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.

中文翻译：

---

通过建模和参数调整，自适应陷波滤波器PLL与反向Park PLL之间的等效性

同步算法在微电网转换器中起着重要作用，并且对于转换器与主电网之间的潮流控制至关重要。在孤岛运行中，同步算法为转换器提供重要的频率和电压数据，以使其在稳态下正常运行，并与主电网连接和断开连接。在这种情况下，这项工作提出了单相PLL的两种结构的建模和参数设计：逆停泊PLL（Park-PLL）和自适应陷波滤波器PLL（ANF-PLL）。详细介绍了先前在文献中讨论的Park-PLL线性化模型的推导。另外，作为本文的主要贡献，提出了ANF-PLL的线性化模型并将其与第一个模型进行比较。因此，当通过所提出的方法调整它们的参数时，有可能证明两个评估的PLL结构之间的等效性。实际和仿真结果从动态响应和稳态误差方面验证了PLL结构的奇偶性。