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 paper. In order to avoid inaccuracies introduced by simplification or assumptions, the analysis is performed entirely using a versatile geometrical method in the normalized domain. Unlike previous approaches, 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, the leading to a pure geometrical treatment that is general and applicable to any possible inverter. As a result of a rigorous analysis, 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 pulsewidth modulation (PWM) equivalent is performed, revealing duality between boundary control using curved SS and traditional PWM. This is a significant advancement toward 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 zero voltage cross (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.