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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


4/100

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: [email protected]


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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.

2-8


34/100

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

2-9


35/100

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

2-12


38/100

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-

2-13


39/100

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,

2-14


40/100

(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


41/100

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

2-16


42/100

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

2-17


43/100

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

2-18


44/100

*

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,

2-19


45/100

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].

-1-

2-20


46/100


47/100

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.

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1994.

14. J. R. Willis, G. J. Brook and J. S. Edmonds, Derivation

of induction motor models from standstill frequency re

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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

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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.

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of

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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

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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

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power semiconductors using the

EMTP , Proceedings

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on Power Systems Transients (IPST'95), Lisbon (Portu

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2-22


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49/100

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-


50/100

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-

3-2


51/100

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-

3-3


52/100

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

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