A probability box representation method for power flow analysis considering both interval and probabilistic uncertainties

In the modern power system, the uncertainties such as renewable generation and electric vehicles are usually modelled as either interval or probabilistic variables for the power flow analysis. It is meaningful to study the mixed impacts of the interval and probabilistic variables on the power flow, but the existing methods considering the mixed impacts lack accuracy. This paper proposes a novel power flow analysis method considering both interval and probabilistic uncertainties, in which the probability box (P-box) model is established to investigate the power flow influenced by multi-type uncertainties. A probability-interval sample classification method combined with interpolation is proposed to achieve an accurate P-box representation of the power flow. Also, the correlation of uncertainties is fully considered where a novel extended optimizing-scenario method is proposed for obtaining the P-box model considering the multi-dimensional correlation of interval variables. Three test cases are carried out to verify the effectiveness of the proposed method. The P-box represented results clearly reflect the fluctuation range and the corresponding probability of the power flow. The specific influences of the sample size, correlation, capacity of multi-type uncertainties on the power flow and the P-box model are also determined and summarized.