ELECTRICAL MODEL OF THE HYBRID PHOTOVOLTAIC THERMAL COLLECTOR
The article is devoted to the creation of electrical models of a hybrid photovoltaic thermal. The objective of the article is to create electrical models of the thermal and photovoltaic parts of the hybrid collector. The paper focuses on the spectrum of solar radiation and shows that absorption occu...
Збережено в:
| Дата: | 2025 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Institute of Renewable Energy National Academy of Sciences of Ukraine
2025
|
| Теми: | |
| Онлайн доступ: | https://ve.org.ua/index.php/journal/article/view/505 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Vidnovluvana energetika |
| Завантажити файл: |  |
Репозитарії
Vidnovluvana energetika| _version_ | 1871103869215309824 |
|---|---|
| author | Bondarenko , D. |
| author_facet | Bondarenko , D. |
| author_institution_txt_mv | [
{
"author": "D. Bondarenko ",
"institution": "Institute of Renewable Energy of NAS of Ukraine, Kyiv, Ukraine"
}
] |
| author_sort | Bondarenko , D. |
| baseUrl_str | https://ve.org.ua/index.php/journal/oai |
| collection | OJS |
| datestamp_date | 2026-07-18T06:32:21Z |
| description | The article is devoted to the creation of electrical models of a hybrid photovoltaic thermal. The objective of the article is to create electrical models of the thermal and photovoltaic parts of the hybrid collector. The paper focuses on the spectrum of solar radiation and shows that absorption occurs both in the photovoltaic part and in the thermal part of the hybrid collector. The advantages of combining thermal and photovoltaic parts in one en-ergy-generating device are shown. The construction of a photovoltaic thermal solar collector is shown. A table of electrothermal analogies, both for thermal conductivity and thermal convection, is demonstrated. An approach is presented in which thermal processes of photon absorption are modeled by the creation of phonons. The funda-mental aspects of the choice of modeling values, for example, the flow of entropy instead of the flow of thermal energy, are shown. It is shown that, within the framework of the electrothermal analogy, the calculation of ther-mal processes is reduced to the calculation of electric circuits. Electrical models are created and electrical equa-tions of the created electrical models are recorded. Controlled sources of current and voltage, and derived model-ing resistances in equivalent circuits are shown. A general model of a hybrid photovoltaic thermal collector is constructed, which is placed on a tracker and connected to a pump that pumps the coolant through the thermal part of the collector. This model includes a part that, based on rate equations, shows the separation of photons according to the spectral absorption distribution. Conclusions are drawn, and further research in the direction of connecting storage devices and connecting energy converters using different principles and designs is shown. It was also noted that the use of electrical models is a way to combine generation systems running on various energy sources. |
| doi_str_mv | 10.36296/1819-8058.2025.1(80).44-50 |
| first_indexed | 2025-07-17T11:39:50Z |
| format | Article |
| fulltext |
44
Відновлювана енергетика. №1/2025 | Сонячна енергетика
УДК 621 https://doi.org/10.36296/1819-8058.2025.1(80)44-50
ELECTRICAL MODEL OF THE HYBRID PHOTOVOLTAIC THERMAL COLLECTOR
Received Feb. 13, 2025; accepted Mar. 14, 2025
Available online Apr. 01, 2025
Bondarenko D.
Author for correspondence: Bondarenko Dmytro,
e-mail: dima7007bond@gmail.com
Abstract. The article is devoted to the creation of electrical models of a hybrid photovoltaic thermal. The objective
of the article is to create electrical models of the thermal and photovoltaic parts of the hybrid collector. The paper
focuses on the spectrum of solar radiation and shows that absorption occurs both in the photovoltaic part and in
the thermal part of the hybrid collector. The advantages of combining thermal and photovoltaic parts in one en-
ergy-generating device are shown. The construction of a photovoltaic thermal solar collector is shown. A table of
electrothermal analogies, both for thermal conductivity and thermal convection, is demonstrated. An approach is
presented in which thermal processes of photon absorption are modeled by the creation of phonons. The funda-
mental aspects of the choice of modeling values, for example, the flow of entropy instead of the flow of thermal
energy, are shown. It is shown that, within the framework of the electrothermal analogy, the calculation of ther-
mal processes is reduced to the calculation of electric circuits. Electrical models are created and electrical equa-
tions of the created electrical models are recorded. Controlled sources of current and voltage, and derived model-
ing resistances in equivalent circuits are shown. A general model of a hybrid photovoltaic thermal collector is
constructed, which is placed on a tracker and connected to a pump that pumps the coolant through the thermal
part of the collector. This model includes a part that, based on rate equations, shows the separation of photons
according to the spectral absorption distribution. Conclusions are drawn, and further research in the direction of
connecting storage devices and connecting energy converters using different principles and designs is shown. It
was also noted that the use of electrical models is a way to combine generation systems running on various energy
sources.
Keywords: photovoltaic thermal collector, PV/T-collector, electrical model, electrical-thermal analogy, photons,
phonons
ЕЛЕКТРИЧНА МОДЕЛЬ ГІБРИДНОГО ФОТОЕЛЕКТРИЧНОГО ТЕПЛОВОГО КОЛЕКТОРА
Отримано 13 лют. 2025 р.; рекомендовано до публікації 14 бер. 2025 р.
Доступно онлайн 01 квіт. 2025 р.
Бондаренко Д. В.
Автор для кореспонденції: Бондаренко Дмитро,
e-mail: dima7007bond@gmail.com
Анотація. Стаття присвячена побудові електричних моделей гібридного фотоелектричного тепло-
вого колектора. Метою статті є створення електричних моделей теплової та фотоелектричної ча-
стин гібридного колектора. У роботі акцентовано на спектрі сонячного випромінювання й показано,
що поглинання відбувається як фотовольтаїчною, так і тепловою частиною гібридного колектора.
Показано переваги поєднання теплової та фотоелектричної частини в одному енергогенерувальному
пристрої. Показано конструкцію фотоелектричного теплового сонячного колектора. Продемонстро-
вана таблиця електротеплових аналогій як для теплопровідності, так і для теплової конвекції. Викла-
дено підхід, в якому теплові процеси поглинання фотонів моделюються утворенням фононів. Показані
принципові аспекти вибору моделювальних величин, наприклад потоку ентропії замість потоку теп-
лової енергії. Показано, що в межах електротеплової аналогії розрахунок теплових процесів зводиться
до розрахунку електричних кіл. Побудовані електричні моделі та записані електричні рівняння
PhD in Technical Sciences
https://orcid.org/0000-0002-5629-930X
Institute of Renewable Energy of NAS of Ukraine,
Kyiv, Ukraine
канд. техн. наук
https://orcid.org/0000-0002-5629-930X
Інститут відновлюваної енергетики НАН України,
м. Київ, Україна
45
Відновлювана енергетика. №1/2025 | Сонячна енергетика
побудованих моделей. В еквівалентних схемах показано контрольовані джерела струмів і напруг, та
виведені моделювальні опори. Побудована загальна модель гібридного фотоелектричного теплового
колектора, який розміщений на трекері й підключений до насоса, який прокачує теплоносій через теп-
лову частину колектора. У таку модель вбудовано частину, яка на основі кінетичних рівнянь показує
розділення фотонів згідно зі спектральним поглинальним розподілом. Зроблені висновки та показано
подальший розвиток досліджень в напрямі доєднання акумулювальних пристроїв та доєднання перет-
ворювачів енергії іншого принципу і конструкції. Також відмічено, що використання електричних моде-
лей є шляхом до комбінування систем генерації з різними джерелами енергії.
Ключові слова: фотоелектричний тепловий колектор, PV/T колектор, електрична модель, електро-
теплова аналогія, фотони, фонони.
Index terms
PV/T – photovoltaic thermal
PV – photovoltaic
Introduction. Solar radiation is a fundamental natural en-
ergy source. It serves as the primary input for generating
both electrical and thermal energy. The field of solar energy
is experiencing rapid growth and adoption [1, 2].
To conduct research on energy processes involving renewa-
ble and conventional energy sources, it is expedient to utilize
a device capable of simulating various energy processes and
integrating them. Methods of physical and mathematical
modeling of technological processes and devices in various
fields [3] necessitate the creation of models that accurately
and comprehensively represent all energy processes in a
complex manner. A promising research method is based on
the creation of electrical models and equivalent electrical cir-
cuits. Such a device is convenient for modeling electrical pro-
cesses and electronic circuits [4], as well as thermal, hydrau-
lic, acoustic, mechanical, and other systems and processes.
At present, the approach used to simulate thermal pro-
cesses is one in which so-called thermal circuits are formed
[5], where the elements of the thermal system are repre-
sented in a topological form and the thermal processes,
such as generation, accumulation, resistance, etc., are dis-
played. And then, the thermal circuits are converted into
electrical ones, using the same physical principles.
The work proposes to apply a different approach. Using the
principle of electro-thermal analogies, to move from ther-
mal processes, thermal devices and thermal quantities to
electrical ones. And then, having electrical analogies, to
create electrical circuits that will be electrical models of
thermal devices and processes. This approach is more cor-
rect and quickly makes the transition from thermal quanti-
ties to electrical ones.
Setting objectives. Create an electrical model of the PV/T
collector, considering both electrical and thermal pro-
cesses.
Construction. Typically, photovoltaic converters based on
semiconductors are used to convert solar energy into elec-
trical energy. Solar thermal collectors, on the other hand,
are used to convert solar energy into thermal energy. A
modern and progressive solution is the combination of
these converters into a single photovoltaic thermal (PV/T)
collector, where the absorption of photons from the sun
occurs in multiple layers simultaneously [6, 7]. One layer is
photovoltaic and absorbs photons of the energies required
to generate electric current, while another layer absorbs
the remaining photons from the solar spectrum to create
heat [8] (Fig. 1).
Fig. 1. Photovoltaic thermal collector
46
Відновлювана енергетика. №1/2025 | Сонячна енергетика
As shown in Figure 1, the solar energy converter is a PV/T
collector, which transforms photon flux into electrical and
thermal energy. Electrical energy is directly extracted from
the photovoltaic part of the collector (PV cells), while ther-
mal energy is extracted by a coolant and transferred to the
consumer by a pump.
Analogies and models. To conduct comprehensive model-
ing of systems of various physical nature, it is advisable to
reduce all quantities to a single, convenient model. For this
purpose, the method of analogies is used [9]. To model
electrical and thermal processes in a PV/T collector, it is
proposed to represent the thermal part by equivalent elec-
trical circuits, i.e., electrical models.
The paper [10] shows that, using the corpuscular nature of
electromagnetic radiation, an electrical model of the pro-
cesses of converting a flow of photons into electric charges
and phonons was developed.
Note that the main variable in energy conversion, consump-
tion and distribution is power. Therefore, the construction of
all electrical models must proceed from the general energy
variable – power, which is present in all energy phenomena
and processes. In turn, the primary and basic concepts in the
construction of analogies are basic definitions, such as effort
e and flow f, the product of which is power P.
𝑃 = 𝑒 ∙ 𝑓 (1)
According to these concepts, Tables 1 and 2 make analogies.
Table 1. Analogies for particles
Table 2. Analogies for conduction and convection
Effort e Flow f
Mechanical variable Force F, N Velocity V, м/с
Electrical variable Voltage U, V Current I, А
Thermal variable (convection) Temperature difference dT, К Flow of coolant V/t, m/s
Thermal variable (conduction) Temperature difference dT, К Flow of entropy S/t, J/Ks
Thus, a model was created that, using current and voltage
sources, simulates the flow of charged particles and pho-
nons, and their energy, respectively (Fig. 2).
Fig. 2. Electrical model of conversion from photons to
charges
Electrical equations of a photovoltaic source from Fig.2 are
𝐼𝑜𝑢𝑡 = 𝐼𝑝ℎ + 𝐼𝑈 + 𝐼𝐼 , (2)
𝑈𝑜𝑢𝑡 = 𝑈𝑝ℎ + 𝑈𝑅𝑢 , (3)
𝑈𝑅𝑢 = 𝐼𝑈𝑅𝑈 , (4)
where Iph – current of photon-charge conversion; II – cur-
rent in internal resistivity of current source; IU – current of
voltage source; Iout – output current of a PV-source; RU –
internal resistivity of current source; Uph – voltage on pho-
ton-charge conversion; URu – voltage on internal resistivity
of voltage source; Uout – output voltage of a PV-source.
Fig. 3. Electrical model of conversion from photons to pho-
nons
Electrical equations of a thermal source from Fig.3 are
𝐼𝑡ℎ𝑒𝑟𝑚𝑎𝑙 = 𝐼𝑝𝑛 + 𝐼𝑈𝑝𝑛 + 𝐼𝐼𝑝𝑛 , (5)
𝑈𝑡ℎ𝑒𝑟𝑚𝑎𝑙 = 𝑈𝑝𝑛 + 𝑈𝑅𝑢𝑝𝑛 , (6)
𝑈𝑅𝑢𝑝𝑛 = 𝐼𝑈𝑝𝑛𝑅𝑈𝑝𝑛 , (7)
where Ipn – current of photon-phonon conversion; IIpn – par-
asitic current that simulates phonon scattering; IUpn –
Effort e Flow f
Electrical variable Voltage U, V Current I, А
Photonic Energy of photon/charge Flow of photons
Thermal variable Energy of phonon /quanta of entropy Flow of phonons
47
Відновлювана енергетика. №1/2025 | Сонячна енергетика
current in internal resistivity of source; Ithermal – output cur-
rent that simulates the source phonon flux; RUpn – internal
resistance that models the scattering of source phonons;
Upn – voltage that models the conversion of photon energy
into phonon energy; URupn – voltage on the simulated inter-
nal resistance of the sources; Uthermal – output voltage of a
thermal source model.
It should be noted that the aforementioned method, utiliz-
ing phonons, is useful when considering the process of pho-
ton absorption and its conversion into heat. However, this
approach is overly complex for modelling propagation as it
requires accounting for all modes of vibrational thermal
processes. Therefore, it is more appropriate to use an inte-
gral method, but also employing the method of analogies.
In the case of heat conduction processes, in the vast major-
ity of known models, electric current is considered analo-
gous to the flow of thermal energy, which is incorrect from
a physical standpoint. Therefore, we will consider the en-
tropy flow as an analog of electric current, which physically
reflects, or rather imitates, the flow of particles during ther-
mal motion. The concept of entropy is difficult to represent
in thermal circuits, but it is simpler and has a physical mean-
ing to transition from entropy to charge, then to current,
and to construct a circuit that is an electrical model.
Therefore, we conclude that by using analogies, we can un-
derstand that the heat conduction processes occurring in the
solar collector involve the transfer of thermal energy from
the absorber to the coolant, and are characterized by a tem-
perature difference and entropy flow. These processes are
modeled by electrical circuits. Furthermore, the subsequent
forced convection processes occurring in the solar collector,
which transfer thermal energy from the collector to the heat
consumer using the coolant and are characterized by a tem-
perature difference and the amount of coolant pumped per
unit of time, are also modeled by electrical circuits.
See that there are two mechanisms of heat transfer in the
proposed system: heat transfer and forced convection. Ini-
tially, the heat from photons is transferred to the heat car-
rier, and then the heat carrier transfers the heat to the con-
sumer. However, the first step is the process of photon
absorption with the conversion into heat. Losses due to the
radiation of the PV/T collector during the construction of
this model will be neglected. Based on the analogies de-
scribed in Table 2, we create an electrical model of thermal
processes in the PV/T collector. Thus, when creating a com-
plete electrical model, for heat transfer processes, the
source is a voltage source, and for convection processes,
we choose a current source. Both voltage sources and cur-
rent sources can be controlled by both voltage and current.
Therefore, the general electrical model (Fig. 3) contains
both voltage sources with a series connection of re-
sistances, on which dissipation occurs, and a current source
with a parallel connection of resistances.
Table 2 shows that depending on the heat transfer system,
two types of models are formed. One for convection pro-
cesses:
∆𝑇 → 𝑈 , (8)
𝑉
𝑡⁄ → 𝐼, (9)
where T – temperature difference of the coolant at the
inlet and outlet of the heater; V – volume of the coolant
that is pumped; t – time.
The second model for heat conduction processes:
∆𝑇 → 𝑈 , (10)
𝑆
𝑡⁄ → 𝐼 , (11)
where T – temperature difference; S – entropy.
In this case, the heat-conducting electrical model will have
the following form (Fig. 4):
Fig. 4. Electrical model of thermal conductivity
Then, for the electrical model we have:
𝑈𝑇𝑡ℎ = 𝐼𝑇𝑡ℎ(𝑅𝑇𝑡ℎ + 𝑅𝑇𝑙𝑜𝑠𝑠𝑒𝑠) , (12)
where UTth – voltage source that models the change in tem-
perature of the solar thermal collector under the influence
of solar radiation; ITth – current that simulates the flow of
entropy in the heat-conducting part of the solar thermal
collector; RTth – resistance that models the transfer of heat
from the collector's absorbing structure to the coolant;
RTlosses – resistance that models heat loss in the solar ther-
mal collector.
When defining resistances, in the sense of entropy, heat
dissipation occurs through the conduction of entropy, so
we introduce the concept of thermal-entropic resistance or
resistance to the flow of entropy.
𝑅𝑇𝑡ℎ =
1
(𝑘1𝐴1𝑇𝑎𝑚𝑏)
⁄ , (13)
𝑅𝑇𝑙𝑜𝑠𝑠𝑒𝑠 =
1
(𝑘2𝐴2𝑇𝑎𝑚𝑏)
⁄ , (14)
where k1 – thermal conductivity coefficient of heat transfer
from the solar thermal collector structure to the coolant; k2
– thermal conductivity coefficient of the solar thermal collec-
tor; А1, А2 – heat transfer area; Тamb – ambient temperature.
Subsequently, after heat exchange between the structure
and the coolant, thermal energy is transferred to the con-
sumer using the coolant, where it gives off heat. Convection
heat transfer processes using the coolant are described by
the following equation [11, 12]:
48
Відновлювана енергетика. №1/2025 | Сонячна енергетика
𝑄𝑡ℎ = 𝐶𝑝𝑚(𝑇𝑜𝑢𝑡 − 𝑇𝑖𝑛) = 𝐶𝑝𝜌𝑉(𝑇𝑜𝑢𝑡 − 𝑇𝑖𝑛), (15)
where Qth – thermal energy that is transferred; Cp – heat
capacity of the coolant of the solar thermal collector; m –
mass of the coolant of the solar thermal collector; V – vol-
ume of coolant of the solar thermal collector; – density of
the coolant of the solar thermal collector; Tin, Tout – coolant
temperatures at the inlet and outlet of the solar thermal
collector.
𝑃𝑡ℎ = 𝑈𝐼 = (𝑇𝑜𝑢𝑡 − 𝑇𝑖𝑛)
𝐶𝑝𝑚
𝑡
= (𝑇𝑜𝑢𝑡 − 𝑇𝑖𝑛)
𝐶𝑝𝜌𝑉
𝑡
, (16)
From where, according to the method of analogies:
(𝑇𝑜𝑢𝑡 − 𝑇𝑖𝑛) → 𝑈 (17)
𝐶𝑝𝜌𝑉
𝑡
→ 𝐼 (18)
Then, since the heat exchange process is fluid pumping, the
electrical model has the form (Fig. 5):
From where, for this electrical model we have:
𝐼С𝑡ℎ =
𝑈С𝑙𝑜𝑠𝑠𝑒𝑠
𝑅𝐶𝑙𝑜𝑠𝑠𝑒𝑠
+
𝑈𝑜𝑢𝑡
𝑅𝑜𝑢𝑡
, (19)
where ICth – current source that models heat transfer by a
coolant; Rout – resistance that models the transfer of heat
from the coolant to the consumer; Uout - voltage that simu-
lates the change in coolant temperature at the load; RClosses
– resistance that models heat loss in the coolant during
pumping; UClosses– voltage that simulates the decrease in
coolant temperature during pumping.
Fig. 5. Electrical model of thermal convection
𝑅𝑜𝑢𝑡 =
1
(𝑘3𝐴3𝑇𝑜𝑢𝑡)
⁄ , (20)
𝑅𝐶𝑙𝑜𝑠𝑠𝑒𝑠 =
1
(𝑘4𝐴4𝑇𝑎𝑚𝑏)
⁄ , (21)
where k3 – thermal conductivity coefficient at the load for
heat removal; k4 – thermal conductivity coefficient of struc-
tures through which the coolant is pumped; А3, А4 – corre-
sponding heat transfer areas; Тout – heat sink outlet tem-
perature.
Model of PV/T-collector. The electrical model hybrid PV/T
collector has two parts: electric and thermal (Fig. 6).
Fig. 6. Electrical model of the photovoltaic thermal collector
In Fig. 6, for the thermal part, we obtained a phenomeno-
logical model in which the output of the previous subsys-
tem is the input data for modeling the subsequent subsys-
tem. There, the voltage source UTth is controlled by the
voltage Uthermal, and the current source ICth is controlled by
ITth.
Using the model shown in Figure 6, we can further de-
velop this method of constructing a hybrid solar collector
49
Відновлювана енергетика. №1/2025 | Сонячна енергетика
with additional equipment. The electrical model in Fig. 7
demonstrates the possibility of connecting a pump for cir-
culating a coolant and a solar tracker. This is achieved by
including in the model two electric motors, that drive the
pump for circulating the coolant [13] and that move the
rotary design of the tracker. Furthermore, the model in
Fig. 7 includes a component based on rate equations [14,
15] in stationary mode, that simulates the spectral distri-
bution of photons and their contributions to both electri-
cal and thermal generation.
Fig. 7. Electrical model of the photovoltaic thermal collector with pump and tracker
Conclusion. In conclusion, it should be noted that when
modeling energy processes in PVT collectors, a
comprehensive energy analysis must be conducted, since a
photovoltaic thermal collector has several energy
components. Creating electrical models is a promising and
convenient way to calculate systems with PVT collectors
and other devices. It should be noted that the use of
electrothermal analogies for calculating thermal processes
is reduced to the calculation of electric circuits, using a well-
known and well-developed calculation apparatus.
Modeling thermal processes with the help of electrical
models allows you to understand and effectively simulate
thermal processes.
The models created in the work clearly reflect the thermal
and electrical processes in the PV/T collector. It should be
noted that the electrical model of the thermal part of the
hybrid PV/T collector is a phenomenological model,
because different parts of the thermal collector use
different heat transfer processes, and accordingly are
described by different phenomena and modeled
differently. The paper also proposes a new vision of some
modeling processes. In particular, an approach is used in
which the current in the electrical model of the heat
conduction process during heat transfer to the coolant
corresponds to the entropy flow, and not the heat energy
flow. This representation is more correct from the point of
view of fundamental physics.
It is also clear that the electrical model of the photovoltaic
part of the hybrid PV/T collector presented in the article is
an expanded representation of the conventional equivalent
circuit of the PV-source [16, 17].
The models presented in the article are generalized and do
not consider some less significant phenomena, such as
thermal radiation [18]. The presented model and the
proposed approach can be developed towards full
consideration of losses [19] and dissipative processes [20],
and simulations can also be carried out with storages, for
example, electrochemical storages of electrical energy [21]
or storage tanks of thermal energy. For this, additional
voltage sources and capacitors are introduced. Also, a
further development of the simulation described above is
the addition of other energy converters. Thus, the use of
electrical models is a promising development direction for
combining systems with different energy natures, which
allows to increase the energy characteristics of the
resulting system, and using controlled dynamic
connections, it is possible to create a flexible distributed
generative system [22].
50
Відновлювана енергетика. №1/2025 | Сонячна енергетика
It should also be noted that mathematical simulating
software is traditionally used for simulation [23, 24, 25]. But
we note that the use of electrical models for simulation of
thermal processes allows flexible and convenient
simulation of thermal energy sources using well-known
software tools for simulation of electric circuits in particular
[26, 27]. In addition, the electrical representation of
thermal processes and thermal systems allows creating
prototypes for physical modeling.
REFERENCES
1. Bondarenko D., Matyakh S., Surzhyk Т., Sheiko I. As-
pects of the further development of photoenergy ac-
cording to the materials of the scientific and practical
conference «Renewable energy and energy efficiency in
the 21st century» 2023. Vidnovluvana Energetika. 2023.
No. 4. Pp. 39–44. doi: 10.36296/1819-
8058.2023.4(75).39-44
2. Kudrya S. O. Renewable energy sources: 2nd edition.
Kyiv: Inst. Of renewable energy, 2024. 492 p.
https://doi.org/10.36296/monograph-2024
3. Vennikov V. A., Vennikov V. G. Similitude and simulation
(as applied to problems of electric power engineering):
3d edition. M.: High school. 1984. 439 p.
4. Chua L., Lin Pen-Min. Computer-aided analysis of elec-
tronic circuits. NJ: Prentice-Hall, Inc, 1975. 737 p.
5. Twidell J., Weir A. Renewable energy resources. Lon-
don: E.&F.N.Spon, 1990. 392 p.
6. Huaxu Liang, Fuqiang Wang, Luwei Yang, Ziming Cheng,
Yong Shuai, Heping Tan. Progress in full spectrum solar
energy utilization by spectral beam splitting hybrid PV/T
system. Renewable and Sustainable Energy Reviews.
2021. V. 141, 110785,
https://doi.org/10.1016/j.rser.2021.110785.
7. Bondarenko, D., Matiakh, S., Surzhyk, T., Sheiko, I. Pho-
tovoltaic Thermal Solar Collector for Autonomous and
Energy Cluster Modes. Systems, Decision and Control in
Energy VI. Studies in Systems, Decision and Control.
2024. V. 552. Springer, Cham. Pp. 373–384.
https://doi.org/10.1007/978-3-031-67091-6_16
8. Msirdi N., M’Sirdi N., Benabdellatif M., Tina G. M.,
Naamane A. Dynamic Coupled Electrical and Thermal
Model for PV-T Solar Energy Collectors. EFEA 2018б Va-
lencia. 2018. hal-01927535
9. Mechanical–electrical analogies. Retrieved from
https://https://en.wikipedia.org/wiki/Mechanical–
electrical_analogies . 2024.
10. Bondarenko, D. Developing electrical models to simu-
late the conversion of solar radiation into electrical and
thermal energy. Vidnovluvana Energetika. 2024. No.
4(79). Pp.59–63. https://doi.org/10.36296/1819-
8058.2024.4(79)59-63
11. Huang L. Y., Wen J. X., Karayiannis T. G., Matthews R. D.
Numerical prediction of high efficiency boiler heat
exchanger performance. Applied Thermal Engineering.
1998. Vol. 18. Issue 11. Pp.1089–1099.
https://doi.org/10.1016/S1359-4311(98)00027-1.
12. Roshanzadeh B., Premer L. R., Mohan G. Developing an
Advanced PVT System for Sustainable Domestic Hot
Water Supply. Energies. 2022. No. 7. P. 2346.
https://doi.org/10.3390/en15072346
13. Bondarenko, D. Modeling of systems with the photovol-
taic power source and water pumps. Vidnovluvana Ener-
getika. 2024. No. 3(78). Pp.62–68.
https://doi.org/10.36296/1819-8058.2024.3(78).62- 68.
14. Hofbauer, Josef; Sigmund, Karl (1998). "Dynamical Sys-
tems and Lotka–Volterra Equations". Evolutionary
Games and Population Dynamics. New York: Cambridge
University Press. Pp. 1–54.
15. Tsang W. Semiconductor injection lasers. Dynamics,
modulation, spectrum. M.: Radio and communication,
1990. 320 p.
16. Fahrenbruch A., Bube R. Fundamentals of solar cells.
Photovoltaic solar energy conversion. NY: Academic
Press Inc., 1983. 580 p.
17. Konuhov S. N. Solar energy systems of space ships.
Physical and mathematical modeling. Kharkov: Space
university, 2000. 515 p.
18. Howell J. R., Mengüç M. P., Siegel, R. Thermal radiation
heat transfer (Sixth ed.). 2016. New York: CRC Press,
Taylor & Francis Group.
19. Antonanzas J., Del Amo A., Martinez-Gracia A., Bayod-
Rujula A., Antonanzas-Torres F. Towards the optimiza-
tion of convective losses in photovoltaic–thermal pan-
els, Solar Energy. 2015. Vol. 116. Pp. 323–336.
https://doi.org/10.1016/j.solener.2015.04.013.
20. Dissipation. Retrieved from https://en.wikipe-
dia.org/wiki/Dissipation. 2024.
21. Bondarenko, D. Equivalent circuits of electric power ac-
cumulators connected to solar photocell. Vidnovluvana
Energetika. 2019. No.3. Pp.30–34. doi: 10.36296/1819-
8058.2019.3(58).30-34
22. Bondarenko D. Combination of pvt-collectors with using
of controlled connections. Vidnovluvana Energetika.
2024. No. 2. Pp.86–91. https://doi.org/10.36296/1819-
8058.2024.2(77).86-91
23. Barbu M., Siroux M., Darie G. Numerical model and par-
ametric analysis of a liquid based hybrid photovoltaic
thermal (PVT) collector. Energy Reports. 2021. Vol. 7.
Pp. 7977–7988.
https://doi.org/10.1016/j.egyr.2021.07.058.
24. Arrillaga J. Computer Analysis of Power Systems. John
Wiley & Sons, 1990. 376 p.
25. Grigsby L. Power Systems. CRC Press, 2012. 556 p.
26. About PSpice. Retrieved from
https://www.pspice.com/about - 2024.
27. Bansal, R. Matlab and its application in engineering.
Pearson publication. (2009).
https://www.scopus.com/authid/detail.uri?authorId=57090256200
https://www.scopus.com/authid/detail.uri?authorId=58866652900
https://www.scopus.com/authid/detail.uri?authorId=57971234900
https://www.scopus.com/authid/detail.uri?authorId=58961288700
https://doi.org/10.36296/1819-8058.2023.4(75).39-44
https://doi.org/10.36296/1819-8058.2023.4(75).39-44
https://doi.org/10.1016/j.rser.2021.110785
https://doi.org/10.1007/978-3-031-67091-6_16
https://doi.org/10.1016/S1359-4311(98)00027-1
https://doi.org/10.3390/en15072346
https://en.wikipedia.org/wiki/Dissipation
https://en.wikipedia.org/wiki/Dissipation
https://www.scopus.com/authid/detail.uri?authorId=57090256200
https://doi.org/10.36296/1819-8058.2019.3(58).30-34
https://doi.org/10.36296/1819-8058.2019.3(58).30-34
https://www.scopus.com/authid/detail.uri?authorId=57090256200
https://doi.org/10.36296/1819-8058.2024.1(76).57-61
https://doi.org/10.36296/1819-8058.2024.1(76).57-61
https://doi.org/10.1016/j.egyr.2021.07.058
https://www.pspice.com/about%20-%202024
|
| id | veorgua-article-505 |
| institution | Vidnovluvana energetika |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-19T01:15:03Z |
| publishDate | 2025 |
| publisher | Institute of Renewable Energy National Academy of Sciences of Ukraine |
| record_format | ojs |
| resource_txt_mv | veorgua/a1/602912d11ac089024591e53541415ea1.pdf |
| spelling | veorgua-article-5052026-07-18T06:32:21Z ELECTRICAL MODEL OF THE HYBRID PHOTOVOLTAIC THERMAL COLLECTOR ЕЛЕКТРИЧНА МОДЕЛЬ ГІБРИДНОГО ФОТОЕЛЕКТРИЧНОГО ТЕПЛОВОГО КОЛЕКТОРА Bondarenko , D. photovoltaic thermal collector, PV/T-collector, electrical model, electrical-thermal analogy, photons, phonons фотоелектричний тепловий колектор, PV/T колектор, електрична модель, електро-теплова аналогія, фотони, фонони. The article is devoted to the creation of electrical models of a hybrid photovoltaic thermal. The objective of the article is to create electrical models of the thermal and photovoltaic parts of the hybrid collector. The paper focuses on the spectrum of solar radiation and shows that absorption occurs both in the photovoltaic part and in the thermal part of the hybrid collector. The advantages of combining thermal and photovoltaic parts in one en-ergy-generating device are shown. The construction of a photovoltaic thermal solar collector is shown. A table of electrothermal analogies, both for thermal conductivity and thermal convection, is demonstrated. An approach is presented in which thermal processes of photon absorption are modeled by the creation of phonons. The funda-mental aspects of the choice of modeling values, for example, the flow of entropy instead of the flow of thermal energy, are shown. It is shown that, within the framework of the electrothermal analogy, the calculation of ther-mal processes is reduced to the calculation of electric circuits. Electrical models are created and electrical equa-tions of the created electrical models are recorded. Controlled sources of current and voltage, and derived model-ing resistances in equivalent circuits are shown. A general model of a hybrid photovoltaic thermal collector is constructed, which is placed on a tracker and connected to a pump that pumps the coolant through the thermal part of the collector. This model includes a part that, based on rate equations, shows the separation of photons according to the spectral absorption distribution. Conclusions are drawn, and further research in the direction of connecting storage devices and connecting energy converters using different principles and designs is shown. It was also noted that the use of electrical models is a way to combine generation systems running on various energy sources. Стаття присвячена побудові електричних моделей гібридного фотоелектричного тепло-вого колектора. Метою статті є створення електричних моделей теплової та фотоелектричної ча-стин гібридного колектора. У роботі акцентовано на спектрі сонячного випромінювання й показано, що поглинання відбувається як фотовольтаїчною, так і тепловою частиною гібридного колектора. Показано переваги поєднання теплової та фотоелектричної частини в одному енергогенерувальному пристрої. Показано конструкцію фотоелектричного теплового сонячного колектора. Продемонстро-вана таблиця електротеплових аналогій як для теплопровідності, так і для теплової конвекції. Викла-дено підхід, в якому теплові процеси поглинання фотонів моделюються утворенням фононів. Показані принципові аспекти вибору моделювальних величин, наприклад потоку ентропії замість потоку теплової енергії. Показано, що в межах електротеплової аналогії розрахунок теплових процесів зводиться до розрахунку електричних кіл. Побудовані електричні моделі та записані електричні рівняння побудованих моделей. В еквівалентних схемах показано контрольовані джерела струмів і напруг, та виведені моделювальні опори. Побудована загальна модель гібридного фотоелектричного теплового колектора, який розміщений на трекері й підключений до насоса, який прокачує теплоносій через теплову частину колектора. У таку модель вбудовано частину, яка на основі кінетичних рівнянь показує розділення фотонів згідно зі спектральним поглинальним розподілом. Зроблені висновки та показано подальший розвиток досліджень в напрямі доєднання акумулювальних пристроїв та доєднання перет-ворювачів енергії іншого принципу і конструкції. Також відмічено, що використання електричних моде-лей є шляхом до комбінування систем генерації з різними джерелами енергії. Institute of Renewable Energy National Academy of Sciences of Ukraine 2025-03-31 Article Article application/pdf https://ve.org.ua/index.php/journal/article/view/505 10.36296/1819-8058.2025.1(80).44-50 Vidnovluvana energetika ; No. 1(80) (2025): Scientific and applied Journal renewable energy ; 44-50 Возобновляемая энергетика; ##issue.no## 1(80) (2025): Scientific and applied Journal renewable energy ; 44-50 Відновлювана енергетика; № 1(80) (2025): Науково-прикладний журнал Відновлювана енергетика; 44-50 2664-8172 1819-8058 10.36296/1819-8058.2025.1(80) en https://ve.org.ua/index.php/journal/article/view/505/414 Copyright (c) 2025 D. Bondarenko https://creativecommons.org/licenses/by-nc-nd/4.0 |
| spellingShingle | photovoltaic thermal collector PV/T-collector electrical model electrical-thermal analogy photons phonons Bondarenko , D. ELECTRICAL MODEL OF THE HYBRID PHOTOVOLTAIC THERMAL COLLECTOR |
| title | ELECTRICAL MODEL OF THE HYBRID PHOTOVOLTAIC THERMAL COLLECTOR |
| title_alt | ЕЛЕКТРИЧНА МОДЕЛЬ ГІБРИДНОГО ФОТОЕЛЕКТРИЧНОГО ТЕПЛОВОГО КОЛЕКТОРА |
| title_full | ELECTRICAL MODEL OF THE HYBRID PHOTOVOLTAIC THERMAL COLLECTOR |
| title_fullStr | ELECTRICAL MODEL OF THE HYBRID PHOTOVOLTAIC THERMAL COLLECTOR |
| title_full_unstemmed | ELECTRICAL MODEL OF THE HYBRID PHOTOVOLTAIC THERMAL COLLECTOR |
| title_short | ELECTRICAL MODEL OF THE HYBRID PHOTOVOLTAIC THERMAL COLLECTOR |
| title_sort | electrical model of the hybrid photovoltaic thermal collector |
| topic | photovoltaic thermal collector PV/T-collector electrical model electrical-thermal analogy photons phonons |
| topic_facet | photovoltaic thermal collector PV/T-collector electrical model electrical-thermal analogy photons phonons фотоелектричний тепловий колектор PV/T колектор електрична модель електро-теплова аналогія фотони фонони. |
| url | https://ve.org.ua/index.php/journal/article/view/505 |
| work_keys_str_mv | AT bondarenkod electricalmodelofthehybridphotovoltaicthermalcollector AT bondarenkod električnamodelʹgíbridnogofotoelektričnogoteplovogokolektora |