Variable Virtual Impedance-Based Overcurrent Protection for Grid-Forming Inverters: Small-Signal, Large-Signal Analysis and Improvement

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.