Piecewise Fryze power theory analysis applied to PWM DC–DC converters

Abstract

This study proposes an extension to the well-known Fryze power theory, which allows the development of a mathematical procedure that defines a global factor for the active and non-active power processing in pulse-width modulated (PWM) dc–dc converters. This global factor is the dc power factor. The proposed extension is a vector representation of periodic currents and voltages mapped into a k-dimensional Euclidean space, which permits that all non-active power of all converter elements to be collected into a single figure of merit. To validate the approaches, a 220 W prototype of an isolated dc–dc Ćuk converter architecture was implemented and evaluated. Experimental results have confirmed that both total non-active power, the proposed dc power factor, and system efficiency are correlated. In the worst case of step-down mode, the converter prototype presented the lowest total non-active power of ∼25 var for the turns ratio of 0.567, resulting in the highest dc power factor of 0.135 and prototype efficiency of 80.6%. In step-up mode, it was obtained the lowest total non-active power of ∼1.14 kvar for the turns ratio of 1.764, resulting in the highest efficiency of 88.3% and dc power factor of 0.145.