Back-electromotive-force observer (BEMF observer) based symmetrical PLL for grid synchronization stability enhancement under weak grid conditions

The synchronous reference frame phase-locked loop (SRF-PLL) is widely utilized for grid synchronization in voltage-source converter (VSC) system. However, it fails to eliminate the effect of high grid impedance leading to instability in weak grids. To address this issue, this paper introduces the back-electromotive-force observer (BEMF observer), commonly being utilized in DC motor, to modify the input of the SRF-PLL. To be specific, the equivalent internal electromotive force calculated by the BEMF observer rather than the PCC voltage is used to capture the phase information. Since the BEMF observer is designed in alpha beta$\alpha \beta$-frame while the SRF-PLL is in dq$dq$-frame, the conventional stability analysis method suffers from complicated process. Thus, this paper further reconstructs the SRF-PLL with the BEMF observer to be symmetrical for simplification. Apart from the symmetrical structure, the stability criterion is accordingly modified. As a result, the proposed back electromotive force based symmetrical PLL (BEFS-PLL) offers the following advantages: (i) it effectively enhances the grid synchronization stability and simplifies the stability analysis process simultaneously, (ii) it exhibits a strong robustness even with the calculation error up to 50%, and (iii) it is characteristic of clear physical meanings. Finally, the effectiveness of the BEFS-PLL is verified by simulation.