It all depends on which is the purpose of your PWM pulses. Are they intended to drive the gates of power MOSFETs in a 3-phase bridge? If it is the case, low-pass filtering the PWM waveforms you should get three sine waves displaced in phase of 120° to each other
where the fundamental factor is the amplitude of ur pulse which should be slightly more than minimum threshold required rating of ur gate and the timing of the gate drive pulse arrival..so as far i know symmetry is not the major factor here.go ahead with ur intended work
it is not very clear to me what do you mean with "symmetric". Do you mean the pulse sequences of the three phases are not the same delayed by 1/3 of the period and/or the waveforms are not exactly periodic? This is not, in general, a major concern, nonetheless it can give rise to residual distortion at low frequency which is not suppressed by the output filter. What kind of modulation are you using to generate the PWM waveform? You can get periodic waveforms if you set the sine wave modulation period equal to an integer number of periods of the PWM waveform in your firmware.
are you trying to control all switches with the same pulse per phase ?
if you could share the circuit, i could help with the pulse generation, as of now seeing the attachment there might be a difference in output voltage wave form when there is a RLC load