Modeling of sinewave inverters: a geometric approach

Three fundamental sinewave inverter topologies are analyzed: 2-leg (1-phase, 2-wire); 3-leg (3-phase, 3-wire); and 4-leg (3-phase, 4-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 3-leg inverters are extended to address the expanded capabilities of the 4-leg inverter. A unique 4×4 decoupling transformation matrix is presented for the 4-leg inverter that enables direct transformation between the four degree-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 3-leg inverter. Fully decoupled models for each inverter are presented