Applications of perturbation theory to power electronic converters

Power Electronic converters usually require complex controllers, involving large numbers of state-space variables; their models, moreover, tend to include multiple nonlinearities. These characteristics make assessing the stability of systems dominated by power electronics converters particularly challenging. This work concerns the application of mathematical methods (in particular, attention focused on Singular Perturbation Theory) to power electronic systems, in order to model effectively their behaviour, reduce the size of their state-space systems, and assess their operating stability using simplified methods. Some preliminary work was performed on the ripple modelling of a DC-DC boost converter and a single-phase full-bridge inverter; second-order approximations of the ripple and average behaviour, computed by applying Singular Perturbation methods, were found to agree very well to the solutions computed for the initial-value problem ODEs. Singular Perturbation theory was subsequently applied to perform model reductions of power-electronic-based systems. First, a single-phase rectifier was considered, then AC microgrids. From a mathematical point of view, a similar approach was adopted in both cases to achieve the model reduction, but, given the different technical nature of such systems, they required separate literature reviews and preparatory work. The reductions were performed gradually, and several stages are here presented; results were tested in simulations, and stability analyses were compared to analogous analyses performed on the non-reduced full-sized systems