Probabilistic Optimal Power Flow Calculation Using Weighted Quasi-Monte Carlo Method Based on Homotopy Algorithm and Correlation Correction

IEEE Transactions on Power Systems, vol. 41, pp. 3593–3605

Abstract

This paper proposes a novel method combining Monte Carlo simulation (MCS) and approximation method to improve the high-order moments accuracy of probabilistic optimal power flow (POPF) with less calculation burden. The method assigns optimal weights to a small set of Sobol samples and integrates them with correlation correction, ensuring that their moments and correlation match the ones of input distributions. Fractional moments are introduced as a bridge to facilitate the solution of weights optimization. First, Sobol sequences generate standard normal samples, with their weights determined through the fit of multiple-order raw moments, based on a goodness-of-fit indicator and fractional moments matching. The homotopy algorithm is introduced to solve the determination of sample weights, avoiding the potential unsolvability that probably arises from employing the traditional Newton-Raphson method. Moreover, the proposed correlation correction adjusts the samples to ensure a consistency with the reference distributions and their correlation coefficients. Finally, the probability density function (PDF) of outputs can be reconstructed based on these multiple-order moments derived from the POPF calculations. The proposed methods are verified by the modified IEEE 118-bus and case1354pegase test system, indicating a superior balance between accuracy and efficiency in the POPF analysis, while maintaining robust performance.

Authors 6

1. Junzhou Wang

   Chongqing University

   Affiliation as printed

   Chongqing University

2. Xingyu Lin

   Chongqing University

   Affiliation as printed

   Chongqing University

3. Sui Peng

   Chongqing University

   Affiliation as printed

   Chongqing University

4. Junjie Tang

   Chongqing University

   Affiliation as printed

   Chongqing University

5. Ferdinanda Ponci Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University

6. Antonello Monti Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University