Universitat Politècnica de Catalunya, Barcelona
On Abel differential equations of the 2nd kind and exact inversion with boost DC-AC converters
The use of DC-DC boost-based switched converter for DC-AC step-up inversion applications has been long handicapped by the fact that it requires non-offset, periodic current reference profiles that satisfy an Abel differential equation of the 2nd kind, and this is a challenging problem because the corresponding vector field becomes nonsmooth in zero-crossing points. As a consequence, the proposals made so far considered either offset inversion, which is much less interesting from a practical point of view, or theoretically unsupported approximate non-offset inversion schemes. However, sufficient conditions for the existence of periodic solutions with nonconstant sign in Abel equations of the 2nd kind have been recently reported. In this talk we review these results, and we apply them to the exact inversion problem with a boost DC-AC power converter.