Application of the Filippov Method to PV‐fed DC‐DC converters modeled as hybrid‐DAEs

Abstract

In this article, a method to study the nonlinear dynamics of a PV-fed boost converter is developed. The model for the solar panel introduces an algebraic constraint into the system and the resulting mathematical model is a set of hybrid differential algebraic equations (DAEs). The behavior of the system is observed to exhibit undesired operation as parameter values vary. Conventional mathematical tools developed to analyze DC-DC converters are not directly applicable to systems modeled as a set of hybrid DAEs. In order to find the monodromy matrix to assess the eigenvalues of the system, we modify the Filippov method to calculate the saltation matrix. The derived formula is general and versatile such that it can be applied to any PV-fed DC-DC converter irrespective of the topology or control algorithm employed. Two case studies are investigated: current mode control and maximum power point tracking. Each case study serves to demonstrate different considerations that must be taken into account when conducting stability analysis of hybrid-DAEs. K E Y W O R D S DC-DC converters, hybrid differential algebraic equations, maximum power point tracking, nonlinear dynamics, photovoltaic, saltation matrix This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Multistability and Its Control by the PWM Carrier Signal Modulation in a DC Electric Drive System

“…From the practitioner's point of view, such nonlinear behavior is an undesired feature; therefore, the mechanism of their onset has to be clear. Recent studies are also devoted to the analysis of more complex power converter systems, such as multicell fying capacitor converters [10], LLC resonant converters [11], cascaded DC/DC converters [12], just to name a few, and also those in connection with the nonlinear source or load, such as photovoltaic module [13]. Onset of instability in such complex systems is also caused by the reasons, which difer from those that were depicted in the classic literature, like an interaction between the load and source converter in a cascaded system [14].…”