Exploration of Stability Between Power Grids on Time Scales of Different Variance

Differential equations are useful tools for evaluating the theoretical long-term behavior of systems, particularly control systems. But in real world applications, unlike continuous differential equations, controllers are often unable to react continuously or immediately. For example, the dynamics of power flow between local power grids in Southern California and the Pacific Northwest are maintained by controllers located midway between these areas that use the internet to relay information. The feedback of these controllers is subject to both nonuniform spacing and time delay. Using the theory of Time Scale calculus, as well as the Stability-Almost-Surely Criteria, I will evaluate the stability of power dynamics on different time scales.