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2017 | OriginalPaper | Chapter

6. Power Map Analysis

Authors : Mihály Makai, János Végh

Published in: Reactor Core Monitoring

Publisher: Springer International Publishing

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Abstract

Power distribution in the reactor core is one of the cornerstones of safe and economic operation of a NPP. The present Chapter is dedicated to methods for estimating the coolant temperature and the released power distributions in the cor. The treatises rely on mathematical background. First we discuss the principal component method (PCM), which has gained popularity in the last years. PCM is a useful tool in checking on the measured values, to get a reliable estimation for the non-metered assemblies, and corroborate or refute some assumptions used in the operation. Since there is no measurement without error, statistics also makes us a good service in revealing errors. The third topic is usage of measurements in upgrading the computational model by adjusting some parameters of the computation models to the measurements.

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previous chapter Application of Trial Functions

next chapter Detection of Disturbances and Anomalies

When f is multi-value function, more than one y is rendered to a given x and \(\mathbf {a}\).

The case of multiple roots can be discussed without difficulty but the result is more complicated.

At first glance it is strange that rank of \(\mathbf {M}\), which is a set of measured quantities, has anything to do with goodness of fit. Actually the measured values form a vector, that we arrange into a matrix according to the core geometry. Model (6.65) and (6.66) exploits core geometry by rearranging the measured vector into a matrix, and the structure of the matrix—this time its rank—is used to obtain information on the matrix and transplant it into the structure of the vector.

In some PWR types, the eigenvector has 4, 6 or 8 elements, depending on the symmetry of the core.

If a parameter is measured by different methods and the measured values are different, an accepted value is selected.

Actually, \(M(x_i)\) is a linear expression of \(\varPhi _p(x_i)\).

\((\mathbf {y}_j;\mathbf {p}_i)\) is the dot product in \(\mathbb {R}^m\).

Here “accords” is loosely determined, in mathematical terms it could be formulated this way: in the measured positions the difference between the solution of (6.113) and the measured \(\varPhi _i\) is small.

In the introduced concept. Do not forget, the here presented “mathematics” is only analogue of statistics.

The actual position of the control rod in assembly No. 293 happened to be 250 cm.

PWR families use that core.

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Title: Power Map Analysis
Authors: Mihály Makai
János Végh
Publisher: Springer International Publishing
Book: Reactor Core Monitoring
Print ISBN: 978-3-319-54575-2

Electronic ISBN: 978-3-319-54576-9

Copyright Year: 2017
DOI: https://doi.org/10.1007/978-3-319-54576-9_6

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