Simulation of voltage control processes in low-voltage microgrid nodes with renewable energy sources and energy storage system
Introduction. The development of low-voltage microgrids (LV MG) with renewable energy sources requires effective control of their operating parameters, in particular voltage. The problem of voltage control in MG is exacerbated by the practical use of remote control systems for grid-forming inverters...
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National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine
2026
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Electrical Engineering & Electromechanics| _version_ | 1869562804914094080 |
|---|---|
| author | Trach, I. Belik, M. Rubanenko, O. Miroshnyk, V. Blinov, I. |
| author_facet | Trach, I. Belik, M. Rubanenko, O. Miroshnyk, V. Blinov, I. |
| author_institution_txt_mv | [
{
"author": "I. Trach",
"institution": "Institute of Electrodynamics of NAS of Ukraine"
},
{
"author": "M. Belik",
"institution": "University of West Bohemia"
},
{
"author": "O. Rubanenko",
"institution": "University of West Bohemia"
},
{
"author": "V. Miroshnyk",
"institution": "Institute of Electrodynamics of NAS of Ukraine"
},
{
"author": "I. Blinov",
"institution": "Institute of Electrodynamics of NAS of Ukraine"
}
] |
| author_sort | Trach, I. |
| baseUrl_str | http://eie.khpi.edu.ua/oai |
| collection | OJS |
| datestamp_date | 2026-07-01T21:42:56Z |
| description | Introduction. The development of low-voltage microgrids (LV MG) with renewable energy sources requires effective control of their operating parameters, in particular voltage. The problem of voltage control in MG is exacerbated by the practical use of remote control systems for grid-forming inverters (GFIs) under conditions of limited data transmission speed. Goal. Identification of the features of local voltage control in LV MG nodes connected to distribution systems using reactive power of GFIs, in particular to assess the dependence of the droop-control coefficient on network parameters and to determine quasi-stationary time intervals. Methodology. The study was carried out using a newly developed imitation model in the PowerDynamics.jl environment for analyzing the dynamics of LV MGs, which are characterized by predominantly active feeder resistance and take into account the specific operating features of GFIs. Results. It has been established that the operating modes of LV MG connected to the distribution system can be considered quasi-stationary over intervals longer than 60 s, which allows the use of static control characteristics without taking into account fast transient processes. The operation of the model was analyzed under conditions of reactive power reduction at the MG input using a PI controller and maintaining a specified value of GFI reactive power. Scientific novelty. A new computational model has been developed which, unlike existing ones, enables comparison of different methods of reactive power distributing among a group of distributed energy sources and investigation of the features of voltage regulation using GFIs. Practical value. Using the developed model, an analysis was performed and the dependence of the voltage droop-control coefficient on the GFI reactive power was determined. Quasi-stationary intervals for power and voltage in LV MGs were established. The developed model confirms the effectiveness of voltage control through GFI reactive power in different MG operating modes. Practical recommendations for setting GFI parameters and information transfer speed in LV MG control systems were formed. References 56, tables 2, figures 7. |
| doi_str_mv | 10.20998/2074-272X.2026.4.11 |
| first_indexed | 2026-07-02T01:00:29Z |
| format | Article |
| fulltext |
84 Electrical Engineering & Electromechanics, 2026, no. 4
© I. Trach, M. Belik, O. Rubanenko, V. Miroshnyk, I. Blinov
UDC 621.311 https://doi.org/10.20998/2074-272X.2026.4.11
I. Trach, M. Belik, O. Rubanenko, V. Miroshnyk, I. Blinov
Simulation of voltage control processes in low-voltage microgrid nodes
with renewable energy sources and energy storage system
Introduction. The development of low-voltage microgrids (LV MG) with renewable energy sources requires effective control of their operating
parameters, in particular voltage. The problem of voltage control in MG is exacerbated by the practical use of remote control systems for grid-
forming inverters (GFIs) under conditions of limited data transmission speed. Goal. Identification of the features of local voltage control in LV
MG nodes connected to distribution systems using reactive power of GFIs, in particular to assess the dependence of the droop-control
coefficient on network parameters and to determine quasi-stationary time intervals. Methodology. The study was carried out using a newly
developed imitation model in the PowerDynamics.jl environment for analyzing the dynamics of LV MGs, which are characterized by
predominantly active feeder resistance and take into account the specific operating features of GFIs. Results. It has been established that the
operating modes of LV MG connected to the distribution system can be considered quasi-stationary over intervals longer than 60 s, which
allows the use of static control characteristics without taking into account fast transient processes. The operation of the model was analyzed
under conditions of reactive power reduction at the MG input using a PI controller and maintaining a specified value of GFI reactive power.
Scientific novelty. A new computational model has been developed which, unlike existing ones, enables comparison of different methods of
reactive power distributing among a group of distributed energy sources and investigation of the features of voltage regulation using GFIs.
Practical value. Using the developed model, an analysis was performed and the dependence of the voltage droop-control coefficient on the
GFI reactive power was determined. Quasi-stationary intervals for power and voltage in LV MGs were established. The developed model
confirms the effectiveness of voltage control through GFI reactive power in different MG operating modes. Practical recommendations for
setting GFI parameters and information transfer speed in LV MG control systems were formed. References 56, tables 2, figures 7.
Key words: microgrid, quasi-stationary state intervals, grid-forming inverter, PV-generation, reactive power.
Вступ. Розвиток мікромереж низької напруги (ММ НН) з відновлювальними джерелами енергії потребує забезпечення
ефективного регулювання параметрів їх режимів, зокрема напруги. Проблема регулювання напруги в ММ НН підсилюється
використанням на практиці систем віддаленого управління інверторами, що формують мережу (GFI), в умовах обмеженої
швидкості передавання даних. Мета. Визначення особливостей локального регулювання напруги у вузлах ММ НН, приєднаних до
систем розподілу, з використанням реактивної потужності GFI, зокрема оцінювання залежності коефіцієнта droop-control від
параметрів мережі та визначення часових інтервалів квазі-стаціонарності. Методологія. Дослідження виконано з
використанням нової розробленої розрахункової моделі у середовищі PowerDynamics.jl для аналізу динаміки ММ НН, яка має
переважно активний характер опору фідерів та враховує специфіку роботи GFI. Результати. Встановлено, що режими ММ
НН, приєднаних до системи розподілу, на інтервалах понад 60 с можна вважати квазі-стаціонарними, що дозволяє
застосовувати статичні характеристики регулювання без урахування швидких перехідних процесів. Проаналізовано роботу
моделі в режимах зниження реактивної потужності на вході мікромережі за допомогою PI-контролера та підтримки заданого
значення реактивної потужності GFI. Наукова новизна. Розроблено нову розрахункову модель, використання якої, на відміну від
існуючих, дозволяє виконати порівняння різних методів розподілу реактивної потужності між групою розосереджених джерел
енергії та дослідити особливості локального регулювання напруги з використанням GFI. Практична значимість. З
використанням розробленої моделі виконано аналіз та визначено залежності коефіцієнта droop-control по напрузі від значення
реактивної потужності GFI та встановлені інтервали квазі-стаціонарності для потужності та напруги в ММ НН. З
використанням розробленої моделі підтверджена ефективність локального регулювання напруги з використанням реактивної
потужності GFI в різних режимах роботи мікромережі. Сформовано практичні рекомендації до налаштування параметрів GFI
та швидкості передачі інформації в системах управління ММ НН. Бібл. 56, табл. 2, рис. 7.
Ключові слова: мікромережа, інтервали квазістаціонарності, мережеутворюючий інвертор, сонячна генерація,
реактивна потужність.
Introduction. The development of electrical power
grids and systems is currently driven by the integration of
renewable energy sources (RES) and the formulation of
control models [1] aligned with the Smart Grid concept
[2]. One of the current research focuses in this field is the
control of microgrid (MG) operating modes. MG connects
a group of loads and distributed generation in a single
controlled local object capable of operating both in the
mode of connection to the electric power distribution
system and in the isolated (island) mode [3, 4]. The
terminology used in the paper is presented in [5]. The
group of international IEC TS 62898 standards [6–9]
defines the main options for building MGs and the
features of their functioning.
Often, the MG includes electricity storage facilities
[10] to accumulate its surplus for further use to balance
demand within the MG and provide backup power during
power outages. Electricity storage facilities affect the
voltage regime in the networks [11]. In addition, the
operation of electricity storage facilities as part of the MG
allows optimizing the costs of purchasing electricity [12].
There are also possibilities for interaction between several
inverters to exchange energy resources [13]. The
possibilities of providing services for regulating the
distribution system modes by both a separate MG and a
group of MGs [14] are expanding. The task of improving
voltage levels and reducing losses in the network with RES
is solved using various partitioning methods, in particular,
shifting the current point of the flow to the partitioning site
using available network power plants operating on RES
[15]. Analysis of reactive power optimization in high-
voltage power systems with the participation of transition
system operators is presented in [16], while distribution
system operators are considered in [17].
The main features of low-voltage (LV) MGs,
according to definitions [7], include: short lengths and
low resistance of feeders, small X/R ratios, a significant
impact on the MG modes of RES generating capacities
with unstable generation laws and electricity storage
units, as well as the operation of the MG both
synchronously with the electric grid (EG) and as isolated
from the EG.
Connecting RES to the MG via converters results in
the emergence of modes that are fundamentally different
from the traditional modes of operation of local
distribution systems. In particular, instead of a gradual
voltage droop from the power center to electricity
Electrical Engineering & Electromechanics, 2026, no. 4 85
consumers, nodes with a local voltage increase at the
points of connection of RES are formed in the LV MG.
As a result, power flows arise in different directions in
different periods of time in individual sections of the LV
MG [18]. This significantly complicates the procedures
for planning and controlling the modes of the LV MG
operation. However, the main problem of ensuring the
stability of the LV MG operation, especially in the island
mode, is the absence of inertia of electromechanical
processes in modern RES and inverters, which is inherent
in synchronous generators of power plants and contributes
to providing for the stability of electric power systems.
Today, the direction of local voltage regulation in
MGs using reactive power of RES is actively developing
in the world. At the same time, the problem of voltage
regulation in LV MG is exacerbated by the practical use
of remote control systems (MG controller) of grid-
forming inverters (GFI) in conditions of limited data
transfer rate. This justifies the need to create simulation
models to determine the intervals of quasi-stationarity of
low-voltage MG modes, which allows developing on their
basis effective algorithms for reactive power regulation in
LV MG of various composition, determining restrictions
on the choice of the number of mode parameters taking
into account their transfer rate.
One of the promising directions for solving this
problem is to build a digital model that simulates the
electromechanical processes of synchronous generators
and generates the relative signals for controlling the LV
MG mode. Means of control of the LV MG based on the
models of synchronous generators are called grid-forming
inverters (GFI) and allow to effectively regulate modes
not only of the LV MG in the island mode but also
increase the efficiency of control of modes of distribution
systems. But at the same time there is an additional
problem of creating means of simulating the GFI
functions, taking into account the features of the electric
grid structure in different modes in order to clarify the
characteristics of such a digital model and build the laws
of regulation for the LV MG control system.
Review of the literature. A description of modern
developments in the field of the GFI simulating and
analysis of the experience of operating such systems is
provided in a number of review publications [19, 20]. For
example, a comprehensive review of scientific and
technical literature, which covers simulating methods,
control methods, protection schemes, applications and
actual implementations of the GFI. A large number of
publications in scientific and technical literature detail
individual components of the problem of building and
using the GFI. The study [12] is devoted to the analysis of
modern developments in the use of the GFI to maintain the
stability and fault tolerance of power systems. Research
shows that GFM control significantly outperforms grid-
following inverter in stabilizing voltage, more robust
support in low-inertia systems. Thus, different control
approaches for grid-forming inverters are discussed and
compared with the grid-forming properties of synchronous
machines [21]. A comparative review of methods for
simulating the operating modes of the MG with RES is
provided in [22]. To solve the problems of simulating the
MG functions and its individual components, software
tools such as Pandapower, Matpower, Simulink and others
are used. To conduct research on the impact of the GFI on
the EG modes, standard EG test schemes with RES [23]
have been developed.
There are various mathematical models for
simulating the functions of a synchronous generator. For
example, in [24], a virtual oscillator model based on the
nonlinear Andronov-Hopf oscillator is studied. In [25], a
model is provided for identifying the dynamic interaction
of voltage and frequency values using the feedback effect.
In [26], a unified sequence impedance model with
harmonic linearization is presented, which characterizes
multi-loop GFIs based on synchronous generator and
virtual generator models.
However, a significant number of researchers prefer
simplified simulation of the behavior of a synchronous
generator without taking into account dynamic transient
processes. Such important practical results of simulating
the MG modes are obtained by simulating the continuous-
time characteristics of the MG by analyzing quasi-
stationary discrete states. For this purpose, the processes
are simulated as a series of snapshots of the stationary
states of the electrical grid without taking into account the
transitional processes between them. For example, in [27],
a method for analyzing processes in the MG without
taking into account dynamic transient processes, which
are microseconds to seconds, is presented. The equivalent
scheme for calculations includes elements exclusively
with linear characteristics. The simplification of
mathematical models for the analysis of quasi-stationary
states is carried out based on the following assumptions: it
is assumed that the voltage and current graphs have a
regular sinusoid, higher harmonics in the voltage and
current graphs are not taken into account, in addition,
electrical transient effects are not considered. The
theoretical foundations of simulating quasi-stationary
states in dynamic systems are covered in detail in [28].
In the study of voltage dynamics in real high and
medium voltage networks, a 3rd order dynamic model of
the power grid was built using DigSILENT PowerFactory
software. The study showed a significant transient time of
15 s [29] in a real HV power grid. At the same time, there
is no publication that would offer a method for analyzing
voltage regulation processes within the day using a droop
control method with local regulation in accordance with
the requirements of the IEC TS 62898-3-1 standard [7]
for the MG. Therefore, this publication considers the
features of using quasi-stationary states in a daily
optimization model of the MG functions with solar panels
and an electricity storage unit according to the
requirements of the IEC TS 62898-3-1 standard. The
research was carried out using the PowerDynamics.jl
tools [30]. Synthetic networks can be used to study the
dynamic regimes of MG [31].
The goal of the paper is to determine the features
of local voltage regulation in LV MG nodes connected to
distribution systems, using the reactive power of GFIs
installed in such LV MGs, using a newly developed
imitation model in a unified package for analyzing the
dynamics of energy systems with a significant share of
RES. Such features within the article include the
assessment of the dependence of the droop-control
coefficient on the voltage on the value of the GFI reactive
power, as well as the determination of quasi-stationarity
intervals for power and voltage in LV MG in accordance
with the requirements of international standards, which
are determining parameters when developing algorithms
for controlling the GFI reactive power in LV MG
connected to the distribution system.
86 Electrical Engineering & Electromechanics, 2026, no. 4
Features of using quasi-stationary states in
simulating the GFI functions. The justification of the
admissibility of using quasi-stationary states in simulating
the GFI functions is given in [32]. For a quasi-stationary
state with an interval [t, t+1] at the beginning of the quasi-
stationary interval in the node, there are voltage V(t),
power S(t). A jump in power of in the node at time t+1
results in a transient process and setting of a new quasi-
stationary state of the grid, new values of voltage in the
node V(t+1) and power S(t+1). Therefore, for voltage
control, quasi-stationary states of the grid are considered
and fast transient processes are not taken into account, as
shown in Fig. 1. Further, the processes of voltage control
in the MG and optimization of mode parameters occur for
a sequence of quasi-stationary states of the MG.
Q, V
t, s
Fig. 1. Quasi-stationary states of the MG
At the same time, for calculations of the EG modes
when forecasting the power of RES, imbalances [33] in
power systems and optimal operation of electricity
storage units, the models of the grids are used, which
operate at 15- and 30-minute intervals that are represented
in the form of quasi-stationary grid states. In particular,
for voltage control with the specified time intervals of
forecasting the power of renewable sources and loads,
sequences of quasi-stationary grid states are used.
Objectives of voltage regulation in the MG by
changing the reactive power in the GFI. In the
problems of simulating the MG with the GFI, two
alternative objectives of the MG voltage control may be
used: minimizing the root mean square value of the
voltages deviation in the MG nodes or maintaining the
rated voltage value in the GFI connection node. Planning
of the MG modes with minimization of the root mean
square value deviation of the square value of the voltage
of all MG nodes [34] or at the GFI setting node [35] is
carried out by solving the problem of multi-criteria
optimization of voltages in the nodes and minimizing the
total value of active losses in the MG [34]. In [37], the
“based on improved marine predator algorithm” is
presented for solving such a multi-criteria optimization
problem. The main advantage of planning the MG modes
by solving the multi-criteria optimization problem is the
complex equalization of voltages in all nodes of the
electrical grid. However, to implement such a MG mode,
it is necessary to monitor voltages in all controlled nodes
with a measurement frequency of 0.1 s, which requires
setting of a monitoring system with appropriate technical
capabilities and significantly increases the cost of the MG
mode control system.
For the analysis of the control of the MGs, useful
data on the configuration of low-voltage networks and
changes in loads over time are presented in [38]. Another
source of data on the consumption of active power,
voltage and current of the low-voltage network for a
group of residential buildings recorded at intervals of 10 s
is presented in [39]. Also, synthetic network models are
useful for modeling voltage regulation in MGs [40]. The
choice of MG operating modes from the point of view of
the criterion of economic efficiency is presented in [41].
Therefore, the implementation of complex monitoring
and voltage control systems requires a technical and
economic justification. Another disadvantage of this approach
is the low reliability of the MG mode control system. In order
to implement the complex optimization systems task,
operational information on voltages in all controlled MG
nodes is required. In case of disappearance of operational
information on voltages in individual MG nodes, the process
of complex control of the MG modes is terminated.
Planning the MG modes with support for the rated
voltage value in the GFI connection node allows avoiding
the need for monitoring voltage in all nodes of the local
electrical grid. This leads to a decrease in the cost of MG
mode monitoring and control systems, as well as
simplifying the control algorithms. Justification of the
compliance of voltage values in uncontrolled nodes with
permissible limits is carried out at the step of designing
the electrical grid scheme. Features of the MG operation
with control of voltage values in the GFI connection node
are studied in [32].
In [42], a method of virtual voltage regulation for an
isolated MG with a predominance of an active component of
the resistance of power transmission lines is presented, taking
into account the quadratic dependence between voltage and
reactive power for MG with predominance of the inductive
component. The proposed method provides for a more
accurate reactive power response. The study [43] proposes to
increase the accuracy of the inverter reactive power
response based on virtual impedance. However, taking into
account the virtual impedance of the MG significantly
complicates the calculation model. One of the methods of
voltage regulation using the fuzzy logic controller of the
MATLAB package is presented in the study [44].
Normalization of the MG operating modes. The
standard [7] defines the term “dynamic control in the
MG” as transient disturbance control and dynamic
disturbance control. Transient disturbance control
suppresses disturbances in the MG caused by forced or
unintentional sudden and strong changes in voltage and
current due to switching of power sources or loads,
configuration switching or troubleshooting. Transient
processes last for milliseconds and are characterized by
significant amplitudes and phase changes.
The MG control system has a hierarchical structure
and is divided into 3 levels. When regulating the voltage,
according to item 6.3.4.2 in [7], the primary control of the
MG is based exclusively on local measurements, local
calculations and local implementation and does not
require a communication component. The standards [8, 9]
describe the technical requirements that MGs and their
operating scenarios must meet.
The main control elements of the MG according to
item 3.3.1 [7] include: multi-level control functions
implemented through a central controller for the overall
stable operation of the system and individual local control
Electrical Engineering & Electromechanics, 2026, no. 4 87
units for the output power of generating units and load
consumption.
For the first level of the MG control system, voltage
droop control is used. Voltage droop control is a process
of linearizing the dependence of voltage and reactive
power to minimize load transient processes, in most cases
using a fixed coefficient:
,)( '
000 VQQKVref (1)
where Vref is reference voltage of the grid; V′0 is targeted
(set) voltage of the grid; Q is the reactive power; Q0 is
preset reactive power; K0 is constant voltage droop.
The secondary level of the MG control system has a
slower dynamic response compared to the primary control
due to the integration function. The voltage amplitude on
the MG main bus is compared with the corresponding
reference values and has the following form:
tVVKVVKV refiVrefpV d)()( , (2)
where δV is a voltage error, KpV is the power regulation
coefficient proportional to voltage; KiV is the integration
coefficient. The third level covers optimization processes,
in particular voltage optimization in the MG nodes,
minimization of the total reactive power of the sources, as
well as minimization of reactive power at the MG input.
The EN 50549-2 standard [45] defines the restraints on
reactive power for voltage regulation in the range
[–0.484PD, 0.484PD], where PD = 0.9 (Fig. 2).
Fig. 2. Reactive power restraints [37]
At the same time, the IEC TS 62898-1 standard states:
since the LV MG transmission lines have short length,
there is no need to optimize the active losses in the MG.
The definition of “dynamic control” in the MG
according to IEC TS 62898-1 is characterized by changes
in amplitude and phase that go beyond the limits of
normal operation and have a duration of up to seconds.
The EN 50549-2 standard, item 4.7.2.3.3 “Voltage-
Related Control Mode” normalizes the integration constant
of the first-order low-pass filter, which can be adjusted for
at least 3 s. This means that when the reactive power jumps
by 1 r.u., voltage output to the level of 0.95 of the new
constant value occurs in 6.91 s. The range of adjustment of
the constant integration of the first-order low-pass filter is
also normalized for more than 3 s. Accordingly, the interval
of voltage output at the level of 0.95 of the constant value
is at least 6.91 s. Thus, depending on the constant
integration of the first-order low-pass filter in the GFI
device, when regulating the voltage using the reactive
power of the GFI, the intervals of individual quasi-
stationary states of the MG should exceed, respectively, the
interval of voltage output at the level of 0.95 of the constant
value from the range of 6.91 s.
Therefore, in this work, the optimization objective is
limited to minimizing voltage deviations in the GFI
connection node by changing the reactive power. In this
case the system of constraints takes into account: the
ranges of generation of active and reactive power of the
GFI, technical maximums of active and reactive power of
the GFI, the maximum capacity and charge/discharge
power of the energy storage unit [46–48].
Description of the LV MG model for experimental
studies. For experimental studies, the PowerDynamics.jl
tools were used. The tools are designed to simulate and
analyze transient processes in electrical grids. In particular, a
mathematical apparatus is provided for simulating a
disturbance of one of the mode parameters [49], for example:
a jump in active or reactive power of one load, a shutdown of
one power transmission line, or other individual deviations
of the initial parameters of the steady mode.
For simulating the GFI functions, the
“MyDroopControl” component from the
PowerDynamics.jl tool package was used. The block
diagram of the GFI model is shown in Fig. 3. A detailed
description of the functions of the “droop-control” block
with a low-pass filter is provided in [50]. In the
calculations, it is assumed that the GFI controls the solar
station and the electric energy storage units connected to it.
Q droop-control (Q, K0) + low-pass filter (TV)
V
Q
Fig. 3. GFI block diagram
Experimental calculations were performed for 0.4 kV
radial electrical grid, which consists of 4 0.4 kV cable
lines and 6 buses (Fig. 4). The phase shift value for the
lines is tg = 0.24, which allows to consider them as lines
with predominantly active resistance.
Fig. 4. LV MG diagram with the GFI
The GFI is connected to bus 4. When simulating the
MG modes, the active and reactive power of the load
connected to bus 6 is controlled. The MG is synchronized
with the distribution system via an 11/0.4 kV 1000 kVA
transformer. The main characteristics of the local grid are
provided in the Table 1.
Table 1
Main characteristics of the MG
Parameters Description Length, km
HV/LV grid, kV 11.0 / 0.4
Transformer
P = 1 MVA, voltage 11/0.4,
Usc = 5.5 %, ∆Psc = 12 kW
ETL 1, 3
R = 0.1649 Ω/km, X = 0.04 Ω/km,
Cpf = 261 pF/km, Imax = 0.394 kA
0.5
ETL 2, 4
R = 0.1649 Ω/km, X = 0.04 Ω/km,
Cpf = 261 pF/km, Imax = 0.394 kA
0.05
Load cosφ = 0.9
The voltage control function is simulated according
to the requirements of [7]. The essence of the control is to
generate inductive or reactive power proportional to the
88 Electrical Engineering & Electromechanics, 2026, no. 4
difference between the voltage on the GFI bus and the
predetermined voltage Vref. The reactive power regulates
the low-pass filter qfilter, which smoothes the oscillations
of the signal and qdroop according to (1). The simulation of
this principle is implemented in the model “Design,
Operation, and Control of Remote Microgrid,”
modelName = ”RemoteMicrogrid” from the MATLAB
package. The GFI parameters for two options for constant
integration of reactive power are presented in Table 2.
Table 2
GFI characteristics for experimental studies
Option 1 Option 2
Rated power GFI, MVA 0.08
Rated reactive power of GFI, MVAr 0.0348
Reference voltage of MG Vref, r.u. 0.985
Low-pass filter, constant reactive power
integration τv, s (time constant reactive power
measurement)
3 12
Droop constant voltage droop coefficient KQ 0.1764
The GFI model has the following restraints: reactive
power according to EN-50549-2, active power of solar
panels and energy storage unit are restrained by their
datasheet parameters. The GFI model is implemented by a
voltage source.
When simulating, it is assumed that the active and
reactive power of the load at node 6, the active power of
the solar panels, and the active power of the energy
storage unit change during the day. The GFI, which
converts the energy of the solar panels and of the storage
unit, releases both active and reactive power to the MG.
When simulating, it is taken into account that
according to the requirements of DSTU EN 50549-2, item
4.7.2.2, Note 4 [45], the GFI should be able to generate
reactive power throughout the day.
The total number of simulation cycles of the MG
modes with an interval of 60 s is 1440 cycles per day. The
coefficient of load power on bus 6 is cos = 0.9. The
maximum load value is 231 kW. The maximum active
power generated by the solar panels is 45 kW. The
nominal GFI power is 80 kVA, the rated GFI reactive
power is 34.5 kVAr. Since it is planned to control the
voltage at quasi-stationary intervals of 60 s, the hourly
graphs are modified by linear interpolation of each time
interval of 60 s and adding noise in the form of uniformly
distributed random numbers in the range [–0.01, 0.01]
from the current power of the loads and the solar panel.
Analysis of the simulation results. In order to
determine the quasi-stationary states of the LV MG with
the GFI, an analysis of the dynamic disturbance in the LV
MG with the predominance of the active component of
the resistance of the transmission lines was carried out.
The time interval in Ts of setting the LV MG to a steady
state after a dynamic disturbance was determined. The
voltage response in the LV MG nodes was analyzed, and
a jump in the reactive power of the load in the remote MG
bus 6 node was used as a disturbance. Figure 5 shows the
dynamic mode of the process of changing the voltage in
the GFI node to a new steady state with a jump in the
reactive power of the load of 10 kVAR in the bus 6 node.
The voltage response on the GFI bus is indicated by dots,
the jump in the reactive power of the load in the bus 6
node is indicated by a solid line. The transfer function Ts
(blue color) is used to estimate the jump. The quantization
time interval is 0.1 s. The constant integration of the
active power is restrained to the range of 3 to 12 s.
V, r.u.
t, s
step
Fig. 5. Voltage response at node 4 during transients
After the jump in the reactive power of the load, the
time interval of setting the voltage to a steady value in the
range [0.95, 1.05] is Ts = 6.2 s. The transfer function is:
439.4174.2278.9
1843.01587.009.24
23
2
sss
ss
T f . (3)
Tf has 3 poles and two zeros and corresponds to the
low-pass filter. The transfer function was estimated by the
tfest function of the MATLAB package [51]. Accuracy of
the estimate: Status: Estimated using Еstimate transfer
function model tfest on time domain data; Fit to estimation
data: 99.34 %, FPE: 1.36110–6, MSE: 1.28210–8. The
accuracy of the transfer function estimate Tf is high. All poles
of Tf are real and negative, therefore the system is stable.
Similar results of the time interval for setting Ts to a
steady state after dynamic disturbances were obtained for
all LV MG nodes, the maximum time for setting to a
steady state Ts ≤ 6.2 s.
It was established that for the pair “node voltage –
GFI reactive power,” taking into account the calculations
and requirements of the standards, quasi-stationary states
may be considered at intervals of 60 s, while the transient
process during voltage regulation by controlling the GFI
reactive power may not be considered.
Simulation of quasi-stationary states of the MG at a
daily time interval was carried out with clock intervals of
60 s. Accordingly, the adopted interval of 60 s may be
used for voltage regulation in the case of a daily forecast
of consumption capacities, renewable sources and storage
units. It should be noted that for research, parameters of
modes of European electrical grids with intervals of 60 s,
as well as 15 and 60 min are available.
Daily graphs of mode characteristics obtained based
on the simulation results are shown in Fig. 6.
Fig. 6. Daily voltage and power graphs at controlled nodes
Electrical Engineering & Electromechanics, 2026, no. 4 89
The GFI power restraints is 72 kW for active power,
34.8 kVA for reactive power in accordance with the rated
GFI power and in accordance with the requirements of the
EN 50549-2 standard. The effect of maintaining voltage at
node 4 is achieved by regulating the reactive component of
the GFI power. Thus, when the voltage at node 4 increases
above the predetermined value, the value of the reactive
component of the GFI power changes towards increasing
inductance. When the voltage at node 4 droops below the
predetermined value, the value of the reactive power
component of the GFI changes towards increasing capacity.
When using the GFI exclusively to maintain voltage at
node 4, the reactive power component at node 1 (the node
of connecting the MG to the distribution system) is not
controlled. Therefore, if a Distribution System Operator
imposes restraints on the values of the reactive power
component at the input to the MG, such restraints should be
additionally taken into account in the mathematical model.
The use of the GFI in the MG allows implementing
additional useful functions, for which the MG modes
were analyzed. Firstly, this is a reduction in reactive
power and cos at the MG input, which refers to the third
level of the MG control system. The objective is achieved
using a PI controller [52] by selecting its parameters
based on expert estimates. As a result of the GFI reactive
power regulation, the reactive power at the distribution
boundary of the LV MG and the MV EG is reduced.
Accordingly, the MG reduces the payment for consumed
or transmitted reactive power and reduces the flow of
reactive power into an external EG. Secondly, based on
the mutual agreement with a Distribution System
Operator, it is possible to form a predetermined inductive
or reactive power, taking into account maintaining the
normalized voltage level in the MG. The results of the
MG operation in different modes are presented in Fig. 7.
It shows the following daily graphs: 1 is normal GFI
operation; 2 is maximum GFI inductive power during the
day; 3 is maximum GFI capacitive power during the day;
4 is the MG operation without the GFI; 5 is minimization
of reactive power at the distribution boundary of the LV
MG and MV ES using a PI-regulator.
Fig. 7. Reactive power at the MG input for different modes of
GFI reactive power control
As a result, the model proposal can provide reactive
power control for one of the modes – constant power
factor cos, reactive power as a function of active power
Q(P), fixed reactive power Qfix.
Thus, the proposed new model allows for a specific LV
MG connected to the distribution system, indirectly through
the estimation of the transfer function coefficients to
determine the quasi-stationarity intervals, as well as to vary
the value of the droop control coefficient in order to optimize
its value. At the same time, the operating parameters of the
LV MG meet the requirements of the standards for LV MG.
For specific LV MGs, the model generates the parameters
necessary for the subsequent creation of an optimal voltage
or reactive power control system.
Discussion. During the experimental studies, a tool
was developed for estimating methods of voltage
regulation and optimization in the MG, taking into
account the requirements of standards for the MG such as
restraints on active and reactive power of the GFI and
energy storage systems. The ability of the
PowerDynamics.jl tools to perform simulation of the LV
MG modes with a significant number of nodes, in
particular using standard LV, MV and MG groups
connected to the MV grid, was confirmed.
The provided model allows optimizing the LV MG
voltage profile by selecting the droop control coefficient
KQ when using the day-ahead forecast of consumption
capacities, generation from renewable sources and
characteristics of electricity storage systems. The provided
model allows solving the problem of selecting the optimal
value of the droop control coefficient for a specific MG
mode. The optimal values of this coefficient may be
determined in the problems of reactive power distribution
in the RES group [53], as well as in the problems of
interpolation by a sequence of linear segments of droop
control coefficients to improve the efficiency of voltage
regulation in the MG [39]. The conclusion on the
admissibility of using quasi-stationary state models with a
discreteness of 60 s for simulating modes and analyzing the
MG states allows taking into account retrospective
information on the modes of electrical grids provided in
particular in [54]. The use of such retrospective information
allows verifying the MG control methods and models, as
well as performing machine learning of artificial
intelligence tools that may be used in solving individual
problems of controlling the MG modes.
To enhance the responsiveness and efficiency of
voltage control strategies in LV MGs, the integration of
digital twin technology offers a promising direction. A
digital twin constitutes a dynamic, data-driven virtual
representation of the physical energy system, capable of
real-time synchronization with sensor data and predictive
modeling. Recent work [16] demonstrated the feasibility of
applying digital twin architecture for increasing the
operational efficiency of RES through predictive analytics
and real-time system monitoring.
The developed model will allow further simulating
of simultaneous local voltage regulation by several GFIs,
which meets the requirements of primary local voltage
regulation provided in the IEC TS 62898-1 standard. The
provided LV MG model allows comparing methods of
proportional power distribution between MG energy
sources, in particular with an energy storage unit.
Another expected use of the developed MG model is
aimed at selecting optimal parameters, for example, of a
PI controller in order to regulate reactive power at the MG
input. The latter requires additional research on the
comparison of the use of PI reactive power regulation and
other methods for reducing reactive power at the MG
input. In particular, it is possible to analyze the change in
MG parameters when the inertia of LV MG changes [55].
The obtained results of voltage transfer function
modeling are useful in developing an improved reactive
power control system for a LV MG connected to the
distribution network [56].
90 Electrical Engineering & Electromechanics, 2026, no. 4
Conclusions. A new imitation model has been
developed for analyzing the dynamics of voltage and
reactive power in LV MG connected to the distribution
network, with a predominant active component of resistance
in the feeders connecting load nodes and GFIs in accordance
with the requirements of modern standards. Using the model
allows to analyze and determine the dependence of the
droop-control coefficient on the voltage on the value of the
GFI reactive power and the quasi-stationarity intervals for
power and voltage in the LV MG, which are the determining
parameters for the development of algorithms for remote
control of the GFI reactive power with limited-speed
information transmission systems in the LV MG.
The peculiarities of local voltage control in the LV
MG connected to the distribution network include
intervals of quasi-stationarity of voltage. The transfer
function for the dependence of the voltage at the nodes on
the reactive power of the load and the transient process
setting time was estimated. It is shown that the LV MG
modes at intervals of more than 60 s may be considered
quasi-stationary, which allows voltage droop control to be
used when regulating the voltage and not taking into
account fast transient processes.
The intervals of individual quasi-stationary states of
the LV MG were determined to exceed the intervals of the
relative output voltage at a level of 0.95 of the constant
value. An example of voltage regulation at quasi-stationary
intervals of 60 s is shown. The established quasi-
stationarity intervals confirmed the possibility of using a
limited-speed data transmission system in LV MG.
The model operation in the reactive power reduction
mode at the MG input using a PI controller and for
generating a predetermined reactive power at the MG
input is analyzed.
The constructed model allows creating practical
requirements for setting the voltage droop control GFI
value. Examples of using the model in the implementation
of local voltage and reactive power regulation in the MG
with RES are provided, taking into account changes in their
operating parameters, namely: when choosing the optimal
parameters of the PI controller in order to reduce reactive
power at the MG input; when generating the predetermined
reactive power at the MG input. The provided model is
intended for simulating the processes of voltage regulation
of the LV MG, in particular when using the forecast of load
power, electricity supply from RES, and existing parameters
of the storage system. The developed model is the basis for
its further development in order to build control systems for
the GFI reactive power regulation in the MG.
Acknowledgement. This paper was supported by
’Regime-3’ (0125U000609),’Innovate Ukraine’ program
(project OMM 10092144).
Conflict of interest. The authors declare that they
have no conflicts of interest.
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Received 04.12.2025
Accepted 03.02.2026
Published 02.07.2026
I. Trach1, PhD, Senior Researcher,
M. Belik2, D.Tech.Sc., Leading Researcher,
O. Rubanenko3,4,5, D.Tech.Sc., Senior Researcher,
V. Miroshnyk1, Senior Researcher,
I. Blinov1, D.Tech.Sc., Leading Researcher,
1 Institute of Electrodynamics of NAS of Ukraine,
56, Beresteysky Avenue, Kyiv, 03057, Ukraine,
igor.trach@gmail.com (Corresponding Author)
2 Department of Electrical Power Engineering,
University of West Bohemia,
Univerzitní 26, Pilsen, 30614, Czech Republic.
3 Research and Innovation Center for Electrical Engineering (RICE),
Faculty of Electrical Engineering of the University of West
Bohemia, Univerzitní 26, Pilsen, 30614, Czech Republic.
4 Institute of Renewable Energy,
20-a, Hnata Khotkevych Str., Kyiv, 02094, Ukraine.
5 Vinnitsya National Technical University,
95, Khmelnytskyi Highway, Vinnitsya, 21021, Ukraine.
How to cite this article:
Trach I., Belik M., Rubanenko O., Miroshnyk V., Blinov I. Simulation of voltage control processes in low-voltage microgrid nodes with
renewable energy sources and energy storage system. Electrical Engineering & Electromechanics, 2026, no. 4, pp. 84-91. doi:
https://doi.org/10.20998/2074-272X.2026.4.11
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| id | eiekhpieduua-article-366081 |
| institution | Electrical Engineering & Electromechanics |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-02T01:00:29Z |
| publishDate | 2026 |
| publisher | National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | eiekhpieduua/b4/a119e3192666664eee9d025f53b969b4.pdf |
| spelling | eiekhpieduua-article-3660812026-07-01T21:42:56Z Simulation of voltage control processes in low-voltage microgrid nodes with renewable energy sources and energy storage system Simulation of voltage control processes in low-voltage microgrid nodes with renewable energy sources and energy storage system Trach, I. Belik, M. Rubanenko, O. Miroshnyk, V. Blinov, I. microgrid quasi-stationary state intervals grid-forming inverter PV-generation reactive power мікромережа інтервали квазістаціонарності мережеутворюючий інвертор сонячна генерація реактивна потужність Introduction. The development of low-voltage microgrids (LV MG) with renewable energy sources requires effective control of their operating parameters, in particular voltage. The problem of voltage control in MG is exacerbated by the practical use of remote control systems for grid-forming inverters (GFIs) under conditions of limited data transmission speed. Goal. Identification of the features of local voltage control in LV MG nodes connected to distribution systems using reactive power of GFIs, in particular to assess the dependence of the droop-control coefficient on network parameters and to determine quasi-stationary time intervals. Methodology. The study was carried out using a newly developed imitation model in the PowerDynamics.jl environment for analyzing the dynamics of LV MGs, which are characterized by predominantly active feeder resistance and take into account the specific operating features of GFIs. Results. It has been established that the operating modes of LV MG connected to the distribution system can be considered quasi-stationary over intervals longer than 60 s, which allows the use of static control characteristics without taking into account fast transient processes. The operation of the model was analyzed under conditions of reactive power reduction at the MG input using a PI controller and maintaining a specified value of GFI reactive power. Scientific novelty. A new computational model has been developed which, unlike existing ones, enables comparison of different methods of reactive power distributing among a group of distributed energy sources and investigation of the features of voltage regulation using GFIs. Practical value. Using the developed model, an analysis was performed and the dependence of the voltage droop-control coefficient on the GFI reactive power was determined. Quasi-stationary intervals for power and voltage in LV MGs were established. The developed model confirms the effectiveness of voltage control through GFI reactive power in different MG operating modes. Practical recommendations for setting GFI parameters and information transfer speed in LV MG control systems were formed. References 56, tables 2, figures 7. Вступ. Розвиток мікромереж низької напруги (ММ НН) з відновлювальними джерелами енергії потребує забезпечення ефективного регулювання параметрів їх режимів, зокрема напруги. Проблема регулювання напруги в ММ НН підсилюється використанням на практиці систем віддаленого управління інверторами, що формують мережу (GFI), в умовах обмеженої швидкості передавання даних. Мета. Визначення особливостей локального регулювання напруги у вузлах ММ НН, приєднаних до систем розподілу, з використанням реактивної потужності GFI, зокрема оцінювання залежності коефіцієнта droop-control від параметрів мережі та визначення часових інтервалів квазі-стаціонарності. Методологія. Дослідження виконано з використанням нової розробленої розрахункової моделі у середовищі PowerDynamics.jl для аналізу динаміки ММ НН, яка має переважно активний характер опору фідерів та враховує специфіку роботи GFI. Результати. Встановлено, що режими ММ НН, приєднаних до системи розподілу, на інтервалах понад 60 с можна вважати квазі-стаціонарними, що дозволяє застосовувати статичні характеристики регулювання без урахування швидких перехідних процесів. Проаналізовано роботу моделі в режимах зниження реактивної потужності на вході мікромережі за допомогою PI-контролера та підтримки заданого значення реактивної потужності GFI. Наукова новизна. Розроблено нову розрахункову модель, використання якої, на відміну від існуючих, дозволяє виконати порівняння різних методів розподілу реактивної потужності між групою розосереджених джерел енергії та дослідити особливості локального регулювання напруги з використанням GFI. Практична значимість. З використанням розробленої моделі виконано аналіз та визначено залежності коефіцієнта droop-control по напрузі від значення реактивної потужності GFI та встановлені інтервали квазі-стаціонарності для потужності та напруги в ММ НН. З використанням розробленої моделі підтверджена ефективність локального регулювання напруги з використанням реактивної потужності GFI в різних режимах роботи мікромережі. Сформовано практичні рекомендації до налаштування параметрів GFI та швидкості передачі інформації в системах управління ММ НН. Бібл. 56, табл. 2, рис. 7. National Technical University "Kharkiv Polytechnic Institute" and Аnatolii Pidhornyi Institute of Power Machines and Systems of NAS of Ukraine 2026-07-02 Article Article application/pdf https://eie.khpi.edu.ua/article/view/366081 10.20998/2074-272X.2026.4.11 Electrical Engineering & Electromechanics; No. 4 (2026); 84-91 Электротехника и Электромеханика; № 4 (2026); 84-91 Електротехніка і Електромеханіка; № 4 (2026); 84-91 2309-3404 2074-272X en https://eie.khpi.edu.ua/article/view/366081/351650 Copyright (c) 2026 I. Trach, M. Belik, O. Rubanenko, V. Miroshnyk, I. Blinov http://creativecommons.org/licenses/by-nc/4.0 |
| spellingShingle | microgrid quasi-stationary state intervals grid-forming inverter PV-generation reactive power Trach, I. Belik, M. Rubanenko, O. Miroshnyk, V. Blinov, I. Simulation of voltage control processes in low-voltage microgrid nodes with renewable energy sources and energy storage system |
| title | Simulation of voltage control processes in low-voltage microgrid nodes with renewable energy sources and energy storage system |
| title_alt | Simulation of voltage control processes in low-voltage microgrid nodes with renewable energy sources and energy storage system |
| title_full | Simulation of voltage control processes in low-voltage microgrid nodes with renewable energy sources and energy storage system |
| title_fullStr | Simulation of voltage control processes in low-voltage microgrid nodes with renewable energy sources and energy storage system |
| title_full_unstemmed | Simulation of voltage control processes in low-voltage microgrid nodes with renewable energy sources and energy storage system |
| title_short | Simulation of voltage control processes in low-voltage microgrid nodes with renewable energy sources and energy storage system |
| title_sort | simulation of voltage control processes in low-voltage microgrid nodes with renewable energy sources and energy storage system |
| topic | microgrid quasi-stationary state intervals grid-forming inverter PV-generation reactive power |
| topic_facet | microgrid quasi-stationary state intervals grid-forming inverter PV-generation reactive power мікромережа інтервали квазістаціонарності мережеутворюючий інвертор сонячна генерація реактивна потужність |
| url | https://eie.khpi.edu.ua/article/view/366081 |
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