This paper discusses an efficient method for handling the mixed Differential and Algebraic Equations (DAE's) of a stand-alone Photovoltaic Power System (PvPS). The beginning of the paper is a description of the PvPS DAE's. Next, one of most popular techniques for solving DAE's, the Backward Differentiation Formula (BDF), is applied to the PvPS problem. At the end, the solver performances are improved in order to obtain a suitable integrator for chaotic modes simulations.