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Considering the increasing penetration of renewable energy sources andelectrical vehicles in utility distribution feeders, it is imperative to studythe impacts of the resulting increasing uncertainty on the delivery capabilityof a distribution network. In this paper, probabilistic available deliverycapability (ADC) is formulated for a general distribution network integratingvarious RES and load variations. To reduce the computational efforts by usingconventional Monte Carlo simulations, we develop and employ a computationallyefficient method to assess the probabilistic ADC, which combines the up-to-datesparse polynomial chaos expansion (PCE) and the continuation method.Particularly, the proposed method is able to handle a large number ofcorrelated random inputs with different marginal distributions. Numericalexamples in the IEEE 13 and IEEE 123 node test feeders are presented, showingthat the proposed method can achieve accuracy and efficiency simultaneously.Numerical results also demonstrate that the randomness brought about by the RESand loads indeed leads to a reduction in the delivery capability of adistribution network.

Applying Polynomial Chaos Expansion to Assess Probabilistic Available Delivery Capability for Distribution Networks with Renewables