Detection of impulsive effects in switched DAEs with applications to power electronics reliability analysis

This paper presents an analytical framework for detecting the presence of jumps and impulses in the solutions of switched differential algebraic equations (switched DAEs). The framework can be applied in the early design stage of fault-tolerant power electronics systems to identify design flaws that could jeopardize its reliability. The system is described by a switched differential algebraic equation, accounting for both fault-free system configurations and the configurations that arise after component faults, where each configuration p is defined by a pair of matrices (E_p, A_p). For each configuration p, the so called consistency projector is obtained from the pair (E_p, A_p). Based on the consistency projectors of all possible configurations, conditions for impulse-free and jump-free solutions of the switched DAE are established. A case-study of a dual redundant buck converter is presented to illustrate the framework.