Large-signal tools for power electronics: State space analysis and averaging theory

This thesis explores the application of nonlinear methods to the practical problems of switching power converter analysis and design. Based on switching algebra, a formalism for large-signal component modeling is developed. The governing equation is formulated for a general class of mixed-mode circuit models containing ideal switches. The geometric interpretation of the governing equation in the state space is developed. This interpretation provides a cogent framework for understanding feedback control and unusual instability phenomena. The classical theory of averaging for systems of ordinary differential equations is applied to power electronic systems. A theoretical basis for widely used averaging approximation techniques is developed. Three new large-signal tools are introduced which are an outgrowth of the basic theory developed. Three large-signal experiments are reported which test the modeling formalism and the geometric and averaging concepts introduced.