An Extended Impedance Model for Power Electronics Converters Retaining Explicit Synchronization Dynamics

In power systems with a high penetration of renewable energy, grid-forming (GFM) and grid-following (GFL) inverters coexist with synchronous generators (SGs). The wide-frequency-band dynamic interactions among various machines result in intricate interactions involving electromagnetic dynamics and synchronous behaviors, posing challenges for stability analysis. Thus, this paper proposes an extended impedance model (EIM) that introduces an additional degree of freedom to separate the synchronous dynamics from the electromagnetic dynamics. Input and output (I/O) variables corresponding to the electromagnetic and synchronous dynamics are independently retained in the proposed EIM. It allows for analyzing specific stability issues by selecting an appropriate dominant loop of concern. Subsequently, a method to identify the dominant loop associated with weakly dampened modes is presented, and an index is introduced to assess the applicability of the derived models. Note that the EIM is obtained without introducing any model redundancy, while it maintains the scalability of impedance models. Using the proposed EIM for stability analysis enables a more extensive and flexible selection of the dominant loops, facilitating the pinpointing of the root cause of instability. The efficacy of the model has been validated through simulations and experimental tests.