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PROBLEMS IN THE CONTROL OF A NUCLEAR REACTOR -- STEAM ELECTRIC POWER PLANT William Kerr University of Michigan Ann Arbor A nuclear reactor-steam electric power the resulting environment impose problems on a plant (Fig. 1) may conveniently be divided into control system which are peculiar to this three parts for descriptive purposes. situation. 1. The reactor proper. One of these problems has to do with core 2. The heat transfer loop. size in relation to heat generated. Typically in a 3. The load. nuclear power reactor the heat generation may be as much as about 4 kilowatts per cubic inch. 1 For control purposes, information is Compare this with around 0. 6 kilowatts per cubic needed concerning the dynamic characteristics inch, typical of a high pressure naval boiler, and of each of these separately, and the performance it-becomes clear that the core structure must of an integrated system containing all three. operate at a high temperature. In fact the upper limit of operating temperature is fixed by what In many of the proposed systems for the core structure can withstand. generating electric power the turbine-generator combination will be of conventional design. In order to get maximum power out of the Hence the items of primary interest are the reactor one operates the core structure at a reactor and the heat transfer loop. Although one temperature just as near its upper limit as one of the most important parts of the heat transfer dares. Hence it is important that the control loop is within the reactor itself, namely the system chosen inhibit any serious oscillation of transfer of heat from fuel to coolant, it is con- power and temperature about the operating level venient for analysis to think of the reactor and lest the core be irreparably damaged. the heat transfer loop as separate elements with a connection from one to the other. One may Another problem peculiar to reactors has refer to the kinetics of the reactor as primarily to do with the intense nuclear radiation fields nuclear kinetics. The kinetics of the' heat trans- present in the core region. Much of this radiation fer loop have then to do with its dynamic heat results from the fission process itself, which transfer characteristics. One is concerned with produces gamma rays and neutrons, and from the nuclear kinetics of the reactor, the thermal the products of the fission process which are kinetics of the heat transfer loop, and inter- radioactive. These radiations are injurious to relationships which may exist between the two. personnel and hence the core region must be surrounded by absorbing shields which contain The Reactor most of this radiation. A nuclear reactor consists of an assembly These radiations also produce structural of fissionable material associated with an changes in many materials. The radiation fields appropriate arrangement of non-fissionable existing in the core of a power reactor may pro- material. The non-fissionable material fre- serious damage in such things as electrical in- quently plays a multi-purpose role. It may have sulation, or organic gaskets or diaphragms. important structural functions, it may participate Hence much conventional measuring equipment in the removal of heat, it may play a part in the cannot be used in the core region without nuclear reactions. appropriate modification. The fissionable- material is contained with- The core may be of the heterogeneous or in a region called the core. It is in the core that homogeneous type. The heterogeneous type is the fission takes place producing energy which is used when the fuel is in solid form as a metallic primarily converted into heat. The fact that this alloy, and the homogeneous type when the fuel heat energy arises from the fission of certain is in solution. Heat is removed from the nuclei is only incidental to its subsequent use. heterogeneous type by an appropriate coolant which Howev.er, the assembly which is necessary for flows through the fixed core structure. The obtaining the controlled fission reaction, and coolant is chosen both for its heat transfer and its

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Page 1: Problems in the Control of a Nuclear Reactor -- Steam Electric Power Plant

PROBLEMS IN THE CONTROL OF A NUCLEAR REACTOR --STEAM ELECTRIC POWER PLANT

William KerrUniversity of Michigan

Ann Arbor

A nuclear reactor-steam electric power the resulting environment impose problems on aplant (Fig. 1) may conveniently be divided into control system which are peculiar to thisthree parts for descriptive purposes. situation.

1. The reactor proper. One of these problems has to do with core2. The heat transfer loop. size in relation to heat generated. Typically in a3. The load. nuclear power reactor the heat generation may be

as much as about 4 kilowatts per cubic inch. 1For control purposes, information is Compare this with around 0. 6 kilowatts per cubic

needed concerning the dynamic characteristics inch, typical of a high pressure naval boiler, andof each of these separately, and the performance it-becomes clear that the core structure mustof an integrated system containing all three. operate at a high temperature. In fact the upper

limit of operating temperature is fixed by whatIn many of the proposed systems for the core structure can withstand.

generating electric power the turbine-generatorcombination will be of conventional design. In order to get maximum power out of theHence the items of primary interest are the reactor one operates the core structure at areactor and the heat transfer loop. Although one temperature just as near its upper limit as oneof the most important parts of the heat transfer dares. Hence it is important that the controlloop is within the reactor itself, namely the system chosen inhibit any serious oscillation oftransfer of heat from fuel to coolant, it is con- power and temperature about the operating levelvenient for analysis to think of the reactor and lest the core be irreparably damaged.the heat transfer loop as separate elements witha connection from one to the other. One may Another problem peculiar to reactors hasrefer to the kinetics of the reactor as primarily to do with the intense nuclear radiation fieldsnuclear kinetics. The kinetics of the' heat trans- present in the core region. Much of this radiationfer loop have then to do with its dynamic heat results from the fission process itself, whichtransfer characteristics. One is concerned with produces gamma rays and neutrons, and fromthe nuclear kinetics of the reactor, the thermal the products of the fission process which arekinetics of the heat transfer loop, and inter- radioactive. These radiations are injurious torelationships which may exist between the two. personnel and hence the core region must be

surrounded by absorbing shields which containThe Reactor most of this radiation.

A nuclear reactor consists of an assembly These radiations also produce structuralof fissionable material associated with an changes in many materials. The radiation fieldsappropriate arrangement of non-fissionable existing in the core of a power reactor may pro-material. The non-fissionable material fre- serious damage in such things as electrical in-quently plays a multi-purpose role. It may have sulation, or organic gaskets or diaphragms.important structural functions, it may participate Hence much conventional measuring equipmentin the removal of heat, it may play a part in the cannot be used in the core region withoutnuclear reactions. appropriate modification.

The fissionable-material is contained with- The core may be of the heterogeneous orin a region called the core. It is in the core that homogeneous type. The heterogeneous type isthe fission takes place producing energy which is used when the fuel is in solid form as a metallicprimarily converted into heat. The fact that this alloy, and the homogeneous type when the fuelheat energy arises from the fission of certain is in solution. Heat is removed from thenuclei is only incidental to its subsequent use. heterogeneous type by an appropriate coolant whichHowev.er, the assembly which is necessary for flows through the fixed core structure. Theobtaining the controlled fission reaction, and coolant is chosen both for its heat transfer and its

Page 2: Problems in the Control of a Nuclear Reactor -- Steam Electric Power Plant

Fig. 1. Block Diagram of Nuclear Power Plant Showing Essential Elements.

nuclear characteristics. In the niomogeneous radioactive) and the turbine-generator system.type heat may be removed by moving the hot fuel- An example is one proposed power reactor whichcontaining solution out of the core and through a uses liquid sodium to cool the core, a sodium--heat exchanger. In this case the fuel itself serves NaK heat exchanger to transfer heat fromto remove heat from the core region. sodium to liquid NaK (a sodium potassium alloy),

and a NaK water exchanger to generate steam.Surrounding the core may be a blanket The extra isolation is considered necessary in

which uses neutrons escaping from the core this system not only because a sodium-water re-region to produce additional fissionable materiaLe action proceeds with considerable violence, butThe blanket may also serve as a reflector which also because the sodium becomes radioactive intends to prevent the escape of neutrons from the flowing through the core. Hence a sodium-core region. water reaction in such a system would produce

the additional hazard of releasing a radioactiveThe Heat Transfer Loop material. The NaK also reacts with water, but

such a reaction would not involve release of aThe heat removed from the core region, radioactive material. In addition, it is extremely

either by a coolant or by circulating the fuel it- important that water not be allowed to reach theself, may be used to generate steam. This steam 'core in a fast reactor;^ the extra isolationgeneration usually takes place in a heat exchang- minimizes this danger.er external to the core. In some reactors,called boiling water reactors, the coolant is The dynamics8 of the heat transfer in theboiled within the core region and the resultant heat transfer loop depend not only on thesteam goes directly to a turbine, characteristics of the heat exchangers, but also

on such things as the coolant pump characteris-Since most coolants become radioactive in tics and the amount.of heat storage capacity in

passing through the high-neutron flux in the core the loop. This latter is influenced considerablyregion, the use of steam generated in the core by the total mass of coolant in the loop. Anyregion makes the turbine radioactive. The use large mass of coolant produces a large heatof a heat exchanger between reactor core and storage capacity and tends to make the systemturbine isolates the turbine and its associated sluggish in its response to changes in load.equipment from the radioactive coolant.

In this respect the reactor heat transferOne notable exception to this situation is loop may differ markedly from a conventional

the use of helium as a coolant. The capture fuel-fired steam boiler. The fuel-fired boilercross section of helium for neutrons is practi- may have appreciable steam and heat storage,cally zero. Thus it will not become radioactive whereas the steam generator part of the heatin passing through the core region and might transfer loop may have almost negligible thermalwell be used in a closed cycle system with a gas storage. The storage that does exist will resideturbine. in the part of the coolant loop between reactor

core and steam generator. In the case of theIn some cases two heat exchangers may be boiling water reactor the steam storage might be

used to secure additional isolation between the made large through the use of some type ofcoolant (which flows through the core and is thus header, or it might be relatively small, leading

Page 3: Problems in the Control of a Nuclear Reactor -- Steam Electric Power Plant

to a situation in which any change in load is ful, particularly in the initial investigation. Asquickly reflected into the reactor. the analysis develops, an analogue computer will

give useful information concerning system be-Load havior.

It is assumed that the load on a nuclear re- For each of the methods mentioned aboveactor-steam generator will be a conventional a mathematical model is necessary. The choiceturbo-generator combination. The characteris- of the model will depend somewhat upon thetics of such a combination are well known. accuracy desired and the detailed problem being

studie.d. However, for system stability studiesInsofar as it affects the performance of the at or near rated load a rather unsophisticated

reactor--heat transfer--load system, the model may suffice.operating program characteristic of the load isimportant. In usual operating practice the output The Reactor Modelof a turbo-generator combination or of a wholeplant is made to follow normal system load fluc- For a nuclear reactor operating very neartuations. In systems of reasonable size these critical the following set of equations has beenfluctuations are not rapid except in emergency found to be a very good description of the nuclearsituations. kinetics3

In the case of a nuclear power plant which dn 8k nis economically usuable in a large utility, X- = i- n - - CXiC1economic considerations probably dictate that it (1)carry full rated load except when it is completelyshut down for repair or routine maintenance. pinThis means that in a system analysis particular dt xiciattention is given to operation at or near fullload.

In addition, care must be used in examining Here n = neutron population in the reactorthe dynamic characteristics of the system during 8k = excess reactivity of reactorstartup. The characteristics of a nuclear power X = mean lifetime of prompt neutrons inthereactor make it particularly susceptible to the r_eactorpossibility of an unstable situation during startup. P = fraction of neutrons per generation

w hich are delayedAnalysis of the System Ppi 1P

1 CGi population of delayed neutron pre-According to H. Hurwitz2 "properly de- cursors of ith group in reactor.

signed nuclear reactors are easy to control and l/Xi = mean life of ith group of delayedsafe to operate. " As he shows, the energy re- neutron precursors.lease to be expected from even a serious reactoraccident is about that to be expected from a small At least three items should be pointed outchemical explosion. However, because of the here. The first is that the mathematical modelpossibility that an accident may release the radio- is that of a "point reactor"--that is, one whoseactive fission products which accumulate during space variation of neutron population is ignored.operation, extreme care must be taken to prevent Experience has shown, however, that for systemany serious power excursion in a reactor. studies near full load this model is entirely

satisfactory.In the case of the power reactor, where

coupling between reactor and load plays an im- The second item is that the neutronportant part in the system dynamics, a careful population, n, is being described. However,analysis not only of reactor performance but also since the fission rate in the reactor is directlyof the complete system is indicated. This analysis proportional to the neutron population, it followsshould indicate whether the system is inherently that the reactor heat generation is very nearlystable and well behaved. If it is not, an appro- proportional to the neutron population. Hencepriate analysis should indicate the steps that mist power generation in the core can be describedasbe taken to produce the desired stable system be- n multiplied by an appropriate constant.havior.

The third item is the presence of a termAt least two approaches to this problem referred to as delayed neutron precursors.may be used, each of which supplements the These are fission products which ultimatelydecayother. An analytical approach is found to be use- to produce neutrons. At least six separate groups

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Page 4: Problems in the Control of a Nuclear Reactor -- Steam Electric Power Plant

have been recognized, 4 each having a character- In some cases Equation (2) should be re-istic mean life for decay. One notes that since placed by an equation which accoutits for thethis is a source of neutrons in addition to the different elements which contribute to the tem-neutrons produced promptly at fission, that the perature coefficient. For example, in areactor may be either "prompt critical" or "de- heterogeneous reactor both fuel and coolant willlayed critical." usually contribute to the temperature coefficient.

This may be represented by an equation of theReactors which are to be controlled are following type.

always operated delayed critical. The reasonfor this is seen when one puts numbers into 8k = bko + pf (Tf - Tfo) + pc (Tc - Tco). (3)equation (1). For a Uranium-235 fuel, j3 is about0. 0075, T may be typically 10-4 for a thermal re- Here ako is the excess reactivity when Tf = Tfoactor, and a mean value for I/A is about 12. 5 and Tc = Tco. Tf and Tc are fuel and coolantsecs. If one computes a mean generation time temperatures respectively, and Tfo and Tco arefor the reactor operated delayed critical it is reference temperatures for each.around 0. 1 sec. Hence the delayed critical re-actor is comparatively sluggish when compared When either Iquation (Z) or (3) is sub-to the prompt criticil reactor characterized.by stituted into the set of Equations (1) there resultsits 10-4 second generation time. a set of equations which is in general non-linear

in n. This can be seen by determining the re-Examination of Equation (1) reveals that lationship between n (the neutron population) and,equilibrium can exist independently of the values in the case of Equation (3), the fuel and theof n and C provided only that dn/dt and dCi/dt coolant temperatures.are zero. In order to change n, dn/dt may bechanged by changing bk. In practice, changes The reactivity of the reactor may also inin bk are usually produced either by deliberately some cases be affected during operation by thechanging the amount of fuel or of neutron absorb- formation of the fission products. One of theer in the core region, or by changes in the isotopes produced in comparatively largequan-nuclear characteristics of the core due to a tities by fission of Uranium is Xenon 135. Thischange in its temperature, isotope has a very high cross section for capture

The first type of change in 8k is frequently of thermal neutrons and hence absorbs neutronsaccomplished by arranging to insert into or with- very readily in a thermal reactor, Since the re-draw from the core region either absorber or actor reactivity depends upon the amount offissionable material. Devices for this purpose abscorbing material in the core it is a function ofare referred to as control rods. The second Xenon concentration.type of change occurs -automatically as the coretemperature rises. Since the core temperature The Xenon is produced by fission. It maydepends upon both the rate-of heat generationand disappear either as a result of radioactive decaythe rate of heat removal, the rate at which heat or by absorbing an additional neutron. Theis removed from the reactor directly influences Xeion concentration at any time thus depends boththe operating power level. This effect of tem- on neutron concentration and on the characteristicperature on reactivity is described quantitatively mean decay time of the radioactive Xenon 135.as a temperature coefficient of reactivity. Forsystem stability it is desirable to have this co- Insofar as Xenon concentration depends onefficient negative- -i. e., such that an increase neutron population it can be seen that, like thein temperature decreases reactivity, temperature coefficient, it is- effectively a re-

activity feedback. That is, a change in reactivityFrom the previous paragraph it is seen changes neutron population which changes either

that a more complete description of 8k as it temperature or Xenon concentration or both, andappears in Equation (1) may be written as these in turn affect reactivity.

8k = bko + pT (T - T0). (2) It should be pointed out that the Xenon"poisoning" effect is important only in the thernml

Here 8ko is the reactivity at T0, pT is the reactor. The cross section for absorption of thetemperature coefficient of reactivity, and T is faster moving neutrons of a fast reactor by Xenonthe reactor temperature. The excess reactivity, 135 is negligible.8ko, is in general a function of time. In order The HeatTransfer Equationsto study the set of equations (1) an additional set - -of equations relating neutron population, n, to The method of heat transfer depends on thereactor temperature, T, is necessary. reactor. For illustrative purposes, let us assume

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Page 5: Problems in the Control of a Nuclear Reactor -- Steam Electric Power Plant

a solid fuel element with coolant flowing through Here a = cociant transit time in a channela channel in the element. The heat transfer can W = coolant mass flow ratebe described in this situation to a good approxi- Cc = coolant specific heatmation by an equation of the type, Tco, Tci = coolant outlet and inlet tempera-

tures respectively.QT ~(Tf - Tc) (4)

In many cases a good approximation resultsHere QT = heat transferred from setting Tcequal to (Tco + Tci)/2. The tem-Tf = average temperature of the fuel peratures Tco and Tci are load dependent. For

element example, if the reactor is delivering no load,

Tc = average coolant temperature Tco = Tci.-is a constant which is character-

istic of the heat transfer. In general, in addition to the load, there willbe in the coolant loop both transport delay due to

The heat, Q, generated in a reactor the travel time of the coolant in its piping, and lagoperating near full load is equal to a constant due to heat capacity of coolant and container. Thetimes the neutron population. Hence the heat magnitudes of these will of course vary widelytransfer fuel to coolant may be described by an with the installation.equation of the type,

With these known, however, a block diagramQ = K1n = MfCt d- + Y (Tf - Tc) (5) can be set up similar to that shown in Fig. 2. A+t study of the integrated system may now be carried

out by means of an appropriate combination ofHere K, a constant of proportionalityHereMKf = ah constan of

proportionality pencil and paper analysis and an analog computer.Mf = the mass of the fuel The standard techniques which have been develop-Cf = the specific heat of the fuel ed for the treatment of controlled systems with

feedback may be applied both to study the inherentExamination of Equation (5) shows that if Q stability of the system without control, and to de-and Tc are known, Tf is completely determined. termine an optimum automatic control system.5 6Since Tc is the average coolant temperature itwill be influenced by the load. The heat genera- The analog computer has proved to be ation, Q, depends on the operating level of the powerful tool in the study of power-producingreactor. However, this will in turn depend on reactor systems. It serves not only as a conven-both Tf and Tc through a relationship such as that ient and flexible method of analysis, but can alsodescribed in equation (3). be used to study the performance of different com-

ponents of the system under simulated operatingThe transfer of heat to the coolant and its conditions; In addition, the computer can be used,subsequent removal may be described by an equa- when appropriately connected to an actual controltion of the type panel, to train operators. This is a particularlv

dTc important function in the case of a reactor systemy(Tf - TFc) =awCc -dt + WCc(Tco - Tci) (6) which is the first of its kind to be constructed.

|aKO 8K | l n | FUEL ELEMENT COOLANT TCbC ) REACTOR r ~~~THERMAL 1, _ THERMALoi b _ - ~~~~~~~KINETICS K INETICS

COEFFICIENTS _;l TRANSPORTIOF REACTI VITY DELAY

Fig. 2. Block Diagram of Reactor and Coolant Loop.

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Page 6: Problems in the Control of a Nuclear Reactor -- Steam Electric Power Plant

Reactor Startup toward automatic startup systems is necessary.Since most of the difficulty is associated with

As in the case of the conventional power measurement of power level at very low levels,plant, startup or shutdown must be accomplished effort must be concentrated in this area.in the light of such considerations as permissablethermal stresses in the heat transfer system and Summaryin the turbine. These are important, however,over at most about three decades below full power The problems of controlling a nuclearlevel. A nuclear power reactor at shutdown may reactor-steam electric power plant are asso-be operating at a power level of ten decades below ciated both with nuclear reactor control and withfull load power. Hence the reactor must be control of the integrated system, which includesbrought through about seven decades of power the reactor as a heat source. The problems canlevel before it reaches the level at which thermal be attacked by appropriate use of existing methodsconsiderations become important. for analyzing controlled systems. Existing nuclear

power plants demonstrate the feasibility of usingAs pointed out previously, the reactor power these methods. They also indicate that not all the

level is changed by inserting into the reactor an problems are completely solved.excess of reactivity over that necessary to makeit delayed critical. As was also pointed out, care Referencesmust be taken to insure that the amount of reac-tivity inserted is not sufficient to make the reactr 1. Zinn, W. H., Nucleonics, 10, No. 9, 8,prompt critical. Since about the only way to judge -the amount of excess reactivity present is through (Sept. 1952).measurements of the power level and the rate at 2. Hurwitz, H. Jr., Safeguard Considerationswhich it is changing, precise measurements of for Nuclear Power Plants, Proceedings 1953reactor power level and rate of change of power Conference on Nuclear Enginee-ring, Univ. oflevel are required in many cases over about ten California, Berkeley.decades.

3. Hurwitz, H. Jr., Nucleonics, 5, No. 1, 61,At the present time, methods of -measuring (July 1949).

power level below about three decades down fromfull power involve measurement of the neutron 4. Paxton, H. C., Nucleonics, 13, No. 10, 49,population. The status of the present methods and (October 1955).equipment for measuring these low power levels 5. Schultz, M. A., Control of Nuclear Reactorsis not altogether satisfactory, and Power Plants, McGraw-Hill Book Company,

Inc., New York, 1955.The startup of most existing nuclear re-actors is accomplished almost entirely by manual 6. Siegel, R. and Hurwitz, H., KAPL-1138,methods. It is clear that further work aimed March 1, 1955.

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