Global performance metrics for synchronization of heterogeneously rated power systems: The role of machine models and inertia

TL;DR

This paper extends the analysis of power system synchronization metrics to more realistic scenarios by incorporating machine heterogeneity and detailed models, revealing nuanced roles of inertia and turbine dynamics in system performance.

Contribution

It introduces a comprehensive framework for evaluating power system synchronization using realistic machine models and heterogeneity, linking classical metrics to modern control insights.

Findings

Inertia plays a secondary role in classical swing dynamics.

Turbine dynamics highlight the importance of inertia for system performance.

Heterogeneity of machine ratings affects synchronization metrics significantly.

Abstract

A recent trend in control of power systems has sought to quantify the synchronization dynamics in terms of a global performance metric, compute it under very simplified assumptions, and use it to gain insight on the role of system parameters, in particular, inertia. In this paper, we wish to extend this approach to more realistic scenarios, by incorporating the heterogeneity of machine ratings, more complete machine models, and also to more closely map it to classical power engineering notions such as Nadir, Rate of Change of Frequency (RoCoF), and inter-area oscillations. We consider the system response to a step change in power excitation, and define the system frequency as a weighted average of generator frequencies (with weights proportional to each machine's rating); we characterize Nadir and RoCoF by the $L_\infty$ norm of the system frequency and its derivative, respectively, and inter-areas oscillations by the $L_2$ norm of the error of the vector of bus frequencies w.r.t. the system frequency. For machine models where the dynamic parameters (inertia, damping, etc.) are proportional to rating, we analytically compute these norms and use them to show that the role of inertia is more nuanced than in the conventional wisdom. With the classical swing dynamics, inertia constant plays a secondary role in performance. It is only when the turbine dynamics are introduced that the benefits of inertia become more prominent.