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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.

Capacitor-current-feedback active damping is an effective method to suppress the LCL-filter resonance in gridconnected inverters. However, due to the variation of grid impedance, the LCL-filter resonance frequency will vary in a wide range, which challenges the design of capacitor-currentfeedback coefficient. Moreover, if the resonance frequency is equal to one-sixth of the sampling frequency (f s /6), the digitally controlled LCL-type grid-connected inverter can hardly be stable no matter how much the capacitor-current-feedback coefficient is. In this paper, the optimal design of capacitor-current-feedback coefficient is presented to deal with the wide range variation of grid impedance. First, the gain margin requirements for system stability are derived under various resonance frequencies. By evaluating the effect of grid impedance on the gain margins, an optimal capacitor-current-feedback coefficient is obtained. With this feedback coefficient, stable operations will be retained for all resonance frequencies except f s /6. Second, in order to improve system stability for the resonance frequency of f s /6, a phase-lag compensation for the loop gain is proposed. Finally, a 6-kW prototype is tested to verify the proposed design procedure.

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