Transient Algebraic Impedance Derivations and Applications for PLL-Synchronized IBRs

In system-level dynamic studies, grid-following inverter-based resources (IBRs) have been treated as current sources synchronized to the main grid via phase-locked-loops (PLL), while the interconnected transmission line is usually treated as a constant complex impedance. In this letter, we present the derivation of transient algebraic impedance of the transmission line and demonstrate its superiority over constant impedance. We show significant accuracy improvement in predicting transient stability and oscillations when the constant impedance is replaced by a transient algebraic impedance. Furthermore, we derive a small-signal model by use of the transient algebraic impedance and this model is successful in explaining the interaction between the PLL and the grid. On the other hand, if constant impedance is assumed, such stability issues cannot be predicted.