# Global analysis of synchronization performance for power systems: bridging the theory-practice gap

## TL;DR

This paper extends the analysis of power grid synchronization to realistic scenarios with heterogeneous generators, providing new metrics and insights that bridge theoretical models and practical engineering applications.

## Contribution

It introduces a decomposition of frequency responses, defines new metrics for synchronization, and validates these through simulations, connecting theory with real-world power system practice.

## Key findings

- System frequency captures grid behavior and steady-state deviations.
- New metrics like Nadir, RoCoF, and synchronization cost quantify dynamic performance.
- System frequency remains accurate as network connectivity increases.

## Abstract

The issue of synchronization in the power grid is receiving renewed attention, as new energy sources with different dynamics enter the picture. Global metrics have been proposed to evaluate performance and analyzed under highly simplified assumptions. In this paper, we extend this approach to more realistic network scenarios and more closely connect it with metrics used in power engineering practice. In particular, our analysis covers networks with generators of heterogeneous ratings and richer dynamic models of machines. Under a suitable proportionality assumption in the parameters, we show that the step response of bus frequencies can be decomposed in two components. The first component is a {system-wide frequency} that captures the aggregate grid behavior, and the residual component represents the individual bus frequency deviations from the aggregate. Using this decomposition, we define --and compute in closed form-- several metrics that capture dynamic behaviors that are of relevance for power engineers. In particular, using the \emph{system frequency}, we define industry-style metrics (Nadir, RoCoF) that are evaluated through a representative machine. We further use the norm of the residual component to define a \emph{synchronization cost} that can appropriately quantify inter-area oscillations. Finally, we employ robustness analysis tools to evaluate deviations from our proportionality assumption. We show that the system frequency still captures the grid steady-state deviation, and becomes an accurate reduced-order model of the grid as the network connectivity grows. Simulation studies with practically relevant data are included to validate the theory and further illustrate the impact of network structure and parameters on synchronization. Our analysis gives conclusions of practical interest, sometimes challenging the conventional wisdom in the field.