  This article explores the effects of a single bus perturbation in the
electrical grid using a Graph Signal Processing (GSP) perspective. The
perturbation is characterized by a sudden change in real-power load demand or
generation. The study focuses on analyzing the spread of the perturbation
throughout the grid and proposes a measure of spreadability based on GSP.
Moreover, the global and local smoothness properties of the difference bus
voltage angle graph signals are evaluated for understanding their embedded
patterns of spreadability property. It is demonstrated that the global
smoothness of the bus voltage angle graph signal follows a quadratic
relationship with the perturbation strength, which helps in characterizing the
critical perturbation strength after which the power flow diverges indicating a
stressed system. The impact of a single bus perturbation on power system graph
signals has been investigated through both analytical derivations using the DC
power flow model and simulation using the AC power flow model. The results
reveal that the proposed measure of spreadability as well as local and global
smoothness properties of the graph signals are independent of the perturbation
strength and instead mainly depend on the perturbation's location.
