  Considering the increasing penetration of renewable energy sources and
electrical vehicles in utility distribution feeders, it is imperative to study
the impacts of the resulting increasing uncertainty on the delivery capability
of a distribution network. In this paper, probabilistic available delivery
capability (ADC) is formulated for a general distribution network integrating
various RES and load variations. To reduce the computational efforts by using
conventional Monte Carlo simulations, we develop and employ a computationally
efficient method to assess the probabilistic ADC, which combines the up-to-date
sparse polynomial chaos expansion (PCE) and the continuation method.
Particularly, the proposed method is able to handle a large number of
correlated random inputs with different marginal distributions. Numerical
examples in the IEEE 13 and IEEE 123 node test feeders are presented, showing
that the proposed method can achieve accuracy and efficiency simultaneously.
Numerical results also demonstrate that the randomness brought about by the RES
and loads indeed leads to a reduction in the delivery capability of a
distribution network.
