Power System Stability and Robustness of Synchronous Machine’s Excitation Control with Magnitude-Phase Voltage Regulator
The conditions necessary to provide the robust stability and robust control of synchronous machine’s excitation control with magnitude-phase automatic voltage regulator are determined.
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| Zitieren: | Power System Stability and Robustness of Synchronous Machine’s Excitation Control with Magnitude-Phase Voltage Regulator / O.F. Butkevych, O.M. Agamalov // Технічна електродинаміка. — 2014. — № 5. — С. 41-43. — Бібліогр.: 4 назв. — англ. |
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irk-123456789-1356422018-06-16T03:07:45Z Power System Stability and Robustness of Synchronous Machine’s Excitation Control with Magnitude-Phase Voltage Regulator Butkevych, O.F. Agamalov, O.M. Електроенергетичні комплекси, системи та керування ними The conditions necessary to provide the robust stability and robust control of synchronous machine’s excitation control with magnitude-phase automatic voltage regulator are determined. Визначено умови, необхідні для забезпечення робастної стійкості та робастного керування збудженням синхронної машини з амплітудно-фазовим автоматичним регулятором напруги. Определены условия, необходимые для обеспечения робастной устойчивости и робастного управления возбуждением синхронной машины с амплитудно-фазовым автоматическим регулятором напряжения. 2014 Article Power System Stability and Robustness of Synchronous Machine’s Excitation Control with Magnitude-Phase Voltage Regulator / O.F. Butkevych, O.M. Agamalov // Технічна електродинаміка. — 2014. — № 5. — С. 41-43. — Бібліогр.: 4 назв. — англ. 1607-7970 http://dspace.nbuv.gov.ua/handle/123456789/135642 621.311 en Технічна електродинаміка Інститут електродинаміки НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
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Електроенергетичні комплекси, системи та керування ними Електроенергетичні комплекси, системи та керування ними |
| spellingShingle |
Електроенергетичні комплекси, системи та керування ними Електроенергетичні комплекси, системи та керування ними Butkevych, O.F. Agamalov, O.M. Power System Stability and Robustness of Synchronous Machine’s Excitation Control with Magnitude-Phase Voltage Regulator Технічна електродинаміка |
| description |
The conditions necessary to provide the robust stability and robust control of synchronous machine’s excitation control with magnitude-phase automatic voltage regulator are determined. |
| format |
Article |
| author |
Butkevych, O.F. Agamalov, O.M. |
| author_facet |
Butkevych, O.F. Agamalov, O.M. |
| author_sort |
Butkevych, O.F. |
| title |
Power System Stability and Robustness of Synchronous Machine’s Excitation Control with Magnitude-Phase Voltage Regulator |
| title_short |
Power System Stability and Robustness of Synchronous Machine’s Excitation Control with Magnitude-Phase Voltage Regulator |
| title_full |
Power System Stability and Robustness of Synchronous Machine’s Excitation Control with Magnitude-Phase Voltage Regulator |
| title_fullStr |
Power System Stability and Robustness of Synchronous Machine’s Excitation Control with Magnitude-Phase Voltage Regulator |
| title_full_unstemmed |
Power System Stability and Robustness of Synchronous Machine’s Excitation Control with Magnitude-Phase Voltage Regulator |
| title_sort |
power system stability and robustness of synchronous machine’s excitation control with magnitude-phase voltage regulator |
| publisher |
Інститут електродинаміки НАН України |
| publishDate |
2014 |
| topic_facet |
Електроенергетичні комплекси, системи та керування ними |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/135642 |
| citation_txt |
Power System Stability and Robustness of Synchronous Machine’s Excitation Control with Magnitude-Phase Voltage Regulator / O.F. Butkevych, O.M. Agamalov // Технічна електродинаміка. — 2014. — № 5. — С. 41-43. — Бібліогр.: 4 назв. — англ. |
| series |
Технічна електродинаміка |
| work_keys_str_mv |
AT butkevychof powersystemstabilityandrobustnessofsynchronousmachinesexcitationcontrolwithmagnitudephasevoltageregulator AT agamalovom powersystemstabilityandrobustnessofsynchronousmachinesexcitationcontrolwithmagnitudephasevoltageregulator |
| first_indexed |
2025-07-09T23:45:42Z |
| last_indexed |
2025-07-09T23:45:42Z |
| _version_ |
1837214984090681344 |
| fulltext |
ISSN 1607-7970. Техн. електродинаміка. 2014. № 5 41
УДК 621.311
POWER SYSTEM STABILITY AND ROBUSTNESS OF SYNCHRONOUS MACHINE’S EXCITATION
CONTROL WITH MAGNITUDE-PHASE VOLTAGE REGULATOR*
О.F.Butkevych 1, O.M.Agamalov 2
1 − Institute of Electrodynamics of the National Academy of Sciences of Ukraine,
Peremohy av., 56, Kyiv-57, 03680, Ukraine, e-mail: butkevych@ied.org.ua
2 − Tashlyk Pump Storage Power Plant, Yuzhnoukrainsk, Ukraine.
The conditions necessary to provide the robust stability and robust control of synchronous machine’s excitation control
with magnitude-phase automatic voltage regulator are determined. References 4, figures 1.
Key words: power system stability, synchronous machine, voltage phasor, magnitude-phase automatic voltage
regulator, robustness.
Power System stability depends on different factors, but considerably depends on excitation control of
synchronous machines (SM) with used types and settings of automatic voltage regulators [1, 2]. Therefore the
improvement of SM’s excitation control effectiveness is an important power system problem. Conventional excitation
control systems are designed based on linearized models of SM and power system. These models are designed for a
given operation mode, and therefore the conventional excitation controllers sometimes work improperly if power
system operation conditions are changed considerably. Nonlinear excitation controllers usually have a more
complicated structure and more parameters, and therefore are harder to implement in practice.
Excitation control is based on the evaluation of the scalar mismatch error between a reference voltage refV and
a measured terminal voltage tV . The obtained scalar error tref VVV −=Δ is used as the input of a PID controller or its
simplified variants (PD, PI) to control the excitation current fI of SM. The purpose of this control is the precise
maintenance of the SM terminal voltage tV according to the reference voltage refV in all possible operation conditions.
In order to achieve this, it is necessary to set the greatest possible value of the automatic voltage regulator’s (AVR)
proportional gain. However, in some operation conditions of SM this leads to a decrease of damping component of the
electric moment that is proportional to the rotor speed deviation ωΔ and to electromechanical oscillations. Therefore,
additionally in SM excitation control the feedbacks on the parameters which characterize the rotor motion (a frequency
deviation fΔ , a rotor speed deviation ωΔ , a field current deviation fIΔ or an accelerating power aP ) are used. These
additional feedbacks are implemented as stabilizing channels in automatic excitation regulators of a strong action in
Russia [4] or as separate devices - power system stabilizers (PSS) [2]. This greatly complicates the design, subsequent
coordination of regulation and stabilization channels, holding of the commissioning works and operation of excitation
control systems. Therefore the development of an excitation control system which implements a new feedback type is
the urgent problem. The structure of such a feedback reflects both the electromagnetic state, determined by terminal
voltage magnitude, and electro-mechanical state, defined by the SM rotor movement. In order to achieve this, it is
necessary to increase the dimension of the mismatch error in such a way that this error is able to reflect both the
deviations of the terminal voltage and the deviations of rotor angle of the SM. According to this requirement the
terminal voltage phasor of the SM is used as input of the magnitude-phase automatic voltage regulator (MP-AVR).
Parameters and sometimes even structure of power system elements under the different operation conditions
are subjected to significant nonlinear changes. Therefore the MP-AVR should have the property of robustness to these
changes, providing the required robust stability and robust performance of control under a given structured and
unstructured uncertainty of synchronous machine and power system models.
We define a setpoint of the SM excitation controller as some phasor refV (p. u.), which coincides in the steady-
state with the field current fI (p. u.) or synchronous EMF phasor qE (p. u.). The magnitudes of the setpoint and terminal
voltage phasors are equal 0tref VV = , (p. u.), but these phasors are shifted by the steady-state rotor angle 0SMδ , in
accordance with the diagram presented in Figure, where eΔ is an error for MP-AVR, and VΔ is an error for existent
AVR. In transient, as a result of disturbance in the power system, the increment ( eΔ ) of an error function of a complex
argument (CAEF) is defined as
)()()sinsin()coscos(),( 01010011001110 ddqqSMtSMtSMtSMtNSMt VVjVVVVjVVeeVfe −+−=−+−=−=ΔΔ=Δ δδδδδ
(1)
Taking into account reft VV =0
the CAEF increment eΔ reflects the increments of the terminal voltage magnitude tVΔ
and rotor’s angles ( SMδΔ ), and generalizes the traditional definition of the error by magnitude terminal voltage:
______________________________________
*The studies were carried out by the project of the research programme of NAS of Ukraine "Ob'ednannya-2".
© Butkevych O.F., Agamalov O.M., 2014
42 ISSN 1607-7970. Техн. електродинаміка. 2014. № 5
2 2 2 2
0 1 1 1 1 0 1 02 cos( ) ( ) ( ) ,t t ref t ref t SM q q d de V V V V V V V V V VΔ = − = + − Δδ = − + − 2 2 2 2
1 0 1 0 0 1 1 .t ref t t t q d q dV V V V V V V V VΔ = − = − = + − +
(2)
The calculation of the CAEF increment based
on the Wirtinger partial derivatives. Taking
into account that output of the excitation
control is oriented in the direction of the
antigradient (1) we obtain the following
control law with MP-AVR
( )
( )
( )( )
cos
cos
sec ,
2
1 2
SM
f ref t
SM
ref SM t
N
V K V V
N
K V N V
⎛ ⎞Δδ
Δ = Δ − Δ =⎜ ⎟⎜ ⎟+ Δδ⎝ ⎠
= Δ − Δδ Δ
(3)
where K – a gain of the proportional channel
by the magnitude deviation of the terminal
voltage phasor tVΔ , and N – a gain by rotor
angle deviation SMδΔ . When 0=Δ refV the
equation (3) in increments is
,tFf VKV Δ=Δ
where ( )SMF NKK δΔ−= sec – an adaptive
feedback gain of the excitation control by
terminal voltage phasor.
Using the expression for the rotor angle deviation by means of the rotor speed deviation we obtain
→Δ⋅Δ=Δ tωδ ( ) tf VtNKV ΔΔΔ−=Δ ωsec ,
( ) ( ).sec tC
V
V
tNK AVRMP
t
f
−=
Δ
Δ
=ΔΔ− ω (4)
Let us define a transfer function of MP-AVR ( AVRMPC − ). Taking into account that for the trigonometric function
secant the direct Laplace transform does not exist we present this function in the expression (4) by the series expansion
( ) ( )
( ) ( ) ( ) ( ) ...
720
61
24
5
2
11
!2
||sec 642
0
2
+ΔΔ+ΔΔ+ΔΔ+=
ΔΔ
=ΔΔ ∑
∞
=
tNtNtN
n
tNEtN
n
n
n ωωωωω , (5)
where nE – the Euler number.
Using first three terms of the series (5), we obtain the “restricted” direct Laplace transform, and then the
transfer function AVRMPC − will be presented at s≡Δω in the form:
.)51( 421 NNsKC AVRMP ++−= −
−
To ensure the robust stability and robust performance of SM excitation control it is necessary to find a
stabilizing controller such as [3]
( )( ) ( )( )
( )
sup , 1, inf sup , ,l lC sR R
F SM C j F SM C j
ω∈ ω∈
μ ω < μ ω⎡ ⎤ ⎡ ⎤⎣ ⎦ ⎣ ⎦ (6)
where μ – structural singular values of the matrix ( )( )ωjCSMFl , , ω – frequencies of the electromechanical transient,
SM – transfer function (matrix) of the SM model, C – transfer function (matrix) of the excitation controller model. The
maximum μ of the many input-many output (MIMO) system is considered the worst gain in the worst direction. The
requirement of the robustness of excitation control system is achieved with a large feedback gain in low frequency range
and with small values of the feedback gain in the high frequency band. If the conventional notations for sensitivity
function ( )ωjS and complementary sensitivity function ( )ωjT are used [3]
( ) ( ) ( ) ( ) ( ) ( )
( ) ( )ωω
ωωω
ωω
ω
jCjSM
jCjSMjT
jCjSM
jS
+
=
+
=
1
,
1
1 ,
then the next trade-off must be executed
( ) ( ) 1=+ ωω jTjS .
ISSN 1607-7970. Техн. електродинаміка. 2014. № 5 43
Therefore it is necessary to maintain these functions’ values low enough at the appropriate points in time which
correspond to the stages of the operation modes. Also, in accordance with Bode's stability criterion [3], the feedback gain
should be less than 1 at the critical frequency wherein the closed loop’s phase delay is 180º. In order to achieve this aim,
the gain N is introduced in the MP-AVR, thus in the feedback the polarity change at rotor angle deviation N2/πδ >Δ is
achieved. After some substitution in the first of the expressions (6) we can obtain the inequality that allows to determine
the vector of parameters ),( NK for MP-AVR, depending on the transfer function of the nominal model SM.
Conclusions. The non-complicated structure of the nonlinear MP-AVR with complex input signal is proposed.
The parameters of such signal are used to regulate the terminal voltage magnitude and to damp the SM's
electromechanical oscillations. The control law and transfer function of MP-AVR are presented. The conditions of the
robustness of excitation control system are determined. Experimental studies have confirmed the effectiveness and
robustness of the proposed MP-AVR.
1. Butkevych O.F. Problem-oriented monitoring of Ukrainian IPS operation conditions. // Tekhnichna Elektrodynamika. −
2007. − No 5. − Pp. 39-52. (Ukr.)
2.Kundur P. Power System Stability and Control. − New York: McGraw-Hill, 1994. − 1176 p.
3. Skogestad S., Postlethwaite I. Multivariable Feedback Control Analysis and Design. − Chichester: John Wiley&Sons,
2001. − 572 p.
4. Yurganov A.A., Kozhevnikov V.A. Excitation Control of Synchronous Generators. − St.-Petersburg: Nauka, 1996. − 138 p.
(Rus)
УДК 621.311
СТІЙКІСТЬ ЕНЕРГОСИСТЕМИ ТА РОБАСТНІСТЬ КЕРУВАНИЯ ЗБУДЖЕННЯМ СИНХРОННОЇ
МАШИНИ З АМПЛІТУДНО-ФАЗОВИМ РЕГУЛЯТОРОМ НАПРУГИ
О.Ф. Буткевич1, докт.техн.наук, О.М.Агамалов2, канд.техн.наук
1−Інститут електродинаміки НАН України,
пр. Перемоги, 56, Київ-57, 03680, Україна.
e-mail: butkevych@ied.org.ua
2−Taшлицька гідроакумулююча електростанція,
Южноукраїнськ, Україна.
Визначено умови, необхідні для забезпечення робастної стійкості та робастного керування збудженням син-
хронної машини з амплітудно-фазовим автоматичним регулятором напруги. Бібл. 4, рис. 1.
Ключові слова: стійкість енергосистеми, синхронна машина, вектор напруги, амплітудно-фазовий регулятор
напруги, робастність.
1. Буткевич О.Ф. Проблемно-орієнтований моніторинг режимів ОЕС України // Техн. електродинаміка. – 2007. − №
5. – С. 39-52.
2.Kundur P. Power System Stability and Control. − New York: McGraw-Hill, 1994. − 1176 p.
3. Skogestad S., Postlethwaite I. Multivariable Feedback Control Analysis and Design. − Chichester: John Wiley&Sons,
2001. − 572 p.
4. Юрганов А.А., Кожевников В.А. Регулирование возбуждения синхронных генераторов. – СПб.: Наука, 1996. – 138 с.
УДК 621.311
УСТОЙЧИВОСТЬ ЭНЕРГОСИСТЕМЫ И РОБАСТНОСТЬ УПРАВЛЕНИЯ ВОЗБУЖДЕНИЕМ
СИНХРОННОЙ МАШИНЫ С АМПЛИТУДНО-ФАЗОВЫМ РЕГУЛЯТОРОМ НАПРЯЖЕНИЯ
А.Ф.Буткевич1, докт.техн.наук, О.Н.Агамалов2, канд.техн.наук
1−Институт электродинамики НАН Украины,
пр. Победы, 56, Киев-57, 03680, Украина.
e-mail: butkevych@ied.org.ua
2−Taшлыкская гидроаккумулирующая электростанция,
Южноукраинск, Украина.
Определены условия, необходимые для обеспечения робастной устойчивости и робастного управления воз-
буждением синхронной машины с амплитудно-фазовым автоматическим регулятором напряжения.
Библ. 4, рис. 1.
Ключевые слова: устойчивость энергосистемы, синхронная машина, вектор напряжения, амплитудно-фазовый
регулятор напряжения, робастность.
Надійшла 25.02.2014
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