Dynamic phasor-based reduced-order models of wireless power transfer systems

Wireless power transfer (WPT) systems in dynamical applications, such as roadway-powered electrical vehicles, require dynamical models for the analysis and control. Conventional modeling methods for WPT systems lead to high-order models as each resonant voltage or current is described by two slowly varying real-valued variables. Other modeling methods may reduce the order but suffer from disadvantages, such as the lack of analytical expressions, loss of generality, and incomplete modeling. This paper develops a systematic and intuitive modeling approach using time-domain dynamic phasors and proposes reduced-order models by applying appropriate s-domain approximations to the linear parts of the system. A dual-side pulse-density-modulation WPT system is completely modeled as an example. Both the equivalent circuits and the mathematical descriptions are presented. The derived models are verified by large-signal step responses and small-signal frequency responses measured during experiments. As compared with the full-order models, the proposed reduced-order models have much more concise formulae while retaining high accuracy.