Page 180 - Dynamics and Control of Nuclear Reactors

13.7 BWR dynamic models 177

13.6 Total reactivity balance
For steady state, zero reactivity is required. The total reactivity balance is as
follows:

ρ ¼ Control rod reactivity + Recirculation flow reactivity + Feedback reactivity ¼ 0
The externally-controlled reactivity may be achieved by a combination of control rod
reactivity and recirculation flow reactivity. Thus, a desired reactivity setting for
either externally-controlled reactivity can be achieved by adjusting the other
externally-controlled reactivity.

13.7 BWR dynamic models
Detailed BWR dynamic models include treatment of all of the complex neutronic
and thermal-hydraulic effects that contribute to the dynamics of the system. Both
linear and nonlinear models exist. Detailed models are too complex for inclusion
here. Interested readers can find information in the literature [4, 5].
Linear models provide estimates of the small-perturbation time response and fre-
quency response. An approximate, low-order model provides simple simulation
capability. It accounts for the neutronic and thermal-hydraulic processes that deter-
mine feedback reactivity. A low-order model [4] was developed by fitting a low-
order transfer function to match the closed-loop frequency response calculated with
a detailed model [5]. The results obtained with the low-order model are essentially
identical with results from the detailed model. Note that the author of Ref. [4] chose
to express the frequency in Hz rather than in rad/s as used elsewhere in this book.
Figures in this chapter use rad/s for frequency units.
The low-order closed loop transfer function used in the fit [4] is
2
ð
Ks + as + bÞ s + cÞ
ð
G c sðÞ ¼ 2 (13.1)
ð s + ds + eÞ s + fð Þ s + gÞ
ð
The following values of the low-order model parameters are typical for BWR sim-
ulation [4]:
K ¼ a gain that varies with power level
a ¼ 0.36
b ¼ 0.1055
c ¼ 0.03
d ¼ 0.09
e ¼ 0.1044
f ¼ 0.25
g ¼ 21.0
The low-order model from Ref. [4] provides the capability to further investigate
BWR dynamics and the cause for potential stability issues. The low-order model