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POWER SYSTEM PROTECTION IEEE Press 445 Hoes Lane, P.O. Box 1331 Piscataway, NJ 08855-1331 IEEE Press Editorial Board Roger F. Hoyt, Editor in Chief John B. Anderson A. H. Haddad M. Padgett ~ M. Anderson R. Herrick W. D. Reeve M. Eden S. Kartalopoulos G. Zobrist M. E. El-Hawary D. Kirk S. Furui P Lap...

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POWER SYSTEM PROTECTION

IEEE Press 445 Hoes Lane, P.O. Box 1331 Piscataway, NJ 08855-1331

IEEE Press Editorial Board

Roger F. Hoyt, Editor in Chief John B. Anderson ~ M. Anderson M. Eden M. E. El-Hawary S. Furui

A. H. Haddad R. Herrick S. Kartalopoulos D. Kirk P Laplante

M. Padgett W. D. Reeve G. Zobrist

Kenneth Moore, Director of IEEE Press Marilyn G. Catis, Assistant Editor Surendra Bhimani, Production Editor IEEE Power Engineering Society, Sponsor PES Liaison to IEEE Press, Roger King Cover Design: William T. Donnelly, WT Design

Technical Reviewers Dr. Xusheng Chen, Seattle University Dr. Charles A. Gross, Auburn University Mladen Kezunovic, Texas A & M University W. C. Kotheimer, Kotheimer Associates Stephen L. Larsen, S & S Larsen Associates, Inc. Dr. Bruce F. Wollenberg, University of Minnesota S. E. Zocholl, IEEE Fellow, Schweitzer Engineering Labs, Inc. IEEE PRESS POWER ENGINEERING SERIES P M. Anderson, Series Editor Power Math Associates, Inc.

Series Editorial Advisory Committee

Roy Billington

Stephen A. Sebo

Ohio State University

Arizona State University

M. El-Hawary

E. Keith Stanek

Roger L. King

Richard F. Farmer

S. S. (Mani) Venkata

Donald B. Novotny

Charles A. Gross

Atif S. Debs

Raymond R. Shoults

University of Saskatchewan

Dalhousie University

Arizona State University

University of Missouri-Rolla

Iowa State University

George Karady

Mississippi State University University of Wisconsin

Auburn University

Decision Systems International

Mladen Kezunovic Texas A & M University

Mehdi Etezadi-Amoli University of Nevada

Siemens Power Transmission and Distribution

John W. Lamont

Antonio G. Flores

~

Iowa State University

Texas Utilities

University of Texas at Arlington

Keith B. Stump M. Anderson

Power Math Associates

POWER SYSTEM PROTECTION

P. M. Anderson Power Math Associates, Inc.

IEEE Power Engineering Society, Sponsor IEEE Press Power Engineering Series P. M. Anderson, Series Editor

ffi WILEY-

~INTERSCIENCE

A JOHN WILEY & SONS, INC., PUBLICATION

.A.. T

IEEE PRESS

The Institute of Electrical and Electronics Engineers, Inc., New York

(91999 THE INSTITUTE OF ELECTRICAL AND ELECTRONICS ENGINEERS, INC. All rights reserved Published simultaneously in Canada.

No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, .or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008.

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Library ofCongress Cataloging-in-Publication Data Anderson, P.M. (Paul M.), 1926Power system protection / by P.M. Anderson. p.

em. -- (IEEE Press power engineering series)

Includes bibliographical references and index. ISBN 0-7803-3427-2 1. Electric power systems-Protection. I. Title. II Series. TLI0I0.A53 1998 621.31'7-dc21

98-28659

CW

Printed in the United States of America 10 9 8 7 6 5 4 3

To Ginny

BOOKS IN THE IEEE PRESS POWER ENGINEERING SERIES ELECTRIC POWER APPLICATIONS OF FUZZY SYSTEMS Mohamed E. El-Hawary, Dalhousie University 1998 Hardcover 384 pp IEEE Order No. PC5666

ISBN 0-7803-1197-3

RATING OF ELECTRIC POWER CABLES: Ampacity Computations for Transmission, Distribution, and Industrial Applications George J. Anders, Ontario Hydro Technologies 1997 Hardcover 464 pp IEEE Order No. PC5647 ISBN 0-7803-1177-9 ANALYSIS OF FAULTED POWER SYSTEMS, Revised Printing Paul M. Anderson, Power Math Associates, Inc. 1995 Hardcover 536 pp IEEE Order No. PC5616

ISBN 0-7803-1145-0

ELECTRIC POWER SYSTEMS: Design and Analysis, Revised Printing Mohamed E. El-Hawary, Dalhousie University 1995 Hardcover 808 pp IEEE Order No. PC5606 ISBN 0-7803-1 140-X POWER SYSTEM STABILITY, VOLUMES I, II, III An IEEE Press Classic Reissue Set Edward Wilson Kimbark, Iowa State University 1995 Softcover 1008 pp IEEE Order No. PC5600

ISBN 0-7803-1135-3

ANALYSIS OF ELECTRIC MACHINERY Paul C. Krause and Oleg Wasynczuk, Purdue University Scott D. Sudhoff, University of Missouri at Rolla 1994 Hardcover 584 pp IEEE Order No. PC4556

ISBN 0-7803-1101-9

POWER SYSTEM CONTROL AND STABILITY, Revised Printing Paul M. Anderson, Power Math Associates, Inc. A. A. Fouad, Iowa State University 1993 Hardcover 480 pp IEEE Order No. PC3789

ISBN 0-7803-1029-2

SUBSYNCHRONOUS RESONANCE IN POWER SYSTEMS P. M. Anderson, Power Math Associates, Inc. B. L. Agrawal, Arizona Public Service Company J. E. Van Ness, Northwestern University 1990 Softcover 282 pp IEEE Order No. PP2477

ISBN 0-7803-5350-1

Contents

Preface

xxi

Acknowledgments List of Symbols PART I

xxiii

xxv

PR<

VII

~

~

"'C ~ 0 CJ

1

//1

WVlI 1I

1

o: (1)

777

7

17

)11 .1

/~~

.001

VI

~

J

V) /1/

.01

II

100"'"

/

VI,,-

V~ V V~ I

v IIIJ

300-5

I

/

I

/

I V

/

--

.... 200-5 150-5 I- 100-5

250-5

50-5

1I

/

Typical Excitation Curve Type BYM Bushing CT Ratio 600-5, 60 Hz

.1 1 Secondary Exciting Current, L

10

100

Figure 2.10 Excitation curves for a multiratio bushing CT with an ANSI accuracy classification of CIOO [4].

ondary voltages to the current transformer with the primary circuit open, and give approximate exciting current requirements for the CT for a given secondary voltage. These curves can be used very simply to determine if the CT becomes saturated at any given fault current. From (2.1), given the fault current and CT ratio, one can determine the secondary voltage. From Figure 2.8, for the computed voltage, one can readily see if the operating point is in the saturated region without making any further computation. This method, including several examples, is discussed further in [4].

2.4.1.3 The Formula Method. An excellent method estimating the CT performance is based on a knowledge of CT design principles. Table 2.1 shows the relationship between the standard secondary burden of the C Class of current transformers and the rated secondary

27

Section 2.4 • Instrument Transformers

voltage. The rated voltage is based on voltage the CT will support across a standard burden with 20 times rated current without exceeding 10% ratio correction. TABLE 2.1 Standard Burden and Rated Voltage of C Class CT's

C Class

Standard ZB (1)

Rated Voltage (2)

CIOO

IQ

100V

C200

2Q

200 V

C400

4Q

400 V

C800

8Q

800 V

(1) Assumed impedance angle of 60°

(2) Computed as 20 x 5A secondary current = A

The secondary voltage is a function of the CT secondary fault current 1F and the total secondary burden Z B. We may write this voltage as d N ¢ v (2.2) dt where N is the number of secondary turns and ¢ is the core flux in webers. Rearranging, we compute the total flux in terms of the flux density as

==

v

N¢ =NBA

For a fully offset voltage this becomes N¢ = NBA = = ZBi F

=

l'

vdt

l' ZBiF(e~R'/L -

[~(l e~R'/L) -

(2.3)

- coswt) dt (2.4)

Sinwt]

Using the maximum value of the expression in square brackets, we write NBAw

= ZBi F

(~ +

1)

(2.5)

Now, the secondary voltage rating of the CT is the voltage that the C'l' will support across a standard burden with 20 times rated current, without exceeding a 10% ratio error. Thus, we can write

(2.6) where the burden is in per unit based on the standard CT burden and the fault current is in per unit based on the CT rated current. Since we use an extreme value of the quantity in parentheses, this will yield a conservatively small value of the maximum tolerable secondary burden [6]. For example, for a transmission line with XIR of 12 and a maximum fault current of four times rated current of a C800 CT, saturation will be avoided when ZB is less than 0.38 per unit of the standard 8 ohm burden, or about 3 ohms.

28

Chapter 2 • Protection Measurements and Controls

2.4.1.4 The Simulation Method. The ANSI accuracy charts, such as Figures 2.8 and 2.9, do not provide an accurate insight as to the waveform distortion that occurs when a large primary current drives the current transformer into saturation. This problem has been addressed and results published to show the type of distortion that may occur, especially from fully offset primary currents of large magnitude [7], [8]. These publications show that substantial waveform distortion is likely with high primary currents, especially if the current is fully offset. A computer simulation has been prepared to permit the engineer to examine any case of interest [8]. EXAMPLE 2.1 An example of a current transformer simulation is to be run for a current transformer of the C400 accuracy class and with 40,000 amperes rms primary current, fully offset. Specifications for the current transformer are shown in Table 2.2. TABLE 2.2 Calculation

Data for C400 Current Transformer

CTratio

15015

CT relaying accuracy class

C400

Core cross-section area

43.1 in. 2

Length of magnetic path

24 in.

Secondary winding resistance

0.10

Secondary burden

CT secondary cable resistance

0.1 +j on

0.10

Frequency

60Hz

Primary current

40,000 A rms

Incident angle

0 0 (fully offset)

Primary current time constant

0.1 sec

Solution The results of the computer simulation are shown in Figure 2.11, where the primary current is fully offset with a typical decrement time constant. 2 The secondary current has an initial high pulse that persists for less than 4 milliseconds in each half cycle. The performance of conventional overcurrent relays is not specified when confronted with such currents. The relay will be affected by saturation in the armature circuit and will have eddy currents induced due to the fast current rise. Note that this example is determined for a CT that is operating at over 266 times its rating, but such a condition can occur in power systems, depending on the availability of fault currents of high magnitude. The simulation method is flexible since any transformer operating under any specified condition can be studied. •

Since the performance of relays under the conditions described in the example are not predictable, laboratory testing of the relay is advised to determine the relay behavior [8].

2.4.2 Instrument Transformer Types and Connections Instrument transformers are available in a number of types and can be connected in a number of different ways to provide the required relay quantities. 2.4.2.1 Current Transformers. Current transformers are available primarily in two types: bushing CT's and wound CT's. Bushing CT's are usually less expensive than wound 2The author is indebted to W. C. Kotheimer of Kotheimer Associates for information regarding the saturation of current transformers and for the plot data for Figure 2.11.

29

Secti on 2.4 • Instru ment Tran sform ers 120

~ .S 80 ....r:::

......

40

...>.Ol

0

0..

-40

~

::l

o

S .;:;

C400

2

0

~

.S

....r::: ...... ::l ~

()

Q

20 -

Ol

"0

r::: -10

0

'" en ~

j ......

10 0

-20

l Il

'-\ :

-

~

...

1

I

2

5

6

7

8

9

10

.. ..

J

~ ; ~ \1}j})\ ~i · ~ ~ . : :

I

4

Ti me in cycles

······__·(········i--·······;......... ..

C400

o

3

I

3

. ..,

,. _,

I

I

:

4

....

< •..

:

I

56

Tim e in cycles

I

7

: I

8

I

9

10

Figure 2.11 Example ofCT secondary saturation due to large. fully offset primary curren\.

CT's, but they have lower accura cy. The y are often used for relaying because of their favorable cost and because their accuracy is often adequate for relay applications. Moreover, bushing CT's are convenientl y located in the bushing s of transformers and circuit breakers. and therefore take up no appre ciable space in the substation. Bushing CT's are designed with a core encircling an insulating bushing. through which the primary current lead of the bushing passes. Thi s means that the diamet er of the core is relati vely large , giving a large mean magnetic path length compared to other types. The bushing CT also has only one primary turn. namely, the metallic connection through the center of the bushing . To compensate for the long path length and minimum primary tum conditi on, the cross-sectional area of iron is increased . Thi s has the advantag e for relaying that the bushing CT tends to be more acc urate than wound CT's at large multiples of secondary current rating . The bushing CT, howe ver, is less accurate at low current s becau se of its large exciting current. Thi s makes the bushing CT a poor choice for applic ations. such as meterin g, which requir e good accuracy at norm al currents. Current tran sformers are labeled with termin al markings to ensure correct polarity of a given connection. The markin gs label the primary wind ing H and the secondary windin g X. each with appropriate subscripts, as shown in Figure 2. 12. The usual practic e is to indicate

Figure 2.12 Polarity convention for current transformers [91.

30

Chapter 2 • Protection Measurements and Controls

polarity by dots, as shown in the two right-hand illustrations in Figure 2.12. Polarity marks are essential where two or more current transformers are connected together so that the resulting current definition can be clearly determined. For the bushing CT on the right in Figure 2.12, the polarity designation can be omitted since the primary current is, by definition, assumed to be flowing toward the breaker from the system. Figure 2.13 shows a wye connection of current transformers, where the phasor primary and secondary currents in each phase are exactly in phase, but differ by the magnitude of the turns ratio.

_ ..._ ............._ . .

t,

~

a

Ib

~b

.i: -...-. . . . ..----.. .-. . ----c ~-

Phase Relays

Figure 2.13 Wye connection of current transformers [9].

The delta connection of CT's can be made in two ways, and these are shown in Figure 2.14, together with the resulting phasor diagrams for each connection. It can be easily shown that the output secondary currents for these connections contain no zero sequence component. Note that delta connection B is the reverse of connection A. The delta connection of current transformers is important for distance relaying". The subject is explored in Chapter 11.

2.4.2.2 Voltage (Potential) Transformers. Two types of voltage measuring devices are used in protective relaying: These are the instrument potential transformer, which is a two-winding transformer, and the capacitance potential device or coupling capacitor voltage transformer (CCVT), which is a capacitive voltage divider. The wound potential transformer is much like a conventional transformer except that it is designed for a small constant load and hence cooling is not as important as accuracy. The capacitance potential devices in common use are of two types: the coupling-capacitor device and the bushing device. These are shown in Figure 2.15. The coupling capacitor device is a series stack of capacitors with the secondary tap taken from the last unit, which is called the auxiliary capacitor. Bushing voltage dividers are constructed from capacitance bushings, where a particular level is tapped as a secondary voltage. The equivalent circuit of a capacitance potential device is shown in Figure 2.16. The equivalent reactance of this circuit is defined by the equation

XCIXC2

XL = - - - XCI + X C2

(2.7)

This reactance is adjusted to make the applied voltage and the tapped voltage in phase, in which case the device is called a resonant potential device. Since the bottom capacitor is much larger than the top capacitor XC2

«

XCI

(2.8)

31

Section 2.4 • Instrument Transformers

_ _............

_ _................__~ I a

~Ia

.....................__~Ib

-............-t-t...._ _ :!'E-- I b

..................

- ....................

t,

Ie -

~

t,>

I

..

t, -

a

Ib

t,

--~

_--~

-

t, Ia - I b

i,

Ie

I

b

Ib

-

t, I a - i,

Ib

Figure 2.14 Delta connection of current transformers and the phasor diagrams for balanced three-phase currents [9).

- - - . . - - - - High-voltage conductor Bushing

Capacity units

Capacitance Tap Shield Bushing Ground Shield

Bushing I J