Importance Sampling of Rare Events for Distribution Networks with Stochastic Loads

Distribution networks are low-voltage electricity grids at the neighborhood level. Within these networks, failures can occur as rare events, triggered by stochastic loads that push voltage levels beyond safe limits. To assess the resilience and reliability of these networks, estimating voltage exceedance probabilities is therefore important. We develop importance-sampling strategies to estimate failure probabilities. We do so using two components. First, we propose a change of measure, using either the Large Deviations Principle and linear power flow equations or the Cross-Entropy method to improve sampling efficiency. Second, we determine feasibility of loads by using our previously developed duality method to overcome the computational complexity of directly solving nonlinear power flow equations using methods such as Newton-Raphson and backward-forward sweep algorithms. Experiments on a IEEE-15 bus network show that this methodology offers a fast and accurate estimation of failure probabilities in distribution networks.