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EFFECT OF SEMICONDUCTOR-CONTROLLED VOLTAGE INJECTION
BY UPFC AND W C ON
PO'WER SYSTEM S W n l r r r
bY
Ihlireza Alavian Mehr
A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy,
Graduate Department of Electrical and Compter Engineering UniversiSr of Toronto
@ Copyright by Alireza Alavian Mehr 1998
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EFFECT OF SEMICONDUCTOR-CONTROLLED VOWAGE INJECTION
BY UPFC AND UETC ON
POWER SYSTEM STABILITY
Doctor of Philosophy Degree, 1998
AIireza Alavian Mehr Department of Electrical and Computer Engineering
University of Toronto
Commercial availability of various power semiconductor switches indicates
proliferation of power electronic based apparatus in utility power systems.
Furthemore, existing power system apparatus, e-g. mechanical phase shiRers
and mechanical tap changing transformers, will be retrofitted to utilize higher
switching speed of serniconductor switches. A group of these apparatus, i.e.,
unined power flow controuer W F C ) , static phase shifter (SPS), under-load
tap-changing (ULTC) transformer and static series capacitor (SSC), perform their
respective functions by means of injecting series controlled voltages in power
systems.
This thesis demonstrates that fast series voltage injection, for dynamic power
flow regdation, can result in voltage dynamics and even voltage instability. This
indicates that fast voltage injection by means of power electronic based apparatus
can couple voltage stability and angle stability phenomena. To investigate this
couphg phenomena, the voltage dependency of the load must be adequately
represented in the load model. The reported studies in this work is based on
representing the load by a combination of static and dynamic loads.
This thesis primarily investigates impacts of UPFC and semiconductor-
controlled ULTC on voltage stability and angle stability phenomena. An eigen
analysis approach is used for the studies. The eigen analysis results are validated
by digital the-domain simulations using a transient stability sofhare. Both the
eigen analysis and the transient stabdity software tools are tailored to account for
angle and voltage stability phenomena.
iii
Acknowledgments
1 wish to express m y sincere gratitude and appreciation to my supervisor,
Professor M.R. Iravani for his invaluable guidance, support and encouragement
throughout the preparation of this thesis.
1 extend m y appreciation to the members of my Ph.D. committee for their
carefid review of m y thesis and for many useful comments.
1 also thank graduate students and staff in the Power Group at the University
of Toronto for creating an atmosphere of friendship, mutual understanding and
cooperation. Special thanks are due to Dr. M. Parniani, Di. A. Nabavi-Niaki,
Dr. H. Karshenas, Mr. A. Mousavi and Mr. M. Tartibi for their helpful discussions
and suggestions.
Financial support f?om the Iranian Ministry of Culture and Higher Education,
and also from the University of Toronto are gratefully acknowiedged.
1 am grateM to my parents for their continued love, support and patience
throughout my studies.
The last but not the least, 1 offer m y heartfelt thanks to m y d e Fahimeh and
to my son Mshin for their invaluable encouragement and understanding.
Contents Abstract
Acknowledgments
Contents
CHApTExc1 1
Introduction ........................................................ 1 1.1 Overview ................................................................................................... . 1 1.2 Objectives ....................................................................................................... 3
1.3 Thesis organization ...................................................................................... 3
c-2 4
Methods of Analyses of Voltage Instability ............................. 4 Introduction ...................................................................................................... 4
Voltage Collapse ............................................................................................... 5
Voltage Instability Analysis ............................................................................ 6
Static Approach ................................................................................................ 7
........................*........ .. ...... 2 .4.1 V-Q SeILSitivity .. ... -8 ..................................................................... 2.4.2 Singdar Value Decomposition 8
......................................................................................... 2.4.3 Modal Analysis 1 0 ........................................................................... 2.4.4 Continuation Power Flow II
.................................................................. Small-Signal Dynamic Approach 12
.................................................................. Large-Signal Dynamic Approach 12
.................................................................................................... Conclusions 13
CHAPTER 3 15
System Representation for Simultaneous
................................... Voltage rrnd Angle Stability Study -15
.................................................................................................... 3.1 Introduction 15
........................................................................ 3.2 Synchronous Machine Model 16
3.3 Induction Machine ................................................................................... 18
3.4 Static Load Model ......................................................................................... 20
....................................................................... 3.5 Transmission Network Model 21
.................................................. 3.6 Mode1 of Conventional ULTC Transformer 22
................................................... ......................... 3.6.1 Principle of Operation ., 22 3.6.2 ULTC Mode1 ................................................................................................ 24
........................................................... 3.7 Model of Phase ShiRing Transformer 25
................................................................. 3.8 Static Phase ShiRer (SPS) Mode1 28
3.8.1 UPFC Mode1 ................................................................................................ 30 ................................................................... 3.8.2 Reduced-order Mode1 of UPFC 33
3.9 Mode1 of Two-terminal HVDC Systems ....................... .. ........................ 34
3.10 System Equations .......................................................................................... 37 .................................................................... 3.10.1 Eigen Analysis S o h a r e Tool 37
............................... 3 .10.2 Transient Stability Software Tao1 .................... ... -38
................................................................................................... 3.11 Conclusions 38
C-4 40
................ Impact of Fast Voltage Regdation on Voltage Stability -40
........................................................... ....................... 4.1 Introduction ...... .... 40
...................................... 4.2 Voltage Behaviour Under Steady-State Operation 41
......................................... 4.3 Voltage Behaviour Under Dynamic Conditions 4 4
4.3.1 Effect of Conventional and Fast Voltage Regulator .................................................................................. on Voltage Dynamics 46
.................................................................................... 4.3.2 Region of Attraction 48 ................. 4.3.3 Effect of Limits of a Voltage Regulator on Voltage Dynamics 51
...................... 4.3.4 Effect of UPFC overd time constant on Voltage Stability 53
4.4 Conclusions .................................................................................................... 53
c-5
Effect of Semiconductor Controiled ULTC
...................................... on Voltage and Angle Dynamics 54
.................................................................................................... 5.1 Introduction 54
5.2 Study System ................................................................................................. 54 .......................................................... 5.3 Effect of ULTC on Voltage Dynamics 55
................................... 5.3.1 Effect of Load Composition on Voltage Dynamics -58 .............................. 5.3.2 Effect of Transmission System on Voltage Dynamics 61
....................................................... 5.3.3 Effect of ULTC on System Dynamics -63 5.3.4 Combined Effect of ULTC and Transmission Network
on System D y n d c s ..................... .. ....................................................... 66
............................................................ 5.4 Validation of Eigen Analpis Resulta 68
.............................................................................................. 5.4.1 Software Tool 68 ............................................. 5.4.2 System Mode1 for Time-Domain Simulation 69
C-6 77
........................ EfEect of UPFC on Voltage and Angle Dynamics 77
................................................................. 6.1 Introduction .............................. .,., 77
6.2 Study System ................................................................................................. 78
6.3 Principles of Voltage Stability Enhancement by Means of a UPFC ........... 78 6.4 UPFC Control System ...................... .. .................................................. 80
........................................................ 6.4.1 Effect of UPFC on Voltage Dynamics 84 .............................. 6.4.2 Effect of System Configuration on Voltage D ynamics 85
..................... ..................... 6.4.3 Validation of Eigen Analysis Results ......... 87
................ 6.5 UPFC Control Strategy to PreventMitigate Voltage InstabiEty 90
.................................................................... 6.6 Voltage Stability Enhancement 94 ........................................... 6.6.1 Effect of UPFC on Voltage Dynamics ..... 94
.................................................................................................. 6.7 Conclusions 9 8
CEAP'mR7 100
.................. Conclusions and Recornmendations for Future Work 100
7.1 Conclusions .................................................................................................. 100
............................... 7.2 Suggestions for Future Work .. .................................. 102
...................................................................... A . 1 Synchronous Machine Mode1 107 ......................... .......................... A . 1.1 Stator Dynamics Not Included ...... 1 0 7
........................................................................ A.1.2 Stator Dynamics hcluded 113
....................................................................................... A.2 Induction Machine 117 ............................................... ..................................... k2.1 SimplXed Mode1 ... 118
.............................................................................................. A.3 HVDC System 122
.................................................... B . 1 Data for the Power System of Chapter 4 126
B.2 Parameters of the AC/DC Test System of Chapter 5 ................................. 127
B.3 Parameters of the Exciters of Chapter 5 .................................................... 128
v i i
Chapter
Introduction
1.1 Overview
Stability problems of interconnected power systems are traditionally
addressed under either (1) voltage stability problems or (2) angle stability
problems. Angle stability deals with electromechanical oscillations which are
closely associated with real-power flow Voltage stability deals with oscillatory or
monotonie variations of voltage, and primarily is due to insufficient reactive
power a t load centers.
Voltage instability, as compared with angle instability, is a relatively slow
process, such that the time span of a typical voltage collapse is in the range of a
few seconds up to tens of minutes. To the contrary, angle instability can occur
within a fraction of second to about a few seconds. Due to the major difference in
the time-intervals associated mith the phenomena of voltage and angle
instability they are treated and investigated as decoupled phenomena.
Conventionally, angle instability phenomenon is treated as a dynamic
phenomenon and voltage-instability is dealt with as a (quasi-) steady-state
phenomenon.
A widely accepted approach for enhancement of voltage stability is to inject
reactive power (VAR allocation) a t critical nodes of the system. There are
various techniques proposedladopted for enhancement of angle stability. These
indude utilization of semiconductor-controIled appmatus, e.g. static VAR Compensator
(SVC), thyristor-controlled series capacitor (TCSC), STATCOM, Unified Power Flow
Controller (UPFC), Static Series Capacitor (SSC), Static Phase-ShiRer (SPS), and
semiconductor-controlled Under-Load Tap Changing (ULTC) transformer. Selection of
either of these apparatus for angle stability enhancement depends on specific conditions
of the system under consideration, e.g. system configuration and the steady-state
function of the apparatus.
SVC and STATCOM inject reactive power in the system and enhance angle stability
by regulating the corresponding terminal voltage at a desired value. Either of SSC, SPS,
UPFC and ULTC injects a controlled series voltage in the system and enhances angle
stability by means of regulating phase-angle andlor magnifxde of the injected voltage.
For ease of reference, this group of apparatus which are capable of injecting controlled
series voltage in a system are referred to as dynamic voltage regulators (DVRs). TCSC
assists in angle stability enhancement through dynamic control of the series impedance
of the corresponding transmission Iine.
- The main objective and contribution of this work is to demonstrate that fast voltage
injection by means of DVRs, primarily for enhancement of angle stabiliQ can result in a
strong coupling between voltage stability and angle stabilitg phenornena. This indicates
that enhancement of angle stability by a fast acting DVR can lead to voltage instabiliw,
unless appropriate precautions are in place. This coupling phenomenon has not been
reported in the technical Eterature and the reasons are:
(1) Introduction of SSC, SPS, UPFC and thyristor-controlled ULTC in power systems is
a relatively new idea and no operational experience exists.
(2) This coupling phenomenon cannot be detectediinvestigated by existing
analytical (eigen analysis) and time-domain simulation tools. The reason is that
existing production grade bols are not capable of representing adequately the
load dynamics with respect to voltage phenomenon in the systern model.
The other contribution of this thesis is the enhancement of the existing eigen analysis .
and transient stability (TS) software tools to demonstrate the coupling phenomenon in a
large realistically sized power system. This thesis concentrates on the impact of fast voltage regulation, by means of UPFC, SPS and semiconductor-controlled ULTC, on
voltage and angle instabiliity phenornena.
1.2 Objectives
1.2 Objectives
The main objectives of the thesis are:
To explain the detrimentai effect of fast DVRs on the phenomenon of voltage
ins tability.
To demonstrate voltage instability phenomenon when either UPFC, SPS or
thyristor controlled ULTC is adopted for angle stabiliw enhancement in a
realistic sized and interconnected system.
To develop analytical (eigen analysis) and digital time-domain simulation tools
capable of demonstrating couphg between voltage and angle stabiliw
phenomena.
Chapter 2 provides an overview of existing methods for investigation of voltage
instabiliw and their limitations.
Chapter 3 introduces component models used for simultaneous investigation of
voltage and angle stability phenomenon. This chapter also briefiy introduces the eigen
analysis software tool and the transient stability software tool which have been
developed for investigation of coupling phenomenon between voltage and.angle
dynamics.
Chapter 4 presents the concept of voltage instability due to fast voltage control by
means of DVRs.
Chapter 5 demonstrates the effect of conventional (mechanical) under-load
tap-changing (ULTC) transformer and fast (semiconductor-controlled) ULTC on voltage
and angle instability phenomena. The studies are conducted o n a real size,
interconnected power system.
Chapter 6 investigates the effect of a UPFC on voltage and angle instability
phenomena. The studies are d s o conducted on a real sized power system.
Final conclusions are summdzed in Chapter 7.
Chapter
Methods of Analyses of Voltage Instability
2.1 Introduction
The phenornena of voltage instabilitg/collapse have been observed in power
systems and analyzed extensively during the past decade [1,2,3]. The
seriousneas of the consequences of these incidences presents strong motivations
for research in the causes of voltage instabilities. Normdy, a large number of
parameters and device controllers are involved in the performance and
dynamics of a power system with respect to voltage instability, and voltage
dynamic (instability) phenomenon can be observed and investigated in
realistically sized power transmission/distribution systems. The objective of this
chapter is to provide an oveMew of the existing techniques for investigation of
voltage dynamic phenomenon.
The primary function of an electrical power system is to generate power at a
satisfactory voltage and fiequency for the consumer. In the early development
stages of electriciQ the generators were situated close to the consumers and
very simple electrical networks were sufficient to Mfil this function. With the
increasing demand for electrical energy, considerable new developments
occurred on the electrical systems. The electricity supplied to consumers
increased in both magnitude and the geographicd area covered. The size of the
generators increased and higher voltage transmission networks were
superllnposed over the lower voltage distribution networks. Interconnection of
2.2 Voltage Collapse
electricie suppliers made it economically more attractive to locate generators at sources
of coal or water power at considerable distances from the consuners. Thus, instead of a
simple network between the generator and the consumer, a fa r more complex
transmission system is utilized.
The elements of a transmission system consume more reactive power as an attempt
is made to transfer more real power. Therefore, although the basic function of an
electrical system remains unaltered, namely, to deïiver power from the generator to the
consumer, in the interconnected power systems, another essential consideration is to
supply the reactive power to the intemediate elements of the system. As the reactive
losses of the elements are proportional to the square of the current components passing
through them, the reactive requirement of a power system can alter drastically with the
real power variations of the load.
As transmission line voltages are increased, greater conductor spacings are
necessary, thus creating higher line reactances which results in higher reactive losses
and higher line voltage drops. Thus, EHV transmission installations have increased the
reactive power requirements of a power system relative to the real power demand to such
a degree that the gross reactive power demand of a power systern is in the same order of
magnitude as the real power demand. EHV transmission systems are usually developed
for systems with major power stations remotely located from load centres. In such
developments, the significant reactive reserves carried by these generators is attenuated
by the relative high reactances between the generators and the loads. The tripping of a
heavily loaded E W line produces a major increase in the system reactive demand, and
may eventudy cause voltage collapse in the bulk power system.
2.2 Voltage Collapse
Stability is one of the most important issues in a power system operation and control.
Behavior of active power has been studied by the conventional stabilitp criteria, such as
steady state stability, dynamic stability, and transient stability. Voltage stability is
associated with the abiliw of a power system to maintain bus voltage magnitudes within
specifïed operating limits. hadequate voltage control has caused major blackouts in
some of the existing power grids which have been very costly to the systems [3,4].
Inability of the power systems to supply the required reactive power demands are
evident in al l the reported incidents.
Voltage collapse & a power system can occur following a sudden increase in reactive
2.3 Voltage I m a bility Analysis
power demand if there are inadequate effective reserves available. The scenarios of
voltage collapse situations in a power system vary depending on the nature of the system
and disturbances applied to the system. A conventional voltage conapse scenario has a
pattèrn as follows [l,2,3].
Assume that a power system is under medium to heavy load demand and certain key
transmission lines are more heavily loaded than their normal conditions. Voltage
instability, and eventually voltage collapse, can be triggered by loss of a heavily loaded
transmission line, loss of a generator and so on. Such disturbances impose a
substantially higher reactive power demand from the system by the extra loading of the
remaining lines, thus, resulting in voltage drops throughout the power system. The voltage levels will be quicldy restored at the power stations by the generator voltage
control systems, but will be below the required levels at the Ioad centres. Then, the MW
and MVAr of the system generators will increase. The transformer taps a t the load
centres will be raised to their maximum settings to restore the load voltages. Thus, active load demand inmeases, and results in further voltage &op dong the transmission lines.
Therefore, installed capacitor banks and the transmission iine capacitances supply less
reactive power. Consequently, some or dl the system generators will reach their full
excitation levels, and the generator terminal voltage will decrease. If the voltage level
drops below the critical value, protection systems trip the overloaded generators, which in turn will trigger a cascading drop of voltage and eventually the initiation of a
widespread voltage sagicollapse.
2.3 Voltage Instability Analysis
Voltage stability is the ability of a power system to maintain a steady acceptable
voltage at each bus under normal operating conditions, and aRer being subjected to a
disturbance. A system enters a state of voltage instability when a disturbance; e.g., an
increase in the load demand or a change in the system conditions, causes a progressive
and uncontrollable voltage decrease 151. The &EE working group on voltage stability has defined voltage stability as the ability to maintain voltage so that when load admittance
is increased, load power will increase, and both power and voltage are controllable [3].
Based on the time frames of the reported voltage collapse incidences, voltage
instability can be categorized as transient and midterm voltage instability. The time
fiame involved in transient voltage instabiiity is nom fiactions of seconds to several
seconds. Induction motor dynamics aiid HVDC converters can be the major causes of
2.4 Static Appmach
instabilities in this t h e frame [3,6].
A voltage dip in the transmission system results i n more reactive demand by
induction motors, and in the stalling of induction motors, which worsens the voltage
instability condition. In this time fiame, generators and induction motors, due to their
dynamic interactions, should be represented as dynamic devices.
Midtem voltage instabilie has a time fiame of a few minutes. Load tap changers,
over-excitation of generators, load buildup by loads with constant energy controllers are
the main causes of voltage instabilities in this tirne name.
For the evaluation and analysis of voltage stability of power systems, three dinerent
approaches have been considered:
(1) Static approach
(2) Sm&-signal dynamic approach
(3) Large-signal dgnamic approach
A brief discussion of each approach folIows.
2.4 Static Approach
The static approach is based on dgebraic equations such as load flow equations. It
includes either a sensitivity analysis such as dQ/dV and dE/dV [7,8], a multiple load
flow solutions approach [9] or a feasibility of load flow [IO]. In a static approach, the
feasibiliw region, defked as the region with feasible load flow solutions, is studied. The
steady state region SS is described as [11,12]
SS(N) = { U ] ( U E FR) A ( y e S y ) )
where cl is the system driving function such as Vmf and omf. FR denotes the feasibility region given by
where x is a vector of state variables such as generator angle 6, anguiar frequency q generator interna1 voltage E, stator and rotor flux Y and system voltages Il In (2-2), h is a set of nonlinear fùnctions of the transmission system, and N is the network varying parameters.
The region in which all the operating limits are saeisfied, is given by S, such that:
where y is a vector of system variables, e.g. bus voltages, line fiows and reactive power
supplies, g(k,u) is a set of nonlinear functions of operating constraints.
To determine the voltage stability margin, the system is stressed until voltage
instability occurs. System conditions at different stress levels are obtained by solving the
load flow equations- In this approach properties such as sensitivities, existence and
multiple solutions of power flow equations are studied [13-161.
Various techniques based on the static approach have been developed for voltage
stability studies as described in the following sections.
V-Q sensitivi@ technique is based on sensitivity of bus voltage magnitude to reactive
. power injection at the same bus. A positive V-Q sensitivity means that the voltage at the
bus increases if reactive poweris injected into the bus. The system is voltage stable if all
V-Q sensitivities of the system buses are positive, and the system is unstable if V-Q sensitivity is negative for at least one bus.
V-Q sensitivity method does not identify unstable modes of the system. GeneraUy.
systern voltage instability does not occur due to voltage fluctuation of individual buses,
rather for individual modes to which each bus participates. Since the V-Q sensitivity
method does not give the unstable modes, it has limited application in the study ~f
voltage instability.
2.4.2 Singular Value Decomposition
The linearized steady state system equations are [19,20]
where, incremental change in bus real power injection,
incremental change in bus reactive power injection,
incrementd change in bus voltage angle,
AV = incremental change in bus voltage magnitude.
The jacobian matrix, 4 in the above equation contains the first derivatives of the
active power part, P. and reactive power part, Q, of the power flow equations with respect
to voltage magnitudes, V; and node angles, 8. If singular value decomposition is applied
to the power flow jacobian matrix, 4 then the matrix decomposition can be written as
i = t
- where n x n orthogonal matrices U and W are the right and left singular vector matrices
of J. The singular vectors ai and coi are the columns of the matrices U and W respectively,
and C is a diagonal matrizr with
where 0, 2 O for all i. The diagonal elements in the matrix Z are ordered so that
The minimum singular value, G, (J) , is a measure of how close toa singularity the power flow jacobian m a t h is. If the minimum singular value is equd to zero, then the
studied matrix is singular and no power flow solution can be obtained. The sin&&@ of
the jacobian matrix indicates that the inverse of the ma& does not exist. This can be
interpreted as an infinite sensitivity of the power flow solution to small perturbations in
the parameter values. At the point where on (J) = O several branches of equilibria corne together and the studied system will experience a qualitative change in the
structure of the solutions due to a small change in a parameter value. This point is called
a static bifurcation point of the power system [21-241.
The [AB ~ f j vector is then computed as
The inverse of the minimum singular value, a;', fkom a small disturbance point of
view, indicates the largest change in the state variables. Let
where un in the last colllmn of U. Then,
where w, is the last column of W. Voltage stability can be evaluated by on, un, and w,.
The smallest singular value, on, is an indicator of the distance to the steady-state
stability b i t . Also, un and w, corresponding to an indicate the most sensitive direction for changes of active and reactive power injections and sensitive voltages.
The modal analysis technique involves the computation of a small number of
eigenvalues and the associated eigenvectors of a reduced-order of the steady state
jacobian mat* of a power system [25]. The magnitudes of eigenvalues provide a relative
measure of proximity to instability. The eigenvectors, on the other hand, provide
information related to the mechanism of loss of voltage stabilitp.
Voltage stabiliw is afZected by both P and Q. Nevertheless, at each operating point we
can assume P t o be constant and evaluate voltage stability by considering the
incremental relationship between V and Q.
In (2-71, let
then
and,
where, .
J~ = JQV- J Q ~ J ; ~ JPV (2-13)
JR is cded the reduced jacobian matrix of the system, and it directly relates changes
in bus voltage magnitudes to increments in reactive power injection at the buses. Let,
where,
Therefore,
JR = R U
R = right eigenvector ma* of JR,
L = left eigenvector ma& of JR,
A = diagonal eigenvalue matrix of JR.
2.4 Static Approach
(2-14)
where Ri is the ia right eigenvector, and Li is the i* leR eigenvector of JR-
The magnitude of each eigenvalue determines the weakness of the corresponding
rnodai voltage. The srnaller the magnitude of X, the weaker the corresponding modal
voltage. If [Ail = 0, the i* modal voltage will collapse.
Singular value decomposition (SVD) technique and modal analysis technique
examine voltage stability of modes. Both techniques provide information regardhg the
voltage instability of the entire system.
2.4.4 Continuation Power Flow
The continuation method (or pathfinding method) is another class of methods for
soiving nonlinear steady-state equations which are used to determine voltage instability of power systems [26].
Multiple power flow solutions are likely to appear under heavy load conditions [9].
This is related to voltage instabüiQ especially when a pair of solutions are located close
to each other. However, when used to analyze voltage instability problems, most
conventional power flow tools break d m . The continuation power flow is a bo l capable
of dealing with the mathematical problems encountered during the analyses of voltage
problems.
Consider the solution of n nonlinear algebraic equations f ( x ) = O , where x is a
vector of n unknowns. Using the path-hding method, the problem is solved by analmg an easier version of the original problem, and then adding to the complexity until it becomes the original one.
2.5 Small-Signal Dynamic ApprocrcA
2.5 Small-Signal Dynamic Approach
In the analysis of voltage instabilities based on small-signal dynamic approaches,
dynamic devices are represented by differential equations, and then the linearized
differential equations dong with those representing the static part of the system are
solved to examine voltage stabiliw [1,17,18]. These linearized models are obtained nom a
nonlinear system model, which can be described as:
Machine and load dynamics: x' = f (x . u, t) Transmission System: h ( x , u,t) = O
Operating conditions: g ( x , u. t ) 5 0
From the dynamic equations of machines and loads, the general form of the
hearized dynamic model is:
hz' = L(X,U,N)AX+H(X.U,N)AU (2-19)
where hr, and Au are perturbations about an operating point. L(x,u,N) and H(xyuyN) are the linearized system and input matrices which depend on the states x, inputs u and the
network N. Since the system model is hem, the region of stable solutions of (2-19) in the
u space can be defïned by
where & is the ilh eigenvalue of L(x,,uJV).
2.6 Large-Signal Dynamic Approach
Most of the investigations associated with voltage instability involve the steady-state
response of the power system. This is as a resdt of the fact that the dynamics of a voltage
collapse process is complicated and has not been thoroughly understood. It is clear that
the voltage collapse dynamics cannot be descnbed solely by generator dynamics which is
traditionally believed to be responsible for transient angle instabiliw.
Various system components are involved in the dynamics of voltage collapse.
Unfortunately, the computation of the dynamics for large scale systems is an extremely
time consuming task and for some systems practicdly impossible. The key in this type of
analysis is to find the critical dynamic components. One approach to achieve this goal is
to eliminate the dynamic states which do not contribute to the a i t i ca i states.
2- 7 Conclusions
Conventionalls three mechanisms are assumed to play major roles in the dynamics of
a voltage collapse process. These are tap-changer dynamics, load dynamics particularly
those involving large percentage of induction motor loads, and generator field excitation
dgnamics [31. There are cases where the operating Iimits for a voltage collapse may not
be determined based on the system static models. This occurs when a static mode1 cannot
predict whether the system is stable or unstable at the bifurcation point.
Most multimachine dynamics can be described by a set of equations of
differential-algebraic form:
where r is a set of state variables, andy is a set of system variables and parameters. These differential-algebraic set of equations should be solved by digital time-domain techniques.
It is essential to employ appropriate models of the system components for evaluation and analysis of system voltage stability In this thesis, appropriate models for voltage stability analysis are introduced, and the voltage instability phenomenon caused by
interactions due to loads, ULTCs, UPFCs, AC/DC transmission systems and generators are analyzed using s m d signal and large signal dynamic methods described here.
2.7 Conclusions
A comprehensive review of the technical literature related to the phenornenon of
voltage stability in power systems reveals that voltage phenomenon is conventionally
viewed as a quasi-steady-state phenomenon. Therefore, extension of steady-state
andysis techniques are used for investigation/prediction of voltage collapse. Roliferation
of semiconductor-controlled power apparatus, e.g., HVDC converters, dynamic voltage
regulators, (DVR), static phase shifters, static under-load tap changers and unined power
flow controllers indicate that voltage dynamics cannot be viewed as a quasi-steady-state
phenomenon. This is as a result of rapid reactive power exchange among various
locations within a power system by means of semiconductor controlled devices. To the
best of our knowledge, as of now, no comprehensive investigation regarding the Wpact of
semiconductor-controlled devices on voltage dynamics has been published. The reasons
are: (1) analytical approaches and the corresponding existing software tools for
investigation of power system dynamics do not have adequate capabilities to represent
2-7 Conclusions
semiconductor-controlled devices and loads with respect to voltage dynamic
phenomenon, and (2) there are not enough operational experience and measurement
results to reveal the importance of the issue. It shodd be mentioned that a few reports
dealing with the phenomenon of voltage dynamics due to HVDC converter systems have
been recently published, which ernphasize the need for investigation of voltage stabiliw as a dynamic phenomenon.
Chapter
System Representation for Sirnultaneous Voltage and Angle Stability Study
rn 3.1 Introduction
The objective of this chapter is to introduce power system component models
and an overall system representation necessary for dynamic voltage stability
studies. The components are divided into two groups. The first group includes
conventional components, e.g., synchronous generators and transmission
networks. The second group consists of those components whose behaviors c a n
directly contribute and/or result in voltage instability. This group includes
induction machine loads, static loads with voltage dependency, under-load
tap-changers (ULTC), phase-shifting transformers, static phase shiRers (SPS), unifïed power flow controllers (UPFC), and HVDC converters.
This chapter introduces equivalent models of power system apparatus for
investigating voltage dynamics based on an small singnal stability approach
(linearized model) and a transient stabiIity simulation approach (nonlinear
model). When low-frequency dynamics, Le., f < 2 Hz, are of cancern, the
dynamics of transmission lines can be neglected and consequently the overall
system mode1 is substantially simplified. This chapter also provides the
component models when only low-Eequency dynamics are of concem.
3.2 Synchmnous Machine Model
Figure 3.1: Synchmnous machine d-axis and q-axis equivdent circuits
3.2 Synchronous Machine Model
Figure 3.1 shows the equivalent circuit representation of a synchronous machine in
the corresponding rotor d-q &ame [2q. The stator ia represented by one winding per axis.
The rotor is represented by (1) one equivalent damper circuit and one field winding on
the d-axis, and (2) two equivalent damper circuits on the q-axis. Based on the equivaent circuits of Figure 3.1, the dynamic behavior of the electrical system of the machine is given by (3-1) to (3-6).
3.2 Synchmnous Machine Mode1
where v, i, and R with d or q indices in (3-1) to (3-6) refer to the voltage, current, flux,
and resistance in d- or q- axes, respectively a> and CO, are rotor angdar frequency and the base angular fiequency of the synchronous machine. Also, indices f , 1, and 2 refer to the
field circuit and damper windings, and Ra is the armature resistance. Further details of (3-1) to (3-6) are given in Appendix A. The mechanical system of a synchronous machine which includes rotor body, rotating exciter and turbine sections is represented by a single
mass and its dynamics are given by (3-7) and (3-8).
where, H, Tm, kD and S are the inertia constant, mechanical torque, damping factor, and
the rotor angle of the synchronous machine, respectively The overall dynamic model of the synchronous machine, based on (3-1) to (3-8) is derived in Appendix A. Small-signal
dynamics of the machine is obtained by linearizing the &chronous machine differential
equations about an operating point. If the stator dynamics are neglected, the smd-signal model is given by
The pre-index i refers to the i-th synchronous machine variables, and As B, B, Cs, and Dus are given in Appendix A. AuDg and AiDQ are D-Q fkarne voltage and current vecturs
of the synchronous machine. QU includes control signals n o m governor and exciter se
systems. The vector of state variables is defined as
where 4 represents the state variables of the exciter system.
Small-signal dynamics of a synchronous machine, in the general case, when the
stator dynamics are included is given by
3.3 Induction Machine
where, the machine state variables are defïned as
Variables, input and output signals, and the associated matrices of (3-11) and (3-12)
are given in Appendix A.
3.3 Induction Machine
An induction machine as a nonlinear dynamic load has considerable impact on the
voltage dynamics of power systems. Consider an induction machine with a chosen
reference frame revolving at speed o. The machine equivalent circuits in the d and q axes
of the rotating reference fiame are shown in Figure 3.2 [28]. The machine dynamic mode1 is given by (3-13) to (3-19).
Figure 3.2: Equivalent circuits for an induction machine in a two axes rotating reference hune
3.3 Induction Machine
where or is the rotor angular fiequency, and a, is the base electncal angular fkequency. Indices s and r refer to the stator and rotor variables, respectively. m and TL are constants which depend on mechanical load. Te and Tm are the electrical and mechanical torques, and H is the inertial constant of the induction motor.
The small-signal dynamics of the induction machine j is developed from linearization
of (3- 13) to (3-19) about an operating point as given by (3-20) and (3-2 1); details are given in Appendix A.
Ai, = .c.(Az,) J J L~
where
,ATL is the mechanical load torque for the j-th induction machine. Matrices fii3 PiU pin and pi, are aiso given in Appendix A. If the stator dynamics are ignored, the
srnaIl-signal dynamic mode1 of the machine reduces to:
3.4 Static Load Madel
where,
/lin piun pin ,Ci,, and ,üiw are &O introduced in Appendix A.
3.4 Static Load Mode1
Voltage dependency of static loads is an important consideration in the phenornenon
of voltage dynamics. In general, a static load at bus Z including its voltage dependency
can be represented as [NI.
where, apb a~~ mi, and ni are constants which depend on the nature of the load. It should be noted that (3-24) and (3-25) are based on the assumption that network dynamics can
be neglected and the transmission network can be represented by algebraic equations which relate current and voltage phasors. If network dynamics are considered, then, static loads are mathematically modeled by ordinary differential equations and are represented as part of the network as will be described in Section 3.5.
Linearizing (3-24) and (3-25) provides a smd-signal mode1 of a static load:
where Ai, Aii, Au, and Aui are real and imaginary components of load current and voltage, and
3.5 Transmission Network Malel
3.5 Transmission Network Model
If network dynamics can be neglected, then algebrgc (phasor model) equations
representing relationships among network electrlcal quantities are used to represent the
electrical transmission network. In this case, the dynamics of machine stators are
neglected. Network dynamics can be neglected if only dynamics of interest are slow, e.g.
fkequencies about 2 Hz and less. This approach is used for network representation for
conventional angle stability studies.
If network dynamics are t o be taken into account, then each three-phase
transmission line is represented by its Ii model. Three-phase seriedparallel inductors,
capacitors and static loads are also represented by the corresponding lumped elements.
Thus the differential equations governing the dynamic behaviors of each set of
three-phase R, L and C components are developed. These equations are transformed into
the system globd d-q fiame as given by [28]:
u, = Ri,
where, (uJdq are the voltages and currents of the components in a dq frame. The overd network model is developed by combining the component equations and extracting a
state-space representation. It should be noted that the network state-space model is Iinear and consequently its small-signal and large-signal dynamics are given by one set of equations.
Ignoring the network dgnamics, inductor and capacitor equations will reduce to:
where XI and Y, are the reactance and susceptance of the network elements.
3.6 Model of Conventional ULTC Transformer
3.6 Mode1 of Conventional UlLTC Transfomer
3.6.1 Principle of Operation
F'dlowing a disturbance in a power system, normally, voltage a t the load side either
sags or rises; however, tap changing equipment starts to restore the load-side voltage to a
controlled level, and thus the load. Under ioad tap changing (ULTC) transformers and
distribution voltage regdators act similarly in regulating load-side voltage. A voltage
relay monitors load-side voltage. If voltage drifts, or jumps, outside a dead-band, a time
delay is energized. If the relay times out, the tap changing mechanism will be energized
and tapping takes place until the voltage is located in-band, or until the maximum or
minimum tap is reached. Once in-band, the voltage relay and timer mechanism are reset.
The fûnctional block diagram of a ULTC is shown in Figure 3.3, which consists of the
following elements [27] :
Tap changing mechanisrn driven by a motor unit,
Voltage regulator which consists of a measuring element and a time-delay
element
Figure 3.4 shows a block diagram of a ULTC ccntrol system. The measuTing element
Measured Voltages I I Tap Position
Reference Voltages
Figure 3.3: h c t i o n a l block diagram of ULTC
of the voltage regulator consists of an adjustable dead band relay with hysteresis. The input to the regulator is a voltage error, namely V,, .
Measuring Motor Drive
Unit
Tirne Delay - Element
Tap-Changer Element
3.6 Modd of Conventional ULTC Transfomer
The output of the measuring element is e, which takes values of O, 1, or - 1 , depending
on the input V, With a reguiator dead band of D and a hysteresis band of E, the output is:
O for -D 5 V,,$ D
O for D < V e , s D + e ; K, increasing
O for -D -E S Ver$-D ; Km decreasing
1 for V, ,>D+E
1 for DCV, , ,SD+E ; V, decreasing
-1 for Vorr<-D-&
-1 for -D-ESV',S-D ; Lincreasing
An adjustable time delay relay is used to reduce the effect of short-time voltage
Transformer
figure 3.4: Block diagram of ULTC control system
variations and to avoid unnecessary tap-position changes. The output of the time-delay
element is
O for t S Td; e arbitrary
1 for t > T d ; e = l
-1 for t > T d ; e = - 1
where Td is the adjustable time delay of the regulator. Td it is constant ( Td = Th ) for a regulator with independent tune delay. For a regulator with variable time-delay characteristics, Td is a function of initial tirne delay settïng Th, voltage error V, and dead-band D:
D Td = ,TT
err do
The motor drive unit and the tap-changer mechanism may be represented by a .
simple time delay TM inherent to the equipment. The output signal Ani represents an
incremental change in tap position, and is equal to O, 1, or -1. Incremental change of tap
. position hi in the i-th operation is:
O for tsTM p b arbitrary
1 for t > T M 3 b = l
-1 for t>TM 9 b = - 1
The per unit tums ratio after the i-th operation is
where Ani represents the per unit turns ratio step corresponding to a change in tap position by one step.
Figure 3.5 shows the tap changing logic for the tap movement. AV is the dead-band
and An is the step size corresponding to the tap movement logic of Figure 3.5. Each tap
change is a discrete t h e event. When the load-side voltage of a ULTC stays over V,+AV (or below V,-AV' for a certain time period, known as time-delay, the turns-ratio n is
decreased (increased) by hn. The continuous mode1 of the tapchanger can be represented
by the fist-order differential equation (3-35) which is the first-order approximation to
discrete t h e event tap changing.
3.7 Model of Phase Shifting Transformer
Figure 3.5: bgic'for tap movement of a ULTC
where T is the ULTC the-constant, and it is in the order of several seconds to minutes.
Having VI and V' representing the primary and secondas. side voltages of the
tap-changer, linearizing (3-35) and expressing it in a d q fkame, we deduce:
where - -
The primary and secondary voltages are related by:
Simiiar expressions relating currents at both sides of the tap-changer can be derived
as:
3.7 Model of Phase Shifting Transformer
A phase shifter injects a voltage in series with the transmission line voltage. The
injected voltage may be in quadrature angle, in-phase, or at any angle with respect to the
line voltage. The phase shifter's ability to control magnitude and phase angle of the
3.7 Model of Phase Shifing Transfomer
injected voltage is used to improve transient stabilitg, to eenhance damping and to control
steady-state power flow (29321.
A conventional phase-shifter can be approximated by a transformer having a complex
turns ratio, = nL0. Therefore, the voltage equations of a conventional phase shifter
in a d q fiame are:
Linearizing (3-39) about an operating point,
where indices 1 and 2 refer to the primary and secondary sides of the phase shif'ter, respectively 8 is the phase shift £kom the primary side to the secondary side of phase shifter; it is positive when Y1 leads V2, and
Similady, the current equation can be found to be:
Linearizing (3-41) leads to:
where
3-7 Model of Phase Shifting Transformer
It should be noted that the ULTC model is a special case of the phase shifting
transformer model given by (3-40) and (3-43) where phase shiR angle 0 is set equal to a
fuced value; i.e-, zero in this case.
In most practical system configurations, a phase shiRing transformer (or a ULTC) is
located at the texminal bus of the load for which voltage regdation must be carried out.
For such a condition, the load model and the phase shifting transformer model can be
combined and represented by a single mode1 as follows.
Consider a dynamic load with the atate space equations given by (3-22), and a phase
shifter which is represented by (3-36). Combining the load dynamic equations with the
ULTC or the phase shifber dynamic equation, and based on (3-40) and (3-42):
where, index 1 refers to the primary side of the phase shifter, and
The combination of load and phase shifter models is summarized in the block diagram of Figure 3.6.
3.8 Static Phase Shifier (SPS) Model
Figure 3.6: Block diagram of combination of dynamic load and phase shifter
3.8 Static Phase Shifter (SPS) Model
Figure 3.7 shows a schematic diagram of a phase shifter. The input to the phase
shifier is the three-phase voltage provided by an excitation transformer (ET). The output
of the phase shifter is a three-phase voltage (Vp) injected in the system by the series
boosting transformer (BT). The converter controls the magnitude andor phase-angle of
the injected voltage.
Converter l -
Figure 3.7: Schematic diagram of a static phase shiRsr
A conventional phase-shifter utilizes mechanical switches to control the injected
voltage Vp. A static phase shifter (SPS) utüizes semiconductor controlled converters ta
regulate the injected voltage. The speed of operation of a SPS is sigaincantly higher than
that of a conventional phase shifter. The impact of high speed voltage regulation, by
means of either a SPS or a thyristor controlled UETC, on voltage dynamics is the prime
concem of this fhesis work. There exists various power eIectronic converter topologies for
implementation in a SPS [29,35,40]. Principles of operations, limitations, and technical
merits of various SPS configurations have been reported in the technical fiterature [35]
and are not forther explained here. Among various circuit configurations proposed for a
SPS, the configuration shown in Figure 3.8 has attracted significant attention and is
referred to as Unined Power Flow Controller (UPFC). A UPFC uses two Voltage Source
Converters (VSCs) and a dc link as the interface between ET and BT. Each VSC has
independent control over phase-angle, magnitude and fkequency of its ac side voltage.
Depending upon the ccntrol strategy adopted, a UPFC can independently perforn the
following control fiuictions within a transmission system:
0 Line power flow regulation
Line reactive power flow regulation - Voltage regdation at bus B - Voltage regulation at bus E
Line , E
ET Inverter Inverter
figure 3.8: Schematic diagram of a UPFC
A UPFC is capable of performing the above functions during steady-state,
small-signal dynamics and large signal dynamics of power systems. Various control
strategies, applications and modelling requirements of a UPFC are addressed in E341. As mentioned previously, investigation of the impact of rapid voltage control at bus B of Figure 3.8, on voltage stabilitg, is one of the objectives of this thesis.
3.8 Static Phase S h i , , r (SPS) Mo&
figure 3.9: UPFC equivalent circuit at niadamental fkequency
3.8.3 UPFC Mode1 -
Based upon the principles of operation of a VSC, the UPFC of Figure 3.8 can be
represented by the equivalent circuit of Figure 3.9 1341. The circuit diagram of Figure 3.9
is a UPF'C representation only at the fundamental fiequency of operation. Fundamental
fkequency is defined as the nominal fiecpency of the power system. In Figure 3.9, each
VSC is represented by a three-phase voltage source and a unidirectional curent source
at the ac side and dc side respectively. Resistances and inductances identifg leakage
eiements of boosting and excitation transformers.
The three-phase voltages representing inverter 1 are expressed as [34]:
u,, = V,,cos (ot + 6,) Ueb = Vem Cos ( ~ t + 6e - 120') u,, = V,, COS ( ~ t + 6, - 240°)
1 where, V,, = ~ r n , v ~ , ; me and 6, are amplitude and phase angle of PWM control signal of the excitation inverter, and v h is the dc link voltage. Similar expressions are valid for
the boosting inverter with rnb and &, as the amplitude and phase angle of its control signal. With reference to Figure 3.9, the dynamic mode1 of the ac side can be written as:
" e a + reiea = us,, - V,,cos (ot + 6,)
3.8 Static Phase Shi'fter (SPS) ModeL
(3-47)
The dc iink dynamics are expressed by:
Equations (3-47) to (3-49) describe the overdl dynamic model of the UPFC. The UPFC mathematical model is expressed in a d-q frame, using matrix Pu as the transformation matrix.
3 Pu = diag {P, P, 2)
where P is the Park's transformation ma&
A state space small-signal model for the UPFC is obtained aRer transformation of
(3-47) to (3-49) to a dq name and linearization about an operating point:
3.8 Static Phase Shifter (SPS) Model
where,
A, = COI
1 1 1 1 B , = d i a g l y . p r g - 1
e e b b
3.8 Static Phase Shifter (SPS) Model
The state variables and control signals are:
3.8.4 Reduced-order Model of UPFC
Similar to the reduced-order equations of synchronous and induction machine, by
ignoring the network dynamics a reduced-order mode1 can be obtained for the UPFC. Denning,
equation (3-52) can be written as:
Let A i i , = O, then ikom (3-531,
3.9 M&l of ?ho-teminal NVDC Systems
A, = --5#-'9 I l 1
Bu, = -3#,'B,
Bu, = A, - S#r:A,
In order to combine UPFC model with the nefmork model, we d e h e a set of currents
pointing out f?om UPFC busses from both excitation and boosting sides as:
such that:
Moreover, (3-54) can be partitioned to separate indices related to the excitation and
boosting sides of UPFC such that
Ce, Cbv..., Dbm are sub-matrices obtained according ta the partitioning of (3-54). Substituting (3 -59) into (3-57) gives the 6nd output UPFC. currents:
Ai, = C,,Axvu + D,Avdq + D,AU,, (3-60)
where,
3.9 Mode1 of Two-terminal HVDC Systems
High voltage direct current transmission systems are integral parts of interconnected
power systems. HVDC connections are either in the form of a link, where the converter
stations are interfaced by a dc transmission line, or in the form of a back-to-back system,
where the converters are physically a t the same location. Multi-terminal HVDC systems
are not considered in this thesis. Operation of an HVDC converter either as a rectifier or
as an inverter is accompanied by consumption of reactive power. This reactive power is to
be provided by the system (transmitted to the converter station) or locally supplied by
capacitor banks, fdters and static (rotating) VAR generators. hadequate reactive power
at an inverter station can result in commutation failure and collapse of the EKûC Iink. Reactive power demaad of a HVDC converter under those operating conditions where
reactive power supply to the system is not optimal, can result in voltage instability and
even voltage collapse.
Neglecting harmonies and representing curent and voltages of a HVDC converter
only a t the fundamental fkequency, the equations that govem the relationship of current
and voltages of rectifier and inverter stations in a d q ficame are [26,27,36] :
- 3& 3 . "' - 'q Di i COS yi-EX,iti
where i,, i i , u, and vi are dc currents and voltages at rectifier and inverter sides. T, and Ti are tap changers of rectifier and inverter bridges:~, and vii are ac side voltages at
rectifier and inverter bridges. COS@, and cos(+ are the power factors given at the ac sides of the rectifier and inverter terminais. a, and yi are the rectifier ignition angle and inverter extinction angle, respectivelp. Also, voltages and currents with indices of d and q
refer to those in d-q h e .
The rectifier current controller can be modelled as:
Figure 3.10: DC transmission
cos a, = x, + k, [ iref - i,]
where x, is an intemal state variable, and imfis the seference current for i, . K i and kp are coefficients used in the control circuit of the rectifier. Simiiarly, the inverter extinction angle control at the inverter side can be represented as:
Using the Tkection representation of DC transmission line of Figure 3.10
where, p is a denvative operator. Equations (3-61) to (3-75) provide a state-space model of a two-terminal HVDC system. Linearizing (3-61) to (3-75) gives a smdl-signal dynamic
model of the HVDC system:
where
3.10 System Equations
Matrices As, B,, B,,, B,, Cs, D,, Qu. and Dm are given in Appendix A.
Rearranging (3-76) yields:
where
A d = l ~ i ~ ~ Aiqr Aidi A$J
3.10 System Equations
The mathematical models of the power system components deduced in Section 3.2 to
3.9, including mathematical models of controls, are used to develop the overall
mathematical model of a power system for
eigenvalue analysis, and
transient stability studies.
3.10.1 Eigen halysis Software Tool
The developed eigenvalue analysis package utilizes the linearized mathematical
models of the system components and (1) constructs a state-spacs mathematical model of
the system, and (2) uses a Q-R eigen analysis approach to calculate al1 the system
eigenvalues. The developed state-space formulation also provides eigenvectors,
3.11 Conclusions
participation factor and the transfer fiuiction with respect to a defhed set of single-input
single-outputs (SISO).
The approach adopted to systematically construct the system matrix is described in
[44,46]. Contribution of this thesis t o the development of the eigen-analysis package is:
r Extemion of the approach provided in [44,461 for systematic inclusion of models of
induction motor load, static voltage dependent load, ULTC, UPFC, static
phase-shifter, two-terminal INDC system and their correspondhg control in the
overall system matris;.
The eigen analysis package utilizes MATLAB routines for numerical eigen-value
calculations. The package provides the option either to include dynamics of transmission
lines in the overall system equations or to represent Iines as static components based on
their phasor models. Steady-state values, about which the linearization process is carried
out, are calculated fkom a three-phase power flow program [43].
3.10.2 Transient Stability Software Tool
The non-linear mathematical models of the power system components descnbed in
Section 3.2 to 3.9 and mathematical models of control system were formulated as a
system of differential-dgebraic equations [42]. The Werentid equations describe the
dpnamics of the system and the algebraic equations represent the network phasor model.
Systematic development of the overd system equations fkom the mathematical models
of the components are deseribed in 1431. A multi-step integration algorithm [47,48] is
adopted to numerically integrate the equations. The main feature of multi-step
integration techniques over other techniques, e.g., Runge-Kutta methods is that they can
handle stiE equations very efficiently. Thus, the sof'tware package can be used as a
computationally efficient tool t o investigate both short-term and mid-term transient
stability. The steady-state initial values for multi-step numerical integration were
calcdated fiom a three-phase power-flow program [431. The contribution of this thesis to
the development of the s o h a r e package for transient stability studies is systematic
inclusion of the dynamic models of induction machine load, voltage dependent static
loads, UWC, UPFC and static phase shifker in the overall system differential-algebraic
equations [48].
3.11 Conclusions
The main objective of this chapter is to develop power system study tools applicable
3.11 Conclusions
for simultaneous voltage and angle stability studies, in particular when the system
under investigation includes semiconductor-controlled apparatus, e-g. stat ic
phase-shifters. To meet the objective, state-space models of induction motor load,
under-load tap-changer m T C ) , H M C two terminal system, static phase-shifter and
their controls are developed. The developed models are combined with the state space
models of conventional power system components, i.e., synchronous machines,
transmission lines and static loads.
The overall system model is tdored for (1) eigen-analysis and (2) transient stabiliw
studies. Eigen analysis is based on the Iinearized system mathematical mode1 about an
operating point. The developed eigen-analysis s o h a r e bol permits both inclusion and
exclusion of network dynamics in the overall system model. The Iinearized model can
represent system dpamics within the fkequency range of a fiaction of a Hz (e.g., 0.001
Hz) up t o about 60 Hz. Transient stability studies are performed based on step-by-step
numerical integration of the system (nonlinear) equations.
The eigen-analysis and t rans ien t stabil i ty software packages provide a
comprehensive set of tools to investigate voltage and angle dynamics of power systems
under small-signal perturbations and large signal transients. Application of the software
tools are reported in Chapter 5 and 6 of this thesis.
The salient advantage of the above software packages over the exissting production
grade eigen-analysis and transient stability programs is that they can simultaneously
represent both angle and voltage dynamics of a power system. Thus, they can be used for
comprehensive stability analysis of power systems. The existing software tools are
fomulated with respect to angle stability phenomenon and do not accurately predict
voltage dynamics. This shortcoming is due to lack andlor inadequacy of cornponent
models with respect to voltage dynamic phenomenon.
Chapter
4.1 Introduction
Realistic scenarios corresponding to voltage dynamics and instability only
can be observed and investigated in large, interco~ected power systems, i.e.,
systems which include tens of buses and several generating and load centers.
Such studies are conducted based upon the time-domain simulation approach,
and plots of voltage versus time are used to identify voltage behaviour. The
studies provide accurate results but do not give much insight into the nature of
voltage dynamics. Eigen-analysis is an approximate method which provides
more information on the nature of voltage dynamicslinstability, e.g. level of
participation of each component in voltage behaviour. However, this method also
does not provide a clear picture with respect to the nature of voltage dynamics,
particularly in large systems.
The objective of this chapter is t o investigate the phenomenon of voltage
dynamics in a simple, srnall system and provide a qualitative explanation of how
fast voltage regdation may have an adverse impact on voltage stability. Instead
of using tirne-domain simulation and eigen analysis software tools described in
Chapter 3, basic equations which govern voltage behaviour of the system are
developed in a step-by-step fashion to provide a better explanation of the
phenomenon.
4.2 Voltage Behaviour Under Steady-State Operation
D m Y Load
figure 4.1: A power system with voltage regdator
4.2 Voltage Behaviour Under Steady-State Operation
To demonstrate the effects of dynamic loads and fast voltage regdation by either a
ULTC or a UPFC on voltage stability ofpower systems, the radial power systern shown in
Figure 4.1 is considered. The network shown in Figure 4.1 coaaects a generating area to
a load area through a voltage regulating device, and the system data are given in
Appendix B.
In voltage stabiüty studies, not only the effects of voltage dependency of load should be considered, but also the dependency of the load to voltage deviations dV/d t should
be taken into account. Different models for power system loads which include voltage
dependency a d o r voltage deviation ( d V / d t ) dependency, have been reported in the
literature [37-391. A general yet simple mode1 of load for voltage stability studies can be
expressed by
The load mode1 of (4.1) consists of two parts; i.e., a voltage dependent static part, and
a dynamic part which is dependent on the voltage rate of change. The system nequency
is assumed t o remain unchanged as it is the case in most voltage collapse incidents. The
static parts of the load are described by polynomial models, and the dpamic parts by the
e s t order dinerential equations:
4 2 Vottage Behaviour Under Steady-State Operation
k, and kp are positive constant parameters which represent the dynamic nature of the load. JP and iq are constant power loads. b1 and al represent constant current loads, and
b2 and a2 refer tO constant impedance loads.
Equation (4.4) states that a reduction in reactive power is an indication of voltage
reduction and vise versa. Under a steady state condition the dynarnic term vanishes, and
the static equations describe the load behaviour.
O .5 1 Load Voitage [PU]
Figure 4.2: Q-V plots of the study system (V, = 1. I pu, Xl = 0.5 pu).
Neglecting the system losses, the load active power and reactive power, in terms of
the parameters of the system of Figure 4.1, are given by:
where q represents the overall reactance of the transmission network interfacing the generating area and the load centez V, and V are the sendîng and receiving end voltages,
4.2 Voltuge Bekuiour Un&r Steady-State Operation
Figure 4.3: Leaf diagrams of the study system for various values of the load level J!Q
respectively. n is the voltage ratio of 'the second- side with respect to the primary side of the voltage regulator. In a ULTC this ratio is referred to as the tap ratio. Figure 4.2 shows the Q-V characteristics of the system. Figure 4.2 identifies P and Q that can be
delivered to the load centre under steady-state conditions.
Figure 4.3 depicts n-V plots of the voltage regulator for various levels of constant
power load. Equations (4.2) and (4.3) are used to represent the static part of the load. In
a conventional ULTC, n varies within 20% to 30% of the nominal tap ratio. However,
steady-state voltage regdation of a UPFC can be within S O % of the nominal voltage
value. Each plot in Figure 4.3 is referred to as a Ieaf diagram. The area of each leaf
diagram is a measure of relative proximity to voltage instability corresponding to the
steady-state conditions [3]. This is due to the fact that a leaf diagram with a large area
4.3 Voltage Behavwur Under Dynamic Condifions
also has a large region of attraction, while a leaf diagram with small area has small region of attraction and it is more prone to voltage instabiliw.
When load increases, the area of the corresponding leaf diagram shrinks until it
vanishes a t the bifurcation point. The shrinkage is a result of load dependency on
voltage. The smaller the area of the diagram, the more prone is the system to voltage
instability. Variables Q, V; and n in Figures 4.2 and 4.3 also assume some numerical
values which camot be permitted in a real system. Therefore, the reader should be
cautioned that only a limited portion of Q-V and P n region of Figures 4.2 and 4.3 are
practically acceptable. However, the whole Q-Vand P n region are illustrated to provide a
better description of the systern behaviour.
4.3 Voltage Behaviour Under Dynamic Conditions
Voltage dynamics of the power system in Figure 4.1 is described by (4.1) to (4.6) and
can be simplified as:
where,
such that
1 vsv PSzn v f l = , [ q ' o d " ' " V " V ) - ~ - ~ s ] Q
P, and Qs are the static parts of the loads. The equilibrium points associated with the systern correspond to li = O. With V, and n, as the voltage and tums-ratio of the voltage regulator at the equilibrium point, and Pso and Qs, as the load power values when evaluated at Vo, the equilibrium points for V, are obtrcined firom:
4.3 Vol fage Behav w ur Under ISynamic Conditions
Equation (4.8) identifies a leafdiagram which depends upon load level ho (P,,, Q,) . Figure 4.4 depicts a schematic graph of (4.8) for an arbitrary load level to ident* the
structure of equilibrium points. The nature of equilibrie points, obtained by solving
(4.8) at V,, are identified by an eigenvalue analysis of (4.9) which is obtained from
linearization of (4.7).
where
1 An, = -T A,, = O
The equilibrium points of the linearized system in Figure 4.4 are shown by points A
and B, where point A is a spiral point or a stable node, and point B is a saddle point. The
left part of the leaf diagram of Figure 4.4, corresponding to the spiral points as well as
stable nodes, contains stable equilibrium points. To the contrary, the right part of the leaf
diagram, corresponding to the saddle points, contains unstable equilibrium conditions.
Figure 4.4 also shows that the trajectories near to a spiral point (point A) eventudly rest
at that point, and the system is stable. Conversely, the trajectories close to a saddle point
(point B) detract and indicate unstable conditions.
Consequently, fkom a small-signal analysis point of view, equilibrium points located
on the leR part of the leaf diagram are stable. Therefore, any incoming trajectories to the equilibrium points are attracted by these points. On the other hand, the right part of the
leaf diagram identines unstable equilibrium points where no trajecto~es can rest. This is
4.3 Voltage Behauiour Under Dynarnic Conditions
Figure 4.4: Equilibrium points and the corresponding trajedories of the study system.
an important characteristic of the leaf diagram which can show the behaviour of the
system under both small-signal and large-signal dynamics. A description of large-signal
stability in close relation with the leaf diagram will be given in the next sections. The following sections also explore the efZects of time constant of voltage control devices such
as under load tap changer and UPFC on voltage stability of a power system, under
different operating conditions.
4.3.1 Effect of Conventional and Fast Voltage Regulator on Voltage Dynamics
Figure 4.5 shows the system dynamic response to a disturbance. Figure 4.5 is
obtained by solving the se t of nonlinear dynamic equations given by (4.7). The
disturbance is introduced as a result of a sudden change in the Ioad characteristic fiom
load level LI to load level L2 as given in Figure 4.5. The pre- and post-disturbance load
parameters are also given in Figure 4.5.
Point O in Figure 4.5 corresponds to the pre-disturbance operating condition. Point A
is the desired post-disturbance steady-state operating condition which is also a stable
spiral point. Point A is determined &om the system steady-state equations based on the
post-disturbance load parameters. Although the steady-state equations indicate stable
operating points (O and A) corresponding to pre- and post-disturbance load parameters,
due tu the system nonlinear characteristic, the deparhire fiom O may not conclude a t A
and the system c a n become unstable. Figure 4.5 shows that slow behaviour of voltage
regulator CT =300.0s and T=25.0s) results in stable departure of the operating point from
4.3 Voltage Behuiour Under Dynarnic Conditions
O to A. To the contrary, due to the fast response of voltage regulator (T=20.0s and
T=l.Os), the departure is not successful and voltage instability is experienced. The voltage coilapse phenornenon in the latter two cases can be described as follows.
When T is large, the Q-V trajectory follows the system conditions, as shown in
Figure 4.5 (a), and directly approaches the equilibrium point without becoming close to
the saddle node. Thus, the system remains voltage stable. A better insight is obtained
from doser examination of Figures 4.4 and 4.6. Figure 4.6 shows plots of V(n) for various
values of 2: which are obtained by solving the set of nonlinear equations of (4.6). Figure
4.6 also shows t h e leaf diagram corresponding t o the desired post disturbance
stëady-state condition. The starting point for trajectories is point O. The desired end
point for trajectories is the spiral point A- When T is relatively large, the trajectory
approaches to an equilibrium point (either A or B) via a spiral path - which is also a
stable path - shown in Figure 4.4, and finally is attracted by the stable operating point A.
In contrast, when T is relatively small (c25s), the trajectory approaches to an
equilibrium point towards the saddle node shown in Figure 4.4. Thus, the trajectory is
Figure 4.5: Trajedories of Q-V to identify departure fkom the pre-disturbance point O to the desired post-disturbance point A for various values of voltage regulator time-constant. Load parameters at O are aOz0.28, al=-0.28,a2=0.2, bO=bl=b2=0, Load parameters at A are a0=0.68, al=-0.28, a2=0.2, bO=bI=b2=0.
4.3 Voltage Behavwur Under Dynarnic Conditions
figure 4.6: Plots of V(n) for various T values and the post-disturbance leaf diagram.
placed among the system eigenvectors such that state n increases and state V decreases.
In this case, voltage sags monotonicdy, and voltage collapse occurs.
4.3.2 Region of Attraction
Voltage behaviour also can be determined by examination of steady-state and
dynamic characteristics of the system given by (4.101, (4.11), and Figure 4.7.
Equations (4.8) and (4.10) give all the equilibrium points, $ for which = O . This is shown by the leaf diagram corresponding to the post-disturbance load level in Figure
4.6. The a x a bounded by the leaf diagram 3 corresponds to O> 0, and the area outside
that to < 0. 3 consists of two çubsets: %! and ZR. is loci of all stable points, while 36! is that of unstable points. These regions are marked in Figure 4.7. Similarly, equation
(4.81, shown by a dashed line in Figure 4.6, corresponds to li = O . For any point on the
system trajectory above that lins, is negative. On the other hand, points on the system
trajectory which are below that, are characterized by >i > 0 .
4.3 Voltage Behavwur Under Qmarnic Conditions
Figure 4.7: Dynamic characteriatics of the system trajectories.
The region of attraction is defined by the set of alI trajectories. gr$, such that following
a disturbance, they start from a stable operating point and rest a t another stable
operating point. The pertinent trajectory is a stable trajectory, by definition. The region
of instability is complernentary to the region of attraction, and the trajectories are
entitled by unstable set of f i
Based on the above defînitions, (4.7). (4.10), and (4.12). the region of instability can be
characterized by
4.3 Voltage Behvwur Under Dynarnic Conditions
where,
If a disturbance, e.g. reduction in load level, forces the system trajectory to move
above V,, the origin of trajectory will be inside the target leaf diagram. Therefore,
V > 0, and voltage rises. This resdts in a negative n , and the fxajectory would be a
stable one.
However, oRen the voltage drops &ter most disturbances, due to an increase in load
level, o r a generator/bansmission outage. In this case, the pattern of a trajectory can
reveal if the trajectory is stable or unstable. The trajectorg, stable or unstable, starts with
a direction characterized by lh O and < 0. The reason can be described using
Figure 4.7. Following a disturbance, the initial condition is located outside the target leaf
diagram which results in falling the voltage below 5.
Consequently, following a voltage reduction, a trajectory can have three patterns:
(1) It terminates at the stable operating point, A, without passing it. The trajectory is an
element of rh with very large T.
(ii) It passes the stable operating point, A, inside the leaf diagram and crosses line
V = V, , n = O . The trajectory is an element of 34 with moderate III
(üi) It passes the stable operating point, A, and crosses the subset 3R of the leaf
diagram. The trajectory is an element of with smail T.
The trajectories in the former two patterns are in the region of attraction, and thoae
in the latter pattern are in the region of instabiliw. AU trajectories enter the leaf diagram
during which voltage recovers. h pattern 2, there is an instance in which n = O ; fiom then on, the trajectory returns to the stable operating point from outside the leaf
diagram. The reason is that, inside the leaf diagram, V > O and voltage keeps rising
until it hits the leaf diagram and passes it. Then, becomes negative and voltage
stabilizes, as f i É O .
In contrast, in pattern 3, the trajectories cross region 3& with = O , and enter the
4-3 Voltage Behviour Under Dynamic Conditions
region with v< O . Voltage will then falI monotonicallg, for 6 > O . The plane shown in Figure 4.8 illustrates the voltage instability region. The region of instability is a set of
hyperbolic functions with respect to voltage regulator's time constants. As it is shown,
the smder the II: the more prone the system to instabili@
Figure 4.8: Region of instability
4.3.3 Effect of Limits of a Voltage Regulator on Voltage Dynamics
For a voltage control limited to 20%, Figure 4.9 shows the system response t o the
slow and the fast voltage regulator operations. Figure 4.9 indicates that voltage
regulator action stabilizes the load voltage at 0.78 per unit. Figure 4.9 concludes that
imposing the voltage control lixniters in a DVR can result in stabilizing the voltage
dynamics at a reduced voltage.
4.3 Voltage Behaviaur Under Dynarnic Conditions
Figure 4.9: Changes in the load voltage and reactive power as a r e d t of the disturbance when the tap setting of the voltage regdator is limited.
Figure 4.10: Dynamic response of the system of to a sudden inerease in the load reactive power demand for UPFC
4.4 Conclusions
4.3.4 Effect of UPFC overd time constant on Voltage Stabiüty
Figure 4.10 shows the response of the system of Figure 4.1 to the same disturbance
and operating conditions as described in section 4.3.1, if the voltage regulator consists of
a UPFC. The UPFC confzols the magnitude of the voltage, and does not injectlabsorb
reactive power. Figure 4.10 indicates that if the UPFC's time-constant is relatively large
(about 3091, a new steady-state operating point is achieved and the system is voltage
stable. However, if UPFC rapidly responds to the disturbance (T=ls), voltage collapse
occurs.
4.4 Conclusions
The impact of a fast voltage regulator on the phenomenon of voltage instability is
investigated and compared with that of a conventional (slow) voltage regulator. The
studies conclude that a fast dynamic voltage regdator accelerates and causes voltage
collapse phenomenon in a power system as compared to a slow voltage regulator. The
concept and fundarnentals of this phenomenon is demoykated in a radial power system.
The inability of a power system to supply the required reactive power is the main cause
of the voltage instability. A power system with a fast dynamic voltage regulator becomes
voltage unstable as it cannot supply this requirement. On the other hand, the dynamic
trajectory of a voltage regulator with a 'slow speed of response is attracted by the region
of attraction, and the system is relatively more stable with respect to voltage *
phenomenon.
Chapter
Effect of Semiconductor Controlled ULTC on Voltage and Angle Dynamics
5.1 Introduction
Throughout the world there have been several reported incidents of voltage
instability caused by unexpected changes i n load levels, sometimes in
combination with unusual conditions in the systems, or by network disturbances
such as the loss of an important transmission line, a transformer o r a generator.
In addition to the present severe operating conditions of power systems there
are newly introduced system components, such as semiconductor controlled
ULTC and WFC, which exhibit adverse effects on voltage stability and these
effects have not been studied,
This chapter examines the phenomenon of voltage dynamics in contrast with
angle dynamics, due to rapid voltage control in a relatively large (28-busbar),
inter-connected HVDC/AC power transmission system with potential problems
in t e m s of angle stability. Effects of load model and ULTC time-constant on
voltage dynamics are discussed. The studies are conducted based on an eigen
analpsis appmach. The eigen study results are validated by digital the-domain
solution of the nonlinear system model, using a transient stabiliw program.
5.2 Study System
Figure 5.1 shows schematic diagram of the power system selected for the
5.3 Efect of UZTC on Voltage Dynamics
studies. Figure 5.1 represents a skeleton of the high voltage transmission system at the
western part of the United States. The system includes eight equivalent generating
stations with a total capacity of 20050 MVA. The system supplies nine major load
centers. The AC transmission lines are at 500 kV and the DC tie is composed of a bipole
DC Link rated at k450 kV, 2000 MW. The system parameters are given in Appendix B.
Under a Ml-load condition, Load#3 requires 950 MVA at 500 kV G5 is rated at 150
MVA. Therefore, under fiIl-load conditions, Load#3 is dominantly supplied by remote
generators through the transmission grid, primarily through the comdor composed of
lines LI0 to L13. The system is to provide this load without experiencing voltage o r angle
instability when lines LI1 t o L16, L25, L30 and L31 are in service. If line L25 is
disconnected, Load#3 and Load#4 are to be supplied through the transmission comdor
which is composed of lines L10 to L13. If Load#3 and load#4 are at their rated values,
then voltage sag at buses A, B, C and D is experienced. This voltage sag at buses C and D is beyond the acceptable limits. Thus, partial load shedding at bus D has to be performed
to maintain the rest of the load in service. The approaches to overcome this problem are:
(1) to install multiple static VAr compensators at buses A, C and D, (2) to install
controlledseries capacitors in lines LI0 to L13, or (3) to install a power regulator to
maintain the required power flow within the acceptable voltage limits. The aim in this
thesis is not to provide guidelines to choose among alternative DVRs, but to investigate
impact of a selected DM( on voltage/angle dynamics. Figure 5.1 shows that a power flow
regulator between buses A and B can be Lsed to maintain the required power flow within
acceptable voltage lirnits. Therequired voltage regdation to ensure power flow can be
carried out by either a ULTC or a UPFC.
This chapter examines the impact of a thyristor-controlled ULTC on voltage and
angle dynamics of the system.
5.3 Effect of UETC on Voltage Dynamics
The system component for eigen analysis are represented according to the models
described in Chapter 3. Excitation system models of generating units G1 to G5 are
represented by the block diagram of Figure 5.2 [41]. Excitation systems of generating
units G6 and G8 are represented by the block diagram of Figure 5.3. ~ara.m&rs of the
excitation systems are given in Appendix B. Dynamics of the governor systems are
neglected and input mechanical power to each unit is assumed to remain cbnstant during system dynamics.
5.3 Eficf of ULTC on Voltage Dynarnics
Figure 5.1: Schematic diagram of study system
5.3 Efict of ULTC on Voltage Dynamics
Generator 1 Terminal Voltage
Figure 5.2: Ercitation system Tgpe ST3 used for generating units 01 to 05
Generatxu Terminal Voltage
U~rnin Figure 5.3: Excitation system Type BBCI used for generating Utlits G7 and G8
The ULTC is installed between buses A and B of Figure 5.1. The ULTC injects a
quadrature phase-angle voltage, with respect to the voltage phasor a t bus A. The
magnitude of the injected voltage can be up to 46% of its rated terminal voltage. The
ULTC is rated at 800 MVA, 550 kV. The leakage impedance of the ULTC is assumed to
remain constant at 0.001+j0.06 per unit.
Figure 5.4 shows the block diagram of the ULTC control system. Measured power Pm is compared with the reference value (Pref) and the power deviation (AP) is used as the
error signal to adjust changes in the magnitude (AV) of voltage at busbar B of Figure 5.1.
the power deviation signal is conditioned by means of a low-pass filter. The fûnction of .
the low-pass filter is to minimize the effect of power oscillatory signals due to system
resonance modes and mechanical torsional modes which are usually within the
fkequency range of 10 to 50 Hz. The conditioned &P is fed to a PI controller. Transfer
fùnction k3/ (1 + sTd) represents the time-constant associated with the operation of
5.3 E ' c t of ULTC on Voltage Dynarnics
Auxifiary Signal 1
Figure 5.4: Block diagram of ULTC control
the ULTC. Time constant Td varies in a wide range depending upon the type of ULTC. Impact of Q on the stability of the overall system is investigated in the following
sections. In a semiconductor-controlled ULTC, auxiliary s i p a l s can be added to either
junctions (1) or (2) to enhance system damping for higher fkequency modes, e.g. torsional
modes. Such stability signal has not been considered in the reported studies. Typical
parameters of the control system of Figure 5.4 is given in Appendia B.
5.3.1 Effect of Load Composition on Voltage Dynamics
Figure 5.5 shows loci of the eigenvalues associated with the two least stable voltage
modes of the system at different load levels corresponding to Load#3. The ULTC control
is disabled, and the magnitude of the injected voltage is adjusted according to the load
flow study results. Load#3 is cornposed of 20% induction motor load a t 0.87 lagging
power factor and 80% k e d impedance load at 0.91 lagging power factor. Contribution
factors indicate that one mode is primarily innuenced by Load#3 and one mode by the
voltage regulator of the HVDC inverter. Both modes are well damped and changes in damping factors and frequencies of both modes, due to changes in Load#S, are
insignifïcant.
Figure 5.6 shows loci of the voltage mode eigenvalues associated with Load#3 and the
HVDC converter when Load#3 is composed of 60% induction motor at 0.87 lagging power
factor and 40% fixed impedance at 0.91 lagging power factor. Cornparison of Figure 5.5
5.3 Efict of ULTC on Voltage Dynamics
-25 -20 -15 -10 Real WS)
Figure 5.5: Least stable voltage mode eigenvalues of the test system. ULTC control is disabled. Load#3 is composed of 20% induction motor and 80% h e d - impedance.
I I I 0.15
-25 -20 -15 -10 Real W s ) ]Figure 5.6: Least stable voltage mode eigenvaiues of the test system.ULn: contml is
disabled. Load#3 is composed of 60% induction motor and 40% fked impedance.
5.3 Efict of ULTC on Voltage Dynamics
and Figure 5.6 shows that for the given condition, the voltage mode eigenvalues
associated with Load#3 change as a function of load#3 composition, but these changes
are practically insignismt. Comparison of Figure 5.5 and Figure 5.6 also indicates that
the impact of Load#3 composition on the voltage mode associated with the HVDC is
Figure 5.7: Voltage mode eigenvalues of the test system associated with Load#3.ULTC control is disabled. Load#3 is composed of 100% indudion motor.
Figure 5.7 shows loci of the eigenvalue of the voltage mode associated with Load#3
when it is composed of 100% induction motor operating at about 0.87 lagging power
factor. Comparison of Figure 5.7 with Figure 5.5 and Figure 5.6 shows that:
0 Increase in the percentage of induction motur load for a given operating condition
( k e d load MVA) reduces the damping of the voltage mode.
0 For the given system configuration and the operating condition (ULTC control
disabled), the voltage mode eigenvalue associated with Load#3 is well damped
and is not of any practical concem.
The voltage mode eigenvalue associated with the KVDC inverter control is not
iduenced by various conditions considered for Load#3, and is not discussed any M e r .
5.3 Effect of ULTC on Voltage Dynarnics
5.3.2 Effect of Transmission System on Voltage Dynamics
Figures 5.8 to 5.11 illustrate eigenvalue loci of the voltage mode associated with
Load#3 and the inertial mode of G5 when either of lines LI0 or L25 are out of service and
the ULTC control is disabled. Figure 5.8 shows the impact of magnitude and composition
of Load#3 on the eigenvalue of voltage mode when line LI0 is out of s e ~ c e . Figure 5.8
shows that the damping of the voltage mode is signincantly affected by the composition
of the load, i.e. percentage of induction rnotor load. Figure 5.8 also indicates that the
instability of the voltage mode can be of practical concern when the load is
predominantly induction motor. Figure 5.9 shows the effect of magnitude and - composition of Load#3 on the loci of the eigenvalue associated with the inertial mode of
G5 when line LI0 is out of service. Figure 5.9 indicates that when Load#3 is adjusted a t
about 100% of its rated value, generator G5 becomes unstable (locus C) or very close to
instability point (loci A and BI. Thus, for the system to be operational when line LI0 is
out of service, either Load#3 must be adequately reduced or other counter-measures, e.g.
ULTCILTPFC, must be adopted to maintain angle s tabw.
Figure . 5.10 . shows loci of the eigenvalue associated with the voltage mode when line
L25 is out of service and load#4 is adjusted to 765 MVA and a power factor of 0.87
lagging. Figure 5.10 indicates that voltage instability can occur when Load#3 becomes
1 Im (rad/s)
-20 -15 -10 -5 Real (Lfs) fime 5.8: Voltage mode eigenvalue associated with Load#3 when L10 is out of
service (ULTC control disabled). A.- Load#3 is composed of 20% induction motor and 80% fixed impedance. B: Load#3 is composed of 60% induction motor and 40% e e d impedance. C: Load#3 is composed of 100% induction motor.
5.3 Efict of ULTC on Voltage Llynamics
O Real 0e2
Figure 5.9: InertiaI mode eigenvalue of generator G5 when LI0 is out of service (ULTC control is disabled). A: Load#3 is composed of 20% induction motor and 80% fked impedance. B: Load#3 is composed of 60% induction motor and 40% fixed impedance. C: Load#3 is composed of 100% induction motor.
more than 40%. Figure 5.11 shows loci of the eigenvalue of the inertial mode of generator
G5 under the same operating conditions. Figure 5.11 indicates that angle instabiïity i s
also experienced when Load#3 is larger than 40% of the rated value. Figures 5.5 to 5.11
demonstrate that:
+ When the transmission system is fully in service (Lines LI0 and L25 are in
service), the osciliatory voltage mode associated with Load#3 is stable and its
damping is adequately large so that the mode is not of any practical concern with
respect to voltage instability (Figures 5.5 to 5.7).
When line LI0 is out of service, damping of the voltage mode is noticeably
reduced, however, it remains stable (Figure 5.8). When LI0 is out of service and Load#3 is composed of only induction motor load, Go experiences angle instability
(Figure 5.8).
5.3 Effect of ULTC on Voltage Dynarnics
Real (Us)
Figure 5.10: Voltage mode eigenvalue associated with Load#3 when L25 is out of seMce m T C control disabled). A. Luad#3 is composed of 20% induction motor and 80% k e d impedance. B: Load#3 is composed of 60% induction motor and 40% fixed impedance. C: Load#3 is composed of 100% induction motor.
When line L25 is out of service both the inertial mode of G5 and the voltage mode
of Load#3 exhibit instability (Figures 5.10 and 5.11). Since system disruption due
to angle instability occurs much faster than that of voltage instabiliw, the angle
instabilitp becomes of more iqunediate concern and remedial measures for
enhancement of angle stability must be activated fi&.
5.3.3 Effect of ULTC on System Dynamics
Figures 5.13 and 5.12 show the effect of the speed of response of the ULTC, i.e.
5.3 Efict of ULTC on Voltage Dynamics
-0.8 -0.6 -0.4 -0.2 O 0.2 Red (Us)
Figure 5.11: Inertial mode eigenvalues of generator G5 when L25 is out of senke (ULTC control disabled). A: Load#3 is composed of 20% induction motor and 80% fked impedance. B: Load#3 is composed of 60% induction motor .and 40% fked irnpedance. C: Load#3 is composed of 100% induction motor.
time-constant Td, on the inertial mode of G5 and the osdatory voltage mode of Load#3.
The initial steady-state operating conditions for the study case reported in Figures 5.13
and 5.12 are: (1) Load#3 is adjusted at 100% induction motur load, (2) lines LI0 and L25
are in service, and (3) G5 delivers 142 M'VA at 0.96 lagging power factor. Steady state
power flow studies show that under the given operating conditions, the ULTC should
adjust the steady-state magnitude ofinjectedvoltage at 0.16 per unit so that the system
can meet the load requirements.
Figure 5.13 shows the locus of the eigenvaIue of the inertial mode of G5 when
time-constant Td varies nom 0.50 seconds to 0.015 seconds. Figure 5.13 indicates that
the inertial mode can be made stable by decreasing the speed of response of the ULTC. This pattern of change of the inertial eigenvalue is predictable, since smaller
time-constant (G) indicates that power transfer is adjusted more rapidly by the ULTC.
5.3 Efict of ULTC on Voltage Dynamics
-20 -15 -10 Real (Us)
Figure 5.12: EEect of the speed of response of UETC qn the voltage mode of Load#3
I A) ULTC control disabled B) Td = 0.50 s
C) Td = 0.10 s
Real (Us)
Figure 5.13: Impact of the speed ofresponse of ULTC on the inertial mode of 05.
5.3 Efic tof ULTCon Voltage Dynarnics
Therefore, the power-angle of G5 does not have to be readjusted to meet the load
requirements. Figure 5.12 shows the locus of the eigenvalue of the voltage mode
corresponding to the same time-constant and other control parameters obtained for the
study cases of Figure 5.13. Figure 5.12 shows that the damping of the voltage oscillatory
mode is reduced as the speed of response of the ULTC is increased (Td decreased).
However, for the given operating conditions, the voltage mode is highly stable and
reduction of its damping is not of practical concern. Figure 5.12 also illustrates that
on-load tap-changing for real power flow regulation (points B, C and D) has adverse
effect on the stability of voltage mode as compared with the case where no on-load
tap-changing (point A) is introduced.
Cornparison of Figure 5.13 and Figure 5.12 indicates that changes in the speed of
response of a ULTC, which is controlled for real power flow regulation, has the opposite
effect on the direction of movement of the eigenvalues associated with the inertial mode
(e.g. for G5) and voltage mode (e-g. foreLoad#3). This cornparison also shows that the
effect of ULTC time-constant on the bestial mode is more signincant as compared with
that of voltage mode, i.e. the damping of the inertial mode is changed fmm about 0.2 to
0.5 (60%), while the damping of the voltage mode is changed firom about 14 to 19 (26%). A
series of eigenvalue studies, similar to those reported in Figures 5.13 and 5.12, are
conducted to examine the impact of various ULTC control parameters (Figure 5.4) on the
inertial and voltage modes of the system. The studies conclude that:
Damping of the voltage modes is only sensitive to Td (Figure 5.4) and other
control parameters do not noticeably influence the voltage mode.
Frequency of the voltage mode is insensitive (fairly constant) to al l parameters
of the control system as long as the voltage mode is highly s table
( 1 real part 1 > 5 US 1. The fkequency of the voltage mode is also affected by Td when damping of the mode is small (e.g., point (1) of curve C in Figure 5.8).
5.3.4 Combined Effect of ULTC and Transmission Network on System Dynamics
Figures 5.14 and 5.15 show the combined effect of the speed of response of ULTC (Td) and the transmission system on the voltage mode of load#3 and the inertial mode of G5. .
Initially Iine LI0 is out of service, Load#3 is adjusted a t 100% induction motor load and
G5 delivers 142 MW at 0.96 to the system.
Figure 5.14 clearly shows that to maintain angle stability of G5, the ULTC must have
5.3 Efict of VLTC on Voltage Dynumics
A) ULTC control disabled B) Td = 0.50 s
C) Td = 0.10 s
D) = 0.015 s
-
3 0.2 Real W s )
. . Figure 5.14: Impact of the speed of response of uL'I!C on the inertial
mode of G5 (Line L10 is out of service).
I A) ITLTC control disabled B) Td = 0.50 s
c) Td = 0.10 S
Figure 5.15: Impact of the speed of reapome of ULTC on the voltage mo'de of Load#3 (line LI0 is out of service).
5-4 VaCiihtion of Eigen Analysis Results
a rapid response (Td 10.01 s ) to be able to meet real power flow transfer to the load
area. Only a semiconductor-controlled ULTC can have the required speed of response
and a conventiond ULTC cannot be used under the given condition when LI0 is out of
service. ln contrast to the locus of the eigenvalue of the inertial mode, Figure 5-15 shows
that if a fast response of ULTC is adopted to maintain angle stabilitp, voltage mode of
Load#3 can become unstable (point D of Figure 5.15). It is interesting to note that if
Load#3 is represented by a fixed impedance instead of an induction machine, no
oscillatory instability corresponding to the voltage mode can be detected in the analysis.
Cornparison of the study results reported in Section 5.3.3 and 5.3.4 show that:
kicreasing the speed of response of the ULTC has opposite effects on the
dampings of the inertial and voltage modes of the system.
Due to the selected initial operating conditions and the system configuration, the
results of Section 5.3.3 do not show system instabiliw while the results of Section
5.3.4 indicate either voltage or angle instability
5.4 Validation of Eigen Analysis Results
The study results reported in Section 5.3 are based on the Iùiearized mathematical
model of the study system of Figure 5.1. The eigen andysis results do not include the
effect of nonlinearities, e.g., magnetic saturations of generators, transfomers and control
limits. To validate the eigen analysis results, the case studies reported in Section 5.3 are
also conducted on a detailed nonlinear mathematical mode1 of the study system. This r eqùes (a) development of the set of nonlinear equations which govern the system
dynamic behaviour and (b) numencal integration of the equations to obtain time-domain
responses associated with the test cases. Quantitative agreement between the
corresponding eigen analysis and the-domain response is used as the measure for
validity of modehg approach, assumptions, numencal results and conclusions.
5.4.1 Software Tool
The software tu01 used for time-domain simulation of the study system is a Transient Stability Program (TSP) developed at the Universitg of Toronto [42]. The TSP version
used for the studies reported in this thesis is an enhanced version of the original
program. The major program enhancements which were canied for the purpose of these
studies are (1) the addition of an induction machine model, (2) the addition of HVDC
5.4 V d i d a h of Eigen Analysis ~ e s u i t s
converter and DC line models, (3) the addition of UPFC and ULTC models and (4) the
addition of control models for HVDC, ULTC, UPFC and a synchronous machine
excitation system.
5.4.2 System Mode1 for Time-Domain Simulation
The mathematical model of each apparatus of the studied system of Figure 5.1 is
briefly described in the following paragraphs.
The electrical system models of the synchronous machines G1 to G8 are represented
in the corresponding d-q reference fkame as described by (3-1) to (3-8). Magnetic
saturation characteristic of each machine is also included in the model [283.
Excitation system of each synchronous machine is also included in the model
according to the block diagrams of Figures 5.2 and 5.3. The nodinear limits associated
with each excitation system are also included in the model. The dynamics of the
governors are not included in the TSP model and the mech8ILical input of each machine
is assumed to remain constant.
Therotating shaR system of each turbine-generator unit is represented by a single,
rigid rotating mass. Damping of each mass is also represented by a constant damping
coefficient. The dynamics of each rotating mass is represented by a second-order
differential equation with constant coefficients.
Except Load#3, dl loads are represented by fixed RL elements which is referred to as
fixed impedance load. Load #3 is represented by a shunt combination of an equivalent
induction motor and a fixed impedance load.
Electrical systems of the equivalent induction machine is represented by (3-13) to
(3-19) of Chapter 3. The magnetic saturation characteristic of the machine is also
included in the model [28]. the mechanical system of the induction machine is
represented by a single, rotating mass. The mathematical models described in Chapter 3
are used to represent the ULTC for tirne-domain studies.
The steady-state initial conditions for each case study (eigen analysis and TSP simulation) are obtained f?om a power flow program. The power flow program generates
steady-state initial values in formats which are directly used by the eigen analysis and
the TSP s o m m e tools. Detailed procedures for systematic development of the overall
system model âom individual component models are described in [43].
5-4 VaCidation of Eigen Analysks Results
The following approach is adopted to obtain a quantitative comparison between the
eigen analysis and the corresponding TSP results. Modal fiequenues and dampings are
calculated Çom the TSP results and compared with the corresponding values obtained
Born eigen analysis [34]. Damping and frequency of the oscillatory modes are determined
by (a) performing the simulation for several (up to 10) cycles of the oscillatory mode of
concern, and (b) n u m e r i d y fitting
to the oscilIations. a and o correspond to the damping and fkequency of the oscillatory mode. Modal frequency o is obtained by performing an FFT on the time response obtained from the TSP. If the time response includes more than one (dominant) oscillatory mode, then: (a) fïrst the frequencies of the modes outside the a~ceptable~range
are determined based on an FFT analysis, and (2) then no& filters are used to eIiminate
the oscillations from the time response [34].
Figure 5.16: The-domain response (O < t < 90 s) of rotor angle of 0 5 to a smd-signal disturbance (80% motor load, LI0 out of s e ~ c e , ULTC controUer disabled)
Figure 5.16 shows deviations in the generator angle (6) of unit G5 as a result of a
small-signal disturbance. The small-signal disturbance is introduced by energizing a
three-phase constant-impedance load at busbar D at time t = O S . The load is rated at
45 MVA and 0.80 lagging power factor. Prior to the disturbance, Load#3 is adjusted at
80% induction motor load and iine L10 is out of service. The ULTC controller is disabled
5.4 Validation of Eigen Analysis Results
Figure 5.17: Time-domain response (90 < t c 120 s) ofrotor angle of G5 to a smd-signal disturbance (80% induction motor load, LI0 out of service, ULTC controner disabled)
and its tap position is adjusted for steady-state power transfer corresponding to 80%
induction motor load at busbar D- Figure 5.16 indicates that the disturbance excites rotor
oscillations a t the frequency of o = 7.932 rad/s (1.26 Hz) and the damping of
u = +0.052 (Us). Eigen analyses studies predict the same unstable behaviour at o> = 8.069
radis and damping coefficient of a = 0.061(1/s). Both eigen analysis and TSP results
closely agree with respect to the rotor behaviour during smd-signal dynamics.
Figure 5.17 shows the rotor dynamic for the time period of 90 s to 120 S. Figure 5.17
indicates that approximately after t = 95 s, the rotor oscillations become nonlinear and
f indy at about t = 117 s, G5 losses synchronization. In practice, power system stabilizer
(PSS) of G5 must mitigate the rotor oscillations before angle instability occurs.
Figures 5.18 compares eigen values corresponding to the voltage mode of Load#3
obtained from eigen value analysis- (linear model) and time-domain simulation -
(nonlinear mode). Figure 5.18 shows close agreement between the eigen analysis and
time-domain simulation results for the operating conditions B, C and D. Under operating
condition A, i.e. when the ULTC control is disabled, unit G5 experiences angle instabiütg
approximately 22 seconds after the disturbance. Within the time interval of 22 seconds,
5.4 Validation of E@en Analysis Results
A) ULTC control disabled B) Td = 0.50 s
C) T, = 0.10 s D) Td = 0.015 s
Eigen Analysis -
i
1
TSP
-0.6 -0.4 -0.2 O 0.2 Real (Ys)
figure 5.18: Cornparison of eigenvalues of voltage mode obtained fkom eigen andysis and time-domain simulation Une LI0 is out of service, Load#3 is 100% induction motor load)
Voltage
(pu)
Figure 5.19: Voltage dynamic at bus D due to a small-signal disturbance (Line LI0 is out of service, Load#3 is 100% induction motor load), time constant of L E C is Td = 0.015 S.
5.4 VdicEafion of Eigen Analysis Resdts
the voltage mode does not complete even one swing and consequently the damping and
nequency of the voltage mode cannot be determined from the simulation results.
Figure 5.19 shows time-domain voltage response of the system (at busbar D) due to
the small-signal disturbance obtained fiom TSP. Figure 5.19 shows that the disturbance
results in an aperiodic voltage collapae. This highly nonlinear behaviour cannot be
predicted based on the eigenvalue studies. However, the eigenvalue results indicate that
the operatiag point is not stable and even a small disturbance will lead to voltage
instabZty
-Figure 5.20 compares the eigenvalue analysis results and the simulation results
corresponding to the inertial o s d a t o r y mode of unit G5 under the same initial operating
- conditions and small-signal disturbance described for Figure 5.18. Time-domain
response of the rotor angle of unit G5 corresponding to the operating conditions B, C and
D of Figure 5.20 are illustrateci in Figure 5.21. Both tirne-domain simulation results and
the eigen analysis results for the corresponding conditions predict the same pattern of
behaviour.
I A) ULTC control disabled B) Td = 0.50 s
C) Td = 0.10 s
Im (radfs) Eigen Analysis
,' #'
/'
/ TSP
Figure 5.20: Cornparison of eigenvalues of the inertial mode of 65 obtained fîom eigen analysis and the-domain simulation (Line L10 is out of service, Load#3 is 100% induction motor load)
5.4 VCrticEation of Eigen Analysis Results
-401 I 1 I t I 1 1 * ? J
O 2 4 6 8 10 12 14 16 18 20 Time (Seconds)
(BI 1 O
A8 5
(degree) O
-5 O 2 4 6 8 10 12 14 16 18 20
Tirne (Seconds)
Time (Seconds)
(Dl 4 I 1 1 1 1 , I ,
4 1 1 l I 1 I t I * O 2 4 6 8 t O 12 14 16 18 20
Tirne (Seconds)
Figure 5.21: Power-angle dynamies ofunit 6 5 due to a smd-signal disturbance (Line LI0 is out of senrice, had#3 is 100% induction motor load) A: ULTC controller disabled B: Time-constant of ULTC Td = 0.50 s C: Time-constant of ULTC Td = 0.10 s D: Time-constant of ULTC Td = 0.015 s
5.5 Conclusions
Cornparison of Figure 5.18 and Figure 5.20 indicates that:
Power flow regulation by means of the ULTC has opposite efTects on the
stability of the angle and the voltage modes.
Angle mode instability occurs when power flow regulation of the ULTC is slow
and thus the generator has to supply power to the load during the system
dynamics. This instability is prevented if the ULTC power flow regulation is
carried out façt enough to prevent rotor oscillations.
Voltage mode instability is due to the systems inability t o provide reactive
power to the loads.
5.5 Conclusions
This chapter examines the effects of a semiconductor-controlled under-load
tap-changing (ULTC) transformer on smd-signal dynarnics of an interco~ected power
system. Both voltage modes and electromechanical modes are sirnultaneously considered
in the stabïlity evaluation. The studies are conducted based on an eigenvalue analysis
approach. The eigen-analysis results are validated based on a digital time-domain
simulation of the study system, using a transient stability program. The studies conclude
that:
Under heavy-load condi t ions (s t ressed system), a fas t - response
(semiconductor-controlled) ULTC is required to dynamically regulate real power
flow and to maintain small-signal angle stability of the system. The UXTC must
be fast enough to dynamically modulate real power flow to counteract the
inertial mode of synchronous machines. The studies show the conventional
ULTCs (slow-response) can not provide the required damping for angle stab-
Although real-power modulation by means of a fast-response ULTC can enhance
angle stability, it can reduce the damping of voltage mode(s). Therefore,
enhancement of small-signal angle stability can result in voltage instabilitp.
Therefore, in contrast to the conventional practice, the phenomena of voltage
and angle stability, in the presence of semiconductor-controlled ULTC, &mnot be
independently investigated.
Under light-load conditions, the stability of the oscillatorg voltage mode is not
sensitive t o the speed of response of the ULTC. Therefore, it is a fairly
5.5 Conclusions
reasonable assumption to decouple voltage and angle small-signal instability
under such conditions. Such an assumption si@cantly simplines the system
model which is of importance .in the stability evaluation of large, intercomected
systems.
To detect smd-signal voltage instabilitg, the load must be properly modelled in
the overd system formulation, Le., dynamic voltage dependency of load has to
be incorporated in the model. If the load is represented by fixed RLC components, then the oscillatory voltage dynamics and consequently voltage
instability cannot be identified in neither the eigen analysis nor in the
time-domain simulation approaches.
Chapter
Effect of UPFC on Voltage and Angle Dvnamics
6.1 Introduction
Among the proposed/installed semiconductor-controlled power equipment,
the Unifïed Power Flow Controller (UPFC) as emerged as the most technically
attractive apparatus for stability enhancement and optimal steady-state power
flow regulation of large power systems. The studies reported in this chapter
demonstrate that if a UPFC is adopted to perform the function of either a
phase-shifter or a ULTC, it can contribute to and even cause voltage instability
However, a UPFC has the capability to regulate real-power flow and inject
reactive-power in t h e system. If these two capabilities of a UPFC are
simultaneously adopted, both voltage and angle stability c m be enhanced by a
UPFC.
This chapter proposes and examines a UPFC control strategy for
simultaneously enhancing of voltage and angle stability. The studies are
conducted on the test system presented in Chapter 5 using the eigenvalue
analysis approach described in Chapter 3. Eigen analysis results are validated
by digital computer tirne-domain simulations, based upon the use of the
Transient Stability Rogram (TSP) described in Chapter 3.
6.2 Study System
6.2 Study System
Figure 6.1 shows a single line diagram of the study system which is used to
investigate the effect of a UPFC on voltage and angle dynamics. The systern parameters
are the same as those used for the study cases of Chapter 5, Figure 5.1. The UPFC is installed between buses A and B of the study system. The shunt converter of the UPFC is connected to bus A The UPFC injects a controlled voltage in the system and dynamically
regulates the voltage at bus B.
6.3 Principles of Voltage Stability Enhancement by Means of a UPFC
Figure 6.2 shows the schematic diagram of a radiai transmission system which is equipped witb a UPFC. The UPFC is p h d y installed to regdate real power flow fkom
sending end (source) to the receiving end (load). Real power flow is dynamically
regulated by controlling phase-angle ( S B ) and magnitude (V') of the injected voltage.
Increase of real power flow fiom the source to the load is accompanied by reactive power
demand fkom both ends of the transmission line 1343. The amount and direction of flow of
reactive power from each end is a function of XI, Xz, XB, XE, VB, VE, 6*, ÔB and 6 [34],
where,
In practice, the sending-end and the receiving-end have limitations on the amount of
reactive power they can supply to the line to meet the requirement for the desired real
power hansfer. This limit is usually more stringent at the load end. This reactive power
demand is a major contributor to the phenornenon of voltage instability when real power
fiow nom sending- to the receiving-end is to be increased by means of a UPFC. Chapter 5
shows that rapid real power flow regulation is another factor which can initiate
oscillatory voltage dynamics and even voltage instabiliw.
When either a ULTC or a phase shifter is used ta control real power flow of a
transmission corridor, demand for reactive power fkom both ends of the comdor changes
as real power flow is varied. In practical configurations, the corridor ends are not usually
connected to stiff voltage sources; thus a change in reactive power is accompanied by
changes in voltage magnitude. An increase in reactive power demand results in voltage
drop. Voltage drop is followed by reduction in real power transfer. Thus, the ULTC (phase-shiRer) further increases the phase-shifk angle to meet the demand for real power
6.3 Principles of Voltage Stability Enhancement by Means of a UPFC
Figure 6.1: Schematic diagram of the studied system
6.4 UPFC Control Systern
1 - UPFC 1
Schematic diagram of a radial line equivalent with a UPFC for power fiow control.
t r d e r . hcrease in the phase-shift angle ca. be accoxnpanied by further reactive power
demand. This process can result in monotonic voltage decline or voltage swings
depending on the overall system parameters, nature of the load and operating conditions.
Voltage instabilitg may result if no couritermeasure is provided. Conceptua&, this type
of voltage instabilitp can be avoided if reactive power demand of the line is limited while
real power flow is increased (regulated at the desired value).
Power system apparatus which provide direct control over phase-angle, i.e. ULTCs, conventional mechanical phase-shifters and thyristor-controlled phase-shifters can only
regulate real power flow, and the required reactive power for the transfer of the real
power must be provided by the system. Under such circumstances, the phenomenon of
voltage instability can be avoided either by limiting the amount of real power flow or
installing reactive power sources, e.g. SVCs and fked capacitors, preferably at multiple
locations within the system. This approach is not cost effective. Furthemore dynamic
coordination of controllers among reactive power sources and a real power fiow controller
is not a trivial task.
The above voltage instability phenomenon can be prevented based on the use of a
UPFC to (1) control real power flow through the line and (2) inject reactive power in the
system t o meet voltage stability criteria. In this respect, the UPFC is utilized as a
combination of a phase-shifter (or ULTC) and a static VAR compensator. The following
sections present two different UPFC control strategies and their effects on voltage
dynamics of the test system of Figure 6.1.
6.4 UPFC Control System
The objective of this section is to study the impact of a UPFC on voltage dynamics
6-4 UPFC Control Systern
associated with Load#3 when the UPFC is instded between buses A and B of the study
system of Figure 6.1. The primary function of the UPFC is to adjust power flow to meet
real power requirements of Load#3. The UPFC carries out this function by controlling
magnitude and/or phase-angle of voltage at bus B. The real power requirement of Load#3
is primarily provided through the transmission comdor which is composed of line LI0 to
L13, Figure 6.1. Reactive power requirement of Load#3 is also p d a l l y provided through
the same corridor by means of the UPFC. The sending-end of the corridor is not
connected t o a stifholtage source and it varies between the upper and lower limits on
the voltage of the sending-end, e.g., 1.11 per unit and 0.84 per unit respectively. These
limits are identified based on optimal steady-state operation of the overall system. Thus, during steady-state condition, there is a limit to the amount of reactive power that can be
supplied through the comdor to Load#3.
During dynamic conditions, voltage limits are temporarily violated. A dpnamic
reduction in voltage results in a smaller amount of reactive power transfer to Load#3. In response, the UPFC may change the magnituddphase-angle of the injected voltage to
compensate for the reduction in reactive power flow. Without proper provisions, the
UPFC operation can result in M e r voltage &op and consequently voltage instability.
collapse. This type of instability can be prevented, if the UPFC can maintain the voltage
at bus A within a Iimit by injecting reactive power in the system. This is achieved if the
shunt converter of the UPFC is operated in the capacitive mode. It should be noted that
thyristor-controlled phase-shifters and ULTCs are not capable of injecting reactive power
in the system and therefore cannot assist in enhancing voltage stability under the
described scenario.
Figure 6.3 shows the UPFC control system for power fïow regdation [34]. The UPFC
controls power flow to Load#3 by regdating phase-angle of voltage at bus B. Figure 6.4 shows the details of the UPFC control system. Figure 6.4(a) shows a block diagram of
the feedback loop for controlling Measured three-phase power Pm is compared with
the reference power signal, and the error signal is fed to a PI controller. The control block
with the time constant TpZ represents the signal generating system. It should be noted
that in the studied system of Figure 6.1 torsional oscillations are not included in the
formulation. Thus, signal hP does not include any high eequency oseillatory components.
In practical applications where high fkequency power components are present, adequate
filtering must be provided to avoid sustained (unstable) high frequency oscillations of
generating units due to the cont~ol hop. Similady, if the power signal is derived from a
transmission comdor where inter-area oscillations are experienced, provisions must be
I I V&nf 1 I A d a r y Al.udïaxy Signais
Signals Figure 6.3: The UPFC control system
made to eliminate the effect of tie oscillations on the control. In the system of Figure 6.1,
due to the relatively small size of G5 with respect to the other generating units, no
oscillations associated with inter-area modes are present in the measured power signal.
However, disturbances at Iines L14, LIS, L30, and Load#3 area wilI excite the inertial mode of unit G5. Consequently, frequency deviation signal A q measured at bus B,
includes the effect of rotor oscillations of unit G5. Aco is used as the auxiliary signal of the
control system of &, Figure 6.4(a), to mitigate the inertial mode of G5. The compensator
block is used to provide phase and gain conditioning for Acri The block with time constant
Td is used to Vary the speed of response of the auxiliarg loop. .
Figure 6.4(b) shows that the control system regulates the rms magnitude of the
injected voltage. During steady-state conditions, modulation index Mg corresponds to
0.16 per unit voltage injection. This is to ensure that changes in SB by means of the
controller of Figure 6.4(a) can effectively regulate real power transfer to Load#3 under al1 operating conditions. This control strategy for 6B and Mg gives the priority to real
power flow control of Load#3 area and determines the reactive power flow according to
the system operating conditions. This indicates that the control loops of Figure 6.4(a) and
(b) reach their limits due to power fiow requkments and not due to reactive power flow
requirements.
Figure 6.4(c) shows the voltage control system of the dc-1Uik capacitor of the UPFC. Measured capacitor voltage is compared with a fixed reference value and the error is
used to regulate power exchange between the excitation converter and the system to
maintain capacitor voltage. Voltage a t bus B of the system (Figure 6.1) during
steady-state condition, depending upon the magnitude of Load#3, varies &om 0.73 per
6.4 UPFC Cuntrol System
HPF Am L
Compensaior 1 +sTd
Figure 6.4: Block diagram of UPFC control system
(a) Control loop of SB (c) DC link voltage control loop
Qmf ~urjliary signal
(b) Voltage control loop of bus B (d) Control loop of mE
6-4 UPFC Control System
unit up to 0.94 per unit. This voltage is not regulated by the UPFC. The excitation
converter of the UPFC is controlled not to exchange any reactive power with the system.
Figure 6.4(d) shows the control block diagram of r n ~ which performs this function.
Theréfore, the UPFC neither absorbs nor injects reactive power in the system.
A) UPFC conttol disabled B) Td = 0.20 s
C) Td = 0.10 s
- i 0.20
D) Td = 0.015 s
Figure 6.5: Effect of UPFC time-constant on the voltage mode associated with Load#3.
1 i
6.4.1 Effect of UPFC on Voltage Dynamics
0.15
Figure 6.5 shows the effect of UPFC time-constant (Td of Figure 6.4(a)) on the
eigenvalue associated with the voltage dynamics of Load#3. Load#3 is initially adjusted
at 100% induction motor load. Lines L10 and L25 are in s e ~ c e , and G5 delivers 142
MVA at 0.96 lagging power factor. Eigenvalue A on Figure 6.5 corresponds to the voltage
mode of Load#3 when the UPFC controls a& disabled, and according to the power flow
conditions, the injected voltage is adjusted so that the required power of Load#3 is
provided by G5 and the system. Figure 6.5 indicates that under this operating condition
the voltage mode of Load#3 is highly stable and the phenornenon of voltage dynamics is
not a concern. Points B, C, and D on Figure 6.5 show the eigenvalue of the voltage mode
under the same steady-state operating condition when the UPFC control is in s e ~ c e .
Figure 6.5 indicates that reducing Td can effectively reduce darnping of the voltage mode
associated with Load#3. However, for all the conditions, the voltage mode is well damped
-20 -15 -10 Real (Us)
6.4 UPFC Control System
Figure 6.6: Effect of UPFC tirnecorntant Td on the hertial mode of G5.
and voltage instability is not a concern for the given operating conditions and the UPFC control parameters.
Figure 6.6 shows the locus of the eigenvalue associated with the inertial mode of G5 when the UPFC time-constant Td is varied fkom 0.015 s to 0.20 S. Figure 6.6 indicates
that slower response of the UPFC results in smaller damping of the inertial mode.
However, for d l the given operating conditions, the inertial mode of G5 is positively
damped for the whole range of variation Td. Faster response (smaller time-constant) of
the UPFC results in lesser dependance of Load#3 on G5 and more on power hansfer 6om
the system. Thus, the inertial mode of G5 exhibits higher damping (Point D of Figure 6.6)
when the UPFC the-constant has its smallest value. Cornparison of Figure 6.5 and
Figure 6.6 indicates that reducing the time constant of power flow controller of the UPFC has the opposite effects on the damping of the voltage mode of Load#3 and the inertial
mode of G5. Increasing the time constant (1) reduces the damping of the voltage mode and (21.increases the damping of the inertial mode.
6.4.2 Effect of System Codguration on Voltage Dynamics
The impact of the UPFC on the voltage mode, when line LI0 of Figure 6.1 is out of
service, is illustrated in Figure 6.7. It is assumed that Load#3 is 100% induction motor
- A) UPFC control disabled B) Td = 0.20 8
c) Td = 0.10 s D) Td = 0.015 s
4
-0.6 -0.4 . -0.2 O 0.2 R e d (Ys)
Figure 6.7: EfFect of UPFC tirneanstant on the eigenvalue of voltage mode associated with Load#3 when line LI0 is out of service.
l A) UPFC conhl disabled
B) Td = 0.20 s
C) Td=O.lOs
D) Td = 0.015 s
Figure 6.8:
0.2 Real (Us)
Effect of UPFC tirneamtant rd on the eigenvalue of the inertial mode of G5 when Iine LI0 ia out of service.
6.4 UPFC Control System
load. Figure 6.7 shows the locus of the eigenvalue associated with the voltage mode when
Td is varied Born 0.015 s to 0.20 S. When the UPFC control is disabled and the initial
injected voltage is adjusted to meet the load requirement, the voltage mode is stable
(Point A of Figure 6.7). If the UPFC control is activated to adjust the power flow
according to the requirsments of Load#3, the stabiliw of the voltage mode depends on the
value of Td. Figure 6.7 shows that when T , is either 0.20 s or 0.10 s, the voltage mode is
stable. However, when Td is 0.015 s, voltage instability is experienced.
In contra& to the detrimental eEect of UPF'C on the voltage mode eigenvalue (Figure
6.7) when Tdis s m d , faster response of the UPFC enhances stabiliw of the inertial mode + of generator G5. Figure 6.8 shows that when the time constant of the UPF'C power flow
regulator is large, the inertid mode of G5 is unstable, i.e., points A and B. However, the
inertial mode is stable when the tirne-constant is small (Point D of Figure 6.8), and the
damping is adequately large to provide reliable operation of the system.
6.4.3 Validation of Eigen Analysis Results
The study results reported in Sections 6.4.1 and 6.4.2 are based on the linearized
mathematical model of the study system of Fïgure 6.1. The eigen analysis resdts do not
include the effect of nonlinearities, e.g. magnetic saturations of generators and
transformer and control limits. To validate the results of the linearized model, test cases
of Sections 6-4.1 and 6.4.2 are also conducted on a detailed nonlinear mathematical
model of the study system. The digital time-domain transient stability program and the
component modeIs of the system are the same as those described in Chapters 3 and 5.
However, the ULTC model is replaced by the UPFC model. Details of the UPFC-mode1
are also given in Chapter 3.
Figures 6.9 and 6.10 compare corresponding eigenvalues obtained from the
eigen analysis (linear model) approach and time-domain simulation (nonlinear
model) approach. The methodology to obtain eigenvalues of the oscillatory modes
fkom time-domain simulation results are descfibed in Section 5.4.2 of Chapter 5.
Figures 6.9 and 6.10 show quantitative agreement between the time-domain
results and the fkequency-domain eigen analysis results.
Figure 6.11 shows the tirne-domain simulation resdt comesponding to the dynamics
of voltage at bus D of the study system when the UPFC is in service to regulate power
flow (Td = 0.015 s) to Load#3 area. The oscillations in the voltage are excited as a result
6.4 UPFC Contrul System
Tirne-Domain Simulation
Eigen Analysis
1 0.2 Real (Us)
Figure 6.9: Compmison of eigenvalues of voltage mode obtained h m eigen analysis and tirne-domain simulation (Line LI0 is out of service, Load#3 is 100% induction motor load)
I A) UPFC controI disabled B) Td = 0.20 s
Cl Td= 0.10 s
TSP Simulation
Method
Eigenvalue Analysis 1
O 0.2 Red (Us)
Figure 6.10: Cornparison of eigenvalues of the inertid &ode of 0 5 obtained h m eigen analysis and time-domain simulation (Line LI0 is out of service, Load#3 is 100% indudion motor load)
of a sudden energization of a fixed impedance Ioad at bus D. The load is rated at 63 MVA
and 0.83 lagging power factor. Prior t o the disturbance, Load#S is h e d at 100% induction
motor Ioad and h e LI0 is disconnected. Figure 6.11 indicates that the voltage oscillatory
mode is unstable and its amplitude increases with time. This is consistent with the
eigenvalue results (Eigenvalue D of Figure 6.9).
For the given operating condition and parameters, the disturbance also excites the
inertial mode of G5, but the UPFC control can effectively mitigate the inertial mode, and
therefore, angle instability is not experienced. Figure 6.11 also shows that about 45
seconds after the disturbance, the system experiences nonlkiear voltage behaviour and
finally voltage collapse. The instant of voltage collapse cannot be predicted based upon
eigen analysis results.
0L 1 I I I I J
O 1 O 20 3 0 4 O 5 0 6 O Tim e (Seconds)
Figure 6.11: Voltage dynamics at bus D to a smaii-signal disturbance (Line LI0 is out of service, Load#3 is 100% induction motor load, UPFC time-constant is 0.015 s)
Figure 6.12 shows deviation in the rotor position of unit G5 as a result of the above
disturbance when the UPFC is in service to regulate power flow to Load#3 (Td = 0.20 s).
Figure 6.12 shows that the rotor oscillation cannot be mitigated by the UPFC and the
amplitude of oscillation grows. This is consistent with the eigen analysis results of
Figure 6.10, point B. Figure 6.12 shows that approximateb 35 seconds after the
disturbance, the rotor oscillations become nonlinear and the system experiences angle
6.5 UPFC Control Sttategy to Prevent/Mitigate Voltage Instability
Cornparison of Figure 6.11 and Figure 6.12 indicates that the post disturbance time
intemals for which either angle or voltage collapse is expenenced are comparable.
-50 I I 1 I I I , 1 1 1 O 5 10 15 20 2 5 30 35 40 45 50
Tirne (Seconds)
Figure 6.12: Inertial mode dynamics of unit G5 due ta a small signal disturbance (Line LI0 is out of senrice, Load#3 is 100% induction motor load, UPFC time-constant is 0.20 SI
6.5 UPFC Control Strategy to Prevent/Mitigate Voltage Instability
Figure 6.13 shows a control strategy adopted for the UPFC to prevent instability of
the voltage oscillatory mode associated with Load#3, under heavy real power transfer to
the load area. Further details of each control loop are illustrated in Figure 6.14. The main difference between the control strategies described in this section and that of
Section 6.4 is as foIlows. The control strategy of Section 6.4 does not permit any reactive
power exchange between the shunt converter of the UPFC and the system. The control
strategy of this section utilizes the shunt converter of UPFC as a static VAR system to
regulate the voltage at bus B (Figure 6.1) at a pre-specified reference value. Under heavy
load conditions of Load#3 area, the shunt converter is operated in the capacitive mode
and injects reactive power in the systern.
Figure 6.14(a) shows the details of the control loop associated with power flow
6.5 UPFC Contml Stnrtegy to Prevent/M&gate Voltage Insta6iZii-y
regdation. Measured power Pm is passed thmugh a low-pass filter (LPF,) to eliminate
high fiequency modes. The fïltered signal is then compared with the reference signal
(Pd. and the error signal is provided to a PI controller to determine the angle of the
injected voltage t jB. To enhance angle stability for unit G5, an auxiliary controller is
added to the controi loop to provide power flow modulation by means of the UPFC, Figure 6.14(a). A frequency deviation signal (ho) is measured and passed through a high-pass
(EIPF,). The function of this filter is to eliminate the effect of inter-area modes on the
control loop. The fIltered signal is then passed through a Iead-lag compensator for phase
and gain adjustment. The transfer function with the time constant Td is used to
investigate the impact of the au.x%ary loop time-constant on the voltage mode. Instead of
junction (Z ) , the a d a r y signal (Ma) can also be added to junction (1).
Vdcmf A d a r y Auxiliary Signais
Signals
VE: Figure 6.13: (a): UPFC control system to prevent voltage ïnstability
(b): Voltage phasors of the UPFC system
Figure 6.14(b) shows the block diagram of the dc link voltage control syst.em. The
capacitor voltage (V&) is compared with the desired value (Vk+) and the error signal is
provided to a PI controller t o control $. 6E controls power exchange betweenthe dc
capacitor and the transmission system by means of VSC-E.
6.5 UPFC ControL Stnztegy to Pmvent lMitigate Voltage Ikstability
AuxiIiary Signal
Atilcillary Signai Awciliary Signal
Figure 6.14: Alternative UPFC control scheme.
(a) A8B controller, (b) AQontroller, (cl AmfiontrolIer
6-5 UPFC Control Strategy to Preuent/Mitigate Voltage Instubility
Figure 6.14(b) shows the control system used to regulate voltage a t the terminal of
the shunt converter (V'). In the study system of Figure 6.1, the shunt converter of the
UPFC is connected to bus A Depending upon the line loading condition, the magnitude
of VEt for the study system of Figure 6.1 c a n Vary fkom 0.73 per unit to 0.94 per unit.
Lower values of Vn correspond to higher levels of real power flow. To minimize reactive
power demand from the system during heavy loading conditions of the line, the
magnitude of Va is dynamically adjusted to 1.02 per unit. This requires the operation of
VSC-E (Figure 6.13) as a VAR compensator under ail operating conditions of the UPFC
system. This is accomplished by comparing the magnitude of V' with the set value of Vset =1.02 per unit and using the error signal to adjust the interna1 voltage of VSC-E by
means of modulation index m ~ . The amount of injected reactive power in the system is a
function of real power transfer to the load area. The injected reactive power reduces
reactive power burden f?om the sending ends with respect to Load#3.
Injected reactive power by VSC-E ensures that the required reactive power demand
of Load#3, under stressed conditions, is available. Thus, voltage collapse and instability
at Load#3 can be prevented regardless of the amount of real power exchange between the
Load#3 iiiea and the rest of the system.
Figure 6.13(b) shows that for a given value of VEt, dependhg upon the magnitude and
phase angle of injected voltage VB, the magnitude of VBt can Vary over a relatively wide range. Existing insrdation coordination- practice of HVAC transmission systems permits
steady-state operation up to 1.5 per unit voltage at a busbar when there exists no direct
load comection to the bus. This indicates ihat the magnitude of the injected voltage by
the UPFC can be up to 0.48 per unit.
I V ~ d m o + = I V ~ t l m m + IV~Imax = 1 .O2 + 0.48 = 1 -5 per unit (6-2)
Magnitude of the injected voltage can be dynamically controlled by the UPFC
through modulation index mg- Dunng time intervals where maximum real power
transfer to Load #3 is required, it is advantageous to inject maximum voltage in the
system by means of the UPFC. The reason can be explained using the phasor diagram of
Figure 6.13b). The dominant variable for real power fiow contml is 6. The desired value
of 6 can be achieved by means of simultaneous adjustment of 6B and 1 VB 1 . For a given
vdue of 6, a larger 1 VB 1 results in a s m d e r vdue of 6 ~ . Thus, to ensure that control
system of SB, Figure 6.14(a), can provide power flow control under extreme load
conditions, the injected voltage 1 V' ( must have its largest value. In the studies reported
in this chapter, the magnitude of the injected voltage is kept constant at 0.48 per unit.
6-6 Voltage Stabilie Enhancement
6.6 Voltage Stability Enhancement
This section demonstrates that the control strategy of Section 6.5 enables the UPFC to provide rapid dynamic power flow regulation to Load#3 and simultaneously prevent
voltage instabilie of the system.
6.6.1 Effect of UPFC on Voltage Dynamics
Initidy, line LI0 is out of semice and Load#3 is set at 950 MVA (100%) of the rated
value) which is composed of 100% equivalent induction motor load. The UPFC which is installed between buses A and B, Figure 6.1, adjusts the power fiow to the requirement of
Load#3 under the given system condition. Figure 6.15 shows the eigenvalue of the
voltage mode associated with Load#3 when time constant Td of the UPFC (Figure
6.14(a)) is varied fkom 0.015 s to 0.2 S. Figure 6.15 shows that for the whole range of
variation of the time constant, the oscillatory voltage mode is stable. Figure 6.15 also
illustrates the voltage mode eigenvalues when the control strategy of Section 6.4 is
adopted for the UPFC. Cornparison of the corresponding eigenvalues demonstrate that
when the UPFC is controlled to inject reactive power in the spstem a t bus A, the
phenomenon of voltage instability is prevented regardless of the speed of voltage
regulation.
A) UPFC mntrol disabled B) Td = 0.20 s
C) Td = 0.10 s 0.204 D) Td = 0.015 a
0.202
-1.2 -1.0 -0.8 -0.6 -0.4 -0.2 O 0.2 Real (l/s)
Figure 6.15: Effect of UPFC time-codstant Td on the eigenvdue of voltage mode associated with Load#3 when line L10 is out of service.
Figure 6.16 shows the effect of the UPFC power flow control on the inertial mode of
G5. Figure 6.16 indicates that slow response of the voltage regulator (Td = 0.20 s) does
6.6 Voltage Stability Enhancement
I a UPFC eontrol of Section 6.5 r UPFC control of Section 6.4
-0.6 -0.4 -0.2 O 0.2 Real (Us)
Fi- 6.16: Ened ofUPFC time-constant Td on the eigenvaiue ofthe inertial mode ofG5 when line LI0 is out of service.
not maintain the stability of the inertial mode. However, faster power regulation, e.g.
Td = 0.10 s or Td = 0.015 s, can ensve that the inertial mode remains stable. Figure 6.16
also provides a quantitative cornparison between the corresponding eigenvalues for the
cases that control strategies of Section 4 and Section 5 are adopted for the UPFC. The cornparison demonstrates that: (1) slow voltage regulation (Td = 0.20 s) cannot maintain
angle stability for both control strategies, and (2) control strategy of Section 5 increases
the damping of the inertial mode.
Evaluation of Figures 6.15 and 6.16 indicates that simultaneous stability of voltage
and angle can be maintained if (1) rapid voltage regulation is camed out (Td L 0.10 s 1 and (2) adequate reactive power is injected in the system at bus A (control strategy of
Section 6.5).
Figure 6.17 compares eigenvalues of the voltage mode obtained from (1) the
linearized model of the system based on the eigenvalue approach and the nonlinear
model of the system based on the digital tirne-domain simulation method. The approach
described in Section 5.4 is used to calculate eigenvalues of the voltage mode from the
time-domain responses. Figure 6.17 depicts close quantitative agreement between the
corresponding eigenvalues obtained fkom the two methods. Figure 6.18 compares the
tirne-domain simulation and eigen analysis results corresponding to the inertial mode of
6.6 Voltage StabiZity Enhancement
B) Td = 0.20 s
CI Td =O.Io s 0.208 D) Td = 0.015 s
0.206
Tim~ime-Domain Simulation Methoci 0.204
0.202
1 I 1 I 1 1 1 I I 1 1 1 1 I
-1.2 -1.0 -0.8 -0-6 -0.4 -0.2 O 0.2 Real (l/d
Figure 6.17: Cornparison of eigenvalues of voltage mode obtained h m eigen andysis and he-domain simulation when line L10 is out of service.
0 Eigen Annipis The-Domain Simulatin0
-0.6 -0.4 -0.2 O 0.2 Real (Us)
Figaw 6.10: Cornpariaon of eigenvalues of the inertial mode of G!5 obtained h m eigen analysis and tirnedomain simulation when line L10 is out of service. (contml strategy of Figure 6.13 is used for the UPFC).
6.6 Voltage Stubility Enhancement
unit G5. Agreement between the tirne-domain simulation results and the eigen andysis
results in the indication of the vdidity of the resuIts and conclusions.
Figure 6.19 shows variations of voltage at bus D corresponding to a small-signal
disturbance in the system. The system is initidy supplying 950 MVA at a power factor of
0.91 to Load#3 and G5 provides 148 MVA at 0.98 lagging power factor. The UPFC operates based on the control strategy of Figure 6.13. Td is adjusted at 0.015 S. A
smd-signal disturbance is imposed on the system by energizing a passive load at bus D. The disturbance load is rated at 63 MVA and 0.82 lagging power factor. Figure 6.19
-121 I I I I l . , I
O 10 20 30 40 50 60 70 80 9 0 Tirne (Seconds)
Figure 6.19: Voltage mode dynamics at bus D due to a srnail-si al disturbance (line LI0 is out ofaervïce, control strate of(contro~ strategy o f R w e 6.13 is us& for the UPFC, and Td = o.oI~%.
shows tirne-domain variations of voltage at the bus after the disturbance. Figure 6.19
illustrates that the disturbance results in voltage oscillations at a fkequency of about
0.03 Hz. The voltage oscillations are positively damped and the system remallis voltage
stable. This is consistent with the corresponding eigen analysis results which is depicted
on Figure 6.17, data point D. To the contrast, Figure 6.11 shows that for the same
operating conditions and disturbance scenario, voltage becomes unstable and finally
voltage collapse occurs if the control strategy of Section 6.4 is adopted for the UPFC.
Figure 6.20 shows dynamics of the inertial mode of unit G5 for the same operating
condition, when the UPFC is operated based on the control strategy of Figure 6.13 and
6.7 Conclusions
1 1 1 1 I 1
O 10 20 30 40 50 60 Tirne (Seconds)
Figure 6.20: Inertial mode dynamics of u+t G5 due to a am&-signal distubance (2ine LO is out of service, control strategy of Figure 6.13 ii used for the UPFC, and Td = 0.20 S)
Td is adjusted at 0.20 S. Figure 6.20 indicates that slow power flow control by means of
the UPFC cannot maintain angle stability of G5. This is also in agreement with the
eigenvdue results (data point B of Figure 6.16).
6.7 Conclusions
This chapter examines the effect of voltage control, by means of a Unified Power Flow
Controller (UPFC), on the damping of the system eigenvdues associated with the
inertial modeb) and voltage mode(s) of a power system. The UPFC is used primady to
regulate power flow t o a load area through dynamic control of magnitude and
phase-angle of the injected voltage. Two control strategies for the UPFC are examined:
First Strategy: The UPFC regulates a senes injected voltage (phase-angle and
magnitude) and does not exchange reactive power with the system. Under this
strategy, the UPFC operates similar to a phase-shifter or an on-load
tap-changing transformer.
6.7 Conclusions
Second Strategy: The UPFC regulates the series injected voltage (both
magnitude and phase angle), and its shun t converter maintains i t s
corresponding terminal voltage at a pre-specified value. Thus, the shunt
converter of the UPFC is controlled to perform as a forced-commutated static
VAR compensator (STATCOMI.
Eigen andysis and digital time-domain simulation results show that:
When a UPFC adopts the first control strategy, to regulate real power flow of a
voltage dependent load, damping(s) of voltage oscillatory mode(s) can be noticeably
affected by the UPFC control system. OsciIlatoiy voltage instability is observed
when rapid voltage regulation is carried out. Slow voltage regulation may not result
in voltage instability; however, it may cause angle instability. The conceptual reason
behind the voltage instability is inadequate capacity of the system to provide the
required reactive power for the load. The results indicate that based on the rirst
control strategy full speed of response of a UPFC cannot be exploited.
When the UPFC adopts the second control strategy, stability of both voltage and
angle oscillatory modes are enhanced. The reason is that the second control
strategy guarantees that the UPFC provides control over real power flow and
reduces (minimizes) the system dependance on the sending-end reactive power.
In contrast to the conventional practice, voltage instability and angle instability
cannot be considered as decoupled dynamic phenomena when a power system is
equi p ped with semiconductor-controlled apparatus.
The phenornenon of voltage dynamics c m be evaluated only if the voltage
dependency of the load is incorporated in the load model. Therefore, based on
conventional practice, where load is represented by constant power loads or
constant impedance loads, the interdependency of angle and voltage dynamics
cannot be studied.
Chapter
Conclusions and Recommendations for Future Work
7.1 Conclusions
This thesis examines effect of dynamic voltage regulators (DVRs) on the
angle stability and voltage stability phenomena of power systems. DVRs are
power electronic based apparatus which are capable of injecting a series
controlled voltage in a power system. Two specific DVR circuit topologies which
are considered in this thesis are: (1) semiconductor-controlled under-load
tap-changing (ULTC) transformer and (2) unined power flow controller (UPFC).
The studies are conducted on a realistically-sized, interconnected power
system which include eight generating stations, 31 transmission lines, 20 high voltage buses and one HVDC link. The studies reported in this thesis carried out
using an eigen analysis technique. Eigen analysis results are validated by
digital time-domain simulation of the system, using a transient stability
software tool. Both the eigen analysis and the transient stability tools are
developed and tailored for the studies reported in the thesis.
The thesis concludes that:
Fast voltage injection by means of a DVR, for enhancement of angle
stability, c m result in voltage instabiliQ. This indicates that in contrast
to the conventional approach, the phenomena of angle stability and
7.1 Conclusions
voltage stability cannot be treated as decoupled phenomena. This is in spite of
the fact that the t h e &ames associated with angle instability and voltage
instability are significantly different. The reason for this type of voltage
instability is incapability of the system to supply required reactive power
agsociated with the real power transfer imposed by series voltage injection. In
mathematical terms, fast voltage injection may result in voltage instability by
imposing unstable dynamic trajectones which are retarded e01n the region of
attraction.
The couphg phenomenon between voltage and angle dynamics can be detected
from the analysis, if voltage dependency of the load is adequately represented in
the load model. In these studies, the load is represented by equivalent induction
motors which dynamically incorporates voltage dependency in its model.
Under light load conditions, fast voltage injection, for enhancement of angle
stabiliw, does not affect voltage dynamics, i.e. no couphg between voltage and
angle dynamics is detectable.
4 C o u p h g between voltage and angle dynamics is reduced if series voltage
injection is camied out slower, i.e. voltage instability due to fast voltage injection
can be prevented if the overall time constant associated with the voltage control
loop of DVR is increased to a pre-specifïed value. This value depends upon the
system configuration, parameters and load characteristics. However, slow
voltage injection may not be useful in enhancing angle s t a b w .
Conventional phase-shifters which use mechanical switches (instead of
electronic switches) do not cause voltage instability since the time constants of
their responses are much larger than the limit value which causes voltage
ins tability.
A semiconductor-controlled ULTC which is equipped with an a d a r y control
for enhancing angle stability, can cause voltage instability
A UPFC, which is used to enhance angle stability through series voltage
injection, can also lead to voltage instability. However, shunt converter of a
UPFC can be independently controlled to act as a VAR generator. Thus the
reactive power demand of the load can be fully or partially met by the shunt
converter, and as a result voltage instability due to fast voltage injection be
prevented. This is another salient advantage of a UPFC as compared with other
7.2 Suggestkons for Future Work
power electronic apparatus which have been adopted/proposed for power system
applications.
Investigation of the coupling phenomenon of voltage and angle dynamics
requires representation of voltage dependency of the load in the study tools, i.e.
eigen analysis and transient stabilitp software programs. The lack of a proper
load mode1 obscures the voltage instability phenomenon, however, it does not
affect the results with respect to angle instabifiw.
7.2 Suggestions for Future Work
The following suggestions are for further studies in continuation of this work
The ULTC and the UPFC control systems provided in Chapters 5 and 6 have not
been optimized to achieve the best performance fkom the system. Therefore,
there is a need to establish criteria for achieving the optimum response of the
system based on adjustment of the control parameters. This may be carried by
considering the system as a multiple input - multiple output (MIMO) rather
than the single input - single output (SIS01 which has been used in Chapters 5
and 6.
0 The IEEE Working Group on Load M o d e h g has suggested various load models
for voltage stabilitg studies. This work only considers induction motor load and
does not investigate the coupling phenomenon of voltage and angle dynamics
with different load models. It is to be mentioned that none of the above load
models have been verinedlvalidated. Thus, it is recommended to investigate the
degree of coupling between voltage and angle dynamics for diffeient load
models, to establish accuracy and sensitivity of such models.
References
Voltage Stabilitg and Securitf Proceedihgs of international Sernimr on Bulk Power System Voltage Phenomena II, Deep Creek Lake, Maryland, Aug. 1991.
C.W. Taylor, Power System Voltage Stability, McGraw Hill, 1994.
IEEE Working Group on Voltage Stability, Voltage Stability of Power Systems: Concepts, Analytical Tools, and Industry Experience,' IEEE Special Publication, 90TW0358-2-PWR, 1990.
A. Kurita, T. Sakurai, "The Power System Failure on July 23, 1987 in Tokyo," Proceedings of the 27th Conference on Decision and Control, Austin, Texas, pp. 2093-2097, December 1988.
F? Kundur, G.K. Morison, "A Review of Classes of Stabilitg Problems in Todays Power Systems," lEEE PES Winter Meeting, 1993.
IEEE Committee report, T V D C Controls for System Dynamic Performance," IEEE Dansactions on Power Systems, Vol 6 pp. 743-752, May 1991.
VA. Venikof; VA. Strov, VI. Idelchick, VI. Tarasov, "Estimation of Electrical Power System Steady-State in Load Flow Calculations," IEEE lYansactions on Power Apparatus and Systems, Vol. PAS-94, No. 3, pp. 1034-1041,1975.
B.M. Weedy, B.R. Cox, Voltage Stabiliw of Power Links," Proc IEE, Vol. 115, pp. 528,1964.
Y. Tamura, M. Mon, S. Iwamoto, Telationship Between Voltage Instability and Multiple Load Flow Solution in Electric Power Systems", lEEE
ll-ansactions on Power Systems, NO. 5, pp. 1115-1123, May 1983.
1101 P. Kessel, H. Glavitsch, "Estimating the Voltage Stability of a Power System," IEEE D-ansactions on Power Delivery, Vol. PWRD-1, No. 3, pp. 346,1986.
[il] 'R. Fischl, J-C. Chow, H. Yan, F- Mercede, F X Wu, "A Cornparison of Indices for Predicting Voltage Collapse in Power Systems," Proceedings of the 2 7th Conference on Decision and Control, Austin, Texas, pp. 2098-2103, Dec. 1988.
1121 J-C Chow, R. Fiscbl, H. Yao, "On the Evaluation of Voltage Collapse Criteria" IEEE Dansaction on Power Systems, Vol, 5, No. 2, pp. 612-620, May 1990.
1131 Y Tamura, Y. Nakanishi, S. Iwamoto, u O ~ the Multiple Solution Structure, Singular Point and Existence Condition of the Multiple Load-Flow Solutions," IEEE PES Winter Meeting, New York, Feb. 1980.
[14] Y. Tamura, K Sakomoto, Y Tayama, "Voltage ZnstabXty Proximity Index NIPI) Based on Multiple Load Flow Solutions in IU-Conditioned Power Systems," Proceedings of the 27th Conference on Deciswn and Control, Austin, Texas, pp. 2114-2119, Dec. 1988.
[15] B.K. Johnson, "Extraneouç and False Load Flow Solutions," E E E îYansactions on Power Apparatus and Systems, Vol. PAS-96, No. 2, pp. 524-534,1977.
1161 F.D. Galiana, %ad Flow Feasibility and the Voltage Collapse Problem," Proceedings of the 23th Colrference on Decision and Control, Las Vegas, NV, pp. 485-487, Dec. 1984,
[17] P.W. Sauer, B.C. Lesieutre, MA. Pai, Wynamic vs. Static Aspects of Voltage Problems," Proceedings of Intematio ml Workshop on Bu& Po wer System Voltage Phenornena: Voltage Stability and Securie Deep Creek Lake, Margland, pp. 207-216, August 47,1991.
[18] J.H. Chow, A. Gebreselassie, "Dynamic Voltage Stabiüty Analysis of A Single Machine Constant Power Load System," Proceedings of the 29th Conference on Decision and Control, Honolulu, Hawaii, pp. 3057-3062, Dec. 1990.
[19] A. Tiranuchit, R.J. Thomas, "A Posturing Strategy Against Voltage Instabilities in Electrk Power Systems," IEEE Dansactions on Power Systems, Vo1.3, No. 1, pp. 87-93, Feb. 1988.
[201 PA. Lof, G. Anderson, D.J. Hill, "Fast Calculation of a Voltage Stability Index," IEEE nansactions on Power Systems, Vo1.7, No. 1, pp. 54-64, Feb. 1992.
[211 C. Christy, V. Aiarapu, B. Srinivasu, "An Approach to Study Steady-State Voltage Stability of Large Scale Power Systems," Proceedings of International Workshop on Bulk Power System Voltage Phenomena: Voltage Stability and Security, Deep Creek Lake, Maryland, pp. 333-340, August 4-7,1991.
[22] V Ajjarapu, B. Lee, %furcation Theory and its Application ta Nonlinear Dynaxnical Phenomena in an Electricai Power system," PICA-2991, Conference in Baltimore, Md. May 740,1991.
[23] H.G. Kwnna A.K Pasrijan, L X Bahar, "Loss of Steady State Stability and Voltage
CoUapse in Electric Power Systems," IEEE Conférence on Decision and Control, m., pp. 804-811, Dec. 1985.
[24] H.G. K w a n ~ , kK Pasrijan, L X Bahar, "Static Bifurcation in Electric Puwer Networks: Loss of Steady-State Stability and Voltage Collapse," IEEE D-ansactions on Circuits and Systems, Vol. CAS-33, No. 10, pp. 981-991, 1986.
[25] B. Gao, G.K. Morison, P. Kundur, "Voltage Stability Evaluation Using Modal Analysis," IEEE Dansactions on Power Syskms, Vol. 7, No. 4, pp. 1529-1536, NOK 1992.
1261 CA- Canizares, EL. Alvarado, C.L. DeMarco, 1. Dobson, W.F. Long, "Point of Collapse Methods Applied to ACIDC Power Systems," B E Paper # 91 SM491-1 PWS, PES, Summer Meeting, San Diego, Cal3ornia, July 28-August 1, 1991.
[27] P. Kundur, Power System Stability and Control, McGraw-HiIl Book C o m p w 1994.
[281 P.C. Krause, Annlysis of Electric Machinary, McGraw-Hill Book Companv. 1986.
1291 R.M- Mathur, R.S. Basati, "A Thyristor-controlled Static Phase-shifter for Ac Power Transmission," B E E Dansactions On Power Apparatus And Systems, Vol. PAS-100, pp. 2650-2655,1981.
[30] EPRI EL-6079, "Study of Improved Load-Tap-Cbanging for Tramformers and Phase-Angle Regdators," EPRI Publicutwns, Final Report, NOK 1988.
[311 A-E. H~mmad, J. Dobsa, "Application of Thyristor Controlled Phase Angle Regulating Transformer For Damping Subsynchronous Oscillations," lEEE PESC Record, pp. 111-120,1983.
[321 G.W. Stagg, A.H. Al-Abiad, Cornputer Methods In Pozuez Systems Analysis, . McGraw-Hill Book Company, 1998.
[331 L. Gyugyi, Wnified Power-Flow Control Concept for Flexible AC Transmission Systems," IEE Proceedings-C, Vol. 139, No. 4, pp. 323-331, 1992.
[34] S A Nabavi-Niaki, YHodelling and Applications of Unified Power Flow Controller (UPFC) for Power Systems," University of Toronto, Ph.D. Thesis Disserfation, 1996.
[35] M.R. Iravani, D. Maratukulam, "Review of Semiconductor-Controlled (Static) Phase Shifters for Power System Applications,' B E nansactwns on Power System, Vol. 9, N0.4, pp. 1833-1839, NOK 1994.
[361 HA. Peterson, P.C. Kiause, "A Direct- and Quadrature- Axis Representation of a . P a r d e l AC and DC Power System," IEEE fiansactions on PAS, Vol. PAS 85, No. 3,
pp. 210-225, Mar& 1966.
[37] IEEE Task Force on Load Representation for Dynamic Performance, "Bibliography on Load Models for Power Flow and Dynamic Performance Simulation," IEEE IPES Sumrner Meeting, San Francisco, CA, July 24028,1994.
[381 K. Wdve, Wodelling of Power System Components at Severe Disturbances," CIGRE, Report 38-18,1986.
[39] K Jimma, A. Tomac, K. Vu, C.C. Liu, 'A Study of Dynamic Load Models for Voltage CoIlapse Analysis," Proceedings Bulk Power System Voltage Phenornena II, Deep Creek Lake, Maryland, pp. 423-429, Aug. 1991.
[40] Westinghouse Elechic Corporation, %udy of Improved Load-Tap-Changing for Transformers and Phase-Angle Regdators," EPRl EL-6079, Project 2763-1, NOK 1988.
[41] P.M. Anderson, kk Fouad, Power System Stability and Control, Revised Rinting, IEEE Press, 1994.
[421 H.W. Dommel, N. Sato, Tast Transient Stabilify Solution," IEEE Trans. Vol. PAS-91, pp. 1643-1650, Jul~dA~gustl972.
[43J J. Arrillaga, C.P. Arnold. Computer AMlysis of Power Systems, John Wiley, 1990
[a] M. Parniani, "Smd-Signal Stability Analysis and Robust Control Design of Static VAR Compensator," University of lbronto, Ph.D. Thesis Dissertation, 1995.
[451 M. Parniani, M.R. Iravani, "Computer Analysis of Smd-Signal Stability of Power S ystem Including Network Dynamics,' ZEE Proc, Cener. Dans.Distrib. Bans. Vol. -
142, No. 6, pp. 613-617, November 1995
[46] C.W. Gear, Numerical Initial Value Problems in Ordinary Differential Equations, Rentice-HaIl, 1971.
[47] G. Gross, A R . Burgen, % GClass of New Multistep Intevation Algorithms fm the Computation of Power System Dynamic Response,' lEEE Dans, Vol. PAS-96, No. 1, pp. 293-306, JanJFeb. 1997.
[48] M.R. kavani, "A Sofbvare Tool for Coordination of Controllers in Power Systems," IEEE Dans., Vol. PWRS-5, NU. 1, pp. 119-125, 1990.
Appendîx
Al Synchronous Machine Model
Per unit stator and rotor flux linkage equations are [27,28]:
kl.1 Stator Dynamics Not Imicliided
Mer eliminating the stator dynamics and linearizing (3-1) to (3-81, and (A-1)
and (A-2), we get:
A1 Synchronous Machine Model
AS Synchronous M d i n e Model
ad. -Zn a d . ~ " a q . ~ " a q . 1
The reference &ame of machine's d-q axes is transferred to the common D-Q axes using the transformation shown in Figure k2. This transformation can be f o d a t e d as:
where
A I Synchronous Machine Mo&Z
Therefore, the state space equations of each synchronous machine in the common
reference f k n e are:
where the pre-index i refers to the i-th synchronous machine. .AuDg and AiDQ are the z z
voltage terminal and the stator D-Q axes currents of the i-th synchronous machine in the common reference frame, and
Figure k 1: Coordinate transformation.
IL0
AS Synchronous Machine Model
1-2 BaiMoid,, + B,Z;,!$frC6 A,, + BaiZ;A C,
Figure A.2 shows the representation of the exciter block diagram associated with the
synchronous machine. State space equations of the exciter system can be written in a general form as [27]:
adu
A I Synchronous Machine M&l
Figure A.2: Block diagram representation of syachronous machine with exciter
where Xdu is the unsaturated value of Xd, and h+Ez is the vector of exciter state space variables. Overall state space equations of synchronous machine is obtained from (A-9) to
(A-13) as:
where
k l . 2 Stator Dynamics Included
In a similar manner described in the preceding sub-section, the exact mode1 of
synchronous machine including stator dynamics can be derived £kom (3-1) to (3-8). Let
L (:,:2) = The sub-mah consisting of the fist two columns of L-' .
A I Synchronous Machine Model
L ( 3 = The sub-matrix consisüng of the third column of L-l .
Exact mode1 of synchronous machine which indudes stator dynamics is
A I Synchronous Machine Model
.B = L vsy
.D L vsny
Including the exciter model nom (A-11) to (A-13) into (A-16) and (A-17) yields:
where
Psn =
L
r
A1 Spchmnous Machine Mode2
A2 Induction Machine
A2 Induction Machine
Expressing flux linkages of induction machine relating to currents, we get:
where,
Linearizing (3-13) to (3-19) and (A-201, and setting the rotor voltage to zero, yields the induction machine state equation:
where,
A2 Induction Mcrchine
T h e induction machine state equations may be written in a standard form as:
where,
p p p p p p p p p p p p - - - - - - - - - - - - - - - - -
- - - - - -
E 1 ( : 1 : denotes a mat* consisting the first two columns of E-1, and E-1 (3) consists of the f3kh col- of E-l . The pre-index j refers to the? induction machine in the power system.
With the dynamics of the stator equations of induction machine neglected, voltage
equations written in a synchronously rotating reference Game, from (3-13) to (3-16)
becomes:
A 2 Induction Machine
where p is a derivative operator, and
Including torque equation in (A-24), and linearizing the equations give:
Partitioning the matrix in (A-25) yields:
where 111 l, II i2, IIz1, I Ip , and IIu are defined based on (A-25), and
A2 Induction Machine
Further, the stator and rotor cments can be calculated f2om state variables by
linearizing (A-20).
where,
Eliminating Aydqs in (A-25) and (A-28) and rearranging the outcome with respect to
the machine inputs and outputs yields:
where,
A2 Induction Mahine
A3 HVDC System
Makices A , B,, Bs,, B, Cm D,, Qu, and Dm in (3-76) are as the following:
- a b - * if (i, JI = (32) "dc
- ; if (i, JI = (5,3)
O ; Otherwise
- 1 O -kiuii sin bi
O -kivii sin yi 1 - l u d i o -v ~ E o
O O
1 kicos ai ki cos ai
- Cui = -'di0 -'qio
k p s $i ki cos di
Appendix
Test Systems
. - _ .- ., .,". . /- .
B.l Data for the Power System of Chapter 4
Transfomers and the equivalent transmission line data in Figure 4.1 are as
Table B-1: Transformer and transmission line data
Transmission Zr 0.2150 UEh
Transformer X, 0.0006 pu
Per unit system is based on 100 MVA and 500 KV as the base power and base
voltage, respectively The per unit voltage at the sending end terminal is set at
1.1 pu.
B.2 Parameters of the AC/DC Test Systern of Chcrpter 5
B.2 Parameters of the ACIDC Test System of Chapter 5
'liab1e B-2: Generator data
Generator -ber
B.3 Putameîers of the Excifers of Chapter 5
B.3 Parameters of the Ekciters of Chapter 5
Table B-3: Excitation system data for nnits G1 to 6 5
Table B-4: Excitation system data for units G6 and GS
B.3 Parameters of the Exciters of Chapter 5
Table B-5: AC line parameters
Line No.
LI
L2
L3
L4
L5
L6
Length(de1
108
210
210
185
185
160
Xi (CUmiIe)
O. 1043
0.3618
0.3618
0.3618
0.3618
0.3618
R(Wmile)
0.0019
0.0028
0.0028
0,0028
0.0028
0.0028
X& (Wmile)
0.4616
0.4516
0.4516
0.4516
O .45 16
0.4516
k* (%)
O
O
O
O
O
O
B.3 Parameters of the Erciters of Chapter 5
* k is the seriea compemation level
130
RWmile)
0.0118
0,0019
0.0023
0.0064
0.0064
0.0064
0.0064
0,0064
0.0064
0.0116
0.0084
0.0084
0.0084
0.0140
0.184
O. 181
X, «Unde)
0.5227
0.4618
0.3714
0.4762
0.4762
0.4762
0.4762
0.4762
0.4762
0.3962
0.3742
0.3742
0.1023
O. 1642
0.3216
0.2123
<
Line No.
L16
LI7
L18
LI9
L20
L21
L22
L23
L24
L25
L26
L27
L28
L29
L30
L31
Length(mi1e)
115
210
164
145
145
145
123
123
123
136
187
187
69 +
73
50
78
& (Nmile)
0.2373
0.4611
0.4322
0.3914
0.3914
0.3914
0.3914
0.3914
0.3914
0.3412
0.4118
0.4118
0.4102
0.3714
O. 1684
0.4311
- k* (%)
35
40
O
O
O
O -
O
O
O
40
35
35
O
O
O
O
B.3 Parameters of the Exfiters of Chapter 5
Table B-6: Load data
Load# 1 MW 1 Power Factor 1 1
2
1470
3
4
0.79 Lagging 1
0.85 Lagging
1572
5
0.93 Lagging
Induction Motor h a d +
Passive Load
1720
1200
7
0.79 Lagging
0.85 Lagging
8
2100
9
0.84 Lagging
2700 0.93 Lagging
1650 0.95 Lagging
B.3 Parameters of the Exciters of Chapter 5
Table B-?= Transformer Data - --
Transformer #
Tl
kV
25/525
X%
10%
R%
1%
B.3 Parameters of the Exciters of Chapter 5
!t'able B4k Generator data - -
G1 G2 G3 G4
# of paraIlel uiits 2 4 3 4
Rated voltage (kV) 25 26 25 20
# of poIes 2 2 2 2
Rated fkequency (Hz) 60 60 60 60
~1 (PU) 0.223 0.205 0.241 0.246
H (s) 2.74 3.06 2.60 3.43
G7 is an infinite bus at 25 kV
B.3 Parameters of the Exciters of Chapter 5
Tàble B-9= Induction machine data
TSble B-10: Data for the UEI'C control
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