Modeling PWM DC-to-DC Power Converters using Graphs

摘要

In this paper, we illustrate, through examples, a novel graph-based modeling technique of two-state (on-off) PWM power converters. Differential equations of power converters are derived by inspection, based on two incident matrices, β(u) and J(u). We associate to each circuit (on, u = 1, or off, u = 0, circuits) a digraph and identify current loops (inductor-capacitor, voltage source-inductor, current source-capacitor). Effectively, B(u) and J(u) represents, resp., the core of energy injection and energy transfers inside the converter. These digraphs and incident matrices serve to obtain also classical dual models, evaluate semiconductor stresses, compute models for power converters with multiple states (active independent switches), and synthesize DC-to-DC power converters.