Technical Bivariate empirical mode decomposition applied to the estimation of out-of-phase oscillations in BWR Alfonso Prieto-Guerrero, Gilberto Espinosa-Paredes ⇑ División de Ciencias Básicas e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186 Col. Vicentina, México, D.F. 09340, Mexico article info Article history: Received 6 October 2013 Accepted 11 November 2013 Available online 4 December 2013 Keywords: Bivariate empirical mode decomposition Out-of-phase oscillations Boiling water reactors Intrinsic mode functions abstract In this paper a new method based on the bivariate empirical mode decomposition to estimate the phase of regional (out-of-phase) or global (in-phase) modes associated with instabilities in boiling water reac- tors (BWR), is explored. The proposed method allows decomposing the analyzed signal (constructed from two different Local Power Range Monitors, LPRMs) in different levels or intrinsic mode functions (IMF). The estimation of the phase between these LPRM signals can be achieved by tracking the modes associ- ated to the instability of the BWR and obtaining the cross-correlation function of their corresponding IMF. This phase determines possible out-of-phase oscillations, which play an important role in the BWR insta- bility. The method is relatively simple to implement and it does not represent a high computational com- plexity. The methodology was tested with simulated signals and validated with two events reported in the Forsmark and Ringhals stability benchmarks. The results of the cases studied show that the proposed method clearly contributes on the fact to detect possible cases of out-of-phase oscillations. Ó 2013 Elsevier Ltd. All rights reserved. 1. Introduction In BWR instability events, two kinds of instabilities are found: in-phase (global and core-wide) oscillations, and out-of-phase (re- gional) oscillations. In-phase oscillations are caused by the lag introduced into the thermal–hydraulic system by the finite speed of propagation of density perturbation (Lahey and Podoswski, 1989). At high-core void fractions and low flow conditions, the feedback becomes so strong that it induces oscillations at fre- quency about 0.5 Hz. When this feedback increases, the oscillation becomes more pronounced, and oscillatory instability is reached. The occurrence of out-of-phase instabilities is relevant because of safety implications, i.e., large-amplitude out-phase power oscilla- tions could be established in the core without resulting in an auto- matic scram. The term out-of-phase oscillation is applied to those instabilities in which different core zones show a considerable phase shift (180°) in neutron flux oscillation. March-Leuba and Blakeman (March-Leuba and Blakeman, 1991) examined the sta- bility of subcritical higher harmonic neutronic modes that could result in out-of-phase power oscillations under certain conditions, even when the fundamental mode is stable and the subcritical reactivity of the spatial harmonic mode as another indication of the stability is employed. In the out-of-phase instability, the usually subcritical first harmonic mode dominates the reactor response (March-Leuba and Blakeman, 1991). The mechanism for the BWR out-of-phase stability has been explained as a phenome- non in which the neutron higher harmonic mode (the first azimuthal mode) is excited by the thermal–hydraulics feedback ef- fect. Thus, the out-of-phase oscillation is dominated strongly by the momentum conservation among different in-core channel regions. In a large commercial BWR core, the first azimuthal harmonic mode usually appears as the first harmonic whose eigen- value is the largest for all but the fundamental mode (Takeuchi et al., 1994). The reactivity feedback causes a spatial coupling that leads to a synthesized out-of-phase oscillation in the entire core. In the out-of-phase instability, the power increases in one half of the core and it decreases in the other half, so that the average power remains essentially constant. Therefore, in order to avoid the core instability events occurrence, the stability analyses need to calculate the global and regional decay ratios of the reactor core. The most reported cases are in-phase instability. However, a few events are out-of-phase instability, which have occurred in Cofrentes (Mata et al., 1992; IBERINCO, 2002), Caorso (Gialdi et al., 1985; Takigawa et al., 1987), Ringhals (Van Der Hagen et al., 1994; Hotta et al., 1997, 2000a), etc. Experience shows that the out-of-oscillations occur suddenly and they rapidly grows in magnitude and hence risk causing damage to the fuel. The risk of fuel is greater during out-of-phase oscillations than during in-phase oscillations since the in-phase oscillations grow 0306-4549/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.anucene.2013.11.024 ⇑ Corresponding author. E-mail address: gepe@xanum.uam.mx (G. Espinosa-Paredes). Annals of Nuclear Energy 65 (2014) 247–252 Contents lists available at ScienceDirect Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene