**Valid Ranges For Using The Cross-Power Spectral Density
Phase Angle For Moderator Temperature Coefficient Sign Determination**

Keith E. Holbert, Nikhil Venkatesh

Abstract

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 using the root-mean-square method and 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° 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.

Nuclear Science and Engineering, Vol. 119, No. 3, pp. 203-211, 1995.

**Determining the Moderator Temperature Coefficient
by Fitting the Noise Analysis Transfer Function**

K. E. Holbert, N. Venkatesh

Previous researchers have established that 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 earlier quantitative methods yield only the magnitude of the MTC independent of the sign. Normally, these methods are used in conjunction with the phase angle technique that is used to ascertain the MTC sign; however, a recent study has determined that a boundary exists on the range of MTC values for which the phase angle from noise analysis can be used. Described below is a fitting method to determine both the MTC sign and magnitude in a single analysis in order to overcome such limitations. The MTC is determed by fitting noise analysis results to a transfer function model. The next stage of this investigation is the analysis of noise data obtained from an operational PWR.

Transactions of the American Nuclear Society, Vol. 69, pp. 236-237, 1993.

**Determination of Moderator Temperature Coefficient in
PWRs**

Keith E. Holbert

Abstract

The moderator temperature coefficient (MTC) quantifies the reactivity feedback due to changes in the coolant temperature of a pressurized water reactor (PWR). Therefore the MTC is an important safety parameter and the Nuclear Regulatory Commission (NRC) requires its periodic measurement. Previous researchers have established that the value of the MTC is contained in correlations between fluctuations of the in-core neutron flux and core-exit coolant temperature.

Currently, two different noise analysis techniques may be used to determine the magnitude of the MTC. Both are used in conjunction with the phase angle method which states that the cross power spectral density (CPSD) phase angle between in-core neutron flux and core-exit temperature near zero frequency approaches -180° for negative MTCs and 0° for positive MTCs. This study has determined that a limitation exists on the range of MTC values for which the phase angle from noise analysis can be used to determine the MTC sign.

A model of the core of a typical PWR is created, and the analytical transfer function between the neutron flux and core-exit temperature is solved for. It is shown in this investigation that the above theory does not hold true in the case of small positive values of the MTC, where the phase angle extrapolates to -180° instead of 0°. Similarly, there is a discrepancy for the case of large negative MTC values which result in a phase angle extrapolation to 0° rather than -180°. Comparison of the indeterminate regions of the MTC to actual MTC ranges in an operating PWR have shown that the indeterminate sign regions are of importance.

Electric Power Research for the 90's, Proceedings of the Third Annual Industrial Partnership Program Conference, April 21, 1993.

Return to Dr. Holbert's Publications