Weighted Total Harmonic Distortion
Weighted THD is preferred over THD when an inverter is generating non-sinus waveforms. Take a BLDC machine, this is usually excited with a trapezoidal current waveform 

THD aims to express the quality of a sinus so if what is being generated isn't a sinus its benefit of determining how pure the output waveform is (w.r.t. what it is expected to be) has been diminished.

WTHD aims to to predict the distortion in the current (and thus the additional losses)