A small signal state space model of single stage three level resonant AC/DC converters

This paper presents a small signal state space modeling approach for a single stage three level resonant power factor correction converter operating with either variable frequency phase shift modulation or variable frequency asymmetrical pulse width modulation control. Modeling is achieved using a combined averaging and multiple-frequency approach. The model gives good prediction of both the transient and steady state operations of the converter. The dynamics of the output filter can also be represented as well as the influence of parasitic parameters such as the capacitor equivalent series resistance (ESR). This method also allows the separation of both the frequency and duty cycle as the control variables. All state variables are broken down into their frequency components, including high and low frequency components (the high frequency components being in the order of the switching frequency and the low frequency components being in the order of power line frequency) and the amplitudes of the frequency components are used as the new state variables. This can then be linearized, thus a small signal model is obtained. The model has the switching frequency as well as the required duty ratio for the pulse-width or phase shift modulation as separated control input variables, which facilitates a better and more accurate controller design. The developed model is verified analytically and experimentally on a 2.3 kW, 48V, input voltage 90-265 V RMS.