General Polynomial Chaos vs Crude Monte Carlo for Probabilistic Evaluation of Distribution Systems

Recent evolutions in low voltage distribution system (LVDS), e.g., distributed generation and electric vehicles, have introduced a higher level of uncertainty. To determine the probability of violating grid constraints, e.g., undervoltage, such system must be assessed using a probabilistic power flow, which considers these uncertainties. Several approaches exist, including simulation-based and analytical methods. A well-known example of the simulation-based methods is the crude Monte Carlo (MC) approach which is very common in scientific computation due to its simplicity. Recently, analytical methods such as the general polynomial chaos (gPC) approach have gained increasing interest. This paper illustrates the effectiveness of the gPC approach compared to the MC method in determining the uncertainty of certain grid measures. Both methods are compared with respect to computational time and accuracy using a small test case with stochastic input which coheres to a univariate continuous distribution.