A Lagrange Interpolation Based Probabilistic Modeling Method and Its Application in Probabilistic Power Flow Analysis

Grid-connection of vast renewable energy sources brings a lot of probabilistic uncertain sources to power system, so it tremendously increases computational burden in probabilistic modeling for uncertain sources during probabilistic power flow (PPF) analysis of power system. In practical application, the Nataf transformation is an effective approach to achieve the probabilistic modeling for such Pearson correlated random variables, where the core step is to determine the Pearson correlation coefficients (PCC) in standard normal distribution scope. However, traditional correlation coefficient solving method, which combines the Simpson’s numerical integration with the bisection method, is so time-consuming that the whole procedure of Nataf transformation is hard to satisfy the demand of realtime computation. To address this issue, an approach based on Lagrange interpolation and simplified Newton method was adopted to implement efficient computation of correlation coefficients to speed up the process of probabilistic modeling, thus the efficiency of PPF analysis could be further improved. Based on the modified IEEE118-bus system, the accuracy and efficiency of the proposed method is tested, and the influence of calculation error on the accuracy of total PPF calculation results was further tested. Test results show that utilizing the proposed method the solution of correlation coefficients of standard normal distribution field in Nataf transformation can be completed efficiently and accurately, thus, on the premise of ensuring the accuracy of PPF results, the efficiency of PPF analysis can be improved.