Symmetrical PLL for SISO Impedance Modeling and Enhanced Stability in Weak Grids

This paper proposes a symmetrical phase-locked loop (PLL) that can eliminate the frequency-coupling terms caused by the asymmetric dynamics of conventional PLLs. In the approach, a concept of complex phase angle vector with both real and imaginary phase components is introduced, which enables to control the direct- and quadrature-axis components with symmetrical dynamics. The small-signal impedance model that characterizes the dynamic effect of the symmetrical PLL on the current control loop is also derived, which, differing from the conventional multiple-input multiple-output impedance matrix, is in a single-input single-output (SISO) form based on complex transfer functions. This SISO representation allows for a design-oriented analysis. Moreover, the undesired sub-synchronous oscillation caused by the conventional asymmetrical PLL can be avoided, and the classical SISO impedance shaping can be utilized to cancel the negative resistor behavior caused by PLL; thus can greatly enhance the grid synchronization stability under weak grid conditions. The effectiveness of the theoretical analysis is validated by experimental tests.