Modeling Discrete Random Variables with Linear and Nonlinear Dependence for Probabilistic Load Flow

A majority of probabilistic load flow studies assume independence or arbitrarily set linear correlation coefficients between the various loads and other inputs on the distribution system. These assumptions may not be applicable to the real world. A methodology is proposed that can model continuous and discrete random variables considering both linear and non-linear dependence through several transformations and inverse transform sampling. The methodology is validated looking at the summation of two random variables and a probabilistic load flow analysis of a residential distribution system with 50% penetration of electric vehicles. This paper hopes to continue the discussion and push for future research in understanding dependence between system inputs and its effects on distribution systems, and how to apply this knowledge in future studies.