A Stochastic Variational Optimization Approach for Reliability Assessment of Renewable Energy Networks

Abstract

The power systems face reliability threats due to intermittent renewable energy and variable line behavior. Traditional probabilistic models such as Loss of Load Expectation can assess the reliability risks under predetermined events, but cannot reflect the worst-case scenario spatial and temporal dependency, as well as topological vulnerability under ambiguity. This article presents an approach based on stochastic variational optimization theory and describes the reliability problem as minimax robust stochastic optimization with respect to a Wasserstein ambiguity set, combining network feasibility with chance-constrained reliability. To reduce the complexity of the problem, robust chance constraints are derived using conditional value-at-risk combined with generalized subdifferential calculus. Stochastic variational inequalities allow for deriving stationarity conditions using normal cones and stochastic gradients, thus defining the minimax problem. The sample average approximation to stochastic variational problem is proved to be consistent and a symptocally normal, while adapted concentration inequalities characterize the probability of cascading failures in terms of the ambiguity radius. A stochastic proximal gradient method combined with a bundle method based on variance reduction technique is proposed for computational purposes. Numerical examples show both convergence of the proposed algorithms and growth of the worst-case reliability bound with ambiguity radius.