Study of the bias of the MTC estimate by noise analysis due to the presence of feedback

This paper discusses the bias of the non-parametric Moderator Temperature Coefficient (MTC) estimate due to the presence of feedback. Up to now the non-parametric estimation of the Frequency Response Function (FRF) is the most commonly used method to estimate the MTC by noise analysis. This estimation method is proportional to the Cross Power Spectral Density between the total neutron flux variation and total temperature variation divided by the auto power spectral density of the total temperature variation. The estimation method is very popular since feedback is considered to be negligible in the frequency band of interest. Unfortunately this is not the case in practice. Measurements at a Nuclear Power Plant in Belgium will be used to confirm that this feedback cannot be neglected. In case of feedback the chosen estimator always results in a biased estimate when there are external neutron flux variations present. It will be seen that the ratio between the external neutron flux and external temperature variation in combination with the amplitude of the feedback determines the bias. The theoretical analysis of the bias is based on a simplified scheme of the MTC measurement setup. A simulation in MATLAB is used to confirm the theoretical results. In order to avoid a biased estimate due to the feedback we will advise to measure the external temperature variation and to use another non-parametric estimator.