Table Of ContentControl of Nuclear Reactors
and Power Plants
M. A. SCHULTZ
Westinghouse Electric Corporation
Pittsburgh, Pennsylvania
McGRAW-HILL BOOK COMPANY, INC.
New York Toronto London
1955
FUND FOR PEACEFUL ATOMIC D£V£LOPM£HT, INft,
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Phoenix
TK
. 2L
CONTROL OF NUCLEAR REACTORS AND POWER PLANTS
Copyright © 1955 by the McGraw-Hill Book Company, Inc. Printed in the
United States of America. All rights reserved. This book, or parts thereof,
may not be reproduced in any form without permission of the publishers.
Library of Congress Catalog Card Number 55-7283
THE MAPLE PRESS COMPANY, YORK, PA.
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PREFACE
This preface is being written as President Eisenhower waves the wand
to start construction of the first commercial nuclear power plant at
Shippingport, Pennsylvania. This event, symbolizing the entrance of
the age of nuclear power, focuses attention on the background of nuclear-
power-plant control. Historically, the early nuclear-reactor-control
designers were concerned only with the similarity of the reactor to a
bomb. The problems they faced were ones of safety and of complete
distrust for refined control elements. The legend is told in the industry
that in the first reactor, constructed under the west stands of the Uni-
versity of Chicago stadium, there existed, in addition to the normal
pneumatic safety-rod mechanism, another safety rod suspended by a
rope, with a hatchet placed conveniently nearby. The progress in
nuclear control from this point to where useful power could be safely
handled has been monumental. Now, in this new age, the problem is
simply stated: Given a nuclear power plant, what is the best way of con-
trolling it? The answer is presented in engineering terms similar to those
used in any complex control problem. The newly developed techniques
of servomechanisms are quickly brought forth as a basic design method,
and now a nuclear power plant, a jet engine, or a guided missile is treated
with confident engineering certainty.
This book, one record of nuclear-control progress, is therefore largely
in elementary servo form and language. Some concessions are made to
the nuclear physicist in recognition of the essential partnership involved
between the physicist and control engineer in the design of a control
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system foglr a nuclear power plant. The entire field of reactor and power-
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plant conotrol is far from covered in this book. Only one specific type of
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reactor, thd-e solid-fuel heterogeneous reactor, is used for descriptive and
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illustrativ#e purposes. More complication is generally involved in the
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design of splants containing different reactors such as circulating-fuel
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homogens_eous reactors. However, the basic techniques for the solution
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of the nucelear-control problem are presented in such a manner that the
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design of accontrol systems for other types of reactor plants may be obtained
by extensorg/ion of the methods presented.
At this post.int it is customary to acknowledge a few of one's coworkers
in the fielud and to ignore the remainder as being too numerous to men-
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vi PREFACE
tion. Because of the pioneering efforts of the small and somewhat closed
fraternity of engineers in this new industry, I should very much like to
acknowledge the tremendous historic labors of my associates in this field.
First, since all the present activity in this country in the field of nuclear
power plants is under the direction of the United States Atomic Energy
Commission, most of the references originally came from the basic work
accomplished under the commission. Grateful acknowledgment is made
to the AEC for permission to publish this material. Second, I should
like to thank the Westinghouse Electric Corporation for supplying me
with the necessary educational background for this project. I should
also like to thank Westinghouse and Radiation Counter Laboratories
for the use of some of the illustrations used in this book. Finally, I must
mention specifically the people at various AEC-sponsored projects who
have directly or indirectly contributed.
At Westinghouse I am particularly grateful to J. N. Grace for his basic
work, assistance, and criticism. I have borrowed liberally from my
friends and colleagues G. Anderson, W. Baer, R. T. Bayard, G. Conley,
J. C. Connor, R. C. Cunningham, R. Durnal, F. Engel, W. Esselman,
T. Fairey, J. Franz, E. F. Frisch, W. Hamilton, A. Henry, J. Kostalos,
R. Leonard, H. McCreary, W. Pagels, W. Ramage, V. Shaw, J. C. Simonds,
C. Single, G. Stubbs, O. Swift, S. Wallach, and J. Wolff.
At the General Electric Company's Knolls Atomic Power Laboratories
the initial servomechanism concept of the reactor transfer function was
achieved by J. Owens and J. Piggott. E. Wade of this laboratory also
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made maglny contributions to reactor-control instrumentation.
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I am indeobted to my friend W. Pease, formerly of the Massachusetts
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Institute od-f Technology, for my initial education in the control of nuclear
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reactors. #He, of course, was responsible for the automatic control design
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of the Brosokhaven reactor.
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At the Args_onne National Laboratory J. M. Harrer, J. Dietrich,
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J. Deshoneg, and D. Krukoff, among others, were responsible for the
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tremendoacus effort to make an engineering science of reactor control. It
was their org/initial work on the oscillation of a reactor that gave the servo
engineer st.respectability in the nuclear field.
At the Oauk Ridge National Laboratory T. Cole and W. Jordan were
always ofhitr assistance to me on power-plant-control problems while they
pioneeredhat with their colleagues on the Materials Testing Reactor control
system.w.
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My thanksw go to J. Newgard, R. Longini, and W. Brazeale for reading
this book p://in manuscript form.
M. A. SCHhttULTZ
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CONTENTS
Preface v
CHAPTER 1. INTRODUCTION 1
1-1. Introduction and Purpose. 1-2. Analogy of a Nuclear Power Plant to
a Direct-current-generator System. 1-3. Example of Analogy of a Nuclear
Power Plant to a Direct-current-generator System. 1-4. Philosophy of
Reactor and Plant Control. 1-5. Control-system Specification. 1-6.
Scope of Text.
CHAPTER 2. ELEMENTARY PHYSICS OF REACTOR CONTROL 10
2-1. Description of a Reactor. 2-2. Fission Process. 2-3. Neutron Level.
2-4. Reactor Period. 2-5. Reactor State. 2-6. Prompt Critical. 2-7.
Subcritical Level Operation. 2-8. Subcritical Period. 2-9. Critical Opera-
tion. 2-10. Supercritical Operation. 2-11. Elementary Reactor Operation.
2-12. Depletion. 2-13. Elementary Reactor Operation with Negative Tem-
perature Coefficient. 2-14. Fission-product Poisoning. 2-15. Inventory of
Items Affecting Reactivity. 2-16. Control-rod Effectiveness.
CHAPTER 3. REACTOR KINETICS 29
3-1. Introduction. 3-2. Solution of Kinetic Equations for Step-function
Input in Sk. 3-3. Solution of Kinetic Equations for Ramp Function. 3-4.
Approximate Solution of Kinetic Equations for a Ramp Function for a
Critical Reactor. 3-5. Solution of Kinetic Equations for Sinusoidal Input
Sk.
CHAPTER 4. ^AUTOMATIC REACTOR CONTROL 48
4-1. Elementary Reactor as a Control Device. 4-2. Reactor Representa-
tion with Temperature Coefficient and Poisoning Feedback Loops. 4-3.
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Negative glTemperature Coefficient Feedback. 4-4. Poisoning Feedback.
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4-5. Geneoral Requirements for Automatic Power-level Control. 4-6. Gen-
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eral Descd-ription of a Reactor Automatic-control System. 4-7. Control-
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loop Resp#onse. 4-8. On-Off-type Reactor-control-system Operation. 4-9.
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Transients Response of Control Loop. 4-10. Determination of Control-loop
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Performans_ce by Simulation Technique. 4-11. Peak Limiting by Negative
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Temperateure Coefficient. 4-12. Evaluation of Transient Response. 4-13.
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Procedureac for the Selection of Control-system Constants.
CHAPTERorg/ 5. REACTOR CONTROL MECHANISMS 98
5-1. Genest.ral Requirements of Control-rod Mechanisms. 5-2. Motors and
Mechanisums for Control Rods: Nonpressurized Systems. 5-3. Pressurized
Control-rohitrd Drive Systems. 5-4. Scramming Mechanisms. 5-5. Energy
Storage Dhatevices. 5-6. Buffers. 5-7. Rod Position Indication. 5-8.
Horsepoww.er Requirements.
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viii CONTENTS
CHAPTER 6. NUCLEAR POWER PLANT CONTROL 124
6-1. Introduction. 6-2. Description of Basic Elements of a Nuclear Power
Plant. 6-3. Steady-state Programming. 6-4. Elementary Thermo-
dynamics of the Basic Loop. 6-5. Transfer Function Representation of
Basic Plant Components. 6-6. General Recapitulation of the Dynamic
Performance of the Basic Plant. 6-7. Temperature Feedback Loop Analy-
sis. 6-8. Coolant Mixing. 6-9. Flow Changes. 6-10. Analysis for Multi-
ple-section Reactor. 6-11. Application and Limitations of Temperature
Feedback Loop Transfer Functions. 6-12. Temperature Coefficient Reac-
tivity Feedback Loop. 6-13. Transient Analysis. 6-14. External Reactor
Control System. 6-15. Automatic Plant Control. 6-16. Stability Analysis
for Demand Loop.
CHAPTER 7. REACTOR CONTROL RADIATION DETECTORS 187
7-1. Measurement Problem. 7-2. Ranges of Measurements. 7-3. Descrip-
tion of Instruments. 7-4. Effect of Gamma Radiation on Instrument
Responses. 7-5. Effects of Reactor Operation and Rod Shadowing on
Neutron Measurements. 7-6. Temperature Effects on Neutron-measuring
Instruments. 7-7. Instrument Calibration and Intercalibration. 7-8.
Instrument Circuits.
CHAPTER 8. OPERATIONAL CONTROL PROBLEMS: STARTUP 213
8-1. Neutron Sources. 8-2. Initial Reactor Startup. 8-3. Subsequent
Reactor Startups. 8-4. Operational Startup Requirements. 8-5. Safety
Startup Considerations. 8-6. Poison Considerations. 8-7. Startup Con-
trol Systems.
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CHAPTERgl 9. OPERATIONAL CONTROL PROBLEMS: POWER OPERATION . . . 245
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9-1. Requoirements for Reactivity Changes at Power Level. 9-2. Automatic
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Control.d-
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CHAPTER# 10. OPERATIONAL CONTROL PROBLEMS: SHUTDOWN 256
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10-1. Shustdown Philosophy. 10-2. Fundamentals of Scram Protection.
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10-3. Accs_idents. 10-4. Alarms and Cutbacks. 10-5. Last-ditch Emer-
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gency Shuetoff Measures. 10-6. Scramming Circuits.
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CHAPTERac 11. SIMULATORS 282
11-1. Elemorg/entary Analogue Computing Techniques. 11-2. Reactor
Kinetic Simst.ulators. 11-3. Subcritical Reactor Simulator. 11-4. Xenon
Simulatoru. 11-5. Power-plant Simulators.
Problems hitr303
Index 309hat
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CHAPTER 1
I NTRODU CTION
1-1. Introduction and Purpose. At present the state of nuclear power
plants in this country is a fluid one, with many technical ramifications
being entwined with political considerations. Nevertheless, in the fields
of reactor and nuclear-plant control several ideas have been crystallized
and are already regarded in terms of long-standing theory. As there is
no universal agreement regarding the best type of power plant, there
obviously can be no agreement as to the best type of control system.
Each reactor plant that has been built thus far contains a different con-
trol system. These control systems differ radically in mechanical design,
but many common theoretical problems and basic design concepts have
arisen. An attempt will be made in this text to present these common
points.
Another aim of this book is to present an elementary picture of reactor
and nuclear-plant control for the new group of control engineers now
entering this field. Historically, nuclear power plants grew from nuclear
reactors, which in turn grew from basic nuclear physics. The detailed
understanding of the design and synthesis of a nuclear reactor is a com-
plex subject steeped in intricate mathematics and clothed in security.
It is fortunate that the control problems of nuclear reactors can be han-
dled by simplified conventional methods which are now familiar to those
in the servomechanisms field. However, it is often necessary for the
control designer to make certain assumptions and simplifications con-
cerning nuclear reactors, which in some cases may create concern on the
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part of thgle nuclear physicists that they and the control designers are not
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talking aboout the same terms.
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It is now gd-enerally recognized that the nuclear-power business is in a
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transition# stage from the physicists to the engineers. The plants that
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have beens constructed are as complex in their own way as are the basic
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physical es_quations upon which the reactors are founded. The engineer
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thereforee tends to regard the reactor only as a component in a much
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larger sysactem, and consequently he deals with it in conventional engineer-
ing termsorg/ which are compatible with the rest of the system. The phys-
1 st.
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2 CONTROL OF NUCLEAR REACTORS AND POWER PLANTS
icist in turn has been more concerned with the intricate details of the
internal reactor structure and tends to regard the plant as an auxiliary
device which is a necessary evil.
The problem of reactor control has existed since the first reactor and
has been the subject of extensive study for many years. The problem
of nuclear plant control is a newer one, and the answers are not as well
known.
1-2. Analogy of a Nuclear Power Plant to a Direct-current-generator
System. Let us consider a reactor operating by itself serving no function
other than perpetuating a chain reaction. This type of operation might
be compared with the open-circuit no-load opefation of a d-c generator.
Tying a load onto the reactor and extracting power from it would corre-
COOLANT
PUMP CONDENSATE
PUMP
FIG. 1-1. Block diagram of elementary nuclear power plant containing pressurized water
reactor and conventional steam system.
spond to tying a load onto the d-c generator. In the case of the generator
it would easily be anticipated that the load would affect the generator
characteristics. Historically, it was not quite so apparent that the power
plant would affect the characteristics of the reactor. This reaction could
occur in a complex plant from many sources. Even minor auxiliary
devices could find their performances reflected back on the basic reactor
performance. In order to gain a better appreciation of this problem
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from an oglver-all point of view, the reactor plant, d-c generator analogy
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can be puorsued further by an illustrative example.
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1-3. Examd-ple of Analogy of a Nuclear Power Plant to a Direct-
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current-ge#nerator System.1! Let us assume that our nuclear power
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plant conssists of a pressurized water-cooled reactor system and a conven-
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t Superiors_ numerals in the text correspond to the numbered References at the end
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of each cheapter.
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INTRODUCTION 3
tional steam-turbine system as shown in Fig. 1-1. In this plant high-
pressure water is used to cool the reactor and extract heat from it. This
heat is transferred to the secondary loop in a steam-generator system
consisting of a boiler and a steam separator. The output loop of the
plant contains a steam turbine, condenser, and all the necessary auxil-
iaries. The turbine is directly coupled to a load, in this case presumably
an electric generator. Both the primary coolant and steam systems are
closed loops.
Control Program. Many types of programs of primary and secondary
parameters can be set up for a plant of this sort, depending upon the
components and local specifications. As a direct relationship exists
between the water temperatures of the primary loop and the steam tem-
perature and pressure of the secondary loop, a control program may be
specified from either loop. For the purpose of this discussion the plant
operation will be specified from the primary loop in terms of the coolant
temperatures at the reactor inlet and at the reactor outlet as functions
of power level. The following symbols are used:
Q = total reactor power output
Th = coolant temperature at reactor outlet
Tc = coolant temperature at boiler outlet
Tw = average coolant temperature = (Th + Tc)/2
Ts = steam temperature at outlet of steam generator
ps — absolute steam pressure at outlet of steam generator
Hs = enthalpy of steam at outlet of steam generator
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Hx = enthglalpy of exhaust steam at turbine outlet, for isentropic
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expansiono
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Hw = entd-halpy of feed water
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F, = rate #of steam flow
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Let us asssume that our control program is such that the average tempera-
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ture of ths_e primary loop coolant is held constant regardless of the load
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requiremeents of the secondary portion of the plant. This so-called con-
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stant-T.v acprogram causes no change in primary coolant volume as the
power ouorg/tput is changed, and a small simple water pressurizer may be
used. Thest. flow of water created by the pump is at a fixed rate and does
not changue as a function of the power level. The specific relationships
between thitrhe primary and secondary temperatures of this type of plant
control arhate shown in Fig. 1-2, for the arbitrary condition of T.v = 500°F.
It can be w.seen in this plant that the steam temperatures fall off very
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rapidly asw the power output is increased. This fall in steam temperature
calls for ap:// corresponding drop in steam pressure.
Thermodyhttnamic Analysis. In analyzing this plant it can be seen that
the powerd / output of the reactor is proportional to Th — Tc. The con-
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4 CONTROL OF NUCLEAR REACTORS AND POWER PLANTS
stant primary coolant flow is assumed such that, again using arbitrary
numbers, at full output of the reactor Th — Tc = 50°F. The power
transferred from the primary-coolant water to the secondary loop is
proportional to T,v — Ts. The proportionality constant depends on the
power rating and on the boiler dimensions. For illustrative purposes
let us again assume that at unity power T.v — T, = 60°F, which will be
designated as rated full power. The numerical values of all these tem-
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REACTORs_ POWER
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FIG. 1-2. Teemperature and pressure control conditions for plant having constant-Tat,
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program.ac
peraturesorg/ are the ones given in Fig. 1-2. In this elementary plant the
steam least.ving the steam generator is of high quality, but it is not super-
heated. Huowever, we can assume that the steam generator furnishes
dry and shitraturated steam at all power levels. The steam pressure then
depends ohatnly on the steam temperature and may be obtained from steam
tables.w.
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If we assuwme that the changes in potential energy and kinetic energy
of the step://am are negligible compared with changes in enthalpy throughout
the steamhtt loop, the power delivered to any component becomes simply
Fe,n &thHa,l pwyh d / derroep F a, c(Irbo/shsr )t hise tchoem spteoanmen-ftl.o Twh reant eF ,a, nHdw &, aHn (dB tHux/l bca) nis bteh ecal-
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