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Modeling and Analysis ofSystem Transients Using
Digital ProgramsPREPARED BY THEIEEE Working Group 15.08.09
IEEE Power & Energy Society
1998
TECHNICAL REPORT
PES-TR7Formerly TP133
IEEE 2013 The Institute of Electr ical and Electronic Engineers, Inc.No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publis
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IEEE PES
pecial ublication
MODELING AND ANALYSIS
OF
SYSTEM
TRANSIENTS
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Prepared
By
IEEE
Working
Group
15.08.09
MODELING AND ANALYSIS OF SYSTEM TRANSIENTS USING
DIGITAL PROGRAMS
Working
Group Chairman
A. J. F. Keri American Electric Power
Task
Forces and Chairmen
1 Power Electronics
2 Slow Transients
3 Switching Transients
4 Fast Front Transients
5 Very Fast Front Transients
Siemens
6 Protection and Controls
7 Bibliography
K. K. Sen Siemens , Le Tang ABB
R. Iravani Univ. of Toronto
A. M. Gole Univ. ofManitoba ,
D. W. Durbak PTI
A. F. Imece ABB
J.A. Martinez-Velasco Univ. Politec.
de Catalunya* , D. Povh
A.K.S. Chaudhary Cooper Power
System , R.E. Wilson WAPA
T.E. Grebe Electrotek Concepts, Inc
J.A. Martinez-Velasco *
Editors:
A. M. Gole, J. Martinez-Velasco, A. J. F. Keri
Acknowledgments: The Working group was originated and technically
supported by Dr. B. R. Shperling New York Power Authority . T.E. Grebe
was also the Secretary
of
the Working Group. Dr. A. M. Gole had also the
difficult job
of
organizing Task Force reports into this Special Publication.
Tutorial On
Modeling And Analysis or SystemTransients Using Digital Programs
Abstracting is permitted with credit to the source. For other copying, reprint, or republication permission, write to the IEEE
Copyright Manager, IEEE Service Center, 445 Hoes Lane, Piscataway, NJ 08855-1331. All rights reserved. Copyright 1998
by The Institute of Electrical and Electronics Engineers, Inc.
IEEE Catalog Number: 99TP133-0
Additional copies of this publication are available from
IEEE Operations Center
P. O. Box 1331
445 Hoes Lane
Piscataway, NJ 08855-1331 USA
1-800-678-IEEE IndividuaUMember Orders
1-800-701-IEEE Institutional Orders
1-732-981-0060
1-732-981-9667 FAX
email: customer.service@ieee.org
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TABLE OF
CONTENTS
Introduction
i
1. Background 1-1
2.
Power
Electronics 2-1
3. Slow
Transients
3-1
4. Switching Transients 4-1
5. Fast
Front
Transients 5 -1
6.
Very
Fast Front
Transients
6-1
7. Protection and Controls 7-1
8. BibIi
0grap
hy ....................... ..... ....... .. .. .. 8-1
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Modelingand Analysis ofSystem TransientsUsing
Digital Programs
Introduction
IEEE PES Working Group 15.08.09
A J F
Keri Chairman ,
A M
Gole
1. INTRODUCTION
Thisdocumentis written in orderto provideguide-
lines for the modelingof power systemapparatusfor use in
time- domainsolutionof electromagnetic transientphenom-
enon. This publication has been arrangedin the following
eight 8 parts.
Part
:Background
Part 2 :PowerElectronics
Part 3:SlowTransients
Part
:Switching Transients
Part 5 :FastFrontTransients
Part 6
Very
Fast FrontTransients
Part 7 :ProtectionAndControl
Part 8 :Bibliography
A
generalstatementof each area is as
follows
BACKGROUND
This sectionpresentsa comprehensive summary of
thebackground andstateof theart for thetransientsolutions,
representation of control systems, and modeling of power
systemcomponents.
2
POWERELECTRONICS
Theguideline presentsthe basicissuesthat arecriti-
cal for successfullymodeling of power electronics devices
andthe interfacebetweenpowerelectronics andtheutilityor
industrial system. Modelingaspectsare presentedfor simu-
lation of the semiconductorswitchingdevices, power elec-
tronics system,snubbertreatment, and simulation errors and
control . A number of simulation examples, including
FACTS
modeling, are presented.
3SLOW TRANSIENTS
Modeling guidelines are presented for investiga-
tionsof smallsignaltorsional oscillations, large -signalshaft
transientstresses, turbine-bladevibrations, fastbus transfer,
controllerinteractions, harmonics interaction, and resonance
phenomena. Sample test systemsand simulationresults are
provided.
i-I
4
SWITCHING TRANSIENTS
The range of frequencies of primary interest in a
switching transients studyvary fromthe fundamental power
frequency up to
10kHz.
Switchingsurgemodelingguide-
lines are presentedincluding modelingof the variouspower
systemcomponents suchas transmission lines, cables,trans-
formers, sourceequivalents, loads and circuit breakers. In
addition, typicalcasestudiesare alsopresented.
5FASTFRONTTRANSIENTS
Modeling guidelines are presented for fast front
transients i.e., frequency rangefrom
10 kHz
up to
1 MHz ,
withparticularemphasison lightningsurgeanalysisof over-
head lines and substation. Modelingphilosophies, simpli-
fiedmathematical relationships,typical data, and examples
are given for various power system components. A case
studyis presentedin order to illustrate the overallmodeling
procedure.
6V RYFASTFRONTTRANSIENTS
Theobjective of this sectionis to providean expla-
nation of the phenomena of very fast transients, in the fre-
quencyrangeof
100
kHz to
50 MHz.
Thistypeof transients
typically occur in the gas insulated substations GIS .
Effects andmodelingguidelines forGIS are presented. An
example of a GIScalculationwith detailedinput data is pro-
vided. A simulation accuracyis verifiedwith fieldmeasure-
ments
7PROTECTIONAND ONTROL
Generalguidelinesformodelingof protection sys-
tems is presented. Because digital modeling
of
protection
systemsin the electromagnetic transients programsis a rela-
tivelynewprocedure, this section describes the advantages
and limitations of theprotectionsystemmodeling. Model-
ing of instrument transformers, relays - electromechanical,
staticandmicroprocessor based are summarizedandmodels
are presented.
8BIBLIOGRAPHY
A
comprehensive list of references on the subject-
are provided.
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Digital Computation of Eelectromagnetic
Transients in Power Systems:
Current
Status
JuanA.Martinez-Velasco
Departament d Enginyeria Electrica
Universitat Politecnica deCatalunya, Spain
Abstract-
Thisdocumentpresentsan introductionto time-domain
solution of electromagnetic transients in power systems using a
digitalcomputerCurrently, themostwidely usedsimulation tools
to
solve
electromagnetictransientsare basedonthe trapezoidalrule
andthemethodofcharacteristics(Bergeron smethod). Onlyworks
related to this solutionalgorithmare considered in this
document
whichcoverstwomaintopics: solution techniques and
modeling
of
powercomponents.
Keywords : Electromagnetic Transients, Time-domain
Simulation, TrapezoidalRule, Numerical Oscillations, Control
Systems, Modeling.
1. INTRODUCTION
Transient phenomena in power systems are caused by
switching operations, faults, and other disturbances, such as
lightning strokes. They involve a frequency range from DC to
several MHz. A rough distinction is usually made between
electromechanical transients, traditionally covered by transient
stability studies, and electromagnetic transients. The latter type
of transients can occur on a time scale that goes from
microseconds to several cycles; they are a combination of
travelling waves on lines, cables and buses, and ofoscillations
in lumped-element circuitsofgenerators, transformers andother
devices. Some electromechanical transients, such as
subsynchronous resonance, for which detailed machine models
are needed, are usually included in this class of transients.
Several tools have been used over the years to analyze
electromagnetic transients. At early stages, miniature power
systemmodels, known as Transient Network Analyzers INA),
were used. At present, the digital computer is the most popular
tool, although INAs are still used; in addition, the new
generation of real-time digital systems are probably the most
adequate tool in some applications for which either a very
high-speed or a real-time simulation is required.
Many techniques have been developed to solve electromagnetic
transients using a digital computer. They can be classified into
two main groups : frequency-domain and time-domain
1-1
techniques. The subject of this document is the digital
simulation ofelectromagnetic transients inpower systems, using
time-domain techniques. Presently, the most widely used
solution method is based on the application of
the trapezoidal
rule and the Bergeron s method, also known as method
of
characteristics [1] - [6].
This document has been arranged as follows. Section 2 deals
with the basic solution techniques either already implemented
or proposed for implementation in electromagnetic transients
programs (emtps). It covers not only the algorithms aimed at
solving the transient solution, but procedures to reduce
numerical oscillations produced by the trapezoidal rule,
initialization methods, and procedures to solve the interface
between power networks and control systems.
Section 3 presents a summary ofmodeling works related to the
most important power components taking into account their
frequency-dependent behaviour.
Due to difficulties for developing power component models
accurate enough for a wide frequency range, much work has
been done toprovidemodeling guidelines for digital simulation
of every type of transient phenomenon. Section 4 summarizes
the work done in this area and reports about works still in
progress.
Some topics, such as parallel computation or real-time emtp
based simulation of electromagnetic transients, which are
closely related to the main subjects of this document are not
covered here.
A selected bibliography related to topics
of
each part has been
included at the end
of
this document.
2. SOLUTION METHODS
2.1 TRANSIENT SOLUTION
The studies to solve travelling wave problems by means
of
a
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Thetrapezoidal ruleisusedto convertthedifferential equations
of thenetworkcomponents into algebraic
equations
involving
voltages, currentsandpast
values.
Thesealgebraic equations are
assembled usinga nodalapproach
digital computer were started in the early
1960
s using two
different techniques, the Bewley s lattice
diagram
[7] and the
Bergeron
s
method
[8]. Thesetechniqueswere
applied
tosolve
small
networks,
withlinearandnonlinear lumped- parameter, as
well as distributed-parameter
elements.
The extension to
multinode networks was made by H.W. Dommel [1]. The
Dommel s scheme combined
the Bergeron s
method
and the
trapezoidal rule intoan algorithm
capable
of
solving
transients
insingle- andmulti-phase
networks
withlumped anddistributed
parameters. This solution method was the origin of the
ElectroMagnetic Transients Program (EMTP), whose
development was supported by Bonneville Power
Administration (BPA).
Using
compensation,
nonlinear elements are represented as
currentinjectionswhicharesuperimposed to thesolutionof the
linear
network
afterthis solution hasbeen computed. Figure1
shows the scheme of the compensation method for a single
nonlinear
element.
proposed to cope with nonlinear and time-varying elements
[11] . These modifications were based on a current source
representation, a piecewise-linear representation or the
compensation method. Someof theadvantages anddrawbacks
shownby theseapproaches werediscussed in [5]and
[11].
r
Nonlinear
V
km
e q u a t i o
-
l
ACS g)
ref
a
Vb
JOO
Vc
100
100
0
0 10
Fig. 20The BlockDiagramof a PLL
' 0
lime
mS
60
Fig.24DerivedFrequency Reference
() 00
Iime(mS)
DO
PLLO>TACS IH['AR T
yp
e 9)
10
- -
i
i
I
/
/ I / /
/
I
+:
f
...
....
__
....
Ii.
I
-+
I
:::
f-
-
_
..._
i
/
7f / /
]
/
J
1/
17
I
1
1
i
/
Iime (mS)
10
Fig. 21 Input three-phase Voltage Signal
Fig. 25 Outputof VCO
0.5 -1-- --- -- -- L-- - -i-.:---f- I----+--------,-j
Fig. 22DQVoltage Components
Fig. 26 Comparison ofInput andObtainedSyn. Signals
The response of this control circuitry to a system
disturbance is illustrated in Fig. 27. A balanced system fault
is placed on and removed from the system, resulting a three
cycle voltage sag.
Three phase fault
Rf=0.01 ohms
Tin=0.025s
Tcl=0.075s
Kpro= 100
Kint =8.3E-3
100
0
0 60
Time mS
DO-PLLO >l
ACS
-DU MD13 lype g)
10
v ,
:
,
0.1000
0.0500
0 . O O
-0.1000
o
-urseo
Fig. 23DerivedPhaseError
With above given control parameters, it takes the
PLL
about three cycles to be relocked into the system volt
age.
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1
40.0
SNUBBC
SNUBBR
ATRMNL
i
GTRMNL
SNUBBC \... i
A model for a general, unidirectional conducting,
three terminal, controllable
power
electronic device
with
snubber connections is shown in Fig. 29. An actual snubber
configuration can be different
from
one application to
another. However, if the purpose
of
a simulation is not to
design the snubber, a sample snubber configuration shown in
this figure can often provide satisfactory results.
The fmite nature of the simulation time step that the
EMTP type programs use also poses another problem for
power electronic circuit simulation which necessitates the
use
of
snubber circuits across fast acting power electronic
switches. Note that in some situations the snubber Rand C
values
of
the actual system
mayor
may
not work in simula
tions using some programs. In this case, the
Rand
C values
of
the snubbers needed for stable simulation is primarily
dependent on the time step and secondarily on systemconfig
uration (capacitors and inductors in the system) and the load
current level. Programs using special features such as vari
able time steps (very short time steps during switching) or
interpolated switching [59] (simulate the switching very
close to the required instant using linear interpolation
between time steps) do not require fictitious snubber circuits.
Therefore, one of the following measures or their combina
tions can be taken to prevent numerical inaccuracies in the
simulation:
Select a smaller time step
Use artificial snubber circuits
Introduce a small smoothing reactor for DC links
Introduce proper stray capacitances in the system model
Provide a parallel damping for lumped system.
oscillations in which case it
is
not a concern to the simulation
engineer. Otherwise, some of the measures listed later in this
section may have to be implemented to obtain correct results.
Note that this example of PLL logic based on the
three phase to DQ transformation is valid for three-phase bal
anced application. Also, its performance characteristic is
highly affected by the parameter settings.
Fig. 28 The PLLCircuitry Responseto a SystemDisturbance
Three phase fault
Rf=O.OI
ohms
Tin=0.025s
Tcl=0.075s
With Modified:
Kpro = 1000
Kint = 8.3E-4
If the circuit parameters are changed from the above
given values to the values listed below, for the same system
and fault, one can observe that the same PLL logic can be
relocked into the system voltage within a half cycle period
of
the time as shown in Fig. 28.
Fig. 27The PLLCircuitryResponseto a SystemDisturbance
3.5. Snubber
Treatment
inEMTPtypePEModeling
The simulation programs using trapezoidal integra
tion method are inherently prone to spurious oscillations
(also known as chatter) in capacitive and inductive circuits
when subjected to sudden changes such as step change in
voltage, current injection and switching. Some EMTP type
programs take special measures to detect and remove these
CTRMNL
Fig. 29 A Sample Snubber Circuit
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3.6.Simulation ErrorsandControl
DC Link
rrors in a Power Electronics simulation can come
through the following sources:
1. switching device approximation and system reduction
2. added circuit elements for numerical oscillation control
3. control system simplification
4. time step related truncation
5. program structure and solution method introduced inter
facing time delay
6. incorrect system initial conditions
AC Supply
~
Six Pulse
Diode Rectifier
PWM
Inverter
Induct ion
Motor
For application simulations, some errors resulting
from the system simplification and measures of numerical
oscillation control are acceptable. The fourth and fifth items
in the list can be controlled by reducing the time step size. A
recommended time step size should not be greater than 1/5 to
1/20
of the
period
of
the highest concerned
frequency
cycle. For an example, for an IGBT inverter simulation with
5000Hz PWM switching, a selected time step could be 10
ms. However, if the objective
of
the simulation is to see the
detailed transient at the terminal of the induction motor
which is fed by the inverter through a section of the cable
with an 1.0 ms travel time, an adequate time step should be
0.2 ms or smaller.
Fig. 30. Electrical Circuit Configuration of an Adjustable Speed
Drive
The built-in diode models are used to construct the
front end rectifier. The same switching devices with added
open/close controls are used to represent output inverter
IGBTs. The EMTP input data modules are use to build this
example case. Both the output reference frequency and the
PWM carrier frequency are made to be controllable. Model
ing of a signal processing and firing pulse generation is illus
trated in
this example . The
motor load of the
drive
is
represented by its R+jX equivalent branch. The simulated
AC input current, carrier and reference signal for the PWM
control, AC output voltage and current are presented in Fig.
31 through Fig. 33.
PW
vS
I>T
ACS - D
JM
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Fig.33.Simulated ACOutputLine-to-line Voltage ofA PWM-VSI
Adjustable SpeedDrive
4.2.Simulation ofVoltage Notching Causedby
Operation
of
Current Source Inverter
CSI)
ASD
8:xJ
PWVSI>NVRTA-
INVRTB(Type
8)
i
600,
II
II
II
00
i :
slOO
I i
rio
1
Ig
-lOO
t
.
I
i
I
I
.
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Vo ltoge 01
4160
Vo lt Surge Copocitor - Bose
Cose
-6000
-8000
--
----:. . .-------cc----------I
tl
nous condenser (SC) and half-and-half mix of the two
(SVC+SC).
Fig. 38 shows the typical results obtained from the
simulation for a permanentDC block. The fixed compensator
case does not control the overvoltage; however, all other
optionsdo. The SVC option is the fastest to respond followed
by the SVC+SCoption and lastly the SCoption. This simula
tion setup can be used to conduct almost any type of perfor
mance study including a thyristor miss-fire in HVDC valve
group or in the SVC itself.
0.6
.5
.2 0.3 0.4
Time (s)
0.1
1-
- - - - - ,- - - - - - - YG:- - - - - - - - - -
1.6
1.5
, - . .
1.4
;:3
5
Q)
1 3
eo
S
~
1.2
/ )
~
1 1
u
1.0
)
t:
Q)
>
s::
0.9
-
0.8
0.7
0.0
The third example is an illustration case for model
ing of an HYDC system with shunt TscrrCR compensation
at the inverter bus [54]. The simulation example is made
using PSCAD/EMTDC. The schematic systemshown inFig.
37 is a modified version of the GlGRE BenchmarkModel for
HYDC Control Studies [55].
Fig. 36.Simulated waveform
at
surge
capacitor
location (4.16
kV
bus
ofcustomer on
parallel feeder)
The inverter short circuit ratio has been reduced
from its original value of 2.5 to 1.5to make the study more
interesting. The DC link is a 1000MW, 500kV, 12 pulse
monopolar system. There are damped low and high pass fil
ters at each converter terminal to reduce the distortionon the
AC bus. The control scheme for the HYDC system consists
of a rectifier current controller with the gamma controller.
4.3. Simulation ofHVDC
Terminal
and Shunt TSCITCR
Compensation
The SVC system is a -200/+300 MVAr, 12 pulse,
TCR and TSC (two stage) combination connected to the
inverter bus through a step up
transformer,
The SVCcontrols
are designed to coordinate the control of TCR and TSC in
such a way that the combined susceptance of the SVC is con
tinuous over its entire operating range. The basic control
mode is voltage control and has as a voltage droop built into
the controls. Several studies to evaluate the recovery to full
power after a contingency were simulated [54]. The perfor
mances of
several compensation options were compared.
These options included fixed capacitors (FC), SVC, synchro-
Rectifier AC
System
1000MW
500kV
12 Pulse
Fig. 37. Study
System
Inverte
r AC
System
Fig.
38
Inverter
AC
Voltage
Follo
winga
Permanent DC
Block
4.4. ModelingofRotatingMachines
Two possible situations can be considered for mod
eling a rotatingmachine when simulating a power electronic
system
1. The machine is a component of a larger system where
one or several power electronic devices are operating,
for instance a synchronousmachine connected to a
transmissionnetworkwhere FACTSdevices are used to
control power flows and improve transient stability.
2. The machine is part of the power electronic system, for
instance an adjustable speed drive.
Similar modeling guidelines for representing rotat
ing machine in both situations can be used, however some
particular considerations can be taken into account in some
cases andstudies.Modelingguidelines provided in this docu
ment assume that power electronic systems operate at low
frequencies, betweenDC and 3 kHz. Therefore only the rep
resentation of rotating machines for this frequency range is
discussed. Regardless of the application to be simulated a
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detailed modeling for the electrical and the mechanical parts
is usually required, saturation effects should be included, and
capacitance effects can be neglected. Frequency dependent
of
electrical parameters, mainly rotor parameters might also be
considered. If frequencies of the transient case to be simu
lated are higher than 3 kHz, the simulation time is no longer
than a few milliseconds and the machine is not close to any
power
electronic system (Le. a synchronous machine con
nected to a transmission system), the mechanical part can be
usually neglected and
the machine
can
be represented by
means of an ideal source behind its subtransient reactance
and a frequency-dependent resistor; capacitance effects
become important , they can be represented by a parallel
capacitance-to-ground [1].
Other representations should be considered for spe
cific applications
A) An
aggregated
representation of several
machines can be used to reduce complexity and simulation
time. Ref. [2] resents an aggregated induction model to be
used in power quality studies where short term interruptions
(i.e. sags) are
of
concern.
B) A very simplified representation for synchronous
and induction machines
can
be
used
in harmonic studies
when the machine is not directly connected to the harmonic
source [3].
An important aspect of the simulation of a rotating
machine is the procedure to obtain machine parameters and
the information where these parameters are derived. Electri
cal
parameters of
synchronous machines
may usually
be
obtained in one of the following forms: (1) data supplied
from manufacturer (conventional stability format data, stand
still frequency response), (2) data from field tests (on-line
frequency response, load rejection test, other tests) and (3)
computer calculation using the finite-element method [4]. A
good discussion about methods to obtain electrical and also
mechanical parameters can be found in [5]. Data from steady
state and short circuit tests include reactances and time con
stants, armature resistance as well as saturation effects. Sev
eral procedures have been proposed to pass from these data
to electrical parameters which are used in the transient solu
tion of the machine [6-8]. Although these tests and the corre
sponding procedures can also be used to obtain electrical
parameters
of
an induction machine, data conversion proce
dures for this type of machines are performed from different
specifications [9-10].
Frequency response tests have received much atten
tion during the last 25 years. Several methods have beenpro
posed to obtain parameters of d-
and
q-axis
equivalent
circuits; they are based on standstill frequency response
(SSFR) [11-14], and on-line frequency response [15-16].
Some techniques have also been developed to account for
saturation effects [17].
4.5. VoltageSource InverterBased FACTSDevices and their
Modeling Techniques Using EMTP
This section describes the fundamentals
and
the
modeling techniques of VoltageSource Inverter-based Flexi
ble lternating Current Transmission Systems
(FACTS)
devices, namely, STATic synchronous COMpensator (STAT
COM),
Static Synchronous Series Compensator
(SSSC), and
Unified Power Flow Controller (UPFC) using an EMTP sim
ulation package. The FACTS model includes all the neces
sary components - a voltage source inverter with a DC link
capacitor, a magnetic circuit, and a realizable controller. The
UPFC model consists of two solid-state
voltage
source
inverters which are connected through a common DC link
capacitor. Each inverter is coupled with a transformer at its
output. The first voltage source inverter,
known
as STAT
COM, injects an almost sinusoidal current, of variable mag
nitude, at the point of connection. The second voltage source
inverter, known as SSSC, injects an almost sinusoidal volt
age, of variable magnitude, in series with the transmission
line. When the STATCOM and the SSSC operate as stand
alone devices, they exchange almost exclusively reactive
power at their terminals. While operating both the inverters
together as a UPFC, the injected voltage in series
with
the
transmission line can be at any angle with respect to the line
current. The exchanged real
power
at the terminals of one
inverter
with
the line f lows to the terminals of the
other
inverter through the common DC link capacitor. The func
tionalities of the models have been verified.
4.5.1 VSI BasedFacts Devices
Flexible Alternating Current Transmission Systems
(FACTS) devices, namely STATic synchronous COMpensa
tor
(STATCOM),
Static Synchronous Series Compensator
(SSSC) and
Unified Power Flow Controller
(UPFC), are
used to control the power flow through an electrical transmis
sion line connecting various generators and loads at its send
ing and receiving ends. Each of the STATCOM and the SSSC
consists
of
a solid-state voltage source inverter with several
Gate Tum
Off
(GTO) thyristor switch-based valves and a DC
link capacitor, a magnetic circuit, and a controller. The num
ber
of
valves and the various configurations
of
the magnetic
circuit depend on the desired quality of AC waveforms gen
erated by the FACTS devices. When the STATCOM and the
SSSC operate as stand-alone devices, they exchange almost
exclusively reactive power at their terminals. While operat
ing
both
the inverters
together
as a UPFC, the
exchanged
powerat the terminals of each inverter can be reactive as well
as real. The exchanged line flows to the terminals of the other
inverter through the common DC link capacitor. The objec
tive in this section is to describe each component, such as a
voltage source inverter, a magnetic circuit, and a controller
of
FACTS devices and its modeling techniques using an EMTP
simulation package. Since, the emphasis
of
modeling is
purely on FACTS devices,
the power
system in
which
the
FACTS devices are connected to has been modeled in a sim-
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Fig.40 A Static
Synchronous
SeriesCompensatorModelin EMTP
sssc
12=
_
~ ~ i i
v, i;
- ES22
E, -
1DC2 ES2
-
VSI2
t.Cl
C 9 r t r : ' o l
~
plistic way. A simple transmission line, shown in Fig. 39, has
an inductive reactance, X
s
and a voltage source V
s
at the
sending end and an inductive reactance, X,., and a voltage
source.P, at the receiving end, respectively. The STATCOM
is connected at BUS 1
of
the transmission line as shown in
Fig. 39 . The STATCOM model in EMTP consists
of
a har
monic neutralized voltage source inverter,
VSIl,
a magnetic
circuit,
MCI
a coupling
transformer
,
TI
a mechanical
switch, MS I , current and voltage sensors, and a controller.
The STATCOM injects an almost sinusoidal current at the
point
of connection .
This injected
current is
almost
in
quadrature with the line voltage, thereby emulating an induc
tive reactance or a capacitive reactance at the point of con
nection. To achieve the basic function
of
a STATCOM, the
inverter is operated by regulating the reactive current flow
through it.
BUS1
ii,
Fig. 39A StaticSynchronous Compensator Modelin
EMTP
The UPFC which is connected to the simple trans
mission line is shown in Fig. 41. The UPFC model in EMTP
consists of two harmonic neutralized voltage source invert
ers, VSIl and VSI2, two magnetic circuits, MCI and MC2 ,
two
coupling transformers
,
Tl
and
T2,
four mechanical
switches ,
MSI
MS2, MS3, andMS4, two electronic switches,
ES2 and ES22, current and voltage sensors, and a controller.
The voltage source inverters are connected through a com
mon DC link capacitor.
In
a basic operation of a UPFC, the
STATCOM is operated by regulating the reactive current
flow through it and the SSSC is operated by injecting a volt
age in series with the transmission line.
Fig. 40 shows an SSSC connected in series with the
simple transmission line between BUS 1 and BUS 2. The
SSSC model in EMTP consists of a harmonic neutralized
voltage source inverter, VSI2, a magnetic circuit, MC2, a
coupling transformer, T2, a mechanical switch, MS2, two
electronic switches,
ES2
and
ES22,
current and voltage sen
sors, and a controller. The SSSC injects an almost sinusoidal
voltage, of variable magnitude, in series with the transmis
sion line. This injected voltage is almost in quadrature with
the line current, thereby emulating an inductive reactance or
a capacitive reactance in series with the transmission line.
ii,
UPFC
12=
_ ~ ~ i i
v, i;
- ES22
E,. -
. ES2
'DC2
MS3
-
P.C1
VSl1 MS4\ISI2 t.Cl
C Q n t r : Q I
Fig. 41A UnifiedPowerFlowController Modelin EMTP
4.5.2 DESCRIPTIONOF THE INVERTER
Fig.
42 shows a single phase
inverter
circuit,
referred to as a 3-level pole, which consists of a positive
valve, A+, a negat ive valve, A-, and an AC valve , AAC '
When a pole is connected across a series of capacitors which
are charged with a total DC voltage of vDC and the valves are
closed and opened alternately, the pole output voltage, v
AD,
at the midpoint of the pole A with respect to the midpoint, 0,
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(1)
N
InverterOEF
-300
.
3 0
o
E
VE,1
V0,1
Vx
x
r---o:-
Vy
MAGNETIC
y
f c:>
-
ORCUIT
r
Vz
B lJc
zf--c:>-
A l
VC,1
VA,1
. 5 V a : : ~
o
O . 5 V a : : ~
Fig. 44 shows two 6-pulse inverters (ABC and DEF)
which are operated from the same DC link capacitor. On the
AC side, they are connected to a 3-phase load (XYZ) through
a magnetic circuit. The poles D, E, and F are operated in such
a way t ha t th e pole voltage fundamental phasors
VE,
1,
Ve,1
and
VF,1
and are 120 apart and the funda
mental voltage phasor set
of
the DEF inverter lags the funda
mental voltage phasor set of the ABC inver ter by 30. The
displacement angle between two consecutive 6-pulse invert
ers in a multipulse inverter arrangement is 21t
/6m,
where
m
is
the total number
of
6-pulse inverters used. The configuration
of the magnetic circuit in Fig . 44 is
such
that if an inverter
pole voltage is time shifted by an angle of -e, the fundamen
tal and all the harmonic components of the pole voltage get a
phase shift by an angle of +e in the positive direction, irre
spective of their sequence.
Fig.44 A 12-Pulse HarmonicNeutralized InverterConfiguration
with3-Level poles
VNO consists of only a fundamental component and odd har
monic components
n)
given by the equation (1) where
n
=6k
1 for k =1,2,3, etc.
2
fA
n = n7/
DC
ccsn):
where
y
is the
dead
period during which the AC
valve operates in each quarter cycle and the pole output volt
age is zero and n=2k
+
1 for k =0, 1, 2, 3, etc. For
y
=0, the
fundamental as well as all the harmonic components have the
highest possible amplitudes.
Fig. 42 A 3-Level Inverter Pole and itsOutputVoltage
The amplitude
of any
odd multiple
of
fundamental compo
nent is
At- c=a:cJ
aT
3 Levellnverter
Pole I>r
aT
W
A ,cNJ
aT
rav
aT
COl
O . 5 v o c ~ At-
o
o 5 v < t : ~
7 t
, Vf (j 1t-l'y Y
. 5 v o c
I>r
1
VIC Oy
1t - ( 1 t .
..{ .
5v
-
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ing
output
voltage exhibits a fundamental
component
and
odd harmonic components n) given by
the
equation
(1)
where
n
= 12k
1 for
k =
1, 2, 3, etc. Note tha t the output
voltage of a 12-pulse inverter with 3-level poles is referred to
as a 12-pulse
waveform
when
the poles are operated
with
dead angle
y
=
o.
Fig. 45 shows a possible configuration of the mag
netic circuit
which can
be
used
to generate a 12-pulse har
monic neutralized voltage. The ABC 6-pulse inverter voltage
is fed to a
Y-Y
transformer and
the
DEF
6-pulse
inverter
voltage
is fed to a
Y
transformer.
The
inverter
s ide A
winding and
DE
winding
wil l have
pe r tum
fundamental
component voltages which
are of
same magni tude and
in
phase and
the fif th
and
the seventh harmonic components
each of which are of same magnitude but in opposite phase.
Therefore, if the l ine side of the transformer windings are
connected in series, the phase-X voltage will exhibit only a
fundamental component and 12-pulse harmonic components.
Note that the inverter side ( winding has
J
times the turns
as the inverter side
Y
winding has. This is needed in order to
keep the same volts
per
turn in both windings. The line side
inverter windings
can
have any turns ratio other than 0.5 to
increase or decrease the output voltage.
component and odd harmonic components n)where n
=
12k
1 for
k
=1, 2, 3, etc. The presence of 12-pulse harmonic
components in the inverter output voltage may not be accept
able in many applications.
Therefore,
an inverter with a
higher pulse output voltage should be considered [56-58].
4.5.3 MODELING TECHNIQUE
ig. 46 shows the block diagram
of
the
EMTP
simu
lation
program
layout.
Sample EMTP program
files
are
given in [56-58]. First, some general constants are defined.
Next, the control or the Transient Analysis of Control Sys
tems (TACS) section receives its input signals from the sen
sors or measuring switches. This section generates the gating
signals for the pole valves on the fly. The ideal pole volt
ages are mathematically combined to produce
harmonic
neu
tralized
inverter
voltages, eI,
which
are fed to the
source
section. In an actual simulation case, the gating signals are
used to operate the pole valves of an inverter structure such
as the one shown in Fig. 42.
IGeneral
Qlnsta1Is
I
n
timeshift
phase
final time shift phase
final
shift phase
shift
phase
pole A
angle
poleD
angle
5
-5*(0)
0
0
-5*
-1tI6
+1t/6 1t
7
+7*(0)
0
0
+7*-1tI6
+1t/6 1t
11
-11*(0)
0
0
-11*(
-1tI6
+1t/6
0
13
+13*(0)
0
0
+
I3*(-1tI6) +1tI6
0
17
-17*(0)
0
0
-17*
-1tI6
+1tI6 1t
19
+19*(0)
0
0
+19*(-1t/6 +1t/6
1t
23
-23*(0) 0
0
-23*(
-1t/6
+1t/6
0
25
+25*(0)
0
0
+25* -1tI6) +1t/6
0
Table 1 PhaseAnglesof a 12-PulseInverter Phasors
ConboI/TACS
Brmch
Transnission
Li1e
Tn ISformeI
Solrnes
T
oobo ed
.1CIepeI1dert
Inverter
Voltages
Fig.45 A Magnetic Circuitfora
12-Pulse Harmonic
Neutralized In
verter
The 12-pulse inverter configuration, shown in Fig.
45, presents a 3-phase voltage which contains a fundamental
Fig. 46 EMTP Modeling Structure
Each valve,
located
in the switch section, can be
modeled with a number of
GTO
thyristors connected in
series
each
having
an
antiparallel diode
and appropriate
snubber circuits. The pole output voltages are fed to a mag
netic circuit, located in the branch section, which produces a
3-phase vol tage set. In this way, the effects of a
nonideal
magnetic circuit, which includes leakage reactance, magnetic
saturation, etc.
can
be studied. However , in this paper, the
valves and the magnetic circuit are assumed to be ideal. The
voltage, vDC across the DC link capacitor is maintained by
the power balance equation at both
AC
and
DC
sides of
the
inverter. This modeling technique gives sufficient insight to
the operation of the power circuit which produces a 3-phase
voltage set. The source section has some independent volt
age sources which establish the power flow in a transmission
ri
VF
Ve
Vx
Vo
Vy
VA
Vz
VB
Vc
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line. Next, the control led and the independent sources are
fed to the branch section which contains the transmission line
and
the
coupling transformer
.
The
l ine voltage set,
vb
at
BUS 1, the inverters' current sets, i
l
and i
2
, and the line cur
rent,
i,
are measured by the measuring switches. Finally, the
output section is defmed.
In
reality, the magnetic circuit can
also serve as the coupling transformer. Therefore, there is no
need for an additional coupling transformer.
The
modeling
may
be done at various levels.
For
example, to study the functionality of a FACTS device on an
elaborated
power system
network, a FACTS device with a
simplified model consisting of sinusoidal voltage sources and
detailed control
and
protection
schemes may
be adequate.
For magnetic circuit and valve designers, the primary focus
should be on the modeling of the detailed power circuit. The
modeling techniques described in this section are useful tools
to the FACTS designers.
The
various control techniques
of
FACTS devices
and simulation results are described in the next section. In
each case, an instantaneous 3-phase set
ofline
voltages,
vI>
at
BUS 1 is
used
to calculate the reference angle, e
which
is
phase-locked to the phase
a
of the line voltage, Via'
A. STATCOM
The controller of a STATCOM is used to operate the
inverter
in
such
a
way tha t
the phase angle
between the
inverter voltage and the line voltage is dynamically adjusted
so that the STATCOM generates or absorbs desired VAR at
the point of connection [56]. Fig. 47 shows the control block
diagram of the STATCOM. An instantaneous 3-phase
calculated by
adding
the
relative
angle, 0. , of the
inverter
voltage
and
the
phase-lock-loop
angle
,
e. The
reference
quadrature component,
h
q
.,
of the inverter current is defined
to be either positive i f the STATCOM is emulating an induc
tive reactance or negative
i f
it is emulating a capacitive reac
tance. The DC
link
capacitor voltage, VDC, is dynamically
adjusted in relationship with the inverter voltage.
The
con
trol scheme used in this section shows the implementation of
the inner current control loop
which
regulates the reactive
current flow through the inverter regardless
of
the line volt
age. However, if one is interested in regulating the line volt
age, an outer voltage control loop must be implemented. The
outer voltage control loop will automatically determine the
reference reactive current for the inner current control loop
which, in turn, will regulate the line voltage.
Fig. 48 shows the digital simulation results from the
reactive current control operation of
a STATCOM. Between
o
and 50 ms, the mechanical switch,
MSJ,
stays open, discon
necting the STATCOM from the transmission line .
The
DC
link capacitor is precharged. The inverter output 12-pulse
voltage
of
phase a, el
a,
and the line voltage
of
phase a,
Via,
are in phase. At 50 ms, MSJ closes and the quadrature cur-
rent
demand, h
q
, of the invert er is set to zero. Since the
inverter current is zero, the inverter voltage of phase a, el
a
,
and the line voltage of phase a, Via, have equal amplitudes.
At 125
ms, the
quadrature
current demand
, Il q
,
of the
inver ter is set to one per
unit
capacitive, which
means
the
STATCOM
should see
the
system
as an
inductive
reac
tance and the inverter current of
phase a,
i la , lags the l ine
voltage
of
phase
a,
Via, by almost 90
0
.
Gale
PatIem
1...cJge
V,A
(PU)
1
-1
1
I
I
I
I
I
V1 I
I
I I
Fig. 47 Control BlockDiagram
ofa
Static Synchronous Compensa
tor
set of measured inverter currents,
iJ,
is decomposed
into its real or direct component, hd, and reactive or quadra
ture component,
h
q
, respectively. The quadrature compo-
nent is compared with the desired rference value,
h
q
,
and
the error is passed through an error amplifier which produces
a relative angle, 0. , of the inverter voltage with respect to the
line voltage. The phase angle, eJ, of the inverter voltage is
-1-
Fig. 48 Performance of a Static Synchronous Compensator witha
12-Pulse
Harmonic
Neutralized InverterOperating inCapacitive and
Inductive
Modes
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B. SSSC
Fig.49 Waveformsfroma StaticSynchronous Compensator witha
12-PulseHarmonicNeutralizedInverterOperatinginCapacitiveand
InductiveModes
Fig.50 ControlBlockDiagramofa StaticSynchronousSeriesCom
pensator
I
I
I
I
I
V1
I
I
I I
inverter in such a way that the injected alternating voltage in
series with the transmission line is proportional to the line
current with the
emulated
reactance
being
the
constant
of
proportionality [57].
When
an SSSC injects an alternating
voltage
leading
the l ine current , it
emulates
an
inductive
reactance in series
with
the
transmission
line
causing
the
power flow as well as the line current to decrease as the level
of compensation increases and the SSSC is considered to be
operating in an inductive mode. When an SSSC injects an
alternating voltage
lagging
the l ine current , it
emulates
a
capacitive reactance in series with the transmission line caus
ing the power flow as well as the line current to increase as
the level
of
compensation increases and the SSSC is consid
ered to be operating in a capacit ive mode. An SSSC control
ler can also be used for stable reversal of
power
flow in the
transmission line.
Fig. 50 shows a control block diagram of an SSSC.
An instantaneous 3-phase set
of
measured line currents, i, is
first decomposed into its real or direct component,
Id, and
reactive or quadrature component,
I
q
, and then the amplitude,
I, and the relative angle, 0
in
of the line current with respect
to the phase-lock-loop angle, E>, are calculated. The phase
angle, E>;, of the line current is calculated
by
adding the rela-
tive angle,
E>ir of
the line current and the phase-lock-loop
angle, 0.
The
calculated amplitude,
I,
of the l ine
current
*
multiplied by the compensating reactance demand,X
q
,i s the
*
insertion voltage amplitude demand,
V
q
. The phase angle,
0 of this insertion voltage demand is either 0
i
+900 if the
demanding compensating reactance is inductive or
0;-90
if
the demanding compensating reactance is capacitive.
The
DC link capacitor voltage is dynamically regulated in rela
t ionship with the insertion voltage amplitude demand. The
*
insertion voltage amplitude demand, V
q
,and the DC link
*
capacitor voltage demand,
V
DC , are related by the inverter
DC-to-fundamental AC amplitude gain factor
K;nv = 2/n
for
a true harmonic netralized voltage source inverter). The DC
250
tine
(ms)
-1
-1
1-
Fig. 49 shows the expanded view of two sections of
Fig. 48. The inverter voltage and current show the presence
of
12-pulse harmonic components.
The inverter voltage set,
el ,
is greater than the line
voltage set,
VI.
At 175 ms, the quadrature current demand,
*
IIq
, of the invert er is set to one
per unit
inductive,
which
means the STATCOM should
see
the system as a capaci
tive reactance and the inverter current in phase
a,
i la, leads
the line voltage at phase
a, VIa,
by almost
90.
The inverter
voltage set,
el ,
is less than the line vol tage set, VI. At 250
*
IDS,
the quadrature current demand,
IIq ,
of
the inverter is set
to one
per
unit capacit ive and the transit ion takes place in a
subcycle time.
The phase
angle, a, between the
inverter
voltage and the line voltage is dynamically adjusted so that
the inverter maintains proper DC link capacitorvoltage.
V,A
(pu)
1-
An SSSC controller uses a solid-state voltage source
inverter to inject an
almost
sinusoidal voltage, of variable
magnitude, in series with a transmission line. This injected
voltage is almost in quadrature with the line current. A small
part of
the injected vol tage which is in phase with the l ine
current provides
the
losses
in
the
inverter.
Most
of
the
injected voltage which is in quadrature with the line current
emulates an inductive or a capacitive reactance in series with
the
transmission
line.
This
emulated variable
reactance,
insertedby the injected voltage source, influences the electric
power flow in the transmission line.
If
an SSSC is operated
with
an
energy
storage system, the controller
becomes
an
impedance compensation controller which can compensate
for the transmission line resistance as well as reactance. The
reactance
compensation controller is used to
operate
the
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*
link capacitor voltage demand,
VDC ,
and the measured DC
voltage, VDC, are compared and the error is passed through an
error amplifier which produces an angle, p. The phase angle,
02, of the inverter voltage is calculated by adding the angle,
p, of the DC voltage regulator and the phase angle, 0\1> of the
insertion voltage demand. The compensating reactance
*
demand,
X
q
, is either negative
if
the SSSC is emulating an
inductive reactance or positive i f it is emulating a capacitive
reactance. In
another
application, the insertion voltage
*
amplitude demand, V
q
may directly be specified and the
SSSC will inject the desired voltage almost in quadrature
with the line current.
neous DC link capacitor voltage is proportional to the ampli
tude of the inverter voltage.
Therefore, when an SSSC emulates a reactance in
series with the transmission line, the power flow in the trans
mission line always decreases
if
the emulated reactance is
inductive. Also, the power flow always increases if the emu
lated reactance is capacitive.
Fig. 52 shows the expanded view
of
the two sections
of
Fig.
51. The inverter voltage show the presence
of
24-pulse har
monic components.
2-
V,A,X,P
1 - ~ ~ P
PU)
/i
a
1
~ ~ ~
- q
0
P
q
1-
-1
*
q
X
q
tiTle
-2-
I
(ms)
200
400
600
Fig. 51 Performance of a Static Synchronous Series Compensator
with a 24-Pulse Harmonic Neutralized Inverter Operating in Induc
tive and Capacitive Modes
Fig. 51 shows the digital simulation results when an
SSSC emulates a reactance in series with the transmission
line. At the beginning
of
the operation, the mechanical
switch,
MS2,
and the electronic switch,
S22,
are open and
the electronic switch, S2, is closed. The inverter, VSI2,
injects no voltage. The DC link capacitor voltage, VDC, is
zero. At 50 ms, an inductive reactance compensation
of
0.15
per unit is requested. The inverter output 24-pulse voltage,
e2a,
of phase a leads the line current, i
a
,
by almost 90
0
. At
175 ms, the inductive reactance demand is increased to 0.3
per unit. As the inductive reactance demand increases, the
line current, i
a
, and the power flow, Pq and
Qq,
in the trans
mission line decrease. At 300 ms, a capacitive reactance
compensation
of
0.1 per unit is requested. The inverter volt-
age,
e2a,
lags the line current,
i
a,
by almost 90
0
.
At 450 ms,
the capacitive reactance demand is increased to 0.15 per unit.
As the capacitive reactance demand increases, the line cur
rent, i
a
, and the power flow, Pq and Qq, in the transmission
line increase. In reality, the SSSC would encounter power
losses in the valves and in the magnetic circuit. Therefore,
there will always be a small part of real current component,
lId, flowing into the inverter and the inverter voltage will be
almost 90
0
out of phase with the line current. The instanta-
Fig. 52 Waveforms from a Static Synchronous Series Compensator
with a 24-Pulse Harmonic Neutralized Inverter Operating in Induc
tive and Capacitive Modes
C. UPFC
The stand alone operations
of
the STATCOM and
the SSSC, as just described,
only allow
the inverters to
exchange almost exclusively reactive power at their termi
nals. However, ifboth the inverters are operated from a com
mon DC link capacitor, the injected voltage by the SSSC can
be at any angle with respect to the line current. The real
power exchanged at the terminals of the SSSC appears at the
terminals
of
the STATCOM through the DC link capacitor.
The STATCOMcan still be used to control the reactive cur
rent flow through it independently [58]. The current injected
by the STATCOM has two components. First, a real or direct
component, which is in phase with the line voltage, absorbs
or delivers the real power exchanged by the SSSC with the
line. Second, a reactive or quadrature component, which is
in quadrature with the line voltage, emulates an inductive or
a capacitive reactance at the point
of
connection with the
transmission line.
The SSSC can be operated in many different modes,
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i
a
1
-1-
Fig. 55 shows the expanded view of two sections of
Fig. 54. The inverter voltage and current show the presence
of
harmonic components.
Fig. 54 Performance of a Unified PowerFlowControllerwith a 24
PulseQuasi Harmonic Neutralized Inverterwith3-LevelPolesOp
eratingin a VoltageInjectionMode
At the beginning
of
the operation, the mechanical
switch, MS2, and the electronic switch, ES22, are open and
the electronic switch,
ES2,
is closed. The inverter,
VSI2,
injects no voltage. The voltage , VIZa, at the terminals of the
coupling transformer, T2, is the voltage across its leakage
reactance. The mechanical switch,MSI , is open, disconnect
ing the STATCOM from the transmission line. The DC link
capacitor is precharged. At 50 ms , MSI closes and the
quadrature current demand, Il q
,
of the inverter is set to zero.
At 100 ms, a series voltage injection
of
0.2 per unit at an
angle of 60
0
leading the reference phase-lock-loop angle is
requested. The series inverter output voltage, ez
a
, of phase a
leads the line current, i
a
, by an angle o. The real power
absorbed by the series inverter appears at the BUS 1 through
the STATCOM. The shunt inverter output voltage, el
a
,
of
phase a is in phase with the current, ;I a, flowing through it.
The power delivered at the receiving end decreases. At 175
ms, the injected voltage request is increased to 0.4 per unit
while maintaining the same angle. As the voltage injection
demand increases, the line current, i
a
, and the power flow, P,
and Q in the transmission line decrease. By injecting a volt
age by the SSSC
of
any magnitude, within the rating
of
the
inverter, and at any angle with respect to the line current, the
real power,
P,.,
and the reactive power, Q at the receiving
end of the transmission line can be increased, decreased or
even reversed selectively.
ime
(ms)
Va:
P- t-
- - - - - --,
V,A
,P,Q
(pu)
1
t - ~ : : - - - - - - - - - - . : . . . . A - - - - - ~
1
*
Vd:I
Fig. 53 ControlBlockDiagram
ofa
StaticSynchronous SeriesCom
pensator
Fig. 54 shows the digital simulation results from the
voltage injection mode of operation
of
an SSSC while the
STATCOMis operated to deliver no reactive current.
vo:;
t
such as voltage injection, phase angle shifter emulation, line
impedance emulation, automatic power flow control, etc. In
each mode
of
operation, the final outcome is such that the
SSSC injects a voltage in series with the transmission line
[58]. In this section, the SSSC is operated in a voltage injec
tion mode. The control block diagram for the SSSC is shown
in Fig. 53.
The desired peak fundamental voltage , Vdq*, at the
output
of
the inverter and its relative angle,
P,
with respect to
the reference phase-lock-loop angle are specified. The phase
angle, 0z,
of
the inverter voltage is calculated by adding the
relative angle, P, of the inverter voltage and the phase-lock
loop angle ,
0 .
The dead angle
of
each pole is calculated in
accordance with the operation of 24-pulse quasi harmonic
neutralized inverter [58].
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13. A. Keyhani and H. Tsai, Identification
of
high-order
synchronous generatormodels from SSFR test data , pre
sented at the 1994 IEEE/PES Winter Meeting, Paper no.
94 WM 022-4 EC, New York, January 30-February 3,
1994.
14. J. R. Willis, G. J. Brook and J. S. Edmonds, Derivation
of induction motor models from standstill frequency re
sponse , IEEE Trans. on Energy Conversion, vol. 4, no.
4, pp. 608-615, December 1989.
15. P. L. Dandeno, P. Kundur, A. T. Poray and H. M. Zein
El-din, Adaptation and validation
of
turbogenerator
model parameters through on-line frequency response
measurements , IEEE Trans. on Power Apparatus and
Systems, vol. 100, no. 4, pp. 1656-1645, April 1981.
16. P.L. Dandeno, P.Kundur, A. T.Poray andM. E.Coultes,
Validation of turbogenerator stability models by com
parison with power system tests , IEEE Trans. on Power
Apparatus and Systems, vol. 100, no. 4, pp. 1637-1645,
April 1981.
17. F. P. de Mello, L. N. Hannett, J. R. Willis, Determina
tion
of
synchronous machine stator and field leakage in
ductances standstill frequency response tests , IEEE
Trans. on Power Systems, vol. 3, no. 4, pp. 1625-1632,
November 1988.
18. L. Dube, H.W. Dommel, Simulation
of
control system
in an Electromagnetic Transient Program with TACS ,
IEEE Trans. on Power Industry and Computer Applica
tions, 1977
rs, EMTP Rule Book, EPRIIDCG Version 1.0.
20. D. Goldsworthy, 1. J. Vithayathil, EMTP model of an
HVDC transmission system , Proceedings of the IEEE
Montech '86 Conference onHVDC Power Transmission,
September 26-0ctober 1, 1986, pp. 39-46
21. L. X. Bui, S. Casoria, G. Morin, Modeling
of
digital
controls with EMTP , CEA Meeting, March 25-29,
1989, Montreal, Canada
22. J. Reeve and S. P. Chen, Versatile interactive digital
simulatorbased on EMTP for AC/DC power system tran
sient studies , IEEE Trans. on Power Apparatus and Sys
tems, Vol. 103,No. 12, December 1984, pp. 3625-3633
23. K. G. Fehrle, R. H. Lasseter, Simulation
of
control sys
tems and application to HVDC converters , IEEE Tuto
rial Course 81 EHOI73-PWR on Digital Simulation
of
Electrical Transient Phenomena, 1981.
24. L. X. Bui, G. Morin, J. Reeve, EMTP TACS-FOR
TRAN interface development for digital controls model
ing , 91 SM 417-6 PWRS
25. G. Morin, L. X. Bui, S. Casoria, J. Reeve, Modeling of
the Hydro-Quebec - New England HVDC system and
digital controls with EMTP , IEEE Trans. on Power De
livery, Vol. 8,No.2, April 1993, pp. 559-566.
26. R. H. Lasseter and S. Y. Lee, Digital simulation
of
static
var system transients , IEEE Trans. on Power Apparatus
and Systems, Vol. PAS-I0l, No. 10, pp. 4171-4177, Oc
tober 1982.
27. A. M. Gole and V. K. Sood, A static compensator model
for use with electromagnetic transients simulation pro
grams , IEEE Trans. on Power Delivery, Vol. PWRS-5,
No.3,
pp. 1398-1407, July 1990
28. A.N. Vasconcelos et. al. Detailedmodeling
of
an actual
static Var compensator for electromagnetic transients
studies , IEEE Trans. on Power Systems, Vol. PWRS-7,
no. l,pp. 11-19, February 1992
29. S.Y. Lee et aI., Detailedmodeling ofstatic Var compen
sators using the Electromagnetic Transients Program
(EMTP) , IEEE Trans. on Power Delivery, Vol. 7, no. 2,
pp. 836-847, April 1992
30. S. Lefebvre and L. Gerin-Lajoie, A static compensator
model for the EMTP , IEEE PES Meeting, San Diego,
July 28-August 1, 1991, Paper 91 SM 461-4 PWRS.
31. L. Dube and I. Bonfanti, MODELS: A new simulation
tool in the EMTP , European Transactions on Electrical
Power Engineering, Vol. 2, no. 1, pp. 45-50, January/
February 1992.
32. Leuven EMTP Center (ed.),
ATP Rule
BOQk, 1990.
33. J. A. Martinez, Simulation
of
a microprocessor-con
trolled SVC , 21th European EMTP Meeting, June 5-7,
1992, Crete (Greece).
34. H.W. Dommel,
EMTP Reference-Manual
(EMIP
Theo
ry Book), BPA, 1986.
35. J. A. Martinez, Simulation of power electronics using
the EMTP, Part I: Power converters, A survey , UP
EC'94, September 14-16, 1994, Galway.
36. G. A. Capolino, H. Henao, ATP simulation for power
electronics and AC drives , 15thEuropean EMTP Users
Group Meeting, Paper 88R-027, October 17-18, 1988,
Leuven.
37. G. A. Capolino, H. Henao, Simulation
of
electrical ma
chine drives with EMTP , 18th European EMTP Users
Group Meeting, Paper M7, May 28-29, 1990, Marseille
38. J. A. Martinez, G. A. Capolino, TACS and MODELS:
Drive simulation languages
in
a general purpose pro
gram , Proc. MCED'91, Marseille, July 1-2, 1991, pp.
RI-RI3.
39. G. A. Capolino, H. Henao, ATP advanced usage for
electrical drives , EMTP Summer Course, July 5-8,
1993,Leuven.
40. H.Knudsen, ExtendedPark's transformation for 2 by 3
phase synchronous machine and converter phasor model
with representation
of
harmonics , IEEE PES Summer
Meeting, Paper 94 SM 350-9 EC, July 24-28, 1994, San
Francisco.
41. M. Mazzucchelli, G. Sciutto, Digital simulation of AC
electrical drives based on field-oriented control method
using a general purpose program , Proceedings PCIM,
pp.350-364, 1986, Munchen
42. Z. Daboussi, N. Mohan, Digital simulation of field-ori
ented control
of
induction motor drives using EMTP ,
IEEE Trans. on Energy Conversion, Vol. 3, pp. 667-673,
September 1988.
43. L. Tang, M. McGranaghan, Modeling an active power
line conditioner for compensation
of
switching tran
sients , Proceedings of First International Conference on
Power Systems Transients (IPST'95), Lisbon (Portugal),
pp. 403-408.
44. X. Z. Meng, J. G. J. Sloot, H. Rijanto, Modelling
of
semiconductor fuses in EMTP , Proceedings
of
First In
ternational Conference on Power Systems Transients (IP
ST'95), Lisbon (Portugal), pp. 481-486.
45. J. A. Martinez-Velasco, R. Abdo, G.A. Capolino, Ad
vanced representation
of
power semiconductors using the
EMTP , Proceedings
of
First International Conference
on Power Systems Transients (IPST'95), Lisbon (Portu
gal), pp. 505-510.
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Modeling Guidelines for Low Frequency Transients
Report Prepared by the Low-Frequency Transients Task Force
of the IEEE Modeling and Analysis of System Transients Working Group
ContributingMembers: R. Iravani (Chair), A.K.S. Chandhury,
I.D. Hassan, J.A. Martinez, A.S. Morched,
B.A.Mork, M. Parniani, D. Shirmohammadi, R.A. Walling
Abstract: The objective of this report is to provide guidelines
for modeling and analyses of low-frequency (approximately 5 to
1000
Hz)
transients of electric power systems, based on the use
of digital time-domain simulation methods. For the ease of ref
erence, the low-frequency transients are divided in seven dis
tinct phenomena. This report (1) briefly describes the physical
nature of each phenomenon, (2) identities those power system
components/apparatus which either contribute to or ar e
affected by the phenomenon, (3) provides guidelines for digital
time-domain simulation and analyses of the phenomenon and
(4) provides sample study-system and typical digital time
domain simulation results corresponding to each phenomenon.
A comprehensive list of reference is also included in this report
to provide further in-depth information to the readers.
Keywords: Low-Frequency Transients, Electromechanical
Transients, Modeling, Time-Domain Analysis, Torsional
Dynamics, Turbine Vibrations, Bus-Transfer, Controller
Interactions, Harmonic Interactions, Ferroresonance
1. INTRODUCTION
An
interconnected power system can experience undesirable
oscillations and transients as a result
of
small-signal perturba
tions, large-signal disturbances, and nonlinear characteristics
of
the system components. The oscillations cover a wide fre
quency range approximately from 0.01 Hz to 50MHz. Oscil
lations in the frequency range of 0.01 to 1000Hz are defmed
in this report as low-frequency (slow) transients. We inter
changeably use the terms slow transients , low frequen
cy(LF) dynamics , and LF oscillations throughout this
report. All the issues relevant to Iow-frequency inter-area
electromechanical oscillations (approximately 0.1 to 1 Hz)
and classical turbine-generator swing modes (approximately
1 to 2.5 Hz) are discussed by other IEEE working groups, and
are not discussed here. A general guideline for representation
of network elements for electromagnetic transient studies
have been previously published [1.1]. The mandate of the
IEEE Low-Frequency Transients Task Force is to provide
modelling guidelines for time-domain analysis ofLF oscilla
tions within the frequency range
of
5 to 1000 Hz. Low fre
quency dynamics are
of
concern with respect to power system
stability issues and/or temporary overvoltages.
phenomena of 60 Hz power systems in the LF range are di
vided into the following categories:
3-1
l.Torsionaloscillations (5 to 120Hz)
2.Transient torsional torques(5 to 120Hz)
3.Turbine bladevibrations (90to 250Hz)
4.Fastbustransfer(1 to 1000Hz)
5.Controller interactions (10 to 30Hz)
6.Harmonic interactions andresonances (60 to 600Hz)
7.Ferroresonance
(1
to 1000
Hz)
For each of the above phenomenon this report provides (1) a
brief explanation of the physical phenomenon, (2) modeling
guidelines for time-domain simulation and analyses, and (3)
typical sample systems and simulation results.
This report is intended for practicing powersystem engineers
who are involved in system analysis, system control, and sys
tem planning. To use the report efficiently, adequate under
standing
of
the physical phenomenon
of
interest and
familiarity with the concepts and techniques
of
digital com
puter simulation approaches are necessary.
Section 2 of the report deals with low-frequency transients
which involve both electrical and mechanical dynamics, i.e.,
torsional oscillations, transient torsional torques, turbine
blade vibrations and fast bus-transfer. Section 3 discusses
low-frequency electrical dynamics, as a result
of
control sys
tems interactions. Section 4 provides analysis guidelines for
harmonic interactions and resonance phenomena. The phe
nomenon
of
ferroresonance is discussed in Section 5.
2. LOW-FREQUENCY ELECTROMECHANICAL
DYNAMICS
This section provides modeling and analysis guide
lines for low-frequency dynamics which involve electrome
chanical oscillations. The phenomena which are covered in
this section are torsional oscillations, transient torques, tur-
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bine-blade vibrations, and bus-transfer.
2.1DEFINITIONS
2.1.1 Torsional Oscillations [2.1, 2.2, 2.3, 2.4, 2.5J
Shaft system
of
a steam turbine-generator experiences tor
sional oscillations when one or more
of
its natural oscillatory
modes, usually at subsynchronous frequencies, are excited.
Sustained or negatively damped torsional oscillations occur
when a turbine-generator shaft system exchanges energy with
an electrical system at the shaft oscil latory modes. This ex
change of energy can exist if the electrical system is equipped
with eitherseries capacitors orHVDC converterstations. The
phenomenon of torsional oscillations can also exist as a result
of
interaction between the shaft system of a steam turbine
generator and
the generator excitation systems through either AVR or PSS
control loops,
electronically controlled governor system,
voltage control loop of an electricallyclose staticV
AR.
compen
sator (SVC)
large electric arc furnaces.
AlthoughAVR, PSS and governor systemcan excite torsional
oscillations, the excitation is primarily due to inadequate con
trol design considerations and can be avoided by introducing
filters in the control circuitry. Thus, this report does not con
sider the generator controls as the main contributors to the
phenomenon of torsional oscillations (Table 1).
The phenomenon
of
torsional oscillation is referred to as sub
synchronous resonance
(SSR)
when it is a result
of
interaction
between a shaft system and a series capacitor compensated
transmission line. The problems associated with the phenom
enon of small-signal torsional oscillations are:
i ) Sustained or even negatively damped oscillations which
are considered as small-signal instability problems, and
ii )
(loss
of
life
of
turbine-generator shaft segment(s) due to the
fatigue induced in the shaft segment(s) as a result of each
oscillatory cycle.
2.1.2 Transient Torsional
Torques
[2.1, 2.2, 2.3, 2.4, 2.5]
The shaft segments of turbine-generator units are exposed to
large-amplitude, oscillatory, mechanical stresses as a result of
electric network faults, and planned and unplanned switching
incidents. Frequencies of the shaft mechanical stresses are
the natural frequencies of the shaft torsional oscil latory
modes. Usually, the oscillatory mode at the first torsional fre
quency dominates the shaft transient oscillations. The major
incidents which resultin severe shaft stresses are: line-to-line
faults, three-phase faults, fault clearing, automatic reclosures,
and out-of-phase synchronization. The amplitudes of the
shaft transient stresses can be particularly large when the net
work is equipped with series capacitors.
High amplitude shaft mechanical stress can induce significant
fatigue in the shaft segments and result in not iceable shaft
life-time reduction during each oscillatory cycle. Such oscil
lations may even result in catastrophic shaft failure. The pri
mary purpose of time-domain investigation of turbine
generator shaft mechanical stresses is to identify the peak
torques imposed on the shaft segments, after system distur
bances. Transient shaft mechanical stresses calculated based
on time-domain simulation methods also can be used to esti
mate shaft loss of life as a result of system disturbances.
2.1.3 Turbine-Blade
Vibrations
[2.6]
Frequencies of turbine-blade vibrational modes are
usual ly within 90 to 250 Hz,
and
constitute supersynchro
nous frequency modes. Identification of supersynchronous
frequency modes and their corresponding frequencies is best
carried out by solving elasticity equation of the shaft system
as a continuum, based on the use of finite element methods.
This approach is beyond the scope of this report and usually
carried out by turbine manufacturers.
In
this report, the objective is to investigate the impact of
large-signal disturbances on those supersynchronous frequen
cy natural modes which are the reason for turbine-blade vibra
tions. Thus the required model is tailored to represent
particular supersynchronous modes and not all
of
them.
The concern with turbine-blade vibrations is fracture
and loss-of-life of the blades due to the fatigue induced in the
blades
by
repetitive or sustained oscillations. Vibrations
of
tur
bine-blades can be excited by large-signal electrical distur
bances, e.g. faults, fault clearing, line switching, reclosure, and
out-of-phase synchronization.
2.1.4FastBus Transfer
[2. 7,2.8,2.9]
Motors and other loads in utility and heavy industrial applica
tions are supplied during normal operation from a preferred
power source. An alternate power source is normally provid
ed to supply such motors and other loads during planned shut
downs and upon loss of normal power from the preferred
power source. The process of disconnecting the motors and
other loads from one source and reconnecting to an alternate
source is commonly defmed as bus transfer . Manual trans-
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fer means are normally provided to allow transferring the mo
tors and other loads from one power source to the other.
However, upon loss of the preferredpowersource, the motors
and other loads are automatically transferred to the alternate
power source. This automatic transfer is necessary to allow
uninterrupted operation of the motors and other loads impor
tant to personnel safety and process operation. This report
does not address the concept
of
bus transferby means of semi
conductor switches [2.23].
The normal and alternate power source connections are al
ways selected such that they are in phase. Therefore, manual
transfers can be accomplished in a make-before-break, i.e.,
the motors and loads are connected to the second power
source before the first power source is disconnected.
In
this
overlapping transfer, the power supply is not interrupted and
the motors are not subjected to transients. However, during
automatic transfers, the motors may be disconnected from
both power sources for a short duration depending on the type
of
transfer and the associated circuit breakers operating times.
The time duringwhich the motors are disconnected from both
power sources is termedthe dead time . Dead time is usually
between two cycles to 12cycles.
If
the relative angle between
the motor residual voltage and the power source voltage be
comes large enough at the time
of
reconnection with signifi
cant residual voltage remaining, the resultant voltage
between the power source and the motor will produce an in
rush current. The inrush current may be significantly largely
than the normal full voltage staging current. Such high inrush
currents cause high winding stresses and transient shaft
torques which can damage the motor and/or the driven equip
ment.
The most common bus transfer scheme is the fast bus transfer
scheme. In this scheme, opening of the normal power source
breaker initiates closing
of
the alternate power source breaker
without intentional time delay. Fast bus transfer operations
result in the motors being disconnected from both power
sources for a duration of as short as two cycles to as long as
12 or more cycles.
Presently,
there
are no
generic criteria
to
ensure
acceptable fast bus transfer operations. Therefore, it is nec
essary to analyze the transient behavior
of
motors during fast
bus transfer operations. The analysis should be on a case by
case basis to ensure that the motors will not be subjected to
excessive inrush currents and/or shaft transient torques.
2.2 MODELING GUIDELINES
2.2.1 Study Zone
In contrast to an inter-area, electromechanical, oscillatory
mode which propagates almost through the entire
of
an inter
connected electric network, the phenomena described in Sec
tion 2.1 are experienced only within a limited part of the
network. The section of the network which experiences the
phenomenon
of
interest, and
must
be represented in adequate
detail for the study
of
the phenomenon, is referred to as the
StudyZone The rest of the network is referred to as the ex
ternal system The external system is represented by an
equivalent model. Identification
of
border nodes
of
the study
zone for a meshed network requires significant familiari ty
with the network, as well as engineering judgment. As of
now, there is no straightforward and systematic approach to
identify the border nodes. One approach involves multiple
harmonic analyses
of
the sys tem under investigation as
boundaries are extended to identify
if
new resonant frequen
cies (at the frequency range of interest) with low dampings ex
ist.
Proper determination
of
the study zone can exert a major im
pact on the investigations of torsional dynamics and transient
torques. Comparatively, the impact
of
the study zone on the
vibrations of turbine blades is less significant. Identification
of the study zone for bus transfer studies is relatively straight
forward.
2.2.2 Component Model
Table 1 identifies the study zone components and their equiv
alent models for investigations of slow transient phenomena.
Further explanation of the system components are given in the
following sections.
2 2 2 1 Synchronous Generator Electrical System [2 lOJ
Figure 2.1 shows a second-order and a third-order
models of a synchronous machine. Inclusion
of
the differen
tialleakage
inductance Lfld in the second-order model is
recommended.
The different ial leakage inductance has
noticeable influence on the damping, and the range
of
insta
bility of
each torsional mode, (with respect to series compen
sation
level), particularly
fo r
a salient
pole
machine.
However, Lfld does not influence the phenomenon
of
blade
vibrations.
Representation of machine electrical system based on
the third-order model, Fig.
2.1,
is more accurate. Inclusion
of
the differential leakage inductance
Lf 2d
in the third-order
model has the same impact as that
of
Lf l
d
for the second-order
model. Magnetic saturation of a synchronous machine, both on
d-axis and q-axis, does not have any significant impact on the
phenomenon of small-signal torsional oscillations, but has pro-
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Component
Torsional
Transient
Turbine-Blade
Fast Bus
Oscillations
Torques
Vibrations
Transfer
Synchronous
Second-Order
Third-Order
Third-Order Model
Not
Genera tor's
Model and
Model (d-q-o
(d-q-o Model)
applicable
Electrical System
Preferably Third-
Model)
Including
Order
Model (d-q-o Including Saturation
Model)
Saturation
Turbine-Generator
Mass-Spring-
Mass- Spring-
Detail
Not
Shaft
System Dashpot
Model
Dashpot Model Mass-Spring-
Applicable
Dashpot Model
Power
Conventional
Conventional
Conventional
Conventional
Transformer
Low-Frequency
Low-Frequency
Low-Frequency
Low-
Model including
Model including
Model including Frequency
Saturation
Saturation
Saturation Model
Characteristic
Characteristic
Characteristic including
Saturation
Characteristic
Transmiss ion Line
Equivalent-a
Equivalent-a Equivalent-a
Not
Model
Model
Mo
top related