Quadratic state-space modeling technique for analysis and simulation of power electronic converters

This paper presents a quadratic state-space modeling technique for analysis of power electronic converters. The methodology is based on using a least-square-error fitting to derive a quadratic state-space representation for each topology, together with automatic determination of switching topology. The algorithm integrates the advantages of calculating topology responses at the circuit level and determining switching instants at the device level. Several key features of the new model that lead to significant improvements in computational efficiency include: (1) its simple quadratic polynomial representation for the state-transition matrix in solving the differential equations describing each topology; (2) its direct and single-step calculation of the switching instants; and (3) its generality in determining valid topology without a prior understanding of the switching relationships. Several examples illustrating the generality and simulation speed of the proposed approach are presented. The computational efficiency of the new approach is demonstrated by comparing its simulation time with commercial software using the stepwise integration algorithm. The accuracy is verified with the exact method and available literature.