# Secant and Popov-like Conditions in Power Network Stability

## TL;DR

This paper introduces secant and Popov-like conditions to analyze and improve decentralized stability criteria in power networks, effectively addressing nonlinearities and generation dynamics with reduced conservatism.

## Contribution

It develops new stability conditions using secant and Popov-like criteria that incorporate local information, enhancing analysis of complex power system dynamics.

## Key findings

- Secant gain conditions provide less conservative stability criteria.
- Popov-like conditions further reduce conservatism with local coupling info.
- Examples demonstrate improved stability analysis in power networks.

## Abstract

The problem of decentralized frequency control in power networks has received an increasing attention in recent years due to its significance in modern power systems and smart grids. Nevertheless, generation dynamics including turbine-governor dynamics, in conjunction with nonlinearities associated with generation and power flow, increase significantly the complexity in the analysis, and are not adequately addressed in the literature. In this paper we show how incremental secant gain conditions can be used in this context to deduce decentralized stability conditions with reduced conservatism. Furthermore, for linear generation dynamics, we establish Popov-like conditions that are able to reduce the conservatism even further by incorporating additional local information associated with the coupling strength among the bus dynamics. Various examples are discussed throughout the paper to demonstrate the significance of the results presented.