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Center for Nonlinear Studies |
The equilibrium operation of power grid requires that the generation meets the demand at each time instant and any deviation raises critical stability concerns. However with ever increasing load, more so with the imminent release of plug-in electric vehicles en masse, the grids are under greater pressure. On the other hand, the growing penetration of renewable energy sources provides an excellent opportunity to meet the increased electricity demand, but the challenge remains to mitigate the uncertainties associated with renewable generation. The challenge here is to ensure seamless integration of newer forms of generation and load, while maintaining a stable and satisfactory grid-level performance.
Specifically in this talk, I will be covering how we propose to model the aggregate dynamics of a large group of flexible (or “time deferrable”) electric loads, such as plug-in electric vehicle chargers, thermostat-controlled heating/cooling loads, etc. using a hysteresis-based approach, and control their aggregate electricity demand to mitigate fluctuations in renewable generation. It will be shown that, often this population dynamics exhibits interesting nonlinear behavior, such as period adding cascade, and thus need to be understood well to ensure safe electrical grid operations. Finally I would briefly discuss some of the more recent techniques that concern with analyzing the power systems stability from a Lyapunov stability perspective, which is often very complex because of the system’s complexity and high dimensionality. However a recent advancement shows promising results by using sum-of-squares techniques to compute the system’s Lyapunov function.