Effect of Phase Shift on the Dynamics and Stability of Power Networks

Power grids are complex networks; their dynamics have strong nonlinearity due to the symmetry breaking in their topological structure. Synchronization stability, which is essential for secure and reliable operation, is the focus of this study. In this paper, the effects of phase shift on dynamics and stability in symmetry-breaking power networks are investigated. To clarify the influence of phase shift parameters, power networks of different sizes and topological structures are systematically analyzed, including a two-node power network, the Nepal power network, and the UK power network. The results show that phase shift significantly changes the collective dynamical behaviors of power networks, leading to transitions from frequency synchronization to complete synchronization or desynchronization under different parameter conditions. Moreover, the stability region shrinks as the phase shift increases. The stability transition region is further found to be strongly related to network size, topological structure, and the spatial distribution of generators and consumers in the power network. The results indicate that the stronger the symmetry-breaking in a power network, the more significant the impact of the phase shift parameter on the dynamics and stability. The results of the basin stability analysis for the power system provide quantitative support for this result and reveal the mechanism of power system instability under the effect of phase shift parameters. These findings provide a deeper understanding of the effect of phase shift on the dynamics of symmetry-breaking power networks and offer new insights into synchronization stability and structural design in complex power systems.