Application of Mathematics in 3D Space Vector Pulse Width Modulation for 4-Leg Inverter to Generate Unbalanced AC

Three dimensional (3D) Space Vector Pulse Width Modulation (SVPWM) techniques depend on correct mapping of the reference signal vector within a predefined 3D space. The 3D space is defined with 3D switching state vectors for all valid switching states of the bridge circuit of a converter or inverter that has to be modulated. A four leg bridge circuit with two switches per leg has sixteen valid switching states. The space defined with corresponding vectors in alpha-beta-gamma frame is a hexagonal right cylinder. The hexagonal space is subdivided in twenty four tetrahedrons, each of which is bound by three concurrent vectors. This paper presents a mathematical model that determines the exact tetrahedron where the reference vector is located and identifies the relevant three switching state vectors. A Matlab simulation of a four leg voltage source inverter working on the proposed model has been presented as a benchmark program to validate the model. Results obtained demonstrate the tangible potential of the proposed approach.