Analysis of the single-phase four-quadrant PWM converter resulting in steady-state and small-signal dynamic models

The paper describes a mathematical model for the single-phase four-quadrant PWM converter. The model is derived from the averaged state-equations of the converter and is applicable to both the two-level and three-level II-bridge topologies. So that classical control design techniques can be used, the model is required to be linear and time-invariant. To overcome the time-variant nature of the system a new substitution method is developed. The analysis results in separate steady-state and linearised small-signal descriptions. The steady-state model aids design of the converter power circuit. The small-signal model provides a basis for quantitative control design. It demonstrates that the converter is essentially a two-input two-output system with cross-coupling between the inputs and outputs. The work is verified by results from simulation and from a laboratory test-rig.