Probabilistic Load Flow Approach Combining Cumulant Method and K-Means Clustering to Handle Large Fluctuations of Stochastic Variables

The modern electrical power system faces various uncertainties, including load fluctuations, forced outages of conventional generators, network branches. Furthermore, the rising penetration of wind power generation introduces additional uncertainty, causing difficulties in power system planning, operation. This paper uses an analytical probabilistic load flow approach to account for all such uncertainties. The random branch outages are simulated using the fictional powers injections into the relevant nodes. A fuzzy method is used to perform contingency sequencing to avoid masking mistakes that might occur when utilizing performance index-based sequencing methods. The sparse Jacobian inverse is eliminated to preserve storage space, accelerate the computation. A modified Cumulant method is used in conjunction with the K-means clustering process to deal with the substantial fluctuations of the input variables. In the proposed approach, the correlated samples are generated using inverse Nataf transformation. These correlated samples are clustered using K-means clustering. The Cumulant method is applied within each cluster, total probability law is used to integrate each cluster's findings. The proposed PLF is tested on 24-bus, 259-bus wind integrated equivalent systems. Compared with the Monte-Carlo simulation, the proposed PLF yields computationally efficient, more accurate findings.