Page 88 - Dynamics and Control of Nuclear Reactors

7.8 Reactivity feedback effect on the frequency response 81

7.7 Power coefficient of reactivity and the power defect
Changes in reactivity induced by external means (such as a control rod) in a power
reactor trigger power changes and reactivity feedback effects. If the net effect of
all feedback effects is negative, reactor power settles out at a power level in which
feedback reactivity cancels the externally induced reactivity change, giving a net
reactivity of zero as required for steady state.
A measure of the net reactivity change following a power change (Δρ/ΔP) is
called the power coefficient of reactivity. It defines the total feedback reactivity
at equilibrium after a power change. The individual feedbacks follow different tra-
jectories to equilibrium and this time dependence is not addressed in the power coef-
ficient. The power coefficient defines the new steady state power level after a change
in external reactivity. Clearly the power coefficient of reactivity must be negative for
a stable reactor.
Note that the power coefficient of reactivity involves processes that operate on
different time scales and depend on thermal-hydraulic processes that determine
the magnitude of various reactivity changes. For example, the Doppler reactivity
feedback is the product of fuel temperature change, ΔT f and the Doppler coefficient
of reactivity, Δρ/ΔT f .
While the power coefficient defines the incremental change in reactivity per unit
change in power, also of interest is the total reactivity change as the reactor moves
from one steady power level to another steady power level. This measure is called the
power defect (it should be noted that some authors define the term, power coefficient,
as the power defect as defined above). The power defect from zero power to full
power in a LWR is Δρ PD 0.01 to 0.03 (ρ) [1].

7.8 Reactivity feedback effect on the frequency response
As shown in Chapter 3, the overall transfer function for a system with inherent
(negative) feedback may be written as follows:
δO G
¼ (7.3)
δI 1+ GH
where G is the process (feedforward) transfer function and H is the feedback transfer
function.
Now consider the effect that negative reactivity feedback has on the overall
power to reactivity frequency response. As shown earlier, the frequency response
magnitude for a reactor without feedback (given by G) is large at low frequencies.
Rewrite Eq. (7.3) as
δO 1
¼ (7.4)
δI 1
+ H
G