Accelerating splitting algorithms for power grid reliability estimation
With increasing penetration of intermittent power generation sources like wind and solar farms, overload risks in power grids due to imbalances in supply and demand of energy has become a serious concern. We model the flow of electricity through a power grid as a functional transformation of a multidimensional Ornstein-Uhlenbeck process of renewable energy injection. Previously, a rare event simulation technique called splitting, based on large deviations results has been proposed as the risk assessment method. This method requires solving a nonlinear optimization problem for every time step in every generated sample path, so significant computational challenges remain in scaling to realistic networks. We propose a new algorithmic approach to implement the large deviations splitting method that derives and exploits fundamental properties of the rate functions in order to significantly speed up the pathwise optimizations. Experimental results show a significant reduction in effort compared to a conventional numerical approach.