Valid ranges for using the cross-power spectral density phase angle for moderator temperature coefficient sign determination

The value of the moderator temperature coefficient (MTC) of reactivity is contained in correlations between fluctuations of the neutron flux and core-exit coolant temperature. The absolute magnitude of the MTC is obtained from noise analysis by using the root-mean-square method and the frequency response function technique. Both approaches are used in conjunction with the phase angle method, which determines the MTC sign, to obtain complete information about the MTC. Analytical expressions that are derived show that a limitation exists on the range of MTC values for which the cross-power spectral density phase angle can be used to establish the MTC sign. This research shows that small positive values of the MTC (an unstable condition) can result in a -180-deg phase angle shift, contrary to earlier studies that indicated a stable reactor. The range of sign determinate MTC values is dependent on the driving noise source. Simulated noise data are generated for different MTC values and analyzed to verify the theoretical work. A comparison of the indeterminate regions to allowable MTC values for an operating pressurized water reactor is also presented.