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

Abstract

Purpose

This study aims to predict the unstable period-1 orbit (UPO-1) of DC–DC converters and find analytical expressions to describe it.

Design/methodology/approach

Nonlinear 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.

Findings

According 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/value

This 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.

Citation

Chen, X., Chen, Y., Zhang, B., Qiu, D. and Li, Z. (2018), "Predicting the unstable period-1 orbit (UPO-1) of DC–DC converters by extracting harmonic content", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 37 No. 2, pp. 930-947. https://doi.org/10.1108/COMPEL-06-2017-0256