Power system transients : parameter determination

Power System

Transients

Parameter

Determination

CRC Press is an imprint of the

Taylor & Francis Group, an informa business

Boca Raton London New York

Power System

Transients

Parameter

Determination

Edited by

Juan A. Martinez-Velasco

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Library of Congress Cataloging-in-Publication Data

Power system transients : parameter determination / editor, Juan A. Martinez-Velasco.

p. cm.

“A CRC title.”

Includes bibliographical references and index.

ISBN 978-1-4200-6529-9 (hardcover : alk. paper)

1. Electric power system stability. 2. Transients (Electricity) Mathematical models. 3. Arbitrary

constants. 4. Electric power systems--Testing. I. Martinez-Velasco, Juan A.

TK1010.P687 2010

621.319’21--dc22 2009031432

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v

Contents

Preface ............................................................................................................................................ vii

Editor................................................................................................................................................ix

Contributors ....................................................................................................................................xi

1. Parameter Determination for Electromagnetic Transient Analysis in

Power Systems .........................................................................................................................1

Juan A. Martinez-Velasco

2. Overhead Lines ..................................................................................................................... 17

Juan A. Martinez-Velasco, Abner I. Ramirez, and Marisol Dávila

3. Insulated Cables .................................................................................................................. 137

Bjørn Gustavsen, Taku Noda, José L. Naredo, Felipe A. Uribe,

and Juan A. Martinez-Velasco

4. Transformers ........................................................................................................................ 177

Francisco de León, Pablo Gómez, Juan A. Martinez-Velasco, and Michel Rioual

5. Synchronous Machines ..................................................................................................... 251

Ulas Karaagac, Jean Mahseredjian, and Juan A. Martinez-Velasco

6. Surge Arresters .................................................................................................................... 351

Juan A. Martinez-Velasco and Ferley Castro-Aranda

7. Circuit Breakers ...................................................................................................................447

Juan A. Martinez-Velasco and Marjan Popov

Appendix A: Techniques for the Identifi cation of a Linear System from Its

Frequency Response Data ......................................................................... 557

Bjørn Gustavsen and Taku Noda

Appendix B: Simulation Tools for Electromagnetic Transients

in Power Systems ......................................................................................... 591

Jean Mahseredjian, Venkata Dinavahi, Juan A. Martinez-Velasco,

and Luis D. Bellomo

Index ............................................................................................................................................. 619

vii

Preface

The story of this book may be traced back to the Winter Meeting that the IEEE Power

Engineering Society (now the Power and Energy Society) held in January 1999, when the

Task Force (TF) on Data for Modeling Transient Analysis was created. The mandate of

this TF was to produce a series of papers that would help users of transient simulation

tools (e.g., EMTP-like tools) select an adequate technique or procedure for determining

the parameters to be specifi ed in transient models. The TF wrote seven papers that were

published in the July 2005 issue of the IEEE Transactions on Power Delivery.

The determination or estimation of transient parameters is probably the most diffi cult

and time-consuming task of many transient studies. Engineers and researchers spend

only a small percentage of the time running the simulations; most of their time is dedi￾cated to collecting the information from where the parameters of the transient models will

be derived and to testing the complete system model. Even today, with the availability of

powerful numerical techniques, simulation tools, and graphical user interfaces, the selec￾tion of the most adequate model and the determination of parameters are very often the

weakest point of the whole task.

Signifi cant efforts have been made in the last two decades on the development of new

transient models and the proposal of modeling guidelines. Currently, users of transient

tools can take advantage of several sources to select the study zone and choose the most

adequate model for each component involved in the transient process. However, the fol￾lowing drawbacks must still be resolved: (1) the information required for the determination

of some parameters is not always available; (2) some testing setups and measurements to

be performed are not recognized in international standards; (3) more studies are required

to validate models, mainly those that are to be used in high or very high-frequency tran￾sients; and (4) built-in models currently available in simulation tools do not cover all mod￾eling requirements, although most of them are capable of creating custom-made models.

Although procedures and studies of parameter determination are presented for only

seven power components, it is obvious that much more information is required to cover

all important aspects in creating an adequate and reliable transient model. In some cases,

procedures of parameter determination are presented only for low-frequency models; in

other cases, all the procedures required for creating the whole model of a component are

not analyzed. In addition, there is a lack of examples to illustrate how parameters can be

determined for real-world applications.

The core of this book is dedicated to current procedures and techniques for the deter￾mination of transient parameters for six basic power components: overhead line, insulated

cable, transformer, synchronous machine, surge arrester, and circuit breaker. Therefore,

this book can be seen as a setup that has joined an expanded version of the transaction

papers. It will help users of transient tools solve part of the main problems they face when

creating a model adequate for electromagnetic transient simulations.

This book includes two appendices. The fi rst provides updated techniques for the

identifi cation of linear systems from frequency responses; these fi tting techniques can

be useful both for determining parameters and for fi tting frequency-dependent models

of some of the components analyzed in this book (e.g., lines, cables, or transformers). The

second reviews the capabilities and limitations of the most common simulation tools,

taking into consideration both off-line and online (real-time) tools.

viii Preface

A crucial aspect that needs to be emphasized is the importance of standards. As pointed

out in several chapters, standards are a very valuable source of information for the deter￾mination of parameters, for the characterization of components, and even for their selec￾tion (e.g., surge arresters). Whenever possible, recommendations presented in standards

have been summarized and included in the appropriate chapter.

Although this is a book on electromagnetic transients, many of the most important top￾ics related to this fi eld have not been well covered or have not been covered at all. For

instance, Appendix B on simulation tools contains only a short summary of computational

methods for transient analysis.

Most of the topics covered require one to have some basic knowledge of electromagnetic

transient analysis. This book is addressed mainly to graduate students and professionals

involved in transient studies.

I want to conclude this preface by thanking the members of the IEEE TF for their pio￾neering work, and by expressing my gratitude to all our colleagues, friends, and relatives

for their help, and, in many circumstances, for their patience.

Juan A. Martinez-Velasco

Barcelona, Spain

MATLAB® is a registered trademark of The MathWorks, Inc. For product information,

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Tel: 508 647 7000

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E-mail: [email protected]

Web: www.mathworks.com

ix

Editor

Juan A. Martinez-Velasco was born in Barcelona, Spain. He received his Ingeniero Industrial

and Doctor Ingeniero Industrial degrees from the Universitat Politècnica de Catalunya

(UPC), Spain. He is currently with the Departament d’Enginyeria Elèctrica of the UPC.

Martinez-Velasco has authored and coauthored more than 200 journal and conference

papers, most of them on the transient analysis of power systems. He has been involved

in several ElectroMagnetic Transients Program (EMTP) courses and has worked as a

consultant for Spanish companies. His teaching and research areas cover power systems

analysis, transmission and distribution, power quality, and electromagnetic transients.

He is an active member of several IEEE and CIGRE working groups (WGs). Currently, he

is the chair of the IEEE WG on Modeling and Analysis of System Transients Using Digital

Programs.

Dr. Martinez-Velasco has been involved as an editor or a coauthor of eight books. He

is also the coeditor of the IEEE publication Modeling and Analysis of System Transients

Using Digital Programs (1999). In 1999, he received the 1999 PES Working Group Award

for Technical Report, for his participation in the tasks performed by the IEEE Task Force

on Modeling and Analysis of Slow Transients. In 2000, he received the 2000 PES Working

Group Award for Technical Report, for his participation in the publication of the special

edition of Modeling and Analysis of System Transients Using Digital Programs.

xi

Contributors

Luis D. Bellomo

École Polytechnique de Montréal

Montreal, Quebec, Canada

Ferley Castro-Aranda

Universidad del Valle

Escuela de Ingeniería Eléctrica y

ElectrÓnica

Cali, Colombia

Marisol Dávila

Universidad de los Andes

Escuela de Ingeniería Eléctrica

Mérida, Venezuela

Francisco de León

Department of Electrical and Computer

Engineering

Polytechnic Institute of NYU

Brooklyn, New York

Venkata Dinavahi

University of Alberta

Department of Electrical and Computer

Engineering

Edmonton, Alberta, Canada

Pablo Gómez

Instituto Politécnico Nacional

Departmento de Ingeniería Eléctrica

México, Mexico

Bjørn Gustavsen

SINTEF Energy Research

Trondheim, Norway

Ulas Karaagac

École Polytechnique de Montréal

Montreal, Quebec, Canada

Jean Mahseredjian

École Polytechnique de Montréal

Montreal, Quebec, Canada

Juan A. Martinez-Velasco

Universitat Politècnica de Catalunya

Department d’Enginyeria Elèctrica

Barcelona, Spain

José L. Naredo

Centro de Investigación y de Estudios

Avanzados del Instituto Politécnico

Nacional

Guadalajara, Mexico

Taku Noda

Central Research Institute of Electric

Power Industry

Yokosuka, Japan

Marjan Popov

Delft University of Technology

Faculty of Electrical Engineering,

Mathematics and Computer Science

Delft, the Netherlands

Abner I. Ramirez

Centro de Investigación y de Estudios

Avanzados del Instituto Politécnico

Nacional

Guadalajara, Mexico

Michel Rioual

Électricité de France R & D

Clamart, France

Felipe A. Uribe

Universidad de Guadalajara

Departmento de Ingeniería Mecánica

Eléctrica

Guadalajara, Mexico

1

1

Parameter Determination for Electromagnetic

Transient Analysis in Power Systems

Juan A. Martinez-Velasco

CONTENTS

1.1 Introduction ............................................................................................................................1

1.2 Modeling Guidelines .............................................................................................................2

1.3 Parameter Determination .....................................................................................................6

1.4 Scope of the Book ................................................................................................................. 11

References ....................................................................................................................................... 15

1.1 Introduction

Power system transient analysis is usually performed using computer simulation tools

like the Electromagnetic Transients Program (EMTP), although modeling using Transient

Network Analyzers (TNAs) is still done, but decreasingly. There is also a family of tools

based on computerized real-time simulations, which are normally used for testing real

control system components or devices such as relays. Although there are several common

links, this chapter targets only off-line nonreal-time simulations.

Engineers and researchers who perform transient simulations typically spend only a

small amount of their total project time running the simulations. The bulk of their time

is spent obtaining parameters for component models, testing the component models to

confi rm proper behaviors, constructing the overall system model, and benchmarking

the overall system model to verify overall behavior. Only after the component models

and the overall system representation have been verifi ed, one can confi dently proceed

to run meaningful simulations. This is an iterative process. If there are some transient

event records to compare against, more model benchmarking and adjustment may be

required.

This book deals with parameter determination and is aimed at reviewing the proce￾dures to be performed for deriving the mathematical representation data of the most

important power components in electromagnetic transient simulations. This chapter

presents a summary on the current status and practice in this fi eld and emphasizes

needed improvements for increasing the accuracy of modeling tasks in detailed tran￾sient analysis.

2 Power System Transients: Parameter Determination

Figure 1.1 shows a fl ow chart of the procedure suggested to obtain the complete repre￾sentation of a power component [1]:

• First, choose the mathematical model.

• Second, collect the information that could be useful to determine the values of

parameters to be specifi ed.

• Third, decide whether the available data are enough or not to derive all

parameters.

The procedure depicted in Figure 1.1 assumes that the values of the parameters to be speci￾fi ed in some mathematical descriptions are not necessarily readily available and they must

be deduced from other information using, in general, a data conversion procedure.

1.2 Modeling Guidelines

An accurate representation of a power component is essential for reliable transient analy￾sis. The simulation of transient phenomena may require a representation of network com￾ponents valid for a frequency range that varies from DC to several MHz. Although the

ultimate objective in research is to provide wideband models, an acceptable representation

of each component throughout this frequency range is very diffi cult, and for most compo￾nents is not practically possible. In some cases, even if the wideband version is available, it

may exhibit computational ineffi ciency or require very complex data.

Modeling of power components that take into account the frequency-dependence of

parameters can be currently achieved through mathematical models which are accurate

FIGURE 1.1

Procedure to obtain a complete representation of a power component. (From Martinez, J.A. et al., IEEE Power

Energy Mag., 3, 16, 2005. With permission.)

Choose the mathematical

representation of the

power component

Collect the information

needed to derive the

mathematical model

Is this

information

enough?

No

Estimate the value of

some parameters

Perform the conversion

procedure

Yes