  In the traditional load flow analysis, a key assumption is that the input
variables, i.e., generator output and customer demand, are fixed in time and
the associated response has no variability. This assumption, however, is no
longer valid as the adoption of renewable energy resources add more variability
and uncertainty to the modern electrical system. Addressing these concerns is
the definition of the Probabilistic Load Flow (PLF) problem. The challenge of
the PLF problem lies in handling high-dimensional input uncertainties and the
non-linearity of the load flow equations. The most straightforward way to
address these problems, but at the cost of computational time, is to perform a
Monte Carlo method. This work, however, solves these problems -- accuracy,
high-dimensionality, and computational time -- with a coupled Karhunen-Lo\`eve
(KL) expansion and Anisotropic Sparse Grid algorithm. The proposed method is
implemented and tested on the IEEE 118-bus test system and a modernized version
of the IEEE Reliability Test System - 1996, the Reliability Test System - Grid
Modernization Lab Consortium (RTS-GMLC). Results for the 194-dimensional case
show a decrease in computational time when compared to the 10,000 sample Monte
Carlo method given a bound on mean and standard deviation error.
