Modeling of Series Resonant Converter in Synchronous Rotating Frame

Abstract

Small signal model of PWM converters are derived from averaging method. In the case of resonant converters, the averaging method fails because tank currents and voltages have no dc component. Moreover, the phenomenon of “beat frequency dynamics” is not addressed in averaging method. Although numerous modeling techniques are presented in literature to model resonant converter; they are either with complicated math or involves complex numerical computation. The state trajectories of resonant converter exhibits rotating behaviour and are analysed using Fundamental Harmonic Approximation (FHA). This paper proposes a simple and straight-forward modeling technique for Series Resonant Converter (SRC) in synchronous rotating d-q frame. The FHA circuit of SRC is analysed in d-q frame where the alternating state variables becomes dc. The derived equivalent circuit of SRC in d-q frame is able to capture the large signal behaviour of the converter. Subsequent perturbation and linearization of the equivalent circuit model in d-q around an equilibrium point yields us the small signal model of SRC. The proposed small signal model of SRC is able to capture “beat frequency dynamics”. Frequency response characteristics of small signal control to output, input to output, input admittance and output impedance are compared with the switching converter plots and are in close agreements. The proposed small signal circuit of SRC is analytically solved and control to output transfer function is derived.