Fast-scale stability limits of a two-stage boost power converter

Abstract

There are many applications in power electronics that demand high step-up conversion ratio between the source and the load. A simple way of achieving such a high voltage ratio is by cascading DC–DC boost converters in a few stages. The individual converters in such a cascaded system are usually designed separately applying classical design criteria. This paper investigates the stability of the overall system of a cascade connection of two boost converters under current mode control. We first demonstrate the bifurcation behavior of the system, and it is shown that the desired periodic orbit can undergo fast-scale period doubling bifurcation leading to subharmonic oscillations and chaotic regimes under parameter variation. The value of the intermediate capacitor is taken as a design parameter, and we determine the minimum ramp slope in the first stage required to maintain stability. It is shown that smaller capacitance values give rise to wider stability range. We explain the bifurcation phenomena using a full-order model. Then, in order to simplify the analysis and to obtain a closed-form expression to explain the previous observation, we develop a reduced-order model by treating the second stage as a current sink. This allows us to obtain design-oriented stability boundaries in the parameter space by taking into account slope interactions between the state variables in the two stages.