Page 104 - Dynamics and Control of Nuclear Reactors

98 CHAPTER 8 Reactor control

The model used here is a U-235 fueled zero-power reactor with a generation time
of 10 5 s. The proportional controller for reactivity control selected for this example
has a gain of K p ¼1 cent/% power change. That is
½
Δρ tðÞ ¼ K p P Set Ptðފ (8.18)
p
where
Δρ p (t)¼proportional control (reactivity)
5
K p ¼proportional coefficient (in this example K p ¼1 0.0067/100 ¼ 6.7 10 )
P(t)¼reactor power at time, t
P Set ¼reactor power set point.

The integral controller selected for this example has a gain of K i ¼0.1 cents/% power
second. That is
Z t
Δρ tðÞ ¼ K i ð Pset PvðÞÞdv (8.19)
i
o

Δρ i (t)¼integral control (reactivity)
6
K i ¼integral coefficient (in this example K i ¼0.1 0.0067/100¼6.7 10 )
The coefficients used here were selected to illustrate control characteristics. Actual
performance could be improved by optimizing the coefficient values.
First consider a transient initiated by a step increase in external reactivity. Fig. 8.7
shows the responses for a reactor with proportional only, integral only, and propor-
tional plus integral control actions.
Note that proportional only control limits the power increase, but the final power
is different than the set point. This is as expected since there must be an error signal
for non-zero control action as needed to cancel the external reactivity that initiated
the transient.
Now consider a transient initiated by a step increase in the reactor power set
point. Fig. 8.8 shows the responses for a reactor with proportional only, integral only,
and proportional plus integral control actions.
Note that all three control options successfully bring the power to the new set
point. This is as expected since there is no external reactivity for the proportional
controller to cancel. Note also that there is a prompt jump for the cases with propor-
tional control and proportional plus integral control. The explanation of this behavior
is left as an exercise for the reader.
Note that proportional control only fails to return reactor power to its (unchanged)
set point for a reactivity disturbance, but succeeds in bringing reactor power to its
new set point following a change in set point. This happens because achieving steady
state requires that control reactivity changes to cancel the reactivity perturbation. For