Methods, system and apparatus are provided for controlling third harmonic voltages when operating a multi-phase machine in an overmodulation region. The multi-phase machine can be, for example, a five-phase machine in a vector controlled motor drive system that includes a five-phase PWM controlled inverter module that drives the five-phase machine. Techniques for overmodulating a reference voltage vector are provided. For example, when the reference voltage vector is determined to be within the overmodulation region, an angle of the reference voltage vector can be modified to generate a reference voltage overmodulation control angle, and a magnitude of the reference voltage vector can be modified, based on the reference voltage overmodulation control angle, to generate a modified magnitude of the reference voltage vector. By modifying the reference voltage vector, voltage command signals that control a five-phase inverter module can be optimized to increase output voltages generated by the five-phase inverter module.