ABSTRACT
This chapter introduces the dependencies among stochastic variables and the copula theory. It explains a formulation of discrete convolution (DC) under the dependent circumstances using the copula function is proposed for dependent probabilistic sequence operation (DPSO). The chapter presents an efficient approach to power system uncertainty analysis with high-dimensional dependencies, called HD-DPSO. Essentially, the copula-based modeling can be viewed as a multidimensional probability density function (PDF) regression problem. The length of the discrete PDF is determined based on the variation area and the discretized step. The chapter examines an algorithm for the proposed HD-DPSO to accelerate the computation. For each subgroup that does not follow Gaussian distributions, a recursive sample-guided DPSO is proposed to tackle the “curse of dimensionality” originating from high-dimensional dependencies. Three measures including grouping, a Gaussian distribution-based aggregation stage, and a recursive sample-guided DPSO are implemented to ease the computational burden.
