A nested cubature rule for probabilistic optimal power flow computation

The probabilistic optimal power flow (POPF) model aims to quantify the statistical features of POPF outputs, which are affected by hundreds of uncertain POPF inputs. This paper sets out to develop a computationally feasible cubature rule for POPF computation. In the case where POPF inputs include correlated random variables, a Gaussian copula is introduced to accommodate the dependence structure of POPF inputs; the generalized lambda distribution is employed to fit the marginal distribution of each POPF input, and empirical formulae are derived to specify the dependence structure of POPF inputs in the standard normal space. With the aid of moment matching equations, optimization procedures are implemented to derive a D-dimensional cubature rule. Then, this D-dimension cubature rule is expanded to a higher dimension by using Hadamard matrix and Kronecker product; if a Hadamard matrix of order 2R is employed, the resultant nested cubature rule can be used to handle a POPF model including m inputs: m≤D(2R −1). Finally, case studies are performed on a modified IEEE 118-bus system to check the proposed methodologies, the results indicate the feasibility, efficiency, and accuracy of nested cubature rules.