Validation of Small Signal Model of an LLC Resonant Converter Based HVDC Modulator

Abstract

Resonant converter based power supplies are widely deployed in many industrial applications for their high efficiency and high power density. For control and regulation of the output voltage in resonant converters, frequency modulation (FM) is an intuitive and preferred method. However, the control-input-to-output transfer function is non-linear function of the operating frequency. The mean operating frequency determines the DC gain and bandwidth of the system for small signal perturbations. In this regard, third order non-linear model for LLC resonant converters is proposed in the literature. At a fixed operating point (i.e. a fixed output voltage corresponding to a particular operating frequency), the model can be treated as fairly linear for small perturbations. It is observed that the DC gain and bandwidth at different operating points is quite different, so deciding an appropriate operating point for a particular application is an important design choice. This research considers the small signal model of an 8.8kV/2A LLC resonant converter designed with resonant frequency ( <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{r}$</tex> ) of 22.7kHz and quality factor (Q)=4 for an industrial magnetron as a specific load. The model is validated through simulations and hardware experiments using the LLC resonant converter. For our specific system DC gain at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{r}$</tex> is - 65dB and bandwidth is 310Hz. DC gain and bandwidth of the system at different operating frequencies give an insight to decide the appropriate operating point. Hence, this work offers a strong foundation for a controller design for the LLC resonant converter under consideration.