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Analytic solution of the classic probabilistic load flow problem on a full AC model

Since the 1970s the application of probabilistic methods to power system analysis was addressed in many papers. Main objective was and still is to find a probabilistic counterpart to the deterministic Load Flow Calculation techniques that can cope with uncertainty about the grid usage. The term “Classical Probabilistic Load Flow Problem” refers to the problem to determine probability information about a line's absolute current from the probability information about nodal powers. Until now approaches that use model simplifications leading to inherent imprecision were used to address this problem. In this paper the authors present a novel approach that allows for the exact solution of the before described ‘Classical Probabilistic Load Flow Problem’ based on a full-steady state AC-network model.