Driven by the large-scale integration of distributed power resources, grid-connected voltage-source converters (VSCs) are increasingly required to operate as grid-forming units to regulate the system voltage/frequency and emulate the inertia. While various grid-forming control schemes have been reported, their transient behaviors under large-signal disturbances are still not fully explored. This paper addresses this issue by presenting a design-oriented transient stability analysis of the grid-forming VSCs. First, four typical grid-forming control schemes, namely the power-synchronization control (PSC), the basic droop control, the droop control with low-pass filters (LPFs), and the virtual synchronous generator (VSG) control, are systematically reviewed, whose dynamics are characterized by a general largesignal model. Based on this model, a comparative analysis on the transient stabilities of different control schemes is then carried out. It reveals that the PSC and the basic droop control can retain a stable operation as long as there are equilibrium points, due to their non-inertial transient responses; while the droop control with LPFs and the VSG control can be destabilized even if the equilibrium points exist, due to the lack of damping on their inertial transient responses. With the phase portrait, the underlying stability mechanism is explicitly elaborated, and the quantitative impacts of the controller gains and the virtual inertia are clearly identified. Subsequently, controller design guidelines are proposed to enhance the system damping as well as the transient stability. Finally, experimental results are provided to verify the theoretical analysis.

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 multipleinput multiple-output impedance matrix, is in a single-input singleoutput (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.

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