Fig. 1. Schematic diagram of power electronic dominated power systems

Fig. 2. Schematic show for a single-machine-infinite-bus (SMIB) system

Fig. 3. Power-angle relationship^[7].

Fig. 4. (a) Power-angle relationships for three different states of before-fault ( ), during-fault ( ), and post-fault ( ); (b) time-domain responses of the power angle when the system are stable (red curve) and critical stable (blue curve), respectively^[9]

Fig. 5. (a) Potential energy function curve; (b) trajectories in state space corresponding different states: stable, critically stable, and unstable^[10].

Fig. 6. Schematic show of a grid-connected VSC system and its controllers

Fig. 7. Schematic show of the control diagram of the VSC system within the voltage timescale

Fig. 8. Bifurcation diagram with the variation of including a sub-critical Hopf bifurcation and a generalized saddle-node bifurcation. The sub-figure shows the eigenvalue traces when decreases and passes through the Hopf bifurcation point

Fig. 9. Response comparison between the voltage timescale VSC system and the detailed VSC system after transient fault

Fig. 10. (a) A multi-machine power system with VSC devices and synchronous generators and (b) its variable relations in differential algebraic equations