An Affine Arithmetic-Based Model of Interval Power Flow With the Correlated Uncertainties in Distribution System

An interval power flow (IPF) method that considers the interval correlations of input random variables is proposed to improve the calculation accuracy of IPF, i.e., as correlated distributed generations (DGs) and some correlated DGs-loads are integrated into distribution system. The interval correlation for input variables is described by parallelogram model (PM), whose shape and size are determined by the interval correlated level. Based on affine arithmetic (AA) method, the IPF is solved through nonlinear optimization instead of traditional interval iterative computations. The optimization model of IPF is established, and the interval correlations of input variables (DGs-DGs and DGs-loads) are added into the IPF optimization problem in the form of additional constraint, to make the power flow solutions, i.e., bus voltage magnitude, voltage angle, active and reactive power of branches, more accurate. Finally, several cases, i.e., numerical case, IEEE33-bus, PG&E69-bus and IEEE118-bus distribution system, not only demonstrate the effectiveness of the proposed method, but also indicate that the IPF results are affected by uncertainty level, and the widths of IPF increase with the increasing of uncertainty level.