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It is shown that proportional-integral (PI) control in the synchronouslyrotating (d, q)-reference frame and proportional-resonant (PR) control in thestationary ({\alpha}, \b{eta})-reference frame, both with anti-windup, areequivalent if and only if their implementation is done correctly in state spaceand the controller parameters and the initial values are identical. It is shownthat an equivalence in the frequency domain does only hold if simplifyingassumptions are satisfied. As consequence of the equivalence, both closed- loopcontrol performances are identical with respect to closed-loop dynamics andsteady-state accuracy. The control performance will only differ if theirimplementation is not done correctly or the time delay induced by the voltagesource inverter becomes significant. To the best knowledge of the author,equivalence of PR and PI controllers with anti-windup has not been shown before(in particular not in state space).

On the equivalence of proportional-integral and proportional-resonant controllers with anti-windup