A clustering-based analytical method for hybrid probabilistic and interval power flow

Various probabilistic power flow (PPF) and interval power flow (IPF) methods have been developed to deal with random and interval variables in power systems, respectively. However, the co-existence of these two types of variables poses great challenges to PPF and IPF calculations. To cope with this issue, we propose a clusteringbased analytical method for hybrid probabilistic and interval power flow (HPIPF) calculation. The uncertainties of load demands and wind power outputs are treated as random and interval variables, respectively. The remarkable feature of this method is to propose an assumption called the unified optimal scenarios of wind power. On this basis, HPIPF calculation is transformed into IPF and PPF calculations, which can be solved by the optimal-scenarios method and the cumulant method, respectively. The accuracy and efficiency of the proposed method are validated on the IEEE 14-bus and 118-bus test systems through the comparisons with the double layer Monte-Carlo simulation. Furthermore, the impacts of correlated interval variables are analyzed. The simulations indicate that the estimations of output variables may be conservative without considering the cor relations of interval variables.