АНАЛІЗ ЕЛЕКТРОМЕХАНІЧНИХ КОЛИВАНЬ В ОЕС УКРАЇНИ З ВИКОРИСТАННЯМ ПРОГРАМНИХ ЗАСОБІВ EUROSTAG ТА DIGSILENT POWERFACTORY
Poorly damped low frequency oscillations – is one of the most complex and significant problems arising in large-scale power systems. The appearance of such oscillations in the power system can lead to system collapse. In the article the possible low-frequency electromechanical oscillations in IPS of...
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Інститут електродинаміки НАН України, Київ
2015
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Technical Electrodynamics| _version_ | 1870203180571164672 |
|---|---|
| author | Павловський , В.В. Лук'яненко , Л.Н. Леньга , О.В. Ламбилон , В. Ресе , Л. |
| author_facet | Павловський , В.В. Лук'яненко , Л.Н. Леньга , О.В. Ламбилон , В. Ресе , Л. |
| author_institution_txt_mv | [
{
"author": "В.В. Павловський ",
"institution": "Інститут електродинаміки НАН України пр. Перемоги, 56, Київ-57, 03680, Україна"
},
{
"author": "Л.Н. Лук'яненко ",
"institution": "Інститут електродинаміки НАН України пр. Перемоги, 56, Київ-57, 03680, Україна"
},
{
"author": "О.В. Леньга ",
"institution": "Інститут електродинаміки НАН України пр. Перемоги, 56, Київ-57, 03680, Україна"
},
{
"author": "В. Ламбилон ",
"institution": "Tractebel Engineering (GDF SUEZ), Avenue Ariane, 7, Brussels – BELGIUM "
},
{
"author": "Л. Ресе ",
"institution": "Tractebel Engineering (GDF SUEZ), Avenue Ariane, 7, Brussels – BELGIUM "
}
] |
| author_sort | Павловський , В.В. |
| baseUrl_str | https://techned.org.ua/index.php/techned/oai |
| collection | OJS |
| datestamp_date | 2023-01-02T21:34:53Z |
| description | Poorly damped low frequency oscillations – is one of the most complex and significant problems arising in large-scale power systems. The appearance of such oscillations in the power system can lead to system collapse. In the article the possible low-frequency electromechanical oscillations in IPS of Ukraine have been considered. Analysis was performed for three scenarios: 1 – IPS of Ukraine interconnected with united power system of Commonwealth States, 2 – Ukraine operating in isolated (island) mode, 3 – Ukraine interconnected to ENTSO-E. Research was performed involving real practice software. The poorly damped low frequency inter-area oscillations have been determined and compared for each of the scenarios of IPS of Ukraine. References 10, table 3, figures 9. |
| first_indexed | 2026-06-16T01:16:08Z |
| format | Article |
| fulltext |
42 ISSN 1607-7970. Техн. електродинаміка. 2015. № 5
ЕЛЕКТРОЕНЕРГЕТИЧНІ СИСТЕМИ ТА УСТАНОВКИ
УДК 621.311
ANALYSIS OF ELECTROMECHANICAL OSCILLATION IN THE IPS OF UKRAINE USING
EUROSTAG AND DIGSILENT POWERFACTORY SOFTWARE TOOLS
V.Pavlovskyi1, L.Lukianenko1, O.Lenga1, V.Lambillon2, L.Rese2
1 − Institute of Electrodynamics of NAS of Ukraine,
pr. Peremohy, 56, Kyiv-57, 03680, Ukraine,
e-mail: lukianenko.lukian@gmail.com
2 − Tractebel Engineering (GDF SUEZ),
Avenue Ariane, 7, Brussels – BELGIUM
Poorly damped low frequency oscillations – is one of the most complex and significant problems arising in large-scale
power systems. The appearance of such oscillations in the power system can lead to system collapse. In the article the
possible low-frequency electromechanical oscillations in IPS of Ukraine have been considered. Analysis was performed
for three scenarios: 1 – IPS of Ukraine interconnected with united power system of Commonwealth States, 2 – Ukraine
operating in isolated (island) mode, 3 – Ukraine interconnected to ENTSO-E. Research was performed involving real
practice software. The poorly damped low frequency inter-area oscillations have been determined and compared for
each of the scenarios of IPS of Ukraine. References 10, table 3, figures 9.
Key words: Low-frequency oscillations, small signal stability, methodology of study, interconnected to ENTSO-E.
1. Introduction. Poorly damped low frequency inter-area oscillations are of major concern in
operation planning and control of large-scale power systems. In the past decade, many cases of such
oscillations have been recorded with the aid of Wide-Area Measurement System (WAMS) technologies [3,
4, 10] and investigated using modern software tools all over the world.
The last recorded incident caused by poorly damped inter-area oscillations in Continental Europe
power system occurred in February 2011. Due to the high active power oscillations on the Swiss border tie-
lines, Swissgrid has blocked the operation of the Automatic Generation Control (AGC) four times (time
windows of about two minutes) [1]. The unexpected interaction among various system controls like AGCs,
speed governors, HVDCs, etc. initiated by low frequency oscillations can be extremely dangerous.
Therefore, the possible poorly damped oscillations might hazard the system security.
It should be noted that the Ukrainian TSO has never faced with such a phenomenon until today.
Unfortunately, there were not significant achievements in practical methods and tools of small-signal
stability in traditional “Russian school” of power system analysis. The main attention was paid to study
aperiodic steady state (static) stability and transient (dynamic) stability of synchronous machines. An
exception case is the oscillation stability described in [2]. However, a very small test system has been used to
demonstrate modal analysis techniques in that paper.
Recently, several modern PMUs have been installed and commissioned in IPS of Ukraine [9].
However, no low frequency oscillations have been recorded since that. The possible reason might be in the
high damping ratio of inter-area modes in the IPS of Ukraine. Power system operation with quite high
stability margin (about 20% for normal condition) contributes for keeping sufficiently damped
electromechanical oscillations. However, current market rules push the system operator to operate the power
system closer to its stability limits. In such a scenario, the study of inter-area oscillations may be of high
importance for the IPS of Ukraine. It should also be taken into account the future plans for synchronously
interconnecting the IPS of Ukraine with the ENTSO-E system.
Basically, the power system oscillations study is based on the linear systems and modern control
theory. Today, different software vendors that provide various implementations of the mathematical
principles and algorithms use different simplifications and assumptions in their tools. Many engineers have
different visions on modal technique indices like mode shape, observability, controllability etc. Therefore,
the brief theoretical background is presented in this article and it outlines the main steps usually employed in
power system small-signal stability analysis.
© Pavlovskyi V., Lukianenko L., Lenga O., Lambillon V., Rese L., 2015
ISSN 1607-7970. Техн. електродинаміка. 2015. № 5 43
2. Model and Methodology of study. In this paper, small-signal stability studies are performed for the
perspective (2020Y horizon) model of IPS of Ukraine for winter peak load condition. The correspondent
overview diagram of IPS of Ukraine is presented at Fig. 1.
Two nuclear units with installed capacity of 1000 MW at Khmelnitska Nuclear Power Plant (NPP), four units
at Dnestrovska Pumped Storage Hydro Power Plant (PSHPP) and a large amount of renewable energy sources
are planned to be installed before 2020 in Ukraine, which makes this target-year very challenging from the
power system stability point of view.
The objective of this study is to assess the possible inter-area oscillation modes for Ukrainian power
system in different network configurations in 2020. The local oscillation modes are also computed, but not
analysed in details in this study, unless if they indicate system instability.
Ташлыкская ГАЭС
ПС 750 кВ Приморская
ПС 500 кВ Ростовская
ПС 330 кВ ПГУ
ПС 330 кВ Кафа
ПС 220 кВ Алмазная
ПС 330 кВ Дрогобыч
ПС 750 кВ Каховська
6598_Микашевичи
ПС 330 кВ Западная
ПС 330 кВ Тальне
ПС 330 кВ Севастополь
ПС 330 кВ ВДГМК
ПС 220 кВ Титан
ПС 220 кВ Красноперекопск
ПС 330 кВ Гомель
ПС 330 кВ Павлоград
ПС 330 кВ Камянец-Подольская
ПС 330 кВ Черновцы
ПС 330 кВ Бельцы
ПС 330 кВ Кишинев
ПС 330 кВ Страшени
ПС 330 кВ ХБК
ПС 400 кВ Вулканешты
Молдавская ГРЭС
ПС 220 кВ Центролит
ПС 220 кВ Коминтерново
ПС 330 кВ Горная
Симферопольская ТЭЦ
ПС 220 кВ Донузлав
ПС 220 кВ Феодосийская
ПС 220 кВ Камыш-Бурун
ПС 330 кВ Островская
ПС 330 кВ Западнокрымская
ПС 330 кВ Джанкой
ПС 220 кВ Т-15
ПС 220 кВ ХБК
ПС 220 кВ ДМЗ
ПС 220 кВ Смолянка
Мироновская ТЭС
ПС 220 кВ ЛИП
ПС 220 кВ Лисичанск
ПС 220 кВ Юбилейная
ПС 220 кВ Черкасская
ПС 500 кВ Новодонбасская
ПС 220 кВ Коммунарская
ПС 220 кВ Кировская
ПС 500 кВ Шахты
ПС 220 кВ Антрацыт
ПС 220 кВ Краснодон
ПС 220 кВ Зуевская
ПС 220 кВ Амвросиевка
Зуевская ТЭС
ПС 330 кВ Южная'
ПС 220 кВ Сысоево
ПС 330 кВ Лозовская
ПС 330 кВ Первомайская'
ПС 330 кВ Купянск
ПС 330 кВ Лосево
ПС 750 кВ Северо-Украинская
ПС 330 кВ Миргород
ПС 330 кВ Кременчуг
Кременчугская ГЭС
ПС 330 кВ Черкассы
ПС 330 кВ Поляна
Каневская ГЭС
ПС 400 кВ Мукачево
ПС 330 кВ Яворов
ПС 330 кВ Львов Западная
ПС 220 кВ Стрый
ПС 220 кВ Роздол
ПС 220 кВ Львов-2
ПС 220 кВ Борислав
ПС 220 кВ Воловец
ПС 330 кВ Ивано-Франковск
ПС 330 кВ Богородчаны
ПС 220 кВ Калуш
ПС 220 кВ ГПП-1
ПС 330 кВ Шепетовка
ПС 330 кВ Рыбница
ПС 330 кВ Котовск
ПС 330 кВ Первомайская
ПС 330 кВ Прометей
ПС 330 кВ ДНП
ПС 330 кВ ДДЗ
ПС 330 кВ Украинка
ПС 330 кВ Рудная
ПС 330 кВ Кварцит
ПС 330 кВ Побужье
Добротворская ТЭС
ПС 330 кВ Львов Южная
ПС 220 кВ Луцк Южная
ПС 330 кВ Радывылив
ПС 330 кВ Ровно
ПС 330 кВ Грабово
ПС 330 кВ Луцк Северная
ПС 330 кВ Ново-Волынск
ПС 330 кВ Ковель
ПС 330 кВ Казатин
Днестровская ГЭС
ПС 330 кВ Винница
ПС 330 кВ Бар
ПС 330 кВ Хмельницкий
ПС 330 кВ Тернополь
ПС 330 кВ Чернигов
ПС 330 кВ Славутич
ПС 330 кВ Лесная
ПС 330 кВ Житомир
ПС 330 кВ Белая Церковь
КТЭЦ-5
КТЭЦ-6
ПС 330 кВ Нежин
ПС 330 кВ Бровары
ПС 330 кВ Октябрьская
ПС 330 кВ Ново-Киевская
ПС 330 кВ Северная
Курская АЭС
ПС 750 кВ Донбасская
ПС 750 кВ Южнодонбасская
Днестровская ГАЭС
ПС 330 кВ Конотоп
ПС 330 кВ Сумы Северная
ПС 330 кВ Сумы
ПС 330 кВ Шостка
ПС 330 кВ Артема
ПС 330 кВ Залютино (ТЕЦ-5)
ПС 330 кВ Полтава
ПС 330 кВ Арцыз
ПС 330 кВ Симферополь
ПС 330 кВ Мелитополь
ПС 330 кВ Херсон
ПС 330 кВ Николаев
ПС 330 кВ Трихаты
ПС 330 кВ Южная
ПС 330 кВ Кировская
ПС 330 кВ Усатово
ПС 330 кВ Ново-Одесская
ПС 330 кВ Аджалык
ПС 330 кВ Каховская ГПП
ПС 330 кВ Запорожская
ПС 330 кВ ДД
ПС 330 кВ Молочанск
ПС 330 кВ Ферросплавная
ПС 330 кВ Никополь
ПС 330 кВ Ивановка
ПС 330 кВ Заря
ПС 220 кВ Азовская
ПС 330 кВ Мирная
ПС 330 кВ Правобережная
ПС 330 кВ Центральная
ПС 500 кВ Победа
ПС 330 кВ Красноармейская
ПС 330 кВ Майская
ПС 330 кВ Чайкино
ПС 330 кВ Харцизька
ПС 330 кВ Макеевка
ПС 400 кВ Михайловка
Бурштынская ТЭС
Трипольская ТЭС
Приднепровская ТЭС
Луганская ТЭС
Кураховская ТЭC
Старобешевская ТЭС
Углегорская ТЭС
Славянская ТЭС
Криворожская ТЭС
Ладыжинская ТЭС
Ровенская АЭС
Хмельницька АЭС
ПС 750 кВ Киевская
ПС 750 кВ Винница
Южноукраинская АЭС
Запорожская АЭС ..
Запорожская ТЭС ..
ПС 750 кВ Западноукраинская
ПС 750 кВ Запорожская ..
ПС 750 кВ Днепровская
ШебБХЗ
Валуйки
Нововоронежская АЭС
Белгород
шув
ПС 220 кВ Замость
Змиёвская ТЭС
ПС 330 кВ Мозирь
Чернобыльская АЭС
ПС 750 кВ Исакча
Винница-ЮУАЭС
1595. МВт
ОЭС Центра - ОЭС Укрины
-383. МВт
ОЭС Украины - ОЭС Сев.Кавказ
852. МВт
ОЭС Украины - Крым
-418,74
Винница - ХАЭС
-1236. МВт
ХАЭС - Запад
369. МВт
Запад_Киев - ОЭС Украины
976. МВт
ОЭС Украины - Киев
3882. МВт
ОЭС Украины - Одесса_Крым
184. МВт
Днепр - Донбасс
4283. МВт
ОЭС Украины - Днепр_Одесса_Крым
381. МВт
ОЭС Украины - КрТЭС_ЗаТЭС_Одесса_Крым ..
-192. МВт
ОЭС Украины - ЗаТЭС_Одесса_Крым
-1109. МВт
Донбасс - ЛуТЭС
455. МВт
Львов - ОЭС Украины
446. МВт
Донбасс-Днепр с ЕЭС России
-124. МВт
ОЭС Украины-Одесса_Молдова
237. МВт
Запад - Винница
3659. МВт
51
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Fig. 1
Taking into account the numerous of development alternatives of the Ukrainian power system, the
analysis is carried out for the following network configurations:
i. IPS of Ukraine interconnected with united power system of Commonwealth States;
ii. Ukraine operating in isolated (island) mode;
iii. Ukraine interconnected to ENTSO-E.
It should be noted that such comprehensive study has never been performed for the IPS of Ukraine
before. In order to achieve adequate results, proper models of the IPS of Ukraine are needed, especially for
the regulations of generating units, including the well-known “strong action automatic excitation regulator
with relay forcing action” commonly used in Russian power stations [6].
Another feature of this study is the use of different simulation software, according to the network
configuration: DIgSILENT PowerFactory (configurations i and ii) and Eurostag (configuration iii).
3. Theoretical background of small-signal stability analysis. The majority of power system
components, such as generators, excitation systems, governors and loads, have nonlinear characteristics. These
components and their associated controls may include saturation and output limiters. Despite the fact that
nonlinear systems theory can be used to study such a system, this is only applicable for small and simple systems.
On the other hand, the linear systems theory can provide useful insights into the operating behaviour
of an interconnected power system. The use of this theory is based on the principle that the dynamic
behaviour of the system is linear (or quasi-linear) around an equilibrium point. Fortunately, low frequency
oscillations in a power system are fairly linear when caused by disturbances of small magnitude such as
random fluctuations of generation and load. The variations in system dynamic variables such as machine
44 ISSN 1607-7970. Техн. електродинаміка. 2015. № 5
rotor angle and speed are also small under these circumstances and the assumption of a linear system model
around a given operating point provides valid results. These conclusions are generally consistent with what is
observed in the field under similar operating conditions [7].
The advantage of assuming a linear model for the system is that the theory of linear systems is in a
mature state, meaning that methodologies, algorithms and tools able to deal with very large systems in
reasonable computation time are available.
In power systems, the study of system stability using linear models is commonly referred to as
“small-signal stability analysis”. This type of study allows the analysis of the so-called steady-state stability.
The following types of oscillation modes can be detected and identified through small-signal stability
analysis [8]:
• Local modes: associated with the oscillations of units at a power station with respect
to the rest of the system (oscillation frequency between 1 Hz and 2 Hz). These oscillations are
located at one station or a small part of the system.
• Inter-area modes: associated with the swing of many machines in one part of the
system against machines in the other parts (oscillation frequency between 0,1 Hz and 1 Hz). Caused
by two or more groups of coherent (electrically close) machines being interconnected by a weak
transmission network.
• Control modes: associated with generating units and their controls. The usual causes
of instability of such modes are improperly tuned excitation systems, speed governors, HVDC
converters and SVCs.
• Torsional modes: associated with the rotational components of turbine-generator
shaft systems. The usual causes of instability of such modes are interactions with excitation controls,
speed governors, HVDC controls, and series-compensated lines.
It must be emphasized that the stability in the small-signal sense is a necessary (but not sufficient)
condition for the power system operation. As consequence of not being a sufficient condition, the results of
small-signal stability analyses must be assessed through nonlinear time-domain simulations
(electromechanical transients simulations).
The following section presents a set of definitions related to linear systems theory and small-signal
stability that will be used for the definition of the methodology to be adopted in this study.
3.1 Linear system theory aspects applied to power systems small-signal stability problem. Low-
frequency electromechanical oscillations usually range from 0,1 Нz to 3 Нz other than those with sub-
synchronous resonance (SSR). multi-machine power system dynamic behaviour in this frequency range is
usually represented by a set of nonlinear differential and algebraic equations (DAE) in the form of
( )&x = f x,z,u , 0 = g(x,z,u), y = h(x,z,u),
where f and g are sets of differential and algebraic equations and h is a set of output equations. x, z, u and y
are vectors of state variables, algebraic variables, inputs and outputs, respectively.
The linearization around an equilibrium point and Gaussian elimination of the algebraic variables of
this system of nonlinear DAEs results in a linear system in the form of
.&x = Ax + Bu, y = Cx + Du
3.1.1 Eigenvalues and oscillation modes. The eigenvalues ( iλ ) of the state matrix (A) characterize
the dynamic behaviour of the linearized system. These eigenvalues may be real or complex numbers.
Complex eigenvalues always occur in conjugate pairs i i ijλ σ ω= ± .
The eigenvalues of the state matrix correspond to the system modes (oscillation mode, if iλ is
complex). The real part (σ ) relates to the mode damping and the imaginary part ( jω± ) relates to its
oscillation frequency.
The relationship between the eigenvalues and the system stability is defined by the absolute stability criteria,
which follows [7]: “A system is stable according to the absolute stability criteria if all eigenvalues of the system are
located in the left semi-plane of the complex plane (all eigenvalues must have negative real parts)”.
The analysis of the eigenvalues indicates the damping level and the oscillation frequency of the
modes. The requirement for minimum damping level varies from system to system (usual criteria is to
assume a minimum damping ratio of 5% [8]). The oscillation frequency of a mode, in Hertz, is given by
/ 2i if ω π= .
ISSN 1607-7970. Техн. електродинаміка. 2015. № 5 45
The damping ratio of a mode is given by 2 2 1/ 2( )i i i iζ σ σ ω −= − + .
3.1.2 Eigenvectors and mode shapes. In power systems literature, the right eigenvector associated
to an eigenvalue iλ is known as the mode shape of iλ . The mode shape provides valuable information on
the participation of a given state variable in a particular mode. It allows the identification of the participation
of an individual machine or a group of machines in a particular mode.
The mode shapes are very useful for the identification of coherent groups of machines, as well as for
the identification of inter-area modes.
3.1.3 Participation factors. In large power systems it is important to quantify the role of each
generator on each mode. A method generally employed for this purpose is the computation of the
participation factors for each mode. The participation factor is a measure of the relative participation of the
k-th state variable on the i-th mode, and vice-versa.
The participation factor of a state variable in a given mode is calculated by means of combining the
left and right eigenvectors associated to that mode. Through this combination it is possible to produce a
dimensionless index, which is essential when comparing state variables of different physical units.
Through the calculation of the participation factors it is possible to determine the machines that have
more contribution to a given oscillation mode. The generators with highest participation factor on poorly
damped low frequency modes are potential candidates for installing a power system stabilizer (PSS).
A drawback of the participation factors is that they relate only to the state and do not take into
account the input/output (I/O) relationship. Therefore, it cannot effectively identify a controller site and an
optimal feedback signal without information on the most adequate input and output when feedback control is
employed. The effectiveness of control can be indicated through controllability and observability factors, as
described in the following.
3.1.4 Modal controllability and observability. Considering the linearized dynamic system given by
,&x = Ax + Bu, y = Cx
where x is the system state vector, u is the input vector and y is the output vector.
Denoting by Φ the matrix where each column is a right eigenvector of A then the change of variable
Φxz = leads to the following system:
& -1z = Λz +Φ Bu, y = CΦ x,
where Λ is a diagonal matrix composed by the eigenvalues of A, one can see that:
• If the i-th row of BΦ 1− is not null, then it is possible to control the i-th mode through the
control u. If there are different potential controls (u is a vector), then the different elements of the i-
th row give indication on which inputs have the largest impacts on the i-th mode.
• If the i-th column of CΦ is not null, then it is possible to observe the i-th mode trough the
output y. If there are different potential observers (y is a vector) then the different elements of the i-
th column give indication on which output provides the more information on the i-th mode.
This means that the controllability of the input signal and the observability of the feedback signal are
basic requirements for PSS allocation.
4. Methodology for small-signal stability analysis. The first step for the small-signal stability
analysis is the linearization of the power system dynamic model around a given operating condition. The
linearized system is then used to compute the following parameters:
• System eigenvalues and eigenvectors (both right and left);
• Participation factors;
• Controllability and observability indices.
4.1 Identification of inter-area and critical oscillation modes. Critical oscillation modes are
defined as modes with low damping level (a cigré "task force" on electromechanical oscillations in power
systems recommends a minimum damping of 5%). the identification of critical oscillation modes starts by
the computation of the system eigenvalues. as the power system model is very large, the computation of all
system eigenvalues through orthogonal decomposition-based methods (i.e. qr factorization) is not
recommended due to the large computational time and memory usage required by these methods [5].
In this study, the method used for eigenvalue calculation is based on the calculation of all
eigenvalues within a predefined region of the complex plane (Arnoldi method) [5]. This region is defined by
the user and must comprise the modes with oscillation frequency up to 3,5 Hz and damping ratios at least up
46 ISSN 1607-7970. Техн. електродинаміка. 2015. № 5
to 35%. This guarantees the calculation of all critical electromechanical modes of the system, as well as the
inter-area modes.
The result of eigenvalues computation is a table containing all information related to the modes: real
and imaginary parts, damping ratio and oscillation frequency.
4.2 Critical modes are identified as the ones whose damping ratio is less than 5%. Inter-area
modes are pre-identified by selecting the modes whose frequency lie in the range between 0,1 Hz and 1 Hz.
To get the final decision on which modes are in fact inter-area modes a second step is needed: analysis of the
mode shapes, which is explained in the sequel.
4.3 Participation factor and mode shape analysis. The goals of participation factor and mode
shape analysis are twofold:
Identify the machines associated to the critical oscillation modes (analysis of participation factors);
Identify the inter-area modes within the modes with frequency between 0,05 Hz and 2 Hz.
4.4 Analysis of participation factors. The participation factors provide an indication of the
contribution of the machines in a given mode. This is very useful for identifying the machines that have
major contributions to the critical modes as well as to the inter-area modes.
In this study, the participation factors of all modes classified as critical (ζ < 5%) in the eigenvalue
computation phase are calculated and analysed in order to provide indications on which machines have most
participation on the critical modes.
4.5 Analysis of mode shapes. As previously described, the mode shapes give the relative magnitude
and phase of the oscillations as seen from a given state variable. Since the objective of this project is to
analyse electromechanical oscillations, the rotor speed or angle must be chosen as state variable.
In this study, the mode shapes of all oscillation modes with frequency between 0,05 Hz and 2 Hz are
calculated and analysed in order to identify all inter-area modes. After the identification of these modes, their
respective damping ratios are carefully analysed. In case of poorly damped inter-area modes, the necessary
measures to improve the damping are recommended.
4.6 Determination of candidate machines for avr retuning aiming at improving oscillation
damping. In case of the presence of critical inter-area modes, the identification of the candidate machines
for avr parameters retuning is performed.
The choice of the machine and the input signals to be used for the improving the damping of critical
modes is not straightforward. It depends on the calculation of the controllability and observability indices.
In this study, if any critical inter-area mode is detected at a certain operating condition, the necessary
recommendations for AVR parameters retuning are given.
5. Study cases. All simulations related to the scenarios “i” and “ii” are performed in DIgSILENT
PowerFactory, while the simulations for the scenario “iii” are performed in EUROSTAG.
5.1. IPS Ukraine interconnected with united power system of Commonwealth States. The
results of small-signal stability analysis for this scenario show that there exist two main inter-area modes, as
presented in Table 1.
Table 1
Mode Real
part
Imaginary
part
Damping
Ratio [%]
Oscillation
Frequency [Hz] Characterization of the Mode
“Ukr-
Rus”
-0,172 ±3,196 5,360 0,509 Ukrainian PS vs Russian PS inter-area mode
“North-
South”
-0,2259
±4,002
5,636
0,637
Zaporіzhs'ka NPP, Juzhno-Ukrainskaja NPP
vs Khmelnitska NPP, Rovenskaya NPP,
Kurskaya NPP (rus), Smolenskaya NPP (rus)
inter-area mode
To detail these inter-area oscillations and to check the correction of our result, the time domain
simulation has been performed. Figure 2 presents results of time-domain simulations that clearly depicts the
“Ukr-Rus” inter-area mode. The oscillation frequency taken from the time domain simulation results (1/T =
=1/ 1,933 = 0,517 Hz) is very close to the value obtained in the small-signal stability analysis (0,509 Hz).
Figure 3 presents results of time-domain simulations that clearly depicts the “North-South” inter-area
mode. The oscillation frequency taken from the simulation results (1/T = 1/1,561 = 0,640 Hz) is very close to
the value obtained in the small-signal stability analysis (0,637 Hz).
ISSN 1607-7970. Техн. електродинаміка. 2015. № 5 47
5.2. Isolated operation of the IPS Ukraine. The results of small-signal stability analysis for “Isolated
operation of IPS of Ukraine” show that there are two main inter-area modes, as presented in Table 2.
Table 2
Mode
#
Real
part
Imaginary
part
Damping
Ratio [%]
Oscillation
Frequency [Hz]
Characterization of the Mode
“North-
South”
-0,3250 ±5,3884 6,020 0,858 North vs South inter-area mode
“East-West” -0,2564 ±3,5618 7,179 0,567 East vs West inter-area mode
Figure 4 presents results of time-domain simulations that clearly depicts the “North-South” inter-area
mode. The oscillation frequency taken from the simulation results (1/T=1/1,154=0,867 Hz) is very close to
the value obtained in the small-signal stability analysis (0,858 Hz).
Fig. 2
Fig. 3
48 ISSN 1607-7970. Техн. електродинаміка. 2015. № 5
Figure 5 presents results of time-domain simulations that clearly depicts the “East-West” inter-area
mode. The oscillation frequency taken from the simulation results (1/T = 1/1,744 = 0,573 Hz) is very close to
the value obtained in the small-signal stability analysis (0,567 Hz).
5.3. IPS Ukraine interconnected with ENTSO-E. The results of small-signal stability analysis for
this scenario show that there exist two inter-area modes, as presented in Table 3.
Table 3
Mode
# Real Imaginary Damping
Ratio [%]
Oscillation
Frequency [Hz] Characterization of the Mode
1 -0,3623 ±1,7088 20,739 0,272 Ukraine x ENTSO-E inter-area mode
2 -0,1671 ±3,8123 4,379 0,607 East x West inter-area mode
Fig. 4
Fig. 5
ISSN 1607-7970. Техн. електродинаміка. 2015. № 5 49
Mode 1 is an inter-area mode associated to the machines of the Ukrainian system oscillating against
the machines of the ENTSO-E system. Figure 6 shows the mode shape plot for this mode. It clearly depicts
the phase opposition between the ENTSO-E system equivalent machine and the coherent group of machines
of the Ukrainian system. For this mode, the oscillation frequency is equal to 0,272 Hz and the damping ratio
is about 20,7%, which is considered an adequate damping ratio for an inter-area mode.
Mode 2 is an inter-area mode associated to the machines of the Western part of the Ukrainian power
system oscillating against the machines of the Eastern part of the system. Figure 7 shows the mode shape
plot for this mode. It clearly depicts the phase opposition between the Eastern and Western groups of
machines. For this mode, the oscillation frequency is equal to 0,607 Hz and the damping ratio is about 4,4%.
Fig. 6 Fig. 7
This inter-area mode is considered as insufficiently
damped.
Figure 8 shows the participation factors for “Mode 2”.
The machines with major contribution to this oscillation mode
are Rovenskaya AES (G5 and G6) and Khmelnitska (G1 and
G2). The analysis of controllability and observability indices
indicates that this mode is more effectively observable and
controllable through the machines G5 and G6 of Rovenskaya
NPP. It is then recommended to retune the parameters of the
AVR system of these two machines in order to improve the
damping of this inter-area mode. Attention has to be taken on
tuning this AVR system (“Strong Action Automatic Excitation
Regulator - SAAER”) because of its particular structure, which
does not allow the employment of classical PSS tuning methods
to retune the AVR parameters. It is worth noticing that retuning
AVR systems to improve damping of inter-area modes is out of
the scope of this study.
G5
G6
G1
G2
Fig. 8
21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 25.5 26.0 26.5
49.97
49.98
49.99
50.00
50.01
50.02
s
Hz
Luhanskaya TES - G8 Unit : Hz
Zmiyovskaya TES - TG1 Unit : Hz
Zaporozhskaya TES - G1 Unit : Hz
KTETS-5 - G1 Unit : Hz
Khmelnitska AES - G2 Unit : Hz
Rovenskaya AES - G1 Unit : Hz
T = 1.641 s
Fig. 9
50 ISSN 1607-7970. Техн. електродинаміка. 2015. № 5
Figure 9 present results of time-domain simulations that clearly depicts the East-West inter-area mode.
The oscillation frequency measured on the simulation results (1/T=1/1,641=0,609 Hz) is very close
to the value obtained in the small-signal stability analysis (0.607 Hz).
6. Conclusion
Small-signal stability analysis has been performed for the interconnected power system of Ukraine
for time horizon of 2020Y. The oscillations have been identified for three different scenarios of power
system operations: “IPS of Ukraine is interconnected with UPS of Commonwealth State”, “Isolated
operation of IPS of Ukraine” and “IPS of Ukraine is interconnected with ENTSO-E system”. The small-
signal stability analysis for the first and second scenarios has been performed using DIgSILENT
PowerFactory software tool, while the simulation for the third scenario has been carried in EUROSTAG.
There are two inter-area modes in the first operating scenario with damping ratios of about 5%
(5,35% and 5,64%) and low oscillation frequencies (0,51 Hz and 0,64 Hz). The first mode is associated to
the machines of the Ukrainian power system oscillating against the machines of the Russian power system.
The second mode is associated to the machines Southern part oscillating against the machines of the
Northern part of the Ukrainian system.
In the second scenario the last mentioned oscillation mode (machines of the Southern part oscillating
against the machines of the Northern part of the system) is slightly different. The damping ratio increases
(from 5,64% to 6,02%) and frequency of oscillation is also increased (from 0,64 Hz to 0,86 Hz). In addition
to that, in this scenario another inter-area mode has been identified. This mode is associated to the machines
of the Eastern part of the system oscillating against the machines of the Western part (damping ratio equal to
7,18% and oscillation frequency of 0,57 Hz).
For the scenario “IPS of Ukraine interconnected with ENTSO-E system”, also two inter-area modes
are identified. The first one is associated to the machines of the Eastern part of the Ukrainian power system
oscillating against the machines of the Western part, whose damping ratio is lower than 5% (oscillation
frequency equal to 0,61 Hz). Further investigation aiming at improving the damping of this mode is
recommended, but is outside of the scope of this paper. The second mode is related to the machines of the
Ukrainian system oscillating against the machines of the ENTSO-E system. This mode has a very low
oscillation frequency (0,27 Hz) and is well damped (damping ratio equal to 20,7%).
The results of this small-signal stability analysis show necessity of preventing measure for damping
oscillations in inter area mode within Ukraine for scenario of parallel operation with ENTSO-E system. In
addition, it should be noted that same additional study is advisable to perform after validation/calibration of
Ukrainian power system dynamic model.
1. Analysis of CE inter-area Oscillations of 19 and 24 February 2011. ENTSO-E SG SPD Report. 21.08.2011.
Available at: https://www.entsoe.eu/fileadmin/user_upload/_library/
publications/entsoe/RG_SOC_CE/Top7_110913_CE_inter-area-oscil_feb_19th_24th_final.pdf. (accessed 10.06.2015)
2. Butkevych O. Problem-oriented monitoring of Ukrainian operation condition // Tekhnichna
Elektrodynamika. – 2007. – № 5. – Pp. 39–52. (Ukr)
3. Bobba R.B., Dagle J., Heine E., Khurana H., Sanders W.H., Sauer P., Yardley T. Enhancing Grid
Measurements: Wide Area Measurement Systems, NASPInet, and Security // IEEE Power and Energy Magazine. −
2012. − Vol. 10. − No 1. − Pp. 67−73.
4. Dong Xinwei1, Huang Qian1, Chang Yong. The Monitor of Inter-area Oscillation Based on Wide Area
Measurement System // 2012 International Conference on Future Energy, Environment and Materials. − 2012. − Vol.
16. − Part C. − Pp. 2033–2043.
5. Golub G.H., Van Loan C.F. Matrix Computations. − The John Hopkins University Press, 2013. − 728 p.
6. Malik O.P, Stroev V.A., Shtrobel V.A., Hancock G.C., Beim R.S. Experimental studies with power system
stabilizers on a physical model of a multimachine power system // IEEE Transactions on Power Systems. −1996. − Vol.
2. − Issue 11. − Pp. 807−812.
7. Pal B., Chaudhuri B. Robust Control in Power Systems. − Springer US, 2005. − 190 p.
8. Paserba J. Analysis and Control of Power System Oscillations. − Special Publication 38.01.07. − 1996. −
Vol. Technical Brochure.
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9. Stogny B.S., Kirilenko A.V., Butkevich A.F., Pavlovsky V.V. Innovative Smart Grid Technologies in Electric
Power Industry of Ukraine // 2nd IEEE PES International Conference “Innovative Smart Grid Technologies – Europe
2011”, Dec. 5-7, 2011, Manchester, UK.
10. Uhlen K., Warland L., Gjerde J.O., Breidablik O., Uusitalo M., Leirbukt A.B., Korba P. Monitoring
amplitude, frequency and damping of power system oscillations with PMU measurements // Power and Energy Society
General Meeting - Conversion and Delivery of Electrical Energy in the 21st Century. – 2008. − Pp. 1−7.
УДК 621.311
АНАЛІЗ ЕЛЕКТРОМЕХАНІЧНИХ КОЛИВАНЬ В ОЕС УКРАЇНИ З ВИКОРИСТАННЯМ
ПРОГРАМНИХ ЗАСОБІВ EUROSTAG ТА DIGSILENT POWERFACTORY
В.В. Павловський1, докт.техн.наук, Л.Н. Лук'яненко1, канд.техн.наук, О.В.Леньга1, В. Ламбилон2, Л. Ресе2
1 − Інститут електродинаміки НАН України
пр. Перемоги, 56, Київ-57, 03680, Україна.
e-mail: lukianenko.lukian@gmail.com
2 − Tractebel Engineering (GDF SUEZ),
Avenue Ariane, 7, Brussels – BELGIUM.
Низькочастотні коливання потужності – це одна із найбільш складних і значних проблем, які виникають у
великих енергооб’єднаннях. Поява таких коливань у енергосистемі може призвести до розвитку системних
аварій. У статті розглянуто можливі електромеханічні низькочастотні коливання в ОЕС України. Аналіз
виконано для трьох сценаріїв роботи: 1 − паралельна робота ОЕС України з енергооб’єднанням ЄЕС Росії/
Білорусії, 2 − ізольована від енергосистем сусідніх країн робота ОЕС України, 3 – паралельна робота ОЕС
України з ENTSO-E. Дослідження виконані із залученням перевірених на практиці програмних засобів. За
результатами проведених розрахунків було визначено небезпечні, погано демпфовані моди коливань для
кожного із сценаріїв роботи ОЕС України та проаналізовано, як ці моди можуть змінюватися в залежності
від сценарію роботи ОЕС України. Бібл. 10, рис. 9, табл. 3.
Ключові слова: низькочастотні коливання, розрахунки, коливна стійкість, методика розрахунку, інтеграція до
ENTSO-E.
УДК 621.311
АНАЛИЗ ЭЛЕКТРОМЕХАНИЧЕСКИХ КОЛЕБАНИЙ В ОЭС УКРАИНЫ С ИСПОЛЬЗОВАНИЕМ
ПРОГРАММНЫХ СРЕДСТВ EUROSTAG И DIGSILENT POWERFACTORY
В.В. Павловский1, докт.техн.наук, Л.Н. Лукьяненко1, канд.техн.наук, О.В.Леньга1, В. Ламбилон2, Л. Ресе2
1 − Институт электродинамики НАН Украины,
пр. Победы, 56, Киев-57, 03680, Украина,
email: lukianenko.lukian@gmail.com
2 − Tractebel Engineering (GDF SUEZ),
Avenue Ariane, 7, Brussels – BELGIUM.
Низкочастотные колебания мощности – это одна из самых сложных и серьезных проблем, которые возни-
кают в больших энергообъединениях. Появление таких колебаний в энергосистеме может привести к разви-
тию системных аварий. В статье рассмотрены возможные электромеханические низкочастотные колебания
в ОЭС Украины. Анализ выполнен для трех возможных сценариев работы: 1 − параллельная работа ОЭС
Украины с энергообъединением ЕЭС России / Белоруссии, 2 – изолированная от энергосистем соседних стран
работа ОЭС Украины, 3 – параллельная работа ОЭС Украины с ENTSO-E. Исследования выполнены с
привлечением проверенных на практике программных средств. По результатам проведенных расчетов были
определены опасные, плохо демпфированные моды колебаний для каждого из сценариев работы ОЭС Украины
и проанализировано, как эти моды могут изменяться в зависимости от сценария работы ОЭС Украины.
Библ. 10, рис. 9. табл. 3.
Ключевые слова: низкочастотные колебания, расчеты, колебательная устойчивость, методика расчета,
интеграция в ENTSO-E.
Надійшла 19.06.2015
|
| id | techned_org_ua-article-959 |
| institution | Technical Electrodynamics |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-06-16T01:16:08Z |
| publishDate | 2015 |
| publisher | Інститут електродинаміки НАН України, Київ |
| record_format | ojs |
| resource_txt_mv | technedorgua/14/c66d31d4208591836c56a8b5a5b1e314.pdf |
| spelling | techned_org_ua-article-9592023-01-02T21:34:53Z ANALYSIS OF ELECTROMECHANICAL OSCILLATION IN THE IPS OF UKRAINE USING EUROSTAG AND DIGSILENT POWERFACTORY SOFTWARE TOOLS АНАЛІЗ ЕЛЕКТРОМЕХАНІЧНИХ КОЛИВАНЬ В ОЕС УКРАЇНИ З ВИКОРИСТАННЯМ ПРОГРАМНИХ ЗАСОБІВ EUROSTAG ТА DIGSILENT POWERFACTORY Павловський , В.В. Лук'яненко , Л.Н. Леньга , О.В. Ламбилон , В. Ресе , Л. Low-frequency oscillations small signal stability methodology of study interconnected to ENTSO-E низькочастотні коливання розрахунки коливна стійкість методика розрахунку інтеграція до ENTSO-E Poorly damped low frequency oscillations – is one of the most complex and significant problems arising in large-scale power systems. The appearance of such oscillations in the power system can lead to system collapse. In the article the possible low-frequency electromechanical oscillations in IPS of Ukraine have been considered. Analysis was performed for three scenarios: 1 – IPS of Ukraine interconnected with united power system of Commonwealth States, 2 – Ukraine operating in isolated (island) mode, 3 – Ukraine interconnected to ENTSO-E. Research was performed involving real practice software. The poorly damped low frequency inter-area oscillations have been determined and compared for each of the scenarios of IPS of Ukraine. References 10, table 3, figures 9. Низькочастотні коливання потужності – це одна із найбільш складних і значних проблем, які виникають у великих енергооб’єднаннях. Поява таких коливань у енергосистемі може призвести до розвитку системних аварій. У статті розглянуто можливі електромеханічні низькочастотні коливання в ОЕС України. Аналіз виконано для трьох сценаріїв роботи: 1 − паралельна робота ОЕС України з енергооб’єднанням ЄЕС Росії/ Білорусії, 2 − ізольована від енергосистем сусідніх країн робота ОЕС України, 3 – паралельна робота ОЕС України з ENTSO-E. Дослідження виконані із залученням перевірених на практиці програмних засобів. За результатами проведених розрахунків було визначено небезпечні, погано демпфовані моди коливань для кожного із сценаріїв роботи ОЕС України та проаналізовано, як ці моди можуть змінюватися в залежності від сценарію роботи ОЕС України. Бібл. 10, рис. 9, табл. 3. Інститут електродинаміки НАН України, Київ 2015-09-01 Article Article application/pdf https://techned.org.ua/index.php/techned/article/view/959 Tekhnichna Elektrodynamika; No. 5 (2015): TEKHNICHNA ELEKTRODYNAMIKA; 042 ТЕХНІЧНА ЕЛЕКТРОДИНАМІКА; № 5 (2015): ТЕХНІЧНА ЕЛЕКТРОДИНАМІКА; 042 2218-1903 1607-7970 en https://techned.org.ua/index.php/techned/article/view/959/837 Авторське право (c) 2023 ТЕХНІЧНА ЕЛЕКТРОДИНАМІКА https://creativecommons.org/licenses/by-nc-nd/4.0 |
| spellingShingle | низькочастотні коливання розрахунки коливна стійкість методика розрахунку інтеграція до ENTSO-E Павловський , В.В. Лук'яненко , Л.Н. Леньга , О.В. Ламбилон , В. Ресе , Л. АНАЛІЗ ЕЛЕКТРОМЕХАНІЧНИХ КОЛИВАНЬ В ОЕС УКРАЇНИ З ВИКОРИСТАННЯМ ПРОГРАМНИХ ЗАСОБІВ EUROSTAG ТА DIGSILENT POWERFACTORY |
| title | АНАЛІЗ ЕЛЕКТРОМЕХАНІЧНИХ КОЛИВАНЬ В ОЕС УКРАЇНИ З ВИКОРИСТАННЯМ ПРОГРАМНИХ ЗАСОБІВ EUROSTAG ТА DIGSILENT POWERFACTORY |
| title_alt | ANALYSIS OF ELECTROMECHANICAL OSCILLATION IN THE IPS OF UKRAINE USING EUROSTAG AND DIGSILENT POWERFACTORY SOFTWARE TOOLS |
| title_full | АНАЛІЗ ЕЛЕКТРОМЕХАНІЧНИХ КОЛИВАНЬ В ОЕС УКРАЇНИ З ВИКОРИСТАННЯМ ПРОГРАМНИХ ЗАСОБІВ EUROSTAG ТА DIGSILENT POWERFACTORY |
| title_fullStr | АНАЛІЗ ЕЛЕКТРОМЕХАНІЧНИХ КОЛИВАНЬ В ОЕС УКРАЇНИ З ВИКОРИСТАННЯМ ПРОГРАМНИХ ЗАСОБІВ EUROSTAG ТА DIGSILENT POWERFACTORY |
| title_full_unstemmed | АНАЛІЗ ЕЛЕКТРОМЕХАНІЧНИХ КОЛИВАНЬ В ОЕС УКРАЇНИ З ВИКОРИСТАННЯМ ПРОГРАМНИХ ЗАСОБІВ EUROSTAG ТА DIGSILENT POWERFACTORY |
| title_short | АНАЛІЗ ЕЛЕКТРОМЕХАНІЧНИХ КОЛИВАНЬ В ОЕС УКРАЇНИ З ВИКОРИСТАННЯМ ПРОГРАМНИХ ЗАСОБІВ EUROSTAG ТА DIGSILENT POWERFACTORY |
| title_sort | аналіз електромеханічних коливань в оес україни з використанням програмних засобів eurostag та digsilent powerfactory |
| topic | низькочастотні коливання розрахунки коливна стійкість методика розрахунку інтеграція до ENTSO-E |
| topic_facet | Low-frequency oscillations small signal stability methodology of study interconnected to ENTSO-E низькочастотні коливання розрахунки коливна стійкість методика розрахунку інтеграція до ENTSO-E |
| url | https://techned.org.ua/index.php/techned/article/view/959 |
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