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

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.