Page 188 - Dynamics and Control of Nuclear Reactors

13.11 Power maneuvering 185

As the number of data points, N, increases, the estimates of (a 1 ,a 2 ) converge to the
actual values with least error. Once the AR coefficients are determined, the resulting
model can be used to compute the impulse response of the system. The above dis-
cussion shows the basic idea of time series modeling from observed data. Recursive
parameter estimation techniques are available to compute the (n+1)-th order model
from the n-th order model; these do not require the inversion of large matrices. These
are computationally fast and more accurate than methods using direct matrix
inversion [12].
An AR analysis of neutron power fluctuations using average power range
monitor (APRM) detector signals from two operating BWRs provides the power-
to-reactivity impulse response. The developed modeled may be used directly to
compute this impulse response in a time recursive fashion. The impulse response
may then be used to estimate a decay ratio of the neutron power response to a change
in the reactivity.
The decay ratio is defined as the ratio between successive positive peaks or suc-
cessive negative peaks calculated from the impulse response function. For stable
reactor operation the decay ratio must be less than 1, and must be less than a value
specified by the regulatory agency. An increased power-to-flow ratio indicates a sys-
tem with a smaller stability margin. A case study [10] provides a stochastic time
series model of a measured neutron signal. The developed model was then used
to generate the response to an impulse change in the reactivity as its input.
Fig. 13.11 shows impulse response results for the case study. Data from two
BWRs operating at different power-to-flow ratios were processed using the AR
model. The upper plot in Fig. 13.11 shows the power-to-reactivity impulse response
of a BWR-4 plant operating at 100% power and 100% recirculation flow rate. The
calculated decay ratio is, DR¼0.024. The lower plot in Fig. 13.11 shows the impulse
response of a BWR-4 plant operating at 100% power and 65% recirculation flow rate
(this is a test case). The calculated decay ratio is, DR¼0.37.
The decay ratio of the impulse response function is less than one, and thus
both the systems are stable. As the power-to-flow ratio increases this stability margin
decreases, indicating a change in the reactor operating characteristic. The flow-to-
power ratio for the two operating cases are 100% and 65%, respectively. Both BWRs
are rated around 1100 MWe. This method of stability monitoring is recommended
as a criterion applied to operating reactors by the U.S. Nuclear Regulatory
Commission [13].

13.11 Power maneuvering

The scenario following opening of the main steam valve in an uncontrolled BWR is
as follows:

• Main steam valve opening "
• Steam flow to turbine "