Complex-Vector PLL for Enhanced Synchronization with Weak Power Grids

This paper proposes a complex-vector based phase-locked loop (PLL) that can eliminate the frequency-coupling terms caused by the asymmetric dynamics of the conventional PLL. In the approach, a complex phase angle with both real and imaginary components is introduced, which enables to control the direct- and quadrature-axis components symmetrically. As a result, the original multiple-input multiple-output (MIMO) system can be simplified to single-input-single-output (SISO) complex transfer functions, which greatly facilitates the system stability analysis. Moreover, the dangerous subsynchronous oscillation hazard caused by the frequency coupling of the conventional PLL can be avoided, and SISO impedance shaping technique can be utilized to enhance the grid synchronization stability under the weak grid condition. The complex-vector PLL is verified by both the theoretical analysis and experimental tests.