EEG-based brain connectivity analysis distinguishes children with low math achievements from their schoolmates

Abstract

A mature mathematical technique to model power systems, aimed at computation of harmonics dynamics in a step-by-step fashion, is the extended harmonic domain (EHD). The EHD is capable of accounting for an arbitrary number of linearly-spaced sequentially-numbered harmonics; however, the dimensions of an EHD-based model are prone to explode if a large number of harmonics are considered. This fact makes computationally impossible the harmonics dynamics study when high-frequencies, inherent of electronic devices, are involved.This paper presents a flexible extended harmonic domain (FEHD) approach that permits to include an arbitrary number of (non-sequential) harmonics in any state variable of the system. The reasoning to use distinct harmonic content for each state variable is that in a general network (especially those involving alternative energy sources), state-variables exhibit distinct harmonic content. Such different contents mainly depend on the network topology, e.g., switched devices involved, filter arrangements utilized, etc.As shown in the paper, the proposed FEHD approach is able to provide reduced-order EHD models including high-frequency ripple information; thus, leading to computational savings while keeping accuracy compared to traditional EHD-based models and averaged-value models. A case study, involving a three-phase photovoltaic system in closed-loop operation, is presented to validate the proposed methodology. The results provided by the proposed methodology are verified with those given by the power system computer-aided design/electromagnetic transients including DC (PSCAD/EMTDC) simulation tool.