Small-signal stability of power systems with voltage droop

Guaranteeing the stability of future, inverter-dominated power grids is a central challenge for grid operators, especially when devices from multiple vendors interact. In this work, we derive novel conditions that guarantee small-signal stability. They are independent of device specifics and are locally verifiable in the neighborhood of each bus. The inverters can be highly heterogeneous and implement any control law of frequency, voltage amplitude, active and reactive power, and internal states. The only structural assumptions we make are that the control implements an exact droop relationship between voltage magnitude and reactive power, and that we have a constant R/X ratio throughout the grid. When applied to established models of control designs, we reproduce and generalize established results. To achieve this, we build on the recent small-phase theorem and adapt it to networked systems. The central novelty on the grid modeling side is the use of complex frequency to capture the relevant dynamical behavior of the inverters. While the conditions are sufficient but not necessary, we find that they are not overly conservative in practice. Furthermore, we find that they can identify individual inverters that are the cause of instability.