Multistability and anomalies in oscillator models of lossy power grids

TL;DR

This paper introduces a geometric framework for analyzing dissipatively coupled oscillators in power grids, revealing how dissipation can enhance transfer capacity and promote multistability, with practical computations on a standard test system.

Contribution

It develops a novel geometric and computational approach to identify all synchronous states and anomalies in lossy power grid models, addressing challenges posed by dissipative couplings.

Findings

Loop flows and dissipation can increase transfer capacity.

Dissipation can promote multistability in power grids.

Identification of multiple high voltage solutions in IEEE RTS-96.

Abstract

The analysis of dissipatively coupled oscillators is challenging and highly relevant in power grids. Standard mathematical methods are not applicable, due to the lack of network symmetry induced by dissipative couplings. Here we demonstrate a close correspondence between stable synchronous states in dissipatively coupled oscillators, and the {winding partition} of their state space, a geometric notion induced by the network topology. Leveraging this winding partition, we accompany this article with an algorithms to compute all synchronous solutions of complex networks of dissipatively coupled oscillators. These geometric and computational tools allow us to identify anomalous behaviors of lossy networked systems. Counterintuitively, we show that loop flows and dissipation can increase the system's transfer capacity, and that dissipation can promote multistability. We apply our geometric framework to compute power flows on the IEEE RTS-96 test system, where we identify two high voltage solutions with distinct loop flows.