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In the traditional load flow analysis, a key assumption is that the inputvariables, i.e., generator output and customer demand, are fixed in time andthe associated response has no variability. This assumption, however, is nolonger valid as the adoption of renewable energy resources add more variabilityand uncertainty to the modern electrical system. Addressing these concerns isthe definition of the Probabilistic Load Flow (PLF) problem. The challenge ofthe PLF problem lies in handling high-dimensional input uncertainties and thenon-linearity of the load flow equations. The most straightforward way toaddress these problems, but at the cost of computational time, is to perform aMonte 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 isimplemented and tested on the IEEE 118-bus test system and a modernized versionof the IEEE Reliability Test System - 1996, the Reliability Test System - GridModernization Lab Consortium (RTS-GMLC). Results for the 194-dimensional caseshow a decrease in computational time when compared to the 10,000 sample MonteCarlo method given a bound on mean and standard deviation error.

A Coupled Karhunen--Lo\`eve and Anisotropic Sparse Grid Interpolation Method for the Probabilistic Load Flow Problem