Discrete Fourier Transformation Matrix for Global Sensitivity Analysis in Probabilistic Optimal Power Flow Calculation

The commonly used global sensitivity analysis (GSA) can quantify the influence of random input variables on the variance of target outputs. To avoid the extremely large computational burden of the Monte Carlo simulation method (MCSM), a discrete Fourier transformation matrix (DFTM) method is developed for the first time to efficiently tackle the variance-based GSA of transmission systems in the probabilistic optimal power flow (POPF) with correlated random inputs. The proposed DFTM method has a flexible sampling strategy and includes two sub-methods named the discrete sine/cosine transformation matrix (DSTM/DCTM). The superiority of the DFTM in both accuracy and efficiency for the variance-based GSA in POPF is demonstrated by its comparisons with Hong’s point estimate method (HPEM), the unscented transformation method (UTM) and the first-order second-moment method (FOSMM). Based on Nataf transformation, it is found through a theoretical derivation in the paper that both HPEM and UTM may lead to a negative variance of output in some cases, which will cause erroneous results of the GSA. In contrast, the proposed DFTM has an immunity to such variance abnormality. The tests and comparisons are implemented on a modified IEEE 118-bus power system, where MCSM is used as a reference for accuracy.