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

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.