A Design Oriented Dynamical Perspective on Proportional-Resonant Controller with 1-$\Phi$ Inverter

A combined Filippov-Floquet approach based rigorous analysis of a single phase inverter with proportionalresonant controller has been performed, which can detect onset of both slow- and fast-scale instabilities. Dynamics of resonant controller is similar to the integral component in proportionalintegral controller as both induces slow-scale instability. Detailed parasitic switched nonlinear model has been derived in addition to the idealized non-parasitic switched nonlinear model. Resistive parasitic elements such as switch on-state resistance, equivalent series and dc resistance, within the power circuit cause delayed onset of slow-scale instability, while having negligible effect on onset of fast-scale instability. Inherent time delay arising in analog controller remains a nonsmooth slow-scale instability inducing phenomenon, causing earlier onset of slow-scale, while having negligible effect on fast-scale instability. Variation in switching frequency around the nominal value also causes earlier and delayed onset of fast- and slow-scale instabilities at lower frequency. Thus, to what extent the analytically determined results of the idealized model shall deviate from the actual physical behavior depends on how all the phenomena are compensating or aggravating each other.