ORIG. RUSSIAN: ON DYNAMIC STABILITY OF NUCLEAR POWER PLANTS

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP88-00904R000100110019-9
• Release Decision: RIPPUB
• Original Classification: U
• Document Page Count: 19
• Document Creation Date: December 22, 2016
• Document Release Date: August 26, 2009
• Sequence Number: 19
• Publication Date: May 1, 1964
• Content Type: STUDY

 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
flow rate and its temperature) run with great time delay, slowly
as compared to the reactor traneiento. Because of this the latter
may be considered to be quasi-static and studying the system
dynamic stability as a whole the reactor should be considered
only in a quasi-static asymptotic approximation. It means that
the influence of terms of high orders in the reactor transfer
function is neglected. The whole system may turn out to be ape-
rigciically stable-even at oscillatory stability of the reactor.
As far as high oscillation frequencies, which can be caused in
the reactor by different reasons, are filtered at a steam genera-
tor and in other primary circuit units great enough and does not
pass to reactor input, the system proves to be "unclosed" over
high frequencies. The closed system stability problem can be re-
duced to the dynamic stability study of the reactor at these
frequencies and of the closed system, in which the reactor is
represented in a quasi-stationary approximation.
While writing down the system of the dynamics equations we
have taken a series of simplifying assumption, validity of which
is evident enough. The main of them are as follows:
a) Roimary circuit coolant flow rate is constant.
b) Steam extraction to the turbine is directly proportional to
the load.
c) Feed water supply depends on the change of steam flow rate to
the turbine and is carried out through an aperiodic network.
d) One group of delayed neutrons was considered in the equations
of kinetics.
e) Feed water subcooling was taken into account in the t ital
steam gener&tor heat balance.
f) The final velocity of upward steam flow in the boiling zone
was neglected, that is, boiling water level change because of
the void steam content change was ignored.
g) Saturation temperature - pressure dependence is linear.
h) Heat-transfer coefficients are constant. For the reactor it
is the consequence of the assumption of the coolant flow rate
permanency. It is true for a steam generator if the heat-
transf
er coefficient is slightly dependent on heat flux.
37 1
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
i) Reactivity changes are small and the equations of kinetics
may be linearized.
j) Transport delays in pipings were approximate by an aperiodic
network,
The solution of the system of the reactor dynamics equations
can be expressed with these rather general approximations as the
transfer function oc (5) which describes coolant temperature
changes at the reactor outlet with temperature fluctuations at
the reactor inlet. Let this function be conventionally "the reac-
tor transfer function" though it usually denotes the function
which is characteristic of power changes versus reactivity chan-
gee:
outlet_ F_
Vinlet FO ( S)
(1)
where
F. ( s ) = s ( s + T I V , ) (s t T P+ 05 T F ) - 0 5 s 7 , f P *107 (s~7)
F(s)=s(s-i)(t'- 5T9+D,SsTPTP*AT /stT (2)
M 11 c)
o /
The functions oe (s) and as(s) are correspondingly equal.
c (c) = o ~ j505
~e = D!Soc e
1 ""T
0 .2 [I~(f2)-J
A
4T)
The reactivity changes can be represented as a function of
reactor inlet and outlet coolant temperature:
1-0
U caC~ S 17
?T inlet + () outlet (4)
It Is Been from equations (1) and (2) that the reactor as a
dynamic system has a characteristic equation of the third order.
However, in most cases the function oC (s) can be simplified by
nog;"IIcting the terms a~ and ~2 an the heat-transfer coeffi-
cient and the fuel element heat conductivity and hence the
reactor dynaamic constants usually are proved to be great enough.
-3~-
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
Besides that, high frequency components in the function of inlet
coolant temperature changes in a closed reactor system are negli-
gible.
If the steam generator boiling water level is assumed to be
held approximately constant at all transients due to controlled
feed water supply and is assumed to be left cove the coi levels,
then it is easy to get the relation between 'U inlet and outlet
solving steam generator heat transfer equations
where
~q = (s) (s rT, l A2 p"
Vinlet outlet /
(5)
T V . T, T2
(s+T1)(s~T,)(s*T2)
The function (5~ can be considered the transient function
of series-connected aperiodic networks. The dynamic coefficients
T 59' T,, TZ are always positive. Therefore, the steam genera-
tor, as a dynamic system, is absolutely stable as to the inlet
temperature disturbances and to the second circuit pressure.
Introducin effective delay time G -f-Z + G s~
r 2 ,
the function (s) can be ex
(S) ressed as an aperiodic network
- r s+ (7)
where
r
Go
In case of a reactor with a control system it is necessary
to introduce the equations of an automatic power regulator into
the system of equationa of the reactor dynamics. The former can
be written down considering possible corrections for the process
parameters (pressure, temperature and etc.) in the form
6n- - rz.
5li=06t'U + Pt2(;+s)V 3
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
In this case the system reactivity changes at pressure disturv
bancee (external load) and at introducing the correction fbr the
steam pressure power demand can"be decomposed" into two compo-
nents: a "temperature" component J T N due to coolant temperature
changes and a "pressure" component YP Also, the third compo-
nent J , characterizing a random uncontrolled reactivity
fluctuations, can be introduced. Thus
where
PTe4k(,) f fp (~;) + J J (s)
5) _ ~(5) ~niet f `al eb (s)'f~utiet
P
?P X,4 (S) ,
(10)
Then, effective "temperature" coefficients of reactivity
(c4 (s) ; oz e (s) ) and an effective "pressure" coefficient
of reactivity can be expressed in terms of reactor process para-
meters and of power regulator parameters as follows:
,4(-
LI 5) -
cit(S-~~)s s
(s_L)(s2_s
(sl = sl--z s-x T
4xf xL
5
P (s- Z)(s-, s x, T)
(12)
Hence, due to linearity of the system of the dynamics equa-
tions, the other process parameter changes (e.g. Voutlet , n
n1so can "be decomposed" formally into "temperature", "pressure"
and "reactivity jump" components.
For example,
371
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
+ + E
Doutlet `.nlet
Fo(s) Fo(s) C (s) j (13)
where Fo (s) and F ~s) coincide in form with the functions
(2) which incorporate the relations (12) instead of c>C and
C G< but Fp'(s) and F? (s) are equal, respe ctivily :
P
P 40 T1 (s _P TO )
Fp(s)_ s (s-t-7,)fIoTl
~c- Vr'2_ro C--P1T_)
ae`' s) ) P T Ps s tT
~S (s + f; T = tqO o )
-L -
(S4) S Z '2e s -a=,
(14)
It should be noted that to provide the best quality of the tran-
sients the automatic power control systeuB are designed so that
time constants of reactor power setting changes and corrections
are turned out to be much greater than a time constant of a
neutron power regulator, i.e.
I c2, X-3 , xq, a-5 I
It means, that the rate of a neutron power change is much
greater than that of a power setting change, power follows chan-
ges of a power demand setting, i.e. 71 =123 at any time instant.
Furthermore, the automatic control rod (AP) insertion rate at
autonomous regulator adjustment is usually selected so that a
control rod (AP) could overcome the "resistance" of a negative
temperature reactivity effect and assure a good quality of reac-
tor power transients. It means t the first addend in the nume-
rator of the expressions for c41 and oCt in (12) must be
much less at all frequencies characteristic of the reactor.
Hence, neglecting the influence of the temperature effect, while
the automatic control rod (AP) in operation and assuming that AP
is adjusted so well that it does not cause systematic disturban-
ces of low frequencies in a closed reactor dynamic system, the
following equations can be written down instead of equations (12) :
371
- 6-
0
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
"4P (S P (S~ C + d?5 SS
() e - Z s f _
z o
(s)
ce3 5
(s-)(s + T')
(S +TO )
(15)
With power automatic control system and with due regard for
equations (15), the functions F (S) and F, (s) take the form:
F(s)=(-5-je,*-S +TP s+ 7+05TP) `05TMTP]- JP(
ey+ .S)
a
Fo (s)=(s -)[Cs*T~)(T,P o5T~)+O,5ThT1]+ i + s)
1( ~ 5
(16)
(17)
The multiplier (S- 2) in the dominator is omitted as being
unessential.
As an example, some results of the APEYC plant dynamic
property studies are to be given. As the time characteristics
of processes, run at the APBYC plant, are calculated to be a
few tens of seconds, then the reactor thermal processes can be
considered in a quasi-static approximation. It allows to write
down the functions FO(S) and F, (5) from the equations (2)
in the form
Fp(s)Ke (S+Te)
F(s)zK1(s+Ti)
Expressions for Ke, Ki, Ti, Te are given in Table III.
In this case the system characteristic equation will be
written down as
371
S' fjs2+fS+B. =0
(18)
(19)
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
.P T
~11(7 + TI)
(2 -
T, TZ
47
3
'T K) +
t)'T, (2, +
T, TZ
+ I qr 'T 4 )IJ
77 -
where
G r
B0 ~T4Te A,)(1
Ke Te 3
Similarity factor To is determined, if Bo in the equation (22)
is equal to a unit.
Coefficients of the equation (19) and Lo being applicable
to the APBYC plant, are equal
Le = 81
= 3.2
2.6.
To study the roots of the characteristic equation (19), one can
use diagrams (Pig.1), represented in the paper by Vyshnegradsky
(2).
Notations,ueed in Fig.1, are as follows:
V5, Lai - doubling period of a transient exponential component
ft dimentionleeoscillation frequency of a transient
periodic component
p - damping characteristic of oscillation amplitude of
J a transient periodic component.
Region I - aperiodic stability region
371 _ 8
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
Region II - oscillatory stability region
The position of a determining point with coordinates
corresponding to a system dynamic parameters on Vyshnegradsky
diagrams, allows to judge of the transient character in the
system.
It is seen from Fig.1, that the APEYC plant as a dynamic
system is a stable low oscillatory system; a doubling period of
a transient aperiodic component is
to- ZoGs /#0 see
o 693 ,
an oscillatory period is
T . 2r1 r0 500 sec;
the degree or an aper odic component damping is:
d_ 2i / 31
Time power and steam pressure change curves at a Jump change ii:
external load of 4596 from nominal received on an analogue compu-
ter for a full initial non-linear system and without reactor
simplifying assumptions are shown in Pig.2. It is evident from
the given evaluations and curves that transients at the APBYC
plant are almost aperiodic, so that practically an oscillatory
component can be neglected. It means that the transient can be
practically approximated to a transfer function, equivalent to
an aperiodic network of a type (s + ~-! where is
depends on the plant parameters through the coefficients Y
and 7 .
The comparison of transients investigation results on the
analogue computer by using the complete non-linear system of
equations with those received from Vyshnegradsky diagrams (1,2),
while using the third order characteristic equation (19), has
shown that this characteristic equation gives quite exact re-
sults and can be used for studies in the influence of different
dynamic factors on the reactor stability.
Lei, us note that the dynamic coefficients D. Toff g A and
KT/Ke, Ti, Te, included in the characteristic equation coeffi-
cients (19), depend on: 3 7 1
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
D - thermal-physical and design parameters of the secondary
circuit ;
A Teff - heat transfer in the steam generator and transport beat
transfer along the pipings and steam generators of the
primary circuit;
i K , Ti, To - the reactor physical, thermal and design parameters.
It allows to investigate independently the influence of pa-
rameters of the reactor, steam generator and primary and secondary
circuit coolant units on the position of the determining point
at VyehnegradBky diagram and correspondingly on the change in the
plant dynamic characteristic by varing only some generalized pa-
rameters.
The influence of Tef f , O/7 and D on the space position of
the determining point of the parameters Y and is shown in
Fig.3.
Let us note, that the increase in Taff is physically equi-
valent to the time decrease in the transport delay in primary
circuit piping and steam generator and to improvement of the
heat transfer conditions in the circuit.
It is seen from the curves in Fig.3, that the determining
point shifts to an aperiodic stability region when increasing
Tef f to about 0.15 (i.e. 10 times as high), other conditions
being equal.
The influence of the reactor dynamic parameters on the sta-
bility of a closed power system, being self-regulated, can be
evaluated, if the coefficients Ki/Ke, Ti, Te are expressed in the
reactivity temperature coefficient (oh.) .
In Pig.3 the curve of changes in the determining point posi-
tion in a phase space versus the value of O( with constant
PT and complex oC~,fo being determined with reactor characte-
ristics is shown. It is seen from the curve that the determining
point shifts into the aperiodic stability region, the negative
reactivity coefficient increasing.
If IC>4, I decreases the curve limits the aperiodic stabi-
lity region, being in the oscillatory stability region. With
positive reactivity coefficient a4T>O close to the fuel
legating reactivity coefficient the
I dynamic closed system
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
is tranafered by jump into the region of absolute instability.
In the same Fig. 3 the determining point position is shown ver-
sus the secondary circuit parameters, expressed in the generali-
zed dynamic coefficient D.
Studying the curves in Pig.3, one can conclude that the
change in the AP1YC type nuclear power plant parameters in a
wide range does not shift it into the dynamic instability region,
if the reactivity temperature coefficients remaines negative.
As with these changes the determining point is moving near
the aperiodic stability region, rounding it, dimensionless time
transient character is of a small change (i.e. the transients
have almost an aperiodic character with the great damping dec-
rement).
With a large negative temperature coefficient and primary
circuit small transport delays the reactor system of APEYC
type tend3 to transfer into the region of an aperiodic stability.
On the basis of equations (20-22), table III and also of
curves, in Fig.3, one can evaluate the influence of some control
system parameters.
Thus, for example, coefficients X., d?.5 are similar to
the reactivity "temperature" coefficients exZ and c . Coeffi-
cients X4 5 increasing, the determining point will tends to
an aperiodic stability boundary as in case of (oc.4 increase.
The coefficient W. is similar to fl, .
While choosing the optimum dynamic parameters both the
character of a transient and the magnitude of asymptotic devia-
tion of the plant process parameters are of importance, in parti-
cular, the minimum deviation of steam pressure from a nominal
value at any load disturbances.
The calculations have shown that the less the asymptotic
pressure value (S--w- 0), the plant operating under self-regula-
tion conditions, the better the steam generator heat transfer
conditions (SF) and this value depends on the initial pressure
value :
LiP
.i
(r4.~-tA5)(I f CVU
Al
MAI- +Q z ?! X23
3 (j+A,) (/f- ) rF
CV.C
VP Po
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
For the APEYC plant under self-regulation conditions of
operation the relative pressure change is equal to about 25- of
(io ee about 6 atm.) while tripping out the full external load ,
which amounts to about 60% of full power.
While taking into account transient character being close
to aperiodic and pressure deviation from the nominal, it is pos-
sible to say, that the APEYC plant can be in stable operation
under self-regulation conditions (without AP), at least, under
conditions when external load changes do not exceed 30% of the
full power.
Pressure deviation from the nominal value (d Po) for the
given type of a steam generator can be reduced by making correc-
tions for pressure in automatic power regulator reading and by
selecting corresponding parameters X2 and i,Z . Then APao
will be equal
'd PC,, = -
D (/ +Aj)=s1-p + -9L )
In case of the APEYC plant pressure correction allows to
reduce relative pressure change at trippingout 60% of full power
to about 12% Po (i. e. to p Pe :,q = 3 atm).
However, at large ratios ?' /X2 transients quality becomes
slightly worse, their oscillations being increased. Indeed, in-
creasing 1X,( f is decreased, and ? being increased, this
is equivalent to the oscillation frequency increase and to the
decrease in oscillation damping degree.
The theoretical results of dynamic properties investigations
according to the methods described were verified in the course
of preliminary experimental studies at the APEYC plant start-up
and test operations (3). Experimental and design curves of power
and pressure variations with 24% external electric load removing
are compared in Fig.4.
Due to correction for pressure change in the setter of an
automatic power regulator stable operation of the APEYC pl.Pun t
can be provided at full external load removing and increase.
Then, steam pressure deviation from the nominal value will not
e.xceed 2.5 atm.
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
Table I
Nomenclature
I
- time scale
- radioactive decay constant of the delayed neutron
emitter
- reactivity
- control rods reactivity
- coolant reactivity temperature coefficient
- fuel reactivity temperature coefficient
- specific heat
Al - mass
KF - total heat flow per unit of temperature drop
G - primary circuit coolant flow rate
Wtur - turbine steam flow rate
YO - nominal reactor power
go - nominal average reactor coolant temperature
YID(" - saturation water and steam densities, respectively
r - steam generation specific heat
1 l - saturation water enthalpy
lsw - reactor input water enthalpy
Vsteam- secondary circuit steam volume
Vwater secondary circuit boiling water volume
Tsatur saturation water temperature
~~ - automatic control system coefficients
`1 L2 - transfer time delay in pipings from the reactor to
the steam generator and in the opposite direction,
respectively
II - relative reactor power change
C - delayed neutron emitters relative concentration
change
t'in' t'out- primary circuit coolant relative temperature c
han e
g
at the reactor inlet and outlet, respectively
primary circuit coolant relative temperature
change
at the steam generator inlet and outlet, respectively
U - fuel elements relative average temperature change
P - secondary circuit steam relative pressure change.
371
- 13 -
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
ymbols
S,
P < coefficient applied to the reactor
Is- coefficient applied to the steam generator
o - it denotes that a given value corresponds to plant
parameters initial values.
Table 2.
Plant dynamio parameters
TL
.1
L -LSw
IM )
Tw
G
v tea,
Vwater
A? TLI
c- TPTP
M ii
- 14 -
TV= TS? -r 05 T1,52
T WT
? (43P,)O%team
T rFe ?
P 2
P '/ Vteam
_ a Ts P?
o 00
-b A
z T`6
TI T T2,
Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
 Approved For Release 2009/08/26: CIA-RDP88-00904R000100110019-9
Table 3. Reactor effective dynamic parameters
With the automatic control system I
! Self-regulation
I
K =/PTP T??- 0,57' _
1/ 1 ?T2 l7? p ~5 0(-
Ke ; T '? ~-~ p 1 _ ~z T '?f o, 5 7 Pt T, P
s P
T1 /, 0
Ti
X'? f xv0<
0, f
7 P P -
d
I - Zz TVf T?? f? 5 71
T P Tp
KIP
TPT11
ToJdP
Oki 01-P % o
O