Query on PI Tuning of Three Phase Inverter

I am working on tuning a PI controller for a three phase 3level PWM inverter as part of our larger project. But i am facing issues with the said tuning using sustained oscillation method.

To better handle the three phase quantities I translated them using alpha-beta transform. After trying my hand at tuning, which I think is wrong, I have obtained a very large Ki value and relatively small Kp value. And these parameters are not helping in improving the system response. In fact I observed that changing the value of Ki is not affecting the system in any way.

When I checked the THD of the control parameter, all the three phases were displaying different values for the THD and noticed even order harmonics in 2nd and 3rd phase. Shouldn't a symmetrical system have the same Kp and Ki value for all phases?

I would be grateful if you could provide resources for tuning the inverter or guide me in correcting my mistakes. Would be willing to provide more info if needed.

Thanks in advance.