Advanced boundary control of inverters using the natural switching surface: Normalized geometrical derivation

A curved switching surface (SS) for inverters control with superior characteristics is geometrically derived in this work. In order to avoid inaccuracies introduced by simplification or assumptions, the analysis is entirely performed using a versatile geometrical method in the normalized domain. Both the output voltage and the capacitor current are considered as varying references to establish a more accurate control law with enhanced performance. The proposed normalization technique provides remarkable insight into the behavior of system leading to a pure geometrical treatment that is general and applicable to any possible inverter. As a result, a control law for inverters defined as natural SS is proposed and thoroughly characterized. In addition to the enhanced dynamic response, fixed frequency operation is one of the key features of the proposed control scheme. In order to formally demonstrate fixed frequency operation, a transformation from the natural SS to its PWM equivalent is performed, revealing duality between boundary control using curved SS and traditional PWM. This is a significant advancement towards the unification and understanding of traditional modulation against modulation produced by curved SSs. Finally, an additional novel concept is explored: operation in mixed monopolar and bipolar mode using the natural SS. This new mixed operating mode overcomes physical limitations of the inverter structure in monopolar mode around the region of output voltage zero crossing (both the problem identification and solution are investigated). Experimental results of a 1.5 kVA inverter operating at fixed moderate frequency are presented to validate the natural SS performance, illustrate the benefits of the normalization technique, and demonstrate the monopolar and mixed operating mode.