*3.3. The Proposed PLL Structure*

The proposed PLL structure is based on the QT1-PLL structure which is depicted in Figure 10. ω*n* is the nominal frequency of the grid. ωˆ *g* is the estimated grid frequency. θ ˆ+ 1 is the estimated phase of FFPS. The arc tangent function can remove the impact of amplitude variation of the input voltage vector. *k* is the only control parameter of QT1-PLL.

**Figure 10.** Block diagram of quasi-type-1 (QT1)-PLL.

Replacing the MAFs in QT1-PLL by the proposed hybrid filtering stage yields the proposed PLL structure as shown in Figure 11. While arc tangent function can remove the impact of amplitude variation, phase deviation still exists. Hence, to compensate a π/4 phase deviation introduced by MDSC*<sup>m</sup>*=4, *<sup>n</sup>*=8, which is mentioned above, −<sup>π</sup>/4 is added at the output of proposed PLL. *k* is the only one control parameter to be designed.

**Figure 11.** Block diagram of the proposed PLL.

### **4. Mathematics Model and Parameters Design Procedure**

According to Figure 11, the mathematics model is derived in this section. To achieve a desired dynamic response, the parameter design procedure is also given. After providing the mathematics model, the stability of the system is also examined.
