The power reactor is routinely measured and has been widely used for characterization of the reactor core dynamics. This signal exhibits complex dynamics, including a combination of large- and small-amplitude fluctuations. This work proposed a method based on singular value decomposition (SVD) to quantify the complexity of the power signal. The underlying idea is to assess the signal complexity in terms of the entropy computed from the singular value distribution and compare such entropy with that obtained from a random process. In this way, a distance to randomness was introduced, which was used as an index for monitoring the signal dynamics. The methodology was used to study benchmark power instability events of Laguna Verde, Forsmark and Ringhals NPPs. The analysis was carried out for a wide range of time scales and showed that instabilities are associated to marked reductions of the SVD entropy, and hence to large distances from randomness. The results were contrasted with a traditional statistical method based on the autocovariance function, and the results showed that the SVD entropy approach was more sensible to stability variations. The SVD entropy showed sufficient sensitivity to detect short-lasted unstable events appearing in in-phase and out-of-phase power oscillations.