Multistability and anomalies in oscillator models of lossy power grids

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.

Automated summary

The analysis of dissipatively coupled oscillators in power grids is challenging but relevant. This study establishes a close correspondence between stable synchronous states and the winding partition of the state space, providing a geometric framework for computing synchronous solutions. It is shown that loop flows and dissipation can have counterintuitive effects on the system's transfer capacity and multistability. The proposed geometric framework is applied to calculate power flows in the IEEE RTS-96 test system, identifying high voltage solutions with distinct loop flows.