Modeling of multileg sine-wave inverters: a geometric approach

Three fundamental sine-wave inverter topologies are analyzed: two-leg (one-phase, two-wire); three-leg (three-phase, three-wire); and four-leg (three-phase, four-wire). The topologies are “full-bridge” voltage-source inverters with LC filters suitable for producing sinusoidal output voltages. The switching states and corresponding output voltage vectors produced by each inverter are identified and presented along with an analysis of the geometric arrangement of these voltage vectors. A pattern of characteristics is established whereby the “qd” modeling forms commonly used with three-leg inverters are extended to address the expanded capabilities of the four-leg inverter. A unique 4 4 decoupling transformation matrix is presented for the four-leg inverter that enables direct transformation between the fourdegree-of-freedom (DOF) leg-modulation space of the inverter and its corresponding 3-DOF output-voltage space. This is shown to be directly analogous to the well-known “abc–qd” transformation developed for the three-leg inverter. Fully decoupled models for each inverter are presented.