Hybrid Probabilistic and Interval Load Flow Calculation based on Data Clustering

In power systems, there exist various uncertainty factors such as renewable energy and load demand, and they follow either probability or interval distributions. However, it is challenging to perform load flow calculations considering hybrid uncertainties. To address this issue, we develop a data clustering-based method for solving hybrid probabilistic and interval load flow (HPILF). In this method, the K-means clustering technique is applied to category the uncertainties of probabilistic input variables into finite subintervals. Then, HPILF can be transformed into a number of interval load flow (ILF) calculations and solved by the well-established affine arithmetic methods. The performance of the proposed method is evaluated on the IEEE 30-bus system. The uncertainties of load demands and wind power are considered, as well as the correlation between loads. The simulation results demonstrate that the proposed method can provide slightly conservative estimations to the maximum and minimum probability distributions of outputs with a low computational burden.