𝑛
=
𝑐𝜌𝑎𝑏ℎ(𝑇
1
−𝑇
2
)
𝑘
𝑐𝑜𝑜𝑙.𝑓.𝑖.𝑘
𝑘
𝑐𝑜𝑜𝑙
: [kJ]
(40)
Using the law of conservation of energy, the photoelectric effect, and heat exchange processes, the equation for
the dependence of the device
’
s power on time, taking into account the operating time of the device and the
F.I.K of the accumulator, was obtained [6], a mathematical expression that allows determining the electrical
energy consumed by the device in accordance with the dimensions of the room.
RESULTS
Obtaining the characteristics and validation of the electrical energy consumed by the device.
When determining
the electrical energy consumption of a device
’
s heating and cooling system, we use the following expression to
obtain its characteristics using the values from experimental research results [5].
𝑊
𝑒𝑙.𝑒𝑛
=
𝑐𝜌𝑎𝑏ℎ(𝑇
1
−𝑇
2
)
𝑘
𝑐𝑜𝑜𝑙.𝑓.𝑖.𝑘
𝑘
𝑐𝑜𝑜𝑙
; [kJ]
(41)
Based on the above, we obtain the characteristic "Energy consumption in cooling mode according to room size
changes" by entering the following values, based on the results of experimental studies.
Then, we obtain the characteristic of the electrical energy consumed by the device during the initialization of
the
𝜌 −
1,29;
𝑎 · 𝑏 −
16
𝑚
2
÷ 40
𝑚
2
;
ℎ −
2,7 m;
𝑠 −
1,0;
𝑘
𝑐𝑜𝑜𝑙.𝑓.𝑖.𝑘
−
0,65;
𝑇
1
− 25
S ÷ 35 S;
𝑇
2
−
15 S;
𝑘
𝑠𝑜𝑣
−
0,5 values in the MATLAB program.
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Figure 9: Energy consumption in cooling mode according to room size variation
In the same view, by entering the following values, we obtain the characteristic "Energy consumption in heating
mode according to the change in room dimensions".
Then, we obtain the characteristic of the electrical energy consumed by the device during the initialization of
the
𝜌 −
1,29;
𝑎 · 𝑏 −
16
𝑚
2
÷ 40
𝑚
2
;
ℎ −
2,7 m;
𝑠 −
1,0;
𝑘
𝑠𝑜𝑣.𝑓.𝑖.𝑘
−
0,65;
𝑇
1
− 0
S ÷ 10 S;
𝑇
2
−
25 S;
𝑘
𝑠𝑜𝑣
−
0,5
values in the MATLAB program.
Figure 10: Energy consumption in heating mode according to room size changes
Confirming the reliability, accuracy, and correctness
of the results obtained is called validation, in which
the results are evaluated for their authenticity before
being used.
Main stages of the result validation process:
Verification of results, Testing and evaluation, Expert
opinion, Statistical analysis, Testing in real conditions,
Importance of result validation, Increasing reliability,
Identifying errors, Creating a basis for acceptance.
For example, if you are studying the effectiveness of
a model as part of a scientific study, the validation
process is necessary to determine how the results of
that model work in real-world conditions.
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Figure 11: Energy consumption in cooling mode according to room size variation
Figure 12: Energy consumption in heating mode according to room size changes
The graphs in Figures 11 and 12 show the validation
results for temperature and energy consumption
evaluation. Their descriptions are given below:
1. In the top graphs:
𝑑𝑊
𝑒𝑙.𝑒𝑛
𝑑𝑡
⁄
−
heating and
cooling energy consumption is expressed.
The vertical axes show the values of
𝑑𝑊
𝑒𝑙.𝑒𝑛
𝑑𝑡
⁄
(watt-hours), the amounts of energy required for
cooling and heating.
The horizontal arrows indicate the time it took in
hours.
The analysis shows that energy consumption has a
sinusoidal variation. Maximum values are observed in
the middle of the day. Minimum values occur in the
evening and morning, which is of course directly
related to temperature changes.
2. In the graphs below:
𝑇
1
−
expressed as outdoor
temperature.
The vertical axis shows the ambient temperature T
1
,
measured at
∁
.
The horizontal arrows indicate the time it took in
hours.
The analysis shows that T
1
varies sinusoidally, with
maximum values observed during the day, which
increases energy consumption. Minimum values are
observed at dawn and at night, which reduces the
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need for cooling or heating depending on its
temperature change.
Validation results:
The energy consumption graph values will have
positive values only when the conditions T
1
>T
2
or
T
2
>T
1
are met. This is confirmed by validation.
If T
1
>T
2
, energy consumption is directed towards
cooling, or vice versa, if T
2
>T
1
, then energy
consumption is directed towards heating.
So the conclusion from the graph is that:
Validation is working successfully because values are
generated only in accordance with physical laws.
As you can see from the graphs, energy consumption
is calculated only under necessary conditions. This
allows you to increase the efficiency of the system.
Development of a device operating algorithm. When
developing the device's operating algorithm, the
necessary quantities were initially selected and
through them the active power generated by the
solar photovoltaic panel and the active power
supplied to the device were determined. Then, by
entering the necessary conditions, it was possible to
determine the power consumed by the device in
heating and cooling and the electricity consumed.
-
Start: Start the device's processing algorithm.
-
𝑃
2𝑚𝑖𝑛
−
minimum usable active capacity of the
battery;
𝑃
2𝑚𝑎𝑥
−
maximum usable active capacity of
the battery;
𝑃
4
−
active power from the power grid;
𝑦𝑒
0
−
solar intensity;
𝑆 −
solar photovoltaic panel
surfacing surface;
𝑘
𝑖𝑛𝑣𝑒𝑟.𝑓.𝑖.𝑘
−
inverter efficiency;
𝑘
𝑎𝑐𝑐𝑢𝑚.𝑓.𝑖.𝑘
−
accumulator efficiency;
𝑘
𝑖𝑐
−
power
loss coefficient in the heating system;
𝑘
ℎ𝑒𝑎𝑡.𝑓.𝑖.𝑘
−
heating efficiency;
𝑘
𝑐𝑜𝑜𝑙.𝑓.𝑖.𝑘
−
cooling efficiency;
𝑘
𝑐𝑜𝑜𝑙
−
power dissipation coefficient in the cooling
system;
𝑡
0
−
The actual power generated by the solar
panel is operating time;
𝑡
1
−
Active power output
from the inverter to the battery operating
time;
𝑡
2𝑚𝑖𝑛
−
minimum time of active power output
from the battery;
t
3
−
Active power output from the
inverter to the device operating time;
t
4
−
The
operating time of the active power entering the
inverter from the power grid;
T
1
−
outside
temperature;
T
2
−
required temperature;
ρ −
air
density;
a −
room length; b
−
room side;
h −
room
height; c
−
specific heat capacity of air.
Figure 13: Device operation algorithm
- After the above parameters are entered, the total
active power generated, taking into account the
change in the angle of incidence of sunlight on the
solar photovoltaic panel during the day, is calculated
from expression (3). The solar photovoltaic panel is
directly connected to the inverter, and the active
power output from the inverter is calculated from
expression (4.1). If the battery supplies active power
to the device in the minimum operating mode, then
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the active power supplied to the device is calculated
from expression (10).
After the given expressions are calculated, the
algorithm moves to the next step and the following
conditions are introduced:
If the power of the solar photovoltaic panel is greater
than or equal to the power consumed, that is, P
0
≥P
3
,
then the algorithm accepts the condition "x" and
calculates the following expression:
P
3
= k
inv.f.i.k
∙ P
0
∙ t
0
/t
3
;
(42)
If the power of the solar photovoltaic panel is less
than or equal to the power consumed, that is, P
0
≤P
3
,
then the algorithm assumes the “no” condition and
proceeds to the next stage, where the following
condition is introduced:
If the power consumed by the device is greater than
or equal to the battery capacity or the power of the
solar photovoltaic panel is greater than or equal to
zero, that is, P
3
≥P
2
min and P
0
≥0, then the algorithm
accepts the condition "yes" and the following
expression is calculated:
P
3
= (k
inv.f.i.k
(P
0
t
0
+ k
ak.fik
P
2min
t
2min
) − P
1
t
1
)/t
3
;
(43)
If the power consumed by the device is less than or
equal to the battery capacity or the power of the solar
photovoltaic panel is less than or equal to zero, that
is, P
3
≤P
2
min and P
0
≤0, then the algorithm assumes the
“no” condition and the following expression is
calculated:
P
3
= k
inv.f.i.k
P
4
t
4
/t
3
;
(44)
Once the power consumption of the device is
determined based on the above conditions, the
algorithm moves to the next step and the following
conditions are introduced:
If the external temperature is lower than the
temperature specified in GOST 30494-2011, i.e.
T
1
<T
norm
, then the algorithm assumes the condition
“yes” and calculates the following expressions:
R
heat
= k
ic
R
3
;
(45)
W
el.en
=
cρabh(T
2
−T
1
)
k
heat.f.i.k
k
ic
;
(46)
If the external temperature is not lower than the
temperature specified in GOST 30494-2011, then the
a
lgorithm accepts the “no” condition and proceeds to
the next stage, where the following condition is
introduced.
If the external temperature is equal to the
temperature specified in GOST 30494-2011, i.e.
T1=T
norm
, then the algorithm accepts the condition
“
yes
” and the device switches to the standby mode.
If the external temperature is not equal to the
temperature specified in GOST 30494-2011, that is,
T
1
<T
norm
, then the algorithm
accepts the “no”
condition and the following expressions are
calculated:
R
cool
= k
cool
R
3
;
(47)
W
el.en
=
cρabh(T
2
−T
1
)
k
cool.f.i.k
k
cool
;
(48)
The energy consumed in heating and cooling, as well
as the electricity consumed, are displayed as a result
of the conditions and calculated expressions provided
in the algorithm.
End: The device processing algorithm ends.
CONCLUSIONS
1.
An energy-efficient structural scheme of the
device was developed based on changing the internal
elements of the heating and cooling system, and a
mathematical model was developed using the Matlab
program that allows determining the electrical energy
consumed by the device, taking into account the
room dimensions and external temperature;
2.
A structural diagram of the device was
developed. As a result, a prototype of the device was
developed based on the diagram.
3.
A mathematical model was developed using
Matlab software to determine the electrical energy
consumption of the device, taking into account the
room dimensions and external temperature. As a
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American Journal of Applied Science and Technology (ISSN: 2771-2745)
result, it was possible to compare the results of
theoretical and experimental studies.
4.
An algorithm for operating an innovative
device that controls room temperature at set values
in heating and cooling buildings of social importance
was developed. As a result, based on this algorithm,
moderate climate control was created in the room
where the device is installed.
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