DEVELOPING ELECTRICAL MODELS TO SIMULATE THE CONVERSION OF SOLAR RADIATION INTO ELECTRICAL AND THERMAL ENERGY
This article focuses on developing electrical models to investigate the conversion of solar radiation into both electrical and thermal energy. Our findings indicate that semiconductor converters are unable to harness the entire electromagnetic spectrum emitted by the sun. A substantial portion of so...
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Institute of Renewable Energy National Academy of Sciences of Ukraine
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| 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. |
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| description | This article focuses on developing electrical models to investigate the conversion of solar radiation into both electrical and thermal energy. Our findings indicate that semiconductor converters are unable to harness the entire electromagnetic spectrum emitted by the sun. A substantial portion of solar radiation is transformed into heat. To achieve these results, we employed a corpuscular model to represent the solar radiation flow and a quantum mechanical framework to describe the energy associated with electromagnetic radiation and thermal processes within the crystal. To derive electrical modeling parameters, this study leveraged the principle of electrical and electrothermal analogies. We established a direct equivalence between the flow of solar photons and the flow of charge carriers represented by the electric current. Additionally, we demonstrated that the energy carried by photons is analogous to the voltage generated across the photovoltaic device. When modeling thermal energy using electrical circuits, we found that the electric current can be used to represent the flow of phonons, quasiparticles associated with thermal vibrations in the crystal, while the voltage corresponds to the energy of phonons. This study developed electrical models to simulate the conversion of solar radiation into both electrical and thermal energy. Current and voltage sources were employed to represent the energy conversion processes. It is shown that the internal resistances of energy sources in electrical models simulate the losses during the generation of electrical and thermal energy. It is noted that the proposed electrical model of a photovoltaic power source corresponds to the traditional equivalent circuit with a diode. The paper concludes by discussing the potential applications of the proposed modeling framework. |
| doi_str_mv | 10.36296/1819-8058.2024.4(79).59-63 |
| first_indexed | 2025-07-17T11:39:42Z |
| format | Article |
| fulltext |
59
Відновлювана енергетика. №4/2024 | Сонячна енергетика
UDK 621 https://doi.org/10.36296/1819-8058.2024.4(79)59-63
DEVELOPING ELECTRICAL MODELS TO SIMULATE THE CONVERSION OF SOLAR RADIATION INTO
ELECTRICAL AND THERMAL ENERGY
Received Oct. 28, 2024; accepted Nov. 27, 2024
Available online Dec. 11, 2024
Bondarenko D.
Author for correspondence: Bondarenko Dmytro,
e-mail: dima7007bond@gmail.com
Abstract. This article focuses on developing electrical models to
investigate the conversion of solar radiation into both electrical and thermal energy. Our findings indicate
that semiconductor converters are unable to harness the entire electromagnetic spectrum emitted by the
sun. A substantial portion of solar radiation is transformed into heat. To achieve these results, we employed
a corpuscular model to represent the solar radiation flow and a quantum mechanical framework to describe
the energy associated with electromagnetic radiation and thermal processes within the crystal. To derive
electrical modeling parameters, this study leveraged the principle of electrical and electrothermal analogies.
We established a direct equivalence between the flow of solar photons and the flow of charge carriers rep-
resented by the electric current. Additionally, we demonstrated that the energy carried by photons is analo-
gous to the voltage generated across the photovoltaic device. When modeling thermal energy using electrical
circuits, we found that the electric current can be used to represent the flow of phonons, quasiparticles asso-
ciated with thermal vibrations in the crystal, while the voltage corresponds to the energy of phonons. This
study developed electrical models to simulate the conversion of solar radiation into both electrical and ther-
mal energy. Current and voltage sources were employed to represent the energy conversion processes. It is
shown that the internal resistances of energy sources in electrical models simulate the losses during the gen-
eration of electrical and thermal energy. It is noted that the proposed electrical model of a photovoltaic
power source corresponds to the traditional equivalent circuit with a diode. The paper concludes by discussing
the potential applications of the proposed modeling framework.
Keywords: electrical model, solar radiation, electrical energy, thermal energy, analogies, photon, phonon
СТВОРЕННЯ ЕЛЕКТРИЧНИХ МОДЕЛЕЙ ДЛЯ МОДЕЛЮВАННЯ ПРОЦЕСІВ ПЕРЕТВОРЕННЯ
СОНЯЧНОГО ВИПРОМІНЕННЯ НА ЕЛЕКТРИЧНУ І ТЕПЛОВУ ЕНЕРГІЇ
Отримано 28 жов. 2024 р.; рекомендовано до публікації 27 лист. 2024 р.
Доступно онлайн 11 груд. 2024 р.
Бондаренко Д. В.
Автор для кореспонденції: Бондаренко Дмитро,
e-mail: dima7007bond@gmail.com
Анотація. Стаття присвячена побудові електричних моде-
лей для дослідження процесів перетворення енергії сонячного випромінювання на електричну і теплову
енергії. В роботі показано, що не весь спектр електромагнітного випромінювання Сонця перетворю-
ється в напівпровідниковому перетворювачі на електричну енергію. Значна частина сонячного випро-
мінювання перетворюється на теплову енергію. В статті було використано корпускулярне предста-
влення потоку сонячного випромінювання та квантово-механічне представлення енергії
електромагнітного випромінювання та енергії теплових процесів у кристалі. Для отримання елект-
ричних моделювальних величин у роботі було застосовано принцип електричних та електротеплових
аналогій. Було показано відповідність потоку частинок сонячного електромагнітного випромінювання,
фотонів, потоку згенерованих носіїв заряду, тобто струму. Також було показано, що енергія фотонів
відповідає напрузі, яка створюється на електродах фотоелектричного перетворювача. В роботі по-
казано, що в разі моделювання теплової енергії за допомогою електричних моделей струм моделює
PhD
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
60
Відновлювана енергетика. №4/2024 | Сонячна енергетика
потік квазічастинок теплових коливальних процесів у кристалі, фононів, а енергія фононів моделю-
ється напругою.
У роботі були побудовані електричні моделі процесу перетворення сонячного випромінювання на елек-
тричну енергію та процесу перетворення сонячного випромінювання на теплову енергію. При цьому
було використано джерело струму та джерело напруги, які саме й моделюють процеси перетворення
однієї енергії на іншу. Показано, що внутрішні опори джерел енергії в електричних моделях моделюють
втрати при генерації електричної та теплової енергії. Відмічено, що запропонована в роботі електри-
чна модель фотовольтаїчного джерела електричної енергії відповідає традиційній еквівалентній схемі
з діодом. Були зроблені висновки та показано область застосування запропонованих принципів та мо-
делей.
Ключові слова: електрична модель, сонячне випромінювання, електрична енергія, теплова енергія, ана-
логії, фотон, фонон.
Introduction. The widespread use of solar energy has high-
lighted the need for comprehensive modeling of various so-
lar energy systems, such as centralized and distributed sys-
tems [1]. As a result, there is a growing demand for
research into different applications of solar radiation [2]. A
fundamental aspect of this research is the detailed study of
solar radiation characteristics.
For the calculation, modeling, and analysis of solar energy
systems, a thorough understanding of the processes in-
volved in converting the electromagnetic energy of solar ra-
diation into electrical and thermal energy is essential. Clas-
sically, electromagnetic energy is carried by waves,
whereas in quantum mechanics, it is carried by photons.
Developing models of solar radiation energy carriers is an
effective and practical approach to conducting such re-
search. Given that electrical energy is the most efficient end
product of electromagnetic energy conversion, the use of
electrical models of absorption, emission, and conversion
processes of electromagnetic waves or photons is highly ef-
fective.
To create effective electrical models, it is recommended to
employ electrical analogy methods [3] that establish corre-
spondences between fundamental physical quantities and
electrical parameters.
Objective of the work. To develop electrical models of the
processes of converting solar radiation into electrical and
thermal energy based on electrical analogy methods and
the corpuscular nature of light and heat.
Materials and methods
Spectrum and energy. The electromagnetic energy flux in-
cident on Earth from the Sun exhibits a distinct spectral dis-
tribution, and a substantial fraction of this spectrum can be
transformed into electrical energy via the photovoltaic ef-
fect in semiconductors. Nevertheless, due to the mismatch
between the absorption spectrum of solar radiation in sem-
iconductor photovoltaic devices and the spectrum of the
conversion of radiation energy into electrical energy (Fig. 1)
[4], the development of electrical models for the processes
of solar radiation conversion into both electrical and ther-
mal energy is imperative.
Fig. 1. Spectrum of solar radiation
When considering the classical interpretation of solar radi-
ation, the electric and magnetic field intensities are not par-
ticularly suitable for model development due to the lack of
corresponding quantities in circuit theory. However, ac-
cording to quantum theory, solar radiation consists of pho-
tons, and the energy of each photon is given by the formula
[5, 6]:
𝐸𝑝ℎ = ℎ𝜈, (1)
where Еph – energy of photon, h – Plank’s constant; – fre-
quency of photon.
Quantum theory views light as consisting of particles –pho-
tons – which aligns well with the particle-based nature of
electrical circuits (where electrons are the charge carriers).
Hence, when creating electrical models, photons can be di-
rectly analogous to electrical charge carriers (p -> e). This
analogy can be extended to thermal processes as well.
The number of photons incident on a semiconductor per
unit time is essentially the light intensity or luminous flux,
as it is directly proportional to the number of photons.
Therefore, the energy of a monochromatic photon flux is:
𝐸𝑝ℎ_𝑓𝑙𝑜𝑤 = 𝑛ℎ𝜈, (2)
where n – number of particles.
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Відновлювана енергетика. №4/2024 | Сонячна енергетика
The main energy transition responsible for the photovoltaic
effect in semiconductors involves the absorption of quanta,
causing electrons to be excited from the valence band EV to
the conduction band EC. This intrinsic light absorption gen-
erates both free electrons and holes. For such transitions to
occur, the photon energy must exceed the bandgap energy
hv ≥ ∆E, where ∆E represents the energy required to excite
the intrinsic atoms of the semiconductor. Impurity levels
also play a role in the absorption process. The excitation of
donor and acceptor impurities requires photon energies of
hv ≥ ∆Ed and hv ≥ ∆Ea, respectively, where ∆Ed and ∆Ea are
the excitation energies of donor and acceptor atoms. Fur-
thermore, other non-main energy transitions within the
crystal can occur.
Electricity. If every absorbed photon has a probability of
generating a free charge carrier or an electron-hole pair,
then the rate at which charge carriers are generated is di-
rectly proportional to the photon flux. Consequently, a di-
rect correlation exists between the electrical current and
the photon flux:
𝑑(𝑛𝑝ℎ)
𝑑𝑡
→
𝑑(𝑛𝑒)
𝑑𝑡
, (3)
where nph – number of photons; ne – number of electrons
By introducing the elementary charge e, we can formulate
an expression for the integrated power associated with the
photon flux:
𝜂𝑃𝑝ℎ_𝑓𝑙𝑜𝑤 = 𝑃𝑒_𝑓𝑙𝑜𝑤 =
ℎ𝜈𝑛
𝑡
𝑒
𝑒
, (4)
where Pph_flow – power of photon flux; Pe_flow – power of
charge flux; – efficiency of conversation photons to elec-
tricity; e – elementary charge.
Electrically, power P is expressed as the product of current
I and voltage U:
𝑃 = 𝐼𝑈. (5)
Comparing equations (4), (5), and (3), it is evident that
𝑛𝑒
𝑡
→ 𝐼, (6)
and
ℎ𝜈
𝑒
→ 𝑈. (7)
Heat. Thermal energy arises when excess or insufficient
photon energy, incident upon a semiconductor, is absorbed
by the solid's crystalline structure. Atoms in a solid are in
constant motion, with the amplitude of their oscillations
around the lattice points increasing with temperature. Ac-
cording to quantum theory, an atom can only change its en-
ergy in discrete quanta. Consequently, the energy of an
atom is quantized, changing in discrete portions, and the
magnitude of these energy portions, similar to photons, is
determined by formula (1), where f is the frequency of
atomic oscillation. The quantization of energy absorption
by an atom significantly influences both the motion of indi-
vidual atoms and the overall state of the solid. Waves are
formed within the solid. Since any wave can be considered
as a stream of quanta, thermal vibrations in a solid consist
of quasiparticles of lattice vibrations – phonons [7].
A phonon, like any quantum, possesses energy ΔEpn = hf. If
a crystal consists of m unit cells, then the energy flux of the
total number of phonons will be
𝐸𝑝𝑛_𝑓𝑙𝑜𝑤 = 𝑚ℎ𝑓, (8)
where m is the number of phonons; f is the vibrational fre-
quency of atoms in the crystal lattice.
Given the above, a direct correlation exists between the
thermal energy and the photon flux:
𝑑(𝑛𝑝ℎ)
𝑑𝑡
→
𝑑(𝑛𝑝𝑛)
𝑑𝑡
, (9)
where nph – number of photons; npn – number of phonons.
By introducing the quasi-particle of entropy s, we can for-
mulate an expression for the integrated power associated
with the photon flux:
(1 − 𝜂)𝑃𝑝ℎ_𝑓𝑙𝑜𝑤 = 𝑃𝑝𝑛_𝑓𝑙𝑜𝑤 =
ℎ𝑓𝑚
𝑡
𝑠
𝑠
, (10)
where Ppn_flow – power of phonon flux; s – quanta of en-
tropy.
Comparing equations (9), (10), and expression of electric
power (5), it is evident that
𝑚𝑠
𝑡
→ 𝐼𝑝𝑛, (11)
and
ℎ𝑓
𝑠
→ 𝑈𝑝𝑛. (12)
Results. Using the derived relationships, we can develop
electrical models to simulate the processes of converting
solar radiation into electricity and heat.
From relations (6) and (7), we can see that the presence of
a certain number of photons being converted into charge
carriers is modeled by a current source, while the energy of
the photons required for absorption during the creation of
an electron-hole pair is modeled by a voltage source. Thus,
the electrical model of the charge carrier generation pro-
cess is a current source with an internal resistance, while
the electrical model of the potential difference creation
across the photocell electrodes is a voltage source with a
certain internal resistance. Therefore, the electrical model
of the photon conversion processes into electron-hole pairs
can be represented as shown in Fig. 2.
Fig. 2. Electric model of photon-electricity conversation in
PV cell
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Відновлювана енергетика. №4/2024 | Сонячна енергетика
As seen in Figure 2, the voltage source Uph and resistance
RU correspond to the linearized equivalent circuit of a diode
[8]. Therefore, the electrical model in Figure 2 can be sim-
plified to the classic equivalent circuit of a photovoltaic cell
as shown in Fig. 3 [9].
Fig. 3. Electric model of PV cell
The internal resistance of the current source RI in Fig. 2 and
3 models various physical processes of photon and charge
carrier losses, and can consist of a group of parallel resistors
modeling losses due to reflection and shading, photon ab-
sorption in the semiconductor without the generation of
electron-hole pairs, scattering on lattice vibrations, and re-
combination of generated charge carriers at defects [10].
On the other hand, according to the electrical model in Fig.
2, the voltage Uph generated during photogeneration is de-
termined by the energy barriers within the semiconductor.
The electromotive force of the voltage source represents
the bandgap, while the voltage drop across the internal re-
sistance RU accounts for the effects of impurities, tempera-
ture, and other semiconductor properties that reduce the
potential barrier for electron-hole pair formation [11, 12].
Electrical equations of a photovoltaic source from Fig. 2 are
𝐼𝑜𝑢𝑡 = 𝐼𝑝ℎ + 𝐼𝑈 + 𝐼𝐼 , (13)
𝑈𝑜𝑢𝑡 = 𝑈𝑝ℎ + 𝑈𝑅𝑢, (14)
𝑈𝑅𝑢 = 𝐼𝑈𝑅𝑈, (15)
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.
The current IU could give by the standard diode theory
(Shockley diode equation) [13]:
𝐼𝑈 = 𝐼𝑑 = 𝐼0 (𝑒
𝑒𝑈𝑜𝑢𝑡
𝑘𝑇 − 1), (16)
where Id – current of diode; I0 – saturation current; k –
Boltzmann’s constant; T – cell temperature [14].
Considering equations (11) and (12), we see that a certain
number of photons are converted into phonons, and this
process is modeled by a current source, while the energy of
the photons transferred to the crystal lattice is modeled by
a voltage source. Thus, the electrical model of the heat gen-
eration process, namely the entropy flow, is a current
source, and the electrical model of the temperature differ-
ence creation between the absorbing element and the ex-
ternal environment is a voltage source with a certain inter-
nal resistance (Fig. 4).
Fig. 4. Electric model of photon-heat conversion in PV cell
The resistance RIpn in Fig. 4 models various physical pro-
cesses of phonon losses and can consist of a group of par-
allel resistors modeling phonon losses due to useless heat
radiation, photon absorption in the semiconductor without
phonon generation, and phonon losses due to useless con-
vective heat losses [15, 16].
On the other hand, the processes of obtaining a tempera-
ture difference and, consequently, a model voltage during
heat generation, according to the electrical model (Fig.4),
also depend on the energy of photons. Specifically, the
model electromotive force of the voltage source in Fig.4 is
formed from the frequency of phonons, which is trans-
ferred to the frequency of vibrations of the crystal lattice
cells. Such voltage can have a certain spectrum of values,
since the photons falling on the photocell and the lattice
vibrations are not monochromatic. The decrease in voltage
in this electrical model resulting from internal resistance,
occurs due to dissipative processes in the crystal lattice of
the solid (photocell) [17].
Conclusion. Our findings demonstrate that electrical mod-
els can be effectively developed for both electrical and
thermal processes in solar photovoltaic and thermal gener-
ating elements by utilizing analogy principles and analyzing
the corpuscular nature of solar energy conversion.
In this work, electrical models were developed for photo-
voltaic and thermal generation based on quantum pro-
cesses of solar radiation absorption. In constructing the
electrical model of thermal generation, quantum processes
for the formation of quasiparticles such as phonons –
quanta of vibrational processes within a crystal lattice, i.e.,
the processes of generation and propagation of thermal en-
ergy – were taken as a basis.
The transition from photon energy to the voltage gener-
ated by a photovoltaic cell and the transition from photon
flow to the electrical current generated by a PV cell are nat-
ural and fully describe the conversion processes. It is shown
that the resulting electrical model corresponds to the
63
Відновлювана енергетика. №4/2024 | Сонячна енергетика
traditional equivalent circuit with a diode. It was also estab-
lished that the modeled energy of phonons, formed by the
absorption of photons that do not participate in electrical
generation, corresponds to the modelled voltage, and the
modelled entropy flow of phonons, under the same condi-
tions, corresponds to the modelled current of the electrical
model's power source.
An effective example of the application of the theory pre-
sented in this article is the calculation of solar hybrid PVT
collectors, which combine the generation of electrical and
thermal energy [18]. Given that cogeneration hybrid energy
equipment is a complex system, for example, with coolant
pumping devices, pumps that require electrical power [19],
and includes mutual influence between the electrical and
thermal subsystems, the approach described above allows
for the analysis, research, and simulation of the entire en-
ergy system. In addition, small, unified generating devices
can be combined into larger systems [20], so a convenient
modeling method, such as the one proposed in the article,
allows for quick calculation of scalable generating systems
and energy clusters.
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| id | veorgua-article-487 |
| institution | Vidnovluvana energetika |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-19T01:14:21Z |
| publishDate | 2024 |
| publisher | Institute of Renewable Energy National Academy of Sciences of Ukraine |
| record_format | ojs |
| resource_txt_mv | veorgua/a0/58c071b43af1d4aab74853abae99d3a0.pdf |
| spelling | veorgua-article-4872026-07-18T06:32:20Z DEVELOPING ELECTRICAL MODELS TO SIMULATE THE CONVERSION OF SOLAR RADIATION INTO ELECTRICAL AND THERMAL ENERGY СТВОРЕННЯ ЕЛЕКТРИЧНИХ МОДЕЛЕЙ ДЛЯ МОДЕЛЮВАННЯ ПРОЦЕСІВ ПЕРЕТВОРЕННЯ СОНЯЧНОГО ВИПРОМІНЕННЯ НА ЕЛЕКТРИЧНУ І ТЕПЛОВУ ЕНЕРГІЇ Bondarenko , D. electrical model, solar radiation, electrical energy, thermal energy, analogies, photon, phonon електрична модель, сонячне випромінювання, електрична енергія, теплова енергія, аналогії, фотон, фонон. This article focuses on developing electrical models to investigate the conversion of solar radiation into both electrical and thermal energy. Our findings indicate that semiconductor converters are unable to harness the entire electromagnetic spectrum emitted by the sun. A substantial portion of solar radiation is transformed into heat. To achieve these results, we employed a corpuscular model to represent the solar radiation flow and a quantum mechanical framework to describe the energy associated with electromagnetic radiation and thermal processes within the crystal. To derive electrical modeling parameters, this study leveraged the principle of electrical and electrothermal analogies. We established a direct equivalence between the flow of solar photons and the flow of charge carriers represented by the electric current. Additionally, we demonstrated that the energy carried by photons is analogous to the voltage generated across the photovoltaic device. When modeling thermal energy using electrical circuits, we found that the electric current can be used to represent the flow of phonons, quasiparticles associated with thermal vibrations in the crystal, while the voltage corresponds to the energy of phonons. This study developed electrical models to simulate the conversion of solar radiation into both electrical and thermal energy. Current and voltage sources were employed to represent the energy conversion processes. It is shown that the internal resistances of energy sources in electrical models simulate the losses during the generation of electrical and thermal energy. It is noted that the proposed electrical model of a photovoltaic power source corresponds to the traditional equivalent circuit with a diode. The paper concludes by discussing the potential applications of the proposed modeling framework. Стаття присвячена побудові електричних моделей для дослідження процесів перетворення енергії сонячного випромінювання на електричну і теплову енергії. В роботі показано, що не весь спектр електромагнітного випромінювання Сонця перетворюється в напівпровідниковому перетворювачі на електричну енергію. Значна частина сонячного випромінювання перетворюється на теплову енергію. В статті було використано корпускулярне представлення потоку сонячного випромінювання та квантово-механічне представлення енергії електромагнітного випромінювання та енергії теплових процесів у кристалі. Для отримання електричних моделювальних величин у роботі було застосовано принцип електричних та електротеплових аналогій. Було показано відповідність потоку частинок сонячного електромагнітного випромінювання, фотонів, потоку згенерованих носіїв заряду, тобто струму. Також було показано, що енергія фотонів відповідає напрузі, яка створюється на електродах фотоелектричного перетворювача. В роботі показано, що в разі моделювання теплової енергії за допомогою електричних моделей струм моделює потік квазічастинок теплових коливальних процесів у кристалі, фононів, а енергія фононів моделюється напругою. У роботі були побудовані електричні моделі процесу перетворення сонячного випромінювання на електричну енергію та процесу перетворення сонячного випромінювання на теплову енергію. При цьому було використано джерело струму та джерело напруги, які саме й моделюють процеси перетворення однієї енергії на іншу. Показано, що внутрішні опори джерел енергії в електричних моделях моделюють втрати при генерації електричної та теплової енергії. Відмічено, що запропонована в роботі електрична модель фотовольтаїчного джерела електричної енергії відповідає традиційній еквівалентній схемі з діодом. Були зроблені висновки та показано область застосування запропонованих принципів та моделей. Institute of Renewable Energy National Academy of Sciences of Ukraine 2024-12-10 Article Article application/pdf https://ve.org.ua/index.php/journal/article/view/487 10.36296/1819-8058.2024.4(79).59-63 Vidnovluvana energetika ; No. 4(79) (2024): Scientific and applied Journal renewable energy ; 59-63 Возобновляемая энергетика; ##issue.no## 4(79) (2024): Scientific and applied Journal renewable energy ; 59-63 Відновлювана енергетика; № 4(79) (2024): Науково-прикладний журнал Відновлювана енергетика; 59-63 2664-8172 1819-8058 10.36296/1819-8058.2024.4(79) en https://ve.org.ua/index.php/journal/article/view/487/396 Copyright (c) 2024 D. Bondarenko https://creativecommons.org/licenses/by-nc-nd/4.0 |
| spellingShingle | electrical model solar radiation electrical energy thermal energy analogies photon phonon Bondarenko , D. DEVELOPING ELECTRICAL MODELS TO SIMULATE THE CONVERSION OF SOLAR RADIATION INTO ELECTRICAL AND THERMAL ENERGY |
| title | DEVELOPING ELECTRICAL MODELS TO SIMULATE THE CONVERSION OF SOLAR RADIATION INTO ELECTRICAL AND THERMAL ENERGY |
| title_alt | СТВОРЕННЯ ЕЛЕКТРИЧНИХ МОДЕЛЕЙ ДЛЯ МОДЕЛЮВАННЯ ПРОЦЕСІВ ПЕРЕТВОРЕННЯ СОНЯЧНОГО ВИПРОМІНЕННЯ НА ЕЛЕКТРИЧНУ І ТЕПЛОВУ ЕНЕРГІЇ |
| title_full | DEVELOPING ELECTRICAL MODELS TO SIMULATE THE CONVERSION OF SOLAR RADIATION INTO ELECTRICAL AND THERMAL ENERGY |
| title_fullStr | DEVELOPING ELECTRICAL MODELS TO SIMULATE THE CONVERSION OF SOLAR RADIATION INTO ELECTRICAL AND THERMAL ENERGY |
| title_full_unstemmed | DEVELOPING ELECTRICAL MODELS TO SIMULATE THE CONVERSION OF SOLAR RADIATION INTO ELECTRICAL AND THERMAL ENERGY |
| title_short | DEVELOPING ELECTRICAL MODELS TO SIMULATE THE CONVERSION OF SOLAR RADIATION INTO ELECTRICAL AND THERMAL ENERGY |
| title_sort | developing electrical models to simulate the conversion of solar radiation into electrical and thermal energy |
| topic | electrical model solar radiation electrical energy thermal energy analogies photon phonon |
| topic_facet | electrical model solar radiation electrical energy thermal energy analogies photon phonon електрична модель сонячне випромінювання електрична енергія теплова енергія аналогії фотон фонон. |
| url | https://ve.org.ua/index.php/journal/article/view/487 |
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