Application of Barycentric Coordinates in Space Vector PWM Computations

This paper proposes the use of barycentric coordinates in the development and implementation of space-vector pulse-width modulation (SVPWM) methods, especially for inverters with deformed space-vector diagrams. The proposed approach is capable of explicit calculation of vector duty cycles, independent of whether they assume ideal positions or are displaced due to the DC-link voltage imbalance. The use of barycentric coordinates also permits a well-defined and universal approach to the problem of identifying the region in which the reference vector is located. It completely avoids the use of angles, trigonometric functions, and inverse trigonometric functions and is chiefly based on matrix operations which are well suited for digital signal processor implementation. The proposed approach is exposed and validated for the special case of three-level neutral-point clamped (NPC) inverter controlled by a discontinuous space-vector PWM.