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I am using the book "

*Instantaneous Power Theory and Applications to Power Condition*" which I found as a pdf on the web.

The authors write:

- The only way for the PLL to reach a stable point is if the input to the PI controller in steady state has an average value of zero.

*ia*and voltage

*va*has to be orthogonal to each other, i.e. [itex]cos(\phi) = 0[/itex].

The author also write that the frequency [itex]\omega[/itex] has to be equal to the system frequency and the current and voltages has to be orthogonal to reach a stable point of operation.

Why must [itex]\omega[/itex] be equal to system frequency to reach a stable point of operation?

I would appreciate if someone help me fully understood how this circuit works

EDIT: I forgot to write 2pi/3 at the left bottom block, i wrote pi/3.