MATHEMATICAL MODEL AND ALGORITHM FOR THE DETERMINATION OF THE ORIGIN OF ELECTRICITY FROM RENEWABLE ENERGY SOURCES IN THE ELECTRIC POWER SYSTEM
The article deals with the development of a method and algorithm for calculation of individual compo-nents of electricity flows in the branches of an electric power grid circuit caused by generation and con-sumption in its nodes. In particular, it is about estimating the share of renewable energy so...
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Institute of Renewable Energy National Academy of Sciences of Ukraine
2024
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Vidnovluvana energetika| _version_ | 1871103750329860096 |
|---|---|
| author | Hunko, I. Kudrya , S. Komar , V. Lezhniuk, P. |
| author_facet | Hunko, I. Kudrya , S. Komar , V. Lezhniuk, P. |
| author_institution_txt_mv | [
{
"author": " I. Hunko",
"institution": "Institute of Re-newable Energy, NAS of Ukraine, Kyiv, Ukraine. "
},
{
"author": "S. Kudrya ",
"institution": "Institute of Re-newable Energy, NAS of Ukraine, Kyiv, Ukraine. "
},
{
"author": "V. Komar ",
"institution": "Vinnytsia National Tech-nical University, Vinnytsia, Ukraine."
},
{
"author": " P. Lezhniuk",
"institution": "Institute of Re-newable Energy, NAS of Ukraine, Kyiv, Ukraine; Vinnytsia National Tech-nical University, Vinnytsia, Ukraine."
}
] |
| author_sort | Hunko, I. |
| baseUrl_str | https://ve.org.ua/index.php/journal/oai |
| collection | OJS |
| datestamp_date | 2026-07-18T06:32:19Z |
| description | The article deals with the development of a method and algorithm for calculation of individual compo-nents of electricity flows in the branches of an electric power grid circuit caused by generation and con-sumption in its nodes. In particular, it is about estimating the share of renewable energy sources (RES) in the electricity consumption of a given consumer. The method is based on methods and algorithms for the calculation of steady-state modes of power grids, integrating a mathematical model for determining the components of current flows in the branches of the power system circuit. The model employs distribution coefficients of currents in the circuit branches from RES nodes and node voltages to form a matrix of cur-rent distribution coefficients for RES across the power grid branches. Since RES in electric power systems (EPS) use general power grids to transmit the electricity they generate, accurate determination of their power share within overall flows enables the impact of RES on the EPS mode parameters to be considered. The peculiarity of the algorithm for estimating the share of RES in the electricity consumption of a given consumer is its consideration of physical processes in the power system. The input data for the calculation are the power system parameters, the node loads (specified by capacity or schedules), as well as arrays of RES generation and centralized power supply nodes and consumers with a controlled value of the Guar-anteed Origin of electricity from RES. The voltages during the formation of the matrix of power distribu-tion coefficients at nodes along the branches of the power grid are determined by the calculation results of the power grid steady-state modes or by experimental measurement data. The method's efficacy and the accuracy of estimating the RES share in the power consumption of a given consumer are verified and demonstrated through a practical example. Determination of the share of the consumer's electricity con-sumption, which origin from renewable sources can be guaranteed, creates an enabling environment that would foster producers and consumers to increase the use of renewable energy sources and promotes the development of the green energy market. Ref. 18. Fig.3. |
| doi_str_mv | 10.36296/1819-8058.2024.2(77).6-12 |
| first_indexed | 2025-07-17T11:39:24Z |
| format | Article |
| fulltext |
6
Відновлювана енергетика. №2/2024 | Комплексні проблеми енергетичних систем на основі НВДЕ
УДК 621.311. https://doi.org/10.36296/1819-8058.2024.2(77)6-12
MATHEMATICAL MODEL AND ALGORITHM FOR THE DETERMINATION OF THE ORIGIN
OF ELECTRICITY FROM RENEWABLE ENERGY SOURCES IN THE ELECTRIC POWER SYSTEM
Received Mar. 18, 2024; accepted Jun. 21, 2024
Available online Jul. 01, 2024
Hunko I. 1, Kudrya S. 2, Komar V.3, Lezhniuk P.4
Author for correspondence: Hunko Iryna
e-mail: iryna_hunko@ukr.net
Abstract. The article deals with the development of a method and
algorithm for calculation of individual compo-nents of electricity
flows in the branches of an electric power grid circuit caused by gen-
eration and con-sumption in its nodes. In particular, it is about esti-
mating the share of renewable energy sources (RES) in the electric-
ity consumption of a given consumer. The method is based on
methods and algorithms for the calculation of steady-state modes
of power grids, integrating a mathematical model for determining
the components of current flows in the branches of the power sys-
tem circuit. The model employs distribution coefficients of currents in the circuit branches from RES nodes and
node voltages to form a matrix of cur-rent distribution coefficients for RES across the power grid branches. Since
RES in electric power systems (EPS) use general power grids to transmit the electricity they generate, accurate
determination of their power share within overall flows enables the impact of RES on the EPS mode parameters
to be considered. The peculiarity of the algorithm for estimating the share of RES in the electricity consumption of
a given consumer is its consideration of physical processes in the power system. The input data for the calculation
are the power system parameters, the node loads (specified by capacity or schedules), as well as arrays of RES
generation and centralized power supply nodes and consumers with a controlled value of the Guar-anteed Origin
of electricity from RES. The voltages during the formation of the matrix of power distribu-tion coefficients at nodes
along the branches of the power grid are determined by the calculation results of the power grid steady-state
modes or by experimental measurement data. The method's efficacy and the accuracy of estimating the RES share
in the power consumption of a given consumer are verified and demonstrated through a practical example. De-
termination of the share of the consumer's electricity con-sumption, which origin from renewable sources can be
guaranteed, creates an enabling environment that would foster producers and consumers to increase the use of
renewable energy sources and promotes the development of the green energy market. Ref. 18. Fig.3.
Кеy words: renewable energy sources, power grids, matrix of power distribution coefficients of nodes by
branches of the power grid, share of consumer electricity from RES.
МАТЕМАТИЧНА МОДЕЛЬ ТА АЛГОРИТМ ВИЗНАЧЕННЯ ПОХОДЖЕННЯ ЕЛЕКТРОЕНЕРГІЇ
СПОЖИВАЧА ВІД ВІДНОВЛЮВАНИХ ДЖЕРЕЛ ЕНЕРГІЇ В ЕЛЕКТРОЕНЕРГЕТИЧНІЙ СИСТЕМІ
Отримано 18 бер. 2024 р.; рекомендовано до публікації 21 чер. 2024 р.
Доступно онлайн 01 лип. 2024 р.
Гунько І. О.1, Кудря С. О.2, Комар В. О.3, Лежнюк П. Д.4
Автор для кореспонденції: Гунько Ірина
e-mail: iryna_hunko@ukr.net
Стаття присвячена розробленню методу та алгоритму ро-
зрахунку окремих складових перетікань електроенергії у віт-
ках схеми електричної мережі, що зумовлені генеруванням
та споживанням у вузлах. Зокрема йдеться про оцінювання
частки електроспоживання певного споживача електроене-
ргії, що забезпечується з відновлюваних джерел енергії (ВДЕ).
1 PhD, Doc.
https://orcid.org/0000-0003-2868-4056
2 Corresponding member of NAS of Ukraine,
Dr. of Tech. Science., Prof.
https://orcid.org/0000-0002-4798-6853
3 Dr. of Tech. Science., Prof.
https://orcid.org/0000-0003-4969-8553
4 Dr. of Tech. Science., Prof.
https://orcid.org/0000-0002-9366-3553
1,2,4 Institute of Re-newable Energy, NAS of
Ukraine, Kyiv, Ukraine.
3,4 Vinnytsia National Tech-nical University,
Vinnytsia, Ukraine.
1 к-т. техн. наук, доц.
https://orcid.org/0000-0003-2868-4056
2 чл.-кор. НАН України, д-р техн. наук, проф.
https://orcid.org/0000-0002-4798-6853
3 д-р. техн. наук, проф.
https://orcid.org/0000-0003-4969-8553
4 д-р. техн. наук, проф.
https://orcid.org/0000-0002-9366-3553
1,2,4 Інститут відновлюваної енергетики НАН
України, м. Київ, Україна.
3,4 Вінницький національний технічний
університет, м. Вінниця, Україна.
7
Відновлювана енергетика. №2/2024 | Комплексні проблеми енергетичних систем на основі НВДЕ
Метод ґрунтується на методах та алгоритмах розра хунку
усталених режимів електричних мереж. В основу методу пок-
ладено математичну модель для визначення складових переті-
кань електроенергії у вітках схеми електричної мережі, в якій
використовуються коефіцієнти розподілу струмів у вітках
схеми від вузлів з ВДЕ та вузлові напруги. В результаті формується матриця коефіцієнтів розподілу
потужності ВДЕ у вітках електричної мережі. Оскільки ВДЕ в електроенергетичних системах (ЕЕС) для
передачі генерованої ними електроенергії використовують електричні мережі загального призначення,
то визначення їх частки потужності в перетоках дозволяє враховувати вплив ВДЕ на параметри ре-
жиму ЕЕС. Особливістю алгоритму оцінювання частки електроспоживання заданого споживача, яка
забезпечується з ВДЕ, є врахування фізичних процесів у електричній мережі. Вхідними даними для роз-
рахунку є параметри електричної мережі, навантаження вузлів, заданих потужністю або графіками,
а також масиви вузлів генерування ВДЕ і централізованого живлення та споживачів з контрольованим
значенням гарантованого походження електроенергії від ВДЕ. Напруги під час формування матриці ко-
ефіцієнтів розподілу потужності вузлів по вітках електричної мережі визначаються за результатами
розрахунку усталених режимів електричної мережі або за експериментальними даними вимірювання.
На прикладі перевірена працездатність розробленого методу та адекватність результатів оціню-
вання частки електроспоживання заданого споживача, яка забезпечується з відновлюваних джерел
енергії. Визначення частки електроенергії споживачів, яку вони гарантовано отримують від ВДЕ, фор-
мує умови для стимулювання генерувальних компаній і споживачів збільшувати використання віднов-
лювальної енергії та сприяти розвитку ринку «зеленої» енергетики. Біб. 18. Рис. 3.
Ключові слова: відновлювані джерела енергії, електричні мережі, матриця коефіцієнтів розподілу
потужності вузлів по вітках електричної мережі, частка електроенергії споживача від ВДЕ.
Використані скорочення
List of Abbreviations and Symbols
EPS – electric power system
GO – Guarantees of Origin
PL – power line
PVPP – photovoltaic power plants
RES – renewable energy sources
WPP – wind power plant
Introduction and task statement. Renewable energy
sources, in particular wind and photovoltaic power plants
(WPP and PVPP), typically use general purpose power grids
to transmit the generated electricity to consumers. There-
fore, it is important to know how they affect the technical
and economic parameters of power grids. This applies to
voltage levels, load and capacity of power lines (PL) and
transformers, short-circuit currents and their conformance
with switching device values [1-4]. In addition, the develop-
ment and increase of the share of renewable energy in
power supply systems give rise to a number of issues not
directly related to the impact on grid parameters. First and
foremost, using renewable energy helps to reduce emis-
sions of harmful substances such as carbon dioxide and
other pollutants that adversely affect human health and
the environment. It is necessary to know the real origin of
electricity from renewable energy sources in order to ob-
jectively assess the impact of renewable energy generation
on the technical and economic parameters of power grids
and the process of decarbonization, i. e. the replacement of
traditional fossil fuel sources in the electricity balance. This
problem is currently referred to in the energy community
as "Guaranteeing the Origin of Electricity" [5, 6]. Guaran-
tees of Origin (GO) for renewable energy allow generation
companies and consumers to increase the use of renewa-
ble energy and promote the development of the green
energy market. Guarantees of origin of electricity from re-
newable energy sources make it possible to: stimulate re-
newable energy producers to expand their capacities and
invest in new technologies; increase consumer responsibil-
ity and awareness of their contribution to the reduction of
greenhouse gas emissions and climate change; and im-
prove energy security by creating conditions for the decen-
tralization of energy supply and the formation of local elec-
tric power systems based on renewable energy sources.
Since it is not yet feasible or practical to fully replace elec-
tricity consumption with renewable energy, differentiating
between the degrees of "greenness" is essential for both
renewable energy producers and industrial consumers
seeking to reduce CO2 emissions [7]. This is especially appli-
cable to power systems where nuclear and thermal power
plants, as well as renewable energy sources, are involved in
balancing the mode of the electric power system (EPS).
In addition to the environmental aspect, this is mainly due
to the need for auditable reporting [8], as shareholders ex-
pect companies to disclose the amount of CO2 emitted [9].
As a result, manufacturers are increasingly demanding au-
ditable environmental products in order to position them-
selves favorably among competitors by having a smaller
carbon footprint, and to meet their customers' desire for
carbon-friendly products [10]. The latter is also reflected in
1,2,4 Інститут відновлюваної енергетики
НАН України, м. Київ, Україна.
3,4 Вінницький національний технічний
університет, м. Вінниця, Україна.
8
Відновлювана енергетика. №2/2024 | Комплексні проблеми енергетичних систем на основі НВДЕ
the growing demand for green energy from residential con-
sumers.
The peculiarities of the physical processes of electricity
transmission make it impossible to separate the flow of
"green" energy from RES to the consumer without certain
assumptions [11]. Therefore, in order to ensure that a given
consumer receives green energy, a number of European
countries use an artificial approach to separating the phys-
ical processes from the commercial ones, which consists of
using "Certificates of Origin" to label each unit of renewa-
ble energy. Interested parties can trade these certificates
separately from the physical energy. Once the electricity is
consumed, the certificates are cancelled [12].
In the engineering practices of different countries, a num-
ber of methods are used to calculate power flows from
each individual generator or entity of the power associa-
tion, both with unambiguously specified information and
with probabilistic and statistical estimation of losses (re-
gression analysis) [13-15]. All available methods for the dis-
tribution of transmission losses can be divided into groups
of methods based on proportional distribution [13], specific
increases in power losses [14] and share distribution [15],
depending on the assumptions and approximations made.
Existing approaches to organizing the work of national elec-
tronic registers of Guarantees of Origin do not take into ac-
count the topology of the grid and the place of electricity
generation. The registers are organized on the principles of
separating physical processes from commercial ones.
Therefore, it is relevant to supplement the existing struc-
ture of the organization of the Guarantees of Origin by tak-
ing into account physical processes in the electricity trans-
mission and distribution systems, which requires the
development of an appropriate mathematical apparatus.
The goal of the article is to develop a method for estimating
the share of electricity in the consumption of a given con-
sumer that is provided by renewable energy sources.
Determining the origin of electricity in the branches of the
power grid. The idea of the method for determining the
share of power flows in power grids from a set of RES to
certain load nodes is to first determine the value of the to-
tal power at the beginning and at the end of each branch of
the circuit, which is determined by the formula [16]:
3b d d=S U M I , (1)
where bS is a power matrix where the columns represent
the power at the beginning and the end of the power grid
branches. dU is the diagonal matrix of voltages in the
nodes, including the balancing nodes;
M matrix of
branch connections in nodes, including balancing nodes;
dI diagonal matrix of currents in the branches of the circuit
(hereinafter, the sign means that the matrix or vector is
conjugated).
In order to obtain the part of power that is transferred from
RES to a particular consumer, we first write down the
values of the beginning and end power in the i-th branch of
the power grid from (1):
S 3( )Ibi d i i= U M , (2)
where iM is a vector-column of the matrix of branch con-
nections in nodes M ; Ii is the current in the i-th branch.
To convert from currents in branches and nodes to power,
we can rewrite equation (2) accordingly. To accomplish
this, the currents in the branches Ii are defined by the cur-
rents in the nodes.
Ii i=C J , (3)
where iC is the i-th vector-row of the matrix of distribu-
tion of specified currents in the nodes J along the
branches of the circuit.
The current distribution matrix is calculated by the method
of single currents or by the formula [16]:
-1 -1 -1( )b t b t =C z M M z M , (4)
where zb is the diagonal matrix of complex impedances in
the branches of an electrical grid circuit.
If the scheme and parameters of the EPS are relatively per-
manent, then the method of determining currents in
branches using the current distribution matrix C is more ap-
propriate.
Taking into account (3) and (4), expression (2) will be re-
written:
S 3( )bi d i i= U M C J , (5)
Given that
11
3
d
−=J U S , (5)
takes the form:
1S ( )bi d i i d
−
= U M C U S , (6)
where S is the vector of consumer loads and generation,
including RES, at nodes, including balancing nodes.
Let’s denote in (6)
1( )i d i i d
−
=D U M C U , (7)
where vector-row iD consists of coefficients that repre-
sent the share of the total power of the i-th branch that is
caused by the power flowing through it from each node.
Taking into account (7), the formula (6) of the power in the
i-th branch will be rewritten:
Sbi i=D S , (8)
In general, we can write that
b =S DS , (9)
9
Відновлювана енергетика. №2/2024 | Комплексні проблеми енергетичних систем на основі НВДЕ
where D is a matrix of coefficients of power distribution
in the nodes over the branches of the power grid, which is
formed from n rows iD , n is number of branches in the
power grid.
Using formula (9), we can determine the power compo-
nents in the power grid's branches from the nodes' power.
To determine the flows from RES in the branches of the
scheme, only RES power should be included in S from for-
mula (9):
b RES RES
=S DS , (10)
where
b RES
S is the vector of power flows in the branches
of the circuit caused by the power of RES nodes;
RES
S is a
vector of node power corresponding to the nodes of the
RES scheme.
To determine the power
RES j
S , that the consumer receives
at the j-th node from RES, the corresponding power bal-
ance is compiled (see Fig. 1):
RES j RES j RES j
S S S+ −= − , (11)
where
RES j
S + ,
RES j
S − are the powers that are generated by
RES and that enter or leave the j-th node, respectively.
Fig. 1. Consumer’s power from RES in the j-th node
The power
RES j
S + and
RES j
S − are determined by formula (9),
in which the first connection matrix
M , compiled for all
nodes of the circuit, is represented as the sum of two ma-
trices:
,+ −
= +M M M , (12)
where +
M is a matrix consisting of a fragment of the con-
nection matrix, the elements of which are zeros and ones
with sign "+"; −
M is the same matrix, but its elements are
zeros and ones with the sign "-".
It can be seen from (7) and (8) that the coefficients of the
distribution of node power S to branch power iD de-
pend not only on the parameters of the power system, but
also on the voltage of the nodes. Therefore, to ensure the
adequacy of the mathematical model, the voltage values
U of the nodes must correspond to the power values of the
nodes S In this case, the EPS mode would be balanced and
the nonlinear dependence of electricity losses in power
grids on the power of nodes S , including
RES
S [17], would
remain.
An algorithm for estimating the share of electricity sup-
plied from renewable energy sources in the consumption
of a given consumer. Fig. 2 shows an algorithm for deter-
mining the share of electricity generated by RES and trans-
mitted to a given electricity consumer. The approach in the
algorithm is such that, using (9), the power flows are deter-
mined in the branches of the power grid that are incidental
to the nodes with the list of RES electricity consumers spec-
ified in it. Directly in the node, we can calculate, from the
power balance of a group of different consumers, the
power of a specific consumer, which is oriented to the con-
sumption of electricity from a particular RES, taking into ac-
count the physical processes in the power system. Thus, it
is possible to estimate the degree of load coverage of a
given consumer by RES supplying energy to the power sys-
tem during a controlled time period T. The input data for
the calculation are the parameters of the power grid, the
load of nodes specified by power or schedules, and the
amounts of nodes of RES generation
RES
θ and centralized
generation
CS
θ and consumers with a controlled value of
the guaranteed origin of electricity from RES
RES
S .
In order to convert the consumer's power to the electricity
consumed, the average or maximum load methods are
used. Depending on the chosen method, the average
aver
S
or maximum
max
S value of the consumer's power for the pe-
riod T is given. A more accurate method is when the fore-
casted hourly consumption schedule for the day ahead is
set and the actual consumption data is based on the auto-
mated commercial electricity metering system (ACEMS). In
the first case, the forecasted amount of electricity planned
to be consumed from RES is determined. In the other case,
the actual amount of electricity consumed from RES is de-
termined. This data is sent to the register of guarantees of
origin, taking into account the amount of guaranteed cov-
erage of the consumer's load with energy from renewable
energy sources [6, 18].
Depending on the need and technical capabilities of the
metering system, the program is initiated on an hourly or
scheduled basis in accordance with the schedules of elec-
tricity generation and consumption in the power grid.
The array of node voltages required for the calculations can
be obtained in two ways: as a result of steady-state calcu-
lations or based on the data from the ACEMS. If the hourly
forecasted values of RES generation and consumption are
determined, the voltage is determined based on the results
of steady-state calculations or, where the accuracy is ac-
ceptable, based on average statistical data. If the actual val-
ues are determined accordingly, the output data are the re-
sults of voltage measurements in the ACEMS.
After forming the array of node voltages, the incident ma-
trix
M and the matrix of coefficients of distribution of
node-specified currents in the branches of the power grid
10
Відновлювана енергетика. №2/2024 | Комплексні проблеми енергетичних систем на основі НВДЕ
Fig. 2. Algorithm for the determination of the consumer's
electricity supply from renewable energy sources
C are formed. Then, the matrix of power distribution coef-
ficients of nodes over the branches of the power grid D is
calculated, which consists of the rows
i
D .
Using the matrix D , we identify those parts of the total
power
b RES
S in the grid branches that flow from RES. By
summing the power
b RES
S of the branches incidental to the
j-th nodes with controlled consumption from RES, their
guaranteed value of electricity from RES is determined.
These nodes can be of two types. If a node is a dead-end,
i.e. only branch with RES power
RES j
S approaches it, then that power is the RES power for
that consumer. If the node is an intermediate node, as
shown in Fig. 1, the power
RES j
S is determined from the
power balance in the j-th node. In the "Results output"
block, depending on the form of the input data, the power
RES j
S is recalculated into consumer electricity originating
from RES and is appropriately protocoled [6, 18].
The effectiveness of the developed method for determin-
ing the origin of the electricity from renewable energy
sources in the electric power system is demonstrated
through the example of a 110 kV power grid, the scheme of
which is shown in Fig. 3. The resistance of the branches,
load and generation are shown in the scheme. The balanc-
ing node is node 1 and the RES is located at node 6. The
steady-state mode test calculation for the maximum gen-
eration of the PV system (at 13:00) was performed using
PowerFactory 15.1. Based on the results of the steady-state
mode calculation, the node voltages were determined (on
Fig.3, the modules and voltage phases are shown in the
scheme near the nodes).
Using the values of the calculated node voltages, according
to (9), we calculate the matrix of power distribution coeffi-
cients of the 6th RES node for the power in the branches
(13).
Multiplying the matrix of power distribution coefficients of
the nodes by the power of the 6th node, we obtain the
power matrix for the branches of the power grid from RES
of the 6th node (14).
For example, branches 5 and 6 transmit the power of
5.254+5.292=10.546 MW to node 5. The power losses in
these branches are (5.292-5.254)+(5.319-5.292)=0.065
MW. Since the active load power of the 5th node in
maximum mode is 25 MW, the remaining power 25-
10.546=14.454 MW is transmitted by the balancing node 1.
6
0 0.567 0.001 0.567 0.001 0 0 0 0
0.452 0.002 0 0 0.091 0.0 0.361 0.001 0 0
0 0.562 0.001 0 0.090 0.0 0 0 0.653 0.001
0 0 0 0 0.349 0.002 0.349 0.002 0
0 0 0 0 0 0.355 0.645
j j
j j j
j j j
j j
− − +
− − + − +
= − + − +
− − +
1 2 3 4 5 6 7
D
2
3
4
5
6
(13)
11
Відновлювана енергетика. №2/2024 | Комплексні проблеми енергетичних систем на основі НВДЕ
Fig. 3. Scheme of the electrical grid
Conclusions
The method and algorithm for calculating separate compo-
nents of electricity flows in the branches of the power grid
circuit caused by generation and consumption in the nodes
are developed. The method determines the share of elec-
tricity, supplied by RES facilities connected to the power
grid, in the total consumption of a given consumer of elec-
tricity. The method is based on a mathematical model for
determining the coefficients of RES power distribution in
the branches of the power grid. The proposed method can
be a tool for confirming the Guarantee of Origin of the en-
ergy consumed in the retail market. Since RES use general
power grids to transmit the electricity they generate, the
determination of their share in the power flows to consum-
ers allows taking into account the impact of RES on the pa-
rameters of the power system mode and can be used in the
operational planning of the electricity balance.
An algorithm has been developed to determine the amount
of guaranteed coverage of the consumer's load with energy
from renewable energy sources. This algorithm can be used
to perform a qualitative and quantitative assessment of the
possibility of providing electricity of Guaranteed Origin for
each energy consumer. Such assessments are transparent
to end users and take into account physical processes in the
electricity grid, which will help to increase consumer confi-
dence in the results of calculations of electricity supply
from renewable-energy power plants. Determining the
share of consumers' electricity that they are guaranteed to
receive from renewable energy sources creates conditions
to encourage generating companies to produce and con-
sumers to increase their use of renewable energy and pro-
motes the development of the green energy market.
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0 8.223 – 0.105 –8.223 0.105 0 0 0 0
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|
| id | veorgua-article-450 |
| institution | Vidnovluvana energetika |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-07-19T01:13:09Z |
| publishDate | 2024 |
| publisher | Institute of Renewable Energy National Academy of Sciences of Ukraine |
| record_format | ojs |
| resource_txt_mv | veorgua/78/95b7a456dc604d6ead48b2cf47bcf578.pdf |
| spelling | veorgua-article-4502026-07-18T06:32:19Z MATHEMATICAL MODEL AND ALGORITHM FOR THE DETERMINATION OF THE ORIGIN OF ELECTRICITY FROM RENEWABLE ENERGY SOURCES IN THE ELECTRIC POWER SYSTEM МАТЕМАТИЧНА МОДЕЛЬ ТА АЛГОРИТМ ВИЗНАЧЕННЯ ПОХОДЖЕННЯ ЕЛЕКТРОЕНЕРГІЇ СПОЖИВАЧА ВІД ВІДНОВЛЮВАНИХ ДЖЕРЕЛ ЕНЕРГІЇ В ЕЛЕКТРОЕНЕРГЕТИЧНІЙ СИСТЕМІ Hunko, I. Kudrya , S. Komar , V. Lezhniuk, P. renewable energy sources, power grids, matrix of power distribution coefficients of nodes by branches of the power grid, share of consumer electricity from RES. відновлювані джерела енергії, електричні мережі, матриця коефіцієнтів розподілу потужності вузлів по вітках електричної мережі, частка електроенергії споживача від ВДЕ. The article deals with the development of a method and algorithm for calculation of individual compo-nents of electricity flows in the branches of an electric power grid circuit caused by generation and con-sumption in its nodes. In particular, it is about estimating the share of renewable energy sources (RES) in the electricity consumption of a given consumer. The method is based on methods and algorithms for the calculation of steady-state modes of power grids, integrating a mathematical model for determining the components of current flows in the branches of the power system circuit. The model employs distribution coefficients of currents in the circuit branches from RES nodes and node voltages to form a matrix of cur-rent distribution coefficients for RES across the power grid branches. Since RES in electric power systems (EPS) use general power grids to transmit the electricity they generate, accurate determination of their power share within overall flows enables the impact of RES on the EPS mode parameters to be considered. The peculiarity of the algorithm for estimating the share of RES in the electricity consumption of a given consumer is its consideration of physical processes in the power system. The input data for the calculation are the power system parameters, the node loads (specified by capacity or schedules), as well as arrays of RES generation and centralized power supply nodes and consumers with a controlled value of the Guar-anteed Origin of electricity from RES. The voltages during the formation of the matrix of power distribu-tion coefficients at nodes along the branches of the power grid are determined by the calculation results of the power grid steady-state modes or by experimental measurement data. The method's efficacy and the accuracy of estimating the RES share in the power consumption of a given consumer are verified and demonstrated through a practical example. Determination of the share of the consumer's electricity con-sumption, which origin from renewable sources can be guaranteed, creates an enabling environment that would foster producers and consumers to increase the use of renewable energy sources and promotes the development of the green energy market. Ref. 18. Fig.3. Стаття присвячена розробленню методу та алгоритму розрахунку окремих складових перетікань електроенергії у вітках схеми електричної мережі, що зумовлені генеруванням та споживанням у вузлах. Зокрема йдеться про оцінювання частки електроспоживання певного споживача електроенергії, що забезпечується з відновлюваних джерел енергії (ВДЕ). Метод 1,2,4 Інститут відновлюваної енергетики НАН України, м. Київ, Україна. 3,4 Вінницький національний технічний університет, м. Вінниця, Україна. ґрунтується на методах та алгоритмах розра хунку усталених режимів електричних мереж. В основу методу покладено математичну модель для визначення складових перетікань електроенергії у вітках схеми електричної мережі, в якій використовуються коефіцієнти розподілу струмів у вітках схеми від вузлів з ВДЕ та вузлові напруги. В результаті формується матриця коефіцієнтів розподілу потужності ВДЕ у вітках електричної мережі. Оскільки ВДЕ в електроенергетичних системах (ЕЕС) для передачі генерованої ними електроенергії використовують електричні мережі загального призначення, то визначення їх частки потужності в перетоках дозволяє враховувати вплив ВДЕ на параметри режиму ЕЕС. Особливістю алгоритму оцінювання частки електроспоживання заданого споживача, яка забезпечується з ВДЕ, є врахування фізичних процесів у електричній мережі. Вхідними даними для розрахунку є параметри електричної мережі, навантаження вузлів, заданих потужністю або графіками, а також масиви вузлів генерування ВДЕ і централізованого живлення та споживачів з контрольованим значенням гарантованого походження електроенергії від ВДЕ. Напруги під час формування матриці коефіцієнтів розподілу потужності вузлів по вітках електричної мережі визначаються за результатами розрахунку усталених режимів електричної мережі або за експериментальними даними вимірювання. На прикладі перевірена працездатність розробленого методу та адекватність результатів оцінювання частки електроспоживання заданого споживача, яка забезпечується з відновлюваних джерел енергії. Визначення частки електроенергії споживачів, яку вони гарантовано отримують від ВДЕ, формує умови для стимулювання генерувальних компаній і споживачів збільшувати використання відновлювальної енергії та сприяти розвитку ринку «зеленої» енергетики. Біб. 18. Рис. 3. Institute of Renewable Energy National Academy of Sciences of Ukraine 2024-07-01 Article Article application/pdf https://ve.org.ua/index.php/journal/article/view/450 10.36296/1819-8058.2024.2(77).6-12 Vidnovluvana energetika ; No. 2(77) (2024): Scientific and applied Journal renewable energy ; 6-12 Возобновляемая энергетика; ##issue.no## 2(77) (2024): Scientific and applied Journal renewable energy ; 6-12 Відновлювана енергетика; № 2(77) (2024): Науково-прикладний журнал Відновлювана енергетика; 6-12 2664-8172 1819-8058 10.36296/1819-8058.2024.2(77) uk https://ve.org.ua/index.php/journal/article/view/450/359 Copyright (c) 2024 I. Hunko, S. Kudrya , V. Komar , P. Lezhniuk https://creativecommons.org/licenses/by-nc-nd/4.0 |
| spellingShingle | renewable energy sources power grids matrix of power distribution coefficients of nodes by branches of the power grid share of consumer electricity from RES. Hunko, I. Kudrya , S. Komar , V. Lezhniuk, P. MATHEMATICAL MODEL AND ALGORITHM FOR THE DETERMINATION OF THE ORIGIN OF ELECTRICITY FROM RENEWABLE ENERGY SOURCES IN THE ELECTRIC POWER SYSTEM |
| title | MATHEMATICAL MODEL AND ALGORITHM FOR THE DETERMINATION OF THE ORIGIN OF ELECTRICITY FROM RENEWABLE ENERGY SOURCES IN THE ELECTRIC POWER SYSTEM |
| title_alt | МАТЕМАТИЧНА МОДЕЛЬ ТА АЛГОРИТМ ВИЗНАЧЕННЯ ПОХОДЖЕННЯ ЕЛЕКТРОЕНЕРГІЇ СПОЖИВАЧА ВІД ВІДНОВЛЮВАНИХ ДЖЕРЕЛ ЕНЕРГІЇ В ЕЛЕКТРОЕНЕРГЕТИЧНІЙ СИСТЕМІ |
| title_full | MATHEMATICAL MODEL AND ALGORITHM FOR THE DETERMINATION OF THE ORIGIN OF ELECTRICITY FROM RENEWABLE ENERGY SOURCES IN THE ELECTRIC POWER SYSTEM |
| title_fullStr | MATHEMATICAL MODEL AND ALGORITHM FOR THE DETERMINATION OF THE ORIGIN OF ELECTRICITY FROM RENEWABLE ENERGY SOURCES IN THE ELECTRIC POWER SYSTEM |
| title_full_unstemmed | MATHEMATICAL MODEL AND ALGORITHM FOR THE DETERMINATION OF THE ORIGIN OF ELECTRICITY FROM RENEWABLE ENERGY SOURCES IN THE ELECTRIC POWER SYSTEM |
| title_short | MATHEMATICAL MODEL AND ALGORITHM FOR THE DETERMINATION OF THE ORIGIN OF ELECTRICITY FROM RENEWABLE ENERGY SOURCES IN THE ELECTRIC POWER SYSTEM |
| title_sort | mathematical model and algorithm for the determination of the origin of electricity from renewable energy sources in the electric power system |
| topic | renewable energy sources power grids matrix of power distribution coefficients of nodes by branches of the power grid share of consumer electricity from RES. |
| topic_facet | renewable energy sources power grids matrix of power distribution coefficients of nodes by branches of the power grid share of consumer electricity from RES. відновлювані джерела енергії електричні мережі матриця коефіцієнтів розподілу потужності вузлів по вітках електричної мережі частка електроенергії споживача від ВДЕ. |
| url | https://ve.org.ua/index.php/journal/article/view/450 |
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