Exact and Efficient Algorithm to Discover Extreme Stochastic Events in Wind Generation over Transmission Power Grids

In this manuscript we continue the thread of [M. Chertkov, F. Pan, M. Stepanov, Predicting Failures in Power Grids: The Case of Static Overloads, IEEE Smart Grid 2011] and suggest a new algorithm discovering most probable extreme stochastic events in static power grids associated with intermittent generation of wind turbines. The algorithm becomes EXACT and EFFICIENT (polynomial) in the case of the proportional (or other low parametric) control of standard generation, and log-concave probability distribution of the renewable generation, assumed known from the wind forecast. We illustrate the algorithm’s ability to discover problematic extreme events on the example of the IEEE RTS-96 model of transmission with additions of 10%, 20% and 30% of renewable generation. We observe that the probability of failure may grow but it may also decrease with increase in renewable penetration, if the latter is sufficiently diversified and distributed.

💡 Research Summary

The paper addresses the critical problem of assessing the reliability of power transmission networks under the stochastic fluctuations introduced by wind power generation. Building on earlier work that treated static overloads as rare events, the authors develop a mathematically rigorous framework for identifying the most probable extreme stochastic events—referred to as “instantons”—that can cause line overloads or violate generator limits when no corrective actions (curtailment, load shedding, or line switching) are employed.

The authors model the network using the DC power‑flow approximation, which yields a linear relationship between nodal phase angles and net injections. Loads are assumed fixed over the short time horizon of interest (seconds to minutes), while wind power injections at a set of renewable nodes are described by a known multivariate probability density (P(\rho) \propto \exp