MODELING OF SYSTEMS WITH THE PHOTOVOLTAIC POWER SOURCE AND WATER PUMPS
The article is devoted to the calculation of systems consisting of a solar photovoltaic power source and water pumps. It is noted that such systems can be used both in households or industry, and in agriculture, in particular for irrigation. Several variants of water pumps are shown. An analysis of...
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"author": "D. Bondarenko ",
"institution": "Institute of Renewable Energy of NAS of Ukraine, Kyiv, Ukraine "
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| description | The article is devoted to the calculation of systems consisting of a solar photovoltaic power source and water pumps. It is noted that such systems can be used both in households or industry, and in agriculture, in particular for irrigation. Several variants of water pumps are shown. An analysis of the operational modes where the photovoltaic power source is connected to the pump has been carried out. The selection of equipment was carried out and the expediency of using a system with an electric energy booster was indicated. A booster for providing current during start-up modes can be a capacitor, a battery of capacitors or an ionistor. Emphasis is placed on the fact that for doing of such systems it is necessary to apply modeling with the use of electrical models. It is shown that for developing of electric models of solenoid-based pumps and pumps based on rotating direct current motors, it is necessary to use the methods of electromechanical analogies. Electrical models of a photovoltaic power source and, based on analogies, a solenoid-based pump and a direct current motor-based pump with permanent magnet excitation and parallel excitation were developed. When developing electrical models, controlled sources of voltage and current were used with mutual influence of the electrical and mechanical parts of the pumps. The need to use direct current motors with parallel excitation is indicated, as they are more stable to emergency modes. It is also stated that in general, the mechanical load of the rotating part of motors is non-linear and depends on the number of revolutions of the shaft. A nonlinear resistance that models a nonlinear mechanical load is shown, and it is noted that the higher-order nonlinearity is insignificant. Conclusions are drawn and further development in the direction of the use of digital technologies is outlined. |
| doi_str_mv | 10.36296/1819-8058.2024.3(78).62-68 |
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62
Відновлювана енергетика. №3/2024 | Сонячна енергетика
UDK 621 https://doi.org/10.36296/1819-8058.2024.3(78)62-68
MODELING OF SYSTEMS WITH THE PHOTOVOLTAIC POWER SOURCE AND WATER PUMPS
Received Aug. 29, 2024; accepted Sep. 16, 2024
Available online Oct. 01, 2024
Bondarenko D.
Author for correspondence: Bondarenko Dmytro,
e-mail: dima7007bond@gmail.com
The article is devoted to the calculation of systems consisting of
a solar photovoltaic power source and water pumps. It is noted that such systems can be used both in house-
holds or industry, and in agriculture, in particular for irrigation. Several variants of water pumps are shown.
An analysis of the operational modes where the photovoltaic power source is connected to the pump has
been carried out. The selection of equipment was carried out and the expediency of using a system with an
electric energy booster was indicated. A booster for providing current during start-up modes can be a capac-
itor, a battery of capacitors or an ionistor. Emphasis is placed on the fact that for doing of such systems it is
necessary to apply modeling with the use of electrical models. It is shown that for developing of electric
models of solenoid-based pumps and pumps based on rotating direct current motors, it is necessary to use
the methods of electromechanical analogies. Electrical models of a photovoltaic power source and, based on
analogies, a solenoid-based pump and a direct current motor-based pump with permanent magnet excitation
and parallel excitation were developed. When developing electrical models, controlled sources of voltage and
current were used with mutual influence of the electrical and mechanical parts of the pumps. The need to use
direct current motors with parallel excitation is indicated, as they are more stable to emergency modes. It is
also stated that in general, the mechanical load of the rotating part of motors is non-linear and depends on
the number of revolutions of the shaft. A nonlinear resistance that models a nonlinear mechanical load is
shown, and it is noted that the higher-order nonlinearity is insignificant. Conclusions are drawn and further
development in the direction of the use of digital technologies is outlined.
Keywords: photovoltaic power source, water pump, photovoltaic pump, electrical model, electromechanical anal-
ogy, solenoid, direct current motor.
МОДЕЛЮВАННЯ СИСТЕМ З ФОТОЕЛЕКТРИЧНИМ ДЖЕРЕЛОМ ЕНЕРГІЇ
ТА ВОДЯНИМИ НАСОСАМИ
Отримано 29 сер. 2024 р.; рекомендовано до публікації 16 вер. 2024 р.
Доступно онлайн 01 жов. 2024 р.
Бондаренко Д. В.
Автор для кореспонденції: Бондаренко Дмитро,
e-mail: dima7007bond@gmail.com
Стаття присвячена розрахунку систем, які складаються з
сонячного фотоелектричного джерела живлення та водяних насосів. Зазначено, що такі системи мо-
жуть використовуватись, як в побуті чи промисловості, так і сільському господарстві, зокрема для
здійснення зрошення. Показано декілька варіантів водяних насосів. Проведено аналіз режимів роботи
під час підключення фотоелектричного джерела живлення до насоса. Здійснено підбір обладнання та
вказано на доцільність використання системи з бустером електричної енергії. Бустером для забезпе-
чення струмом під час пускових режимів може бути конденсатор, батарея конденсаторів чи іоністор.
Акцентовано на тому, що для побудови таких систем необхідно застосувати моделювання з викорис-
танням електричних моделей. Показано, що для побудови електричних моделей насосів на основі соле-
ноїда та насосів на основі обертових двигунів постійного струму потрібно використовувати методи
електромеханічних аналогій. Було побудовано електричні моделі фотоелектричного джерела жив-
лення і, з використанням аналогій, насоса на основі соленоїда й насоса на основі двигуна постійного
струму зі збудженням на постійних магнітах та з паралельним збудженням. При побудові електричних
моделей використовувались керовані джерела напруги та струму з взаємним впливом електричної та
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
63
Відновлювана енергетика. №3/2024 | Сонячна енергетика
механічної частин насосів. Наголошено на необхідності використання саме двигунів постійного струму
з паралельним збудженням, оскільки вони стійкіші до аварійних режимів. Також зазначено, що в загаль-
ному випадку механічне навантаження обертової частини двигунів є нелінійним і залежить від кілько-
сті обертів валу. Показано нелінійний опір, який моделює нелінійне механічне навантаження та заува-
жено, що нелінійність високих порядків є несуттєвою. Зроблено висновки та окреслено подальший
розвиток в напрямі застосування цифрових технологій.
Ключові слова: фотоелектричне джерело енергії, водяний насос, фотоелектричний насос, електрична
модель, електромеханічна аналогія, соленоїд, двигун постійного струму.
Introduction
The development of renewable energy sources, especially
solar energy, prompts us to search for technical solutions
where such sources would be most appropriate [1]. It would
be convenient to use solar energy when it is available be-
cause solar generation is highly variable and depends on the
meteorological conditions of the environment, geographical
location and time of day. One of such applications is power-
ing a water pump from solar energy generators. This is espe-
cially appropriate in the sector of agriculture and landscap-
ing, where irrigation and pumping of water for agricultural
purposes is required, as well as in autonomous water supply
systems, especially with the use of thermal collectors [2].
There are quite a few implementations for such use [3,4],
but from the point of view of efficiency, convenience and
versatility, the most appropriate is the use of pumps with
electric motors, which are connected to solar photovoltaic
energy sources directly [5]. Also note that to simplify the
system, it is advisable to use direct current (DC) motors
with a rated operating voltage that corresponds to the
rated operating voltage of the vast majority of solar photo-
voltaic sources. This approach will avoid the use of addi-
tional converting equipment, which will lead to the compli-
cation and increase in the cost of the system.
In order to choose the proper equipment, we face a num-
ber of challenges, such as technological, economic, social,
etc. [6]. Therefore, it is very important to choose the cor-
rect equipment and carry out its modeling and simulation.
To conduct research on energy and mechanical processes
involving energy sources and electric motors, it is advisable
to use a way that performs modeling of energy processes
of various nature and combines them. One of these devices
can be a research method based on the creation of electri-
cal models and equivalent electrical circuits [7]. This ap-
proach is convenient to use both for modeling electrical
processes and electronic circuits, as well as mechanical sys-
tems and processes. That is, the main task is to build a sys-
tem from a photovoltaic energy source and a water pump
and create an electrical model.
Materials and methods
Two main types of water pumps are used to pumping wa-
ter: centrifugal and positive displacement. In centrifugal
pumps, rotation of an impeller sucks water in through the
middle of the pump and gives out water at the edge [8]. In
positive displacement pumps, parts of water are transfer-
red by a primary mover, like a piston or a screw-type device
[9]. In centrifugal pumps, rotary engines are primarily used,
and in positive displacement pumps, both rotary engines
and solenoid-based mechanisms can be used.
Source of electrical energy is a PV-panel or PV-array. Pho-
tovoltaic power sources could be connected to motors of
pumps by different ways [10].
Direct connection of a photovoltaic (PV) panel or PV-array
to the pump is possible only if the pump has a DC-motor
[11]. The operating point results from the intersection of
the pump volt-ampere (VI) curve with the PV-source VI-
curve. If the curve of pump is too high (array current is un-
dersized), the pumping threshold will be high, that is penal-
izing during low irradiances (low season, cloudy days and
morning/evening). If it is too low, the full potential power
of the array is not used during bright hours. The optimal
sizing therefore depends either on the irradiance distribu-
tion (i. e. location, orientation, meteorological data), and
on the periods when the water needs are more important.
Another way of the direct connection is through configura-
tion of PV-array [12]. Getting necessary parameters of volt-
age and current may be improved by performing a PV-array
reconfiguration by reconnecting of PV-panels [13]. If we
use two identical groups of PV-panels, at low irradiance all
groups are connected in parallel, providing the high cur-
rents necessary to start the pump. From a given irradiance
level, the groups are connected in series, increasing the
voltage and decreasing the current of the PV array. This
configuration requires electric or electronic switches [14].
However, the better method is a direct connection of the
PV-panel to a booster and to motor of the pump. Thus, the
direct coupling configuration is improved, especially, that
of DC displacement pumps. Most displacement pumps re-
quire significant current when DC-motor starts. The current
of PV-panel or array may not be able to provide the peak,
increasing the irradiance threshold. Help is usually provided
by a booster device, which stores the PV energy in a big ca-
pacitor and gives it back as a peak current. Also, one could
use a supercapacitor (ionistor) or electric battery with sig-
nificant peak of the output current [15].
The high-tech method supposes using of converters and
controllers, for example maximum power point tracker.
This electronic device connects PV-panels to a load with
fixed voltage and current for maximum output power, and
behaves as a current generator for supplying the DC motor
of the pump. At the input side, the voltage may be chosen
close to the maximum power point. At the output side, the
power is supposed to be transmitted to the motor at the
64
Відновлювана енергетика. №3/2024 | Сонячна енергетика
optimal current/voltage point corresponding to the availa-
ble power and the motor needs.
The opposite option is to use alternate current (AC)
pumps. It includes a DC/AC inverter with harmonic output
of supplying power and some requirements to voltage and
frequency that must be met for proper operation of the
pump.
Having analyzed connection options as per the list
above, we can come to the conclusion that the optimal
way, at the initial level, to structure a system with a PV-
source and a pump - from an economic and operational
point of view - is to use a direct connection with a boos-
ter (Fig. 1).
The method of using electromechanical analogies [16, 17]
(Table 1) was applied to build the electric model of the en-
gine [18, 19]. The main and basic concepts when building
analogies are basic definitions, such as effort and flow.
Fig. 1. PV-panel with a booster connected to a pump
(where M is DC-motor)
Table.1. Mechanical–electrical analogies
Effort e Flow f
Mechanical translation variable Force F, N Velocity V, m/s
Mechanical rotates variable Torque М, Nm Angular velocity w, rad/s
Electrical variable Voltage U, V Current I, А
It can be seen from Table 1 that the following dependence
is formed for motors with translational motion:
𝐹 → 𝑈 , (1)
𝑉 → 𝐼 . (2)
It can be seen from Table 1 that the following dependence
is formed for motors with rotating motion:
𝑀 → 𝑈, (3)
𝜔 → 𝐼. (4)
Results
A modeling mechanism using electrical models was used
for the calculation.
Considering the electrical model of an energy source with a
booster, we have a circuit that comprises an ideal ISUN cur-
rent source, a diode D (which can be represented by a non-
linear resistor), a shunt resistor RP and a series resistor RS,
as well as a capacitor C, which is a booster (Fig. 2).
Fig. 2. PV power source with a booster
Electrical equations of a photovoltaic source with a con-
nected booster:
𝐼𝑆𝑈𝑁 = 𝐼𝑑 + 𝐼𝑅𝑝 + 𝐼𝑅𝑠 , (5)
𝐼𝑃𝑉 = 𝐼𝑅𝑠 + 𝐼𝐶 , (6)
𝑈𝑆𝑈𝑁 = 𝑈𝑅𝑠 + 𝑈𝑃𝑉 , (7)
where ISUN – current of a photon-charge conversion; Id –
current of a reverse diode; IRp – current of a shunt resistor;
IRs – current of a series resistor; IPV – current of a PV-source;
IC – current of a booster; USUN – voltage of a pn-junction;
URs – voltage of a series resistor; UPV – voltage of a PV-
source
𝐼𝐶 = 𝐶
𝑑𝑈𝑃𝑉
𝑑𝑡
, (8)
𝐼𝑅𝑠 =
𝑈𝑅𝑠
𝑅𝑆
, (9)
where C – capacity of booster.
𝐼𝑆𝑈𝑁 = 𝛼𝐺𝐴𝑐𝑒𝑙𝑙𝑠, (10)
where G – solar global irradiance at the level of solar cells;
α – the effective transmittance–absorptance product of the
cell; Acelsl – the surface area of cells.
65
Відновлювана енергетика. №3/2024 | Сонячна енергетика
The reverse current is given by the standard diode theory [20]:
𝐼𝑑 = 𝐼0 (𝑒
𝑒𝑈
𝑘𝑇 − 1)
where I0 – saturation current [21]; U – voltage of a diode;
e – charge of electron; k – Boltzmann’s constant; T – cell
temperature.
Series resistance Rs and shunt current Rp of PV cells can be
determined by different ways from materials and analysis
of V-I-curves [22].
Electrical equations of pumps with solenoid [23]:
𝑈𝐼𝑁 = 𝐼𝑆𝑙𝑅𝑠𝑙 + 𝐿𝑠𝑙
𝑑𝐼𝑆𝑙
𝑑𝑡
+ 𝑈𝑆𝐿𝑁 , (11)
𝑈𝑆𝐿𝑁 = 𝐼𝑆𝑙
𝑑𝐿𝑠𝑙𝑛(𝑥)
𝑑𝑥
𝑑𝑥
𝑑𝑡
, (12)
where UIN – input voltage of a pump; ISl – current of a sole-
noid; USLN – voltage of a nonlinear part of solenoid; Rsl – re-
sistance of solenoid; Lsl – linear inductance of a solenoid;
Lsln(x) – nonlinear inductance of a solenoid.
Equation of motion of pumps with solenoid [24]:
𝑚
𝑑2𝑥
𝑑𝑡2
+ 𝑏
𝑑𝑥
𝑑𝑡
+ 𝑘𝑥 + 𝐹 = 0 . (13)
where x – displacement of piston of a solenoid; m – mass
of piston of a solenoid; b – dissipation coefficient; k – elas-
ticity coefficient; F – input force.
𝐿𝑃𝐷𝑃
𝑑𝐼𝑃𝐷𝑃
𝑑𝑡
+ 𝐼𝑃𝐷𝑃𝑅𝑃𝐷𝑃 +
1
𝐶𝑃𝐷𝑃
∫ 𝐼𝑃𝐷𝑃𝑑𝑡 + 𝑈𝑃𝐷𝑃(𝑈𝑆𝐿𝑁) = 0.
(14)
where IPDP – modeling current of a positive displacement
pump; UPDP – modeling voltage of a positive displacement
pump; LPDP – modeling inductance of a positive displace-
ment pump; RDPD – modeling resistance of a positive dis-
placement pump, CPDP – modeling capacity of a positive dis-
placement pump.
Proceeding from the equivalent circuit of solenoid and
equations (11), (12), (14) an electric model of a solenoid-
based pump is presented (Fig. 3).
Fig. 3. Electric model of a solenoid-based pump
From equation (12) and the electrical model (Fig. 3), we can
see that there is a dependence of the nonlinear inductance
on the IPDP current, which models the speed of movement
of the core in the solenoid:
𝐿𝑠𝑙𝑛 = 𝛼(𝑥)𝐼𝑃𝐷𝑃 , (15)
where a(x) – nonlinear factor.
The electrical model from Fig. 3 contains a controlled
power source UPDP [25], in which the voltage depends on
the USLN voltage:
𝑈𝑃𝐷𝑃 = 𝛽𝑈𝑆𝐿𝑁 , (16)
where b – factor of transformation.
DC motor equation [26]:
𝑈𝑖𝑛 = 𝜇𝜑𝜔 + 𝐼𝑟𝑜𝑡𝑅𝑟𝑜𝑡 + 𝐿𝑟𝑜𝑡
𝑑𝐼𝑟𝑜𝑡
𝑑𝑡
, (17)
𝐽
𝑑𝜔
𝑑𝑡
= 𝜇𝜑𝐼𝑟𝑜𝑡 −𝑀 , (18)
where Uin – input voltage of a pump; m – proportionality
coefficient; φ – magnetic flux in the gap; ω – angular veloc-
ity; Irot – current of rotor; Rrot – resistance of rotor; Lrot – in-
ductance of rotor; J – moment of inertia; M – torque.
According to expressions (3)-(4), (17)-(18) we have the fol-
lowing equations for the electrical model of pumps and a
rotating DC motor:
𝑈𝑃𝑉 = 𝑈1 + 𝐼𝑟𝑜𝑡𝑅𝑟𝑜𝑡 + 𝐿𝑟𝑜𝑡
𝑑𝐼𝑟𝑜𝑡
𝑑𝑡
, (19)
𝐿𝑀
𝑑𝐼𝑀
𝑑𝑡
= 𝑈2 − 𝑈𝑀. (20)
where U1 and U2 – mutually controlled voltage sources that
simulate the joining of armature (rotor) current and angu-
lar velocity; UM м voltage that simulates the torque; IM –
current that simulates the angular velocity; LM – inductor
that simulates the moment of inertia.
Fig. 4 presents an electrical model based on equations (19),
(20). RM is modeling resistance of mechanical loads and
equals voltage that simulates the torque divided by current
that simulates the angular velocity.
This electrical model (Fig. 4) contains controlled power
sources U1 and U2, in which the voltage depends on the cur-
rents IM and Irot:
𝑈1 = 𝛾1𝐼𝑀 , (21)
𝑈2 = 𝛾2𝐼𝑟𝑜𝑡 , (22)
where 1, 2 – conversion factors.
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Відновлювана енергетика. №3/2024 | Сонячна енергетика
Fig. 4. Electric model of a pump with DC motor
The electrical model of the DC motor in Fig. 4 does not take
into account the presence of excitation windings, which can
be dependent and independent. In motors, where the mag-
netic field of the stator is created by inductors, they must
be taken into account in the circuit and in the calculation.
Having considered the various configurations of such
motors, it should be noted that when the excitation wind-
ing is connected in parallel to the armature winding, the di-
rect current motor provides the maximum stable number
of revolutions [27], which we need for stable and controlled
pumping of water. In this case, the electrical model looks as
shown in Fig. 5.
Fig. 5. Electric model of DC-motor pump with parallel excitation
The electrical model from Fig. 4 contains controlled power
sources U1 and U2, in which the voltage depends on the cur-
rents IM and Iarm:
𝑈1 = 𝛾3𝐼𝑀 , (23)
𝑈2 = 𝛾4𝐼𝑎𝑟𝑚 , (24)
where 3, 4 – conversion factors.
It should be noted that when the excitation winding and the
armature winding are connected in series, in the absence
of a load or a small load, an emergency mode may occur in
which the revolutions will begin to increase uncontrollably.
This mode is not permissible in our case. Motors with mixed
(parallel and series) excitation [28], which is an intermedi-
ate option between parallel and series excitation, do not
have the mentioned disadvantages.
Another aspect of water pump operation is that, in general,
the mechanical load is non-linear [29]. Accordingly, the
value of the mechanical torque M and the value of the re-
sistance that models the mechanical torque, RM, are also
non-linear.
In this case, we present the mechanical torque in the form
of a polynomial:
𝑀 = 𝑎 + 𝑏𝜔 + 𝑐𝜔𝑛, (25)
where a is the static torque of the rotating parts; b reflects
the proportional component of the load torque; c and n de-
pend on the nonlinear properties of the mechanical load. The
properties of mechanical loads are such that the main part of
the mechanical torque consists of the first two terms, that is,
the coefficient c can be considered a small parameter.
According to (25), the resistance simulating the mechanical
load looks as follows:
𝑅𝑀 = 𝐴 + 𝐵(𝐼𝑀) + 𝐶(𝐼𝑀
𝑛 ), (26)
where A is a linear resistance that simulates the mechanical
load of rotating parts; B is a non-linear resistance that de-
pends on the current IM and simulates a mechanical load
that is proportional to the revolutions; C is a resistance that
depends on higher harmonics and is, as noted above, insig-
nificant.
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Відновлювана енергетика. №3/2024 | Сонячна енергетика
It should be noted that the inclusion in the calculation and
modeling of the nonlinear component of the mechanical
moment is the process that doesn’t depend on the motor
type (with dependent or independent excitation winding)
process. Thus, we can simulate the entire range of DC mo-
tors for different load modes.
Conclusion
As a result, we have produced electric models of various
types of pumps that are connected to solar photovoltaic
power sources. The obtained models make it possible to
conduct simulations both with the help of specialized soft-
ware for simulation of electrical circuits [30] and with the
help of software for general modeling [31, 32].
Modeling is a productive means of calculating renewable
energy systems, especially using electrical models. Analysis
and calculation of circuits containing electromechanical
converters should be carried out using analogies that rep-
resent mechanical values via electrical values.
Conducting modeling and simulation before building real
water supply systems in agriculture and in everyday life
based on solar power sources is an expedient and rational
step. Further development in this research area would be
via the application of digital technologies, namely the use
of brushless DC motors controlled by a microcontroller.
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|
| id | veorgua-article-471 |
| institution | Vidnovluvana energetika |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-07-19T01:13:54Z |
| publishDate | 2024 |
| publisher | Institute of Renewable Energy National Academy of Sciences of Ukraine |
| record_format | ojs |
| resource_txt_mv | veorgua/fb/9517298b1da280f6737302108c2052fb.pdf |
| spelling | veorgua-article-4712026-07-18T06:32:20Z MODELING OF SYSTEMS WITH THE PHOTOVOLTAIC POWER SOURCE AND WATER PUMPS МОДЕЛЮВАННЯ СИСТЕМ З ФОТОЕЛЕКТРИЧНИМ ДЖЕРЕЛОМ ЕНЕРГІЇ ТА ВОДЯНИМИ НАСОСАМИ Bondarenko , D. photovoltaic power source, water pump, photovoltaic pump, electrical model, electromechanical analogy, solenoid, direct current motor. фотоелектричне джерело енергії, водяний насос, фотоелектричний насос, електрична модель, електромеханічна аналогія, соленоїд, двигун постійного струму. The article is devoted to the calculation of systems consisting of a solar photovoltaic power source and water pumps. It is noted that such systems can be used both in households or industry, and in agriculture, in particular for irrigation. Several variants of water pumps are shown. An analysis of the operational modes where the photovoltaic power source is connected to the pump has been carried out. The selection of equipment was carried out and the expediency of using a system with an electric energy booster was indicated. A booster for providing current during start-up modes can be a capacitor, a battery of capacitors or an ionistor. Emphasis is placed on the fact that for doing of such systems it is necessary to apply modeling with the use of electrical models. It is shown that for developing of electric models of solenoid-based pumps and pumps based on rotating direct current motors, it is necessary to use the methods of electromechanical analogies. Electrical models of a photovoltaic power source and, based on analogies, a solenoid-based pump and a direct current motor-based pump with permanent magnet excitation and parallel excitation were developed. When developing electrical models, controlled sources of voltage and current were used with mutual influence of the electrical and mechanical parts of the pumps. The need to use direct current motors with parallel excitation is indicated, as they are more stable to emergency modes. It is also stated that in general, the mechanical load of the rotating part of motors is non-linear and depends on the number of revolutions of the shaft. A nonlinear resistance that models a nonlinear mechanical load is shown, and it is noted that the higher-order nonlinearity is insignificant. Conclusions are drawn and further development in the direction of the use of digital technologies is outlined. Стаття присвячена розрахунку систем, які складаються з сонячного фотоелектричного джерела живлення та водяних насосів. Зазначено, що такі системи можуть використовуватись, як в побуті чи промисловості, так і сільському господарстві, зокрема для здійснення зрошення. Показано декілька варіантів водяних насосів. Проведено аналіз режимів роботи під час підключення фотоелектричного джерела живлення до насоса. Здійснено підбір обладнання та вказано на доцільність використання системи з бустером електричної енергії. Бустером для забезпечення струмом під час пускових режимів може бути конденсатор, батарея конденсаторів чи іоністор. Акцентовано на тому, що для побудови таких систем необхідно застосувати моделювання з використанням електричних моделей. Показано, що для побудови електричних моделей насосів на основі соленоїда та насосів на основі обертових двигунів постійного струму потрібно використовувати методи електромеханічних аналогій. Було побудовано електричні моделі фотоелектричного джерела живлення і, з використанням аналогій, насоса на основі соленоїда й насоса на основі двигуна постійного струму зі збудженням на постійних магнітах та з паралельним збудженням. При побудові електричних моделей використовувались керовані джерела напруги та струму з взаємним впливом електричної та механічної частин насосів. Наголошено на необхідності використання саме двигунів постійного струму з паралельним збудженням, оскільки вони стійкіші до аварійних режимів. Також зазначено, що в загальному випадку механічне навантаження обертової частини двигунів є нелінійним і залежить від кількості обертів валу. Показано нелінійний опір, який моделює нелінійне механічне навантаження та зауважено, що нелінійність високих порядків є несуттєвою. Зроблено висновки та окреслено подальший розвиток в напрямі застосування цифрових технологій. Institute of Renewable Energy National Academy of Sciences of Ukraine 2024-09-29 Article Article application/pdf https://ve.org.ua/index.php/journal/article/view/471 10.36296/1819-8058.2024.3(78).62-68 Vidnovluvana energetika ; No. 3(78) (2024): Scientific and applied Journal renewable energy ; 62-68 Возобновляемая энергетика; ##issue.no## 3(78) (2024): Scientific and applied Journal renewable energy ; 62-68 Відновлювана енергетика; № 3(78) (2024): Науково-прикладний журнал Відновлювана енергетика; 62-68 2664-8172 1819-8058 10.36296/1819-8058.2024.3(78) uk https://ve.org.ua/index.php/journal/article/view/471/380 Copyright (c) 2024 D. Bondarenko https://creativecommons.org/licenses/by-nc-nd/4.0 |
| spellingShingle | photovoltaic power source water pump photovoltaic pump electrical model electromechanical analogy solenoid direct current motor. Bondarenko , D. MODELING OF SYSTEMS WITH THE PHOTOVOLTAIC POWER SOURCE AND WATER PUMPS |
| title | MODELING OF SYSTEMS WITH THE PHOTOVOLTAIC POWER SOURCE AND WATER PUMPS |
| title_alt | МОДЕЛЮВАННЯ СИСТЕМ З ФОТОЕЛЕКТРИЧНИМ ДЖЕРЕЛОМ ЕНЕРГІЇ ТА ВОДЯНИМИ НАСОСАМИ |
| title_full | MODELING OF SYSTEMS WITH THE PHOTOVOLTAIC POWER SOURCE AND WATER PUMPS |
| title_fullStr | MODELING OF SYSTEMS WITH THE PHOTOVOLTAIC POWER SOURCE AND WATER PUMPS |
| title_full_unstemmed | MODELING OF SYSTEMS WITH THE PHOTOVOLTAIC POWER SOURCE AND WATER PUMPS |
| title_short | MODELING OF SYSTEMS WITH THE PHOTOVOLTAIC POWER SOURCE AND WATER PUMPS |
| title_sort | modeling of systems with the photovoltaic power source and water pumps |
| topic | photovoltaic power source water pump photovoltaic pump electrical model electromechanical analogy solenoid direct current motor. |
| topic_facet | photovoltaic power source water pump photovoltaic pump electrical model electromechanical analogy solenoid direct current motor. фотоелектричне джерело енергії водяний насос фотоелектричний насос електрична модель електромеханічна аналогія соленоїд двигун постійного струму. |
| url | https://ve.org.ua/index.php/journal/article/view/471 |
| work_keys_str_mv | AT bondarenkod modelingofsystemswiththephotovoltaicpowersourceandwaterpumps AT bondarenkod modelûvannâsistemzfotoelektričnimdžerelomenergíítavodâniminasosami |