Whats the reason for triangular carrier PWM
In a sawtooth PWM, the centre of each pulse and thus the phase of the reconstructed waveform varies with the signal amplitude or PWM duty cycle. 

Double sided modulation, using a triangular waveform, avoids this problem, keeping the centre of each PWM pulse at a constant phase relative to the PWM sampling interval.

And yes, the phase distortion does appear as unwanted harmonic content when you PWM modulate a sine wave with triangular PWM.