Modulation in Voltage Source Inverters: An Algebraic Approach

Pulse width modulation in voltage source inverters with an arbitrary number of phases is analyzed in this paper. The problem is treated as purely algebraic, without any use of space vectors. Regardless of avoiding space vectors, the same results are achieved. It is shown that the problem of determining duty ratio values does not have a unique solution, and that there is one degree of freedom to choose one duty ratio, but within a limited range. Limits of the range are derived. Feasibility constraints for the required set of line voltages are derived, reducing to the requirement that the highest of the line voltages should be lower than the DC bus voltage. The analysis is illustrated in cases varying from two to five phases, and experimentally verified in the case of three phases. The method is simple and could be applied to any number of phases, even for the voltages that are not sinusoidal.