This paper deals with the transient stability of a grid-forming converter while embedding a current reference saturation strategy. The novelty of this work consists in investigating the impact of the current reference angle on the transient stability. In case of a balanced voltage sag, analytical formulas to estimate the critical clearing angle (CCA) and critical clearing time (CCT) while considering different values of the current reference angle are derived. It is demonstrated that the choice of this angle is constrained by the ability of the power converter to switch back to the voltage control mode. Based on that, its optimal value that enhances the transient stability and allows a switching from the saturated current control mode to the voltage control mode is calculated. Thereafter, the effectiveness of this optimal choice to guarantee the stability in case of a phase shift caused by a line re-closing event is verified. Time-domain simulations and experimental tests validate the correctness of the presented theoretical approaches.

The present paper deals with the post-fault synchronization of a voltage source converter based on the droop control. In case of large disturbances on the grid, the current is limited via current limitation algorithms such as the virtual impedance. During the fault, the power converter internal frequency deviates resulting in a converter angle divergence. Thereby, the system may lose the synchronism after fault clearing and which may lead to instability. Hence, this paper proposes a theoretical approach to explain the dynamic behavior of the grid forming converter subject to a three phase bolted fault. A literal expression of the critical clearing time is defined. Due to the precise analysis of the phenomenon, a simple algorithm can be derived to enhance the transient stability. It is based on adaptive gain included in the droop control. These objectives have been achieved with no external information and without switching from one control to the other. To prove the effectiveness of the developed control, experimental test cases have been performed in different faulted conditions.

Grid-forming inverters are sensitive to large grid disturbances that may engender overcurrent due to their voltage source behavior. To overcome this critical issue and ensure the safety of the system, current limitation techniques have to be implemented. In this context, the variable virtual impedance (VI) appears as a suitable solution for this problem. The design of the variable virtual impedance basically rests on static considerations, while, its impact on the system stability and dynamics considering both small-signal and large-signal aspects can be significant. This paper proposes small-signal and nonlinear power models to assess the impact of the virtual impedance parameters on the grid current dynamics and on the angle stability. Thanks to the proposed approach, it has been demonstrated that the virtual impedance ratio $\sigma _{X_{VI}/R_{VI}}$ has a contradictory effect on the system dynamics and the transient stability, i.e., a resistive virtual impedance results in a well-damped current response but a very limited transient stability margin, while an inductive virtual impedance results in a poorly-damped current response but an acceptable transient stability margin. Based on that, it has been concluded that the conventional virtual impedance cannot cope at once with the current dynamic performances and the transient stability. To overcome this constraint, a Variable Transient Virtual Resistance (VTVR) has been proposed as an additional degree of freedom to vary $\sigma _{X_{VI}/R_{VI}}$ . It decreases $\sigma _{X_{VI}/R_{VI}}$ in the transient to damp the current response and it increases $\sigma _{X_{VI}/R_{VI}}$ in the quasi-static and steady-state to guarantee the maximum angle stability margin allowed by the variable virtual impedance. The effectiveness of the proposed control has been proven through time-domain simulations.