Influence of Stochastic Dependence on Small-Disturbance Stability and Ranking Uncertainties

A high level of stochastic dependence (or correlation) exists between different uncertainties (i.e., loads and renewable generation), which is nonlinear and non-Gaussian and it affects power system stability. Accurate modeling of stochastic dependence becomes more important and influential as the penetration of correlated uncertainties (such as renewable generation) increases in the network. The stochastic dependence between uncertainties can be modeled using 1) copula theory and 2) joint probability distributions. These methods have been implemented in this paper and their performances have been compared in assessing the small-disturbance stability of a power system. The value of modeling stochastic dependence with increased renewables has been assessed. Subsequently, the critical uncertainties that most affect the damping of the most critical oscillatory mode have been identified and ranked in terms of their influence using advanced global sensitivity analysis techniques. This has enabled the quantification and identification of the impact of modeling stochastic dependence on the raking of critical uncertainties. The results suggest that multivariate Gaussian copula is the most suitable approach for modeling correlation as it shows consistently low error even at higher levels of renewable energy penetration into the power system.