  This paper studies the probabilistic hosting capacity analysis (PHCA) problem
in distribution networks considering uncertainties from distributed energy
resources (DERs) and residential loads. PHCA aims to compute the hosting
capacity, which is defined as the maximal level of DERs that can be securely
integrated into a distribution network while satisfying operational constraints
with high probability. We formulate PHCA as a chance-constrained optimization
problem, and model the uncertainties from DERs and loads using historical data.
Due to non-convexities and a substantial number of historical scenarios being
used, PHCA is often formulated as large-scale nonlinear optimization problem,
thus computationally intractable to solve. To address the core computational
challenges, we propose a fast and extensible framework to solve PHCA based on
Bayesian Optimization (BayesOpt). Comparing with state-of-the-art algorithms
such as interior point and active set, numerical results show that the proposed
BayesOpt approach is able to find better solutions (25% higher hosting
capacity) with 70% savings in computation time on average.
