Equivalency between Adaptive Notch Filter PLL and Inverse Park PLL by Modeling and Parameter Adjustment

Synchronism algorithms play an important role in microgrid converters, and they are fundamental to the power flow control between the converters and the main grid. In island operation, synchronism algorithms provide important frequency and voltage data for converters to operate properly at steady state, and also connect and disconnect from the main grid. In this context, this work presents modeling and parameter design of two structures of single-phase PLLs: the inverse park PLL (Park-PLL) and the adaptive notch filter PLL (ANF-PLL). The derivation of the linearized model of Park-PLL, previously discussed in the literature, is detailed. In addition, as main contribution this paper, a linearized model of the ANF-PLL is presented and compared with the first one. As a result, it is possible to demonstrate equivalency between the two evaluated PLL structures when their parameters are adjusted by the proposed methodology. Practical and simulated results validate the parity of the PLL structures in terms of the dynamic response and steady-state error.