A Coupled Karhunen-Loève and Anisotropic Sparse Grid Interpolation Method for the Probabilistic Load Flow Problem

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 This assumption, however, is no longer valid as the adoption of renewable energy resources add more variability and uncertainty to the modern electrical system.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-Loève (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.

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