Certifying Frequency Stability for Systems with Line Dynamics and Heterogeneous Bus Dynamics

Abstract

This work presents a framework for certifying small-signal frequency stability of a power system with line dynamics and heterogeneous bus dynamics. This framework can certify the stability of systems which include synchronous generators, synchronous condensers, and converter-interfaced resources with a wide range of controls. Moreover, it can do so without detailed or precise knowledge of the network topology. With this framework, we also provide a detailed analysis of how proportional-derivative (PD) droop can improve the stability margin of the frequency response. The stability certificates presented in this work, which extend prior results by incorporating line dynamics, provide insight into how the control parameters for different units in the system impact the overall frequency stability. While damper windings have long been understood to improve the frequency synchronization between machines, the dynamics of the damper windings are complex, making them difficult to analyze. To address this gap, this paper derives a novel reduced-order model of the damper windings in the form of a derivative droop term. Moreover, we show that derivative droop terms used in grid-forming (GFM) control can be understood as a form of damper winding emulation. Our analytical stability conditions highlight the importance of damper windings (or their emulation) in facilitating frequency synchronization and suppressing unstable interactions between GFM converters. These results are validated with electromagnetic-transient (EMT) simulation.

15 pages, 14 figures