Understand the effect of line losses on resonant energy flow

Investigate how transmission line losses interact with the resonant energy flow between a solitary node and the synchronized cluster in the inertial Kuramoto model on complex networks, and characterize the impact of lossy coupling on the existence, frequency, and stability of resonant solitary states.

Background

The main theory is developed for sinusoidal coupling without explicit treatment of transmission losses, focusing on how resonant excitation of network modes leads to non-zero mean power flow p_s that sustains intermediate solitary frequencies. Prior work indicates that lossy coupling can qualitatively alter multistability and solitary phenomena, but its specific interaction with resonant energy transfer is not addressed here.

Clarifying this interaction is needed to connect the proposed mechanism to more realistic power-grid models in which line losses are present, potentially modifying resonance conditions, energy balances, and stability of solitary states.