Predicting the unstable period-1 orbit (UPO-1) of DC–DC converters by extracting harmonic content

Abstract

PurposeThis study aims to predict the unstable period-1 orbit (UPO-1) of DC–DC converters and find analytical expressions to describe it. Design/methodology/approachNonlinear dynamical phenomena of a peak–current–mode controlled direct current–direct current (DC–DC) Boost converter are discussed briefly first. Then fast fourier transform (FFT) analysis of state variables under different dynamic states is provided, and the characteristic of the harmonic content in different states is summarized. Following these, a scientific hypothesis on the harmonic content of the UPO-1 is presented, and the Equivalent Small Parameter method is adopted then, thus analytic-form expressions of the UPO-1 can be derived. FindingsAccording to results of theoretical analysis, numerical simulations and experiments, this paper illustrates that, like stable period-1 orbit, the UPO-1 is also made up of the DC component and harmonics with integer times of switching frequency. Originality/valueThis work provides an unreported approach for extracting the UPO-1 of DC–DC converters, which is mainly based on predicting the harmonic structure information of the orbit. According to experimental parts of the work, it shows that the stabilizer can be designed easier by using the proposed method. Additionally, from a broader perspective, the results could also have implications in a wide class of forced oscillation systems.

Transient modeling and analysis of fractional-order resonant very high frequency boost converter

“…In addition, Bertrand has shown that VHF or ultra-high frequency would lead to energy storage elements with fractional calculus characteristics, and the fractional component model can more accurately predict the equivalent series resistance and capacitance value of capacitors at high frequency operation (Bertrand et al , 2010). And in recent years, research on the fractional calculus and its applications in modeling fractional-order pulse-width modulated (PWM) DC-DC converters with operating frequency of kHz level, along with further analyzing the influences of fractional-order components on the converters’ characteristics, has been deeply conducted (Diethelm, 2010; Oustaloup, 2014; Fa-Qiang and Xi-Kui, 2013; Chen et al , 2017a; Chen et al , 2018; Wei et al , 2019; Jiang and Zhang, 2020). However, there are few studies on the modeling and analysis of fractional VHF converters.…”