Solution Manual For Protective Relaying: Principles and Applications, 4th Edition

solutions MANUAL FOR Protective Relaying Principles and Applications F o u rt h E d i t i o n by J. Lewis Blackburn Thomas J. Domin A CHAPMAN & HALL BOOK solutionS MANUAL FOR Protective Relaying Principles and Applications F o u rt h E d i t i o n by J. Lewis Blackburn Thomas J. Domin Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2014 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper Version Date: 20140227 International Standard Book Number-13: 978-1-4822-0201-4 (Ancillary) This book contains information obtained from authentic and highly regarded sources. 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For permission to photocopy or use material electronically from this work, please access www.copyright.com (http://www.copyright.com/) or contact the Copyright Clearance Center, Inc. (CCC), 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400. CCC is a not-for-profit organization that provides licenses and registration for a variety of users. For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged. Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com Protective Relaying Principles and Applications 4th Edition J. Lewis Blackburn (Deceased) Thomas Domain Solutions Manual Prepared by the following contributors: Sean W. Carr, P.E. Sr. Engineer-Relay & Protection Services Commonwealth Edison Company [email protected] James K. Niemira, P.E., ME-EPE Principal Engineer-Power Systems Solutions S&C Electric Company [email protected] John R. Bettler, P.E., MSEE Principal Engineer-Relay & Protection Services Commonwealth Edison Company [email protected] William J. Niemira, MSEE Associate-Power Delivery Services Sargent & Lundy LLC [email protected] Anthony D. Locatelli, P.E., MSEE Sr. Engineer-Relay & Protection Services Commonwealth Edison Company The classic work of J . Lewis Blackburn is well known to all of those practicing in the field of protecti ve relaying and it is a humbling honor to have been invited to contribute to the latest revision of this work. The vario us collaborators to thi s solutions manual have worked many hours on the soluti ons to the exercise problems for thi s classic text. We hope that we have illustrated the solution techniques in a manner that is clear and educational for the users of thi s manual. It is important to note that in working out these so lutions, the collaborators have drawn upon their own Some engineering assumptions and simplifying years of ex perience working in this field. approximations are sometimes made and it is experience that guides one in the validity of the si mplifying approximations and assumptions used. For the sake of those learning the craft, we have attempted to highlight approximations and assumptions when used, but there may be some occasions where we have forgotten to point out an assumption or approximation. We hope that thi s does not cause undue confusion. It is also possible that other justifiable assumptions may lead to somewhat different, equally valid solutions. Re lay system design and settings selections are inherently a balance between competing considerations. Safety and protection being primary, other considerations of security, dependability, cost, and system performance may lead to different solutions depending upon which of these other considerations are emphasized in any particular app lication. It is our hope that the users of thi s so lutions manual wi ll find it to be a useful educational tool and will benefit from it. If any errors are found, we apo logize and would appreciate these being brought to our attention. Sea n Carr, Chicago, IL February 20, 20 14 CHAPTER 2 2.1 A wye-connected generator ha s a namep late rating of 200 MVA, 20 kV, and its subtransient reactance (X;’) is 1.2 pu. Detennine its reactance in ohms. 2.2 The generator of Problem 2.1 is connected in a power system where the base is specifi ed as 100 MY A , 13 .8 k V. What is the generator reactance (X;’) in per unit on this system ba se? 2.3 Convert the per-unit answer calculated in Prob lem 2.2 to ohms. Does this match the va lue determined in Problem 2.1? 2.4 Three 5 MVA sing le-phase transformers, each rated 8: 1.39 kY, have a leakage impedance of 6%. These can be connected in a number of different ways to supply three identical 5 n resisti ve loads. Various transformer and load connections are out lined in Table P2.4. Complete the table columns. Use a three-phase base of 15 MV A. TABLE P2.4 Transformer connection Case No. Pri mary Se cond al)’ Wye Wye Wye Wye De lta Delta De lta De lta 2 3 4 5 6 7 8 2.5 Load conn ce.tion to secondary HV Wye Wye Delta Delta Wye Wye Delta Delta Line-lo-Iine base kV Load R in per un it LV Total Z as ‘icwcd from t he high side Per unit Q Wye Delta Wye Wye Wye Delta Wye Delta A three-phase generator feeds three large synchronous motors over a 16 km, 11 5 kV transmi ssion line, through a trans former bank, as shown in Figure P2.S. Draw an e qui valent sing le-line reactance diagram with all reactances indicated in per unit ofa 100 MVA , 13.8 or l i S kV base. Transformer #1 Transformer #2 <l do Generator 50 MVA 13.2 kV = 20% Xd ~ ~ I ~ .’alt 2·<I'cf' -.1' r+-v jo .IJ " ~.'1of /'$ .iS 1 /, H o d 0.01. n.es;, I, ~c;oc jO " I ;,< ff) f .J P. Ob Y ~I 8 Y A 8' ,2. <fOg 6. Y g- 1, 39() JO .D 1- &' V 02- A ~ I.Y iD /J ~il4 SdZe_~lr£",~d~. t)." b i3. 8S 1 ?;kV¥ f3 ~ 15.j56 Jd ~ P4 . ~ ~IA fUIIJ!… ~R– Y 'I .'" r J .J P, 04 f). bfV ~y -'e ~ Jl . I' " r t.l. (, 1 ~~•:'J& 'J • S- r . ~ ,.'67 ~. /.1.17 S /. "6 7 • p- :: /2 V~ :e-&; V UIS;-&'MW "" '"' VI f . J Problem 2.4 Col A Col B Col C Col D Winding connection LV wye wye delta delta wye wye delta delta Load connection wye delta wye delta wye delta wye delta Col E Col F Col G Col H LL Voltage Base (kV) Base Impedance (ohms) HV 13.856 13.856 13.856 13.856 8.000 8.000 8.000 8.000 HV 12.799 12.799 12.799 12.799 4.267 4.267 4.267 4.267 Case 1 2 3 4 5 6 7 8 HV wye wye wye wye delta delta delta delta LV 2.407 2.407 1.390 1.390 2.407 2.407 1.390 1.390 Base power (3‐phase MVA) 15.000 HV winding voltage (kV) 8.000 HV delta LL voltage HV wye LL Zbase for HV Zbase for HV (kV) voltage (kV) delta wye 8.000 13.856 4.267 12.799 Base power (3‐phase MVA) 15.000 LV winding voltage (kV) 1.390 LV delta LL voltage LV wye LL Zbase for LV Zbase for LV (kV) voltage (kV) delta wye 1.390 2.407 0.129 0.386 LV 0.386 0.386 0.129 0.129 0.386 0.386 0.129 0.129 Intermediate calculations Col I Col J Col K equivalent Y‐connected PU equivalent wye‐ resistive load connected load PU leakage resistance reactance (ohms on LV side) equivalent in line (Col J / Col H) 0.060 5.000 12.940 0.060 1.667 4.313 0.060 5.000 38.818 0.060 1.667 12.939 0.060 5.000 12.940 0.060 1.667 4.313 0.020 5.000 38.818 0.020 1.667 12.939 Col L Col M Total Z viewed from HV side per unit ohms (Col K + j*Col i) (Col L * Col G) 12.940 + j0.060 165.623 + j0.768 4.313 + j0.060 55.208 + j0.768 38.818 + j0.060 496.840 + j0.768 12.939 + j0.060 165.613 + j0.768 12.940 + j0.060 55.211 + j0.256 4.313 + j0.060 18.404 + j0.256 38.818 + j0.020 165.623 + j0.085 12.939 + j0.020 55.208 + j0.085 c.k;yj 13~: /Mv'lttJE..t) (kVoL-P Y ~fu·tJW ;: : ~O'-VV-w~OLD ~thr k[~~J "1/':; 2D1.(~)(~~:;tc ~6."1. o.~{,£/"< I 1-1 X:: I;;<'/; C~) =- Zrn.~ O.~Yf"'-0 f”’- ;t( / Xd “” Jo1, (p.) ~ ;Wll %/ IA1 Z- y./’. 2tJ ~ C~) ‘” foz> 7. tA13 ‘f.J” -;; /11, t~ (‘,~.} ) I ~d) rI ~ ar y ~ 3111.) ‘3. 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