A Modeling Approach for the VIRT and Other Coupled Electronic and Magnetic Systems

Recently, a new class of magnetic component has emerged in which the electronics that connect to these components are fundamental to defining the conductive loops that comprise them. In these “coupled electronic and magnetic systems” (CEMSs), a clear partition cannot be made between the electrical and magnetic domains and this prevents the application of established modeling techniques for deriving their circuit representation. One such CEMS is the variable inverter/rectifier transformer (VIRT), which enables a transformer with fractional effective turns and a variable effective turns ratio. Previous investigations into the VIRT have invoked simplifying assumptions to synthesize a circuit representation, omitting the full details of operation such as the possibility and implications of ac currents induced on conductors that encircle the VIRT. Other fractional-turn transformers have simply assumed a circuit representation without undertaking modeling. In this work, a modeling approach is proposed which enables the circuit representation of a CEMS to be extracted directly from first principles. Two case studies are explored and the derived models are shown to match well with experiment. The proposed approach is suitable both for assessing the finer details of the VIRT, and other fractional-turn transformers, and as a framework for deriving and understanding new CEMS implementations.